K4- 
 
The Publishers and the Authors will be grateful to 
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 their attention to any errors of omission or of commis- 
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 oui* publications standard works of study and reference, 
 and, to that end, the greatest accuracy is sought. It 
 rarely happens that the early editions of works of any 
 size are free from errors; but it is the endeavor of the 
 Publishers to have them removed immediately upon being 
 discovered, and it is therefore desired that the Authors 
 may be aided in their task of revision, from time to time, 
 by the kindly criticism of their readers. 
 
 JOHN WILEY & SONS, Inc. 
 432 4TH AVENUE. 
 
WORKS OF WILLIAM KENT 
 
 PUBLISHED BY 
 
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 Bookkeeping and Cost Accounting for Fac- 
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 vii +261 pages. 8M by 10^. Profusely illus- 
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 The Mechanical Engineers Pocket-Book. 
 
 A Reference Book 01 Rules, Tables, Data, and 
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 and Students. Ninth edition. Thoroughly 
 revised with the assistance of Robert T. Kent. 
 xiv+1526 pages, 4 by 6%. Flexible "Fabrikoid" 
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 Steam-Boiler Economy 
 
 A Treatise on the Theory and Practice of Fuel 
 Economy in the Operation of Steam-Boilers. 
 Second edition, 1915. xvii +717 pages, 6 by 9, 
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THE 
 
 MECHANICAL ENGINEERS' 
 POCKET-BOOK. 
 
 A REFERENCE-BOOK OF RULES, TABLES, 
 DATA, AND FORMULA. 
 
 WILLIAM KENT, M.E., Sc.D., 
 
 Consulting Engineer. 
 Member Amer. Soc'y Mechl. Engrs. and Amer. Inst. Mining Engrs. 
 
 NINTH EDITION, THOROUGHLY REVISED 
 
 WITH THE ASSISTANCE OF 
 
 ROBERT THURSTON KENT, M. E., 
 
 Consulting Engineer. 
 Junior American Society of Mechanical Engineers. 
 
 TOTAL I3SJW, 
 ONE HUNDRED AND THIRTY-FIVE THOUSAND. 
 
 NEW YORK 
 
 JOHN WILEY & SONS, INC. 
 
 LONDON: CHAPMAN & HALL, LIMITED 
 
 1916 
 
COPYRIGHT, 1895, 1902, 1910, 1915, 
 
 BY 
 
 WILLIAM KENT. 
 
 Eighth Edition entered at Stationers' Hall. 
 
 Composition and Electrotyping by the STANHOPE PRESS, Boston, Mass., and 
 
 the PUBLISHERS PRINTING COMPANY, New York. 
 Printing and Binding by BRAUNWORTH & COMPANY, Brooklyn, N. Y. 
 
PREFACE TO THE NINTH EDITION. 
 
 NOVEMBER, 1915. 
 
 SINCE the eighth edition was published, five years ago, there have 
 been notable advances in many branches of engineering, rendering 
 obsolete portions of the book which at that time were in accord with 
 practice. In addition, many engineering standards have been changed 
 during the five-year period, necessitating a thorough revision of many 
 sections of the work. The absolutely necessary revisions to bring the 
 book up to date -have involved changes in over 400 pages of the eighth 
 edition, and the addition of over 150 pages of new matter. The 
 treatment of many subjects in the earlier edition has been condensed 
 into smaller space to enable the insertion of the new matter without 
 increasing the size of the book to unwieldy proportions. Extensive 
 revisions have been made in the subjects of materials, mechanics, 
 fans and blowers, heating and ventilation, fuel, steam-boilers and 
 engines, and steam-turbines. The chapter on machine-shop practice 
 has been rewritten and doubled in size, and now covers many subjects 
 which were omitted in earlier editions. The new matter includes 
 many data on planing, milling, drilling and grinding, together with 
 an elaborate treatment of the subject of machine-tool driving. The 
 subject of electrical engineering has been completely rewritten and 
 brought into agreement with present practice. Of the new tables 
 added the following are considered of special importance. Square 
 roots of fifth powers; Four-place logarithms; Standard sizes of welded 
 steel pipe; Standard pipe flanges; Properties of wire rope; Fire brick 
 and other refractories; Properties of structural sections and columns; 
 Chemical standards for iron castings; Flow of air, water and steam; 
 Analyses and heating values of coals; Rankine efficiency; Cooling 
 towers; Properties of ammonia; -Power required for driving machine 
 tools of all types, both singly and in groups; Electric resistance and 
 conductivity of wires; Street railway installation; Electric lamp char- 
 acteristics; Illuminating data. 
 
 NOTE TO SECOND PRINTING OF THE NINTH 
 EDITION. 
 
 In line with the policy of keeping the book up to date and elimi- 
 nating all obsolete matter, the section on hydraulic turbines has been 
 completely rewritten for the second printing of the ninth edition. 
 The presentation of the theory has been improved, new design con- 
 stants have been given, and the tables of capacity, etc., represent the 
 performance of the most recent types of turbines. 
 
 MARCH, 1917. 
 
 iii 
 
 40223,3 
 
IV PREFACE. 
 
 ABSTRACT FROM PREFACE TO THE 
 FIRST EDITION, 1895. 
 
 MORE than twenty years ago the author began to follow the advice 
 given by Nystrom: " Every engineer should make his own pocket-book, 
 as he proceeds in study and practice, to suit his particular business." 
 The manuscript pocket-book thus begun, however, soon gave place to 
 more modern means for disposing of the accumulation of engineering 
 facts and figures, viz., the index rerum, the scrap-book, the collection of 
 indexed envelopes, portfolios and boxes, the card catalogue, etc. Four 
 years ago, at the request of the publishers, the labor was begun of selecting 
 from this accumulated mass such matter as pertained to mechanical 
 engineering, and of condensing, digesting, and arranging it in form for 
 publication. In addition to this, a careful examination was made of the 
 transactions of engineering societies, and of the most important recent 
 works on mechanical engineering, in order to fill gaps that might be left 
 in the original collection, and insure that no important facts had been 
 overlooked. 
 
 Some ideas have been kept in mind during the preparation of the 
 Pocket-book that will, it is believed, cause it to differ from other works 
 of its class. In the first place it was considered that the field of mechani- 
 cal engineering was so great, and the literature of the subject so vast, that 
 as little space as possible should be given to subjects which especially 
 belong to civil engineering. While the mechanical engineer must con- 
 tinually deal with problems which belong properly to civil engineering, 
 this latter branch is so well covered by Traut wine's " Civil Engineer's 
 Pocket-book " that any attempt to treat it exhaustively would not only 
 fill no " long-felt want," but would occupy space which should be given 
 to mechanical engineering. 
 
 Another idea prominently kept in view by the author has been that he 
 would not assume the position of an " authority " in giving rules and 
 formulae for designing, but only that of compiler, giving not only the 
 name of the originator of the rule, where it was known, but also the volume 
 and page from which it was taken, so that its derivation may be traced 
 when desired. When different formulas for the same problem have been 
 found they have been given in contrast, and in many cases examples 
 have been calculated by each to show the difference between them. In 
 some cases these differences are quite remarkable, as will be seen under 
 Safety-valves and Crank-pins. Occasionally the study of these differences 
 has led to the author's devising a new formula, in which case the deriva- 
 tion of the formula is given. 
 
 Much attention has been paid to the abstracting of data of experiments 
 from recent periodical literature, and numerous references to other data 
 are given. In this respect the present work will be found to differ from 
 other Pocket-books. 
 
 The author desires to express his obligation to the many persons who 
 huve assisted him in the preparation of the work, to manufacturers who 
 
PREFACE. V 
 
 have furnished their catalogues and given permission for the use of their 
 tables, and to many engineers who have contributed original data and 
 tables. The names of these persons are mentioned in their proper places 
 in the text, and in all cases it has been endeavored to give credit to whom 
 credit is due. 
 
 WILLIAM KENT. 
 
 PREFACE TO THE EIGHTH EDITION. 
 
 SEPTEMBER, 1910. 
 
 DURING the first ten years following the issue of the first edition of this 
 book, in 1895, the attempt was made to keep it up to date by the method 
 of cutting out pages and paragraphs, inserting new ones in their places, by 
 inserting new pages lettered a, b, c, etc., and by putting some new matter 
 in an appendix. In this way the book passed to its 7th edition in October, 
 1904. After 50,000 copies had been printed it was found that the electro- 
 typed plates were beginning to wear out, so that extensive resetting of type 
 would soon be necessary. The advances in engineering practice also had 
 been so great that it was evident that many chapters required to be entirely 
 rewritten. It was therefore determined to make a thorough revision of the 
 book, and to reset the type throughout. This has now been accomplished 
 after four years of hard labor. The size of the book has increased over 300 
 pages, in spite of all efforts to save space by condensation and elision of 
 much of the old matter and by resetting many of the tables and formulae 
 in shorter form. A new style of type for the tables has been designed for 
 the book, which is believed to be much more easily read than the old. 
 
 The thanks of the author are due to many manufacturers who ha^re fur- 
 nished new tables of materials and machines, and to many engineers who 
 have made valuable contributions and helpful suggestions. He is especially 
 indebted to his son, Robert Thurston Kent, M.E., who has done the work 
 of revising manufacturers' tables of materials and has done practically all 
 of the revising of the subjects of Compressed Air, Fans and Blowers, Hoist- 
 ing and Conveying, and Machine Shop. 
 
CONTENTS. 
 
 (For Alphabetical Index see page 1479.) 
 
 MATHEMATICS. 
 
 Arithmetic. 
 
 PAGE 
 
 Arithmetical and Algebraical Signs 1 
 
 Greatest Common Divisor 2 
 
 Least Common Multiple 
 
 Fractions 
 
 Decimals 
 
 Table. Decimal Equivalents of Fractions of One Inch 3 
 
 Table. Products of Fractions expressed in Decimals 
 
 Compound or Denominate Numbers 5 
 
 Reduction Descending and Ascending 5 
 
 Decimals of a Foot Equivalent to Fractions of an Inch 5 
 
 Ratio and Proportion 6 
 
 Involution, or Powers of Numbers 7 
 
 Table. First Nine Powers of the First Nine Numbers 7 
 
 Table. First Forty Powers of 2 8 
 
 Evolution. Square Root 8 
 
 Cube Root 9 
 
 Alligation 9 
 
 Permutation 10 
 
 Combination 10 
 
 Arithmetical Progression 10 
 
 Geometrical Progression 11 
 
 Percentage, Profit and Loss, Efficiency 12 
 
 Interest 12 
 
 Discount 13 
 
 Compound Interest 
 
 Compound Interest Table, 3, 4, 5, and 6 per cent 
 
 Equation of Payments >, 
 
 Partial Payments 14 
 
 Annuities 15 
 
 Tables of Amount, Present Values, etc., of Annuities 15 
 
 Weights and Measures. 
 
 Long Measure 17 
 
 Old Land Measure 17 
 
 Nautical Measure 17 
 
 Square Measure 
 
 Solid or Cubic Measure 
 
 Liquid Measure 
 
 The Miners' Inch 
 
 Apothecaries' Fluid Measure 
 
 Dry Measure i ~ 19 
 
 Shipping Measure 
 
 Avoirdupois Weight 19 
 
 Troy Weight 19 
 
 Apothecaries' Weight 20 
 
 To Weigh Correctly on an Incorrect Balance 20 
 
 Circular Measure 20 
 
 Measure of Time 20 
 
 vii 
 
Vlll CONTENTS. 
 
 PAGE 
 
 Board and Timber Measure 20 
 
 Table. Contents in Feet of Joists, Scantlings, and Timber. ... 21 
 
 French or Metric Measures 21 
 
 British and French Equivalents 22 
 
 Metric Conversion Tables 23 
 
 Compound Units 
 
 of Pressure and Weight 27 
 
 of Water, Weight and Bulk 27 
 
 of Air, Weight and Volume 27 
 
 of Work, Power, and Duty . 27 
 
 of Velocity 4 27 
 
 Wire and Sheet Metal Gages 28 
 
 Circular-mil Wire Gage 29, 30 
 
 U. S. Standard Wire and Sheet Gage (1893) 29, 32 
 
 Twist-drill and Steel-wire Gages 31 
 
 Decimal Gage 32 
 
 Algebra. 
 
 Addition, Multiplication, etc 33 
 
 Powers of Numbers 
 
 Parentheses, Division 
 
 Simple Equations and Problems 
 
 Equations containing two or more Unknown Quantities 
 
 Elimination 
 
 Quadratic Equations 
 
 Theory of Exponents 
 
 Binominal Theorem 
 
 Geometrical Problems of Construction 
 
 of Straight Lines 37 
 
 ^f Angles 38 
 
 of Circles 39 
 
 of Triangles 
 
 of Squares and Polygons 
 
 of the Ellipse 45 
 
 of the Parabola 
 
 of the Hyperbola 
 
 of the Cycloid 50 
 
 of the Tractrix or Schiele Anti-friction Curve 50 
 
 of the Spiral 51 
 
 of Rings inside a Circle '51 
 
 of Arc of a Large Circle 51 
 
 of the Catenary 52 
 
 of the Involute 52 
 
 of plotting Angles 
 
 Geometrical Propositions 53 
 
 Degree of a Railway Curve 54 
 
 Mensuration, Plane Surfaces. 
 
 Quadrilateral, Parallelogram, etc 54 
 
 Trapezium and Trapezoid 54 
 
 Triangles 54 
 
 Polygons. Table of Polygons 55 
 
 Irregular Figures 56 
 
 Properties of the Circle 57 
 
 Values of TT and its Multiples, etc 57 
 
 Relations of arc, chord, etc 58 
 
 Relations of circle to inscribed square, etc 59 
 
 Formulse for a Circular Curve 59 
 
 Sectors and Segments 60 
 
 Circular Ring 60 
 
 The Ellipse 60 
 
 The Helix 61 
 
 The Spiral 61 
 
 Surfaces and Volumes of Similar Solids 61 
 
CONTENTS. ix 
 
 Mensuration, Solid Bodies. PAGE 
 
 Prism 62 
 
 Pyramid 62 
 
 Wedge 62 
 
 Rectangular Prismoid 62 
 
 Cylinder 62 
 
 Cone 62 
 
 Sphere 62 
 
 Spherical Triangle 63 
 
 Spherical Polygon 63 
 
 The Prismoid 63 
 
 The Prismoidal Formula 63 
 
 Polyedron 63 
 
 Spherical Zone 64 
 
 Spherical Segment 64 
 
 Spheroid or Ellipsoid 64 
 
 Cylindrical Ring ; 64 
 
 Solids of Revolution 64 
 
 Spindles 64 
 
 Frustum of a Spheroid 64 
 
 Parabolic Conoid 65 
 
 Volume of a Cask 65 
 
 'Irregular Solids 65 
 
 Plane Trigonometry. 
 
 Solution of Plane Triangles 66 
 
 Sine, Tangent, Secant, etc ...'..' 66 
 
 Signs of the Trigonometric Functions 67 
 
 Trigonometrical Formulae 68 
 
 Solution of Plane Right-angled Triangles 69 
 
 Solution of Oblique-angled Triangles 69 
 
 Analytical Geometry. 
 
 Ordinates and Abscissas 70 
 
 Equations of a Straight Line, Intersections, etc 70 
 
 Equations of the Circle 71 
 
 Equations of the Ellipse 71 
 
 Equations of the Parabola 72 
 
 Equations of the Hyperbola 72 
 
 Logarithmic Curves 73 
 
 Differential Calculus. 
 
 Definitions 73 
 
 Differentials of Algebraic Functions 74 
 
 Formulae for Differentiating 74 
 
 Partial Differentials 75 
 
 Integrals 75 
 
 Formulae for Integration 75 
 
 Integration between Limits 76 
 
 Quadrature of a Plane Surface 76 
 
 Quadrature of Surfaces of Revolution 77 
 
 Cubature of Volumes of Revolution ' 77 
 
 Second, Third, etc., Differentials 77 
 
 Maclaurin's and Taylor's Theorems 78 
 
 Maxima arid Minima 78 
 
 Differential of an Exponential Function 79 
 
 Logarithms 79 
 
 Differential Forms which have Known Integrals 80 
 
 Exponential Functions . . 80 
 
 Circular Functions 81 
 
 The Cycloid 81 
 
 Integral Calculus 82 
 
X CONTENTS. 
 
 The Slide Bule. 
 
 Examples solved by the Slide Rule . . . 82 
 
 Logarithmic Ruled Paper. 
 
 Plotting on Logarithmic Paper 84 
 
 Mathematical Tables. 
 
 Formula for Interpolation 86 
 
 Reciprocals of Numbers 1 to 2000 
 
 Squares, Cubes, Square Roots and Cube Roots from 0.1 to 1600 
 
 Squares and Cubes of Decimals 108 
 
 Fifth Roots and Fifth Powers 109 
 
 Square Roots of Fifth Powers of Pipe Sizes 
 
 Circumferences and Areas of Circles Ill 
 
 Circumferences of Circles in Feet and Inches from 1 inch to 32 
 
 feet 11 inches in diameter 
 
 Areas of the Segments of a Circle 
 
 Lengths of Circular Arcs, Degrees Given 
 
 Lengths of Circular Arcs, Height of Arc Given 
 
 Circles and Squares of Equal Area 125 
 
 Number of Circles Inscribed within a Large Circle 125 
 
 Spheres 126 
 
 Square Feet in Plates 3 to 32 feet long and 1 inch wide 128 
 
 Gallons in a Number of Cubic Feet 
 
 Cubic Feet in a Number of Gallons 130 
 
 Contents of Pipes and Cylinders, Cubic Feet and Gallons 
 
 Cylindrical Vessels, Tanks, Cisterns, etc 132 
 
 Capacities of Rectangular Tanks in Gallons 
 
 Number of Barrels in Cylindrical Cisterns and Tanks 
 
 Logarithms 135 
 
 Table of Logarithms 
 
 Hyperbolic Logarithms 
 
 Four-place Logarithms of Numbers from 1 to 1000 167 
 
 Natural Trigonometric Functions 169 
 
 Logarithmic Trigonometric Functions 172 
 
 MATERIALS. 
 
 Chemical Elements 173 
 
 Specific Gravity and Weight of Materials 173 
 
 The Hydrometer : 175 
 
 Metals, Properties of 
 
 Aluminum 177 
 
 Antimony 177 
 
 Bismuth 178 
 
 Cadmium 178 
 
 Copper 178 
 
 Gold 178 
 
 Iridium 178 
 
 Iron 178 
 
 Lead 178 
 
 Magnesium 179 
 
 Manganese 179 
 
 Mercury : 179 
 
 Nickel 179 
 
 Platinum 179 
 
 Silver 179 
 
 Tin 179 
 
 Zinc 179 
 
 Miscellaneous Materials. 
 
 Order of Malleability, etc., of Metals 180 
 
 Measures and Weights of Various Materials 180 
 
CONTENTS. XI 
 
 PAGE 
 
 Formulae and Table for Weight of Rods, Plates, etc 181 
 
 Commercial Sizes of Iron and Steel Bars 182 
 
 Weights of Iron and Steel Sheets 183 
 
 of Iron Bars 184 
 
 of Round Steel Bars 185 
 
 of Fillets 185 
 
 of Round, Square, and Hexagon Steel 186 
 
 of Plate Iron 187 
 
 of Flat Rolled Iron 188 
 
 of Steel Blooms 190 
 
 of Roofing Materials 191-196 
 
 Snow and Wind Loads on Roofs 191 
 
 Roof Construction 191 
 
 Specifications for Tin and Terne Plates 194 
 
 Corrugated Sheets 194 
 
 Weights and Thickness of Cast-iron Pipe 196-199 
 
 Weights of Cast-iron Pipe Columns 200 
 
 Weight of Open-end Cast-iron Cylinders 200 
 
 Standard Sizes of Welded Pipe 201-205 
 
 Weight and Bursting Strength of Welded Pipe 205 
 
 Tubular Electric Line Poles 206 
 
 Protective Coatings for Pipes 206 
 
 Valves and Fittings 206-217 
 
 Standard Pipe Flanges 208-212 
 
 Forged Steel Flanges 211 
 
 Standard Hose Couplings 218 
 
 Wooden Stave Pipe. . . 218 
 
 Riveted Hydraulic Pipe 219 
 
 Riveted Iron Pipes 220 
 
 Spiral Riveted Pipe 220 
 
 Weight of Steel for Riveted Pipe 221 
 
 Bent and Coiled Pipes 221 
 
 Flexibility of Pipe Bends 221 
 
 Shelby Cold-drawn Steel Tubing 222 
 
 Seamless Brass and Copper Tubes 224, 225 
 
 Aluminum Tubing 226 
 
 Lead and Tin-lined Lead Pipe 226 
 
 Iron Pipe Lined with Tin, Lead, Brass, and Copper 227 
 
 Weight of Sheet and Bar Brass 228 
 
 of Sheet Zinc 228 
 
 of Copper and Brass Wire and Plates 229 
 
 of Aluminum Sheets, Bars, and Plates 230 
 
 of Copper Rods 230 
 
 Screw-threads, U. S. Standard 231 
 
 Whitworth Screw-threads 232 
 
 Limit-gages for Screw-threads . . . . : 232 
 
 Automobile Screws and Nuts 233 
 
 International Screw-thread 233 
 
 Acme Screw-thread 234 
 
 Machine Screws, A. S. M. E. Standard 234 
 
 Standard Taps 235 
 
 Wood Screws 236 
 
 Machine Screw Heads 237 
 
 Set Screws and Cap Screws 238 
 
 Weights of Rivets 238, 239 
 
 Shearing Value of Rivets. Bearing Value of Riveted Plates 240 
 
 Length of Rivets for Various Grips 241 
 
 Lag Screws 241 
 
 Weight of Bolts with Square Heads and Nuts 242 
 
 Washers .242, 243 
 
 Hanger Bolts 243 
 
 Turnbuckles 243 
 
 Track Bolts 244 
 
 Cut Nails 244 
 
 Material Required per Mile of Railroad Track 245 
 
 Wire Nails 246 
 
 Spikes. .,,,,,,,*,, 248 
 
Xii CONTENTS. 
 
 PAGE 
 
 Wires of Different Metals 248 
 
 Steel Wire, Size, Strength, etc 249 
 
 Piano Wire 250 
 
 Telegraph Wire 250-252 
 
 Plow-steel Wire 250, 258 
 
 Galvanized Iron Wire 250 
 
 Copper Wire, Bare and Insulated 251, 252 
 
 Notes on Wire Rope 253 
 
 Wire Rope Tables 255-262 
 
 Varieties and Uses of Wire Rope 256 
 
 Splicing of Wire Ropes 263 
 
 Chains and Chain Cables 264 
 
 Sizes of Fire Brick 266 
 
 Refractoriness of American Fire-brick 268 
 
 Slag Bricks and Slag Blocks 268 
 
 Magnesia Bricks 269 
 
 Fire Clay Analysis 269 
 
 Zirconia 270 
 
 Asbestos 270 
 
 Standard Cross-sections of Materials, for Draftsmen 271 
 
 Strength of Materials. 
 
 Stress and Strain 272 
 
 Elastic Limit 273 
 
 Yield Point 273 
 
 Modulus of Elasticity 274 
 
 Resilience 274 
 
 Elastic Limit and Ultimate Stress 275 
 
 Repeated Stresses 275 
 
 Repeated Shocks 276 
 
 Stresses due to Sudden Shocks 278 
 
 Tensile Strength 278 
 
 Measurement of Elongation 279 
 
 Shapes of Test Specimens 280 
 
 Increasing Tensile Strength of Bars by Twisting 280 
 
 Compressive Strength 281 
 
 Columns, Pillars, or Struts 283 
 
 Hodgkinson's Formula. Euler's Formula 
 
 Gordon's Formula. Rankine's Formula 
 
 Wrought-iron Columns 2S5 
 
 Built Columns 285-286 
 
 The Straight-line Formula 285 
 
 Comparison of Column Formulae 286 
 
 Tests of Large Built Steel Columns 287 
 
 Working Strains in Bridge Members 287 
 
 Strength of Cast-iron Columns 
 
 Safe Load on Cast-iron Columns 291 
 
 Strength of Brackets on Cast-iron Columns 292 
 
 Moment of Inertia 293 
 
 Radius of Gyration 293 
 
 Elements of Usual Sections 
 
 Eccentric Loading of Columns 296 
 
 Transverse Strength 297 
 
 Formulae for Flexure of Beams 297 
 
 Safe Loads on Steel Beams 298, 309 
 
 Beams 9f Uniform Strength 301 
 
 Dimensions and Weights of Structural Steel Sections 302 
 
 Allowable Tension in Steel Bars 305 
 
 Properties of Rolled Structural Shapes 305 
 
 " Steel I-Beams , 307 
 
 " Steel Wrought Plates 308 
 
 " Corrugated Plates 310 
 
 Spacing of Steel I-Beams 311 
 
 Properties of Steel Channels 312 
 
 " T Shapes 313 
 
CONTENTS. . Xlll 
 
 PAGE 
 
 Properties of Angles 316 
 
 " Z-bars 317 
 
 Rivet Spacing for Structural Work 321 
 
 Dimensions and Safe Load on Built Steel Columns 323-330 
 
 Bethlehem Girder and I-beams and H-columns 331 
 
 Torsional Strength 334 
 
 Elastic Resistance to Torsion 334 
 
 Combined Stresses 335 
 
 Stress due toTemperature 335 
 
 Strength of Flat Plates 336 
 
 Thickness of Flat Cast-iron Plates 336 
 
 Strength of Unstayed Flat Surfaces 337 
 
 Unbraced Heads of Boilers 337 
 
 Strength of Stayed Surfaces 338 
 
 Stresses in Steel Plating under Water Pressure 338 
 
 Spherical Shells and Domed Heads 339 
 
 Thick Hollow Cylinders under Tension 339 
 
 Thin Cylinders under Tension 340 
 
 Carrying Capacity of Steel Rollers and Balls 340 
 
 Resistance of Hollow Cylinders to Collapse 341, 343 
 
 Formula for Corrugated Furnaces 342 
 
 Hollow Copper Balls 345 
 
 Holding. Power of Nails, Spikes, Bolts, and Screws 346 
 
 Cut versus Wire Nails 347 
 
 Strength of Bolts 347 
 
 Initial Strain on Bolts 347 
 
 Strength of Chains 348 
 
 Stand Pipes and their Design 349 
 
 Riveted Steel Water-pipes 351 
 
 Kirkaldy's Tests of Materials 352-358 
 
 Cast Iron 352 
 
 Iron Castings 352 
 
 Iron Bars, Forgings, etc 352--. 
 
 Steel Rails and Tires 353 
 
 Spring Steel, Steel Axles, Shafts 354 
 
 Riveted Joints, Welds 355 
 
 Copper, Brass, Bronze, etc 356 
 
 Wire-rope 356 
 
 Wire 357 
 
 Ropes, Hemp, and Cotton . . 357 
 
 Belting, Canvas 357 
 
 Stones 357 
 
 Brick, Cement, Wood 358 
 
 Tensile Strength of Wire 358 
 
 Watertown Testing-machine Tests 359 
 
 Riveted Joints 359 
 
 Wrought-iron Bars, Compression Tests 359 
 
 Steel Eye-bars 360 
 
 Wrought-iron Columns 360 
 
 Cold Drawn Steel 361 
 
 Tests of Steel Angles x . . 362 
 
 Shearing Strength 362 
 
 Relation of Shearing to Tensile Strength 362 
 
 Strength of Iron and Steel Pipe 363 
 
 Threading Tests of Pipe 363 
 
 Old Tubes used as Columns 363 
 
 Methods of Testing Hardness of Metals 364 
 
 Holding Power of Boiler-tubes 364 
 
 Strength of Glass 365 
 
 Strength of Ice 366 
 
 Strength of Timber 366 
 
 Expansion of Timber 367, 369 
 
 Tests of American Woods . 367 
 
 Shearing Strength of Woods 367 
 
 Copper at High Temperatures 368 
 
 Drying of Wood 368 
 
 Preservation of Timber 368 
 
XIV CONTENTS. 
 
 PAGE 
 
 Copper Castings of High Conductivity 368 
 
 Tensile Strength of Rolled Zinc Plates 369 
 
 Strength of Brick, Stone, etc. . '. 369 
 
 " Lime and Cement Mortar. 372 
 
 " Flagging .'.'.' 373 
 
 Tests of Portland Cement 373 
 
 Moduli of Elasticity of Various Materials 374 
 
 Factors of Safety 374 
 
 Properties of Cork 377 
 
 Vulcanized India-Rubber 378 
 
 Specifications for Air Hose 379 
 
 Nickel 379 
 
 Aliuninum, Properties and Uses 380 
 
 Alloys. 
 
 Alloys of Copper and Tin, Bronze 384 
 
 Alloys of Copper and Zinc, Brass 386 
 
 Variation in Strength of Bronze 386 
 
 Copper-tin-zinc Alloys 387 
 
 Liquation or Separation of Metals 388 
 
 Alloys used in Brass Foundries 390 
 
 Tobin Bronze 392 
 
 Qualities of Miscellaneous Alloys 392 
 
 Copper-zinc-iron Alloys 393 
 
 ' Alloys of Copper, Tin, and Lead 394 
 
 Phosphor Bronze 394 
 
 Alloys for Casting under Pressure 395 
 
 Aluminum Alloys 396 
 
 Caution as to Strength of Alloys 398 
 
 Alloys of Aluminum, Silicon, and Iron 398 
 
 Tungsten-aluminum Alloys 399 
 
 The Thermit Process 400 
 
 Aluminum-tin Alloys 400 
 
 Manganese Alloys 401 
 
 Manganese Bronze 401 
 
 German Silver 402 
 
 Monel Metal 403 
 
 Copper-nickel Alloys 403 
 
 Alloys of Bismuth .404 
 
 Fusible Alloys 404 
 
 Bearing Metal Alloys 405 
 
 Bearing Metal Practice, 1907 407 
 
 White Metal for Engine Bearings 407 
 
 Alloys containing Antimony 407 
 
 White-metal Alloys 407 
 
 Babbitt Metals 407, 408 
 
 Type-metal 408 
 
 Solders 409 
 
 Ropes and Cables. 
 
 Strength of Hemp, Iron, and Steel Ropes 410 
 
 Rope for Hoisting or Transmission 411 
 
 Cordage, Technical Terms of 411 
 
 Splicing of Ropes 412 
 
 Cargo Hoisting 414 
 
 Working Loads for Manila Rope . . 414 
 
 Knots 415 
 
 Life of Hoisting and Transmission Rope 415 
 
 Efficiency of Rope Tackles 415 
 
 Springs. 
 
 Laminated Steel Springs 417 
 
 Helical Steel Springs 418 
 
CONTENTS. XV 
 
 PAGE 
 
 Carrying Capacity of Springs 419 
 
 Elliptical Springs 423 
 
 Springs to Resist Torsional Force 423 
 
 Phosphor-bronze Springs 424 
 
 Chromium-Vanadium Spring Steel 424 
 
 Test of a Vanadium Steel Spring 424 
 
 Riveted Joints. 
 
 Fairbairn's Experiments 424 
 
 Loss of Strength by Punching 424 
 
 Strength of Perforated Plates 424 
 
 Hand versus Hydraulic Riveting 424 
 
 Formulae for Pitch of Rivets 427, 434 
 
 Proportions of Joints 427 
 
 Efficiencies of Joints 428 
 
 Diameter of Rivets 429 
 
 Shearing Resistance of Rivet Iron and Steel 430 
 
 Strength of Riveted Joints 431 
 
 Riveting Pressures 435 
 
 Tests of Soft Steel Rivets 435 
 
 Iron and Steel. 
 
 Classification of Iron and Steel 436 
 
 Grading of Pig Iron 437 
 
 Manufacture of Cast Iron 437 
 
 Influence of Silicon Sulphur, Phos. and Mn on Cast Iron 438 
 
 Microscopic Constituents 439 
 
 Analyses of Cast Iron 439 
 
 Specifications for Pig Iron and Castings 441, 443 
 
 Specifications for Cast-iron Pipe 441 
 
 Chemical Standards for Castings 441 
 
 Strength of Cast Iron 444, 451 
 
 Strength in Relation to Cross-section 446, 447 
 
 " Semi-steel " 446, 453 
 
 Shrinkage of Cast Iron 447 
 
 White Iron Converted into Gray 448 
 
 Mobility of Molecules of Cast Iron 449 
 
 Expansion of Iron by Heat 449, 465 
 
 Permanent Expansion of Cast Iron by Heating 449 
 
 Castings from Blast Furnace Metal 450 
 
 Effect of Cupola Melting 450 
 
 Additions of Titanium, etc., to Cast Iron 450, 451 
 
 Mixture of Cast Iron with Steel 453 
 
 Bessemerized Cast Iron 453 
 
 Bad Cast Iron -. 453 
 
 Malleable Cast Iron ! 454 
 
 Design of Malleable Castings 457 
 
 Specifications of Malleable Iron 457 
 
 Strength of Malleable Cast Iron 458 
 
 Wrought Iron 459 
 
 Chemistry of Wrought Iron 460 
 
 Electrolytic Iron 460 
 
 Influence of Rolling on Wrought Iron 460 
 
 Specifications for Wrought Iron 461 
 
 Stay-bolt Iron 462 
 
 Tenacity of Iron at High Temperatures 463 
 
 Effect of Cold on Strength of Iron 464 
 
 Durability of Cast Iron 465 
 
 Corrosion of Iron and Steel 466 
 
 Corrosion of Iron and Steel Pipes 467 
 
 Electrolytic Theory, and Prevention of Corrosion 468 
 
 Chrome Paints, Anti-corrosive 469 
 
 Corrosion Caused by Stray Electric Currents 470 
 
 Electrolytic Corrosion due to Overstrain 470 
 
XVI CONTENTS. 
 
 PAGE 
 
 Preservative Coatings, Paints, etc 471 
 
 Inoxydation Processes, Bower-Barff, etc 472 
 
 Aluminum Coatings 473 
 
 Galvanizing 473 
 
 Sherardizing, Galvanizing by Cementation 474 
 
 Lead Coatings 474 
 
 Steel. 
 
 Manufacture of Steel 475 
 
 Crucible, Bessemer, and Open Hearth Steel 475 
 
 Relation between Chemical and Physical Properties 476 
 
 Electric Conductivity 477 
 
 " Armco Ingot Iron " 477 
 
 Variation in Strength 477, 478 
 
 Bending Tests of Steel 478 
 
 Effect of Heat Treatment and of Work 478 
 
 Hardening Soft Steel 479 
 
 Effect of Cold Rolling 479 
 
 Comparison of Full-sized and Small Pieces 480 
 
 Recalescence of Steel 480 
 
 Critical Point 480 
 
 Metallography 480 
 
 Burning, Overheating, and Restoring Steel 481 
 
 Working Steel at a Blue Heat 482 
 
 Oil Tempering and Annealing 482 
 
 Brittleness due to Long-continued Heating 483 
 
 Influence of Annealing upon Magnetic Capacity 483 
 
 Treatment of Structural Steel 483 
 
 May Carbon be Burned out of Steel? 485 
 
 Effect of Nicking a Bar 485 
 
 Dangerous Low Carbon Steel 486 
 
 Specific Gravity 486 
 
 Occasional Failures 486 
 
 Segregation in Ingots and Plates 487 
 
 Endurance of Steel under Repeated Stresses 487 
 
 Welding of Steel 488 
 
 The Thermit Welding Process 488 
 
 Oxy-acetylene Welding and Cutting of Metals 488 
 
 Hydraulic Forging 488 
 
 Fluid-compressed .Steel 488 
 
 Steel Castings 489 
 
 Crucible Steel 490 
 
 Effect of Heat on Gram 491 
 
 Heating and Forging 491 
 
 Tempering Steel 493 
 
 Kinds of Steel used for Different Purposes 494 
 
 High-speed Tool Steel 
 
 Manganese Steel- 494 
 
 Chrome Steel 496 
 
 Aluminum Steel 496 
 
 Tungsten Steel 496 
 
 Nickel Steel 497 
 
 Copper Steel 499 
 
 Nickel- Vanadium Steel 499 
 
 Static and Dynamic Properties of Steel 500 
 
 Strength and Fatigue Resistance of Steels 501 
 
 Chromium- Vanadium Steel 502 
 
 Heat Treatment of Alloy Steels 502, 503 
 
 Specifications for Steel 504-51 1 
 
 High-strength Steel for Shipbuilding 507 
 
 Fire-box Steel 508 
 
 Steel Rails 508 
 
 MECHANICS. 
 
 Matter, Weight, Mass 511 
 
 Force, Unit of Force 512 
 
CONTENTS. XVli 
 
 PAGE 
 
 Local Weight * 512 
 
 Inertia 513 
 
 Newton's Laws of Motion 513 
 
 Resolution of Forces 513 
 
 Parallelogram of Forces 513 
 
 Moment of a Force . . 514 
 
 Statical Moment, Stability 515 
 
 Stability of a Dam 515 
 
 Parallel Forces 515 
 
 Couples 515 
 
 Equilibrium of Forces 516 
 
 Center of Gravity 516 
 
 Moment of Inertia 517 
 
 Centers of Oscillation and Percussion 518 
 
 Center and Radius of Gyration 518 
 
 The Pendulum 520 
 
 Conical Pendulum 520 
 
 Centrifugal Force 521 
 
 Velocity, Acceleration, Falling Bodies 521 
 
 Value of g 522 
 
 Angular Velocity 522 
 
 Height due to Velocity 523 
 
 Parallelogram of Velocities 522 
 
 Velocity due to Falling a Given Height 524 
 
 Fundamental Equations in Dynamics 525 
 
 Force of Acceleration 526 
 
 Formulae for Accelerated Motion 527 
 
 Motion on Inclined Planes '.- 527 
 
 Momentum 527 
 
 Work, Energy, Power 528 
 
 Work of Acceleration 529 
 
 Work of Accelerated Rotation . . 529 
 
 Force of a Blow 529 
 
 Impact of Bodies 530 
 
 Energy of Recoil of Guns 531 
 
 Conservation of Energy. . . T 531 
 
 Sources of Energy 531 
 
 Perpetual Motion 532 
 
 Efficiency of a Machine 532 
 
 Animal-power, Man-power 532 
 
 Man-wheel, Tread Mills 533 
 
 Work of a Horse 533 
 
 Horse-gin 534 
 
 Resistance of Vehicles 534 
 
 Elements of Mechanics. 
 
 The Lever. . 535 
 
 The Bent Lever 536 
 
 The Moving Strut 536 
 
 The Toggle-joint 536 
 
 The Inclined Plane 537 
 
 The Wedge 537 
 
 The Screw 537 
 
 The Cam 537 
 
 Efficiency of a Screw 538 
 
 Efficiency of Screw Bolts 538 
 
 Pulleys or Blocks '. 539 
 
 Differential Pulley 539 
 
 Wheel and Axle 539 
 
 Toothed- wheel Gearing 539 
 
 Endless Screw, Worm Gear 540 
 
 Differential Windlass 540 
 
 Differential Screw 540 
 
 Efficiency of a Differential Screw 641 
 
XV1U CONTENTS. 
 
 Stresses in Framed Structures. 
 
 Cranes and Derricks 541 
 
 Shear Poles and Guys 542 
 
 King Post Truss or Bridge 543 
 
 Queen Post Truss 543 
 
 Burr Truss 544 
 
 Pratt or Whipple Truss 544 
 
 Method of Moments 545 
 
 Howe Truss 546 
 
 Warren Girder 546 
 
 Roof Truss 547 
 
 The Economical Angle 548 
 
 HEAT. 
 
 Thermometers and Pyrometers 549 
 
 Centigrade and Fahrenheit degrees compared . 550 
 
 Temperature Conversion Table 552 
 
 Copper-ball Pyrometer 553 
 
 Thermo-electric Pyrometer 554 
 
 Temperatures in Furnaces 554 
 
 Seger's Fire-clay Pyrometer 555 
 
 Wiborgh Air Pyrometer 655 
 
 Mesure and Nouel's Pyrometer 556 
 
 Uehling and Steinbart Pyrometer 557 
 
 Air- thermometer 557 
 
 High Temperatures Judged by Color 558 
 
 Boiling-points of Substances 559 
 
 Melting-points 559 
 
 Unit of Heat 560 
 
 Mechanical Equivalent of Heat 560 
 
 Heat of Combustion 560 
 
 Heat Absorbed by Decomposition 561 
 
 Specific Heat 562 
 
 Thermal Capacity of Gases 564 
 
 Expansion by Heat 565 
 
 Absolute Temperature, Absolute Zero 567 
 
 Latent Heat of Fusion 68 
 
 Latent Heat of Evaporation 568 
 
 Total Heat of Evaporation 569 
 
 Evaporation and Drying 569 
 
 Evaporation from Reservoirs 569 
 
 Evaporation by the Multiple System 570 
 
 Resistance to Boiling * . . 570 
 
 Manufacture of Salt 570 
 
 Solubility of Salt 571 
 
 Salt Contents of Brines 571 
 
 Concentration of Sugar Solutions 572 
 
 Evaporating by Exhaust Steam 572 
 
 Drying in Vacuum 573 
 
 Driers and Drying 574 
 
 Design of Drying Apparatus 576 
 
 Humidity Table 577 
 
 Radiation of Heat 578 
 
 Black-body Radiation 579 
 
 Conduction and Convection of Heat 579 
 
 Rate of External Conduction 580 
 
 Heat Conduction of Insulating Materials 581 
 
 Heat Resistance, Reciprocal of Heat Conductivity 582 
 
 Steam-pipe Coverings 584 
 
 Transmission through Plates 587 
 
 Transmission in Condenser Tubes 588 
 
 Transmission of Heat in Feed-water Heaters 590 
 
 Transmission through Cast-iron Plates 591 
 
 Heating Water by Steam Coils 591 
 
 Transmission from Air or Gases to Water 592 
 
CONTENTS. XIX 
 
 PAGE 
 
 Transmission from Flame to Water 593 
 
 Cooling of Air 594 
 
 Transmission from Steam or Hot Water to Air 595 
 
 Thermodynamics 597 
 
 Entropy 599 
 
 Reversed Carnot Cycle, Refrigeration . . , 600 
 
 Principal Equations of a Perfect Gas 600 
 
 Construction of the Curve PV = C 602 
 
 Temperature-Entropy Diagram of Water and Steam 602 
 
 PHYSICAL PROPERTIES OF GASES. 
 
 Expansion of Gases 603 
 
 Boyle and Marriotte's Law 603 
 
 Law of Charles, Avogadro's Law 604 
 
 Saturation Point of Vapors 604 
 
 Law of Gaseous Pressure 604 
 
 Flow of Gases 605 
 
 Absorption by Liquids 605 
 
 Liquefaction of Gases, Liquid Air 605 
 
 AIR. 
 
 Properties of Air 606 
 
 Barometric Pressures 606 
 
 Air-manometer 607 
 
 Conversion Table for Air Pressures 607 
 
 Pressure at Different Altitudes 607, 609 
 
 Leveling by the Barometer and by Boiling Water 607 
 
 To find Difference in Altitude 608 
 
 Weight of Air at Different Pressures and Temperatures 609 
 
 Moisture in Atmosphere 609, 611 
 
 Humidity Table 610 
 
 Weight of Air and Mixtures of Air and Vapor 610, 613 
 
 Specific Heat of Air 614 
 
 Flow of Air. 
 
 Flow of Air through Orifices 615 
 
 Flow of Air in Pipes 617 
 
 Tables of Flow of Air 622, 623 
 
 Effects of Bends in Pipe 624 
 
 Anemometer Measurements 624 
 
 Equalization of Pipes 625 
 
 Wind. 
 
 Force of the Wind 626 
 
 Wind Pressure in Storms 627 
 
 Windmills 627 
 
 Capacity of Windmills 629 
 
 Economy of Windmills 630 
 
 Electric Power from Windmills 632 
 
 Compressed Air. 
 
 Heating of Air by Compression 632 
 
 Loss of Energy in Compressed Air 632 
 
 Loss due to Heating 633 
 
 Work of Adiabatic Compression of Air 634 
 
 Compound Air-compression 635 
 
XX CONTENTS. 
 
 PAGE 
 
 Mean Effective Pressures 635, 636 
 
 Horse-power Required for Compression 637 
 
 Compressed-air Engines 638 
 
 Mean and Terminal Pressures 638 
 
 Air-compression at Altitudes 639 
 
 Popp Compressed-air System 639 
 
 Small Compressed-air Motors 640 
 
 Efficiency of Air-heating Stoves 640 
 
 Efficiency of Compressed-air Transmission 640 
 
 Efficiency of Compressed-air Engines 640 
 
 Air-compressors .- 641 
 
 Tests of Air compressors 643 
 
 Steam Required to Compress 100 Cu. Ft. of Air. 644 
 
 Requirements of Rock-drills 645 
 
 Compressed Air for Pumping Plants 645 
 
 Compressed Air for Hoisting Engines 646 
 
 Practical Results with Air Transmission 647 
 
 Effect of Intake Temperature 647 
 
 Compressed-air Motors with Return Circuit 648 
 
 Intercoolers for Air-compressors 64.8 
 
 Centrifugal Air-compressors 648 
 
 High-pressure Centrifugal Fans 649 
 
 Test of a Hydraulic Air-compressor 650 
 
 Mekarski Compressed-air Tramways 652 
 
 Compressed Air Working Pumps in Mines . , 652 
 
 Compressed Air for Street Railways 652 
 
 Fans and Blowers. 
 
 Centrifugal Fans 653 
 
 Best Proportions of Fans 653 
 
 Pressure due to Velocity 653 
 
 Blast Area or Capacity Area 655 
 
 Pressure Characteristics of Fans 655 
 
 Quantity of Air Delivered 655 
 
 Efficiency of Fans and Positive Blowers 657 
 
 Tables of Centrifugal Fans t 658-666 
 
 Effect of Resistance on Capacity of Fans 664 
 
 Sirocco or Multivane Fans '664 
 
 Methods of Testing Fans 667 
 
 Horse-power of a Fan 668 
 
 Pitot Tube Measurements 669 
 
 Thomas Electric Air and Gas Meter 669 
 
 Flow of Air through an Orifice 670 
 
 Diameter of Blast-pipes 670 
 
 Centrifugal Ventilators for Mines 672 
 
 Experiments on Mine Ventilators 673 
 
 Disk Fans 675 
 
 Efficiency of Disk Fans 676 
 
 Positive Rotary Blowers 677 
 
 Steam-jet Blowers and Exhausters 679 
 
 Blowing Engines 680 
 
 HEATING AND VENTILATION. 
 
 Ventilation 681 
 
 Quantity of Air Discharged through a Ventilating Duct 683 
 
 Heating and Ventilating of Large Buildings 684 
 
 Comfortable Temperatures and Humidities 685 
 
 Carbon Dioxide Allowable in Factories 685 
 
 Standards of Ventilation 686 
 
 Air Washing 687 
 
 Contamination of Air 687 
 
 Standards for Calculating Heating Problems 687 
 
CONTENTS. XXI 
 
 PAGE 
 
 Heating Value of Coal 687 
 
 Heat Transmission through Walls, etc 688 
 
 Allowance for Exposure and Leakage 689 
 
 Heating by Hot-air Furnaces . 690 
 
 Carrying Capacity of Air-pipes 691 
 
 Volume of Air at Different Temperatures 692 
 
 Sizes of Pipes Used in Furnace Heating 692 
 
 Furnace Heating with Forced Air Supply 693 
 
 Rated Capacity of Boilers for House Heating 693 
 
 Capacity of Grate-surface 694 
 
 Steam Heating, Rating of Boilers 694 
 
 Testing Cast-iron Heating Boilers 696 
 
 Proportioning House Heating Boilers 696 
 
 Coefficient of Transmission in Direct Radiation 697 
 
 Heat Transmitted in Indirect Radiation 698 
 
 Short Rules for Computing Radiating Surface 698 
 
 Carrying Capacity of Steam Pipes in Low Pressure .Heating .... 698 
 
 Proportioning Pipes to Radiating Surface 700 
 
 Sizes of Pipes in Steam Heating Plants 701 
 
 Resistance of Fittings 701 
 
 Removal of Air, Vacuum Systems 702 
 
 Overhead Steam-pipes 702 
 
 Steam-consumption in Car-heating 702 
 
 Heating a Greenhouse by Steam 702 
 
 Heating a Greenhouse by Hot Water 703 
 
 Hot-water Heating 703 
 
 Velocity of Flow in Hot- water Heating 703 
 
 Sizes of Pipe for Hot- water Heating 704 
 
 Sizes of Flow and Return Pipes 705 
 
 Heating by Hot-water, with Forced Circulation 707 
 
 Corrosion of Pipe in Hot- water Heating 708 
 
 Blower System of Heating and Ventilating 708 
 
 Advantages and Disadvantages of the Plenum System 708 
 
 Heat Radiated from Coils in the Blower System 708 
 
 Test of Cast-iron Heaters for Hot-blast Work 709 
 
 Factory Heating by the Fan System 710 
 
 Artificial Cooling of Air 710 
 
 Capacities of Fans for Hot-blast Heating 711 
 
 Relative Efficiency of Fans and Heated Chimneys 712 
 
 Heating a Building to 70 F 712 
 
 Heating by Electricity 713 
 
 Mine- ventilation 714 
 
 Friction of Air in Underground Passages 714 
 
 Equivalent Orifices - 715 
 
 WATER. 
 
 Expansion of Water 716 
 
 Weight of Water at Different Temperatures. 716, 717 
 
 Pressure of Water due to its Weight 718, 719 
 
 Head Corresponding to Pressures 718 
 
 Buoyancy 719 
 
 Boiling-point 719 
 
 Freezing-point 719 
 
 Sea-water 719 
 
 Ice and Snow 720 
 
 Specific Heat of Water 720 
 
 Compressibility of Water '. . . 720 
 
 Impurities of Water 720 
 
 Causes of Incrustation 721 
 
 Means for Preventing Incrustation 721 
 
 Analyses of Boiler-scale 722 
 
 Hardness of Water 723 
 
 Purifying Feed-water 723 
 
 Softening Hard Water 724 
 
XX11 CONTENTS. 
 
 Hydraulics. Flow of Water. PAGE 
 
 Formulae for Discharge through Orifices and Weirs 726 
 
 Flow of Water from Orifices 727 
 
 Flow in Open and Closed Channels 728 
 
 General Formulae for Flow . . . : 728 
 
 Chezy's Formula 728 
 
 Values of the Coefficient c 728, 732 
 
 Table, Fall in_Feet per mile, etc 729 
 
 Values of \/r for Circular Pipes 730 
 
 Kutter's Formula 730 
 
 D'Arcy's Formula 732 
 
 Values of a \/r for Chezy's Formula 733 
 
 Values of the Coefficient of Friction 734 
 
 Loss of Head 735 
 
 Resistance at the Inlet of a pipe 735 
 
 Exponential Formulae, Williams' and Hazen's Tables 736 
 
 Short Formulas 737 
 
 Flow of Water in a 20-inch Pipe , 737 
 
 Coefficients for Reducing H. and W. to Chezy's Formula 737 
 
 Tables of Flow of Water in Circular Pipes 738-743 
 
 Flow of Water in Riveted Pipes 743 
 
 Long Pipe Lines 743 
 
 Flow of Water in House-service Pipes 744 
 
 Friction Loss in Clean Cast-iron Pipe 745 
 
 Approximate Hydraulic Formulae 746 
 
 Compound Pipes, and Pipes with Branches 746 
 
 Rifled Pipes for Conveying Oils 746 
 
 Effect of Bend and Curves 747 
 
 Loss of Pressure Caused by Valves, etc 747, 748 
 
 Hydraulic Grade-line 748 
 
 Air-bound Pipes 748 
 
 Water Hammer 749 
 
 Vertical Jets 749 
 
 Water Delivered through Meters 749 
 
 Price Charged for Water in Cities 749 
 
 Fire Streams 749 
 
 Hydrant Pressures Required with Different Lengths and Sizes of 
 
 Hose 750 
 
 Pump Inspection Table 751 
 
 Pipe Sizes for Ordinary Fire Streams 752 
 
 Friction Losses in Hose 752 
 
 Rated Capacity of Steam Fire-engines 752 
 
 Flow of Water through Nozzles 753 
 
 The Siphon 754 
 
 Velocity of Water in Open Channels 755 
 
 Mean Surface and Bottom Velocities 755 
 
 Safe Bottom and Mean Velocities 755 
 
 Resistance of Soil to Erosion 755 
 
 Abrading and Transporting Power of Water 755 
 
 Frictional Resistance of Surfaces Moved in Water 756 
 
 Grade of Sewers 757 
 
 Measurement of Flowing Water 757 
 
 Piezometer 757 
 
 Pitot Tube Gauge 
 
 Maximum and Mean Velocities in Pipes. 758 
 
 The Venturi Meter 758 
 
 Measurement of Discharge by Means of Nozzles 759 
 
 The Lea V-notch Recording Meter 759 
 
 Flow through Rectangular Orifices 760 
 
 Measurement of an Open Stream 760 
 
 Miners' Inch Measurements 761 
 
 Flow of Water over Weirs 762 
 
 Francis's Formica for Weirs 762 
 
 Weir Table 763 
 
 Bazin's Experiments 763 
 
 The Cippoleti, or Trapezoidal Weir 764 
 
 The Triangular Weir :...... 764 
 

 CONTENTS. xxiii 
 
 WATER-POWER. 
 
 Power of a Fall of Water 765 
 
 Horse-power of a Running Stream 765 
 
 Current Motors 765 
 
 Bernouilli's Theorem 765 
 
 Maximum Efficiency of a Long Conduit 766 
 
 Mill-power . 766 
 
 Value of Water-power 76(j 
 
 Water Wheels. Hydraulic Turbines. 
 
 Theory of Turbines 768 
 
 Determination of Dimensions of Turbine Runners 769A 
 
 Comparison of Formulae for Dimensions of Turbines 769A 
 
 Comparison of American High Speed Runners 770 
 
 Type Characteristics of Turbines 770 
 
 Specific Discharge 770B 
 
 Use of Type Characteristics to Determine Size and Type of 
 
 Turbines 770B 
 
 Classes of Radial Inward Flow Turbines 771 
 
 Estimating Weight of Turbines 771A 
 
 Selection of Turbines 771A 
 
 Eifficiency of Turbine wheels 771s 
 
 Relation of Efficiency and Water Consumption to Speed ...... 772 
 
 Tests at the Philadelphia Exposition 772 
 
 Relation of Gare Openings to Efficiency 773 
 
 Tests of Turbine Discharge by Salt Solution 774' 
 
 Efficiency Tables for Turbines 776-777 
 
 Draft Tubes 778 
 
 Recent Turbine Practice 778 
 
 Some Large Turbines 779 
 
 The Fall-increaser for Turbines 780 
 
 Tangential or Impulse Water Wheels.- 
 
 The Pelton Water Wheel 780 
 
 Considerations in the Choice of a Tangential Wheel 781 
 
 Control of Tangential Water Wheels 781 
 
 Efficiency of the Doble Nozzle 782 
 
 Tests of a 12-inch Doble Motor 782 
 
 Water-power Plants Operating under High Pressures 782 
 
 Amount of Water Required to Develop a Given Horse-Power . 783 
 
 Formulae for Calculating the Power of Jet Water Wheels 784 
 
 Tangential Water-wheel Table 787 
 
 The Power of Ocean Waves. 
 
 Energy of Deep Sea Waves 786 
 
 Utilization of Tidal Power 787 
 
 PUMPS AND PUMPING ENGINES. 
 
 Theoretical Capacity of a Pump 788 
 
 Depth of Suction 788 
 
 The Deane Pump 7X9 
 
 Sizes of Direct-acting Pumps 789, 791 
 
 Amount of Water Raised by a Single-acting Lift-pump 790 
 
 Proportioning the Steam-cylinder of a Direct-acting Pump 790 
 
 Speed of Water through Pipes and Pump-passages 790 
 
 Efficiency of Small Pumps 790 
 
 The Worthington Duplex Pump 791 
 
 Speed of Piston 791-792 
 
 Speed of Water through Valves 792 
 
 Underwriters' Pumps, Standard Sizes 792 
 
 Boiler-feed Pumps 792 
 
 Pump Valves 793 
 
 The Worthington High-duty Pumping PJngine 793 
 
CONTENTS. 
 
 The d'Auria Pumping Engine 793 
 
 A 72,000,000-Gallon Pumping Engine 793 
 
 The Screw Pumping Engine 794 
 
 Finance of Pumping Engine Economy 794 
 
 Cost of Pumping 1000 Gallons per Minute 795 
 
 Centrifugal Pumps 796 
 
 Design of a Four-stage Turbine Pump 797 
 
 Relation of Peripheral Speed to Head 797 
 
 Tests of De Laval Centrifugal Pump 798 
 
 A High-duty Centrifugal Pump 801 
 
 Rotary Pumps 801 
 
 Tests of Centrifugal and Rotary Pumps 802 
 
 Duty Trials of Pumping Engines 802 
 
 Leakage Tests of Pumps 803 
 
 Notable High-duty Pump Records 805 
 
 Vacuum Pumps 806 
 
 The Pulsometer 806 
 
 The Jet Pump 807 
 
 The Injector 807 
 
 Pumping by Compressed Air 808 
 
 Gas-engine Pumps ; The Humphrey Gas Pump 808 
 
 Air-lift Pump 808 
 
 Air-lifts for Deep Oil-wells 809 
 
 The Hydraulic Ram 810 
 
 Quantity of Water Delivered by the Hydraulic Ram 810 
 
 Hydraulic Pressure Transmission. 
 
 Energy of Water under Pressure 812 
 
 Efficiency of Apparatus 812 
 
 Hydraulic Presses 813 
 
 Hydraulic Power in London 814 
 
 Hydraulic Riveting Machines 814 
 
 Hydraulic Forging 814 
 
 Hydraulic Engine 815 
 
 FUEL. 
 
 Theory of Combustion 816 
 
 Analyses of the Gases of Combustion 817 
 
 Temperature of the Fire 818 
 
 Classification of Solid Fuels 818 
 
 Classification of Coals 819 
 
 Analyses of Coals 820 
 
 Caking and Non-Caking Coals 820 
 
 Cannel Coals 821 
 
 Rhode Island Graphitic Anthracite 821 
 
 Analysis and Heating Value of Coals 821-828 
 
 Approximate Heating Values 822 
 
 Lord and Haas's Tests 823 
 
 Sizes of Anthracite Coal 823 
 
 Space occupied by Anthracite 823 
 
 Bernice Basin, Pa., Coal 824 
 
 Connellsville Coal and Coke 824 
 
 Bituminous Coals of the Western States 824 
 
 Analysis of Foreign Coals 825 
 
 Sampling Coal for Analyses 825 
 
 Relative Value of Steam Coals 826 
 
 Calorimetric Tests of Coals 826 
 
 Classified Lists of Coals 828-830 
 
 Purchase of Coal Under Specifications 830 
 
 Weathering of Coal 830 
 
 Pressed Fuel 831 
 
 Spontaneous Combustion of Coal 832 
 
 Coke 832 
 
 Experiments in Coking 833 
 
 Coal Washing 833 
 
CONTENTS. XXV 
 
 PAGE 
 
 Recovery of By-products in Coke Manufacture 833 
 
 Generation of Steam from the Waste Heat and Gases from Coke- 
 ovens 834 
 
 Products of the Distillation of Coal 834 
 
 Wood as Fuel 835 
 
 Heating Value of Wood 835 
 
 Composition of Wood 835 
 
 Charcoal 836 
 
 Yield of Charcoal from a Cord of Wood 836 
 
 Consumption of Charcoal in Blast Furnaces 837 
 
 Absorption of Water and of Gases by Charcoal 837 
 
 Miscellaneous Solid Fuels 837 
 
 Dust-fuel Dust Explosions 837 
 
 Peat or Turf 838 
 
 Sawdust as Fuel 838 
 
 Wet Tan-bark as Fuel 838 
 
 Straw as Fuel 839 
 
 Bagasse as Fuel in Sugar Manufacture 839 
 
 Liquid Fuel. 
 
 Products of Distillation of Petroleum 840 
 
 Lima Petroleum 840 
 
 Value of Petroleum as Fuel 840 
 
 Fuel Oil Burners 842 
 
 Specifications for Purchase of Fuel Oil 843 
 
 Alcohol as Fuel 843 
 
 Specific Gravity of Ethyl Alcohol 844 
 
 Vapor Pressures of Saturation of Alcohol and other Liquids .... 844 
 
 Fuel Gas. 
 
 Carbon Gas 845 
 
 Anthracite Gas 845 
 
 Bituminous Gas 846 
 
 Water Gas 846 
 
 Natural Gas in Ohio and Indiana 847 
 
 Natural Gas as a Fuel for Boilers 847 
 
 Producer-gas from One Ton of Coal 848 
 
 Combustion of Producer-gas 849 
 
 Proportions of Gas Producers and Scrubbers 849 
 
 Gas Producer Practice 851 
 
 Capacity of Producers 851 
 
 High Temperature Required for Production of CO 852 
 
 The Mond Gas Producer 852 
 
 Relative Efficiency of Different Coals in Gas-engine Tests 853 
 
 Use of Steam in Producers and Boiler Furnaces 854 
 
 Gas Analyses by Volume and by Weight 854 
 
 Gas Fuel for Small Furnaces 854 
 
 Blast-furnace Gas 855 
 
 Acetylene and Calcium Carbide. 
 
 Acetylene 855 
 
 Calcium Carbide 856 
 
 Acetylene Generators and Burners 857 
 
 The Acetylene Blowpipe 857 
 
 Ignition Temperature of Gases 858 
 
 Illuminating Gas. 
 
 Coal-gas 858 
 
 Water-gas 858 
 
 Analyses of Water-gas and Coal-gas 860 
 
 Calorific Equivalents of Constituents 860 
 
 Efficiency of a Water-gas Plant 861 
 
 Space Required for a Water-gas Plant 862 
 
 Fuel- value of Illuminating Gas 863 
 
XXVI CONTENTS. 
 
 PAGE 
 
 Flow of Gas in Pipes. **, 864-866 
 
 Services for Lamps 864 
 
 Factors for Reducing Volumes of Gas 865 
 
 STEAM. 
 
 Temperature and Pressure 867 
 
 Total Heat 867 
 
 Latent Heat of Steam 867 
 
 Specific Heat of Saturated -Steam 867 
 
 The Mechanical Equivalent of Heat 868 
 
 Pressure of Saturated Steam 868 
 
 Volume of Saturated Steam 868 
 
 Specific Heat of Superheated Steam 869 
 
 Specific Density of Gaseous Steam 870 
 
 Table of the Properties of Saturated Steam 871-874 
 
 Table of the Properties of Superheated Steam 874, 875 
 
 Flow of Steam. 
 
 Flow of Steam through a Nozzle 876 
 
 Napier's Approximate Rule 876 
 
 Flow of Steam in Pipes 877 
 
 Flow of Steam in Long Pipes, Ledoux's Formula 877 
 
 Table of Flow of Steam in Pipes 878 
 
 Carrying Capacity of Extra Heavy Steam Pipes 879 
 
 Resistance to Flow by Bends, Valves, etc 879 
 
 Sizes of Steam-pipes for Stationary Engines 879 
 
 Sizes of Steam-pipes for Marine Engines 880 
 
 Proportioning Pipes for Minimum Loss by Radiation and Friction 880 
 
 Available Maximum Efficiency of Expanded Steam 881 
 
 Steam-pipes. 
 
 Bursting-tests of Copper Steam-pipes 882 
 
 Failure of a Copper Steam-pipe 882 
 
 Wire-wound Steam-pipes 882 
 
 Materials for Pipes and Valves for Superheated Steam 882 
 
 Riveted Steel Steam-pipes 883 
 
 Valves in Steam-pipes 883 
 
 The Steam Loop 883 
 
 Loss from an Uncovered Steam-pipe 884 
 
 Condensation in an Underground Pipe Line 884 
 
 Steam Receivers in Pipe Lines 884 
 
 Equation of Pipes 884 
 
 Identification of Power House Piping by Colors 885 
 
 THE STEAM-BOILER. 
 
 The Horse-power of a Steam-boiler 885 
 
 Measures for Comparing the Duty of Boilers 886 
 
 Unit of Evaporation 886 
 
 Steam-boiler Proportions 887 
 
 Heating-surface 887 
 
 Horse-power, Builders' Rating 888 
 
 Grate-surface 888 
 
 Areas of Flues 889 
 
 Air-passages Through Grate-bars 889 
 
 Performance of Boilers 889 
 
 Conditions which Secure Economy 890 
 
 Air Leakage in Boiler Settings 891 
 
 Efficiency of a Boiler 891 
 
 Autographic CO2 Recorders 891 
 
 Relation of Efficiency to Rate of Driving, Air Supply, etc 893 
 
 Effect of Quality of Coal upon Efficiency 895 
 
 Effect of Imperfect Combustions and Excess Air Supply 896 
 
 Theoretical Efficiency with Pittsburgh Coal 896 
 
CONTENTS. XXVII 
 
 / 
 
 The Straight Line Formula for Efficiency 896 
 
 High Rates of Evaporation 898 
 
 Boilers Using Waste Gases 898 
 
 Maximum Efficiencies at Different Rates of Driving 898 
 
 Rules for Conducting Boiler Tests 899 
 
 Heat Balance in Boiler Tests 907 
 
 Factors of Evaporation 908 
 
 Strength of Steam-boilers. 
 
 Rules for Construction 908 
 
 Shell-plate Formulae 913 
 
 Efficiency of Riveted Joints 914 
 
 Loads Allowed on Stays 916 
 
 Holding Power of Boiler Tubes 916 
 
 Safe-working Pressures 918 
 
 Boiler Attachments, Furnaces, etc. 
 
 Fusible Plugs 2 918 
 
 Steam Domes 918 
 
 Mechanical Stokers 918 
 
 The Hawley Down-draught Furnace 919 
 
 Under-feed Stokers 919 
 
 Smoke Prevention 920 
 
 Burning Illinois Coal without Smoke 921 
 
 Conditions of Smoke Prevention 922 
 
 Forced Combustion 923 
 
 Fuel Economizers 924 
 
 Thermal Storage 927 
 
 Incrustation and Corrosion 927 
 
 Boiler-scale Compounds 929 
 
 Removal of Hard Scale 930 
 
 Corrosion in Marine Boilers 930 
 
 Use of Zinc '. 931 
 
 Effect of Deposit on Flues 931 
 
 Dangerous Boilers 932 
 
 Safety-valves. 
 
 Rules for Area of Safety-valves 932 
 
 Spring-loaded Safety-valves 933 
 
 Safety Valves for Locomotives 935 
 
 The Injector. 
 
 Equation of the Injector 936 
 
 Performance of Injectors 937 
 
 Boiler-feeding Pumps 937 
 
 Feed-water Heaters. 
 
 Percentage of Saving Due to Use of Heaters 938 
 
 Strains Caused by Cold Feed-water 939 
 
 Calculation of Surface of Heaters and^Condensers 939 
 
 Open vs. Closed Feed-water Heaters 940 
 
 Steam Separators. 
 
 Efficiency of Steam Separators 941 
 
 Determination of Moisture in Steam. 
 
 Steam Calorimeters 942 
 
 Coil Calorimeter 942 
 
 Throttling Calorimeters 943 
 
 Separating Calorimeters 943 
 
XXV111 CONTENTS. 
 
 PAGE 
 
 Identification of Dry Steam 944 
 
 Usual Amount of Moisture in Steam 944 
 
 Chimneys. 
 
 Chimney Draught Theory 944 
 
 Force of Intensity of Draught 945 
 
 Rate of Combustion Due to Height of Chimney 947 
 
 High Chimneys not Necessary 948 
 
 Height of Chimneys Required for Different Fuels 948 
 
 Protection of Chimney from Lightning 949 
 
 Table of Size of Chimneys 950 
 
 Velocity of Gas in Chimneys 951 
 
 Size of Chimneys for Oil Fuel 951 
 
 Chimneys with Forced Draught 952 
 
 Largest Chimney in the World 952 
 
 Some Tall Brick Chimneys 953, 954 
 
 Stability of Chimneys 954 
 
 Steel Chimneys 956 
 
 Reinforced Concrete Chimneys 958 
 
 Sheet-iron Chimneys 958 
 
 THE STEAM ENGINE. 
 
 Expansion of Steam ; 959 
 
 Mean and Terminal Absolute Pressures 960 
 
 Calculation of Mean Effective Pressure 961 
 
 Mechanical Energy of Steam Expanded Adiabatically 963 
 
 Measures for Comparing the Duty of Engines 963 
 
 Efficiency, Thermal Units per Minute 964 
 
 Real Ratio of Expansion 965 
 
 Effect of Compression 965 
 
 Clearance in Low- and High-speed Engines 966 
 
 Cylinder-condensation 966 
 
 Water-consumption of Automatic Cut-off Engines 967 
 
 Experiments on Cylinder-condensation 967 
 
 Indicator Diagrams 968 
 
 Errors of Indicators 969 
 
 Pendulum Indicator Rig 969 
 
 The Manograph 969 
 
 The Lea Continuous Recorder 970 
 
 Indicated Horse-power 970 
 
 Rules for Estimating Horse-power 970 
 
 Horse-power Constants 971 
 
 Table of Engine Constants 972 
 
 To Draw Clearance on Indicator-diagram 974 
 
 To Draw Hyperbola Curve on Indicator-diagram 974 
 
 Theoretical Water Consumption 975 
 
 Leakage of Steam 976 
 
 Compound Engines. 
 
 Advantages of Compounding 976 
 
 Woolf and Receiver Types of Engines 977 
 
 Combined Diagrams > 979 
 
 Proportions of Cylinders in Compound Engines 980 
 
 Receiver Space 980 
 
 Formula for Calculating Work of Steam 981 
 
 Calculation of Diameters of Cylinders 982 
 
 Triple-expansion Engines 983 
 
 Proportions of Cylinders 983 
 
 Formulae for Proportioning Cylinders 983 
 
 Types of Three-stage Expansion Engines 985 
 
 Sequence of Cranks 986 
 
 Velocity of Steam through Passages , 986 
 
 A Double-tandem Triple-expansion Engine 986 
 
 Quadruple-expansion Engines 986 
 
CONTENTS. XXIX 
 Steam-engine Economy. 
 
 JrALriU 
 
 Economic Performance of Steam-engines 987 
 
 Feed- water Consumption of Different Types 987 
 
 Sizes and Calculated Performances of Vertical High-speed Engine 988 
 
 The Willans Law, Steam Consumption at Different Loads 991 
 
 Relative Economy of Engines under Variable Loads 992 
 
 Steam Consumption of Various Sizes 992 
 
 Steam Consumption in Small Engines 993 
 
 Steam Consumption at Various Speeds '993 
 
 Capacity and Economy of Steam Fire Engines 993 
 
 Economy Tests of High-speed Engines 994 
 
 Limitation of Engine Speed 995 
 
 British High-speed Engines 995 
 
 Advantage of High Initial and Low-back Pressure 996 
 
 Comparison of Compound and Single-cylinder Engines 997 
 
 Two-cylinder and Three-cylinder Engines 997 
 
 Steam Consumption of Engines with Superheated Steam 998 
 
 Steam Consumption of Different Types of Engine 999 
 
 The Lentz Compound Engine 999 
 
 Efficiency of Non-condensing Compound Engines 1000 
 
 Economy of Engines under Varying Loads 1000 
 
 Effect of Water in Steam on Efficiency 1001 
 
 Influence of Vacuum and Superheat on Steam Consumption. . . . 1001 
 
 Practical Application of Superheated Steam 1002 
 
 Performance of a Quadruple Engine 1003 
 
 Influence of the Steam-jacket 1004 
 
 Best Economy of the Piston Steam Engine 1005 
 
 Highest Economy of Pumping-engines 1006 
 
 Sulphur-dioxide Addendum to Steam-engine 1007 
 
 Standard Dimensions of Direct-connected Generator Sets 1007 
 
 Dimensions of Parts of Large Engines 1007 
 
 Large Rolling-mill Engines , 1008 
 
 Counterbalancing Engines 1008 
 
 Preventing Vibrations of Engines * 1008 
 
 Foundations Embedded in Air 1009 
 
 Most Economical Point of Cut-off 1009 
 
 Type of Engine used when Exhaust-steam is used for Heating. . 1009 
 
 Cost of Steam-power 1009 
 
 Cost of Coal for Steam-power 1010 
 
 Power-plant Economics 1011 
 
 Analysis of Operating Costs of Power-plants 1013 
 
 Economy of Combination of Gas Engines and Turbines 1014 
 
 Storing Steam Heat in Hot Water 1014 
 
 Utilizing the Sun's Heat as a Source of Power 1015 
 
 Rules for Conducting Steam-engine Tests 1015 
 
 Dimensions of Parts of Engines. 
 
 Cylinder. 1021 
 
 Clearance of Piston 1021 
 
 Thickness of Cylinder 1021 
 
 Cylinder Heads 1022 
 
 Cylinder-head Bolts 1022 
 
 The Piston 1023 
 
 Piston Packing-rings 1023 
 
 Fit of Piston-rod 1024 
 
 Diameter of Piston-rods 1024 
 
 Piston-rod Guides 1024 
 
 The Connecting-rod 1025 
 
 Connecting-rod Ends 1026 
 
 Tapered Connecting-rods 1026 
 
 The Crank-pin 1027 
 
 Crosshead-pin or Wrist-pin . 1029 
 
 The Crank-arm 1029 
 
 The Shaft, Twisting Resistance 1030 
 
 * iistance to Bending . . , X032 
 
XXX CONTENTS. 
 
 _ PAGE 
 
 Equivalent Twisting Moment 1032 
 
 Fly-wheel Shafts 1033 
 
 Length of Shaft-bearings 1034 
 
 Crank-shafts with Center-crank and Double-crank Arms 1036 
 
 Crank-shaft with two Cranks Coupled at 90 1037 
 
 Crank-shaft with three Cranks at 120 1038 
 
 Valve-stem or Valve-rod 1038 
 
 The Eccentric 1039 
 
 The Eccentric-rod 1039 
 
 Reversing-gear 1039 
 
 Current Practice in Engine Proportions, 1897 1039 
 
 Current Practice in Steam-engine Design, 1909 1040 
 
 Shafts and Bearings of Engines 1042 
 
 Calculating the Dimensions Of Bearings 1042 
 
 Engine-frames or Bed-plates 1044 
 
 Fly-wheels. 
 
 Weight of Fly-wheels 1044 
 
 Weight of Fly-wheels for Alternating-current Units 1047 
 
 Centrifugal Force in Fly-wheels 1047 
 
 Diameters for Various Speeds 1048 
 
 Strains in the Runs 1049 
 
 Arms of Fly-wheels and Pulleys 1050 
 
 Thickness of Rims 1050 
 
 A Wooden Rim Fly-wheel 1051 
 
 Wire- wound Fly-wheels 1052 
 
 The Slide-Valve. 
 
 Definitions, Lap, Lead, etc 1052 
 
 Sweet's Valve-diagram , 1054 
 
 The Zeuner Valve-diagram 1054 
 
 Port Opening, Lead, and Inside Lead 1057 
 
 Crank Angles for Connecting-rods of Different Lengths 1058 
 
 Ratio of Lap and of Port-opening to Valve- travel 1058 
 
 Relative Motions of Crosshead and Crank 1060 
 
 Periods of Admission or Cut-off for Various Laps and Travels. . 1060 
 
 Piston- valves 1061 
 
 Setting the Valves of an Engine 1061 
 
 To put an Engine on its Center 1061 
 
 Link-motion 1062 
 
 The Walschaerts Valve-gear 1064 
 
 Governors. 
 
 Pendulum or Fly-ball Governors 1065 
 
 To Change the Speed of an Engine 1066 
 
 Fly-wheel or Shaft Governors 1066 
 
 The Rites Inertia Governor 1066 
 
 Calculation of Springs for Shaft-governors 1066 
 
 Condensers, Air-pumps, Circulating-pumps, etc.. 
 
 The Jet Condenser 1068 
 
 Quantity of Cooling Water 1068 
 
 Ejector Condensers 1069 
 
 The Barometric Condensers 1069 
 
 The Surface Condenser 1069 
 
 Coefficient of Heat Transference in Condensers 
 
 The Power Used for Condensing Apparatus 
 
 Vacuum, Inches of Mercury and Absolute Pressure 
 
 Temperatures, Pressures and Volumes of Saturated Air 
 
 Condenser Tubes 1072 
 
 Tube-plates 1073 
 
 Spacing of Tubes 1073 
 
 Air-pump 
 
 Area through Valve-seats 1 73 
 
CONTENTS. 
 
 PAGE 
 
 Work done by an Air-pump 1074 
 
 Most Economical Vacuum for Turbines 1075 
 
 Circulating-pump 1075 
 
 The Leblanc Condenser 1076 
 
 Feed-pumps for Marine Engines 1076 
 
 An Evaporative Surface Condenser 1076 
 
 Continuous Use of Condensing Water 1076 
 
 Increase of Power by Condensers 1077 
 
 Advantage of High Vacuum in Reciprocating Engines 1078 
 
 The Choice of a Condenser 1078 
 
 Cooling Towers 1079 
 
 Calculation of Air Supply for Cooling Towers 1080 
 
 Tests of a Cooling Tower and Condenser 1080 
 
 Water Evaporated in a Cooling Tower 1080 
 
 Weight of Water Vapor mixed with One Pound of Air -. . . . 1081 
 
 Evaporators and Distillers 1082 
 
 Rotary Steam Engines Steam Turbines. 
 
 Rotary Steam Engines 1082 
 
 Impulse and Reaction Turbines 1082 
 
 The DeLaval Turbine 1082 
 
 The Zolley or Rateau Turbine 1083 
 
 The Parsons Turbine 1083 
 
 The Westinghouse Double-flow Turbine 1083 
 
 Mechanical Theory of the Steam Turbine 1084 
 
 Heat Theory of the Steam Turbine 1084 
 
 Velocity of Steam in Nozzles 1085 
 
 Speed of the Blades 1086 
 
 Comparison of Impulse and Reaction Turbines 1087 
 
 Loss due to Windage 1087 
 
 Efficiency of the Machine 1087 
 
 Steam Consumption of Turbines 1088 
 
 Effect of Vacuum on Steam Turbines 1088 
 
 Tests of Turbines 1088 
 
 Efficiency of the Rankine Cycle 1089 
 
 Factors for Reduction to Equivalent Efficiency 1090 
 
 Effect of Pressure, Vacuum and Superheat 1090 
 
 Steam and Heat Consumption of the Ideal Engine 1091 
 
 Westinghouse Turbines at 74th St. Station, New York 1092 
 
 A Steam Turbine Guarantee 1092 
 
 Efficiency of a 5000-K. W. Steam Turbine Generator 1092 
 
 Comparison of Large Turbines and Reciprocating Engines ..... 1092 
 
 Steam Consumption of Small Steam Turbines 1093 
 
 Low-pressure Steam Turbines 1093 
 
 Tests of a 15,000-K.W. Steam-engine Turbine Unit 1095 
 
 Reduction Gear for Steam Turbines 1095 
 
 Hot-air Engines. 
 
 Hot-air or Caloric Engines * 1095 
 
 Test of a Hot-air Engine , 1095 
 
 INTERNAL, COMBUSTION ENGINES. 
 
 Four-cycle and Two-cycle Gas-engines 1096 
 
 Temperatures and Pressures Developed 1096 
 
 Calculation of the Power of Gas-engines 1097 
 
 Pressures and Temperatures at End of Compression 1098 
 
 Pressures and Temperature at Release 1099 
 
 after Combustion 1099 
 
 Mean Effective Pressures 1099 
 
 Sizes of Large Gas-engines 1100 
 
 Engine Constants for Gas-engines 1101 
 
 Rated Capacity of Automobile Engines 1101 
 
 Estimate of the Horse-power of a Gas-engine 1101 
 
XXX11 CONTENTS. 
 
 PAGE 
 
 Oil and Gasoline Engines 1101 
 
 The Diesel Oil Engine 1102 
 
 The De La Vergne Oil Engine 1102 
 
 Alcohol Engines 1102 
 
 Ignition 1102 
 
 Timing 1103 
 
 Governing 1103 
 
 Gas and Oil Engine Troubles 1103 
 
 Conditions of Maximum Efficiency 1103 
 
 Heat Losses in the Gas-engine 1104 
 
 Economical Performance of Gas-engines 1104 
 
 Utilization of Waste Heat from Gas-engines 1105 
 
 Rules for Conducting Tests of Gas and Oil Engines 1105 
 
 LOCOMOTIVES. 
 
 Resistance of Trains 1108 
 
 Resistance of Electric Railway Cars and Trains 1110 
 
 Efficiency of the Mechanism of a Locomotive 1111 
 
 Adhesion 1111 
 
 Tractive Force 1111 
 
 Size of Locomotive Cylinders 1112 
 
 Horse-power of a Locomotive 1113 
 
 Size of Locomotive Boilers 1113 
 
 Wootten's Locomotive 1114 
 
 Grate-surface, Smokestacks, and Exhaust-nozzles 1115 
 
 Fire-brick Arches 1115 
 
 Economy of High Pressures 1116 
 
 Leading American Types 1116 
 
 Classification of Locomotives 1116 
 
 Steam Distribution for High Speed 1117 
 
 Formulae for Curves . 1117 
 
 Speed of Railway Trains 1118 
 
 Performance of a High-speed Locomotive 1118 
 
 Fuel Efficiency of American Locomotives 1119 
 
 Locomotive Link-motion 1119 
 
 Dimensions of Some American Locomotives 1120 
 
 The Mallet Compound Locomotive 1120 
 
 Indicated Water Consumption 1122 
 
 Indicator Tests of a Locomotive at High-speed 1122 
 
 Locomotive Testing Apparatus 1123 
 
 Weights and Prices of Locomotives 1124 
 
 Waste of Fuel in Locomotives 1 125 
 
 Advantages of Compounding 1 125 
 
 Depreciation of Locomotives 1125 
 
 Average Train Loads 1125 
 
 Tractive Force of Locomotives, 1893 and 1905 1125 
 
 Superheating in Locomotives 1126 
 
 Counterbalancing Locomotives 
 
 Narrow-gauge Railways 1127 
 
 Petroleum-burning Locomotives 
 
 Fireless Locomotives :....-.... 1127 
 
 Self-propelled Railway Cars 
 
 Compressed-air Locomotives 1128 
 
 Air Locomotives with Compound Cylinders 1129 
 
 SHAFTING. 
 
 Diameters to Resist Torsional Strain 1130 
 
 Deflection of Shafting 1131 
 
 Horse-power Transmitted by Shafting 1132 
 
 Flange Couplings 1133 
 
 Effect of Cold Rolling 1133 
 
 Hollow Shafts. . 1133 
 
 Sizes of Collars for Shafting 1133 
 
 Table for Laying Out Shafting , , , , , , U34 
 
* 
 
 CONTENTS. XXxiii 
 
 ^ 
 
 PULLETS. PAGE 
 
 Proportions of Pulleys 1135 
 
 Convexity of Pulleys 1136 
 
 Cone or Step Pulleys 1 136 
 
 Method of Determining Diameter^ of Cone Pulleys 1136 
 
 Speeds of Shafts with Cone Pulleys 1137 
 
 Speeds in Geometrical Progression , 1138 
 
 BELTING. 
 
 Theory of Belts and Bands 1138 
 
 Centrifugal Tension 1139 
 
 Belting Practice, Formulae for Belting 1139 
 
 Horse-power of a Belt one inch wide 1140 
 
 A. F. Nagle's Formula 1141 
 
 Width of Belt for Given Horse-power , . . . 1141 
 
 Belt Factors 1 142 
 
 Taylor's Rules for Belting 1143 
 
 Earth's Studies on Belting 1146 
 
 Notes on Belting 1146 
 
 Lacing of Belts 1147 
 
 Setting a Belt on Quarter-twist 1147 
 
 To Find the Length of Belt 1148 
 
 To Find the Angle of the Arc of Contact 1148 
 
 To Find the Length of Belt when Closely Rolled 1148 
 
 To Find the Approximate Weight of Belts 1148 
 
 Relations of the Size and Speeds of Driving and Driven Pulleys. 1148 
 
 Evils of Tight Belts 1149 
 
 Sag of Belts 1149 
 
 Arrangement of Belts and Pulleys 1149 
 
 Care of Belts 1150 
 
 Strength of Belting ( . . 1150 
 
 Adhesion, Independent of Diameter rv. 1151 
 
 Endless Belts 1151 
 
 Belt Data 1151 
 
 U. S. Navy Specifications for Leather Belting 1151 
 
 Belt Dressings 1151 
 
 Cement for Cloth or Leather 1152 
 
 Rubber Belting 1152 
 
 Steel Belts 1152 
 
 Chain Drives. 
 
 Roller Chain and Sprocket Drives 1153 
 
 Belting versus Chain Drives 1155 
 
 Data used in Design of Chain Drives 1156 
 
 Comparison of Rope and Chain Drives 1157 
 
 GEARING. 
 
 Pitch, Pitch-circle, etc 3157 
 
 Diametral and Circular Pitch 1158 
 
 Diameter of Pitch-line of Wheels from 10 to 100 Teeth 1159 
 
 Chordal Pitch 1159 
 
 Proportions of Teeth 1 159 
 
 Gears with Short Teeth 1160 
 
 Formulae for Dimensions of Teeth 1160 
 
 Width of Teeth 1161 
 
 Proportions of Gear-wheels 1161 
 
 Rules for Calculating the Speed of Gears and Pulleys 1162 
 
 Milling Cutters for Interchangeable Gears 1162 
 
 Forms of the Teeth. 
 
 The Cycloidal Tooth 1162 
 
 The Involute Tooth 1165 
 
XXXiV CONTENTS, 
 
 PAGE 
 
 Approximation by Circular Arcs -. 1166 
 
 Stub Gear Teeth for Automobiles 1167 
 
 Stepped Gears 1168 
 
 Twisted Teeth 1168 
 
 Spiral Gears 1168 
 
 Worm Gearing 1168 
 
 The Hindley Worm 1169 
 
 Teeth of Bevel-wheels 1169 
 
 Annular and Differential Gearing 1169 
 
 Efficiency of Gearing 1170 
 
 Efficiency of Worm Gearing 1171 
 
 Efficiency of Automobile Gears 1172 
 
 Strength of Gear Teeth. 
 
 Various Formulae for Strength 1172 
 
 Comparison of Formulae 1 174 
 
 Raw-hide Pinions 1177 
 
 Maximum Speed of Gearing 1177 
 
 A Heavy Machine-cut Spur-gear 1 178 
 
 Frictional Gearing 1178 
 
 Frictional Grooved Gearing 1178 
 
 Power Transmitted by Friction Drives 1178 
 
 Friction Clutches 1179 
 
 Coil Friction Clutches 1180 
 
 HOISTING AND CONVEYING. 
 
 Working Strength of Blocks 1181 
 
 Chain-blocks 1181 
 
 Efficiency of Hoisting Tackle 1182 
 
 Proportions of Hooks 1182 
 
 Heavy Crane Hooks 1183 
 
 Strength of Hooks and Shackles 1184 
 
 Power of Hoisting Engines 1184 
 
 Effect of Slack Rope on Strain in Hoisting 1186 
 
 Limit of Depth for Hoisting 1 186 
 
 Large Hoisting Records \ 1186 
 
 Safe Loads for Ropes and Chains 1187 
 
 Pneumatic Hoisting 1 187 
 
 Counterbalancing of Winding-engines 1188 
 
 Cranes. 
 
 Classification of Cranes 1189 
 
 Position of the Inclined Brace in a Jib Crane 1190 
 
 Electric Overhead Traveling Cranes 1190 
 
 Power Required to Drive Cranes 1191 
 
 Dimensions, Loads and Speeds of Electric Cranes 1191 
 
 Notable Crane Installations 1192 
 
 A 150-ton Pillar Crane 1192 
 
 Compressed-air Traveling Cranes 1192 
 
 Electric versus Hydraulic Cranes 
 
 Power Required for Traveling Cranes and Hoists 1193 
 
 Lifting Magnets 1193 
 
 Telpherage 1196 
 
 ' Coal-handling Machinery. 
 
 Weight of Overhead Bins 1196 
 
 Supply-pipes from Bins 1196 
 
 Types of Coal Elevators 1196 
 
 Combined Elevators and Conveyors 1197 
 
 Coal Conveyors 1 197 
 
 Horse-power of Conveyors 1 198 
 

 CONTENTS. XXXV 
 
 PAGE 
 
 Bucket, Screw, and Belt Conveyors 1198 
 
 Weight of Chain and of Flights 1199 
 
 Capacity of Belt Conveyors 1 199 
 
 Belt Conveyor Construction 1200 
 
 Horse-power to Drive Belt Conveyors 1200 
 
 Relative Wearing Power of Conveyor Belts * 1200 
 
 Pneumatic Conveying 1201 
 
 Pneumatic Postal Transmission 1201 
 
 , 
 
 Wire-rope Haulage. 
 
 Self-acting Inclined Plane 1202 
 
 Simple Engine Plane 1203 
 
 Tail-rope System 1203 
 
 Endless Rope System 1203 
 
 Wire-rope Tramways 1204 
 
 Stress in Hoisting-ropes on Inclined Planes 1204 
 
 An Aerial Tramway 21 miles long .. . . 1205 
 
 Suspension Cableways and Cable Hoists 1205 
 
 Tension Required to Prevent Wire Slipping on Drums 1206 
 
 Formulae for Deflection of a Wire Cable 1207 
 
 Taper Ropes of Uniform Tensile Strength 1208 
 
 WIRE-ROPE TRANSMISSION. 
 
 Working Tension of Wire Ropes 1208 
 
 Sheaves for Wire-rope Transmission 1208 
 
 Breaking Strength of Wire Ropes. 1209 
 
 Bending Stresses of Wire Ropes 1209 
 
 Horse-power Transmitted 1210 
 
 Diameters of Minimum Sheaves 1211 
 
 Deflection of the Rope 1211 
 
 Limits of Span 1212 
 
 Long-distance Transmission 1212 
 
 Inclined Transmissions 1212 
 
 Bending Curvature of Wire Ropes 1213 
 
 ROPE-DRIVING. 
 
 Formulae for Rope-driving 1214 
 
 Horse-power of Transmission at Various Speeds 1215 
 
 Sag of the Rope between Pulleys. 1216 
 
 Tension on the Slack Part of the Rope 12*16 
 
 Miscellaneous Notes on Rope-driving . . , 1217 
 
 Data of Manila. Transmission Rope 1218 
 
 Cotton Ropes 1218 
 
 FRICTION AND LUBRICATION. 
 
 Coefficient of Friction 1219 
 
 Rolling Friction '. 1219 
 
 Friction of Solids < 1219 
 
 Friction of Rest , 1219 
 
 Laws of Unlubricated Friction 1219 
 
 Friction of Tires Sliding on Rails 1219 
 
 Coefficient of Rolling Friction 1220 
 
 Laws of Fluid Friction .' 1220 
 
 Angles of Repose of Building Materials 1220 
 
 Coefficient of Friction of Journals 1220 
 
 Friction of Motion 1221 
 
 Experiments on Friction of a Journal 1221 
 
 Coefficients of Friction of Journal with Oil Bath 1221, 1223 
 
 Coefficients of Friction of Motion and of Rest 1222 
 
 Value of Anti-friction Metals . . 1223 
 
 Cast-iron for Bearings 1223 
 
x ^y CONTENTS. 
 
 PAGE 
 
 Friction of Metal under Steam-pressure 1223 
 
 Morin's Laws of Friction 1223 
 
 Laws of Friction of Well-lubricated Journals 1225 
 
 Allowable Pressures on Bearing-surfaces 1226 
 
 Oil-pressure in a Bearing 1228 
 
 Friction of Car-journal Brasses 1228 
 
 Experiments on Overheating of Bearings 1228 
 
 Moment of Friction and Work of Friction 1229 
 
 Tests of Large Shaft Bearings 1230 
 
 Clearance between Journal and Bearing 1230 
 
 Allowable Pressures on Bearings 1230 
 
 Bearing Pressures for Heavy Intermittent Loads 1231 
 
 Bearings for Very High Rotative Speed 1231 
 
 Bearing Pressures in Shafts of Parsons Turbine 1232 
 
 Thrust Bearings in Marine Practice 1232 
 
 Bearings for Locomotives 1232 
 
 Bearings of Corliss Engines 1232 
 
 Temperature of Engine Bearings 1232 
 
 Pivot Bearings 1232 
 
 The Schiele Curve 1232 
 
 Friction of a Flat Pivot-bearing 1233 
 
 Mercury-bath Pivot 1233 
 
 Ball Bearings, Roller Bearings, etc 1233 
 
 Friction Rollers 1233 
 
 Conical Roller Thrust Bearings. 1234 
 
 The Hyatt Roller Bearing 1235 
 
 Notes on Ball Bearings 1235 
 
 Saving of Power by Use of Ball Bearings 1237 
 
 Knife-edge Bearings 1238 
 
 Friction of Steam-engines 1238 
 
 Distribution of the Friction of Engines 1238 
 
 Friction Brakes and Friction Clutches. 
 
 Friction Brakes 1239 
 
 Friction Clutches 1239 
 
 Magnetic and Electric Brakes 1240 
 
 Design of Band Brakes 1240 
 
 Friction of Hydaulic Plunger Packing 1241 
 
 Lubrication. 
 
 Durability of Lubricants 1241 
 
 ualifications of Lubricants 1242 
 
 xamination of Oils 1242 
 
 Specifications for Petroleum Lubricants 1243 
 
 Penna. R. R. Specifications 1244 
 
 Grease Lubricants 
 
 Testing Oil for Steam Turbines 1244 
 
 8uantity of Oil to Run an Engine 
 
 ylinder Lubrication 1245 
 
 Soda Mixture for Machine Tools 
 
 Water as a Lubricant 124 
 
 Acheson's Deflocculated Graphite 1246 
 
 Solid Lubricants 1246 
 
 Graphite, Soapstone, Metaline 1246 
 
 THE FOUNDRY. 
 
 Cupola Practice 1247 
 
 Melting Capacity of Different Cupolas 1248 
 
 Charging a Cupola 1248 
 
 Improvement of Cupola Practice 
 
 Charges in Stove Foundries 1250 
 
 Foundry Blower Practice 1250 
 

 CONTENTS. XXXV11 
 
 PAGE 
 
 Results of Increased Driving 1252 
 
 Power Required for a Cupola Fan 1253 
 
 Utilization of Cupola Gases 1253 
 
 Loss of Iron in Melting 1253 
 
 Use of Softeners ; . . 1253 
 
 Weakness of Large Castings 1253 
 
 Shrinkage of Castings 1254 
 
 Growth of Cast Iron by Heating 1254 
 
 Hard Iron due to Excessive Silicon 1254 
 
 Ferro Alloys for Foundry Use 1255 
 
 Dangerous Ferro-silicon 1255 
 
 Quality of Foundry Coke 1255 
 
 Castings made in Permanent Cast-iron Molds 1255 
 
 Weight of Castings from Weight of Pattern 1256 
 
 Molding Sand 1256 
 
 Foundry Ladles 1257 
 
 : 
 
 THE MACHINE-SHOP. 
 
 Speed of Cutting Tools 1258 
 
 Table of Cutting Speeds 1258 
 
 Spindle Speeds of Lathes 1259 
 
 Rule for Gearing Lathes 1259 
 
 Change-gears for Lathes 1260 
 
 Quick Change Gears 1260 
 
 Metric Screw-threads 1261 
 
 Cold Chisels 1261 
 
 Setting the Taper in a Lathe 1261 
 
 Lubricants for Lathe Centers 1261 
 
 Taylor's Experiments on Tool Steel 1261 
 
 Proper Shape of Lathe Tool 1261 
 
 Forging and Grinding Tools 1263 
 
 Best Grinding Wheel for Tools 1263 -~- 
 
 Chatter 1264 
 
 Use of Water on Tool 1264 
 
 Interval between Grindings 1264 
 
 Effect of Feed and Depth of Cut on Speed 1264 
 
 Best High Speed Tool Steel Heat Treatment 1265 
 
 Table, Cutting Speeds of Taylor- White Tools 1266 
 
 Best Method of Treating Tools in Small Shops 1268 
 
 Quality of Different Tool Steels 1268 
 
 Parting and Thread Tools 1268 
 
 Durability of Cutting Tools 1268 
 
 Economical Cutting Speeds 1268 -^ 
 
 New High Speed Steels, 1909 1269 
 
 Stellite 1269 
 
 Planer Work 1270-1275 
 
 Cutting and Return Speeds of Planers 1270 
 
 Power Required for Planing 1270 
 
 Time Required for Planing 1271 
 
 Standard Planer Tools 1271-1275 
 
 Milling Machine Practice <, 1275-1284 
 
 Forms of Milling Cutters 1275 
 
 Number of Teeth in Milling Cutters 1276 
 
 Keyways in Milling Cutters 1277 
 
 Power Required for Milling 1278 
 
 Modern Milling Practice, 1914 1279 
 
 Milling wiJi or against the Feed 1280 
 
 Lubricant for Milling Cutters :. . . 1281 
 
 Typica 
 High-s 
 
 Jigh-speed Milling 1282 
 
 Limiting Factors of Milling Practice 1283 
 
 Speeds and Feeds for Gear Cutting 1284 
 
 Drills and Drilling 1285-1290 
 
 Forms of Drills 1285 
 
 Drilling Compounds 1286 
 
XXXV111 CONTENTS. 
 
 1>AGE 
 
 Twist Drill and Steel Wire Gages ...;>...,.. 1286 
 
 Power Required to Drive Drills 1286, 1287 
 
 Feeds and Speeds of Drills 1288 
 
 Extreme Results with Drills ; 1289 
 
 Experiments on Twist Drills 1289 
 
 Cutting Speeds for Tapping and Threading 1290 
 
 Sawing Metals 1291 
 
 Case-hardening, Cementation, Harvey izing 1291 
 
 Change of Shape due to Hardening and Tempering 1291 
 
 Power Required for Machine Tools. 
 
 Resistance Overcome in Cutting Metal :. . 1292 
 
 Power Required to Run Lathes 1292-1295 
 
 Sizes of Motors for Machine Tools 1294-1298 
 
 Horse-power Constants for Cutting Metals 1299 
 
 Pulley Diameters for Motors 1300 
 
 Geared Connections for Motors, Table 1301 
 
 Motor Requirements for Planers 1302 
 
 Tests on a Motor-driven Planer 1303 
 
 Power Required for Wood-working Machinery 1303 
 
 Power Required to Drive Shafting 1305 
 
 Power Required to Drive Machines in Groups 1305 
 
 Machine Tool Drives, Speeds and Feeds 1307 
 
 Geometrical Progression of Speeds and Feeds 1307 
 
 Methods of Driving Machine Tools 1307 
 
 Abrasive Processes. 
 
 The Cold Saw 1309 
 
 Reese's Fusing-disk 1309 
 
 Cutting Stone with Wire 1309 
 
 The Sand-blast 1309 
 
 Polishing and Buffing '. 1310 
 
 Laps and Lapping 1310 
 
 Emery-wheels 131 1-1317 
 
 Artificial Abrasives 1313 
 
 Mounting Grinding Wheels, Safety Devices 1314 
 
 Grinding as a Substitute for Finish Turning 1317 
 
 Grindstones 1317 
 
 Various Tools and Processes. 
 
 Taper Bolts, Pins, Reamers, etc 1318 
 
 Morse Tapers 1319 
 
 Jarno Taper 1319 
 
 Tap Drills 1320 
 
 Taper Pins 1321 
 
 T-slots, T-bolts and T-nuts 1321 
 
 Punches and Dies, Presses, etc 1321 
 
 Punch and Die Clearances > . . 1321 
 
 Kennedy's Spiral Punch 1322 
 
 . Sizes of Blanks Used in the Drawing Press 1322 
 
 Pressure Obtained by the Drop Press 1322 
 
 Flow of Metals 1323 
 
 Fly-wheels for Presses, Punches, Shears, etc. 1323 
 
 Forcing, Shrinking, and Running Fits 1324 
 
 Pressures for Mounting Wheels and Crank Pins 1324 
 
 Fits for Machine Parts 1325 
 
 Running Fits 1325 
 
 Shop Allowances for Electrical Machinery 
 
 Pressure Required for Press Fits 
 
 Stresses due to Force and Shrink Fits 1326 
 
 Force Required to Start Force and Shrink Fits 1327 
 
 Formulae for Flat and Square Keys 1328 
 
CONTENTS. XXXIX 
 
 PAGE 
 
 Keys of Various Forms 1328-1331 
 
 Depth of Key Seats 1329 
 
 Gib Keys 1332 
 
 Holding Power of Keys and Set Screws 1332 
 
 DYNAMOMETERS. 
 
 Traction Dynamometers 1333 
 
 The Prony Brake 1333 
 
 The Alden Dynamometer 1334 
 
 Capacity of Friction-brakes 1334 
 
 Transmission Dynamometers 1335 
 
 ICE MAKING OR REFRIGERATING-MACHINES. 
 
 Operations of a Refrigerating-Machine 1336 
 
 Pressures, etc., of Available Liquids 1337 
 
 Properties of Sulphur Dioxide Gas 1338 
 
 Properties of Ammonia 1339, 1340 
 
 Solubility of Ammonia 1341 
 
 Properties of Saturated Vapors 1341 
 
 Heat Generated by Absorption of Ammonia 1341 
 
 Cooling Effect, Compressor Volume and Power Required, with 
 
 Different Cooling Agents 1341 
 
 Ratios of Condenser, Mean Effective, and Vaporizer Pressures . . 1342 
 
 Properties of Brine used to absorb Refrigerating Effect 1343 
 
 Chloride-of-calcium Solution 1343 
 
 Ice-melting Effect 1344 
 
 Ether-machines 1344 
 
 Air-machines 1344 
 
 Carbon Dioxide Machines 1344 
 
 Methyl Chloride Machines 1345 
 
 Sulphur-dioxide Machines 1345 
 
 Machines Using Vapor of Water 1345 
 
 Ammonia Compression-machines 1345 
 
 Dry, Wet and Flooded Systems 1345 
 
 Ammonia Absorption-machines 1346 
 
 Relative Performance of Compression and Absorption Machines 1346 
 
 Efficiency of a Refrigerating-machine 1347 
 
 Diagrams of Ammonia Machine Operation 1348 
 
 Cylinder-heating 1349 
 
 Volumetric Efficiency 1349 
 
 Pounds of Ammonia per Ton of Refrigeration 1350, 1351 
 
 Mean Effective Pressure, and Horse-power 1350 
 
 The Voorhees Multiple Effect Compressor 1350 
 
 Size and Capacities of Ammonia Machines , . . . . 1352 
 
 Piston Speeds and Revolutions per Minute 1353 
 
 Condensers for Refrigera ting-machines 1353 
 
 Cooling Tower Practice in Refrigerating Plants 1354 
 
 Test Trials of Refrigerating-machines 1355 
 
 Comparison of Actual and Theoretical Capacity 1355 
 
 Performance of Ammonia Compression-machines 1 356 
 
 Economy of Ammonia Compression-machines 1357 
 
 Form of Report of Test 1358 
 
 Temperature Range 1359 
 
 Metering the Ammonia 1359 
 
 Performance of Ice-making Machines 1359 
 
 Performance of a 75-ton Refrigerating-machine 1361-1363 
 
 Ammonia Compression-machine, Results of Tests '. . 1364 
 
 Performance of a Single-acting Ammonia Compressor 1364 
 
 Performance of Ammonia Absorption-machine 1364 
 
 Means for Applying the Cold 1365 
 
 Artificial Ice-manufacture , Ib66 
 
 Test of the New York Hygeia Ice-making Plant 1367 
 
 An Absorption Evaporator Ice-making System 1367 
 
 Ice-making with Exhaust Steam 1367 
 
Xl CONTENTS. 
 
 PAGE 
 
 Tons of Ice per Ton of Coal 1367 
 
 Standard Ice Cans or Molds 1368 
 
 Cubic Feet of Insulated Space per Ton Refrigeration 1368 
 
 MARINE ENGINEERING. 
 
 Rules for Measuring and Obtaining Tonnage of Vessels 1368 
 
 The Displacement of a Vessel 1369 
 
 Coefficient of Fineness 1369 
 
 Coefficient of Water-line 1369 
 
 Resistance of Ships 1369 
 
 Coefficient of Performance of Vessels 1370 
 
 Defects of the Common Formula for Resistance 1370 
 
 Rankine's Formula 1370 
 
 Empirical Equations for Wetted Surface 1371 
 
 E. R. Mumford's Method 1371 
 
 Dr. Kirk's Method 1372 
 
 To find the I.H.P. from the Wetted Surface. 1372 
 
 Relative Horse-power required for Different Speeds of Vessels . . 1373 
 
 Resistance per Horse-power for Different Speeds 1373 
 
 Estimated Displacement, Horse-power, etc., of S team- vessels. . . 1374 
 
 Speed of Boats with Internal Combustion Engines 1374 
 
 Data of Ships of Various Types 1376 
 
 Relation of Horse-power to Speed 1376 
 
 The Screw-propeller. 
 
 Pitch and Size of Screw 1377 
 
 Propeller Coefficients 1378 
 
 Efficiency of the Propeller 1379 
 
 Pitch-ratio and Slip for Screws of Standard Form 1379 
 
 Table for Calculating Dimensions of Screws 1380 
 
 Marine Practice. 
 
 Comparison of Marine Engines, 1872, 1881, 1891, 1901 1380 
 
 Turbines and Boilers of the " Lusitania" 1381 
 
 Performance of the "Lusitania," 1908 1381 
 
 Dimensions and Performance of Notable Atlantic Steamers. . . . 
 
 Relative Economy of Turbines and Reciprocating Engines 1382 
 
 Reciprocating Engines with a Low-pressure Turbine 1383 
 
 The Paddle-wheel. 
 
 Paddle-wheels with Radial Floats 1383 
 
 Feathering Paddle-wheels 1383 
 
 Efficiency of Paddle-wheels 1384 
 
 Jet Propulsion. 
 
 Reaction of a Jet 1384 
 
 CONSTRUCTION OF BUILDINGS. 
 
 Foundations. 
 
 Bearing Power of Soils 1385 
 
 Bearing Power of Piles 1386 
 
 Safe Strength of Brick Piers 1386 
 
 Thickness of Foundation Walls 1386 
 
 Masonry. 
 
 Allowable Pressures on Masonry 1386 
 
 Crushing Strength of Concrete 1386 
 
 Reinforced Concrete 1386 
 
CONTENTS. Xll 
 
 Beams and Girders. PAGE 
 
 Safe Loads on Beams 1387 
 
 Safe Loads on Wooden Beams 1387 
 
 Maximum Permissible Stresses in Structural Materials 1388 
 
 Walls. 
 
 Thickness of Walls of Buildings 1388 
 
 Walls of Warehouses, Stores, Factories, and Stables 1388 
 
 Floors, Columns and Posts. 
 
 Strength of Floors, Roofs, and Supports 1389 
 
 Columns and Posts 1389 
 
 Fireproof Buildings 1389 
 
 Iron and Steel Columns 1389 
 
 Lintels, Bearings, and Supports 1390 
 
 Strains on Girders and Rivets 1390 
 
 Maximum Load on Floors 1390 
 
 Strength of Floors 1391 
 
 Maximum Spans for 1, 2 and 3 inch Plank 1392 
 
 Mill C9lumns . , 1393 
 
 Safe Distributed Loads on Southern-pine Beams 1393 
 
 Approximate Cost of Mill Buildings 1394 
 
 ELECTRICAL ENGINEERING. 
 
 C. G. S. System of Physical Measurement 1396 
 
 Practical Units used in Electrical Calculations 1396 
 
 Relations of Various Units 1397 
 
 Units of the Magnetic Circuit 1398 
 
 Equivalent Electrical and Mechanical Units 1399 
 
 Permeability 1400 
 
 logics between Flow of Water and Electricity 1400 
 
 Electrical Resistance. 
 
 Laws of Electrical Resistance 1400 
 
 Electrical Conductivity of Different Metals and Alloys 1401 
 
 Conductors and Insulators 1402 
 
 Resistance Varies with Temperature : 1402 
 
 Annealing 1402 
 
 Standard of Resistance of Copper Wire 1402 
 
 Wire Table, Standard Annealed Copper 1404 
 
 Direct Electric Currents. 
 
 Ohm's Law 1406 
 
 Series and Parallel or Multiple Circuits 1406 
 
 Resistance of Conductors in Series and Parallel 1407 
 
 Internal Resistance 1408 
 
 Power of the Circuit 1408 
 
 Electrical, Indicated, and Brake Horse-power 1408 
 
 Heat Generated by a Current 1408 
 
 Heating of Conductors 1409 
 
 Heating of Coils 1409 
 
 Fusion of Wires 1409 
 
 Allowable Carrying Capacity of Copper Wires : . 1410 
 
 Underwriters' Insulation 1410 
 
 Electric Transmission, Direct-Currents. 
 
 Drop of Voltage in Wires Carrying Allowed Currents 1410 
 
 Section of Wire Required for a Given Current 1410 
 
 Weight of Copper for a Given Power 1411 
 
Xlii CONTENTS. 
 
 PAGE 
 
 Short-circuiting 1411 
 
 Economy of Electric Transmission 1411 
 
 Efficiency of Electric Systems 1412 
 
 Wire Table for 110, 220, 500, 1000, and 2000 volt Circuits 1413 
 
 Resistances of Pure Aluminum Wire 1414 
 
 Electric Railways. 
 
 Schedule Speeds, Miles per Hour 1414 
 
 Train Resistance 1415 
 
 Rates of Acceleration 1415 
 
 Safe Maximum Speed on Curves 1416 
 
 Electric Resistance of Rails and Bonds 1416 
 
 Electric Locomotives 1416 
 
 Efficiencies of Distributing Systems 1417 
 
 Steam Railroad Electrifications 1418 
 
 Electric Welding. 
 
 Arc Welding 1419 
 
 Data of Electric Welding in Railway Shops 1419 
 
 Resistance Welding 1419 
 
 Cost of Welding 1420 
 
 Electric Heaters. 
 
 Elementary Form of Heater 1420 
 
 Relative Efficiency of Electric and Steam Heating 1421 
 
 Heat Required to Warm and Ventilate a Room 1421 
 
 Domestic Heating 1421 
 
 Electric Furnaces. 
 
 Arc Furnaces and Resistance Furnaces 1422 
 
 Uses of Electric Furnaces 1423 
 
 Electric Smelting of Pig-iron 1424 
 
 Ferro-alloys 1424 
 
 Non-ferrous Metals 1424 
 
 Electric Batteries. 
 
 Primary Batteries 1425 
 
 Description of Storage-batteries or Accumulators 1425 
 
 Rules for Care of Storage-batteries 1426 
 
 Efficiency of a Storage Cell 1427 
 
 Uses of Storage-batteries '. 1427 
 
 Edison Alkaline Battery 1428 
 
 Electrolysis 1428 
 
 Electro-chemical Equivalents 1429 
 
 The Magnetic Circuit. 
 
 Lines and Loops of Force 1430 
 
 Values of B and H 1431 
 
 Tractive or Lifting Force of a Magnet 1431 
 
 Determining the Polarity of Electro-magnets 
 
 Determining the Direction of a Current 1432 
 
 Dynamo-electric Machines. 
 
 Rating of Generators and Motors 1432 
 
 Temperature Limitations of Capacity 143 
 
 Methods of Determining Temperatures 143 
 
 Temperature Limits of Hottest Spot 
 
 Moving Force of a Dynamo-electric Machine 1435 
 
CONTENTS. xliii 
 
 PAGE 
 
 Torque of an Armature 1435 
 
 Torque, Horse-power and Revolutions 1436 
 
 Electro-motive Force of the Armature Circuit 1436 
 
 Strength of the Magnetic Field 1436 
 
 Direct-Current Generators. 
 
 Series-, Shunt- and Compound- wound 1437 
 
 Commutating Pole Machines 1438 
 
 Parallel Operation 1439 
 
 Three- Wire System 1439 
 
 Alternating Currents. 
 
 Maximum, Average and Effective Values 1440 
 
 Frequency 1440 
 
 Inductance 1440 
 
 Capacity 1440 
 
 Power Factor 1440 
 
 Reactance, Impedance, Admittance 1441 
 
 Skin Effect 1442 
 
 Ohm's Law Applied to Alternating Current Circuits 1442 
 
 Impedance Polygons 1442 
 
 Self-inductance of Lines and Circuits 1446 
 
 Capacity of Conductors 1446 
 
 Single-phase and Polyphase Currents t 1446 
 
 Measurement of Power in Polyphase Circuits 1447 
 
 Alternating Current Generators. 
 
 Synchronous Generators 1448 
 
 Rating 1448 
 
 Efficiency 1448 
 
 Regulation ; 1449 
 
 Rating of a Generator Unit 1449 
 
 Windings 1449 
 
 Voltages 1450 
 
 Parallel Operation 1450 
 
 Exciters 1450 
 
 Transformers. 
 
 Primary and Secondary 1451 
 
 Voltage Ratio 1451 
 
 Rating 1451 
 
 Efficiency 1451 
 
 Connections 1452 
 
 Auto Transformers 1453 
 
 Constant-Current Transformers . , 1453 
 
 Synchronous Converters. 
 
 Description 1453 
 
 Effective E.M.F. between Collector Rings 1454 
 
 Voltage Regulation 1455 
 
 Starting Synchronous Converters 1455 
 
 Motor-Generators. 
 
 Balancers 1456 
 
 Boosters 1456 
 
 Dynamotors 1457 
 
 Frequency Changers 1457 
 
 Mercury Arc Rectifier 1457 
 
xliv CONTENTS. 
 
 Alternating'Current Circuits. 
 
 PAGfi 
 
 Calculation of Alternating Current Circuits 1457 
 
 Relative Weight of Copper Required in Different Systems ..... 1459 
 
 Rule for Size of Wires for Three-phase Transmission Lines 1459 
 
 Notes on High-tension Transmission 1459 
 
 Voltages Advisable for Various Line Lengths 1460 
 
 Line Spacing 1460 
 
 Size of Line Conductors 1460 
 
 A 135,000- volt Three-phase Transmission System 1461 
 
 Electric Motors. 
 
 Classification of Motors 1461 
 
 Characteristics of Motors 1461 
 
 Series Motor 1461 
 
 Speed Control of Motors 1462 
 
 Shunt IMotor 1462 
 
 Compound Motor 1462 
 
 Induction Motor; Squirrel-cage Motor 1463 
 
 Multi-speed Induction Motors 1463 
 
 Synchronous Motors 1463 
 
 Single-phase Series Motor 1464 
 
 Repulsion Induction Motor 1464 
 
 Reversible Repulsion Motor 1464 
 
 Variable-speed Repulsion Motor 1464 
 
 Motor Applications. 
 
 Pumps 1464 
 
 Fans 1465 
 
 Air Compressors 1465 
 
 Hoists . . 1465 
 
 Machine Tools 1466 
 
 Motors for Machine Tools 1467 
 
 Illumination Electric and Gas Lighting. 
 
 Illumination 1468 
 
 Terms, Units, Definitions .... 1468 
 
 Relative Color Values of Illuminants 1469 
 
 Relation of Illumination to Vision . . . 1469 
 
 Types of Electric Lamps 1470 
 
 Street Lighting 1470 
 
 Illumination by Arc Lamps at Different Distances 1471 
 
 Data of Some Arc Lamps 1471 
 
 Relative Efficiency of Illuminants 1472 
 
 Characteristics of Tungsten Lamps 1473 
 
 Interior Illumination 1473 
 
 Quantity of Electricity or Gas Required for Illuminating 1474 
 
 Standard Units; Mazda and Welsbach 1475 
 
 Cost of Electric Lighting 1475 
 
 Recent Street Lighting Installations 1476 
 
 Symbols Used in Electric Diagrams 1477 
 
NAMES AND ABBREVIATIONS OF PERIODICALS AND 
 TEXT -BOOKS FREQUENTLY REFERRED TO IN 
 THIS WORK. 
 
 Am. Mach. American Machinist. 
 
 App. Cyl. Mech. Appleton's Cyclopaedia of Mechanics, Vols. I and II. 
 
 Bull. I. & S. A. Bulletin of the American Iron and Steel Association. 
 
 Burr's Elasticity and Resistance of Materials. 
 
 Clark, R. T. D. D. K. Clark's Rules, Tables, and Data for Mechanical 
 Engineers. 
 
 Clark, S. E. D. K. Clark's Treatise on the Steam-Engine. 
 
 Col. Coll. Qly. Columbia College Quarterly. 
 
 El. Rev. Electrical Review. 
 
 El. World. Electrical World and Engineer. 
 
 Engg. Engineering (London). 
 
 Eng. News. Engineering News. 
 
 Eng. Rec. Engineering Record. 
 
 Engr. The Engineer (London). 
 
 Fairbairn's Useful Information for Engineers. 
 
 Flynn's Irrigation Canals and Flow of Water. 
 
 Indust. Eng. Industrial Engineering. 
 
 Jour. A. C. I. W. Journal of American Charcoal Iron Workers' 
 Association. 
 
 Jour. Ass. Eng. Soc. Journal of the Association of Engineering 
 Societies. 
 
 Jour. F. I. Journal of the Franklin Institute. 
 
 Lanza's Applied Mechanics. 
 
 Machy. Machinery. 
 
 Merriman's Strength of Materials. 
 
 Modern Mechanism. Supplementary volume of Appleton's Cyclo- 
 paedia of Mechanics. 
 
 Peabody's Thermodynamics. 
 
 Proc. A. S. H. V. E. Proceedings. Am. Soc'y of Heating and Ventilat- 
 ing Engineers. 
 
 Proc. A. S. T. M. Proceedings Amer. Soc'y for Testing Materials. 
 
 Proc. Inst. C. E. Proceedings Institution of Civil Engineers (London). 
 
 Proc. Inst. M. E. Proceedings Institution of Mechanical Engineers 
 (London) . 
 
 Proceedings Engineers' Club of Philadelphia. 
 
 Rankine, S. E. Rankine's The Steam Engine and other Prime Movers. 
 
 Rankine's Machinery and Millwork. 
 
 Rankine, R. T. D. Rankine's Rules, Tables, and Data. 
 
 Reports of U. S. Iron and Steel Test Board. 
 
 Reports of U. S. Testing Machine at Watertown, Massachusetts. 
 
 Rontgen's Thermodynamics. 
 
 Seaton's Manual of Marine Engineering. 
 
 Hamilton Smith, Jr.'s Hydraulics. 
 
 Stevens Indicator. 
 
 Thompson's Dynamo-electric Machinery. 
 
 Thurston's Manual of the Steam Engine. 
 
 Thurston's Materials of Engineering. 
 
 Trans. A. I. E. E. Transactions American Institute of Electrical 
 Engineers. 
 
 Trans. A. I. M. E. Transactions American Institute of Mining 
 Engineers. 
 
 Trans. A. S. C. E. Transactions American Society of Civil Engineers. 
 
 Trans. A. S. M. E. Transactions American Society of Mechanical 
 Engineers. 
 
 Trautwine's Civil Engineer's Pocket Book. 
 
 The Locomotive (Hartford, Connecticut). 
 
 Unwin's Elements of Machine Design. 
 
 Weisbach's Mechanics of Engineering, 
 
 Wood's Resistance of Materials. 
 
 Wood's Thermodynamics, _, 
 
MATHEMATICS. 
 
 Greek Letter. 
 
 a Alpha 
 
 j8 Beta 
 
 y Gamma 
 
 8 Delta 
 
 e Epsilon 
 
 C Zeta 
 
 Eta 
 
 N v 
 
 Nu 
 
 T 
 
 T Tan 
 
 9 Theta 
 
 H 
 
 Xi 
 
 Y 
 
 v Upsilon 
 
 Iota 
 
 o 
 
 Omicron 
 
 $ 
 
 <t> Phi 
 
 Kappa 
 Lambda 
 
 II 7T 
 P P 
 
 Pi 
 
 Kho 
 
 X 
 
 Y Chi 
 $ Psi 
 
 Mu 
 
 2 as 
 
 Sigma 
 
 O 
 
 w Omega 
 
 Arithmetical and Algebraical Signs and Abbreviations* 
 
 + plus (addition). 
 + positive. 
 minus (subtraction). 
 - negative. 
 plus or minus. 
 T minus or plus. 
 = equals. 
 X multiplied by. 
 ab or a.b = a X b. 
 -5- divided by. 
 / divided by. 
 
 2 _/6 _.. 15-16 = if - 
 0.2 -; 0.002 -jJL. 
 
 V square root. 
 ^ cube root. 
 M 4th root. 
 
 : is to, :: so is, : to (proportion). 
 2 : 4 :: 3 : 6, 2 is to 4 as 3 is to 6. 
 : ratio; divided by. 
 2 : 4, ratio of 2 to 4 = 2/4. 
 .*. therefore. 
 > greater than. 
 < less than. 
 D square. 
 O round. 
 
 degrees, arc or thermometer. 
 ' minutes or feet. 
 " seconds or inches. 
 
 "' accents to distinguish letters, 
 
 as a', a", a'". 
 <*! 2, 03, ab, etc, read a sub 1, a sub 
 
 ft, etc. 
 
 on) 
 
 - parenthesis, braclr^ts, 
 
 braces, vinculum ; denoting 
 that the numbers enclosed are 
 to be taken together; as, 
 (a + b)c = 4 + 3 X 5 = 35, 
 
 a 2 , a 3 , a squared, a cubed. 
 
 a n , a raised to the nth power. 
 
 10 9 = 10 to the 9th power = 
 
 1,000,000,000. 
 sin a = the sine of a. 
 sin" 1 a = the arc whose sine is a. 
 
 sin a- = ^ 
 
 sin a 
 
 log = logarithm. 
 
 loge or hyp log = hyperbolic loga- 
 rithm. 
 % per cent. 
 A angle. 
 
 ,L right angle. 
 
 JL perpendicular to. 
 
 sin, sine. 
 
 cos, cosine. 
 
 tan, tangent. 
 
 sec, secant. 
 
 versin, versed sine. 
 
 cot, cotangent. 
 
 cosec, cosecant. 
 
 covers, co-versed sine. 
 
 In Algebra, the first letters of 
 the alphabet, a, b, c, d, etc., are 
 generally used to denote known 
 quantities, and the last letters, 
 w, x, y, z, etc., unknown quantities. 
 
 Abbreviations and Symbols com- 
 monly used, 
 d, differential (in calculus). 
 
 , integral (in calculus). 
 
 , integral between limits a and b. 
 
 A, delta, difference. 
 
 2, sigma, sign of summation. 
 
 n, pi, ratio of circumference of 
 
 circle to diameter = 3.14159. 
 g, acceleration due to gravity = 
 
 32.16 ft. per second per second. 
 
 Abbreviations frequently used in 
 
 this Book. 
 
 L., 1., length in feet and inches. 
 B., b., breadth in feet and inches. 
 D., d., depth or diameter. 
 H., h., height, feet and inches. 
 T., t., thickness or temperature. 
 V., v., velocity. 
 F., force, or factor of safety, 
 f., coefficient of fricti9n. 
 E., coefficient of elasticity. 
 11., r., radius. 
 W., w., weight. 
 P., p., pressure or load. 
 H.P., horse-power. 
 I.H.P., indicated horse-power. 
 B.H.P., brake horse-power, 
 h. p., high pressure, 
 i. p., intermediate pressure. 
 I. p., low pressure. 
 A.W.G., American Wire Gauge 
 
 (Brown & Sharpe). 
 B.W.G., Birmingham W ire Gauge. 
 r. p. m., or revs, per min.. revolu- 
 tions per minute. 
 Q. =* quantity, or volume. 
 
ARITHMETIC. 
 
 . ARITHMETIC. 
 
 The user of this book is supposed to have had a training in arithmetic as 
 well as in elementary algebra. Only those rules are given here which are 
 apt to be easily forgotten. 
 
 GREATEST COMMON MEASURE, OR GREATEST 
 COMMON DIVISOR OF TWO NUMBERS. 
 
 Rule. Divide the greater number by the less; then divide the divisor 
 by the remainder, and so on, dividing always the last divisor by the last 
 remainder, until there is no remainder, and the last divisor is the greatest 
 common measure required. 
 
 LEAST COMMON MULTIPLE OF TWO OR MORE 
 NUMBERS. 
 
 Rule. Divide the given numbers by any number that will divide the 
 greatest number of them without a remainder, and set the quotients with 
 the undivided numbers in a line beneath. 
 
 Divide the second line as before, and so on, until there are no two num- 
 bers that can be divided; then the continued product of the divisors, last 
 quotients, and undivided numbers will give the multiple required. 
 
 FRACTIONS. 
 
 To reduce a common fraction to its lowest terms. Divide both 
 terms by their greatest common divisor: 39/ 52 = 3/ 4 . 
 
 To change an improper fraction to a mixed number. Divide the 
 numerator by the denominator; the quotient is the whole number, and 
 the remainder placed over the denominator is the fraction: 39/ 4 = 93/4. 
 
 To change a mixed number to an improper fraction. Multiply 
 the whole number by the denominator of the fraction; to the product add 
 the numerator; place the sum over the denominator: 17/g = i5/ 8 . 
 
 To express a whole number in the form of a fraction with a given 
 denominator. Multiply the whole number by the given denominator, 
 and place the product over that denominator: 13 = 39/ 3 . 
 
 To reduce a compound to a simple fraction, also to multiply 
 fractions. Multiply the numerators together for a new numerator and 
 the denominators together for a new denominator: 
 
 2.4 8 . 2^4 8 
 3 f 3 = 9' alS 3 X 3 = 9' 
 
 To reduce a complex to a simple fraction. The numerator and 
 denominator must each first be given the form of a simple fraction; then 
 multiply the numerator of the upper fraction by the denominator of the 
 lower for the new numerator, and the denominator of the upper by the 
 numerator of the lower for the new denominator: 
 
 7/8 = 7/8 = 28 = 1 
 l3/ 4 7/4 56 2* 
 
 To divide fractions. Reduce both to the form of simple fractions, 
 Invert the divisor, and proceed as in multiplication: 
 
 3 35 34 12 3 
 
 4 +1V4 -5 + 4~ 4 X 5~20- 5' 
 
 Cancellation of fractions. In compound or multiplied fractions, 
 divide any numerator and any denominator by any number which will 
 divide them both without remainder, striking out the numbers thus 
 divided and setting down the quotients in their stead. 
 
 To reduce fractions to a common denominator. Reduce each 
 fraction to the form of a simple fraction; then multiply each numerator 
 
DECIMALS. 
 
 fcy all the denominators except its own for the new numerator, and all 
 the denominators together for the common denominator: 
 
 , 
 
 42* 
 
 14 f 
 42* 
 
 IS 
 42* 
 
 To add fractions. Reduce them to a common denominator, then 
 add the numerators and place their sum over the common denominator: 
 
 21 + 14 4- 18 
 42 
 
 53 
 43 
 
 To subtract fractions. Reduce them to a common denominator, 
 subtract the numerators and place the difference over the common denom- 
 inator: 
 
 1 _ 3 7-6 J_ 
 
 2 7 ~ 14 " 14 
 
 DECIMALS. 
 
 To add decimals. Set down the figures so that the decimal points 
 are one above the other, then proceed as in simple addition: 18.75' 4- 0.012 
 = 18.762. 
 
 To subtract decimals. Set down the figures so that the decimal 
 points are one above the other, then proceed as in simple subtraction: 
 18.75 - 0.012 = 18.738. 
 
 To multiply decimals. Multiply as in multiplication of whole num- 
 bers, then point off as many decimal places as there are in multiplier and 
 multiplicand taken together: 1.5 X 0.02 = .030 = 0.03. 
 
 To divide decimals. Divide as in whole numbers, and point off in 
 the quotient as many decimal places as those in the dividend exceed those 
 in the divisor. Ciphers must be added to the dividend to make its decimal 
 places at least equal those in the divisor, and as many more as it is desired 
 to have in the quotient: 1.5 -J- 0.25 = 6. 0.1 -i- 0.3 = 0.10000 -i- 0.3 
 = 0.3333 +. 
 
 Decimal Equivalents of Fractions of One Inch. 
 
 1-64 
 
 .015625 
 
 17-64 
 
 .265625 
 
 33-64 
 
 .515625 
 
 49-64 
 
 .765625 
 
 1-32 
 
 .03125 
 
 9-32 
 
 .28125 
 
 17-32 
 
 .53125 
 
 25-32 
 
 .78125 
 
 3-64 
 
 .046875 
 
 19-64 
 
 .296875 
 
 35-64 
 
 .546875 
 
 51-64 
 
 .796875 
 
 1-16 
 
 .0625 
 
 5-16 
 
 .3125 
 
 9-16 
 
 .5625 
 
 13-16 
 
 .8125 
 
 5-64 
 
 .078125 
 
 21-64 
 
 .328125 
 
 37-64 
 
 .578125 
 
 53-64 
 
 .828125 
 
 3-32 
 
 .09375 
 
 11-32 
 
 .34375 
 
 19-32 
 
 .59375 
 
 27-32 
 
 .84375 
 
 7-64 
 
 .109375 
 
 23-64 
 
 .359375 
 
 39-64 
 
 .609375 
 
 55-64 
 
 .859375 
 
 1-8 
 
 .125 
 
 3-8 
 
 .375 
 
 5-8 
 
 .625 
 
 7-8 
 
 .875 
 
 9-64 
 
 .140625 
 
 25-64 
 
 .390625 
 
 41-64 
 
 .640625 
 
 57-64 
 
 .890625 
 
 5-32 
 
 .15625 
 
 13-32 
 
 .40625 
 
 21-32 
 
 .65625 
 
 29-32 
 
 .90625 
 
 11-64 
 
 .171875 
 
 27-64 
 
 .421875 
 
 43-64 
 
 .671875 
 
 59-64 
 
 .921875 
 
 3-16 
 
 .1875 
 
 7-16 
 
 .4375 
 
 11-16 
 
 .6875 
 
 15-16 
 
 .9375 
 
 13-64 
 
 .203125 
 
 29-64 
 
 .453125 
 
 45-64 
 
 .703125 
 
 61-64 
 
 .953123 
 
 7-32 
 
 .21875 
 
 15-32 
 
 .46875 
 
 23-32 
 
 ,71875 
 
 31-32 
 
 .96875 
 
 15-64 
 
 .234375 
 
 31-64 
 
 .484375 
 
 47-64 
 
 .734375 
 
 63-64 
 
 .984375 
 
 1-4 
 
 .25 
 
 1-3 
 
 .50 
 
 3-4 
 
 .75 
 
 1 
 
 1. 
 
 To convert a common fraction into a decimal. Divide the nume- 
 rator by the denominator, adding to the numerator as many ciphers 
 prefixed by a decimal point as are necessary to give the number of decimal 
 places desired in the result: 1/3 = 1.0000 * 3 = 0.3333 +. 
 
 To convert a decimal into a common fraction. Set down the 
 decimal as a numerator, and place as the denominator 1 with as many 
 ciphers annexed as there are decimal places in the numerator; erase the 
 
ARITHMETIC. 
 
 S3. $ 
 
 $ 2 8 
 
 NO <s rx 
 t> 00 CO 
 
 i 5 3 
 
 >q t>* r> cq 
 
 in T en Q 
 
 eM ON NO en O 
 
 \O o in o m 
 
 m NO \o !> t> 
 
 t> \o \o NO m m 
 
 rq m oo T i> 
 
 t> m o -<r GO 
 
 r n in \o NO vo 
 
 O ON oo fN >o n in 
 en 5r ^T S in S 2 
 
 ^ ^o t>i o* o R SS iS 
 vo* \O' rNtsr-NC^ 
 moofS>nON<SNO 
 c<^ en en "^ ^t ^. "^ *f\ 
 
 O en ir\ 06 O en iin oo O 
 o fScnnspr>.GOO 
 moo. ^t>OenvOO 
 
 ^ oo ^- 06 ' >n GO <s n 
 
 oovOcnoooineNOrs 
 
 ON ^rNOCNimcO' en 
 
 "1 ; ts c^i CM en en en en ^ ^ 
 
 O n O^ ^ 00 en t>, \O O 
 O'^-t>.O^r>'-^cO in 
 ^NOoo enmooor4inr>. 
 
 ~~. ^~. ". ^ N . ^ i ^ **! ^ "i 
 
 t> <N t^ (S 00 en OO ^ O^ TO n 
 fNrNNOvOininT-tenenenfN 
 
 -. -. -. -. 2 jq cs CM cs ^ Jn 
 
 u^ F> <n o v5 Fi ON in ^ F> ^ O 
 eNQOenONinONO rxenoo^O 
 Ot>ONO(M'^-inrNOOO' enm 
 o O o 4 cs cs cs CM 
 
 c\i ^ \o en o oo in <s ON so en * oo n 
 inOoOOSenint>,oooeN'<rr>tN, 
 enTmt>ooONO^~eN'^'inNOt>oo 
 OOOOOO ~^ 1 ^^^ 
 
 sO^en ONi>tnen' ONCOO^TP^O 
 
 inen^ O^NO^<SOoomen^- ONt>n 
 ^-fNenen-*inNOt>r>.ooONOO c^ 
 o o o o o o o o o o o '-;-;'-; *~. 
 
 ONOot^^om^fenmvN oONcor%>ovn 
 c ^J5;^.iX O vcnr>.'-inoNenvOo^oocN 
 OO (SeNenenrn^^mininN 
 OOOOOOOOOOOOOOOC3 
 
 fMoom r>enNN'- 
 
 ;j ~^ sj en en "t r> in o. <q r>. cq cq O; 
 
COMPOUND NUMBERS. 
 
 decimal point In the numerator, and reduce the fraction thus formed to Its 
 lowest terms: 
 
 To reduce a recurring decimal to a common fraction. Subtract 
 the decimal figures that do not recur from the whole decimal including 
 one set of recurring figures; set down the remainder as the numerator of 
 the fraction, and as many nines as there are recurring figures, followed by 
 as many ciphers as there are non-recurring figures, in the denominator. 
 Thus: 
 
 0.79054054, the recurring figures being 054. 
 Subtract __ 79 
 
 7807 'i 117 
 
 99900 "* ( redllced to its lwest terms) * 
 
 .COMPOUND OR DENOMINATE NUMBERS. 
 
 Reduction descending. To reduce a compound number to a lower 
 denomination. Multiply the number by as many units of the lower 
 denomination as makes one of the higher. 
 
 , 
 
 fr 
 ae 
 
 3 yards to inches: 3 X 36 = 108 inches. 
 0.04 square feet to square inches: .04 X 144 
 
 5.76 sq. in. 
 
 _ the given number is in more than one denomination proceed in steps 
 from the highest denomination to the next lower, and so on to the lowest, 
 adding in the units of each denomination as the operation proceeds. 
 
 3 yds. 1 ft. 7 in. to inches: 3X3 = 9,4-1=10, 10 X 12 = 120, +7 = 127 in. 
 
 Reduction ascending. To express a number of a lower denomina- 
 tion in terras of a higher, divide the number by the number of units of 
 the lower denomination contained in one of the next higher; the quotient 
 is in the higher denomination, and the remainder, if any, in the lower. 
 127 inches to higher denomination. 
 
 127 -^ 12 = 10 feet + 7 inches; 10 feet *- 3 = 3 yards 4- 1 foot. 
 
 Ans. 3 yds. 1 ft. 7 in. 
 
 To express the result in decimals of the higher denomination, divide the 
 given number by the number of units of the given denomination contained 
 in one of the required denomination, carrying the result to as many places 
 of decimals as may be desired. 
 
 127 inches to yards: 127 -^ 36 = 319/ae = 3.5277 4- yards. 
 
 Decimals of a Foot Equivalent to Inches and Fractions 
 of an Inch. 
 
 Inches 
 
 
 
 H 
 
 X 
 
 H 
 
 H 
 
 ft 
 
 X 
 
 % 
 
 
 
 
 
 .01042 
 
 .02083 
 
 .03125 
 
 .04167 
 
 .05208 
 
 .06250 
 
 .07292 
 
 1 
 
 .0833 
 
 .0938 
 
 .1042 
 
 .1146 
 
 .1250 
 
 .1354 
 
 .1458 
 
 .1563 
 
 2 
 
 .1667 
 
 .1771 
 
 .1875 
 
 .1979 
 
 .2083 
 
 .2188 
 
 .2292 
 
 .2396 
 
 3 
 
 .2500 
 
 .2604 
 
 .2708 
 
 .2813 
 
 .2917 
 
 .3021 
 
 .3125 
 
 .3229 
 
 4 
 
 .3333 
 
 .3438 
 
 .3542 
 
 .3646 
 
 .3750 
 
 .3854 
 
 .3958 
 
 .4063 
 
 5 
 
 .4167 
 
 .4271 
 
 .4375 
 
 .4479 
 
 .4583 
 
 .4688 
 
 .4792 
 
 .4896 
 
 . 6 
 
 .5000 
 
 .5104 
 
 .5208 
 
 .5313 
 
 .5417 
 
 .5521 
 
 .5625 
 
 .5729 
 
 7 
 
 .5833 
 
 .5938 
 
 .6042 
 
 .6146 
 
 .6250 
 
 .6354 
 
 .6458 
 
 .6563 
 
 8 
 
 .6667 
 
 .6771 
 
 .6875 
 
 .6979 
 
 .7083 
 
 .7188 
 
 .7292 
 
 .7396 
 
 9 
 
 .7500 
 
 .7604 
 
 .7708 
 
 .7813 
 
 .7917 
 
 .8021 
 
 .8125 
 
 .8229 
 
 10 
 
 .8333 
 
 .8438 
 
 .8542 
 
 .8646 
 
 .8750 
 
 .8854 
 
 .8958 
 
 .9063 
 
 11 
 
 .9167 
 
 .9271 
 
 .9375 
 
 .9479 
 
 .9583 
 
 .9688 
 
 .9792 
 
 .9896 
 
ARITHMETIC. 
 
 RATIO AND PROPORTION. 
 
 Ratio Is the relation of one number to another, as obtained by dividing 
 the first number by the second. Synonymous with quotient. 
 
 Ratio of 2 to 4, or 2 : 4 = 2/ 4 = l/ 2 . 
 Ratio of 4 to 2, or 4 : 2 = 2. 
 
 Proportion is the equality of two ratios. Ratio of 2 to 4 equals ratio 
 of 3 to 6, 2/4=3/ 6 ; expressed thus, 2 : 4 :: 3 : 6; read, 2 is to 4 as 3 is to 6. 
 
 The first and fourth terms are called the extremes or outer terms, the 
 second and third the means or inner terms. 
 
 The product of the means equals the product of the extremes: 
 
 2 : 4 : : 3 : 6; 2 X 6 = 12; 3 X 4 = 12. 
 
 Hence, given the first three terms to find the fourth, multiply the 
 second and third terms together and divide by the first. 
 
 2 : 4 : : 3 : what number? Ans. ~-^ = 6. 
 
 Algebraic expression of proportion. a : b : : c : d; r = -; ad *5c; 
 
 be be , ad, ad 
 
 from which a = -r ; d= ; 6= ; c = -7- 
 a a c o 
 
 From the above equations may also be derived the following: 
 6 : a::d : c a + b : a : :c + d : c' a + b : a b : : c + d ; c d 
 a : c : : b : d a + b : b : : c + d : d a n : b : _: c n : d n 
 a-.b^cid a -b:b::c - d:d ^ : ty : : ^/c ^ 
 a b : a: :c d : c 
 
 Mean proportional between two given numbers, 1st and 2d, is such 
 a number that the ratio which the first bears to it equals the ratio which it 
 bears to the second. Thus, 2:4::4:8;4isa mean proportional between 
 
 2 and 8. To find the mean proportional between two numbers, extract 
 the square root of their product. 
 
 Mean proportional of 2 and 8 = V2 X 8 = 4. 
 
 Single Rule of Three; or, finding the fourth term of a proportion 
 when three terms are given. Rule, as above, when the terms are stated 
 in their proper order, multiply the second by the third and divide by the 
 first. The difficulty is to state the terms in their proper order. The 
 term which is of the same kind as the required or fourth term is made the 
 third; the first and second must be like each other in kind and denomina- 
 tion. To determine which is to be made second and which first requires 
 a little reasoning. If an inspection of the problem shows that the answer 
 should be greater than the third term, then the greater of the other two 
 given terms should be made the second term otherwise the first. Thus, 
 
 3 men remove 54 cubic feet of rock in a day; how many men will remove 
 in the same time 10 cubic yards? The answer is to be men make men 
 third term; the answer is to be more than three men, therefore make the 
 greater quantity, 10 cubic yards, the second term; but as it is not the same 
 denomination as the other term it must be reduced, = 270 cubic feet. 
 The proportion is then stated: 
 
 3 X 270 
 54 : 270 : : 3 : x (the required number); x = ^ir~ = 15 men. 
 
 O'x 
 
 The problem is more complicated if we increase the number of given 
 terms. Thus, in the above question, substitute for the words "in the 
 same time" the words '* in 3 days." First solve it as above, as if the work 
 were to be done in the same time; then make another proportion, stating 
 it thus: If 15 men do it in the same time, it will take fewer men to do it in 
 3 days; make 1 day the second terra and 3 days the first term, 3:1:: 
 15 men : 5 men. 
 
POWERS OF NUMBERS. 
 
 . 
 
 FJ 
 
 Compound Proportion, or Double Rule of Three. By this rule 
 are solved questions like the one just given, in which two or more statings 
 are required by the single rule of three. In it, as in the single rule, there 
 is one third term, which is of the same kind and denomination as the 
 fourth or required term, but there may be two or more first and second 
 terms. Set down the third term, take each pair of terms of the same kinc 1 
 separately, and arrange them as first and second by the same reasoning as 
 is adopted in the single rule of three, making the greater of the pair the 
 second if this pair considered alone should require the answer to begreater. 
 
 Set down all the first terms one under the other, and likewise all the 
 second terms. Multiply all the first terms together and all the second 
 terms together. Multiply the product of all the second terms by the third 
 term, and divide this product by the product of all the first terms. 
 Example: If 3 men remove 4 cubic yards in one day, working 12 hours a 
 day, how many men working 10 hours a day will remove 20 cubic yards 
 in 3 days? 
 
 Yards 4 90 
 
 : : 3 men : x men . 
 
 Products 120 240 : : 3 : 6 men. Ans. 
 
 To abbreviate by cancellation, any one of the first terms may cancel 
 either the third or any of the second terms; thus, 3 in first cancels 3 in 
 third, making it 1, 10 cancels into 20 making the latter 2, which into 4 
 makes it 2, which into 12 makes it 6. and the figures remaining are only 
 1 : 6 : : 1 : 6. 
 
 Yards 
 Days 
 Hours 
 
 4 
 3 
 10 
 
 20 
 1 
 12 
 
 INVOLUTION, OR POWERS OF NUMBERS. 
 
 Involution is the continued multiplication of a number by itself a given 
 number of times. The number is called the root, or first power, and the 
 products are called powers. The second power is called the square and 
 the third power the cube. The operation may be indicated without being 
 performed by writing a small figure called the index or exponent to the 
 right of and a little above the root; thus, 3 3 = cube of 3, = 27. 
 
 To multiply two or more powers of the same number, add their expo- 
 nents; thus, 2 2 X 2 3 = 2 5 , or 4 X 8 = 32 = 2 5 . 
 
 To divide two powers of the same number, subtract their exponents; 
 
 thus, 2 3 -* 2 2 = 2 l = 2; 2 2 -s- 2 4 = 2~ 2 =.5 
 
 The exponent may 
 
 thus be negative. 2 3 -f- 2 3 = 2 = 1, whence the zero power of any 
 number = 1. The first power of a number is the number itself. The 
 exponent may be fractional, as 2*, 2$, which means that the root is to be 
 raised to a power whose exponent is the numerator of the fraction, and 
 the root whose sign is the denominator is to be extracted (see Evolution). 
 The exponent may be a decimal, as 2' 5 , 2 1 ' 5 ; read, two to the five-tenths 
 power, two to the one and five-tenths power. These powers are solved by 
 means of Logarithms (which see). 
 
 First Nine Powers of the First Nine Numbers. 
 
 ^1 
 
 b 
 
 o 
 
 ^ 
 
 4th 
 
 5th 
 
 6th 
 
 7th 
 
 8th 
 
 9th 
 
 J 
 
 s 
 
 en 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 PL. 
 
 PH 
 
 PH 
 
 
 
 
 
 
 
 1 
 
 , 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 2 
 
 4 
 
 8 
 
 16 
 
 32 
 
 64 
 
 128 
 
 256 
 
 512 
 
 3 
 
 9 
 
 27 
 
 81 
 
 243 
 
 729 
 
 2187 
 
 6561 
 
 19683 
 
 A 
 
 16 
 
 64 
 
 256 
 
 1024 
 
 4096 
 
 16384 
 
 65536 
 
 262144 
 
 5 
 
 25 
 
 125 
 
 625 
 
 3125 
 
 15625 
 
 78125 
 
 390625 
 
 1953125 
 
 6 
 
 36 
 
 216 
 
 1296 
 
 7776 
 
 46656 
 
 279936 
 
 1679616 
 
 10077696 
 
 7 
 
 49 
 
 343 
 
 2401 
 
 16807 
 
 1 1 7649 
 
 823543 
 
 5764801 
 
 40353607 
 
 8 
 
 64 
 
 512 
 
 4096 
 
 32768 
 
 262144 
 
 2097152 
 
 16777216 
 
 134217728 
 
 9 
 
 81 
 
 729 
 
 6561 
 
 59049 
 
 531441 
 
 4782969 
 
 43046721 
 
 387420489 
 
ARITHMETIC, 
 
 The First Forty Powers of 2. 
 
 
 
 I 
 
 o 
 
 Q 
 
 J3 
 
 o 
 
 QJ 
 
 1 
 
 1 
 
 J3 
 
 i 
 
 O 
 
 1 
 
 
 
 > 
 
 
 ^ 
 
 PH 
 
 *" 
 
 ft 
 
 > 
 
 ft 
 
 
 
 
 , 
 
 9 
 
 512 
 
 18 
 
 262144 
 
 27 
 
 134217728 
 
 36 
 
 68719476736 
 
 1 
 
 2 
 
 10 
 
 1024 
 
 19 
 
 524288 
 
 28 
 
 268435456 
 
 37 
 
 137438953472 
 
 2 
 
 4 
 
 11 
 
 2048 
 
 20 
 
 1048576 
 
 29 
 
 536870912 
 
 38 
 
 274877906944 
 
 3 
 
 8 
 
 12 
 
 4096 
 
 21 
 
 2097152 
 
 30 
 
 1073741824 
 
 39 
 
 549755813888 
 
 4 
 
 16 
 
 13 
 
 8192 
 
 22 
 
 4194304 
 
 31 
 
 2147483648 
 
 40 
 
 1099511627776 
 
 5 
 
 32 
 
 14 
 
 16384 
 
 23 
 
 8388608 
 
 32 
 
 4294967296 
 
 
 
 6 
 
 64 
 
 15 
 
 32768 
 
 24 
 
 16777216 
 
 33 
 
 8589934592 
 
 
 
 7 
 
 128 
 
 16 
 
 65536 
 
 25 
 
 33554432 
 
 34 
 
 17179869184 
 
 
 
 8 
 
 256 
 
 17 
 
 131072 
 
 26 
 
 67108864 
 
 35 
 
 34359738368 
 
 
 
 EVOLUTION. 
 
 Evolution is the finding of the root (or extracting the root) of any 
 number the power of which is given. 
 
 The sign V indicates that the square root is to be extracted: ^ <\J <^/ 
 the cube root, 4th root, nth root. 
 
 A fractional exponent with 1 for the numerator of the fraction is also 
 used to indicate that the operation of extracting the root is to be per- 
 formed; thus, 2*, 2* = <\/2, -\/2. 
 
 When the power of a number is indicated, the involution not being per- 
 formed, the extraction of any root of that power may also be indicated by 
 dividing the index of the power by the index of the root, indicating the 
 division by a fraction. Thus, extract the square root of the 6th power 
 of 2: 
 
 */2 = 2* = 2* = 2 3 = 8. 
 
 The 6th power of 2, as in the table above, is 64: v'ei = 8. 
 
 Difficult problems in evolution are performed by logarithms, but the 
 square root and the cube root may be extracted directly according to the 
 rules given below. The 4th root is the square root of the square root. 
 The 6th root is the cube root of the square root, or the square root of the 
 cube root; the 9th root is the cube root of the cube root; etc. 
 
 To Extract the Square Root. Point off the given number into 
 periods of two places each, beginning with units. If there are decimals, 
 point these off likewise, beginning at the decimal point, and supplying 
 as many ciphers as may be needed. Find the greatest number whose 
 square is less than the first left-hand period, and place it as the first 
 figure in the quotient. Subtract its square from the left-hand period, 
 and to the remainder annex the two figures of the second period for 
 a dividend. Double the first figure of the quotient for a partial divisor; 
 find how many times the latter is contained in the dividend exclusive 
 of the right-hand figure, and set the figure representing that number of 
 times as the second figure in the quotient, and annex it to the right of 
 the partial divisor, forming the complete divisor. Multiply this divisor 
 by the second figure in the quotient and Subtract the product from the 
 dividend. To the remainder bring down the next period and proceed as 
 before, in each case doubling the figures in the root already found to obtain 
 the trial divisor. Should the product of the second figure in the root by 
 the completed divisor be greater than the dividend, erase the second 
 figure both from the quotient and from the divisor, and substitute the 
 next smaller figure, or one small enough to make the product of the second 
 figure by the divisor less than or equal to the dividend. 
 
6QUA 
 o i A 1 rcnofl 
 
 CUBE ROOT. 
 
 SQUARE ROOT. 
 
 3.1415926536 U/77245 -f 
 1 
 
 27(214 
 1189 
 
 34712515 
 (2429 
 
 354218692 
 7084 
 
 CUBE ROOT. 
 
 35444 160865 
 1141776 
 
 55448511908936 
 )1772425 
 
 300 X I 2 
 30 X 1 
 
 1.881.365.963.6251 12345 
 1 
 
 = 300 881 
 X2 = 60 
 22= 4 
 
 364 728 
 
 300X122 =43200 
 
 30 X 12 X 3 = 1080 
 
 32 = 9 
 
 44289 
 
 I 
 
 300 X 1232 = 4538700 
 
 30 X 123 X 4 = 14760 
 
 42= 16 
 
 4553476 
 
 300X1234 2 =456826800 
 
 30X1234X5= 185100 
 
 5 2 = 25 
 
 457011925 
 
 20498963 
 
 18213904 
 
 2285059625 
 
 2285059625 
 
 To extract the square root of a fraction, extract the root of a numerator 
 
 /4~ 2 
 and denominator separately, 1/g = ~ or first convert the fraction into 
 
 a decimal, *\| = V.4444 4- = 0.6666 -K 
 
 To Extract the Cube Root. Point off the number into periods of 3 
 figures each, beginning at the right hand, or unit's place. Point off 
 decimals in periods of 3 figures from the decimal point. Find the greatest 
 cube that does not exceed the left-hand period; write its root as the first 
 figure in the required root. Subtract the cube from the left-hand period, 
 and to the remainder bring down the next period for a dividend. 
 
 Square the first figure of the root; multiply by 300, and divide the 
 product into the dividend for a trial divisor; write the quotient after 
 the first figure of the root as a trial second figure. 
 
 Complete the divisor by adding to 300 times the square of the first 
 figure, 30 times the product of the first by the second figure, and the 
 square of the second figure. Multiply this divisor by the second figure; 
 subtract the product from the remainder. (Should the product be greater 
 than the remainder, the last figure of the root and the complete divisor 
 are too large; substitute for the last figure the next smaller number, and 
 correct the trial divisor accordingly.) 
 
 To the remainder bring down the next period, and proceed as before to 
 find the third figure of the root that is, square the two figures of the 
 root already found; multiply by 300 for a trial divisor, etc. 
 
 If at any time the trial divisor is greater than the dividend, bring down 
 another period of 3 figures, and place in the root and proceed. 
 
 The cube root of a number will contain as many figures as there are 
 periods of 3 in the number. 
 
 To Extract a Higher Root than the Cube. The fourth root is the 
 square root of the square root; the sixth root is the cube root of the square 
 root or the square root of the cube root. Other roots are most conve- 
 niently found by the use of logarithms. 
 
 ALLIGATION. 
 
 shows the value of a mixture of different ingredients when the quantity 
 and value of each are known. 
 
 Let the ingredients be a, b, c, d, etc., and their respective values per 
 unit w, x, y, z, etc. 
 
10 ARITHMETIC. 
 
 A = the sum of the quantities = a+b+c+d t etc. 
 P = mean value or price per unit of A. 
 AP = aw + bx + cy + dz, etc. 
 P = aw + bx + cy + dz 
 A 
 
 PERMUTATION 
 
 shows in how many positions any number of things may be arranged in a 
 row; thus, the letters a, b, c may be arranged in six positions, viz. abc, acb, 
 cab, cba, bac, bca. 
 
 Rule. Multiply together all the numbers used in counting the things; 
 thus, permutations of 1, 2, and 3 = 1X2X3 = 6. In how many 
 positions can 9 things in a row be placed? 
 
 1X2X3X4X5X6X7X8X9 = 362880. 
 
 COMBINATION 
 
 shows how many arrangements of a few things may be made out of a 
 greater number. Rule: Set down that figure which indicates the greater 
 number, and after it a series of figures diminishing by 1, until as many are 
 set down as the number of the few things to be taken in each combination. 
 Then beginning under the last one, set down said number of few things; 
 then going backward set down a series diminishing by 1 until arriving 
 under the first of the upper numbers. Multiply together all the upper 
 numbers to form one product, and all the lower numbers to form another; 
 divide the upper product by the lower one. 
 
 How many combinations of 9 things can be made, taking 3 in each com- 
 bination? 
 
 9X8X7 _ 504 _ 
 
 1X2X3" 6 
 
 ARITHMETICAL PROGRESSION, 
 
 in a series of numbers, is a progressive increase or decrease in each succes- 
 sive number by the addition or subtraction of the same amount at each 
 step, as 1, 2, 3, 4, 5, etc., or 15, 12, 9, 6, etc. The numbers are called terms, 
 and the equal increase or decrease the difference. Examples in arithmeti- 
 cal progression may be solved by the following formulae: 
 
 Let a = first term, I = last term, d = common difference, n = number 
 
 of terms, s = sum of the terms; 
 
 1 / / 1 \ 2 
 
 I = a + (n l)d, = - d y 2ds -f I a - d\ 9 
 
 2s s , (n I)d 
 
 ~ ~n ~~ a> = ri 2 
 
 X "* J * 2 2d 
 
 2 2 
 
 == i d Id 4-ldV-- 
 
 l-a 
 d -^-l* 
 
 P - a 
 
 ' 2s - I a 
 
 I - a , 
 
 ~T~ *" * 
 
 2s 
 ! I + a ' 2d 
 
 2(s - an) 
 
 
 n(n - 1) ' 
 2(nl - s) 
 
 n(n - 1) 
 
 d 2a V(2a - < 
 
 *)2 + 8ds 
 
 2d 
 
 21 + d ^(21 -f d) ! 
 
 * - Sds 
 
GEOMETRICAL PROGRESSION. 
 
 GEOMETRICAL PROGRESSION. 
 
 11 
 
 ix ci series of numbers, is a progressive increase or decrease in each suc- 
 cessive number by the same multiplier or divisor at each step, as 1, 2, 4, 8, 
 16, etc., or 243, 81, 27, 9, etc. The common multiplier is called the ratio. 
 Let a = first term, I = last term, r = ratio or constant multiplier, n = 
 number of terms, m = any term, as 1st, 2d, etc., s = sum of the terms: 
 
 log I = log a + (n - 1) logr, l(s J) 71 "" 1 - a(s - a) n ~ l = 0, 
 
 m = arm 1 log m = log a + (m 1) log r. 
 
 n ~^- n ^/a^ _ lr n_ l 
 
 rl-a 
 
 log? - log a 
 
 logr h1 ' 
 log I log a 
 
 ~~ log (s a) log (s - I) 
 
 log [a + (r - l)s] - log a ( 
 
 logr 
 log? log [Ir (r l)s] 
 
 logr 
 
 Population of the United States. 
 
 (A problem in geometrical progression.) 
 
 Year. 
 
 1860 
 1870 
 1880 
 1890 
 1900 
 1910 
 1920 
 
 Population. 
 
 31,443,321 
 39,818,449* 
 50,155,783 
 62,622,250 
 76,295,220 
 91,972,267 
 Est. 110,367,000 
 
 Increase in 10 Annual Increase, 
 Years, per cent. per cent. 
 
 26.63 
 25.96 
 24.86 
 21.834 
 20.53 
 Est. 20.0 
 
 2.39 
 2.33 
 2.25 
 1.994 
 1.886 
 Est. 1.840 
 
 Estimated Population in Each Year from 1880 to 1919. 
 (Based on the above rates of increase, in even thousands.) 
 
 I860. 
 
 50,156 
 
 1890. 
 
 62.622 
 
 1900. 
 
 76.295 
 
 1910.. 
 
 91.972 
 
 1881. 
 
 51,281 
 
 1891. 
 
 63.871 
 
 1901 . 
 
 77.734 
 
 1911 .. 
 
 93.665 
 
 1882. 
 
 52.433 
 
 1892. 
 
 65.145 
 
 1902. 
 
 79.201 
 
 1912.. 
 
 95.388 
 
 1883. 
 
 53.610 
 
 1893. 
 
 66444 
 
 1903. 
 
 80.695 
 
 1913.. 
 
 97,143 
 
 1884. 
 
 54.813 
 
 1894. 
 
 67.770 
 
 1904. 
 
 82.217 
 
 1914.. 
 
 98.930 
 
 1885. 
 
 56,043 
 
 1895. 
 
 69,122 
 
 1905. 
 
 83.768 
 
 1915.. 
 
 100.750 
 
 1886. 
 
 57.301 
 
 1896. 
 
 70.500 
 
 1906. 
 
 85.348 
 
 1916.. 
 
 102.604 
 
 1887. 
 
 58,588 
 
 1897. 
 
 71.906 
 
 1907. 
 
 86.958 
 
 1917.. 
 
 104.492 
 
 1888. 
 
 59.903 
 
 1898. 
 
 73.341 
 
 1908. 
 
 88.598 
 
 1918.. 
 
 106.414 
 
 1889. 
 
 61,247 
 
 1899. 
 
 74.803 
 
 1909. 
 
 90.269 
 
 1919.. 
 
 108.373 
 
 * Corrected by addition of 1,260,078, estimated error of the census of 
 1870, Census Bulletin No. 16, Dec, 13, 1890. 
 
12 ARITHMETIC. 
 
 The preceding table has been calculated by logarithms as follows: 
 log r = log I log a -5- (n 1), log m = log a + (m - 1) log f 
 
 Pop. 1900. . .76,295,220 log = 7.8824988 = log I 
 
 1890. . .62,622,250 log = 7.7967285 = log a 
 
 diff. = .0857703 
 
 n = 11, n - 1 = 10; diff. -J- 10 = .00857703 = log r, 
 add log for 1890 7.7967285 = log a 
 
 log for 1891 = 7.80530553 No. = 63,871 . . 
 add again .00857703 
 
 log for 1892 7.81388256 No. = 65,145 . . . 
 
 Compound interest is a form of geometrical progression; the ratio 
 being 1 plus the percentage. 
 
 PERCENTAGE: PROFIT AND LOSS: PER CENT 
 OF EFFICIENCY. 
 
 Per cent means "by the hundred." A profit of 10 per cent means a 
 gain of $10 on every $100 expended. If a thing is bought for $1 and sold 
 for $2 the profit is 100 per cent; but if it is bought for $2 and sold for $1 
 the loss is not 100 per cent, but only 50 per cent. 
 
 Rule for percentage: Per cent gain or loss is the gain or loss divided by 
 the original cost, and the quotient multiplied by 100. 
 
 Efficiency is defined in engineering as the quotient "output divided by 
 input," that is, the energy utilized divided by the energy expended. The 
 difference between the input and the output is the loss or waste of energy. 
 Expressed as a fraction, efficiency is nearly always less than unity. Ex- 
 pressed as a per cent, it is this fraction multiplied by 100. Thus we may 
 say that a motor has an efficiency of 0.9 or of 90 per cent. 
 
 The efficiency of a boiler is the ratio of the heat units absorbed by the 
 boiler in heating water and making steam to the heating value of the coal 
 burned. The saving in fuel due to increasing the efficiency of a boiler 
 from 60 to 75% is not 25%, but only 20%. The rule is: Divide the gain 
 in efficiency (15) by the greater figure (75). The amount of fuel used is 
 inversely proportional to the efficiency; that is, 60 Ibs. of fuel with 75% 
 efficiency will do as much work as 75 Ibs. with 60% efficiency. The 
 saving of fuel is 15 lb*. which is 20% of 75 Ibs. 
 
 INTEREST AND DISCOUNT. 
 
 Interest is money paid for the use of money for a given time; tho 
 factors are: 
 
 p, the sum loaned, or the principal; 
 
 t, the time in years; 
 
 r, the rate of interest ; 
 
 i, the amount of interest for the given rate and time; 
 
 a = p + i = the amount of the principal with interest 
 
 at the end of the time. 
 Formulas: 
 
 i interest = principal X time X rate per cent = i = J-QQ I 
 
 a amount = principal + interest = p + ^g ' 
 lOOi 
 
 r -rate- 
 
INTEREST AND DISCOUNT. 33 
 
 If the rate is expressed decimally, thus, 6 per cent = .06, the 
 formulse become 
 
 Rules for finding Interest. Multiply the principal by the rate per 
 annum divided by 100, and by the time in years and fractions of a year. 
 
 If the time is given in days, interest = Principal X rate X no. of Jays _ 
 
 ooo X 100 
 
 In banks interest is sometimes calculated on the basis of 360 days to a 
 year, or 12 months of 30 days each. 
 
 Short rules for interest at 6 per cent, when 360 days are taken as 1 year: 
 
 Multiply the principal by number of days and divide by 6000. 
 
 Multiply the principal by number of months and divide by 200. 
 
 The interest of 1 dollar for one month is cent. 
 
 Interest of 10O Dollars for Different Times and Rates. 
 
 Time 3% 3% 4% 5% 6% 8% 10% 
 
 lyear $2.00 $3.00 $4.00 $5.00 $6.00 $8.00 $10.00 
 
 1 month .16| .25 .33 .41 .50 .66| .83$ 
 
 lday= g | 5 year.0055i .0083 .0111$ .0138f .0166 .0222 .02775 
 
 is year .005479 .008219 .010959 .013699 .016438 .0219178 .0273973 
 
 Discount is interest deducted for payment of money before it is due. 
 
 True discount is the difference between the amount of a debt payable 
 at a future date without interest and its present worth. The present 
 worth is that sum which put at interest at the legal rate will amount to 
 the debt when it is due. 
 
 To find the present worth of an amount due at a future date, divide the 
 amount by the amount of $1 placed at interest for the given time. The 
 discount equals the amount minus the present worth. 
 
 What discount should be allowed on $103 paid six months before it is 
 due, interest being 6 per cent per annum? 
 
 ? = $100 present worth, discount = 3.00. 
 1 +1 X .06 X ^ 
 
 Bank discount is the amount deducted by a bank as interest on money 
 loaned on promissory notes. It is interest calculated not on the actual 
 sum loaned, but on the gross amount of the note, from which the discount 
 is deducted in advance. It is also calculated on the basis of 360 days 
 in the year, and for 3 (in some banks 4) days more than the time specified 
 in the note. These are called days of grace, and the note is not payable 
 till the last of these days. In some States days of grace have been 
 abolished. 
 
 What discount will be deducted by a bank in discounting a note for $103 
 payable 6 months hence? Six months = 182 days, add 3 days grace = 185 
 
 Compound Interest. In compound interest the interest is added to 
 the principal at the end of each year, (or shorter period if agreed upon). 
 
 Let p = the principal, r = the rate expressed decimally, n = no. of 
 years, and a the amount: 
 
 o amount p(l + r) n ; r rate = u - - 1. 
 p principal = (l . n ; no. of y.ears=- n = 
 
14 
 
 ARITHMETIC. 
 
 Compound Interest Table. 
 
 (Value of one dollar at compound interest, compounded yearly, at 
 3, 4, 5, and 6 per cent, from 1 to 50 years.) 
 
 
 
 Per cent 
 
 t 
 
 
 ** 
 
 Per cent 
 
 3 
 
 4 
 
 5 
 
 6 
 
 3 
 
 4 
 
 5 
 
 6 
 
 i 
 
 .03 
 
 .04 
 
 .05 
 
 .06 
 
 16 
 
 .6047 
 
 1 .8730 
 
 2.1829 
 
 2.5403 
 
 2 
 
 .0609 
 
 .0816 
 
 .1025 
 
 .1236 
 
 17 
 
 .6528 
 
 1.9479 
 
 2.2920 
 
 2.6928 
 
 3 
 
 .0927 
 
 .1249 
 
 .1576 
 
 .1910 
 
 18 
 
 .7024 
 
 2.0258 
 
 2.4066 
 
 2.8543 
 
 4 
 
 .1255 
 
 .1699 
 
 .2155 
 
 .2625 
 
 19 
 
 .7535 
 
 2.1068 
 
 2.5269 
 
 3.0256 
 
 5 
 
 .1593 
 
 .2166 
 
 .2763 
 
 .3382 
 
 20 
 
 .8061 
 
 2.1911 
 
 2.6533 
 
 3.2071 
 
 6 
 
 .1941 
 
 .2653 
 
 .3401 
 
 .4185 
 
 21 
 
 .8603 
 
 2.2787 
 
 2.7859 
 
 3.3995 
 
 7 
 
 .2299 
 
 .3159 
 
 .4071 
 
 .5036 
 
 22 
 
 .9161 
 
 2.3699 
 
 2.9252 
 
 3.6035 
 
 8 
 
 .2668 
 
 .3686 
 
 .4774 
 
 .5938 
 
 23 
 
 .9736 
 
 2.4647 
 
 3.0715 
 
 3.8197 
 
 9 
 
 .3048 
 
 .4233 
 
 .5513 
 
 .6895 
 
 24 
 
 2.0328 
 
 2.5633 
 
 3.2251 
 
 4.0487 
 
 10 
 
 .3439 
 
 .4802 
 
 .6289 
 
 .7908 
 
 25 
 
 2.0937 
 
 2.6658 
 
 3.3863 
 
 4.2919 
 
 11 
 
 .3842 
 
 .5394 
 
 .7103 
 
 1.8983 
 
 30 
 
 2.4272 
 
 3.2433 
 
 4.3219 
 
 5.7435 
 
 12 
 
 .4258 
 
 .6010 
 
 .7958 
 
 2.0122 
 
 35 
 
 2.8138 
 
 3.9460 
 
 5.5159 
 
 7.6862 
 
 13 
 
 .4685 
 
 .6651 
 
 .8856 
 
 2.1329 
 
 40 
 
 3.2620 
 
 4.8009 
 
 7.0398 
 
 10.2858 
 
 14 
 
 1.5126 
 
 .7317 
 
 .9799 
 
 2.2609 
 
 45 
 
 3.7815 
 
 5.8410 
 
 8.9847 
 
 13.7648 
 
 15 
 
 1.5580 
 
 .8009 
 
 2.0789 
 
 2.3965 
 
 50 
 
 4.3838 
 
 7.1064 
 
 11.4670 
 
 18.4204 
 
 At compound interest at 3 per cent money will double itself in 23 1/2 years, 
 at 4 per cent in 172/3 years, at 5 per cent in 14.2 years, and at 6 per cent io 
 11. 9 years. 
 
 EQUATION OF PAYMENTS. 
 
 By equation of payments we find the equivalent or average time in 
 which one payment should be made to cancel a number of obligations due 
 at different dates; also the number of days upon which to calculate interest 
 or discount upon a gross sum which is composed of several smaller sums 
 payable at different dates. 
 
 Rule. Multiply each item by the time of its maturity in days from a 
 fixed date, taken as a standard, and divide the sum of the products by 
 the sum of the items: the result is the average time in days from the stand- 
 ard date. 
 
 A owes B $100 due in 30 days, $200 due in 60 days, and $300 due in 90 
 days. In how many days may the whole be paid in one sum of $600? 
 
 100X30+200X60+300X90 = 42,000; 42,000-^600 = 70 days, ans. 
 
 A owes B $100, $200, and $300, which amounts are overdue respectively 
 30, 60, and 90 days. If he now pays the whole amount, $600, how many 
 days' interest should he pay on that sum? Ans. 70 days. 
 
 PARTIAL, PAYMENTS. 
 
 To compute interest on notes and bonds when partial payments have 
 been made. 
 
 United States Rule. Find the amount of the principal to the time 
 of the first payment, and, subtracting the payment from it, find the 
 amount of the remainder as a new principal to the time of the next pay* 
 meat. 
 
ANNUITIES. 
 
 15 
 
 If the payment is less than the interest, find the amount of the principal 
 to the time when the sum of the payments equals or exceeds the interest 
 due, and subtract the sum of the payments from this amount. 
 
 Proceed in this manner till the time of settlement. 
 
 Note. The principles upon which the preceding rule is founded are: 
 
 1st. That payments must be applied first to discharge accrued interest, 
 and then the remainder, if any, toward the discharge of the principal. 
 
 2d. That only unpaid principal can draw interest. 
 
 Mercantile Method. When partial payments are made on short 
 notes or interest accounts, business men commonly employ the following 
 method: 
 
 Find the amount of the whole debt to the time of settlement ; also find 
 the amount of each payment from the time it was made to the time of 
 settlement. Subtract the amount of payments from the amount of the 
 debt: the remainder will be the balance due. 
 
 ANNUITIES. 
 
 An Annuity is a fixed sum of money paid yearly, or at other equ^l times 
 agreed upon. The values of annuities are calculated by the principles of 
 compound interest. 
 
 1. Let i denote interest on $ 1 for a year, then at the end of a year trier 
 amount will be 1 + i. At the end of n years it will be (1 -f i) n . 
 
 2. The sum which in n years will amount to 1 is or (1 + i) n f 
 
 or the present value of 1 due in n years. 
 
 3. The amount of an annuity of 1 in any number of years n is ' : 
 
 4. The present value of an annuity of 1 for any number of years n is 
 
 5. The annuity which 1 will purchase for any number of years n la 
 
 i 
 
 6. The annuity which would amount to 1 in n years is 
 
 (1 + i) n - , 
 Amounts, Present Values, etc., at 5% Interest. 
 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 Years 
 
 CH-t) 
 
 (l-fzT n 
 
 (l+i)n_i 
 
 1-0+0-" 
 
 i 
 
 i 
 
 
 
 
 I 
 
 i 
 
 1-0 + 0- n 
 
 (1 +t -)n_* 
 
 1 . 
 
 .05 
 
 .952381 
 
 1.00 
 
 .952381 
 
 1.05 
 
 1.00 
 
 2. 
 
 .1025 
 
 .907029 ' 
 
 2.05 
 
 1.859410 
 
 .537805 
 
 .487805 
 
 3. 
 
 .157625 
 
 .863838 
 
 3.1525 
 
 2.723248 
 
 .367209 
 
 .317209 
 
 4. 
 
 .215506 
 
 .822702 
 
 4.310125 
 
 3.545951 
 
 .282012 
 
 .232012 
 
 5. 
 
 .276282 
 
 .783526 
 
 5.525631 
 
 4.329477 
 
 .230975 
 
 .180975 
 
 6. 
 
 .340096 
 
 .746215 
 
 6.801913 
 
 5.075692 
 
 .197017 
 
 .147018 
 
 7. 
 
 .407100 
 
 .710681 
 
 8.142008 
 
 5.786373 
 
 .172820 
 
 .122820 
 
 8. 
 
 .477455 
 
 .676839 
 
 9.549109 
 
 6.463213 
 
 .154722 
 
 .104722 
 
 9. 
 
 .551328 
 
 .644609 
 
 1 1 .026564 
 
 7.107822 
 
 . 1 40690 
 
 .090690 
 
 10. 
 
 .628895 
 
 .613913 
 
 12.577893 
 
 7.721735 
 
 .129505 
 
 .079505 
 
16 
 
 ARITHMETIC. 
 
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 GO fNixTt- QGOIN.VO mm T T en tnencNCN 
 
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 SzrJTJ^^" f^ocoi^O NOin-tn-T enenencN w 
 
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 [ "f ao "1 
 '' 
 
 tn in-^-i^Tr^ OO-^-oo c^G 
 
 s tr \q >o\ oo ts o^ m O oq 
 
 K-* vOO^'o'in csl ad >O <n * hs' 
 - 
 
 O* NO' m* fx o^' in T m ix in o NO" 
 Tents ~ ^^ nmT 
 
 t^mO 
 
 oo O 
 
 T- oor> 
 
 TencN ^ "^"^ 
 
 p i fx T NO n T -f csj o f O m r> , NO o^ t>. oq CN m IN. in eN 
 
 NO m o en vq In -^ -^r f 
 '' ' 
 
 ) O ^r o in ix NO O^ r> ; oq ?N -T o n csi r>. oq 
 ' ' ' '' 
 
 
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 fO in-t-^-fNiO roini>.Nq C^.'O.***"^*** 
 
 'in "m'o^'ooo* in'o^^'o vom'ooooo' 
 
 om n ONOOI> t> NO m m m T ^ ^r en CN 
 
 rn'inoONo' rin-'oao 
 o<vj^rcMn m ooooo 
 ^rmN - 
 
 . 
 
 " o in r>. NO t a^ NO r> r^ 
 
 'oin r>.'"r '&<* 
 
 NOmm T T T en cq 
 
 V in ' t>C en in o tntx NO'CN co'intNO 
 OfN^om m*-oONOO txvONOinm T T T "t 
 
 > *^ rsi %o O in o^ o 
 O' en ^t" O NO' en 
 
 rT^cn CSCN 
 
 IH o 
 
WEIGHTS AND MEASURES. 17 
 
 TABLES FOB CALCULATING SINKING-FUNDS AND 
 PRESENT VALUES. 
 
 Engineers and others connected with municipal work and industrial 
 enterprises often find it necessary to calculate payments to sinking-funds 
 which will provide a sum of money sufficient to pay off a bond issue or 
 other debt at the end of a given period, or to determine the present value 
 of certain annual charges. The accompanying tables were computed by 
 Mr. John W. Hill, of Cincinnati, Eng'g News, Jan. 25, 1894. 
 
 Table I (opposite page) shows the annual sum at various rates of interest 
 required to net $1000 in from 2 to 50 years, and Table II shows the present 
 value at various rates of interest of an annual charge of $1000 for from 5 
 to 50 years, at five-year intervals, and for 100 years. 
 
 Table II. Capitalization of Annuity of $1000 for 
 from 5 to 10O Years. 
 
 1 
 
 Rate of IL terest, per cent. 
 
 5 
 10 
 15 
 20 
 25 
 
 30 
 35 
 40 
 45 
 50 
 100 
 
 31/2 
 
 3 
 
 3V2 
 
 4 
 
 4V2 
 
 5 
 
 5V2 
 
 6 
 
 4,645.88 
 8,752.17 
 12,381.41 
 15,589.215 
 18,424.67 
 
 20,930.59 
 23,145.31 
 25,103.53 
 26,833.15 
 28,362.48 
 36,614.21 
 
 4.579.60 
 8,530.13 
 11,937.80 
 
 4,5 1 4. 92 
 8,316.45 
 11,517.23 
 
 4,451.68 
 8,110.74 
 11,118.06 
 
 4,389.91 
 7,912.67 
 10,739.42 
 
 4,329.45 
 7,721.73 
 10,379.53 
 
 4,268.09 
 7,537.54 
 10,037.48 
 
 4,212.40 
 7,360.19 
 9,712.30 
 
 14,877.27 
 17,413.01 
 
 19,600.21 
 
 14,212.12 
 16,481.28 
 
 18,391.85 
 
 13,590.21 
 15,621.93 
 
 17,291.86 
 
 13,007.88 
 14,828.12 
 
 16,288.77 
 
 12,462.13 
 14,093.86 
 
 15,372.36 
 
 11,950.26 
 13,413.82 
 
 14,533.63 
 
 11,469.96 
 12,783.38 
 
 13,764.85 
 
 21,487.04 
 23,114.36 
 24,518.49 
 25,729.58 
 31,598.81 
 
 20,000.43 
 21,354.83 
 22,495.23 
 23,455.21 
 27,655.36 
 
 18,664.37 
 19,792.65 
 20,719.89 
 21,482.08 
 24,504.96 
 
 17,460.89 
 18,401.49 
 19,156.24 
 19,761.93 
 21,949.21 
 
 16,374.36 
 17,159.01 
 17,773.99 
 18,255.86 
 19,847.90 
 
 15,390.48 
 16,044.92 
 16,547.65 
 16,931.97 
 18,095.83 
 
 14,488.65 
 15,046.31 
 15,455.85 
 15,761.87 
 16,612.64 
 
 WEIGHTS AND MEASURES. 
 
 Long Measure. Measures of Length. 
 
 12 inches = 1 foot. 
 
 3 feet = 1 yard. 
 
 1760 yards, or 5280 feet = 1 mile. 
 
 Additional measures of length in occasional use: 1000 mils = 1 inch; 
 4 inches = 1 hand; 9 inches = 1 span; 2 1/2 feet = 1 military pace; 2 yards 
 = 1 fathom; 5 1/2 yards, or 161/2 feet = 1 rod (formerly also called pole or 
 perch). 
 
 Old Land Measure. 7.92 inches = 1 link; 100 links, or 66 feet, or 4 
 rods = 1 chain; 10 chains, or 220 yards = 1 furlong; 8 furlongs, or 80 
 chains = 1 mile; 10 square chains = 1 acre. 
 
 Nautical Measure. 
 
 6080.26JeeU.or 1.15156 stat- J =1 nautical 
 
 3 nautical miles =1 league. 
 
 60 nautical miles, or 69.168 ) _ 
 statute miles J - 
 
 / nt thp pmiatnr^ 
 l at tne equator). 
 
 360 degrees 
 
 circumference of the earth at the equator. 
 
 * The British Admiralty takes the round figure of 6080 ft. which is the 
 length of the " measured mile" used in trials of vessels. The value varies 
 from 6080.26 to 6088.44 ft. according to different measures of the earth's 
 diameter. There is a difference of opinion among writers as to the use 
 of the word " knot" to mean length or a distance some holding that 
 it should be used only to denote a rate of speed. The length between 
 knots on the log line is 1/120 of a nautical mile, or 50.7 ft., when a half- 
 minute glass is used; so that a speed of 10 knots is equal to 10 nautical 
 miles per hour. 
 
18 ARITHMETIC. 
 
 Square Measure. Measures of Surface. 
 
 144 square inches, or 183.35 circular ) _ , f . 
 
 inches )or 
 
 9 square feet = 1 square yard. 
 
 30V4 square yards, or 2721/4 square feet = 1 square rod. 
 10 sq. chains, or 160 sq. rods, or 4840 sq. ) , 
 
 yards, or 43560 sq. feet 
 
 640 acres or 27,878,400 sq. ft. =1 square mile. 
 
 An acre equals a square whose side is 208.71 feet. 
 Circular Inch; Circular Mil. A circular inch is the area of a circle 
 
 1 inch m diameter = 0.7854 square inch. 
 
 1 square inch = 1.2732 circular inches. 
 
 A circular mil is the area of a circle 1 mil, or 0.001 inch in diameter. 
 10002 or 1,000,000 circular mils =- 1 circular inch. 
 
 1 square inch = 1,273,239 circular mils. 
 
 t The mil and circular mil are used in electrical calculations involving 
 tne diameter and area of wires. 
 
 Solid or Cubic Measure. Measures of Volume. 
 
 1728 cubic inches = 1 cubic foot. 
 27 cubic feet = 1 cubic yard. 
 
 1 cord of wood = a pile, 4X4X8 feet = 128 cubic feet. 
 1 perch of masonry = 161/2 X 11/2 X 1 foot = 243/ 4 cubic feet. 
 
 Liquid Measure. 
 
 4 pills = 1 pint. 
 2 pints = 1 quart. 
 4 nnart i p-niirm J U. S. 231 cubic inches. 
 
 - 1 gallon j Eng 277.274 cubic inches. 
 
 Old Liquid Measures. 31 1/2 gallons = 1 barrel; 42 gallons = 1 tierce; 
 
 2 barrels, or 63 gallons = 1 hogshead; 84 gallons, or 2 tierces = 1 pun- 
 cheon; 2 hogsheads, or 126 gallons = 1 pipe or butt; 2 pipes, or 3 pun- 
 cheons = 1 tun. 
 
 A gallon of water at 62 F. weighs 8.33531b. (air free, weighed in vacuo). 
 
 The U. S. gallon contains 231 cubic inches; 7.4805 gallons = 1 cubic 
 foot. A cylinder 7 in. diam. and 6 in. high contains 1 gallon, very nearly, 
 or 230.9 cubic inches. The British Imperial gallon contains 277.274 cubic 
 inches = 1.20032 U. S. gallon, or 10 ibs. of water at 62 F. 
 
 The gallon is a very troublesome unit for engineers. Much labor might 
 be saved if it were abandoned and the cubic fo9t used instead. The 
 capacity of a tank or reservoir should.be stated in cubic feet, and the 
 delivery of a pump in cubic feet per second or in millions of cubic feet in 
 24 hours. One cubic foot per second = 86,400 cu. ft. in 24 hours. One 
 million cu. ft. per 24 hours = 11.5741 cu. ft. per sec. 
 
 The Miner's Inch. (Western U. S. for measuring flow of a stream 
 of water.) An act of the California legislature, May 23, 1901, makes the 
 standard miner's inch 1.5 cu. ft. per minute, measured through any aper- 
 ture or orifice. 
 
 The term Miner's Inch is more or less indefinite, for the reason that Cali- 
 fornia water companies do not all use the same head above the centre of 
 the aperture, and the inch varies from 1.36 to 1.73 cu. ft. per min., but 
 the most common measurement is through an aperture 2 ins. high and 
 whatever length is required, and through a plank 11/4 ins. thick. The 
 lower edge of the aperture should be 2 ins. above the bottom of the meas- 
 uring-box, and the plank 5 ins. high above the aperture, thus making a 6-in. 
 head above the centre of the stream. Each square inch of this opening 
 represents a miner's inch, which is equal to a flow of 1 1/2 cu. ft. per min. 
 
 Apothecaries' Fluid Measure. 
 
 60 minims = 1 fluid drachm. 8 drachms = 1 fluid ounce. 
 
 In the U. S. a fluid ounce is the 128th part of a U. S. gallon, or 1.805 
 cu. ins. It contains 456.3 grains of water at 39 F. In Great Britain 
 the fluid ounce is 1.732 cu. ins. and contains 1 ounce avoirdupois, or 437.5 
 grains of water at 62 F. 
 
WEIGHTS AND MEASURES. 19 
 
 Dry Measure, U. S. 
 
 2 pints = 1 quart. 8 quarts = 1 peck. 4 pecks = 1 bushel. 
 
 The standard U. S. bushel is the Winchester bushel, which is, in 
 cylinder form, 18 1/2 inches diameter and 8 inches deep, and contains 
 2150.42 cubic inches. 
 
 A struck bushel contains 2150.42 cubic inches = 1.2445 cu. ft.; 1 
 cubic foot = 0.80356 struck bushel. A heaped bushel is a cylinder 18 1/2 
 inches diameter and 8 inches deep, with a heaped cone not less than 
 6 inches high. It is equal to 1 V* struck bushels. (When applied to 
 apples and pears the bushel should be heaped so as to contain 2737.715 
 cu. in. = 1.2731 struck bushels. Decision of U. S. Court of Customs 
 Appeals, 1912.) 
 
 The British Imperial bushel = 8 imperial gallons or 2218.192 cu. in. = 
 1.2837 cu. ft. The British quarter = 8 imperial bushels. 
 
 Capacity of a cylinder in U. S. gallons = square of diameter, in inches 
 X height in inches X .0034. (Accurate within 1 part in 100,000.) 
 
 Capacity of a cylinder in U. S. bushels = square of diameter in inches 
 X height in inches X 0.0003652. 
 
 Shipping Measure. 
 
 Register Ton. For register tonnage or for measurement of the entire 
 ternal capacity of a vessel: 
 
 100 cubic feet = 1 register ton. 
 
 This number is arbitrarily assumed to facilitate computation. 
 Shipping Ton. For the measurement of cargo: 
 
 40 cubic feet = 1 U. S. shipping ton = 32.143 U. S. bushels. 
 
 42 cubic feet = 1 .British shipping ton = 32.719 imperial bushels. 
 
 Carpenter's Rule. Weight a vessel will carry = length of keel X 
 breadth at main beam X depth of hold in feet -h 95 (the cubic feet 
 allowed for a ton). The result will be the tonnage. For a double- 
 decker instead of the depth of the hold take half the breadth of the 
 
 
 Measures of Weight. Avoirdupois or Commercial 
 Weight. 
 
 16 drachms, or 437.5 grains = 1 ounce, oz. 
 16 ounces, or 7000 grains = 1 pound, Ib. 
 28 pounds = 1 quarter, qr. 
 
 4 quarters = 1 hundredweight, cwt. = 112 Ib. 
 
 20 hundredweight = 1 ton of 2240 Ib., gross or long ton. 
 
 2000 pounds = 1 net, or short ton. 
 
 2204.6 pounds = 1 metric ton. 
 
 1 stone = 14 pounds; 1 quintal = 100 pounds. 
 
 The drachm, quarter, hundredweight, stone, and quintal are now 
 seldom used in the United States. 
 
 Troy Weight 
 
 24 grains = 1 pennyweight, dwt. 
 
 20 pennyweights = 1 ounce, oz. = 480 grains. 
 
 12 ounces = 1 pound, Ib. = 5760 grains. 
 
 Troy weight is used for weighting gold and silver. The grain is the 
 same in Avoirdupois. Troy, and Apothecaries' weights. A carat, for 
 weighing diamonds = 3.086 grains = 0.200 gramme. (International 
 Standard, 1913.) 
 
 Apothecaries' Weight. 
 
 20 grains = 1 scruple, 3 
 
 3 scruples 1 drachm, 3 - 60 grains. 
 
 8 drachms 1 ounce, 5 480 grains. 
 
 12 ounces 1 pound, Ib. 5760 grains. 
 
20 ARITHMETIC. 
 
 To determine whether a balance has unequal arms. After weigh- 
 ing an article and obtaining equilibrium, transpose the article and the 
 weights. If the balance is true, it will remain in equilibrium; if untrue, 
 the pan suspended from the longer arm will descend. 
 
 To weigh correctly on an incorrect balance. First, by substitu- 
 tion. Put the article to be weighed in one pan of the balance and counter- 
 poise it by any convenient heavy articles placed on the other pan. 
 Remove the article to be weighed and substitute for it standard weights 
 until equipoise is again established. The amount of these weights is the 
 weight of the article. 
 
 Second, by transposition. Determine the apparent weight of the 
 article as usual, then its apparent weight after transposing the article and 
 the weights. If the difference is small, add half the difference to the 
 smaller of the apparent weights to obtain the true weight. If the differ- 
 ence is 2 per cent the error of * his method is 1 part in 10,000. For larger 
 differences, or to obtain a perfectly accurate result, multiply the two 
 apparent weights together and extract the square root of the product. 
 
 Circular Measure. 
 
 60 seconds, * = 1 minute, '. 
 60 minutes, ' = 1 degree, . 
 90 degrees = 1 quadrant. 
 380 = circumference. 
 
 Arc of angle of 57.3, or 360 * 6.2832 = 1 radian the arc whose length 
 is equal to the radius. 
 
 Time. 
 
 60 seconds = 1 minute. 
 60 minutes = 1 hour. 
 24 hours = 1 day. 
 
 7 days = 1 week. 
 365 days, 5 hours, 48 minutes, 48 seconds 1 year. 
 
 By the Gregorian Calendar every year whose number is divisible by 4 
 is a leap year, and contains 366 days, the other years containing 365 days, 
 except that the centesimal years are leap years only when the number of 
 the year is divisible by 400. 
 
 The comparative values of mean solar and sidereal time are shown by 
 the following relations according to Bessel: 
 
 365.24222 mean solar days = 366.24222 sidereal days, whence 
 1 mean solar day = 1.00273791 sidereal days; 
 
 1 sidereal day = 0.99726957 mean solar day; 
 24 hours mean solar time = 24* 3 56.555 sidereal time; 
 24 hours sidereal time = 23* 56*n 4.091 mean solar time, 
 
 whence 1 mean solar day is 3 55.91 longer than a sidereal day, reckoned 
 in mean solar time. 
 
 BOARD AND TIMBER MEASURE. 
 
 Board Measure. 
 
 In board measure boards are assumed to be one inch in thickness. To 
 obtain the number of feet board measure (B. M.) of a board or stick of 
 square timber, multiply together the length in feet, the breadth in feet, 
 and the thickness in inches. 
 
 To compute the measure or surface in square feet. When all 
 dimensions are in feet, multiply the length by the breadth, and the prod- 
 uct will give the surface required. 
 
 When either of the dimensions are in inches, multiply as above and 
 divide the product by 12. 
 
 When all dimensions are in inches, multiply as before and divide product 
 by 144. 
 
 Timber Measure. 
 
 To compute the volume of round timber. When all dimensions 
 are in feet, multiply the length by one quarter of the product of the mean 
 
WEIGHTS AND MEASURES. 
 
 21 
 
 girth and diameter, and the product will give the measurement in cubic 
 feet. When length is given in feet, and girth and diameter in inches 
 divide the product by 144; when all the dimensions are in inches, divide 
 by 1728. 
 
 To compute the volume of square timber. When all dimensions 
 are in feet, multiply together the length, breadth, and depth; the product 
 will be the volume in cubic feet. When one dimension is given in inches, 
 divide by 12; when two dimensions are in inches, divide by 144: when all 
 three dimensions are in inches, divide by 1728. 
 
 Contents in Feet of Joists, Scantling, and Timber, 
 
 Length in Feet. 
 
 Size. 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 Feet Board Measure. 
 
 2X4 
 
 8 
 
 9 
 
 11 
 
 12 
 
 13 
 
 15 
 
 16 
 
 17 
 
 19 
 
 20 
 
 2X6 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 2X8 
 
 16 
 
 19 
 
 21 
 
 24 
 
 27 
 
 29 
 
 32 
 
 35 
 
 37 
 
 40 
 
 2 X 10 
 
 20 
 
 23 
 
 27 
 
 30 
 
 33 
 
 37 
 
 40 
 
 43 
 
 47 
 
 50 
 
 2 X 12 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 52 
 
 56 
 
 60 
 
 2 X 14 
 
 28 
 
 33 
 
 37 
 
 42 
 
 47 
 
 51 
 
 56 
 
 61 
 
 65 
 
 70 
 
 3X8 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 52 
 
 56 
 
 60 
 
 3 X 10 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 3 X 12 
 
 36 
 
 42 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 84 
 
 90 
 
 3 X 14 
 
 42 
 
 49 
 
 56 
 
 63 
 
 70 
 
 77 
 
 64 
 
 91 
 
 98 
 
 105 
 
 4X4 
 
 16 
 
 19 
 
 21 
 
 24 
 
 27 
 
 29 
 
 32 
 
 35 
 
 37 
 
 40 
 
 4X6 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 43 
 
 52 
 
 56 
 
 60 
 
 4X8 
 
 32 
 
 37 
 
 43 
 
 43 
 
 53 
 
 59 
 
 64 
 
 69 
 
 75 
 
 80 
 
 4 X 10 
 
 40 
 
 47 
 
 53 
 
 60 
 
 67 
 
 73 
 
 80 
 
 87 
 
 93 
 
 100 
 
 4 X 12 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 83 
 
 96 
 
 104 
 
 112 
 
 120 
 
 4 X 14 
 
 56 
 
 65 
 
 75 
 
 84 
 
 93 
 
 103 
 
 112 
 
 121 
 
 131 
 
 140 
 
 6X6 
 
 36 
 
 42 
 
 43 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 84 
 
 90 
 
 6X8 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 83 
 
 96 
 
 104 
 
 112 
 
 120 
 
 6 X 10 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 6 X 12 
 
 72 
 
 84 
 
 96 
 
 108 
 
 120 
 
 132 
 
 144 
 
 156 
 
 168 
 
 180 
 
 6X 14 
 
 84 
 
 98 
 
 112 
 
 126 
 
 140 
 
 154 
 
 168 
 
 182 
 
 196 
 
 210 
 
 8X8 
 
 64 
 
 75 
 
 85 
 
 96 
 
 107 
 
 117 
 
 128 
 
 139 
 
 149 
 
 160 
 
 8 X 10 
 
 80 
 
 93 
 
 107 
 
 120 
 
 133 
 
 147 
 
 160 
 
 173 
 
 187 
 
 200 
 
 8 X 12 
 
 96 
 
 112 
 
 128 
 
 144 
 
 160 
 
 176 
 
 192 
 
 208 
 
 224 
 
 240 
 
 8 X 14 
 
 112 
 
 131 
 
 149 
 
 168 
 
 187 
 
 205 
 
 224 
 
 243 
 
 261 
 
 280 
 
 10 X 10 
 
 100 
 
 117 
 
 133 
 
 150 
 
 167 
 
 183 
 
 200 
 
 217 
 
 233 
 
 250 
 
 10 X 12 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 220 
 
 240 
 
 260 
 
 2ttO 
 
 300 
 
 10 X 14 
 
 140 
 
 163 
 
 187 
 
 210 
 
 233 
 
 257 
 
 280 
 
 303 
 
 327 
 
 350 
 
 12 X 12 
 
 144 
 
 168 
 
 192 
 
 216 
 
 240 
 
 264 
 
 288 
 
 312 
 
 336 
 
 360 
 
 12 X 14 
 
 168 
 
 196 
 
 224 
 
 252 
 
 280 
 
 308 
 
 336 
 
 364 
 
 392 
 
 420 
 
 14 X 14 
 
 196 
 
 229 
 
 261 
 
 294 
 
 327 
 
 359 
 
 392 
 
 425 
 
 457 
 
 490 
 
 FRENCH OB METRIC MEASURES. 
 
 The metric unit of length is the metre = 39.37 inches. 
 
 The metric unit of weight is the gram = 15.432 grains. 
 
 1 he following prefixes are used for subdivisions and multiples: Milli = 
 Viooq, Centi = Vioo, Deci = 1/10, Deca = 10, Hecto = 100, Kilo = 1000. 
 i.yna = 10,000. 
 
22 ARITHMETIC. 
 
 FRENCH AND BRITISH (AND AMERICAN) 
 EQUIVALENT MEASURES. 
 
 Measures of Length. 
 
 FRENCH. BRITISH and U. S. 
 
 1 metre = 39.37 inches, or 3.28083 feet, or 1.09361 yards. 
 
 0.3048 metre = 1 foot. 
 
 1 centimetre = 0.3937 inch. 
 2.54 centimetres = 1 inch. 
 
 1 millimetre = 0.03937 inch, or 1 /25 inch, nearly. 
 25.4 millimetres = 1 inch. 
 
 1 kilometre = 1093. Gl yards, or 0.62137 mile. 
 
 Of Surface 
 
 FRENCH BRITISH and U. S. 
 
 1 omiarp mptrp - j 10.7639 square feet. 
 
 ~ 1 1.196 square yards. 
 
 0.836 square metre = 1 square yard. 
 
 0.0929 square metre = 1 square foot. 
 
 1 square centimetre = 0. 15500 square inch. 
 6.452 square centimetres = 1 square inch. 
 
 1 square millimetre = 0.00155 sq. in. = 1973.5 circ. mils. 
 
 645.2 square millimetres = 1 square inch. 
 
 1 centiare = 1 sq. metre = 10.764 square feet. 
 
 1 are = 1 sq. decametre = 1076.41 
 
 1 hectare = 100 ares = 107641 = 2.4711 acres. 
 
 1 sq. kilometre = 0.386109 sq. miles = 247.11 
 
 1 sq. myriametre = 38.6109 
 
 Of Volume 
 
 FRENCH. BRITISH and U. S. 
 
 i miVnV rnpfro J 35.314 cubic feet, 
 
 1 cubic metre = -j 13QS cubic yards 
 
 0.7645 cubic metre = 1 cubic yard. 
 
 0.02832 cubic metre = 1 cubic foot. 
 
 1 oiibio rlpHmptrP - i 61.0234 cubic inches. 
 1 0.035314 cubic foot. 
 28.32 cubic decimetres = 1 cubic foot. 
 
 1 cubic centimetre = 0.061 cubic inch. 
 16.387 cubic centimetres = 1 cubic inch. 
 1 cubic centimetre = 1 millilitre = 0.061 cubic inch. 
 1 decilitre =6.102 " 
 
 1 litre = 1 cubic decimetre = 61.0234 ' = 1.05671 
 
 quarts, U. S. 
 
 1 hectolitre or decistere = 3.5314 cubic feet = 2.8375 bu., U. S. 
 
 1 stere, kilolitre, or cubic metre = 1.308 cubic yards = 28.37 bu., 
 
 Of Capacity 
 
 FRENCH. BRITISH and U. S. 
 
 f 6 1.0234 cubic inches. 
 oiil'gaUoi? (American), 
 2.202 pounds of water at 62 F. 
 28.317 litres = 1 cubic foot. 
 
 4.543 litres = 1 gallon (British). 
 
 3.785 litres = 1 gallon (American). 
 
 Of Weight. 
 
 FRENCH. BRITISH and U. S. 
 
 1 gramme = 15,432 grains. 
 
 0.0648 gramme = 1 grain. 
 
 1 kilogramme = 2.204622 pounds. 
 
 0.4536 kilogramme = 1 pound. 
 
 1 tonne or metric ton I = j 0.9842 ton of 2240 pounds. 
 1000 kilogrammes f = j 22G4. 6 pounds. 
 
 1.016 metric tons 1 ton of 2240 pounds. 
 
WEIGHTS AND MEASURES. 
 
 23 
 
 Mr. O. H. Titmann, in Bulletin No. 9 of the U. S. Coast and Geodetic 
 Survey, discusses the work of various authorities who have compared the 
 yard and the metre, and by referring all the observations to a common 
 standard has succeeded in reconciling the discrepancies within very 
 narrow limits. The following are his results for the number of inches in a 
 metre according to the comparisons of the authorities named: 1817. 
 Hassler, 39.36994 in. 1818. Kater, 39.36990 in. 1835. Baily, 39.36973 
 in. 1866. Clarke, 39.36970 in. 1885. Comstock, 39.36984 in. The mean 
 of these is 39.36982 in. 
 
 The value of the metre is now denned in the U. S. laws as 39.37 inches. 
 
 French and British Equivalents of Compound Units. 
 
 FRENCH. BRITISH. 
 
 gramme per square millimetre = 1.422 Ibs. per sq. in. 
 
 kilogramme per square ' = 1422.32 
 
 centimetre = 14.223 " 
 
 .0335 kg. per sq. cm. = 1 atmosphere = 14.7 " " " " 
 
 0.070308 kilogramme per square centimetre = 1 Ib. per square inch. 
 
 kilogrammetre = 7.2330 foot-pounds. 
 
 gramme per litre = 0.062428 Ib. per cu. ft. = 58.349 grains per U. S gal. 
 
 of water at 62 F. 
 1 grain per U. S. gallon=l part in 58,349 = 1.7138 parts per 100,000 
 
 0.017138 grammes per litre. 
 
 METRIC CONVERSION TABLES. 
 
 The following tables, with the subjoined memoranda, were published 
 in 1890 by the United States Coast and Geodetic Survey, office of standard 
 weights and measures, T. C. Mendenhall, Superintendent. 
 
 - 
 
 Tables for Converting TJ. S. Weights and Measures 
 Customary to Metric. 
 
 LINEAR. 
 
 
 Inches to Milli- 
 metres. 
 
 Feet to Metres. 
 
 Yards to Metres. 
 
 Miles to Kilo- 
 metres. 
 
 2 = 
 
 3 = 
 4 = 
 5 = 
 
 25.4001 
 50.8001 
 76.2002 
 101.6002 
 127.0003 
 
 0.304801 
 0.609601 
 0.914402 
 1.219202 
 1.524003 
 
 0.914402 
 1 .828804 
 2.743205 
 3.657607' 
 4.572009 
 
 1.60935 
 3.21869 
 4.82804 
 6.43739 
 8.04674 
 
 8 = 
 
 152.4003 
 177.8004 
 203.2004 
 228.6005 
 
 1.828804 
 2.133604 
 2.438405 
 2:743205 
 
 5.486411 
 6.400813 
 7.315215 
 8.229616 
 
 9.65608 
 11.26543 
 12.87478 
 14.48412 
 
 SQUARE. 
 
 
 Square Inches to 
 Square Centi- 
 metres. 
 
 Square Feet to 
 Square Deci- 
 metres. 
 
 Square Yards to 
 Square Metres. 
 
 Acres to 
 Hectares. 
 
 K 
 
 1 = 
 
 6.452 
 
 9.290 
 
 0.836 
 
 04047 
 
 2 = 
 
 12.903 
 
 18.581 
 
 1.672 
 
 0.8094 
 
 3 = 
 
 19.355 
 
 27.871 
 
 2.508 
 
 1.2141 
 
 A 
 
 25.807 
 
 37.161 
 
 3.344 
 
 1.6187 
 
 5 = 
 
 32.258 
 
 46.452 
 
 4.181 
 
 2.0234 
 
 6 = 
 
 38.710 
 
 55.742 
 
 5.017 
 
 2.4281 
 
 7 = 
 
 45.161 
 
 65.032 
 
 5.853 
 
 2.8328 
 
 8 = 
 
 51.613 
 
 74.323 
 
 6.689 
 
 3.2375 
 
 9 = 
 
 58.065 
 
 83.613 
 
 7.525 
 
 3.6422 
 
ARITHMETIC. 
 
 CUBIC. 
 
 
 Cubic Inches to 
 Cubic Centi- 
 metres. 
 
 Cubic Feet to 
 Cubic Metres. 
 
 Cubic Yards to 
 Cubic Metres. 
 
 Bushels to 
 Hectolitres. 
 
 Ui-UUJ Si- 
 ll II II II 11 
 
 16.387 
 32.774 
 49.161 
 65.549 
 81.936 
 
 0.02832 
 0.05663 
 0.08495 
 0.11327 
 0.14158 
 
 0.765 
 1.529 
 2.294 
 3.058 
 3.823 
 
 0.35242 
 0.70485 
 1.05727 
 1 .40969 
 1.76211 
 
 6 = 
 
 8 = 
 
 98.323 
 114.710 
 131.097 
 147.484 
 
 0.16990 
 0.19822 
 0.22654 
 0.25485 
 
 4.587 
 5.352 
 6.116 
 6.881 
 
 2.11454 
 2.46696 
 2.81938 
 3.17181 
 
 CAPACITY. 
 
 
 Fluid Dracnms 
 to Millilitres or 
 Cubic Centi- 
 metres. 
 
 Fluid Ounces to 
 Millilitres . 
 
 Quarts to Litres. 
 
 Gallons to 
 Litres. 
 
 1 = 
 
 2 = 
 3 = 
 4 = 
 5 = 
 
 6 = 
 
 8 = 
 9 = 
 
 3.70 
 7.39 
 11.09 
 14.79 
 18.48 
 
 22.18 
 25.88 
 29.57 
 33.28 
 
 29.57 
 59.15 
 88.72 
 118.30 
 147.87 
 
 177.44 
 207.02 
 236.59 
 266.16 
 
 0.94636 
 1 .89272 
 2.83908 
 3.78544 
 4.73180 
 
 5.67816 
 6.62452 
 7.57088 
 8.51724 
 
 3.78544 
 7.57088 
 11.35632 
 15.14176 
 18.92720 
 
 22.71264 
 26.49808 
 30.28352 
 34.06896 
 
 WEIGHT. 
 
 
 Grains to Milli- 
 grammes. 
 
 Avoirdupois 
 Ounces to 
 Grammes. 
 
 Avoirdupois 
 Pounds to Kilo- 
 grammes. 
 
 Troy Ounces to 
 Grammes. 
 
 1 = 
 
 2 
 
 4 = 
 5 = 
 
 6 = 
 
 8-= 
 9- 
 
 64.7989 
 129.5978 
 194.3968 
 259.1957 
 323.9946 
 
 388.7935 
 453.5924 
 518.3914 
 583.1903 
 
 28.3495 
 56.6991 
 85.0486 
 113.3981 
 141.7476 
 
 170.0972 
 198.4467 
 226.7962 
 255.1457 
 
 0.45359 
 0.90719 
 1 .36078 
 1.81437 
 2.26796 
 
 2.72156 
 3.17515 
 3.62874 
 4.08233 
 
 31.10348 
 62.20696 
 93.31044 
 124.41392 
 155.51740 
 
 186.62089 
 217.72437 
 248.82785 
 279.93133 
 
 1 chain = 20.11 69 metres. 
 1 square mile = 259 hectares. 
 1 fathom = 1 .829 metres. 
 1 nautical mile = 1853.27 metres. 
 1 foot = 0.304801 metre. 
 1 avoir, pound = 453.5924277 gram. 
 15432.35639 grains = 1 kilogramme. 
 
METRIC CONVERSION TABLES. 
 
 25 
 
 Tables for Converting U. S. Weights and Measures 
 Metric to Customary. 
 
 LINEAR. 
 
 
 Metres to 
 Inches. 
 
 Metres to 
 Feet. 
 
 Metres to 
 Yards. 
 
 Kilometres to 
 Miles. 
 
 1 = 
 
 2 = 
 
 4 = 
 5 = 
 
 39.3700 
 78.7400 
 118.1100 
 157.4800 
 196.8500 
 
 3.28083 
 6.56167 
 9.84250 
 13.12333 
 16.40417 
 
 1.093611 
 2.187222 
 3.280833 
 4.374444 
 5.468056 
 
 0.62137 
 1 .24274 
 1.86411 
 2.48548 
 3.10685 
 
 1: 
 
 236.2200 
 275.5900 
 314.9600 
 354.3300 
 
 19.68500 
 22.96583 
 26.24667 
 29.52750 
 
 6.561667 
 7.655278 
 8.748889 
 9.842500 
 
 3.72822 
 4.34959 
 4.97096 
 5.59233 
 
 SQUARE. 
 
 
 Square Centi- 
 metres to 
 Square Inches. 
 
 Square Metres 
 to Square Feet. 
 
 Square Metres 
 to Square Yards. 
 
 Hectares to 
 Acres. 
 
 1 = 
 
 0.1550 
 
 10.764 
 
 1.196 
 
 2.471 
 
 2 = 
 
 0.3100 
 
 21.528 
 
 2.392 
 
 4.942 
 
 3 = 
 
 0.4650 
 
 32.292 
 
 3.588 
 
 7.413 
 
 4 = 
 
 0.6200 
 
 43.055 
 
 4.784 
 
 9.884 
 
 5 = 
 
 0.7750 
 
 53.819 
 
 5.980 
 
 12.355 
 
 6 = 
 
 0.9300 
 
 64.583 
 
 7.176 
 
 14826 
 
 7 = 
 
 1.0850 
 
 75.347 
 
 8.372 
 
 17.297 
 
 8 = 
 
 1.2400 
 
 86.111 
 
 9.563 
 
 19.768 
 
 9 = 
 
 1.3950 
 
 96.874 
 
 10.764 
 
 22.239 
 
 CUBIC. 
 
 
 Cubic Centi- 
 metres to Cubic 
 Inches. 
 
 Cubic Deci- 
 metres to Cubic 
 Inches. 
 
 Cubic Metres to 
 Cubic Feet. 
 
 Cubic Metres to 
 Cubic Yards. 
 
 1 = 
 
 0.0610 
 
 61.023 
 
 35.314 
 
 1.308 
 
 2 - 
 
 0.1220 
 
 122.047 
 
 70.629 
 
 2.616 
 
 3 = 
 
 0.1831 
 
 183.070 
 
 105.943 
 
 3.924 
 
 4 = 
 
 0.2441 
 
 244.093 
 
 141.258 
 
 5.232 
 
 5 = 
 
 0.3051 
 
 305.117 
 
 176.572 
 
 6.540 
 
 6 = 
 
 0.3661 
 
 366.140 
 
 211.887 
 
 7.848 
 
 j 
 
 0.4272 
 
 427.163 
 
 247.201 
 
 9.156 
 
 8 = 
 
 0.4882 
 
 488.187 
 
 282.516 
 
 10.464 
 
 9 = 
 
 0.5492 
 
 549.210 
 
 317.830 
 
 11.771 
 
 CAPACITY. 
 
 
 Milhlitres or 
 Cubic Centi- 
 metres toFluid 
 
 Centimetres 
 to Fluid 
 Ounces. 
 
 Litres to 
 Quarts. 
 
 Dekalitres 
 to 
 Gallons. 
 
 Hektolitres 
 to 
 Bushels. 
 
 
 Drachms. 
 
 
 
 
 
 1 = 
 
 0.27 
 
 0.338 
 
 1.0567 
 
 2.6417 
 
 2.8375 
 
 2 = 
 
 0.54 
 
 0.676 
 
 2.1134 
 
 5.2834 
 
 5.6750 
 
 3 = 
 
 0.81 
 
 1.014 
 
 3.1700 
 
 7.9251 
 
 8.5125 
 
 4 = 
 
 1.08 
 
 1.352 
 
 4.2267 
 
 10.5668 
 
 11.3500 
 
 5 = 
 
 1.35 
 
 1.691 
 
 5.2834 
 
 13.2085 
 
 14.1875 
 
 6 = 
 
 1.62 
 
 2.029 
 
 6.3401 
 
 15.8502 
 
 17.0250 
 
 j 
 
 1.89 
 
 2.363 
 
 7.3968 
 
 18.4919 
 
 . 19.8625 
 
 8 = 
 
 2.16 
 
 2.706 
 
 8.4534 
 
 21.1336 
 
 22.7000 
 
 9 = 
 
 2.43 
 
 3.043 
 
 9.5101 
 
 23.7753 
 
 25.5375 
 
26 
 
 ARITHMETIC. 
 WEIGHT. 
 
 
 Milligrammes 
 to Grains. 
 
 Kilogrammes 
 to Grains. 
 
 Hectogrammes 
 ( 1 00 grammes) 
 to Ounces Av. 
 
 Kilogrammes 
 to Pounds 
 Avoirdupois. 
 
 1 = 
 
 2 = 
 3 = 
 4 = 
 5 = 
 
 0.01543 
 0.03086 
 0.04630 
 0.06173 
 0.07716 
 
 15432.36 
 30864.71 
 46297.07 
 61729.43 
 77161.78 
 
 3.5274 
 7.0548 
 10.5822 
 14.1096 
 17.6370 
 
 2.20462 
 4.40924 
 6.61386 
 8.81849 
 11.02311 
 
 6 = 
 
 j 
 
 8 = 
 9 = 
 
 0.09259 
 0.10803 
 0.12346 
 0.13839 
 
 92594.14 
 108026.49 
 123458.85 
 138891.21 
 
 21.1644 
 24.6918 
 28.2192 
 31.7466 
 
 13.22773 
 15.43235 
 17.63697 
 19.84159 
 
 
 Quintals to 
 Pounds Av. 
 
 Milliers or Tonnes to 
 Pounds Av. 
 
 Grammes to Ounces. 
 Troy. 
 
 1 =, 
 
 220.46 
 
 2204.6 
 
 0.03215 
 
 2 = 
 
 440.92 
 
 4409.2 
 
 0.06430 
 
 3 = 
 
 661.38 
 
 6613.8 
 
 0.09645 
 
 4 = 
 
 881.84 
 
 8818.4 
 
 0.12860 
 
 5 - 
 
 1102.30 
 
 11023.0 
 
 0.16075 
 
 6 = 
 
 1322.76 
 
 13227.6 
 
 0.19290 
 
 7 - 
 
 1543.22 
 
 15432.2 
 
 22505 
 
 8== 
 
 1763.68 
 
 17636.8 
 
 0.25721 
 
 9 = 
 
 1984.14 
 
 19841.4 
 
 0.28936 
 
 The British Avoirdupois pound was derived from the British standard 
 Troy pound of 1758 by direct comparison, and it contains 7000 grains Troy. 
 
 The grain Troy is therefore the same as the grain Avoirdupois, and the 
 pound Avoirdupois in use in the United States is equal to the British 
 pound Avoirdupois. 
 
 By the concurrent action of the principal governments of the world an 
 International Bureau of Weights and Measures has been established near 
 Paris. 
 
 The International Standard Metre is derived from the Metre des 
 Archives, and its length is defined by the distance between two lines at 
 Centigrade, on a platinum-iridium bar deposited at the International 
 Bureau. 
 
 The International Standard Kilogramme is a mass of platinum-indium 
 deposited at the same place, and its weight in vacua is the same as that of 
 the Kilogramme des Archives. 
 
 Copies of these international standard weights and measures are 
 deposited in the office of the United States Bureau of Standards. 
 
 The litre is equal to a cubic decimetre of water, and it is measured by 
 the quantity of distilled water which, at its maximum density, will 
 counterpoise the standard kilogramme in a vacuum; the volume of such 
 a quantity of water being, as nearly as has been ascertained, equal to a 
 cubic decimetre. 
 
 The metric system was legalized in the United States in 1866. Many 
 attempts were made during the 50 years following to have the U. S. 
 Congress pass laws to make the metric system the legal standard, but they 
 have all failed. Similar attempts in Great Britain have also failed. For 
 arguments for and against the metric system see the report of a committee 
 of the American Society of Mechanical Engineers, 1903, Vol. 24. 
 
WEIGHTS AND MEASURES. 27 
 
 COMPOUND UNITS. 
 
 Measures of Pressure and Weight. 
 
 One pound force (or pressure) = the force exerted by gravity on 1 Ib. 
 of matter at a place where the acceleration due to gravity is 32.1740 
 feet-per-second per second; that is (very nearly) the force of gravity on 
 1 Ib. of matter at latitude 45 at the sea level. 
 
 1 Ib. per square inch 
 
 144 Ib. per square foot. 
 
 2.0355 in. of mercury at 32 P. 
 2.0416 " " " "62F. 
 2.309 ft. of water at 62 F. 
 27.71 ins. " " "62 F. 
 
 j 0.1276 in. of mercury at 62 F. 
 1 ounce per sq. in. 1.732 in. of water at 62 F. 
 
 2116.3 Ib. per square foot. 
 I 33.947 ft. of water at 62 F. 
 
 ;i4.71b. per sqJn.) - j %i>21in, ofm^curfat 32' F, 
 
 760 millimetres of mercury at 32 F. 
 i 0.03609 Ib. or .5774 oz. per sq. in. 
 1 inch of water at 62 F. = < 5.196 Ib. per square foot. 
 
 0.0735 in. of mercury at 62 F. 
 
 1 foot of water at 62 F. - P 
 
 _j 
 
 H 
 
 0.491 Ib. or 7.86 oz. per sq. in. 
 
 1 inch of mercury at 62 F. = -{ 1.134 ft. of water at 62 F. 
 
 ( 13.61 in. of water at 62 F. 
 
 Weight of One Cubic Foot of Pure Water. 
 
 At 32 F. (freezing-point) 62.418 Ib. 
 
 " 39.1 F. (maximum density) 62.425 ' 
 
 " 62 F. (standard temperature) in vacuo 62.355 " 
 
 " 212 F. (boiling-point, under 1 atmosphere) 59.76 
 
 American gallon = 231 cubic ins. of water at 62 F. = 8.3356 Ib. 
 British " = 277.274 " " " " " = 10 Ib. 
 
 Weight of 1 cu. ft. of air-free distilled water at 62, weighed in air at 
 62 with brass weights of 8. 4 density = 62.287 Ib. = 8.3267 Ib. per U. S. 
 gallon. 
 
 Weight and Volume of Air. 
 
 1 cubic ft. of air at 32 F. and atmospheric pressure weighs 0.080728 Ib. 
 i tt. v.~'~i~4- f +. ooo i 0.0005606 Ib. per sq. in. 
 
 . in height of air at 3. \ 0.015534 inches of water at 62 F. 
 
 For air at any other temperature T Fahr. multiply by 492 -=- (460 + T). 
 1 Ib. pressure per sq. ft. = 12.387 ft. of air at 32 F. 
 
 1 " " sq. in. = 1784. " " " " 
 
 1 inch of water at 62 F. = 64.37 " " " " 
 For air at any other temperature multiply by (460 + T) -~ 492. 
 
 At any fixed temperature the weight of a given volume is proportional 
 to the absolute pressure. 
 
 Measures of Work, Power, and Duty. 
 
 Unit of work. One foot-pound, i.e., a pressure of one pound exerted 
 through a space of one foot. 
 
 Horse-power. The rate of work. Unit of horse-power = 33,000 
 f t.-lb. per minute, or 550 ft.-lb. per second = 1 ,980,000 ft.-lb. per hour. 
 
 Heat unit. = heat required to raise 1 Ib. of water 1 F. (see page 560). 
 
 00 (")(")() 
 
 Horse-power expressed in heat-units = ' ~ = 42.442 heat-units per 
 
 minute = 0.7074 heat-unit per second = 2546.5 heat units per hour. 
 1 Ib. of fuel per H.P. per hour = 1,980,000 ft.-lb. per Ib. of fuel. 
 1,000,000 ft.-lb. per Ib. of fuel = 1.98 Ib. of fuel per H.P. per hour. 
 
 5280 ^2 
 Velocity. Feet per second = %QQQ = Is x miles P er hour. 
 
 tons per mile = 2240 = 14 lb< per yarci ( sin le rail ) 
 
28 
 
 ARITHMETIC. 
 
 WIRE AND SHEET-METAL GAUGES COMPARED. 
 
 8^ 
 
 <jj 3 
 * 
 
 So 
 
 Irl 
 
 .po 
 
 S * 5s 
 
 g i 
 
 ing's and 
 iburn & 
 :'s Gauge. 
 
 
 
 ajo 
 
 - O o 
 J a)- 22 
 
 yt'G nj 
 %% 
 
 !"2 
 ^B . 
 
 <gl|i 
 
 Ui 
 la- 
 
 ;s o> c^ 05 
 <* cS 
 
 9 
 
 |a 
 
 S c8 
 
 go 
 
 g-2 ^ 
 oc 
 
 Sg 
 
 |2& 
 
 " 
 
 ||| 
 
 J-li 
 
 pill 
 
 3 c8 
 
 *ei 
 p s 
 
 1 
 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 
 0000000 
 
 
 
 .49 
 
 
 .500 
 
 .6666 
 
 .5 
 
 7/o 
 
 000000 
 
 
 
 .46 
 
 
 464 
 
 .625 
 
 .469 
 
 6,0 
 
 00000 
 
 
 
 .43 
 
 
 .432 
 
 .5883 
 
 .438 
 
 5/o 
 
 0000 
 
 .454 
 
 .46 
 
 .393 
 
 
 .4 
 
 
 .406 
 
 
 000 
 
 .425 
 
 .40964 
 
 .362 
 
 
 .372 
 
 .500 
 
 .375 
 
 3/2 
 
 00 
 
 .38 
 
 .3648 
 
 .331 
 
 
 .348 
 
 .4452 
 
 344 
 
 2/n 
 
 
 
 .34 
 
 .32486 
 
 .307 
 
 
 .324 
 
 .3964 
 
 .313 
 
 
 
 
 .3 
 
 .2893 
 
 .283 
 
 227 
 
 .3 
 
 .3532 
 
 .281 
 
 1 
 
 2 
 
 .284 
 
 .25763 
 
 .263 
 
 .219 
 
 .276 
 
 .3147 
 
 266 
 
 2 
 
 3 
 
 .259 
 
 .22942 
 
 .244 
 
 .212 
 
 .252 
 
 .2804 
 
 .25 
 
 3 
 
 4 
 
 .238 
 
 J20431 
 
 .225 
 
 .207 
 
 .232 
 
 .250 
 
 .234 
 
 4 
 
 5 
 
 .22 
 
 .18194 
 
 .207 
 
 .204 
 
 .212 
 
 .2225 
 
 ,219 
 
 5 
 
 6 
 
 .203 
 
 .16202 
 
 .192 
 
 .201 
 
 .192 
 
 .1981 
 
 .203 
 
 6 
 
 7 
 
 .18 
 
 .14428 
 
 .177 
 
 .199 
 
 .176 
 
 .1764 
 
 .188 
 
 7 
 
 6 
 
 .165 
 
 .12849 
 
 .162 
 
 .197 
 
 .16 
 
 .1570 
 
 .172 
 
 8 
 
 9 
 
 .148 
 
 .11443 
 
 .148 
 
 .194 
 
 .144 
 
 .1398 
 
 .156 
 
 9 
 
 10 
 
 .134 
 
 .10189 
 
 .135 
 
 .191 
 
 .128 
 
 .1250 
 
 .141 
 
 10 
 
 11 
 
 .12 
 
 .09074 
 
 .12 
 
 .188 
 
 .116 
 
 .1113 
 
 .125 
 
 11 
 
 12 
 
 .109 
 
 .08081 
 
 .105 
 
 .185 
 
 .104 
 
 .0991 
 
 .109 
 
 12 
 
 13 
 
 .095 
 
 .07196 
 
 .092 
 
 .182 
 
 .092 
 
 .0882 
 
 .094 
 
 13 
 
 14 
 
 .033 
 
 .06403 
 
 ,08 
 
 .180 
 
 .08 
 
 .0785 
 
 078 
 
 14 
 
 15 
 
 .072 
 
 .05707 
 
 .072 
 
 .178 
 
 .072 
 
 .0699 
 
 .07 
 
 15 
 
 16 
 
 .065 
 
 .05082 
 
 .063 
 
 .175 
 
 .064 
 
 .0625 
 
 .0625 
 
 16 
 
 17 
 
 .058 
 
 .04526 
 
 .054 
 
 .172 
 
 .056 
 
 .0556 
 
 .0563 
 
 17 
 
 18 
 
 .049 
 
 .0403 
 
 .047 
 
 .168 
 
 .048 
 
 .0495 
 
 .05 
 
 18 
 
 19 
 
 .042 
 
 .03589 
 
 .041 
 
 164 
 
 .04 
 
 .0440 
 
 .0433 
 
 19 
 
 20 
 
 .035 
 
 .03196 
 
 .035 
 
 .161 
 
 .036 
 
 .0392 
 
 .0375 
 
 20 
 
 21 
 
 .032 
 
 .02846 
 
 .032 
 
 .157 
 
 .032 
 
 .0349 
 
 .0344 
 
 21 
 
 22 
 
 .028 
 
 .02535 
 
 .028 
 
 .155 
 
 .028 
 
 .03125 
 
 .0313 
 
 22 
 
 23 
 
 .025 
 
 .02257 
 
 .025 
 
 .153 
 
 .024 
 
 .02782 
 
 0281 
 
 23 
 
 24 
 
 .022 
 
 .0201 
 
 .023 
 
 .151 
 
 .022 
 
 .02476 
 
 .025 
 
 24 
 
 25 
 
 .02 
 
 .0179 
 
 .02 
 
 .148 
 
 .02 
 
 .02204 
 
 .0219 
 
 25 
 
 26 
 
 .018 
 
 .01594 
 
 .018 
 
 .146 
 
 .018 
 
 .01961 
 
 .0188 
 
 26 
 
 27 
 
 .016 
 
 .01419 
 
 .017 
 
 .143 .0164 
 
 .01745 
 
 .0172 
 
 27 
 
 28 
 
 .014 
 
 .01264 
 
 .016 
 
 .139 .0148 
 
 .015625 
 
 .0156 
 
 28 
 
 29 
 
 .013 
 
 .01126 
 
 .015 
 
 .134 .0136 
 
 .0139 
 
 .0141 
 
 29 
 
 30 
 
 .012 
 
 .01002 
 
 .014 
 
 .127 .0124 
 
 .0123 
 
 .0125 
 
 30 
 
 31 
 
 .01 
 
 .00893 
 
 .013 
 
 .120 
 
 .0116 
 
 .0110 
 
 .0109 
 
 31 
 
 32 
 
 .009 
 
 .00795 
 
 .013 
 
 .115 
 
 .0108 
 
 .0098 
 
 .0101 
 
 32 
 
 33 
 
 .008 
 
 .00708 
 
 .011 
 
 .112 
 
 .01 
 
 .0037 
 
 .0094 
 
 33 
 
 34 
 
 .007 
 
 ,0063 
 
 .01 
 
 .110 
 
 .0092 
 
 .0077 
 
 .0086 
 
 34 
 
 35 
 
 .005 
 
 .00561 
 
 .0095 
 
 .103 
 
 .0084 
 
 .0069 
 
 .0078 
 
 35 
 
 36 
 
 .004 
 
 .005 
 
 .009 
 
 .106 
 
 .0076 
 
 .0061 
 
 .007 
 
 36 
 
 37 
 
 
 .00445 
 
 .0085 
 
 .103 
 
 .0068 
 
 .0054 
 
 .0066 
 
 37 
 
 38 
 
 
 .00396 
 
 .008 
 
 .101 
 
 .006 
 
 .0048 
 
 .0063 
 
 38 
 
 39 
 
 
 .00353 
 
 .0075 
 
 .099 
 
 .0052 
 
 .0043 
 
 
 39 
 
 40 
 
 
 .00314 
 
 .007 
 
 .097 
 
 .0048 
 
 .00386 
 
 
 40 
 
 41 
 
 
 
 
 .095 
 
 .0044 
 
 .00343 
 
 
 41 
 
 42 
 
 
 
 
 .092 
 
 .004 
 
 .00306 
 
 
 42 
 
 43 
 
 
 
 
 .088 
 
 .0036 
 
 .00272 
 
 
 43 
 
 44 
 
 
 
 
 .085 
 
 .0032 
 
 .00242 
 
 
 44 
 
 45 
 
 
 
 
 .081 
 
 .0028 
 
 .00215 
 
 
 45 
 
 46 
 
 
 
 
 .079 
 
 .0024 
 
 .00192 
 
 
 46 
 
 47 
 
 
 
 
 .077 
 
 .002 
 
 .00170 
 
 
 47 
 
 48 
 
 
 
 
 .075 
 
 .0016 
 
 .00152 
 
 
 48 
 
 49 
 
 
 
 
 .072 
 
 .0012 
 
 .00135 
 
 
 49 
 
 50 
 
 
 
 
 .065 
 
 .001 
 
 .00120 
 
 
 50 
 
WIRE AND SHEET METAL GAUGES , 29 
 
 THE EDISON OB CIRCULAR MIL WIRE GAUGE. 
 
 (For table of copper wires by this gauge, giving weights, electrical 
 resistances, etc., see Copper Wire.) 
 
 Mr. C. J. Field (Stevens Indicator, July, 1887) thus describes the origin 
 of the Edison gauge: 
 
 The Edison company experienced inconvenience and loss by not having 
 a wide enough range nor sufficient number of sizes in the existing gauges. 
 This was felt more particularly in the central-station work in making 
 electrical determinations for the street system. They were compelled to 
 make use of two of the existing gauges at least, thereby introducing a 
 complication that was liable to lead to mistakes by the contractors and 
 linemen. 
 
 In the incandescent system an even distribution throughout the entire 
 system and a uniform pressure at the point of delivery are obtained by 
 calculating for a given maximum percentage of loss from the potential as 
 delivered from the dynamo. In carrying this out, on account of lack of 
 regular sizes, it was often necessary to use larger sizes than the occasion 
 demanded, and even to assume new sizes for large underground conductors. 
 The engineering department of the Edison company, knowing the require- 
 ments, have designed a gauge that has the widest range obtainable and 
 a large number of sizes which increase in a regular and uniform manner. 
 The basis of the graduation is the sectional area, and the number of the 
 wire corresponds. A wire of 100,000 circular mils area is No. 100; a wire 
 of one half the size will be No. 50; twice the size No. 200. 
 
 In the older gauges, as the number increased the size decreased. With 
 this gauge, however, the number increases with the wire, and the number 
 multiplied by 1000 will give the circular mils. 
 
 The weight per mil-foot, 0.00000302705 pounds, agrees with a specific 
 gravity of 8.889, which is the latest figure given for copper. The ampere 
 capacity which is given was deduced from experiments made in the com- 
 pany's laboratory, and is based on a rise of temperature of 50 F. in the 
 wire. 
 
 In 1893 Mr. Field writes, concerning gauges in use by electrical engineers: 
 
 The B. and S. gauge seems to be in general use for the smaller sizes, up 
 to 100,000 c.m., and in some cases a little larger. From between one and 
 two hundred thousand circular mils upwards, the Edison gauge or its 
 equivalent is practically in use, and there is a general tendency to desig- 
 nate all sizes above this in circular mils, specifying a wire as 200,000, 
 400,000, 500,000, or 1,000,000 C.M. 
 
 In the electrical business there is a large use of copper wire and rod and 
 other materials of these large sizes, and in ordering them, speaking of 
 them, specifying, and in every other use, the general method is to simply 
 specify the circular milage. I think it is going to be the only system in 
 the future for the designation of wires, and the attaining of it means 
 practically the adoption of the Edison gauge or the method and basis of 
 this gauge as the correct one for wire sizes. 
 
 THE U. S. STANDARD GAUGE FOR SHEET AND 
 PLATE IRON AND STEEL, 1893. 
 
 There is in this country no uniform or standard gauge, and the same 
 numbers in different gauges represent different thicknesses of sheets or 
 plates. This has given rise to much misunderstanding and friction 
 between employers and workmen and mistakes and fraud between dealers 
 and consumers. 
 
 An Act of Congress in 1893 established the Standard Gauge for sheet 
 Iron and steel which is given on the next page. It is based on the fact that 
 a cubic foot of iron weighs 480 pounds. 
 
 A sheet of iron 1 foot square and 1 inch thick weighs 40 pounds, or 640 
 ounces, and 1 ounce in weight should be 1/640 inch thick. The scale has 
 been arranged so that each descriptive number represents a certain 
 number of ounces in weight and an equal number of 640ths of an inch in 
 thickness. 
 
 The law enacts that on and after July 1, 1893, the new gauge shall be 
 used in determining duties and taxes levied on sheet and plate iron and 
 (Continued on page 32.} 
 
30 
 
 ARITHMETIC. 
 
 Edison, or Circular Mil Gauge for Electrical Wires. 
 
 Gauge 
 Num- 
 ber. 
 
 Circular 
 Mils. 
 
 Diam- 
 eter in 
 Mils. 
 
 Gauge 
 Num- 
 ber. 
 
 Circular 
 Mils. 
 
 Diam- 
 eter in 
 
 Mils. 
 
 Gauge 
 Num- 
 ber. 
 
 Circular 
 Mils. 
 
 Diam- 
 eter in 
 Mils. 
 
 3 
 
 3,000 
 
 54.78 
 
 70 
 
 70,000 
 
 264.58 
 
 190 
 
 190,000 
 
 435.89 
 
 5 
 
 5,000 
 
 70.72 
 
 75 
 
 75,000 
 
 273.87 
 
 200 
 
 200,000 
 
 447.22 
 
 8 
 
 8,000 
 
 89.45 
 
 80 
 
 80,000 
 
 282.85 
 
 220 
 
 220,000 
 
 469.05 
 
 12 
 
 12,000 
 
 109.55 
 
 85 
 
 85,000 
 
 291.55 
 
 240 
 
 240,000 
 
 489.90 
 
 15 
 
 15,000 
 
 122.48 
 
 90 
 
 90,000 
 
 300.00 
 
 260 
 
 260,000 
 
 509.91 
 
 20 
 
 20,000 
 
 141.43 
 
 95 
 
 95,000 
 
 308.23 
 
 280 
 
 280,000 
 
 529.16 
 
 25 
 
 25,000 
 
 158.12 
 
 100 
 
 100,000 
 
 316.23 
 
 300 
 
 300,000 
 
 547.73 
 
 30 
 
 30,000 
 
 173.21 
 
 110 
 
 110,000 
 
 331.67 
 
 320 
 
 320,000 
 
 565.69 
 
 35 
 
 35,000 
 
 187.09 
 
 120 
 
 120,000 
 
 346.42 
 
 340 
 
 340,000 
 
 583.10 
 
 40 
 
 40,000 
 
 200.00 
 
 130 
 
 130,000 
 
 360.56 
 
 360 
 
 360,000 
 
 600.00 
 
 45 
 
 45,000 
 
 212.14 
 
 140 
 
 140,000 
 
 374.17 
 
 
 
 
 50 
 
 50,000 
 
 223.61 
 
 150 
 
 150,000 
 
 387.30 
 
 
 
 
 55 
 
 55,000 
 
 234.53 
 
 160 
 
 160,000 
 
 400.00 
 
 
 
 
 60 
 
 60,000 
 
 244.95 
 
 170 
 
 170,000 
 
 412.32 
 
 
 
 
 65 
 
 65,000 
 
 254.96 
 
 180 
 
 180,000 
 
 424.27 
 
 
 
 
 Twist Drill and Steel Wire Gauge. 
 
 (Manufacturers Standard) 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 1 
 
 0.2280 
 
 14 
 
 0.1820 
 
 27 
 
 0.1440 
 
 40 
 
 0.0980 
 
 53 
 
 0.0595 
 
 67 
 
 0.0320 
 
 2 
 
 .2210 
 
 15 
 
 .1800 
 
 28 
 
 .1405 
 
 41 
 
 .0960 
 
 54 
 
 .0550 
 
 68 
 
 .0310 
 
 
 .2130 
 
 16 
 
 .1770 
 
 29 
 
 .1360 
 
 42 
 
 .0935 
 
 55 
 
 .0520 
 
 69 
 
 .0292 
 
 4 
 
 .2090 
 
 17 
 
 .1730 
 
 30 
 
 .1285 
 
 43 
 
 .0890 
 
 56 
 
 .0465 
 
 70 
 
 .0280 
 
 5 
 
 .2055 
 
 18 
 
 .1695 
 
 31 
 
 .1200 
 
 44 
 
 .0860 
 
 57 
 
 .0430 
 
 71 
 
 .0260 
 
 6 
 
 .2040 
 
 19 
 
 .1660 
 
 32 
 
 .1160 
 
 45 
 
 .0820 
 
 58 
 
 .0420 
 
 72 
 
 .0250 
 
 7 
 
 .2010 
 
 20 
 
 .1610 
 
 33 
 
 .1130 
 
 46 
 
 .0810 
 
 59 
 
 .0410 
 
 73 
 
 .0240 
 
 8 
 
 .1990 
 
 21 
 
 .1590 
 
 34 
 
 .1110 
 
 47 
 
 .0785 
 
 60 
 
 .0400 
 
 74 
 
 .0225 
 
 9 
 
 .1960 
 
 22 
 
 .1570 
 
 35 
 
 .1100 
 
 48 
 
 .0760 
 
 61 
 
 .0390 
 
 75 
 
 .0210 
 
 10 
 
 .1935 
 
 23 
 
 .1540 
 
 36 
 
 .1065 
 
 49 
 
 .0730 
 
 62 
 
 .0380 
 
 76 
 
 .0200 
 
 11 
 
 .1910 
 
 24 
 
 .1520 
 
 37 
 
 .1040 
 
 50 
 
 .0700 
 
 63 
 
 .0370 
 
 77 
 
 .0180 
 
 12 
 
 .1890 
 
 25 
 
 .1495 
 
 38 
 
 .1015 
 
 51 
 
 .0670 
 
 64 
 
 .0360 
 
 78 
 
 .0160 
 
 13 
 
 .1850 
 
 26 
 
 .1470 
 
 39 
 
 .0995 
 
 52 
 
 .0635 
 
 65 
 
 .0350 
 
 79 
 
 .0145 
 
 
 
 
 
 
 
 
 
 66 
 
 .0330 
 
 80 
 
 .0135 
 
 Stubs' Steel Wire Gauge. 
 
 (For Nos. 1 to 50 see table on page 31.) 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 z 
 
 inch. 
 .413 
 
 P 
 
 inch. 
 .323 
 
 F 
 
 inch. 
 .257 
 
 51 
 
 inch. 
 .066 
 
 61 
 
 inch. 
 .038 
 
 71 
 
 inch. 
 .026 
 
 Y 
 
 .404 
 
 O 
 
 .316 
 
 Fi 
 
 .250 
 
 52 
 
 .063 
 
 62 
 
 .037 
 
 72 
 
 .024 
 
 X 
 
 .397 
 
 N 
 
 .302 
 
 D 
 
 .246 
 
 53 
 
 .058 
 
 63 
 
 .036 
 
 73 
 
 .023 
 
 w 
 
 .386 
 
 M 
 
 .295 
 
 
 
 .242 
 
 54 
 
 .055 
 
 64 
 
 .035 
 
 74 
 
 .022 
 
 V 
 
 .377 
 
 T, 
 
 .290 
 
 B 
 
 .238 
 
 55 
 
 .050 
 
 65 
 
 .033 
 
 75 
 
 .020 
 
 TT 
 
 .368 
 
 K 
 
 .281 
 
 A 
 
 .234 
 
 56 
 
 .045 
 
 66 
 
 .032 
 
 76 
 
 .018 
 
 T 
 
 .358 
 
 ,T 
 
 .277 
 
 1 
 
 (See 
 
 57 
 
 .042 
 
 67 
 
 .031 
 
 77 
 
 .016 
 
 8 
 
 .348 
 
 T 
 
 .272 
 
 to 
 
 {page 
 
 58 
 
 .041 
 
 68 
 
 .030 
 
 78 
 
 .015 
 
 fi 
 
 .339 
 
 H 
 
 .266 
 
 50 
 
 (29 
 
 59 
 
 .040 
 
 69 
 
 .029 
 
 79 
 
 .014 
 
 Q 
 
 .332 
 
 G 
 
 .261 
 
 
 
 60 
 
 .039 
 
 70 
 
 .027 
 
 80 
 
 .013 
 
 The Stubs' Steel Wire Gauge is used in measuring drawn steel wire or 
 drill rods of Stubs' make, and is also used by many makers of American 
 drill rods. 
 
WIRE AND SHEET METAL GAUGES. 
 
 31 
 
 U. S. STANDARD GAUGE FOR SHEET AND PLATE 
 IRON AND STEEL, 1893. 
 
 Number of 
 Gauge. 
 
 Approximate 
 Thickness in 
 Fractions of 
 an Inch. 
 
 ** 9 
 8 -a * . 
 
 HIP 
 
 fr* 
 
 Approximate 
 Thickness 
 in 
 
 Millimeters. 
 
 Weight per 
 Square Foot 
 in Ounces 
 Avoirdupois. 
 
 Weight per 
 Square Foot 
 in Pounds 
 Avoirdupois. 
 
 fit 
 
 ^ 5 
 
 |S 
 
 ^.2 
 
 Weight per 
 Square Meter 
 in Kilograms. 
 
 1 Weight per Sq. 1 
 M eter in Founds! 
 Avoirdupois. | 
 
 0000000 
 
 1-2 
 
 0.5 
 
 12.7 
 
 320 
 
 20. 
 
 9.072 
 
 97.65 
 
 215.28 
 
 000000 
 
 15-32 
 
 0.46875 
 
 1 1 .90625 
 
 300 
 
 18.75 
 
 8.505 
 
 91.55 
 
 201.82 
 
 00000 
 
 7-16 
 
 0.4375 
 
 11.1125 
 
 280 
 
 17.50 
 
 7.938 
 
 85.44 
 
 188.37 
 
 0000 
 
 13-32 
 
 0.40625 
 
 10.31875 
 
 260 
 
 16.25 
 
 7.371 
 
 79.33 
 
 174.91 
 
 000 
 
 3-8 
 
 0.375 
 
 9.525 
 
 240 
 
 15. 
 
 6.804 
 
 73.24 
 
 161.46 
 
 00 
 
 11-32 
 
 0.34375 
 
 8.73125 
 
 220 
 
 13.75 
 
 6.237 
 
 67.13 
 
 148.00 
 
 
 
 5-16 
 
 0.3125 
 
 7.9375 
 
 200 
 
 12.50 
 
 5.67 
 
 61.03 
 
 134.55 
 
 1 
 
 9-32 
 
 0.28125 
 
 7.14375 
 
 180 
 
 11.25 
 
 5.103 
 
 54.93 
 
 121.09 
 
 2 
 
 17-64 
 
 0.265625 
 
 6.746875 
 
 170 
 
 10.625 
 
 4.819 
 
 51.88 
 
 114.37 
 
 3 
 
 1-4 
 
 0.25 
 
 6.35 
 
 160 
 
 10. 
 
 4.536 
 
 48.82 
 
 107,64 
 
 4 
 
 15-64 
 
 0.234375 
 
 5.953125 
 
 150 
 
 9.375 
 
 4.252 
 
 45.77 
 
 100.91 
 
 5 
 
 7-32 
 
 0.21875 
 
 5.55625 
 
 140 
 
 8.75 
 
 3.969 
 
 42.72 
 
 94.18 
 
 6 
 
 13-64 
 
 0.203125 
 
 5.159375 
 
 130 
 
 8.125 
 
 3.685 
 
 39.67 
 
 87.45 
 
 7 
 
 3-16 
 
 0.1875 
 
 4.7625 
 
 120 
 
 7.5 
 
 3.402 
 
 36.62 
 
 80.72 
 
 . 8 
 
 11-64 
 
 0.171875 
 
 4.365625 
 
 110 
 
 6.875 
 
 3.118 
 
 33.57 
 
 74.00 
 
 9 
 
 5-32 
 
 0.15625 
 
 3.96875 
 
 100 
 
 6.25 
 
 2.835 
 
 30.52 
 
 67.27 
 
 10 
 
 9-64 
 
 0.140625 
 
 3.571875 
 
 90 
 
 5.625 
 
 2.552 
 
 27.46 
 
 60.55 
 
 11 
 
 1-8 
 
 0.125 
 
 3.175 
 
 80 
 
 5. 
 
 2.268 
 
 24.41 
 
 53.82 
 
 12 
 
 7-64 
 
 0.109375 
 
 2.778125 
 
 70 
 
 4.375 
 
 .984 
 
 21.36 
 
 47.09 
 
 13 
 
 3-32 
 
 0.09375 
 
 2.38125 
 
 60 
 
 3.75 
 
 .701 
 
 18.31 
 
 40.36 
 
 14 
 
 5-64 
 
 0.078125 
 
 1 .984375 
 
 50 
 
 3.125 
 
 .417 
 
 15.26 
 
 33.64 
 
 15 
 
 9-128 
 
 0.0/03125 
 
 1 .7859375 
 
 45 
 
 2.8125 
 
 .276 
 
 13.73 
 
 30.27 
 
 16 
 
 1-16 
 
 0.0625 
 
 1.5875 
 
 40 
 
 2.5 
 
 .134 
 
 12.21 
 
 26.91 
 
 17 
 
 9-160 
 
 0.05625 
 
 1 .42875 
 
 36 
 
 2.25 
 
 .021 
 
 10.99 
 
 24.22 
 
 18 
 
 1-20 
 
 0.05 
 
 1.27 
 
 32 
 
 2. 
 
 0.9072 
 
 9.765 
 
 21.53 
 
 19 
 
 7-160 
 
 0.04375 
 
 1.11125 
 
 28 
 
 .75 
 
 0.7938 
 
 8.544 
 
 18.84 
 
 20 
 
 3-80 
 
 0.0375 
 
 0.9525 
 
 24 
 
 .50 
 
 0.6804 
 
 7.324 
 
 16.15 
 
 21 
 
 1 1-320 
 
 0.034375 
 
 0.873125 
 
 22 
 
 .375 
 
 0.6237 
 
 6.713 
 
 14.80 
 
 22 
 
 1-32 
 
 0.03125 
 
 0.793750 
 
 20 
 
 .25 
 
 0.567 
 
 6.103 
 
 13.46 
 
 23 
 
 9-320 
 
 0.028125 
 
 0.714375 
 
 18 
 
 .125 
 
 0.5103 
 
 5.49 
 
 12.11 
 
 24 
 
 1-40 
 
 0.025 
 
 0.635 
 
 16 
 
 1. 
 
 0.4536 
 
 4.882 
 
 10.76 
 
 25 
 
 7-320 
 
 0.021875 
 
 0.555625 
 
 14 
 
 0.875 
 
 0.3969 
 
 4.272 
 
 9.42 
 
 26 
 
 3-160 
 
 0.01875 
 
 0.47625 
 
 12 
 
 0.75 
 
 0.3402 
 
 3.662 
 
 8.07 
 
 27 
 
 1 1-640 
 
 0.0171875 
 
 0.4365625 
 
 11 
 
 0.6875 
 
 0.3119 
 
 3.357 
 
 7.40 
 
 28 
 
 1-64 
 
 0.015625 
 
 0.396875 
 
 10 
 
 0.625 
 
 0.2835 
 
 3.052 
 
 6.73 
 
 29 
 
 9-640 
 
 0.0140625 
 
 0.3571875 
 
 9 
 
 0.5625 
 
 0.2551 
 
 7746 
 
 6.05 
 
 30 
 
 1-80 
 
 0.0125 
 
 0.3175 
 
 8 
 
 0.5 
 
 0.2268 
 
 2.441 
 
 5.38 
 
 31 
 
 7-640 
 
 0.0109375 
 
 0.2778125 
 
 7 
 
 0.4375 
 
 0.1984 
 
 2.136 
 
 4.71 
 
 32 
 
 13-1280 
 
 0.01015625 
 
 0.25796875 
 
 ' < 61/2 
 
 0.40625 
 
 0.1843 
 
 1.983 
 
 4.37 
 
 (33 
 
 3-320 
 
 0.009375 
 
 0.238125 
 
 6 
 
 0.375 
 
 0.1701 
 
 1.831 
 
 4.04 
 
 34 
 
 11-1280 
 
 0.00859375 
 
 0.21828125 
 
 51/2 
 
 0.34375 
 
 0.1559 
 
 1.678 
 
 3.70 
 
 35 
 
 5-640 
 
 0.0078125 
 
 0.1984375 
 
 5 
 
 0.3125 
 
 0.1417 
 
 1.526 
 
 3.36 
 
 36 
 
 9-1280 
 
 0.00703125 
 
 0.17859375 
 
 4V2 
 
 0.28125 
 
 0.1276 
 
 1.373 
 
 3.03 
 
 37 
 
 17-2560 
 
 0.00664062 
 
 0.16867187 
 
 41/4 
 
 0.26562 
 
 0.1205 
 
 1.297 
 
 2.87 
 
 38 
 
 1-160 
 
 0.00625 
 
 0.15875 
 
 
 0.25 
 
 0.1134 
 
 1.221 
 
 2.69 
 
 - 
 
32 
 
 THE DECIMAL GAUGE. 
 
 (continued from page 29) steel; and that in its application a variation of 
 2 1/2 per cent either way may be allowed. 
 
 The Decimal Gauge. The legalization of the standard sheet- 
 metal gauge of 1893 and its adoption by some manufacturers of 
 sheet iron have only added to the existing confusion of gauges. A joint 
 committee of the American Society of Mechanical Engineers and the 
 American Railway Master Mechanics' Association in 1895 agreed to 
 recommend the use of the decimal gauge, that is, a gauge whose number 
 for each thickness is the number of thousandths of an inch in that thick- 
 ness, and also to recommend " the abandonment and disuse of the various 
 other gauges now in use, as tending to confusion and error." A notched 
 gauge of oval form, shown in the cut below, has come into use as a standard 
 form of the decimal gauge. 
 
 In 1904 The Westinghouse Electric & Mfg. Co. abandoned the use of 
 gauge numbers in referring to wire, sheet metal, etc. 
 
 Weight of Sheet Iron and Steel. Thickness by Decimal Gauge. 
 
 
 
 
 i 
 
 Weight per 
 Square Foot 
 
 6 
 
 
 
 m 
 
 Weight per 
 Square Foot 
 
 3 
 
 .2 
 
 J* 
 
 in Pounds. 
 
 !> 
 
 ' ' 
 
 " 
 
 in Pounds. 
 
 
 
 "OBO 
 
 
 
 
 
 09 
 
 t>o 
 
 1 
 
 
 
 
 
 
 d 
 
 
 JO ^ 
 
 o. 
 
 O 
 
 E 
 
 
 - -tJ 
 
 "O 
 
 a 
 
 feh fl 
 
 i 
 
 o^. 
 
 ft-^ 
 
 'd 
 
 ^ 
 
 iS 
 
 o ~ 
 
 & 4) 
 
 00 ft,*^ 
 
 .3 
 
 X * 
 
 M 
 
 *O 
 
 "i- ^ 
 
 .5 
 
 o 
 
 X 
 
 $5 
 
 "*"__ r* 
 
 Q 
 
 I 
 
 ft 
 
 ft 
 M 
 
 135 
 
 02 
 
 Q 
 
 P 
 
 2 
 1 
 
 
 'a)^ 3 
 
 
 
 0.002 
 
 1/500 
 
 0.05 
 
 0.08 
 
 0.082 
 
 0.060 
 
 1/16- 
 
 1.52 
 
 2.40 
 
 2.448 
 
 0.004 
 
 1/250 
 
 0.10 
 
 0.16 
 
 0.163 
 
 0.065 
 
 13/200 
 
 1.65 
 
 2.60 
 
 2.652 
 
 0.006 
 
 3/500 
 
 0.15 
 
 0.24 
 
 0.245 
 
 0.070 
 
 7/100 
 
 1.78 
 
 2.80 
 
 2.856 
 
 0.008 
 
 Vl25 
 
 0.20 
 
 0.32 
 
 0.326 
 
 0.075 
 
 3/40 
 
 1.90 
 
 3.00 
 
 3.060 
 
 0.010 
 
 1/100 
 
 0.25 
 
 0.40 
 
 0.408 
 
 0.080 
 
 2/25 
 
 2.03 
 
 3.20 
 
 3.264 
 
 0.012 
 
 3/250 
 
 0.30 
 
 0.48 
 
 0.490 
 
 0.085 
 
 17/200 
 
 2.16 
 
 3.40 
 
 3.468 
 
 0.014 
 
 7/500 
 
 0.36 
 
 0.56 
 
 0.571 
 
 0.090 
 
 9/100 
 
 2.28 
 
 3.60 
 
 3.672 
 
 0.016 
 
 1/64 + 
 
 0.41 
 
 0.64 
 
 0.653 
 
 0.095 
 
 19/200 
 
 2.41 
 
 3.80 
 
 3.876 
 
 0.018 
 
 9/500 
 
 0.46 
 
 0.72 
 
 0.734 
 
 0.100 
 
 1/10 
 
 2.54 
 
 4.00 
 
 4.080 
 
 0.020 
 
 1/50 
 
 0.51 
 
 0.80 
 
 0.816 
 
 0.110 
 
 H/100 
 
 2.79 
 
 4.40 
 
 4.488 
 
 0.022 
 
 H/500 
 
 0.56 
 
 0.88 
 
 0.898 
 
 0.125 
 
 1/8 
 
 3.18 
 
 5.00 
 
 5.100 
 
 0.025 
 
 1/40 
 
 0.64 
 
 .00 
 
 .020 
 
 0.135 
 
 27/200 
 
 3.43 
 
 5.40 
 
 5.508 
 
 0.028 
 
 7/250 
 
 0.71 
 
 .12 
 
 .142 
 
 0.150 
 
 3/20 
 
 3.81 
 
 6.00 
 
 6.120 
 
 0.032 
 
 1/32 + 
 
 0.81 
 
 .28 
 
 .306 
 
 0.165 
 
 33/200 
 
 4.19 
 
 6.60 
 
 6.732 
 
 0.036 
 
 9/250 
 
 0.91 
 
 .44 
 
 .469 
 
 0.180 
 
 9/50 
 
 4.57 
 
 7.20 
 
 7.344 
 
 0.040 
 
 1/25 
 
 1.02 
 
 .60 
 
 .632 
 
 0.200 
 
 1/5 
 
 5.08 
 
 8.00 
 
 8.160 
 
 0.045 
 
 9/200 
 
 1.14 
 
 .80 
 
 .836 
 
 0.220 
 
 n/50 
 
 5.59 
 
 8.80 
 
 8.976 
 
 0.050 
 
 1/20 
 
 1.27 
 
 2.00 
 
 2.040 
 
 0.240 
 
 
 6.10 
 
 9.60 
 
 9.792 
 
 0.055 
 
 11/200 
 
 1.40 
 
 2.20 
 
 2.244 
 
 0.250 
 
 i/f 
 
 6.35 
 
 10.00 
 
 10.20C 
 
ALGEBRA. 33 
 
 ALGEBRA. 
 
 Addition. Add a, b, and c. Ans. a 4 b c. 
 Add 2a and - 3a. Ans. - a. Add 2ab, - Sab, - c, - 3c. Ans, 
 - ab - 4c. Add a 2 and 2a. Ans. a 2 -f 2a. 
 Subtraction. Subtract a from b. Ans. & a. Subtract a from 
 
 6. Ans. b + a. 
 
 Subtract b + c from a. Ans. a 6 c. Subtract 3a 2 6 9c from 
 4a 2 6 -f c. Ans. a 2 6 + lOc. RULE: Change the signs of the subtrahend 
 and proceed as in addition. 
 
 Multiplication. Multiply a by b. Ans. ab. Multiply ab by a + b. 
 Ans. a 2 6 + ab 2 . 
 
 Multiply a 4- b by a 4 6. Ans. (a 4-6) (a46)=a 2 4-2a&+6 2 . 
 
 Multiply a by b. Ans. ab. Multiply a by b. Ans. a&. 
 Like signs give plus, unlike signs minus. 
 
 Powers of numbers. The product of two or more powers of any 
 number is the number with an exponent equal to the sum of the powers: 
 a 2 x a 3 = a 5 ; a 2 6 2 X ab = a 3 6 3 ; - 7ab X 2ac = - 14ft 2 6c. 
 
 To multiply a polynomial by a monomial, multiply each term of the 
 polynomial by the monomial and add the partial products: (6a 36) 
 X 3c = I8ac - 96c. 
 
 To multiply two polynomials, multiply each term of one factor by each 
 term of the other and add the partial products: (5a 66) X (3a 46) 
 = 15a 2 - 38a6 4- 246 2 . 
 
 The square of the sum of two numbers = sum of their squares + twice 
 their product. 
 
 The square of the difference of two numbers = the sum of their squares 
 
 twice their product. 
 
 The product of the sum and difference of two numbers = the difference 
 of their squares: 
 
 (a 4- 6) 2 = a 2 4- 2a6 4- 6 2 ; (a - 6) 2 = a 2 - 2a6 4- & 2 ; 
 (a 4- 6) X (a - 6) = a 2 - 6 2 . 
 
 The square of half the sums of two quantities is equal to their product 
 plus the square of half their difference: (^^Y = ab + (^- b Y- 
 
 The square of the sum of two quantities is equal to four times their 
 products, plus the square of their difference: (a + 6) 2 = 4a6 4- (a 6) 2 . 
 
 The sum of the squares of two quantities equals twice their product, 
 plus the square of their difference: a 2 + 6 2 = 2a6 4- (a 6) 2 . 
 
 The square of a trinomial == square of each term 4 twice the product 
 of each term by each of the terms that follow it: (a + 6 4 c) 2 = a 2 4 6 2 
 4 c 2 4- 2a6 4- 2ac + 2bc; (a b - c) ? = -a 2 + 6 2 + c* - 2a6- 2ac + 2bc. 
 
 The square of (any number 4- 1/2) = square of the number + the number 
 + 1/4; = the number X (the number 4- 1) 4- 1/ 4 : (a+ i/2) 2 = a 2 4- a 4- 1/4, 
 = a (a + 1) 4- 1/4- (4l/2) 2 = 4 2 + 4 4- 1/4=4 X 5 + 1/4 = 201/4. 
 
 The product of any number 4- 1/2 by any other number + 1/2 = product 
 of the numbers 4- half their sum 4- 1/4. (a + i/ 2 ) X (6 4- 1/2) = ab + 1/2(0 46) 
 4 1/4. 4l/ 2 X 6V 2 = 4X64- i/ 2 (4 4- 6) 4- V 4 = 24 4- 5 4- 1/4 = 29V4. 
 
 Square, cube, 4th power, etc., of a binomial a 4- 6. 
 
 (a 4 6) 2 = a 2 4- 2a6 4- 6 2 ; (a 4- 6) 3 = a 3 4- 3a 2 6 + 3a6 2 4- 6 
 (a 4- 6) 4 = a 4 4- 4a 3 6 4- 6a 2 6 2 4- 4a6 3 4- 6 4 . 
 
 In each case the number of terms is one greater than the exponent of 
 the power to which the binomial is raised. 
 
 2. In the first term the exponent of a is the same as the exponent of the 
 power to which the binomial is raised, and it decreases by 1 in each suc- 
 ceeding term. 
 
 3. 6 appears in the second term with the exponent 1, and its exponent 
 increases by 1 in each succeeding term. 
 
 4. The coefficient of the first term is 1. 
 
 5. The coefficient of the second term is the exponent of the power to 
 which the binomial is raised. 
 
34 ALGEBRA. 
 
 6. The coefficient of each succeeding term is found from the next pre- 
 ceding term by multiplying its coefficient by the exponent of a, and 
 dividing the product by a number greater by 1 than the exponent of b. 
 (See Binomial Theorem, below.) 
 
 Parentheses. When a parenthesis is preceded by a plus sign it may 
 be removed without changing the yalue of the expression: a + b + (a + 
 b) = 2a + 2b. When a parenthesis is preceded by a minus sign it may 
 be removed if we change the signs of all the terms within the parenthesis: 
 1 (a b c) = 1 a + b + c. When a parenthesis is within a 
 parenthesis remove the inner one first: a [6 {c (d e)}] = a [ft 
 {c d + ej]= a - [b - c + d - e] = a - b + c d + e. 
 
 A multiplication sign, X, has the effect of a parenthesis, in that the 
 operation indicated by it must be performed before the operations of 
 addition or subtraction, a 4- b X a + b = a + ab + b; while (a -f- 6) 
 X (a + 6) = a 2 + 2ab + 6 2 , and (a + b) X a + b = a 2 + ab + b. 
 
 The absence of any sign between two parentheses, or between a quan- 
 tity and a parenthesis, indicates that the parenthesis is to be multiplied by 
 the quantity or parenthesis: a(a + b + c) = a 2 + ab + ac. 
 
 Division. The quotient is positive when the dividend and divisor 
 have like signs, and negative when they have unlike signs: abc -*- b = ac; 
 abc * 6 = ac. 
 
 To divide a monomial by a monomial, write the dividend over the 
 divisor with a line between them. If the expressions have common factors, 
 remove the common factors: 
 
 a z bx ax a 4 a 3 1 
 
 a z bx -* aby = -r = ; , = a; -7 = -^ = a~~ 2 . 
 aby y a 3 'a 6 a 2 
 
 To divide a polynomial by a monomial, divide each term of the poly- 
 nomial by the monomial: (Sab 12ac) -5- 4a = 26 3c. 
 
 To divide a polynomial by a polynomial, arrange both dividend and 
 divisor in the order of the ascending or descending powers of some common 
 letter, and keep this arrangement throughout the operation. 
 
 Divide the first term of the dividend by the first term of the divisor, and 
 write the result as the first term of the quotient. 
 
 Multiply all the terms of the divisor by the first term of the quotient 
 and subtract the product from the dividend. If there be a remainder, 
 consider it as a new dividend and proceed as before: (a 2 b 2 ) -* (a + b). 
 
 a 2 - 6 2 I a + b. 
 a 2 + ab I a b. 
 
 - ab -~~&~ 
 
 - ab - ft 2 . 
 
 The difference of two equal odd powers of any two numbers is divisible 
 by their difference but not by their sum: 
 
 The difference of two equal even powers of two numbers is divisible by 
 their difference and also by their sum: (a 2 b 2 ) -5- (a 6) = a -4- 6. 
 
 The sum of two equal even powers of two numbers is not divisible by 
 either the difference or the sum of the numbers; but when the exponent 
 of each of the two equal powers is composed of an odd and an even factor, 
 the sum of the given power is divisible by the sum of the powers expressed 
 by the even factor. Thus x 6 + y 6 is not divisible by x -f y or by x y, 
 but is divisible by x 2 + if. 
 
 Simple equations. An equation is a statement of equality between 
 two expressions; as, a + b = c + d. 
 
 A simple equation, or equation of the first degree, is one which contains 
 only the first power of the unknown quantity. If equal changes be made 
 (by addition, subtraction, multiplication, or division) in both sides of an 
 equation, the results will be equal. 
 
 Any term may be changed from one side of an equation to another, 
 provided its sign be changed: a+b = c+d\a^c+d b. To solve 
 
ALGEBRA. 35 
 
 an equation having one unknown quantity, transpose all the terms involv- 
 ing the unknown quantity to one side of the equation, and- all the other 
 terms to the other side; combine like terms, and divide both sides by the 
 coefficient of the unknown quantity. 
 
 Solve Sx - 29 - 26 - 3x. Sx + 3x = 29 4- 26; llx = 55; x = 5, ans. 
 
 Simple algebraic problems containing one unknown quantity are solved 
 by making x = the unknown quantity, and stating the conditions of the 
 problem in the form of an algebraic equation, and then solving the equa- 
 tion. What two numbers are those whose sum is 48 and difference 14? 
 Let x = the smaller number, re 4- 14 the greater, x + x + 14 = 48. 
 2x = 34, x = 17; x -I- 14 = 31, ans. 
 
 Find a number whose treble exceeds 50 as much as its double falls short 
 of 40. Lets = the number. 3x - 50 = 40 - 2x; 5x 90; a; = 18, ans. 
 Proving, 54 - 50 = 40 - 36. 
 
 Equations containing two unknown quantities. If one equation 
 contains two unknown quantities, x and y, an indefinite number of pairs 
 of values of x and y may be found that will satisfy the equation, but if a 
 second equation be given only one pair of values can be found that will 
 satisfy both equations. Simultaneous equations, or those that may be 
 satisfied by the same values of the unknown quantities, are solved by 
 combining the equations so as to obtain a single equation containing only 
 one unknown quantity. This process is called elimination. 
 
 Elimination by addition or subtraction. Multiply the equation by 
 such numbers as will make the coefficients of one of the unknown quanti- 
 ties equal in the resulting equation. Add or subtract the resulting equa- 
 tions according as they have unlike or like signs. 
 
 M 
 
 Substituting value of ?/ in first equation, 2x 4- 3 = 7; x = 2. 
 
 Elimination by substitution. From one of the equations obtain the 
 value of one of the unknown quantities in terms of the other. Substi- 
 tute for this unknown quantity its value in the other equation and reduce 
 the resulting equations. 
 
 4 3y ^ 7. Multiply by 2: . _ 
 
 - by = 3. Subtract : 4a? 5y 3 l\y - 11 ; y => 1 
 
 c^irr^ f 2.r + 3y = 8. (1). From (1) we find x 
 bolve l3z +7y = 7. (2). 
 
 Substitute this value in (2): 3 ( 8 ~ 3?/ ) 4-7^ = 7; = 
 
 whence y = - 2. Substitute this value in (1): 2x 6 = 8; x = 7. 
 
 Elimination by comparison. From each equation obtain the value of 
 one of the unknown quantities in terms of the 9ther. Form an equation 
 from these equal values, and reduce this equation. 
 
 Solve 2x 9y = 11. (1) and 3x - 4y = 7. (2). From (1) we find 
 
 
 From (2) we find x 
 
 Equating these values of x, ll t 9 ^ = 7 ~t 4y ; IQy - - 19; y = - 1. 
 
 j O 
 
 Substitute this value of y in (1): 2x 4-9 = 11; x = 1. 
 
 If three simultaneous equations are given containing three unknown 
 quantities, one of the unknown quantities must be eliminated between two 
 pairs of the equations; then a second between the two resulting equations. 
 
 Quadratic equations. A quadratic equation contains the square of 
 the unknown quantity, but no higher power. A pure quadratic contains 
 the square only; an affected quadratic both the square and the first power. 
 
 To solve a pure quadratic, collect the unknown quantities on one side, 
 
 id the known quantities on the other; divide by the coefficient of the 
 
 iknown quantity and extract the square root of each side of the resulting 
 
 [nation. 
 
 Solve 3z 2 - 15 = 0. 3z* = 15; x* = 5; x = >/5. 
 
 A root like x/5, which is indicated, but which can be found only approxi- 
 ' Ay. is called a surd. 
 
36 ALGEBRA. 
 
 Solve 3a* + 15 - 0. 3z?= - 15; a* = - 5; x = v. 
 
 The square root of 5 cannot be found even approximately, fo/ tha 
 square of any number positive or negative is positive; therefore a root 
 which is indicated, but cannot be found even approximately, is called 
 imaginary. 
 
 To solve an affected quadratic, 1. Convert the equation into the form 
 a*x 2 2abx = c, multiplying or dividing the equation if necessary, so as 
 to make the coefficient of x 2 a square number. 
 
 2. Complete the square of the first member of the equation, so as to 
 convert it to the form of a 2 x 2 2abx + b 2 , which is the square of the 
 binomial ax &, as follows: add to each side of the equation the square of 
 the quotient obtained by dividing the second term by twice the square 
 root of the first term. 
 
 3. Extract the square root of each side of the resulting equation. 
 Solve 3.* 2 - 4.r = 32. To make the coefficient of x 2 a square number, 
 
 multiply by 3 : 9x 2 - I2x = 96; I2x + (2 X 3x) = 2; 2 2 = 4. 
 
 Complete the square: 9x 2 I2x + 4 = 100. Extract the root: 
 3x 2 = 10, whence x = 4 or 22/3. The square root of 100 is 
 either + 10 or 10, since the square of 10 as well as + 10 2 = 100. 
 
 Every affected quadratic may be reduced to the form ax*+bx+c=-Q. 
 
 The solution of this equation is x = -- - 
 
 Problems involving quadratic equations have apparently two solutions, 
 as a quadratic has two roots. Sometimes both will be true solutions, but 
 generally one only will be a solution and the other be inconsistent with the 
 conditions of the problem. 
 
 The sum of the squares of two consecutive positive numbers is 481. 
 Find the numbers. 
 
 Let x =. one number, x+1 the other. z 2 + (x -f I) 2 = 481. 2x* -f 
 2x + 1 = 481. 
 
 x 2 + x = 240. Completing the square, x 2 +x -f 0.25 = 240.25. 
 Extracting the root we obtain x + 0.5 = 15.5; x = 15 or - 16. The 
 negative root 16 is inconsistent with the conditions of the problem. 
 
 Quadratic equations containing two unknown quantities require 
 different methods for their solution, according to the form of the equations. 
 For these methods reference must be made to works on algebra. 
 
 Theory of exponents. %a when n is a positive integer is one of n 
 
 equal factors of a. \o means a is to be raised to the with power and the 
 nth root extracted. 
 
 tnat the nth root of a is to be taken and the result 
 raised to the with power. 
 
 \/a = ( \l~a\ m = an. When the exponent is a fraction, the numera- 
 
 tor indicates a power, and the denominator a root. a 6 /2 = v / a 6 = a 3 ; 
 a 3 /2 = V a 3 = a 1 - s. 
 
 To extract the root of a quantity raised to an indicated power, divide 
 the exponent by the index of the required root; as, 
 
 Subtracting 1 from the exponent of a is equivalent to dividing by a: 
 2-i= a' =o; a'-i = a - ^- 1; a-i = a~> ~ i; a--i=a-2=l. 
 
 A number with a negative exponent denotes the reciprocal of the num- 
 ber with the corresponding positive exponent. 
 
 A factor under the radical sign whose root can be taken may, by having 
 the root taken, be removed from under the radical sign: 
 
GEOMETRICAL PROBLEMS. 
 
 37 
 
 A factor outside the radical sign may be raised to the corresponding 
 power and placed under it: 
 
 Binomial Theorem. 
 
 sion of the form x + a 
 
 - To obtain any power, as the nth, of an expres- 
 
 x* + 
 
 etc. *~* i- 2 - 3 - 
 
 The following laws hold for any term in the expansion of (a 4- x) n . 
 
 The exponent of x is less by one than the number of terms. 
 
 The exponent of a is n minus the exponent of x. 
 
 The last factor of the numerator is greater by one than the exponent of a. 
 
 The last factor of the denominator is the same as the exponent of x. 
 
 In the rth term the exponent of x will be r 1. 
 
 The exponent of a will be n (r 1), or n r 4- 1. 
 
 The last factor of the numerator will be n r 4- 2. 
 
 The last factor of the denominator will be = r 1. 
 
 Hence the rth term = "( - D( - 2) . ( - r+ 2) ^ 
 
 l.^.O....^?* 1^ 
 
 GEOMETRICAL PROBLEMS. 
 
 1. To bisect a straight line, or 
 an arc of a circle (Fig. 1). From 
 the ends A, B, as centres, describe 
 arcs intersecting at C and D, and 
 draw a line through C and D which 
 will bisect the line at E or the arc 
 at F. 
 
 2. To draw a perpendicular to 
 a straight line, or a radial line to 
 a circular arc. Same as in 
 Problem 1. C D is perpendicular to 
 the line A B, and also radial to the 
 arc. 
 
 3. To draw a perpendicular to 
 a straight line from a given point 
 in that line (Fig. 2). With any 
 radius, from the given point A in the 
 line B C, cut the line at B and C. 
 With a longer radius describe arcs 
 from B and C, cutting each other at 
 D, and draw the perpendicular D A. 
 
 4. From the end A of a given 
 line A D to erect a perpendicular 
 AE (Fig. 3). From any centre F, 
 above A D, describe a circle passing 
 through the given point A , and cut- 
 ting the given line at D. Draw D F 
 and produce it to cut the circle at E t 
 and draw the perpendicular A E. 
 
 Second Method (Fig. 4). From 
 the given point A set off a distance 
 A E equal to .three parts, by any 
 scale; and on the centres A and E, 
 with radii of four and five parts 
 respectively, describe arcs intersect- 
 ing at C, Draw the perpendicular 
 A C. 
 
 NOTE. This method is most 
 useful on very large scales, where 
 straight edges are inapplicable. Any 
 multiples of the numbers 3, 4, 5 may 
 be taken with the same effect, as 6, & 
 10, or 9, 12. 15. 
 
38 
 
 GEOMETRICAL PROBLEMS. 
 
 5. To draw a perpendicular to 
 a straight line from any point 
 without it (Fig. 5). From the 
 point A, with a sufficient radius cut 
 the given line at F and G, and from 
 these points describe arcs cutting at 
 E. Draw the perpendicular A E. 
 
 6. To draw a straight line 
 parallel to a given line, at a given 
 distance apart (Fig. 6). From 
 the centres A, B, in the given line, 
 with the given distance as radius, 
 describe arcs (7, D, and draw the 
 parallel lines C D touching the arcs. 
 
 7. To divide a straight line into 
 a number of equal parts (Fig. 7). 
 To divide the line A B into, say, 
 five parts, draw the line A C at an 
 angle from A ; set off five equal parts; 
 draw B5 and draw parallels to it 
 from the other points of division in 
 A C. These parallels divide A B as 
 required. 
 
 NOTE. By a similar process a 
 line may be divided into a number 
 of unequal parts; setting off divisions 
 on A C, proportional by a scale to the 
 required divisions, and drawing 
 parallels cutting A B. The triangles 
 All, A 22, A33, etc., are similar 
 triangles. 
 
 8. Upon a straight line to draw 
 an angle equal to a given angle 
 
 (Fig. 8). Let A be the given angle 
 and F G the line. From the point A 
 with any radius describe the arc D E. 
 From F with the same radius 
 describe I H. Set off the arc I H 
 equal to D E, and draw F H. The 
 angle F is equal to A, as required. 
 
 9. To draw angles of 60 and 
 
 80 (Fig. 9). From F, with any 
 radius F /, describe an arc / H ; and 
 from /, with the same radius, cut 
 the arc at H and draw F H to form 
 the required angle I F H. Draw the 
 perpendicular H K to the base line to 
 form the angle of 30 F H K. 
 
 10. To draw an angle of 45 
 
 (Fig. 10). Set off the distance F /; 
 draw the perpendicular / H equal to 
 / F t and join H " 
 
 \. 
 
 FIG. 9. 
 
 F. 
 
 Fto form the angle at 
 The angle at H is "also 45. 
 
 FIG. 10. 
 
GEOMETRICAL PROBLEMS. 
 
 39 
 
 FIG. 11. 
 
 Fia. 15. 
 
 11. To bisect an angle (Fig. 11). 
 Let ACB be the angle; with C as 
 a centre draw an arc cutting the 
 sides at A, B. From A and B as 
 centres, describe arcs cutting each 
 other at Z>. Draw C D, dividing the 
 angle into two equal parts. 
 
 12. Through two given points 
 to describe an arc of a circle with 
 a given radius (Fig. 12). From 
 the ppints A and B as centres, with 
 the given radius, describe arcs cut- 
 ting at C; and from C with the same 
 radius describe an arc A B. 
 
 13. To find the centre of a circle 
 or of an arc of a circle (Fig. 13). 
 Select three points, A, B, C, in the 
 circumference, well apart; with the 
 same radius describe arcs from these 
 three points, cutting each other, and 
 draw the two lines, D E, FG, 
 through their intersections. The 
 point O, where they cut, is the centre 
 of the circle or arc. 
 
 To describe a circle passing 
 through three given points. 
 Let A, B, C be the given points, and 
 proceed as in last problem to find the 
 centre O, from which the circle may 
 be described. 
 
 14. To describe an arc of a 
 circle passing through three 
 given points when the centre is 
 not available (Fig. 14). From 
 the extreme points A, B, as 
 centres, describe arcs AH, B G. 
 Through the third point C draw 
 A E : B F, cutting the arcs. 
 Divide A F and B E into any 
 number of equal parts, and set 
 off a series of equal parts of the 
 same length on the upper por- 
 tions of the arcs beyond the 
 points E F. Draw straight 
 lines, B L, BM, etc., to the 
 divisions in A F, and A I, A K, 
 etc., to the divisions in EG. 
 The successive intersections N, 
 O, etc., of these lines are points 
 in the circle required between the 
 given points A and C, which may 
 be drawn in; similarly the remain- 
 ing part of the curve BC may 
 be described. (See also Problem 
 54.) 
 
 15. To draw a tangent to a 
 circle from a given point in the 
 circumference (Fig. 15). Through 
 the given point A, draw the radial 
 line A C, and a perpendicular to it, 
 FG t which is "the tangent required. 
 
40 
 
 GEOMETRICAL PROBLEMS. 
 
 16. To draw tangents to a 
 circle from a point without it (Fig. 
 16). From A, with the radius 
 A C, describe an arc BCD, and 
 from C, with a radius equal to the 
 diameter of the circle, cut the arc at 
 BD. Join BC, CD, cutting the 
 circle at E F, and draw A E, AF, 
 the tangents. 
 
 NOTE. When a tangent is 
 already drawn, the exact point of 
 contact may be found by drawing a 
 perpendicular to it from the centre. 
 
 17. Between two inclined lines 
 to draw a series of circles touching 
 these lines and touching each 
 other (Fig. 17). Bisect the inclina- 
 tion of the given lines A B, C D, by 
 the line N O. From a point P in this 
 line draw the perpendicular P B to the 
 line A B, and on P describe the circle 
 B D, touching the lines and cutting 
 the centre line at E. From E draw 
 E F perpendicular to the centre line, 
 cutting A B at F, and from F 
 describe an arc E G, cutting A B at 
 G. Draw GH parallel to B P, 
 giving H, the centre of the next 
 circle, to be described with the 
 radius HE, and so on for the next 
 circle IN. 
 
 Inversely, the largest circle may 
 be described first, and the smaller 
 ones in succession. This problem is 
 of frequent use in scroll-work. 
 
 18. Between two inclined lines 
 to draw a circular segment tan- 
 gent to the lines and passing 
 through a point F on the line FC 
 which bisects the angle of the 
 lines (Fig. 18). Through F draw 
 DA at right angles to FC; bisect 
 the angles A and Z), as in Problem 
 11, by lines cutting at C, and from 
 C with radius C F draw the arc H F G 
 required. 
 
 19. To draw a circular arc that 
 will be tangent to two given lines 
 AB and C D inclined to one another, 
 one tangential point E being given 
 
 (Fig. 19). Draw the centre line 
 GF. From E draw E F at right 
 angles to A B ; then F is the centre 
 of the circle required. 
 
 20. To describe a circular arc 
 Joining two circles, and touching 
 one of them at a given point (Fig. 
 20). To join the circles A B, FG, 
 by an arc touching one of them at 
 F, draw the radius E F, and produce 
 it both ways. Set off F H equal to 
 the radius A C of the other circle; 
 join CH and bisect it with the per- 
 pendicular L I, cutting E F at I. 
 On the centre 7, with radius IF, 
 describe the arc FA as required. 
 
GEOMETRICAL PROBLEMS. 
 
 FIG. 22. 
 E 
 
 FIG. 23. 
 
 FIG. 24. 
 
 FIG. 25. 
 
 FIG. 26. 
 
 21. To draw a circle with a 
 given radius R that will be tan- 
 gent to two given circles A and B 
 
 (Fig. 21). From centre of circle 
 A with radius equal R plus radius 
 of A, and from centre of B with 
 radius equal to R + radius of B, 
 draw two arcs cutting each other in 
 C, which will be the centre of the 
 circle required. 
 
 22. To construct an equilateral 
 triangle, the sides being given 
 
 (Fig. 22). On the ends of one side, 
 A, B, with A B as radius, describe 
 arcs cutting at C, and draw A C, C B. 
 
 23. To construct a triangle of 
 unequal sides (Fig. 23). On 
 either end of the base A D, with the 
 side B as radius, describe an arc; 
 and with the side C as radius, on the 
 other end of the base as a centre, cut 
 the arc at E. Join A E, D E. 
 
 24. To construct a square on 
 given straight line A B (Fig. 24). 
 With A B as radius and A and B 
 as centres, draw arcs A D and B C, 
 intersecting at E. Bisect E B at 
 F. With E as centre and E F as 
 radius, cut the arcs A D and B C 
 in D and C. Join A C, C D t and 
 D B to form the square. 
 
 25. To construct a rectangle 
 with given base E F and height EH 
 
 (Fig. 25). On the base E F draw 
 the perpendiculars E //, F O equal 
 to the height, and join G H. 
 
 26. To describe a circle about 
 a triangle (Fig. 26). Bisect two 
 sides A B, A C of the triangle at 
 E F, and from these points draw 
 perpendiculars cutting at K. On 
 the centre K, with the radius K A, 
 draw the circle ABC. 
 
 27. To inscribe a circle in a 
 triangle (Fig. 27). Bisect two of 
 the angles A, C, of the triangle by 
 
42 
 
 GEOMETRICAL PROBLEMS. 
 
 lines cutting at D; from D draw a 
 perpendicular D E to any side, and 
 with D E as radius describe a circle. 
 When the triangle is equilateral, 
 draw a perpendicular from one of the 
 angles to the opposite side, and from 
 the side set off one third of the 
 perpendicular. 
 
 28. To describe a circle about 
 a square, and to inscribe a square 
 in a circle (Fig. 28). To describe 
 the circle, draw the diagonals A B, 
 C D of the square, cutting at E. On 
 the centre E, with the radius A E, 
 describe the circle. 
 
 To inscribe the square. Draw 
 the two diameters, A B,C D, at right 
 angles, and join the points A, B, 
 C D, to form the square. 
 
 NOTE. In the same way a circle 
 may be described about a rectangle. 
 
 29. To inscribe a circle in a 
 square (Fig. 29). To inscribe the 
 circle, draw the diagonals A B, C D 
 of the square, cutting at E; draw the 
 perpendicular E F to one side, and 
 with the radius E F describe the 
 circle. 
 
 FIG. 28. 
 A G C 
 
 30. To describe a square about 
 a circle (Fig. 30). Draw two 
 diameters A B, C D at right angles. 
 With the radius of the circle and 
 A, B, C and D as centres, draw the 
 four half circles which cross one 
 another in the corners of the square. 
 
 31. To inscribe a pentagon in 
 a circle (Fig. 31). Draw diam- 
 eters A C, B D at right angles, cut- 
 ting at o. Bisect A o at E, and from 
 E, with radius E B, cut A C at F; 
 from B, with radius B F, cut the 
 circumference at G, H, and with the 
 same radius step round the circle to 
 / and K\ join the points so found to 
 form the pentagon. 
 
 32. To construct a pentagon 
 on a given line A B (Fig. 32). 
 From B erect a perpendicular B C 
 half the length of A B ; join A C and 
 prolong it to D, making C D = B C. 
 Then B D is the radius of the circle 
 circumscribing the pentagon. From 
 A and B as centres, with B D as 
 radius, draw arcs cutting each other 
 in O, which is the centre of the circle. 
 
 FIG. 32. 
 
GEOMETRICAL PROBLEMS. 
 
 43 
 
 FIG. 34. 
 
 33. To construct a hexagon 
 upon a given straight line (Fig. 
 
 33). From A and B, the ends of 
 the given line, with radius A B, 
 describe arcs cutting at g; from g t 
 with the radius g A, describe a circle; 
 with the same radius set off the arcs 
 A G, G F, and B D, D E. Join the 
 points so found to form the hexagon. 
 The side of a hexagon = radius of its 
 circumscribed circle. 
 
 34. To inscribe a hexagon in a 
 circle (Fig. 34). Draw a diam- 
 eter ACS. From A and B as 
 centres, with the radius of the circle 
 A C, cut the circumference, at D, E, 
 F, G, and draw A D, D E, etc., to 
 form the hexagon. The radius of 
 the circle is equal to the side of the 
 hexagon; therefore the points D, E t 
 etc., may also be found by stepping 
 the radius six times round the circle. 
 The angle between the diameter and 
 the sides of a hexagon and also the 
 exterior angle between a side and an 
 adjacent side prolonged is 60 degrees; 
 therefore a hexagon may conven- 
 iently be drawn by the use of a 60- 
 degree triangle. 
 
 35. To describe a hexagon 
 about a circle (Fig. 35). Draw a 
 diameter A D B, and with the radius 
 A D, on the centre A, cut the circum- 
 ference at C; join A C, and bisect it 
 with the radius D E ; through E draw 
 FG, parallel to A C, cutting the diam- 
 eter at F, and with the radius D F 
 describe the circumscribing circle 
 F H. Within this circle describe a 
 hexagon by the preceding problem. 
 A more convenient method is by use 
 of a 60-degree triangle. Four of the 
 sides make angles of 60 degrees with 
 the diameter, and the other two are 
 parallel to the diameter. 
 
 36. To describe an octagon on 
 a given straight line (Fig. 36). 
 Produce the given line 'A B both 
 ways, and draw perpendiculars A E. 
 BF; bisect the external angles^, and 
 B by the lines A H, B C, which make 
 equal to A B. Draw C D and H G 
 parallel to A E, and equal to A B; 
 from the centres G, D, with the 
 radius A B, cut the perpendiculars at 
 E, F, and draw E F to complete the 
 octagon. 
 
 37. To convert a sqaare into 
 an octagon (Fig. 37). Draw the 
 diagonals of the square cutting at e; 
 from the corners A, B, C, D, with 
 A e as radius, describe arcs cutting 
 the sides at gn, fk, hm, and ol, and 
 join the points so found to form the 
 octagon. Adjacent sides of an octa- 
 gon make an angle of 135 degrees. 
 
GEOMETRICAL PROBLEMS. 
 
 38. To inscribe an octagon in 
 a circle (Fig. 38). Draw two 
 diameters, A C, B D at right angles; 
 bisect the arcs A B, B C, etc., at e f, 
 etc., and join A e, B, etc., to form 
 the octagon, 
 
 39. To describe an octagon 
 about a circle (Fig. 39). P -scribe 
 a square about the given circle A B; 
 draw perpendiculars h k, etc., to the 
 diagonals, touching the circle to 
 form the octagon. 
 
 40. To describe a polygon of 
 any number of sides upon a given 
 straight line (Fig. 40). Produce 
 the given .line A B, and on A, with the 
 radius A B, describe a semicircle; 
 divide the semi-circumference into 
 as many equal parts as there are to 
 be sides in the polygon say, in 
 this example, five sides. Draw lines 
 from A through the divisional points 
 D, b, and c, omitting one point a; 
 and on the centres B, D, with the 
 radius A B, cut A b at E and A c at F. 
 Draw D E, E F t F B to complete the 
 polygon. 
 
 41. To inscribe a circle within 
 a polygon (Figs. 41, 42). When 
 the polygon has an even number of 
 sides (Fig. 41), bisect two opposite 
 sides at A and B; draw A B, and 
 bisect it at C by a diagonal D E, and 
 with the radius C A describe the 
 circle. 
 
 When the number of sides is odd 
 (Fig. 42), bisect two of the sides at A 
 and B, and draw lines A E, B D to the 
 opposite angles, intersecting at C; 
 from <7, with the radius C A, describe 
 the circle. 
 
 42. To describe a circle without 
 a polygon (Figs. 41, 42). Find 
 the centre C as before, and with the 
 radius C D describe the circle. 
 
 43. To inscribe a polygon of 
 any number of sides within a circle 
 
 (Fig. 43). Draw the diameter A B 
 and through the centre E draw the 
 
 H D G 
 
 FIG. 39. 
 
 Fio. 42. 
 
GEOMETRICAL PROBLEMS. 
 
 45 
 
 perpendicular E C, cutting the circle 
 at F. Divide E F into four equal 
 parts, and set off three parts equal 
 to those from F to C. Divide the 
 diameter A B into as many equal 
 parts as the polygon is to have sides; 
 and from C draw C D, through the 
 second point of division, cutting the 
 circle at D. Then A D is equal to one 
 side of the polygon, and by stepping 
 round the circumference with the 
 length A D the polygon may be com- 
 pleted. 
 
 Table of Polygonal Angles. 
 
 Number 
 of Sides. 
 
 Angle 
 at Centre. 
 
 Number 
 of Sides. 
 
 Angle 
 at Centre. 
 
 Number 
 of Sides. 
 
 Angle 
 at Centre. 
 
 No. 
 
 4 
 5 
 6 
 
 8 
 
 Degrees. 
 120 
 90 
 72 
 60 
 
 g* 
 
 No. 
 9 
 10 
 11 
 12 
 13 
 14 
 
 Degrees. 
 40 
 36 
 
 gw 
 i 
 
 No. 
 15 
 16 
 17 
 18 
 19 
 20 
 
 Degrees. 
 22l/ 2 
 
 iH 
 
 19 
 18 
 
 In this table the angle at the centre is found by dividing 360 degrees, the 
 number of degrees in a circle, by the number of sides in the polygon; and 
 by setting off round the centre of the circle a succession of angles by means 
 of the protractor, equal to the angle in the table due to a given number of 
 sides, the radii so drawn will divide the circumference into the same num- 
 ber of parts. 
 
 44. To describe an ellipse when 
 the length and breadth are given 
 (Fig. 44). A B, transverse axis; 
 C Z>, conjugate axis; F G, foci. The 
 sum of the distances from C to F 
 and G, also the sum of the distances 
 from F and G to any other point in 
 the curve, is equal to the transverse 
 axis. From the centre C, with A E 
 as radius, cut the axis A B at F and 
 G, the foci; fix a couple of pins into 
 the axis at F and G, and loop on a 
 thread or cord upon them equal in 
 length to the axis A B, so as when 
 stretched to reach to the extremity 
 C of the conjugate axis, as shown in 
 dot-lining. Place a pencil inside the 
 cord as at //, and guiding the pencil 
 in this way, keeping the cord equally 
 in tension, carry the pencil round the 
 pins F, G, and so describe the 
 ellipse. 
 
 NOTE. This method is employed 
 in setting off elliptical garden-plots, 
 walks, etc. 
 
 2d Method (Fig. 45). Along the 
 straight edge of a slip of stiff paper 
 mark off a distance a c equal to A C, 
 half the transverse axis; and from 
 the same point a distance a b equal 
 to C G, half the conjugate axis. 
 
 FIG. 44. 
 
GEOMETRICAL PROBLEMS. 
 
 Place the slip so as to bring the point b on the line A B of the transverse 
 axis, and the ppint c on the line D E; and set off on the drawing the posi- 
 tion of the point a. Shifting the slip so that the point b travels on the 
 transverse axis, and the x point c on the conjugate axis, any number of 
 points in the curve may be found, through which the curve may be 
 traced. 
 
 3d Method (Fig. 46). The action 
 of the preceding method may be 
 embodied so as to afford the means 
 of describing a large curve contin- 
 uously by means of a bar m k, with 
 steel points m, I, k, riveted into brass 
 slides adjusted to the length of the 
 semi-axis and fixed with set-screws. 
 A rectangular cross E G, with guiding- 
 slots is placed, coinciding with the 
 two axes of the ellipse A C and B H. 
 B7 sliding the points k, I in the slots, 
 and carrying round the point m, the 
 curve may be continuously described. 
 A pen or pencil may be fixed at m. 
 
 4th Method (Fig. 47). Bisect the 
 transverse axis at C, and through C * 
 draw the perpendicular D E, making 
 C D and C E each equal to half the 
 conjugate axis. From D or E, with 
 the radius AC, cut the transverse 
 axis at F, F f , for the foci. Divide 
 A C into a number of parts at the 
 points 1, 2, 3, etc. With the radius 
 Al on. F and F' as centres, describe 
 arcs, and with the radius B 1 on the 
 same centres cut these arcs as shown. 
 Repeat the operation for the other 
 divisions of the transverse axis. The 
 series of intersections thus made are 
 points in the curve, through which 
 the curve may be traced. 
 
 5th Method (Fig. 48). On the 
 two axes A B, D E as diameters, on 
 centre C, describe circles; from a 
 number of points a, b, etc., in the 
 circumference A F B, draw radii cut- 
 ting the inner circle at a', 6', etc. 
 From a, b, etc., draw perpendiculars 
 to AB; and from a', b' t etc., draw 
 parallels to A B, cutting the respec- 
 tive perpendiculars at n, o, etc. The 
 intersections are points in the curve, 
 through which the curve may be 
 traced. 
 
 6to Method (Fig. 49). When the 
 transverse and conjugate diameters 
 are given, A B, CD, draw the tangent 
 EF parallel to A B. Produce CD, 
 and on the centre G with the radius 
 of half A B, describe a semicircle 
 H D K; from the centre G draw any 
 number of straight lines to the points 
 E, r, etc., in the line E F t cutting the 
 circumference at /, m, n, etc.; from 
 the centre O of the ellipse draw 
 straight lines to the points E, r, etc.; 
 and from the points I, m, n, etc., 
 draw parallels to G C, cutting the 
 tines O E, O r t etc., at L t M t 3v, etc. Fio. 49. 
 
GEOMETRICAL PROBLEMS. 
 
 47 
 
 These are points in the circumference of the ellipse, and the curve may be 
 traced through them. Points in the other half of the ellipse are formed 
 by extending the intersecting lines as indicated in the figure. 
 
 45. To describe an ellipse 
 approximately by means of cir- 
 cular arcs. First. With arcs 
 of two radii (Fig. 50). Find the 
 difference of the semi-axes, and set 
 it off from the centre O to a and c on 
 O A and O C; draw ac, and set off 
 half a c to d; draw d i parallel to a c; 
 set off O e equal to O d; join e i, and 
 draw the parallels e m, d m. From 
 m, with radius m C, describe an arc 
 through C; and from i describe an 
 arc through D ; from d and e describe 
 arcs through A and B. The four 
 arcs form the ellipse approximately. 
 NOTE. This method does not 
 apply satisfactorily when the con- 
 jugate axis is less than two thirds of 
 the transverse axis. 
 
 2d Method (by Carl G. Barth, Fig. 
 51). In Fig. 51 a b is the major and 
 c d the minor axis of the ellipse to be 
 approximated. Lay off b e equal to 
 the semi-minor axis c O, and use a e 
 as radius for the arc at each extrem- 
 ity of the minor axis. Bisect e o at / 
 and lay off eg equal toef, and use gb 
 as radius for the arc at each extrem- 
 ity of the major axis. 
 
 method is not considered applicable for cases in which the minor 
 less than two thirds of the major. 
 
 3d Method: With arcs of three radii 
 (Fig. 52). On the transverse axis 
 A B draw the rectangle B G on the 
 height O C; to the diagonal A C 
 draw the perpendicular G H D; set 
 off O K equal to O C, and describe & 
 semicircle on A K, and produce O C 
 to L; set off O M equal to C L, and 
 from D describe an arc with radius 
 D M] from A, with radius O L, cut 
 A B at N; from H, with radius HN, 
 cut arc a b at a. Thus the five 
 centres D, a, b, H, H f are found, 
 from which the arcs are described to 
 form the ellipse. 
 
 This process works well for nearly 
 all proportions of ellipses. It is used 
 in striking out vaults and stone 
 bridges. 
 
 4th Method (by F. R. Honey, 
 Figs. 53 and 54). Three 
 radii are employed. With 
 the shortest radius describe 
 the two arcs which pass 
 through the vertices of the 
 major axis, with the longest 
 the two arcs which pass 
 
 through the vertices of the 
 
 minor axis, and with the third 
 radius the four arcs which 
 connect the former. 
 
 The 
 axis is 
 
 b Jid 
 
 FIG. 53. 
 
48 
 
 GEOMETRICAL PROBLEMS. 
 
 A simple method of determining the radii of curvature is illustrated in 
 Fig. 53. Draw the straight lines a f and a c, forming any angle at a. With 
 a as a centre, and with radii a b and a c, respectively, equal to the semi- 
 minor and semi-major axes, draw the arcs b e and c d. Join e d, and 
 through b and c respectively draw b g and c f parallel to e d, intersecting 
 a c at g, and a / at /; a f is the radius of curvature at the vertex of 
 the minor axis; and a g the radius of curvature at the vertex of the 
 major axis. 
 
 Lay off d h (Fig. 53) equal to one eighth of 6 d. Join e h, and draw c k 
 and b I parallel to e h. Take a k for the longest radius ( = R), a I for the 
 shortest radius (= r), and the arithmetical mean, or one half the sum of 
 the semi-axes, for the third radius (= p), and employ these radii for the 
 eight-centred oval as follows: 
 
 Let a Sander/ (Fig. 54) 
 be the major and minor 
 axes. Lay off a e equal 
 to r, and a f equal to p; 
 also lay off c g equal to R, 
 and c h equal to p'. With 
 g as a centre and gfi as a 
 radius, draw the arc h k; 
 with the centre e and 
 radius e f draw the arc / k, a 
 intersecting h k at k. 
 Draw the line g k and 
 
 produce it, making g I 
 equal to R. Draw k e 
 
 and produce it, making 
 k m equal to p. With the 
 centre g and radius g c 
 (= R) draw the arc c I; 
 with the centre k and 
 radius kl (= p) draw the 
 arc I m, and with the 
 centre e and radius e m 
 (= r) draw the arc m a. 
 
 The remainder of the work is symmetrical with respect ,o the 
 axes. 
 
 46. The Parabola. A parabola (D A C, Fig. 55) is a curve such 
 that every point in the curve is equally distant from the directrix K L 
 and the focus F. The focus lies in the axis 
 
 A B drawn from the vertex or head of the K P \ 
 
 curve A, so as to divide the figure into two 
 equal parts. The vertex A is equidistant 
 from the directrix and the focus, or A e = A F. 
 Any line parallel to the axis is a diameter. 
 A straight line, as E G or DC, drawn across 
 the figure at right angles to the axis is a 
 double ordinate, and either half of it is an 
 ordinp.te. The ordinate to the axis E F G, 
 drawn through the focus, is called the para- 
 meter of the axis. A segment of the axis, 
 reckoned from the vertex, is an abscissa of 
 the axis, and it is an abscissa of the ordinate 
 drawn from the base of the abscissa. Thus, 
 A B is an abscissa of the ordinate B C. 
 
 E 
 / 
 
 
 A 
 
 L 
 
 /^ 
 
 \^\ 
 
 F 
 
 \ 
 
 n/ 
 
 O 
 
 \ 
 
 
 
 o 
 
 \ 
 
 \ 
 
 T 
 
 o 
 
 
 
 D B 
 
 b 
 
 ^-a C 
 
 FIG. 55. 
 
 Abscissae of a parabola are as the squares of their ordinates. 
 
 To describe a parabola when an abscissa and its ordinate are given 
 
 (Fig. 55). Bisect the given ordinate B C at a, draw A a, and then a b 
 perpendicular to it, meeting the axis at 6. Set off A e, A F, each equal to 
 B b; and draw K e L perpendicular to the axis. Then K L is the directrix 
 and F is the focus. Through F and any number of points, o, o, etc., in the 
 axis, draw double ordinates, n o n, etc., and from the centre F, with the 
 radii F e t o e, etc., cut the respective ordinates at E, G, n, n, etc.. The 
 curve may be traced through these points as shown. 
 
 2d Method: By means of a square and a cord (Fig. 56). Place a 
 
GEOMETRICAL PROBLEMS. 
 
 49 
 
 FIG. 56. 
 
 / 
 
 { 
 
 y 
 
 7 
 
 
 
 * 
 
 9 
 
 ^ 
 
 'j_ 
 
 
 
 
 
 
 
 
 'i 
 
 ) d cbaBabad 
 
 FIG. 57. 
 
 straight-edge to the directrix E N, 
 and apply to it a square LEG. 
 Fasten to the end G one end of a 
 thread or cord equal in length to the 
 edge E (7, and attach the other end 
 to the focus F; slide the square along 
 the straight-edge, holding the cord 
 taut against the edge of the square 
 by a pencil D, by which the curve is 
 described. 
 
 3d Method: When the height and 
 the base are given (Fig. 57). Let 
 A B be the given axis, and C D a 
 double ordinate or base; to describe 
 a parabola of which the vertex is at 
 A. Through A draw E F parallel to 
 C D, and through C and D draw C E 
 and D F parallel to the axis. Divide 
 B C arid B D into any number of 
 equal parts, say five, at a, 6, etc., and 
 divide C E and D F into the same 
 number of parts. Through the 
 points a, b, c, d in the base CD on 
 each side of the axis draw perpen- 
 diculars, and through a, b, c, d in C E 
 and D F draw lines to the vertex A , 
 cutting the perpendiculars at e, /, g, h. 
 These are points in the parabola, and 
 the curve CAD may be traced as 
 shown, passing through them. 
 47. The Hyperbola (Fig. 58). A hyperbola is a. plane curve, such 
 that the difference of the distances from any point of it to two fixed points 
 
 is equal to a given distance. The 
 fixed points are called the foci. 
 
 To construct a hyperbola. 
 Let F/ and F be the foci, and F e F 
 the distance Between them. Take a 
 ruler longer than the distance F 1 F, 
 and fasten one of its extremities vj 
 the focus F' . At the other extrem 
 ity, H, attach a thread of such a 
 length that the length of the ruler 
 shall exceed the length of the thread 
 by a given distance A B. Attach 
 the other extremity of the thread at 
 the focus F. 
 
 Press a pencil, P, against the ruler, 
 and keep the thread constantly tense, 
 while the ruler is turned around F' as 
 a centre. The point of the pencil 
 will describe one branch of the curve. 
 2d Method: By points (Fig. 59). 
 From the focus F' lay off a distance 
 F' N equal to the transverse axis, or 
 distance between the two branches of 
 the curve, and take any other dis- 
 tance, as F' II, greater than F' N. 
 
 With F' as a centre and F' H as a 
 radius describe the arc of a circle. 
 
 hen with F as a centre and N H as a radius describe an arc intersecting 
 he arc before described at p and q. These will be points of the hyper- 
 oia, for F' q F q is equal to the transverse axis A B. 
 If, with F as a centre and F' H as a radius, an arc be described, and a 
 second arc be described with F' as a centre and N H as a radius, two points 
 in the other branch of the curve will be determined. Hence, by changing 
 the centres, each pair of radii will determine two points in each branch. 
 The Equilateral Hyperbola. The transverse axis of a hyperbola is 
 
 FIG. 58. 
 
 \P/ 
 
 FIG. 59. 
 
50 
 
 GEOMETRICAL PROBLEMS. 
 
 
 the distance, on a line joining the foci, between the two branches of the 
 curve. The conjugate axis is a line perpendicular to the transverse axis, 
 drawn from its centre, and of such a length that the diagonal of the rect- 
 angle of the transverse and conjugate axes is equal to the distance between 
 the foci. The diagonals of this rectangle, indefinitely prolonged, are the 
 asymptotes of the hyperbola, lines which the curve continually approaches, 
 but touches only at an infinite distance. If these asymptotes are perpen- 
 dicular to each other, the hyperbola is called a rectangular or equilateral 
 hyperbola. It is a property of this hyperbola that if the asymptotes are 
 taken as axes of a rectangular system of coordinates (see Analytical Geom- 
 etry), the product of the abscissa and ordinate of any point in the curve is 
 equal to the product of the abscissa and ordinate of any other point ; or, if 
 p is the ordinate of any point and v its abscissa, and p\, and vi are the 
 ordinate and abscissa of any other point, pv = p\v\\ or pv = a constant. 
 
 48. The Cycloid (Fig. 
 
 60). If a circle A a be 6 f 
 
 rolled along a straight 
 line A 6, any point of the 
 circumference as A will 
 describe a curve, which is 
 called a cycloid. The 
 circle is called the gene- 
 rating circle, and A the 
 generating point. 
 
 To draw a cycloid. 
 Divide the circumference 
 of the generating circle 
 
 into an even number of equal parts, as A 1, 12, etc., and set off these dis- 
 tances on the base. Through the points 1, 2, 3, etc., on the circle 
 draw horizontal lines, and on them 
 set off distances la = A 1 , 2b = A 2, 3c = 
 A3, etc. The points A , a, ft, c, etc., 
 will be points in the cycloid, through 
 which draw the curve. 
 
 49. The Epicycloid (Fig. 61) is 
 generated by a point D in one circle 
 D C rolling upon the circumference of 
 another circle A C B, instead of on a 
 flat surface or line; the former being 
 the generating circle, and the latter 
 the fundamental circle. The generat- 
 ing circle is shown in four positions, 
 in which the generating point is 
 successively marked D, D', D", D'". 
 A D'" B is the epicycloid. 
 
 FIG. 61. 
 
 50. The Hypocycloid (Fig. 62) 
 is generated by a point in the gener- 
 ating circle rolling on the inside of 
 the fundamental circle. 
 
 When the generating circle = 
 Tadius of the other circle, the hypo- 
 cycloid becomes a straight line. 
 
 51. The Tractrix or Schiele's 
 anti-friction curve (Fig. 63). R 
 is the radius of the shaft, C, 1, 2, etc., 
 ihe axis. From O set off on R a 
 rmall distance, oa; with radius A and 
 centre a cut the axis at 1, join a 1, 
 and set off a like small distance a b; 
 from b with radius R cut axis at 2, 
 join b 2, and so on, thus finding 
 points o, a, b, c, d, etc., through which 
 the curve is to be drawn. 
 
GEOMETRICAL PROBLEMS. 
 
 51 
 
 52. The Spiral. The spiral is a curve described by a point which 
 moves along a straight line according to any given law, the line at the same 
 time having a uniform angular motion. The line is called the radius vector. 
 
 If the radius vector increases directly 
 as the measuring angle, the spires, 
 or parts described in each revolution, 
 thus gradually increasing their dis- 
 tance from each other, the curve is 
 known as the spiral of Archimedes 
 
 FIG. 64. 
 
 his curve is commonly used for 
 cams. To describe it draw the 
 radius vector in several different 
 directions around the centre, with 
 equal angles between them; set off 
 
 the distances 1, 2, 3, 4, etc., corresponding to the scale upon which the 
 
 curve is drawn, as shown in Fig. 64. 
 
 In the common spiral (Fig. 64) the 
 pitch is uniform; that is, the spires 
 are equidistant. Such a spiral is 
 made by rolling up a belt of uniform 
 thickness. 
 
 To construct a spiral with four 
 centres (Fig. 65). Given the 
 pitch of the spiral, construct a square 
 about the centre, with the sum of 
 the four sides equal to the pitch. 
 Prolong the sides in one direction as 
 shown; the corners are the centres for 
 each arc of the external^ angles, 
 forming a quadrant of a spire. 
 
 FIG. 65. 
 
 53. To find the diameter of a circle into which a certain number of 
 rings will fit on its inside (Fig. 66). For instance, what is the diameter 
 of a circle into which twelve i/2-inch rings will fit, as per sketch? Assume 
 that we have found the diameter of the required circle, and have drawn 
 
 the rings inside of it. Join the 
 centres of the rings by straight lines, 
 as shown: we then obtain a regular 
 polygon with 12 sides, each side 
 being equal to the diameter of a 
 
 fiven ring. We have now to find 
 he diameter of a circle circum- 
 scribed about this polygon, and add 
 the diameter of one ring to it; the 
 sum will be the diameter of the circle 
 into which the rings will fit. 
 Through the centres A and D of two 
 adjacent rings draw the radii C A 
 
 R\( \^ } __ _,' / }/ and CD; since the polygon has twelve 
 
 X-NC^^JT S sides the angle A C D = 30 and 
 
 N^^===^K^ AC B = 15. One half of the side 
 
 ^^^S^^^ A D is equal to A B. We now give 
 
 7 the following proportion: The sine 
 
 FIG. 66. of the angle A C B is to A B as 1 is to 
 
 the required radius. From this we 
 
 . 
 
 _ t the following rule: Divide A B by the sine of the angle A C B\ the 
 quotient will be the radius of the circumscribed circle; add to the corre- 
 sponding diameter the diameter of one ring; the sum will be the required 
 diameter F G. 
 
 54. To describe an arc of a circle which is too large to be drawn 
 by a beam compass, by means of points in the arc, radius being given. 
 Suppose the radius is 20 feet and it is desired to obtain five points in an 
 arc whose half chord is 4 feet. Draw a line equal to the half chord, full 
 
 uAvuiais ui> yuiiua i, 2, o, uuu * icci iiuui me mat pcipciiuicuiai. ciuu 
 
 Talues of y in the formula of the circle, x* * j/ a R\ by substituting for 
 
52 
 
 GEOMETRICAL PROBLEMS. 
 
 x the values 0, 1, 2, 3, and 4, etc., and for R 2 the square of the radius, or 
 400. The values will be y = ^R 2 ~ x 2 = V400, ^399, V396, V391, 
 
 V384; = 20, 19.975, 19.90, 19.774, 19.596. 
 Subtract the smallest, 
 
 or 19.596, leaving 0.404, 0.379, 0.304, 0.178, feet. 
 
 Lay off these distances on the five perpendiculars, as ordinates from the 
 half chord, and the positions of five points on the arc will be found. 
 Through these the curve may be 
 drawn. (See also Problem 14.) 
 
 55. The Catenary is the curve 
 assumed by a perfectly flexible cord 
 when its ends are fastened at two 
 points, the weight of a unit length 
 being constant. 
 
 The equation of the catenary is 
 
 / x _?\ 
 y =^(e a -}-e a ), in which e is the 
 
 base of the Napierian system of log- 
 arithms. 
 
 To plot the catenary. Let o 
 (Fig. 67) be the origin of coordinates. 
 Assigning to a any value as 3, the 
 equation becomes 
 
 ( 
 
 To find the lowest point of the 
 curve. 
 
 Puts = 0; /. y = - 
 
 Then put x = \\ .'. fgl 
 
 Put z = 2; .'. 1/=|( 
 
 H^ (1.396 +0.717) =3.17. 
 ) = ? (1.948 +0.513) =3.69. 
 
 Put x = 3, 4, 5, etc., etc., and find the corresponding values of y. For 
 each value of y we obtain two symmetrical points, as for example p and, p r . 
 In this way, by making a successively equal to 2, 3, 4, 5, 6, 7, and 8, the 
 curves of Fig. 67 were plotted. 
 
 In each case the distance from the origin to 
 the lowest point of the curve is equal to a; for 
 putting x = o, the general equation reduces to 
 
 For values of a 6, 7, and 8 the catenary 
 closely approaches the parabola. For deriva- 
 tion of the equation of the catenary see Bow- 
 ser's Analytic Mechanics. 
 
 56. The Involute is a name given to the 
 curve which is formed by the end of a string 
 which is unwound from a cylinder and kept 
 taut; consequently the string as it is unwound 
 will always lie in the direction of a tangent 
 to the cylinder. To describe the involute of 
 any given circle, Fig. 68, take any point A on 
 its circumference, draw a diameter A B, and 
 from B draw B b perpendicular to A B. Make 
 B b equal in length to half the circumference 
 of the circle. Divide B b nnd the semi-circum- 
 ference into the same number of equal parts, 
 say six. From each point of division 1, 2, 
 3, etc., on the circumference draw lines to the centre C of the circle. 
 Then draw lai perpendicular to (71; 2 a^ perpendicular to (72; and 
 80 on. Make \a\ equal to b 6 t ; 2 dz equal to b 6 2 ; 3 a equal to b b&; and 
 so on. Join the points A, a lt ctz, 03, etc., by a curve; this curve will be 
 t&e required involute. 
 
 FIG. 68. 
 

 GEOMETRICAL PROPOSITIONS. 53 
 
 57. Method of plotting angles without using a protractor. The 
 
 radius of a circle whose circumference is 360 is 57.3 (more accurately 
 57.296). Striking a semicircle with a radius 57.3 by any scale, spacers 
 set to 10 by the same scale will divide the arc into 18 spaces of 10 each 
 and intermediates can bo measured indirectly at the rate of 1 by scale for 
 each 1, or interpolated by eye according to the degree of accuracy required 
 The following table shows the chords to the above-mentioned radius, for 
 every 10 degrees from up to 110. By means of one of these a 10 
 point is fixed upon the paper next less than the required angle, and the 
 remainder is laid oft at the rate of 1 by scale for each degree. 
 
 Angle. Chord. Angle. Chord. Angle. Chord. 
 
 1 0.999 40 39.192 80 73658 
 
 10 9.988 50 48.429 90.., 81029 
 
 20 19.899 60 57.296 100 '. 87>82 
 
 30 29.658 70 65.727 110 93.869 
 
 GEOMETRICAL PROPOSITIONS. 
 
 In a right-angled triangle the square on the hypothenuse is equal to the 
 sum of the squares on the other two sides. 
 
 If a triangle is equilateral, it is equiangular, and vice versa. 
 
 If a straight line from the vertex of an isosceles triangle bisects the base, 
 It bisects the vertical angle and is perpendicular to the base. 
 
 If one side of a triangle is produced, the exterior angle is equal to the 
 sum of the two interior and opposite angles. 
 
 If two triangles are mutually equiangular, they are similar and their 
 corresponding sides are proportional. 
 
 If the sides of a polygon are produced in the same order, the sum of the 
 exterior angles equals four right angles. (Not true if the polygon has 
 re-entering angles.) 
 
 In a quadrilateral, the sum of the interior angles equals four right 
 angles. 
 
 In a parallelogram, the opposite sides are equal; the opposite angles are 
 equal; it is bisected by its diagonal, and its diagonals bisect each other. 
 
 If three points are not in the same straight line, a circle may be passed 
 through them. 
 
 If two arcs are intercepted on the same circle, they are proportional to 
 the corresponding angles at the centre. 
 
 If two arcs are similar, they are proportional to their radii. 
 
 The areas of two circles are proportional to the squares of their radii. 
 
 If a radius is perpendicular to a chord, it bisects the chord and it bisects 
 the arc subtended by the chord. 
 
 A straight line tangent to a circle meets it in only one point, and it 13 
 perpendicular to the radius drawn to that point. 
 
 If from a point without a circle tangents are drawn to touch the circle, 
 there are but two; they are equal, and they make equal angles with the 
 chord joining the tangent points. 
 
 If two lines are parallel chords or a tangent ,and parallel chord, they 
 intercept equal arcs of a circle. 
 
 If an angle at the circumference of a circle, between two chords, is sub- 
 tended by the same arc as an angle at the centre, between two radii, tho 
 angle at the circumference is equal to half the angle at the centre. 
 
 If a triangle is inscribed in a semicircle, it is right-angled. 
 
 If two chords intersect each other in a circle, the rectangle of the seg- 
 ments of the one equals the rectangle of the segments of the other. 
 
 And if one chord is a diameter and the other perpendicular to it, the 
 rectangle of the segments of the diameter is equal to the square on 
 half the other chord, and the half chord is a mean proportional between 
 the segments of the diameter. 
 
 If an angle is formed by a tangent and chord, it is measured by one half 
 of the arc intercepted by the chord; that is, it is equal to half the angle at 
 the centre subtended by the chord. 
 
54 MENSURATION PLANE SURFACES. 
 
 a Railway Curve. This last proposition is useful in staking 
 out railway curves. A curve is designated as one of so many degrees, and 
 the degree is the angle at the centre subtended by a chord of 100 ft. To 
 lay out a curve of n degrees the transit is set at its beginning or " point of 
 curve," pointed in the direction of the tangent, and turned through i/2?i 
 degrees; a point 100 ft. distant in the line of sight will be a point in the 
 curve. The transit is then swung 1/2 n degrees further and a 100 ft. chord 
 is measured from the point already found t9 a point in the new line of 
 sight, which is a second point or " station " in the curve. 
 
 The radius of a 1 curve is 5729.65 ft., and the radius of a curve of any 
 degree is 5729.65 ft. divided by the number of degrees. 
 
 Some authors use the angle subtended by an arc (instead of chord) of 
 100 ft. in defining the degree of a curve. For a statement of the relative 
 advantages of the two definitions, see Eng. News, Feb. 16, 1911. 
 
 MENSURATION. 
 
 PLANE SURFACES. 
 
 Quadrilateral* A four-sided figure. 
 
 Parallelogram. A quadrilateral with opposite sides parallel. 
 
 Varieties. Square: four sides equal, all angles right angles. Rect- 
 angle: opposite sides equal, all angles right angles. Rhombus: four sides 
 equal, opposite angles equal, angles not right angles. Rhomboid: opposite 
 sides equal, opposite angles equal, angles not right angles. 
 
 Trapezium. A quadrilateral with unequal sides. 
 
 Trapezoid. A quadrilateral with only one pair of opposite sides 
 parallel. _ 
 
 Diagonal of a square = ^2 X side 2 = 1.4142 X side. _ 
 
 Diag. of a rectangle = v sum of squares of two adjacent sides. 
 
 Area of any parallelogram = base X altitude. 
 
 Area of rhombus or rhomboid = product of two adjacent sides X sine 
 of angle included between them. 
 
 Area of a trapezoid = product of half the sum of the two parallel sidea 
 by the perpendicular distance between them. 
 
 To find the area of any quadrilateral figure. Divide the quad- 
 rilateral into two triangles; the sum of the areas of the triangles is the 
 area. 
 
 Or, multiply half the product of the two diagonals by the sine of the 
 angle at their intersection. 
 
 To find the area of a quadrilateral which may be inscribed in a 
 circle. From half the sum of the four sides subtract each side severally; 
 multiply the four remainders together; the square root of the product is 
 the area. 
 
 Triangle. A three-sided plane figure. 
 
 Varieties. Right-angled, having one right angle; obtuse-angled, hav- 
 ing one obtuse angle; isosceles, having two equal angles and two equal 
 sides; equilateral, having three equal sides and equal angles. 
 
 The sum of the three angles of every triangle = 180. 
 
 The sum of the two acute angles of a right-angled triangle = 90. 
 
 Hypothenuse of a right-angled triangle, the side opposite the right 
 angle, = Vsum of the squares of the other two sides. If a and 6 are the 
 two sides and c the hypothenuse, c 2 =a 2 + & 2 ; a = Vc 2 -& 2 =V( c +&)(/-&). 
 
 If the two sides are equal, side = hyp -9- 1.4142; or hyp X.7071. 
 
 To find the area of a triangle : 
 
 RULE 1. Multiply the base by half the altitude. 
 
 RULE 2. Multiply half the product of two sides by the sine of the 
 included angle. 
 
 RULE 3. From half the sum of the three sides subtract each side 
 severally; multiply together the half sum and the three remainders, and 
 extract the square root of the product. 
 
 The area of an equilateral triangle is equal to one fourth _the square of 
 
 one of its sides multiplied by the square root of 3, = a . , a being tht 
 tide; or a 8 X 0,433013, 
 
MENSURATION. 
 
 55 
 
 Area of a triangle given, to find base: Base = twice area * perpendicular 
 height. 
 
 Area of a triangle given, to find height: Height = twice area -s- base. 
 
 Two sides and base given, to find perpendicular height (in a triangle in 
 which both of the angles at the base are acute). 
 
 RULE. As the base is to the sum of the sides, so is the difference of the 
 sides to the difference of the divisions of the base made bv drawing the 
 perpendicular. Half this difference being added to or subtracted from 
 half the base will give the two divisions there9f. As each side and its 
 opposite division of the base constitutes a right-angled triangle., the 
 perpendicular is ascertained by the rule: Perpendicular = Vhyp 2 base 2 * 
 
 Areas of similar figures are to each other as the squares of their 
 respective linear dimensions. If the area of an equilateral triangle of 
 side = 1 is 0.433013 and its height 0.86603, what is the area of a similai 
 triangle whose height = 1? 0.86603 2 : I 2 :: 0.433013 : 0.57735, Ans. 
 
 Polygon. A plane figure having three or more sides. Regular or 
 irregular, according as the sides or angles are equal or unequal. Polygons 
 are named from the number of their sides and angles. 
 
 To find the area of an irregular polygon. Draw diagonals dividing 
 the polygon into triangles, and find the sum of the areas of these triangles. 
 
 To find the area of a regular polygon: 
 
 RULE. Multiply the length of a side by the perpendicular distance to 
 the centre; multiply the product by the number of sides, and divide it by 
 2. Or, multiply half the perimeter by the perpendicular let fall from the 
 centre on one of the sides. 
 
 The perpendicular from the centre is equal to half of one of the sides of 
 the polygon multiplied by the cotangent of the angle subtended by the 
 half side. 
 
 The angle at the centre = 360 divided by the number of sides. 
 
 Table of Regular Polygons^ 
 
 
 
 
 H 
 
 Radius of Cir- 
 
 
 
 
 
 
 
 
 II 
 
 cumscribed 
 
 12 
 
 c3 o 
 
 
 t 
 
 
 d 
 
 
 ft 
 
 Circle. 
 
 ^Q 1 " 1 
 
 ^ d 
 
 
 2 
 
 1 
 
 1 
 
 iH 
 
 
 
 ~ 
 
 K3 
 t 
 
 
 1.1 
 
 2 
 
 C-TJ 
 
 si 
 
 i;' 
 
 1 
 
 "d 
 
 6 
 
 S $ 
 
 m 
 
 1- 
 
 
 w 
 
 *o 
 
 02 
 
 J 
 
 i i II 
 
 i" 1 
 
 
 
 S^^j 
 
 "S 
 
 0)^9 
 
 ^ a 
 
 o 
 
 g 
 
 
 OQ 
 
 o 
 
 II 
 
 11 
 
 "S'S 2 
 
 o 
 
 ^ S 
 
 & 
 
 i 
 
 1 
 
 1 
 
 
 
 1 
 
 
 J' 3 
 
 1 
 
 r 
 
 3 
 
 Triangle 
 
 0.4330 
 
 0.5773 
 
 2.000 
 
 0.5773 
 
 0.2887 
 
 1.732 
 
 120 
 
 60 
 
 4 
 
 Square 
 
 1.0000 
 
 1.0000 
 
 .414 
 
 0.7071 
 
 0.5000 
 
 1.4142 
 
 90 
 
 90 
 
 5 
 
 Pentagon 
 
 1 . 7205 
 
 0.7265 
 
 .236 
 
 0.8506 
 
 0.6882 
 
 1 . 1 756 
 
 72 
 
 108 
 
 6 
 
 Hexagon 
 
 2.5981 
 
 0.8660 
 
 .155 
 
 1 . 0000 
 
 0.866 
 
 1 . 0000 
 
 60 
 
 120 
 
 7 
 
 Heptagon 
 
 3.6339 
 
 0.7572 
 
 .11 
 
 1 . 1 524 
 
 1 . 0383 
 
 0.8677 
 
 51 26' 
 
 1284-7 
 
 8 
 
 Octagon 
 
 4.8284 
 
 0.8284 
 
 .082 
 
 1 . 3066 
 
 .2071 
 
 0.7653 
 
 45 
 
 135 
 
 9 
 
 Nonagon 
 
 6.1818 
 
 0.7688 
 
 .064 
 
 1 4619 
 
 .3737 
 
 0.684 
 
 40 
 
 140 
 
 10 
 11 
 
 Decagon 
 Undecagon 
 
 7.6942 
 9.3656 
 
 0.8123 
 0.7744 
 
 .051 
 .042 
 
 1.618 
 1 . 7747 
 
 .5388 
 .7028 
 
 0.618 
 0.5634 
 
 36 
 3243' 
 
 144 
 1473-11 
 
 12 
 
 Dodecagon 
 
 11.1962 
 
 0.8038 
 
 .035 
 
 1.9319 
 
 .866 
 
 0.5176 
 
 30 
 
 150 
 
 
 * Short diameter, even number of sides, = diam. of inscribed circle: 
 short diam., odd number of sides, = rad. of inscribed circle + rad. ol 
 circumscribed circle. 
 
56 
 
 AREA OF IRREGULAR FIGURES. 
 
 To find the area of a regular polygon, when the length of a side 
 only is given: 
 
 RULE. Multiply the square of the side by the figure for "area, side 
 1," opposite to the name of the polygon in the table. 
 
 Length of a side of a regular polygon inscribed in a circle = diam. 
 X sin (180 *- no. of sides). 
 
 No. of sides sin (180 /n) No. sin (180 /n) 
 
 0.86603 
 .70711 
 .58778 
 .50000 
 .43388 
 .38268 
 
 9 0.34202 
 
 10 .30902 
 
 11 .28173 
 
 12 .25882 
 
 13 .23931 
 
 14 .22252 
 
 No. sin (180/n) 
 
 15 0.20791 
 
 16 .19509 
 
 17 .18375 
 
 18 .17365 
 
 19 .16458 
 
 20 .15643 
 
 To find the area of an irregular 
 i^gure (Fig. 69). Draw ordinates 
 f, cross its breadth at equal distances 
 apart, the first and the last ordinate 
 each being one half space from the 
 ends of the figure. Find the average 
 breadth by adding together the 
 lengths of these lines included be- 
 tween the boundaries of the figure, 
 and divide by the number of the lines 
 added; multiply this mean breadth 
 by the length. The greater the num- 
 ber of lines the nearer the approxi- 
 mation. 
 
 \l* 3 4 $ 
 
 
 
 FIG. 69. 
 
 In a figure of very irregular outline, as an indicator-diagram from a 
 high-speed steam-engine, mean lines may be substituted for the actual 
 lines of the figure, being so traced as to intersect the undulations, so that 
 the total area of the spaces cut off may be compensated by that of the 
 extra spaces inclosed. 
 
 2d Method: THE TRAPEZOIDAL RULE. Divide the figure into any 
 sufficient number of equal parts; add half the sum of the two end ordinates 
 to the sum of all the other ordinates; divide by the number of spaces 
 (that is, one less than the number of ordinates) to obtain the mean 
 ordinate, and multiply this by the length to obtain the area. 
 
 3d Method: SIMPSON'S RULE. Divide the length of the figure into any 
 even number of equal parts, at the common distance D apart, and draw 
 ordinates through the points of division to touch the boundary lines 
 Add together the first and last ordinates and call the sum A ; add together 
 the even ordinates and call the sum J5; add together the odd ordinates, 
 except the first and last, and call the sum C. Then, 
 
 area of the figure = 
 
 A+4B+2C 
 
 XD. 
 
 4/fe Method: DURAND'S RULE. Add together */io the sum of the first 
 and last ordinates, 1 Vio the sum of the second and the next to the last 
 (or the penultimates), and the sum of all the intermediate ordinates. 
 Multiply the sum thus gained by the common distance between the ordi- 
 nates to obtain the area, or divide this sum by the number of spaces to 
 f btain the mean ordinate. 
 
 Prof. Durand describes the method of obtaining his rule in Engineering 
 News, Jan. 18, 1894. He claims that it is more accurate than Simpson's 
 rule, and practically as simple as the trapezoidal rule. He thus describes 
 its application for approximate integration of differential equations. Any 
 definite integral may be represented graphically by an area. Thus, let 
 
 Q = fu dx 
 
 be an integral in which u is some function of x, either known or admitting 
 of computation or measurement. Any curve plotted with x as abscissa 
 and u as ordinate will then represent the variation of u with x, and tht 
 
MENSURATION. 
 
 57 
 
 area between such curve and the axis X will represent the integral in 
 question, no matter how simple or complex may be the real nature of the 
 function u. 
 
 Substituting in the rule as above given the word " volume" for " area" 
 and the W9rd "section" for " ordinate," it becomes applicable to the 
 determination of volumes from equidistant sections as well as of areas 
 from equidistant ordinates. 
 
 Having approximately obtained an area by the trapezoidal rule, the 
 area by Durand's rule may be found by adding algebraically to the sum of 
 the ordinates used in the trapezoidal rule (that is, half the sum of the end 
 ordinates -f sum of the other ordinates) 1/10 of (sum of penultimates 
 sum of first and last) and multiplying by the common distance between 
 the ordinates. 
 
 5ih Method. Draw the figure on cross-section paper. Count the 
 number of squares that are entirely included within the boundary; then 
 estimate the fractional parts of. squares that are cut by the boundary, add 
 together these fractions, and add the sum to the number of whole squares. 
 The result is the area in units of the dimensions of the squares. The finer 
 the ruling of the cross-section paper the more accurate the result. 
 
 6th Method. Use a planimeter. 
 
 7th Method. With a chemical balance, sensitive to one milligram, 
 draw the figure on paper of uniform thickness and cut it out carefully; 
 weigh the piece cut out, and compare its weight with the weight per 
 square inch of the paper as tested by weighing a piece of rectangular shape. 
 
 
 THE CIRCLE. 
 
 Circumference = diameter X 3. 1416, nearly; more accurately, 3.14159265359. 
 
 99 "^^^ 
 
 Approximations, = 3.143; = 3.1415929. 
 
 The ratio of circum. to diam. is represented by the symbol 
 Area = 0.7854 X square of the diameter. 
 
 (called Pi). 
 
 Multiples of r. 
 
 1* = 3.14159265359 
 In = 6.28318530718 
 37r = 9.42477796077 
 4* = 12.56637061436 
 5x = 15.70796326795 
 6^ = 18.84955592154 
 In = 21.99114857513 
 8;: = 25.13274122872 
 9* = 28.27433388231 
 
 7T/4 
 
 Multiples of|- 
 
 = 0.7853982 
 X 2 = 1.5707963 
 X 3 = 2.356194r 
 X 4 = 3.1415927 
 X 5 = 3.9269908 
 X 6 = 4.7123890 
 X 7 = 5.4977871 
 X 8 = 6.2831853 
 X 9 = 7.0685835 
 
 Ratio of diam. to circumference = reciprocal of = 0.3183099. 
 
 1/7^=0.101321 
 VK= 1.772453 
 V7/7 =0.564189 
 vV/4 =0.886226 
 LogTr =0.497 14987 
 Log ir/4_= 1.895090 
 Log vV =0.248575 
 Log vV/4= 1.947545 
 
 iprocal of /4 = 1.27324. 
 
 10/7r= 3.18310 
 
 Multiples of I/TT. 
 
 12/x= 3.81972 
 
 I/TT = 0.31831 
 
 x/2 = 1.570796 
 
 2/7T = 0.63662 
 
 7T/3 = 1.047197 
 
 3/?r = 0.95493 
 
 7T/6 = 0.523599 
 
 4/7r= 1.27324 
 
 7T/12 = 0.261799 
 
 5/7T = 1.59155 
 
 ir/64 = 0.049087 
 
 6/7r= 1.90986 
 
 Tr/360 = 0.0087266 
 
 7/7r= 2.22817 
 
 360/7r= 114.5915 
 
 8/7T = 2.54648 
 
 ** = 9.86960 
 
 9/7T = 2.86479 
 
 1-^-4*-= 0.0795775 
 
 
 Diam. in ins. = 13.5405 Varea in sq. ft. 
 
 Area in sq. ft. = (diam in inches) 2 X .0054542. 
 
 D = diameter, R = radius, C = circumference, 
 
 ; area. 
 
58 
 
 THE CIRCLE. 
 
 . = ; = .0795802 ;= - 
 
 R = - 
 
 0.31831(7; 
 
 0.159155C; 
 
 ; = 2 4/-; = 1. 
 
 V * 
 
 12838 
 
 ~ ; = 0.564189 
 
 Areas of circles are to each other as the squares of their diameters. 
 To find the length of an arc of a circle: 
 
 RULE 1. As 360 is to the number of degrees in the arc, so is the circum- 
 ference of the circle to the length of the arc. 
 
 RULE 2. Multiply the diameter of the circle by the number of degrees 
 in the arc, and this product by 0.0087266. 
 
 Relations of Arc, Chord, Chord of Half the Arc, etc. 
 
 Let R = radius, D = diameter, L = length of arc, 
 C = chord of the arc, c = chord of half the arc, 
 V = rise, or height of the arc, 
 
 9/> V 1 F 
 
 Length of the arc = L 
 
 - (very nearly), = 
 
 + 2c ' nearly 
 
 4F 2 X 
 
 15CS+33FS 
 Chord of the arc C, = 2 >/c 2 - F 2 ; = 
 
 .. nearly. 
 
 - (D - 2F) 2 ; = 8c - 3L 
 = 2 \/(D - F) X F. 
 Chord of half the arc, c = i/ 2 v / <7 2 + 4F 2 ; = VD x F; = (3L -f C) * 8. 
 Diameter of the circle, D = ;= V4 C 2 4- F^ ; 
 
 Rise of the arc, F = ^ ; = 1/2 (D - ' 
 
 (or if F is greater than radius 1/2 (I> + ' 
 
 - <7 2 ) ; 
 
 Half the chord of the arc is a mean proportional between the rise and 
 the diameter minus the rise: 1/2 C = V'F X ( - F). 
 
 Length of the Chord subtending an angle at the centre = twice the 
 sine of half the angle. (See Table of Sines.) 
 
 Ordinates to Circular Arcs. C = chord, F = height of the arc, or 
 middle ordinate, x = abscissa, or distance measured on the chord from its 
 central point, y = ordinate, or distance from the arc to the chord at the 
 point x, V = R - ^R 2 - 1/4C' 2 ; y = ^R 2 - x 2 - (R - F). 
 
 Length of a Circular Arc. Huyghens's Approximation. 
 
 Length of the arc, L = (8c C) * 3. Professor Williamson shows 
 that when the arc subtends an angle of 30, the radius being 100,000 feet 
 (nearly 19 miles), the error by this formula is about two inches, or 1/600000 
 part of the radius. When the length of the arc is equal to the radius, i.e., 
 when it subtends an angle of 57. 3, the error is less than 1/7680 part of the 
 radius. Therefore, if the radius is 100,000 feet, the error is less than 
 100000/7680 = 13 feet. The error increases rapidly with the increase of 
 the angle subtended. For an arc of 120 the error is 1 part in 400; for an 
 arc of 180 the error is 1.18%, 
 
MENSURATION. 
 
 59 
 
 In the measurement of an arc which is described with a short radius the 
 error is so small that it may be neglected. Describing an arc with a radius 
 of 12 inches subtending an angle of 30, the error is 1/50000 of an inch. 
 
 To measure an arc when it subtends a large angle, bisect it and measure 
 each half as before in this case making B = length of the chord of half the 
 arc, and b = length of the chord of one fourth the arc; then L = (166 - 25) -*- 3. 
 
 Formulas for a Circular Curve. 
 
 J. C. Locke, Eng. News, March 16, 1908. 
 c 
 
 u 
 
 ;- = ^2R (R- V(R +&)(#_ 6) 
 = 2\S m (2R m), = 2R sin 1/27, 
 = 2 1 7 cos 1/2 7. 
 
 e = R exsec 1/27, = R tan l/ 2 7 tan 1/47, 
 = T tan 1/4 7. 
 
 7i ) sin7 l = a cot 1/2 7. 
 
 2a 
 
 2m ' 
 
 - c) (2R - c)), = 2R sin 1/47. 
 Y = R vers i/ 2 7, 
 
 JK sin 1/2 / tan 1/4 /, = 1/2 c tan 1/4 /. 
 
 -i f 
 
 +6) (fi - 
 
 (sin 1/2 7) 2 , = R vers 7, 
 
 R sin 7 tan 1/27, = & tan 1/27, = T sin 7. 
 = #tani/ 2 7. r L ^ 
 
 I = L x 57.295780. 
 
 I c 
 
 = IR X 0.01745329, 
 
 Area of Segment = -- 
 
 2 sin 7 
 
 X 57.295780. 
 
 1Z& 
 2 * 
 
 Relation of the Circle to its Equal, Inscribed, and Circum- 
 scribed Squares. 
 
 
 Diameter of circle X 
 
 Circumference of circle X 
 Circumference of circle X 
 Diameter of circle X 
 
 Circumference of circle X 
 Area of circle X 0.90031 -f- 
 Area of circle X 
 Area of circle X 
 Side of square X 
 X 
 
 " X 
 X 
 
 Perimeter of square X 
 Square inches X 
 
 0.88623 ) 
 0.28209 J 
 1.1284 
 0.7071 ) 
 0.22508} = 
 liameter) 
 
 diameter 
 1.2732 
 0.63662 
 1.4142 
 4.4428 
 1.1284 
 3.5449 
 0.88623 
 1.2.732 
 
 side of equal square, 
 perimeter of equal square. 
 
 side of inscribed square. 
 
 = area of circumscribed square. 
 = area of inscribed square. 
 = diam. of circumscribed circle. 
 = circum. 
 
 = diam. of equal circle. 
 = circum. ^ ^ 
 
 = circular inches. 
 
GO MENSURATION. 
 
 Sectors and Segments. To find the area of a sector of a circle. 
 
 RULE 1. Multiply the arc of the sector by half its radius. 
 
 RULE 2. As 360 is to the number of degrees in the arc, so is the area of 
 the circle to the area of the sector. 
 
 RULE 3. Multiply the number of degrees in the arc by the square of the 
 radius and by 0.008727. 
 
 To find the area of a segment of a circle: Find the area of the sector 
 which has the same arc, and also the area of the triangle formed by the 
 chord of the segment and the radii of the sector. 
 
 Then take the sum of these areas, if the segment is greater than a semi- 
 circle, but take their difference if it is less. (See Table of Segments.) 
 
 Another Method: Ar^a of segment = V2.R 2 (arc sin A), in which A is 
 the central angle, R the radius, and arc the length of arc to radius 1 . 
 
 To find the area of a segment of a circle when its chord and height only 
 are given. First find radius, as follows: 
 
 radius - 1 [sq^e f ^ ChOrd + height ] . 
 
 2. Find the angle subtended by the arc, as follows: half chord * 
 radius = sine of half the angle. Take the corresponding angle from a 
 table of sines, and double it to get the angle of the arc. 
 
 3. Find area of the sector of which the segment is a part: 
 
 area of sector = area of circle X degrees of arc -* 360. 
 
 4. Subtract area of triangle under the segment: 
 
 Area of triangle = half chord X (radius height of segment). . 
 
 The remainder is the area of the segment. 
 
 When the chord, arc, and diameter are given, to find the area. From 
 the length of the arc subtract the length of the chord. Multiply the 
 remainder by the radius or one-half diameter; to the product add the 
 chord multiplied by the height, and divide the sum by 2. 
 
 Given diameter, d,'and height of segment, h. 
 
 When h is from to 1/4 c?, area = feVl.766(/fe - fe 2 ; 
 
 1/2 d, area = h\ / Q.Ol7d 2 + \.ldh - h 2 
 
 (approx.). Greatest error 0.23%, when h = i/4rf. 
 
 To find the chord: From the diameter subtract the height; multiply 
 the remainder by four times the height and extract the square root. 
 
 When the chords of the arc and of half the arc and the rise are given: 
 To the chord of the arc add four thirds of the chord of half the arc; mul- 
 tiply the sum by the rise and the product by 0.40426 (approximate). 
 
 Circular Ring. To find the area of a ring included between the cir- 
 cumferences of two concentric circles: Take the difference between the. areas 
 of the two circles; or, subtract the square of the less radius from the square 
 of the greater, and multiply their difference by 3.14159. 
 
 The area of the greater circle is equal to nR*; 
 and the area of the smaller, ~r 2 . 
 
 Their difference, or the area of the ring, is n(R* - r 2 ). 
 The Ellipse. Area of an ellipse = product of its semi-axes X3.14159 
 
 = product of its axes X 0.785398. 
 
 The Ellipse. Circumference (approximate) = 3.1416 y - - , D 
 
 and d being the two axes. 
 
 Trautwine gives the following as more accurate: When the longer axis 
 D is not more than five times the length of the shorter axis, d t 
 
 Circumference - 3.1416 
 
MENSURATION. 61 
 
 "When D is more than 5d, the divisor 8.8 is to be replaced by the fallowings 
 
 ForD/d = 6 789 10 12 14 16 18 20 30 40 50 
 Divisor = 9 9.2 9.3 9.35 9.4 9.5 9.6 9.68 9.75 9.8 9.92 9.98 10 
 
 in which A = - Ingenieurs Taschenbuch, 1896. (a and 6, semi-axes.) 
 
 Carl G. Earth (Machinery, Sept., 1900) gives as a very close approxi- 
 mation to this formula 
 
 Area of a segment, of an ellipse the base of which is parallel to one of 
 the axes of the ellipse. Divide the height of the segment by the axis of 
 which it is part, and find the area of a circular segment, in a table 9f circu- 
 lar segments, of which the height is equal to the quotient; multiply the 
 area thus found by the product of the two axes of the ellipse. 
 
 Cycloid. A curve generated by the rolling of a circle on a plane. 
 
 Length of a cycloidal curve = 4 X diameter of the generating circle. 
 Length of the base = circumference of the generating circle. 
 Area of a cycloid = 3 X area of generating circle. 
 
 Helix (Screw). A line generated by the progressive rotation cf a 
 point around an axis and equidistant from its center. 
 
 Length of a helix. To the square of the circumference described by the 
 generating point add the square of the distance advanced in one revolution, 
 and take the square root of their sum multiplied by the number of revolu- 
 tions of the generating point. Or, 
 
 length, n being number of revolutions. 
 
 Spirals. Lines generated by the progressive rotation of a point 
 around a fixed axis, with a constantly increasing distance from the axis. 
 
 A plane spiral is made when the point rotates in one plane. 
 
 A conical spiral is made when the point rotates around an axis at a 
 progressing distance from its center, and advancing in the direction of the 
 axis, as around a cone. 
 
 Length of a plane spiral line. When the distance between the coils is 
 uniform. 
 
 RULE. Add together the greater and less diameters; divide their sum 
 by 2; multiply the quotient by 3.1416, and again by the number of revo- 
 lutions. Or, take the mean of the length of the greater and less circum- 
 ferences and multiply it by the number of revolutions. Or, 
 
 length = im(R +r), R and r being the outer and inner radii. To find n, 
 
 let t = thickness of coil or band, s = space between the coils, n = . . 
 
 i ~r s 
 
 Length of a conical spiral line. Add together the greater and less 
 diameters; divide their sum by 2 and multiply the quotient by 3.1416. 
 To the square of the product of this circumference and the number of 
 revolutions of the spiral add the square of the height of its axis and take 
 the square root of the sum. 
 
 Or, length 
 
 SOLID BODIES. 
 
 Surfaces and Volumes of Similar Solids. The surfaces of two 
 similar solids are to each other as the squares of their linear dimensions; 
 the volumes are as the cubes of their linear dimensions. If L = the side 
 
62 MENSURATION. 
 
 of a cube or other solid, and / the side of a similar body of different size, 
 S, s, the surfaces and V, v, the volumes respectively, S : s :: L 2 : /*; 
 V : v :: L 3 : J. 
 
 The Prism. To find the surface of a right prism: Multiply the perim- 
 eter of the base by the altitude for the convex surface. To this add the 
 areas of the two ends when the entire surface is required. 
 
 Volume of a prism = area of its base X its altitude. 
 
 The pyramid. Convex surface of a regular pyramid = perimeter of 
 its base X half the slant height. To this add area of the base if the whole 
 surface is required. 
 
 Volume of a pyramid = area of base X one third of the altitude. 
 
 To find the surface of a frustum of a regular pyramid: Multiply half the 
 slant height by the sum of the perimeters of the' two bases for the convex 
 surface. To this add the areas of the two bases when the entire surface is 
 required . 
 
 To find the volume of a frustum of a pyramid: Add together the areas of 
 the two bases and a mean proportional between them," and multiply the 
 sum by one third of the altitude. (Mean proportional between two 
 numbers = square root of their product.) 
 
 Wedge. A wedge is a solid bounded by five planes, viz.: a rectangular 
 base, two trapezoids, or two rectangles, meeting in an edge, and two 
 triangular ends. The altitude is the perpendicular drawn from any point 
 in the edge to the plane of the base. 
 
 To find the volume of a wedge: Add the length of the edge to twice the 
 length of the base, and multiply the sum by one sixth of the product of 
 the height of the wedge and the breadth of the base. 
 
 Rectangular prismoid. A rectangular prisrnoid is a solid bounded 
 by six planes, of which the two bases are rectangles, having their corre- 
 sponding sides parallel, and the four upright sides of the solid are trape- 
 zoids. 
 
 To find the volume of a rectangular prismoid: Add together the areas of 
 the two bases and four times the area of a parallel section equally distant 
 from the bases, and multiply the sum by one sixth of the altitude. 
 
 Cylinder. Convex surface of a cylinder = perimeter of base X 
 altitude. To this add the areas of the two ends when the entire surface is 
 required. 
 
 Volume of a cylinder area of base X altitude. 
 
 Cone. Convex surface of a cone = circumference of base X half the 
 slant height. To this add the area of the base when the entire surface is 
 required. 
 
 Volume of a cone = area of base X one third of the altitude. 
 
 To find the surface of a frustum of a cone: Multiply half the side by the 
 sum of the circumferences of the two bases for the convex surface; to this 
 add the areas of the two bases when the entire surface is required. 
 
 To find the volume of a frustu?n of a cone: Add together the areas of 
 the two bases and a mean proDortional between them, and multiply 
 the sum by one third of the altitude. Or, Vol. = 0.261Sa(6 2 4- c 2 + be); 
 a = altitude; b and c, diams. of the two bases. 
 
 Sphere. To find the surface of a sphere: Multiply the diameter by the 
 circumference of a great circle; or, multiply the square of the diameter by 
 3.14159. 
 
 Surface of sphere 4 x area of its great circle. 
 *' *' ** =i convex surface of its circumscribing cylinder. 
 
 Surfaces of spheres are to each other as the squares of their diameters. 
 To find the volume of a sphere: Multiply the surface by one third of the 
 radius; or, multiply the cube of the diameter by ;r/6; that is, by 0.5236, 
 Value of 7T/6 to' 10 decimal places = 0.5235987756. 
 The volume of a sphere = 2/3 the volume of its circumscribing cylinder. 
 Volumes of spheres are to each other as the cubes of their diameters. 
 
MENSURATION. 63 
 
 Spherical triangle. To find the area of a spherical triangle: Compute 
 the surface of the quadrantal triangle, or one eighth of the surface of 
 the sphere. From the sum of the three angles subtract two right angles; 
 divide the remainder by 90, and multiply the quotient by the area of the 
 quadrantal triangle. 
 
 Spherical polygon. To find the area of-a spherical polygon: Compute 
 the surface of the quadrantal triangle. From the sum of all the angles 
 subtract the product of two right angles by the number of sides less two; 
 divide the remainder by 90 and multiply the quotient by the area of the 
 quadrantal triangle. 
 
 The prismoid. The prismoid is a solid having parallel end areas, and 
 may be composed of any combination of prisms, cylinders, wedges, pyra- 
 mids, or cones or frustums of the same, whose bases and apices lie in the 
 end areas. 
 
 Inasmuch as cylinders and cones are but special forms of prisms and 
 pyramids, and warped, surface solids may be divided into elementary 
 forms of them, and since frustums may also be subdivided into the elemen- 
 tary forms, it is sufficient to say that all prismoids may be decomposed 
 into prisms, wedges, and pyramids. If a formula can be found which is 
 equally applicable to all of these forms, then it will apply to any combi- 
 nation of them. {Such a formula is called 
 
 The Prismoictal Formula. 
 
 Let A = area of the base of a prism,, wedge, or pyramid: 
 Ai, Az t A m = the two end and the middle areas of a prismoid, or of any ol 
 its elementary solids; h = altitude of the prismoid or elementary solid? 
 V = its volume; 
 
 For a prism, Ai, A m and A* are equal, = A; V = ^ X SA = hA. 
 
 Fora wedge with parallel ends, 4 2 = 0, A m =-- \ Xi;V=|(4i+2A:)=- 
 
 For a cone or pyramid, Az = 0, A m = - AI; V = - (A\ + A\) = -^-- 
 
 The prismoidal formula is a rigid formula for all prismoids. The only 
 approximation involved in its use is in the assumption that the given solid 
 may be generated by a right line moving over the boundaries of the end 
 areas. 
 
 The area of the middle section is never the mean of the two end areas if 
 the prismoid contains any pyramids or cones among its elementary forms. 
 When the three sections are similar in form the dimensions of the middle 
 area are always the means of the corresponding end dimensions. This 
 fact often enables the dimensions, and hence the area of the middle section, 
 to be computed from the end areas. 
 
 Polyedrons. A polyedron is a solid bounded by plane polygons. A 
 regular polyedron is one whose sides are all equal regular polygons. 
 
 To find the surface of a regular polyedron. Multiply the area of one of 
 the faces by the number of faces; 9r, multiply the square of one of the 
 edges by the surface of a similar solid whose edge is unity. 
 
 A TABLE OP THE' REGULAR POLYEDRONS WHOSE EDGES ARE UNITY. 
 
 Names. No*, of Faces. Surface. Volume. 
 
 Tetraedron 4 1.7320508 0.1178513 
 
 Hexaedron 6 6.0000000 1.0000000 
 
 Octaedron 8 3.4641016 0.4714045 
 
 Dodecaedron 12 20.6457288 7.6631189 
 
 Icosaedroa 20 8.6602540 2.1816950 
 
g4 MENSURATION. 
 
 To find the volume of a regular polyedron. Multiply the surface 
 by one third of the perpendicular let fall from the centre on one of the 
 faces; or, multiply the cube of one of the edges by the solidity of a similar 
 polyedron whose edge is unity. 
 
 Solid of revolution. The volume of any solid of revolution is equal 
 to the product of the area of its generating surface by the length of the 
 path of the centre of gravity of that surface. 
 
 The convex surface of any solid of revolution is equal to the product of 
 the perimeter of its generating surface by the length of path of its centre 
 of gravity. 
 
 Cylindrical ring. Let d = outer diameter; d' = inner diameter; 
 1/2 (d - d') = thickness = t; 1/4* I 2 = sectional area; 1/2 (d +d') = mean 
 diameter = M; m = circumference of section; IT M = mean circum- 
 ference of ring; surface = n t X n M; = 1/4 ^ (d 2 - d /2 ); = 9.86965 t M ; 
 = 2.46741 (d 2 - d /2 ); volume = 1/4 * t z M n\ = 2.467241 . 2 M. 
 
 Spherical zone. Surface of a spherical zone, or segment of a sphere 
 = its altitude X the circumference of a great circle of the sphere. A 
 great circle is one v/hose plane passes through the centre of the sphere. 
 
 Volume of a zone of a sphere. To the sum of the squares of the radii 
 of the ends add one third of the square of the height; multiply the sum 
 by the height and by 1.5708. 
 
 Spherical segment. Volume of a spherical segment with one base. 
 Multiply half the height of the segment by the area of the base, and the 
 cube of the height by 0.5236 and add the two products. Or, from three 
 times the diameter of the sphere subtract twice the height of the segment; 
 multiply the difference by the square of the height and by 0.5236. Or, to 
 three times the square of the radius of the base of the segment add the 
 square of its height, and multiply the sum by the height and by 0.5236. 
 
 Spheroid or ellipsoid. When the revolution of the generating sur- 
 face of the spheroid is about the transverse diameter the spheroid is 
 prolate, and when about the conjugate it is oblate. 
 
 Convex surface of a segment of a spheroid. Square the diameters of the 
 spheroid, and take the square root of half their sum; then, as the diameter 
 from which the segment is cut is to this root so is the height of the segment 
 to the proportionate height of the segment to the mean diameter. Multiply 
 the product of the other diameter and 3. 1416 by the proportionate height. 
 
 Convex surface of a frustum or zone of a spheroid. Proceed as by 
 previous rule for the surface of a segment, and obtain the proportionate 
 height of the frustum. Multiply the product of the diameter parallel to 
 the base of the frustum and 3.1416 by the proportionate height of the 
 frustum. 
 
 Volume of a spheroid is equal to the product of the square of the revol v- 
 ing axis by the fixed axis and by 0.5236. The volume of a spheroid is two 
 thirds of that of the circumscribing cylinder. 
 
 Volume of a segment of a spheroid. 1. When the base is parallel to the 
 revolving axis, multiply the difference between three times the fixed axis 
 and twice the height of the segment, by the square of the height and by 
 0.5236. Multiply the product by the square of the revolving axis, and 
 divide by the square of the fixed axis. 
 
 2. When the base is perpendicular to the revolving axis, multiply the 
 difference between three times the revolving axis and twice the height of 
 the segment by the square of the height and by 0.5236. Multiply the 
 product by the length of the fixed axis, and divide by the length of the 
 revolving axis. 
 
 Volume of the middle frustum of a spheroid. 1. When the ends are 
 circular, or parallel to the revolving axis: To twice the square of the middle 
 diameter add the square of the diameter of one end; multiply the sum by 
 the length of the frustum and by 0.2618. 
 
 2. When the ends are elliptical, or perpendicular to the revolving axis: 
 To twice the product of the transverse and conjugate diameters of the 
 middle section add the product of the transverse and conjugate diameters 
 of one end; multiply the sum by the length of the frustum and by 0.2618. 
 
 Spindles. Figures generated by the revolution of a plane area, 
 bounded by a ctirve other than a circle, when th j curve is revolved about 
 a chord perpendicular to its axis, or about its double ordinate. They are 
 designated by the name of the arc or curve from which they are generated, 
 as Circular, Elliptic, Parabolic, etc., etc. 
 
MENSURATION. 65 
 
 Convex surface of a circular spindle, zone, or segment of it. Rule: Mul- 
 tiply the length by the radius of the revolving arc; multiply this arc by the 
 central distance, or distance between the centre of the spindle and centre 
 of the revolving arc; subtract this product from the former, double the 
 remainder, and multiply it by 3.1416. 
 
 Volume of a circular spindle. Multiply the central distance by half 
 the area of the revolving segment; subtract the product from one third of 
 the cube of half the length, and multiply the remainder by 12.5664. 
 
 Volume of fruslum or zone of a circular spindle. From the square of 
 half the length of the whole spindle take one third of the square of half the 
 length of the frustum, and multiply the remainder by the said half length 
 of the frustum; multiply the central distance by the revolving area which 
 generates the frustum; subtract this product from the former, and multi- 
 ply the remainder by 6.2832. 
 
 Volume of a segment of a circular spindle. Subtract the length of the 
 segment from the half length of the spindle; double the remainder and 
 ascertain the volume of a middle frustum of this length; subtract the 
 result from the volume of the whole spindle and halve the remainder. 
 
 this product by 8. 
 
 Parabolic conoid. Volume of a parabolic conoid (generated by the 
 revolution of a parabola on its axis). Multiply the area of the base by 
 half the height. 
 
 Or multiply the square of the diameter of the base by the height and by 
 
 Volume of a fruslum of a parabolic conoid. Multiply half the sum of 
 xne areas of the two ends by the height. 
 
 Volume of a -parabolic spindle (generated by the revolution of a parabola 
 on its base). Multiply the square of the middle diameter by the length 
 and by 0.4189. The volume of a parabolic spindle is to that of a cylinder 
 of the same height and diameter as 8 to 15. 
 
 Volume of the middle frustum of a parabolic spindle. Add together 
 8 times the square of the maximum diameter, 3 times the square of the 
 end diameter, and 4 times the product of the diameters. Multiply the 
 sum by the length of the frustum and by 0.05236. This rule is applicable 
 for calculating the content of casks of parabolic form. 
 
 Casks. To find the volume of a cask of any form. Add together 39 
 times the square of the bung diameter, 25 times the square of the head 
 diameter, and 26 times the product of the diameters. Multiply the sum 
 by the length, and divide by 31,773 for the content in Imperial gallons, or 
 by 26,470 for U. S. gallons. 
 
 This rule was framed by Dr. Hutton, on the supposition that the middle 
 third of the length of the cask was a frustum of a parabolic spindle, and 
 each outer third was a frustum of a cone. 
 
 To find the ullage of a cask, the quantity of liquor in it when it is not full. 
 1. For a lying cask: Divide the number of wet or dry inches by the bung 
 diameter in inches. If the quotient is less than 0.5, deduct from it one 
 fourth part of what it wants of 0.5. If it exceeds 0.5, add to it one fourth 
 part of the excess above 0.5. Multiply the remainder or the sum by the 
 whole content of the cask. The product is the quantity of liquor in the 
 cask, in gallons, when the dividend is wet inches; or the empty space, if 
 dry inches. 
 
 2. For a standing cask: Divide the number of wet or dry inches by the 
 length of the cask. If the quotient exceeds 0.5, add to it one tenth of its 
 excess above 0.5; if less than 0.5, subtract from it one tenth of what it 
 wants of 0.5. Multiply the sum or the remainder by the whole content of 
 the cask. The product is the quantity of liquor in the cask, when the 
 dividend is wet inches; or the empty space, if dry inches. 
 
 Volume of cask (approximate) U. S. gallons = square of mean diam. 
 X length in inches X 0.0034. Mean diameter = half the sum of the 
 bung and head diameters. 
 
 Volume of an irregular solid. Suppose it divided into parts, resem- 
 bling prisms or other bodies measurable by preceding rules. Find the con- 
 lent of each part; the sum of the contents is the cubic contents of the solid. 
 
66 PLANE TRIGONOMETRY. 
 
 The content of a small part is found nearly by multiplying half the sum 
 of the areas of each end by the perpendicular distance between them. 
 
 The contents of small irregular solids may sometimes be found by im- 
 mersing them under water in a prismatic or cylindrical vessel, and observ- 
 ing the amount by which the level of the water descends when the solid is 
 withdrawn. The sectional area of the vessel being multiplied by the 
 descent of the level gives the cubic contents. 
 
 Or, weigh the solid in air and in water; the difference is the weight of 
 water it displaces. Divide the weight in pounds by 62.4 to obtain volume 
 in cubic feet, or multiply it by 27.7 to obtain the volume in cubic inches. 
 
 When the solid is very large and a great degree of accuracy is not 
 requisite, measure its length, breadth, and depth in several different 
 places, and take the mean of the measurement for each dimension, and 
 multiply the three means together. 
 
 When the surface of the solid is very extensive it is better to divide it 
 into triangles, to find the area of each triangle, and to multiply it by the 
 mean depth of the triangle for the contents of each triangular portion; the 
 contents of the triangular sections are to be added together. 
 
 The mean depth of a triangular section is obtained by measuring the 
 depth at each angle, adding together the three measurements, and taking 
 one third of the sum. 
 
 PLANE TRIGONOMETRY. 
 
 Trigonometrical Functions. 
 
 Every triangle has six parts three angles and three sides. When any 
 three of these parts are given, provided one of them is a side, the other 
 parts may be determined. By the solution of a triangle is meant the 
 determination of the unknown parts of a triangle when certain parts are 
 given. 
 
 The complement of an angle or arc is what remains after subtracting the 
 angle or arc from 90. 
 
 In general, if we represent any arc by A, its complement is 90 - A. 
 Hence the complement of an arc that exceeds 90 is negative. 
 
 The supplement of an angle or arc is what remains after subtracting the 
 angle or arc from 180. If A is an arc its supplement is 180 A. The 
 supplement of an arc that exceeds 180 is negative. 
 
 The sum of the three angles of a triangle is equal to ISO . Either angle is 
 the supplement of the other two. In a right-angled triangle, the right 
 angle being equal to 90, each of the acute angles is the complement of 
 the other. 
 
 In all right-angled triangles having the same acute angle, the sides have to 
 each other the same ratio. These ratios have received special names, as 
 follows: 
 
 If A is one of the acute angles, a the opposite side, b the adjacent side, 
 and c the hypothenuse. 
 
 The sine of the angle A is the quotient of the opposite side divided by the 
 
 hypothenuse. Sin A == - 
 
 The tangent of the angle A is the quotient of the opposite side divided by 
 the adjacent side. Tan A = j-- 
 
 The secant of the angle A is the quotient of the hypothenuse divided by the 
 adjacent side. Sec A = -r 
 
 The cosine (cos), cotangent (cot), and cosecant (coscc) of an angle 
 are respectively the sine, tangent, and secant of the complement of that 
 angle. The terms sine, cosine, etc., are called trigonometrical functions. 
 
 In a circle whose radius is unity, the sine of an arc, or of the angle at the 
 centre measured by that arc, is the perpendicular let fall from one extremity of 
 the arc upon the diameter passing through the other extremity. 
 
 The tangent of an arc is the line which touches the circle at one extremity 
 
PLANE TRIGONOMETRY. 
 
 67 
 
 of the arc, and is limited by the diameter (produced) passing through the other 
 extremity. 
 
 The secant of an arc is that part of the produced diameter which is inter" 
 cepted between the centre and the tangent. 
 
 The versed sine of an arc is that part of the diameter intercepted between 
 the extremity of the arc and the foot of the sine. 
 
 In a circle whose radius is not unity, the trigonometric functions of an 
 arc will be equal to the lines here denned, divided by the radius of the 
 circle. 
 
 it 1C A (Fig. 71) is an angle in the first quadrant, and CF = radius, 
 
 The sine of the angle = 
 
 FG 
 Rad 
 
 Cos = 
 
 Tan 
 
 I A 
 
 '' Had ' 
 
 Cosec = 
 
 Secant 
 
 CL 
 Rad ' 
 
 CT 
 
 Rad ' 
 
 Versin = 
 
 CG 
 
 Rad 
 
 Cot = 
 
 GA 
 
 '' Rad * 
 
 = 
 
 Rad* 
 PL 
 Rad* 
 
 FIG. 
 
 If radius is 1, then Rad in the denominator is 
 omitted, and sine = F G, etc. 
 
 The sine of an arc = half the chord of twice the 
 arc. 
 
 The sine of the supplement of the arc is the 
 same as that of the arc itself. Sine of arc B D F 
 = F G = sin arc F A. 
 The tangent of the supplement is equal to the tangent of the arc, but 
 with a contrary sign. Tan BDF = BM. 
 
 The secant of the supplement is equal to the secant of the arc, but with 
 a contrary sign. Sec BDF = CM. 
 
 Signs of the functions in the four quadrants. If we divide a 
 circle into four quadrants by a vertical and a horizontal diameter, the 
 upper right-hand quadrant is called the first, the upper left the second, 
 the lower left the third, and the lower right the fourth. The signs of the 
 functions in the four quadrants are as follows: 
 
 First quad. Second quad. Third quad. Fourth quad. 
 Sine and cosecant, + + 
 
 Cosine and secant, -4- + 
 
 Tangent and cotangent, 4- + 
 
 The values of the functions are as follows for the angles specified: 
 
 Angle 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 30 
 
 45 
 
 60 
 
 QO 
 
 120 
 
 135 
 
 150 
 
 180 
 
 9 70 
 
 S60 
 
 Sine 
 
 
 
 1 
 2 
 
 1 
 
 V2 
 
 v/3 
 2 
 
 1 
 
 T~ 
 
 1 
 
 1 
 2 
 
 
 
 -1 
 
 
 
 
 
 
 X/o 
 
 I 
 
 1 
 
 
 1 
 
 1 
 
 \/^~ 
 
 
 
 
 Cosine 
 
 1 
 
 ~2 
 
 V~2 
 
 2* 
 
 U 
 
 2" 
 
 
 2~ 
 
 -1 
 
 
 
 1 
 
 
 Tangent 
 
 
 
 J_ 
 
 1 
 
 Vs 
 
 00 
 
 -V3~ 
 
 -1 
 
 1 
 
 
 
 GO 
 
 
 
 
 Cotangent .... 
 
 00 
 
 vf 
 
 1 
 
 I 
 
 
 
 J_ 
 
 -1 
 
 -\/3~ 3 
 
 oo 
 
 
 
 
 
 
 
 
 \/3 
 
 
 x/3 
 
 
 
 
 
 
 Secant 
 
 1 
 
 2 
 
 X/2 
 
 2 
 
 oo 
 
 -2 
 
 _x/2~ 
 
 2 
 
 -1 
 
 00 
 
 1 
 
 Cosecant 
 
 oc 
 
 2 
 
 \/2 
 
 2 
 
 v/3 
 
 1 
 
 2 
 
 v? 
 
 2 
 
 oo 
 
 -1 
 
 to 
 
 Versed sine ... 
 
 d 
 
 2-\/3 
 
 \/2 i 
 
 1 
 2 
 
 1 
 
 3 
 
 2 
 
 V/J-f-l 
 
 2+Va 
 
 2 
 
 1 
 
 
 
 2 
 
 V 2 
 
 V2 
 
 2 
 
68 PLANE TRIGONOMETRY. 
 
 TRIGONOMETRICAL, FORMULAE. 
 
 The following relations are deduced from the properties of similai 
 triangles (Radius = 1): 
 
 cos A : sin A : : 1 : tan A, whence tan A r ; 
 
 cos A 
 
 sin A : cos A : : 1 : cot A. " cotan A = . 7 ; 
 
 sin A 
 
 cos Ail nl i sec A, " sec A 
 
 cos A' 
 
 sin A 1 1 : : 1 : cosec A, " cosec A -: 7- ; 
 
 sin A 
 
 tan A 1 1 . 1 1 1 i cot A tan A = 1 
 
 cot A 
 
 The sum of the square of the sine of an arc and the square of its cosine 
 equals unity. Sin 2 A 4- cos 2 A = 1. 
 
 Also, 1 4- tan 2 A = sec 2 A; I + cot 2 A = cosec 2 A. 
 
 Functions of the sum and difference of two angles : 
 
 Let the two angles be denoted by A and B, their sum A 4- B =* C, and 
 their difference A - B by D. 
 
 sin (A + B) = sin A cos B 4- cos A sin B; (1) 
 
 cos (A + B) = cos A cos B sin A sin B; (2) 
 
 sin (A . B) = sin A cos B cos A sin B; (3) 
 
 cos (A B) = cos A cos B + sin A sin B (4) 
 
 From these four formulae by addition and subtraction we obtain 
 
 sin (A + B) + sin (A - B) = 2 sin A cos B; . . . . (5 
 
 sin (A + B) sin (A B) = 2 cos A sin B; . . . . (6 
 
 cos (A + B) + cos (A B) = 2 cos A cos 5; . . . . (7 
 
 cos (A B) cos (A 4- B) = 2 sin A sin 5 (8 
 
 If we put A + B = C, and A B = Z>, then A = 1/2 (C 4- D) and 5 = 
 v and we have 
 
 sin (7 + sin D = 2 sin 1/2(C 4- D) cos i/2? - D); . (9) 
 
 sin C - sin D = 2 cos 1/2 (C 4- D) sin 1/2 (C7 - Z>); . . (10) 
 
 cos C + cos Z>= 20031/2(0 4- D) cos i/ 2 ((7 - D); . . (11) 
 
 cos D - cos C = 2 sin 1/2 (C 4- Z>) sin V 2 (C - Z>). . . (12) 
 
 Equation (9) may be enunciated thus: The sum of the sines of any two 
 angles is equal to twice the sine of half the sum of the angles multiplied by 
 the cosine 9f half their difference. These formulae enable us to transform 
 a sum or difference into a product. 
 
 The sum of the sines of two angles is to their difference as the tangent of 
 half the sum of those angles is to the tangent of half their difference. 
 
 sin A 4- sin B = 2 sin V 2 (A 4- B) cos V 2 (A -B) tan V 2 (A 4- B} 
 sin A - sin B 2 cos i/ 2 (A + B) sin i/ 2 (A - B) **" tan i/ 2 (A - B)' 
 
 The sum of the cosines of two angles is to their difference as the cotan- 
 gent.of half the sum of those angles is to the tangent of half their difference. 
 
 cos A 4- cos B = 2 cos l/ 2 (A 4- B} cos V 2 (A -B) = cot l/ 2 (A4-) [ ( . 
 cos B - cos A 2 sin 1/2 (A 4- B) sin 1/2 (A - B) tan i/ 2 (A - B) ' 
 
 The sine of the sum of two angles is to the sine of their difference as the 
 sum of the tangents of those angles is to the difference of the tangents. 
 
 sin (A 4- B) ^ tan A + tan B . 
 sin (A - ) tan A - tan B ' 
 
 (15) 
 
PLANE TRK 
 MnU+A) ! jj. 
 
 3ONOMET 
 
 tan (A-f 
 tan (A 
 cot (A + 
 cot (A 
 
 cos 2 A 
 cot 2A 
 
 cos 1/2 A 
 cot 1/2 A 
 
 BY. 69 
 
 . tan A -f tan 3 . 
 
 cos A cos 5 
 
 sin (A 5) 
 
 P tan A - tan B . 
 
 cosAcosl?" ^ *' 
 cos (A 4- B) itanJB- 
 
 1 + tan A tan ,6 * 
 
 cos A cos 5 
 cos (A J5) t 
 
 cot B + cot A ' 
 
 cos A cos 5 
 Functions of twice an angle: 
 
 sin' 2 A = 2 sin A cos A; 
 tin 01 2 tan A 
 
 cot B cot A 
 
 = cos 2 A sin 2 A ; 
 cot 2 A - 1 
 
 ~ 1 - tan 2 A * 
 Functions of half an angle: 
 
 2 cot A 
 
 . / 1 cos A 
 
 J 1 + cos A. 
 
 cm 1/2 A- -J. y 2 ; 
 
 !a *- L V 2 
 \/l 4- cos A 
 
 tin I/* 1 f i/ 1 ~ C S A - 
 
 1 4- cos A ' 
 
 V i cos A 
 
 
 For tables of Trigonometric Functions, see Mathematical Tables. 
 
 Solution of Plane Right-angled Triangles. 
 
 Let A and B be the two acute angles and C the right angle, and a, 6, and 
 c the sides opposite these angles, respectively, then we have 
 
 d " 
 
 1. sin A = cos B = ~ ; 3. tan A 
 
 2. cos A = sin 
 
 4. cot A = tan B 
 
 1. In any plane right-angled triangle the sine of either of the acute 
 angles is equal to the quotient of the opposite leg divided by the hypothe- 
 nuse. 
 
 2. The cosine of either of the acute angles is equal to the quotient of 
 the adjacent leg divided by the hypothenuse. 
 
 3. The tangent of either of the acute angles is equal to the quotient of 
 the opposite leg divided by .the adjacent leg. 
 
 4. The cotangent of either of the acute angles is equal to the quotient 
 of the adjacent Teg divided by the opposite leg. 
 
 5. The square of the hypothenuse equals the sum of the squares of the 
 other two sides. 
 
 Solution of Oblique-angled Triangles. 
 
 The following propositions are proved in works on plane trigonometry. 
 In any plane triangle 
 
 Theorem 1. The sines of the angles are proportional to the opposite 
 sides. 
 
 Theorem 2. The' sum of any two sides is to their difference as the tan- 
 gent of half the sum of the opposite angles is to the tangent of half their 
 difference. 
 
 Theorem 3. If from any angle of a triangle a perpendicular be drawn to 
 the opposite side or base, the whole base will be to the sum of the other 
 two sides as the difference of those two sides is to the difference of the 
 segments of the base. 
 
 CASE I. Given two angles and a side, to find the third angle and the 
 other two sides. 1. The third angle 180 sum of the two angles. 
 2. The sides may be found by tlie following proportion; 
 
70 ANALYTICAL GEOMETRY. 
 
 The sine of the angle opposite the given side is to the sine of the angle 
 opposite the required side as the given side is to the required side. 
 
 CASE II. Given two sides and an angle opposite one of them, to find 
 the third side and the remaining angles. 
 
 The side opposite the given angle is to the side opposite the required 
 angle as the sine of the given angle is to the sine of the required angle. 
 
 The third angle is found by subtracting the sum of the other two from 
 180, and the third side is found as in Case I. 
 
 CASE III. Given two sides and the included angle, to find the third 
 side and the remaining angles. 
 
 The sum of the required angles is found by subtracting the given angle 
 from 180. The difference of the required angles is then found by Theorem 
 II. Half the difference added to half the sum gives the greater angle, and 
 half the difference subtracted from half the sum gives the less angle. The 
 third side is then found by Theorem I. 
 
 Another method: 
 
 Given the sides c, 6, and the included angle A, to find the remaining side 
 a and the remaining angles B and C. 
 
 From either of the unknown angles, as B, draw a perpendicular Be to 
 the opposite side. 
 
 Then 
 
 Ae = c cos A, Be = c sin A, eC = b Ac Be * eC = tan C. 
 
 Or, in other words, solve Be, Ae and BeC as right-angled triangles. 
 
 CASE IV. Given the three sides, to find the angles. 
 
 Let fall a perpendicular upon the longest side from the opposite angle, 
 dividing the given triangle into two right-angled triangles. The two seg- 
 ments of the base may be found by Theorem III. There will then be 
 given the hypothenuse and one side of a right-angled triangle to find the 
 angles. 
 
 For areas of triangles, see Mensuration. 
 
 ANALYTICAL GEOMETRY. 
 
 Analytical geometry is that branch of Mathematics which has for its 
 object the determination of the forms and magnitudes of geometrical 
 magnitudes by means of analysis. 
 
 Ordinates and abscissas. In analytical geometry two intersecting 
 lines YY', XX' are used as coordinate axes, 
 XX' being the axis of abscissas or axis of X, 
 and YY' the axis of ordinates or axis of Y. 
 
 A, the intersection, is called the origin of co- /:; 7 
 
 ordinates. The distance of any point P / u / 
 
 from the axis of Y measured parallel to the / 
 
 axis of X is called the abscissa of the point, 
 as AD or CP, Fig. 72. Its distance from the 
 
 f 
 
 V' 
 
 axis of X, measured parallel to the axis of 
 
 Y, is called the ordinate, as AC or PD. 
 
 The abscissa and ordinate taken together 
 
 are called the coordinates of the point P. 
 
 The angle of intersection is usually taken as Y 
 
 a right angle, in which case the axes of X p IG 72 
 
 and Y are called rectangular coordinates. 
 
 The abscissa of a point is designated by the letter x and the ordinate 
 oy y. 
 
 The equations of a point are the equations which express the distances 
 of the point from the axis. Thus x = a, y = b are the equations of the 
 point P. 
 
 Equations referred to rectangular coordinates. The equation of 
 a line expresses the relation which exists between the coordinates of every 
 point of the line. 
 
 Equation of a straight line, y = ax b, in which a is the tangent of the 
 angle the line makes with the axis of -Y, and b the distance above A in 
 which the line cuts the axis of Y. 
 
 Every equation of the first degree between two variables is the equation 
 
ANALYTICAL GEOMETRY. 71 
 
 of a straight line, as Ay 4- Bx f C 0, which can be reduced to the form 
 y = o# 6. 
 
 Equation of the distance between two points: 
 
 D = vV' - z') 2 + (y" - I/O 2 , 
 
 in which x'y', x"y" are the coordinates of the two points. 
 Equation of a line passing through a given point: 
 
 y - y' = a(x - x'), 
 
 in which x'y' are the coordinates of the given point, a, the tangent of the 
 angle the line makes with the axis of x, being undetermined, since any 
 number of lines may be drawn through a given point. 
 Equation of a line passing through two given points: 
 
 
 Equation of a line parallel to a given line and through a given point: 
 
 y y' = a(x x'}. 
 Equation of an angle V included between two given lines: 
 
 a' a 
 
 in which a and a' are the tangents of the angles the lines make with the 
 axis of abscissas. 
 
 If the lines are at right angles to each other tang V = oo, and 
 
 1 + a'a = 0. 
 
 Equations of an intersection of two lines, whose equations are 
 y = ax f b, and y = a'x + &', 
 b - b' ab' - a'b 
 
 x - ~ ^r-rf* and y = T^5T 
 
 Equation of a perpendicular from a given point to a given line: 
 
 y - y' = - - (x* - x'). 
 Equation of the length of the perpendicular Pi 
 
 The circle. Equation of a circle, the origin of coordinates being at 
 the centre, and radius -= A': 
 
 x2 -f 2/2 = R*. 
 II the origin is at the left extremity of the diameter, on the axis of X: 
 
 y 2 = 2Rx - x 2 . 
 
 If the origin is at any point, and the coordinates of the centre are x'y' 
 (x - z') 2 + (y - 2/') 2 = # 2 . 
 
 Equation of a tangent to a circle, the coordinates of the point of tan- 
 gency being x"y" and the origin at the centre, 
 
 yy" + xx" = R 2 . 
 
 The ellipse. Equation of an ellipse, referred to rectangular coordi- 
 nates with axis at the centre: 
 
 AW + 2x2 = A*B\ 
 in which 4 is half tUe transverse axis and qajf the conjugate **fs. 
 
72 ANALYTICAL GEOMETRY. 
 
 Equation of the ellipse wiien the origin is at the vertex of the transverse 
 axis; 
 
 B 2 
 y* = ~j(2Ax - *'). 
 
 The eccentricity of an ellipse is the distance from the centre to either 
 focus, divided by the semi-transverse axis, or 
 
 The parameter of an ellipse is the double ordinate passing through the 
 focus. It is a third proportional to the transverse axis and its conjugate, 
 or 
 
 22 
 
 2 A : 2B :: 2B : parameter; or parameter = -^ 
 
 Any ordinate of a circle circumscribing an ellipse is to the corresponding 
 ordinate of the ellipse as the semi -trans verse axis to the semi-conjugate. 
 Any ordinate of a circle inscribed in an ellipse is to the corresponding 
 ordinate of the ellipse as the semi -conjugate axis to the semi-transverse. 
 
 Equation of the tangent to an ellipse, origin of axes at the centre: 
 
 A*yy" + B z xx" = A*B*. 
 
 y"x" being the coordinates of the point of tangency. 
 
 Equation of the normal, passing through the point of tangency, and 
 perpendicular to the tangent: 
 
 -v-s5?<*-*">- 
 
 The normal bisects the angle of the two lines drawn from the point of 
 tangency to the foci. 
 
 The lines drawn from the foci make equal angles with the tangent. 
 
 The parabola. Equation of the parabola referred to rectangular 
 coordinates, the origin being at the vertex of its axis, y 2 = 2px, in which 
 2p is the parameter or double ordinate through the focus. 
 
 The parameter is a third proportional to any abscissa and its correspond- 
 ing ordinate, or 
 
 x : y :: y : 2p. 
 
 Equation of the tangent: 
 
 yy" = p(x 
 
 y"x" being coordinates of the point of tangency. 
 Equation of the normal: 
 
 y - y" - - ~(x - x"). 
 
 The sub-normal, or projection of the normal on the axis, is constant, and 
 equal to half the parameter. 
 
 The tangent at any point makes equal angles with the axis and with the 
 line drawn from the pDint of tangency to the focus. 
 
 The hyperbola. Equation of the hyperbola referred to rectangular 
 coordinates, origin at the centre: 
 
 in which A is the semi-transverse axis and B the semi-conjugate axis. 
 Equation when the origin is at the right vertex of the transverse axis: 
 
 Conjugate and equilateral hyperbolas. If on the conjugate axis 
 

 DIFFERENTIAL CALCULUS. 73 
 
 as a transverse, and a focal distance equal to ^A 2 + B z , we construct 
 the two branches of a hyperbola, the two hyperbolas thus constructed are 
 called conjugate hyperbolas. If the transverse and conjugate axes are 
 equal, the hyperbolas are called equilateral, in which case y*-x 2 = -A* 
 when A is the transverse axis, and x 2 - ?/ 2 = B 2 when B is the trans- 
 
 The parameter of the transverse axis is a third proportional to the trans- 
 r erse axis and its conjugate. 
 
 2 A : 2B :: 2J5 : parameter. 
 
 The tangent to a hyperbola bisects the angle of the two lines drawn from 
 the point of tangency to the foci. 
 
 The asymptotes of a hyperbola are the diagonals of the rectangle 
 described on the axes, indefinitely produced in both directions. 
 
 The asymptotes continually approach the hyperbola, and become 
 tangent to it "at an infinite distance from the centre. 
 
 Equilateral hyperbola. In an equilateral hyperbola the asymptotes 
 make equal angles with the transverse axis, and are at right angles to each 
 other. With the asymptotes as axes, and P = ordinate, V abscissa, 
 py = a constant. This equation is that of the expansion of a perfect 
 gas, in which P = absolute pressure, V = volume. 
 
 Curveof Expansion of Gases. PV = a constant, or Pi Vi n =PzVz n , 
 in which Fi and 2 are the volumes at the pressures Pi and Pz. When 
 these are given, the exponent n may be found from the formula 
 
 . 
 
 1 
 
 log Pi - log Pz 
 
 log Vz log Vi 
 
 Conic sections, Every equation of the second degree between two 
 variables will represent either a circle, an ellipse, a parabola or a hyperbola. 
 These curves are those which are obtained by intersecting the surface of a 
 cone by planes, and for this reason they are called conic sections. 
 
 Logarithmic curve, A logarithmic curve is one in which one of the 
 coordinates of any point is the logarithm of the other. 
 
 The coordinate axis to which the lines denoting the logarithms are 
 parallel is called the axis of logarithms, and the other the axis of numbers. 
 If y is the axis of logarithms and x the axis of numbers, the equation of the 
 curve is y = log x. 
 
 If the base of a system of logarithms is a, we have a y = x, in which y is 
 the logarithm of x. 
 
 Each system of logarithms will give a different logarithmic curve. If 
 y ^ o, x = 1. Hence every logarithmic curve will intersect the axis of 
 numbers at a distance from the origin equal to 1. 
 
 DIFFERENTIAL CALCULUS. 
 
 The differential of a variable quantity is the difference between any two 
 of its consecutive values; hence it is indefinitely small. It is expressed by 
 writing d before the quantity, as dx, which is read differential of x. 
 
 The term ^ is called the differential coefficient of y regarded as a func- 
 tion of x. It is also called the first derived function or the derivative. 
 
 The differential of a function is equal .to its differential coefficient mul- 
 tiplied by the differential of the independent variable; thus, -^dx = dy. 
 
 The limit of a variable quantity is that value to which it continually 
 approaches, so as at last to differ from it by less than any assignable 
 quantity^ 
 
 The differential coefficient is the limit of the ratio of the increment of 
 the independent variable to the increment of the function. 
 
 The differential of a constant quantity is equal to 0. 
 
 The differential of a product of a constant by a variable is equal to the 
 constant multiplied by the differential of the variable. 
 
 If u = Av, du = A dv* 
 
74 DIFFERENTIAL CALCULUS. 
 
 In any curve whose equation is y = /(#), the differential coefficient 
 5T- = tan a; hence, the rate of increase of the function, or the ascension of 
 
 the curve at any point, is equal to the tangent of the angle which the 
 tangent line makes with the axis of abscissas. 
 
 All the operations of the Differential Calculus comprise but two objects: 
 
 1. To find the rate of change in a function when it passes from one state 
 of value to another, consecutive with it. 
 
 2. To find the actual change in the function: The rate of change is the 
 differential coefficient, and the actual change the differential. 
 
 Differentials of algebraic functions. The differential of the sum 
 or difference of any number of functions, dependent on the same variable, 
 is equal to the sum or difference of their differentials taken separately: 
 
 If u = y 4- z w, du dy + dz dw. 
 
 The differential of a product of two functions dependent on the same 
 variable is equal to the sum of the products of each by the differential of 
 the other: 
 
 _ 74. fj d(uv) _ du_ dv 
 uv u v 
 
 The differential of the product of any number ol functions is equal to 
 the sum of the products which arise by multiplying the differential of each 
 function by the product of all the others: 
 
 d(uts) tsdu + usdt + utds. 
 
 The differential of a fraction equals the denominator into the diffeiential 
 of the numerator minus the numerator into the differential of the denom- 
 inator, divided by the square of the denominator: 
 
 _ (tL\ v ^ u ~ u d v 
 
 If the denominator is constant, dv = 0, and dt 5- = 
 
 v v 
 
 If the numerator is constant, du = 0, and dt = -$ 
 
 The differential of the square root of a quantity is equal to the differen- 
 tial of the quantity divided by twice the square root of the quantity: 
 
 If v = it 1 / 2 ' or v - 
 
 2V u 
 
 2 
 
 The differential of any power of a function is equal to the exponent multi- 
 plied by the function raised to a powerless one, multiplied by the differen- 
 tial of the function, d(u n ) = nu n ~ l du. 
 
 Formulas for differentiating algebraic functions. 
 
 1. d (a) = 0. 
 
 2. d (ax) = a dx. 
 
 3. d (x + y) = dx + dy. 
 
 4. d (x y) = dx dy. 
 
 5. d (xy) = x dy + y dx. 
 
 To find the differential of the form u = (a + bx n ) m : 
 Multiply the exponent of the parenthesis into the exponent of the vari- 
 able within the parenthesis, into the coefficient of the variable, into the 
 
DIFFERENTIAL CALCULUS. 75 
 
 binomial raised to a power less 1 , into the variable within the parenthesis 
 raised to a power less 1, into the differential of the variable. 
 
 du = d(a + bx n ) m = mnb(a + bx n ) m ~ l x n ~ l dx. 
 
 To find the rate of change for a given value of the variable: 
 Find the differential coefficient, and substitute the value of the variable 
 in the second member of the equation. 
 
 EXAMPLE. If x is the side of a cube and u its volume, u = x 3 , -r- = 3x 2 . 
 
 Hence the rate of change in the volume is three times the square of the 
 edge. If the edge is denoted by 1, the rate of change is 3. 
 
 Application. The coefficient of expansion by heat of the volume of a 
 body is three times the linear coefficient of expansion. Thus if the side 
 of a cube expands 0.001 inch, its volume expands 0.003 cubic inch. 1.001 3 
 = 1.003003001. 
 
 A partial differential coefficient is the differential coefficient of a 
 function of two or more variables under the supposition that only one 
 of them has changed its value. 
 
 A partial differential is the differential of a function of two or more 
 variables under the supposition that only one of them has changed its 
 value. 
 
 The total differential of a function of any number of variables is equal 
 to the sum of the partial differentials. 
 
 If u = f (xy), the partial differentials are -r- dx, ~rdy. 
 
 ' 
 
 Integrals. An integral is a functional 'expression derived from a 
 differential. Integration is the operation of finding the primitive func- 
 tion from the differential function. It is indicated by the sign/i which is 
 
 read "the integral of." Thus fix dx = z 2 ; read, the integral of 2xdx 
 equals x 2 . 
 
 To integrate an expression of the form mx m ~ 1 dx or x m dx, add 1 to the 
 exponent of the variable, and divide by the new exponent and by the 
 
 differential of the variable: JZx^dx = a: 3 . (Applicable in all cases except 
 
 when m = 1. For Jx dx see formula 2, page 81.) 
 
 The integral of the product of a constant by the differential of a vari- 
 *)le is equal to the constant multiplied by the integral of the differential: 
 
 If u -= x* + y3 - z, du = - dx + dy + dz; = 2xdx + 3y* dy - dz. 
 
 fax dx = a f 
 
 x m dx = a 
 
 m + 1* 
 
 The integral of the algebraic sum of any number of differentials is 
 equal to the algebraic sum of their integrals: 
 
 du = 2ax z dx bydy z 2 dz; ( du= - 
 
 Since the differential of a constant is 0, a constant connected with a 
 variable by the sign + or disappears in the differentiation; thus 
 d(a -4- x m ) = dx m = mx m ~ l dx. Hence in integrating a differential 
 expression we must annex to the integral obtained a constant represented 
 by C to compensate for the term which may have been lost in differen- 
 tiation. Thus if we have dy = adx^fdy = afdx. Integrating, 
 
 y = ax C. 
 
76 DIFFERENTIAL CALCULUS. 
 
 The constant C, which is added to the first integral, must have such a 
 value as to render the functional equation true for every possible value 
 that may be attributed to the variable. Hence, after having found the 
 first integral equation and added the constant C, if we then make 
 the variable equal to zero, the value which the function assumes will be 
 the true value of C. 
 
 An indefinite integral is the first integral obtained before the value of 
 the constant C is determined. 
 
 A particular integral is the integral after the value of C has been found. 
 
 A definite integral is the integral corresponding to a given value of the 
 '-ariable. 
 
 Integration between limits. Having found the indefinite integral 
 and the particular integral, the next step is to find the definite integral 
 and then the definite integral between given limits of the variable. 
 
 The integral of a function, taken between two limits, indicated by given 
 values of x, is equal to the difference of the definite integrals correspond- 
 ing to those limits. The expression 
 
 X 
 
 X" 
 
 dy 
 
 is read: Integral of the differential of y, taken between the limits x f and 
 x"\ the least limit, or the limit corresponding to the subtractive integral, 
 being placed below. 
 
 Integrate du 9x z dx between the limits x = 1 and x = 3, u being equal 
 
 to 81 when x = 0. /du = /Qx z dx = 3x 3 -f C; C = 81 when x = 0, then 
 
 = 3 
 
 du = 3(3)3 + 8i > minus 3(1)3 + i = 73. 
 
 Integration of particular forms. 
 
 To integrate a differential of the form du = (a + bx n ) m x n l dx. 
 
 1. If there is a constant factor, place it without the sign of the integral, 
 and omit the power of the variable without the parenthesis and the differ- 
 ential ; 
 
 2. Augment the exponent of the parenthesis by 1, and then divide 
 this quantity, with the exponent so increased, by the exponent of the 
 parenthesis, into the exponent of the variable within the parenthesis, 
 into the coefficient of the variable. Whence 
 
 (wH-Dnd 
 
 The differential of an arc is the hypothenuse of a right-angle triangle of 
 which the base is dx and the perpendicular dy. 
 
 If 2 is an arc, dz = ^dx z + dy z z =J ^dx 2 + dy*. 
 
 Quadrature of a plane figure. 
 
 The differential of the area of a plane surface is equal to the ordmate int^ 
 the differential of the abscissa. 
 
 ds = y dx. 
 
 To apply the principle enunciated in the last equation, in finding the area 
 of any particular plane surface: 
 
 Find the value of y in terms of x, from the equation of the bounding line; 
 substitute this value in the differential equation, and then integrate 
 between the required limits of x. 
 
 Area of the parabola. Find the area of any portion of the com- 
 mon parabola whose equation is 
 
 y z = 2px; whence y = 
 
DIFFERENTIAL CALCULUS. 77 
 
 Substituting this value of y in the differential equation ds = y dx gives 
 
 If we estimate the area from the principal vertex, x = 0, y = 0, and 
 
 o 
 C = 0; and denoting the particular integral by s 7 , s' = ^ zi/. 
 
 o 
 
 That is, the area of any portion of the parabola, estimated from the 
 vertex, is equal to 2/3 of the rectangle of the abscissa and ordinate of the 
 extreme point. The curve is therefore quadrable. 
 
 Quadrature of surfaces of revolution. The differential of a surface 
 of revolution is equal to the circumference of a circle perpendicular to the 
 axis into the differential of the arc of the meridian curve. 
 
 ds = 
 
 in which y is the radius of a circle of the bounding surface in a i 
 pendicular to the axis of revolution, and r is the abscissa, or distance of 
 the plane from the origin of coordinate axes. 
 
 Therefore, to find the volume of any surface of revolution: 
 
 Find the value of y and dy from the equation of the meridian curve in 
 terms of x and dx, then substitute these values in the differential equation, 
 and integrate between the proper limits of x. 
 
 By application of this rule we may find: 
 
 The curved surface of a cylinder equals the product of the circum- 
 ference of the base into the altitude. 
 
 The convex surface of a cone equals the product of the circumference of 
 the base into half the slant height. 
 
 The surface of a sphere is equal to the area of four great circles, or equal 
 to the curved surface of the circumscribing cylinder. 
 
 Cubature of volumes of revolution. A volume of revolution is a 
 volume generated by the revolution of a plane figure about a fixed line 
 called the axis. 
 
 If we denote the volume by V, dV = xy 2 dx. 
 
 The area of a circle described by any ordinate y is ny 2 ; hence the differ- 
 ential of a volume of revolution is equal t9 the area of a circle perpendicular 
 to the axis into the differential of the axis. 
 
 The differential of a volume generated by the revolution of a plane 
 figure about the axis of Y is nx 2 dy. 
 
 To find the value of V for any given volume of revolution : 
 
 Find the value of y 2 in terms of x from the equation of the meridian 
 curve, substitute this value in the differential equation, and then integrate 
 between the required limits of x. 
 
 By application of this rule we may find: 
 
 The volume of a cylinder is equal to the area of the base multiplied 
 by the altitude. 
 
 The volume of a cone is equal to the area of the base into one third the 
 altitude. 
 
 The volume of a prolate spheroid and of an oblate spheroid (formed by 
 the revolution of an ellipse around its transverse and its conjugate axis 
 respectively) are each equal to two thirds of the circumscribing cylinder. 
 
 If the axes are equal, the spheroid becomes a sphere and its volume = 
 
 - nR z X D = - 7rZ> 3 ; R being radius and D diameter. 
 o o 
 
 The volume of a paraboloid is equal to half the cylinder having the same 
 base and altitude. 
 
 The volume of a pyramid equals the area of the base multiplied by one 
 third the altitude. 
 
 Second, third, etc., differentials. The differential coefficient being 
 a function of the independent variable, it may be differentiated, and we 
 thus obtain the second differential coefficient; 
 
78 DIFFERENTIAL CALCULUS 
 
 ^\ =- Dividing by dx t we have for the second differential 
 
 coefficient -r-^, which is read : second differential of u divided by the square 
 of the differential of x (or dx squared). 
 
 The third differential coefficient ^ is read: third differential of u 
 
 divided by dx cubed. 
 
 The differentials of the different orders are obtained by multiplying 
 the differential coefficient by the corresponding powers of dx; thus 
 
 ^ dx 3 = third differential of u. 
 dx 3 
 
 Sign of the first differential coefficient. If we have a curve 
 Artiose equation is y = fx, referred to rectangular coordinates, the curve 
 
 will recede from the axis of X when -~ is positive, and approach the 
 
 axis when it is negative, when the curve lies within the first angle of the 
 coordinate axes. For all angles and every relation of y and x the curve 
 will recede from the axis of X when the ordinate and first differential 
 coefficient have the same sign, and approach it .when they have different 
 signs. If the tangent of the curve becomes parallel to the axis of X at any 
 
 point ~- = 0. If the tangent becomes perpendicular to the axis of X at 
 
 any point ^| = oo. t 
 
 Sign of the second differential coefficient. The second differential 
 coefficient has the same sign as the ordinate when the curve is convex 
 toward the axis of abscissa and a contrary sign when it is concave. 
 
 Maclaurin's Theorem. For developing into a series any function 
 of a single variable as u = A + Bx + Cx z + Dx 3 + Ex*, etc., in which 
 A, B, C, etc., are independent of x: 
 
 In applying the formula, omit the expressions x = 0, although the 
 coefficients are always found under this hypothesis. 
 EXAMPLES: 
 
 (a + x) m = a m + ma m ~ l x + 
 
 . - i - 4 + 
 
 a + x a a 2 a 3 a 4 a n + 1 
 
 Taylor's Theorem. For developing into a series any function of the 
 sum or difference of two independent variables, as u' = j(x y): 
 
 in which u is what u' becomes when y 0, ~ is what becomes when 
 
 y 0, etc. 
 
 Maxima and minima. To find the maximum or minimum value 
 of a function of a single variable: 
 
 1. Find the first differential coefficient of the function, place it equal 
 to 0, and determine the roots of the equation. 
 
 2. Find the second differential coefficient, and substitute each real root, 
 
DIFFERENTIAL CALCULUS. 79 
 
 In succession, for the variable in the second member of the equation. 
 Each root which gives a negative result will correspond to a maximum 
 value of the function, and each which gives a positive result will corre- 
 spond to a minimum value. 
 
 EXAMPLE. To find the value of x which will render the function y a 
 maximum or minimum in the equation of the circle, y 2 + x 2 = R 2 ; 
 
 f| - - y; making - jj ~ gives x - 0. 
 
 The second differential coefficient is: ~ = - x + 3 y * 
 
 When x 0, y R; hence -^ = - ^ which being negative, y is a 
 
 maximum for R positive. 
 
 In applying the rule to practical examples we first find an expression for 
 the function which is to be made a maximum or minimum. 
 
 2. If in such expression a constant quantity is found as a factor, it may 
 be omitted in the operation; for the product will be a maximum or a mini- 
 mum when the variable factor is a maximum or a minimum. 
 
 3. Any value 9f the independent variable which renders a function a 
 maximum or a minimum will render any power or root of that function a 
 maximum or minimum; hence we may square both members of an equa- 
 tion to free it of radicals before differentiating. 
 
 By these rules we may find : 
 
 The maximum rectangle which can be inscribed in a triangle is one 
 whose altitude is half the altitude of the triangle. 
 
 The altitude of the maximum cylinder which can be inscribed in a cone 
 is one third the altitude of the cone. 
 
 'The surface of a cylindrical vessel of a given volume, open at the top, 
 is a minimum when the altitude equals half the diameter. 
 
 The altitude of a cylinder inscribed in a sphere when its convex surface is 
 a maximum is r v^2. r = radius. 
 
 The altitude of a cylinder inscribed in a sphere when the volume is a 
 maximum is 2r * Vs. 
 
 Maxima and Minima without the Calculus. In the equation 
 y = a : 4- bx + ex 2 , in which a, &, and c are constants, either positive or 
 negative, if c be positive y is a minimum when x = b -*- 2c; if c be 
 negative y is a maximum when x = b * 2c. In the equation y = a + 
 bx +c/x, y is a, minimum when bx = c/x. 
 
 APPLICATION. The cost of electrical transmission is made up (1) of 
 fixed charges, such as superintendence, repairs, cost of poles, etc., which 
 may be represented by a; (2) of interest on cost of the wire, which varies 
 with the sectional area, and may be represented by bx; and (3) of cost of 
 the energy wasted in transmission, which varies inversely with the area 
 of the wire, or c/x. The total cost, y = a 4- bx + c/x, is a minimum 
 when item 2 = item 3, or bx = c/x. 
 
 Differential of an exponential function. 
 
 If u = a x . . . (1) 
 
 then du = da x = a x kdx (2) 
 
 in which k is a constant dependent on a. 
 
 The relation bet ween a and k is o* = e; whence a = e* .... (3) 
 in which e = 2.7182818 . . . the base of the Naperian system of loga- 
 rithms. 
 
 Logarithms. The logarithms in the Naperian system are denoted by 
 I, Nap. log or hyperbolic log, hyp. log, or log e ; and in the common system 
 Iways by log. 
 
 fc Nap. logo; log a = k log e (4) 
 
 
80 DIFFERENTIAL CALCULUS. 
 
 The common logarithm of e, = log 2.7182818 . . . * 0.4342945 . . . ; 
 Is called the modulus of the common system, and is denoted by Af. 
 Hence, if we have the Naperian logarithm of a number we can find the 
 common logarithm of the same number by multiplying by the modulus. 
 Reciprocally, Nap. log = com. log X 2.3025851. 
 
 If in equation (4) we make a = 10, we have 
 
 1 = k log e, or ? = log e = M . 
 
 That is, the modulus of the common system is equal to 1, divided by the 
 Naperian logarithm of the common base. 
 From equation (2) we have 
 
 du da x 
 * - kdx. 
 u a x 
 
 If we make a = 10, the base of the common system, x = log u, and 
 
 j /i j du 1 du ^ f 
 
 d (log u) - dx = ~ X - - X M. 
 
 That is, the differential of a common logarithm of a quantity is equal to 
 the differential of the quantity divided by the quantity, into the modulus. 
 If we make a = e, the base of the Naperian system, x becomes the Nape- 
 rian logarithm of u, and k becomes 1 (see equation (3)); hence M = 1, 
 and 
 
 du du 
 
 d (Nap. log u) = dx - ; = 
 a x u 
 
 That is, the differential of a Naperian logarithm of a quantity is equal to 
 the differential of the quantity divided by the quantity; and in the 
 Naperian system the modulus is 1. 
 
 Since k is the Naperian logarithm of a, du = a x I a dx. That is, the 
 differential of a function of the form a x is equal to the function, into the 
 Naperian logarithm of the base .a, into the differential of the exponent. 
 
 If we have a differential in a fractional form, in which the numerator is 
 the differential of the denominator, the integral is the Naperian logarithm 
 of the denominator. Integrals of fractional differentials of other forms 
 are given below: 
 
 Differential forms which have known integrals; exponential 
 functions. (I = Nap. log.) 
 
 + C; 
 
 4. 
 
 6. I , "^ - l(x a + Vx*~ 2ax) + C; 
 
CALCULUS. 
 
 81. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 2a cte 
 
 -j 
 
 f |^ 
 
 J x \/a* + x* 
 
 2a<ta = l la - Va 2 - x~A + C; 
 a 2 - a: 2 \ a + ^a 2 - z 2 / 
 
 r *~ 2 ^ = _ z fi + vi + os\ [ c 
 
 x -{- x * 
 
 Circular functions. Let z denote an arc in the first quadrant, y its 
 sine, x its cosine, y its versed sine, and t its tangent; and the following nota- 
 tion be employed to designate an arc by any one of its functions, viz., 
 
 sin" 1 y denotes an arc of which y is the sine, 
 cos" 1 ^ " " " " " x is the cosine, 
 tan"^ " " " " " Ms the tangent, 
 
 (read "arc whose sine is ?/," etc.), we have the following differential 
 forms which have known integrals (r = radius): 
 
 | cos zdz = sin z+ C\ 
 I sin z dz = cos z + C\ 
 
 sin z dz = versin z + (7; 
 
 The cycloid. If a circle be rolled along a straight line, any point of 
 the circumference, as P, will describe a curve which is called a cycloid. 
 The circle is called the generating circle, and P the generating point. 
 
SLIDE 
 
 The transcendental equation of the cycloid is 
 
 x = versin ~i v 
 
 and the differential equation is dx = 
 
 The area of the cycloid is equal to three times the 
 area of the generating circle. 
 
 The surface described by the arc of a cycloid when 
 revolved about its base is equal to 64 thirds of the 
 generating circle. 
 
 The volume of the solid generated by revolving 
 a cycloid about its base is equal to five eighths of the 
 circumscribing cylinder. 
 
 Integral calculus. In the integral calculus we 
 have to return from the differential to the function 
 from which it was derived. A number of differential 
 expressions are given above, each of which has a 
 known integral corresponding to it, which, being 
 differentiated, will produce the given differential. 
 
 In all classes of functions any differential expression 
 may be integrated when it is reduced to one of the 
 known forms; and the operations of the integral cal- 
 culus consist mainly in making such transformations 
 of given differential expressions as shall reduce them 
 to equivalent ones whose integrals are known. 
 
 For methods of making these transformations 
 reference must be made to the text-books on differen- 
 tial and integral calculus. 
 
 THE SLIDE RULE. 
 
 The slide rule is based on the principles that the 
 addition of logarithms multiplies the numbers which 
 they represent, and subtracting logarithms divides 
 the numbers. By its use the operations of multiplica- 
 tion, division, the finding of powers and the extraction 
 of roots, may be performed rapidly and with an ap- 
 proximation to accuracy which is sufficient for many 
 purposes. With a good 10-inch Mannheim rule the 
 results obtained are usually accurate to 1/4 of 1 per 
 cent. Much greater accuracy is obtained with cylin- 
 drical rules like the Thacher. 
 
 The rule (see Fig. 73) consists of a fixed and a 
 sliding part both of which are ruled with logarithmic 
 scales; that is, with consecutive divisions spaced not 
 equally, as in an ordinary scale, but in proportion 
 to the logarithms of a series of numbers from 1 to 
 10. By moving the slide to the right or left the loga- 
 rithms are added or subtracted, and multiplication 
 or division of the numbers thereby effected. The 
 scales on the fixed part of the rule are known as the 
 A and D scales, and those on the slide as the B and 
 C scales. A and B are the upper and C and D 
 are the lower scales. The A and B scales are each 
 divided into two, left hand and right hand, each 
 being a reproduction, one half the size, of the C and 
 D scales. A "runner," which consists of a framed 
 glass plate with a fine vertical line on it, is used to 
 facilitate some of the operations. The numbering on 
 each scale begins with the figure 1, which is called 
 
 FIG. 73. 
 
THE SLIDE RULE. 83 
 
 the "index" of the scale. In using the scale the figures 1, 2, 3, etc., are 
 to be taken either as representing these numbers, or as 10, 20, 30, etc., 
 100, 200, 300, etc., 0.1, 0.2, 0.3, etc., that is, the numbers multiplied or 
 divided by 10, 100, etc., as may be most convenient for the solution of a 
 given problem. 
 
 The following examples will give an idea of the method of using the 
 glide rule,, 
 
 Proportion. Set the first term of a proportion on the C scale opposite 
 the second term on the D scale, then opposite the third term on the C 
 scale read the fourth term on the D scale. 
 
 EXAMPLE, Find the fourth term in the proportion 12 : 21 :: 30 : x. 
 Move the slide to the right until 12 on C coincides with 21 on Z), then 
 opposite 30 on C read x on D = 52.5. The A and B scales may be used 
 instead of C and D. 
 
 Multiplication. Set the index or figure 1 of the C scale to one of the 
 factors on ZX 
 
 EXAMPLE. 25 X 3. Move the slide to the right until the left index 
 of C coincides with 25 on the D scale. Under 3 on the C scale will be 
 found the product on the Z) scale, = 75. 
 
 Division, Place the divisor on C opposite the dividend on D, and the 
 quotient will be found on D under the index of C. 
 
 EXAMPLE. 750 *- 25. Move the slide to the right until 25 on C coin- 
 cides with 750 on D. Under the left index of C is found the quotient on 
 D, = 30. 
 
 Combined Multiplication and Division. Arrange the factors to be 
 multiplied and divided in the form of a fraction with one more factor in 
 the numerator than in the denominator, supplying the factor 1 if necessary. 
 Then perform alternate division and multiplication, using the runner to 
 Indicate the several partial results. 
 
 4X5X8 
 EXAMPLE^ 3 .. g = 8.9 nearly. Set 3 on C over 4 on D, set 
 
 O X O 
 
 runner to 5 on C, then set 6 on C under the runner, and read under 8 on 
 C the result 8*9 - on D. 
 
 Involution and Evolution. The numbers on scales A and B are the 
 squares of their coinciding numbers on the scales C and D, and also the 
 numbers on scales C and D are the square roots of their coinciding num- 
 bers on scales A and B. 
 
 EXAMPLE, 4 2 = 16. Set the runner over 4 on scale D and read 16 
 on A.__ 
 
 ^16 = 4. Set the runner over 16 on A and read 4 on D. 
 
 In extracting square roots, if the number of digits is odd, take the num- 
 ber on the left-hand scale of A ; if the number of digits is even, take the 
 number on the right-hand scale of A. 
 
 To cube a number perform the operations of squaring and multiplica- 
 tion. 
 
 EXAMPLEO 2 s = 8. Set the index of C over 2 on D, and above 2 
 on B read the result 8 on A 
 
 Extraction of the Cube Root. Set the runner over the number on A, 
 then move the slide until there is found under the runner on B, the same 
 number which is found under the index of C on D; this number is the 
 cube root desired. 
 
 EXAMPLE ^8=2. Set the runner over 8 on A, move the slide 
 along until the same number appears under the runner on B and under 
 the index of C on D; this will be the number 2. 
 
 Trigonometrical Computations. On the under side of the slide (which 
 is reversible) are placed three scales, a scale of natural sines marked S t 
 a scale of natural tangents marked T, and between these a scale of equal 
 parts. To use these scales, reverse the slide, bringing its under side to 
 the top. Coinciding with an angle on S its sine will be found on A t and 
 coinciding with an angle on T will be found the tangent on D. Sines and 
 tangents can be multiplied or divided like numbers. 
 
84 LOGARITHMIC RULED PAPER* 
 
 LOGARITHMIC RULED PAPER. 
 
 W. F. Durand (Eng. News, Sept. 28, 1893.) 
 
 As plotted on ordinary cross-section paper the lines which express 
 relations between two variables are usually curved, and must be plotted 
 point by point from a table previously computed. It is only where the 
 exponents involved in the relationship are unity that the line becomes 
 straight and may be drawn immediately on the determination of two of 
 its points. It is the peculiar property of logarithmic section paper that 
 for all relationships which involve multiplication, division, raising to 
 powers, or extraction of roots, the lines representing them are straight. 
 Any such relationship may be represented by an equation of the form: 
 y = Bx n . Taking logarithms we have: log y = log B 4- n log x. 
 
 Logarithmic section paper is a short and ready means of plotting such 
 logarithmic equations. The scales on each side are logarithmic instead 
 of uniform, as in ordinary cross-section paper. The numbers and divi- 
 sions marked are placed at such points that their distances from the origin 
 are proportional to the logarithms of such numbers instead of to the 
 numbers themselves. If we take any point, as 3, for example, on such a 
 scale, the real distance we are dealing with is log 3 to some particular 
 base, and not 3 itself. The number at the origin 9f such a scale is always 
 1 and not 0, because 1 is the number whose logarithm is 0. This 1 may, 
 however, represent a unit of any order, so that quantities of any size 
 whatever may be dealt with. 
 
 If we have a series of values of x and of Bx , and plot on logarithmic 
 section paper x horizontally and Bx n vertically, the actual distances 
 Involved will be log x and log (Bx n ), or log B + n log x. But these dis- 
 tances will give a straight line as the locus. Hence all relationships 
 expressible in this form are represented on logarithmic section paper by 
 straight lines. It follows that the entire locus may be determined from 
 any two points; that is, from any two values of Bx n \ or, again, by any one 
 point and the angle of inclination; that is, by one value of Bx n and the 
 value of ft, remembering that n is the tangent of the angle of inclination 
 to the horizontal. 
 
 A single square plotted on each edge with a logarithmic scale from 1 
 fco 10 may be made to serve for any number whatever from to oo. Thus 
 to express graphically the locus of the equation: y = rr s /2. Let Fig. 74 
 denote a square cross-sectioned with logarithmic scales, as described. 
 Suppose that there were joined to it and to each other on the right and 
 above, an indefinite series of such squares similarly divided. Then, con- 
 sidering, in passing from one square to an adjacent one to the right or 
 above, that the unit becomes of next higher order, such a series of squares 
 would, with the proper variation of the unit, represent all values of either 
 x or y between and oo, 
 
 Suppose the original square divided on the horizontal edge into 3 parts, 
 and on the vertical edge into 2 parts, the points of division being at A, 
 B, D, F, G, I. Then lines joining these points, as shown, will be at an 
 inclination to the horizontal whose tangent is 3/ 2 . Now, beginning at 0, 
 OF will give the value of a^/2 for values of x from 1 to that denoted by HF, 
 or OB, or about 4.6. For greater values of x the line would run into the 
 adjacent square above, but the location of this line, if continued, would 
 be exactly similar to that of BD in the square before us. Therefore the 
 line BD will give values of :r 3 /2 for x between B and C, or 4.6 and 10, the 
 corresponding values of y being of the order of tens, and ranging from 10 
 to 31.3. For larger values of x the unit of x is of the higher order, and 
 we run into an adjacent square to the right without change of unit for y. 
 In this square we should traverse a line similar to IG. Therefore, by a 
 proper choice of units we may make use of IG for the determination of 
 values of 3 /2 where x lies between 10 and the value at G, or about 21.5. 
 We should then run into an adjacent square above, requiring the unit on 
 y to be of the next higher order, and traverse a line similar to AE t which 
 
takes us finall 
 
 LOGARITHMIC RULED PAPER. 
 
 85 
 
 takes us finally to the opposite corner and completes the cycle. Follow- 
 ing this, the same series of lines would result for numbers of succeeding 
 orders. 
 
 The value of x 3 /2 for any value of x between 1 and oo may thus be read 
 from one or another of these lines, and likewise for any value between 
 and 1. The location of the decimal point is readily found by a little 
 attention to the numbers involved. The limiting values of x for any 
 given line may be marked on it, thus enabling a proper choice to be readily 
 made. Thus, in Fig. 74 we mark OF as - 4.6, BD as 4.6 - 10, 1G as 
 
 O p 
 
 10 21.5, and A E as 21.5 100. If values of x less than 1 are to be 
 dealt with, AE will serve for values of x between 1 and 0.215, IG for 
 values between 0.215 and 0.1, BD for values between 0.1 and 0.046, and 
 OF for values between 0.046 and 0.001. 
 
 The principles involved in this case may be readily extended to any 
 other, and in general if the exponent be represented by m/n, the complete 
 set of lines may be drawn by dividing one side of the square into m and 
 the other into n parts, and joining the points of division as in Fig. 74. In 
 all there will be (m -f n 1) lines, and opposite t9 any point on X there 
 will be n lines corresponding to the n different beginnings of the nth root 
 
86 MATHEMATICAL TABLES. 
 
 of the mth power, while opposite to any point on Y will be m lines corre- 
 sponding to the different beginnings of the mth root of the nth power. 
 Where the complete number of lines would be quite large, it is usually 
 unnecessary to draw them all, and the number may be limited to those 
 necessary to cover the needed range in the values of x. 
 
 If, instead of the equation y = x n t we have a constant term as a multi- 
 plier, giving an equation in the more general form y = Bx n , or Bx m/n, 
 there will be the same number of lines and at the same inclination, but 
 all shifted vertically through a distance equal to log B. If, therefore, 
 we start on the axis of Y at the point B, we may draw in the same series 
 of lines and in a similar manner. In this way PQ represents the locus 
 giving the values of the areas of circles in terms of their diameters, being 
 the locus of the equation A = 1/4 d 2 or y = 1/4"' 2 - 
 
 If in any case we have x in the denominator such that the equation is 
 in the form y = B/x n , this is equal to y = Bx~ n . and the same general 
 rules hold. The lines in such case slant downward to the right instead of 
 upward. Logarithmic ruled paper, with directions for the use, may be 
 obtained from Keuffel & Esser Co., 127 Fulton St., New York. 
 
 MATHEMATICAL TABLES. 
 
 Formula for Interpolation. 
 
 (n-1) (n-2) ^ , (n-1) (n-2) (n-3) 
 - -- - ^ - 
 
 (n 
 
 
 
 ai = the first term of the series; n, number of the required term; a n , the 
 required term; di, dz, d 3 , first terms of successive orders of differences 
 between ai, a2, a 3 , a 4 , successive terms. 
 
 EXAMPLE. Required the log of 40.7, logs of 40, 41 , 42, 43 being given as 
 below. 
 
 Terms a lt a 2 , as, a 4( : 1.6021 1.6128 1.6232 1.6335 
 
 1st differences: 0.0107 0.0104 0.0103 
 2d - 0.0003 - 0.0001 
 
 3d + 0.0002 
 
 For log. 40, n = 1; log 41, n= 2; for log 40.7, n 1.7; n 1 = 0.7: n 2 
 = - 0.3; n - 3 =- 1.3. 
 
 a n =1.6021+0.7 (0.0107) + (0.7)(-0.3K-0.0003) + (0.7)(-0.3)(- 1.3)(0.0002!| 
 = 1.6021 4- 0.00749 + 0.000031 4- 0.000009 = 1.6096 +. 
 
RECIPROCALS OF NUMBERS. 
 
 RECIPROCALS OF NUMBERS. 
 
 87 
 
 No. 
 
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 cal. 
 
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 cal. 
 
 No. 
 
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 cal. 
 
 No. 
 
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 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 1 
 
 1.00000000 
 
 64 
 
 01562500 
 
 127 
 
 00787402 
 
 190 
 
 .00526316 
 
 253 
 
 .00395257 
 
 2 
 
 .50000000 
 
 5 
 
 01538461 
 
 8 
 
 00781250 
 
 1 
 
 .C0523560 
 
 4 
 
 .00393701 
 
 3 
 
 .33333333 
 
 6 
 
 01515151 
 
 9 
 
 00775194 
 
 2 
 
 .00520833 
 
 5 
 
 .00392157 
 
 4 
 
 .25000000 
 
 7 
 
 01492537 
 
 130 
 
 00769231 
 
 3 
 
 .00518135 
 
 6 
 
 .00390625 
 
 5 
 
 .20000000 
 
 8 
 
 01470588 
 
 1 
 
 00763359 
 
 4 
 
 .00515464 
 
 7 
 
 .00389105 
 
 6 
 
 .16666667 
 
 9 
 
 01449275 
 
 2 
 
 00757576 
 
 5 
 
 .00512820 
 
 8 
 
 .0038/597 
 
 7 
 
 .14285714 
 
 70 
 
 01428571 
 
 3 
 
 00751880 
 
 6 
 
 .00510204 
 
 9 
 
 .00386100 
 
 8 
 
 .12500COO 
 
 1 
 
 01408451 
 
 4 
 
 00746269 
 
 7 
 
 .00507614 
 
 260 
 
 .00384615 
 
 9 
 
 11111111 
 
 2 
 
 01388889 
 
 5 
 
 00740741 
 
 8 
 
 .00505051 
 
 1 
 
 .00383142 
 
 10 
 
 '.10000000 
 
 3 
 
 01369863 
 
 6 
 
 00735294 
 
 9 
 
 .00502513 
 
 2 
 
 .00381679 
 
 11 
 
 .09090909 
 
 4 
 
 01351351 
 
 7 
 
 -00729927 
 
 200 
 
 .00500000 
 
 3 
 
 .00380228 
 
 12 
 
 .08333333 
 
 5 
 
 01333333 
 
 8 
 
 -00724638 
 
 1 
 
 .00497512 
 
 4 
 
 .00378786 
 
 13 
 
 .07692308 
 
 6 
 
 01315789 
 
 9 
 
 -00719424 
 
 2 
 
 .00495049 
 
 5 
 
 .00377358 
 
 14 
 
 .07142857 
 
 7 
 
 01298701 
 
 140 
 
 00714286 
 
 3 
 
 .0049261 1 
 
 6 
 
 .00375940 
 
 15 
 
 .06666667 
 
 8 
 
 01282051 
 
 1 
 
 00709220 
 
 4 
 
 .004901% 
 
 7 
 
 .00374532 
 
 16 
 
 .06250000 
 
 9 
 
 01265823 
 
 2 
 
 00704225 
 
 5 
 
 .00487805 
 
 8 
 
 .00373134 
 
 17 
 
 .05882353 
 
 80 
 
 01250000 
 
 3 
 
 -00699301 
 
 6 
 
 .00485437 
 
 9 
 
 .00371747 
 
 18 
 
 .05555556 
 
 1 
 
 01234568 
 
 4 
 
 00694444 
 
 7 
 
 .00483092 
 
 270 
 
 .00370370 
 
 19 
 
 .05263158 
 
 2 
 
 01219512 
 
 5 
 
 .00689655 
 
 8 
 
 .00480769 
 
 1 
 
 .00369004 
 
 20 
 
 .05000000 
 
 3 
 
 01204819 
 
 6 
 
 .00684931 
 
 9 
 
 .00478469 
 
 2 
 
 .00367647 
 
 
 .04761905 
 
 4 
 
 01190476 
 
 7 
 
 .00680272 
 
 210 
 
 .00476190 
 
 3 
 
 .00366300 
 
 ^ 
 
 .04545455 
 
 
 
 01176471 
 
 8 
 
 .00675676 
 
 11 
 
 .00473934 
 
 4 
 
 .00364%3 
 
 2 
 
 .04347826 
 
 e 
 
 01 162791 
 
 9 
 
 -00671141 
 
 12 
 
 .00471698 
 
 5 
 
 .00363636 
 
 4 
 
 .04166667 
 
 7 
 
 01149425 
 
 150 
 
 -00666667 
 
 13 
 
 .00469484 
 
 6 
 
 .00362319 
 
 c 
 
 .04000000 
 
 8 
 
 01136364 
 
 1 
 
 .00662252 
 
 14 
 
 .00467290 
 
 7 
 
 .00361011 
 
 6 
 
 .03846154 
 
 9 
 
 01 123595 
 
 2 
 
 .00657895 
 
 15 
 
 .00465116 
 
 8 
 
 .00359712 
 
 T 
 
 .03703704 
 
 90 
 
 01111111 
 
 3 
 
 .00653595 
 
 16 
 
 .00462963 
 
 9 
 
 .00358423 
 
 8 
 
 .03571429 
 
 1 
 
 01098901 
 
 4 
 
 .00649351 
 
 17 
 
 .00460829 
 
 280 
 
 .00357143 
 
 g 
 
 .03448276 
 
 2 
 
 010S6956 
 
 5 
 
 .00645161 
 
 18 
 
 .00458716 
 
 1 
 
 .00355872 
 
 30 
 
 .03333333 
 
 3 
 
 01075269 
 
 6 
 
 .00641026 
 
 19 
 
 .00456621 
 
 2 
 
 .00354610 
 
 
 .03225806 
 
 4 
 
 01063830 
 
 7 
 
 .00636943 
 
 220 
 
 .00454545 
 
 3 
 
 .00353357 
 
 j 
 
 .03125000 
 
 c 
 
 01052632 
 
 8 
 
 .0063291 1 
 
 | 
 
 .00452489 
 
 4 
 
 .00352113 
 
 
 
 .03030303 
 
 6 
 
 01041667 
 
 9 
 
 .00628931 
 
 2 
 
 .00450450 
 
 5 
 
 .00350877 
 
 4 
 
 .02941176 
 
 7 
 
 01030928 
 
 160 
 
 .00625000 
 
 3 
 
 .00448430 
 
 6 
 
 .0034%50 
 
 
 
 .02857143 
 
 8 
 
 01020408 
 
 1 
 
 .00621118 
 
 4 
 
 .00446429 
 
 7 
 
 .00348432 
 
 6 
 
 .027/7778 
 
 9 
 
 01010101 
 
 2 
 
 .00617284 
 
 5 
 
 .00444444 
 
 8 
 
 .00347222 
 
 j 
 
 .02702703 
 
 100 
 
 01000000 
 
 3 
 
 .00613497 
 
 6 
 
 .00442478 
 
 9 
 
 .00346021 
 
 8 
 
 .02631579 
 
 1 
 
 00990099 
 
 4 
 
 .00609756 
 
 7 
 
 .00440529 
 
 290 
 
 .00344828 
 
 g 
 
 .02564103 
 
 2 
 
 00980392 
 
 5 
 
 .00606061 
 
 8 
 
 .004385% 
 
 1 
 
 .00343643 
 
 40 
 
 .02500000 
 
 2 
 
 00970874 
 
 6 
 
 .00602410 
 
 9 
 
 .00436681 
 
 2 
 
 .00342466 
 
 | 
 
 .02439024 
 
 A 
 
 00% 1538 
 
 7 
 
 .00598802 
 
 230 
 
 .00434783 
 
 3 
 
 .00341297 
 
 ' 4 
 
 .02380952 
 
 c 
 
 00952381 
 
 8 
 
 .00595238 
 
 1 
 
 .00432900 
 
 4 
 
 .00340136 
 
 \ 
 
 .02325581 
 
 t 
 
 009433% 
 
 9 
 
 00591716 
 
 2 
 
 .00431034 
 
 5 
 
 .00338983 
 
 t 
 
 .02272727 
 
 7 
 
 .00934579 
 
 170 
 
 .00588235 
 
 3 
 
 .00429184 
 
 6 
 
 .00337838 
 
 i 
 
 02222222 
 
 8 
 
 -00925926 
 
 1 
 
 .00584795 
 
 4 
 
 .00427350 
 
 7 
 
 .00336700 
 
 6 
 
 .02173913 
 
 9 
 
 .00917431 
 
 2 
 
 .00581395 
 
 5 
 
 .00425532 
 
 8 
 
 .00335570 
 
 7 
 
 .02127660 
 
 110 
 
 .00909091 
 
 3 
 
 .00578035 
 
 6 
 
 .00423729 
 
 9 
 
 00334448 
 
 8 
 
 .02083333 
 
 11 
 
 .00900901 
 
 4 
 
 .00574713 
 
 7 
 
 .00421941 
 
 300 
 
 .00333333 
 
 c 
 
 .02040816 
 
 12 
 
 .00892857 
 
 5 
 
 .00571429 
 
 8 
 
 .00420168 
 
 
 .00332226 
 
 50 
 
 .02000000 
 
 13 
 
 .00884956 
 
 6 
 
 .00568182 
 
 9 
 
 .00418410 
 
 2 
 
 .00331126 
 
 1 
 
 .01960784 
 
 14 
 
 .00877193 
 
 7 
 
 .00564972 
 
 240 
 
 .00416667 
 
 3 
 
 .00330033 
 
 j 
 
 .01923077 
 
 15 
 
 .00869565 
 
 8 
 
 .00561798 
 
 1 
 
 .00414938 
 
 4 
 
 .00328947 
 
 - 
 
 .01886792 
 
 16 
 
 .00862069 
 
 9 
 
 .00558659 
 
 2 
 
 .00413223 
 
 5 
 
 .00327869 
 
 / 
 
 .01851852 
 
 17 
 
 .00854701 
 
 180 
 
 .00555556 
 
 3 
 
 .00411523 
 
 6 
 
 .00326797 
 
 c 
 
 .01818182 
 
 18 
 
 .00847458 
 
 1 
 
 .00552486 
 
 4 
 
 .00409836 
 
 7 
 
 .00325733 
 
 ( 
 
 .01785714 
 
 19 
 
 .00840336 
 
 2 
 
 .00549451 
 
 5 
 
 .00408163 
 
 8 
 
 .00324675 
 
 7 
 
 .01754386 
 
 120 
 
 .00833333 
 
 3 
 
 .00546448 
 
 6 
 
 .00406504 
 
 9 
 
 .00323625 
 
 8 
 
 .01724138 
 
 1 
 
 .00826446 
 
 4 
 
 .00543478 
 
 7 
 
 .00404858 
 
 310 
 
 .00322581 
 
 9 
 
 .01694915 
 
 2 
 
 .00819672 
 
 5 
 
 .00540540 
 
 8 
 
 .00403226 
 
 11 
 
 .00321543 
 
 60 
 
 .01666667 
 
 3 
 
 .00813008 
 
 6 
 
 .00537634 
 
 9 
 
 .00401606 
 
 12 
 
 .00320513 
 
 1 
 
 .01639344 
 
 4 
 
 .00806452 
 
 7 
 
 .00534759 
 
 250 
 
 .00400000 
 
 -13 
 
 .00319489 
 
 2 
 
 .01612903 
 
 5 
 
 .00800000 
 
 8 
 
 .00531914 
 
 1 
 
 .00398406 
 
 14 
 
 .00318471 
 
 3 
 
 .01587302 
 
 6 
 
 .00793651 
 
 9 
 
 .00529100 
 
 Z 
 
 .00396825 
 
 15 
 
 .00317460 
 
88 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 ~ 316 
 
 .00316456 
 
 381 
 
 .00262467 
 
 446 
 
 .00224215 
 
 511 
 
 .00195695 
 
 576 
 
 .00173611 
 
 17 
 
 .00315457 
 
 2 
 
 .00261780 
 
 7 
 
 .00223714 
 
 12 
 
 .00195312 
 
 7 
 
 .00173310 
 
 18 
 
 .00314465 
 
 3 
 
 .00261097 
 
 8 
 
 .00223214 
 
 13 
 
 .00194932 
 
 8 
 
 .00173010 
 
 19 
 
 .00313480 
 
 4 
 
 .00260417 
 
 9 
 
 .00222717 
 
 14 
 
 .00194552 
 
 9 
 
 .00172712 
 
 320 
 
 .00312500 
 
 5 
 
 .00259740 
 
 450 
 
 .00222222 
 
 15 
 
 .00194175 
 
 580 
 
 .00172414 
 
 1 
 
 .00311526 
 
 6 
 
 .00259067 
 
 1 
 
 .00221729 
 
 16 
 
 .00193798 
 
 1 
 
 .00172117 
 
 2 
 
 .00310559 
 
 7 
 
 .00258398 
 
 2 
 
 .00221239 
 
 17 
 
 .00193424 
 
 2 
 
 .00171821 
 
 3 
 
 .00309597 
 
 8 
 
 .00257732 
 
 3 
 
 .00220751 
 
 18 
 
 .00193050 
 
 3 
 
 .00171527 
 
 4 
 
 .00308642 
 
 9 
 
 .00257069 
 
 4 
 
 .00220264 
 
 19 
 
 .00192678 
 
 4 
 
 .00171233 
 
 5 
 
 .00307692 
 
 390 
 
 .00256410 
 
 5 
 
 .00219780 
 
 520 
 
 .00192308 
 
 5 
 
 .00170940 
 
 6 
 
 .00306748 
 
 1 
 
 .00255754 
 
 6 
 
 .00219298 
 
 1 
 
 00191939 
 
 6 
 
 .00170648 
 
 7 
 
 .00305810 
 
 2 
 
 .00255102 
 
 7 
 
 .00218818 
 
 2 
 
 .00191571 
 
 7 
 
 .00170358 
 
 8 
 
 .00304878 
 
 3 
 
 .00254453 
 
 8 
 
 .00218341 
 
 3 
 
 .00191205 
 
 8 
 
 .00170068 
 
 9 
 
 .00303951 
 
 4 
 
 .00253807 
 
 9 
 
 .00217865 
 
 4 
 
 00190840 
 
 9 
 
 .00169779 
 
 330 
 
 .00303030 
 
 5 
 
 .00253165 
 
 460 
 
 .00217391 
 
 5 
 
 .00190476 
 
 590 
 
 .00169491 
 
 1 
 
 .00302115 
 
 6 
 
 .00252525 
 
 1 
 
 .00216920 
 
 6 
 
 .00190114 
 
 1 
 
 .00169205 
 
 2 
 
 .00301205 
 
 7 
 
 .00251889 
 
 2 
 
 .00216450 
 
 7 
 
 .00189753 
 
 2 
 
 .00168919 
 
 3 
 
 .00300300 
 
 8 
 
 .00251256 
 
 3 
 
 .00215983 
 
 8 
 
 .00189394 
 
 3 
 
 .00168634 
 
 4 
 
 .00299401 
 
 9 
 
 .00250627 
 
 4 
 
 .00215517 
 
 9 
 
 .00189036 
 
 4 
 
 .00168350 
 
 5 
 
 .00298507 
 
 400 
 
 .00250000 
 
 5 
 
 .00215054 
 
 530 
 
 .00188679 
 
 5 
 
 .00168067 
 
 6 
 
 .00297619 
 
 1 
 
 .00249377 
 
 6 
 
 .00214592 
 
 1 
 
 .00188324 
 
 6 
 
 .00167785 
 
 7 
 
 .00296736 
 
 2 
 
 .00248756 
 
 7 
 
 .00214133 
 
 2 
 
 .00187970 
 
 7 
 
 .00167504 
 
 8 
 
 .00295858 
 
 3 
 
 .00248139 
 
 8 
 
 .00213675 
 
 3 
 
 .00187617 
 
 8 
 
 .00167224 
 
 9 
 
 .00294985 
 
 4 
 
 .00247525 
 
 9 
 
 .00213220 
 
 4 
 
 .00187266 
 
 9 
 
 .00166945 
 
 340 
 
 .00294118 
 
 5 
 
 .00246914 
 
 470 
 
 .00212766 
 
 5 
 
 .00186916 
 
 600 
 
 .00166667 
 
 1 
 
 .00293255 
 
 6 
 
 .00246305 
 
 1 
 
 .00212314 
 
 6 
 
 .00186567 
 
 1 
 
 00166389 
 
 2 
 
 .00292398 
 
 7 
 
 .00245700 
 
 2 
 
 .00211864 
 
 7 
 
 .00186220 
 
 2 
 
 .00166113 
 
 3 
 
 .00291545 
 
 8 
 
 .00245098 
 
 3 
 
 .00211416 
 
 8 
 
 .00185874 
 
 3 
 
 .00165837 
 
 4 
 
 .00290698 
 
 9 
 
 .00244499 
 
 4 
 
 .00210970 
 
 9 
 
 .00185528 
 
 4 
 
 .00165563 
 
 5 
 
 .00289855 
 
 410 
 
 .00243902 
 
 5 
 
 .00210526 
 
 540 
 
 .00185185 
 
 5 
 
 .00165289 
 
 6 
 
 .00289017 
 
 11 
 
 .00243309 
 
 6 
 
 .00210084 
 
 1 
 
 .00184843 
 
 6 
 
 00165016 
 
 7 
 
 .00288184 
 
 12 
 
 .00242718 
 
 7 
 
 .00209644 
 
 2 
 
 .00184502 
 
 7 
 
 .00164745 
 
 8 
 
 .00287356 
 
 13 
 
 .00242131 
 
 8 
 
 .00209205 
 
 3 
 
 .00184162 
 
 8 
 
 .00164474 
 
 9 
 
 .00286533 
 
 14 
 
 .00241546 
 
 9 
 
 .00208768 
 
 4 
 
 .00183823 
 
 9 
 
 .00164204 
 
 350 
 
 ,00285714 
 
 15 
 
 .00240964 
 
 480 
 
 .00208333 
 
 5 
 
 .00183486 
 
 610 
 
 .00163934 
 
 1 
 
 .00284900 
 
 16 
 
 .00240385 
 
 1 
 
 .00207900 
 
 6 
 
 00183150 
 
 11 
 
 00163666 
 
 2 
 
 .00284091 
 
 17 
 
 .00239808 
 
 2 
 
 .00207469 
 
 7 
 
 .00182815 
 
 12 
 
 .00163399 
 
 3 
 
 .00283286 
 
 18 
 
 .00239234 
 
 3 
 
 .00207039 
 
 8 
 
 .00182482 
 
 13 
 
 00163132 
 
 4 
 
 .00282486 
 
 19 
 
 .00238663 
 
 4 
 
 .00206612 
 
 9 
 
 00182149 
 
 14 
 
 .00162866 
 
 5 
 
 .00281690 
 
 420 
 
 .00238095 
 
 5 
 
 .00206186 
 
 550 
 
 .00181818 
 
 15 
 
 .00162602 
 
 6 
 
 .00280899 
 
 1 
 
 .00237530 
 
 6 
 
 .00205761 
 
 1 
 
 00181488 
 
 16 
 
 00162338 
 
 7 
 
 .00280112 
 
 2 
 
 .00236967 
 
 7 
 
 .00205339 
 
 2 
 
 .00181159 
 
 17 
 
 .00162075 
 
 8 
 
 .00279330 
 
 3 
 
 .00236407 
 
 8 
 
 .00204918 
 
 3 
 
 .00180832 
 
 18 
 
 00161812 
 
 9 
 
 .00278551 
 
 4 
 
 .00235849 
 
 9 
 
 .00204499 
 
 4 
 
 00180505 
 
 19 
 
 .00161551 
 
 360 
 
 .00277778 
 
 5 
 
 .00235294 
 
 490 
 
 .00204082 
 
 5 
 
 .00180180 
 
 620 
 
 00161290 
 
 1 
 
 .00277008 
 
 6 
 
 .00234742 
 
 1 
 
 .00203666 
 
 6 
 
 00179856 
 
 1 
 
 .00161031 
 
 2 
 
 .00276243 
 
 7 
 
 .00234192 
 
 2 
 
 .00203252 
 
 7 
 
 .00179533 
 
 2 
 
 00160772 
 
 3 
 
 .00275482 
 
 8 
 
 .00233645 
 
 3 .00202840 
 
 8 
 
 00179211 
 
 . 3 
 
 00160514 
 
 4 
 
 .00274725 
 
 9 
 
 .00233100 
 
 4 
 
 .00202429 
 
 9 
 
 .00178891 
 
 4 
 
 .00160256 
 
 5 
 
 .00273973 
 
 430 
 
 .00232558 
 
 5 
 
 .00202020 
 
 560 
 
 .00178571 
 
 5 
 
 00160000 
 
 6 
 
 .00273224 
 
 1 
 
 .00232019 
 
 6 
 
 .00201613 
 
 1 
 
 .00178253 
 
 6 
 
 .00159744 
 
 7 
 
 .00272480 
 
 2 
 
 .00231481 
 
 7 
 
 .00201207 
 
 2 
 
 .00177936 
 
 7 
 
 00159490 
 
 8 
 
 .00271739 
 
 3 
 
 .00230947 
 
 8 
 
 .00200803 
 
 3 
 
 .00177620 
 
 8 
 
 .00159236 
 
 9 
 
 .00271003 
 
 4 
 
 .00230415 
 
 9 
 
 .00200401 
 
 4 
 
 .00177305 
 
 9 
 
 00158982 
 
 370 
 
 .00270270 
 
 5 
 
 .00229885 
 
 500 
 
 .00200000 
 
 5 
 
 .00176991 
 
 630 
 
 .00158730 
 
 1 
 
 .00269542 
 
 6 
 
 .00229358 
 
 1 
 
 .00199601 
 
 6 
 
 .00176678 
 
 1 
 
 00158479 
 
 2 
 
 .00268817 
 
 7 
 
 .00228833 
 
 2 
 
 .00199203 
 
 7 
 
 00176367 
 
 2 
 
 .00158228 
 
 ^ 
 
 .00268096 
 
 8 
 
 .00228310 
 
 3 
 
 .00198807 
 
 8 
 
 .00176056 
 
 3 
 
 00157978 
 
 4 
 
 .00267380 
 
 9 
 
 .00227790 
 
 4 
 
 .00198413 
 
 9 
 
 .00175747 
 
 4 
 
 .00157729 
 
 e 
 
 .00266667 
 
 440 
 
 .00227273 
 
 5 
 
 .00198020 
 
 570 
 
 .00175439 
 
 5 
 
 00157480 
 
 t 
 
 .00265957 
 
 1 
 
 .00226757 
 
 6 
 
 .00197628 
 
 1 
 
 00175131 
 
 6 
 
 .00157233 
 
 7 
 
 .00265252 
 
 2 
 
 .00226244 
 
 7 
 
 .00197239 
 
 2 
 
 .00174825 
 
 7 
 
 .00156986 
 
 8 
 
 .00264550 
 
 3 
 
 .00225734 
 
 8 
 
 .00196850 
 
 3 
 
 .00174520 
 
 8 
 
 .00156740 
 
 9 
 
 .00263852 
 
 4 
 
 .00225225 
 
 9 
 
 .00196464 
 
 
 .00174216 
 
 9 
 
 .00156494 
 
 380 
 
 .00263158 
 
 5 
 
 .00224719 
 
 510 
 
 .00196078 
 
 5 
 
 .00173913 
 
 640 
 
 .00156250 
 
RECIPROCALS OF NUMBERS. 
 
 89 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipnx 
 cal. 
 
 641 
 
 .001560% 
 
 706 
 
 .00141643 
 
 771 
 
 .00129702 
 
 836 
 
 .00119617 
 
 901 
 
 .001 10988 
 
 2 
 
 .00155763 
 
 7 
 
 00141443 
 
 2 
 
 .00129534 
 
 7 
 
 .001 19474 
 
 2 
 
 .001 10865 
 
 3 
 
 .00155521 
 
 8 
 
 00141243 
 
 3 
 
 .00129366 
 
 8 
 
 .00119332 
 
 3 
 
 .00110742 
 
 4 
 
 .00155279 
 
 9 
 
 .00141044 
 
 4 
 
 .00129199 
 
 9 
 
 .00119189 
 
 4 
 
 .00110619 
 
 5 
 
 .00155039 
 
 710 
 
 00140345 
 
 5 
 
 .00129032 
 
 840 
 
 .00119048 
 
 5 
 
 .00110497 
 
 6 
 
 .00154799 
 
 11 
 
 .00140647 
 
 6 
 
 .00128866 
 
 1 
 
 .001 18906 
 
 6 
 
 .001 10375 
 
 7 
 
 .00154559 
 
 12 
 
 .00140449 
 
 7 
 
 .00128700 
 
 2 
 
 .001 18765 
 
 7 
 
 .00110254 
 
 8 
 
 .00154321 
 
 13 
 
 .00140252 
 
 8 
 
 .00128535 
 
 3 
 
 .001 18624 
 
 8 
 
 .00110132 
 
 9 
 
 .00154033 
 
 14 
 
 .00140056 
 
 9 
 
 .00128370 
 
 4 
 
 .00118483 
 
 9 
 
 .00110011 
 
 650 
 
 .00153846 
 
 15 
 
 .00139860 
 
 780 
 
 .00128205 
 
 5 
 
 .001 18343 
 
 910 
 
 .00109890 
 
 1 
 
 .00153610 
 
 16 
 
 .00139665 
 
 1 
 
 .00128041 
 
 6 
 
 .001 18203 
 
 11 
 
 .00109769 
 
 2 
 
 .00153374 
 
 17 
 
 .00139470 
 
 2 
 
 .00127877 
 
 7 
 
 .00118064 
 
 12 
 
 .00109649 
 
 3 
 
 .00153140 
 
 18 
 
 .00139276 
 
 3 
 
 .00127714 
 
 8 
 
 .00117924 
 
 13 
 
 .00109529 
 
 4 
 
 .00152905 
 
 19 
 
 .00139032 
 
 4 
 
 .00127551 
 
 9 
 
 .00117786 
 
 14 
 
 .00109409 
 
 5 
 
 .00152672 
 
 720 
 
 .00138889 
 
 5 
 
 .00127388 
 
 850 
 
 .00117647 
 
 15 
 
 .00109290 
 
 6 
 
 .00152439 
 
 1 
 
 .00138696 
 
 6 
 
 .00127226 
 
 1 
 
 .00117509 
 
 16 
 
 .00109170 
 
 7 
 
 .00152207 
 
 2 
 
 .00138504 
 
 7 
 
 .00127065 
 
 2 
 
 .00117371 
 
 17 
 
 .00109051 
 
 8 
 
 .00151975 
 
 3 
 
 .00138313 
 
 8 
 
 .00126904 
 
 3 
 
 .00117233 
 
 18 
 
 .00108932 
 
 9 
 
 .00151745 
 
 4 
 
 .00138121 
 
 9 
 
 .00126743 
 
 4 
 
 .001170% 
 
 19 
 
 00108814 
 
 660 
 
 .00151515 
 
 5 
 
 00137931 
 
 790 
 
 .00126582 
 
 5 
 
 .001 16959 
 
 920 
 
 .00108696 
 
 
 .00151236 
 
 6 
 
 .00137741 
 
 1 
 
 .00126422 
 
 6 
 
 .001 16822 
 
 1 
 
 .00108578 
 
 2 
 
 .00151057 
 
 7 
 
 .00137552 
 
 2 
 
 .00126263 
 
 7 
 
 .001 16686 
 
 2 
 
 .00108460 
 
 3 
 
 .00150330 
 
 8 
 
 .00137363 
 
 3 
 
 .00126103 
 
 8 
 
 .00116550 
 
 3 
 
 .00108342 
 
 4 
 
 .00150602 
 
 9 
 
 .00137174 
 
 4 
 
 .00125945 
 
 9 
 
 .00116414 
 
 4 
 
 .00108225 
 
 5 
 
 .00150376 
 
 730 
 
 00136936 
 
 5 
 
 .00125786 
 
 860 
 
 .00116279 
 
 5 
 
 .00108108 
 
 6 
 
 .00150150 
 
 1 
 
 .00136799 
 
 6 
 
 .00125628 
 
 1 
 
 .00116144 
 
 6 
 
 .00107991 
 
 7 
 
 .00149925 
 
 2 
 
 00136612 
 
 7 
 
 .00125470 
 
 2 
 
 .00116009 
 
 7 
 
 .00107875 
 
 8 
 
 .00149701 
 
 3 
 
 .00136426 
 
 8 
 
 .00125313 
 
 3 
 
 .00115875 
 
 8 
 
 .00107759 
 
 9 
 
 .00149477 
 
 4 
 
 00136240 
 
 9 
 
 .00125156 
 
 4 
 
 .00115741 
 
 9 
 
 .00107.643 
 
 670 
 
 .00149254 
 
 5 
 
 .00136054 
 
 800 
 
 .00125000 
 
 5 
 
 .00115607 
 
 930 
 
 .00107527 
 
 1 
 
 .00149031 
 
 6 
 
 00135870 
 
 1 
 
 .00124844 
 
 6 
 
 .00115473 
 
 1 
 
 .00107411 
 
 2 
 
 .00148809 
 
 7 
 
 .00135685 
 
 2 
 
 .00124688 
 
 7 
 
 .00115340 
 
 2 
 
 .00107296 
 
 4 
 
 .00148588 
 
 8 
 
 00135501 
 
 3 
 
 .00124533 
 
 8 
 
 .00115207 
 
 3 
 
 .00107181 
 
 4 
 
 .00148368 
 
 9 
 
 .00135318 
 
 4 
 
 .00124378 
 
 9 
 
 .00115075 
 
 4 
 
 .00107066 
 
 j 
 
 .00148148 
 
 740 
 
 00135135 
 
 5 
 
 .00124224 
 
 870 
 
 .001 14942 
 
 5 
 
 .00106952 
 
 ( 
 
 .00147929 
 
 1 
 
 .00134953 
 
 6 
 
 .00124069 
 
 1 
 
 .00114811 
 
 6 
 
 .00106838 
 
 7 
 
 .00147710 
 
 2 
 
 00134771 
 
 7 
 
 .00123916 
 
 2 
 
 .00114679 
 
 7 
 
 .00106724 
 
 8 
 
 .00147493 
 
 3 
 
 .00134589 
 
 8 
 
 .00123762 
 
 3 
 
 .00114547 
 
 8 
 
 .00106610 
 
 9 
 
 .00147275 
 
 4 
 
 .00134409 
 
 9 
 
 .00123609 
 
 4 
 
 .00114416 
 
 9 
 
 .00106496 
 
 680 
 
 .00147059 
 
 c 
 
 .00134228 
 
 810 
 
 .00123457 
 
 5 
 
 .00114286 
 
 940 
 
 .00106383 
 
 1 
 
 .00146843 
 
 6 
 
 00134048 
 
 11 
 
 .00123305 
 
 6 
 
 .00114155 
 
 1 
 
 .00] 06270 
 
 2 
 
 .00146628 
 
 7 
 
 .00133869 
 
 12 
 
 .00123153 
 
 7 
 
 .00114025 
 
 2 
 
 .00106157 
 
 3 
 
 .00146413 
 
 8 
 
 00133690 
 
 13 
 
 .00123001 
 
 8 
 
 .00113895 
 
 3 
 
 00106044 
 
 z 
 
 .00146199 
 
 9 
 
 .00133511 
 
 14 
 
 .00122850 
 
 9 
 
 .00113766 
 
 4 
 
 .00105932 
 
 c 
 
 .00145985 
 
 750 
 
 00133333 
 
 15 
 
 .00122699 
 
 880 
 
 .00113636 
 
 5 
 
 00105820 
 
 ( 
 
 .00145773 
 
 1 
 
 .00133156 
 
 16 
 
 .00122549 
 
 1 
 
 .00113507 
 
 6 
 
 00105708 
 
 j 
 
 .00145560 
 
 2 
 
 00132979 
 
 17 
 
 .00122399 
 
 2 
 
 .00113379 
 
 7 
 
 00105597 
 
 8 
 
 .00145349 
 
 
 .00132802* 
 
 18 
 
 .00122249 
 
 3 
 
 .00113250 
 
 8 
 
 .00105485 
 
 9 
 
 .00145137 
 
 4 
 
 00132626 
 
 19 
 
 .00122100 
 
 4 
 
 .00113122 
 
 9 
 
 00105374 
 
 690 
 
 .00144927 
 
 c 
 
 .00132450 
 
 820 
 
 .00121951 
 
 5 
 
 .001 12994 
 
 950 
 
 .00105263 
 
 J 
 
 .00144718 
 
 6 
 
 00132275 
 
 ] 
 
 .00121803 
 
 6 
 
 .00 H 2867 
 
 1 
 
 .00105152 
 
 4 
 
 .00144509 
 
 7 
 
 .00132100 
 
 2 
 
 .00121654 
 
 7 
 
 .00112740 
 
 2 
 
 .00105042 
 
 2 
 
 .00144300 
 
 8 
 
 .00131926 
 
 3 
 
 .00121507 
 
 8 
 
 .00112613 
 
 3 
 
 .00104932 
 
 4 
 
 .00144092 
 
 9 
 
 .00131752 
 
 4 
 
 .00121359 
 
 9 
 
 .001 12486 
 
 4 
 
 .00104822 
 
 c 
 
 .00143885 
 
 760 
 
 .00131579 
 
 5 
 
 .00121212 
 
 890 
 
 .001 12360 
 
 5 
 
 .00104712 
 
 6 
 
 .00143678 
 
 1 
 
 .00131406 
 
 6 
 
 .00121065 
 
 1 
 
 .00112233 
 
 6 
 
 00104602 
 
 7 
 
 .00143472 
 
 2 
 
 .00131234 
 
 7 
 
 .00120919 
 
 2 
 
 .00112108 
 
 7 
 
 .00104493 
 
 8 
 
 .00143266 
 
 3 
 
 .00131062 
 
 8 
 
 .00120773 
 
 3 
 
 .001 1 1982 
 
 8 
 
 00104384 
 
 9 
 
 .00143061 
 
 4 
 
 .00130890 
 
 9 
 
 .00120627 
 
 4 
 
 00111857 
 
 9 
 
 .00104275 
 
 700 
 
 .00142857 
 
 5 
 
 .00130719 
 
 830 
 
 .00120482 
 
 5 
 
 .00111732 
 
 960 
 
 .00104167 
 
 1 
 
 .00142653 
 
 6 
 
 .00130548 
 
 1 
 
 .00120337 
 
 6 
 
 .00111607 
 
 1 
 
 .00104058 
 
 2 
 
 .00142450 
 
 7 
 
 00130378 
 
 2 
 
 .00120192 
 
 7 
 
 .001 1 1483 
 
 2 
 
 .00103950 
 
 3 
 
 .00142247 
 
 8 
 
 .00130208 
 
 3 
 
 .00120048 
 
 8 
 
 .00111359 
 
 3 
 
 .00103842 
 
 4 
 
 .00142045 
 
 9 
 
 .00130039 
 
 4 
 
 .00119904 
 
 9 
 
 .00111235 
 
 4 
 
 .00103734 
 
 3 
 
 .00141844 
 
 770 
 
 .00129870 
 
 5 
 
 .001 19760 
 
 900 
 
 .00111111 
 
 5 
 
 .00103627 
 
00 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 
 No. 
 
 Recipro- 
 cal. 
 
 .000815661 
 
 966 
 
 .00103520 
 
 1031 
 
 .000969932 
 
 10% 
 
 .000912409 
 
 1161 
 
 .000861326 
 
 1226 
 
 7 
 
 .00103413 
 
 2 
 
 .000968992 
 
 7 
 
 .000911577 
 
 2 
 
 .000860585 
 
 7 
 
 .0008149% 
 
 8 
 
 .00103306 
 
 3 
 
 .000968054 
 
 8 
 
 .000910747 
 
 3 
 
 .000859845 
 
 8 
 
 .000814332 
 
 9 
 
 .00103199 
 
 4 
 
 .000967118 
 
 9 
 
 .000909918 
 
 4 
 
 .000859106 
 
 9 
 
 .000813670 
 
 970 
 
 .00103093 
 
 5 
 
 .000966184 
 
 1100 
 
 .000909091 
 
 5 
 
 .000858369 
 
 1230 
 
 .000813008 
 
 I 
 
 .00102987 
 
 6 
 
 .000965251 
 
 1 
 
 .000908265 
 
 6 
 
 .000857633 
 
 1 
 
 .000812348 
 
 2 
 
 .00102881 
 
 7 
 
 .000964320 
 
 2 
 
 000907441 
 
 7 
 
 .000856898 
 
 2 
 
 .000811688 
 
 3 
 
 .00102775 
 
 8 
 
 .000963391 
 
 3 
 
 .000906618 
 
 8 
 
 .000856164 
 
 3 
 
 .000811030 
 
 4 
 
 .00102669 
 
 9 
 
 .000962464 
 
 4 
 
 .000905797 
 
 9 
 
 .000855432 
 
 4 
 
 .000810373 
 
 5 
 
 .00102564 
 
 1040 
 
 000% 1538 
 
 5 
 
 .000904977 
 
 1170 
 
 .000854701 
 
 5 
 
 .000809717 
 
 6 
 
 .00102459 
 
 1 
 
 .000960615 
 
 6 
 
 .000904159 
 
 1 
 
 .000853971 
 
 6 
 
 .000809061 
 
 7 
 
 .00102354 
 
 2 
 
 .000959693 
 
 7 
 
 .000903342 
 
 2 
 
 .000853242 
 
 7 
 
 .000808407 
 
 8 
 
 .00102250 
 
 3 
 
 .000958774 
 
 8 
 
 .000902527 
 
 3 
 
 .000852515 
 
 8 
 
 .000807754 
 
 9 
 
 .00102145 
 
 4 
 
 .000957854 
 
 9 
 
 .000901713 
 
 4 
 
 .000851789 
 
 9 
 
 .000807102 
 
 980 
 
 .00102041 
 
 5 
 
 .000956938 
 
 1110 
 
 .000900901 
 
 5 
 
 .000851064 
 
 1240 
 
 .000806452 
 
 1 
 
 .00101937 
 
 6 
 
 .000956023 
 
 1 1 
 
 .000900090 
 
 6 
 
 .000850340 
 
 1 
 
 .000805802 
 
 2 
 
 .00101833 
 
 7 
 
 .000955110 
 
 12 
 
 .000899281 
 
 7 
 
 .00084% 18 
 
 2 
 
 .000805153 
 
 3 
 
 .00101729 
 
 8 
 
 .000954198 
 
 13 
 
 .000898473 
 
 8 
 
 .0008488% 
 
 3 
 
 .000804505 
 
 4 
 
 .00101626 
 
 9 
 
 .000953289 
 
 14 
 
 .000897666 
 
 9 
 
 .000848176 
 
 4 
 
 .000803858 
 
 5 
 
 .00101523 
 
 1050 
 
 .000952381 
 
 15 
 
 0008%861 
 
 1180 
 
 .000847457 
 
 5 
 
 .000803213 
 
 6 
 
 .00101420 
 
 1 
 
 .000951475 
 
 16 
 
 .0008%057 
 
 1 
 
 .000846740 
 
 6 
 
 .000802568 
 
 7 
 
 .00101317 
 
 2 
 
 .000950570 
 
 17 
 
 .000895255 
 
 2 
 
 .000846024 
 
 7 
 
 .000801925 
 
 8 
 
 .00101215 
 
 3 
 
 .000949668 
 
 18 
 
 .000894454 
 
 3 
 
 000845308 
 
 8 
 
 .000801282 
 
 9 
 
 .00101112 
 
 4 
 
 .000948767 
 
 191.000893655 
 
 4 
 
 .000844595 
 
 9 
 
 .000800640 
 
 990 
 
 .00101010 
 
 5 
 
 .000947867 
 
 1120 
 
 000892857 
 
 5 
 
 .000843882 
 
 1250 
 
 .000800000 
 
 1 
 
 .00100908 
 
 6 
 
 .000946970 
 
 1 
 
 .000892061 
 
 6 
 
 .000843170 
 
 1 
 
 .000799360 
 
 2 
 
 .00100806 
 
 7 
 
 .000946074 
 
 2 
 
 .000891266 
 
 7 
 
 .000842460 
 
 2 
 
 .000798722 
 
 3 
 
 .00100705 
 
 8 
 
 .000945180 
 
 3 
 
 .000890472 
 
 8 
 
 .000841751 
 
 3 
 
 .000798085 
 
 4 
 
 .00100604 
 
 9 
 
 .000944287 
 
 4 
 
 .00088%80 
 
 9 
 
 .000841043 
 
 4 
 
 .000797448 
 
 5 
 
 .00100502 
 
 1060 
 
 .0009433% 
 
 5 
 
 .000888889 
 
 1190 
 
 .000840336 
 
 5 
 
 .0007%813 
 
 6 
 
 .00100402 
 
 1 
 
 .000942507 
 
 6 
 
 .000888099 
 
 1 
 
 00083%31 
 
 6 
 
 .0007% 178 
 
 7 
 
 .00100301 
 
 2 
 
 .000941620 
 
 7 
 
 .000887311 
 
 2 
 
 .000838926 
 
 7 
 
 .000795545 
 
 8 
 
 .00100200 
 
 3 
 
 .000940734 
 
 8 
 
 .000886525 
 
 3 
 
 .000838222 
 
 8 
 
 .000794913 
 
 9 
 
 .00100100 
 
 4 
 
 .000939850 
 
 9 
 
 .000885740 
 
 4 
 
 .000837521 
 
 9 
 
 .000794281 
 
 1000 
 
 .00100000 
 
 5 
 
 .000938%7 
 
 1130 
 
 .000884956 
 
 5 
 
 .000836820 
 
 1260 
 
 .000793651 
 
 1 
 
 .000999001 
 
 6 
 
 000938086 
 
 1 
 
 .000884173 
 
 6 
 
 .000836120 
 
 1 
 
 .000793021 
 
 2 
 
 .000998004 
 
 7 
 
 .000937207 
 
 2 
 
 .000883392 
 
 7 
 
 .000835422 
 
 2 
 
 .000792393 
 
 3 
 
 .000997009 
 
 8 
 
 .000936330 
 
 3 
 
 .000882612 
 
 8 
 
 .000834724 
 
 3 
 
 .000791766 
 
 4 
 
 .000996016 
 
 9 
 
 .000935454 
 
 4 
 
 .000881834 
 
 9 
 
 .000834028 
 
 4 
 
 000791139 
 
 5 
 
 .000995025 
 
 1070 
 
 .000934579 
 
 5 
 
 .000881057 
 
 1200 
 
 .000833333 
 
 5 
 
 .000790514 
 
 6. 
 
 .000994036 
 
 1 
 
 .000933707 
 
 6 
 
 000880282 
 
 ] 
 
 000832639 
 
 6 
 
 .000789889 
 
 7 
 
 .000993049 
 
 2 
 
 .000932836 
 
 7 
 
 .000879508 
 
 2 
 
 .000831947 
 
 7 
 
 .000789266 
 
 8 
 
 .000992063 
 
 3 
 
 .00093 1%6 
 
 8 
 
 .000878735 
 
 3 
 
 .000831255 
 
 8 
 
 .000788643 
 
 9 
 
 .000991080 
 
 4 
 
 000931099 
 
 9 
 
 .000877%3 
 
 4 
 
 .000830565 
 
 9 
 
 000788022 
 
 1010 
 
 .000990099 
 
 5 
 
 .000930233 
 
 1140 
 
 .000877193 
 
 5 
 
 .000829875 
 
 1270 
 
 .000787402 
 
 11 
 
 .000989120 
 
 6 
 
 .000929368 
 
 1 
 
 000876424 
 
 6 
 
 000829187 
 
 1 000786782 
 
 12 
 
 .000988142 
 
 7 
 
 .000928505 
 
 2 
 
 .000875657 
 
 7 
 
 .000828500 
 
 21.000786163 
 
 13 
 
 .000987167 
 
 8 
 
 .000927644 
 
 3 
 
 .000874891 
 
 8 
 
 .000827815 
 
 3|.000785546 
 
 14 
 
 .000986193 
 
 9 
 
 000926784 
 
 4 
 
 .000874126 
 
 9 
 
 .000827130 
 
 4 
 
 000784929 
 
 15 
 
 .000985222 
 
 1080 
 
 .000925926 
 
 5 
 
 .000873362 
 
 1210 
 
 .000826446 
 
 5 
 
 000784314 
 
 16 
 
 .000984252 
 
 1 
 
 000925069 
 
 6 
 
 000872600 
 
 11 .000825764 
 
 6 
 
 .UUU/tf>699 
 
 17 
 
 .000983284 
 
 2 
 
 .000924214 
 
 7 
 
 .000871840 
 
 12 .000825082 
 
 7 
 
 .000783085 
 
 18 
 
 .000982318 
 
 3 
 
 .000923361 
 
 8 
 
 .000871080 
 
 13 000824402 
 
 8 
 
 000782473 
 
 19 
 
 .000981354 
 
 4 
 
 .000922509 
 
 9 
 
 .000870322 
 
 14 
 
 000823723 
 
 9 
 
 .000781861 
 
 1020 
 
 .000980392 
 
 5 
 
 .000921659 
 
 1150 
 
 .000869565 
 
 15 
 
 .000823045 
 
 1280 
 
 000781250 
 
 1 
 
 .000979432 
 
 6 
 
 000920810 
 
 1 
 
 000868810 
 
 161.000822368 
 
 1 
 
 .000780640 
 
 2 
 
 .000978474 
 
 7 
 
 .0009 19%3 
 
 2 
 
 .000868056 
 
 17 
 
 .000821693 
 
 2 
 
 .000780031 
 
 3 
 
 .000977517 
 
 8 
 
 .000919118 
 
 3 
 
 .000867303 
 
 18 
 
 .000821018 
 
 3 
 
 .000779423 
 
 4 
 
 .000976562 
 
 9 
 
 .000918274 
 
 4 
 
 .000866551 
 
 19 
 
 .000820344 
 
 4 
 
 .000778816 
 
 5 
 
 .000975610 
 
 1090 
 
 .000917431 
 
 5 
 
 .000865801 
 
 1220 
 
 .0008 1%72 
 
 5 
 
 .000778210 
 
 6 
 
 .000974659 
 
 1 
 
 .000916590 
 
 6 
 
 .000865052 
 
 1 
 
 .000819001 
 
 6 
 
 .000777605 
 
 7 
 
 .000973710 
 
 2 
 
 .00091575 
 
 7 
 
 .000864304 
 
 2 
 
 .000818331 
 
 7 
 
 .000777001 
 
 8 
 
 .000972763 
 
 3 
 
 .000914913 
 
 8 
 
 .000863558 
 
 3 
 
 .000817661 
 
 8 
 
 .000776397 
 
 9 
 
 .000971817 
 
 4 
 
 .00091407: 
 
 9 
 
 .000862813 
 
 4 
 
 000816993 
 
 9 
 
 .000775795 
 
 1030 
 
 .000970874 
 
 5 
 
 .000913242 
 
 1160 
 
 .000862069 
 
 5 
 
 .000816326 
 
 1290 
 
 .000775194 
 
RECIPROCALS OP NUMBERS. 
 
 91 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 
 No. 
 
 Recipro- 
 
 No. 
 
 Recipro* 
 cal. 
 
 1291 
 
 .000774593 
 
 1356 
 
 .000737463 
 
 1421 
 
 .000703730 
 
 i486 
 
 .000672948 
 
 1551 
 
 .000644745 
 
 2 
 
 .000773994 
 
 7 
 
 .000736920 
 
 2 
 
 .000703235 
 
 7 
 
 .000672495 
 
 2 
 
 .000644330 
 
 3 
 
 .000773395 
 
 8 
 
 .000736377 
 
 3 
 
 .000702741 
 
 8 
 
 .000672043 
 
 ? 
 
 .000643915 
 
 4 
 
 .000772797 
 
 9 
 
 .000735835 
 
 4 
 
 .000702247 
 
 g 
 
 .000671592 
 
 t 
 
 .000643501 
 
 5 
 
 .000772201 
 
 1360 
 
 .000735294 
 
 5 
 
 .000701754 
 
 1490 
 
 .000671141 
 
 c 
 
 .000643087 
 
 6 
 
 .000771605 
 
 1 
 
 .000734754 
 
 6 
 
 .000701262 
 
 1 
 
 .000670691 
 
 \ 
 
 .000642673 
 
 7 
 
 .000771010 
 
 2 
 
 .000734214 
 
 7 
 
 .000700771 
 
 2 
 
 .000670241 
 
 7 
 
 .000642261 
 
 8 
 
 .000770416 
 
 3 
 
 .000733676 
 
 8 
 
 .000700280 
 
 3 
 
 .000669792 
 
 8 
 
 .000641848 
 
 9 
 
 .000769823 
 
 4 
 
 .000733138 
 
 9 
 
 .000699790 
 
 4 
 
 .000669344 
 
 9 
 
 .000641437 
 
 1300 
 
 .000769231 
 
 5 
 
 .000732601 
 
 1430 
 
 .000699301 
 
 5 
 
 .0006688% 
 
 1560 
 
 .000641026 
 
 1 
 
 .000768639 
 
 6 
 
 .000732064 
 
 1 
 
 .000698812 
 
 6 
 
 .000668449 
 
 
 .000640615 
 
 2 
 
 .000768049 
 
 7 
 
 .000731529 
 
 2 
 
 .000698324 
 
 7 
 
 .000668003 
 
 2 
 
 .000640205 
 
 3 
 
 .000767459 
 
 8 
 
 .000730994 
 
 3 
 
 .000697837 
 
 8 
 
 .000667557 
 
 g 
 
 .000639795 
 
 4 
 
 .000766871 
 
 9 
 
 .000730460 
 
 4 
 
 .000697350 
 
 9 
 
 .000667111 
 
 ^ 
 
 .000639386 
 
 5 
 
 .000766283 
 
 1370 
 
 .000729927 
 
 5 
 
 .000696864 
 
 1500 
 
 .000666667 
 
 
 
 .000638978 
 
 6 
 
 .000765697 
 
 1 
 
 .000729395 
 
 6 
 
 000696379 
 
 1 
 
 .000666223 
 
 t 
 
 .000638570 
 
 7 
 
 .000765111 
 
 2 
 
 .000728863 
 
 7 
 
 000695894 
 
 2 
 
 .000665779 
 
 7 
 
 .000638162 
 
 8 
 
 .000764526 
 
 3 
 
 .000728332 
 
 8 
 
 000695410 
 
 3 
 
 .000665336 
 
 8 
 
 .000637755 
 
 9 
 
 .000763942 
 
 4 
 
 .000727802 
 
 9 
 
 000694927 
 
 4 
 
 .000664894 
 
 9 
 
 .000637349 
 
 1310 
 
 .000763359 
 
 5 
 
 .000727273 
 
 1440 
 
 000694444 
 
 5 
 
 .000664452 
 
 1570 
 
 .000636943 
 
 11 
 
 .000762776 
 
 6 
 
 .000726744 
 
 1 
 
 000693962 
 
 6 
 
 .000664011 
 
 1 
 
 .000636537 
 
 12 
 
 .000762195 
 
 7 
 
 .000726216 
 
 2 
 
 000693481 
 
 7 
 
 .000663570 
 
 2 
 
 .000636132 
 
 13 
 
 .000761615 
 
 8 
 
 .000725689 
 
 3 
 
 000693001 
 
 8 
 
 .000663130 
 
 3 
 
 .000635728 
 
 14 
 
 .000761035 
 
 9 
 
 .000725163 
 
 4 
 
 000692521 
 
 9 
 
 .000662691 
 
 4 
 
 .000635324 
 
 15 
 
 .000760456 
 
 1380 
 
 .000724638 
 
 5 
 
 000692041 
 
 1510 
 
 000662252 
 
 5 
 
 .000634921 
 
 16 
 
 .000759878 
 
 1 
 
 .000724113 
 
 6 
 
 000691563 
 
 11 
 
 000661813 
 
 6 
 
 .000634518 
 
 17 
 
 .000759301 
 
 2 
 
 .000723589 
 
 7 
 
 000691085 
 
 12 
 
 000661376 
 
 7 
 
 .000634115 
 
 18 
 
 .000758725 
 
 3 
 
 .000723066 
 
 8 
 
 000690608 
 
 13 
 
 000660939 
 
 8 
 
 .000633714 
 
 19 
 
 .000758150 
 
 4 
 
 .000722543 
 
 9 
 
 000690131 
 
 14 
 
 000660502 
 
 9 
 
 .000633312 
 
 1320 
 
 .000757576 
 
 5 
 
 .000722022 
 
 1450 
 
 000689655 
 
 15 
 
 000660066 
 
 580 
 
 .000632911 
 
 
 .000757002 
 
 6 
 
 .000721501 
 
 1 
 
 000689180 
 
 16 
 
 00065%31 
 
 
 .000632511 
 
 2 
 
 .000756430 
 
 7 
 
 .000720980 
 
 2 
 
 000688705 
 
 17 
 
 0006591% 
 
 2 
 
 .000632111 
 
 3 
 
 .000755858 
 
 8 
 
 .000720461 
 
 3 
 
 000688231 
 
 18 
 
 000658761 
 
 3 
 
 000631712 
 
 4 
 
 .000755287 
 
 9 
 
 .000719942 
 
 4 
 
 000687758 
 
 19 
 
 000658328 
 
 4 
 
 .000631313 
 
 5 
 
 .000754717 
 
 1390 
 
 .000719424 
 
 5 
 
 000687285 
 
 1520 
 
 000657895 
 
 5 
 
 000630915 
 
 6 
 
 .000754148 
 
 1 
 
 .000718907 
 
 6 
 
 000686813 
 
 1 
 
 000657462 
 
 6 
 
 000630517 
 
 7 
 
 .000753579 
 
 2 
 
 .000718391 
 
 7 
 
 000686341 
 
 2 
 
 000657030 
 
 7 
 
 C00630I20 
 
 8 
 
 .000753012 
 
 3 
 
 .000717875 
 
 8 
 
 000685871 
 
 3 
 
 000656598 
 
 8 
 
 000629723 
 
 9 
 
 .000752445 
 
 4 
 
 .000717360 
 
 9l 000685401 
 
 4 
 
 000656168 
 
 9 
 
 000629327 
 
 1330 
 
 .000751880 
 
 5 
 
 .000716846 
 
 1460 
 
 .000684932 
 
 5 
 
 000655738 
 
 590 
 
 000628931 
 
 1 
 
 .000751315 
 
 6 
 
 000716332 
 
 1 
 
 000684463 
 
 6 
 
 000655308 
 
 1 
 
 000628536 
 
 2 
 
 .000750750 
 
 7 
 
 .000715820 
 
 2 
 
 .000683994 
 
 7 
 
 000654879 
 
 2 
 
 000628141 
 
 3 
 
 .000750187 
 
 8 
 
 000715308 
 
 3 
 
 .000683527 
 
 8 
 
 000654450 
 
 3 
 
 000627746 
 
 4 
 
 .000749625 
 
 9 
 
 .0007147% 
 
 4 
 
 .000683060 
 
 9 
 
 000654022 
 
 4 
 
 000627353 
 
 5 
 
 .000749064 
 
 1400 
 
 .000714286 
 
 5 
 
 000682594 
 
 1530 
 
 000653595 
 
 5 
 
 000626959 
 
 6 
 
 .000748503 
 
 1 
 
 .000713776 
 
 6 
 
 .000682128 
 
 1 
 
 000653168 
 
 6 
 
 000626566 
 
 7 
 
 .000747943 
 
 2 
 
 .000713267 
 
 7 
 
 .000681663 
 
 2 
 
 000652742 
 
 7 
 
 000626174 
 
 8 
 
 .000747384 
 
 3 
 
 .000712758 
 
 8 
 
 .000681199 
 
 3 
 
 000652316 
 
 8 
 
 000625782 
 
 9 
 
 .000746826 
 
 4 
 
 .000712251 
 
 9 
 
 .000680735 
 
 4 
 
 000651890 
 
 9 
 
 000625391 
 
 1340 
 
 .000746269 
 
 5 
 
 .000711744 
 
 1470 
 
 .000680272 
 
 5 
 
 000651466 
 
 600 
 
 000625000 
 
 1 
 
 .000745712 
 
 6 
 
 .000711238 
 
 1 
 
 .000679810 
 
 6 
 
 000651042 
 
 2 
 
 000624219 
 
 2 
 
 .000745156 
 
 7 
 
 .000710732 
 
 2 
 
 .000679348 
 
 7 
 
 000650618 
 
 4 
 
 000623441 
 
 3 
 
 .000744602 
 
 8 
 
 .000710227 
 
 3 
 
 000678887 
 
 8 
 
 000650195 
 
 6 
 
 000622665 
 
 4 
 
 .000744048 
 
 9 
 
 .000709723 
 
 4 
 
 .000678426 
 
 9 
 
 000649773 
 
 8 
 
 000621890 
 
 5 
 
 .000743494 
 
 1410 
 
 .000709220 
 
 5 
 
 000677966 
 
 1540 
 
 000649351 
 
 610 
 
 000621 1 18 
 
 6 
 
 .000742942 
 
 11 
 
 .000708717 
 
 6 
 
 .000677507 
 
 1 
 
 000648929 
 
 12 
 
 000620347 
 
 7 
 
 .000742390 
 
 12 
 
 .000708215 
 
 7 
 
 .000677048 
 
 2 
 
 000648508 
 
 14 
 
 000619578 
 
 8 
 
 .000741840 
 
 13 
 
 .000707714 
 
 8 
 
 .000676590 
 
 3 
 
 000648088 
 
 16 
 
 000618812 
 
 9 
 
 .000741290 
 
 14 
 
 .000707214 
 
 9 
 
 .000676132 
 
 4 
 
 000647668 
 
 18 
 
 000618047 
 
 1350 
 
 .000740741 
 
 15 
 
 .000706714 
 
 1480 
 
 .000675676 
 
 5 
 
 000647249 
 
 620 
 
 000617284 
 
 1 
 
 .000740192 
 
 16 
 
 .000706215 
 
 1 
 
 .000675219 
 
 6 
 
 000646830 
 
 2 
 
 000616523 
 
 2 
 
 .000739645 
 
 17 
 
 .000705716 
 
 2 
 
 .000674764 
 
 7 
 
 000646412 
 
 A 
 
 000615763 
 
 3 
 
 .000739098 
 
 18 
 
 .000705219 
 
 3 
 
 .000674309 
 
 8 
 
 000645995 
 
 6 
 
 000615006 
 
 4 
 
 .000738552 
 
 19 000704722 
 
 4 
 
 .000673854 
 
 9 
 
 000645578 
 
 8 
 
 000614250 
 
 5 
 
 .000738007 
 
 1 420 1. 000704225 
 
 5 
 
 .000673401 
 
 1550 
 
 .000645161 
 
 630 
 
 000613497 
 
MATHEMATICAL TABLES. 
 
 No. 
 "1632 
 
 Recipro- 
 cal* 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 .000612745 
 
 1706 
 
 .000586166 
 
 1780 
 
 .000561798 
 
 1854 
 
 .000539374 
 
 1928 
 
 .000518672 
 
 4 
 
 .00061 1995 
 
 8 
 
 .000585480 
 
 2 
 
 000561167 
 
 6 
 
 .000538793 
 
 1930 
 
 .000518135 
 
 6 
 
 .00061 1247 
 
 1710 
 
 .000584795 
 
 4 
 
 .000560538 
 
 8 
 
 .000538213 
 
 2 
 
 .000517599 
 
 8 
 
 .000610500 
 
 12 
 
 .0005841 12 
 
 6 
 
 .000559910 
 
 1860 
 
 .000537634 
 
 4 
 
 .000517063 
 
 1640 
 
 .000609756 
 
 14 
 
 .000583430 
 
 8 
 
 000559284 
 
 2 
 
 .000537057 
 
 6 
 
 .000516528 
 
 2 
 
 .000609013 
 
 16 
 
 .000582750 
 
 1790 
 
 .000558659 
 
 4 
 
 .000536480 
 
 8 
 
 .0005159% 
 
 4 
 
 .000608272 
 
 18 
 
 000582072 
 
 2 
 
 .000558035 
 
 6 
 
 .000535905 
 
 1940 
 
 .000515464 
 
 6 
 
 .000607533 
 
 1720 
 
 .000581395 
 
 4 
 
 .000557413 
 
 8 
 
 .000535332 
 
 2 
 
 .000514933 
 
 8 
 
 .0006067% 
 
 2 
 
 .000580720 
 
 6 
 
 .000556793 
 
 1870 
 
 .000534759 
 
 4 
 
 .000514403 
 
 1650 
 
 .000506061 
 
 4 
 
 .000580046 
 
 8 
 
 .000556174 
 
 2 
 
 .000534188 
 
 6 
 
 .000513874 
 
 2 
 
 .000605327 
 
 6 
 
 .000579374 
 
 1800 
 
 .000555556 
 
 4 
 
 .000533618 
 
 8 
 
 .000513347 
 
 4 
 
 .000604595 
 
 8 
 
 .000578704 
 
 '2 
 
 000554939 
 
 6 
 
 000533049 
 
 1950 
 
 .000512820 
 
 6 
 
 .000503865 
 
 1730 
 
 .000578035 
 
 4 
 
 .000554324 
 
 8 
 
 .000532481 
 
 2 
 
 .000512295 
 
 8 
 
 .000603136 
 
 2 
 
 .000577367 
 
 6 
 
 .000553710 
 
 1880 
 
 .000531915 
 
 4 
 
 .000511770 
 
 1660 
 
 .000602110 
 
 4 
 
 .000576701 
 
 8 
 
 .000553097 
 
 2 
 
 .000531350 
 
 6 
 
 .000511247 
 
 2 
 
 .000601585 
 
 6 
 
 .000576037 
 
 1810 
 
 .000552486 
 
 4 
 
 .000530785 
 
 8 
 
 .000510725 
 
 4 
 
 .000500962 
 
 8 
 
 .000575374 
 
 12 
 
 .000551876 
 
 6 
 
 .000530222 
 
 1960 
 
 .000510204 
 
 6 
 
 .000600240 
 
 1740 
 
 000574713 
 
 14 
 
 .000551268 
 
 8 
 
 000529661 
 
 2 
 
 .000509684 
 
 8 
 
 .000599520 
 
 2 
 
 .000574053 
 
 16 
 
 .000550661 
 
 1890 
 
 .000529100 
 
 4 
 
 .000509165 
 
 1670 
 
 .000598802 
 
 4 
 
 .000573394 
 
 18 
 
 .000550055 
 
 2 
 
 .000528541 
 
 6 
 
 .000508647 
 
 2 
 
 .000598086 
 
 6 
 
 .000572737 
 
 1820 
 
 .000549451 
 
 4 
 
 .000527983 
 
 8 
 
 .000508130 
 
 4 
 
 .000597371 
 
 8 
 
 .000572082 
 
 2 
 
 .000548848 
 
 6 
 
 .000527426 
 
 197C 
 
 .000507614 
 
 6 
 
 .000596658 
 
 1750 
 
 .000571429 
 
 4 
 
 .000548246 
 
 8 
 
 .000526870 
 
 2 
 
 .000507099 
 
 8 
 
 .000595947 
 
 2 
 
 .000570776 
 
 6 
 
 .000547645 
 
 1900 
 
 .000526316 
 
 4 
 
 .000506585 
 
 1680 
 
 .000595238 
 
 4 
 
 .000570125 
 
 8 
 
 .000547046 
 
 2 
 
 .000525762 
 
 6 
 
 .000506073 
 
 2 
 
 000594530 
 
 6 
 
 000569476 
 
 1830 
 
 000546448 
 
 4 
 
 000525210 
 
 8 
 
 .000505561 
 
 4 
 
 .000593824 
 
 8 
 
 .000568828 
 
 2 
 
 .000545851 
 
 6 
 
 .000524659 
 
 1980 
 
 .000505051 
 
 6 
 
 .000593120 
 
 1760 
 
 .000568182 
 
 4 
 
 .000545256 
 
 8 
 
 .000524109 
 
 2 
 
 .000504541 
 
 8 
 
 .000592417 
 
 2 
 
 .000567537 
 
 6 
 
 .000544662 
 
 1910 
 
 .000523560 
 
 4 
 
 .000504032 
 
 1690 
 
 .000591716 
 
 4 
 
 .000566893 
 
 8 
 
 .000544069 
 
 12 
 
 .000523012 
 
 6 
 
 .000503524 
 
 2 
 
 .000591017 
 
 6 
 
 .000566251 
 
 1840 
 
 000543478 
 
 14 
 
 .000522466 
 
 8 
 
 .000503018 
 
 4 
 
 .000590319 
 
 8 
 
 .00056561 1 
 
 2 
 
 .000542888 
 
 16 
 
 .000521920 
 
 1990 
 
 .000502513 
 
 6 
 
 .000589622 
 
 1770 
 
 .000564972 
 
 4 
 
 .000542299 
 
 18 
 
 .000521376 
 
 2 
 
 .000502008 
 
 8 
 
 .000588928 
 
 2 
 
 .000564334 
 
 6 
 
 .000541711 
 
 1920 
 
 .000520833 
 
 4 
 
 .000501504 
 
 1700 
 
 .000588235 
 
 4 
 
 .000563698 
 
 8 
 
 .000541125 
 
 2 
 
 .000520291 
 
 6 
 
 .000501002 
 
 2 
 
 .000587544 
 
 6 
 
 .000563063 
 
 1850 
 
 .000540540 
 
 4 
 
 .000519750 
 
 8 
 
 .000500501 
 
 4 
 
 .000586854 
 
 8 
 
 .000562430 
 
 2 
 
 .000539957 
 
 6 
 
 .000519211 
 
 2000 
 
 .000500000 
 
 Use of reciprocals. Reciprocals may be conveniently used to facili- 
 tate computations in long division. Instead of dividing as usual, multiply 
 the dividend by the reciprocal of the divisor. The method is especially 
 useful when many different dividends are required to be divided by the 
 same divisor. In this case find the reciprocal of the divisor, and make a 
 small table of its multiples up to 9 times, and use this as a multiplication- 
 table instead of actually performing the multiplication in each case. 
 
 EXAMPLE. 9871 and several other numbers are to be divided by 1638. 
 The reciprocal of 1638 is .000610500. 
 Multiples of the 
 
 reciprocal: 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. 
 9. 
 10. 
 
 .0006105 
 .0012210 
 .0018315 
 .0024420 
 .0030525 
 .0036630 
 .0042735 
 .0048840 
 .0054945 
 .0061050 
 
 The table of multiples is made by continuous addi- 
 tion of 6105. The tenth line is written to check the 
 accuracy of the addition, but it is not afterwards used. 
 Operation. 
 
 Dividend 9871 
 
 Take from table 1 0006105 
 
 7 0.042735 
 
 8 00.48840 
 
 9 005.4945 
 
 Quotient 6.0262455 
 
 Correct quotient by direct division 6.0262515 
 
 The result will generally be correct to as many figures as there are signi- 
 ficant figures in the reciprocal, less one, and the error of the next figure will 
 in general not exceed one. In the above example the reciprocal has six 
 significant figures, 610500, and the result is correct to five places of figures. 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 03 
 
 SQUARES, CUBES, SQUARE BOOTS AND CUBE ROOTS OF 
 NUMBERS FROM 0.1 TO 1600. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 1 
 
 .01 
 
 .001 
 
 .3162 
 
 .4642 
 
 3.1 
 
 9.61 
 
 29.791 
 
 .761 
 
 1.458' 
 
 .15 
 
 .0225 
 
 .0034 
 
 .3873 
 
 .5313 
 
 .2 
 
 10.24 
 
 32.768 
 
 .789 
 
 1.474 
 
 .2 
 
 .04 
 
 .008 
 
 .4472 
 
 .5848 
 
 .3 
 
 10.89 
 
 35.937 
 
 .817 
 
 1.489 
 
 .25 
 
 .0625 
 
 .0156 
 
 .500 
 
 .6300 
 
 .4 
 
 11.56 
 
 39.304 
 
 .844 
 
 1.504 
 
 .3 
 
 .09 
 
 .027 
 
 .5477 
 
 .6694 
 
 .5 
 
 12.25 
 
 42.875 
 
 .871 
 
 1.518 
 
 .35 
 
 .1225 
 
 .0429 
 
 .5916 
 
 .7047 
 
 .6 
 
 12.96 
 
 46.656 
 
 .897 
 
 1.533 
 
 .4 
 
 16 
 
 .064 
 
 .6325 
 
 .7368 
 
 .7 
 
 13.69 
 
 50.653 
 
 .924 
 
 1.547 
 
 .45 
 
 .2025 
 
 .0911 
 
 .6708 
 
 .7663 
 
 .8 
 
 14.44 
 
 54.872 
 
 .949 
 
 1.560 
 
 .5 
 
 .25 
 
 .125 
 
 .7071 
 
 .7937 
 
 .9 
 
 15.21 
 
 59.319 
 
 .975 
 
 1.574 
 
 .55 
 
 .3025 
 
 .1664 
 
 .7416 
 
 .8193 
 
 4. 
 
 16. 
 
 64. 
 
 2. 
 
 1.5874 
 
 .6 
 
 .36 
 
 . .216 
 
 .7746 
 
 .8434 
 
 .1 
 
 16.81 
 
 68.921 
 
 2.025 
 
 1.601 
 
 .65 
 
 .4225 
 
 .2746 
 
 .8062 
 
 .8662 
 
 .2 
 
 17.64 
 
 74.088 
 
 2.049 
 
 1.613 
 
 .7 
 
 .49 
 
 .343 
 
 .8367 
 
 .8879 
 
 .3 
 
 18.49 
 
 79.507 
 
 2.074 
 
 1.626 
 
 .75 
 
 .5625 
 
 .4219 
 
 .8660 
 
 .9086 
 
 .4 
 
 19.36 
 
 85..184 
 
 2.098 
 
 1.639 
 
 .8 
 
 .64 
 
 .512 
 
 .8944 
 
 .9283 
 
 .5 
 
 20.25 
 
 91.125 
 
 2.121 
 
 1.651 
 
 .85 
 
 .7225 
 
 .6141 
 
 .9219 
 
 .9473 
 
 .6 
 
 21.16 
 
 97.336 
 
 2.145 
 
 1.663 
 
 .9 
 
 .81 
 
 .729 
 
 .9487 
 
 .9655 
 
 .7 
 
 22.09 
 
 103.823 
 
 2.168 
 
 1.675 
 
 .95 
 
 .9025 
 
 .8574 
 
 .9747 
 
 .9830 
 
 .8 
 
 23.04 
 
 110.592 
 
 2.191 
 
 1.687 
 
 1. 
 
 
 
 
 1. 
 
 .9 
 
 24.01 
 
 1 1 7.649 
 
 2.214 
 
 1.698 
 
 1.05 
 
 '.1025 
 
 J58 
 
 !025 
 
 1.016 
 
 5. 
 
 25. 
 
 125. 
 
 2.2361 
 
 1.7100 
 
 j 
 
 .21 
 
 .331 
 
 .049 
 
 1.032 
 
 .1 
 
 26.01 
 
 132.651 
 
 2.258 
 
 1.721 
 
 J5 
 
 .3225 
 
 .521 
 
 .072 
 
 1.048 
 
 .2 
 
 27.04 
 
 140.608 
 
 2.280 
 
 1.732 
 
 .2 
 
 .44 
 
 728 
 
 .095 
 
 1.063 
 
 .3 
 
 28.09 
 
 148.877 
 
 2.302 
 
 1.744 
 
 .25 
 
 .5625 
 
 .953 
 
 .118 
 
 1.077 
 
 .4 
 
 29.16 
 
 157.464 
 
 2.324 
 
 1.754 
 
 .3 
 
 .69 
 
 2.197 
 
 .140 
 
 1.091 
 
 .5 
 
 30.25 
 
 166.375 
 
 2.345 
 
 1.765 
 
 .35 
 
 .8225 
 
 2.460 
 
 .162 
 
 1.105 
 
 .6 
 
 31.36 
 
 175.616 
 
 2.366 
 
 1.776 
 
 .4 
 
 .96 
 
 2.744 
 
 .183 
 
 1.119 
 
 .7 
 
 32.49 
 
 185.193 
 
 2.387 
 
 1.786 
 
 .45 
 
 2.1025 
 
 3.049 
 
 .204 
 
 1.132 
 
 .8 
 
 33.64 
 
 195.112 
 
 2.408 
 
 1.797 
 
 .5 
 
 2.25 
 
 3.375 
 
 .2247 
 
 1.1447 
 
 .9 
 
 34.81 
 
 205.379 
 
 2.429 
 
 1.807 
 
 .55 
 
 2.4025 
 
 3.724 
 
 .245 
 
 1.157 
 
 6. 
 
 36. 
 
 216. 
 
 2.4495 
 
 1.8171 
 
 .6 
 
 2.56 
 
 4.096 
 
 .265 
 
 1.170 
 
 .1 
 
 37.21 
 
 226.981 
 
 2.470 
 
 1.827 
 
 .65 
 
 2.7225 
 
 4.492 
 
 .285 
 
 K182 
 
 .2 
 
 38.44 
 
 238.328 
 
 2.490 
 
 1.837 
 
 .7 
 
 2.89 
 
 4.913 
 
 .304 
 
 1.193 
 
 .3 
 
 39.69 
 
 250.047 
 
 2.510 
 
 1.847 
 
 .75 
 
 3.0625 
 
 5.359 
 
 .323 
 
 1.205 
 
 .4 
 
 40.96 
 
 262.144 
 
 2.530 
 
 1.857 
 
 .8 
 
 3.24 
 
 5.832 
 
 .342 
 
 1.216 
 
 .5 
 
 42.25 
 
 274.625 
 
 2.550 
 
 1.866 
 
 1.85 
 
 3.4225 
 
 6.332 
 
 .360 
 
 1.228 
 
 .6 
 
 43.56 
 
 287.496 
 
 2.569 
 
 1.876 
 
 1.9 
 
 3.61 
 
 6.859 
 
 .378 
 
 1.239 
 
 .7 
 
 44.89 
 
 300.763 
 
 2.588 
 
 1.885 
 
 1.95 
 
 3.8025 
 
 7.415 
 
 .396 
 
 1.249 
 
 .8 
 
 46.24 
 
 314.432 
 
 2.608 
 
 1.895 
 
 2. 
 
 4. 
 
 8. 
 
 .4142 
 
 1 .2599 
 
 .9 
 
 47.61 
 
 328.509 
 
 2.627 
 
 1.904 
 
 .1 
 
 4.41 
 
 9.261 
 
 .449 
 
 1.281 
 
 7. 
 
 49. 
 
 343*. 
 
 2.6458 
 
 1.9129 
 
 .2 
 
 4.84 
 
 10.648 
 
 .483 
 
 1.301 
 
 j 
 
 50.41 
 
 357.911 
 
 2.665 
 
 1.922 
 
 .3 
 
 5.29 
 
 12.167 
 
 .517 
 
 1.320 
 
 \2 
 
 51.84 
 
 373.248 
 
 2.683 
 
 1.931 
 
 .4 
 
 5.76 
 
 13.824 
 
 .549 
 
 1.339 
 
 .3 
 
 53.29 
 
 389.017 
 
 2.702 
 
 1.940 
 
 .5 
 
 6.25 
 
 15.625 
 
 .581 
 
 1.357 
 
 .4 
 
 54.76 
 
 405.224 
 
 2.720 
 
 1.949 
 
 .6 
 
 6.76 
 
 17.576 
 
 .612 
 
 1.375 
 
 .5 
 
 56.25 
 
 421.875 
 
 2.739 
 
 1.957 
 
 .7 
 
 7.29 
 
 19.683 
 
 .643 
 
 1.392 
 
 .6 
 
 57.76 
 
 438.976 
 
 2.757 
 
 1.966 
 
 .8 
 
 7.84 
 
 21.952 
 
 .673 
 
 1.409 
 
 .7 
 
 59.29 
 
 456.533 
 
 2.775 
 
 1.975 
 
 .9 
 
 8.41 
 
 24.389 
 
 .703 
 
 1.426 
 
 .8 
 
 60.84 
 
 474.552 
 
 2.793 
 
 1.983 
 
 3. 
 
 
 
 9. 
 
 27. 
 
 .7321 
 
 1 .4422 
 
 .9 
 
 62.41 
 
 493.039 
 
 2.811 
 
 1.992 
 
94 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root, 
 
 sT~ 
 
 64. 
 
 512. 
 
 2.8284 
 
 2. 
 
 45 
 
 2025 
 
 91123 
 
 6.7082 
 
 3.5569 
 
 
 65.61 
 
 531.441 
 
 2.846 
 
 2.008 
 
 46 
 
 2116 
 
 97336 
 
 6.7823 
 
 3.5830 
 
 \2 
 
 67.24 
 
 551.368 
 
 2.864 
 
 2.017 
 
 47 
 
 2209 
 
 103823 
 
 6.8557 
 
 3.6088 
 
 .3 
 
 68.89 
 
 571.787 
 
 2.881 
 
 2.025 
 
 48 
 
 2304 
 
 110592 
 
 6.9282 
 
 3.6342 
 
 .4 
 
 70.56 
 
 592.704 
 
 2.898 
 
 2.033 
 
 49 
 
 2401 
 
 1 1 7649 
 
 7. 
 
 3.6593 
 
 .5 
 
 72.25 
 
 614.125 
 
 2.915 
 
 2.041 
 
 50 
 
 2500 
 
 125000 
 
 7.0711 
 
 3.6840 
 
 .6 
 
 73.96 
 
 636.056 
 
 2.933 
 
 2.049 
 
 51 
 
 2601 
 
 132651 
 
 7.1414 
 
 3.7084 
 
 .7 
 
 75.69 
 
 658.503 
 
 2.950 
 
 2.057 
 
 52 
 
 2704 
 
 140608 
 
 7.2111 
 
 3.7325 
 
 .8 
 
 77.44 
 
 681.472 
 
 2.966 
 
 2.065 
 
 53 
 
 2809 
 
 148877 
 
 7.2801 
 
 3.7563 
 
 .9 
 
 79.21 
 
 704.969 
 
 2.983 
 
 2.072 
 
 54 
 
 2916 
 
 ] 57 464 
 
 7.3485 
 
 3.7798 
 
 9. 
 
 81. 
 
 729. 
 
 3. 
 
 2.0801 
 
 55 
 
 3025 
 
 166375 
 
 7.4162 
 
 3.8030 
 
 .1 
 
 82.81 
 
 753.571 
 
 3.017 
 
 2.088 
 
 56 
 
 3136 
 
 175616 
 
 7.4833 
 
 3.8259 
 
 .2 
 
 84.64 
 
 778.688 
 
 3.033 
 
 2.095 
 
 57 
 
 3249 
 
 185193 
 
 7.5498 
 
 3.8485 
 
 .3 
 
 86.49 
 
 804.357 
 
 3.050 
 
 2.103 
 
 58 
 
 3364 
 
 195112 
 
 7.6158 
 
 3.8709 
 
 .4 
 
 88.36 
 
 830.584 
 
 3.066 
 
 2.110 
 
 59 
 
 3481 
 
 205379 
 
 7.6811 
 
 3.8930 
 
 .5 
 
 90.25 
 
 857.375 
 
 3.082 
 
 2.118 
 
 60 
 
 3600 
 
 216000 
 
 7.7460 
 
 3.9149 
 
 .6 
 
 92.16 
 
 884.736 
 
 3.098 
 
 2.125 
 
 61 
 
 3721 
 
 226981 
 
 7.8102 
 
 3.9365 
 
 .7 
 
 94.09 
 
 912.673 
 
 3.114 
 
 2.133 
 
 62 
 
 3844 
 
 238328 
 
 7.8740 
 
 3.9579 
 
 .8 
 
 96.04 
 
 941.192 
 
 3.130 
 
 2.140 
 
 63 
 
 3969 
 
 250047 
 
 7.9373 
 
 3.9791 
 
 .9 
 
 98.01 
 
 970.299 
 
 3.146 
 
 2.147 
 
 64 
 
 4096 
 
 262144 
 
 8. 
 
 4. 
 
 10 
 
 100 
 
 1000 
 
 3.1623 
 
 2.1544 
 
 65 
 
 4225 
 
 274625 
 
 8.0623 
 
 4.0207 
 
 11 
 
 121 
 
 1331 
 
 3.3166 
 
 2.2240 
 
 66 
 
 4356 
 
 287496 
 
 8.1240 
 
 4.0412 
 
 12 
 
 144 
 
 1728 
 
 3.4641 
 
 2.2894 
 
 67 
 
 4489 
 
 300763 
 
 8.1854 
 
 4.0615 
 
 13 
 
 169 
 
 2197 
 
 3.6056 
 
 2.3513 
 
 68 
 
 4624 
 
 314432 
 
 8.2462 
 
 4.0817 
 
 14 
 
 196 
 
 2744 
 
 3.7417 
 
 2.4101 
 
 69 
 
 4761 
 
 328509 
 
 8.3066 
 
 4.1016 
 
 15 
 
 225 
 
 3375 
 
 3.8730 
 
 2.4662 
 
 70 
 
 4900 
 
 343000 
 
 8.3666 
 
 4.1213 
 
 16 
 
 256 
 
 4096 
 
 4. 
 
 2.5198 
 
 71 
 
 5041 
 
 357911 
 
 8.4261 
 
 4.1408 
 
 17 
 
 289 
 
 4913 
 
 4.1231 
 
 2.5713 
 
 72 
 
 5184 
 
 373248 
 
 8.4853 
 
 4.1602 
 
 18 
 
 324 
 
 5832 
 
 4.2426 
 
 2.6207 
 
 73 
 
 5329 
 
 389017 
 
 8.5440 
 
 4.1793 
 
 19 
 
 361 
 
 6859 
 
 4.3589 
 
 2.6684 
 
 74 
 
 5476 
 
 405224 
 
 8.6023 
 
 4.1983 
 
 20 
 
 400 
 
 8000 
 
 4.4721 
 
 2.7144 
 
 75 
 
 5625 
 
 421875 
 
 8.6603 
 
 4.2172 
 
 21 
 
 441 
 
 9261 
 
 4.5826 
 
 2.7589 
 
 76 
 
 5776 
 
 438976 
 
 8.7178 
 
 4.2358 
 
 22 
 
 484 
 
 10648 
 
 4.6904 
 
 2.8020 
 
 77 
 
 5929 
 
 456533 
 
 8.7750 
 
 4.2543 
 
 23 
 
 529 
 
 12167 
 
 4.7958 
 
 2.8439 
 
 78 
 
 6084 
 
 474552 
 
 8.8318 
 
 4.2727 
 
 24 
 
 576 
 
 13824 
 
 4.8990 
 
 2.8845 
 
 79 
 
 6241 
 
 493039 
 
 8.8882 
 
 4.2908 
 
 25 
 
 625 
 
 15625 
 
 5. 
 
 2.9240 
 
 80 
 
 6400 
 
 5.12000 
 
 8.9443 
 
 4.3089 
 
 26 
 
 676 
 
 17576 
 
 5.0990 
 
 2.9625 
 
 81 
 
 6561 
 
 531441 
 
 9. 
 
 4.3267 
 
 27 
 
 729 
 
 19683 
 
 5.1962 
 
 3. 
 
 82 
 
 6724 
 
 551368 
 
 9.0554 
 
 4.3445 
 
 28 
 
 784 
 
 21952 
 
 5.2915 
 
 3.0366 
 
 83 
 
 6889 
 
 571787 
 
 9.1104 
 
 4.3621 
 
 29 
 
 841 
 
 24389 
 
 5.3852 
 
 3.0723 
 
 84 
 
 7056 
 
 592704 
 
 9.1652 
 
 4.3795 
 
 30 
 
 900 
 
 27000 
 
 5.4772 
 
 3.1072 
 
 85 
 
 7225 
 
 614125 
 
 9.2195 
 
 4.3968 
 
 31 
 
 961 
 
 29791 
 
 5.5678 
 
 3.1414 
 
 86 
 
 7396 
 
 636056 
 
 9.2736 
 
 4.4140 
 
 32 
 
 024 
 
 32768 
 
 5.6569 
 
 3.1748 
 
 87 
 
 7569 
 
 658503 
 
 9.3276 
 
 4.4310 
 
 33 
 
 089 
 
 35937 
 
 5.74^6 
 
 3.2075 
 
 88 
 
 7744 
 
 681472 
 
 9.3808 
 
 4.4480 
 
 34 
 
 156 
 
 39304' 
 
 5.8310 
 
 3.2396 
 
 89 
 
 7921 
 
 704969 
 
 9.4340 
 
 4.4647 
 
 35 
 
 225 
 
 42875 
 
 5.9161 
 
 3.2711 
 
 90 
 
 8100 
 
 729000 
 
 9.4868 
 
 4.4814 
 
 36 
 
 296 
 
 46656 
 
 6. 
 
 3.3019 
 
 91 
 
 8281 
 
 753571 
 
 9.5394 
 
 4.4979 
 
 37 
 
 369 
 
 50653 
 
 6.0828 
 
 3.3322 
 
 92 
 
 8464 
 
 778688 
 
 9.5917 
 
 4.5144 
 
 38 
 
 444 
 
 54872 
 
 6.1644 
 
 3.3620 
 
 93 
 
 8649 
 
 804357 
 
 9.6437 
 
 4.5307 
 
 39 
 
 521 
 
 59319 
 
 6.2450 
 
 3.3912 
 
 94 
 
 8836 
 
 830584 
 
 9.6954 
 
 4.5468 
 
 40 
 
 600 
 
 64000 
 
 6.3246 
 
 3.4200 
 
 95 
 
 9025 
 
 857375 
 
 9.7468 
 
 4.5629 
 
 41 
 
 681 
 
 68921 
 
 64031 
 
 3.4482 
 
 96 
 
 9216 
 
 884736 
 
 9.7980 
 
 4.5789 
 
 42 
 
 764 
 
 74088 
 
 6.4807 
 
 3.4760 
 
 97 
 
 9409 
 
 912673 
 
 98489 
 
 4.5947 
 
 43 
 
 849 
 
 79507 
 
 6.5574 
 
 3.5034 
 
 98 
 
 9604 
 
 941 192 
 
 9.8995 
 
 4.6104 
 
 44 
 
 936 
 
 85184 
 
 6.6332 
 
 3.5303 
 
 99 
 
 9801 
 
 970299 j 
 
 9.9499 
 
 4.6261 
 

 SQUARES, CUBES, SQUARE AND CUBE ROOTS. 95 
 
 No. 
 
 Sq. 
 
 Cube 
 
 Sq. 
 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube.. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 Too" 
 
 10000 
 
 1000000 
 
 10. 
 
 4.6416 
 
 155 
 
 24025 
 
 3723875 
 
 12.4499 
 
 5.3717 
 
 101 
 
 10201 
 
 1030301 
 
 10.0499 
 
 4.6570 
 
 156 
 
 24336 
 
 3796416 
 
 12.4900 
 
 5.3832 
 
 102 
 
 10404 
 
 1061208 
 
 10.0995 
 
 4.6723 
 
 157 
 
 24649 
 
 3869893 
 
 12.5300 
 
 5.3947 
 
 103 
 
 10609 
 
 1092727 
 
 10.1489 
 
 4.6875 
 
 158 
 
 24964 
 
 3944312 
 
 12.5698 
 
 5 4061 
 
 104 
 
 10816 
 
 1124864 
 
 10.1980 
 
 4.7027 
 
 159 
 
 25281 
 
 4019679 
 
 12.6095 
 
 5.4175 
 
 105 
 
 11025 
 
 1157625 
 
 10.2470 
 
 4.7177 
 
 160 
 
 25600 
 
 4096000 
 
 12.6491 
 
 5.4288 
 
 106 
 
 11236 
 
 1191016 
 
 10.2956 
 
 4.7326 
 
 161 
 
 25921 
 
 4173281 
 
 12.6886 
 
 5.4401 
 
 107 
 
 11449 
 
 1225043 
 
 10.3441 
 
 4.7475 
 
 162 
 
 26244 
 
 425 1 528 
 
 12.7279 
 
 5.4514 
 
 10S 
 
 11664 
 
 1259712 
 
 10.3923 
 
 4.7622 
 
 163 
 
 26569 
 
 4330747 
 
 12.7671 
 
 5.^26 
 
 109 
 
 11881 
 
 1295029 
 
 10.4403 
 
 4.7769 
 
 164 
 
 26896 
 
 4410944 
 
 12.8062 
 
 5.W37 
 
 110 
 
 12100 
 
 1331000 
 
 10.4881 
 
 4.7914 
 
 165 
 
 27225 
 
 4492125 
 
 12.8452 
 
 5.4848 
 
 1 1 1 
 
 12321 
 
 1367631 
 
 10.5357 
 
 4.8059 
 
 166 
 
 27556 
 
 4574296 
 
 12.8841 
 
 5.4959 
 
 112 
 
 12544 
 
 1404928 
 
 10.5830 
 
 4.8203 
 
 167 
 
 27889 
 
 4657463 
 
 12.9228 
 
 5.5069 
 
 113 
 
 12769 
 
 1442897 
 
 10.6301 
 
 4.8346 
 
 168 
 
 28224 
 
 4741632 
 
 12.9615 
 
 5.5178 
 
 114 
 
 12996 
 
 1481544 
 
 10.6771 
 
 4.8488 
 
 169 
 
 28561 
 
 4826809 
 
 13.0000 
 
 5.5288 
 
 115 
 
 13225 
 
 1 520875 
 
 10.7238 
 
 4.8629 
 
 170 
 
 28900 
 
 4913000 
 
 13.0384 
 
 5.5397 
 
 116 
 
 13456 
 
 1560896 
 
 10.7703 
 
 4.8770 
 
 171 
 
 29241 
 
 5000211 
 
 13.0767 
 
 5.5505 
 
 117 
 
 13689 
 
 1601613 
 
 10.8167 
 
 4.8910 
 
 172 
 
 29584 
 
 5088448 
 
 13.1149 
 
 5.5613 
 
 118 
 
 13924 
 
 1643032 
 
 10.8628 
 
 4.9049 
 
 173 
 
 29929 
 
 5177717 
 
 13.1529 
 
 5.5721 
 
 119 
 
 14161 
 
 1685159 
 
 10.9087 
 
 4.9187 
 
 174 
 
 30276 
 
 5268024 
 
 13.1909 
 
 5.5828 
 
 120 
 
 14400 
 
 1728000 
 
 10.9545 
 
 4.9324 
 
 175 
 
 30625 
 
 5359375 
 
 13.2288 
 
 5.5934 
 
 121 
 
 14641 
 
 1771561 
 
 1 1 .0000 
 
 4.9461 
 
 176 
 
 30976 
 
 5451776 
 
 13.2665 
 
 5.6041 
 
 122 
 
 14884 
 
 1815848 
 
 1 1 .0454 
 
 4.9597 
 
 177 
 
 31329 
 
 5545233 
 
 13.3041 
 
 5.6147 
 
 123 
 
 15129 
 
 1860867 
 
 1 1 .0905 
 
 4.9732 
 
 178 
 
 31684 
 
 5639752 
 
 13.3417 
 
 5.6252 
 
 124 
 
 15376 
 
 1906624 
 
 11.1355 
 
 4.9866 
 
 179 
 
 32041 
 
 5735339 
 
 13.3791 
 
 5.6357 
 
 125 
 
 15625 
 
 1953125 
 
 11.1803 
 
 5.0000 
 
 180 
 
 32400 
 
 5832000 
 
 13.4164 
 
 5.6462 
 
 126 
 
 15876 
 
 2000376 
 
 11.2250 
 
 5.0133 
 
 181 
 
 32761 
 
 5929741 
 
 13.4536 
 
 5.6567 
 
 127 
 
 16129 
 
 2048383 
 
 1 1 .2694 
 
 5.0265 
 
 182 
 
 33124 
 
 6028568 
 
 13.4907 
 
 5.6671 
 
 12S 
 
 16384 
 
 2097152 
 
 11.313" 
 
 5.0397 
 
 183 
 
 33489 
 
 6128487 
 
 13.5277 
 
 5.6774 
 
 129 
 
 16641 
 
 2146689 
 
 11.3578 
 
 5.0528 
 
 184 
 
 33856 
 
 6229504 
 
 13.5647 
 
 5.6873 
 
 130 
 
 16900 
 
 2197000 
 
 11.4018 
 
 5.0658 
 
 185 
 
 34225 
 
 6331625 
 
 13.6015 
 
 5.6980 
 
 131 
 
 17161 
 
 2248091 
 
 11.4455 
 
 5.0788 
 
 186 
 
 34596 
 
 6434856 
 
 13.6382 
 
 5.7083 
 
 132 
 
 17424 
 
 2299963 
 
 11.4891 
 
 5.0916 
 
 187 
 
 34969 
 
 6539203 
 
 13.6748 
 
 5.7185 
 
 133 
 
 17689 
 
 2352637 
 
 11.5326 
 
 5.1045 
 
 188 
 
 35344 
 
 6644672 
 
 13.7113 
 
 5.7287 
 
 134 
 
 17956 
 
 2406104 
 
 11.5758 
 
 5.1172 
 
 189 
 
 35721 
 
 6751269 
 
 13.7477 
 
 5.7388 
 
 135 
 
 18225 
 
 2460375 
 
 11.6190 
 
 5.1299 
 
 190 
 
 36100 
 
 6859000 
 
 13.7840 
 
 5.7489 
 
 136 
 
 18496 
 
 2515456 
 
 11.6619 
 
 5.1426 
 
 191 
 
 36481 
 
 6967871 
 
 13.8203 
 
 5.7590 
 
 137 
 
 18769 
 
 2571353 
 
 11.7047 
 
 5.1551 
 
 192 
 
 36864 
 
 7077888 
 
 13.8564 
 
 5.7690 
 
 138 
 
 19044 
 
 2628072 
 
 11.7473 
 
 5.1676 
 
 193 
 
 37249 
 
 7189057 
 
 13.8924 
 
 5.7790 
 
 139 
 
 19321 
 
 2685619 
 
 11.7898 
 
 5.1801 
 
 194 
 
 37636 
 
 7301384 
 
 13.9284 
 
 5.7890 
 
 140 
 
 19600 
 
 2744000 
 
 11.8322 
 
 5.1925 
 
 195 
 
 38025 
 
 7414875 
 
 13.9642 
 
 5.7989 
 
 141 
 
 19331 
 
 2803221 
 
 11.8743 
 
 5.2048 
 
 196 
 
 38416 
 
 7529536 
 
 14.0000 
 
 5.8088 
 
 142 
 
 20164 
 
 2863288 
 
 11.9164 
 
 5.2171 
 
 1.97 
 
 38809 
 
 7645373 
 
 14.0357 
 
 5.8186 
 
 143 
 
 20449 
 
 2924207 
 
 1 1 .9583 
 
 '5.2293 
 
 198 
 
 39204 
 
 7762392 
 
 14.0712 
 
 5.8285 
 
 144 
 
 20736 
 
 2985984 
 
 12.0000 
 
 5.2415 
 
 199 
 
 39601 
 
 7880599 
 
 14.1067 
 
 5.8383 
 
 145 
 
 21025 
 
 3048625 
 
 120416 
 
 5.2536 
 
 200 
 
 40000 
 
 8000000 
 
 14.1421 
 
 5.8480 
 
 146 
 
 21316 
 
 3112136 
 
 12.0830 
 
 5.2656 
 
 201 
 
 40401 
 
 8120601 
 
 14.1774 
 
 5.8578 
 
 147 
 
 21609 
 
 3176523 
 
 12.1244 
 
 5.2776 
 
 202 
 
 40804 
 
 8242408 
 
 14.2127 
 
 5.8675 
 
 148 
 
 21904 
 
 3241792 
 
 12 1655 
 
 5.2896 
 
 203 
 
 41209 
 
 8365427 
 
 14.2478 
 
 5.8771 
 
 149 
 
 22201 
 
 3307949 
 
 12.2066 
 
 5.3015 
 
 204 
 
 41616 
 
 8489664 
 
 14.2829 
 
 5.8868 
 
 150 
 
 22500 
 
 3375000 
 
 12.2474 
 
 5.3133 
 
 205 
 
 42025 
 
 8615125 
 
 14.3178 
 
 5.8964 
 
 151 
 
 22801 
 
 344295 1 
 
 12.2882 
 
 5.3251 
 
 206 
 
 42436 
 
 8741816 
 
 14.3527 
 
 5.9059 
 
 152 
 
 23104 
 
 3511808 
 
 12.3288 
 
 5.3368 
 
 207 
 
 42849 
 
 8869743 
 
 14.3875 
 
 5.9155 
 
 153 
 
 23409 
 
 3581577 
 
 12.3693 
 
 5.3485 
 
 208 
 
 43264 
 
 8998912 
 
 14.4222 
 
 5.9250 
 
 154 23716 
 
 3652264 
 
 12.4097 
 
 5.3601 
 
 209 
 
 43681 
 
 9129329 
 
 14.4568 
 
 5.9345 
 
96 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Sq. 
 
 Cube. 
 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 2H)" 
 
 44100 
 
 9261000 
 
 14.4914 
 
 5.9439 
 
 265 
 
 70225 
 
 18609625 
 
 16.2788 
 
 6.4232 
 
 211 
 
 44521 
 
 939393 1 
 
 14.5258 
 
 5.9533 
 
 266 
 
 70756 
 
 18821096 
 
 16.3095 
 
 6.4312 
 
 212 
 
 44944 
 
 9528128 
 
 14.5602 
 
 5.9627 
 
 267 
 
 71289 
 
 19034163 
 
 16.3401 
 
 6.4393 
 
 213 
 
 45369 
 
 9663597 
 
 14.5945 
 
 5.9721 
 
 268 
 
 71824 
 
 19248832 
 
 16.3707 
 
 6.4473 
 
 214 
 
 45796 
 
 9800344 
 
 14.6287 
 
 5.9814 
 
 269 
 
 72361 
 
 19465109 
 
 16.4012 
 
 6.4553 
 
 215 
 
 46225 
 
 9938375 
 
 14.6629 
 
 5.9907 
 
 270 
 
 72900 
 
 19683000 
 
 16.4317 
 
 6.4633 
 
 216 
 
 46656 
 
 10077696 
 
 14.6969 
 
 6.0000 
 
 271 
 
 73441 
 
 19902511 
 
 16.4621 
 
 6.4713_ 
 
 217 
 
 47089 
 
 1 02 1 83 1 3 
 
 14.7309 
 
 6.0092 
 
 272 
 
 73984 
 
 20123648 
 
 16.4924 
 
 6.4792 
 
 21S 
 
 47524 
 
 10360232 
 
 14.7648 
 
 6.0185 
 
 273 
 
 74529 
 
 20346417 
 
 16.5227 
 
 6.4872 
 
 1 
 
 47961 
 
 10503459 
 
 14.7986 
 
 6.0277 
 
 274 
 
 75076 
 
 20570824 
 
 16.5529 
 
 6.4951 
 
 220 
 
 48400 
 
 10648000 
 
 14.8324 
 
 6.0368 
 
 275 
 
 75625 
 
 20796875 
 
 16.5831 
 
 6.5030 
 
 221 
 
 48841 
 
 10793861 
 
 14.8661 
 
 6.0459 
 
 276 
 
 76176 
 
 21024576 
 
 16.6132 
 
 6.5108 
 
 222 
 
 49284 
 
 1 094 1 048 
 
 14.8997 
 
 6.0550 
 
 277 
 
 76729 
 
 21253933 
 
 16.6433 
 
 6.5187 
 
 223 
 
 49729 
 
 11089567 
 
 14.9332 
 
 6.0641 
 
 278 
 
 77284 
 
 21484952 
 
 16.6733 
 
 6.5265 
 
 224 
 
 50176 
 
 11239424 
 
 14.9666 
 
 6.0732 
 
 279 
 
 77841 
 
 21717639 
 
 16.7033 
 
 6.5343 
 
 225 
 
 50625 
 
 11390625 
 
 15.0000 
 
 6.0822 
 
 280 
 
 78400 
 
 21952000 
 
 16.7332 
 
 6.5421 
 
 226 
 
 51076 
 
 11543176 
 
 15.0333 
 
 6.0912 
 
 281 
 
 78961 
 
 22188041 
 
 16.7631 
 
 6.5499 
 
 227 
 
 51529 
 
 11697083 
 
 15.0665 
 
 6.1002 
 
 282 
 
 79524 
 
 22425768 
 
 16.7929 
 
 6.5577 
 
 228 
 
 51984 
 
 11852352 
 
 15.0997 
 
 6.1091 
 
 283 
 
 80089 
 
 22665187 
 
 16.8226 
 
 6.5654 
 
 229 
 
 52441 
 
 12008989 
 
 15.1327 
 
 6.1180 
 
 284 
 
 80656 
 
 22906304 
 
 16.8523 
 
 6.5731 
 
 230 
 
 52900 
 
 12167000 
 
 15.1658 
 
 6.1269 
 
 285 
 
 81225 
 
 23149125 
 
 16.8819 
 
 6.5808 
 
 231 
 
 53361 
 
 12326391 
 
 15.1987 
 
 6.1358 
 
 286 
 
 81796 
 
 23393656 
 
 16.9115 
 
 6.5885 
 
 232 
 
 53824 
 
 12487168 
 
 15.2315 
 
 6. 1 446 
 
 287 
 
 82369 
 
 23639903 
 
 16.9411 
 
 6.5962 
 
 233 
 
 54289 
 
 12649337 
 
 15.2643 
 
 6.1534 
 
 288 
 
 82944 
 
 23887872 
 
 16.9706 
 
 6.6039 
 
 234 
 
 54756 
 
 12812904 
 
 15.2971 
 
 6.1622 
 
 289 
 
 83521 
 
 24137569 
 
 17.0000 
 
 6.6115 
 
 235 
 
 55225 
 
 12977875 
 
 15.3297 
 
 6.1710 
 
 290 
 
 84100 
 
 24389000 
 
 17.0294 
 
 6.6191 
 
 236 
 
 55696 
 
 13144256 
 
 15.3623 
 
 6.1797 
 
 291 
 
 84681 
 
 24642171 
 
 17.0587 
 
 6.6267 
 
 237 
 
 56169 
 
 13312053 
 
 153948 
 
 6.1885 
 
 292 
 
 85264 
 
 24897088 
 
 17.0880 
 
 6.6343 
 
 238 
 
 56644 
 
 13481272 
 
 15.4272 
 
 6.1972 
 
 293 
 
 85849 
 
 25153757 
 
 17.1172 
 
 6.6419 
 
 239 
 
 57121 
 
 13651919 
 
 15.4596 
 
 6.2058 
 
 294 
 
 86436 
 
 25412184 
 
 17.1464 
 
 6.6494 
 
 240 
 
 57600 
 
 13824000 
 
 15.4919 
 
 6.2145 
 
 295 
 
 87025 
 
 25672375 
 
 17.1756 
 
 6.6569 
 
 241 
 
 58081 
 
 13997521 
 
 15.5242 
 
 6.223 1 
 
 296 
 
 87616 
 
 25934336 
 
 17.2047 
 
 6.6644 
 
 242 
 
 58564 
 
 14172488 
 
 15.5563 
 
 6.2317 
 
 297 
 
 88209 
 
 26198073 
 
 17.2337 
 
 6.6719 
 
 243 
 
 59049 
 
 14348907 
 
 15.5885 
 
 6.2403 
 
 298 
 
 88804 
 
 26463592 
 
 17.2627 
 
 6.6794 
 
 244 
 
 59536 
 
 14526784 
 
 15.6205 
 
 6.2488 
 
 299 
 
 89401 
 
 26730899 
 
 17.2916 
 
 6.6869 
 
 245 
 
 60025 
 
 14706125 
 
 15.6525 
 
 6.2573 
 
 300 
 
 90000 
 
 27000000 
 
 17.3205 
 
 6.6943 
 
 246 
 
 60516 
 
 14886936 
 
 15.6844 
 
 6.2658 
 
 301 
 
 90601 
 
 27270901 
 
 17.3494 
 
 6.7018 
 
 247 
 
 61009 
 
 1 5069223 
 
 15.7162 
 
 6.2743 
 
 302 
 
 91204 
 
 27543608 
 
 17.3781 
 
 6.7092 
 
 248 
 
 61504 
 
 15252992 
 
 15.7480 
 
 6.2828 
 
 303 
 
 91809 
 
 27818127 
 
 17.4069 
 
 6.7166 
 
 249 
 
 62001 
 
 15438249 
 
 15.7797 
 
 6.2912 
 
 304 
 
 92416 
 
 28094464 
 
 17.4356 
 
 6.7240 
 
 250 
 
 62500 
 
 1 5625000 
 
 15.8114 
 
 6.2996 
 
 305 
 
 93025 
 
 28372625 
 
 1 7.4642 
 
 6.7313 
 
 251 
 
 63001 
 
 15813251 
 
 15.8430 
 
 6.3080 
 
 306 
 
 93636 
 
 28652616 
 
 17.4929 
 
 6.7387 
 
 252 
 
 63504 
 
 16003008 
 
 15.8745 
 
 6.3164 
 
 307 
 
 94249 
 
 28934443 
 
 17.5214 
 
 6.7460 
 
 253 
 
 64009 
 
 16194277 
 
 15.9060 
 
 6.3247 
 
 308 
 
 94864 
 
 29218112 
 
 17.5499 
 
 6.7533 
 
 254 
 
 64516 
 
 16387064 
 
 15.9374 
 
 6.3330 
 
 309 
 
 95481 
 
 29503629 
 
 17.5784 
 
 6.7606 
 
 255 
 
 65025 
 
 16581375 
 
 15.9687 
 
 6.3413 
 
 310 
 
 96100 
 
 29791000 
 
 1 7.6068 
 
 6.7679 
 
 256 
 
 65536 
 
 16777216 
 
 16.0000 
 
 6.3496 
 
 311 
 
 96721 
 
 3008023 1 
 
 17.6352 
 
 6.7752 
 
 257 
 
 66049 
 
 16974593 
 
 16.0312 
 
 6,3579 
 
 312 
 
 97344 
 
 30371328 
 
 17.6635 
 
 6.7824 
 
 258 
 
 66564 
 
 17173512 
 
 16.0624 
 
 6.3661 
 
 313 
 
 97969 
 
 30664297 
 
 17.6918 
 
 6.7897 
 
 259 
 
 67081 
 
 17373979 
 
 16.0935 
 
 6.3743 
 
 314 
 
 98596 
 
 30959144 
 
 17.7200 
 
 6.7969 
 
 260 
 
 67600 
 
 17576000 
 
 16.1245 
 
 6.3825 
 
 315 
 
 99225 
 
 31255875 
 
 17.7482 
 
 6.8041 
 
 261 
 
 68121 
 
 17779581 
 
 16.1555 
 
 63907 
 
 316 
 
 99856 
 
 31554496 
 
 17.7764 
 
 6.8113 
 
 262 
 
 68644 
 
 1 7984728 
 
 16.1864 
 
 6.3988 
 
 317 
 
 100489 
 
 31855013 
 
 17.8045 
 
 6.8185 
 
 263 
 
 69169 
 
 18191447 
 
 16.2173 
 
 6.4070 
 
 318 
 
 101124 
 
 32157432 
 
 17.8326 
 
 6.8256 
 
 264 
 
 69696 
 
 18399744 16.2481 
 
 6.4151 
 
 319 
 
 101761 
 
 32461759 
 
 17.8606 
 
 6.8328 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 97 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 320 
 
 102400 
 
 32768000 
 
 17.8885 
 
 6.8399 
 
 375 
 
 1 40625 
 
 52734375 
 
 19.3649 
 
 7.2112 
 
 321 
 
 103041 
 
 33076161 
 
 17.9165 
 
 6.8470 
 
 376 
 
 141376 
 
 53157376 
 
 19.3907 
 
 7.2177 
 
 322 
 
 1 03684 
 
 33386248 
 
 17.9444 
 
 6.8541 
 
 377 
 
 142129 
 
 53582633 
 
 19.4165 
 
 7.2240 
 
 323 
 
 104329 
 
 33698267 
 
 17.9722 
 
 6.8612 
 
 378 
 
 1 42884 
 
 54010152 
 
 1 9.4422 
 
 7.2304 
 
 324 
 
 104976 
 
 34012224 
 
 18.0000 
 
 6.8683 
 
 379 
 
 143641 
 
 54439939 
 
 19.4679 
 
 7.2368 
 
 325 
 
 105625 
 
 34328125 
 
 18.0278 
 
 6.8753 
 
 380 
 
 1 44400 
 
 54872000 
 
 1 9.4936 
 
 7.2432 
 
 326 
 
 106276 
 
 34645976 
 
 18.0555 
 
 6.8824 
 
 381 
 
 145161 
 
 55306341 
 
 19.5192 
 
 72495 
 
 327 
 
 106929 
 
 34965783 
 
 18.0831 
 
 6.8894 
 
 382 
 
 145924 
 
 55742968 
 
 19.5448 
 
 7.2558 
 
 328 
 
 107584 
 
 35287552 
 
 18.1108 
 
 6.8964 
 
 383 
 
 1 46689 
 
 56181887 
 
 19.5704 
 
 7.2622 
 
 329 
 
 108241 
 
 35611289 
 
 18.1384 
 
 6.9034 
 
 384 
 
 147456 
 
 56623104 
 
 19.5959 
 
 7.2685 
 
 330 
 
 108900 
 
 35937000 
 
 18.1659 
 
 6.9104 
 
 385 
 
 148225 
 
 57066625 
 
 19.6214 
 
 7.2748 
 
 331 
 
 109561 
 
 36264691 
 
 18.1934 
 
 6.9174 
 
 386 
 
 1 48996 
 
 57512456 
 
 19.6469 
 
 7.2811 
 
 332 
 
 110224 
 
 36594368 
 
 18.2209 
 
 6.9244 
 
 387 
 
 149769 
 
 57960603 
 
 19.6723 
 
 7.2874 
 
 333 
 
 110889 
 
 36926037 
 
 18.2483 
 
 6.9313 
 
 388 
 
 150544 
 
 58411072 
 
 19.6977 
 
 7.2936 
 
 334 
 
 111556 
 
 37259704 
 
 18.2757 
 
 6.9382 
 
 389 
 
 151321 
 
 58863869 
 
 19.7231 
 
 7.2999 
 
 335 
 
 112225 
 
 37595375 
 
 18.3030 
 
 6.9451 
 
 390 
 
 152100 
 
 59319000 
 
 19.7484 
 
 7.306! 
 
 336 
 
 1 1 2896 
 
 37933056 
 
 18.3303 
 
 6.9521 
 
 391 
 
 152881 
 
 59776471 
 
 19.7737 
 
 7.3124 
 
 337 
 
 113569 
 
 38272753 
 
 183576 
 
 6.9589 
 
 392 
 
 153664 
 
 60236288 
 
 19.7990 
 
 7.3186 
 
 338 
 
 114244 
 
 38614472 
 
 18.3848 
 
 6.9658 
 
 393 
 
 1 54449 
 
 60698457 
 
 1 9.8242 
 
 7.3248 
 
 339 
 
 114921 
 
 38958219 
 
 18.4120 
 
 6.9727 
 
 394 
 
 155236 
 
 61162984 
 
 1 9.8494 
 
 7.3310 
 
 340 
 
 1 1 5600 
 
 39304000 
 
 18.4391 
 
 6.9795 
 
 395 
 
 156025 
 
 61629875 
 
 19.8746 
 
 7.3372 
 
 341 
 
 116281 
 
 39651821 
 
 18.4662 
 
 6.9864 
 
 396 
 
 156816 
 
 62099136 
 
 1 9.8997 
 
 7.3434 
 
 342 
 
 116964 
 
 40001688 
 
 18.4932 
 
 6.9932 
 
 397 
 
 157609 
 
 62570773 
 
 19.9249 
 
 7.3496 
 
 343 
 
 1 1 7649 
 
 40353607 
 
 18.521)3 
 
 7.0000 
 
 398 
 
 1 58404 
 
 63044792 
 
 19.9499 
 
 7.35*8 
 
 344 
 
 118336 
 
 40707584 
 
 18.5472 
 
 7.0068 
 
 399 
 
 159201 
 
 63521199 
 
 19.9750 
 
 7.361$ 
 
 345 
 
 119025 
 
 41063625 
 
 18.5742 
 
 7.0136 
 
 400 
 
 1 60000 
 
 64000000 
 
 20.0000 
 
 7.3681 
 
 346 
 
 119716 
 
 41421736 
 
 18.6011 7.0203 
 
 401 
 
 160801 
 
 64481201 
 
 20.0250 
 
 7.3742 
 
 347 
 
 120409 
 
 41781923 
 
 18.62797.0271 
 
 402 
 
 161604 
 
 64964808 
 
 20.0499 
 
 7.3803 
 
 348 
 
 121104 
 
 42144192 
 
 18.6548 
 
 7.0338 
 
 403 
 
 162409 
 
 65450827 
 
 20.0749 
 
 7.3864 
 
 349 
 
 121801 
 
 42508549 
 
 18.6815 
 
 7.0406 
 
 404 
 
 163216 
 
 65939264 
 
 20.0998 
 
 7.3925 
 
 350 
 
 122500 
 
 42875000 
 
 18.7083 
 
 7.0473 
 
 405 
 
 164025 
 
 66430125 
 
 20.1246 
 
 7.3986 
 
 351 
 
 123201 
 
 43243551 
 
 18.7350 
 
 7.0540 
 
 406 
 
 164836 
 
 66923416 
 
 20.1494 
 
 7.4047 
 
 352 
 
 123904 
 
 43614208 
 
 18.7617 
 
 7.0607 
 
 407 
 
 165649 
 
 67419143 
 
 20.1742 
 
 7.4108 
 
 353 
 
 124609 
 
 43986977 
 
 18.7883 
 
 7.0674 
 
 408 
 
 166464 
 
 67917312 
 
 20.1990 
 
 7.4169 
 
 354 
 
 125316 
 
 44361864 
 
 18.8149 
 
 7.0740 
 
 409 
 
 167281 
 
 68417929 
 
 20.2237 
 
 7.4229 
 
 355 
 
 126025 
 
 44738875 
 
 18.8414 
 
 7.0807 
 
 410 
 
 168100 
 
 68921 COO 
 
 202485 
 
 7.4290 
 
 356 
 
 126736 
 
 45118016 
 
 18.8680 
 
 7.0873 
 
 411 
 
 168921 
 
 69426531 
 
 20.2731 
 
 7.4350 
 
 357 
 
 127449 
 
 45499293 
 
 18.8944 
 
 7.0940 
 
 412 
 
 1 697 44 
 
 69934528 
 
 20.2978 
 
 7.4410 
 
 358 
 
 128164 
 
 45882712 
 
 18.9209 
 
 7.1006 
 
 413 
 
 170569 
 
 70444997 
 
 20.3224 
 
 7.4470 
 
 359 
 
 128881 
 
 46268279 
 
 18.9473 
 
 7.1072 
 
 414 
 
 171396 
 
 70957944 
 
 20.3470 
 
 7.4530 
 
 360 
 
 129600 
 
 46656000 
 
 189737 
 
 7.1138 
 
 415 
 
 172225 
 
 71473375 
 
 20.3715 
 
 7.4590 
 
 361 
 
 130321 
 
 47045881 
 
 19.0000 
 
 7.1204 
 
 416 
 
 173056 
 
 71991296 
 
 20.3961 
 
 7.4650 
 
 362 
 
 131044 
 
 47437928 
 
 19.0263 
 
 7.1269 
 
 417 
 
 1 73889 
 
 72511713 
 
 20.4206 
 
 7.4710 
 
 363 
 
 131769 
 
 47832147 
 
 19.0526 
 
 7.1335 
 
 418 
 
 1 74724 
 
 73034632 
 
 20.4450 
 
 7.4770 
 
 364 
 
 132496 
 
 48228544 
 
 19.0788 
 
 7.1400 
 
 419 
 
 175561 
 
 73560059 
 
 20.4695 
 
 7.4829 
 
 365 
 
 133225 
 
 48627125 
 
 19.1050 
 
 7.1466 
 
 420 
 
 1 76400 
 
 74088000 
 
 20.4939 
 
 74889 
 
 366 
 
 133956 
 
 49027896 
 
 19.1311 
 
 7.1531 
 
 421 
 
 177241 
 
 74618461 
 
 20.5183 
 
 7.4948 
 
 367 
 
 134689 
 
 49430863 
 
 19.1572 
 
 7.1596 
 
 422 
 
 1 78084 
 
 75151448 
 
 20.5426 
 
 7.5007 
 
 368 
 
 135424 
 
 49836032 
 
 19.1833 
 
 7.1661 
 
 423 
 
 1 78929 
 
 75686967 
 
 20.5670 
 
 7.5067 
 
 369 
 
 136161 
 
 50243409 
 
 19.2094 
 
 7.1726 
 
 424 
 
 179776 
 
 76225024 
 
 20.5913 
 
 7.5126 
 
 370 
 
 1 36900 
 
 50653000 
 
 19.2354 
 
 7.1791 
 
 425 
 
 180625 
 
 76765625 
 
 20.6155 
 
 7.5185 
 
 371 
 
 137641 
 
 51064811 
 
 19.2614 
 
 7.1855 
 
 426 
 
 18M76 
 
 77308776 
 
 20 6398 
 
 7 5244 
 
 372 
 
 138384 
 
 51478848 
 
 19.2873 
 
 7.1920 
 
 427 
 
 182329 
 
 77854483 
 
 20.6640 
 
 7 5302 
 
 373 
 
 374 
 
 139129 
 139876 
 
 51895117 19313217 1984 
 52313624 19.3391 '7.2048 
 
 428 
 429 
 
 183184 
 184041 
 
 78402752 
 78953589 
 
 20.6882 
 20.7123 
 
 7.5361 
 7.5420 
 
'98 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 430 
 431 
 432 
 433 
 434 
 
 184900 
 185761 
 186624 
 187489 
 188356 
 
 79507000 
 80062991 
 80621568 
 81182737 
 81746504 
 
 20.7364 
 20.7605 
 20.7846 
 20.8087 
 20.8327 
 
 7.5478 
 7.5537 
 7.5595 
 7.5654 
 7.5712 
 
 485 
 486 
 487 
 488 
 489 
 
 235225 
 236196 
 237169 
 238144 
 239121 
 
 114084125 
 114791256 
 115501303 
 116214272 
 116930169 
 
 22.0227 
 22.0454 
 22.0681 
 22.0907 
 22.1133 
 
 7.8568 
 7.8622 
 7.8676 
 7.8730 
 7.8784 
 
 435 
 436 
 437 
 438 
 439 
 
 189225 
 190096 
 1 90969 
 191844 
 192721 
 
 82312875 
 82881856 
 83453453 
 84027672 
 846045 1 9 
 
 20.8567 
 20.8806 
 20.9045 
 20.9284 
 20.9523 
 
 7.5770 
 
 7.5828 
 7.5886 
 7.5944 
 76001 
 
 490 
 491 
 492 
 493 
 494 
 
 240100 
 241081 
 242064 
 243049 
 244036 
 
 1 1 7649000 
 118370771 
 119095488 
 119823157 
 120553784 
 
 22.1359 
 22.1585 
 22.1811 
 22.2036 
 22.2261 
 
 7.8837 
 7.8891 
 7.8944 
 7.8998 
 7.9051 
 
 440 
 441 
 442 
 443 
 444 
 
 193600 
 194481 
 195364 
 196249 
 197136 
 
 85184000 
 85766121 
 86350888 
 86938307 
 87528384 
 
 20.9762 
 21.0000 
 21.0238 
 21.0476 
 21.0713 
 
 7.6059 
 7.6117 
 7.6174 
 7.6232 
 7.6289 
 
 495 
 496 
 497 
 498 
 499 
 
 245025 
 246016 
 247009 
 248004 
 249001 
 
 121287375 
 122023936 
 122763473 
 123505992 
 124251499 
 
 22.2486 
 22.2711 
 22.2935 
 22.3159 
 22.3383 
 
 7.9105 
 7.9158 
 7.9211 
 7.9264 
 7.9317 
 
 445 
 446 
 447 
 448 
 449 
 
 198025 
 198916 
 199809 
 200704 
 201601 
 
 88121125 
 88716536 
 893 1 4623 
 89915392 
 90518849 
 
 21 0950 
 21.1187 
 21.1424 
 21.1660 
 21.1896 
 
 7.6346 
 7.6403 
 7.6460 
 7.6517 
 7.6574 
 
 500 
 501 
 502 
 503 
 504 
 
 250000 
 251001 
 252004 
 253009 
 254016 
 
 125000000 
 125751501 
 1 26506008 
 127263527 
 128024064 
 
 22.3607 
 22.3830 
 22.4054 
 22.4277 
 22.4499 
 
 7.9370 
 7.9423 
 7.9476 
 7.9528 
 7.9581 
 
 450 
 451 
 452 
 453 
 454 
 
 202500 
 203401 
 204304 
 205209 
 206116 
 
 91125000 
 91733851 
 92345408 
 92959677 
 93576664 
 
 21.2132 
 21.2368 
 21.2603 
 21.2838 
 21.3073 
 
 7.6631 
 7.6688 
 7.6744 
 7.6800 
 7.6857 
 
 505 
 506 
 507 
 508 
 509 
 
 255025 
 256036 
 257049 
 258064 
 259081 
 
 128787625 
 129554216 
 130323843 
 131096512 
 131872229 
 
 22.4722 
 22.4944 
 22.5167 
 22.5389 
 22.5610 
 
 7.9634 
 7.9686 
 79739 
 7.9791 
 7.9843 
 
 455 
 456 
 457 
 458 
 459 
 
 207025 
 207936 
 208849 
 209764 
 210681 
 
 94196375 
 94818816 
 95443993 
 96071912 
 96702579 
 
 21.3307 
 21.3542 
 21.3776 
 21.4009 
 21.4243 
 
 7.6914 
 7.6970 
 7.7026 
 7.7082 
 7.7138 
 
 510 
 511 
 512 
 513 
 514 
 
 260100 
 261121 
 262144 
 263169 
 264196 
 
 132651000 
 133432831 
 134217728 
 135005697 
 135796744 
 
 22.5832 
 22.6053 
 22.6274 
 22.6495 
 22.6716 
 
 7.9896 
 7.9948 
 8.0000 
 8.0052 
 8.0104 
 
 460 
 461 
 462 
 463 
 464 
 
 211600 
 212521 
 213444 
 214369 
 215296 
 
 97336000 
 
 97972181 
 98611128 
 99252847 
 99897344 
 
 21.4476 
 21.4709 
 21.4942 
 21.5174 
 21.5407 
 
 7.7194 
 7.7250 
 7.7306 
 7.7362 
 7.7418 
 
 515 
 516 
 517 
 518 
 519 
 
 265225 
 266256 
 267289 
 268324 
 269361 
 
 136590875 
 137388096 
 138188413 
 138991832 
 139798359 
 
 22 6936 
 22.7156 
 22.7376 
 22.7596 
 22.7816 
 
 8.0156 
 8.0208 
 8.0260 
 8.0311 
 8.0363 
 
 465 
 466 
 467 
 468 
 469 
 
 216225 
 217156 
 218089 
 219024 
 219961 
 
 100544625 
 101194696 
 101847563 
 102503232 
 103161709 
 
 21.5639 
 21.5870 
 21.6102 
 21.6333 
 21.6564 
 
 7.7473 
 7.7529 
 7.7584 
 7.7639 
 7.7695 
 
 520 
 521 
 522 
 523 
 524 
 
 270400 
 271441 
 272484 
 273529 
 274576 
 
 140608000 
 141420761 
 142236648 
 143055667 
 143877824 
 
 22.8035 
 22.8254 
 22.8473 
 22.8692 
 22.8910 
 
 8.0415 
 8.0466 
 8.0517 
 8.0569 
 8.0620 
 
 470 
 471 
 472 
 473 
 474 
 
 220900 
 221841 
 222784 
 223729 
 224676 
 
 103823000 
 104487111 
 105154048 
 105823817 
 106496424 
 
 21.6795 
 21.7025 
 21.7256 
 21.7486 
 21.7715 
 
 7.7750 
 7.7805 
 7.7860 
 7.7915 
 7.7970 
 
 525 
 526 
 527 
 
 528 
 529 
 
 275625 
 276676 
 277729 
 
 278784 
 279841 
 
 144703125 
 145531576 
 146363183 
 147197952 
 148035889 
 
 22.9129 
 22.9347 
 22.9565 
 22.9783 
 23.0000 
 
 8.0671 
 8.0723 
 8.0774 
 8.0825 
 8.0876 
 
 475 
 476 
 477 
 478 
 479 
 
 225625 
 226576 
 227529 
 228484 
 22944 1 
 
 107171875 
 107850176 
 108531333 
 109215352 
 109902239 
 
 21.7945 
 21.8174 
 21 8403 
 21.8632 
 21.8861 
 
 7.8025 
 7.8079 
 7.8134 
 7.8188 
 7.8243 
 
 530 
 531 
 532 
 533 
 534 
 
 280900 
 281961 
 283024 
 284089 
 285156 
 
 148877000 
 149721291 
 1 50568768 
 151419437 
 152273304 
 
 23.0217 
 23.0434 
 23.0651 
 23 0868 
 23.1084 
 
 80927 
 8.0978 
 8.1028 
 8.1079 
 8.1130 
 
 480 
 481 
 482 
 483 
 484 
 
 230400 
 231361 
 232324 
 233289 
 234256 
 
 110592000 
 111284641 
 111980168 
 112678587 
 1 13379904 
 
 21.9089 
 21.9317 
 21.9545 
 21.9773 
 22.0000 
 
 7.8297 
 7.8352 
 7.8406 
 7.8460 
 7.8514 
 
 535 
 536 
 537 
 538 
 539 
 
 286225 
 287296 
 288369 
 289444 
 290521 
 
 153130375 
 1 53990656 
 154854153 
 155720S72 
 156590819 
 
 23.1301 
 23.1517 
 23.1733 
 23.1948 
 23.2164 
 
 8.1180 
 8.123! 
 8.128! 
 8.1332 
 8.1332 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 99 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 540 
 541 
 542 
 543 
 544 
 
 291600 
 292681 
 293764 
 294849 
 295936 
 
 157464000 
 158340421 
 159220088 
 160103007 
 160989184 
 
 23.2379 
 23.2594 
 23.2809 
 23.3024 
 23.3238 
 
 8.1433 
 8.1483 
 8.1533 
 8.1583 
 8.1633 
 
 595 
 
 596 
 597 
 598 
 599 
 
 354025 
 355216 
 356409 
 357604 
 358801 
 
 210644875 
 211708736 
 212776173 
 213847192 
 214921799 
 
 24.3926 
 24.4131 
 24.4336 
 24.4540 
 24.4745 
 
 8.4108 
 8.4155 
 8.4202 
 8.4249 
 8.4296 
 
 545 
 
 546 
 547 
 548 
 549 
 
 297025 
 298116 
 299209 
 300304 
 301401 
 
 161878625 
 162771336 
 163667323 
 164566592 
 165469149 
 
 23.3452 
 23.3666 
 23.3880 
 23.4094 
 23.4307 
 
 8.1683 
 8.1733 
 8.1783 
 8.1833 
 8.1882 
 
 600 
 601 
 602 
 603 
 604 
 
 360000 
 361201 
 362404 
 363609 
 364816 
 
 216000000 
 217081801 
 218167208 
 219256227 
 220348864 
 
 24.4949 
 24.5153 
 24.5357 
 24.5561 
 24.5764 
 
 8.4343 
 8.4390 
 8.4437 
 8.4484 
 8.4530 
 
 550 
 551 
 552 
 553 
 554 
 
 302500 
 303601 
 304704 
 305809 
 306916 
 
 166375000 
 167284151 
 168196608 
 169112377 
 170031464 
 
 23.4521 
 23.4734 
 23.4947 
 23.5160 
 23.5372 
 
 8.1932 
 8.1982 
 8.2031 
 8.2081 
 8.2130 
 
 605 
 606 
 607 
 608 
 609 
 
 366025 
 367236 
 36S449 
 369664 
 370881 
 
 221445125 
 222545016 
 223648543 
 224755712 
 225866529 
 
 24.5967 
 24.6171 
 24.6374 
 24.6577 
 24.6779 
 
 8.4577 
 8.4623 
 8.4670 
 8.4716 
 8.4763 
 
 555 
 
 556 
 557 
 
 558 
 559 
 
 308025 
 309136 
 310249 
 311364 
 312481 
 
 170953875 
 171879616 
 1 72808693 
 173741112 
 174676879 
 
 23.5584 
 23.5797 
 23.6008 
 23.6220 
 23.6432 
 
 8.2180 
 8.2229 
 8.2278 
 8.2327 
 8.2377 
 
 610 
 611 
 612 
 613 
 614 
 
 372100 
 373321 
 374544 
 375769 
 376996 
 
 226981000 
 228099131 
 229220928 
 230346397 
 231475544 
 
 24.6982 
 24.7184 
 24.7386 
 24.7588 
 24.7790 
 
 8.4809 
 8.4856 
 8.4902 
 8.4948 
 8.4994 
 
 560 
 561 
 562 
 563 
 564 
 
 313600 
 314721 
 315844 
 316969 
 318096 
 
 175616000 
 176558481 
 177504328 
 178453547 
 179406144 
 
 23.6643 
 23.6854 
 23.7065 
 23.7276 
 23.7487 
 
 8.2426 
 8.2475 
 8.2524 
 8.2573 
 8.2621 
 
 615 
 616 
 617 
 618 
 619 
 
 378225 
 379456 
 380689 
 381924 
 383161 
 
 232608375 
 233744896 
 234885113 
 236029032 
 237176659 
 
 24.7992 
 24.8193 
 24.8395 
 24.8596 
 24.8797 
 
 8.5040 
 8.5C86 
 8.5132 
 8.5178 
 8.5224 
 
 565 
 566 
 567 
 568 
 569 
 
 319225 
 320356 
 321489 
 322624 
 323761 
 
 180362125 
 181321496 
 182284263 
 183250432 
 184220009 
 
 23.7697 
 23.7908 
 23.8118 
 23.8328 
 23.8537 
 
 8.2670 
 8.2719 
 8.2768 
 8.2816 
 8.2865 
 
 620 
 621 
 622 
 623 
 624 
 
 384400 
 385641 
 386884 
 388129 
 389376 
 
 238328000 
 239483061 
 240641848 
 241804367 
 242970624 
 
 24.8998 
 24.9199 
 24.9399 
 24.9600 
 24.9800 
 
 8.5270 
 8.5316 
 8.5362 
 8.5408 
 8.5453 
 
 570 
 571 
 572 
 573 
 574 
 
 324900 
 326041 
 327184 
 328329 
 329476 
 
 185193000 
 186169411 
 187149248 
 188132517 
 189119224 
 
 23.8747 
 23.8956 
 23.9165 
 23.9374 
 23.9583 
 
 8.2913 
 8.2962 
 8.3010 
 8.3059 
 8.3107 
 
 625 
 626 
 627 
 628 
 629 
 
 390625 
 391876 
 393129 
 394384 
 395641 
 
 244140625 
 245314376 
 246491883 
 247673152 
 248858189 
 
 25.0000 
 25.0200 
 25.0400 
 25.0599 
 25.0799 
 
 8.5499 
 8.5544 
 85590 
 8.5635 
 8.5681 
 
 575 
 576 
 577 
 578 
 579 
 
 330625 
 331776 
 332929 
 334084 
 335241 
 
 190109375 
 191102976 
 192100033 
 193100552 
 194104539 
 
 23.9792 
 24.0000 
 24.0208 
 24.0416 
 24.0624 
 
 8.3155 
 8.3203 
 8.3251 
 8.3300 
 8.3348 
 
 630 
 631 
 632 
 633 
 634 
 
 396900 
 398161 
 399424 
 400689 
 401956 
 
 250047000 
 251239591 
 252435968 
 253636137 
 254840104 
 
 25.0998 
 25.1197 
 25.1396 
 25.1595 
 25.1794 
 
 8.5726 
 8.5772 
 8.5817 
 8.5862 
 8.5907 
 
 580 
 581 
 582 
 583 
 584 
 
 336400 
 337561 
 338724 
 339889 
 341056 
 
 195112000 
 196122941 
 197137368 
 198155287 
 199176704 
 
 24.0832 
 24.1039 
 24.1247 
 24.1454 
 24.1661 
 
 8.3396 
 8.3443 
 8.3491 
 8.3539 
 8.3587 
 
 635 
 636 
 637 
 638 
 639 
 
 403225 
 404496 
 405769 
 407044 
 408321 
 
 256047875 
 257259456 
 258474853 
 259694072 
 260917119 
 
 25.1992 
 25.2190 
 25.2389 
 25.2587 
 25.2784 
 
 8.5952 
 8.5997 
 8.6043 
 8.6088 
 8.6132 
 
 585 
 586 
 587 
 588 
 589 
 
 342225 
 343396 
 344569 
 345744 
 34692 1 
 
 200201625 
 201230056 
 202262003 
 203297472 
 204336469 
 
 24.1868 
 24.2074 
 24.2281 
 24.2487 
 24.2693 
 
 8.3634 
 8.3682 
 8.3730 
 8.3777 
 8.3825 
 
 640 
 641 
 642 
 643 
 644 
 
 409600 
 410881 
 412164 
 413449 
 414736 
 
 262144000 
 263374721 
 264609288 
 265847707 
 267089984 
 
 25.2982 
 25.3180 
 25.3377 
 25.3574 
 25.3772 
 
 8.6177 
 8.6222 
 8.6267 
 8.6312 
 8.6357 
 
 590 
 591 
 592 
 593 
 594 
 
 348100 
 349281 
 350464 
 351649 
 352836 
 
 205379000 
 206425071 
 207474688 
 208527857 
 209584584 
 
 24.2899 
 24.3105 
 24.3311 
 24.3516 
 24.3721 
 
 8.3872 
 8.3919 
 8.3967 
 8.4014 
 8.4061 
 
 645 
 646 
 647 
 648 
 649 
 
 416025 
 417316 
 4 1 8609 
 419904 
 421201 
 
 268336125 
 269586136 
 27084002.3 
 272097792 
 273359449 
 
 25.3969 
 25.416 
 25.436 
 25.4558 
 25.475 
 
 8.6401 
 8.6446 
 8.6490 
 8.6535 
 8.6579 
 
100 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 650 
 651 
 652 
 653 
 654 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 705 
 706 
 707 
 708 
 709 
 
 Square 
 
 Cube* 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 422500 
 42380! 
 425104 
 426409 
 427716 
 
 274625000 
 275894451 
 277167808 
 278445077 
 279726264 
 
 25.4951 
 25.5147 
 25.5343 
 25.5539 
 25.5734 
 
 6.6624 
 8.6668 
 8.6713 
 8.6757 
 8.6801 
 
 497625 
 498436 
 499849 
 501264 
 502681 
 
 350402625 
 351895816 
 353393243 
 354894912 
 356400829 
 
 26.5518 
 26.5707 
 26.5895 
 26.6083 
 26.6271 
 
 8.9001 
 8.9043 
 8.9085 
 8.9127 
 8.9169 
 
 655 
 656 
 657 
 658 
 659 
 
 429025 
 430336 
 431649 
 432964 
 434281 
 
 281011375 
 282300416 
 283593393 
 284890312 
 286191179 
 
 25.5930 
 25.6125 
 25.6320 
 25.6515 
 25.6710 
 
 8.6845 
 8.6890 
 8.6934 
 8.6978 
 8.7022 
 
 710 
 711 
 712 
 713 
 714 
 
 504100 
 505521 
 506944 
 508369 
 509796 
 
 35791 100C 
 359425431 
 360944128 
 362467097 
 363994344 
 
 26.6458 
 26.6646 
 26.6833 
 26.7021 
 26.7208 
 
 8.9211 
 8.9253 
 8.9295 
 8.9337 
 8.9378 
 
 660 
 661 
 662 
 663 
 664 
 
 435600 
 43692 1 
 438244 
 439569 
 440896 
 
 287496000 
 288804781 
 290117528 
 291434247 
 292754944 
 
 25.6905 
 25.7099 
 25.7294 
 25.7488 
 25.7682 
 
 8.7066 
 8.7110 
 8.7154 
 8.7198 
 8.7241 
 
 715 
 716 
 717 
 718 
 719 
 
 511225 
 512656 
 5 1 4089 
 515524 
 516961 
 
 365525875 
 367061696 
 368601813 
 370146232 
 371694959 
 
 26.7395 
 26.7582 
 26.7769 
 26.7955 
 26.8142 
 
 8.9420 
 8.9462 
 8.9503 
 8.9545 
 8.9587 
 
 665 
 566 
 667 
 663 
 669 
 
 442225 
 443556 
 444889 
 446224 
 447561 
 
 294079625 
 295408296 
 296740963 
 298077632 
 299418309 
 
 25.7876 
 25.8070 
 25.8263 
 25.8457 
 25.8650 
 
 8.7285 
 87329 
 
 8.7373 
 8.7<16 
 8.7460 
 
 720 
 
 721 
 722 
 723 
 724 
 
 518400 
 519841 
 521284 
 522729 
 524176 
 
 373248000 
 374805361 
 376367048 
 377933067 
 379503424 
 
 26.8328 
 26.8514 
 26.8701 
 26.8887 
 26.9072 
 
 8.9628 
 8.9670 
 8.9711 
 8.9752 
 8.9794 
 
 670 
 671 
 672 
 673 
 674 
 
 448900 
 450241 
 451584 
 452929 
 454276 
 
 300763000 
 302111711 
 303464448 
 304821217 
 306182024 
 
 25.8844 
 25.9037 
 25.9230 
 25.9422 
 25.9615 
 
 8.7503 
 8.7547 
 8.7590 
 8.7634 
 8.7677 
 
 725 
 726 
 727 
 728 
 729 
 
 525625 
 527076 
 528529 
 529984 
 531441 
 
 381078125 
 382657176 
 384240583 
 385828352 
 387420489 
 
 26.9258 
 26.9444 
 26.9629 
 26.9815 
 27.0000 
 
 8.9835 
 8.9876 
 8.9918 
 8.9959 
 9.0000 
 
 675 
 676 
 677 
 673 
 679 
 
 455625 
 456976 
 458329 
 459684 
 461041 
 
 307546875 
 308915776 
 310288733 
 311665752 
 313046839 
 
 25.9808 
 26.0000 
 26.0192 
 26.0384 
 26.0576 
 
 8.7721 
 8.7764 
 8.7807 
 8.7850 
 8.7893 
 
 730 
 731 
 
 732 
 733 
 734 
 
 532900 
 534361 
 535824 
 537289 
 538756 
 
 389017000 
 390617891 
 392223168 
 393832837 
 395446904 
 
 27.0185 
 27.0370 
 27.0555 
 27.0740 
 27.0924 
 
 9.0041 
 9.0082 
 9.0123 
 9.0164 
 9.0205 
 
 680 
 681 
 682 
 683 
 684 
 
 462400 
 463761 
 465124 
 466489 
 467856 
 
 314432000 
 315821241 
 317214568 
 318611987 
 320013504 
 
 26.0768 
 26.0960 
 26.1151 
 26.1343 
 26.1534 
 
 8.7937 
 8.7980 
 8.8023 
 8.8066 
 8.8109 
 
 735 
 
 736 
 737 
 738 
 739 
 
 540225 
 541696 
 543169 
 5 4464 4 
 546121 
 
 397065375 
 398688256 
 400315553 
 401947272 
 403583419 
 
 27.1109 
 27.1293 
 27.1477 
 27.1662 
 27.1846 
 
 9.0246 
 9.0287 
 9.0328 
 9.0369 
 9.0410 
 
 685 
 686 
 687 
 688 
 689 
 
 469225 
 470596 
 471969 
 473344 
 474721 
 
 321419125 
 322828856 
 324242703 
 325660672 
 327082769 
 
 26.1725 
 26.1916 
 26.2107 
 26.2298 
 26.2488 
 
 8.8152 
 8.8194 
 8.8237 
 8.8280 
 8.8323 
 
 740 
 741 
 742 
 743 
 744 
 
 54760C 
 54908 1 
 550564 
 552049 
 553536 
 
 405224000 
 406869021 
 408518488 
 410172407 
 
 411830784 
 
 27.2029 
 27.2213 
 27.2397 
 27.2580 
 27.2764 
 
 9.0450 
 90491 
 9.0532 
 9.0572 
 9.0613 
 
 690 
 691 
 692 
 693 
 694 
 
 476100 
 477481 
 478864 
 480249 
 481636 
 
 328509000 
 329939371 
 331373888 
 332812557 
 334255384 
 
 26.2679 
 26.2869 
 26.3059 
 26.3249 
 26.3439 
 
 8.8366 
 8.8408 
 8.8451 
 8.8493 
 8.8536 
 
 745 
 
 746 
 747 
 748 
 749 
 
 555025 
 556516 
 558009 
 559504 
 561001 
 
 413493625 
 415160936 
 416832723 
 418508992 
 420189749 
 
 27.2947 
 273130 
 27.3313 
 27.3496 
 27.3679 
 
 9.0654 
 9.0694 
 9.0735 
 9.0775 
 9.0816 
 
 695 
 696 
 697 
 698 
 699 
 
 483025 
 484416 
 485809 
 487204 
 488601 
 
 335702375 
 337153536 
 338608873 
 340068392 
 341532099 
 
 26.3629 
 26.3818 
 26.4008 
 26.4197 
 26.4386 
 
 8.8578 
 8.8621 
 8.8663 
 8.8706 
 8.8748 
 
 750 
 751 
 752 
 753 
 
 754 
 
 562500 
 564001 
 565504 
 567009 
 568516 
 
 421875000 
 423564751 
 425259008 
 426957777 
 428661061 
 
 27.3861 
 27.4044 
 27.4226 
 27.4408 
 27.4591 
 
 9.0856 
 90896 
 9.0937 
 9.0977 
 9.1017 
 
 700 
 701 
 702 
 703 
 704 
 
 490000 
 491401 
 492804 
 494209 
 495616 
 
 343000000 
 344472101 
 345948408 
 347428927 
 348913664 
 
 26.4575 
 26.4764 
 26.4953 
 26.5141 
 26.5330 
 
 88790 
 8.8833 
 8.8875 
 8.8917 
 8.8959 
 
 755 
 756 
 757 
 758 
 759 
 
 570025 
 571536 
 573049 
 574564 
 576081 
 
 430368875 
 432081216 
 433798093 
 435519512 
 437245479 
 
 27.4773 
 27.4955 
 27.5136 
 27.5318 
 27.5500 
 
 9 1057 
 9.1098 
 9.1138 
 9 1178 
 9.1219 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 101 
 
 No 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 760 
 
 577600 
 
 438976000 
 
 27.5681 
 
 9.1258 
 
 ~8l5 
 
 664225 
 
 541343375 
 
 28.5482 
 
 9.3408 
 
 76 
 
 57912 
 
 440711081 
 
 27.5862 
 
 9.1298 
 
 816 
 
 665856 
 
 543338496 
 
 28.5657 
 
 9.3447 
 
 762 
 
 580644 
 
 442450728 
 
 27.6043 
 
 9.1338 
 
 81 
 
 667489 
 
 545338513 
 
 28.5832 
 
 9.3485 
 
 763 
 
 532 1 69 
 
 444194947 
 
 27.6225 
 
 9.1378 
 
 818 
 
 66912 
 
 547343432 
 
 28.6007 
 
 9.3523 
 
 764 
 
 583696 
 
 445943744 
 
 27.6405 
 
 9.1418 
 
 819 
 
 67076 
 
 549353259 
 
 28.6182 
 
 9.3561 
 
 765 
 
 585225 
 
 447697125 
 
 27.6586 
 
 9.1458 
 
 820 
 
 672400 
 
 55136800C 
 
 28.6356 
 
 9.3599 
 
 766 
 
 586756 
 
 449455096 
 
 27.6767 
 
 9. 1 498 
 
 82 
 
 67404 
 
 55338766 
 
 28.6531 
 
 9.3637 
 
 767 
 
 588289 
 
 451217663 
 
 27.6948 
 
 9.1537 
 
 822 
 
 67568 
 
 55541224S 
 
 28.6705 
 
 9.3675 
 
 768 
 
 589824 
 
 452984832 
 
 27.7128 
 
 9.1577 
 
 823 
 
 67732 
 
 55744176 
 
 28.6880 
 
 9.3713 
 
 769 
 
 591361 
 
 454756609 
 
 27.7308 
 
 9.1617 
 
 824 
 
 678976 
 
 559476224 
 
 28.7054 
 
 9.3751 
 
 770 
 
 592900 
 
 456533000 
 
 27.7489 
 
 9.1657 
 
 825 
 
 68062 
 
 561515625 
 
 28.7228 
 
 9.3789 
 
 771 
 
 594441 
 
 458314011 
 
 27.7669 
 
 9.1696 
 
 826 
 
 682276 
 
 563559976 
 
 28.7402 
 
 9.3827 
 
 772 
 
 595984 
 
 460099648 
 
 27.7849 
 
 9.1736 
 
 827 
 
 683929 
 
 565609283 
 
 28.7576 
 
 9.3865 
 
 773 
 
 597529 
 
 461889917 
 
 27.8029 
 
 9.1775 
 
 828 
 
 685584 
 
 567663552 
 
 28.7750 
 
 9.3902 
 
 774 
 
 599076 
 
 463684824 
 
 27.8209 
 
 9.1815 
 
 829 
 
 68724 
 
 569722789 
 
 28.7924 
 
 9.3940 
 
 775 
 
 600625 
 
 465434375 
 
 27.8388 
 
 9.1855 
 
 830 
 
 688900 
 
 571787000 
 
 28.8097 
 
 9.3978 
 
 776 
 
 602176 
 
 467288576 
 
 27.8568 
 
 9.1894 
 
 83 
 
 69056 
 
 57385619 
 
 28.8271 
 
 9.4016 
 
 777 
 
 603729 
 
 469097433 
 
 27.8747 
 
 9.^33 
 
 832 
 
 692224 
 
 575930368 
 
 28.8444 
 
 9.4053 
 
 778 
 
 605284 
 
 470910952 
 
 27.8927 
 
 9.1973 
 
 833 
 
 693889 
 
 578009537 
 
 28.8617 
 
 9.4091 
 
 779 
 
 606341 
 
 472729139 
 
 27.9106 
 
 9.2012 
 
 834 
 
 695556 
 
 580093704 
 
 28.8791 
 
 9.4129 
 
 780 
 
 603400 
 
 474552000 
 
 27.9285 
 
 9.2052 
 
 835 
 
 697225 
 
 582182875 
 
 28.8964 
 
 9.4166 
 
 781 
 
 609961 
 
 476379541 
 
 27.9464 
 
 9.2091 
 
 836 
 
 698896 
 
 584277056 
 
 28.9131 
 
 9.4204 
 
 782 
 
 611524 
 
 478211768 
 
 27.9643 
 
 9.2130 
 
 837 
 
 700569 
 
 586376253 
 
 28.9310 
 
 9.4241 
 
 783 
 
 6(3089 
 
 430048687 
 
 27.9821 
 
 9.2170 
 
 838 
 
 702244 
 
 588480472 
 
 28.9482 
 
 9.4279 
 
 784 
 
 614656 
 
 431890304 
 
 28.0000 
 
 9.2209 
 
 839 
 
 703921 
 
 590589719 
 
 28.9655 
 
 9.4316 
 
 785 
 
 616225 
 
 483736625 
 
 28.0179 
 
 9.2248 
 
 840 
 
 705600 
 
 592704000 
 
 28.9828 
 
 9.4354 
 
 786 
 
 617796 
 
 485587656 
 
 28.0357 
 
 9.2287 
 
 841 
 
 707281 
 
 594823321 
 
 29.0000 
 
 9.4391 
 
 787 
 
 619369 
 
 487443403 
 
 28.0535 
 
 9.2326 
 
 842 
 
 708964 
 
 596947688 
 
 29.0172 
 
 9.4429 
 
 788 
 
 620944 
 
 489303872 
 
 28.0713 
 
 9.2365 
 
 843 
 
 710649 
 
 599077107 
 
 29.0345 
 
 9.4466 
 
 789 
 
 622521 
 
 491169069 
 
 28.0891 
 
 9.2404 
 
 844 
 
 712336 
 
 601211584 
 
 29.0517 
 
 9.4503 
 
 790 
 
 624100 
 
 493039000 
 
 28.1069 
 
 9.2443 
 
 845 
 
 714025 
 
 603351125 
 
 29.0689 
 
 9.4541 
 
 791 
 
 625631 
 
 494913671 
 
 28.1247 
 
 9.2482 
 
 846 
 
 715716 
 
 605495736 
 
 29.0861 
 
 9.4578 
 
 792 
 
 627264 
 
 496793088 
 
 28.1425 
 
 9.2521 
 
 847 
 
 717409 
 
 607645423 
 
 29.1033 
 
 9.4615 
 
 793 
 
 623349 
 
 498677257 
 
 28.1603 
 
 9.2560 
 
 848 
 
 719104 
 
 609800192 
 
 29.1204 
 
 9.4652 
 
 794 
 
 630436 
 
 500566184 
 
 28.1780 
 
 9.2599 
 
 849 
 
 720801 
 
 611960049 
 
 29.1376 
 
 9.4690 
 
 795 
 
 632025 
 
 502459875 
 
 28.1957 
 
 9.2638 
 
 850 
 
 722500 
 
 614125000 
 
 29.1548 
 
 9.4727 
 
 796 
 
 633616 
 
 504358336 
 
 28.2135 
 
 9.2677 
 
 851 
 
 724201 
 
 616295051 
 
 29.1719 
 
 9.4764 
 
 797 
 
 635209 
 
 506261573 
 
 28.23129.2716 
 
 852 
 
 725904 
 
 618470208 
 
 29. 1 890 
 
 9.4801 
 
 798 
 
 636804 
 
 508169592 
 
 28.2489 
 
 9.2754 
 
 853 
 
 727609 
 
 620650477 
 
 29.2062 
 
 9.4838 
 
 799 
 
 638401 
 
 510082399 
 
 28.2666 
 
 9.2793 
 
 854 
 
 729316 
 
 622835864 
 
 79.2233 
 
 9.4875 
 
 800 
 
 640000 
 
 512000000 
 
 28.2843 
 
 9.2832 
 
 855 
 
 731025 
 
 625026375 
 
 29.2404 
 
 9.4912 
 
 801 
 
 641601 
 
 513922401 
 
 28.3019 
 
 9.2870 
 
 856 
 
 732736 
 
 627222016 
 
 29.2575 
 
 9.4949 
 
 802 
 
 643204 
 
 515849608 
 
 28.3196 
 
 9.2909 
 
 857 
 
 734449 
 
 629422793 
 
 29.2746 
 
 9.4986 
 
 803 
 
 644809 
 
 517781627 
 
 28.3373 
 
 9.2948 
 
 858 
 
 736164 
 
 631628712 
 
 29.2916 
 
 9.5023 
 
 804 
 
 646416 
 
 519718464 
 
 28.3549 
 
 9.2986 
 
 859 
 
 737881 
 
 633839779 
 
 29.3087 
 
 9.5060 
 
 805 
 
 648025 
 
 521660125 
 
 28.3725 
 
 9.3025 
 
 860 
 
 739600 
 
 636056000 
 
 29.3258 
 
 9.5097 
 
 806 
 
 649636 
 
 523606616 
 
 28.3901 
 
 9.3063 
 
 861 
 
 741321 
 
 638277381 
 
 29.3428 
 
 9.5134 
 
 807 
 
 651249 
 
 525557943 
 
 28.4077 
 
 9.3102 
 
 862 
 
 743044 
 
 640503928 
 
 29.3598 
 
 9.5171 
 
 808 
 
 652864 
 
 527514112 
 
 28.4253 
 
 9.3140 
 
 863 
 
 744769 
 
 642735647 
 
 29.3769 
 
 9.5207 
 
 809 
 
 654481 
 
 529475129 
 
 28.4429 
 
 9.3179 
 
 864 
 
 746496 
 
 644972544 
 
 29.3939 
 
 9.5244 
 
 810 
 
 656100 
 
 531441000 
 
 28.4605 
 
 5.3217 
 
 865 
 
 748225 
 
 647214625 
 
 9.4109 
 
 9.5231 
 
 811 
 
 657721 
 
 533411731 
 
 28.4781 
 
 5.3255 
 
 866 
 
 49956 
 
 49461896 
 
 9.4279 
 
 9.5317 
 
 812 
 
 659344 
 
 35387328 
 
 28.4956 9.3294 
 
 867 
 
 51689 
 
 51714363 29.4449 
 
 9.5354 
 
 813 
 814 
 
 660969 37367797 
 662596 539353144 
 
 28.51329.3332 
 28.5307 9.3370 
 
 868 5342465397203229.4618 
 869 1 755 1 6 1 1 656234909! 29.4788 
 
 9.5391 
 9.5427 
 
102 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 870 
 
 871 
 872 
 873 
 874 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 ~925 
 926 
 927 
 928 
 929 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 756900 
 758641 
 760384 
 762129 
 763876 
 
 658503000 
 660776311 
 663054848 
 665338617 
 667627624 
 
 29.4958 
 29.5127 
 29.5296 
 29.5466 
 29.5635 
 
 9.5464 
 9.5501 
 9.5537 
 9.5574 
 9.5610 
 
 855625 
 857476 
 859329 
 861184 
 863041 
 
 791453125 
 794022776 
 796597983 
 799178752 
 801765089 
 
 30.4138 
 30.4302 
 30.4467 
 30.4631 
 30.4795 
 
 9.7435 
 9.7470 
 9.7505 
 9.7540 
 9.7575 
 
 875 
 
 876 
 877 
 878 
 879 
 
 765625 
 767376 
 769129 
 770884 
 772641 
 
 669921875 
 672221376 
 674526133 
 676836152 
 679151439 
 
 29.5804 
 29.5973 
 29.6142 
 29.63 1 1 
 29.6479 
 
 9.5647 
 9.5683 
 9.5719 
 9.5756 
 9.5792 
 
 930 
 931 
 932 
 933 
 934 
 
 864900 
 866761 
 868624 
 870489 
 872356 
 
 804357000 
 806954491 
 809557568 
 812166237 
 814780504 
 
 30.4959 
 30.5123 
 30.5287 
 30.5450 
 30.5614 
 
 9.76M 
 9.7645 
 9.7680 
 9.7715 
 9.7750 
 
 880 
 881 
 882 
 883 
 884 
 
 774400 
 776161 
 777924 
 779689 
 781456 
 
 681472000 
 683797841 
 686128968 
 688465387 
 690807104 
 
 29.6648 
 29.6816 
 29.6985 
 29.7153 
 29.7321 
 
 9.5828 
 9.5865 
 9.5901 
 9.5937 
 9.5973 
 
 935 
 936 
 937 
 938 
 939 
 
 874225 
 876096 
 877969 
 879844 
 881721 
 
 817400375 
 820025856 
 822656953 
 825293672 
 827936019 
 
 30.5778 
 30.5941 
 30.6105 
 30.6268 
 30.6431 
 
 9.7785 
 9.7819 
 9.7854 
 9.7889 
 9.7924 
 
 885 
 886 
 887 
 888 
 889 
 
 783225 
 784996 
 786769 
 788544 
 790321 
 
 693154125 
 695506456 
 697864103 
 700227072 
 702595369 
 
 29.7489 
 29.7658 
 29.7825 
 29.7993 
 29.8161 
 
 9.6010 
 9.6046 
 9.6082 
 9.6118 
 9.6154 
 
 940 
 941 
 942 
 943 
 944 
 
 883600 
 885481 
 887364 
 889249 
 891136 
 
 830584000 
 833237621 
 835896888 
 838561807 
 841232384 
 
 30.6594 
 30.6757 
 30.6920 
 30.7083 
 30.7246 
 
 9.7959 
 9.7993 
 9.8028 
 9.8063 
 9.8097 
 
 890 
 891 
 892 
 893 
 694 
 
 792100 
 793881 
 795664 
 797449 
 799236 
 
 704969000 
 707347971 
 709732288 
 712121957 
 714516984 
 
 29.8329 
 29.8496 
 29.8664 
 29.8831 
 29.8998 
 
 9.6190 
 9.6226 
 9.6262 
 9.6298 
 9.6334 
 
 945 
 946 
 947 
 948 
 949 
 
 893025 
 894916 
 896809 
 898704 
 900601 
 
 843908625 
 846590536 
 849278123 
 851971392 
 854670349 
 
 30.7409 
 30.7571 
 30.7734 
 30.7896 
 30.8058 
 
 9.8132 
 9.8167 
 9.8201 
 9.8236 
 9.8270 
 
 895 
 896 
 897 
 898 
 899 
 
 801025 
 802816 
 804609 
 806404 
 808201 
 
 716917375 
 719323136 
 721734273 
 724150792 
 726572699 
 
 29.9166 
 29.9333 
 29.9500 
 29.9666 
 29.9833 
 
 9.6370 
 9.6406 
 9.6442 
 9.6477 
 9.6513 
 
 950 
 951 
 952 
 953 
 954 
 
 902500 
 904401 
 906304 
 908209 
 910116 
 
 857375000 
 860085351 
 862801408 
 865523177 
 868250664 
 
 30.8221 
 30.8383 
 30.8545 
 30.8707 
 30.8869 
 
 9.8305 
 9.8339 
 9.8374 
 9.8408 
 9.8443 
 
 900 
 901 
 902 
 903 
 904 
 
 810000 
 811801 
 813604 
 815409 
 817216 
 
 729000000 
 731432701 
 733870808 
 736314327 
 738763264 
 
 30.0000 
 30.0167 
 30.0333 
 30.0500 
 30.0666 
 
 9.6549 
 9.6585 
 9.6620 
 9.6656 
 9.6692 
 
 955 
 956 
 957 
 958 
 959 
 
 912025 
 913936 
 915849 
 917764 
 919681 
 
 870983875 
 873722816 
 876467493 
 879217912 
 881974079 
 
 30.9031 
 30.9192 
 30.9354 
 30.9516 
 30.9677 
 
 9.8477 
 9.8511 
 9.8546 
 9.8580 
 9.8614 
 
 905 
 906 
 907 
 908 
 909 
 
 819025 
 820836 
 822649 
 824464 
 826281 
 
 741217625 
 743677416 
 746142643 
 748613312 
 751089429 
 
 30.0832 
 30.0998 
 30.1164 
 30.1330 
 30.1496 
 
 9.6727 
 9.6763 
 9.6799 
 9.6834 
 9.6870 
 
 960 
 961 
 962 
 963 
 964 
 
 921600 
 923521 
 925444 
 927369 
 929296 
 
 884736000 
 887503681 
 890277128 
 893056347 
 895841344 
 
 30.9839 
 31.0000 
 31.0161 
 31.0322 
 31.0483 
 
 9.8648 
 9.8683 
 9.8717 
 9.8751 
 9.8785 
 
 910 
 911 
 912 
 913 
 914 
 
 828100 
 829921 
 831744 
 833569 
 835396 
 
 753571000 
 75605803 1 
 758550528 
 761048497 
 763551944 
 
 30.1662 
 30.1828 
 30.1993 
 30.2159 
 30.2324 
 
 9.6905 
 9.6941 
 9.6976 
 9.7012 
 9.7047 
 
 965 
 966 
 967 
 968 
 969 
 
 931225 
 933156 
 935089 
 937024 
 938961 
 
 898632125 
 901428696 
 904231063 
 907039232 
 909853209 
 
 3 1 .0644 
 3 1 .0805 
 3 1 .0966 
 31.1127 
 31.1288 
 
 9.8819 
 9.8854 
 9.8888 
 9.8922 
 9.8956 
 
 915 
 916 
 917 
 918 
 919 
 
 837225 
 839056 
 840889 
 842724 
 844561 
 
 766060875 
 768575296 
 771095213 
 773620632 
 776151559 
 
 30.2490 
 30.2655 
 30.2820 
 30.2985 
 30.3150 
 
 9.7082 
 9.7118 
 9.7153 
 9.7188 
 9.7224 
 
 970 
 971 
 972 
 973 
 
 974 
 
 940900 
 
 942841 
 944784 
 946729 
 948676 
 
 912673000 
 915498611 
 918330048 
 921167317 
 924010424 
 
 31.1448 
 31.1609 
 31.1769 
 31.1929 
 31.2090 
 
 9.8990 
 9.9024 
 9.9058 
 9.9092 
 9.9126 
 
 920 
 921 
 922 
 923 
 924 
 
 846400 
 848241 
 850084 
 851929 
 853776 
 
 778688000 
 781229961 
 783777448 
 786330467 
 7888890241 
 
 30.3315 
 30.3480 
 30.3645 
 30.3809 
 30.3974 
 
 9.7259 
 9.7294 
 9.7329 
 9.7364 
 9.7400 
 
 975 
 976 
 977 
 978 
 979 
 
 950625 
 952576 
 954529 
 956484 
 958441 
 
 926859375 
 929714176 
 932574833 
 935441352 
 938313739 
 
 31.2250 
 31.2410 
 31.2570 
 31.2730 
 31.2890 
 
 9.9160 
 99194 
 9.9227 
 9.9261 
 9.9293 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 103 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 980 
 
 960400 
 
 941 192000 
 
 31.3050 
 
 9.9329 
 
 1035 
 
 1071225 
 
 1108717875 
 
 32.1714 
 
 10.1153 
 
 981 
 
 962361 
 
 944076141 
 
 31.3209 
 
 9.9363 
 
 1036 
 
 10732% 
 
 1111934656 
 
 32.1870 
 
 10.1186 
 
 982 
 
 964324 
 
 946966168 
 
 31.3369 
 
 9.93% 
 
 1037 
 
 1075369 
 
 1115157653 
 
 32.2025 
 
 10.1218 
 
 983 
 
 966289 
 
 949862087 
 
 31.3528 
 
 9.9430 
 
 1038 
 
 1077444 
 
 1 1 18386872 
 
 32.2180 
 
 10.1251 
 
 984 
 
 968256 
 
 952763904 
 
 31.3688 
 
 9.9464 
 
 1039 
 
 1079521 
 
 1121622319 
 
 32.2335 
 
 10.1283 
 
 985 
 
 970225 
 
 955671625 
 
 31.3847 
 
 9.9497 
 
 1040 
 
 1081600 
 
 1124864000 
 
 32.2490 
 
 10.1316 
 
 986 
 
 9721% 
 
 958585256 
 
 31.4006 
 
 9.9531 
 
 1041 
 
 1083681 
 
 1128111921 
 
 32.2645 
 
 10 1348 
 
 987 
 
 974169 
 
 %1 504803 
 
 31.4166 
 
 9.9565 
 
 1042 
 
 1085764 
 
 1131366088 
 
 32.2800 
 
 10.1381 
 
 988 
 
 976144 
 
 964430272 
 
 31.4325 
 
 9.9598 
 
 1043 
 
 1087849 
 
 1134626507 
 
 32.2955 
 
 10.1413 
 
 989 
 
 978121 
 
 %7361669 
 
 31.4484 
 
 9.%32 
 
 1044 
 
 1089936 
 
 1137893184 
 
 32.3110 
 
 10.1446 
 
 990 
 
 980100 
 
 970299000 
 
 31.4643 
 
 9.%66 
 
 1045 
 
 1092025 
 
 1141166125 
 
 32.3265 
 
 10.1478 
 
 991 
 
 982081 
 
 973242271 
 
 31.4802 
 
 9.%99 
 
 1046 
 
 1094116 
 
 1144445336 
 
 32.3419 
 
 10.1510 
 
 992 
 
 984064 
 
 976191488 
 
 31.4960 
 
 9.9733 
 
 1047 
 
 10%209 
 
 1147730823 
 
 32.3574 
 
 10.1543 
 
 993 
 
 986049 
 
 979146657 
 
 31.5119 
 
 9.9766 
 
 1048 
 
 1098304 
 
 1151022592 
 
 32.3728 
 
 10.1575 
 
 994 
 
 988036 
 
 982107784 
 
 31.5278 
 
 9.9800 
 
 1049 
 
 ir00401 
 
 1154320649 
 
 32.3883 
 
 10.1607 
 
 995 
 
 990025 
 
 985074875 
 
 31.5436 
 
 9.9833 
 
 1050 
 
 1 102500 
 
 1157625000 
 
 32.4037 
 
 10.1640 
 
 9% 
 
 992016 
 
 988047936 
 
 31.5595 
 
 9.9866 
 
 1051 
 
 1104601 
 
 1160935651 
 
 32.4191 
 
 10.1672 
 
 997 
 
 994009 
 
 991026973 31.5753 
 
 9.9900 
 
 1052 
 
 1 106704 
 
 1164252608 
 
 32.4345 
 
 10.1704 
 
 998 
 
 996004 
 
 99401 1992 
 
 31.5911 
 
 9.9933 
 
 1053 
 
 1108809 
 
 1167575877 
 
 32.4500 
 
 10.1736 
 
 999 
 
 998001 
 
 997002999 
 
 31.6070 
 
 9.9%7 
 
 1054 
 
 1110916 
 
 1170905464 
 
 32.4654 
 
 10.1769 
 
 1000 
 
 1000000 
 
 1000000000 
 
 31.6228 
 
 10.0000 
 
 1055 
 
 1 1 13025 
 
 1174241375 
 
 32.4808 
 
 10.1801 
 
 1001 
 
 1002001 
 
 1003003001 
 
 31.6386 
 
 10.0033 
 
 1056 
 
 1115136 
 
 1177583616 
 
 32.4%2 
 
 10.1833 
 
 1002 
 
 1004004 
 
 1006012008 
 
 31.6544 
 
 10.0067 
 
 1057 
 
 1117249 
 
 1180932193 
 
 32.5115 
 
 10.1865 
 
 1003 
 
 1006009 
 
 1009027027 
 
 31.6702 
 
 10.0100 
 
 1058 
 
 1 1 19364 
 
 1184287112 
 
 32.5269 
 
 10.1897 
 
 1004 
 
 1008016 
 
 1012048064 
 
 31.6860 
 
 10.0133 
 
 1059 
 
 1121481 
 
 1 187648379 
 
 32.5423 
 
 10.1929 
 
 1005 
 
 1010025 
 
 1015075125 
 
 31.7017 
 
 10.0166 
 
 1060 
 
 1123600 
 
 1191016000 
 
 32.5576 
 
 10.1%1 
 
 1006 
 
 1012036 
 
 1018108216 
 
 31.7175 
 
 10.0200 
 
 1061 
 
 1125721 
 
 1 194389981 
 
 32.5730 
 
 10.1993 
 
 1007 
 
 1014049 
 
 1021147343 
 
 31.7333 
 
 10.0233 
 
 1062 
 
 1127844 
 
 1 197770328 
 
 32.5833 
 
 10.2025 
 
 1008 
 
 1016064 
 
 1024192512 
 
 31.7490 
 
 10.0266 
 
 1063 
 
 1129%9 
 
 1201157047 
 
 32.6036 
 
 10.2057 
 
 1009 
 
 1018081 
 
 1027243729 
 
 31.7648 
 
 10.0299 
 
 1064 
 
 11320% 
 
 1204550144 
 
 32.6190 
 
 10.2089 
 
 1010 
 
 T020100 
 
 1030301000 
 
 31.7805 
 
 10.0332 
 
 1065 
 
 1134225 
 
 120794%25 
 
 32 6343 
 
 10.2121 
 
 1011 
 
 1022121 
 
 1033364331 
 
 31.7962 
 
 10.0365 
 
 1066 
 
 1136356 
 
 12113554% 
 
 32.6497 
 
 10.2153 
 
 1012 
 
 1024144 
 
 1036433728 
 
 31.8119 
 
 10.0398 
 
 1067 
 
 1138489 
 
 1214767763 
 
 32.6650 
 
 10.2185 
 
 1013 
 
 1026169 
 
 1039509197 
 
 31.8277 
 
 10.0431 
 
 1063 
 
 1140624 
 
 1218186432 
 
 32.6803 
 
 10.2217 
 
 1014 
 
 10281% 
 
 1042590744 
 
 31.8434 
 
 10.0465 
 
 1069 
 
 1142761 
 
 1221611509 
 
 32.6956 
 
 10.2249 
 
 1015 
 
 1030225 
 
 1045678375 
 
 31.8591 
 
 10.0498 
 
 1070 
 
 1144900 
 
 1225043000 
 
 32.7109 
 
 10.2281 
 
 1016 
 
 1032256 
 
 10487720% 
 
 31.8748 
 
 10.0531 
 
 1071 
 
 1 147041 
 
 1228480911 
 
 32.7261 
 
 10.2313 
 
 1017 
 
 1034289 
 
 1051871913 
 
 31.8904 
 
 10.0563 
 
 1072 
 
 1149184 
 
 1231925248 
 
 32.7414 
 
 10.2345 
 
 1018 
 
 1036324 
 
 1054977832 
 
 31.9061 
 
 10.0596 
 
 1073 
 
 1151329 
 
 1235376017 
 
 32.7567 
 
 10.2376 
 
 1019 
 
 1038361 
 
 1058089859 
 
 31.9218 
 
 10.0629 
 
 1074 
 
 1153476 
 
 1238833224 
 
 32.7719 
 
 10.2408 
 
 1020 
 
 1040400 
 
 1061208000 
 
 31.9374 
 
 10.0662 
 
 1075 
 
 1155625 
 
 1242296875 
 
 32.7872 
 
 10.2440 
 
 1021 
 
 1042441 
 
 1064332261 
 
 31.9531 
 
 10.0695 
 
 1076 
 
 1157776 
 
 1245766976 
 
 32.8024 
 
 10.2472 
 
 1022 
 
 1044484 
 
 1067462648 
 
 31.9687 
 
 10.0728 
 
 1077 
 
 1159929 
 
 1249243533 
 
 32.8177 
 
 10.2503 
 
 1023 
 
 1046529 
 
 1070599167 
 
 31.9844 
 
 10.0761 
 
 1078 
 
 1162084 
 
 1252726552 
 
 32.8329 
 
 10.2535 
 
 1024 
 
 1048576 
 
 1073741824 
 
 32.0000 
 
 10.0794 
 
 1079 
 
 1 164241 
 
 1256216039 
 
 32.8481 
 
 10.2567 
 
 1025 
 
 1050625 
 
 1076890625 
 
 32.0156 
 
 10.0826 
 
 1080 
 
 1166400 
 
 1259712000 
 
 32.8634 
 
 10.2599 
 
 1026 
 
 1052676 
 
 1080045576 
 
 32.0312 
 
 10.0859 
 
 1081 
 
 1 168561 
 
 1263214441 
 
 32.8786 
 
 10.2630 
 
 1027 
 
 1054729 
 
 1083206683 
 
 32.0468 
 
 10.0892 
 
 1032 
 
 1170724 
 
 1266723368 
 
 32.8938 
 
 10.2662 
 
 1028 
 
 1056784 
 
 1086373952 
 
 32.0624 
 
 10.0925 
 
 1033 
 
 1172889 
 
 1270238787 
 
 32.9090 
 
 10.2693 
 
 1029 
 
 1058841 
 
 1089547389 
 
 32.0780 
 
 10.0957 
 
 1084 
 
 1175056 
 
 1273760704 
 
 32.9242 
 
 10.2725 
 
 1030 
 
 1060900 
 
 1092727000 
 
 32.0936 
 
 10.0990 
 
 1035 
 
 1177225 
 
 1277289125 
 
 32.9393 
 
 10.2757 
 
 1031 
 
 1062%! 
 
 1095912791 
 
 32.1092 
 
 10.1023 
 
 1036 
 
 11793% 
 
 1280824056 
 
 32.9545 
 
 10.2788 
 
 1032 
 
 1065024 
 
 1099104768 
 
 32.1248 
 
 10.1055 
 
 1037 
 
 1181569 
 
 1284365503 
 
 32.%97 
 
 10.2820 
 
 1033 
 
 10670S9 
 
 1 102302937 
 
 32.1403 
 
 10.1088 
 
 1088 
 
 1183744 
 
 1287913472 
 
 32.9848 
 
 10.2851 
 
 1034 
 
 1069156 
 
 1105507304 
 
 32.1559 
 
 10.1121 
 
 1089 
 
 11 8592 1 1 1291 467969 
 
 33.0000 
 
 10.2883 
 
104 
 
 MATHEMATICAL TABLES. 
 
 No. 
 T090 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 1188100 
 
 1295029000 
 
 33.0151 
 
 10.2914 
 
 1145 
 
 1311025 
 
 1501123625 
 
 33.8378 
 
 10.4617 
 
 1091 
 
 1 190281 
 
 12985%571 
 
 33.0303i 10.2946 
 
 1146 
 
 1313316 
 
 1505060136 
 
 33.8526 
 
 10.4647 
 
 1092 
 1093 
 
 1192464 
 1194649 
 
 1302170688 
 1305751357 
 
 33.0454 
 33.0606 
 
 10.297/ 
 10.3009 
 
 1147 
 1148 
 
 1315609 
 1317904 
 
 1509003523 
 1512953792 
 
 33.8674 
 33.882 
 
 10.4678 
 10.4708 
 
 1094 
 
 1196836 
 
 1309338584 
 
 33.0757 
 
 10.3040 
 
 1149 
 
 132020 
 
 1516910949 
 
 33.8%9 
 
 10.4739 
 
 1095 
 
 1199025 
 
 1312932375 
 
 33.0908 
 
 10.307 
 
 1150 
 
 1322500 
 
 1520875000 
 
 33.9116 
 
 10.4769 
 
 10% 
 
 1201216 
 
 1316532736 
 
 33.1059 
 
 10.3103 
 
 1151 
 
 1324801 
 
 1524845951 
 
 33.9264 
 
 10.4799 
 
 1097 
 
 1203409 
 
 1320139673 
 
 33.1210 
 
 10.3134 
 
 1152 
 
 1327104 
 
 1528823808 
 
 33.9411 
 
 10.4830 
 
 1098 
 
 1205604 
 
 1323753192 
 
 33.1361 
 
 10.3165 
 
 1153 
 
 1329409 
 
 1532808577 
 
 33.9559 
 
 10.4860 
 
 1099 
 
 1207801 
 
 1327373299 
 
 33.1512 
 
 10.3197 
 
 1154 
 
 1331716 
 
 1536800264 
 
 33.9706 
 
 10.4890 
 
 1100 
 
 1210000 
 
 1331000000 
 
 33.1662 
 
 10.3228 
 
 1155 
 
 1334025 
 
 1540798875 
 
 33.9853 
 
 10.4921 
 
 1101 
 
 1212201 
 
 1334633301 
 
 33.1813J 10.3259 
 
 1156 
 
 1336336 
 
 1544804416 
 
 34.0000 
 
 10.4951 
 
 1102 
 
 1214404 
 
 1338273208 
 
 33.1964! 10.3290 
 
 1157 
 
 1338649 
 
 1548816893 
 
 34.0147 
 
 10.4981 
 
 1103 
 
 1216609 
 
 1341919727 
 
 33 .21141 10.3322 
 
 1158 
 
 1340964 
 
 1552836312 
 
 34.0294 
 
 10.5011 
 
 1104 
 
 1218816 
 
 1345572864 
 
 33.2264 
 
 103353 
 
 1159 
 
 1343281 
 
 1556862679 
 
 34.0441 
 
 10.5042 
 
 
 
 
 
 
 
 
 
 
 1105 
 
 1221025 
 
 1349232625 
 
 33.2415 
 
 10.3384 
 
 1160 
 
 1345600 
 
 1560896000 
 
 34.0588 
 
 10.5072 
 
 1106 
 
 1223236 
 
 1352899016 
 
 33.2566 
 
 10.3415 
 
 1161 
 
 1347921 
 
 1564936281 
 
 34.0735 
 
 10.5102 
 
 1107 
 
 1225449 
 
 1356572043 
 
 33.2716 
 
 10.3447 
 
 1162 
 
 1350244 
 
 1568933528 
 
 34.0881 
 
 10.5132 
 
 1108 
 
 1227664 
 
 1360251712 
 
 33.2866 
 
 10.3478 
 
 1163 
 
 1352569 
 
 1573037747 
 
 34.1028 
 
 1 0.5 162 
 
 1109 
 
 1229881 
 
 1363938029 
 
 33.3017 
 
 10.3509 
 
 1164 
 
 13548% 
 
 1577098944 
 
 34.1174 
 
 10.5192 
 
 1110 
 
 1232100 
 
 1367631000 
 
 33.3167 
 
 10.3540 
 
 1165 
 
 1357225 
 
 1581167125 
 
 34.1321 
 
 10.5223 
 
 1111 
 
 1234321 
 
 1371330631 
 
 33.3317 
 
 10.3571 
 
 1166 
 
 1359556 
 
 15852422% 
 
 34.1467 
 
 10.5253 
 
 1112 
 
 1236544 
 
 1375036928 
 
 33.3467 
 
 10.3602 
 
 1167 
 
 1361889 
 
 1589324463 
 
 34.1614 
 
 10.5283 
 
 1113 
 
 1238769 
 
 1378749897 
 
 33.3617 
 
 10.3633 
 
 1168 
 
 1364224 
 
 1593413632 
 
 34.1760 
 
 10.5313 
 
 1114 
 
 12409% 
 
 1382469544 
 
 33.3766 
 
 10.3664 
 
 1169 
 
 1366561 
 
 1597509809 
 
 34.1906 
 
 10.5343 
 
 1115 
 
 1243225 
 
 1386195875 
 
 33.3916 
 
 10.3695 
 
 1170 
 
 1368900 
 
 1601613000 
 
 34.2053 
 
 10.5373 
 
 1116 
 
 1245456 
 
 13899288% 
 
 33.4066 
 
 10.3726 
 
 1171 
 
 1371241 
 
 1605723211 
 
 34.2199 
 
 10.5403 
 
 1117 
 
 1247689 
 
 1393668613 
 
 33.4215 
 
 103757 
 
 1172 
 
 1373584 
 
 1609840448 
 
 34.2345 
 
 10.5433 
 
 1118 
 
 1249924 
 
 1397415032 
 
 33.4365 
 
 10.3788 
 
 1173 
 
 1375929 
 
 1613964717 
 
 34.2491 
 
 10.5463 
 
 1119 
 
 1252161 
 
 1401168159 
 
 33.4515 
 
 10.3819 
 
 1174 
 
 1378276 
 
 1618096024 
 
 34.2637 
 
 10.5493 
 
 1120 
 
 1254400 
 
 1404928000 
 
 33.4664 
 
 10.3850 
 
 1175 
 
 1380625 
 
 1622234375 
 
 34.2783 
 
 10.5523 
 
 1121 
 
 1256641 
 
 408694561 
 
 33.4813 
 
 10.3881 
 
 1176 
 
 1382976 
 
 1626379776 
 
 34.2929 
 
 10.5553 
 
 1122 
 
 1258884 
 
 412467848 
 
 33.4%3 
 
 10.3912 
 
 1177 
 
 1385329 
 
 1630532233 
 
 34.3074 
 
 10.5583 
 
 1123 
 
 1261 129 
 
 416247867 
 
 33.5112 
 
 10.3943 
 
 1178 
 
 1387684 
 
 1634691752 
 
 34.3220 
 
 10.5612 
 
 1124 
 
 1263376 
 
 420034624 
 
 33.5261 
 
 10.3973 
 
 1179 
 
 1390041 
 
 638858339 
 
 34.3366 
 
 10.5642 
 
 1125 
 
 1265625 
 
 423828125 
 
 33.5410 
 
 10.4004 
 
 1180 
 
 1392400 
 
 643032000 
 
 34.3511 
 
 10.5672 
 
 1126 
 
 1267876 
 
 427628376 
 
 33.5559 
 
 10.4035 
 
 1181 
 
 1394761 
 
 647212741 
 
 34.3657 
 
 10.5702 
 
 1127 
 
 1270129 
 
 431435383 
 
 33.5708 
 
 10.4066 
 
 1182 
 
 1397124 
 
 65140056834.3802 
 
 10.5732 
 
 1128 
 
 1272384 
 
 435249152 
 
 33.5857 
 
 10.4097 
 
 1183 
 
 1399489 
 
 655595487 
 
 34.3948 
 
 0.5762 
 
 1129 
 
 1274641 
 
 439069689 
 
 33.6006 
 
 10.4127 
 
 1184 
 
 1401856 
 
 659797504 
 
 34.4093 
 
 0.5791 
 
 1130 
 
 1276900 
 
 442897000 
 
 33.6155 
 
 10.4158 
 
 1185 
 
 1404225 
 
 664006625 
 
 34.4238 
 
 0.5821 
 
 \\3\ 
 
 1279161 
 
 446731091 
 
 33.6303 
 
 10.4189 
 
 1186 
 
 1406596 
 
 668222856 
 
 34.4384 
 
 0.5851 
 
 1132 
 
 1281424 
 
 450571968 33.6452 
 
 10.4219 
 
 1187 
 
 140S%9 
 
 672446203 
 
 34.4529 
 
 0.5881 
 
 1133 
 
 1283689 
 
 4544 1%37| 33 .6601 
 
 10.4250 
 
 1158 
 
 1411344 
 
 676676672 
 
 34.4674 
 
 0.5910 
 
 1134 
 
 1285956 
 
 458274104 
 
 33.6749 
 
 10.4281 
 
 1189 
 
 1413721 
 
 680914269 
 
 34.4819 
 
 0.5940 
 
 1135 
 
 1288225 
 
 462135375 
 
 33.6898 
 
 10.4311 
 
 1190 
 
 1416100 
 
 685159000 
 
 34.4964 
 
 0.5970 
 
 1136 
 
 12904% 
 
 466003456133.7046 
 
 10.4342 
 
 1191 
 
 1418481 
 
 689410871 
 
 34.5109 
 
 0.6000 
 
 1137 
 
 1292769 
 
 469878353 33.7174 
 
 10.4373 
 
 1192 
 
 1420864 
 
 693669888 
 
 34.5254 
 
 0.6029 
 
 1138 
 
 1295044 
 
 473760072 33.7342 
 
 10.4404 
 
 1193 
 
 1423249 
 
 697936057 
 
 34.5398 
 
 0.6059 
 
 1139 
 
 1297321 
 
 477648619 
 
 33.7491 
 
 10.4434 
 
 1194 
 
 1425636 
 
 702209384 
 
 34.5543 
 
 0.6088 
 
 1140 
 
 1299600 
 
 481544000 
 
 33.7639 
 
 10.4464 
 
 1195 
 
 1428025 
 
 706489875 
 
 34,5688 
 
 0.6118 
 
 1141 
 
 1301881 
 
 485446221 33.7787 
 
 10.4495 
 
 11% 
 
 1430416 
 
 710777536 
 
 34.5832 
 
 0.6148 
 
 1142 
 
 1304164 
 
 489355288 33.7935 
 
 10 4525 
 
 1197 
 
 1432809 
 
 715072373 
 
 34.5977 
 
 0.6177 
 
 1143 
 
 1306449 
 
 493271207 33.8083 
 
 10.4556 
 
 1198 
 
 1435204 
 
 719374392 
 
 34.6121 
 
 0.6207 
 
 1144 
 
 1308736 
 
 497193934338231 
 
 10.4586 
 
 1199 
 
 1437601 '1723683599 
 
 34.6266 
 
 0.6236 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 105 
 
 No 
 1200 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 1440000 
 
 1728000000 
 
 34.6410 
 
 10.6266 
 
 1255 
 
 1575025 
 
 1976656375 
 
 35.4260 
 
 10.7865 
 
 1201 
 
 1442401 
 
 1732323601 
 
 34.6554 
 
 10.6295 
 
 1256 
 
 1577536 
 
 1981385216 
 
 35.4401 
 
 10.7894 
 
 1202 
 
 1444804 
 
 1 736654408 
 
 34.6699 
 
 10.6325 
 
 1257 
 
 1580049 
 
 1986121593 
 
 35.4542 
 
 10.7922 
 
 1203 
 
 1447209 
 
 1740992427 
 
 34.6843 
 
 10.6354 
 
 1258 
 
 1582564 
 
 1990865512 
 
 35.4683 
 
 10.7951 
 
 1204 
 
 1449616 
 
 1745337664 
 
 34.6987 
 
 10.6384 
 
 1259 
 
 1585081 
 
 1995616979 
 
 35.4824 
 
 10.7980 
 
 1205 
 
 1452025 
 
 1749690125 
 
 34.7131 
 
 10.6413 
 
 1260 
 
 1587600 
 
 2000376000 
 
 35.4%5 
 
 10.8008 
 
 1206 
 
 1454436 
 
 1754049816 
 
 34.7275 
 
 10.6443 
 
 1261 
 
 1590121 
 
 2005142581 
 
 35.5106 
 
 10.8037 
 
 1207 
 
 1456849 
 
 1758416743 
 
 34.7419 
 
 10.6472 
 
 1262 
 
 1592644 
 
 2009916728 
 
 35.5246 
 
 10.8065 
 
 1208 
 
 1459264 
 
 1762790912 
 
 34.7563 
 
 1C.6501 
 
 1263 
 
 1595169 
 
 2014698447 
 
 35.5387 
 
 10.8094 
 
 1209 
 
 1461631 
 
 1767172329 
 
 34.7707 
 
 10.6530 
 
 1264 
 
 15976% 
 
 2019487744 
 
 35.5528 
 
 10.8122 
 
 1210 
 
 1464100 
 
 1771561000 
 
 34.7851 
 
 10.6560 
 
 1265 
 
 1600225 
 
 202428.4625 
 
 35.5668 
 
 10.8151 
 
 1211 
 
 1 466521 
 
 1775956931 
 
 34.7994 
 
 10.6590 
 
 1266 
 
 1602756 
 
 2029089096 
 
 35.5809 
 
 10.8179 
 
 1212 
 
 1463944 
 
 1780360128 
 
 34.8138 
 
 10.6619 
 
 1267 
 
 1605289 
 
 2033901163 
 
 35.5949 
 
 10.8208 
 
 1213 
 
 1471369 
 
 1784770597 
 
 34.8281 
 
 10.6648 
 
 1268 
 
 1607824 
 
 2038720832 
 
 35.6090 
 
 10.8236 
 
 1214 
 
 1473796 
 
 1789188344 
 
 34.8425 
 
 10.6678 
 
 1269 
 
 1610361 
 
 2043548109 
 
 35.6230 
 
 10.8265 
 
 1215 
 
 1476225 
 
 1793613375 
 
 34.8569 
 
 10.6707 
 
 1270 
 
 1612900 
 
 2048383000 
 
 35.6371 
 
 10.8293 
 
 1216 
 
 1478656 
 
 17980456% 
 
 34.8712 
 
 10.6736 
 
 1271 
 
 1615441 
 
 2053225511 
 
 35.6511 
 
 10.8322 
 
 1217 
 
 1481089 
 
 1802485313 
 
 34.8855 
 
 10.6765 
 
 1272 
 
 1617984 
 
 2058075648 
 
 35.6651 
 
 10.8350 
 
 1218 
 
 1433524 
 
 1806932232 
 
 34.8999 
 
 10.6795 
 
 1273 
 
 1620529 
 
 2062933417 
 
 35.6791 
 
 10.8378 
 
 1219 
 
 1485%! 
 
 1811386459 
 
 34.9142 
 
 10.6324 
 
 1274 
 
 1623076 
 
 2067798824 
 
 35.6931 
 
 10.8407 
 
 1220 
 
 1438400 
 
 1815848000 
 
 34.9285 
 
 10.6853 
 
 1275 
 
 1625625 
 
 2072671875 
 
 35.7071 
 
 10.8435 
 
 1221 
 
 1490841 
 
 1820316861 
 
 34.9428 
 
 10.6882 
 
 1276 
 
 1628176 
 
 2077552576 
 
 35.7211 
 
 10.8463 
 
 1222 
 
 1493284 
 
 1824793048 
 
 34.9571 
 
 10.691 1 
 
 1277 
 
 1630729 
 
 2082440933 
 
 35.7351 
 
 10.8492 
 
 1223 
 
 1495729 
 
 1829276567 
 
 34.9714 
 
 10.6940 
 
 1278 
 
 1633284 
 
 2087336952 
 
 35.7491 
 
 10.8520 
 
 1224 
 
 1498176 
 
 1833767424 
 
 34.9357 
 
 10.6970 
 
 1279 
 
 1635841 
 
 2092240639 
 
 35.7631 
 
 10.8548 
 
 1225 
 
 1500625 
 
 1838265625 
 
 35.0000 
 
 10.6999 
 
 1280 
 
 1638400 
 
 2097152000 
 
 35.7771 
 
 10.857; 
 
 1226 
 
 1503076 
 
 1842771176 
 
 35.0143 
 
 10.7028 
 
 1281 
 
 1640%! 
 
 2102071041 
 
 35.791 1 
 
 10.8605 
 
 1227 
 
 1505529 
 
 1847284033 
 
 35.0286 
 
 10.7057 
 
 1282 
 
 1643524 
 
 2106997768 
 
 35.8050 
 
 10.8633 
 
 1223 
 
 1507984 
 
 1851804352 
 
 35.0428 
 
 10.7086 
 
 1283 
 
 1646089 
 
 2111932187 
 
 35.8190 
 
 10.8661 
 
 1229 
 
 1510441 
 
 1856331989 
 
 35.0571 
 
 10.7115 
 
 1284 
 
 1648656 
 
 21 16874304 
 
 35.8329 
 
 10.8690 
 
 1230 
 
 1512900 
 
 1860867000 
 
 35.0714 
 
 10.7144 
 
 1285 
 
 1651225 
 
 2121824125 
 
 35.8469 
 
 10.8718 
 
 1231 
 
 1515361 
 
 1865409391 
 
 35.0856 
 
 10.7173 
 
 1286 
 
 1653796 
 
 2126781656 
 
 35.8608 
 
 10.8746 
 
 1232 
 
 1517824 
 
 1869959163 
 
 35.0999 
 
 10.7202 
 
 1287 
 
 1656369 
 
 2131746903 
 
 35.8748 
 
 10.8774 
 
 1233 
 
 1520239 
 
 1874516337 
 
 35.1141 
 
 10.7231 
 
 1238 
 
 1658944 
 
 2136719872 
 
 35.8887 
 
 10.8802 
 
 1234 
 
 1522756 
 
 1879080904 
 
 35.1283 
 
 10.7260 
 
 1289 
 
 1661521 
 
 2141700569 
 
 35.9026 
 
 10.8831 
 
 1235 
 
 1525225 
 
 1833652875 
 
 35.1426 
 
 10.7289 
 
 1290 
 
 1664100 
 
 2146689000 
 
 35.9166 
 
 10.8859 
 
 1236 
 
 1527696 
 
 1838232256 
 
 35.1568 
 
 10.7318 
 
 1291 
 
 1666681 
 
 2151685171 
 
 35.9305 
 
 10.8887 
 
 1237 
 
 1530169 
 
 1892819053 
 
 35.1710 
 
 10.7347 
 
 1292 
 
 1669264 
 
 2156689088 
 
 35.9444 
 
 10.8915 
 
 1233 
 
 1532644 
 
 1897413272 
 
 35.1852 
 
 10.7376 
 
 1293 
 
 1671849 
 
 2161700757 
 
 35.9583 
 
 10.8943 
 
 1239 
 
 1535121 
 
 1902014919 
 
 35.1994 
 
 10.7405 
 
 1294 
 
 1674436 
 
 2166720184 
 
 35.9722 
 
 10.8971 
 
 1240 
 
 1537600 
 
 1906624000 
 
 35.2136 
 
 10.7434 
 
 1295 
 
 1677025 
 
 2171747375 
 
 35.9fBl 
 
 10.8959 
 
 1241 
 
 1540081 
 
 1911240521 
 
 35.2278 
 
 10.7463 
 
 1296 
 
 167%16 
 
 2176782336 
 
 36.0000 
 
 10.9027 
 
 1242 
 
 1542564 
 
 1915864438 
 
 35.2420 
 
 10.7491 
 
 1297 
 
 1682209 
 
 2181825073 
 
 36.0139 
 
 10.9055 
 
 1243 
 
 1545049 
 
 1920495907 
 
 35.2562 
 
 10.7520 
 
 1298 
 
 1684804 
 
 2186875592 
 
 36.0278 
 
 10.9083 
 
 1244 
 
 1547536 
 
 1925134784 
 
 35.2704 
 
 10.7549 
 
 1299 
 
 1687401 
 
 2191933899 
 
 36.0416 
 
 10.9111 
 
 1245 
 
 1550025 
 
 1929781125 
 
 35.2846 
 
 10.7578 
 
 1300 
 
 1690000 
 
 2197000000 
 
 36.0555 
 
 10.9139 
 
 1246 
 
 1552516 
 
 1934434936 
 
 35.2987 
 
 10.7607 
 
 1301 
 
 1692601 
 
 2^02073901 
 
 36.0694 
 
 10.9167 
 
 1247 
 
 1555005 
 
 1939096223 
 
 35.3129 
 
 10.7635 
 
 1302 
 
 1695204 
 
 2207155608 
 
 36.0832 
 
 10.9195 
 
 1243 
 
 1557504 
 
 1 943764992 
 
 35.3270 
 
 10.7664 
 
 1303 
 
 1697809 
 
 2212245127 
 
 36.0971 
 
 10.9223 
 
 1249 
 
 1560001 
 
 1948441249 
 
 35.3412 
 
 10.7693 
 
 1304 
 
 1700416 
 
 2217342464 
 
 36.1109 
 
 10.9251 
 
 1250 
 
 1562509 
 
 1953125000 
 
 35.3553 
 
 10.7722 
 
 1305 
 
 1703025 
 
 2222447625 
 
 36.1248 
 
 10.9279 
 
 1251 
 
 1555011 
 
 1957816251 
 
 35.3695 
 
 10.7750 
 
 1306 
 
 1705636 
 
 2227560616 
 
 36.1386 
 
 10.9307 
 
 1252 
 
 1567504 
 
 1962515008 
 
 35.3836 
 
 10.7779 
 
 1307 
 
 1708249 
 
 2232681443 
 
 36.1525 
 
 10.9335 
 
 1253 
 
 1570009 
 
 1967221277 
 
 35.3977 
 
 10.7808 
 
 1308 
 
 1710864 
 
 22378101 12 
 
 36.1663 
 
 10.9363 
 
 1254 
 
 1572516 
 
 197193506435.4119 
 
 10.7837 
 
 1309 
 
 1713481 
 
 2242946629 
 
 36.1801 
 
 10.9391 
 
106 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 .Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 T310 
 
 1716100 
 
 2248091000 
 
 36.1939 
 
 10.9418 
 
 1365 
 
 1863225 
 
 2543302125 
 
 36.9459 
 
 1 1 .0929 
 
 1311 
 
 1718721 
 
 2253243231 
 
 36.2077 
 
 10.9446 
 
 1366 
 
 1865956 
 
 25488958% 
 
 36.9594 
 
 1 1 .0956 
 
 1312 
 
 1721344 
 
 2258403328 
 
 36.2215 
 
 10.9474 
 
 1367 
 
 1868689 
 
 2554497863 
 
 36.9730 
 
 1 1 .0983 
 
 1313 
 
 1723969 
 
 2263571297 
 
 36.2353 
 
 10.9502 
 
 1368 
 
 1871424 
 
 2560108032 
 
 36.9865 
 
 11.1010 
 
 1314 
 
 17265% 
 
 2268747144 
 
 36.2491 
 
 10.9530 
 
 1369 
 
 1874161 
 
 2565726409 
 
 37.0000 
 
 11.1037 
 
 1315 
 
 1729225 
 
 2273930875 
 
 36.2629 
 
 10.9557 
 
 1370 
 
 1876900 
 
 2571353000 
 
 37.0135 
 
 11.1064 
 
 1316 
 
 1731856 
 
 22791224% 
 
 36.2767 
 
 10.9585 
 
 1371 
 
 1879641 
 
 257698781 1 
 
 37.0270 
 
 11.1091 
 
 1317 
 
 1734489 
 
 2284322013 
 
 36.2905 
 
 10.%13 
 
 1372 
 
 1882384 
 
 2582630848 
 
 37.0405 
 
 11.1118 
 
 1318 
 
 1737124 
 
 2289529432 
 
 36.3043 
 
 10.9640 
 
 1373 
 
 1885129 
 
 2588282117 
 
 37.0540 
 
 11.1145 
 
 1319 
 
 1739761 
 
 2294744759 
 
 36.3180 
 
 10.9668 
 
 1374 
 
 1887876 
 
 2593941624 
 
 37.0675 
 
 11.1172 
 
 1320 
 
 1742400 
 
 2299968000 
 
 36.3318 
 
 10.%% 
 
 1375 
 
 1890625 
 
 2599609375 
 
 37.0810 
 
 11.1199 
 
 1321 
 
 1745041 
 
 2305199161 
 
 36.3456 
 
 10.9724 
 
 1376 
 
 1893376 
 
 2605285376 
 
 37.0945 
 
 11.1226 
 
 1322 
 
 1747684 
 
 2310438248 
 
 36.3593 
 
 10.9752 
 
 1377 
 
 18%129 
 
 261096%33 
 
 37.1080 
 
 11.1253 
 
 1323 
 
 1750329 
 
 2315685267 
 
 36.3731 
 
 10.9779 
 
 1378 
 
 1898884 
 
 2616662152 
 
 37.1214 
 
 11.1280 
 
 1324 
 
 1752976 
 
 2320940224 
 
 36.3868 
 
 10.9807 
 
 1379 
 
 1901641 
 
 2622362939 
 
 37.1349 
 
 11.1307 
 
 
 
 
 
 
 
 
 
 
 1325 
 
 1755625 
 
 2326203125 
 
 36.4005 
 
 10.9834 
 
 1380 
 
 1904400 
 
 2628072000 
 
 37.1484 
 
 11.1334 
 
 1326 
 
 1758276 
 
 2331473976 
 
 36.4143 
 
 10.9862 
 
 1381 
 
 1907161 
 
 2633789341 
 
 37.1618 
 
 11.1361 
 
 1327 
 
 1760929 
 
 2336752783 
 
 36.4280 
 
 10.9890 
 
 1382 
 
 1909924 
 
 2639514968 
 
 37.1753 
 
 11.1387 
 
 1328 
 
 1763584 
 
 2342039552 
 
 36.4417 
 
 10.9917 
 
 1383 
 
 1912689 
 
 2645248887 
 
 37.1887 
 
 11.1414 
 
 1329 
 
 1766241 
 
 2347334289 
 
 36.4555 
 
 10.9945 
 
 1384 
 
 1915456 
 
 2650991104 
 
 37.2021 
 
 11.1441 
 
 1330 
 
 1768900 
 
 2352637000 
 
 36.4692 
 
 10.9972 
 
 1385 
 
 1918225 
 
 2656741625 
 
 37.2156 
 
 11.1468 
 
 1331 
 
 1771561 
 
 2357947691 
 
 36.4829 
 
 11.0000 
 
 1386 
 
 1920996 
 
 2662500456 
 
 37.2290 
 
 11.1495 
 
 1332 
 
 1774224 
 
 2363266368 
 
 36.4966 
 
 1 1 .0028 
 
 1387 
 
 1923769 
 
 2668267603 
 
 37.2424 
 
 11.1522 
 
 1333 
 
 1776889 
 
 2368593037 
 
 36.5103 
 
 11.0055 
 
 1388 
 
 1926544 
 
 2674043072 
 
 37.2559 
 
 11.1548 
 
 1334 
 
 1779556 
 
 2373927704 
 
 36.5240 
 
 11.0083 
 
 1389 
 
 1929321 
 
 2679826869 
 
 37.2693 
 
 11.1575 
 
 1335 
 
 1782225 
 
 2379270375 
 
 36.5377 
 
 11.0110 
 
 1390 
 
 1932100 
 
 2685619000 
 
 37.2827 
 
 11.1602 
 
 1336 
 
 1784896 
 
 2384621056 
 
 36.5513 
 
 11.0138 
 
 1391 
 
 1934881 
 
 2691419471 
 
 37.2961 
 
 11.1629 
 
 1337 
 
 1787569 
 
 2389979753 
 
 36.5650 
 
 11.0165 
 
 1392 
 
 1937664 
 
 2697228288 
 
 37.3095 
 
 11.1655 
 
 1338 
 
 1790244 
 
 2395346472 
 
 36.5787 
 
 11.0193 
 
 1393 
 
 1940449 
 
 2703045457 
 
 37.3229 
 
 11.1682 
 
 1339 
 
 1792921 
 
 2400721219 
 
 36.5923 
 
 11.0220 
 
 1394 
 
 1943236 
 
 2708870984 
 
 37.3363 
 
 11.1709 
 
 1340 
 
 1795600 
 
 2406104000 
 
 36.6060 
 
 11.0247 
 
 1395 
 
 1946025 
 
 2714704875 
 
 37.3497 
 
 11.1736 
 
 1341 
 
 1798281 
 
 2411494821 
 
 36.6197 
 
 1 1 .0275 
 
 1396 
 
 1948816 
 
 2720547136 
 
 37.3631 
 
 11.1762 
 
 1342 
 
 1800964 
 
 2416893688 
 
 36.6333 
 
 1 1 .0302 
 
 1397 
 
 1951609 
 
 2726397773 
 
 37.3765 
 
 11.1789 
 
 1343 
 
 1803649 
 
 2422300607 
 
 36.6469 
 
 1.0330 
 
 1398 
 
 1954404 
 
 2732256792 
 
 37.3898 
 
 11.1816 
 
 1344 
 
 1806336 
 
 2427715584 
 
 36.6606 
 
 1 .0357 
 
 1399 
 
 1957201 
 
 2738124199 
 
 37.4032 
 
 11.1842 
 
 1345 
 
 1809025 
 
 2433138625 
 
 36.6742 
 
 .0384 
 
 1400 
 
 1960000 
 
 2744000000 
 
 37.4166 
 
 11.1869 
 
 1346 
 
 1811716 
 
 2438569736 
 
 36.6879 
 
 .0412 
 
 1401 
 
 1962801 
 
 2749884201 
 
 37.4299 
 
 11.1896 
 
 1347 
 
 1814409 
 
 2444008923 
 
 36.7015 
 
 .0439 
 
 1402 
 
 1%5604 
 
 2755776808 
 
 37.4433 
 
 11.1922 
 
 1348 
 
 1817104 
 
 2449456192 
 
 36.7151 
 
 .0466 
 
 1403 
 
 1%8409 
 
 2761677827 
 
 37.4566 
 
 11.1949 
 
 1349 
 
 1819801 
 
 2454911549 
 
 36.7287 
 
 .0494 
 
 1404 
 
 1971216 
 
 2767587264 
 
 37.4700 
 
 11.1975 
 
 1350 
 
 1822WO 
 
 2460375000 
 
 36.7423 
 
 .0521 
 
 1405 
 
 1974025 
 
 2773505125 
 
 37.4833 
 
 11.2002 
 
 1351 
 
 1825201 
 
 2465846551 
 
 36.7560 
 
 1 .0548 
 
 1406 
 
 1976836 
 
 2779431416 
 
 37,4967 
 
 1 1 .2028 
 
 1352 
 
 1827904 
 
 2471326208 
 
 36.76% 
 
 1 .0575 
 
 1407 
 
 1979649 
 
 2785366143 
 
 37.5100 
 
 1 1 .2055 
 
 1353 
 
 1830609 
 
 2476813977 
 
 36.7831 
 
 .0603 
 
 1408 
 
 1982464 
 
 2791309312 
 
 37.5233 
 
 1 1 .2082 
 
 1354 
 
 1833316 
 
 2482309864 
 
 36.7967 
 
 1.0630 
 
 1409 
 
 1985281 
 
 2797260929 
 
 37.5366 
 
 11.2108 
 
 1355 
 
 1836025 
 
 2487813875 
 
 36.8103 
 
 .0657 
 
 1410 
 
 1988100 
 
 2803221000 
 
 37.5500 
 
 11.2135 
 
 1356 
 
 1838736 
 
 2493326016 
 
 36.8239 
 
 1.0684 
 
 1411 
 
 1990921 
 
 2809189531 
 
 37.5633 
 
 11.2161 
 
 1357 
 
 1841449 
 
 2498846293 
 
 36.8375 
 
 1.0712 
 
 1412 
 
 1993744 
 
 2815166528 
 
 37.5766 
 
 11. 2 188 
 
 1358 
 
 1844164 
 
 2504374712 
 
 36.8511 
 
 1.0739 
 
 1413 
 
 19%569 
 
 2821151997 
 
 37.5699 
 
 11.2214 
 
 1359 
 
 1846881 
 
 2509911279 
 
 36.8646 
 
 1 .0766 
 
 1414 
 
 1999396 
 
 2827145944 
 
 37.6032 
 
 1 1 .2240 
 
 1360 
 
 1849600 
 
 2515456000 
 
 36.8782 
 
 1 .0793 
 
 1415 
 
 2002225 
 
 2833148375 
 
 37 6165 
 
 11.2267 
 
 1361 
 
 1852321 
 
 2521008881 
 
 36.8917 
 
 1 .0820 
 
 1416 
 
 2005056 
 
 28391592% 
 
 37.6298 
 
 11.2293 
 
 1362 
 
 1855044 
 
 2526569928 
 
 36.9053 
 
 1 .0847 
 
 1417 
 
 2007889 
 
 2845178713 
 
 37.6431 
 
 11.2320 
 
 1363 
 
 1857769 
 
 2532139147 
 
 36.9188 11.0875 
 
 1418 
 
 2010724 
 
 2851206632 
 
 37.6563 
 
 1 1 2346 
 
 1364 18604% 
 
 2537716544 
 
 36.9324 1 1 .0902 
 
 1419 
 
 2013561 
 
 2857243059 
 
 37.66% 
 
 1 1 2373 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 107 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. | 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 1420 
 1421 
 1422 
 1423 
 1424 
 
 2016400 
 2019241 
 2022084 
 2024929 
 2027776 
 
 2863288000 
 2869341461 
 2875403448 
 2881473967 
 2887553024 
 
 37.6829 
 37.6962 
 37.7094 
 37.7227 
 37.7359 
 
 1 1 .2399 
 1 1 .2425 
 1 1 .2452 
 11.2478 
 11.2505 
 
 1475 
 1476 
 1477 
 1478 
 1479 
 
 2175625 
 2178576 
 2181529 
 2184484 
 2187441 
 
 3209046875 
 3215578176 
 3222118333 
 3228667352 
 3235225239 
 
 38.4057 
 
 38 4187 
 38.4318 
 38.4448 
 38.4578 
 
 1 1 .3832 
 1 1 .3858 
 1 1 .3883 
 11.3909 
 11.3935 
 
 1425 
 1426 
 1427 
 1428 
 1429 
 
 2030625 
 2033476 
 2036329 
 2039184 
 2042041 
 
 2893640625 
 2899736776 
 2905841483 
 2911954752 
 2918076589 
 
 37.7492 
 37.7624 
 37.7757 
 37.7889 
 37.8021 
 
 11.2531 
 11.2557 
 1 1 .2583 
 11.2610 
 11.2636 
 
 1480 
 1481 
 1482 
 1483 
 1484 
 
 2190400 
 2193361 
 21%324 
 2199289 
 2202256 
 
 3241792000 
 3248367641 
 3254952168 
 3261545587 
 3268147904 
 
 38.4708 
 38.4838 
 38.4968 
 38.5097 
 38.5227 
 
 11.3960 
 11.3986 
 11.4012 
 11.4037 
 11.4063 
 
 1430 
 1431 
 1432 
 1433 
 1434 
 
 2044900 
 2047761 
 2050624 
 2053489 
 2056356 
 
 2924207000 
 2930345991 
 2936493568 
 2942649737 
 2948814504 
 
 37.8153 
 37.8286 
 37.8418 
 37.8550 
 37.8682 
 
 11.2662 
 11.2689 
 11.2715 
 11.2741 
 11.2767 
 
 1485 
 1486 
 1487 
 1488 
 1489 
 
 2205225 
 2208196 
 2211169 
 2214144 
 2217121 
 
 3274759125 
 3281379256 
 3288008303 
 3294646272 
 3301293169 
 
 38.5357 
 38.5487 
 38.5616 
 38.5746 
 38.5876 
 
 11.4089 
 11.4114 
 11 4140 
 11.4165 
 11.4191 
 
 1435 
 1436 
 1437 
 1438 
 1439 
 
 2059225 
 20620% 
 2064969 
 2067844 
 2070721 
 
 2954987875 
 2961169856 
 2967360453 
 2973559672 
 29797675 19 
 
 37.8814 
 37.8946 
 37.9078 
 37.9210 
 37.9342 
 
 11.2793 
 11.2820 
 1 1 .2846 
 11.2872 
 1 1 .2898 
 
 1490 
 1491 
 1492 
 1493 
 1494 
 
 2220100 
 2223081 
 2226064 
 2229049 
 2232036 
 
 3307949000 
 3314613771 
 3321287488 
 3327970157 
 3334661784 
 
 386005 
 38.6135 
 386264 
 38.6394 
 38.6523 
 
 11.4216 
 11.4242 
 1 1 .4268 
 1 1 .4293 
 11.4319 
 
 1440 
 1441 
 1442 
 1443 
 1444 
 
 2073600 
 2076481 
 2079364 
 2032249 
 2085136 
 
 2985984000 
 2992209121 
 2998442888 
 3004685307 
 3010936384 
 
 37.9473 
 37.9605 
 37.9737 
 37.9868 
 38.0000 
 
 1 1 .2924 
 11.2950 
 1 1 .2977 
 1 1 .3003 
 11.3029 
 
 1495 
 1496 
 1497 
 1493 
 1499 
 
 2235025 
 2238016 
 2241009 
 2244004 
 2247001 
 
 3341362375 
 3348071936 
 3354790473 
 3361517992 
 3368254499 
 
 38.6652 
 38.6782 
 38.691 1 
 38.7040 
 38.7169 
 
 1 1 .4344 
 1 1 .4370 
 11.4395 
 11.4421 
 11.4446 
 
 1445 
 1446 
 1447 
 1448 
 1449 
 
 2088025 
 2090916 
 2093809 
 2096704 
 2099601 
 
 3017196125 
 3023464536 
 3029741623 
 3036027392 
 3042321849 
 
 38.0132 
 38.0263 
 38.0395 
 38 0526 
 38.0657 
 
 1 1 .3055 
 11.3081 
 11.3107 
 11.3133 
 11.3159 
 
 1500 
 1501 
 1502 
 1503 
 1504 
 
 2250000 
 2253001 
 2256004 
 2259009 
 2262016 
 
 3375000000 
 3381754501 
 3388518008 
 3395290527 
 3402072064 
 
 38.7298 
 38.7427 
 38.7556 
 38.7685 
 38.7814 
 
 11.4471 
 1 1 .4497 
 11.4522 
 1 1 .4548 
 11.4573 
 
 1450 
 1451 
 1452 
 1453 
 1454 
 
 2102500 
 2105401 
 2108304 
 2111209 
 2114116 
 
 3048625000 
 3054936851 
 3061257408 
 3067586677 
 3073924664 
 
 38.0789 
 38.0920 
 38.1051 
 38.1182 
 38.1314 
 
 11.3185 
 11.3211 
 1 1 .3237 
 1 1 .3263 
 11.3289 
 
 1505 
 1506 
 1507 
 1508 
 1509 
 
 2265025 
 2268036 
 2271049 
 2274064 
 2277081 
 
 3408862625 
 3415662216 
 3422470843 
 3429288512 
 3436115229 
 
 38.7943 
 38.8072 
 38 8201 
 38.8330 
 38.8458 
 
 11.4598 
 11.4624 
 11.4649 
 11.4675 
 11.4700 
 
 1455 
 1456 
 1457 
 1458 
 1459 
 
 2117025 
 2119936 
 2122849 
 2125764 
 2128681 
 
 3080271375 
 3086626816 
 3092990993 
 3099363912 
 3105745579 
 
 38.1445 
 38.1576 
 38.1707 
 38.1838 
 38.1969 
 
 11.3315 
 11.3341 
 1 1 .3367 
 11.3393 
 11.3419 
 
 1510 
 1511 
 1512 
 1513 
 1514 
 
 2280100 
 2283121 
 2286144 
 2289169 
 22921% 
 
 3442951000 
 3449795831 
 3456649728 
 3463512697 
 3470384744 
 
 38.8587 
 38.8716 
 38.8844 
 38.8973 
 38.9102 
 
 11.4725 
 11.4751 
 11 ,4776 
 11.4801 
 11.4826 
 
 1460 
 1461 
 1462 
 1463 
 1464 
 
 2131600 
 2134521 
 2137444 
 2140369 
 2143296 
 
 3112136000 
 3118535181 
 3124943128 
 3131359847 
 3137785344 
 
 38.2099 
 38.2230 
 38.2361 
 38.2492 
 38.2623 
 
 11.3445 
 11.3471 
 11.34% 
 11.3522 
 11.3548 
 
 1515 
 
 1516 
 1517 
 1518 
 1519 
 
 2295225 
 2298256 
 2301289 
 2304324 
 2307361 
 
 3477265875 
 34841560% 
 3491055413 
 3497%3832 
 3504881359 
 
 38.9230 
 38.9358 
 38.9487 
 38.%15 
 38.9744 
 
 11.4852 
 11.4877 
 11.4902 
 11.4927 
 11.4953 
 
 1465 
 1466 
 1467 
 1468 
 1469 
 
 2146225 
 2149156 
 2152089 
 2155024 
 2157%1 
 
 3144219625 
 3150662696 
 3157114563 
 3163575232 
 3170044709 
 
 38.2753 
 38.2884 
 38.3014 
 38.3145 
 38.3275 
 
 11.3574 
 11.3600 
 11.3626 
 1 1 .3652 
 11.3677 
 
 1520 
 1521 
 1522 
 1523 
 1524 
 
 2310400 
 2313441 
 2316484 
 2319529 
 2322576 
 
 3511808000 
 3518743761 
 3525688648 
 3532642667 
 3539605824 
 
 38.9872 
 39.0000 
 39.0128 
 39.0256 
 39.0384 
 
 11.4978 
 11.5003 
 11.5028 
 11.5054 
 11.5079 
 
 1470 
 1471 
 M72 
 1473 
 1474 
 
 2160900 
 2163841 
 2166784 
 2169729 
 2172676 
 
 3176523000 
 3183010111 
 3189506048 
 3196010817 
 3202524424 
 
 38.3406 
 38.3536 
 38.3667 
 38.3797 
 38 3927 
 
 11.3703 
 1 1 .3729 
 1 1 .3755 
 1 1 3780 
 11.3806 
 
 1525 
 1526 
 1527 
 4528 
 1529 
 
 2325625 
 2328676 
 2331729 
 2334784 
 2337841 
 
 3546578125 
 3553559576 
 3560550183 
 3567549952 
 3574558889 
 
 39.0512 
 39.0640 
 39.0768 
 39.08% 
 39.1024 
 
 11.5104 
 11.5129 
 11.5154 
 11.5179 
 11.5204 
 
108 
 
 MATHEMATICAL TABLES, 
 
 No. 
 
 1530 
 1531 
 1532 
 1533 
 1534 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 "7565 
 1566 
 1567 
 1568 
 1569 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 2340900 
 2343961 
 2347024 
 2350089 
 2353156 
 
 3581577000 
 3588604291 
 3595640768 
 3602686437 
 3609741304 
 
 39.1152 
 39.1280 
 39.1408 
 39.1535 
 39.1663 
 
 1 1 .5230 
 11.5255 
 11.5280 
 11.5305 
 11.5330 
 
 2449225 
 2452356 
 2455489 
 2458624 
 2461761 
 
 3833037125 
 38403894% 
 3847751263 
 3855123432 
 3862503009 
 
 39.5601 
 39.5727 
 39.5854 
 39.5980 
 39.6106 
 
 11.6102 
 11.6126 
 11.6151 
 11.6176 
 11.6200 
 
 1535 
 1536 
 1537 
 1538 
 1539 
 
 2356225 
 23592% 
 2362369 
 2365444 
 2368521 
 
 3616805375 
 3623878656 
 3630% 11 53 
 3638052872 
 3645153819 
 
 39.1791 
 39.1918 
 39.2046 
 39.2173 
 39.2301 
 
 11.5355 
 1 1 .5380 
 1 1 .5405 
 1 1 .5430 
 1 1 .5455 
 
 1570 
 1571 
 1572 
 1573 
 1574 
 
 2464900 
 2468041 
 2471184 
 2474329 
 2477476 
 
 3869893000 
 3877292411 
 3884701248 
 3892119517 
 3899547224 
 
 39.6232 
 39.6358 
 39.6485 
 39.661 1 
 39.6737 
 
 11.6225 
 1 1 .6250 
 1 1 .6274 
 1 1 .6299 
 11.6324 
 
 1540 
 1541 
 1542 
 1543 
 1544 
 
 2371600 
 2374681 
 2377764 
 2380849 
 2383936 
 
 3652264000 
 3659383421 
 3666512088 
 3673650007 
 3680797184 
 
 39.2428 
 39.2556 
 39.2683 
 39.2810 
 39.2938 
 
 1 1 .5480 
 11.5505 
 11.5530 
 11.5555 
 11.5580 
 
 1575 
 1576 
 1577 
 1578 
 1579 
 
 2480625 
 2483776 
 2486929 
 2490084 
 2493241 
 
 3906984375 
 3914430976 
 3921887033 
 3929352552 
 3936827539 
 
 39.6863 
 39.6989 
 39.7115 
 39.7240 
 39.7366 
 
 1 1 .6348 
 1 1 .6373 
 1 1 .6398 
 1 1 .6422 
 1 1 .6447 
 
 1545 
 1546 
 1547 
 1548 
 154Q 
 
 2387025 
 2390116 
 2393209 
 2396304 
 2399401 
 
 3687953625 
 3695119336 
 3702294323 
 3709478592 
 3716672149 
 
 39.3065 
 393192 
 39.3319 
 39.3446 
 39.3573 
 
 1 1 .5605 
 1 1 .5630 
 1 1 .5655 
 11.5680 
 11.5705 
 
 1580 
 1581 
 1582 
 1583 
 1584 
 
 2496400 
 2499561 
 2502724 
 2505889 
 2509056 
 
 3944312000 
 3951805941 
 3959309368 
 3966822287 
 3974344704 
 
 39.7492 
 39.7618 
 39.7744 
 39.7869 
 39.7995 
 
 11.6471 
 11.64% 
 11.6520 
 1 1 .6545 
 1 1 .6570 
 
 1550 
 1551 
 1552 
 1553 
 1554 
 
 2402500 
 2405601 
 2408704 
 2411809 
 2414916 
 
 3723875000 
 3731087151 
 3738308608 
 3745539377 
 3752779464 
 
 39.3700 
 39.3827 
 39.3954 
 39.4081 
 39.4208 
 
 1 1 .5729 
 11.5754 
 1 1 .5779 
 1 1 .5804 
 1 1 .5829 
 
 1585 
 1586 
 1587 
 1588 
 1589 
 
 2512225 
 25153% 
 2518569 
 2521744 
 2524921 
 
 3981876625 
 3989418056 
 3996%9003 
 4004529472 
 4012099469 
 
 39.8121 
 39.8246 
 39.8372 
 39.8497 
 39.8623 
 
 1 1 .6594 
 11.6619 
 1 1 .6643 
 11.6668 
 1 1 .6692 
 
 1555 
 1556 
 1557 
 1558 
 1559 
 
 2418025 
 2421136 
 2424249 
 2427364 
 2430481 
 
 3760028875 
 3767287616 
 3774555693 
 3781833112 
 37891 19879 
 
 39.4335 
 39.4462 
 39.4588 
 39.4715 
 39.4842 
 
 11.5854 
 1 1 .5879 
 1 1 .5903 
 1 1 .5928 
 1 1 .5953 
 
 1590 
 1591 
 1592 
 1593 
 1594 
 
 2528100 
 2531281 
 2534464 
 2537649 
 2540836 
 
 401%79000 
 4027268071 
 4034866688 
 4042474857 
 4050092584 
 
 39.8748 
 39.8873 
 39.8999 
 39.9124 
 39.9249 
 
 11.6717 
 1 1 .6741 
 1 1 .6765 
 1 1 .6790 
 11.6814 
 
 1560 
 1561 
 1562 
 1563 
 1564 
 
 2433600 
 2436721 
 2439844 
 2442969 
 24460% 
 
 3796416000 
 3803721481 
 381 1036328 
 3818360547 
 3825694144 
 
 39.4968 
 39.5095 
 39.5221 
 39.5348 
 39.5474 
 
 1 1 .5978 
 11.6003 
 11.6027 
 1 1 .6052 
 11.6077 
 
 1595 
 15% 
 1597 
 1598 
 1599 
 
 2544025 
 2547216 
 2550409 
 2553604 
 2556801 
 
 4057719875 
 4065356736 
 4073003173 
 4080659192 
 4088324799 
 
 39.9375 
 39.9500 
 39.%25 
 39.9750 
 39.9875 
 
 1 1 .6839 
 1 1 .6863 
 11 6888 
 11.6912 
 11.6936 
 
 
 
 
 
 
 1600 
 
 2560000 
 
 4096000000 
 
 40.0000 
 
 11.6961 
 
 SQUARES AND CUBES OF DECIMALS. 
 
 No. 
 
 Square 
 
 Cube. 
 
 No. 
 
 Square 
 
 Cube. 
 
 No. 
 
 Square. 
 
 ' Cube. 
 
 \2 
 
 .01 
 .04 
 
 .001 
 .008 
 
 .01 
 .02 
 
 .0001 
 .0004 
 
 .000 001 
 .000 008 
 
 .001 
 .002 
 
 .00 00 01 
 .00 00 04 
 
 .000 000 001 
 .000 000 008 
 
 
 .09 
 
 .027 
 
 .03 
 
 .0009 
 
 .000 027 
 
 .003 
 
 .00 00 09 
 
 .000 000 027 
 
 *4 
 
 .16 
 
 .064 
 
 .04 
 
 .0016 
 
 .000 064 
 
 .004 
 
 .00 00 16 
 
 ,000 000 064 
 
 .5 
 
 .25 
 
 .125 
 
 .05 
 
 .0025 
 
 .000 125 
 
 .005 
 
 .00 00 25 
 
 .000 000 125 
 
 6 
 
 .36 
 
 .216 
 
 .06 
 
 .0036 
 
 .000 216 
 
 .006 
 
 .00 00 36 
 
 .000 000 216 
 
 .7 
 
 .49 
 
 .343 
 
 .07 
 
 .0049 
 
 .000 343 
 
 .007 
 
 .00 00 49 
 
 .000 000 343 
 
 8 
 
 .64 
 
 .512 
 
 .08 
 
 .0064 
 
 .000 512 
 
 .008 
 
 .00 00 64 
 
 .000 000 512 
 
 .9 
 
 .81 
 
 .729 
 
 .09 
 
 .0081 
 
 .000 729 
 
 .009 
 
 .00 00 81 
 
 .000 000 729 
 
 1 
 
 1 00 
 
 1.000 
 
 .10 
 
 .0100 
 
 .001 000 
 
 .010 
 
 .00 01 00 
 
 .000 001 000 
 
 
 1.44 
 
 1.728 
 
 .12 
 
 .0144 
 
 .001 728 
 
 .012 
 
 .00 01 44 
 
 .000 001 728 
 
 Note that the square has twice as many decimal places, and the cube 
 .three times as many decimal places, as the root. 
 
FIFTH ROOTS AND FIFTH POWERS, 
 
 109 
 
 FIFTH ROOTS AND FIFTH POWERS. 
 
 (Abridged from TRAUTWINB.) 
 
 *i 
 && 
 
 Power. 
 
 o 3 
 
 
 
 Power. 
 
 (H . 
 
 o -^ 
 
 ll 
 
 Power. 
 
 S<i 
 
 ll 
 
 Power. 
 
 li 
 
 Itf 
 
 Power. 
 
 .10 
 
 .000010 
 
 3.7 
 
 693.440 
 
 9.8 
 
 90392 
 
 21.8 
 
 4923597 
 
 40 
 
 102400000 
 
 .15 
 
 .000075 
 
 3.8 
 
 792.352 
 
 9.9 
 
 95099 
 
 22.0 
 
 5153632 
 
 41 
 
 115856201 
 
 .20 
 
 .000320 
 
 3.9 
 
 902.242 
 
 10.0 
 
 100000 
 
 22.2 
 
 5392186 
 
 42 
 
 130691232 
 
 .25 
 
 .000977 
 
 4.0 
 
 1024.00 
 
 10.2 
 
 110408 
 
 22.4 
 
 5639493 
 
 43 
 
 147008443 
 
 .30 
 
 .002430 
 
 4.1 
 
 1158.56 
 
 10.4 
 
 121665 
 
 22.6 
 
 5895793 
 
 44 
 
 164916224 
 
 .35 
 
 .005252 
 
 4.2 
 
 1306.91 
 
 10.6 
 
 133823 
 
 22.8 
 
 6161327 
 
 45 
 
 184528125 
 
 .40 
 
 .010240 
 
 4.3 
 
 1470.08 
 
 10.8 
 
 146933 
 
 23.0 
 
 6436343 
 
 46 
 
 205962976 
 
 .45 
 
 .018453 
 
 4.4 
 
 1649.16 
 
 11.0 
 
 161051 
 
 23.2 
 
 6721093 
 
 47 
 
 229345007 
 
 .50 
 
 .031250 
 
 4.5 
 
 1845.28 
 
 11.2 
 
 176234 
 
 23.4 
 
 7015834 
 
 48 
 
 254803968 
 
 .55 
 
 .050328 
 
 4.6 
 
 2059.63 
 
 11.4 
 
 192541 
 
 23.6 
 
 7320825 
 
 49 
 
 282475249 
 
 .60 
 
 .077760 
 
 4.7 
 
 2293.45 
 
 11.6 
 
 210034 
 
 23.8 
 
 7636332 
 
 50 
 
 312500000 
 
 .65 
 
 .116029 
 
 4.8 
 
 2548.04 
 
 11.8 
 
 228776 
 
 24.0 
 
 7962624 
 
 51 
 
 345025251 
 
 .70 
 
 .168070 
 
 49 
 
 2824.75 
 
 12.0 
 
 248832 
 
 24.2 
 
 8299976 
 
 52 
 
 380204032 
 
 .75 
 
 .237305 
 
 5.0 
 
 3125.00 
 
 12.2 
 
 270271 
 
 24.4 
 
 8648666 
 
 53 
 
 418195493 
 
 .80 
 
 .327680 
 
 5.1 
 
 3450.25 
 
 12.4 
 
 293163 
 
 24.6 
 
 9008978 
 
 54 
 
 459165024 
 
 .85 
 
 .443705 
 
 5.2 
 
 3802.04 
 
 12.6 
 
 317580 
 
 24.8 
 
 9381200 
 
 55 
 
 503284375 
 
 .90 
 
 .590490 
 
 5.3 
 
 4181.95 
 
 12.8 
 
 343597 
 
 25.0 
 
 9765625 
 
 56 
 
 550731776 
 
 .95 
 
 .773781 
 
 5.4 
 
 4591 65 
 
 13.0 
 
 371293 
 
 25.2 
 
 10162550 
 
 57 
 
 601692057 
 
 .00 
 
 1.00000 
 
 5.5 
 
 5032.84 
 
 13.2 
 
 400746 
 
 25.4 
 
 10572278 
 
 58 
 
 656356768 
 
 .05 
 
 1.27628 
 
 5.6 
 
 5507.32 
 
 13.4 
 
 432040 
 
 25.6 
 
 10995116 
 
 59 
 
 714924299 
 
 .10 
 
 1.61051 
 
 5.7 
 
 6016.92 
 
 13.6 
 
 465259 
 
 25.8 
 
 11431377 
 
 60 
 
 777600000 
 
 .15 
 
 2.01135 
 
 5.8 
 
 6563.57 
 
 13.8 
 
 500490 
 
 26.0 
 
 11881376 
 
 61 
 
 844596301 
 
 .20 
 
 2.48832 
 
 5.9 
 
 7149.24 
 
 14.0 
 
 537824 
 
 26.2 
 
 12345437 
 
 62 
 
 916132832 
 
 .25 
 
 3.05176 
 
 6.0 
 
 7776.00 
 
 14.2 
 
 577353 
 
 26.4 
 
 12823886 
 
 63 
 
 992436543 
 
 .30 
 
 3.71293 
 
 6.1 
 
 8445.96 
 
 14.4 
 
 619174 
 
 26.6 
 
 13317055 
 
 64 
 
 1073741824 
 
 .35 
 
 4.48403 
 
 6.2 
 
 9161.33 
 
 14.6 
 
 663383 
 
 26.8 
 
 13825281 
 
 65 
 
 1160290625 
 
 .40 
 
 5.37824 
 
 6.3 
 
 9924.37 
 
 14.8 
 
 710082 
 
 27.0 
 
 14348907 
 
 66 
 
 1252332576 
 
 .45 
 
 6.40973 
 
 6.4 
 
 10737 
 
 15.0 
 
 759375 
 
 27.2 
 
 14888280 
 
 67 
 
 1350125107 
 
 .50 
 
 7.59375 
 
 6.5 
 
 11603 
 
 15.2 
 
 811368 
 
 27.4 
 
 15443752 
 
 68 
 
 1453933568 
 
 .55 
 
 8.94661 
 
 6.6 
 
 12523 
 
 15.4 
 
 866171 
 
 27.6 
 
 16015681 
 
 69 
 
 1564031349 
 
 .60 
 
 10.4858 
 
 6.7 
 
 13501 
 
 15.6 
 
 923896 
 
 27.8 
 
 1 6604430 
 
 70 
 
 1680700000 
 
 .65 
 
 12.2298 
 
 6.8 
 
 14539 
 
 15.8 
 
 984658 
 
 28.0 
 
 17210368 
 
 71 
 
 1804229351 
 
 .70 
 
 14.1986 
 
 6.9 
 
 15640 
 
 16.0 
 
 1048576 
 
 28.2 
 
 17833868 
 
 72 
 
 1934917632 
 
 .75 
 
 16.4131 
 
 7.0 
 
 16807 
 
 16.2 
 
 1115771 
 
 28.4 
 
 18475309 
 
 73 
 
 2073071593 
 
 .80 
 
 18.8957 
 
 7.1 
 
 18042 
 
 16.4 
 
 1186367 
 
 28.6 
 
 19135075 
 
 74 
 
 2219006624 
 
 .85 
 
 21.6700 
 
 7.2 
 
 19349 
 
 16.6 
 
 1260493 
 
 28.8 
 
 19813557 
 
 75 
 
 2373046875 
 
 .90 
 
 24.7610 
 
 7.3 
 
 20731 
 
 16.8 
 
 1338278 
 
 29.0 
 
 20511149 
 
 76 
 
 2535525376 
 
 .95 
 
 28.1951 
 
 7.4 
 
 22190 
 
 17.0 
 
 1419857 
 
 29.2 
 
 21228253 
 
 77 
 
 2706784157 
 
 2.00 
 
 32.0000 
 
 7.5 
 
 23730 
 
 17.2 
 
 1 505366 
 
 29.4 
 
 21965275 
 
 78 
 
 2887174368 
 
 2.05 
 
 36.2051 
 
 7.6 
 
 25355 
 
 17.4 
 
 1594947 
 
 29.6 
 
 22722628 
 
 79 
 
 3077056399 
 
 2.10 
 
 40.8410 
 
 7.7 
 
 27068 
 
 17.6 
 
 1688742 
 
 298 
 
 23500728 
 
 80 
 
 3276800000 
 
 2.15 
 
 45.9401 
 
 7.8 
 
 28872 
 
 17.8 
 
 1 786899 
 
 30.0 
 
 24300000 
 
 81 
 
 3486784401 
 
 2.20 
 
 51.5363 
 
 7.9 
 
 30771 
 
 18.0 
 
 1889568 
 
 30.5 
 
 26393634 
 
 82 
 
 3707398432 
 
 2.25 
 
 57.6650 
 
 8.0 
 
 32768 
 
 18.2 
 
 1996903 
 
 31.0 
 
 28629151 
 
 83 
 
 3939040643 
 
 2.30 
 
 64.3634 
 
 8.1 
 
 34868 
 
 18.4 
 
 2109061 
 
 31.5 
 
 31013642 
 
 84 
 
 4182119424 
 
 2.35 
 
 71.6703 
 
 8.2 
 
 37074 
 
 18.6 
 
 2226203 
 
 32.0 
 
 33554432 
 
 85 
 
 4437053125 
 
 2.40 
 
 79.6262 
 
 8.3 
 
 39390 
 
 18.8 
 
 2348493 
 
 32.5 
 
 36259082 
 
 86 
 
 4704270176 
 
 2.45 
 
 88.2735 
 
 8.4 
 
 41821 
 
 19.0 
 
 2476099 
 
 33.0 
 
 39135393 
 
 87 
 
 4984209207 
 
 2.50 
 
 97.6562 
 
 8.5 
 
 44371 
 
 19.2 
 
 2609193 
 
 33.5 
 
 42191410 
 
 88 
 
 5277319168 
 
 2.55 
 
 107.820 
 
 8.6 
 
 47043 
 
 19.4 
 
 2747949 
 
 34.0 
 
 45435424 
 
 89 
 
 5584059449 
 
 2.60 
 
 118.814 
 
 8.7 
 
 49842 
 
 19.6 
 
 2892547 
 
 34.5 
 
 48875980 
 
 90 
 
 5904900000 
 
 2.70 
 
 143.489 
 
 8.8 
 
 52773 
 
 19.8 
 
 3043168 
 
 35.0 
 
 52521875 
 
 91 
 
 6240321451 
 
 2.80 
 
 172.104 
 
 8.9 
 
 55841 
 
 20.0 
 
 3200000 
 
 35.5 
 
 56382167 
 
 92 
 
 6590815232 
 
 2.90 
 
 205.111 
 
 9.0 
 
 59049 
 
 20.2 
 
 3363232 
 
 36.0 
 
 60466176 
 
 93 
 
 6956883693 
 
 3.00 
 
 243.000 
 
 9.1 
 
 62403 
 
 20.4 
 
 3533059 
 
 36.5 
 
 64783487 
 
 94 
 
 7339040224 
 
 3.10 
 
 286.292 
 
 9.2 
 
 65908 
 
 20.6 
 
 3709677 
 
 37.0 
 
 69343957 
 
 95 
 
 7737809375 
 
 3.20 
 
 335.544 
 
 9.3 
 
 69569 
 
 20.8 
 
 3893289 
 
 37.5 
 
 74157715 
 
 96 
 
 8153726976 
 
 3.30 
 
 391.354 
 
 9.4 
 
 73390 
 
 21.0 
 
 4084101 
 
 38.0 
 
 79235168 
 
 97 
 
 8587340257 
 
 3.40 
 
 454.354 
 
 9.5 
 
 77378 
 
 21.2 
 
 4282322 
 
 38.5 
 
 84587005 
 
 98 
 
 9039207968 
 
 3.50 
 
 525.219 
 
 9.6 
 
 81537 
 
 21.4 
 
 4488 1 66 
 
 39.0 
 
 90224199 
 
 99 
 
 9509900499 
 
 3.60 
 
 604.662 
 
 9.7 
 
 85873 
 
 21.6 
 
 4701850 
 
 39.5 
 
 96158012 
 
 
 
110 
 
 MATHEMATICAL TABLES. 
 
 tt 
 
 |- 
 
 53 
 
 1 O 
 
 !l 
 
 81 
 Bl 
 
 
 
 
 I 
 
 LO CO C 
 
 O r 
 
 -'' 
 
 --- 
 
 OI>.O^ 
 
 m !> co c 
 
 CNt^ C 
 
 o o O - ri i 
 
 
 
 OvO 
 ^O C 
 - 
 
 ooow^oooooomom. oooinoomoooomtnoro c^.o 
 -1 !>. mo^-OiAOPOOoor^oot > NO'^-vOfNOOio' T t' 
 
 -< '- 
 
 - N N <N (N <S (S (S fS <N C 
 
 ,.. 
 
 f^t^.t^.0 (NpTiOO'^TOOO <N 
 
 oo covo <NPM ir^rt-r>.in 
 
 O O O O O fS CO vO 00 -O CO <N r 
 
 fT 
 
 d OO CO ' 
 
 U^ICN 
 
 SI" 
 
 C.S 
 
 '^fCNfN 
 
 o oooo 
 
 ooooo < 
 
 Is 
 
 1.- 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 
 CIRCUMFERENCES AND AREAS OF CIRCLES. 
 
 Ill 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 1/64 
 
 .04909 
 
 .00019 
 
 23/ 8 
 
 7.4613 
 
 4.4301 
 
 6Vs 
 
 19.242 
 
 29 465 
 
 1/32 
 
 . 098 1 8 
 
 .00077 
 
 7/16 
 
 7.6576 
 
 4 . 6664 
 
 1/4 
 
 19.635 
 
 30 680 
 
 3/64 
 
 .14726 
 
 .00173 
 
 i/3 
 
 7.8540 
 
 4.9087 
 
 3/8 
 
 20.028 
 
 31 919 
 
 Vl6 
 
 .19635 
 
 .00307 
 
 9 /16 
 
 8.0503 
 
 5.1572 
 
 V2 
 
 20.420 
 
 33 183 
 
 3/32 
 
 .29452 
 
 .00690 
 
 5 /8 
 
 8.2467 
 
 5.4119 
 
 5 /8 
 
 20.813 
 
 34.472 
 
 Vs 
 
 .39270 
 
 .01227 
 
 H/16 
 
 8.4430 
 
 5.6727 
 
 3/4 
 
 21.206 
 
 35 785 
 
 5/32 
 
 .49087 
 
 .01917 
 
 3/4 
 
 8.6394 
 
 5.9396 
 
 7/8 
 
 21.598 
 
 37. 122 
 
 3/16 
 
 . 58905 
 
 .02761 
 
 13/16 
 
 8.8357 
 
 6.2126 
 
 
 21.991 
 
 38.485 
 
 7/32 
 
 . 68722 
 
 .03758 
 
 7/8 
 
 9.0321 
 
 6.4918 
 
 *l/8 
 
 22.384 
 
 39.871 
 
 
 
 
 15/16 
 
 9.2284 
 
 6.7771 
 
 V4 
 
 22.776 
 
 41.282 
 
 1/4 
 
 .78540 
 
 . 04909 
 
 
 
 
 3/8 
 
 23 . 1 69 
 
 42.718 
 
 /32 
 
 .88357 
 
 .06213 
 
 3. 
 
 9.4248 
 
 7.0686 
 
 V2 
 
 23.562 
 
 44. 179 
 
 5/16 
 
 .98175 
 
 .07670 
 
 Vl6 
 
 9.6211 
 
 7.3662 
 
 5/8 
 
 23.955 
 
 45 . 664 
 
 H/32 
 
 .0799 
 
 .09281 
 
 Vs 
 
 9.8175 
 
 7 . 6699 
 
 3/4 
 
 24.347 
 
 47.173 
 
 3/8 
 
 . 1781 
 
 .11045 
 
 3/16 
 
 10.014 
 
 7.9798 
 
 7/8 
 
 24.740 
 
 48.707 
 
 13/32 
 
 .2763 
 
 .12962 
 
 !/4 
 
 10.210 
 
 8.2958 
 
 8. 
 
 25.133 
 
 50.265 
 
 7/16 
 
 .3744 
 
 ..15033 
 
 5/16 
 
 10.407 
 
 8.6179 
 
 V8 
 
 25.525 
 
 51.849 
 
 15/32 
 
 .4726 
 
 .17257 
 
 3/8 
 
 10.603 
 
 8.9462 
 
 1/4 
 
 25.918 
 
 53.455 
 
 
 
 
 7/16 
 
 10.799 
 
 9.2806 
 
 3/8 
 
 26.311 
 
 55.088 
 
 1/2 
 
 .5708 
 
 .19635 
 
 1/2 
 
 10.996 
 
 9.6211 
 
 V2 
 
 26.704 
 
 56.745 
 
 17/32 
 
 .6690 
 
 .22166 
 
 9/16 
 
 11. 192 
 
 9.9678 
 
 5 /8 
 
 27.096 
 
 58.426 
 
 9/18 
 
 .7671 
 
 .24850 
 
 5 /8 
 
 1 1 . 388 
 
 10.321 
 
 3/4 
 
 27.489 
 
 60. 132 
 
 19/32 
 
 .8653 
 
 .27688 
 
 H/16 
 
 11.585 
 
 10.680 
 
 7/8 
 
 27.882 
 
 61.862 
 
 5/8 
 
 .9635 
 
 .30680 
 
 3/4 
 
 11.781 
 
 11.045 
 
 9. 
 
 28.274 
 
 63.617 
 
 21/32 
 
 2.0617 
 
 .33824 
 
 13/16 
 
 11.977 
 
 11.416 
 
 1/8 
 
 28.667 
 
 65.397 
 
 H/16 
 
 2.1598 
 
 .37122 
 
 7/8 
 
 12.174 
 
 1 1 . 793 
 
 1/4 
 
 29.060 
 
 67.201 
 
 23/32 
 
 2.2580 
 
 .40574 
 
 15/16 
 
 12.370 
 
 12.177 
 
 3/8 
 
 29.452 
 
 69.029 
 
 
 
 
 4. 
 
 12.566 
 
 12.566 
 
 1/2 
 
 29.845 
 
 70.882 
 
 3/4 
 
 2.3562 
 
 .44179 
 
 Vl6 
 
 12.763 
 
 12.962 
 
 5 /8 
 
 30.238 
 
 72.760 
 
 25/3 2 
 
 2.4544 
 
 .47937 
 
 1/8 
 
 12.959 
 
 13.364 
 
 3/4 
 
 30.631 
 
 74.662 
 
 13/16 
 
 2.5525 
 
 .51849 
 
 3/16 
 
 13. 155 
 
 13.772 
 
 7/8 
 
 3 1 . 023 
 
 76.589 
 
 27/32 
 
 2.6507 
 
 .55914 
 
 1/4 
 
 13.352 
 
 14. 186 
 
 10. 
 
 31.416 
 
 78.540 
 
 7/8 
 
 2.7489 
 
 .60132 
 
 5/16 
 
 13.548 
 
 14.607 
 
 V8 
 
 3 1 . 809 
 
 80.516 
 
 29/32 
 
 2.8471 
 
 .64504 
 
 3/8 
 
 13.744 
 
 15.033 
 
 1/4 
 
 32.201 
 
 82.516 
 
 15/16 
 
 2.9452 
 
 . 69029 
 
 7/16 
 
 13.941 
 
 15.466 
 
 3/8 
 
 32.594 
 
 84.541 
 
 31/32 
 
 3.0434 
 
 .73708 
 
 1/2 
 
 14.137 
 
 1 5 . 904 
 
 V2 
 
 32.987 
 
 86.590 
 
 
 
 
 9 /16 
 
 14.334 
 
 16.349 
 
 5/8 
 
 33.379 
 
 88,664 
 
 1. 
 
 3.1416 
 
 .7854 
 
 5/8 
 
 14.530 
 
 16.800 
 
 3/4 
 
 33.772 
 
 90.763 
 
 Vl6 
 
 3.3379 
 
 .8866 
 
 U/16 
 
 14.726 
 
 17.257 
 
 7/8 
 
 34. 165 
 
 92.886 
 
 1/8 
 
 3.5343 
 
 .9940 
 
 3/4 
 
 14.923 
 
 17.721 
 
 11. 
 
 34.558 
 
 95.033 
 
 3/16 
 
 3.7306 
 
 .1075 
 
 13/16 
 
 15.119 
 
 18. 190 
 
 1/8 
 
 34.950 
 
 97.205 
 
 1/4 
 
 3.9270 
 
 .2272 
 
 7/8 
 
 15.315 
 
 18.665 
 
 1/4 
 
 35.343 
 
 99.402 
 
 5/16 
 
 4.1233 
 
 .3530 
 
 15/16 
 
 15.512 
 
 19.147 
 
 3 /8 
 
 35.736 
 
 101.62 
 
 3/8 
 
 4.3197 
 
 .4849 
 
 5. 
 
 15.708 
 
 19.635 
 
 V2 
 
 36. 128 
 
 103.87 
 
 7/16 
 
 4.5160 
 
 .6230 
 
 Vl6 
 
 1 5 . 904 
 
 20. 129 
 
 5/8 
 
 36.521 
 
 106.14 
 
 1/2 
 
 4.7124 
 
 .7671 
 
 1/8 
 
 16. 101 
 
 20.629 
 
 3/4 
 
 36.914 
 
 108.43 
 
 'Vie 
 
 4.9087 
 
 .9175 
 
 3/16 
 
 16.297 
 
 21.135 
 
 7/8 
 
 37.306 
 
 110.75 
 
 5/8 
 
 5.1051 
 
 2.0739 
 
 1/4 
 
 16.493 
 
 21.648 
 
 13. 
 
 37.699 
 
 113.10 
 
 H/16 
 
 5.3014 
 
 2.2365 
 
 5 /l6 
 
 16.690 
 
 22 . 1 66 
 
 V8 
 
 38.092 
 
 115.47 
 
 3/4 
 
 5.4978 
 
 2.4053 
 
 3 /8 
 
 16.886 
 
 22.691 
 
 1/4 
 
 38.485 
 
 117.86 
 
 13/16 
 
 5.6941 
 
 2.5802 
 
 7/16 
 
 17.082 
 
 23.221 
 
 3/8 
 
 38.877 
 
 120.28 
 
 7/8 
 
 5.8905 
 
 2.7612 
 
 1/2 
 
 17.279 
 
 23.758 
 
 1/2 
 
 39.270 
 
 122.72 
 
 15 /16 
 
 6.0868 
 
 2.9483 
 
 9/16 
 
 17.475 
 
 24.301 
 
 5/8 
 
 39.663 
 
 125.19 
 
 
 
 
 5/8 
 
 17.671 
 
 24.850 
 
 3/4 
 
 40.055 
 
 127.68 
 
 3. 
 
 6.2832 
 
 3.1416 
 
 n/ie 
 
 17.868 
 
 25.406 
 
 7/8 
 
 40.448 
 
 130.19 
 
 Vl6 
 
 6.4795 
 
 3.3410 
 
 3/4 
 
 18.064 
 
 25.967 
 
 13. 
 
 40.841 
 
 132.73 
 
 1/8 
 
 6.6759 
 
 3.5466 
 
 13 /16 
 
 18.261 
 
 26.535 
 
 V8 
 
 41.233 
 
 135 30 
 
 3/16 
 
 6.8722 
 
 3.7583 
 
 7/8 
 
 18.457 
 
 27. 109 
 
 1/4 
 
 41.626 
 
 137.89 
 
 1/4 
 
 7 . 0686 
 
 3.9761 
 
 15/16 
 
 18.653 
 
 27.688 
 
 3/8 
 
 42.019 
 
 140.50 
 
 5/16 
 
 7.2649 
 
 4.2000 
 
 6. 
 
 18.850 
 
 28.274 
 
 1/2 
 
 42.412 
 
 143.14 
 
112 
 
 MATHEMATICAL TABLES. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 135/8 
 
 42.804 
 
 145.80 
 
 217/ 8 
 
 68.722 
 
 375.83 
 
 30 Vs 
 
 94.640 
 
 712.76 
 
 3/4 
 
 43.197 
 
 148.49 
 
 23. 
 
 69. 115 
 
 380.13 
 
 1/4 
 
 95.033 
 
 718.69 
 
 7/8 
 
 43.590 
 
 151.20 
 
 1/8 
 
 69.508 
 
 384.46 
 
 3/8 
 
 95.426 
 
 724 64 
 
 14. 
 
 43 , 982 
 
 153.94 
 
 1/4 
 
 69.900 
 
 388.82 
 
 1/2 
 
 95.819 
 
 730.62 
 
 1/8 
 
 44.375 
 
 156.70 
 
 3/8 
 
 70.293 
 
 393.20 
 
 5/8 
 
 96.211 
 
 736.62 
 
 1/4 
 
 44.768 
 
 159.48 
 
 1/2 
 
 70.686 
 
 397.61 
 
 3/4 
 
 96.604 
 
 742.64 
 
 3/8 
 
 45.160 
 
 162.30 
 
 5 /8 
 
 71.079 
 
 402.04 
 
 7/8 
 
 96.997 
 
 748.69 
 
 V2 
 
 45.553 
 
 165.13 
 
 3/4 
 
 71.471 
 
 406.49 
 
 31. 
 
 97.389 
 
 754.77 
 
 5/8 
 
 45.946 
 
 167.99 
 
 7/8 
 
 71.864 
 
 410.97 
 
 V8 
 
 97.782 
 
 760.87 
 
 3/4 
 
 46.338 
 
 170.87 
 
 23. 
 
 72.257 
 
 415.48 
 
 1/4 
 
 98.175 
 
 766.99 
 
 7/8 
 
 46.731 
 
 173.78 
 
 1/8 
 
 72.649 
 
 420.00 
 
 3/8 
 
 98.567 
 
 773. 14 
 
 15. 
 
 47.124 
 
 176.7! 
 
 1/4 
 
 73.042 
 
 424.56 
 
 1/2 
 
 98.960 
 
 779.31 
 
 J-/8 
 
 47.517 
 
 179.67 
 
 3/8 
 
 73.435 
 
 429.13 
 
 5 /8 
 
 99.353 
 
 785.51 
 
 1/4 
 
 47.909 
 
 182.65 
 
 1/2 
 
 73.827 
 
 433.74 
 
 3/4 
 
 99.746 
 
 791 73 
 
 3/8 
 
 48.302 
 
 185.66 
 
 5/8 
 
 74.220 
 
 438.36 
 
 7/8 
 
 100. 138 
 
 797.98 
 
 V2 
 
 48.695 
 
 188.69 
 
 3/4 
 
 74.613 
 
 443.01 
 
 32. 
 
 100.531 
 
 804.25 
 
 5/8 
 
 49.087 
 
 191.75 
 
 7/8 
 
 75.006 
 
 447.69 
 
 Vs 
 
 100.924 
 
 810.54 
 
 3/4 
 
 49.480 
 
 194.83 
 
 24. 
 
 75.398 
 
 452.39 
 
 1/4 
 
 101.316 
 
 816.86 
 
 7/8 
 
 49.873 
 
 197.93 
 
 1/8 
 
 75.791 
 
 457.11 
 
 3/8 
 
 101.709 
 
 823.21 
 
 16. 
 
 50.265 
 
 201.06 
 
 1/4 
 
 76. 184 
 
 461.86 
 
 1/2 
 
 102.102 
 
 829.58 
 
 Vs 
 
 50.658 
 
 204.22 
 
 3/8 
 
 76.576 
 
 466.64 
 
 5/8 
 
 102.494 
 
 835.97 
 
 V4 
 
 51.051 
 
 207.39 
 
 1/2 
 
 76.969 
 
 471.44 
 
 3/ 4 
 
 102.887 
 
 842.39 
 
 3/8 
 
 51.444 
 
 210.60 
 
 5 /8 
 
 77.362 
 
 476.26 
 
 7/8 
 
 103.280 
 
 848.83 
 
 V2 
 
 51.836 
 
 213.82 
 
 3/ 4 
 
 77.754 
 
 481.11 
 
 33. 
 
 103.673 
 
 855.30 
 
 5/8 
 
 52.229 
 
 217.08 
 
 7/8 
 
 78.147 
 
 485.98 
 
 1/8 
 
 104.065 
 
 861.79 
 
 3/4 
 
 52.622 
 
 220.35 
 
 25. 
 
 78.540 
 
 490.87 
 
 1/4 
 
 104.458 
 
 868.31 
 
 7/ 8 
 
 53.014 
 
 223.65 
 
 1/8 
 
 78.933 
 
 495.79 
 
 3/8 
 
 104.851 
 
 874.85 
 
 17. 
 
 53.407 
 
 226.98 
 
 1/4 
 
 79.325 
 
 500.74 
 
 V2 
 
 105.243 
 
 881.41 
 
 Vs 
 
 53.800 
 
 230.33 
 
 3/8 
 
 79.718 
 
 505.71 
 
 5/8 
 
 105.636 
 
 888.00 
 
 1/4 
 
 54.192 
 
 233.71 
 
 1/2 
 
 80.111 
 
 510.71 
 
 3/4 
 
 106.029 
 
 894.62 
 
 3/8 
 
 54.585 - 
 
 237.10 
 
 5/8 
 
 80.503 
 
 515.72 
 
 7/8 
 
 106.421 
 
 901.26 
 
 1/2 
 
 54.978 
 
 240.53 
 
 3/4 
 
 80.896 
 
 520.77 
 
 34. 
 
 106.814 
 
 907.92 
 
 5 /8 
 
 55.371 
 
 243.98 
 
 7/8 
 
 81.289 
 
 525.84 
 
 V8 
 
 107.207 
 
 914.61 
 
 3/4 
 
 55.763 
 
 247.45 
 
 26. 
 
 81.681 
 
 530.93 
 
 1/4 
 
 107.600 
 
 921.32 
 
 7/8 
 
 56.156 
 
 250.95 
 
 1/8 
 
 82.074 
 
 536.05 
 
 3/8 
 
 107.992 
 
 928.06 
 
 18. 
 
 56.549 
 
 254.47 
 
 1/4 
 
 82.467 
 
 541.19 
 
 1/2 
 
 108.385 
 
 934.82 
 
 1/8 
 
 56.941 
 
 258.02 
 
 3/8 
 
 82.860 
 
 546.35 
 
 5/8 
 
 108.778 
 
 941.61 
 
 1/4 
 
 57.334 
 
 261.59 
 
 1/2 
 
 83.252 
 
 551.55 
 
 3/4 
 
 109. 170 
 
 948.42 
 
 3/8 
 
 57.727 
 
 265.18 
 
 5/8 
 
 83.645 
 
 556.76 
 
 7/8 
 
 109.563 
 
 955.25 
 
 1/2 
 
 58.119 
 
 268.80 
 
 3/4 
 
 -84.038 
 
 562.00 
 
 35. 
 
 109.956 
 
 962 . 1 1 
 
 5/8 
 
 58.512 
 
 272.45 
 
 7/8 
 
 84.430 
 
 567.27 
 
 1/8 
 
 110.348 
 
 969 . 00 
 
 3/4 
 
 58.905 
 
 276.12 
 
 27. 
 
 84.823 
 
 572.56 
 
 1/4 
 
 110.741 
 
 975.91 
 
 7/8 
 
 59.298 
 
 279.81 
 
 Vs 
 
 85.216 
 
 577.87 
 
 3/8 
 
 111. 134 
 
 982.84 
 
 19. 
 
 59.690 
 
 283.53 
 
 1/4 
 
 85.608 
 
 583.21 
 
 1/2 
 
 111.527 
 
 989.80 
 
 1/8 
 
 60.083 
 
 287.27 
 
 3/8 
 
 86.001 
 
 588.57 
 
 5/8 
 
 111.919 
 
 996.78 
 
 1/4 
 
 60.476 
 
 291.04 
 
 1/2 
 
 86.394 
 
 593.96 
 
 3/4 
 
 112.312 
 
 1003.8 
 
 3/8 
 
 60.868 
 
 294.83 
 
 5 /8 
 
 86.786 
 
 599.37 
 
 7/8 
 
 112.705 
 
 1010.8 
 
 1/2 
 
 61.261 
 
 298.65 
 
 3/4 
 
 87.179 
 
 604.81 
 
 36. 
 
 113.097 
 
 1017.9 
 
 5/8 
 
 61.654 
 
 302.49 
 
 7/8 
 
 87.572 
 
 610.27 
 
 1/8 
 
 113.490 
 
 1025.0 
 
 3/4 
 
 62 . 046 
 
 306.35 
 
 28. 
 
 87.965 
 
 615.75 
 
 1/4 
 
 113.883 
 
 1032.1 
 
 7/8 
 
 62.439 
 
 310.24 
 
 V8 
 
 88.357 
 
 621.26 
 
 3/8 
 
 114.275 
 
 1039.2 
 
 20. 
 
 62.832 
 
 314.16 
 
 1/4 
 
 88.750 
 
 626.80 
 
 1/2 
 
 114. 668 
 
 1046.3 
 
 1/8 
 
 63.225 
 
 318.10 
 
 3 /8 
 
 89.143 
 
 632.36 
 
 5/8 
 
 115.061 
 
 1053.5 
 
 1/4 
 
 63.617 
 
 322.06 
 
 1/2 
 
 89.535 
 
 637.94 
 
 3/4 
 
 115.454 
 
 1060.7 
 
 3/8 
 
 64.010 
 
 326.05 
 
 5/8 
 
 89.928 
 
 643.55 
 
 7/8 
 
 115.846 
 
 1068.0 
 
 1/2 
 
 64.403 
 
 330.06 
 
 3/4 
 
 90.321 
 
 649.18 
 
 37. 
 
 116.239 
 
 1075.2 
 
 5/8 
 
 64.795 
 
 334.10 
 
 7/8 
 
 90.713 
 
 654.84 
 
 1/8 
 
 116.632 
 
 1082.5 
 
 3/4 
 
 65.188 
 
 338.16 
 
 29. 
 
 91.106 
 
 660.52 
 
 1/4 
 
 117.024 
 
 1089.8 
 
 7/8 
 
 65.581 
 
 342.25 
 
 1/8 
 
 91.499 
 
 666.23 
 
 3/8 
 
 117.417 
 
 1097.1 
 
 21. 
 
 65.973 
 
 346.36 
 
 V4 
 
 91 .892 
 
 671.96 
 
 1/2 
 
 17.810 
 
 1104.5 
 
 1/8 
 
 66.366 
 
 350.50 
 
 3/8 
 
 92.284 
 
 677.71 
 
 5/8 
 
 18.202 
 
 1111.8 
 
 1/4 
 
 66.759 
 
 354.66 
 
 1/2 
 
 92.677 
 
 683 . 49 
 
 3/4 
 
 1-8.596 
 
 1119.2 
 
 3/8 
 
 67.152 
 
 358.84 
 
 5/8 
 
 93.070 
 
 689.30 
 
 7/8 
 
 18.988 
 
 1126.7 
 
 1/2 
 
 67.544 
 
 363.05 
 
 3/4 
 
 93.462 
 
 695.13 
 
 38. 
 
 19.381 
 
 1134.1 
 
 5/8 
 
 67.937 
 
 367.28 
 
 7/8 
 
 93.855 
 
 700.98 
 
 1/8 
 
 19.773 
 
 1141.6 
 
 3/4 
 
 68.330 
 
 371.54 
 
 30. 
 
 94.248 
 
 706 . 86 
 
 V4 
 
 120.166 
 
 1149.1 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 113 
 
 Dtam 
 
 Circuin. 
 
 Area. 
 
 Diara 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 883/8 
 
 120.559 
 
 1136.6 
 
 465/8 
 
 146.477 
 
 1707.4 
 
 547/ g 
 
 172.395 
 
 2365.0 
 
 1/2 
 
 120.951 
 
 1164.2 
 
 3/4 
 
 146.869 
 
 1716.5 
 
 55. 
 
 172.788 
 
 2375.8 
 
 5/ 8 
 
 121.344 
 
 1171.7 
 
 7/8 
 
 147.262 
 
 1725.7 
 
 1/8 
 
 173.180 
 
 2386.6 
 
 3/ 4 
 
 121.737 
 
 1179.3 
 
 47. 
 
 147.655 
 
 1734.9 
 
 V4 
 
 173.573 
 
 2397.5 
 
 7/8 
 
 122.129 
 
 1186.9 
 
 Vs 
 
 148.048 
 
 1744.2 
 
 3 /8 
 
 173.966 
 
 2408.3 
 
 39. 
 
 122.522 
 
 1194.6 
 
 V4 
 
 148.440 
 
 1753.5 
 
 V2 
 
 174.358 
 
 2419.2 
 
 l/ 8 
 
 122.915 
 
 1202.3 
 
 3/8 
 
 148.833 
 
 1762.7 
 
 5/8 
 
 174.751 
 
 2430. 1 
 
 1/4 
 
 123.308 
 
 1210.0 
 
 V2 
 
 149.226 
 
 1772. 1 
 
 3/4 
 
 175. 144 
 
 2441. 1 
 
 3/8 
 
 123.700 
 
 1217.7 
 
 5/8 
 
 149.618 
 
 1781.4 
 
 7/8 
 
 175.536 
 
 2452.0 
 
 1/2 
 
 124.093 
 
 1225.4 
 
 3/4 
 
 150.011 
 
 1790.8 
 
 56. 
 
 175.929 
 
 2463.0 
 
 5/8 
 
 124.486 
 
 1233.2 
 
 7/8 
 
 150.404 
 
 1800. 1 
 
 Vs 
 
 176.322 
 
 2474.0 
 
 3/4 
 
 124.878 
 
 1241.0 
 
 48. 
 
 150.796 
 
 1809.6 
 
 1/4 
 
 176.715 
 
 2485.0 
 
 7/8 
 
 125.271 
 
 1248.8 
 
 Vs 
 
 151.189 
 
 1819.0 
 
 3/8 
 
 177. 107 
 
 2496. 1 
 
 40. 
 
 125.664 
 
 1256.6 
 
 1/4 
 
 151.582 
 
 1828.5 
 
 1/2 
 
 177.500 
 
 2507.2 
 
 Vs 
 
 126.056 
 
 1264.5 
 
 $ 
 
 151.975 
 
 1837.9 
 
 5 /8 
 
 177.893 
 
 2518.3 
 
 1/4 
 
 126.449 
 
 1272.4 
 
 1/2 
 
 152.367 
 
 1847.5 
 
 3/4 
 
 178.285 
 
 2529.4 
 
 3 /8 
 
 126.842 
 
 1280.3 
 
 5/8 
 
 152.760 
 
 1857.0 
 
 7/8 
 
 178.678 
 
 2540.6 
 
 1/9 
 
 127.235 
 
 1288.2 
 
 3/4 
 
 153. 153 
 
 1866.5 
 
 57. 
 
 179.071 
 
 2551.8 
 
 5 /8 
 
 127.627 
 
 1296.2 
 
 7/8 
 
 153.545 
 
 1876. 1 
 
 1/8 
 
 1 79. 463 
 
 2563.0 
 
 3/ 4 
 
 128.020 
 
 1304.2 
 
 49. 
 
 153.938 
 
 1885.7 
 
 V4 
 
 179.856 
 
 2574.2 
 
 7/a 
 
 128.413 
 
 1312.2 
 
 Vs 
 
 154.331 
 
 1895.4 
 
 3/8 
 
 180.249 
 
 2585.4 
 
 41. 
 
 128.805 
 
 1320.3 
 
 V4 
 
 154.723 
 
 1905.0 
 
 1/2 
 
 180.642 
 
 2596.7 
 
 Vs 
 
 129.198 
 
 1328.3 
 
 3/8 
 
 155.116 
 
 1914.7 
 
 5/8 
 
 181.034 
 
 2608.0 
 
 V4 
 
 129.591 
 
 1336.4 
 
 V2 
 
 155.509 
 
 1924.4 
 
 3/4 
 
 181.427 
 
 2619.4 
 
 3/8 
 
 129.983 
 
 1344.5 
 
 5 /8 
 
 155.902 
 
 1934.2 
 
 7/8 
 
 181.820 
 
 2630.7 
 
 I/O 
 
 130.376 
 
 1352.7 
 
 3/4 
 
 156.294 
 
 1943.9 
 
 58. 
 
 182.212 
 
 2642. 1 
 
 5 /8 
 
 130.769 
 
 1360.8 
 
 7/8 
 
 156.687 
 
 1953.7 
 
 VS 
 
 182.605 
 
 2653.5 
 
 3/4 
 
 131.161 
 
 1369.0 
 
 50. 
 
 157 080 
 
 1963.5 
 
 V4 
 
 182.998 
 
 2664.9 
 
 7/8 
 
 131.554 
 
 1377.2 
 
 Vs 
 
 157.472 
 
 1973.3 
 
 3/8 
 
 183.390 
 
 2676.4 
 
 42. 
 
 131.947 
 
 1385.4 
 
 1/4 
 
 157.865 
 
 1983.2 
 
 1/2 
 
 183.783 
 
 2687.8 
 
 1/8 
 
 132.340 
 
 1393.7 
 
 3/jj 
 
 158.258 
 
 1993.1 
 
 5/8 
 
 184.176 
 
 2699.3 
 
 V? 
 
 132.732 
 
 1 402 . 
 
 1/9 
 
 158.650 
 
 2003.0 
 
 3/4 
 
 184.569 
 
 2710.9 
 
 3 /8 
 
 133.125 
 
 1410.3 
 
 5 /8 
 
 159.043 
 
 2012.9 
 
 7/8 
 
 184.961 
 
 2722.4 
 
 1/9 
 
 133.518 
 
 1418.6 
 
 8/4 
 
 159.436 
 
 2022.8 
 
 59. 
 
 185.354 
 
 2734.0 
 
 5 /8 
 
 133.910 
 
 1427.0 
 
 7/8 
 
 159.829 
 
 2032.8 
 
 i/a 
 
 185.747 
 
 2745.6 
 
 3/4 
 
 134.303 
 
 1435.4 
 
 51. 
 
 160.221 
 
 2042.8 
 
 1/4 
 
 186.139 
 
 2757.2 
 
 7 /8 
 
 134.696 
 
 1443.8 
 
 Vs 
 
 160.614 
 
 2052.8 
 
 3/8 
 
 186.532 
 
 2768.8 
 
 43. 
 
 135.088 
 
 1452.2 
 
 */4 
 
 161.007 
 
 2062.9 
 
 1/2 
 
 186.925 
 
 2780.5 
 
 Vs 
 
 135.481 
 
 1460.7 
 
 3/8 
 
 161.399 
 
 2073.0 
 
 5/8 
 
 187.317 
 
 2792.2 
 
 1/4 
 
 135.874 
 
 1469. 1 
 
 1/2 
 
 161.792 
 
 2083.1 
 
 3/4 
 
 187.710 
 
 2803.9 
 
 3 /8 
 
 136.267 
 
 1477.6 
 
 5/8 
 
 162.185 
 
 2093.2 
 
 7/8 
 
 188.103 
 
 2815.7 
 
 V2 
 
 136.659 
 
 1486.2 
 
 3/4 
 
 162.577 
 
 2103.3 
 
 60. 
 
 188.496 
 
 2827.4 
 
 5/8 
 
 137.052 
 
 1494.7 
 
 7/8 
 
 162.970 
 
 2113.5 
 
 Vs 
 
 188.888 
 
 2839.2 
 
 3/4 
 
 137.445 
 
 1503.3 
 
 53. 
 
 163.363 
 
 2123.7 
 
 1/4 
 
 189.281 
 
 2851.0 
 
 7/8 
 
 137.837 
 
 1511.9 
 
 Vs 
 
 163.756 
 
 2133.9 
 
 3/8 
 
 189.674 
 
 2862.9 
 
 44. 
 
 138.230 
 
 1520.5 
 
 V4 
 
 164.148 
 
 2144.2 
 
 1/2 
 
 190.066 
 
 2874.8 
 
 Vs 
 
 138.623 
 
 1529.2 
 
 3/8 
 
 164.541 
 
 2154.5 
 
 5/8 
 
 190.459 
 
 2886.6 
 
 V4 
 
 139.015 
 
 1537.9 
 
 1/2 
 
 164.934 
 
 2164.8 
 
 3/4 
 
 190.852 
 
 2898.6 
 
 3/8 
 
 139.408 
 
 1546.6 
 
 5/8 
 
 165.326 
 
 2175.1 
 
 7/8 
 
 191.244 
 
 2910.5 
 
 V2 
 
 139.801 
 
 1555.3 
 
 3/4 
 
 165.719 
 
 2185.4 
 
 61. 
 
 191.637 
 
 2922.5 
 
 5 /8 
 
 140.194 
 
 1564.0 
 
 7/8 
 
 166.112 
 
 2195.8 
 
 1/8 
 
 192.030 
 
 2934.5 
 
 3/4 
 
 140.586 
 
 1572.8 
 
 53. 
 
 166.504 
 
 2206.2 
 
 V4 
 
 192.423 
 
 2946.5 
 
 7/8 
 
 140.979 
 
 1581.6 
 
 Vs 
 
 166.897 
 
 2216.6 
 
 3/8 
 
 192.815 
 
 2958.5 
 
 45. 
 
 141.372 
 
 1590.4 
 
 V4 
 
 167.290 
 
 2227.0 
 
 1/2 
 
 193.208 
 
 2970.6 
 
 Vs 
 
 141.764 
 
 1599.3 
 
 3/8 
 
 167.683 
 
 2237.5 
 
 5 /8 
 
 193.601 
 
 2982 . 7 
 
 V4 
 
 142.157 
 
 1608.2 
 
 1/2 
 
 168.075 
 
 2248.0 
 
 3/4 
 
 193.993 
 
 2994.8 
 
 3/8 
 
 142.550 
 
 1617.0 
 
 5/8 
 
 1 68 . 468 
 
 2258.5 
 
 7/8 
 
 194.386 
 
 3006.9 
 
 Va 
 
 142.942 
 
 1626.0 
 
 3/4 
 
 168.861 
 
 2269.1 
 
 62. 
 
 194.779^ 
 
 3019.1 
 
 5/8 
 
 143.335 
 
 1634.9 
 
 7/8 
 
 169.253 
 
 2279.6 
 
 Vs 
 
 195. 171 
 
 3031.3 
 
 3/4 
 
 143.728 
 
 1643.9 
 
 54. 
 
 169.646 
 
 2290.2 
 
 V4 
 
 195.564 
 
 3043.5 
 
 7/8 
 
 144. 121 
 
 1652.9 
 
 1/8 
 
 170.039 
 
 2300.8 
 
 3/8 
 
 195.957 
 
 3055.7 
 
 46. 
 
 144.513 
 
 1661.9 
 
 1/4 
 
 170.431 
 
 2311.5 
 
 V2 
 
 196.350 
 
 3068.0 
 
 Vs 
 
 144.906 
 
 1670.9 
 
 3/8 
 
 170.824 
 
 2322.1 
 
 5/8 
 
 196.742 
 
 3080.3 
 
 V4 
 
 145.299 
 
 1680.0 
 
 1/2 
 
 171.217 
 
 2332.8 
 
 8/4 
 
 197.135 
 
 3092.6 
 
 3/8 
 
 145.691 
 
 1689.1 
 
 5/8 
 
 171.609 
 
 2343.5 
 
 7/8 
 
 197.528 
 
 3 1 04 . 9 
 
 , V 2 
 
 146.084 
 
 1698.2 
 
 3/4 
 
 172.002 
 
 2354.3 
 
 63. 
 
 197.920 
 
 3117.2 
 
114 
 
 MATHEMATICAL TABLES. 
 
 Diam. 
 
 63V8~ 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 "4979.1 
 
 198.313 
 
 3129.6 
 
 713/8 
 
 224.231 
 
 4001.1 
 
 795/ 8 
 
 250.149 
 
 1/4 
 
 198.706 
 
 3142.0 
 
 1/2 
 
 224.624 
 
 4015.2 
 
 3/* 
 
 250.542 
 
 4995 . 2 
 
 3 /8 
 
 199.098 
 
 3154.5 
 
 5/8 
 
 225.017 
 
 4029.2 
 
 7 /8 
 
 250.935 
 
 5010.9 
 
 1/2 
 
 199.491 
 
 3166.9 
 
 3/ 4 
 
 225.409 
 
 4043.3 
 
 80. 
 
 251.327 
 
 5026.5 
 
 5/8 
 
 199.884 
 
 3179.4 
 
 7/8 
 
 225.802 
 
 4057.4 
 
 1/8 
 
 251.720 
 
 5042.3 
 
 3/4 
 
 200.277 
 
 3191.9 
 
 73. 
 
 226. 195 
 
 4071.5 
 
 1/4 
 
 252. 113 
 
 5058.0 
 
 7 /8 
 
 200.669 
 
 3204.4 
 
 Vs 
 
 226.587 
 
 4085.7 
 
 3/8 
 
 252.506 
 
 5073.8 
 
 64. 
 
 201.062 
 
 3217.0 
 
 1/4 
 
 226.980 
 
 4099.8 
 
 !/2 
 
 252.898 
 
 5089.6 
 
 1/8 
 
 201.455 
 
 3229.6 
 
 3/8 
 
 227.373 
 
 4114.0 
 
 5/8 
 
 253.291 
 
 5105.4 
 
 V4 
 
 201.847 
 
 3242.2 
 
 V2 
 
 227.765 
 
 4128.2 
 
 3/4 
 
 253.684 
 
 5121.2 
 
 3 /8 
 
 202.240 
 
 3254.8 
 
 5/8 
 
 228.158 
 
 4142.5 
 
 7/8 
 
 254.076 
 
 5137. 1 
 
 Va 
 
 202.633 
 
 3267.5 
 
 3/4 
 
 228.551 
 
 4156.8 
 
 81. 
 
 254.469 
 
 5153.0 
 
 5 /8 
 
 203.025 
 
 3280.1 
 
 7/8 
 
 228.944 
 
 4171.1 
 
 V8 
 
 254.862 
 
 5 1 68 . 9 
 
 3/4 
 
 203.418 
 
 3292.8 
 
 73. 
 
 229.336 
 
 4185.4 
 
 1/4 
 
 255.254 
 
 5184.9 
 
 7 /8 
 
 203.811 
 
 3305.6 
 
 1/8 
 
 229.729 
 
 4199.7 
 
 3/8 
 
 255.647 
 
 5200.8 
 
 65. 
 
 204.204 
 
 3318.3 
 
 1/4 
 
 230.122 
 
 4214.1 
 
 1/2 
 
 256.040 
 
 5216.8 
 
 Vs 
 
 204.596 
 
 3331.1 
 
 3/8 
 
 230.514 
 
 4228.5 
 
 5/8 
 
 256.433 
 
 5232.8 
 
 V4 
 
 204.989 
 
 3343.9 
 
 V2 
 
 230.907 
 
 4242.9 
 
 3/4 
 
 256.825 
 
 5248.9 
 
 3/8 
 
 205.382 
 
 3356.7 
 
 5/8 
 
 231.300 
 
 4257.4 
 
 7/8 
 
 257.218 
 
 5264.9 
 
 V2 
 
 205.774 
 
 3369.6 
 
 3/4 
 
 231.692 
 
 4271.8 
 
 83. 
 
 257.611 
 
 5281.0 
 
 5/8 
 
 206.167 
 
 3382.4 
 
 7/8 
 
 232.085 
 
 4286.3 
 
 1/8 
 
 258.003 
 
 5297. 1 
 
 3/4 
 
 206.560 
 
 3395.3 
 
 74. 
 
 232.478 
 
 4300.8 
 
 1/4 
 
 258.396 
 
 5313.3 
 
 7/8 
 
 206.952 
 
 3408.2 
 
 1/8 
 
 232.871 
 
 4315.4 
 
 3/8 
 
 258.789 
 
 5329.4 
 
 66. 
 
 207.345 
 
 3421.2 
 
 1/4 
 
 233.263 
 
 4329.9 
 
 1/2 
 
 259.181 
 
 5345.6 
 
 1/8 
 
 207.738 
 
 3434.2 
 
 3/8 
 
 233.656 
 
 4344.5 
 
 5/8 
 
 259.574 
 
 5361.8 
 
 1/4 
 
 208.131 
 
 3447.2 
 
 1/2 
 
 234.049 
 
 4359.2 
 
 3/4 
 
 259.967 
 
 5378. 1 
 
 3/8 
 
 208.523 
 
 3460.2 
 
 5/8 
 
 234.441 
 
 4373.8 
 
 7/8 
 
 260.359 
 
 5394.3 
 
 1/2 
 
 208.916 
 
 3473.2 
 
 3/4 
 
 234.834 
 
 4388.5 
 
 83. 
 
 260.752 
 
 5410.6 
 
 5/8 
 
 209.309 
 
 3486.3 
 
 7/8 
 
 235.227 
 
 4403 . 1 
 
 1/8 
 
 261.145 
 
 5426.9 
 
 3/4 
 
 209.701 
 
 3499.4 
 
 75. 
 
 235.619 
 
 4417.9 
 
 l /4 
 
 261.538 
 
 5443.3 
 
 7/8 
 
 210.094 
 
 3512.5 
 
 1/8 
 
 236.012 
 
 4432.6 
 
 3/8 
 
 261.930 
 
 5459.6 
 
 67. 
 
 210.487 
 
 3525.7 
 
 1/4 
 
 236.405 
 
 4447.4 
 
 1/2 
 
 262.323 
 
 5476.0 
 
 1/8 
 
 210.879 
 
 3538.8 
 
 3 /8 
 
 236.798 
 
 4462.2 
 
 5/8 
 
 262.716 
 
 5492.4 
 
 1/4 
 
 211.272 
 
 3552.0 
 
 V2 
 
 237.190 
 
 4477.0 
 
 3/4 
 
 263.108 
 
 5508.8 
 
 3/8 
 
 211.665 
 
 3565.2 
 
 5/8 
 
 237.583 
 
 -^491.8 
 
 7/8 
 
 263.501 
 
 5525.3 
 
 1/2 
 
 212.058 
 
 3578.5 
 
 3/4 
 
 237.976 
 
 4506.7 
 
 84. 
 
 263.894 
 
 5541.8 
 
 5/8 
 
 212.450 
 
 3591.7 
 
 7/8 
 
 238.368 
 
 4521.5 
 
 1/8 
 
 264.286 
 
 5558.3 
 
 3/4 
 
 212.843 
 
 3605.0 
 
 76c 
 
 238.761 
 
 4536.5 
 
 V4 
 
 264.679 
 
 5574.8 
 
 7/8 
 
 213.236 
 
 3618.3 
 
 1/8 
 
 239.154 
 
 4551.4 
 
 3/8 
 
 265.072 
 
 5591.4 
 
 68. 
 
 213.628 
 
 3631.7 
 
 V4 
 
 239.546 
 
 4566.4 
 
 1/2 
 
 265.465 
 
 5607.9 
 
 Vs 
 
 214.021 
 
 3645.0 
 
 3/8 
 
 239.939 
 
 4581.3 
 
 5/8 
 
 265.857 
 
 5624.5 
 
 V4 
 
 214.414 
 
 3658.4 
 
 1/2 
 
 240.332 
 
 4596.3 
 
 3/4 
 
 266.250 
 
 5641.2 
 
 3/8 
 
 214.806 
 
 3671.8 
 
 5/8 
 
 240.725 
 
 4611.4 
 
 7/8 
 
 266.643 
 
 5657.8 
 
 1/2 
 
 215.199 
 
 3685.3 
 
 3/4 
 
 241. 117 
 
 4626.4 
 
 85. 
 
 267.035 
 
 5674.5 
 
 5/8 
 
 215.592 
 
 3698.7 
 
 7/8 
 
 241.510 
 
 4641.5 
 
 1/8 
 
 267.428 
 
 5691.2 
 
 3/4 
 
 2 1 5 . 984 
 
 3712.2 
 
 77. 
 
 241.903 
 
 4656.6 
 
 V4 
 
 267.821 
 
 5707.9 
 
 7/8 
 
 216.377 
 
 3725.7 
 
 1/8 
 
 242.295 
 
 4671.8 
 
 3/8 
 
 268.213 
 
 '5724.7 
 
 69. 
 
 216.770 
 
 3739.3 
 
 1/4 
 
 242.688 
 
 4686.9 
 
 V2 
 
 268.606 
 
 5741.5 
 
 Vs 
 
 217.163 
 
 3752.8 
 
 3/8 
 
 243.081 
 
 4702.1 
 
 5/8 
 
 268.999 
 
 5758.3 
 
 V4 
 
 217.555 
 
 3766.4 
 
 1/2 
 
 243.473 
 
 4717.3 
 
 3/4 
 
 269.392 
 
 5775.1 
 
 3/8 
 
 2 1 7 . 948 
 
 3780.0 
 
 5 /8 
 
 243.866 
 
 4732.5 
 
 7/8 
 
 269.784 
 
 5791.9 
 
 1/2 
 
 218.341 
 
 3793.7 
 
 3/4 
 
 244.259 
 
 4747.8 
 
 86. 
 
 270.177 
 
 5808.8 
 
 5/8 
 
 218.733 
 
 3807.3 
 
 7/8 
 
 244.652 
 
 4763.1 
 
 1/8 
 
 270.570 
 
 5825.7 
 
 3/4 
 
 219.126 
 
 3821.0 
 
 78. 
 
 245.044 
 
 4778.4 
 
 1/4 
 
 270.962 
 
 5842.6 
 
 7/8 
 
 219.519 
 
 3834.7 
 
 1/8 
 
 245.437 
 
 4793.7 
 
 3/8 
 
 271.355 
 
 5859.6 
 
 70. 
 
 219.911 
 
 3848.5 
 
 1/4 
 
 245.830 
 
 4809.0 
 
 1/9 
 
 271.748 
 
 5876.5 
 
 V8 
 
 220.304 
 
 3862.2 
 
 3/8 
 
 246.222 
 
 4824.4 
 
 5/J 
 
 272.140 
 
 5893.5 
 
 1/4 
 
 220.697 
 
 3876.0 
 
 i/2 
 
 246.615 
 
 4839.8 
 
 3/4 
 
 272.533 
 
 5910.6 
 
 3/8 
 
 221.090 
 
 3889.8 
 
 5 /8 
 
 247.008 
 
 4855.2 
 
 7/8 
 
 272.926 
 
 5927.6 
 
 V2 
 
 221.482 
 
 3903.6 
 
 3/4 
 
 247 400 
 
 4870.7 
 
 87. 
 
 273.319 
 
 5944.7 
 
 5/8 
 
 221.375 
 
 3917.5 
 
 7/8 
 
 247.793 
 
 4886.2 
 
 Vs 
 
 273.711 
 
 5961.8 
 
 3/4 
 
 222.268 
 
 3931.4 
 
 79. 
 
 248. 186 
 
 4901.7 
 
 1/4 
 
 274. 104 
 
 5978.9 
 
 7/8 
 
 222 . 660 
 
 3945.3 
 
 !/8 
 
 248.579 
 
 4917.2 
 
 3/8 
 
 274.497 
 
 5996.0 
 
 71. 
 
 223.053 
 
 3959 2 
 
 1/4 
 
 248.971 
 
 4932.7 
 
 1/2 
 
 274.889 
 
 6013.2 
 
 V8 
 
 223 . 446 
 
 3973 1 
 
 3/8 
 
 249.364 
 
 4948.3 
 
 5 /8 
 
 275.282 
 
 6030.4 
 
 1/4 
 
 223.838 
 
 3987.1 
 
 V 2 
 
 249.757 
 
 4963.9 
 
 3/4 
 
 275.675 
 
 6047.6 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 115 
 
 Diani 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 877/s 
 
 276.067 
 
 6064.9 
 
 957/s 
 
 301.200 
 
 7219.4 
 
 130 
 
 408.41 
 
 13273.23 
 
 88. 
 
 276.460 
 
 6082.1 
 
 96. 
 
 301.593 
 
 7238.2 
 
 131 
 
 411.55 
 
 13478.22 
 
 1/8 
 
 276.853 
 
 6099.4 
 
 1/8 
 
 301.986 
 
 7257.1 
 
 132 
 
 414.69 
 
 13684.78 
 
 1/4 
 
 277.246 
 
 6116.7 
 
 1/4 
 
 302.378 
 
 7276.0 
 
 133 
 
 417.83 
 
 13892.91 
 
 3/8 
 
 277.638 
 
 6134.1 
 
 3/8 
 
 302.771 
 
 7294.9 
 
 134 
 
 420.97 
 
 1 4 1 02 . 6 1 
 
 1/2 
 
 278.031 
 
 6151.4 
 
 1/2 
 
 303. 164 
 
 7313.8 
 
 135 
 
 424. 12 
 
 14313.88 
 
 5/8 
 
 278.424 
 
 6168.8 
 
 5/8 
 
 303.556 
 
 7332.8 
 
 136 
 
 427.26 
 
 14526.72 
 
 3/4 
 
 278.816 
 
 6186.2 
 
 3/4 
 
 303.949 
 
 7351.8 
 
 137 
 
 430.40 
 
 !4741 . 14 
 
 7/8 
 
 279.209 
 
 6203 . 7 
 
 7/8 
 
 304.342 
 
 7370.8 
 
 138 
 
 433.54 
 
 14957.12 
 
 89. 
 
 279.602 
 
 6221.1 
 
 97. 
 
 304.734 
 
 7389.8 
 
 139 
 
 436.68 
 
 15174.68 
 
 V8 
 
 279.994 
 
 6238.6 
 
 1/8 
 
 305. 127 
 
 7408.9 
 
 140 
 
 439.82 
 
 15393.80 
 
 1/4 
 
 280.387 
 
 6256.1 
 
 1/4 
 
 305.520 
 
 7428.0 
 
 141 
 
 442.96 
 
 15614.50 
 
 3/8 
 
 280.780 
 
 6273.7 
 
 3/8 
 
 305.913 
 
 7447.1 
 
 142 
 
 446. 11 
 
 15836.77 
 
 Vz 
 
 281. 173 
 
 6291.2 
 
 1/2 
 
 306.305 
 
 7466.2 
 
 143 
 
 449.25 
 
 16060.61 
 
 5/8 
 
 281.565 
 
 6308.8 
 
 5/8 
 
 306.698 
 
 7485.3 
 
 144 
 
 452.39 
 
 16286.02 
 
 3/4 
 
 281.958 
 
 6326.4 
 
 3/4 
 
 307.091 
 
 7504.5 
 
 145 
 
 455.53 
 
 16513.00 
 
 7/8 
 
 282.351 
 
 6344.1 
 
 7/8 
 
 307.483 
 
 7523.7 
 
 146 
 
 458.67 
 
 16741.55 
 
 90. 
 
 282.743 
 
 6361.7 
 
 98. 
 
 307.876 
 
 7543.0 
 
 147 
 
 461.81 
 
 16971.67 
 
 Vs 
 
 283.136 
 
 6379.4 
 
 1/8 
 
 308.269 
 
 7562.2 
 
 148 
 
 464.96 
 
 17203.36 
 
 1/4 
 
 283.529 
 
 6397.1 
 
 1/4 
 
 308.661 
 
 7581.5 
 
 149 
 
 468.10 
 
 17436.62 
 
 3/8 
 
 283.921 
 
 64 1 4 . 9 
 
 3/8 
 
 309.054 
 
 7600.8 
 
 150 
 
 471.24 
 
 17671.46 
 
 1/2 
 
 284.314 
 
 6432.6 
 
 1/2 
 
 309.447 
 
 7620. 1 
 
 151 
 
 474.38 
 
 17907.86 
 
 5/8 
 
 284.707 
 
 6450.4 
 
 5/8 
 
 309.840 
 
 7639.5 
 
 152 
 
 477.52 
 
 18145.84 
 
 3/4 
 
 285.100 
 
 6468.2 
 
 3/4 
 
 310.232 
 
 7658.9 
 
 153 
 
 480.66 
 
 18385.39 
 
 7 /8 
 
 285.492 
 
 6486.0 
 
 7/8 
 
 310.625 
 
 7678.3 
 
 154 
 
 483.81 
 
 18626.50 
 
 91. 
 
 285.885 
 
 6503.9 
 
 99. 
 
 311.018 
 
 7697.7 
 
 155 
 
 486.95 
 
 18869.19 
 
 Vs 
 
 286.278 
 
 6521.8 
 
 1/8 
 
 311.410 
 
 7717.1 
 
 156 
 
 490 . 09 
 
 19113.45 
 
 1/4 
 
 286.670 
 
 6539.7 
 
 1/4 
 
 311.803 
 
 7736.6 
 
 157 
 
 493.23 
 
 19359.28 
 
 3/8 
 
 287.063 
 
 6557.6 
 
 3/8 
 
 312. 196 
 
 7756.1 
 
 158 
 
 496.37 
 
 19606.68 
 
 V2 
 
 287.456 
 
 6575.5 
 
 1/2 
 
 312.588 
 
 7775.6 
 
 159 
 
 499.51 
 
 19855.65 
 
 5 /8 
 
 287.848 
 
 6593.5 
 
 5/8 
 
 312.981 
 
 7795.2 
 
 160 
 
 502.65 
 
 20106. 19 
 
 3/4 
 
 288.241 
 
 6611.5 
 
 3/4 
 
 313.374 
 
 7814.8 
 
 161 
 
 505 . 80 
 
 20358.31 
 
 7/8 
 
 288.634 
 
 6629.6 
 
 7/8 
 
 313.767 
 
 7834.4 
 
 162 
 
 508.94 
 
 20611.99 
 
 93. 
 
 289.027 
 
 6647.6 
 
 100 
 
 314". 159 
 
 7854.0 
 
 163 
 
 512.08 
 
 20867.24 
 
 Vs 
 
 289.419 
 
 6665 . 7 
 
 101 
 
 317.30 
 
 8011 .85 
 
 164 
 
 515.22 
 
 21124.07 
 
 V4 
 
 289.812 
 
 6683.8 
 
 102 
 
 320.44 
 
 8171.28 
 
 165 
 
 518.36 
 
 21382.46 
 
 3/8 
 
 290.205 
 
 6701.9 
 
 103 
 
 323.58 
 
 8332.29 
 
 166 
 
 521.50 
 
 21642.43 
 
 V2 
 
 290.597 
 
 6720. 1 
 
 104 
 
 326.73 
 
 8494.87 
 
 167 
 
 524.65 
 
 21903.97 
 
 5/8 
 
 290.990 
 
 6738.2 
 
 105 
 
 329.87 
 
 8659.01 
 
 168 
 
 527.79 
 
 22167.08 
 
 3/4 
 
 291.383 
 
 6756.4 
 
 106 
 
 333.01 
 
 8824.73 
 
 169 
 
 530.93 
 
 22431.76 
 
 7/8 
 
 291.775 
 
 6774.7 
 
 107 
 
 336.15 
 
 8992.02 
 
 170 
 
 534.07 
 
 22698.01 
 
 93. 
 
 292.168 
 
 6792.9 
 
 108 
 
 339.29 
 
 9160.88 
 
 171 
 
 537.21 
 
 22965 . 83 
 
 V8 
 
 292.561 
 
 6811.2 
 
 109 
 
 342.43 
 
 9331.32 
 
 172 
 
 540.35 
 
 23235.22 
 
 V4 
 
 292.954 
 
 6829.5 
 
 110 
 
 345.58 
 
 9503.32 
 
 173 
 
 543.50 
 
 23506.18 
 
 3/8 
 
 293.346 
 
 6847.8 
 
 111 
 
 348.72 
 
 9676.89 
 
 174 
 
 546.64 
 
 23778.71 
 
 1/2 
 
 293.739 
 
 6866.1 
 
 112 
 
 351.86 > 
 
 9852.03 
 
 175 
 
 549.78 
 
 24052.82 
 
 5/8 
 
 294. 132 
 
 6884.5 
 
 113 
 
 355.00 
 
 0028.75 
 
 176 
 
 552.92 
 
 24328.49 
 
 3/4 
 
 294.524 
 
 6902 . 9 
 
 114 
 
 358.14 
 
 0207.03 
 
 177 
 
 556.06 
 
 24605 . 74 
 
 7/8 
 
 294.917 
 
 6921.3 
 
 115 
 
 361.28 
 
 0386.89 
 
 178 
 
 559.20 
 
 24884.56 
 
 94. 
 
 295.310 
 
 6939.8 
 
 116 
 
 364.42 
 
 0568.32 
 
 179 
 
 562.35 
 
 25164.94 
 
 1/8 
 
 295 . 702 
 
 6958.2 
 
 117 
 
 367.57 
 
 0751.32 
 
 ISO 
 
 565 . 49 
 
 25446.90 
 
 1/4 
 
 296.095 
 
 6976.7 
 
 118 
 
 370.71 
 
 0935.88 
 
 181 
 
 568.63 
 
 25730.43 
 
 3/8 
 
 296.488 
 
 6995.3 
 
 119 
 
 373.85 
 
 1122.02 
 
 182 
 
 571.77 
 
 26015.53 
 
 1/2 
 
 296.881 
 
 701.3.8 
 
 120 
 
 376.99 
 
 1309.73 
 
 183 
 
 574.91 
 
 26302.20 
 
 5/8 
 
 297.273 
 
 7032.4 
 
 121 
 
 380.13 
 
 1499.01 
 
 184 
 
 578.05 
 
 26590.44 
 
 3/4 
 
 297.666 
 
 7051.0 
 
 122 
 
 383.27 
 
 1689.87 
 
 185 
 
 581.19 
 
 26880.25 
 
 7/8 
 
 298.059 
 
 7069.6 
 
 123 
 
 386.42 
 
 1882.29 
 
 186 
 
 584.34 
 
 27171.63 
 
 95. 
 
 298.451 
 
 7088.2 
 
 124 
 
 389.56 
 
 2076.28 
 
 187 
 
 587.48 
 
 27464.59 
 
 1/8 
 
 298.844 
 
 7106.9 
 
 125 
 
 392.70 
 
 2271.85 
 
 188 
 
 590.62 
 
 27759.11 
 
 1/4 
 
 299.237 
 
 7125.6 
 
 126 
 
 395.84 
 
 2468.98 
 
 189 
 
 593 . 76 
 
 28055.21 
 
 3/8 
 
 299.629 
 
 7144.3 
 
 127 
 
 398.98 
 
 2667.69 
 
 190 
 
 596.90 
 
 28352.87 
 
 1/2 
 
 300.022 
 
 7163.0 
 
 128 
 
 402. 12 
 
 2867.96 
 
 191 
 
 600.04 
 
 28652. 11 
 
 5/8 
 
 300.415 
 
 7181.8 
 
 129 
 
 405.27 
 
 3069.81 
 
 192 
 
 603.19 
 
 28952.92 
 
 3/4 
 
 n i 
 
 300.807 
 
 7200.6 
 
 
 
 
 
 
 
116 
 
 MATHEMATICAL TABLES. 
 
 Diam 
 
 Circum 
 
 Area. 
 
 Diam 
 
 Circum 
 
 Area. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 193 
 
 606.33 
 
 29255.30 
 
 260 
 
 816.81 
 
 53092.92 
 
 327 
 
 1027.30 
 
 83961.84 
 
 194 
 
 609.47 
 
 29559.25 
 
 261 
 
 819.96 
 
 53502.11 
 
 328 
 
 1030.44 
 
 84496.28 
 
 195 
 
 612.61 
 
 29864.77 
 
 262 
 
 823.10 
 
 53912.87 
 
 329 
 
 1033.58 
 
 85012.28 
 
 196 
 
 615.75 
 
 30171.86 
 
 263 
 
 826.24 
 
 54325. 21 
 
 330 
 
 1036.73 
 
 85529.86 
 
 197 
 
 618.89 
 
 30480.52 
 
 264 
 
 829.38 
 
 54739.11 
 
 331 
 
 1039.87 
 
 86049.01 
 
 193 
 
 622.04 
 
 30790.75 
 
 265 
 
 832.52 
 
 55154.59 
 
 332 
 
 1043.01 
 
 86569.73 
 
 199 
 
 625. 18 
 
 31102.55 
 
 266 
 
 835.66 
 
 55571.63 
 
 333 
 
 1046. 15 
 
 87092.02 
 
 200 
 
 628.32 
 
 31415.93 
 
 267 
 
 838.81 
 
 55990.25 
 
 334 
 
 1049.29 
 
 87615.88 
 
 201 
 
 631.46 
 
 31730.87 
 
 268 
 
 841.95 
 
 56410.44 
 
 335 
 
 1052.43 
 
 88141.31 
 
 202 
 
 634.60 
 
 32047.39 
 
 269 
 
 845.09 
 
 56832.20 
 
 336 
 
 1055.58 
 
 88668.31 
 
 203 
 
 637.74 
 
 32365.47 
 
 270 
 
 848.23 
 
 57255.53 
 
 337 
 
 1058.72 
 
 89196.88 
 
 204 
 
 640.88 
 
 32685. 13 
 
 271 
 
 851.37 
 
 57680.43 
 
 338 
 
 1061 .86 
 
 89727.03 
 
 205 
 
 644.03 
 
 33006.36 
 
 272 
 
 854.51 
 
 58106.90 
 
 339 
 
 1065.00 
 
 90258.74 
 
 206 
 
 647. 17 
 
 33329. 16 
 
 273 
 
 857.65 
 
 58534.94 
 
 340 
 
 1068. 14 
 
 90792.03 
 
 207 
 
 650.31 
 
 33653.53 
 
 274 
 
 860.80 
 
 58964.55 
 
 341 
 
 1071.28 
 
 91326.88 
 
 203 
 
 653.45 
 
 33979.47 
 
 275 
 
 863 . 94 
 
 59395.74 
 
 342 
 
 1074.42 
 
 91863.31 
 
 209 
 
 656.59 
 
 34306.98 
 
 276 
 
 867.08 
 
 59828.49 
 
 343 
 
 1077.57 
 
 92401.31 
 
 210 
 
 659.73 
 
 34636.06 
 
 277 
 
 870.22 
 
 60262.82 
 
 344 
 
 1080.71 
 
 92940.88 
 
 211 
 
 662.88 
 
 34966.71 
 
 278 
 
 873.36 
 
 60698.71 
 
 345 
 
 1083.85 
 
 93482.02 
 
 212 
 
 666.02 
 
 35298.94 
 
 279 
 
 876.50 
 
 61136. 18 
 
 346 
 
 1086.99 
 
 94024.73 
 
 213 
 
 669. 16 
 
 35632.73 
 
 280 
 
 879.65 
 
 61575.22 
 
 347 
 
 1090. 13 
 
 94569.01 
 
 214 
 
 672.30 
 
 35968.09 
 
 281 
 
 882.79 
 
 62015.82 
 
 348 
 
 1093.27 
 
 95114.86 
 
 215 
 
 675.44 
 
 36305.03 
 
 282 
 
 885.93 
 
 62458.00 
 
 349 
 
 1096.42 
 
 95662.28 
 
 216 
 
 678.58 
 
 36643.54 
 
 283 
 
 889.07 
 
 62901.75 
 
 350 
 
 1099.56 
 
 96211.28 
 
 217 
 
 681.73 
 
 36983.61 
 
 284 
 
 892.21 
 
 63347.07 
 
 351 
 
 1102.70 
 
 96761.84 
 
 218 
 
 684.87 
 
 37325.26 
 
 285 
 
 895.35 
 
 63793.97 
 
 352 
 
 1105.84 
 
 97313.97 
 
 219 
 
 688.01 
 
 37668.48 
 
 286 
 
 898.50 
 
 64242.43 
 
 353 
 
 1108.98 
 
 97867.68 
 
 230 
 
 691. 15 
 
 38013.27 
 
 287 
 
 901.64 
 
 64692.46 
 
 354 
 
 1112. 12 
 
 98422.96 
 
 221 
 
 694.29 
 
 38359.63 
 
 288 
 
 904.78 
 
 65144.07 
 
 355 
 
 1115.27 
 
 98979.80 
 
 222 
 
 697.43 
 
 38707.56 
 
 289 
 
 907.92 
 
 65597.24 
 
 356 
 
 1118.41 
 
 99538.22 
 
 223 
 
 700.58 
 
 39057.07 
 
 290 
 
 911.06 
 
 66051.99 
 
 357 
 
 1121.55 
 
 100098.21 
 
 224 
 
 703.72 
 
 39408. 14 
 
 291 
 
 914.20 
 
 66508.30 
 
 358 
 
 1124.69 
 
 100659.77 
 
 225 
 
 706.86 
 
 39760.78 
 
 292 
 
 917.35 
 
 66966. 19 
 
 359 
 
 1127.83 
 
 101222.90 
 
 226 
 
 710.00 
 
 401 15.00 
 
 293 
 
 920.49 
 
 67425.65 
 
 360 
 
 1130.97 
 
 101787.60 
 
 227 
 
 713. 14 
 
 40470.78 
 
 294 
 
 923.63 
 
 67886.68 
 
 361 
 
 1134.11 
 
 102353.87 
 
 228 
 
 716.28 
 
 40828. 14 
 
 295 
 
 926.77 
 
 68349.28 
 
 362 
 
 1137.26 
 
 102921.72 
 
 229 
 
 719.42 
 
 41187.07 
 
 296 
 
 929.91 
 
 68813.45 
 
 363 
 
 1140.40 
 
 103491. 13 
 
 230 
 
 722.57 
 
 41547.56 
 
 297 
 
 933.05 
 
 69279. 19 
 
 364 
 
 1143.54 
 
 1 04062 . 1 2 
 
 231 
 
 725.71 
 
 41909.63 
 
 298 
 
 936. 19 
 
 69746.50 
 
 365 
 
 1146.68 
 
 104634.67 
 
 232 
 
 728.85 
 
 42273.27 
 
 299 
 
 939.34 
 
 70215.38 
 
 366 
 
 1149.82 
 
 105208.80 
 
 233 
 
 73 1 . 99 
 
 42638.48 
 
 300 
 
 942.48 
 
 70685.83 
 
 367 
 
 1152.96 
 
 105784.49 
 
 234 
 
 735.13 
 
 43005.26 
 
 301 
 
 945.62 
 
 71157.86 
 
 368 
 
 1156.11 
 
 106361.76 
 
 235 
 
 738.27 
 
 43373.61 
 
 302 
 
 948.76 
 
 71631.45 
 
 369 
 
 1159.25 
 
 106940.60 
 
 236 
 
 741.42 
 
 43743.54 
 
 303 
 
 951.90 
 
 72106.62 
 
 370 
 
 1162.39 
 
 107521.01 
 
 237 
 
 744.56 
 
 44115.03 
 
 304 
 
 955.04 
 
 72583.36 
 
 371 
 
 1165.53 
 
 108102.99 
 
 238 
 
 747.70 
 
 44488.09 
 
 305 
 
 958. 19 
 
 73061.66 
 
 372 
 
 1 168.67 
 
 108686.54 
 
 239 
 
 750.84 
 
 44862.73 
 
 306 
 
 961.33 
 
 73541 .54 
 
 373 
 
 1171.81 
 
 109271.66 
 
 240 
 
 753.98 
 
 45238.93 
 
 307 
 
 964.47 
 
 74022.99 
 
 374 
 
 1174.96 
 
 109858.35 
 
 241 
 
 757. 12 
 
 45616.71 
 
 308 
 
 967.61 
 
 74506.01 
 
 375 
 
 1178.10 
 
 1 10446.62 
 
 242 
 
 760.27 
 
 45996.06 
 
 309 
 
 970.75 
 
 74990.60 
 
 376 
 
 1181.24 
 
 111036.45 
 
 243 
 
 763.41 
 
 46376.98 
 
 310 
 
 973.89 
 
 75476.76 
 
 377 
 
 1184.33 
 
 1 1 1627.86 
 
 244 
 
 766.55 
 
 46759.47 
 
 311 
 
 977.04 
 
 75964.50 
 
 378 
 
 1187.52 
 
 112220.83 
 
 245 
 
 769.69 
 
 47143.52 
 
 312 
 
 980. 18 
 
 76453.80 
 
 379 
 
 1190.66 
 
 112815.38 
 
 246 
 
 772. S3 
 
 47529. 16 
 
 313 
 
 983.32 
 
 76944.67 
 
 380 
 
 1193.81 
 
 113411.49 
 
 247 
 
 775.97 
 
 47916.36 
 
 314 
 
 986.46 
 
 77437.12 
 
 381 
 
 1196.95 
 
 114009.18 
 
 248 
 
 779. 11 
 
 48305.13 
 
 315 
 
 989.60 
 
 77931. 13 
 
 382 
 
 1200.09 
 
 1 14608.44 
 
 249 
 
 782.26 
 
 48695.47 
 
 316 
 
 992 . 74 
 
 78426.72 
 
 383 
 
 1203.23 
 
 115209.27 
 
 250 
 
 785.40 
 
 49087.39 
 
 317 
 
 995.88 
 
 78923.88 
 
 384 
 
 1206.37 
 
 115811;67 
 
 251 
 
 788.54 
 
 49480.87 
 
 318 
 
 999.03 
 
 79422.60 
 
 385 
 
 1209.51 
 
 116415.64 
 
 252 
 
 791.68 
 
 49875.92 
 
 319 
 
 1002.17 
 
 79922 . 90 
 
 386 
 
 1212.65 
 
 117021.18 
 
 253 
 
 794.82 
 
 50272.55 
 
 320 
 
 1005.31 
 
 80424.77 
 
 387 
 
 1215.80 
 
 117628.30 
 
 254 
 
 797.96 
 
 50670.75 
 
 321 
 
 1008.45 
 
 80928.21 
 
 388 
 
 1218.94 
 
 18236.98 
 
 255 
 
 801. 11 
 
 51070.52 
 
 322 
 
 1011.59 
 
 81433.22 
 
 389 
 
 1222.08 
 
 18847.24 
 
 256 
 
 804.25 
 
 51471.85 
 
 323 
 
 1014.73 
 
 81939.80 
 
 390 
 
 1225.22 
 
 19459.06 
 
 257 
 
 807.39 
 
 51874.76 
 
 324 
 
 1017.88 
 
 82447.96 
 
 391 
 
 1228.36 
 
 20072.46 
 
 258 
 
 810.53 
 
 52279.24 
 
 325 
 
 1021.02 
 
 82957.68 
 
 392 
 
 1231.50 
 
 20687.46 
 
 259 
 
 813.67 
 
 52685 . 29 
 
 326 
 
 1024. 16 
 
 83468.98 
 
 393 
 
 1234.65 
 
 21303.96 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 
 
 117 
 
 Diam 
 
 Circum 
 
 Area. 
 
 Diam 
 
 Circum 
 
 Area. 
 
 Diam 
 
 Circum 
 
 Area. 
 
 "394" 
 
 1237.79 
 
 121922.07 
 
 461 
 
 1448.27 
 
 166913.60 
 
 528 
 
 1658.76 
 
 218956.44 
 
 395 
 
 1240.93 
 
 122541.75 
 
 462 
 
 1451.42 
 
 167638.53 
 
 529 
 
 1661.90 
 
 219786.61 
 
 396 
 
 1244.07 
 
 123163.00 
 
 463 
 
 1454.56 
 
 168365.02 
 
 530 
 
 1665.04 
 
 220618.34 
 
 397 
 
 1247.21 
 
 123785.82 
 
 464 
 
 1457.70 
 
 1 69093 . 08 
 
 531 
 
 1668. 19 
 
 221451.65 
 
 398 
 
 1250.35 
 
 124410.21 
 
 465 
 
 1460.84 
 
 169822.72 
 
 532 
 
 1671.33 
 
 222286.53 
 
 399 
 
 1253.50 
 
 125036. 17 
 
 466 
 
 1463.98 
 
 170553.92 
 
 533 
 
 1674.47 
 
 223122.98 
 
 400 
 
 1256.64 
 
 125663.71 
 
 467 
 
 1467. 12 
 
 171286.70 
 
 534 
 
 1677.61 
 
 223961.00 
 
 401 
 
 1259.78 
 
 126292.81 
 
 468 
 
 1470.27 
 
 172021.05 
 
 535 
 
 1680.75 
 
 224800.59 
 
 402 
 
 1262.92 
 
 126923.48 
 
 469 
 
 1473.41 
 
 172756.97 
 
 536 
 
 1683.89 
 
 225641.75 
 
 403 
 
 1266.06 
 
 127555.73 
 
 470 
 
 1476.55 
 
 173494.45 
 
 537 
 
 1687.04 
 
 226484.48 
 
 404 
 
 1269.20 
 
 128189.55 
 
 471 
 
 1479.69 
 
 174233.51 
 
 538 
 
 1690.18 
 
 227328.79 
 
 405 
 
 1272.35 
 
 128824.93 
 
 472 
 
 1482.83 
 
 174974. 14 
 
 539 
 
 1693.32 
 
 228174.66 
 
 406 
 
 1275.49 
 
 129461 .89 
 
 473 
 
 1485.97 
 
 175716.35 
 
 540 
 
 1696.46 
 
 229022. 10 
 
 407 
 
 1278.63 
 
 130100.42 
 
 474 
 
 1489.11 
 
 176460.12 
 
 541 
 
 1699.60 
 
 229871.12 
 
 408 
 
 1281.77 
 
 130740.52 
 
 475 
 
 1492.26 
 
 177205.46 
 
 542 
 
 1702.74 
 
 230721.71 
 
 409 
 
 1284.91 
 
 131382. 19 
 
 476 
 
 1495.40 
 
 177952.37 
 
 543 
 
 1705.88 
 
 231573.86 
 
 410 
 
 1288.05 
 
 132025.43 
 
 477 
 
 1498.54 
 
 178700.86 
 
 544 
 
 1709.03 
 
 232427.59 
 
 411 
 
 1291. 19 
 
 132670.24 
 
 478 
 
 1501.68 
 
 179450.91 
 
 545 
 
 1712.17 
 
 233282.89 
 
 412 
 
 1294.34 
 
 133316.63 
 
 479 
 
 1504.82 
 
 180202.54 
 
 546 
 
 1715.31 
 
 234139.76 
 
 413 
 
 1297.48 
 
 133964.58 
 
 480 
 
 1507.96 
 
 180955.74 
 
 547 
 
 1718.45 
 
 234998.20 
 
 414 
 
 1300.62 
 
 134614.10 
 
 481 
 
 1511.11 
 
 181710.50 
 
 548 
 
 1721.59 
 
 235858.21 
 
 415 
 
 1303.76 
 
 135265.20 
 
 482 
 
 1514.25 
 
 182466.84 
 
 549 
 
 1724.73 
 
 236719.79 
 
 416 
 
 1306.90 
 
 135917.86 
 
 483 
 
 1517.39 
 
 183224.75 
 
 550 
 
 1727.88 
 
 237582.94 
 
 417 
 
 1310.04 
 
 136572.10 
 
 484 
 
 1520.53 
 
 183984.23 
 
 551 
 
 1 73 1 . 02 
 
 238447.67 
 
 418 
 
 1313.19 
 
 137227.91 
 
 485 
 
 1523.67 
 
 184745.28 
 
 552 
 
 1734.16 
 
 239S13.96 
 
 419 
 
 1316.33 
 
 137885.29 
 
 486 
 
 1526.81 
 
 185507.90 
 
 553 
 
 1737.30 
 
 240181.83 
 
 420 
 
 1319.47 
 
 138544.24 
 
 487 
 
 1529.96 
 
 186272.10 
 
 554 
 
 1740.44 
 
 241051.26 
 
 421 
 
 1322.61 
 
 139204.76 
 
 488 
 
 1533.10 
 
 187037.86 
 
 555 
 
 1743.58 
 
 241922.27 
 
 421 
 
 1325.75 
 
 139866.85 
 
 489 
 
 1536.24 
 
 187805.19 
 
 556 
 
 1746.73 
 
 242794.85 
 
 423 
 
 1328.89 
 
 140530.51 
 
 49O 
 
 1539.38 
 
 188574.10 
 
 557 
 
 1749.87 
 
 243668.99 
 
 424 
 
 1332.04 
 
 141195.74 
 
 491 
 
 1542.52 
 
 169344.5. 
 
 558 
 
 1753.01 
 
 244544.71 
 
 425 
 
 1335. 18 
 
 141862.54 
 
 492 
 
 1545.66 
 
 1901 16.62 
 
 559 
 
 1756.15 
 
 245422.00 
 
 426 
 
 1338.32 
 
 142530.92 
 
 493 
 
 1548.81 
 
 190890.2 
 
 560 
 
 1759.29 
 
 246300.86 
 
 427 
 
 1341.46 
 
 143200.86 
 
 494 
 
 1551.95 
 
 191665.43 
 
 561 
 
 1 762 . 43 
 
 247181.30 
 
 428 
 
 1344.60 
 
 143872.38 
 
 495 
 
 1555.09 
 
 192442. 18 
 
 562 
 
 1765.58 
 
 248063.30 
 
 429 
 
 1347.74 
 
 1 44545. 46 
 
 496 
 
 1558.23 
 
 193220.51 
 
 563 
 
 1768.72 
 
 248946.87 
 
 430 
 
 1350.88 
 
 145220. 12 
 
 497 
 
 1561.37 
 
 194000.41 
 
 564 
 
 1771 .86 
 
 249832.01 
 
 431 
 
 1354.03 
 
 145896.35 
 
 498 
 
 1564.51 
 
 194781.89 
 
 565 
 
 1775.00 
 
 250718.73 
 
 432 
 
 1357.17 
 
 146574.15 
 
 499 
 
 1567.65 
 
 195564.93 
 
 566 
 
 1778.14 
 
 251607.01 
 
 433 
 
 1360.31 
 
 147253.52 
 
 500 
 
 1570.80 
 
 196349.54 
 
 567 
 
 1781.28 
 
 252496.87 
 
 434 
 
 1363.45 
 
 147934.46 
 
 501 
 
 1573.94 
 
 197135.72 
 
 568 
 
 1784.42 
 
 253388.30 
 
 435 
 
 1366.59 
 
 148616.97 
 
 502 
 
 1577.03 
 
 197923.48 
 
 569 
 
 1787.57 
 
 254281.29 
 
 436 
 
 1369.73 
 
 149301.05 
 
 503 
 
 1580.22 
 
 198712.80 
 
 570 
 
 1790.71 
 
 255175.86 
 
 437 
 
 1372 88 
 
 149986.70 
 
 504 
 
 1583.36 
 
 199503.70 
 
 571 
 
 1793.85 
 
 256072.00 
 
 438 
 
 1376.02 
 
 150673.93 
 
 505 
 
 1586.50 
 
 200296.17 
 
 572 
 
 1796.99 
 
 256969.71 
 
 439 
 
 1379. 16 
 
 151362.72 
 
 506 
 
 1589.65 
 
 201090.20 
 
 573 
 
 1800. 13 
 
 257868.99 
 
 440 
 
 1382.30 
 
 152053.08 
 
 507 
 
 1592.79 
 
 201885.81 
 
 574 
 
 1803.27 
 
 258769.85 
 
 441 
 
 1385.44 
 
 152745.02 
 
 508 
 
 1595.93 
 
 202682.99 
 
 575 
 
 1806.42 
 
 259672.27 
 
 442 
 
 1388.58 
 
 153438.53 
 
 509 
 
 1599.07 
 
 203481.74 
 
 576 
 
 1809.56 
 
 260576.26 
 
 443 
 
 1391.73 
 
 154133.60 
 
 510 
 
 1602.21 
 
 204282.06 
 
 577 
 
 1812.70 
 
 261481.83 
 
 444 
 
 1394.87 
 
 154830.25 
 
 511 
 
 1605.35 
 
 205083.95 
 
 578 
 
 1815.84 
 
 262388.96 
 
 445 
 
 1398.01 
 
 155528.47 
 
 512 
 
 1608.50 
 
 205887.42 
 
 579 
 
 1818.93 
 
 263297.67 
 
 446 
 
 1401. 15 
 
 156228.26 
 
 513 
 
 1611.64 
 
 206692.45 
 
 580 
 
 1822.12 
 
 264207.94 
 
 447 
 
 1404.29 
 
 156929.62 
 
 514 
 
 1614.78 
 
 207499.05 
 
 581 
 
 1825.27 
 
 265119.79 
 
 448 
 
 1407.43 
 
 157632.55 
 
 515 
 
 1617.92 
 
 208307.23 
 
 582 
 
 1828.41 
 
 266033.21 
 
 449 
 
 1410.58 
 
 158337.06 
 
 516 
 
 1 62 1 . 06 
 
 209116.97 
 
 583 
 
 1831.55 
 
 266948.20 
 
 450 
 
 1413.72 
 
 159043.13 
 
 517 
 
 1624.20 
 
 209928.29 
 
 584 
 
 1834.69 
 
 267864.76 
 
 451 
 
 1 4 1 6 . 86 
 
 159750.77 
 
 518 
 
 1627.34 
 
 210741.18 
 
 585 
 
 1837.83 
 
 268782.89 
 
 452 
 
 1420.00 
 
 160459.99 
 
 519 
 
 1630.49 
 
 211555.63 
 
 586 
 
 1840.97 
 
 269702.59 
 
 453 
 
 1423.14 
 
 161170.77 
 
 520 
 
 1633.63 
 
 212371.66 
 
 587 
 
 1844.11 
 
 270623.86 
 
 454 
 
 1426.28 
 
 161883. 13 
 
 521 
 
 1636.77 
 
 213189.26 
 
 588 
 
 1847.26 
 
 271546.70 
 
 455 
 
 1429.42 
 
 162597.05 
 
 522 
 
 1639.91 
 
 214008.43 
 
 589 
 
 1850.40 
 
 272471. 12 
 
 456 
 
 1432.57 
 
 163312.55 
 
 523 
 
 1643.05 
 
 214829. 17 
 
 59O 
 
 1853.54 
 
 273397.10 
 
 457 
 
 1435.71 
 
 164029.62 
 
 524 
 
 1646. 19 
 
 215651.49 
 
 591 
 
 1856.68 
 
 274324.66 
 
 458 
 
 1438 85 
 
 164748 26 
 
 525 
 
 1649.34 
 
 216475.37 
 
 592 
 
 1859.82 
 
 275253.78 
 
 459 
 460 
 
 1441.99 
 1445.13 
 
 165468.47 
 166190.25 
 
 526 
 527 
 
 1652.48 
 1655.62 
 
 217300.82 
 218127.85 
 
 593 
 594 
 
 1862.96 276184.48 
 1866.1l'277l16.75 
 
118 
 
 MATHEMATICAL TABLES. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 Circum, 
 
 Area. 
 
 Diam 
 
 Circum 
 
 Area. 
 
 595 
 
 1869.25 
 
 278050.58 
 
 663 
 
 2082.88 
 
 345236.69 
 
 731 
 
 2296.50 
 
 419686. 13 
 
 596 
 
 1872.39 
 
 278985.99 
 
 664 
 
 2086.02 
 
 346278.91 
 
 732 
 
 2299.65 
 
 420835 19 
 
 597 
 
 1875.53 
 
 279922.97 
 
 665 
 
 2089.16 
 
 347322.70 
 
 733 
 
 2302.79 
 
 421985* 79 
 
 598 
 
 1878.67 
 
 280861.52 
 
 666 
 
 2092.30 
 
 348368.07 
 
 734 
 
 2305.93 
 
 423137.97 
 
 599 
 
 1881.81 
 
 281801.65 
 
 667 
 
 2095.44 
 
 349415.00 
 
 735 
 
 2309.07 
 
 424291.72 
 
 600 
 
 1884.96 
 
 282743.34 
 
 668 
 
 2098.58 
 
 350463.51 
 
 736 
 
 2312.2 
 
 425447.04 
 
 601 
 
 1888. 10 
 
 283686.60 
 
 669 
 
 2101.73 
 
 351513.59 
 
 737 
 
 2315.35 
 
 426603 . 94 
 
 602 
 
 1891.24 
 
 284631.44 
 
 670 
 
 2104.87 
 
 352565.24 
 
 738 
 
 2318.50 
 
 427762.40 
 
 603 
 
 1894.38 
 
 285577.84 
 
 671 
 
 2108.01 
 
 353618.45 
 
 739 
 
 2321.64 
 
 428922.43 
 
 604 
 
 1897.52 
 
 286525.82 
 
 672 
 
 2111.15 
 
 354673.24 
 
 740 
 
 2324.78 
 
 430084.03 
 
 605 
 
 1900.66 
 
 287475.36 
 
 673 
 
 2114.29 
 
 355729.60 
 
 741 
 
 2327.92 
 
 431247.21 
 
 606 
 
 1903.81 
 
 288426.48 
 
 674 
 
 2117.43 
 
 356787.54 
 
 742 
 
 233 1 . 06 
 
 432411.95 
 
 607 
 
 1906.95 
 
 289379.17 
 
 675 
 
 2120.58 
 
 357847.04 
 
 743 
 
 2334.20 
 
 433578.27 
 
 608 
 
 1910.09 
 
 290333.43 
 
 676 
 
 2123.72 
 
 358908.11 
 
 744 
 
 2337.34 
 
 434746. \6 
 
 609 
 
 1913.23 
 
 291289.26 
 
 677 
 
 2126.86 
 
 359970.75 
 
 745 
 
 2340.49 
 
 435915.62 
 
 610 
 
 1916.37 
 
 292246.66 
 
 678 
 
 2130.00 
 
 361034.97 
 
 746 
 
 2343.63 
 
 437086.64 
 
 611 
 
 1919.51 
 
 293205.63 
 
 679 
 
 2133.14 
 
 362100.75 
 
 747 
 
 2346.77 
 
 438259.24 
 
 612 
 
 1922.65 
 
 294166.17 
 
 680 
 
 2136.28 
 
 363168.11 
 
 748 
 
 2349.91 
 
 439433.41 
 
 613 
 
 1925.80 
 
 295128.28 
 
 681 
 
 2139.42 
 
 364237.04 
 
 749 
 
 2353.05 
 
 440609.16 
 
 614 
 
 1928.94 
 
 296091.97 
 
 682 
 
 2142.57 
 
 365307.54 
 
 750 
 
 2356.19 
 
 441786.47 
 
 615 
 
 1932.08 
 
 297057.22 
 
 683 
 
 2145.71 
 
 366379.60 
 
 751 
 
 2359.34 
 
 442965.35 
 
 616 
 
 1935.22 
 
 298024.05 
 
 684 
 
 2148.85 
 
 367453.24 
 
 752 
 
 2362.48 
 
 444145.80 
 
 617 
 
 1938.36 
 
 298992.44 
 
 685 
 
 2151.99 
 
 368528.45 
 
 753 
 
 2365.62 
 
 445327.83 
 
 618 
 
 1941.50 
 
 299962.41 
 
 686 
 
 2155.13 
 
 369605.23 
 
 754 
 
 2368.76 
 
 446511.42 
 
 619 
 
 1944.65 
 
 300933.95 
 
 687 
 
 2158.27 
 
 370683.59 
 
 755 
 
 2371.90 
 
 447696.59 
 
 620 
 
 1947.79 
 
 301907.05 
 
 688 
 
 2161.42 
 
 371763.51 
 
 756 
 
 2375.04 
 
 448883.32 
 
 621 
 
 1950.93 
 
 302881.73 
 
 689 
 
 2164.56 
 
 372845.00 
 
 757 
 
 2378.19 
 
 450071.63 
 
 622 
 
 1954.07 
 
 303857.98 
 
 690 
 
 2167.70 
 
 373928.07 
 
 758 
 
 2381.33 
 
 451261.51 
 
 623 
 
 1957.21 
 
 304835.80 
 
 691 
 
 2170.84 
 
 375012.70 
 
 759 
 
 2384.47 
 
 452452.96 
 
 624 
 
 1960.35 
 
 305815.20 
 
 692 
 
 2173.98 
 
 376098.91 
 
 760 
 
 2387.61 
 
 453645.98 
 
 625 
 
 1963.50 
 
 306796.16 
 
 693 
 
 2177.12 
 
 377186.68 
 
 761 
 
 2390.75 
 
 454840.57 
 
 626 
 
 1966.64 
 
 307778.69 
 
 694 
 
 2180.27 
 
 378276.03 
 
 762 
 
 2393.89 
 
 456036.73 
 
 627 
 
 1969.78 
 
 308762.79 
 
 695 
 
 2183.41 
 
 379366.95 
 
 763 
 
 2397.04 
 
 457234.46 
 
 628 
 
 1972.92 
 
 309748.47 
 
 696 
 
 2186.55 
 
 380459.44 
 
 764 
 
 2400.18 
 
 458433.77 
 
 629 
 
 1976.06 
 
 310735.71 
 
 697 
 
 2189.69 
 
 381553.50 
 
 765 
 
 2403.32 
 
 459634.64 
 
 630 
 
 1979.20 
 
 311724.53 
 
 698 
 
 2192.83 
 
 382649.13 
 
 766 
 
 2406.46 
 
 460837.08 
 
 631 
 
 1982.35 
 
 312714.92 
 
 699 
 
 2195.97 
 
 383746.33 
 
 767 
 
 2409.60 
 
 462041.10 
 
 632 
 
 1985.49 
 
 313706.88 
 
 700 
 
 2199.11 
 
 384845.10 
 
 768 
 
 2412.74 
 
 463246.69 
 
 633 
 
 1988.63 
 
 314700.40 
 
 701 
 
 2202.26 
 
 385945.44 
 
 769 
 
 2415.88 
 
 464453.84 
 
 634 
 
 1991.77 
 
 315695.50 
 
 702 
 
 2205.40 
 
 387047.36 
 
 770 
 
 2419.03 
 
 465662.57 
 
 635 
 
 1994.91 
 
 316692.17 
 
 703 
 
 2208.54 
 
 388150.84 
 
 771 
 
 2422.17 
 
 466872.87 
 
 636 
 
 1998.05 
 
 317690.42 
 
 704 
 
 2211.68 
 
 389255.90 
 
 772 
 
 2425.31 
 
 468084.74 
 
 637 
 
 2001. 19 
 
 318690.23 
 
 705 
 
 2214.82 
 
 390362.52 
 
 773 
 
 2428.45 
 
 469298. 18 
 
 638 
 
 2004.34 
 
 319691.61 
 
 706 
 
 2217.96 
 
 391470.72 
 
 774 
 
 2431.59 
 
 470513.19 
 
 639 
 
 2007.48 
 
 320694.56 
 
 707 
 
 2221.11 
 
 392580.49 
 
 775 
 
 2434.73 
 
 471729.77 
 
 640 
 
 2010.62 
 
 321699.09 
 
 708 
 
 2224.25 
 
 393691.82 
 
 776 
 
 2437.88 
 
 472947.92 
 
 641 
 
 2013.76 
 
 322705.18 
 
 709 
 
 2227.39 
 
 394804.73 
 
 777 
 
 2441.02 
 
 474167.65 
 
 642 
 
 2016.90 
 
 323712.85 
 
 710 
 
 2230.53 
 
 395919.21 
 
 778 
 
 2444.16 
 
 475388.94 
 
 643 
 
 2020.04 
 
 324722.09 
 
 711 
 
 2233.67 
 
 397035.26 
 
 779 
 
 2447.30 
 
 476611.81 
 
 644 
 
 2023. 19 
 
 325732.89 
 
 712 
 
 2236.81 
 
 398152.89 
 
 780 
 
 2450.44 
 
 477836.24 
 
 645 
 
 2026.33 
 
 326745.27 
 
 713 
 
 2239.96 
 
 399272.08 
 
 781 
 
 2453.58 
 
 479062.25 
 
 646 
 
 2029.47 
 
 327759.22 
 
 714 
 
 2243.10 
 
 400392.84 
 
 782 
 
 2456.73 
 
 480289.83 
 
 647 
 
 2032.61 
 
 328774.74 
 
 715 
 
 2246.24 
 
 401515.18 
 
 783 
 
 2459.87 
 
 481518.97 
 
 648 
 
 2035.75 
 
 329791.83 
 
 716 
 
 2249.38 
 
 402639.08 
 
 784 
 
 2463.01 
 
 482749.69 
 
 649 
 
 2038.89 
 
 330810.49 
 
 717 
 
 2252.52 
 
 403764.56 
 
 785 
 
 2466.15 
 
 483981.98 
 
 650 
 
 2042.04 
 
 331830.72 
 
 718 
 
 2255.66 
 
 404891.60 
 
 786 
 
 2469.29 
 
 485215.84 
 
 651 
 
 2045. 18 
 
 332852.53 
 
 719 
 
 2258.81 
 
 406020.22 
 
 787 
 
 2472.43 
 
 48645 1 . 28 
 
 652 
 
 2048.32 
 
 333875.90 
 
 720 
 
 2261.95 
 
 407150.41 
 
 788 
 
 2475.58 
 
 487688.28 
 
 653 
 
 2051.46 
 
 334900.85 
 
 721 
 
 2265 . 09 
 
 408282.17 
 
 789 
 
 2478.72 
 
 488926.85 
 
 654 
 
 2054.60 
 
 335927.36 
 
 722 
 
 2268.23 
 
 409415.50 
 
 790 
 
 2481.86 
 
 490166.99 
 
 655 
 
 2057.74 
 
 336955.45 
 
 723 
 
 2271.37 
 
 410550.40 
 
 791 
 
 2485.00 
 
 491408.71 
 
 656 
 
 2060.88 
 
 337985.10 
 
 724 
 
 2274.51 
 
 411686.87 
 
 792 
 
 2488.14 
 
 492651.99 
 
 657 
 
 2064.03 
 
 339016.33 
 
 725 
 
 2277.65 
 
 412824.91 
 
 793 
 
 2491.28 
 
 493896.85 
 
 . 658 
 
 2067.17 
 
 340049.13 
 
 726 
 
 2280.80 
 
 413964.52 
 
 794 
 
 2494.42 
 
 495143.28 
 
 659 
 
 2070.31 
 
 341083.50 
 
 727 
 
 2283.94 
 
 415105.71 
 
 795 
 
 2497.57 
 
 496391.27 
 
 660 
 
 2073.45 
 
 342119.44 
 
 728 
 
 2287.085416248.46 
 
 796 
 
 2500.71 
 
 497640.84 
 
 661 
 
 2076.59 
 
 343156.95 
 
 729 
 
 2290.22 
 
 417392.79 
 
 797 
 
 2503.85 
 
 498891.98 
 
 62 
 
 2079.73 344196.03 
 
 730 2293.36 
 
 418538.68 
 
 798 
 
 2506.99500144.69 
 
CIRCUMFERENCES AND AREAS OP CIRCLES. 119 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 Diam. I Circum. 
 
 Area. 
 
 Diam 
 
 Circum. 1 Area. 
 
 799 
 
 2510.13 
 
 501398.97 
 
 867 
 
 2723.76 
 
 590375.16 
 
 935 
 
 2937.39 
 
 686614.71 
 
 8OO 
 
 2513.27 
 
 502654.82 
 
 868 
 
 2726.90 
 
 591737.83 
 
 936 
 
 2940.53 
 
 688084. 19 
 
 801 
 
 2516.42 
 
 503912.25 
 
 869 
 
 2730.04 
 
 593102.06 
 
 937 
 
 2943.67 
 
 689555.24 
 
 802 
 
 2519.56 
 
 505171.24 
 
 870 
 
 2733.19 
 
 594467.87 
 
 938 
 
 2946.81 
 
 691027.86 
 
 803 
 
 2522.70 
 
 50643 1 . 80 
 
 871 
 
 2736.33 
 
 595835.25 
 
 939 
 
 2949.96 
 
 692502 05 
 
 804 
 
 2525.84 
 
 507693.94 
 
 872 
 
 2739.47 
 
 597204.20 
 
 940 
 
 2953.10 
 
 693977.82 
 
 805 
 
 2528.98 
 
 508957.64 
 
 873 
 
 2742.61 
 
 598574.72 
 
 941 
 
 2956.24 
 
 695455. 15 
 
 806 
 
 2532.12 
 
 510222.92 
 
 874 
 
 2745.75 
 
 599946.81 
 
 942 
 
 2959.38 
 
 696934.06 
 
 807 
 
 2535.27 
 
 511489.77 
 
 875 
 
 2748.89 
 
 601320.47 
 
 943 
 
 2962.52 
 
 698414.53 
 
 808 
 
 2538.41 
 
 512758.19 
 
 876 
 
 2752.04 
 
 602695.70 
 
 944 
 
 2965 . 66 
 
 699896.58 
 
 809 
 
 2541.55 
 
 514028.18 
 
 877 
 
 2755.18 
 
 604072.50 
 
 945 
 
 2968.81 
 
 701380.19 
 
 810 
 
 2544.69 
 
 515299.74 
 
 878 
 
 2758.321605450.88 
 
 946 
 
 2971.95 
 
 702865 38 
 
 811 
 
 2547.83 
 
 516572.87 
 
 879 
 
 2761.46 
 
 606830.82 
 
 947 
 
 2975.09 
 
 704352.14 
 
 812 
 
 2550.97 
 
 517847.57 
 
 88O 
 
 2764.60 
 
 608212.34 
 
 948 
 
 2978.23 
 
 705840 47 
 
 813 
 
 2554.11 
 
 519123.84 
 
 881 
 
 27 '67.7 'A 
 
 609595.42 
 
 949 
 
 2981.37 
 
 707330 37 
 
 814 
 
 2557.26 
 
 520401.68 
 
 882 
 
 2770.88 
 
 610980.08 
 
 05O 
 
 2984.51 
 
 708821.84 
 
 815 
 
 2560.40 
 
 521681.10 
 
 883 
 
 2774.03 
 
 612366.31 
 
 951 
 
 2987.65 
 
 7 1 03 1 4 . 88 
 
 816 
 
 2563.54 
 
 522962.08 
 
 884 
 
 2777. 17 
 
 613754.11 
 
 952 
 
 2990.80 
 
 711809.50 
 
 817 
 
 2566.68 
 
 524244.63 
 
 885 
 
 2780.31 
 
 615143.48 
 
 953 
 
 2993 . 94 
 
 713305.68 
 
 818 
 
 2569.82 
 
 525528.76 
 
 886 
 
 2783.45 
 
 616534.42 
 
 954 
 
 2997.08 
 
 714803.43 
 
 819 
 
 2572,96 
 
 526814.46 
 
 887 
 
 2786.59 
 
 617926.93 
 
 955 
 
 3000.22 
 
 716302.76 
 
 820 
 
 2576.11 
 
 528101.73 
 
 888 
 
 2789.73 
 
 619321.01 
 
 956 
 
 3003.36 
 
 717803.66 
 
 821 
 
 2579.25 
 
 529390.56 
 
 889 
 
 2792.88 
 
 620716.66 
 
 957 
 
 3006.50 
 
 719306.12 
 
 822 
 
 2582.39 
 
 530680.97 
 
 890 
 
 2796.02 
 
 622113.89 
 
 958 
 
 3009.65 
 
 720810.16 
 
 823 
 
 2585.53 
 
 531972.95 
 
 891 
 
 2799.16 
 
 623512.68 
 
 959 
 
 3012.79 
 
 722315.77 
 
 824 
 
 2588.67 
 
 533266.50 
 
 892 
 
 2802.30 
 
 624913.04 
 
 960 
 
 3015.93 
 
 723822.95 
 
 825 
 
 2591.81 
 
 534561.62 
 
 893 
 
 2805.44 
 
 626314.98 
 
 961 
 
 3019.07 
 
 725331.70 
 
 826 
 
 2594.96 
 
 535858.32 
 
 894 
 
 2808.58 
 
 627718.49 
 
 962 
 
 3022.21 
 
 726842.02 
 
 827 
 
 2598.10 
 
 537156.58 
 
 895 
 
 2811.73 
 
 629123.56 
 
 963 
 
 3025.35 
 
 728353.91 
 
 828 
 
 2601.24 
 
 538456.41 
 
 896 
 
 2814.87 
 
 630530.21 
 
 964 
 
 3028.50 
 
 729867.37 
 
 829 
 
 2604.38 
 
 539757.82 
 
 897 
 
 2818.01 
 
 631938.43 
 
 965 
 
 3031.64 
 
 731382.40 
 
 830 
 
 2607.52 
 
 541060.79 
 
 898 
 
 2821.15 
 
 633348.22 
 
 966 
 
 3034.78 
 
 732899.01 
 
 831 
 
 2610.66 
 
 542365.34 
 
 899 
 
 2824.29 
 
 634759.58 
 
 967 
 
 3037.92 
 
 734417.18 
 
 832 
 
 2613.81 
 
 543671.46 
 
 900 
 
 2827.43 
 
 636172.51 
 
 968 
 
 3041.06 
 
 735936.93 
 
 833 
 
 2616.95 
 
 544979.15 
 
 901 
 
 2830.58 
 
 637587.01 
 
 969 
 
 3044.20 
 
 737458.24 
 
 834 
 
 2620.09 
 
 546288.40 
 
 902 
 
 2833.72 
 
 639003.09 
 
 970 
 
 3047.34 
 
 738981.13 
 
 835 
 
 2623.23 
 
 547599.23 
 
 903 
 
 2836.86 
 
 640420.73 
 
 971 
 
 3050.49 
 
 740505.59 
 
 836 
 
 2626.37 
 
 548911.63 
 
 904 
 
 2840.00 
 
 641839.95 
 
 972 
 
 3053.63 
 
 74203 1 . 62 
 
 837 
 
 2629.51 
 
 550225.61 
 
 905 
 
 2843.14 
 
 643260.73 
 
 973 
 
 3056.77 
 
 743559.22 
 
 838 
 
 2632.65 
 
 551541.15 
 
 906 
 
 2846.28 
 
 644683 . 09 
 
 974 
 
 3059.91 
 
 745088.39 
 
 839 
 
 2635.80 
 
 552858.26 
 
 907 
 
 2849.42 
 
 646107.01 
 
 975 
 
 3063.05 
 
 746619. 13 
 
 840 
 
 2638.94 
 
 554176.94 
 
 908 
 
 2852.57 
 
 647532.51 
 
 976 
 
 3066.19 
 
 748151.44 
 
 841 
 
 2642.08 
 
 555497.20 
 
 909 
 
 2855.71 
 
 648959.58 
 
 977 
 
 3069.34 
 
 749685.32 
 
 842 
 
 2645.22 
 
 556819.02 
 
 910 
 
 2858.85 
 
 650388.22 
 
 978 
 
 3072.48 
 
 751220.78 
 
 843 
 
 2648.36 
 
 558142.42 
 
 911 
 
 2861.99 
 
 651818.43 
 
 979 
 
 3075.62 
 
 752757.80 
 
 844 
 
 2651.50 
 
 559467.39 
 
 912 
 
 2865.13 
 
 653250.21 
 
 98O 
 
 3078.76 
 
 754296.40 
 
 845 
 
 2654.65 
 
 560793.92 
 
 913 
 
 2868.27 
 
 654683.56 
 
 981 
 
 3081.90 
 
 755836.56 
 
 846 
 
 2657.79 
 
 562122.03 
 
 914 
 
 2871.42 
 
 656118.48 
 
 982 
 
 3085.04 
 
 757378.30 
 
 847 
 
 2660.93 
 
 563451.71 
 
 915 
 
 2874.56 
 
 657554.98 
 
 983 
 
 3088.19 
 
 758921.61 
 
 848 
 
 2664.07 
 
 564782.96 
 
 916 
 
 2877.70 
 
 658993 . 04 
 
 984 
 
 3091 .33 
 
 760466.48 
 
 849 
 
 2667.21 
 
 566115.78 
 
 917 
 
 2880.84 
 
 660432.68 
 
 985 
 
 3094.47 
 
 762012.93 
 
 850 
 
 2670.35 
 
 567450.17 
 
 918 
 
 2883.98 
 
 661873.88 
 
 986 
 
 3097.61 
 
 763560.95 
 
 851 
 
 2673.50 
 
 568786.14 
 
 919 
 
 2887.12 
 
 663316.66 
 
 987 
 
 3100.75 
 
 765110.54 
 
 852 
 
 2676.64 
 
 570123.67 
 
 92O 
 
 2890.27 
 
 664761.01 
 
 988 
 
 3103.89 
 
 766661.70 
 
 853 
 
 2679.78 
 
 571462.77 
 
 921 
 
 2893.41 
 
 666206.92 
 
 989 
 
 3107.04 
 
 768214.44 
 
 854 
 
 2682.92 
 
 572803.45 
 
 922 
 
 2896.55 
 
 667654.41 
 
 99O 
 
 3110.18 
 
 769768.74 
 
 855 
 
 2686.06 
 
 574145.69 
 
 923 
 
 2899.69 
 
 669103.47 
 
 991 
 
 3113.32 
 
 771324.61 
 
 856 
 
 2689.20 
 
 575489.51 
 
 924 
 
 2902.83 
 
 670554.10 
 
 992 
 
 3116.46 
 
 772882.06 
 
 857 
 
 2692.34 
 
 576834.90 
 
 925 
 
 2905.97 
 
 672006.30 
 
 993 
 
 3119.60 
 
 774441.07 
 
 858 
 
 2695.49 
 
 578181.85 
 
 926 
 
 2909.11 
 
 673460.08 
 
 994 
 
 3122.74 
 
 776001.66. 
 
 859 
 
 2698.63 
 
 579530.38 
 
 927 
 
 2912.26 
 
 674915.42 
 
 995 
 
 3125.88 
 
 777563.82 
 
 860 
 861 
 
 2701.77 
 2704.91 
 
 580880.48 
 582232.15 
 
 928 
 929 
 
 2915.40676372.33 
 2918.54 677830.82 
 
 996 
 997 
 
 3129.03 
 3132.17 
 
 779127.54 
 780692 84 
 
 862 
 
 2708.05 
 
 583585.39 
 
 930 
 
 2921.68:679290.87 
 
 998 
 
 3135.31 
 
 782259.7? 
 
 863 
 
 2711.19 
 
 584940.20 
 
 931 
 
 2924.82 680752.50 
 
 999 
 
 3138.45 
 
 783828 15 
 
 864 
 
 2714.34 
 
 586296.59 
 
 932 
 
 2927.96682215.69 
 
 1000 
 
 3141.59 
 
 785398.16 
 
 865 
 
 2717.48 
 
 587654.54 
 
 933 
 
 2931 . 11 683680.46 
 
 
 
 
 866 
 
 m 
 
 2720.62 
 
 589014.07 
 
 934 
 
 2934.25 685146.80 
 
 
 
 
120 CIRCUMFERENCE OF CIRCLES, FEET AND INCHED 
 
 ^OG < *J i N.OenNOOe^\NOONcNmoo^~moo ^ t>. o m r^ o m 
 
 CN CN N en 
 
 1- OOONooh-.NOm-'^-eneN OONOOooi^NOin-feneN o ON~OO r - , 
 
 rNNOenot^'3- ooineNC 
 
 V in t>.' a^ o CN 
 CNmoo ^oo ^4 
 
 rNOoeN-<rmi>.ONOOcNcnmt>.ONOc 
 
 - 
 
 ^B oo in CN ON vo co o r>. * oo in C 
 
 ^jesmoo <j-f>.O'<j-t>.oen\ooNeNNOONeNinoo -<roo j-h>.oenNooenNOONeN 
 p^ mmmi r>,r>, oo ONONQNONO 
 
 r ;oNONoooooooooooooooooooooor>.r>r s .r > ^r>.t>.r>r>r<t>r s .NONONONONONONONONO 
 
 ^*^3^*^w^^^*^or^^"^N^^f<\o^^^^^^^Ndf^ 
 
 ^> ^w--^r>.ocAvOoc 
 -p . CN CN CN en e 
 
 Ninoo-- -!rt>O'rr^OfAvDONCN\ooNC 
 m in o vo so i> t> t> oo oo oo oo ON ON ON 
 
 N ooNoooor>NO>n^tTncN ON 
 
 cnmcNCNCNCNCNCNCNCNCNCN 
 
 - 
 
 voooo c 
 
 o^Ni 
 
 OOOO 
 
 i>, -r oo i 
 
 ' 
 
 oNoot^NOin-^-mfN ooNoot>NOin-j-rncN' o 
 
 ONONONONONONONONONONONOOOOOOOOOOOOOOOOOOOOr. 
 
 NO m or*.-* oo m CN ON so en o t>. * oo >n CN ON NO en o 
 ' ' ' ' ' 
 
 en vn rN oo' o' o en n r>* oo' o o' en in NO oc i o en m NO oo' o en T' NO' oc i o 
 
 ocnr>iOfnNOONCNinoNCNmoo -*r>.o-^-t>.oenvOONCNvOONCNino 
 CN CN CN CN en en en -r if -^- m m m NO NO NO t>. i>. t> r>. oo oo oo ON ON ON o 
 
 < 
 
 ONONONONOu^u 
 O en o r^ ^ o 
 
 ' ' * 
 
 ' t f i ^cncnf 
 - oo in CN 
 
 * 
 
 R m CN ON NO en o r>, 'T oo in CN ON NO en o t>. -* oo m CN ON NO en o t>, 
 o CN en m t>' o' o' o* CN en m r>' oo o o' CN en m' t^.' oo* o' o' en in r>. oo' o o en m NO 
 
 o moo -<i 
 *- 
 
 JeNCNCNCNCNCN OOOOOOOOOOOONQNONC 
 
 ON* o* CN ^ m r>. ON o CN ^' m r> ON o* o CN *r >n t> ON o* o* CN en m t> oo* o o CN en 
 +J fr>t> '__ ~-~- cNCNrNjenenen^r^j--^-minmNONONONOt>t>r^oooooooNO^CNO 
 
 ooin<NONNOenor>.-r 
 ' enn-Noooo en 
 
 NCNmoo moo t-r>.ocnr>.oenNOONCNnON<Nnoo 3-^ ^r^o 
 CN CN CN en en en -<r ^n- >n in m in NO NO NO t>. t>. t>, oo oo oo ON ON ON o 
 
AREAS OF THE SEGMENTS OF A CIRCLE. 
 
 121 
 
 AREAS OF THE SEGMENTS OF A CIRCLE. 
 
 (Diameter=l; Rise or Height in parts of Diameter being given.) 
 
 RULE FOR USE OF THE TABLE. Divide the rise or height of the segment 
 by the diameter. Multiply the area in the table corresponding to the 
 quotient thus found by the square of the diameter. 
 
 // the segment exceeds a semicircle its area is area of circle area of seg- 
 ment whose rise is (diarn. of circle rise of given segment). 
 
 Given chord and rise, to find diameter. Diam. = (square of half chord -*- 
 rise) + rise. The half chord is a mean proportional between the two parts . 
 into which the chord divides the diameter which is perpendicular to it. 
 
 Rise 
 -f- 
 
 Diam. 
 
 Area. 
 
 Rise 
 ^ 
 Diam. 
 
 Area. 
 
 Rise 
 Diam. 
 
 Area. 
 
 Rise 
 Diam. 
 
 Area. 
 
 Rise 
 -i- 
 
 Diam. 
 
 Area. 
 
 .001 
 
 .00004 
 
 .054 
 
 01646 
 
 .107 
 
 .04514 
 
 .16 
 
 .08111 
 
 .213 
 
 .12235 
 
 .002 
 
 .00012 
 
 .055 
 
 .01691 
 
 .108 
 
 .04576 
 
 .161 
 
 .08185 
 
 .214 
 
 .12317 
 
 .003 
 
 .00022 
 
 .056 
 
 .01737 
 
 .109 
 
 .04638 
 
 .162 
 
 .08258 
 
 .215 
 
 .12399 
 
 .004 
 
 .00034 
 
 .057 
 
 .01783 
 
 .11 
 
 .04701 
 
 .163 
 
 .08332 
 
 .216 
 
 .12481 
 
 .005 
 
 .00047 
 
 .058 
 
 .01830 
 
 .111 
 
 .04763 
 
 .164 
 
 .08406 
 
 .217 
 
 .12563 
 
 .006 
 
 .00062 
 
 .059 
 
 .01877 
 
 .112 
 
 .04826 
 
 .165 
 
 .08480 
 
 .218 
 
 .12646 
 
 .007 
 
 .00078 
 
 .06 
 
 .01924 
 
 .113 
 
 .04889 
 
 .166 
 
 .08554 
 
 .219 
 
 .12729 
 
 .008 
 
 .00095 
 
 .061' 
 
 .01972 
 
 .114 
 
 .04953 
 
 .167 
 
 .08629 
 
 .22 
 
 .12811 
 
 .009 
 
 .00113 
 
 .062 
 
 .02020 
 
 .115 
 
 .05016 
 
 .168 
 
 .08704 
 
 .221 
 
 .12894 
 
 .01 
 
 .00133 
 
 .063 
 
 .02068 
 
 .116 
 
 .05080 
 
 .169 
 
 .08779 
 
 .222 
 
 .12977 
 
 .011 
 
 .00153 
 
 .064 
 
 .02117 
 
 .117 
 
 .05145 
 
 .17 
 
 .08854 
 
 .223 
 
 .13060 
 
 .012 
 
 .00175 
 
 .065 
 
 .02166 
 
 .118 
 
 .05209 
 
 .171 
 
 .08929 
 
 .224 
 
 .13144 
 
 .013 
 
 .00197 
 
 .066 
 
 .02215 
 
 .119 
 
 .05274 
 
 .172 
 
 .09004 
 
 .225 
 
 .13227 
 
 .014 
 
 .0022 
 
 .067 
 
 .02265 
 
 .12 
 
 .05338 
 
 .173 
 
 .09080 
 
 .226 
 
 .13311 
 
 .015 
 
 .00244 
 
 .068 
 
 .02315 
 
 .121 
 
 .05404 
 
 .174 
 
 .09155 
 
 .227 
 
 .13395 
 
 .016 
 
 .00268 
 
 .069 
 
 .02366 
 
 .122 
 
 .05469 
 
 .175 
 
 .0923 1 
 
 .228 
 
 .13478 
 
 .017 
 
 .00294 
 
 .07 
 
 .02417 
 
 .123 
 
 .05535 
 
 .176 
 
 .09307 
 
 .229 
 
 .13562 
 
 .018 
 
 .0032 
 
 .071 
 
 .02468 
 
 .124 
 
 .05600 
 
 .177 
 
 .09384 
 
 .23 
 
 .13646 
 
 .019 
 
 .00347 
 
 .072 
 
 .02520 
 
 .125 
 
 .05666 
 
 .178 
 
 .09460 
 
 .231 
 
 .13731 
 
 .02 
 
 .00375 
 
 .073 
 
 .02571 
 
 .126 
 
 .05733 
 
 .179 
 
 .09j37 
 
 .232 
 
 .13815 
 
 .021 
 
 .00403 
 
 .074 
 
 .02624 
 
 .127 
 
 .05799 
 
 .18 
 
 .09613 
 
 .233 
 
 .13900 
 
 .022 
 
 00432 
 
 .075 
 
 .02676 
 
 .128 
 
 .05866 
 
 .181 
 
 .09690 
 
 .234 
 
 .13984 
 
 .023 
 
 .00462 
 
 .076 
 
 .02729 
 
 .129 
 
 .05933 
 
 .182 
 
 .09767 
 
 .235 
 
 .14069 
 
 .024 
 
 .00492 
 
 .077 
 
 .02782 
 
 .13 
 
 .06000 
 
 .183 
 
 .09845 
 
 .236 
 
 .14154 
 
 .025 
 
 .00523 
 
 .078 
 
 .02836 
 
 .131 
 
 .06067 
 
 .184 
 
 .09922 
 
 .237 
 
 .14239 
 
 .026 
 
 .00555 
 
 .079 
 
 .02889 
 
 .132 
 
 .06135 
 
 .185 
 
 .10000 
 
 .238 
 
 .14324 
 
 .027 
 
 .00587 
 
 .08 
 
 .02943 
 
 .133 
 
 .06203 
 
 .186 
 
 .10077 
 
 .239 
 
 .14409 
 
 .028 
 
 .00619 
 
 .081 
 
 .02998 
 
 .134 
 
 .06271 
 
 .187 
 
 .10155 
 
 .24 
 
 .14494 
 
 ,029 
 
 .00653 
 
 .082 
 
 .03053 
 
 .135 
 
 .06339 
 
 .188 
 
 .10233 
 
 .241 
 
 .14580 
 
 .03 
 
 .00687 
 
 .083 
 
 .03108 
 
 .136 
 
 .06407 
 
 .189 
 
 .10312 
 
 .242 
 
 .14666 
 
 .031 
 
 .00721 
 
 .084 
 
 .03163 
 
 .137 
 
 .06476 
 
 .19 
 
 .10390 
 
 .243 
 
 .14751 
 
 .032 
 
 .00756 
 
 .085 
 
 .03219 
 
 .138 
 
 .06545 
 
 .191 
 
 .10469 
 
 .244 
 
 .14837 
 
 .033 
 
 .00791 
 
 .086 
 
 .03275 
 
 .139 
 
 .06614 
 
 .192 
 
 .10547 
 
 .245 
 
 .14923 
 
 .034 
 
 .00827 
 
 .087 
 
 .03331 
 
 .14 
 
 .06683 
 
 .193 
 
 .10626 
 
 .246 
 
 .15009 
 
 .035 
 
 .00864- 
 
 .088 
 
 .03387 
 
 .141 
 
 .06753 
 
 .194 
 
 .10705 
 
 .247 
 
 .15095 
 
 .036 
 
 .00901 
 
 .089 
 
 .03444 
 
 .142 
 
 .06822 
 
 .195 
 
 .10784 
 
 .248 
 
 .15182 
 
 .037 
 
 .00938 
 
 .09 
 
 .03501 
 
 .143 
 
 .06892 
 
 .196 
 
 .10864 
 
 .249 
 
 .15268 
 
 .038 
 
 .00976 
 
 091 
 
 .03559 
 
 .144 
 
 .06963 
 
 .197 
 
 .10943 
 
 .25 
 
 .15355 
 
 .039 
 
 .01015 
 
 .092 
 
 .03616 
 
 .145 
 
 .07033 
 
 .198 
 
 .11023 
 
 .251 
 
 .15441 
 
 .04 
 
 .01054 
 
 .093 
 
 .03674 
 
 .146 
 
 .07103 
 
 .199 
 
 .11102 
 
 .252 
 
 .15528 
 
 .041 
 
 .01093 
 
 .094 
 
 .03732 
 
 .147 
 
 .07174 
 
 .2 
 
 .11182 
 
 .253 
 
 .15615 
 
 .042 
 
 .01133 
 
 .095 
 
 .03791 
 
 .148 
 
 .07245 
 
 .201 
 
 .11262 
 
 .254 
 
 .15702 
 
 .043 
 
 .01173 
 
 .096 
 
 .03850 
 
 .149 
 
 .07316 
 
 .202 
 
 .11343 
 
 .255 
 
 .15789 
 
 .044 
 
 .01214 
 
 .097 
 
 .03909 
 
 .15 
 
 .07387 
 
 .203 
 
 .11423 
 
 .256 
 
 .15876 
 
 .045 
 
 .01255 
 
 .098 
 
 .03968 
 
 .151 
 
 .07459 
 
 .204 
 
 .11504 
 
 .257 
 
 .15964 
 
 .046 
 
 .01297 
 
 .099 
 
 .04028 
 
 .152 
 
 .07531 
 
 .205 
 
 .11584 
 
 .258 
 
 .16051 
 
 .047 
 
 .01339 
 
 | 
 
 .04087 
 
 .153 
 
 .07603 
 
 .206 
 
 .11665 
 
 .259 
 
 .16139 
 
 .048 
 
 .01382 
 
 J01 
 
 .04148 
 
 .154 
 
 .07675 
 
 .207 
 
 . 1 1 746 
 
 .26 
 
 .16226 
 
 .049 
 
 .01425 
 
 .102 
 
 .04208 
 
 .155 
 
 .07747 
 
 .208 
 
 .11827 
 
 .261 
 
 .16314 
 
 .05 
 
 .01468 
 
 .103 
 
 .04269 
 
 .156 
 
 .07819 
 
 .209 
 
 .11908 
 
 .262 
 
 .16402 
 
 .051 
 
 .01512 
 
 .104 
 
 .04330 
 
 .157 
 
 .07892 
 
 .21 
 
 .11990 
 
 .263 
 
 .16490 
 
 .052 
 
 .01556 
 
 .105 
 
 .04391 
 
 .158 
 
 .07965 
 
 .211 
 
 .12071 
 
 .264 
 
 .16578 
 
 .053 
 
 .01601 
 
 .106 
 
 .04452 
 
 .159 
 
 .08038 
 
 .212 
 
 .12153 
 
 .265 
 
 .16666 
 
122 
 
 MATHEMATICAL TABLES, 
 
 Rise 
 
 4- 
 
 Diam. 
 
 Area. 
 
 Rise 
 Diam. 
 
 Area. 
 
 Rise 
 
 *- 
 Diam. 
 
 Area. 
 
 Rise 
 
 * 
 Diana. 
 
 Area. 
 
 Rise 
 
 * 
 Diam. 
 
 Area. 
 
 .266 
 
 .16755 
 
 .313 
 
 .21015 
 
 .36 
 
 .25455 
 
 .407 
 
 .30024 
 
 .454 
 
 .34676 
 
 .267 
 
 .16643 
 
 .314 
 
 .21108 
 
 .361 
 
 .25551 
 
 .408 
 
 .30122 
 
 .455 
 
 -.34776 
 
 .268 
 
 .16932 
 
 .315 
 
 .21201 
 
 .362 
 
 .25647 
 
 .409 
 
 .30220 
 
 .456 
 
 .34876 
 
 .269 
 
 17020 
 
 316 
 
 .21294 
 
 .363 
 
 .25743 
 
 .41 
 
 .30319 
 
 .457 
 
 .34975 
 
 .27 
 
 .17109 
 
 .317 
 
 .21387 
 
 .364 
 
 .25839 
 
 .411 
 
 .30417 
 
 .458 
 
 .35075 
 
 .271 
 
 .17198 
 
 .318 
 
 .21480 
 
 .365 
 
 .25936 
 
 .412 
 
 .30516 
 
 .459 
 
 .35175 
 
 .272 
 
 .17287 
 
 .319 
 
 .21573 
 
 .366 
 
 .26032 
 
 .413 
 
 .30614 
 
 .46 
 
 .35274 
 
 .273 
 
 .17376 
 
 .32 
 
 .21667 
 
 .367 
 
 .26128 
 
 .414 
 
 .30712 
 
 .461 
 
 .35374 
 
 .274 
 
 .17465 
 
 .321 
 
 .21760 
 
 .368 
 
 .26225 
 
 .415 
 
 .30811 
 
 .462 
 
 .35474 
 
 .275 
 
 .17554 
 
 .322 
 
 .21853 
 
 .369 
 
 .26321 
 
 .416 
 
 .30910 
 
 .463 
 
 .35573 
 
 .276 
 
 .17644 
 
 .323 
 
 ,21947 
 
 .37 
 
 .26418 
 
 .417 
 
 .3 1 008 
 
 .464 
 
 .35673 
 
 .277 
 
 .17733 
 
 .324 
 
 .22040 
 
 .37! 
 
 .265 1 4 
 
 .418 
 
 .31107 
 
 .465 
 
 .35773 
 
 .278 
 
 .17823 
 
 .325 
 
 .22134 
 
 .372 
 
 .26611 
 
 .419 
 
 .31205 
 
 .466 
 
 .35873 
 
 .279 
 
 .17912 
 
 .326 
 
 .22228 
 
 .373 
 
 .26708 
 
 .42 
 
 .31304 
 
 .467 
 
 .35972 
 
 .28 
 
 .18002 
 
 .327 
 
 .22322 
 
 .374 
 
 .26805 
 
 .421 
 
 .31403 
 
 .468 
 
 .36072 
 
 .281 
 
 .18092 
 
 .328 
 
 .22415 
 
 .375 
 
 .26901 
 
 .422 
 
 .31502 
 
 .469 
 
 .36172 
 
 .282 
 
 .18182 
 
 .329 
 
 .22509 
 
 .376 
 
 .26998 
 
 .423 
 
 .31600 
 
 .47 
 
 .36272 
 
 .283 
 
 .18272 
 
 .33 
 
 .22603 
 
 .377 
 
 .27095 
 
 .424 
 
 .31699 
 
 .471 
 
 .36372 
 
 .284 
 
 .18362 
 
 .331 
 
 .22697 
 
 .378 
 
 .27192 
 
 .425 
 
 .3 1 798 
 
 .472 
 
 .36471 
 
 .285 
 
 .18452 
 
 .332 
 
 .22792 
 
 .379 
 
 .27289 
 
 .426 
 
 .31897 
 
 .473 
 
 .36571 
 
 .286 
 
 .18542 
 
 .333 
 
 .22886 
 
 .38 
 
 .27386 
 
 .427 
 
 .31996 
 
 .474 
 
 .36671 
 
 .287 
 
 .18633 
 
 .334 
 
 .22980 
 
 .381 
 
 .27483 
 
 .428 
 
 .32095 
 
 .475 
 
 .36771 
 
 .288 
 
 .18723 
 
 .335 
 
 .23074 
 
 .382 
 
 .27580 
 
 .429 
 
 .32194 
 
 .476 
 
 .36871 
 
 .289 
 
 .18814 
 
 .336 
 
 .23169 
 
 .383 
 
 .27678 
 
 .43 
 
 .32293 
 
 .477 
 
 .36971 
 
 .29 
 
 .18905 
 
 .337 
 
 .23263 
 
 .384 
 
 .27775 
 
 .431 
 
 .32392 
 
 .478 
 
 .37071 
 
 .291 
 
 .18996 
 
 .338 
 
 .23358 
 
 .385 
 
 .27872 
 
 .432 
 
 .32491 
 
 .479 
 
 .37171 
 
 .292 
 
 .19086 
 
 .339 
 
 .23453 
 
 .386 
 
 .27969 
 
 .433 
 
 .32590 
 
 .48 
 
 .37270 
 
 293 
 
 .19177 
 
 .34 
 
 .23547 
 
 .387 
 
 .28067 
 
 .434 
 
 .32689 
 
 .481 
 
 .37370 
 
 294 
 
 .19268 
 
 .341 
 
 .23642 
 
 .388 
 
 .28164 
 
 .435 
 
 .32788 
 
 .482 
 
 .37470 
 
 .295 
 
 .19360 
 
 .342 
 
 .23737 
 
 .389 
 
 .28262 
 
 .436 
 
 .32887 
 
 .483 
 
 .37570 
 
 .296 
 
 .19451 
 
 .343 
 
 .23832 
 
 .39 
 
 .28359 
 
 .437 
 
 .32987 
 
 .484 
 
 .37670 
 
 .297 
 
 .19542 
 
 .344 
 
 .23927 
 
 .391 
 
 .28457 
 
 .438 
 
 .33086 
 
 .485 
 
 .37770 
 
 .298 
 
 .19634 
 
 .345 
 
 .24022 
 
 .392 
 
 .28554 
 
 .439 
 
 .33185 
 
 .486 
 
 .37870 
 
 .299 
 
 .19725 
 
 .346 
 
 .24117 
 
 .393 
 
 .28652 
 
 .44 
 
 .33284 
 
 .487 
 
 .37970 
 
 .3 
 
 .19817 
 
 .347 
 
 .24212 
 
 .394 
 
 .28750 
 
 .441 
 
 .33384 
 
 .488 
 
 .38070 
 
 .301 
 
 .19908 
 
 .348 
 
 .24307 
 
 .395 
 
 .28848 
 
 .442 
 
 .33483 
 
 .489 
 
 .38170 
 
 .302 
 
 .20000 
 
 .349 
 
 .24403 
 
 .396 
 
 .28945 
 
 .443 
 
 .33582 
 
 .49 
 
 .38270 
 
 .303 
 
 .20092 
 
 .35 
 
 .24498 
 
 .397 
 
 .29043 
 
 .444 
 
 .33682 
 
 .491 
 
 .38370 
 
 ,304 
 
 .20184 
 
 .351 
 
 .24593 
 
 .398 
 
 .29141 
 
 .445 
 
 .33781 
 
 .492 
 
 .38470 
 
 .305 
 
 .20276 
 
 .352 
 
 .24689 
 
 .399 
 
 .29239 
 
 .446 
 
 .33880 
 
 .493 
 
 .38570 
 
 .306 
 
 .20368 
 
 .353 
 
 .24784 
 
 .4 
 
 .29337 
 
 .447 
 
 .33980 
 
 .494 
 
 .38670 
 
 .307 
 
 .20460 
 
 .354 
 
 .24880 
 
 ".401 
 
 .29435 
 
 .448 
 
 .34079 
 
 .495 
 
 .38770 
 
 .308 
 
 .20553 
 
 .355 
 
 .24976 
 
 .402 
 
 .29533 
 
 .449 
 
 .34179 
 
 .496 
 
 .38870 
 
 .309 
 
 .20645 
 
 .356 
 
 .25071 
 
 .403 
 
 .29631 
 
 .45 
 
 .34278 
 
 .497 
 
 .38970 
 
 .31 
 
 .20738 
 
 .357 
 
 .25167 
 
 .404 
 
 .29729 
 
 .451 
 
 .34378 
 
 .498 
 
 .39070 
 
 .311 
 
 .20830 
 
 .358 
 
 .25263 
 
 .405 
 
 .29827 
 
 .452 
 
 .34477 
 
 .499 
 
 .39170 
 
 .312 
 
 .20923 
 
 .359 
 
 .25359 
 
 .406 
 
 .29926 
 
 .453 
 
 .34577 
 
 .5 
 
 .39270 
 
 For rules for finding the area of a segment see Mensuration, page 60. 
 
 LENGTHS OF CIRCULAR ARCS. 
 
 (Degrees being given. Radius of Circle = 1.) 
 
 FORMULA. Length of arc = g X radius X number of degrees. 
 
 RULE. Multiply the factor in the table (see next page) for any given 
 number of degrees by the radius. 
 EXAMPLE. Given a curve of a radius of 55 feet and an angle of 7 8 20'. 
 
 r Factor from table for 78 1 .3613568 
 
 Factor from table for 20' .0058178 
 
 Factor. 1.3671740 
 
 1.3671746X55 = 
 
LENGTHS OP CIRCULAR ARCS. 
 
 FACTORS FOR LENGTHS OF CIRCULAR ARCS. 
 
 123 
 
 Degrees. 
 
 Minutes. 
 
 1 
 
 .0174533 
 .0349066 
 
 61 
 62 
 
 1 .0646508 
 1.0821041 
 
 121 
 122 
 
 2.1118484 
 2.1293017 
 
 1 
 2 
 
 .0002909 
 .0005818 
 
 3 
 
 .0523599 
 
 63 
 
 1.0995574 
 
 123 
 
 2.1467550 
 
 3 
 
 .0008727 
 
 A 
 
 .0698132 
 
 64 
 
 1.1170107 
 
 124 
 
 2.1642083 
 
 4 
 
 .0011636 
 
 5 
 
 .0872665 
 
 65 
 
 1.1344640 
 
 125 
 
 2.1816616 
 
 5 
 
 .0014544 
 
 6 
 
 .1047198 
 
 66 
 
 1.1519173 
 
 126 
 
 2.1991149 
 
 6 
 
 .0017453 
 
 7 
 
 .1221730 
 
 67 
 
 1.1693706 
 
 127 
 
 2.2165682 
 
 7 
 
 .0020362 
 
 8 
 
 .1396263 
 
 68 
 
 1.1868239 
 
 128 
 
 2.2340214 
 
 8 
 
 .0023271 
 
 9 
 
 .1570796 
 
 69 
 
 1.2042772 
 
 129 
 
 2.2514747 
 
 9 
 
 .0026 1 80 
 
 10 
 
 .1745329 
 
 70 
 
 1.2217305 
 
 130 
 
 2.2689280 
 
 10 
 
 .0029089 
 
 11 
 
 .1919862 
 
 71 
 
 1.2391838 
 
 131 
 
 2.2863813 
 
 11 
 
 .0031998 
 
 12 
 
 .2094395 
 
 72 
 
 1.2566371 
 
 132 
 
 2.3038346 
 
 12 
 
 .0034907 
 
 13 
 
 .2268928 
 
 73 
 
 1 .2740904 
 
 133 
 
 2.3212879 
 
 13 
 
 .0037815 
 
 14 
 
 .2443461 
 
 74 
 
 1.2915436 
 
 134 
 
 2.3387412 
 
 14 
 
 .0040724 
 
 15 
 
 .2617994 
 
 75 
 
 1.3089969 
 
 135 
 
 2.3561945 
 
 15 
 
 .0043633 
 
 16 
 
 .2792527 
 
 ' 76 
 
 1.3264502 
 
 136 
 
 2.3736478 
 
 16 
 
 .0046542 
 
 17 
 
 .2967060 
 
 77 
 
 1.3439035 
 
 137 
 
 2.3911011 
 
 17 
 
 .0049451 
 
 18 
 
 .3141593 
 
 78 
 
 1.3613568 
 
 138 
 
 2.4085544 
 
 18 
 
 .0052360 
 
 19 
 
 .3316126 
 
 79 
 
 1.3788101 
 
 139 
 
 2.4260077 
 
 19 
 
 .0055269 
 
 20 
 
 .3490659 
 
 80 
 
 1.3962634 
 
 140 
 
 2.4434610 
 
 20 
 
 .0058178 
 
 21 
 
 .3665191 
 
 81 
 
 1.4137167 
 
 141 
 
 2.4609142 
 
 21 
 
 .0061087 
 
 22 
 
 .3839724 
 
 82 
 
 1 .43 1 1 700 
 
 142 
 
 2.4783675 
 
 22 
 
 .0063995 
 
 23 
 
 .4014257 
 
 83 
 
 1 .4486233 
 
 143 
 
 2.4958208 
 
 23 
 
 .0066904 
 
 24 
 
 .4188790 
 
 84 
 
 1 .4660766 
 
 144 
 
 2.5132741 
 
 24 
 
 .0069813 
 
 25 
 
 .4363323 
 
 85 
 
 1.4835299 
 
 145 
 
 2.5307274 
 
 25 
 
 .0072722 
 
 26 
 
 .4537856 
 
 86 
 
 1.5009832 
 
 146 
 
 2.5481807 
 
 26 
 
 .0075631 
 
 27 
 
 .4712389 
 
 87 
 
 1.5184364 
 
 147 
 
 2.5656340 
 
 27 
 
 .007854(1 
 
 28 
 
 .4886922 
 
 88 
 
 1.5358897 
 
 148 
 
 2.5830873 
 
 28 
 
 .0081449 
 
 29 
 
 .5061455 
 
 89 
 
 1.5533430 
 
 149 
 
 2.6005406 
 
 29 
 
 .0084358 
 
 30 
 
 .5235988 
 
 90 
 
 1.5707963 
 
 150 
 
 2.6179939 
 
 30 
 
 .008726(1 
 
 31 
 
 .5410521 
 
 91 
 
 1 .5882496 
 
 151 
 
 2.6354472 
 
 31 
 
 .0090175 
 
 32 
 
 .5585054 
 
 92 
 
 1.6057029 
 
 152 
 
 2.6529005 
 
 32 
 
 .0093084 
 
 33 
 
 .5759587 
 
 93 
 
 1.6231562 
 
 153 
 
 2.6703538 
 
 33 
 
 .0095993 
 
 34 
 
 .5934119 
 
 94 
 
 1 .6406095 
 
 154 
 
 2.6878070 
 
 34 
 
 .0098902 
 
 35 
 
 .6108652 
 
 95 
 
 1.6580628 
 
 155 
 
 2.7052603 
 
 35 
 
 .0101811 
 
 36 
 
 .6283185 
 
 96 
 
 1.6755161 
 
 156 
 
 2.7227136 
 
 36 
 
 .0104720 
 
 37 
 
 .6457718 
 
 97 
 
 1 .6929694 
 
 157 
 
 2.7401669 
 
 37 
 
 .0107629 
 
 38 
 
 .6632251 
 
 98 
 
 1.7104227 
 
 158 
 
 2.7576202 
 
 38 
 
 .0110538 
 
 39 
 
 .6806784 
 
 99 
 
 1.7278760 
 
 159 
 
 2.7750735 
 
 39 
 
 .0113446 
 
 40 
 
 .6981317 
 
 100 
 
 1.7453293 
 
 160 
 
 2.7925268 
 
 40 
 
 .0116355 
 
 41 
 
 .7155850 
 
 101 
 
 1.7627825 
 
 161 
 
 2.8099801 
 
 41 
 
 .0119264 
 
 42 
 
 .7330383 
 
 102 
 
 1.7802358 
 
 162 
 
 2.8274334 
 
 42 
 
 .0122173 
 
 43 
 
 .7504916 
 
 103 
 
 1.7976891 
 
 163 
 
 2.8448867 
 
 43 
 
 .0125082 
 
 44 
 
 .7679449 
 
 104 
 
 1.8151424 
 
 164 
 
 2.8623400 
 
 44 
 
 .0127991 
 
 45 
 
 .7853982 
 
 105 
 
 1.8325957 
 
 165 
 
 2.8797933 
 
 45 
 
 .0130900 
 
 46 
 
 .8028515 
 
 106 
 
 1 .8500490 
 
 166 
 
 "2.8972466 
 
 46 
 
 .0133809 
 
 47 
 
 .8203047 
 
 107 
 
 1.8675023 
 
 167 
 
 2.9146999 
 
 47 
 
 .0136717 
 
 48 
 
 .8377580 
 
 108 
 
 1.8849556 
 
 168 
 
 2.9321531 
 
 48 
 
 .0139626 
 
 49 
 
 .8552113 
 
 109 
 
 1 .9024089 
 
 169 
 
 2.9496064 
 
 49 
 
 .0142535 
 
 50 
 
 .8726646 
 
 110 
 
 1.9198622 
 
 170 
 
 2.9670597 
 
 50 
 
 .0145444 
 
 51 
 
 .8901179 
 
 111 
 
 1.9373155 
 
 171 
 
 2.9845130 
 
 51 
 
 .0148353 
 
 52 
 
 .9075712 
 
 112 
 
 1.9547688 
 
 172 
 
 3.0019663 
 
 52 
 
 .0151262 
 
 53 
 
 .9250245 
 
 113 
 
 1 19722221 
 
 173 
 
 3.0194196 
 
 53 
 
 .0154171 
 
 54 
 
 .9424778 
 
 114 
 
 1 .9896753 
 
 174 
 
 3.0368729 
 
 54 
 
 .0157080 
 
 55 
 
 .9599311 
 
 115 
 
 2.0071286 
 
 175 
 
 3.0543262 
 
 55 
 
 .0159989 
 
 56 
 
 .9773844 
 
 116 
 
 2.0245819 
 
 176 
 
 3.0717795 
 
 56 
 
 .0162897 
 
 57 
 
 .9948377 
 
 117 
 
 2.0420352 
 
 177 
 
 3.0892328 
 
 57 
 
 .0165806 
 
 58 
 
 1.0122910 
 
 118 
 
 2.0594885 
 
 178 
 
 3.1066861 
 
 58 
 
 .0168715 
 
 59 
 
 1.0297443 
 
 119 
 
 2.0769418 
 
 179 
 
 3.1241394 
 
 59 
 
 .0171624 
 
 60 
 
 1.0471976 
 
 120 
 
 2.0943951 
 
 180 
 
 3.1415927 
 
 60 
 
 .0174533 
 
124 
 
 MATHEMATICAL 
 
 LENGTHS Off CtHCtJLAll ARCS. 
 
 (Diameter =- 1. Given the Chord and Height of the Arc.) 
 
 RULE FOR USE OF THE TABLE. Divide the height by the chord. Find 
 In the column of heights the number equal to this quotient. Take out the 
 corresponding number from the column of lengths. Multiply this last 
 number by the length of the given chord; the product will be length of the 
 
 If the arc is greater than a semicircle, first find the diameter from the 
 formula, Diam. = (square of half chord -f- rise) + rise; the formula is true 
 whether the arc exceeds a semicircle or not. Then find the circumference. 
 From the diameter subtract the given height of arc, the remainder will be 
 height of the smaller arc of the circle; find its length according to the rule, 
 and subtract it from the circumference. 
 
 Hgts. 
 
 Lgths. 
 
 Hgts. 
 
 Lgths. 
 
 Hgts. 
 
 Lgths. 
 
 Hgts. 
 
 Lgths. 
 
 Hgts. 
 
 Lgths. 
 
 0.001 
 
 .00002 
 
 0.15 
 
 .05896 
 
 0.238 
 
 .14480 
 
 0.326 
 
 .26288 
 
 0.414 
 
 .40788 
 
 .005 
 
 .00007 
 
 .152 
 
 .06051 
 
 .24 
 
 .14714 
 
 .328 
 
 .26588 
 
 .416 
 
 .41145 
 
 .01 
 
 .00027 
 
 .154 
 
 .06209 
 
 .242 
 
 .14951 
 
 .33 
 
 .26892 
 
 .418 
 
 .41503 
 
 .015 
 
 .00061 
 
 .156 
 
 .06368 
 
 .244 
 
 .15189 
 
 .332 
 
 .27196 
 
 .42 
 
 .41861 
 
 .02 
 
 .00107 
 
 .158 
 
 .06530 
 
 .246 
 
 .15428 
 
 .334 
 
 .27502 
 
 .422 
 
 .42221 
 
 .025 
 
 .00167 
 
 .16 
 
 .06693 
 
 .248 
 
 .15670 
 
 .336 
 
 .27810 
 
 .424 
 
 .42583 
 
 .03 
 
 .00240 
 
 .162 
 
 .06858 
 
 .25 
 
 .15912 
 
 .338 
 
 .28118 
 
 .426 
 
 .42945 
 
 .035 
 
 .00327 
 
 .164 
 
 .07025 
 
 .252 
 
 .16156 
 
 .34 
 
 .28428 
 
 .428 
 
 .43309 
 
 .04 
 
 .00426 
 
 .166 
 
 .07194 
 
 .254 
 
 .16402 
 
 :342 
 
 .28739 
 
 .43 
 
 .43673 
 
 .045 
 
 .00539 
 
 .168 
 
 .07365 
 
 .256 
 
 .16650 
 
 .344 
 
 .29052 
 
 .432 
 
 .44039 
 
 .05 
 
 .00665 
 
 .17 
 
 .07537 
 
 .258 
 
 .16899 
 
 .346 
 
 .29366 
 
 .434 
 
 .44405 
 
 .055 
 
 .00805 
 
 .172 
 
 .07711 
 
 .26 
 
 .17150 
 
 .348 
 
 .29681 
 
 .436 
 
 .44773 
 
 .06 
 
 .00957 
 
 .174 
 
 .07888 
 
 .262 
 
 .17403 
 
 .35 
 
 .29997 
 
 .438 
 
 .45142 
 
 .065 
 
 .01123 
 
 .176 
 
 .08066 
 
 .264 
 
 .17657 
 
 .352 
 
 .30315 
 
 .44 
 
 .45512 
 
 .07 
 
 .01302 
 
 .178 
 
 .08246 
 
 .266 
 
 .17912 
 
 .354 
 
 .30634 
 
 .442 
 
 .45883 
 
 .075 
 
 .01493 
 
 .18 
 
 .08428 
 
 .268 
 
 .18169 
 
 .356 
 
 .30954 
 
 .444 
 
 .46255 
 
 .08 
 
 .01698 
 
 .182 
 
 .08611 
 
 .27 
 
 .18429 
 
 .358 
 
 .31276 
 
 .446 
 
 .46628 
 
 .085 
 
 .01916 
 
 .184 
 
 .08797 
 
 .272 
 
 .18689 
 
 .36 
 
 .31599 
 
 .448 
 
 .47002 
 
 .09 
 
 .02146 
 
 .186 
 
 .08984 
 
 .274 
 
 .18951 
 
 .362 
 
 .31923 
 
 .45 
 
 .47377 
 
 .095 
 
 .02389 
 
 .188 
 
 .09174 
 
 .276 
 
 .19214 
 
 .364 
 
 .32249 
 
 .452 
 
 .47753 
 
 .10 
 
 .02646 
 
 .19 
 
 .09365 
 
 .278 
 
 .19479 
 
 .366 
 
 .32577 
 
 .454 
 
 .48131 
 
 .102 
 
 .02752 
 
 .192 
 
 .09557 
 
 .28 
 
 .19746 
 
 .368 
 
 .32905 
 
 .456 
 
 .48509 
 
 .104 
 
 .02860 
 
 .194 
 
 .09752 
 
 .282 
 
 .20014 
 
 .37 
 
 .33234 
 
 .458 
 
 .48889 
 
 .106 
 
 .02970 
 
 .196 
 
 .09949 
 
 .284 
 
 .20284 
 
 .372 
 
 .33564 
 
 .46 
 
 .49269 
 
 .108 
 
 .03082 
 
 .198 
 
 .10147 
 
 .286 
 
 .20555 
 
 .374 
 
 .33896 
 
 .462 
 
 .49651 
 
 .11 
 
 .03196 
 
 .20 
 
 .10347 
 
 .288 
 
 .20827 
 
 .376 
 
 .34229 
 
 .464 
 
 .50033 
 
 .112 
 
 .03312 
 
 .202 
 
 .10548 
 
 .29 
 
 .21102 
 
 .378 
 
 .34563 
 
 .466 
 
 .50416 
 
 .114 
 
 .03430 
 
 .204 
 
 .10752 
 
 .292 
 
 .21377 
 
 .38 
 
 .34899 
 
 .468 
 
 .50800 
 
 .116 
 
 .03551 
 
 .206 
 
 .10958 
 
 .294 
 
 .21654 
 
 .382 
 
 .35237 
 
 .47 
 
 .51185 
 
 .118 
 
 .03672 
 
 .208 
 
 .11165 
 
 .296 
 
 .21933 
 
 .384 
 
 .35575 
 
 .472 
 
 .51571 
 
 .12 
 
 .03797 
 
 .21 
 
 .11374 
 
 .298 
 
 .22213 
 
 .386 
 
 .35914 
 
 .474 
 
 .51958 
 
 .122 
 
 .03923 
 
 .212 
 
 .11584 
 
 .30 
 
 .22495 
 
 .388 
 
 .36254 
 
 .476 
 
 .52346 
 
 .124 
 
 .04051 
 
 .214 
 
 .11796 
 
 .302 
 
 .22778 
 
 .39 
 
 .36596 
 
 .478 
 
 .52736 
 
 .126 
 
 .04181 
 
 .216 
 
 .12011 
 
 .304 
 
 .23063 
 
 .392 
 
 .36939 
 
 .48 
 
 .53126 
 
 .128 
 
 .04313 
 
 .218 
 
 .12225 
 
 .306 
 
 .23349 
 
 .394 
 
 .37283 
 
 .482 
 
 .53518 
 
 .13 
 
 .04447 
 
 .22 
 
 .12444 
 
 .308 
 
 .23636 
 
 .396 
 
 .37628 
 
 .484 
 
 .53910 
 
 .132 
 
 .04584 
 
 .222 
 
 .12664 
 
 .31 
 
 .23926 
 
 .398 
 
 .37974 
 
 .486 
 
 .54302 
 
 .134 
 
 .04722 
 
 .224 
 
 .12885 
 
 .312 
 
 .24216 
 
 > .40 
 
 .38322 
 
 .488 
 
 .54696 
 
 .136 
 
 .04862 
 
 .226 
 
 .13108 
 
 .314 
 
 .24507 
 
 .402 
 
 .38671 
 
 .49 
 
 .55091 
 
 .138 
 
 .05003 
 
 .228 
 
 .13331 
 
 .316 
 
 .24801 
 
 .404 
 
 .39021 
 
 .492 
 
 .55487 
 
 .14 
 
 .05147 
 
 .23 
 
 .13557 
 
 .318 
 
 .25095 
 
 .406 
 
 .39372 
 
 .494 
 
 .55854 
 
 .142 
 
 .05293 
 
 .232 
 
 .13785 
 
 .32 
 
 .25391 
 
 .408 
 
 .39724 
 
 .496 
 
 .56282 
 
 .144 
 
 .05441 
 
 .234 
 
 .14015 
 
 .322 
 
 .25689 
 
 .41 
 
 .40077 
 
 .498 
 
 .56681 
 
 .146 
 
 .05591 
 
 .236 
 
 .14247 
 
 .324 
 
 .25988 
 
 .412 
 
 .40432 
 
 .50 
 
 .57080 
 
 .148 
 
 .05743 
 
 
 
 
 
 
 
 
 
CIRCLES AND SQUARES OF EQUAL AREA. 125 
 
 Diameters of Circles and Sides of Squares of Same Area. 
 
 Diameter of circle * 1.128379 X side of square of same area. 
 Side of square 0.886227 X diameter of circle of same area. 
 
 Diam. of Cir- 
 cle or Side 
 of Square. 
 
 Side of 
 Square 
 Equiva- 
 lent to 
 Circle. 
 
 Diam. of 
 Circle 
 Equiva- 
 lent to 
 Square. 
 
 Diam. of Cir- 
 cle or Side 
 of Square. 
 
 Side of 
 Square 
 Equiva- 
 lent to 
 Circle. 
 
 Diam. of 
 Circle 
 Equiva- 
 lent to 
 Square. 
 
 Diam. of Cir- 
 cle or Side 
 of Square. 
 
 Side of 
 Square 
 Equiva- 
 lent to 
 Circle. 
 
 Diam. of 
 Circle 
 Equiva- 
 lent to 
 Square. 
 
 1 
 
 0.886 
 
 1 .128 
 
 34 
 
 30.132 
 
 38.365 
 
 67 
 
 59.377 
 
 75.601 
 
 2 
 
 1.772 
 
 2.257 
 
 35 
 
 31.018 
 
 39.493 
 
 68 
 
 60.263 
 
 76.730 
 
 3 
 
 2.659 
 
 3.385 
 
 36 
 
 31.904 
 
 40.622 
 
 69 
 
 61 .150 
 
 77.858 
 
 4 
 
 3.545 
 
 4.514 
 
 37 
 
 32.790 
 
 41.750 
 
 70 
 
 62 . 036 
 
 78.987 
 
 5 
 
 4.431 
 
 5.642 
 
 38 
 
 33.677 
 
 42.878 
 
 71 
 
 62.922 
 
 80.115 
 
 6 
 
 5.317 
 
 6.770 
 
 39 
 
 34.563 
 
 44.007 
 
 72 
 
 63.808 
 
 81.243 
 
 7 
 
 6.204 
 
 7.899 
 
 40 
 
 35.449 
 
 45.135 
 
 73 
 
 64.695 
 
 82.372 
 
 8 
 
 7.090 
 
 9.027 
 
 41 
 
 36.335 
 
 46 . 264 
 
 74 
 
 65.581 
 
 83.500 
 
 9 
 
 7.976 
 
 10.155 
 
 42 
 
 37.222 
 
 47.392 
 
 75 
 
 66.467 
 
 84.628 
 
 10 
 
 8.862 
 
 11.284 
 
 43 
 
 38.108 
 
 48.520 
 
 76 
 
 67.353 
 
 85.757 
 
 11 
 
 9.748 
 
 12.412 
 
 44 
 
 38.994 
 
 49.649 
 
 77 
 
 68.239 
 
 86.885 
 
 12 
 
 10.635 
 
 13.541 
 
 45 
 
 39.880 
 
 50.777 
 
 78 
 
 69.126 
 
 tttt.014 
 
 13 
 
 11.521 
 
 14.669 
 
 46 
 
 40.766 
 
 51 .905 
 
 79 
 
 70.012 
 
 89.142 
 
 14 
 
 12.407 
 
 15.797 
 
 47 
 
 41 .653 
 
 53.034 
 
 80 
 
 70.898 
 
 90.270 
 
 15 
 
 13.293 
 
 16.926 
 
 48 
 
 42.539 
 
 54.162 
 
 81 
 
 71 .784 
 
 91 .399 
 
 16 
 
 14.180 
 
 18.054 
 
 49 
 
 43.425 
 
 55.291 
 
 82 
 
 72.671 
 
 92.527 
 
 17 
 
 15.066 
 
 19.182 
 
 50 
 
 44.311 
 
 56.419 
 
 83 
 
 73.557 
 
 93.655 
 
 18 
 
 15.952 
 
 20.311 
 
 51 
 
 45.198 
 
 57.547 
 
 84 
 
 74.443 
 
 94.784 
 
 19 
 
 16.838 
 
 21.439 
 
 52 
 
 46.084 
 
 58.676 
 
 85 
 
 75.330 
 
 95.912 
 
 20 
 
 17.725 
 
 22.568 
 
 53 
 
 46.970 
 
 59.804 
 
 86 
 
 76.216 
 
 97.041 
 
 21 
 
 18.611 
 
 23.696 
 
 54 
 
 47.856 
 
 60.932 
 
 87 
 
 77.102 
 
 98.169 
 
 22 
 
 19.497 
 
 24.824 
 
 55 
 
 48.742 
 
 62.061 
 
 88 
 
 77.988 
 
 99.297 
 
 23 
 
 20.383 
 
 25.953 
 
 56 
 
 49.629 
 
 63.189 
 
 89 
 
 >8.874 
 
 100.426 
 
 24 
 
 21.269 
 
 27.081 
 
 57 
 
 50.515 
 
 64.318 
 
 90 
 
 79.760 
 
 101 .554 
 
 25 
 
 22.156 
 
 28.209 
 
 58 
 
 51.401 
 
 65.446 
 
 91 
 
 80.647 
 
 102.682 
 
 26 
 
 23.042 
 
 29.338 
 
 59 
 
 52.287 
 
 66.574 
 
 92 
 
 81.533 
 
 103.811 
 
 27 
 
 23.928 
 
 30.466 
 
 60 
 
 53.174 
 
 67.703 
 
 93 
 
 82.419 
 
 104.939 
 
 28 
 
 24.814 
 
 31.595 
 
 61 
 
 54.060 
 
 68.831 
 
 94 
 
 83.305 
 
 106.068 
 
 29 
 
 25.701 
 
 32.723 
 
 62 
 
 54.946 
 
 69.959 
 
 95 
 
 84 192 
 
 107.196 
 
 30 
 
 26.587 
 
 33.851 
 
 63 
 
 55.832 
 
 71 .088 
 
 96 
 
 85.078 
 
 108.324 
 
 31 
 
 27.473 
 
 34.980 
 
 64 
 
 56 719 
 
 72.216 
 
 97 
 
 85.964 
 
 109.453 
 
 32 
 
 28.359 
 
 36.108 
 
 65 
 
 57.605 
 
 73.345 
 
 98 
 
 86.850 
 
 110.581 
 
 33 
 
 29.245 
 
 37.237 
 
 66 
 
 58.491 
 
 74.473 
 
 99 
 
 87.736 
 
 111.710 
 
 Number of Circles that can be Inscribed within a Larger Circle. 
 
 N = Number of circles; D = diam. of enclosing circle; d = diam. of 
 inscribed circles. 
 
 Obtain the ratio of D -5- d and find the value nearest to it in the 
 table. Opposite this value under A r , find the number of circles of 
 diameter d that can be inscribed in a circle of diameter D. 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 N 
 
 D/d 
 
 2 
 
 2.00 
 
 13 
 
 4.23 
 
 24 
 
 5.72 
 
 35 
 
 6.86 
 
 46 
 
 7.81 
 
 85 
 
 10.46 
 
 140 
 
 13.26 
 
 3 
 
 2.15 
 
 14 
 
 4.41 
 
 25 
 
 5.81 
 
 36 
 
 7.00 
 
 47 
 
 7.92 
 
 90 
 
 10.73 
 
 145 
 
 13.49 
 
 4 
 
 2.41 
 
 15 
 
 4.55 
 
 26 
 
 5.92 
 
 37 
 
 7.00 
 
 48 
 
 8.00 
 
 95 
 
 11.15 
 
 150 
 
 13.72 
 
 - 5 
 
 2.70 
 
 16 
 
 4.70 
 
 27 
 
 6.00 
 
 38 
 
 7.08 
 
 49 
 
 8.03 
 
 100 
 
 11.34 
 
 155 
 
 13.95 
 
 6 
 
 3.00 
 
 17 
 
 4.86 
 
 28 
 
 6.13 
 
 39 
 
 7.18 
 
 50 
 
 8.13 
 
 105 
 
 11.60 
 
 160 
 
 14.17 
 
 7 
 
 3.00 
 
 18 
 
 5.00 
 
 29 
 
 6.23 
 
 40 
 
 7.31 
 
 55 
 
 8.21 
 
 110 
 
 11.85 
 
 165 
 
 14.39 
 
 8 
 
 3.31 
 
 19 
 
 5.00 
 
 30 
 
 6.40 
 
 41 
 
 7.39 
 
 60 
 
 8.94 
 
 115 
 
 12.10 
 
 170 
 
 14.60 
 
 9 
 
 3.61 
 
 20 
 
 5.18 
 
 31 
 
 6.44 
 
 42 
 
 7.43 
 
 65 
 
 9.25 
 
 120 
 
 12.34 
 
 175 
 
 14.81 
 
 10 
 
 3.80 
 
 21 
 
 5.31 
 
 32 
 
 6.55 
 
 43 
 
 7.61 
 
 70 
 
 9.61 
 
 125 
 
 12.57 
 
 180 
 
 15.01 
 
 11 
 
 3.92 
 
 22 
 
 5.49 
 
 33 
 
 6.70 
 
 44 
 
 7.70 
 
 75 
 
 9.93 
 
 130 
 
 12.80 
 
 185 
 
 15.20 
 
 12 
 
 4.05 
 
 23 
 
 5.61 
 
 34 
 
 6.76 
 
 45 
 
 7.72 
 
 80 
 
 10.20 
 
 135 
 
 13.06 
 
 190 
 
 15.39 
 
126 
 
 MATHEMATICAL TABLES. 
 
 SPHERES. 
 
 (Some errors of 1 in the last figure only. From TRAUTWINE.) 
 
 Diam 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 V32 
 
 .0030 
 
 .0000 
 
 31/4 
 
 33.18 
 
 17.97 
 
 97/ 8 
 
 306.36 
 
 504.21 
 
 Vie 
 
 .0122 
 
 .0001 
 
 5/16 
 
 34.47 
 
 19.03 
 
 10. 
 
 314.16 
 
 523.60 
 
 3/32 
 
 .0276 
 
 .0004 
 
 3/8 
 
 35.78 
 
 20.129 
 
 1/8 
 
 322.06 
 
 543.48 
 
 1/8 
 
 .0490 
 
 .0010 
 
 7/16 
 
 37.122 
 
 21.268 
 
 1/4 
 
 330.06 
 
 563.86 
 
 5/32 
 
 .0767 
 
 .0020 
 
 1/2 
 
 38.484 
 
 22.449 
 
 3/8 
 
 338.16 
 
 584.74 
 
 3/16 
 
 .1104 
 
 .0034 
 
 9/16 
 
 39.872 
 
 23.674 
 
 1/2 
 
 346.36 
 
 606.13 
 
 7/32 
 
 .1503 
 
 .0054 
 
 5/8 
 
 41.283 
 
 24.942 
 
 5/3 
 
 354.66 
 
 628.04 
 
 1/4 
 
 .1963 
 
 .0081 
 
 H/16 
 
 42.719 
 
 26.254 
 
 3/4 
 
 363.05 
 
 650.46 
 
 9/32 
 
 .2485 
 
 .0116 
 
 3/4 
 
 44.179 
 
 27.61 
 
 7/8 
 
 371.54 
 
 673.42 
 
 5/16 
 
 .3068 
 
 .0159 
 
 13/16 
 
 45.664 
 
 29.016 
 
 11. 
 
 380.13 
 
 696.91 
 
 U/32 
 
 .3712 
 
 .0212 
 
 7/8 
 
 47.173 
 
 30.466 
 
 1/8 
 
 388.83 
 
 720.95 
 
 3/8 
 
 .44179 
 
 .0276 
 
 15/16 
 
 48.708 
 
 31.965 
 
 1/4 
 
 397.61 
 
 745.51 
 
 13/32 
 
 .51848 
 
 .0351 
 
 4. 
 
 50.265 
 
 33.510 
 
 3/8 
 
 406.49 
 
 770.64 
 
 7/16 
 
 .60132 
 
 .0438 
 
 1/8 
 
 53.456 
 
 36.751 
 
 V2 
 
 415.48 
 
 796.33 
 
 15/32 
 
 .69028 
 
 .0539 
 
 V4 
 
 56.745 
 
 40.195 
 
 5/8 
 
 424.50 
 
 822.58 
 
 1/2 
 
 .78540 
 
 .0654 
 
 3/8 
 
 60.133 
 
 43.847 
 
 3/4 
 
 433.73 
 
 849.40 
 
 9/16 
 
 .99403 
 
 .0931 
 
 1/2 
 
 63.617 
 
 47.713 
 
 7/8 
 
 443.01 
 
 876.79 
 
 5/8 
 
 1.2272 
 
 .12783 
 
 5/8 
 
 67.201 
 
 51.801 
 
 12. 
 
 452.39 
 
 904.78 
 
 H/16 
 
 1.4849 
 
 .17014 
 
 3/4 
 
 70.883 
 
 56.116 
 
 1/4 
 
 471.44 
 
 962.52 
 
 3/4 
 
 1.7671 
 
 .22089 
 
 7/8 
 
 74.663 
 
 60.663 
 
 V2 
 
 490.87 
 
 1 022.7 
 
 13/16 
 
 2.0739 
 
 .28084 
 
 5. 
 
 78.540 
 
 65.450 
 
 3/4 
 
 510.71 
 
 1085.3 
 
 7/8 
 
 2.4053 
 
 .35077 
 
 1/8 
 
 82.516 
 
 70.482 
 
 13. 
 
 530.93 
 
 1150.3 
 
 15/16 
 
 2.7611 
 
 .43 143 
 
 V4 
 
 86.591 
 
 75.767 
 
 V4 
 
 551.55 
 
 1218.0 
 
 1 
 
 3.1416 
 
 .52360 
 
 3/8 
 
 90.763 
 
 81 .308 
 
 1/2 
 
 572.55 
 
 1288.3 
 
 Vl6 
 
 3.5466 
 
 .62804 
 
 1/2 
 
 95.033 
 
 87.113 
 
 3/4 
 
 593.95 
 
 1361.2 
 
 1/8 
 
 3.9761 
 
 .7455 
 
 5/8 
 
 99.401 
 
 93.189 
 
 14. 
 
 615.75 
 
 1436.8 
 
 3/16 
 
 4.4301 
 
 .8768 
 
 3/4 
 
 103.87 
 
 99.541 
 
 1/4 
 
 637.95 
 
 1515.1 
 
 1/4 
 
 4.9088 
 
 .0227 
 
 7/8 
 
 108.44 
 
 106.18 
 
 1/2 
 
 660.52 
 
 1596.3 
 
 5/16 
 
 5.4119 
 
 .1839 
 
 6. 
 
 113.10 
 
 113.10 
 
 3/4 
 
 683.49 
 
 1680.3 
 
 3/8 
 
 5.9396 
 
 .3611 
 
 1/8 
 
 117.87 
 
 120.31 
 
 15. 
 
 706.85 
 
 1767.2 
 
 7/16 
 
 6.4919 
 
 .5553 
 
 1/4 
 
 122.72 
 
 127.83 
 
 1/4 
 
 730.63 
 
 1857.0 
 
 1/2 
 
 7.0686 
 
 .7671 
 
 3/8 
 
 127.68 
 
 135.66 
 
 1/2 
 
 754.77 
 
 1949.8 
 
 9/16 
 
 7.6699 
 
 .9974 
 
 1/2 
 
 132.73 
 
 143.79 
 
 3/4 
 
 779.32 
 
 2045.7 
 
 5/8 
 
 8.2957 
 
 2.2468 
 
 5/8 
 
 137.89 
 
 152.25 
 
 16. 
 
 804.25 
 
 2144.7 
 
 , U/16 
 
 8.9461 
 
 2.5161 
 
 3/4 
 
 143.14 
 
 161.03 
 
 1/4 
 
 829.57 
 
 2246.8 
 
 I Q/ 
 
 3/4 
 
 9.6211 
 
 2.8062 
 
 7/8 
 
 148.49 
 
 170.14 
 
 1/2 
 
 855.29 
 
 2352.1 
 
 13/16 
 
 0.321 
 
 3.1177 
 
 7. 
 
 153.94 
 
 179.59 
 
 3/4 
 
 881.42 
 
 2460.6 
 
 '7/8 
 
 1.044 
 
 3.4514 
 
 1/8 
 
 159.49 
 
 189.39 
 
 17. 
 
 907.93 
 
 2572.4 
 
 15/16 
 
 1.793 
 
 3.8083 
 
 1/4 
 
 165.13 
 
 199.53 
 
 1/4 
 
 934.83 
 
 2687.6 
 
 2. 
 
 2.566 
 
 4.1888 
 
 3/8 
 
 1 70.87 
 
 210.03 
 
 1/2 
 
 962.12 
 
 2806.2 
 
 1/16 
 
 3.364 
 
 4.5939 
 
 1/2 
 
 176.71 
 
 220.89 
 
 3/4 
 
 989.80 
 
 2928.2 
 
 1/8 
 
 4.186 
 
 5.0243 
 
 5/8 
 
 182.66 
 
 232.13 
 
 18. 
 
 1017.9 
 
 3053.6 
 
 3/16 
 
 5.033 
 
 5.4809 
 
 3/4 
 
 188.69 
 
 243.73 
 
 1/4 
 
 1046.4 
 
 3182.6 
 
 1/4 
 
 5.904 
 
 5.9641 
 
 7/8 
 
 194.83 
 
 255.72 
 
 1/2 
 
 1075.2 
 
 3315.3 
 
 5/16 
 
 6.800 
 
 6.4751 
 
 8. 
 
 201.06 
 
 268.08 
 
 3/4 
 
 1 104.5 
 
 3451.5 
 
 3/8 
 
 7.721 
 
 7.0144 
 
 V8 
 
 207.39 
 
 280.85 
 
 19. 
 
 1 134.1 
 
 3591.4 
 
 Vl6 
 
 8.666 
 
 7.5829 
 
 1/4 
 
 213.82 
 
 294.01 
 
 1/4 
 
 1164.2 
 
 3735.0 
 
 1/2 
 
 9.635 
 
 8.1813 
 
 3/8 
 
 220.36 
 
 307.58 
 
 1/2 
 
 1 194.6 
 
 3882.5 
 
 9/16 
 
 0.629 
 
 8.8103 
 
 1/2 
 
 226.98 
 
 321.56 
 
 3/4 
 
 1225.4 
 
 4033.7 
 
 5/8 
 
 1.648 
 
 9.4708 
 
 5/8 
 
 233.71 
 
 335.95 
 
 20. 
 
 1256.7 
 
 4188.8 
 
 U/16 
 
 2.691 
 
 0.154 
 
 3/4 
 
 240.53 
 
 350.77 
 
 V4 
 
 1288.3 
 
 4347.8 
 
 3/4 
 
 3.758 
 
 0.889 
 
 7/8 
 
 247.45 
 
 366.02 
 
 1/2 
 
 1320.3 
 
 4510.9 
 
 13/16 
 
 4.850 
 
 1.649 
 
 9. 
 
 254.47 
 
 381.70 
 
 3/4 
 
 352.7 
 
 4677.9 
 
 7/8 
 
 5.967 
 
 2.443 
 
 1/8 
 
 261.59 
 
 397.83 
 
 21. 
 
 385.5 
 
 4849.1 
 
 15/16 
 
 7.109 
 
 3.272 
 
 1/4 
 
 268.81 
 
 414.41 
 
 1/4 
 
 418.6 
 
 5024.3 
 
 3. 
 
 8.274 
 
 4.137 
 
 3/8 
 
 270.12 
 
 431.44 
 
 1/2 
 
 452.2 
 
 5203.7 
 
 1/16 
 
 9.465 
 
 5.039 
 
 1/2 
 
 283.53 
 
 448.92 
 
 3/4 
 
 486.2 
 
 5387.4 
 
 1/8 
 
 0.680 
 
 5.979 
 
 5/8 
 
 291.04 
 
 466.87 
 
 23. 
 
 520.5 
 
 5575.3 
 
 3/16 
 
 1.919 
 
 6.957 
 
 3/4 
 
 289.65 
 
 485.31 
 
 1/4 
 
 555.3 
 
 5767.6 
 
SPHERES. 
 
 SPHERES Continued. 
 
 127 
 
 Diam 
 
 Sur- 
 face. 
 
 Vol- 
 urne 
 
 Diam 
 
 Sur- 
 face 
 
 Vol- 
 ume 
 
 Diam 
 
 Sur- 
 face. 
 
 Vol. 
 ume. 
 
 22 1/2 
 
 1590.4 
 
 5964. 
 
 40 1/2 
 
 5153.1 
 
 34783 
 
 70 1/2 
 
 15615 
 
 183471 
 
 3/4 
 
 1626.0 
 
 6165.2 
 
 41. 
 
 5281.1 
 
 36087 
 
 71. 
 
 15837 
 
 187402 
 
 23. 
 
 1661.9 
 
 6370.6 
 
 V2 
 
 5410.7 
 
 37423 
 
 1/2 
 
 16061 
 
 191389 
 
 1/4 
 
 1698.2 
 
 6580.6 
 
 43. 
 
 5541.9 
 
 38792 
 
 73. 
 
 16286 
 
 195433 
 
 1/2 
 
 1735.0 
 
 6795.2 
 
 1/2 
 
 5674.5 
 
 40194 
 
 V2 
 
 16513 
 
 199532 
 
 3/ 4 
 
 1772. 
 
 7014.3 
 
 43. 
 
 5808.8 
 
 41630 
 
 73. 
 
 16742 
 
 203689 
 
 24. 
 
 1809.6 
 
 7238.2 
 
 1/2 
 
 5944.7 
 
 43099 
 
 1/2 
 
 16972 
 
 207903 
 
 V4 
 
 1847.5 
 
 7466.7 
 
 44. 
 
 6082.1 
 
 44602 
 
 74. 
 
 17204 
 
 212175 
 
 1/2 
 
 1885.8 
 
 7700. 
 
 1/2 
 
 6221.2 
 
 46141 
 
 1/2 
 
 17437 
 
 216505 
 
 3 /4 
 
 1924.4 
 
 7938.3 
 
 45. 
 
 6361.7 
 
 47713 
 
 75. 
 
 17672 
 
 220894 
 
 25. 
 
 1963.5 
 
 8181.3 
 
 V2 
 
 6503.9 
 
 49321 
 
 1/2 
 
 17908 
 
 225341 
 
 V4 
 
 2002.9 
 
 8429.2 
 
 46. 
 
 6647.6 
 
 50965 
 
 76. 
 
 18146 
 
 229848 
 
 !/2 
 
 2042.6 
 
 8682.0 
 
 1/2 
 
 6792.9 
 
 52645 
 
 V2 
 
 18386 
 
 234414 
 
 3/4 
 
 2083.0 
 
 8939.9 
 
 47. 
 
 6939.9 
 
 54362 
 
 77. 
 
 18626 
 
 239041 
 
 26. 
 
 2123.7 
 
 9202.8 
 
 1/2 
 
 7088.3 
 
 56115 
 
 V2 
 
 18869 
 
 243728 
 
 1/4 
 
 2164.7 
 
 9470.8 
 
 48. 
 
 7238.3 
 
 57906 
 
 78. 
 
 19114 
 
 248475 
 
 1/2 
 
 2206.2 
 
 9744.0 
 
 1/2 
 
 7389.9 
 
 59734 
 
 1/2 
 
 19360 
 
 253284 
 
 3/4 
 
 2248.0 
 
 10022 
 
 49. 
 
 7543.1 
 
 61601 
 
 79. 
 
 19607 
 
 258155 
 
 27. 
 
 2290.2 
 
 10306 
 
 1/2 
 
 7697.7 
 
 63506 
 
 1/2 
 
 19856 
 
 263088 
 
 1/4 
 
 2332.8 
 
 10595 
 
 50. 
 
 7854.0 
 
 65450 
 
 80. 
 
 20106 
 
 268083 
 
 1/2 
 
 2375.8 
 
 10889 
 
 1/2 
 
 8011.8 
 
 67433 
 
 1/2 
 
 20358 
 
 273147 
 
 3/4 
 
 2419.2 
 
 11189 
 
 51. 
 
 8171.2 
 
 69456 
 
 81. 
 
 20612 
 
 278263 
 
 28. 
 
 2463.0 
 
 11494 
 
 1/2 
 
 8332.3 
 
 71519 
 
 V2 
 
 20867 
 
 283447 
 
 1/4 
 
 2507.2 
 
 11805 
 
 52. 
 
 8494.8 
 
 73622 
 
 83. 
 
 2i<24 
 
 288696 
 
 1/2 
 
 2551.8 
 
 12121 
 
 1/2 
 
 8658.9 
 
 75767 
 
 1/2 
 
 21382 
 
 294010 
 
 3/4 
 
 2596.7 
 
 12443 
 
 53. 
 
 8824.8 
 
 77952 
 
 83. 
 
 21642 
 
 299388 
 
 29. 
 
 2642.1 
 
 12770 
 
 1/2 
 
 8992.0 
 
 80178 
 
 1/2 
 
 21904 
 
 304831 
 
 1/4 
 
 2687.8 
 
 13103 
 
 54. 
 
 9160.8 
 
 82448 
 
 84. 
 
 22167 
 
 310340 
 
 1/2 
 
 2734.0 
 
 13442 
 
 V2 
 
 9331.2 
 
 84760 
 
 1/2 
 
 22432 
 
 315915 
 
 3/4 
 
 2780.5 
 
 13787 
 
 55. 
 
 9503.2 
 
 87114 
 
 85. 
 
 22698 
 
 321556 
 
 30. 
 
 2827.4 
 
 14137 
 
 V2 
 
 9676.8 
 
 89511 
 
 1/2 
 
 22966 
 
 327264 
 
 1/4 
 
 2874.8 
 
 14494 
 
 56. 
 
 9852.0 ' 
 
 91953 
 
 86. 
 
 23235 
 
 333039 
 
 1/2 
 
 2922.5 
 
 14856 
 
 V2 
 
 10029 
 
 94438 
 
 1/2 
 
 23506 
 
 338882 
 
 3/4 
 
 2970.6 
 
 15224 
 
 57. 
 
 10207 
 
 96967 
 
 87. 
 
 23779 
 
 344792 
 
 31. 
 
 3019.1 
 
 15599 
 
 1/2 
 
 10387 
 
 99541 
 
 1/2 
 
 24053 
 
 350771 
 
 1/4 
 
 3068.0 
 
 15979 
 
 58. 
 
 10568 
 
 102161 
 
 88. 
 
 24328 
 
 356819 
 
 1/2 
 
 3117.3 
 
 16366 
 
 1/2 
 
 10751 
 
 104826 
 
 1/2 
 
 24606 
 
 362935 
 
 3/4 
 
 3166.9 
 
 16758 
 
 59. 
 
 10936 
 
 107536 
 
 89. 
 
 24885 
 
 369122 
 
 33. 
 
 3217.0 
 
 17157 
 
 1/2 
 
 11122 
 
 110294 
 
 1/2 
 
 25165 
 
 375378 
 
 V4 
 
 3267.4 
 
 17563 
 
 60. 
 
 11310 
 
 113098 
 
 90. 
 
 25447 
 
 381704 
 
 1/2 
 
 3318.3 
 
 17974 
 
 V2 
 
 11499 
 
 115949 
 
 1/2 
 
 25730 
 
 388102 
 
 3/4 
 
 3369.6 
 
 18392 
 
 61. 
 
 11690 
 
 118847 
 
 91. 
 
 26016 
 
 394570 
 
 33. 
 
 3421.2 
 
 18817 
 
 1/2 
 
 11882 
 
 121794 
 
 V2 
 
 26302 
 
 401109 
 
 V4 
 
 3473.3 
 
 19248 
 
 63. 
 
 12076 
 
 124789 
 
 93. 
 
 26590 
 
 407721 
 
 V2 
 
 3525.7 
 
 19685 
 
 1/2 
 
 12272 
 
 127832 
 
 1/2 
 
 26880 
 
 4 1 4405 
 
 8/4 
 
 3578.5 
 
 20129 
 
 63. 
 
 12469 
 
 130925 
 
 93. 
 
 27172 
 
 421161 
 
 34. 
 
 3631.7 
 
 20580 
 
 1/2 
 
 12668 
 
 134067 
 
 1/2 
 
 27464 
 
 427991 
 
 1/4 
 
 3685.3 
 
 21037 
 
 64. 
 
 12868 
 
 137259 
 
 94. 
 
 27759 
 
 434894 
 
 1/2 
 
 3730.3 
 
 21501 
 
 1/2 
 
 13070 
 
 140501 
 
 1/2 
 
 28055 
 
 441871 
 
 35. 
 
 3848.5 
 
 22449 
 
 65. 
 
 13273 
 
 143794 
 
 95. 
 
 28353 
 
 448920 
 
 V2 
 
 3959.2 
 
 23425 
 
 1/2 
 
 13478 
 
 147138 
 
 V2 
 
 28652 
 
 456047 
 
 36. 
 
 4071.5 
 
 24429 
 
 66. 
 
 13685 
 
 1 50533 
 
 96. 
 
 28953 
 
 463248 
 
 */2 
 
 4185.5 
 
 25461 
 
 1/2 
 
 13893 
 
 153980 
 
 1/2 
 
 29255 
 
 470524 
 
 37. 
 
 4300.9 
 
 26522 
 
 67. 
 
 14103 
 
 157480 
 
 97. 
 
 29559 
 
 477874 
 
 V2 
 
 4417.9 
 
 27612 
 
 V2 
 
 14314 
 
 161032 
 
 1/2 
 
 29865 
 
 485302 
 
 38. 
 
 4536.5 
 
 28731 
 
 68. 
 
 14527 
 
 164637 
 
 98. 
 
 30172 
 
 492808 
 
 V2 
 
 4656.7 
 
 29880 
 
 1/2 
 
 14741 
 
 168295 
 
 1/2 
 
 30481 
 
 500388 
 
 39. 
 
 4778.4 
 
 31059 
 
 69. 
 
 14957 
 
 1 72007 
 
 99. 
 
 30791 
 
 508047 
 
 V2 
 
 4901.7 
 
 32270 
 
 1/2 
 
 15175 
 
 175774 
 
 V2 
 
 31103 
 
 515785 
 
 40. 
 
 5026.5 
 
 33510 
 
 70. 
 
 15394 
 
 1 79595 
 
 00. 
 
 31416 
 
 523598 
 
128 
 
 MATHEMATICAL TABLES. 
 
 NUMBER OF SQUARE FEET IN PLATES 3 TO 32 FEET 
 LONG, AND 1 INCH WIDE. 
 
 For other widths, multiply by the width in inches. 1 sq . in. = 0.00694/9 sq. ft, 
 
 Ft. and 
 Ins. 
 Long. 
 
 Ins. 
 Long. 
 
 Square 
 Feet. 
 
 Ft. and 
 Ins. 
 Long; 
 
 Ins. 
 Long. 
 
 Square 
 Feet. 
 
 Ft. and 
 Ins. 
 Long. 
 
 Ins. 
 Long. 
 
 Square 
 Feet. 
 
 3. 
 
 36 
 
 .25 
 
 7. 10 
 
 94 
 
 .6528 
 
 12. 8 
 
 152 
 
 .056 
 
 
 37 
 
 .2569 
 
 11 
 
 95 
 
 .6597 
 
 9 
 
 153 
 
 .063 
 
 2 
 
 38 
 
 .2639 
 
 8. 
 
 96 
 
 .6667 
 
 10 
 
 154 
 
 .069 
 
 3 
 
 39 
 
 .2708 
 
 1 
 
 97 
 
 .6736 
 
 11 
 
 155 
 
 ,076 
 
 4 
 
 40 
 
 .2778 
 
 2 
 
 98 
 
 .6806 
 
 13. 
 
 156 
 
 ,083 
 
 5 
 
 41 
 
 .2847 
 
 3 
 
 99 
 
 .6875 
 
 1 
 
 157 
 
 09 
 
 6 
 
 42 
 
 .2917 
 
 4 
 
 100 
 
 .6944 
 
 2 
 
 158 
 
 .097 
 
 7 
 
 43 
 
 .2986 
 
 5 
 
 101 
 
 .7014 
 
 3 
 
 159 
 
 .104 
 
 8 
 
 44 
 
 .3056 
 
 6 
 
 102 
 
 .7083 
 
 4 
 
 160 
 
 .1 14 
 
 9 
 
 45 
 
 .3125 
 
 7 
 
 103 
 
 .7153 
 
 5 
 
 161 
 
 .ua 
 
 10 
 
 46 
 
 .3194 
 
 8 
 
 104 
 
 .7222 
 
 6 
 
 162 
 
 .125 
 
 11 
 4. 
 
 47 
 48 
 
 .3264 
 .3333 
 
 9 
 10 
 
 105 
 106 
 
 .7292 
 .7361 
 
 7 
 8 
 
 163 
 164 
 
 .13.? 
 . 1 3V 
 
 
 49 
 
 .3403 
 
 11 
 
 107 
 
 .7431 
 
 9 
 
 165 
 
 .146 
 
 2 
 
 50 
 
 .3472 
 
 9. 
 
 108 
 
 .75 
 
 10 
 
 166 
 
 .153 
 
 3 
 
 51 
 
 .3542 
 
 1 
 
 109 
 
 .7569 
 
 11 
 
 167 
 
 .159 
 
 4 
 
 52 
 
 .3611 
 
 2 
 
 110 
 
 .7639 
 
 14. 
 
 168 
 
 .167 
 
 5 
 
 53 
 
 .3681 
 
 3 
 
 111 
 
 .7708 
 
 1 
 
 169 
 
 .174 
 
 6 
 
 54 
 
 .375 
 
 4 
 
 112 
 
 .7778 
 
 2 
 
 170 
 
 .181 
 
 7 
 
 55 
 
 .3819 
 
 5 
 
 113 
 
 .7847 
 
 3 
 
 171 
 
 .188 
 
 8 
 
 56 
 
 .3889 
 
 6 
 
 114 
 
 .7917 
 
 4 
 
 172 
 
 .194 
 
 9 
 
 57 
 
 .3958 
 
 7 
 
 115 
 
 .7986 
 
 5 
 
 173 
 
 .201 
 
 10 
 
 58 
 
 .4028 
 
 8 
 
 116 
 
 .8056 
 
 6 
 
 174 
 
 .208 
 
 It 
 
 59 
 
 .4097 
 
 9 
 
 117 
 
 .8125 
 
 7 
 
 175 
 
 .215 
 
 5. 
 
 60 
 
 .4167 
 
 10 
 
 118 
 
 .8194 
 
 8 
 
 176 
 
 .222 
 
 
 61 
 
 .4236 
 
 11 
 
 119 
 
 .8264 
 
 9 
 
 177 
 
 .229 
 
 2 
 
 62 
 
 .4306 
 
 10. 
 
 120 
 
 .8333 
 
 10 
 
 178 
 
 .236 
 
 3 
 
 63 
 
 .4375 
 
 
 121 
 
 .8403 
 
 11 
 
 179 
 
 .243 
 
 4 
 
 64 
 
 .4444 
 
 2 
 
 122 
 
 .8472 
 
 15. 
 
 180 
 
 .25 
 
 5 
 
 65 
 
 .4514 
 
 3 
 
 123 
 
 .8542 
 
 
 181 
 
 .257 
 
 6 
 
 66 
 
 .4583 
 
 4 
 
 124 
 
 .8611 
 
 2 
 
 182 
 
 .264 
 
 7 
 
 67 
 
 .4653 
 
 5 
 
 125 
 
 .8681 
 
 3 
 
 183 
 
 .271 
 
 8 
 
 68 
 
 .4722 
 
 6 
 
 126 
 
 .875 
 
 4 
 
 184 
 
 .278 
 
 9 
 
 69 
 
 .4792 
 
 7 
 
 127 
 
 .8819 
 
 5 
 
 185 
 
 .285 
 
 10 
 
 70 
 
 .4861 
 
 8 
 
 128 
 
 .8889 
 
 6 
 
 186 
 
 .292 
 
 11 
 
 71 
 
 .4931 
 
 9 
 
 129 
 
 .8958 
 
 7 
 
 187 
 
 .299 
 
 8. 
 
 72 
 
 .5 
 
 10 
 
 130 
 
 .9028 
 
 8 
 
 188 
 
 .306 
 
 1 
 
 73 
 
 .5069 
 
 11 
 
 131 
 
 .9097 
 
 9 
 
 189 
 
 .313 
 
 2 
 
 74 
 
 .5139 
 
 11. 
 
 132 
 
 .9167 
 
 10 
 
 190 
 
 .319 
 
 3 
 
 75 
 
 .5208 
 
 
 133 
 
 .9236 
 
 11 
 
 191 
 
 .326 
 
 4 
 
 76 
 
 .5278 
 
 2 
 
 134 
 
 .9306 
 
 16. 
 
 192 
 
 .333 
 
 5 
 
 77 
 
 .5347 
 
 3 
 
 135 
 
 .9375 
 
 1 
 
 193 
 
 .34 
 
 6 
 
 78 
 
 .5417 
 
 4 
 
 136 
 
 .9444 
 
 2 
 
 194 
 
 .347 
 
 7 
 
 79 
 
 .5486 
 
 5 
 
 137 
 
 .9514 
 
 3 
 
 195 
 
 .354 
 
 8 
 
 80 
 
 .5556 
 
 6 
 
 138 
 
 .9583 
 
 4 
 
 196 
 
 .361 
 
 9 
 
 81 
 
 .5625 
 
 7 
 
 139 
 
 .9653 
 
 5 
 
 197 
 
 .368 
 
 10 
 
 82 
 
 .5694 
 
 8 
 
 140 
 
 .9722 
 
 6 
 
 198 
 
 .375 
 
 11 
 
 83 
 
 .5764 
 
 9 
 
 141 
 
 .9792 
 
 7 
 
 199 
 
 .382 
 
 7. 
 
 84 
 
 .5834 
 
 10 
 
 142 
 
 .9861 
 
 8 
 
 200 
 
 .389 
 
 
 85 
 
 .5903 
 
 11 
 
 143 
 
 .9931 
 
 9 
 
 201 
 
 .396 
 
 2 
 
 86 
 
 .5972 
 
 12. 
 
 144 
 
 .000 
 
 10 
 
 202 
 
 .403 
 
 3 
 
 87 
 
 .6042 
 
 
 145 
 
 .007 
 
 11 
 
 203 
 
 .41 
 
 4 
 
 88 
 
 .6111 
 
 2 
 
 146 
 
 .014 
 
 17. 
 
 204 
 
 .417 
 
 5 
 
 89 
 
 .6181 
 
 3 
 
 147 
 
 .021 
 
 1 
 
 205 
 
 .424 
 
 6 
 
 90 
 
 .625 
 
 4 
 
 148 
 
 .028 
 
 2 
 
 206 
 
 .431 
 
 7 
 
 91 
 
 .6319 
 
 5 
 
 149 
 
 .035 
 
 3 
 
 207 
 
 .438 
 
 8 
 
 92 
 
 .6389 
 
 6 
 
 150 
 
 1.042 
 
 4 
 
 208 
 
 .444 
 
 9 
 
 93 
 
 .6458 
 
 7 
 
 151 
 
 1.049 
 
 5 
 
 209 
 
 K451 
 
NUMBER OF SQUARE FEET IN PLATES. 
 
 120 
 
 SQUARE FEET IN PLATES. Continued. 
 
 Ft. and 
 Ins. 
 Long. 
 
 Ins. 
 Long. 
 
 Square 
 Feet. 
 
 Ft. and 
 Ins. 
 Long. 
 
 Ins. 
 Long. 
 
 Square 
 Feet. 
 
 Ft. and 
 Ins.. 
 Long. 
 
 Ins. 
 Long 
 
 Square 
 Feet. 
 
 17. 6 
 
 210 
 
 1.458 
 
 22. 5 
 
 269 
 
 1.868 
 
 27. 4 
 
 328 
 
 2.278 
 
 7 
 
 211 
 
 1.465 
 
 6 
 
 270 
 
 1.875 
 
 5 
 
 329 
 
 2.285 
 
 8 
 
 212 
 
 1.472 
 
 7 
 
 271 
 
 1.882 
 
 6 
 
 330 
 
 2.292 
 
 9 
 
 213 
 
 1.479 
 
 8 
 
 272 
 
 1.889 
 
 7 
 
 331 
 
 2.299 
 
 10 
 
 214 
 
 1.486 
 
 9 
 
 273 
 
 1.896 
 
 8 
 
 332 
 
 2.306 
 
 11 
 
 215 
 
 1.493 
 
 10 
 
 274 
 
 1.903 
 
 9 
 
 333 
 
 2.313 
 
 18. 
 
 216. 
 
 1.5 
 
 11 
 
 275 
 
 1.91 
 
 10 
 
 334 
 
 2.319 
 
 
 217 
 
 1.507 
 
 23. 
 
 276 
 
 1.917 
 
 11 
 
 335 
 
 2.326 
 
 2 
 
 218 
 
 1.514 
 
 
 277 
 
 1.924 
 
 28. 
 
 336 
 
 2.333 
 
 3 
 
 219 
 
 1.521 
 
 2 
 
 278. 
 
 1.931 
 
 1 
 
 337 
 
 2.34 
 
 4 
 
 220 
 
 1.528 
 
 3 
 
 279 
 
 1.938 
 
 2 
 
 338 
 
 2.347 
 
 5 
 
 221 
 
 1.535 
 
 4 
 
 280 
 
 1.944 
 
 3 
 
 339 
 
 2.354 
 
 6 
 
 222 
 
 1.542 
 
 5 
 
 281 
 
 1.951 
 
 4 
 
 340 
 
 2.361 
 
 7 
 
 223 
 
 1.549 
 
 6 
 
 282 
 
 1.958 
 
 5 
 
 341 
 
 2.368 
 
 8 
 
 224 
 
 1.556 
 
 7 
 
 283 
 
 1.965 
 
 6 
 
 342 
 
 2.375 
 
 9 
 
 225 
 
 1.563 
 
 8 
 
 284 
 
 1.972 
 
 7 
 
 343 
 
 2.382 
 
 10 
 
 226 
 
 1.569 
 
 9 
 
 285 
 
 1.979 
 
 8 
 
 344 
 
 2.389 
 
 11 
 
 227 
 
 1.576 
 
 10 
 
 286 
 
 1.986 
 
 9 
 
 345 
 
 2.396 
 
 19. 
 
 228 
 
 1.583 
 
 11 
 
 287 
 
 1.993 
 
 10 
 
 346 
 
 2.403 
 
 
 229 
 
 1.59 
 
 24. 
 
 288 
 
 2. 
 
 11 
 
 347 
 
 2.41 
 
 2 
 
 230 
 
 1.597 
 
 1 
 
 289 
 
 2.007 
 
 29. 
 
 348 
 
 2.417 
 
 3 
 
 231 
 
 1.604 
 
 2 
 
 290 
 
 2.014 
 
 
 349 
 
 2.424 
 
 4 
 
 232 
 
 1.611 
 
 3 
 
 291" 
 
 2.021 
 
 2 
 
 350 
 
 2.431 
 
 5 
 
 233 
 
 1.618 
 
 4 
 
 292 
 
 2.028 
 
 3 
 
 351 
 
 2.438 
 
 6 
 
 234 
 
 1.625 
 
 5 
 
 293 
 
 2.035 
 
 4 
 
 352 
 
 2.444 
 
 7 
 
 235 
 
 1.632 
 
 6 
 
 294 
 
 2'.042 
 
 5 
 
 353 
 
 2.451 
 
 8 
 
 236 
 
 1.639 
 
 7 
 
 295 
 
 2.049 
 
 6 
 
 354 
 
 2.458 
 
 9 
 
 237 
 
 1.645 
 
 8 
 
 296 
 
 2.056 
 
 7 
 
 355 
 
 2.465 
 
 10 
 
 238 
 
 1.653 
 
 9 
 
 297 
 
 2.063 
 
 8 
 
 356 
 
 2.472 
 
 11 
 
 239 
 
 1 .659 
 
 10 
 
 298 
 
 2.069 
 
 9 
 
 357 
 
 2.479 
 
 20. 
 
 240 
 
 1.667 
 
 11 
 
 299 
 
 2.076 
 
 10 
 
 358 
 
 2.486 
 
 
 241 
 
 1.674 
 
 25. 
 
 300 
 
 *2.083 
 
 11 
 
 359 
 
 2.493 
 
 2 
 
 242 
 
 1.681 
 
 1 
 
 301 
 
 2.09 
 
 30. 
 
 360 
 
 2.5 
 
 3 
 
 243 
 
 1.688 
 
 2 
 
 302 
 
 2.097 
 
 1 
 
 361 
 
 2.507 
 
 4 
 
 244 
 
 1.694 
 
 3 
 
 303 
 
 2.104 
 
 2 
 
 362 
 
 2.514 
 
 5 
 
 245 
 
 1.701 
 
 4 
 
 304 
 
 2.111 
 
 3 
 
 363 
 
 2.521 
 
 6 
 
 246 
 
 1.708 
 
 5 
 
 305 
 
 2.118 
 
 4 
 
 364 
 
 2.528 
 
 7 
 
 247 
 
 1.715 
 
 6 
 
 306 
 
 2.125 
 
 5 
 
 365 
 
 2.535 
 
 8 
 
 248 
 
 1.722 
 
 7 
 
 307 
 
 2.132 
 
 6 
 
 366 
 
 2.542 
 
 9 
 
 249 
 
 1.729 
 
 8 
 
 308 
 
 2.139 
 
 7 
 
 367 
 
 2.549 
 
 10 
 
 250 
 
 1.736 
 
 9 
 
 309 
 
 2.146 
 
 8 
 
 368 
 
 2.556 
 
 II 
 
 251 
 
 1.743 
 
 10 
 
 310 
 
 2.153 
 
 9 
 
 369 
 
 2.563 
 
 21. 
 
 252 
 
 1.75 
 
 11 
 
 311 
 
 2.16 
 
 10 
 
 370 
 
 2.569 
 
 
 253 
 
 1.757 
 
 26. 
 
 312 
 
 2.167 
 
 11 
 
 371 
 
 2.576 
 
 2 
 
 254 
 
 1.764 
 
 
 313 
 
 2.174 
 
 31. 
 
 372 
 
 2.583 
 
 3 
 
 255 
 
 1.771 
 
 2 
 
 314 
 
 2.18V 
 
 
 373 
 
 2.59 
 
 4 
 
 256 
 
 1.778 
 
 3 
 
 315 
 
 2.188 
 
 2 
 
 374 
 
 2.597 
 
 5 
 
 257 
 
 1.785 
 
 4 
 
 316 
 
 2.194 
 
 3 
 
 375 
 
 2.604 
 
 6 
 
 258 
 
 1.792 
 
 5 
 
 317 
 
 2.201 
 
 4 
 
 376 
 
 2.611 
 
 7 
 
 259 
 
 1.799 
 
 6 
 
 318 
 
 2.208 
 
 5 
 
 377 
 
 2.618 
 
 8 
 
 260 
 
 1.806 
 
 7 
 
 319 
 
 2.215 
 
 6 
 
 378 
 
 2.625 
 
 9 
 
 261 
 
 1.813 
 
 8 
 
 320 
 
 2.222 
 
 7 
 
 379 
 
 2.632 
 
 10 
 
 262 
 
 1.819 
 
 9 
 
 321 
 
 2.229 
 
 8 
 
 380 
 
 2.639 
 
 11 
 
 263 
 
 1.826 
 
 10 
 
 322 
 
 2.236 
 
 9 
 
 381 
 
 2.646 
 
 23.0 
 
 264 
 
 1.833 
 
 11 
 
 323 
 
 2.243 
 
 10 
 
 382 
 
 2.653 
 
 1 
 
 265 
 
 1.84 
 
 27. 
 
 324 
 
 2.25 
 
 11 
 
 383 
 
 2.66 
 
 2 
 
 266 
 
 1.847 
 
 
 325 
 
 2.257 
 
 32. 
 
 384 
 
 2.667 
 
 3 
 
 267 
 
 1.854 
 
 2 
 
 326 
 
 2.264 
 
 1 
 
 385 
 
 2.674 
 
 4 
 
 268 
 
 1.861 
 
 3 
 
 327 
 
 2.271 
 
 2 
 
 386 
 
 2.681 
 
130 
 
 MATHEMATICAL TABLES. 
 
 GALLONS AND CUBIC FEET, 
 
 United States Gallons in a given Number of Cubic Feet. 
 
 1 cubic foot = 7. 4805 19 U.S. gallons; 1 gallon = 231 cu.ir . = 0.13368056cu. ft. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 0.1 
 
 0.75 
 
 50 
 
 374.0 
 
 8,000 
 
 59,844.2 
 
 0.2 
 
 1.50 
 
 60 
 
 448.8 
 
 9,000 
 
 67,324.7 
 
 0.3 
 
 2.24 
 
 70 
 
 523.6 
 
 10,000 
 
 74,805.2 
 
 0.4 
 
 2.99 
 
 80 
 
 598.4 
 
 20,000 
 
 . 149,610.4 
 
 0.5 
 
 3.74 
 
 90 
 
 673.2 
 
 30,000 
 
 224,415.6 
 
 0.6 
 
 4.49 
 
 100 
 
 748.0 
 
 40,000 
 
 299,220.8 
 
 0.7 
 
 5.24 
 
 200 
 
 1,496.1 
 
 50,000 
 
 374,025.9 
 
 0.8 
 
 5.98 
 
 300 
 
 2,244.2 
 
 60,000 
 
 448,831.1 
 
 0.9 
 
 6.73 
 
 400 
 
 2,992.2 
 
 70,000 
 
 523,636.3 
 
 1 
 
 7.48 
 
 500 
 
 3,740.3 
 
 80,000 
 
 598,441.5 
 
 2 
 
 14.96 
 
 600 
 
 4,488.3 
 
 90,000 
 
 673,246. 
 
 3 
 
 22.44 
 
 700 
 
 5,236.4 
 
 100,000 
 
 748,051.9 
 
 4 
 
 29.92 
 
 800 
 
 5,984.4 
 
 200,000 
 
 1,496,103.8 
 
 5 
 
 37.40 
 
 900 
 
 6,732.5 
 
 300,000 
 
 2,244,155.7 
 
 6 
 
 44.88 
 
 1,000 
 
 7,480.5 
 
 400,000 
 
 2,992,207.6 
 
 7 
 
 52.36 
 
 2,000 
 
 14,961.0 
 
 500,000 
 
 3,740,259.5 
 
 8 
 
 59.84 
 
 3,000 
 
 22,441.6 
 
 600,000 
 
 4,488,311.4 
 
 9 
 
 67.32 
 
 4,000 
 
 29,922.1 
 
 700,000 
 
 5,236,363.3 
 
 10 
 
 74.80 
 
 5,000 
 
 37,402.6 
 
 800 000 
 
 5,984,415.2 
 
 20 
 
 149.6 
 
 6,000 
 
 44,883.1 
 
 900,000 
 
 6,732,467.1 
 
 30 
 
 224.4 
 
 7,000 
 
 52,363.6 
 
 1,000,000 
 
 7,480,519.0 
 
 40 
 
 299.2 
 
 
 
 
 
 Cubic Feet in a given Number of Gallons. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 1 
 2 
 
 .134 
 .267 
 
 1,000 
 2,000 
 
 133.681 
 267.361 
 
 1,000,000 
 2,000,000 
 
 133,680.6 
 267,361.1 
 
 3 
 
 .401 
 
 3,000 
 
 401.042 
 
 3,000,000 
 
 401,041.7 
 
 4 
 
 .535 
 
 4,000 
 
 534.722 
 
 4,000,000 
 
 534,722.2 
 
 5 
 
 .668 
 
 5,000 
 
 668.403 
 
 5,000,000 
 
 668,402.8 
 
 6 
 
 .802 
 
 6,000 
 
 802.083 
 
 6,000,000 
 
 802,083.3 
 
 7 
 
 .936 
 
 7,000 
 
 935.764 
 
 7,000,000 
 
 935,763.9 
 
 8 
 
 1.069 
 
 ' 8,000 
 
 1,069.444 
 
 8,000,000 
 
 1,069,444.4 
 
 9 
 
 1.203 
 
 9,000 
 
 1,203.125 
 
 9,000,000 
 
 1,203,125.0 
 
 10 
 
 1.337 
 
 10,000 
 
 1,336.806 
 
 10,000,000 
 
 1,336,805.6 
 
 Cubic Feet per Second, Gallons in 24 hours, etc. 
 
 1/60 I 1.5472 2.2800 
 
 1 60 92.834 133.681 
 
 7.480519 448.83 694.444 1,000. 
 
 10,771.95 646,317 1,000,000 1,440,000 
 
 62.355 3741.3 5788.66 8335.65 
 
 Cu. ft. per sec. 
 Cu. ft. per min. 
 U. S* Gals, per min. 
 
 " " " 24 hrs. 
 Pounds of water ) 
 (at 62 F.) per min. J 
 
 The gallon 'is a troublesome and unnecessary measure. If hydraulic 
 engineers and pump manufacturers would stop using it, and use cubig 
 Jeet instead, many tedious calculations would be saved. 
 
CAPACITY OF CYLINDKICAL VESSELS. 
 
 131 
 
 CONTENTS IN CUBIC FEET AND U. S. GALLONS OF PIPES 
 
 AND CYLINDERS OF VARIOUS DIAMETERS AND ONE 
 
 FOOT IN LENGTH. 
 
 1 gallon = 231 cubic inches. 1 cubic foot = 7.4805 gallons. 
 
 
 For 1 Foot in 
 
 
 For 1 Foot in 
 
 
 For 1 Foot in 
 
 d 
 
 Length. 
 
 .S 
 
 Length. 
 
 d 
 
 Length. 
 
 5 as 
 
 
 0> 3? 
 
 
 fc 
 
 
 2 
 
 
 Cu.Ft. 
 
 U.S. 
 
 -t~ O 
 
 oj^j 
 Jo 
 
 Cu.Ft. 
 
 U.S. 
 
 S 2 
 
 d 
 
 Cu.Ft. 
 
 U.S. 
 
 c c 
 
 also 
 
 Gals., 
 
 d 
 
 also 
 
 Gals., 
 
 d d 
 
 also 
 
 Gals.. 
 
 Q 
 
 Area in 
 
 231 
 
 p 
 
 Area in 
 
 231 
 
 
 Area in 
 
 231 
 
 M 
 
 Sq.Ft. 
 
 Cu.In. 
 
 
 Sq.Ft. 
 
 Cu.In. 
 
 . 
 
 Sq.Ft. 
 
 Cu. In. 
 
 V4 
 
 .0003 
 
 .0025 
 
 63/ 4 
 
 .2485 
 
 1.859 
 
 19 
 
 1.969 
 
 14.73 
 
 5/16 
 
 .0005 
 
 .004 
 
 7 
 
 .2673 
 
 1.999 
 
 191/2 
 
 2074 
 
 15.51 
 
 3/8 
 
 .0008 
 
 .0057 
 
 7V4 
 
 .2867 
 
 2.145 
 
 20 
 
 2.182 
 
 16.32 
 
 7/16 
 
 .001 
 
 .0078 
 
 71/2 
 
 .3068 
 
 2.295 
 
 201/2 
 
 2.292 
 
 17.15 
 
 1/2 
 
 .0014 
 
 .0102 
 
 73/4 
 
 .3276 
 
 2.45 
 
 21 
 
 2.405 
 
 17.99 
 
 9/16 
 
 .0017 
 
 .0129 
 
 8 
 
 .3491 
 
 2.611 
 
 2U/2 
 
 2.521 
 
 18.86 
 
 5/8 
 
 .0021 
 
 .0159 
 
 8l/ 4 
 
 .3712 
 
 2.777 
 
 22 
 
 2.640 
 
 19.75 
 
 11/16 
 
 .0026 
 
 ;0193 
 
 81/2 
 
 .3941 
 
 2.948 
 
 221/2 
 
 2.761 
 
 20.66 
 
 3/4 
 
 .0031 
 
 .0230 
 
 83/ 4 
 
 .4176 
 
 3.125 
 
 23 
 
 2.885 
 
 21.58 
 
 /16 
 
 .0036 
 
 .0269 
 
 9 
 
 .4418 
 
 3.305 
 
 231/2 
 
 3.012 
 
 22.53 
 
 7/8 
 
 .0042 
 
 .0312 
 
 91/4 
 
 .4667 
 
 3.491 
 
 24 
 
 3.142 
 
 23.50 
 
 15/16 
 
 .0048 
 
 .0359 
 
 91/2 
 
 .4922 
 
 3.682 
 
 25 
 
 3.409 
 
 25.50 
 
 1 
 
 .0055 
 
 .0408 
 
 93/4 
 
 .5185 
 
 3.879 
 
 26 
 
 3.687 
 
 27.58 
 
 U/4 
 
 .0085 
 
 .0638 
 
 10 
 
 .5454 
 
 4.08 
 
 27 
 
 3.976 
 
 29.74 
 
 U/2 
 
 .0123 
 
 .0918 
 
 101/4 
 
 .5730 
 
 4.286 
 
 28 
 
 4.276 
 
 31.99 
 
 13/4 
 
 .0167 
 
 .1249 
 
 101/2 
 
 .6013 
 
 4.498 
 
 29 
 
 4.587 
 
 34.31 
 
 2 
 
 .0218 
 
 .1632 
 
 103/4 
 
 .6303 
 
 4.715 
 
 30 
 
 4.909 
 
 36.72 
 
 2V4 - 
 
 .0276 
 
 .2066 
 
 11 
 
 .66 
 
 4.937 
 
 31 
 
 5.241 
 
 39.21 
 
 21/2 
 
 .0341 
 
 .2550 
 
 111/4 
 
 .6903 
 
 5.164 
 
 32 
 
 5.585 
 
 41.78 
 
 23/4 
 
 .0412 
 
 .3085 
 
 111/ 2 
 
 .7213 
 
 5.396 
 
 33 
 
 5.940 
 
 44.43 
 
 3 
 
 .0491 
 
 .3672 
 
 113/4 
 
 .7530 
 
 5.633 
 
 34 
 
 6.305 
 
 47.16 
 
 31/4 
 
 .0576 
 
 .4309 
 
 12 
 
 .7854 
 
 5.875 
 
 35 
 
 6.681 
 
 49.98 
 
 31/2 
 
 .0668 
 
 .4998 
 
 121/2 
 
 .8522 
 
 6.375 
 
 36 
 
 7.069 
 
 52.88 
 
 33/4 
 
 .0767 
 
 .5738 
 
 13 
 
 .9218 
 
 6.895 
 
 37 
 
 7.467 
 
 55.86 
 
 4 
 
 .0873 
 
 .6528 
 
 13V 2 
 
 .994 
 
 7.436 
 
 38 
 
 7.876 
 
 58.92 
 
 41/4 
 
 .0985 
 
 .7369 
 
 14 
 
 1.069 
 
 7.997 
 
 39 
 
 8.296 
 
 62.06 
 
 4V2 
 
 .1104 
 
 .8263 
 
 141/2 
 
 1.147 
 
 8.578 
 
 40 
 
 8.727 
 
 65.28 
 
 43/4 
 
 .1231 
 
 .9206 
 
 15 
 
 1.227 
 
 9.180 
 
 41 
 
 9.168 
 
 68.58 
 
 5 
 
 .1364 
 
 .020 
 
 15l/ 2 
 
 1.310 
 
 9.801 
 
 42 
 
 9.621 
 
 71.97 
 
 5V4 
 
 .1503 
 
 .125 
 
 16 
 
 1.396 
 
 10.44 
 
 43 
 
 10.085 
 
 75.44 
 
 5i/ 2 
 
 .1650 
 
 .234 
 
 161/2 
 
 .485 
 
 11.11 
 
 44 
 
 10.559 
 
 78.99 
 
 53/4 
 
 .1803 
 
 .349 
 
 17 
 
 .576 
 
 11.79 
 
 45 
 
 11.045 
 
 82.62 
 
 6 
 
 .1963 
 
 .469 
 
 171/2 
 
 .670 
 
 12.49 
 
 46 
 
 11.541 
 
 86.33 
 
 61/ 4 
 
 .2131 
 
 .594 
 
 18 
 
 .768 
 
 13.22 
 
 47 
 
 12.048 
 
 90.10 
 
 61/2 
 
 .2304 
 
 .724 
 
 18l/ 2 
 
 .867 
 
 13.96 
 
 48 
 
 12.566 
 
 94.00 
 
 To^find the capacity of pipes greater than the largest given in the table, 
 
 aer n any o z, 
 
 in cubic feet by 621/4 or the gallons by 8 1/3, or, if a closer approximation is 
 required, by the weight of a cubic foot of water at the actual temperature 
 in the pipe. 
 
 Given the dimensions of a cylinder in inches, to find its capacity in U. 8. 
 gallons: Square the diameter, multiply by the length and by 0.0034. If d= 
 
 diameter, I - length, gallons- d * X ^ 54 X * - 0.0034 & 1. If D and L are 
 in feet, gallons - 5.875 D*L. 
 
.132 
 
 MATHEMATICAL TABLES. 
 
 CYLINDRICAL, VESSELS, TANKS, CISTERNS, ETC. 
 
 Diameter In Feet and Inches, Area in Square Feet, and U. S, 
 Gallons Capacity for One Foot in Depth. 
 
 1 gallon = 231 cubic inches = 
 
 1 cubic foot 
 
 7.4805 
 
 ' 0.13368 cubic feet. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 Ft. In. 
 
 Sq.ft. 
 
 1 foot 
 depth. 
 
 Ft. In. 
 
 Sq. ft. 
 
 1 foot 
 depth. 
 
 Ft. In. 
 
 Sq.ft. 
 
 1 foot 
 depth. 
 
 1 
 
 .785 
 
 5.87 
 
 5 8 
 
 25.22 
 
 188 .66 
 
 19 
 
 283 .53 
 
 2120.9 
 
 1 
 
 .922 
 
 6.89 
 
 5 9 
 
 25.97 
 
 194.25 
 
 19 3 
 
 291.04 
 
 2177.1 
 
 2 
 
 .069 
 
 8.00 
 
 510 
 
 26.73 
 
 199.92 
 
 19 6 
 
 298.65 
 
 2234.0 
 
 3 
 
 .227 
 
 9.18 
 
 5 11 
 
 27.49 
 
 205.67 
 
 19 9 
 
 306.35 
 
 2291.7 
 
 A 
 
 .396 
 
 10.44 
 
 6 
 
 28.27 
 
 211.51 
 
 20 
 
 314.16 
 
 2350.1 
 
 5 
 
 .576 
 
 11.79 
 
 6 3 
 
 30.68 
 
 229.50 
 
 20 3 
 
 322.06 
 
 2409.2 
 
 6 
 
 .767 
 
 13.22 
 
 6 6 
 
 33.18 
 
 248.23 
 
 20 6 
 
 330.C6 
 
 2469.1 
 
 7 
 
 .969 
 
 14.73 
 
 6 9 
 
 35.78 
 
 267.69 
 
 20 9 
 
 338.16 
 
 2529,6 
 
 8 
 
 2.182 
 
 16.32 
 
 7 
 
 38.48 
 
 287.88 
 
 21 
 
 346.36 
 
 2591.0 
 
 9 
 
 2.405 
 
 17.99 
 
 7 3 
 
 41.28 
 
 308.81 
 
 21 3 
 
 354.66 
 
 2653.0 
 
 10 
 
 2.640 
 
 19.75 
 
 7 6 
 
 44.18 
 
 330.48 
 
 21 6 
 
 363.05 
 
 2715.8 
 
 11 
 
 2.885 
 
 21.58 
 
 7 9 
 
 47.17 
 
 352.88 
 
 21 9 
 
 371.54 
 
 2779.3 
 
 
 3.142 
 
 23.50 
 
 8 
 
 50.27 
 
 376.01 
 
 22 
 
 380.13 
 
 2843.6 
 
 1 
 
 3.409 
 
 25.50 
 
 8 3 
 
 53.46 
 
 399.88 
 
 22 3 
 
 388.82 
 
 2908.6 
 
 2 2 
 
 3.687 
 
 27.58 
 
 8 6 
 
 56.75 
 
 424.48 
 
 22 6 
 
 397.61 
 
 2974.3 
 
 2 3 
 
 3.976 
 
 29.74 
 
 8 9 
 
 60.13 
 
 449.82 
 
 22 9 
 
 406.49 
 
 3040.8 
 
 2 4 
 
 4.276 
 
 31.99 
 
 9 
 
 63.62 
 
 475.89 
 
 23 
 
 415.48 
 
 3108.0 
 
 2 5 
 
 4.587 
 
 34.31 
 
 9 3 
 
 67.20 
 
 502.70 
 
 23 3 
 
 424.56 
 
 3175.9 
 
 2 6 
 
 4.909 
 
 36.72 
 
 9 6 
 
 70.88 
 
 530.24 
 
 23 6 
 
 433.74 
 
 3244.6 
 
 2 7 
 
 5.241 
 
 39.21 
 
 9 9 
 
 74.66 
 
 558.51 
 
 23 9 
 
 443.01 
 
 3314.0 
 
 2 8 
 
 5.585 
 
 41.78 
 
 10 
 
 78.54 
 
 587.52 
 
 24 
 
 452.39 
 
 3384.1 
 
 2 9 
 
 5.940 
 
 44.43 
 
 10 3 
 
 82.52 
 
 617.26 
 
 24 3 
 
 461.86 
 
 3455.0 
 
 2 10 
 
 6.305 
 
 47.16 
 
 10- 6 
 
 86.59 
 
 647.74 
 
 24 6 
 
 471.44 
 
 3526.6 
 
 2 11 
 
 6.681 
 
 49.98 
 
 10 9 
 
 90.76 
 
 678.95 
 
 24 9 
 
 481.11 
 
 3598.9 
 
 3 
 
 7.069 
 
 52.88 
 
 11 
 
 95.03 
 
 710.90 
 
 25 
 
 490.87 
 
 3672.0 
 
 1 
 
 7.467 
 
 55.86 
 
 11 3 
 
 99.40 
 
 743.58 
 
 25 3 
 
 500.74 
 
 3745.8 
 
 2 
 
 7.876 
 
 58.92 
 
 11 6 
 
 103.87 
 
 776.99 
 
 25 6 
 
 510.71 
 
 3820.3 
 
 3 
 
 8.296 
 
 62.06 
 
 11 9 
 
 108.43 
 
 811.14 
 
 25 9 
 
 520.77 
 
 3895.6 
 
 A 
 
 8.727 
 
 65.28 
 
 12 
 
 113.10 
 
 846.03 
 
 26 
 
 530.93 
 
 3971.6 
 
 5 
 
 9.168 
 
 68.58 
 
 12 3 
 
 117.86 
 
 881.65 
 
 26 3 
 
 541.19 
 
 4048.4 
 
 6 
 
 9.621 
 
 71.97 
 
 12 6 
 
 122.72 
 
 918.00 
 
 26 6 
 
 551.55 
 
 4125.9 
 
 7 
 
 10.085 
 
 75.44 
 
 12 9 
 
 127.68 
 
 955.09 
 
 26 9 
 
 562.00 
 
 4204. 1 
 
 8 
 
 10.559 
 
 78.99 
 
 13 
 
 132.73 
 
 992.91 
 
 27 
 
 572.56 
 
 4283.0 
 
 9 
 
 1 1 .045 
 
 82.62 
 
 13 3 
 
 137.89 
 
 1031.5 
 
 27 3 
 
 583.21 
 
 4362.7 
 
 10 
 
 11.541 
 
 86.33 
 
 13 6 
 
 143.14 
 
 1070.8 
 
 27 6 
 
 593.96 
 
 4443.1 
 
 11 
 
 12.048 
 
 90.13 
 
 13 9 
 
 1 48.49 
 
 1110.8 
 
 27 9 
 
 604.81 
 
 4524.3 
 
 
 12.566 
 
 94.00 
 
 14 
 
 153.94 
 
 1151.5 
 
 28 
 
 615.75 
 
 4606.2 
 
 1 
 
 13.095 
 
 97.96 
 
 14 3 
 
 159.48 
 
 1193.0 
 
 28 3 
 
 626.80 
 
 4688.8 
 
 2 
 
 13.635 
 
 102.00 
 
 14 6 
 
 165.13 
 
 1235.3 
 
 28 6 
 
 637.94 
 
 4772.1 
 
 3 
 
 14.186 
 
 106.12 
 
 14 9 
 
 170.87 
 
 1278.2 
 
 28 9 
 
 649.18 
 
 4856.2 
 
 4 
 
 14.748 
 
 110.32 
 
 15 
 
 176.71 
 
 1321.9 
 
 29 
 
 660.52 
 
 4941.0 
 
 5 
 
 15.321 
 
 114.61 
 
 15 3 
 
 182.65 
 
 1366.4 
 
 29 3 
 
 67 1 .96 
 
 5026.6 
 
 6 
 
 15.90 
 
 118.97 
 
 15 6 
 
 188.69 
 
 1411.5 
 
 29 6 
 
 683.49 
 
 5112.9 
 
 7 
 
 16.50 
 
 123.42 
 
 15 9 
 
 194.83 
 
 1457.4 
 
 29 9 
 
 695.13 
 
 5199.9 
 
 8 
 
 17.10 
 
 127.95 
 
 16 
 
 201.06 
 
 1504.1 
 
 30 
 
 706.86 
 
 5287.7 
 
 9 
 
 17.72 
 
 132.56 
 
 46 3 
 
 207.39 
 
 1551.4 
 
 30 3 
 
 718.69 
 
 5376.2 
 
 10 
 
 18.35 
 
 137.25 
 
 16 6 
 
 213.82 
 
 1 599.5 
 
 30 6 
 
 730.62 
 
 5465.4 
 
 11 
 
 18.99 
 
 142.02 
 
 16 9 
 
 220.35 
 
 1648.4 
 
 30 9 
 
 742.64 
 
 5555.4 
 
 
 19.63 
 
 146.88 
 
 17 
 
 226.98 
 
 1697.9 
 
 31 
 
 754.77 
 
 5646.1 
 
 1 
 
 20.29 
 
 151.82 
 
 17 3 
 
 233.71 
 
 1748.2 
 
 31 3 
 
 766.99 
 
 5737.5 
 
 2 
 
 20.97 
 
 156.83 
 
 17 6 
 
 240.53 
 
 1799.3 
 
 31 6 
 
 779.31 
 
 5829.7 
 
 3 
 
 21.65 
 
 161.93 
 
 17 9 
 
 247.45 
 
 1851.1 
 
 31 9 
 
 791.73 
 
 5922.6 
 
 4 
 
 22.34 
 
 167.12 
 
 18 
 
 254.47 
 
 1903.6 
 
 32 
 
 804.25 
 
 6016.2 
 
 5 
 
 23.04 
 
 172.38 
 
 18 3 
 
 261.59 
 
 1956.8 
 
 32 3 
 
 816.86 
 
 6110.6 
 
 6 
 
 23.76 
 
 177. ,72 
 
 18 6 
 
 268.80 
 
 2010.8 
 
 32 6 
 
 829.58 
 
 6205.7 
 
 7 
 
 24.48 
 
 183.15 
 
 18 9 
 
 276.12 
 
 2065.5 
 
 32 9 
 
 842.39 
 
 6301.5 
 
CAPACITIES OF RECTANGULAR TANKS. 
 
 133 
 
 CAPACITIES OF RECTANGULAR TANKS IN U. S. 
 GALLONS, FOB EACH FOOT IN DEPTH. 
 
 1 cubic foot =- 7.4805 U. S. gallons 
 
 Vidth 
 of 
 Fank. 
 
 Length of Tank. 
 
 feet. 
 
 2 
 
 ft. in. 
 2 6 
 
 feet. 
 3 
 
 ft. in. 
 3 6 
 
 feet. 
 4 
 
 ft. in. 
 4 6 
 
 feet. 
 5 
 
 ft. in. 
 5 6 
 
 feet. 
 6 
 
 ft. in. 
 6 6 
 
 feet. 
 7 
 
 t. in. 
 2 6 
 
 3 6 
 4 
 
 4 6 
 
 5 6 
 6 
 6 6 
 
 7 
 
 29.92 
 
 37.40 
 46.75 
 
 44.88 
 56.10 
 67.32 
 
 52.36 
 65.45 
 78.54 
 91.64 
 
 59.84 
 74.80 
 89.77 
 104.73 
 119.69 
 
 67.32 
 84.16 
 1 00.99 
 117.82 
 134.65 
 
 151.48 
 
 74.81 
 93.51 
 112.21 
 130.91 
 149.61 
 
 168.31 
 187.01 
 
 82.29 
 102.86 
 123.43 
 144.00 
 164.57 
 
 185.14 
 205.71 
 226.28 
 
 89.77 
 112.21 
 134.65 
 157.09 
 179.53 
 
 201.97 
 224.41 
 246.86 
 269.30 
 
 97.25 
 121.56 
 145.87 
 170.18 
 194.49 
 
 218.80 
 243.11 
 267.43 
 291.74 
 316.05 
 
 104.73 
 130.91 
 157.09 
 183.27 
 209.45 
 
 235.62 
 261.82 
 288.00 
 314.18 
 340.36 
 
 366.54 
 
 
 ... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Width 
 of 
 Tank. 
 
 Length of Tank. 
 
 ft. in 
 7 6 
 
 feet. 
 8 
 
 ft. in. 
 8 6 
 
 feet. 
 9 
 
 ft. in 
 9 6 
 
 feet. 
 10 
 
 ft. in 
 10 6 
 
 feet. 
 11 
 
 ft. in 
 11 6 
 
 feet. 
 13 
 
 179.53 
 224.41 
 269.30 
 314.18 
 359.06 
 
 403.94 
 448.83 
 493. 7 1 
 538.59 
 583.47 
 
 628.36 
 673.24 
 718.12 
 763.00 
 807.89 
 
 852.77 
 897.66 
 942.56 
 987.43 
 1032.3 
 
 1077.2 
 
 ft. in 
 2 
 2 6 
 3 
 3 6 
 4 
 
 4 6 
 
 5 6 
 6 
 6 6 
 
 7 6 
 8 
 8 6 
 9 
 
 9 6 
 10 
 10 6 
 11 
 11 6 
 
 12 
 
 112.21 
 140.26 
 168.31 
 196.36 
 224.41 
 
 25247 
 280.52 
 308.57 
 336.62 
 364.67 
 
 392.72 
 420.78 
 
 119.69 
 149.61 
 179.53 
 209.45 
 239.37 
 
 269.30 
 299.22 
 329.14 
 359.06 
 388.98 
 
 418.91 
 448.83 
 478.75 
 
 127.17 
 158.96 
 190.75 
 222.54 
 254.34 
 
 286.13 
 317.92 
 349.71 
 381.50 
 413.30 
 
 445.09 
 476.88 
 508.67 
 540.46 
 
 134.65 
 168.31 
 202.97 
 235.63 
 269.30 
 
 302.96 
 336.62 
 370.28 
 403.94 
 437.60 
 
 471.27 
 504.93 
 538.59 
 572.25 
 605.92 
 
 142.13 
 177.66 
 213.19 
 248.73 
 284.26 
 
 319.79 
 355.32 
 390.85 
 426.39 
 461.92 
 
 497.45 
 532.98 
 568.51 
 604.05 
 639.58 
 
 675.11 
 
 149.61 
 187.01 
 224.41 
 261.82 
 299.22 
 
 336.62 
 374.03 
 411.43 
 448.83 
 486.23 
 
 523.64 
 561.04 
 598.44 
 635.84 
 673.25 
 
 710.65 
 748.05 
 
 157.09 
 196.36 
 235.63 
 274.90 
 314.18 
 
 353.45 
 392.72 
 432.00 
 471.27 
 510.54 
 
 549.81 
 589.08 
 628.36 
 667.63 
 706.90 
 
 746.17 
 
 785.45 
 824.73 
 
 164.57 
 205.71 
 246.86 
 288.00 
 329.14 
 
 370.28 
 411.43 
 452.57 
 493.71 
 534.85 
 
 575.99 
 617.14 
 658.28 
 699.42 
 740.56 
 
 781.71 
 822.86 
 864.00 
 905.14 
 
 172.05 
 215.06 
 258.07 
 301.09 
 344.10 
 
 387.11 
 430.13 
 473.14 
 516.15 
 559.16 
 
 602.18 
 645.19 
 688.20 
 731.21 
 774.23 
 
 817.24 
 860.26 
 903.26 
 946.27 
 989.29 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
134 
 
 MATHEMATICAL TABLES. 
 
 NUMBER OF BARRELS (31 1-3 GALLONS) IN 
 CISTERNS AND TANKS. 
 
 I barrel = 31^ gallons > 
 
 31.5X 231 
 1728 
 
 = 4.21094 cu. ft. Reciprocal -0.2 37 477 
 
 Diameter in Feet. 
 
 Feet. 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 13 
 
 13 
 
 14 
 
 , 
 
 4.663 
 
 6.714 
 
 9.139 
 
 11.937 
 
 15.108 
 
 18.652 , 
 
 >2.569 
 
 26.859 
 
 31.522 
 
 36.557 
 
 5 
 
 23.3 
 
 33.6 
 
 45.7 
 
 59.7 
 
 75.5 
 
 93.3 
 
 12.8 
 
 134.3 
 
 157.6 
 
 182.8 
 
 6 
 
 28.0 
 
 40.3 
 
 54.8 
 
 71.6 
 
 90.6 
 
 111.9 
 
 35.4 
 
 161.2 
 
 189.1 
 
 219.3 
 
 7 
 
 32.6 
 
 47.0 
 
 64.0 
 
 83.6 
 
 105.8 
 
 130.6 
 
 58.0 
 
 188.0 
 
 220.7 
 
 255.9 
 
 8 
 
 37.3 
 
 53.7 
 
 73.1 
 
 95.5 
 
 120.9 
 
 149.2 
 
 80.6 
 
 214.9 
 
 252.2 
 
 292.5 
 
 9 
 
 42.0 
 
 60.4 
 
 82.3 
 
 107.4 
 
 136.0 
 
 167.9 ; 
 
 >03.1 
 
 241.7 
 
 283.7 
 
 329.0 
 
 10 
 
 46.6 
 
 67.1 
 
 91.4 
 
 119.4 
 
 151.1 
 
 186.5 ; 
 
 Z25.7 
 
 268.6 
 
 315.2 
 
 365.6 
 
 11 
 
 51.3 
 
 73.9 
 
 100.5 
 
 131.3 
 
 166.2 
 
 205.2 ; 
 
 548.3 
 
 295.4 
 
 346.7 
 
 402.1 
 
 12 
 
 56.0 
 
 80.6 
 
 109.7 
 
 143.2 
 
 181.3 
 
 223.8 ; 
 
 570.8 
 
 322.3 
 
 378.3 
 
 438.7 
 
 13 
 
 60.6 
 
 87.3 
 
 118.8 
 
 155.2 
 
 196.4 
 
 242.5 : 
 
 593.4 
 
 349.2 
 
 409.8 
 
 475.2 
 
 14 
 
 65.3 
 
 94.0 
 
 127.9 
 
 167.1 
 
 211.5 
 
 261.1 I 
 
 16.0 
 
 376.0 
 
 44 K3 
 
 511.8 
 
 15 
 
 69.9 
 
 100.7 
 
 137.1 
 
 179.1 
 
 226.6 
 
 279.8 2 
 
 38.5 
 
 402.9 
 
 472.8 
 
 548.4 
 
 16 
 
 74.6 
 
 107.4 
 
 146.2 
 
 191.0 
 
 241.7 
 
 298.4 2 
 
 61.1 
 
 429.7 
 
 504.4 
 
 584.9 
 
 17 
 
 79.3 
 
 114.1 
 
 155.4 
 
 202.9 
 
 256.8 
 
 317.1 2 
 
 83.7 
 
 456.6 
 
 535.9 
 
 621.5 
 
 18 
 
 83.9 
 
 120.9 
 
 164.5 
 
 214.9 
 
 271.9 
 
 335.7 ^ 
 
 K)6.2 
 
 483.5 
 
 567.4 
 
 658.0 
 
 19 
 
 88.6 
 
 127.6 
 
 173.6 
 
 226.8 
 
 287.1 
 
 354.4 ^ 
 
 128.8 
 
 510.3 
 
 598.9 
 
 694.6 
 
 20 
 
 93.3 
 
 134.3 
 
 182.8 
 
 238.7 
 
 302.2 
 
 373.0 * 
 
 151.4 
 
 537.2 
 
 630.4 
 
 731.1 
 
 Depth 
 in 
 
 Diameter in Feet. 
 
 Feet. 
 
 
 
 
 
 
 
 
 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 1 
 
 41.966 
 
 47.748 
 
 53.903 
 
 60.431 
 
 67.33. 
 
 I 74.606 
 
 82.253 
 
 90.273 
 
 5 
 
 209.8 
 
 238.7 
 
 269.5 
 
 302.2 
 
 336.7 
 
 373.0 
 
 411.3 
 
 451.4 
 
 6 
 
 251.8 
 
 286.5 
 
 323.4 
 
 362.6 
 
 404.0 
 
 447.6 
 
 493.5 
 
 541.6 
 
 7 
 
 293.8 
 
 334.2 
 
 377.3 
 
 423.0 
 
 471.3 
 
 522.2 
 
 575.8 
 
 631.9 
 
 8 
 
 335.7 
 
 382.0 
 
 431.2 
 
 483.4 
 
 538.7 
 
 596.8 
 
 658.0 
 
 722.2 
 
 9 
 
 377.7 
 
 429.7 
 
 485.1 
 
 543.9 
 
 606.0 
 
 671.5 
 
 740.3 
 
 812.5 
 
 10 
 
 419.7 
 
 477.5 
 
 539.0 
 
 604.3 
 
 673.3 
 
 746.1 
 
 822.5 
 
 902.7 
 
 11 
 
 461.6 
 
 525.2 
 
 592.9 
 
 664.7 
 
 740.7 
 
 820.7 
 
 904.8 
 
 993.0 
 
 12 
 
 503.6 
 
 573.0 
 
 646.8 
 
 725.2 
 
 808.0 
 
 895.3 
 
 987.0 
 
 1083.3 
 
 13 
 
 545.6 
 
 620.7 
 
 700.7 
 
 785.6 
 
 875.3 
 
 969.9 
 
 1069.3 
 
 1173.5 
 
 14 
 
 587.5 
 
 668.5 
 
 754.6 
 
 846.0 
 
 942.6 
 
 1044.5 
 
 1151.5 
 
 1263.8 
 
 15 
 
 629.5 
 
 716.2 
 
 808.5 
 
 906.5 
 
 1010.0 
 
 1119.1 
 
 1233.8 
 
 1354.1 
 
 16 
 
 671.5 
 
 764.0 
 
 862.4 
 
 966.9 
 
 1077.3 
 
 1193.7 
 
 1316.0 
 
 1444.4 
 
 17 
 
 713.4 
 
 811.7 
 
 916.4 
 
 1027.3 
 
 1144.6 
 
 1268.3 
 
 1398.3 
 
 1534.5 
 
 18 
 
 755.4 
 
 859.5 
 
 970.3 
 
 1087.8 
 
 1212.0 
 
 1342.9 
 
 1480.6 
 
 1624.9 
 
 19 
 
 797.4 
 
 907.2 
 
 1024.2 
 
 1148.2 
 
 1279.3 
 
 1417.5 
 
 1562.8 
 
 1715.2 
 
 20 
 
 839.3 
 
 955.0 
 
 1078.1 
 
 1208.6 
 
 1346.6 
 
 1492.1 
 
 1645.1 
 
 1805.5 
 
 
 
 
 
 
 
 
 i 
 
LOGARITHMS OF NUMBERS. 
 
 135 
 
 NUMBER OF BARBELS (31 1-2 GALLONS) IN CISTERNS 
 AND TANKS. Continued. 
 
 Depth 
 in 
 Feet. 
 
 Diameter in Feet. 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 1 
 5 
 
 98.666 
 493.3 
 
 107.432 
 537.2 
 
 116.571 
 582.9 
 
 126.083 
 630.4 
 
 135.968 
 679.8 
 
 146.226 
 731.1 
 
 156.858 
 784.3 
 
 167.863 
 839.3 
 
 6 
 
 592.0 
 
 644.6 
 
 699.4 
 
 756.5 
 
 815.8 
 
 877.4 
 
 941.1 
 
 1007.2 
 
 7 
 
 690.7 
 
 752.0 
 
 316.0 
 
 882.6 
 
 951.8 
 
 1023.6 
 
 1098.0 
 
 1175.0 
 
 8 
 
 789.3 
 
 859.5 
 
 932.6 
 
 1008.7 
 
 1087.7 
 
 1169.8 
 
 1254.9 
 
 1342.9 
 
 9 
 
 888.0 
 
 966.9 
 
 1049.1 
 
 1134.7 
 
 1223.7 
 
 1316.0 
 
 1411.7 
 
 1510.8 
 
 to 
 
 986.7 
 
 1074.3 
 
 1165.7 
 
 1260.8 
 
 1359.7 
 
 1462.2 
 
 1 568.6 
 
 1678.6 
 
 11 
 
 1085.3 
 
 1 181.8 
 
 1282.3 
 
 1386.9 
 
 1495.6 
 
 1608.5 
 
 1725.4 
 
 1846.5 
 
 12 
 
 1184.0 
 
 1289.2 
 
 1398.8 
 
 1513.0 
 
 1631.6 
 
 1754.7 
 
 1882.3 
 
 2014.4 
 
 13 
 
 1282.7 
 
 1396.6 
 
 1515.4 
 
 1639.1 
 
 1767.6 
 
 1900.9 
 
 2039.2 
 
 2182.2 
 
 14 
 
 1381.3 
 
 1504.0 
 
 1632.0 
 
 1765.2 
 
 1903.6 
 
 2047.2 
 
 2196.0 
 
 2350.1 
 
 15 
 
 1480.0 
 
 1611.5 
 
 1 748.6 
 
 1891.2 
 
 2039.5 
 
 2193.4 
 
 2352.9 
 
 2517.9 
 
 16 
 
 1578.7 
 
 1718.9 
 
 1865.1 
 
 2017.3 
 
 2175.5 
 
 2339.6 
 
 2509.7 
 
 2685.8 
 
 17 
 
 1677.3 
 
 1826.3 
 
 1981.7 
 
 2143.4 
 
 2311.5 
 
 2485.8 
 
 2666.6 
 
 2853.7 
 
 18 
 
 1776.0 
 
 1933.8 
 
 2098.3 
 
 2269.5 
 
 2447.4 
 
 2632.0 
 
 2823.4 
 
 3021.5 
 
 19 
 
 1874.7 
 
 2041.2 
 
 2214.8 
 
 2395.6 
 
 2583.4 
 
 2778.3 
 
 2980.3 
 
 3189.4 
 
 20 
 
 1973.3 
 
 2148.6 
 
 2321.4 
 
 2521.7 
 
 2719.4 
 
 2924.5 
 
 3137.2 
 
 3357.3 
 
 LOGARITHMS. 
 
 Logarithms (abbreviation log). The log of a number is the exponent 
 of the power to which it is necessary to raise a fixed number to produce 
 the given number. The fixed number is called the base. Thus if the 
 base is 10, the log of 1000 is 3, for 10 3 = 1000. There are two systems 
 of logs in general use, the common, in which the base is 10, and the Naperian, 
 or hyperbolic, in which the base is 2.718281828 .... The Naperian base 
 is commonly denoted by e, as in the equation e y x, in which y is the 
 Nap. log of a:. The abbreviation log e is commonly used to denote the 
 Nap log. 
 
 In any system of logs, the log of 1 is 0; the log of the base, taken in that 
 system, is 1. In any system the base of which is greater than 1, the logs of 
 all numbers greater than 1 are positive and the logs of all numbers less 
 than 1 are negative. 
 
 The modulus of any system is equal to the reciprocal of the Naperian log 
 of the base of that system. The modulus of the Naperian system is 1 , that 
 of the common system is 0.4342945. 
 
 The log of a number in any system equals the modulus of that system X 
 the Naperian log of the number. 
 
 The hyperbolic or Naperian log of any number equals the common 
 logX 2.3025851. 
 
 Every log consists of two parts, an entire part called the characteristic. 
 or index, and the decimal part, or mantissa. The mantissa only is given 
 in the usual tables of common logs, with the decimal point omitted. The 
 characteristic is found by a simple rule, viz., it is one less than the number 
 of figures to the left of the decimal point in the number whose log is to be 
 found. Thus the characteristic of numbers from 1 to 9.99 + is 0, from 
 10 to 99.99 4- is 1, from 100 to 999 -f is 2, from 0.1 to 0.99 + is - 1, from 
 0.01 to 0.099 + is -2, etc. Thus 
 
 log of 2000 is 3.30103; log of 0.2 
 " oon " 2.30103; " " 0.02 
 
 200 , 
 
 20 " 1.30103; 
 
 2 " Q.30103; 
 
 is - 1.30103, or 9.30103 - 10 
 " - 2.30103, " 8.30103 - 10 
 0.002 " - 3.30103, " 7.30103 - 10 
 1* 0,0002 " - 4,30103, '! Q.301Q3 - IQ 
 
136 LOdARITHMS OF NUMBERS. 
 
 The minus sign is frequently written above the characteristic thusi 
 log 0.002 = 3.30103. The characteristic only is negative, the decimal part, 
 or mantissa, being always positive. 
 
 When a log consists of a negative index and a positive mantissa, it is 
 usual to write the negative sign over the index, or else to add 10 to the 
 index, and to indicate the subtraction of 10 from the resulting logarithm. 
 
 Thus log 0.2 = 1.30103, and this may be written 9.30103 - 10. 
 
 In tables of logarithmic sines, etc., the 10 is generally omitted, as 
 being understood. 
 
 Rules for use of the table of logarithms. To find the log of any 
 whole number. For 1 to 100 inclusive the log is given complete in the 
 small table on page 137. 
 
 For 100 to 999 inclusive the decimal part of the log is given opposite the 
 given number in the column headed in the table (including the two 
 figures to the left, making six figures). Prefix the characteristic, or 
 index, 2. 
 
 For 1000 to 9999 inclusive: The last four figures of the log are found 
 opposite the first three figures of the given number and in the vertical 
 column headed with the fourth figure of the given number ; prefix the two 
 figures under column 0, and the index, which is 3. 
 
 For numbers over 10,000 having five or more digits: Find the decimal 
 part of the log for the first four digits as above, multiply the difference 
 figure in the last column by the remaining digit or digits, and divide by 10 
 if there be only one digit more, by 100 if there be two more, and so on; 
 add the quotient to the log of the first four digits and prefix the index, 
 which is 4 if there are five digits, 5 if there are six digits, and so on. The 
 table of proportional parts may be used, as shown below. 
 
 To find the log of a decimal fraction or of a whole number and a 
 'decimal. First find the log of the quantity as if there were no decimal 
 Doint, then prefix the index according to rule: the index is one less than 
 the number of figures to the left of the decimal point. 
 
 Example, log of 3.14159. log of 3.141 =0.497068. Diff. =-138 
 From proportional parts 5 = 690 
 
 09= 1242 
 
 log 3. 14159 0.4971494 
 
 If the number is a decimal less than unity, the index is negative 
 and is one more than the_ number of zeros to the right of the decimal 
 point. Log of 0.0682 = 2.833784 = 8.833784 - 10. 
 
 To find the number corresponding to a given log. Find in the 
 table the log nearest to tne decimal part of the given log and take the 
 first four digits of the required number from the column N and the top or 
 foot of the column containing the log which is the next less thanthegiven 
 log. To find the 5th and 6th digits subtract the log in the table from the 
 given log, multiply the difference by 100, and divide by the figure in the 
 Diff. column opposite the log; annex the quotient to the four digits 
 already found, and place the decimal point according to the rule; the 
 number of figures to the left of the decimal point is one greater than the 
 index. The number corresponding to a log is called the anti-logarithm. 
 
 Find the anti-log of 0.497150 
 
 Next lowest log in table corresponds to 3141 0.497068 Diff. = 82 
 
 Tabular diff. = 138; 82 -f- 138 = 0.59 -f- 
 The index being 0, the number is therefore 3.14159 -f . 
 
 To multiply two numbers by tlie use of logarithms. Add together 
 the logs of the two numbers, and find' the number whose log is the sum. 
 
 To divide two numbers. Subtract the log of the divisor from the 
 log of the dividend, and find the number whose log is the difference. 
 Log of a fraction. Log of a/b = log a log b. 
 
 To raise a number to any given power. Multiply the log of the 
 number by the exponent of the power, and find the number whose log 
 is the product. 
 
 To find any root of a given number. Divide the log of the number 
 index of the root. The quotient is tlje log, of tfce root. 
 
IiOGAUITHMS OP NUMBERS. 
 
 137 
 
 To find the reciprocal of a number. Subtract the decimal pait 
 of the log of the number from 0, add 1 to the index and change the sign of 
 the index. The result is the log of the reciprocal. 
 
 Required the reciprocal of 3.141593. 
 
 Log of 3.141593, as found above 0.4971498 
 
 Subtract decimal part from gives 0.5028502 
 
 Add 1 to the index, and changing sign of the index gives. . 1. 5028502 
 which is the log of 0.31831. 
 
 To find the fourth term of a proportion by logarithms. Add 
 the logarithms of the second and third terms, and from their sum subtract 
 the logarithm of the first term. 
 
 When one logaithm is to be subtracted from another, it may be more 
 convenient to convert the subtraction into an addition, which may be 
 done by first subtracting the given logarithm from 10, adding the difference 
 to the other logarithm, and afterwards rejecting the 10. 
 
 The difference between a given logarithm and .10 is called its arithmetical 
 complement, or cologarithm. 
 
 To subtract one logarithm from another is the same as to add its com- 
 plement and then reject 10 from the result. For a b = 10 b+ a 10. 
 
 To work a proportion, then, by logarithms, add the complement of the 
 logarithm of the first term to the logarithms of the second and third terms. 
 The characteristic must afterwards be diminished by 10. 
 
 Example in logarithms with a negative index. Solve by 
 
 logarithms 
 
 
 Vioii 
 quotient to the 2.45 power. 
 
 log 526 = 2.720986 
 log 1011 = 3.004751 
 
 which means divide 526 by 1011 and raise the 
 
 log of quotient = 
 Multiply by 
 
 9.716235 - 10 
 2.45 
 
 .48581175 
 3.8864940 
 19.432470 
 
 23. 80477575 -(10X2.45) = 1.30477575 = 0.20173, Ans. 
 LOGARITHMS OF NUMBERS FROM 1 TO 100. 
 
 N. 
 
 Log. 
 
 N. 
 
 Log. 
 
 N. 
 
 Log. 
 
 N. 
 
 Log. 
 
 N. 
 
 Log. 
 
 ! 
 
 0.000000 
 
 21 
 
 .322219 
 
 41 
 
 .612784 
 
 61 
 
 .785330 
 
 81 
 
 .908485 
 
 2 
 
 0.301030 
 
 22 
 
 .342423 
 
 42 
 
 .623249 
 
 62 
 
 .792392 
 
 82 
 
 .913814 
 
 
 0.477121 
 
 23 
 
 .361728 
 
 43 
 
 .633468 
 
 63 
 
 .799341 
 
 83 
 
 .919078 
 
 4 
 
 0.602060 
 
 24 
 
 .380211 
 
 44 
 
 .643453 
 
 64 
 
 .806180 
 
 84 
 
 .924279 
 
 
 0.698970 
 
 25 
 
 .397940 
 
 45 
 
 .653213 
 
 65 
 
 .812913 
 
 85 
 
 .929419 
 
 6 
 
 0.778151 
 
 26 
 
 .414973 
 
 46 
 
 .662758 
 
 66 
 
 .819544 
 
 86 
 
 .934498 
 
 7 
 
 0.845098 
 
 27 
 
 .431364 
 
 47 
 
 .672098 
 
 67 
 
 .826075 
 
 87 
 
 .939519 
 
 8 
 
 0.903090 
 
 28 
 
 .447158 
 
 48 
 
 .681241 
 
 68 
 
 .832509 
 
 88 
 
 .944483 
 
 9 
 
 0.954243 
 
 29 
 
 .462398 
 
 49 
 
 .690196 
 
 69 
 
 .838849 
 
 89 
 
 .949390 
 
 10 
 
 1 .000000 
 
 30 
 
 .477121 
 
 50 
 
 .698970 
 
 70 
 
 .845098 
 
 90 
 
 .954243 
 
 11 
 
 .041393 
 
 31 
 
 .491362 
 
 51 
 
 .707570 
 
 71 
 
 .851258 
 
 91 
 
 .959041 
 
 12 
 
 .079181 
 
 32 
 
 .505150 
 
 52 
 
 .716003 
 
 72 
 
 .857332 
 
 92 
 
 .963788 
 
 13 
 
 .113943 
 
 33 
 
 .518514 
 
 53 
 
 .724276 
 
 73 
 
 .863323 
 
 93 
 
 .968483 
 
 14 
 
 .146128 
 
 34 
 
 .531479 
 
 54 
 
 .732394 
 
 74 
 
 .869232 
 
 94 
 
 .973128 
 
 15 
 
 .176091 
 
 35 
 
 .544068 
 
 55 
 
 .740363 
 
 75 
 
 .875061 
 
 95 
 
 977724 
 
 16 
 
 .204120 
 
 36 
 
 .556303 
 
 56 
 
 .748188 
 
 76 
 
 .880814 
 
 96 
 
 .982271 
 
 17 
 
 230449 
 
 37 
 
 .568202 
 
 57 
 
 .755875 
 
 77 
 
 .886491 
 
 97 
 
 .966772 
 
 18 
 
 .255273 
 
 38 
 
 .579784 
 
 58 
 
 .763428 
 
 78 
 
 .892095 
 
 98 
 
 .991226 
 
 19 
 
 .278754 
 
 39 
 
 .591065 
 
 59 
 
 .770852 
 
 79 
 
 .897627 
 
 99 
 
 .995635 
 
 20 
 
 1.301030 
 
 40 
 
 .602060 
 
 60 
 
 .778151 
 
 80 
 
 .903090 
 
 100 
 
 2.000000 
 
 For four-place logarithms see page 
 
138 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 100 L. OOO.j 
 
 [No. 109 L. 040. 
 
 N. 
 
 
 
 1 
 
 3 
 
 0868 
 5181 
 9451 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 346~1 
 
 7748 
 
 9 
 
 3891 
 8174 
 
 Diff. 
 
 432' 
 428 
 
 424 
 420 
 
 416 
 412 
 408 
 
 404 
 400 
 
 397 
 
 100 
 1 
 2 
 
 3 
 
 4 
 
 5 
 6 
 
 8 
 9 
 
 000000 
 4321 
 8600 
 
 0434 
 4751 
 9026 
 
 1301 
 5609 
 9876 
 
 1734 
 6038 
 
 2166 
 6466 
 
 2598 
 6894 
 
 3029 
 7321 
 
 0300 
 
 4521 
 8700 
 
 0724 
 4940 
 9116 
 
 1147 
 5360 
 9532 
 
 1570 
 5779 
 9947 
 
 1993 
 6197 
 
 2415 
 6616 
 
 012837 
 7033 
 
 3259 
 7451 
 
 3680 
 7868 
 
 4100 
 
 8284 
 
 0361 
 
 4486 
 8571 
 
 2619 
 6629 
 
 0775 
 
 4896 
 8978 
 
 021189 
 5306 
 9384 
 
 1603 
 5715 
 9789 
 
 2016 
 6125 
 
 2428 
 6533 
 
 2841 
 6942 
 
 3252 
 7350 
 
 3664 
 7757 
 
 4075 
 8164 
 
 0195 
 4227 
 8223 
 
 0600 
 4628 
 8620 
 
 1004 
 5029 
 9017 
 
 1408 
 5430 
 9414 
 
 1812 
 5830 
 9811 
 
 2216 
 6230 
 
 3021 
 
 7028 
 
 033424 
 7426 
 04 
 
 3826 
 7825 
 
 0207 
 
 0602 
 
 0998 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 434" 
 
 43.4 
 
 86.8 
 
 130.2 
 
 173.6 
 
 217.0 
 
 260.4 
 
 303.8 
 
 347.2 
 
 390.6 
 
 433 
 
 43.3 
 
 86.6 
 
 129.9 
 
 173.2 
 
 216.5 
 
 259.8 
 
 303.1 
 
 346.4 
 
 389.7 
 
 432 
 
 43.2 
 
 86.4 
 
 129.6 
 
 172.8 
 
 216.0 
 
 259.2 
 
 302.4 
 
 345.6 
 
 388.8 
 
 431 
 
 43.1 
 
 86.2 
 
 129.3 
 
 172.4 
 
 215.5 
 
 258.6 
 
 301.7 
 
 344.8 
 
 387.9 
 
 430 
 
 43.0 
 
 86.0 
 
 129.0 
 
 172.0 
 
 215.0 
 
 258.0 
 
 301.0 
 
 344.0 
 
 387.0 
 
 429 
 
 42.9 
 
 85.8 
 
 128.7 
 
 171.6 
 
 214.5 
 
 257.4 
 
 300.3 
 
 343.2 
 
 386.1 
 
 428 
 
 42.8 
 
 85.6 
 
 128.4 
 
 171.2 
 
 214.0 
 
 256.8 
 
 299.6 
 
 342.4 
 
 385.2 
 
 427 
 
 42.7 
 
 85.4 
 
 128.1 
 
 170.8 
 
 213.5 
 
 256.2 
 
 298.9 
 
 341.6 
 
 384.3 
 
 426 
 
 42.6 
 
 85.2 
 
 127.8 
 
 170.4 
 
 213.0 
 
 255.6 
 
 298.2 
 
 340.8 
 
 383.4 
 
 425 
 
 42.5 
 
 85.0 
 
 127.5 
 
 170.0 
 
 212.5 
 
 255.0 
 
 297.5 
 
 340.0 
 
 382.5 
 
 424 
 
 42.4 
 
 84.8 
 
 127.2 
 
 169.6 
 
 212.0 
 
 254.4 
 
 296.8 
 
 339.2 
 
 381.6 
 
 423 
 
 42.3 
 
 84.6 
 
 126.9 
 
 169.2 
 
 211.5 
 
 253.8 
 
 296.1 
 
 338.4 
 
 380.7 
 
 422 
 
 42.2 
 
 84.4 
 
 126.6 
 
 168.8 
 
 211.0 
 
 253.2 
 
 295.4 
 
 337.6 
 
 379.8 
 
 421 
 
 42.1 
 
 84.2 
 
 126.3 
 
 168.4 
 
 210.5 
 
 252.6 
 
 294.7 
 
 336.8 
 
 378.9 
 
 420 
 
 42.0 
 
 84.0 
 
 126.0 
 
 168.0 
 
 210.0 
 
 252.0 
 
 294.0 
 
 336.0 
 
 373.0 
 
 419 
 
 41.9 
 
 83.8 
 
 125.7 
 
 167.6 
 
 209.5 
 
 251.4 
 
 293.3 
 
 335.2 
 
 377.1 
 
 418 
 
 41.8 
 
 83.6 
 
 125.4 
 
 167.2 
 
 209.0 
 
 250.8 
 
 292.6 
 
 334.4 
 
 376.2 
 
 417 
 
 41.7 
 
 83.4 
 
 125.1 
 
 166.8 
 
 208.5 
 
 250.2 
 
 291.9 
 
 333.6 
 
 375.3 
 
 416 
 
 41.6 
 
 83.2 
 
 124.8 
 
 166.4 
 
 208.0 
 
 249.6 
 
 291.2 
 
 332.8 
 
 374.4 
 
 415 
 
 41.5 
 
 83.0 
 
 124.5 
 
 166.0 
 
 207.5 
 
 249.0 
 
 290.5 
 
 332.0 
 
 373.5 
 
 414 
 
 41.4 
 
 82.8 
 
 124.2 
 
 165.6 
 
 207.0 
 
 248.4 
 
 289.8 
 
 331.2 
 
 372.6 
 
 413 
 
 41.3 
 
 82.6 
 
 123.9 
 
 165.2 
 
 206.5 
 
 247.8 
 
 289.1 
 
 330.4 
 
 371.7 
 
 412 
 
 41.2 
 
 82.4 
 
 123.6 
 
 164.8 
 
 206.0 
 
 247.2 
 
 288.4 
 
 329.6 
 
 370.8 
 
 >11 
 
 41.1 
 
 82.2 
 
 123.3 
 
 164.4 
 
 205.5 
 
 246.6 
 
 287.7 
 
 328.8 
 
 369.9 
 
 410 
 
 41.0 
 
 82.0 
 
 123.0 
 
 164.0 
 
 205.0 
 
 246.0 
 
 287.0 
 
 328.0 
 
 369.0 
 
 409 
 
 40.9 
 
 81.8 
 
 122.7 
 
 163.6 
 
 204.5 
 
 245.4 
 
 286.3 
 
 327.2 
 
 368.1 
 
 408 
 
 40.8 
 
 81.6 
 
 122.4 
 
 163.2 
 
 204.0 
 
 244.8 
 
 285.6 
 
 326.4 
 
 367.2 
 
 407 
 
 40.7 
 
 81.4 
 
 122.1 
 
 162.8 
 
 203.5 
 
 244.2 
 
 284.9 
 
 325.6 
 
 366.3 
 
 406 
 
 40.6 
 
 81.2 
 
 121.8 
 
 162.4 
 
 203.0 
 
 243.6 
 
 284.2 
 
 324.8 
 
 365.4 
 
 405 
 
 40.5 
 
 81.0 
 
 121.5 
 
 162.0 
 
 202.5 
 
 243.0 
 
 283.5 
 
 324.0 
 
 364.5 
 
 404 
 
 40.4 
 
 80.8 
 
 121.2 
 
 161.6 
 
 202.0 
 
 242.4 
 
 282.8 
 
 323.2 
 
 363.6 
 
 403 
 
 40.3 
 
 80.6 
 
 120.9 
 
 161.2 
 
 201.5 
 
 241.8 
 
 282.1 
 
 322.4 
 
 362.7 
 
 402 
 
 40.2 
 
 80.4 
 
 120.6 
 
 160.8 
 
 201.0 
 
 241.2 
 
 281.4 
 
 321.6 
 
 361.8 
 
 401 
 
 40.1 
 
 80.2 
 
 120.3 
 
 160.4 
 
 200.5 
 
 240.6 
 
 280.7 
 
 320.8 
 
 360.9 
 
 400 
 
 40.0 
 
 80.0 
 
 120.0 
 
 160.0 
 
 200.0 
 
 240.0 
 
 280.0 
 
 320.0 
 
 360.0 
 
 399 
 
 39.9 
 
 79.8 
 
 119.7 
 
 159.6 
 
 199.5 
 
 239.4 
 
 279.3 
 
 319.2 
 
 359.1 
 
 398 
 
 39.8 
 
 79.6 
 
 119.4 
 
 159.2 
 
 199.0 
 
 238.8 
 
 278.6 
 
 318.4 
 
 358.2 
 
 397 
 
 39.7 
 
 79.4 
 
 119.1 
 
 158.8 
 
 198.5 
 
 238.2 
 
 277.9 
 
 317.6 
 
 357.3 
 
 396 
 
 39.6 
 
 79.2 
 
 118.8 
 
 158.4 
 
 198.0 
 
 237.6 
 
 277.2 
 
 316.8 
 
 356.4 
 
 395 
 
 39.5 
 
 79.0 
 
 118.5 
 
 158.0 
 
 197.5 
 
 237.0 
 
 276.5 
 
 316.0 
 
 355.5 
 
LOGARITHMS OF NUMBERS. 
 
 139 
 
 No. 110 L. 041.] 
 
 [No. 119 L. 078. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 no 
 i 
 
 2 
 
 3 
 4 
 
 5 
 
 6 
 7 
 
 8 
 9 
 
 041393 
 5323 
 9218 
 
 1787 
 5714 
 9606 
 
 2182 
 6105 
 9993 
 
 2576 
 6495 
 
 0380 
 4230 
 8046 
 
 2969 
 6885 
 
 0766 
 4613 
 8426 
 
 3362 
 7275 
 
 3755 
 7664 
 
 4148 
 8053 
 
 4540 
 8442 
 
 4932 
 8830 
 
 393 
 390 
 
 386 
 383 
 
 379 
 376 
 373 
 
 370 
 366 
 363 
 
 1153 
 4996 
 8805 
 
 1538 
 5378 
 9185 
 
 1924 
 5760 
 9563 
 
 2309 
 6142 
 9942 
 
 2694 
 6524 
 
 0320 
 4083 
 7815 
 
 053078 
 6905 
 
 3463 
 7286 
 
 3846 
 7666 
 
 060698 
 4458 
 8186 
 
 1075 
 4832 
 8557 
 
 1452 
 5206 
 8928 
 
 1829 
 5580 
 9298 
 
 2206 
 5953 
 9668 
 
 2582 
 6326 
 
 2958 
 6699 
 
 3333 
 7071 
 
 3709 
 7443 
 
 0038 
 3718 
 7368 
 
 0407 
 4085 
 7731 
 
 0776 
 4451 
 8094 
 
 1145 
 4816 
 8457 
 
 1514 
 5182 
 8819 
 
 071882 
 5547 
 
 2250 
 5912 
 
 2617 
 6276 
 
 2985 
 6640 
 
 3352 
 7004 
 
 PROPORTIONAL PA.RTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 395 
 
 39.5 
 
 79.0 
 
 118.5 
 
 158.0 
 
 197.5 
 
 237.0 
 
 276.5 
 
 316.0 
 
 355.5 
 
 394 
 
 39.4 
 
 78.8 
 
 T18.2 
 
 157.6 
 
 197.0 
 
 236.4 
 
 275.8 
 
 315.2 
 
 354.6 
 
 393 
 
 39.3 
 
 78.6 
 
 1 17.9 
 
 157.2 
 
 196.5 
 
 235.8 
 
 275.1 
 
 314.4 
 
 353.7 
 
 392 
 
 39.2 
 
 78.4 
 
 117.6 
 
 156.8 
 
 196.0 
 
 235.2 
 
 274.4 
 
 313.6 
 
 352.8 
 
 391 
 
 39.1 
 
 78.2 
 
 117.3 
 
 156.4 
 
 195.5 
 
 234.6 
 
 273.7 
 
 312.8 
 
 351.9 
 
 390 
 
 39.0 
 
 78.0 
 
 117.0 
 
 156.0 
 
 195.0 
 
 234.0 
 
 273.0 
 
 312.0 
 
 351.C 
 
 389 
 
 38.9 
 
 77.8 
 
 116.7 
 
 155.6 
 
 194.5 
 
 233.4 
 
 272.3 
 
 311.2 
 
 350.1 
 
 388 
 
 38.8 
 
 77.6 
 
 116.4 
 
 155.2 
 
 194.0 
 
 232.8 
 
 271.6 
 
 310.4 
 
 349.2 
 
 387 
 
 38.7 
 
 77.4 
 
 116.1 
 
 154.8 
 
 193.5 
 
 232.2 
 
 270.9 
 
 309.6 
 
 348.3 
 
 386 
 
 38.6 
 
 77.2 
 
 115.8 
 
 154.4 
 
 193.0 
 
 231.6 
 
 270.2 
 
 308.8 
 
 347.4 
 
 385 
 
 38.5 
 
 77.0 
 
 115.5 
 
 154.0 
 
 192.5 
 
 231.0 
 
 269.5 
 
 308.0 
 
 346.? 
 
 384 
 
 38.4 
 
 76.8 
 
 115.2 
 
 153.6 
 
 192.0 
 
 230.4 
 
 268.8 
 
 307.2 
 
 345.6 
 
 383 
 
 38.3 
 
 76.6 
 
 114.9 
 
 153.2 
 
 191.5 
 
 229.8 
 
 268.1 
 
 306.4 
 
 344.7 
 
 382 
 
 38.2 
 
 76.4 
 
 114.6 
 
 152.8 
 
 191.0 
 
 229.2 
 
 267.4 
 
 305.6 
 
 343.8 
 
 381 
 
 38.1 
 
 76.2 
 
 114.3 
 
 152.4 
 
 190.5 
 
 228.6 
 
 266.7 
 
 304.8 
 
 342.9 
 
 380 
 
 38.0 
 
 76.0 
 
 114.0 
 
 152.0 
 
 1900 
 
 228.0 
 
 266.0 
 
 304.0 
 
 342.0 
 
 379 
 
 37.9 
 
 75.8 
 
 113.7 
 
 151.6 
 
 189.5 
 
 227.4 
 
 265.3 
 
 303.2 
 
 341.1 
 
 378 
 
 37.8 
 
 75.6 
 
 113.4 
 
 151.2 
 
 189.0 
 
 226.8 
 
 264.6 
 
 302.4 
 
 340.2 
 
 377 
 
 37.7 
 
 75.4 
 
 113.1 
 
 150.8 
 
 188.5 
 
 226.2 
 
 263.9 
 
 301.6 
 
 339.3 
 
 376 
 
 37.6 
 
 75.2 
 
 112.8 
 
 150.4 
 
 188.0 
 
 225.6 
 
 263.2 
 
 300.8 
 
 338.4 
 
 375 
 
 37.5 
 
 75.0 
 
 112.5 
 
 150.0 
 
 187.5 
 
 225.0 
 
 262.5 
 
 300.0 
 
 337.5 
 
 374 
 
 37.4 
 
 74.8 
 
 112.2 
 
 149.6 
 
 187.0 
 
 224.4 
 
 261.8 
 
 299.2 
 
 336.6 
 
 373 
 
 37.3 
 
 74.6 
 
 111.9 
 
 149.2 
 
 186.5 
 
 223.8 
 
 261.1 
 
 298.4 
 
 335.7 
 
 372 
 
 37.2 
 
 74.4 
 
 111.6 
 
 148.8 
 
 186.0 
 
 223.2 
 
 260.4 
 
 297.6 
 
 334.8 
 
 371 
 
 37.1 
 
 74.2 
 
 111.3 
 
 148.4 
 
 185.5 
 
 222.6 
 
 259.7 
 
 296.8 
 
 333.9 
 
 370 
 
 37.0 
 
 74.0 
 
 111.0 
 
 148.0 
 
 185.0 
 
 222.0 
 
 259.0 
 
 296.0 
 
 333.0 
 
 369 
 
 36.9 
 
 73.8 
 
 110.7 
 
 147.6 
 
 184.5 
 
 221.4 
 
 258.3 
 
 295.2 
 
 332.1 
 
 368 
 
 36.8 
 
 73.6 
 
 110.4 
 
 147.2 
 
 184.0 
 
 220.8 
 
 257.6 
 
 294.4 
 
 331.2 
 
 367 
 
 36.7 
 
 73.4 
 
 110.1 
 
 146.8 
 
 183.5 
 
 220.2 
 
 256.9 
 
 293.6 
 
 330.3 
 
 366 
 
 36.6 
 
 73.2 
 
 109.8 
 
 146.4 
 
 183.0 
 
 219.6 
 
 256.2 
 
 292.8 
 
 329.4 
 
 365 
 
 36.5 
 
 73.0 
 
 109.5 
 
 146.0 
 
 182.5 
 
 219.0 
 
 255.5 
 
 292.0 
 
 328.5 
 
 364 
 
 36.4 
 
 72.8 
 
 109.2 
 
 145.6 
 
 182.0 
 
 218.4 
 
 254.8 
 
 291.2 
 
 327.6 
 
 363 
 
 36.3 
 
 72.6 
 
 108.9 
 
 145.2 
 
 181.5 
 
 217.8 
 
 254.1 
 
 290.4 
 
 326.7 
 
 362 
 
 36.2 
 
 72.4 
 
 108.6 
 
 144.8 
 
 181.0 
 
 217.2 
 
 253.4 
 
 289.6 
 
 325.8 
 
 361 
 
 36.1 
 
 72.2 
 
 108.3 
 
 144.4 
 
 180.5 
 
 216.6 
 
 252.7 
 
 288.8 
 
 324.9 
 
 360 
 
 36.0 
 
 72.0 
 
 108.0 
 
 144.0 
 
 180.0 
 
 216.0 
 
 252.0 
 
 288.0 
 
 324.0 
 
 359 
 
 35.9 
 
 71.8 
 
 107.7 
 
 143.6 
 
 179.5 
 
 215.4 
 
 251.3 
 
 287.2 
 
 323.1 
 
 358 
 
 35.8 
 
 71.6 
 
 107.4 
 
 143.2 
 
 179.0 
 
 214.8 
 
 250.6 
 
 286.4 
 
 322.2 
 
 357 
 
 35.7 
 
 71.4 
 
 107.1 
 
 142.8 
 
 178.5 
 
 214.2 
 
 249.9 
 
 285.6 
 
 32!. 3 
 
 356 
 
 35.6 
 
 71.2 
 
 106.8 
 
 142.4 
 
 178.0 
 
 213.6 
 
 249.2 
 
 284.8 
 
 320.4 
 
140 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 120 L. 079.] 
 
 [No. 134 L. 130. 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 120 
 2 
 
 4 
 
 5 
 
 6 
 7 
 
 8 
 
 9 
 
 130 
 
 1 
 
 2 
 3 
 
 4 
 
 079181 
 
 9543 
 
 9904 
 
 0266 
 3861 
 7426 
 
 0626 
 4219 
 7781 
 
 0987 
 4576 
 8136 
 
 1347 
 4934 
 8490 
 
 1707 
 5291 
 8845 
 
 2067 
 5647 
 9198 
 
 2426 
 6004 
 9552 
 
 360 
 357 
 355 
 
 352 
 349 
 
 346 
 343 
 341 
 
 338 
 335 
 
 333 
 
 330 
 328 
 325 
 
 323 
 
 082785 
 6360 
 9905 
 
 3144 
 6716 
 
 3503 
 7071 
 
 0258 
 
 3772 
 7257 
 
 0611 
 
 4122 
 7604 
 
 0963 
 
 4471 
 7951 
 
 1315 
 4820 
 8298 
 
 1667 
 5169 
 8644 
 
 2018 
 5518 
 8990 
 
 2370 
 5866 
 9335 
 
 2721 
 6215 
 9681 
 
 3071 
 6562 
 
 093422 
 6910 
 
 0026 
 3462 
 6871 
 
 100371 
 3804 
 7210 
 
 0715 
 4146 
 7549 
 
 1059 
 4487 
 7888 
 
 1403 
 4828 
 8227 
 
 1747 
 5169 
 8565 
 
 2091 
 5510 
 8903 
 
 2434 
 5851 
 9241 
 
 2777 
 6191 
 9579 
 
 3119 
 6531 
 9916 
 
 0253 
 3609 
 
 6940 
 
 110590 
 
 3943 
 725 '1 
 
 0926 
 
 4277 
 7603 
 
 1263 
 
 4611 
 7934 
 
 1599 
 
 4944 
 8265 
 
 1934 
 
 5278 
 8595 
 
 2270 
 
 5611 
 
 8926 
 
 2605 
 
 5943 
 9256 
 
 2940 
 
 6276 
 9586 
 
 3275 
 
 6608 
 9915 
 
 0245 
 3525 
 6781 
 
 120574 
 3852 
 7105 
 13 
 
 0903 
 4178 
 7429 
 
 1231 
 4504 
 7753 
 
 1560 
 4830 
 8076 
 
 1888 
 5156 
 8399 
 
 2216 
 5481 
 8722 
 
 2544 
 5806 
 9045 
 
 2871 
 6131 
 9368 
 
 3198 
 6456 
 9690 
 
 0012 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 355" 
 
 35.5 
 
 71.0 
 
 106.5 
 
 142.0 
 
 177.5 
 
 213.0 
 
 248.5 
 
 284.0 
 
 319.5 
 
 354 
 
 35.4 
 
 70.8 
 
 106.2 
 
 141.6 
 
 177.0 
 
 212.4 
 
 247.8 
 
 283.2 
 
 318.6 
 
 353 
 
 35.3 
 
 70.6 
 
 105.9 
 
 141.2 
 
 176.5 
 
 211.8 
 
 247.1 
 
 282.4 
 
 317.7 
 
 352 
 
 35.2 
 
 70.4 
 
 105.6 
 
 140.8 
 
 176.0 
 
 211.2 
 
 246.4 
 
 281.6 
 
 316.8 
 
 351 
 
 35.1 
 
 70.2 
 
 105.3 
 
 140.4 
 
 175.5 
 
 210.6 
 
 245.7 
 
 280.8 
 
 315.9 
 
 350 
 
 35.0 
 
 70.0 
 
 105.0 
 
 140.0 
 
 175.0 
 
 210.0 
 
 245.0 
 
 280.0 
 
 315.0 
 
 349 
 
 34.9 
 
 69.8 
 
 104.7 
 
 139.6 
 
 174.5 
 
 209.4 
 
 244.3 
 
 279.2 
 
 314.1 
 
 348 
 
 34.8 
 
 69.6 
 
 104.4 
 
 139.2 
 
 174.0 
 
 208.8 
 
 243.6 
 
 278.4 
 
 313.2 
 
 347 
 
 34.7 
 
 694 
 
 104.1 
 
 138.8 
 
 173.5 
 
 208.2 
 
 242.9 
 
 277.6 
 
 312.3 
 
 346 
 
 34.6 
 
 69.2 
 
 103.8 
 
 138.4 
 
 173.0 
 
 207.6 
 
 242.2 
 
 276.8 
 
 311 4 
 
 345 
 
 34.5 
 
 69.0 
 
 103.5 
 
 138.0 
 
 172.5 
 
 207.0 
 
 241.5 
 
 276.0 
 
 310.5 
 
 344 
 
 34.4 
 
 68.8 
 
 103.2 
 
 137.6 
 
 172.0 
 
 206.4 
 
 240.8 
 
 275.2 
 
 309.6 
 
 343 
 
 34.3 
 
 68.6 
 
 102.9 
 
 137.2 
 
 171.5 
 
 205.8 
 
 240.1 
 
 274.4 
 
 308.7 
 
 342 
 
 34.2 
 
 68.4 
 
 102.6 
 
 136.8 
 
 171.0 
 
 205.2 
 
 239.4 
 
 273.6 
 
 307.8 
 
 341 
 
 34.1 
 
 68.2 
 
 102.3 
 
 136.4 
 
 170.5 
 
 204.6 
 
 238.7 
 
 272.8 
 
 306.9 
 
 340 
 
 34.0 
 
 68.0 
 
 102.0 
 
 136.0 
 
 170.0 
 
 204.0 
 
 238.0 
 
 272.0 
 
 306.0 
 
 339 
 
 33.9 
 
 67.8 
 
 101.7 
 
 135.6 
 
 169.5 
 
 203.4 
 
 237.3 
 
 271.2 
 
 305.1 
 
 338 
 
 33.8 
 
 67.6 
 
 101.4 
 
 135.2 
 
 169.0 
 
 202.8 
 
 236.6 
 
 270.4 
 
 304.2 
 
 337 
 
 33.7 
 
 67.4 
 
 101.1 
 
 134.8 
 
 168.5 
 
 202.2 
 
 235.9 
 
 269.6 
 
 303.3 
 
 336 
 
 33.6 
 
 67.2 
 
 100.8 
 
 134.4 
 
 168.0 
 
 201.6 
 
 235.2 
 
 268.8 
 
 302.4 
 
 335 
 
 33.5 
 
 67.0 
 
 100.5 
 
 134.0 
 
 167.5 
 
 201.0 
 
 234.5 
 
 268.0 
 
 301.5 
 
 334 
 
 33.4 
 
 66.8 
 
 100.2 
 
 133.6 
 
 167.0 
 
 200.4 
 
 233.8 
 
 267.2 
 
 300.6 
 
 333 
 
 33.3 
 
 66.6 
 
 99.9 
 
 133.2 
 
 166.5 
 
 199.8 
 
 233.1 
 
 266.4 
 
 299.7 
 
 332 
 
 33.2 
 
 66.4 
 
 99.6 
 
 132.8 
 
 166.0 
 
 199.2 
 
 232.4 
 
 265.6 
 
 298.8 
 
 331 
 
 33.1 
 
 66.2 
 
 99.3 
 
 132.4 
 
 165.5 
 
 198.6 
 
 231.7 
 
 264.8 
 
 297.9 
 
 330 
 
 33.0 
 
 66.0 
 
 99.0 
 
 132.0 
 
 165.0 
 
 198.0 
 
 231.0 
 
 264.0 
 
 297.0 
 
 329 
 
 32.9 
 
 65.8 
 
 98.7 
 
 131.6 
 
 164.5 
 
 197.4 
 
 230.3 
 
 263.2 
 
 296.1 
 
 328 
 
 32.8 
 
 65.6 
 
 98.4 
 
 131.2 
 
 164.0 
 
 196.8 
 
 229.6 
 
 262.4 
 
 295.2 
 
 327 
 
 32.7 
 
 65.4 
 
 98.1 
 
 130.8 
 
 163.5 
 
 196.2 
 
 228.9 
 
 261.6 
 
 294.3 
 
 326 
 
 32.6. 
 
 65.2 
 
 97.8 
 
 130.4 
 
 163.0 
 
 195.6 
 
 228.2 
 
 260.8 
 
 293.4 
 
 325 
 
 32.5 
 
 65.0 
 
 97.5 
 
 130.0 
 
 162.5 
 
 195.0 
 
 227.5 
 
 260.0 
 
 292.5 
 
 324 
 
 32.4 
 
 64.8 
 
 97.2 
 
 129.6 
 
 162.0 
 
 194.4 
 
 226.8 
 
 259.2 
 
 291.6 
 
 323 
 
 32.3 
 
 64.6 
 
 96.9 
 
 129.2 
 
 161.5 
 
 193.8 
 
 226.1 
 
 258.4 
 
 290.7 
 
 322 
 
 32.2 
 
 64.4 
 
 96.6 
 
 128.8 
 
 161.0 
 
 193.2 
 
 225.4 
 
 257.6 
 
 289.8 
 
LOGARITHMS OF NUMBERS. 
 
 141 
 
 No. 135 L. 130.] 
 
 [No. 149 L. 175. 
 
 N. 
 
 O 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 ~32T 
 318 
 316 
 
 314 
 311 
 
 309 
 
 307 
 305 
 303 
 
 301 
 299 
 297 
 295 
 
 293 
 291 
 
 135 
 6 
 
 7 
 8 
 
 9 
 140 
 
 2 
 3 
 4 
 
 5 
 6 
 
 7 
 
 8 
 9 
 
 130334 
 3539 
 6721 
 9879 
 
 0655 
 3858 
 7037 
 
 0977 
 4177 
 7354 
 
 1298 
 4496 
 7671 
 
 1619 
 4814 
 7987 
 
 1939 
 5133 
 8303 
 
 2260 
 5451 
 8618 
 
 2580 
 5769 
 8934 
 
 2900 
 6086 
 9249 
 
 3219 
 6403 
 9564 
 
 0194 
 3327 
 
 6438 
 9527 
 
 0508 
 3639 
 
 6748 
 9835 
 
 0822 
 3951 
 
 7058 
 
 1136 
 4263 
 
 7367 
 
 1450 
 4574 
 
 7676 
 
 1763 
 4885 
 
 7985 
 
 2076 
 5196 
 
 8294 
 
 2389 
 5507 
 
 8603 
 
 2702 
 5818 
 
 8911 
 
 143015 
 
 6128 
 9219 
 
 0142 
 3205 
 6246 
 9266 
 
 0449 
 3510 
 6549 
 9567 
 
 0756 
 3815 
 6852 
 9868 
 
 1063 
 4120 
 7154 
 
 1370 
 4424 
 7457 
 
 1676 
 4728 
 7759 
 
 1982 
 5032 
 8061 
 
 152288 
 5336 
 8362 
 
 2594 
 5640 
 8664 
 
 2900 
 5943 
 8965 
 
 0168 
 3161 
 6134 
 9086 
 
 0469 
 3460 
 6430 
 9380 
 
 0769 
 3758 
 6726 
 9674 
 
 1068 
 4055 
 7022 
 9968 
 
 161368 
 4353 
 7317 
 
 1667 
 4650 
 7613 
 
 1967 
 4947 
 7908 
 
 2266 
 5244 
 8203 
 
 2564 
 
 5541 
 8497 
 
 2863 
 5838 
 8792 
 
 1 70262 
 3186 
 
 0555 
 
 3478 
 
 0348 
 3769 
 
 1141 
 4060 
 
 1434 
 4351 
 
 1726 
 4641 
 
 2019 
 4932 
 
 2311 
 5222 
 
 2603 
 5512 
 
 2895 
 5802 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 321 
 
 32.1 
 
 64.2 
 
 96.3 
 
 128.4 
 
 160.5 
 
 192.6 
 
 224.7 
 
 256.8 
 
 288.9 
 
 320 
 
 32.0 
 
 64.0 
 
 96.0 
 
 128.0 
 
 160.0 
 
 192.0 
 
 224.0 
 
 256.0 
 
 2880 
 
 319 
 
 31.9 
 
 63.8 
 
 95.7 
 
 127.6 
 
 159.5 
 
 191.4 
 
 223.3 
 
 255.2 
 
 287.1 
 
 318 
 
 31.8 
 
 63.6 
 
 95.4 
 
 127.2 
 
 159.0 
 
 190.8 
 
 222.6 
 
 254.4 
 
 286.2 
 
 317 
 
 31.7 
 
 63.4 
 
 95.1 
 
 126.8 
 
 158.5 
 
 190.2 
 
 221.9 
 
 253.6 
 
 285.3 
 
 316 
 
 31.6 
 
 63.2 
 
 94.8 
 
 126.4 
 
 158.0 
 
 189.6 
 
 221.2 
 
 252.8 
 
 284.4 
 
 315 
 
 31.5 
 
 63.0 
 
 94.5 
 
 126.0 
 
 157.5 
 
 189.0 
 
 220.5 
 
 252.0 
 
 283.5 
 
 314 
 
 31.4 
 
 62.8 
 
 94.2 
 
 125.6 
 
 157.0 
 
 188.4 
 
 219.8 
 
 251.2 
 
 282.6 
 
 313 
 
 31.3 
 
 62.6 
 
 93.9 
 
 125.2 
 
 156.5 
 
 187.8 
 
 219.1 
 
 250.4 
 
 281.7 
 
 312 
 
 31.2 
 
 62.4 
 
 93.6 
 
 124.8 
 
 156.0 
 
 187.2 
 
 218.4 
 
 249.6 
 
 280.8 
 
 311 
 
 31.1 
 
 62.2 
 
 93.3 
 
 124.4 
 
 155.5 
 
 186.6 
 
 217.7 
 
 248.8 
 
 279.9 
 
 310 
 
 31.0 
 
 62.0 
 
 93.0 
 
 124.0 
 
 155.0 
 
 186.0 
 
 217.0 
 
 248.0 
 
 279.0 
 
 309 
 
 30.9 
 
 61.8 
 
 92.7 
 
 123.6 
 
 154.5 
 
 185.4 
 
 216.3 
 
 247.2 
 
 278.1 
 
 308 
 
 30.8 
 
 61.6 
 
 92.4 
 
 123.2 
 
 154.0 
 
 184.8 
 
 215.6 
 
 246.4 
 
 277.2 
 
 307 
 
 30.7 
 
 61.4 
 
 92.1 
 
 122.8 
 
 153.5 
 
 184.2 
 
 214.9 
 
 245.6 
 
 276.3 
 
 306 
 
 30.6 
 
 61.2 
 
 91.8 
 
 122.4 
 
 153.0 
 
 183.6 
 
 214.2 
 
 244.8 
 
 275.4 
 
 305 
 
 30!5 
 
 61.0 
 
 91.5 
 
 122.0 
 
 152 5 
 
 183.0 
 
 213.5 
 
 244.0 
 
 274.5 
 
 304 
 
 30.4 
 
 60.8 
 
 91.2 
 
 121.6 
 
 152.0 
 
 182.4 
 
 212.8 
 
 243.2 
 
 273.6 
 
 303 
 
 30.3 
 
 60.6 
 
 90.9 
 
 121.2 
 
 151.5 
 
 181.8 
 
 212.1 
 
 242.4 
 
 272.7 
 
 302 
 
 30.2 
 
 60.4 
 
 90.6 
 
 120.8 
 
 151.0 
 
 181.2 
 
 211.4 
 
 241.6 
 
 271.8 
 
 301 
 
 30.1 
 
 60.2 
 
 90.3 
 
 120.4 
 
 150.5 
 
 1806 
 
 210.7 
 
 240.8 
 
 270.9 
 
 300 
 
 30.0 
 
 60.0 
 
 90.0 
 
 120.0 
 
 150.0 
 
 180.0 
 
 210.0 
 
 240.0 
 
 270.0 
 
 299 
 
 29.9 
 
 59.8 
 
 89.7 
 
 119.6 
 
 149.5 
 
 179.4 
 
 209.3 
 
 239.2 
 
 269.1 
 
 298 
 
 29.8 
 
 59.6 
 
 89.4 
 
 119.2 
 
 149.0 
 
 178.8 
 
 208.6 
 
 238.4 
 
 268.2 
 
 297 
 
 29.7 
 
 59.4 
 
 89.1 
 
 118.8 
 
 148.5 
 
 178.2 
 
 207.9 
 
 237.6 
 
 267.3 
 
 296 
 
 29.6 
 
 59.2 
 
 88.8 
 
 118.4 
 
 148.0 
 
 177.6 
 
 207.2 
 
 236.8 
 
 266.4 
 
 295 
 
 29.5 
 
 590 
 
 88.5 
 
 118.0 
 
 147.5 
 
 177.0 
 
 206.5 
 
 236.0 
 
 265.5 
 
 294 
 
 29.4 
 
 58.8 
 
 88.2 
 
 117.6 
 
 147.0 
 
 176.4 
 
 205.8 
 
 235.2 
 
 264.6 
 
 293 
 
 29.3 
 
 58.6 
 
 87.9 
 
 117.2 
 
 146.5 
 
 175.8 
 
 205.1 
 
 234.4 
 
 263.7 
 
 292 
 
 29.2 
 
 58.4 
 
 87.6 
 
 116.8 
 
 146,0 
 
 175.2 
 
 204.4 
 
 233.6 
 
 262.8 
 
 291 
 
 29.1 
 
 58.2 
 
 87.3 
 
 116.4 
 
 145.5 
 
 174.6 
 
 203.7 
 
 232.8 
 
 261.9 
 
 290 
 
 29.0 
 
 58.0 
 
 87.0 
 
 116.0 
 
 145.0 
 
 174.0 
 
 203.0 
 
 232.0 
 
 261.. 
 
 289 
 
 28.9 
 
 57.8 
 
 86.7 
 
 115.6 
 
 144.5 
 
 173.4 
 
 202.3 
 
 231.2 
 
 260.1 
 
 288 
 
 28.8 
 
 57.6 
 
 86.4 
 
 115.2 
 
 144.0 
 
 172.3 
 
 201.6 
 
 230.4 
 
 259.2 
 
 287 
 
 28.7 
 
 57.4 
 
 86.1 
 
 114.8 
 
 143.5 
 
 172.2 
 
 200.9 
 
 229.6 
 
 258.3 
 
 286 
 
 28.6 
 
 57.2 
 
 85.8 
 
 114.4 
 
 143.0 
 
 171.6 
 
 200.2 
 
 228.8 
 
 2*7.4 
 
142 
 
 LOGARITHMS OP NUMBERS. 
 
 Wo. 150 L. 176.] 
 
 [No. 109 L. 230 
 
 N. 
 ~T50" 
 
 2 
 
 4 
 
 5 
 6 
 7 
 
 8 
 
 9 
 160 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 9 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 DiflF. 
 -28T 
 
 287 
 285 
 
 283 
 
 281 
 279 
 278 
 276 
 
 274 
 272 
 
 271 
 269 
 
 267 
 266 
 264 
 262 
 
 261 
 259 
 258 
 
 256 
 
 176091 
 8977 
 
 6381 
 9264 
 
 6670 
 9552 
 
 6959 
 9839 
 
 7248 
 
 7536 
 
 7825 
 
 8113 
 
 8401 
 
 8689 
 
 0126 
 2985 
 5825 
 8647 
 
 0413 
 3270 
 6108 
 8928 
 
 0699 
 3555 
 6391 
 9209 
 
 0986 
 3839 
 6674 
 9490 
 
 1272 
 4123 
 6956 
 9771 
 
 1558 
 4407 
 7239 
 
 181844 
 4691 
 7521 
 
 2129 
 4975 
 7803 
 
 2415 
 5259 
 8084 
 
 2700 
 5542 
 8366 
 
 0051 
 2846 
 5623 
 8382 
 
 190332 
 3125 
 5900 
 8657 
 
 0612 
 3403 
 6176 
 8932 
 
 0892 
 3681 
 6453 
 9206 
 
 1171 
 3959 
 6729 
 9481 
 
 1451 
 4237 
 7005 
 9755 
 
 1730 
 4514 
 7281 
 
 2010 
 4792 
 7556 
 
 2289 
 5069 
 7832 
 
 2567 
 5346 
 8107 
 
 0029 
 2761 
 
 5475 
 8173 
 
 0303 
 3033 
 
 5746 
 8441 
 
 0577 
 3305 
 
 6016 
 8710 
 
 0850 
 3577 
 
 6286 
 8979 
 
 1124 
 3848 
 
 6556 
 9247 
 
 201397 
 
 4120 
 6826 
 9515 
 
 1670 
 
 4391 
 7096 
 9783 
 
 1943 
 
 4663 
 7365 
 
 2216 
 
 4934 
 7634 
 
 2488 
 
 5204 
 7904 
 
 0051 
 2720 
 5373 
 8010 
 
 0319 
 2986 
 5638 
 8273 
 
 0586 
 3252 
 5902 
 8536 
 
 0853 
 3518 
 6166 
 8798 
 
 1121 
 3783 
 6430 
 9060 
 
 1388 
 4049 
 6694 
 9323 
 
 1654 
 4314 
 6957 
 9585 
 
 1921 
 4579 
 7221 
 9846 
 
 212188 
 4844 
 7484 
 
 2454 
 5109 
 7747 
 
 220108 
 2716 
 5309 
 7887 
 23 
 
 0370 
 2976 
 5568 
 8144 
 
 0631 
 3236 
 5826 
 8400 
 
 0892 
 3496 
 6084 
 8657 
 
 1153 
 3755 
 6342 
 8913 
 
 1414 
 4015 
 6600 
 9170 
 
 1675 
 4274 
 6858 
 9426 
 
 1936 
 4533 
 7115 
 9682 
 
 2196 
 4792 
 7372 
 9938 
 
 2456 
 5051 
 7630 
 
 0193 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 285 
 
 28.5 
 
 57.0 
 
 85.5 
 
 114.0 
 
 142.5 
 
 171.0 
 
 199.5 
 
 228.0 
 
 256.5 
 
 ,784 
 
 28.4 
 
 56.8 
 
 85.2 
 
 113.6 
 
 142.0 
 
 170.4 
 
 198.8 
 
 227.2 
 
 255.6 
 
 283 
 
 28.3 
 
 56.6 
 
 84.9 
 
 113.2 
 
 141.5 
 
 169.8 
 
 198.1 
 
 226.4 
 
 254.7 
 
 282 
 
 28.2 
 
 56.4 
 
 84.6 
 
 112.8 
 
 141.0 
 
 169.2 
 
 197.4 
 
 225.6 
 
 253.8 
 
 281 
 
 28.1 
 
 56.2 
 
 84.3 
 
 112.4 
 
 140.5 
 
 168.6 
 
 196.7 
 
 224.8 
 
 252.9 
 
 280 
 
 28.0 
 
 56.0 
 
 84.0 
 
 112.0 
 
 140.0 
 
 168.0 
 
 196.0 
 
 224.0 
 
 252.0 
 
 279 
 
 27.9 
 
 55.8 
 
 83.7 
 
 111.6 
 
 139.5 
 
 167.4 
 
 195.3 
 
 223.2 
 
 251.1 
 
 278 
 
 27.8 
 
 55.6 
 
 83.4 
 
 111.2 
 
 139.0 
 
 166.8 
 
 194.6 
 
 222.4 
 
 250.2 
 
 277 
 
 27.7 
 
 55.4 
 
 83.1 
 
 110.8 
 
 138.5 
 
 166.2 
 
 193.9 
 
 221.6 
 
 249.3 
 
 276 
 
 27.6 
 
 55.2 
 
 82.8 
 
 110.4 
 
 138.0 
 
 165.6 
 
 193.2 
 
 220.8 
 
 248.4 
 
 275 
 
 27.5 
 
 55.0 
 
 82.5 
 
 110.0 
 
 137.5 
 
 165.0 
 
 192.5 
 
 220.0 
 
 247.5 
 
 274 
 
 27.4 
 
 54.8 
 
 82.2 
 
 109.6 
 
 137.0 
 
 164.4 
 
 191.8 
 
 219.2 
 
 246.6 
 
 273 
 
 27.3 
 
 54.6 
 
 81.9 
 
 109,2 
 
 136.5 
 
 163.8 
 
 191.1 
 
 218.4 
 
 245.7 
 
 272 
 
 27.2 
 
 54.4 
 
 81.6 
 
 108.8 
 
 136.0 
 
 163.2 
 
 190.4 
 
 217.6 
 
 244.8 
 
 271 
 
 27.1 
 
 54.2 
 
 81.3 
 
 108.4 
 
 135.5 
 
 162.6 
 
 189.7 
 
 216.8 
 
 243.9 
 
 270 
 
 27.0 
 
 54.0 
 
 81.0 
 
 108.0 
 
 135.0 
 
 162.0 
 
 189.0 
 
 216.0 
 
 243.0 
 
 269 
 
 26.9 
 
 53.8 
 
 80.7 
 
 107.6 
 
 134.5 
 
 161.4 
 
 188.3 
 
 215.2 
 
 242.1 
 
 268 
 
 26.8 
 
 53.6 
 
 80.4 
 
 107.2 
 
 134.0 
 
 160.8 
 
 187.6 
 
 214.4 
 
 241.2 
 
 267 
 
 26.7 
 
 53.4 
 
 80.1 
 
 106.8 
 
 133.5 
 
 160.2 
 
 186.9 
 
 213.6 
 
 240.3 
 
 266 
 
 26.6 
 
 53.2 
 
 79.8 
 
 106.4 
 
 133.0 
 
 159.6 
 
 186.2 
 
 212.8 
 
 239.4 
 
 265 
 
 26.5 
 
 53.0 
 
 79.5 
 
 106.0 
 
 132.5 
 
 159.0 
 
 185.5 
 
 212.0 
 
 238.5 
 
 264 
 
 26.4 
 
 52.8 
 
 79.2 
 
 105.6 
 
 132.0 
 
 158.4 
 
 184.8 
 
 211.2 
 
 237.6 
 
 263 
 
 26.3 
 
 52.6 
 
 78.9 
 
 105.2 
 
 131.5 
 
 157.8 
 
 184.1 
 
 210.4 
 
 236.7 
 
 262 
 
 26.2 
 
 52.4 
 
 78.6 
 
 104.8 
 
 131.0 
 
 157.2 
 
 183.4 
 
 209.6 
 
 235.8 
 
 261 
 
 26.1 
 
 52.2 
 
 78.3 
 
 104.4 
 
 130.5 
 
 156.6 
 
 182.7 
 
 208.8 
 
 234.9 
 
 260 
 
 26.0 
 
 52.0 
 
 78.0 
 
 104.0 
 
 130.0 
 
 156.0 
 
 182.0 
 
 208.0 
 
 234.0 
 
 259 
 
 25.9 
 
 51.8 
 
 77.7 
 
 103.6 
 
 129.5 
 
 155.4 
 
 181.3 
 
 207.2 
 
 233.1 
 
 258 
 
 25.8 
 
 51.6 
 
 77.4 
 
 103.2 
 
 129.0 
 
 154.8 
 
 180.6 
 
 206.4 
 
 232.2 
 
 257 
 
 25.7 
 
 51.4 
 
 77.1 
 
 102.8 
 
 128.5 
 
 154.2 
 
 179.9 
 
 205.6 
 
 231.3 
 
 256 
 
 25.6 
 
 51.2 
 
 76,8 
 
 102.4 
 
 128.0 
 
 153.6 
 
 179.2 
 
 204.8 
 
 230.4 
 
 255 
 
 25.5 
 
 51.0 
 
 76.5 ' 
 
 102.0 
 
 127.5 ' 
 
 153.0 
 
 178.5 
 
 204.0 i 
 
 229J 
 
LOGARITHMS OF NUMBERS. 
 
 143 
 
 No. I VOL. 230.] 
 
 [No. 189L.278. 
 
 N. 
 
 17o~ 
 
 i 
 
 2 
 3 
 
 4 
 
 6 
 7 
 
 8 
 9 
 
 180 
 1 
 
 2 
 3 
 
 4 
 5 
 6 
 
 8 
 9 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 230449 
 2996 
 5528 
 8046 
 
 0704 
 3250 
 5781 
 8297 
 
 0960 
 3504 
 6033 
 8548 
 
 1215 
 3757 
 6285 
 8799 
 
 1470 
 4011 
 6537 
 9049 
 
 1724 
 4264 
 6789 
 9299 
 
 1979 
 4517 
 7041 
 9550 
 
 2234 
 4770 
 7292 
 9800 
 
 2488 
 5023 
 7544 
 
 2742 
 5276 
 7795 
 
 255 
 253 
 252 
 
 250 
 
 249 
 248 
 246 
 
 245 
 243 
 242 
 
 241 
 239 
 
 238 
 237 
 235 
 234 
 
 233 
 232 
 230 
 229 
 
 0050 
 2541 
 5019 
 7482 
 9932 
 
 0300 
 2790 
 5266 
 7728 
 
 240549 
 3038 
 5513 
 7973 
 
 0799 
 3286 
 5759 
 8219 
 
 1048 
 3534 
 6006 
 8464 
 
 1297 
 3782 
 6252 
 8709 
 
 1546 
 4030 
 6499 
 8954 
 
 1795 
 4277 
 6745 
 9198 
 
 2044 
 4525 
 6991 
 9443 
 
 2293 
 4772 
 7237 
 9687 
 
 0176 
 2610 
 5031 
 
 7439 
 9833 
 
 250420 
 2853 
 
 5273 
 7679 
 
 0664 
 3096 
 
 5514 
 7918 
 
 0908 
 3338 
 
 5755 
 8158 
 
 1151 
 3580 
 
 5996 
 8398 
 
 1395 
 
 3822 
 
 6237 
 8637 
 
 1638 
 4064 
 
 6477 
 8877 
 
 1881 
 4306 
 
 6718 
 9116 
 
 2125 
 4548 
 
 6958 
 9355 
 
 2368 
 4790 
 
 7198 
 9594 
 
 260071 
 2451 
 4818 
 7172 
 9513 
 
 0310 
 2688 
 5054 
 7406 
 9746 
 
 0548 
 2925 
 5290 
 7641 
 9980 
 
 0787 
 3162 
 5525 
 7875 
 
 1025 
 3399 
 5761 
 81 10 
 
 1263 
 3636 
 5996 
 8344 
 
 1501 
 3873 
 6232 
 8578 
 
 1739 
 4109 
 6467 
 8812 
 
 1976 
 4346 
 6702 
 9046 
 
 2214 
 4582 
 6937 
 9279 
 
 0213 
 2538 
 4850 
 7151 
 
 0446 
 2770 
 5081 
 7380 
 
 0679 
 3001 
 5311 
 7609 
 
 0912 
 3233 
 5542 
 7838 
 
 1144 
 3464 
 5772 
 8067 
 
 1377 
 3696 
 6002 
 8296 
 
 1609 
 3927 
 6232 
 8525 
 
 271842 
 4158 
 6462 
 
 2074 
 4389 
 6692 
 
 2306 
 4620 
 6921 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 255 
 
 25.5 
 
 51.0 
 
 76.5 
 
 102.0 
 
 127.5 
 
 153.0 
 
 178.5 
 
 204.0 
 
 229.5 
 
 254 
 
 25.4 
 
 50.8 
 
 76.2 
 
 101.6 
 
 127.0 
 
 152.4 
 
 177.8 
 
 203.2 
 
 228.6 
 
 253 
 
 25.3 
 
 50.6 
 
 75.9 
 
 101.2 
 
 126.5 
 
 151.8 
 
 177.1 
 
 202.4 
 
 227.7 
 
 252 
 
 25.2 
 
 50.4 
 
 75.6 
 
 100.8 
 
 126.0 
 
 151.2 
 
 176.4 
 
 201.6 
 
 226.8 
 
 251 
 
 25.1 
 
 50.2 
 
 75.3 
 
 100.4 
 
 125.5 
 
 150.6 
 
 175.7 
 
 200.8 
 
 225.9 
 
 250 
 
 25.0 
 
 50.0 
 
 75.0 
 
 100.0 
 
 125.0 
 
 150.0 
 
 175.0 
 
 200.0 
 
 225.0 
 
 249 
 
 24.9 
 
 49.8 
 
 74.7 
 
 99.6 
 
 124.5 
 
 149.4 
 
 174.3 
 
 199.2 
 
 224.1 
 
 248 
 
 24.8 
 
 49.6 
 
 74.4 
 
 99.2 
 
 124.0 
 
 148.8 
 
 173.6 
 
 198.4 
 
 223.2 
 
 247 
 
 24.7 
 
 49.4 
 
 74.1 
 
 98.8 
 
 123.5 
 
 148.2 
 
 172.9 
 
 197.6 
 
 222.3 
 
 246 
 
 24.6 
 
 49.2 
 
 73.8 
 
 98.4 
 
 123.0 
 
 147.6 
 
 172.2 
 
 196.8 
 
 221.4 
 
 245 
 
 24.5 
 
 49.0 
 
 73.5 
 
 98.0 
 
 122.5 
 
 147.0 
 
 171.5 
 
 196.0 
 
 220.5 
 
 244 
 
 24.4 
 
 48.8 
 
 73.2 
 
 97.6 
 
 122.0 
 
 146.4 
 
 170.8 
 
 195.2 
 
 219.6 
 
 243 
 
 24.3 
 
 48.6 
 
 72.9 
 
 97.2 
 
 121.5 
 
 145.8 
 
 170.1 
 
 194.4 
 
 218.7 
 
 242 
 
 24.2 
 
 48.4 
 
 72.6 
 
 96.8 
 
 121.0 
 
 145.2 
 
 1694 
 
 193.6 
 
 217.8 
 
 241 
 
 24.1 
 
 48.2 
 
 72.3 
 
 96.4 
 
 120.5 
 
 144.6 
 
 168.7 
 
 192.8 
 
 216.9 
 
 240 
 
 24.0 
 
 48.0 
 
 72.0 
 
 96.0 
 
 120.0 
 
 144.0 
 
 168.0 
 
 192.0 
 
 216.0 
 
 239 
 
 23.9 
 
 47.8 
 
 71.7 
 
 95.6 
 
 119.5 
 
 143.4 
 
 167.3 
 
 191.2 
 
 215.1 
 
 238 
 
 23.8 
 
 47.6 
 
 71.4 
 
 95.2 
 
 119.0 
 
 142.8 
 
 166.6 
 
 190.4 
 
 214.2 
 
 237 
 
 23.7 
 
 47.4 
 
 71.1 
 
 94.8 
 
 118.5 
 
 142.2 
 
 165.9 
 
 189.6 
 
 213.3 
 
 236 
 
 23.6 
 
 47.2 
 
 70.8 
 
 94.4 
 
 118.0 
 
 141.6 
 
 165.2 
 
 188.8 
 
 212.4 
 
 235 
 
 23.5 
 
 47.0 
 
 70.5 
 
 94.0 
 
 117.5 
 
 141.0 
 
 164.5 
 
 188.0 
 
 211.5 
 
 234 
 
 23.4 
 
 46.8 
 
 70.2 
 
 93.6 
 
 117.0 
 
 140.4 
 
 163.8 
 
 187.2 
 
 210.6 
 
 233 
 
 23.3 
 
 46.6 
 
 69.9 
 
 93.2 
 
 116.5 
 
 139.8 
 
 163.1 
 
 186.4 
 
 209.7 
 
 232 
 
 23.2 
 
 46.4 
 
 69.6 
 
 92.8 
 
 116.0 
 
 139.2 
 
 162.4 
 
 185.6 
 
 208.8 
 
 231 
 
 23.1 
 
 46.2 
 
 69.3 
 
 92.4 
 
 115.5 
 
 138.6 
 
 161.7 
 
 184.8 
 
 207.9 
 
 230 
 
 23.0 
 
 46.0 
 
 69.0 
 
 920 
 
 115.0 
 
 138.0 
 
 161.0 
 
 184.0 
 
 207.0 
 
 229 
 
 22.9 
 
 45.8 
 
 68.7 
 
 91.6 
 
 114.5 
 
 137.4 
 
 160.3 
 
 183.2 
 
 206.1 
 
 228 
 
 22.8 
 
 45.6 
 
 68.4 
 
 91.2 
 
 114.0 
 
 136.8 
 
 159.6 
 
 182.4 
 
 205.2 
 
 227 
 
 22.7 
 
 45.4 
 
 68.1 
 
 90.8 
 
 113.5 
 
 136.2 
 
 158.9 
 
 181.6 
 
 204.3 
 
 226 
 
 22.6 
 
 45.2 
 
 67.8 
 
 90.4 
 
 113.0 
 
 135.6 
 
 158.2 
 
 180.8 
 
 203.4 
 
144 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 190 L. 278.] 
 
 [No. 214 L.332. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 190 
 
 278754 
 
 898;; 
 
 921 1 
 
 9439 
 
 9667 
 
 9895 
 
 
 
 
 
 
 
 
 
 
 
 
 
 m j-i 
 
 nae 
 
 n^7 
 
 flQflA 
 
 
 2 
 3 
 4 
 
 281033 
 3301 
 5557 
 7802 
 
 1261 
 3527 
 5782 
 8026 
 
 1488 
 3753 
 6007 
 8249 
 
 1715 
 3979 
 6232 
 8473 
 
 1942 
 4205 
 6456 
 8696 
 
 2169 
 4431 
 6681 
 8920 
 
 2396 
 4656 
 6905 
 9143 
 
 2622 
 4882 
 7130 
 9366 
 
 2849 
 5107 
 7354 
 9589 
 
 3075 
 5332 
 
 7578 
 9812 
 
 227 
 226 
 225 
 223 
 
 5 
 6 
 7 
 8 
 9 
 
 290035 
 2256 
 4466 
 6665 
 8853 
 
 0257 
 2478 
 4687 
 6884 
 9071 
 
 0480 
 2699 
 4907 
 7104 
 9289 
 
 0702 
 2920 
 5127 
 7323 
 9507 
 
 0925 
 3141 
 5347 
 7542 
 9725 
 
 1147 
 3363 
 5567 
 7761 
 9943 
 
 1369 
 3584 
 5787 
 7979 
 
 1591 
 3804 
 6007 
 8198 
 
 1813 
 4025 
 6226 
 8416 
 
 2034 
 4246 
 6446 
 8635 
 
 222 
 221 
 220 
 219 
 
 
 
 
 
 
 
 
 0161 
 
 0-170 
 
 ft^QS 
 
 no i q 
 
 9 t A 
 
 200 
 1 
 2 
 3 
 4 
 
 301030 
 3196 
 5351 
 7496 
 9630 
 
 1247 
 3412 
 5566 
 7710 
 9843 
 
 1464 
 3628 
 5781 
 7924 
 
 1681 
 3844 
 5996 
 8137 
 
 1898 
 4059 
 6211 
 8351 
 
 2114 
 4275 
 6425 
 8564 
 
 2331 
 
 4491 
 6639 
 
 8778 
 
 2547 
 4706 
 6854 
 8991 
 
 2764 
 4921 
 7068 
 9204 
 
 2980 
 5136 
 7282 
 9417 
 
 217 
 216 
 215 
 213 
 
 
 
 
 0056 
 
 0268 
 
 048 1 
 
 0693 
 
 0906 
 
 1 1 j o 
 
 i -2ar\ 
 
 1 ^49 
 
 919 
 
 5 
 6 
 7 
 8 
 
 311754 
 3867 
 5970 
 8063 
 
 1966 
 4078 
 6180 
 
 8272 
 
 2177 
 4289 
 6390 
 8481 
 
 2389 
 4499 
 6599 
 8689 
 
 2600 
 4710 
 6809 
 8898 
 
 2812 
 4920 
 7018 
 9106 
 
 3023 
 5130 
 
 7227 
 9314 
 
 3234 
 5340 
 7436 
 9522 
 
 3445 
 5551 
 7646 
 9730 
 
 3656 
 5760 
 
 7854 
 9938 
 
 211 
 210 
 209 
 208 
 
 9 
 210 
 
 2 
 3 
 
 320146 
 
 2219 
 4282 
 6336 
 8380 
 
 0354 
 
 2426 
 4488 
 6541 
 8583 
 
 0562 
 
 2633 
 4694 
 6745 
 8787 
 
 0769 
 
 2839 
 4899 
 6950 
 
 8991 
 
 t)977 
 
 3046 
 5105 
 7155 
 9194 
 
 1184 
 
 3252 
 5310 
 7359 
 9398 
 
 1391 
 
 3458 
 5516 
 7563 
 9601 
 
 1598 
 
 3665 
 5721 
 7767 
 9805 
 
 1805 
 
 3871 
 5926 
 7972 
 
 2012 
 
 4077 
 6131 
 8176 
 
 207 
 
 206 
 205 
 204 
 
 
 
 
 
 
 
 
 
 
 noftP. 
 
 O9 i i 
 
 9flT 
 
 4 
 
 330414 
 
 0617 
 
 0819 
 
 1022 
 
 1225 
 
 1427 
 
 1630 
 
 1832 
 
 2034 
 
 2236 
 
 202 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 225 
 
 22.5 
 
 45.0 
 
 67.5 
 
 90.0 
 
 112.5 
 
 135.0 
 
 157.5 
 
 180.0 
 
 202.5 
 
 224 
 
 22.4 
 
 44.8 
 
 67.2 
 
 89 6 
 
 112.0 
 
 134.4 
 
 156.8 
 
 179.2 
 
 201.6 
 
 223 
 
 22.3 
 
 44.6 
 
 66.9 
 
 89.2 
 
 111.5 
 
 133.8 
 
 156.1 
 
 178.4 
 
 200.7 
 
 222 
 
 22.2 
 
 44.4 
 
 66.6 
 
 88.8 
 
 1110 
 
 133.2 
 
 155.4 
 
 177.6 
 
 199.8 
 
 221 
 
 22.1 
 
 44.2 
 
 66.3 
 
 88.4 
 
 110.5 
 
 132.6 
 
 154.7 
 
 176.8 
 
 198.9 
 
 220 
 
 22.0 
 
 44.0 
 
 66.0 
 
 88.0 
 
 110.0 
 
 132.0 
 
 154.0 
 
 176.0 
 
 198.0 
 
 219 
 
 21.9 
 
 43.8 
 
 65.7 
 
 87.6 
 
 109.5 
 
 131.4 
 
 153.3 
 
 175.2 
 
 197.1 
 
 218 
 
 21.8 
 
 43.6 
 
 65.4 
 
 87.2 
 
 109.0 
 
 130.8 
 
 152.6 
 
 174.4 
 
 196.2 
 
 217 
 
 21.7 
 
 43.4 
 
 65.1 
 
 86.8 
 
 108.5 
 
 130.2 
 
 151.9 
 
 173.6 
 
 195.3 
 
 216 
 
 21.6 
 
 43.2 
 
 64.8 
 
 86.4 
 
 108.0 
 
 129.6 
 
 151.2 
 
 172.8 
 
 194.4 
 
 215 
 
 21.5 
 
 43.0 
 
 64.5 
 
 86.0 
 
 107.5 
 
 129.0 
 
 150.5 
 
 172.0 
 
 193.5 
 
 214 
 
 21.4 
 
 42.8 
 
 64.2 
 
 85.6 
 
 107.0 
 
 128.4 
 
 149.8 
 
 171.2 
 
 192.6 
 
 213 
 
 21.3 
 
 42.6 
 
 63.9 
 
 85.2 
 
 106.5 
 
 127.8 
 
 149.1 
 
 170.4 
 
 191.7 
 
 212 
 
 21.2 
 
 42.4 
 
 63.6 
 
 84.8 
 
 106.0 
 
 127.2 
 
 148.4 
 
 169.6 
 
 190.8 
 
 211 
 
 21.1 
 
 42.2 
 
 63.3 
 
 84.4 
 
 105.5 
 
 126.6 
 
 147.7 
 
 168.8 
 
 189.9 
 
 210 
 
 21.0 
 
 42.0 
 
 63.0 
 
 84.0 
 
 105.0 
 
 126.0 
 
 147.0 
 
 168.0 
 
 189.0 
 
 209 
 
 20.9 
 
 41.8 
 
 62.7 
 
 83.6 
 
 104.5 
 
 125.4 
 
 146.3 
 
 167.2 
 
 188.1 
 
 208 
 
 20.8 
 
 41.6 
 
 62.4 
 
 83.2 
 
 104.0 
 
 124.8 
 
 145.6 
 
 166.4 
 
 187.2 
 
 207 
 
 20.7 
 
 41.4 
 
 62.1 
 
 82.8 
 
 103.5 
 
 124.2 
 
 144.9 
 
 165.6 
 
 186.3 
 
 206 
 
 20.6 
 
 41:2 
 
 61.8 
 
 82.4 
 
 103.0 
 
 123.6 
 
 144.2 
 
 164.8 
 
 185.4 
 
 205 
 
 20.5 
 
 41.0 
 
 61.5 
 
 82.0 
 
 102.5 
 
 123.0 
 
 143 5 
 
 164.0 
 
 184.5 
 
 204 
 
 20.4 
 
 40.8 
 
 61.2 
 
 81.6 
 
 102.0 
 
 122.4 
 
 142.8 
 
 163.2 
 
 183.6 
 
 203 
 
 20.3 
 
 40.6 
 
 60.9 
 
 81.2 
 
 101.5 
 
 121.8 
 
 142.1 
 
 162.4 
 
 182.7 
 
 202 
 
 20.2 
 
 40.4 
 
 60.6 
 
 80.8 
 
 101.0 
 
 121.2 1 
 
 141.4 
 
 161.6 
 
 181.8 
 
LOGARITHMS OF NUMBERS. 
 
 145 
 
 No. 215 L. 332.] 
 
 [No. 239 L. 380. 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 "3447 
 5458 
 7459 
 9451 
 
 6 
 
 73649 
 5658 
 7659 
 9650 
 
 7 
 
 ~3850 
 5859 
 7858 
 9849 
 
 8 
 
 ~~4Q5~1 
 6059 
 8058 
 
 9 
 
 "4253 
 6260 
 
 S257 
 
 Diff. 
 
 ~202" 
 201 
 200 
 
 199 
 198 
 
 197 
 196 
 195 
 
 194 
 193 
 193 
 192 
 191 
 190 
 
 189 
 
 188 
 188 
 187 
 186 
 
 215 
 6 
 
 8 
 9 
 220 
 
 2 
 3 
 
 4 
 6 
 
 8 
 9 
 
 230 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 332438 
 4454 
 6460 
 8456 
 
 2640 
 4655 
 6660 
 8656 
 
 2842 
 4856 
 6860 
 8855 
 
 3044 
 5057 
 7060 
 9054 
 
 3246 
 5257 
 7260 
 9253 
 
 0047 
 2028 
 
 3999 
 5962 
 7915 
 9860 
 
 1796 
 3724 
 5643 
 7554 
 9456 
 
 0246 
 2225 
 
 4195 
 6157 
 8110 
 
 340444 
 
 2423 
 4392 
 6353 
 8305 
 
 0642 
 
 2620 
 4589 
 6549 
 8500 
 
 0841 
 
 2817 
 4785 
 6744 
 8694 
 
 1039 
 
 3014 
 4981 
 6939 
 8889 
 
 1237 
 
 3212 
 5178 
 7135 
 9083 
 
 1435 
 
 3409 
 5374 
 7330 
 9278 
 
 1632 
 
 3606 
 5570 
 7525 
 9472 
 
 1830 
 
 3802 
 5766 
 7720 
 9666 
 
 1603 
 3532 
 5452 
 7363 
 9266 
 
 0054 
 1989 
 3916 
 5834 
 7744 
 9646 
 
 350248 
 2183 
 4108 
 6026 
 7935 
 9835 
 
 0442 
 2375 
 4301 
 6217 
 8125 
 
 0636 
 2568 
 4493 
 6408 
 8316 
 
 0829 
 2761 
 4685 
 6599 
 8506 
 
 1023 
 2954 
 4876 
 6790 
 8696 
 
 1216 
 3147 
 5068 
 6981 
 8886 
 
 1410 
 3339 
 5260 
 7172 
 9076 
 
 0025 
 
 1917 
 3800 
 5675 
 7542 
 9401 
 
 0215 
 
 2105 
 3988 
 5862 
 7729 
 9587 
 
 0404 
 
 2294 
 4176 
 6049 
 7915 
 9772 
 
 0593 
 
 2482 
 4363 
 6236 
 8101 
 9958 
 
 0783 
 
 2671 
 4551 
 6423 
 
 8287 
 
 0972 
 
 2859 
 4739 
 6610 
 8473 
 
 1161 
 
 3048 
 4926 
 6796 
 8659 
 
 1350 
 
 3236 
 5113 
 6983 
 8845 
 
 0698 
 2544 
 4382 
 6212 
 8034 
 9849 
 
 1539 
 
 3424 
 5301 
 7169 
 9030 
 
 361728 
 3612 
 5488 
 7356 
 9216 
 
 0143 
 1991 
 3831 
 5664 
 7488 
 9306 
 
 0328 
 2175 
 4015 
 5846 
 7670 
 9487 
 
 0513 
 2360 
 4198 
 6029 
 7852 
 9668 
 
 0883 
 2728 
 4565 
 6394 
 8216 
 
 185 
 184 
 184 
 183 
 182 
 
 181 
 
 37106S 
 2912 
 4748 
 6577 
 8398 
 38 
 
 1253 
 3096 
 4932 
 6759 
 8580 
 
 1437 
 3280 
 5115 
 6942 
 8761 
 
 1622 
 3464 
 5298 
 7124 
 8943 
 
 1806 
 3647 
 5481 
 7306 
 9124 
 
 0030 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 *202~ 
 201 
 
 20.2 
 20.1 
 
 40.4 
 40.2 
 
 60.6 
 60.3 
 
 80.8 
 80.4 
 
 101.0 
 100.5 
 
 121.2 
 120.6 
 
 141.4 
 140.7 
 
 161.6 
 160.8 
 
 181.8 
 180.9 
 
 200 
 
 20.0 
 
 40.0 
 
 60.0 
 
 80.0 
 
 100.0 
 
 120.0 
 
 140.0 
 
 160.0 
 
 180.0 
 
 199 
 
 19.9 
 
 39.8 
 
 59.7 
 
 79.6 
 
 99.5 
 
 119.4 
 
 139.3 
 
 159.2 
 
 179.{ 
 
 198 
 
 19.8 
 
 39.6 
 
 59.4 
 
 79.2 
 
 99.0 
 
 118.8 
 
 138.6 
 
 158.4 
 
 178.2 
 
 197 
 
 19.7 
 
 39.4 
 
 59.1 
 
 78.8 
 
 98.5 
 
 118.2 
 
 137.9 
 
 157.6 
 
 177.3 
 
 196 
 
 19.6 
 
 39.2 
 
 58.8 
 
 78.4 
 
 98.0 
 
 117.6 
 
 137.2 
 
 156.8 
 
 176.4 
 
 195 
 
 19.5 
 
 39.0 
 
 58.5 
 
 78.0 
 
 97.5 
 
 117.0 
 
 136.5 
 
 1 56.0 
 
 175.5 
 
 194 
 
 19.4 
 
 38.8 
 
 58.2 
 
 77.6 
 
 97.0 
 
 116.4 
 
 135.8 
 
 155.2 
 
 174.6 
 
 193 
 
 19.3 
 
 38.6 
 
 57.9 
 
 77.2 
 
 96.5 
 
 115.8 
 
 135.1 
 
 154.4 
 
 173.7 
 
 192 
 
 19.2 
 
 38.4 
 
 57.6 
 
 76.8 
 
 96.0 
 
 ' 115.2 
 
 134.4 
 
 153.6 
 
 172.8 
 
 191 
 
 19.1 
 
 38.2 
 
 57.3 
 
 76.4 
 
 95.5 
 
 114.6 
 
 133.7 
 
 152.8 
 
 171.9 
 
 190 
 
 190 
 
 38.0 
 
 57.0 
 
 76.0 
 
 95.0 
 
 114.0 
 
 133.0 
 
 152.0 
 
 171.0 
 
 189 
 
 18.9 
 
 37.8 
 
 56.7 
 
 75.6 
 
 94.5 
 
 113.4 
 
 132.3 
 
 151.2 
 
 170.1 
 
 188 
 
 18.8 
 
 37.6 
 
 56.4 
 
 75.2 
 
 940 
 
 112.8 
 
 131.6 
 
 150.4 
 
 169.2 
 
 187 
 
 18.7 
 
 37.4 
 
 56.1 
 
 74.8 
 
 93.5 
 
 112.2 
 
 130.9 
 
 149.6 
 
 168.3 
 
 186 
 
 18.6 
 
 37.2 
 
 55.3 
 
 74.4 
 
 93.0 
 
 111.6 
 
 130.2 
 
 148.8 
 
 167.4 
 
 185 
 
 18.5 
 
 37.0 
 
 55.5 
 
 74.0 
 
 92.5 
 
 111.0 
 
 129.5 
 
 148.0 
 
 166.5 
 
 184 
 
 18.4 
 
 36.8 
 
 55.2 
 
 73.6 
 
 92.0 
 
 110.4 
 
 128.8 
 
 147.2 
 
 165.6 
 
 183 
 
 18.3 
 
 36.6 
 
 54.9 
 
 73.2 
 
 91.5 
 
 109.8 
 
 128.1 
 
 146.4 
 
 164.7 
 
 182 
 
 18.2 
 
 36.4 
 
 54.6 
 
 72.8 
 
 91.0 
 
 109.2 
 
 127.4 
 
 145.6 
 
 163.8 
 
 181 
 
 18.1 
 
 36.2 
 
 54.3 
 
 72.4 
 
 90.5 
 
 108.6 
 
 126.7 
 
 144.8 
 
 162.9 
 
 180 
 
 18.0 
 
 36.0 
 
 54.0 
 
 72.0 
 
 90.0 
 
 108.0 
 
 126.0 
 
 1440 
 
 162.0 
 
 179 
 
 17.9 
 
 35.8 
 
 53.7 
 
 71.6 
 
 89.5 
 
 107.4 
 
 125.3 
 
 143.2 
 
 161.1 
 
146 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 240 L. 380.J 
 
 [No. 269 L. 431, 
 
 N. 
 
 1 
 
 3 
 4 
 5 
 
 6 
 
 7 
 8 
 9 
 
 250 
 
 1 
 
 2 
 3 
 
 5 
 6 
 
 7 
 
 8 
 9 
 
 260 
 
 2 
 3 
 
 4 
 6 
 
 8 
 9 
 
 
 
 1 
 
 2 
 
 ~0573 
 2377 
 4174 
 5964 
 7746 
 9520 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 T656 
 3456 
 5249 
 7034 
 8811 
 
 9 
 
 Diff. 
 
 IsT 
 
 180 
 179 
 178 
 178 
 
 177 
 176 
 176 
 175 
 174 
 
 173 
 
 173 
 172 
 171 
 
 17! 
 170 
 169 
 
 169 
 168 
 167 
 
 167 
 166 
 165 
 
 165 
 164 
 164 
 163 
 162 
 162 
 
 161 
 
 380211 
 2017 
 3815 
 5606 
 7390 
 9166 
 
 0392 
 2197 
 3995 
 5785 
 7568 
 9343 
 
 0754 
 2557 
 4353 
 6142 
 7924 
 9698 
 
 0934 
 2737 
 4533 
 6321 
 8101 
 9875 
 
 1115 
 2917 
 4712 
 6499 
 8279 
 
 1296 
 3097 
 4891 
 6677 
 8456 
 
 1476 
 3277 
 5070 
 6856 
 8634 
 
 1837 
 3636 
 5428 
 7212 
 8989 
 
 0051 
 1817 
 3575 
 5326 
 7071 
 
 8808 
 
 0228 
 1993 
 3751 
 5501 
 7245 
 
 8981 
 
 0405 
 2169 
 3926 
 5676 
 7419 
 
 9154 
 
 0582 
 2345 
 4101 
 5850 
 7592 
 
 9328 
 
 0759 
 2521 
 4277 
 6025 
 7766 
 
 9501 
 
 390935 
 2697 
 4452 
 6199 
 
 7940 
 9674 
 
 1112 
 2873 
 4627 
 6374 
 
 8114 
 9847 
 
 1288 
 3048 
 4802 
 6548 
 
 8287 
 
 1464 
 3224 
 4977 
 6722 
 
 8461 
 
 1641 
 3400 
 5152 
 6896 
 
 8634 
 
 0020 
 1745 
 3464 
 '5176 
 6881 
 8579 
 
 0192 
 1917 
 3635 
 5346 
 7051 
 8749 
 
 0365 
 2089 
 3807 
 5517 
 7221 
 8918 
 
 0538 
 2261 
 3978 
 5688 
 7391 
 9087 
 
 0711 
 2433 
 4149 
 5858 
 7561 
 9257 
 
 0883 
 2605 
 4320 
 6029 
 7731 
 9426 
 
 1056 
 2777 
 4492 
 6199 
 7901 
 9595 
 
 1228 
 2949 
 4663 
 6370 
 8070 
 9764 
 
 401401 
 3121 
 4834 
 6540 
 8240 
 9933 
 
 1573 
 3292 
 5005 
 6710 
 8410 
 
 0102 
 1788 
 3467 
 
 5140 
 6807 
 8467 
 
 0271 
 1956 
 3635 
 
 5307 
 6973 
 8633 
 
 0440 
 2124 
 3803 
 
 5474 
 7139 
 8798 
 
 0609 
 2293 
 3970 
 
 5641 
 7306 
 8964 
 
 0777 
 2461 
 4137 
 
 5808 
 7472 
 9129 
 
 0946 
 2629 
 4305 
 
 5974 
 7638 
 9295 
 
 11 14 
 2796 
 4472 
 
 6141 
 7804 
 9460 
 
 1110 
 2754 
 4392 
 6023 
 7648 
 9268 
 
 1283 
 2964 
 4639 
 
 6308 
 7970 
 9625 
 
 1451 
 3132 
 4806 
 
 6474 
 8135 
 9791 
 
 1439 
 3082 
 4718 
 6349 
 7973 
 9591 
 
 411620 
 3300 
 
 4973 
 6641 
 8301 
 9956 
 
 0121 
 1768 
 3410 
 5045 
 6674 
 8297 
 9914 
 
 0286 
 1933 
 3574 
 5208 
 6836 
 8459 
 
 0451 
 2097 
 3737 
 5371 
 6999 
 8621 
 
 0616 
 2261 
 3901 
 5534 
 7161 
 8783 
 
 0781 
 2426 
 4065 
 5697 
 7324 
 8944 
 
 0945 
 2590 
 4228 
 5860 
 7486 
 9106 
 
 1275 
 2918 
 4555 
 6186 
 7811 
 9429 
 
 421604 
 3246 
 4882 
 6511 
 8135 
 9752 
 43 
 
 0075 
 
 0236 
 
 0398 
 
 0559 
 
 0720 
 
 0881 
 
 1042 
 
 1203 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 T78~ 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 17.8 
 
 35.6 
 
 53.4 
 
 71.2 
 
 89.0 
 
 106.8 
 
 124.6 
 
 142.4 
 
 160.2 
 
 177 
 
 17.7 
 
 35.4 
 
 53.1 
 
 70.8 
 
 88.5 
 
 106.2 
 
 23.9 
 
 141.6 
 
 159.3 
 
 176 
 
 17.6 
 
 35.2 
 
 52.8 
 
 70.4 
 
 88.0 
 
 105.6 
 
 123.2 
 
 140.8 
 
 158.4 
 
 175 
 
 17.5 
 
 35.0 
 
 52.5 
 
 70.0 
 
 87.5 
 
 105.0 
 
 122.5 
 
 140.0 
 
 157.5 
 
 174 
 
 17.4 
 
 34.8 
 
 52.2 
 
 69.6 
 
 87.0 
 
 104.4 
 
 121.8 
 
 139.2 
 
 156.6 
 
 173 
 
 173 
 
 34.6 
 
 51.9 
 
 69.2 
 
 86.5 
 
 103.8. 
 
 121.1 
 
 138.4 
 
 155.7 
 
 172 
 
 17.2 
 
 34.4 
 
 51.6 
 
 68.8 
 
 86.0 
 
 103.2 
 
 120.4 
 
 137.6 
 
 154.8 
 
 171 
 
 17.1 
 
 34.2 
 
 51.3 
 
 68.4 
 
 85.5 
 
 102.6 
 
 119.7 
 
 136.8 
 
 153.V 
 
 170 
 
 17.0 
 
 34.0 
 
 51.0 
 
 68.0 
 
 85.0 
 
 102.0 
 
 119.0 
 
 136.0 
 
 153.0 
 
 169 
 
 16.9 
 
 33.8 
 
 50.7 
 
 67.6 
 
 84.5 
 
 101.4 
 
 118.3 
 
 135.2 
 
 152.1 
 
 168 
 
 16.8 
 
 33.6 
 
 50.4 
 
 67.2 
 
 84.0 
 
 100.8 
 
 117.6 
 
 134.4 
 
 151.2 
 
 167 
 
 16.7 
 
 33.4 
 
 50.1 
 
 66.8 
 
 83.5 
 
 100.2 
 
 116.9 
 
 133.6 
 
 150.3 
 
 166 
 
 16.6 
 
 33.2 
 
 49.8 
 
 66.4 
 
 830 
 
 99.6 
 
 116.2 
 
 132.8 
 
 149.4 
 
 165 
 
 16.5 
 
 33.0 
 
 49.5 
 
 66.0 
 
 82.5 
 
 99.0 
 
 115.5 
 
 132.0 
 
 148.5 
 
 164 
 
 16.4 
 
 32.8 
 
 49.2 
 
 65.6 
 
 82.0 
 
 98.4 
 
 114.8 
 
 131.2 
 
 147.6 
 
 163 
 
 16.3 
 
 32.6 
 
 48.9 
 
 65.2 
 
 81.5 97.8 
 
 114.1 
 
 130.4 
 
 146.7 
 
 162 
 
 16.2 
 
 32.4 
 
 48.5 
 
 64.8 
 
 81.0 97.2 
 
 113.4 
 
 129.6 
 
 1458 
 
 161 
 
 16.1 
 
 32.2 
 
 48.3 
 
 64.4 
 
 80.5 1 96.6 
 
 112.7 
 
 128.8 
 
 144.9 
 
LOGARITHMS OF NUMBERS. 147 
 
 No. 270 L. 431.] [No. 299 L. 476. 
 
 N. 
 
 ?70 
 1 
 2 
 3 
 4 
 5 
 
 6 
 
 8 
 9 
 
 280 
 
 2 
 
 4 
 5 
 6 
 7 
 8 
 
 9 
 
 290 
 
 1 
 
 3 
 
 4 
 5 
 
 6 
 
 8 
 9 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 431364 
 2969 
 4569 
 6163 
 7751 
 9333 
 
 1525 
 3130 
 4729 
 6322 
 7909 
 9491 
 
 1685 
 3290 
 4888 
 6481 
 8067 
 9648 
 
 1846 
 3450 
 5048 
 6640 
 8226 
 9806 
 
 2007 
 3610 
 5207 
 6799 
 8384 
 9964 
 
 2167 
 3770 
 5367 
 6957 
 8542 
 
 2328 
 3930 
 5526 
 7116 
 8701 
 
 24tte> 
 4090 
 5685 
 
 7275 
 8859 
 
 2649 
 4249 
 5844 
 7433 
 9017 
 
 2809 
 4409 
 6004 
 7592 
 9175 
 
 161 
 160 
 159 
 159 
 158 
 
 158 
 157 
 157 
 156 
 155 
 
 155 
 
 154 
 154 
 153 
 153 
 152 
 152 
 15} 
 
 151 
 150 
 
 150 
 149 
 149 
 148 
 148 
 
 147 
 146 
 146 
 146 
 145 
 
 0122 
 1695 
 3263 
 4825 
 6382 
 
 7933 
 9478 
 
 0279 
 1852 
 3419 
 4981 
 6537 
 
 8088 
 9633 
 
 0437 
 2009 
 3576 
 5137 
 6692 
 
 8242 
 9787 
 
 0594 
 2166 
 3732 
 5293 
 6848 
 
 8397 
 9941 
 
 0752 
 2323 
 3889 
 5449 
 7003 
 
 8552 
 
 440909 
 2480 
 4045 
 5604 
 
 7158 
 8706 
 
 1066 
 2637 
 4201 
 5760 
 
 7313 
 8861 
 
 1224 
 2793 
 4357 
 5915 
 
 7468 
 QQ15 
 
 1381 
 2950 
 4513 
 6071 
 
 7623 
 9170 
 
 1538 
 3106 
 4669 
 6226 
 
 7778 
 9324 
 
 0095 
 1633 
 3165 
 4692 
 6214 
 7731 
 9242 
 
 450249 
 1786 
 3318 
 4845 
 6366 
 7882 
 9392 
 
 0403 
 1940 
 3471 
 4997 
 6518 
 8033 
 9543 
 
 0557 
 2093 
 3624 
 5150 
 6670 
 8184 
 9694 
 
 0711 
 2247 
 3777 
 5302 
 6821 
 8336 
 9845 
 
 0865 
 2400 
 3930 
 5454 
 6973 
 8487 
 9995 
 
 1018 
 2553 
 4082 
 5606 
 7125 
 8638 
 
 1172 
 2706 
 4235 
 5758 
 7276 
 8789 
 
 1326 
 2859 
 4387 
 5910 
 7428 
 8940 
 
 1479 
 3012 
 4540 
 6062 
 7579 
 9091 
 
 0146 
 1649 
 
 3146 
 4639 
 6126 
 7608 
 9085 
 
 0296 
 1799 
 
 3296 
 4788 
 6274 
 7756 
 9233 
 
 0447 
 1948 
 
 3445 
 4936 
 6423 
 7904 
 9380 
 
 0597 
 2098 
 
 3594 
 5085 
 6571 
 8052 
 9527 
 
 0748 
 2248 
 
 3744 
 5234 
 6719 
 8200 
 9675 
 
 460898 
 
 2398 
 3893 
 5383 
 6868 
 8347 
 9322 
 
 1048 
 
 2548 
 4042 
 5532 
 7016 
 8495 
 9969 
 
 1198 
 
 2697 
 4191 
 5680 
 7164 
 8643 
 
 1348 
 
 2847 
 4340 
 5829 
 7312 
 8790 
 
 1499 
 
 2997 
 4490 
 5977 
 7460 
 8938 
 
 0116 
 1585 
 3049 
 4508 
 5962 
 
 0263 
 1732 
 3195 
 4653 
 6107 
 
 0410 
 1878 
 3341 
 4799 
 6252 
 
 0557 
 2025 
 3487 
 4944 
 6397 
 
 0704 
 2171 
 3633 
 5090 
 6542 
 
 0851 
 2318 
 3779 
 5235 
 6687 
 
 0998 
 2464 
 3925 
 5381 
 6832 
 
 1145 
 2610 
 4071 
 5526 
 6976 
 
 471292 
 2756 
 4216 
 5671 
 
 1438 
 2903 
 4362 
 5816 
 
 PROPORTIONAL, PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7. 
 
 8 
 
 9 
 
 161 
 160 
 
 16.1 
 16.0 
 
 32.2 
 32.0 
 
 48.3' 
 48.0 
 
 64.4 
 64.0 
 
 80.5 
 80.0 
 
 96.6 
 96.0 
 
 112.7 
 112.0 
 
 128.8 
 128.0 
 
 144.9 
 144.0 
 
 159 
 
 15.9 
 
 31.8 
 
 47.7 
 
 63.6 
 
 79.5 
 
 95.4 
 
 111.3 
 
 127.2 
 
 143.1 
 
 158 
 
 15.8 
 
 31.6 
 
 47.4 
 
 63.2 
 
 79.0 
 
 94.8 
 
 110.6 
 
 126.4 
 
 142.2 
 
 157 
 
 15.7 
 
 31.4 
 
 47.1 
 
 62.8 
 
 78.5 
 
 94.2 
 
 109.9 
 
 125.6 
 
 141.3 
 
 156 
 
 15.6 
 
 31.2 
 
 46.8 
 
 62.4 
 
 78.0 
 
 93.6 
 
 109.2 
 
 124.8 
 
 140.4 
 
 155 
 
 15.5 
 
 31.0 
 
 46.5 
 
 62.0 
 
 77.5 
 
 93.0 
 
 108 5 
 
 124.0 
 
 139.5 
 
 154 
 
 15.4 
 
 30.8 
 
 46.2 
 
 61.6 
 
 77.0 
 
 92.4 
 
 107.8 
 
 123.2 
 
 138.6 
 
 153 
 
 15.3 
 
 30.6 
 
 45.9 
 
 61.2 
 
 76:5 
 
 91.8 
 
 107.1 
 
 122.4 
 
 137.7 
 
 152 
 
 15.2 
 
 30.4 
 
 45.6 
 
 60.8 
 
 76.0 
 
 91.2 
 
 106.4 
 
 121.6 
 
 136.8 
 
 151 
 
 15.1 
 
 30.2 
 
 45.3 
 
 60.4 
 
 75.5' 
 
 90.6 
 
 105.7 
 
 120.8 
 
 135.9 
 
 150 
 
 15.0 
 
 30.0 
 
 450 
 
 60.0 
 
 75.0 
 
 90.0 
 
 105.0 
 
 120.0 
 
 135.0 
 
 149 
 
 14.9 
 
 29.8 
 
 44.7 
 
 59.6 
 
 74.5 
 
 89.4 
 
 104.3 
 
 119.2 
 
 134.1 
 
 148 
 
 14.8 
 
 29.6 
 
 44.4 
 
 59.2 
 
 74.0 
 
 88.8 
 
 103.6 
 
 118.4 
 
 133.2 
 
 147 
 
 14.7 
 
 29.4 
 
 44.1 
 
 58.8 
 
 73.5 
 
 88.2 
 
 102.9 
 
 117.6 
 
 132.3 
 
 146 
 
 14.6 
 
 29.2 
 
 43.8 
 
 58.4 
 
 73.0 
 
 87.6 
 
 102.2 
 
 116.8 
 
 131.4 
 
 145 
 
 14.5 
 
 29.0 
 
 43.5 
 
 58.0 
 
 72.5 
 
 87.0 
 
 101.5 
 
 1160 
 
 1305 
 
 144 
 
 14.4 
 
 28.8 
 
 43.2 
 
 57.6 
 
 72.0 
 
 86.4 
 
 100.8 
 
 115.2 
 
 129.6 
 
 143 
 
 14.3 
 
 28.6 
 
 42.9 
 
 57.2 
 
 71.5 
 
 85.8 
 
 100.1 
 
 114.4 
 
 128.7 
 
 142 
 
 14.2 
 
 28.4 
 
 42.6 
 
 56.8 
 
 71.0 
 
 85.2 
 
 99.4 
 
 113.6 
 
 127.8 
 
 141 
 
 14.1 
 
 28.2 
 
 42.3 
 
 56.4 
 
 70.5 
 
 84.6 
 
 98.7 
 
 112.8 
 
 126.9 
 
 140 
 
 14.0 
 
 28.0 
 
 42.0 
 
 56.0 
 
 70.0 
 
 84.0 
 
 98.0 
 
 112.0 ! 
 
 126.0 
 
LOGARITHMS OF NUMBERS. 
 
 No. 300 L. 477.] 
 
 [No. 339 L. 531. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 300 
 
 1 
 
 477121 
 8566 
 
 7266 
 8711 
 
 7411 
 8855 
 
 7555 
 8999 
 
 7700 
 9143 
 
 7844 
 9287 
 
 7989 
 9431 
 
 8133 
 9575 
 
 8278 
 9719 
 
 8422 
 9863 
 
 1 145' 
 144 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 480007 
 1443 
 2874 
 4300 
 5721 
 7138 
 8551 
 
 0151 
 1586 
 3016 
 4442 
 5863 
 7280 
 8692 
 
 0294 
 1729 
 3159 
 4585 
 6005 
 7421 
 8833 
 
 0438 
 1372 
 3302 
 4727 
 6147 
 7563 
 8974 
 
 0582 
 2016 
 3445 
 4869 
 6289 
 7704 
 91 14 
 
 0725 
 2159 
 3587 
 5011 
 6430 
 7845 
 9255 
 
 0369 
 2302 
 3730 
 5153 
 6572 
 7986 
 9396 
 
 1012 
 2445 
 3872 
 5295 
 6714 
 8127 
 9537 
 
 1156 
 2588 
 4015 
 5437 
 6355 
 8269 
 9677 
 
 1299 
 2731 
 4157 
 5579 
 6997 
 8410 
 9818 
 
 144 
 143 
 143 
 142 
 142 
 141 
 141 
 
 9 
 
 9958 
 
 0099 
 
 0239 
 
 0380 
 
 0520 
 
 0661 
 
 0801 
 
 0941 
 
 1081 
 
 1222 
 
 140 
 
 310 
 1 
 2 
 3 
 4 
 5 
 
 491362 
 2760 
 4155 
 5544 
 6930 
 8311 
 
 1502 
 2900 
 4294 
 5683 
 7068 
 8448 
 
 1642 
 3040 
 4433 
 5822 
 7206 
 8586 
 
 1782 
 3179 
 4572 
 5960 
 7344 
 8724 
 
 1922 
 3319 
 4711 
 6099 
 7483 
 8862 
 
 2062 
 3458 
 4850 
 6238 
 7621 
 8999 
 
 2201 
 3597 
 4989 
 6376 
 7759 
 9137 
 
 2341 
 3737 
 5128 
 6515 
 7897 
 9275 
 
 2481 
 3876 
 5267 
 6653 
 8035 
 9412 
 
 2621 
 4015 
 5406 
 6791 
 8173 
 9550 
 
 140 
 139 
 139 
 139 
 138 
 138 
 
 6 
 
 9687 
 
 9824 
 
 9962 
 
 0099 
 
 0236 
 
 0374 
 
 0511 
 
 0648 
 
 0785 
 
 0922 
 
 137 
 
 7 
 8 
 9 
 
 320 
 1 
 2 
 
 501059 
 2427 
 3791 
 
 5150 
 6505 
 7856 
 
 1 196 
 2564 
 3927 
 
 5286 
 6640 
 7991 
 
 1333 
 2700 
 4063 
 
 5421 
 6776 
 8126 
 
 1470 
 
 2837 
 4199 
 
 5557 
 6911 
 8260 
 
 1607 
 2973 
 4335 
 
 5693 
 7046 
 8395 
 
 1744 
 3109 
 4471 
 
 5828 
 7181 
 8530 
 
 1880 
 3246 
 4607 
 
 5964 
 7316 
 8664 
 
 2017 
 3382 
 4743 
 
 6099 
 
 7451 
 8799 
 
 2154 
 3518 
 4878 
 
 6234 
 7586 
 8934 
 
 2291 
 3655 
 5014 
 
 6370 
 7721 
 9068 
 
 137 
 136 
 136 
 
 136 
 135 
 135 
 
 3 
 
 9203 
 
 9337 
 
 947 1 
 
 9606 
 
 9740 
 
 9874 
 
 0009 
 
 0143 
 
 0277 
 
 041 1 
 
 134 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 330 
 
 510545 
 1883 
 3218 
 4548 
 5874 
 7196 
 
 8514 
 
 0679 
 2017 
 3351 
 4681 
 6006 
 7328 
 
 8646 
 
 0813 
 2151 
 3484 
 4813 
 6139 
 7460 
 
 8777 
 
 0947 
 2284 
 3617 
 4946 
 6271 
 7592 
 
 8909 
 
 1081 
 2418 
 3750 
 5079 
 6403 
 7724 
 
 9040 
 
 1215 
 2551 
 3883 
 5211 
 6535 
 7855 
 
 9171 
 
 1349 
 2684 
 4016 
 5344 
 6668 
 7987 
 
 9303 
 
 1482 
 2818 
 4149 
 5476 
 6800 
 8119 
 
 9434 
 
 1616 
 2951 
 4282 
 5609 
 6932 
 8251 
 
 9566 
 
 1750 
 3084 
 4415 
 5741 
 7064 
 8382 
 
 9697 
 
 134 
 133 
 133 
 133 
 132 
 132 
 
 131 
 
 1 
 
 9828 
 
 9959 
 
 0090 
 
 0221 
 
 0353 
 
 0484 
 
 0615 
 
 0745 
 
 0876 
 
 1007 
 
 131 
 
 2 
 3 
 4 
 5 
 6 
 7 
 
 521138 
 2444 
 3746 
 5045 
 6339 
 7630 
 
 1269 
 2575 
 3876 
 5174 
 6469 
 7759 
 
 1400 
 2705 
 4006 
 5304 
 6598 
 7888 
 
 1530 
 2835 
 4136 
 5434 
 6727 
 8016 
 
 1661 
 2966 
 4266 
 5563 
 6856 
 8145 
 
 1792 
 3096 
 4396 
 5693 
 6985 
 8274 
 
 1922 
 3226 
 4526 
 5822 
 7114 
 8402 
 
 2053 
 3356 
 4656 
 5951 
 7243 
 8531 
 
 2183 
 3486 
 4785 
 6081 
 7372 
 8660 
 
 2314 
 3616 
 4915 
 6210 
 7501 
 8788 
 
 131 
 130 
 130 
 129 
 129 
 129 
 
 8 
 
 8917 
 
 9045 
 
 9174 
 
 9302 
 
 9430 
 
 9559 
 
 9687 
 
 9815 
 
 9943 
 
 0072 
 
 128 
 
 9 
 
 530200 
 
 0328 
 
 0456 
 
 0584 
 
 0712 
 
 0840 
 
 0968 
 
 1096 
 
 1223 
 
 1351 
 
 128 
 
 PROPORTIONAL PARTS. 
 
 Diff 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 , 8 
 
 9 
 
 139 
 
 13.9 
 
 27.8 
 
 41.7 
 
 55.6 
 
 69.5 
 
 83.4 
 
 97.3 
 
 11 1.2 
 
 125.1 
 
 138 
 
 13.8 
 
 27.6 
 
 41.4 
 
 55.2 
 
 69.0 
 
 82.8 
 
 96.6 
 
 110.4 
 
 124.2 
 
 137 
 
 13.7 
 
 27.4 
 
 41.1 
 
 54.8 
 
 68.5 
 
 82.2 
 
 95.9 
 
 109.6 
 
 123.3 
 
 136 
 
 13.6 
 
 27.2 
 
 40.8 
 
 54.4 
 
 68.0 
 
 81.6 
 
 95.2 
 
 108.8 
 
 122.4 
 
 135 
 
 13.5 
 
 27.0 
 
 40.5 
 
 54.0 
 
 67.5 
 
 81.0 
 
 94.5 
 
 108.0 
 
 121.5 
 
 134 
 
 13.4 
 
 26.8 
 
 40.2 
 
 53.6 
 
 67.0 
 
 80.4 
 
 93.8 
 
 107.2 
 
 120.6 
 
 133 
 
 13.3 
 
 26.6 
 
 39.9 
 
 53.2 
 
 66.5 
 
 79.8 
 
 93.1 
 
 106.4 
 
 119.7 
 
 132 
 
 13.2 
 
 26.4 
 
 39.6 
 
 52.8 
 
 66.0 
 
 79.2 
 
 92.4 
 
 105.6 
 
 118.8 
 
 131 
 
 13.1 
 
 26.2 
 
 39.3 
 
 52.4 
 
 65.5 
 
 78.6 
 
 91.7 
 
 104.8 
 
 117.9 
 
 130 
 
 13.0 
 
 26.0 
 
 39.0 
 
 52.0 
 
 65.0 
 
 78.0 
 
 91.0 
 
 1040 
 
 117.0 
 
 129 
 
 12.9 
 
 25.8 
 
 38.7 
 
 51.6 
 
 64.5 
 
 77.4 
 
 90.3 
 
 103.2 
 
 M6.1 
 
 128 
 
 12.8 
 
 25.6 
 
 38.4 
 
 51.2 
 
 64 
 
 76.8 
 
 89.6 
 
 102.4 
 
 115.2 
 
 127 
 
 12.7 
 
 25.4 * 
 
 38.1 
 
 50.8 1 
 
 63.5 
 
 76.2 
 
 88.9 1 
 
 101.6 
 
 114.3 
 
LOGARITHMS OF NUMBERS. 
 
 149 
 
 No. 340 L. 531.J ' 
 
 [No. 379 L. 579. 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 340 
 2 
 
 4 
 5 
 6 
 
 7 
 8 
 9 
 
 350 
 1 
 
 3 
 4 
 
 5 
 6 
 
 8 
 9 
 
 360 
 1 
 2 
 3 
 
 4 
 5 
 
 6 
 
 8 
 9 
 
 370 
 
 I 
 
 2 
 
 4 
 5 
 6 
 
 8 
 9 
 
 531479 
 2754 
 4026 
 5294 
 6558 
 7819 
 9076 
 
 1607 
 2882 
 4153 
 5421 
 6685 
 7945 
 9202 
 
 1734 
 3009 
 4280 
 5547 
 6811 
 8071 
 9327 
 
 1862 
 3136 
 4407 
 5674 
 6937 
 8197 
 9452 
 
 1990 
 3264 
 4534 
 5800 
 7063 
 8322 
 9578 
 
 2117 
 3391 
 4661 
 5927 
 7189 
 8448 
 9703 
 
 2245 
 3518 
 4787 
 6053 
 7315 
 8574 
 9829 
 
 2372 
 3645 
 4914 
 6180 
 7441 
 8699 
 9954 
 
 2500 
 3772 
 5041 
 6306 
 7567 
 8825 
 
 2627 
 3899 
 5167 
 6432 
 7693 
 8951 
 
 128 
 127 
 127 
 126 
 126 
 126 
 
 125 
 125 
 125 
 124 
 
 124 
 124 
 123 
 123 
 
 123 
 122 
 122 
 121 
 121 
 121 
 
 120 
 120 
 120 
 
 119 
 119 
 119 
 
 m 
 
 118 
 118 
 118 
 
 117 
 
 117 
 117 
 116 
 116 
 116 
 115 
 115 
 115 
 114 
 
 0079 
 1330 
 2576 
 3820 
 
 5060 
 6296 
 7529 
 8758 
 9984 
 
 0204 
 1454 
 2701 
 3944 
 
 5183 
 6419 
 7652 
 8881 
 
 540329 
 1579 
 2825 
 
 4068 
 5307 
 6543 
 7775 
 9003 
 
 0455 
 1704 
 2950 
 
 4192 
 5431 
 6666 
 7898 
 9126 
 
 0580 
 1829 
 3074 
 
 4316 
 5555 
 6', 89 
 8021 
 9249 
 
 0705 
 1953 
 3199 
 
 4440 
 5678 
 6913 
 8144 
 9371 
 
 0830 
 2078 
 3323 
 
 4564 
 5802 
 7036 
 8267 
 9494 
 
 0955 
 2203 
 
 3447 
 
 4688 
 5925 
 7159 
 8389 
 9616 
 
 1080 
 2327 
 3571 
 
 4812 
 6049 
 7282 
 8512 
 9739 
 
 1205 
 2452 
 3696 
 
 4936 
 6172 
 7405 
 8635 
 9861 
 
 0106 
 1328 
 2547 
 3762 
 4973 
 682 
 
 7387 
 8589 
 9787 
 
 550228 
 1450 
 2668 
 3883 
 5094 
 
 6303 
 7507 
 8709 
 9907 
 
 0351 
 1572 
 2790 
 4004 
 5215 
 
 6423 
 7627 
 8829 
 
 0473 
 1694 
 2911 
 4126 
 5336 
 
 6544 
 7748 
 8948 
 
 0595 
 1816 
 3033 
 
 4247 
 5457 
 
 6664 
 7868 
 9068 
 
 0717 
 1938 
 3155 
 4368 
 5578 
 
 6785 
 7988 
 9188 
 
 0840 
 2060 
 3276 
 4489 
 5699 
 
 6905 
 8108 
 9308 
 
 0962 
 2181 
 3398 
 4610 
 5820 
 
 7026 
 8228 
 9428 
 
 1084 
 2303 
 3519 
 4731 
 5940 
 
 7146 
 8349 
 9548 
 
 1206 
 2425 
 3640 
 4852 
 6061 
 
 7267 
 8469 
 9667 
 
 0026 
 1221 
 2412 
 3600 
 4784 
 5966 
 7144 
 
 8319 
 9491 
 
 0146 
 1340 
 2531 
 3718 
 4903 
 6084 
 7262 
 
 8436 
 9608 
 
 0265 
 1459 
 2650 
 3837 
 5021 
 6202 
 7379 
 
 8554 
 9725 
 
 0385 
 1578 
 2769 
 3955 
 5139 
 6320 
 7497 
 
 8671 
 9842 
 
 0504 
 1698 
 2887 
 4074 
 5257 
 6437 
 7614 
 
 8788 
 9959 
 
 0624 
 1817 
 3006 
 4192 
 5376 
 6555 
 7732 
 
 8905 
 
 0743 
 1936 
 3125 
 4311 
 5494 
 6673 
 7849 
 
 9023 
 
 0863 
 2055 
 3244 
 4429 
 5612 
 6791 
 7967 
 
 9140 
 
 0982 
 
 2174 
 3362 
 4548 
 5730 
 6909 
 8084 
 
 9257 
 
 561101 
 2293 
 3481 
 4666 
 5848 
 7026 
 
 8202 
 9374 
 
 0076 
 1243 
 2407 
 3568 
 4726 
 5880 
 7032 
 8181 
 9326 
 
 0193 
 1359 
 2523 
 3684 
 4841 
 5996 
 7147 
 8295 
 9441 
 
 0309 
 1476 
 2639 
 3800 
 4957 
 6111 
 7262 
 8410 
 9555 
 
 0426 
 1592 
 2755 
 3915 
 5072 
 6226 
 73,77 
 8525 
 9669 
 
 570543 
 1709 
 2872 
 4031 
 5188 
 6341 
 7492 
 8639 
 
 0660 
 1825 
 2988 
 4147 
 5303 
 6457 
 7607 
 8754 
 
 0776 
 1942 
 3104 
 4263 
 5419 
 6572 
 7722 
 8868 
 
 0893 
 2058 
 3220 
 4379 
 5534 
 6687 
 7836 
 8983 
 
 1010 
 2174 
 3336 
 4494 
 5650 
 6802 
 7951 
 9097 
 
 1126 
 2291 
 3452 
 4610 
 5765 
 6917 
 8066 
 9212 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 128 
 
 12.8 
 
 25.6 
 
 38.4 
 
 51.2 
 
 64.0 
 
 76.8 
 
 89.6 
 
 102.4 
 
 115.2 
 
 127 
 
 12.7 
 
 25.4 
 
 38.1 
 
 50.8 
 
 63.5 
 
 76.2 
 
 88:9 
 
 101.6 
 
 114.3 
 
 126 
 
 12.6 
 
 25.2 
 
 37.8 
 
 50.4 
 
 63.0 
 
 75.6 
 
 88.2 
 
 100.8 
 
 113.4 
 
 125 
 
 12.5 
 
 25.0 
 
 37.5 
 
 50.0 
 
 62.5 
 
 75.0 
 
 87.5 
 
 100.0 
 
 112.5 
 
 124 
 
 12.4 
 
 24.8 
 
 37.2 
 
 49.6 
 
 62.0 
 
 74.4 
 
 86.8 
 
 99.2 
 
 111.6 
 
 123 
 
 12.3 
 
 24.6 
 
 36.9 
 
 49.2 
 
 61.5 
 
 73.8 
 
 86.1 
 
 98.4 
 
 110.7 
 
 122 
 
 12.2 
 
 24.4 
 
 36.6 
 
 48.8 
 
 61.0 
 
 73.2 
 
 85.4 
 
 97.6 
 
 109.8 
 
 121 
 
 12.1 
 
 24.2 
 
 36.3 
 
 48.4 
 
 60.5 
 
 72.6 
 
 84.7 
 
 96.8 
 
 108.9 
 
 120 
 
 12.0 
 
 24.0 
 
 36.0 
 
 48.0 
 
 60.0 
 
 72.0 
 
 84.0 
 
 96.0 
 
 108.0 
 
 119 
 
 11.9 
 
 23.8 
 
 35.7 
 
 47.6 
 
 59.5 
 
 71.4 
 
 83.3 
 
 95.2 
 
 107.1 
 
150 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 380 L. 579.J 
 
 [No. 414 L. 617. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 114 
 
 113 
 112 
 
 111 
 
 110 
 109 
 
 108 
 107 
 
 106 
 105 
 
 380 
 
 1 
 2 
 
 4 
 
 6 
 
 7 
 8 
 9 
 
 390 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 9 
 
 400 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 
 8 
 9 
 
 410 
 2 
 4 
 
 579784 
 
 9898 
 
 0012 
 1153 
 2291 
 3426 
 4557 
 5686 
 6812 
 7935 
 9056 
 
 0126 
 1267 
 2404 
 3539 
 4670 
 5799 
 6925 
 8047 
 9167 
 
 0241 
 1381 
 2518 
 3652 
 4783 
 5912 
 7037 
 8160 
 9279 
 
 0355 
 1495 
 2631 
 3765 
 4896 
 6024 
 7149 
 8272 
 9391 
 
 0469 
 1608 
 2745 
 3879 
 5009 
 6137 
 7262 
 8384 
 9503 
 
 0583 
 1722 
 2858 
 3992 
 5122 
 6250 
 7374 
 8496 
 9615 
 
 0697 
 1836 
 2972 
 4105 
 5235 
 6362 
 7486 
 8608 
 9726 
 
 0811 
 1950 
 3085 
 4218 
 5348 
 6475 
 7599 
 8720 
 9838 
 
 580925 
 2063 
 3199 
 4331 
 5461 
 6587 
 7711 
 8832 
 9950 
 
 1039 
 2177 
 3312 
 4444 
 5574 
 6700 
 7823 
 8944 
 
 0061 
 
 1176 
 2288 
 3397 
 4503 
 5606 
 6707 
 7805 
 8900 
 9992 
 
 ~\OS2 
 
 2169 
 3253 
 4334 
 5413 
 6489 
 7562 
 8633 
 9701 
 
 0173 
 
 1287 
 2399 
 3508 
 4614 
 5717 
 6817 
 7914 
 9009 
 
 0284 
 
 1399 
 2510 
 
 3618 
 4724 
 5827 
 6927 
 8024 
 9119 
 
 0396 
 
 1510 
 2621 
 3729 
 4834 
 5937 
 7037 
 8134 
 9228 
 
 0507 
 
 1621 
 2732 
 3840 
 4945 
 6047 
 7146 
 8243 
 9337 
 
 0619 
 
 1732 
 2843 
 3950 
 5055 
 6157 
 7256 
 8353 
 9446 
 
 0730 
 
 1843 
 2954 
 4061 
 5165 
 6267 
 7366 
 8462 
 9556 
 
 0842 
 
 1955 
 3064 
 4171 
 5276 
 6377 
 7476 
 8572 
 9665 
 
 0953 
 
 2066 
 3175 
 4282 
 5386 
 6487 
 7586 
 8681 
 9774 
 
 591065 
 2177 
 3286 
 4393 
 5496 
 6597 
 7695 
 8791 
 9883 
 
 0101 
 1191 
 
 2277 
 3361 
 4442 
 5521 
 6596 
 7669 
 8740 
 9808 
 
 0210 
 1299 
 
 2386 
 3469 
 4550 
 5628 
 6704 
 7777 
 8847 
 9914 
 
 0319 
 1406 
 
 2494 
 3577 
 4658 
 5736 
 681 1 
 7884 
 8954 
 
 0428 
 1517 
 
 2603 
 3686 
 4766 
 5844 
 6919 
 7991 
 9061 
 
 0537 
 1625 
 
 2711 
 3794 
 4874 
 5951 
 7026 
 8098 
 9167 
 
 0646 
 1734 
 
 2819 
 3902 
 4982 
 6059 
 7133 
 8205 
 9274 
 
 0755 
 1843 
 
 2928 
 4010 
 5089 
 6166 
 7241 
 8312 
 9381 
 
 0864 
 1951 
 
 3036 
 4118 
 5197 
 6274 
 7348 
 8419 
 9488 
 
 600973 
 
 2060 
 3144 
 4226 
 5305 
 6381 
 7455 
 8526 
 9594 
 
 0021 
 1086 
 2148 
 
 3207 
 4264 
 5319 
 6370 
 7420 
 
 0128 
 1192 
 2254 
 
 3313 
 4370 
 5424 
 6476 
 7525 
 
 0234 
 1298 
 2360 
 
 3419 
 4475 
 5529 
 6581 
 7629 
 
 0341 
 1405 
 2466 
 
 3525 
 4581 
 5634 
 6686 
 7734 
 
 0447 
 1511 
 2572 
 
 3630 
 4686 
 5740 
 6790 
 7839 
 
 0554 
 1617 
 2678 
 
 3736 
 4792 
 5845 
 6895 
 7943 
 
 610660 
 1723 
 
 2784 
 3842 
 4897 
 5950 
 7000 
 
 0767 
 1829 
 
 2890 
 3947 
 5003 
 6055 
 7105 
 
 0873 
 1936 
 
 2996 
 4053 
 5108 
 6160 
 7210 
 
 0979 
 2042 
 
 3102 
 4159 
 5213 
 6265 
 7315 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 118 
 
 11.8 
 
 23.6 
 
 35.4 
 
 47.2 
 
 59.0 
 
 70.8 
 
 82.6 
 
 94.4 
 
 106.2 
 
 117 
 
 11.7 
 
 23.4 
 
 35.1 
 
 46.8 
 
 58.5 
 
 70.2 
 
 81.9 
 
 93.6 
 
 105.3 
 
 116 
 
 11.6 
 
 23.2 
 
 34.8 
 
 46.4 
 
 58.0 
 
 69.6 
 
 81.2 
 
 92.8 
 
 104.4 
 
 115 
 
 11.5 
 
 23.0 
 
 34.5 
 
 46.0 
 
 57.5 
 
 69.0 
 
 80.5 
 
 92.0 
 
 103.5 
 
 114 
 
 11.4 
 
 22.8 
 
 34.2 
 
 45.6 
 
 57.0 
 
 68.4 
 
 79.8 
 
 9, 7 
 
 102.6 
 
 113 
 
 11.3 
 
 22.6 
 
 33.9 
 
 45.2 
 
 56.5 
 
 67.8 
 
 79.1 
 
 90.4 
 
 101.7 
 
 112 
 
 11.2 
 
 22.4 
 
 33.6 
 
 44.8 
 
 56.0 
 
 67.2 
 
 78.4 
 
 89.6 
 
 100.8 
 
 111 
 
 11.1 
 
 22.2 
 
 33.3 
 
 44.4 
 
 55.5 
 
 66.6 
 
 77.7 
 
 88.8 
 
 99.9 
 
 110 
 
 11.0 
 
 22.0 
 
 33.0 
 
 44.0 
 
 55.0 
 
 66.0 
 
 77.0 
 
 88.0 
 
 99.0 
 
 109 
 
 10.9 
 
 21.8 
 
 32.7 
 
 43.6 
 
 54.5 
 
 65.4 
 
 76.3 
 
 87.2 
 
 98.1 
 
 108 
 
 10.8 
 
 21.6 
 
 32.4 
 
 43.2 
 
 54.0 
 
 64.8 
 
 75.6 
 
 86.4 
 
 97.2 
 
 107 
 
 10.7 
 
 21.4 
 
 32.1 
 
 42.8 
 
 53.5 
 
 64.2 
 
 74.9 
 
 85.6 
 
 96.3 
 
 106 
 
 10.6 
 
 21.2 
 
 31.8 
 
 42.4 
 
 53.0 
 
 63.6 
 
 74.2 
 
 84.8 
 
 95.4 
 
 105 
 
 10.5 
 
 21.0 
 
 31.5 
 
 42.0 
 
 52.5 
 
 63.0 
 
 73.5 
 
 84.0 
 
 94.5 
 
 104 
 
 10.4 
 
 20.8 
 
 31.2 
 
 41.6 
 
 52.0 
 
 62.4 
 
 72.8 
 
 83.2 
 
 93.6 
 
LOGARITHMS OF NUMBERS. 
 
 151 
 
 No. 415 L. 618.] 
 
 [No. 459 L. 662. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 415 
 
 618048 
 
 8153 
 
 8257 
 
 8362 
 
 8466 
 
 8571 
 
 8676 
 
 8780 
 
 8884 
 
 8989 
 
 ~105 
 
 6 
 
 9093 
 
 9198 
 
 9302 
 
 9406 
 
 9511 
 
 9615 
 
 9719 
 
 9824 
 
 9928 
 
 "0032 
 
 
 7 
 
 620136 
 
 0240 
 
 0344 
 
 0448 
 
 0552 
 
 0656 
 
 0760 
 
 0864 
 
 0968 
 
 1072 
 
 104 
 
 8 
 
 1176 
 
 1280 
 
 1384 
 
 1488 
 
 1592 
 
 1695 
 
 1799 
 
 1903 
 
 2007 
 
 2110 
 
 
 9 
 
 2214 
 
 2318 
 
 2421 
 
 2525 
 
 2628 
 
 2732 
 
 2835 
 
 2939 
 
 3042 
 
 3146 
 
 
 420 
 
 3249 
 
 3353 
 
 3456 
 
 3559 
 
 3663 
 
 3766 
 
 3869 
 
 3973 
 
 4076 
 
 4179 
 
 
 1 
 
 4282 
 
 4385 
 
 4488 
 
 4591 
 
 4695 
 
 4793 
 
 4901 
 
 5004 
 
 5107 
 
 5210 
 
 103 
 
 2 
 
 5312 
 
 5415 
 
 5518 
 
 5621 
 
 5724 
 
 5827 
 
 5929 
 
 6032 
 
 6135 
 
 6238 
 
 
 3 
 
 6340 
 
 6443 
 
 6546 
 
 6648 
 
 6751 
 
 6853 
 
 6956 
 
 7058 
 
 7161 
 
 7263 
 
 
 4 
 
 7366 
 
 7463 
 
 7571 
 
 7673 
 
 7775 
 
 7878 
 
 7980 
 
 8082 
 
 8185 
 
 8287 
 
 
 5 
 
 8389 
 
 8491 
 
 8593 
 
 8695 
 
 8797 
 
 8900 
 
 9002 
 
 9104 
 
 9206 
 
 9308 
 
 .102 
 
 6 
 
 9410 
 
 9512 
 
 9613 
 
 9715 
 
 9817 
 
 9919 
 
 0021 
 
 0123 
 
 0224 
 
 0326 
 
 
 7 
 
 630428 
 
 0530 
 
 ~063T 
 
 0733 
 
 0835 
 
 0936 
 
 1038 
 
 1139 
 
 1241 
 
 1342 
 
 
 8 
 
 1444 
 
 1545 
 
 1647 
 
 1748 
 
 1849 
 
 1951 
 
 2052 
 
 2153 
 
 2255 
 
 2356 
 
 
 9 
 
 2457 
 
 2559 
 
 2660 
 
 2761 
 
 2862 
 
 2963 
 
 3064 
 
 3165 
 
 3266 
 
 3367 
 
 
 430 
 
 3468 
 
 3569 
 
 3670 
 
 3771 
 
 3872 
 
 3973 
 
 4074 
 
 4175 
 
 4276 
 
 4376 
 
 101 
 
 1 
 
 4477 
 
 4578 
 
 4679 
 
 4779 
 
 4880 
 
 4981 
 
 5081 
 
 5182 
 
 5283 
 
 5383 
 
 
 2 
 
 5484 
 
 5584 
 
 5635 
 
 5785 
 
 5886 
 
 5986 
 
 6087 
 
 6187 
 
 6287 
 
 6388 
 
 
 3 
 
 6488 
 
 6588 
 
 6638 
 
 6789 
 
 6889 
 
 6989 
 
 7089 
 
 7189 
 
 7290 
 
 7390 
 
 
 4 
 
 7490 
 
 7590 
 
 7690 
 
 7790 
 
 7890 
 
 7990 
 
 8090 
 
 8190 
 
 8290 
 
 8389 
 
 100 
 
 5 
 
 8489 
 
 8589 
 
 8689 
 
 8789 
 
 8888 
 
 8988 
 
 9088 
 
 9188 
 
 9287 
 
 9387 
 
 
 6 
 
 9486 
 
 9586 
 
 9686 
 
 9785 
 
 9885 
 
 9984 
 
 0084 
 
 0183 
 
 0283 
 
 0382 
 
 
 7 
 
 640431 
 
 0581 
 
 0680 
 
 0779 
 
 0879 
 
 0978 
 
 1077 
 
 1177 
 
 1276 
 
 1375 
 
 
 8 
 
 1474 
 
 1573 
 
 1672 
 
 1771 
 
 1871 
 
 1970 
 
 2069 
 
 2168 
 
 2267 
 
 2366 
 
 
 9 
 
 2465 
 
 2563 
 
 2662 
 
 2761 
 
 2860 
 
 2959 
 
 3058 
 
 3156 
 
 3255 
 
 3354 
 
 99 
 
 440 
 
 3453 
 
 3551 
 
 3650 
 
 3749 
 
 3847 
 
 3946 
 
 4044 
 
 4143 
 
 4242 
 
 4340 
 
 
 1 
 
 4439 
 
 4537 
 
 4636 
 
 4734 
 
 4832 
 
 4931 
 
 5029 
 
 5127 
 
 5226 
 
 5324 
 
 
 2 
 
 5422 
 
 5521 
 
 5619 
 
 5717 
 
 5815 
 
 5913 
 
 6011 
 
 6110 
 
 6208 
 
 6306 
 
 
 3 
 
 6404 
 
 6502 
 
 6600 
 
 6698 
 
 6796 
 
 6894 
 
 6992 
 
 7089 
 
 7187 
 
 7285 
 
 98 
 
 4 
 
 7333 
 
 7481 
 
 7579 
 
 7676 
 
 7774 
 
 7872 
 
 7969 
 
 8067 
 
 8165 
 
 8262 
 
 
 5 
 
 8360 
 
 8458 
 
 8555 
 
 8653 
 
 8750 
 
 8848 
 
 8945 
 
 9043 
 
 9140 
 
 9237 
 
 
 6 
 
 9335 
 
 9432 
 
 9530 
 
 9627 
 
 9724 
 
 9821 
 
 9919 
 
 0016 
 
 0113 
 
 0210 
 
 
 7 
 
 650303 
 
 0405 
 
 0502 
 
 "0599 
 
 0696 
 
 0793 
 
 0890 
 
 0987 
 
 1084 
 
 1181 
 
 
 8 
 
 1278 
 
 1375 
 
 1472 
 
 1569 
 
 1666 
 
 1762 
 
 1859 
 
 1956 
 
 2053 
 
 2150 
 
 97 
 
 9 
 
 2246 
 
 2343 
 
 2440 
 
 2536 
 
 2633 
 
 2730 
 
 2826 
 
 2923 
 
 3019 
 
 3116 
 
 
 450 
 
 3213 
 
 3309 
 
 3405 
 
 3502 
 
 3598 
 
 3695 
 
 3791 
 
 3888 
 
 3984 
 
 4080 
 
 
 
 4177 
 
 4273 
 
 4369 
 
 4465 
 
 4562 
 
 4658 
 
 4754 
 
 4850 
 
 4946 
 
 5042 
 
 
 2 
 
 5138 
 
 5235 
 
 5331 
 
 5427 
 
 5523 
 
 5619 
 
 5715 
 
 5810 
 
 5906 
 
 6002 
 
 96 
 
 3 
 
 6098 
 
 6194 
 
 6290 
 
 6386 
 
 6482 
 
 6577 
 
 6673 
 
 6769 
 
 6864 
 
 6960 
 
 
 4 
 
 7056 
 
 7152 
 
 7247 
 
 7343 
 
 7438 
 
 7534 
 
 7629 
 
 7725 
 
 7820 
 
 7916 
 
 
 5 
 
 8011 
 
 8107 
 
 8202 
 
 8298 
 
 8393 
 
 8488 
 
 8584 
 
 8679 
 
 8774 
 
 8870 
 
 
 6 
 
 8965 
 
 9060 
 
 9155 
 
 9250 
 
 9346 
 
 9441 
 
 9536 
 
 9631 
 
 9726 
 
 9821 
 
 
 7 
 
 9916 
 
 0011 
 
 0106 
 
 0201 
 
 0296 
 
 0391 
 
 0486 
 
 0581 
 
 0676 
 
 "0771 
 
 95 
 
 8 
 
 660865 
 
 0960 
 
 1055 
 
 1150 
 
 1245 
 
 1339 
 
 1434 
 
 1529 
 
 1623 
 
 1718 
 
 
 9 
 
 1813 
 
 1907 
 
 2002 
 
 2096 
 
 2191 
 
 2286 
 
 23801 2475 
 
 2569 
 
 2663 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 10.5 
 10.4 
 10.3 
 10.2 
 10.1 
 10.0 
 9.9 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 105 
 104 
 103 
 102 
 101 
 100 
 99 
 
 21.0 
 20.8 
 20.6 
 20.4 
 20.2 
 20.0 
 19.8 
 
 31.5 
 31.2 
 30.9 
 30.6 
 30.3 
 30.0 
 29.7 
 
 42.0 
 41.6 
 41.2 
 40.8 
 40.4 
 40.0 
 39.6 
 
 52.5 
 52.0 
 51.5 
 51.0 
 50.5 
 50.0 
 49.5 
 
 63.0 
 62.4 
 61.8 
 61.2 
 60.6 
 60.0 
 59.4 
 
 73.5 
 72.8 
 72.1 
 71.4 
 70.7 
 70.0 
 69.3 
 
 84.0 
 83.2 
 82.4 
 81.6 
 80.8 
 80.0 
 79.2 
 
 94.5 
 93.6 
 92.7 
 91.8 
 90.9 
 90.0 
 89.1 
 
152 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 460 L. 662.] 
 
 [No. 499 L. 698 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff< 
 
 "46CT 
 
 ' 662758 
 
 2852 
 
 2947 
 
 3041 
 
 3135 
 
 3230 
 
 "3324 
 
 3418 
 
 3512 
 
 3607 
 
 
 
 3701 
 
 3795 
 
 3889 
 
 3983 
 
 4078 
 
 4172 
 
 4266 
 
 4360 
 
 4454 
 
 4548 
 
 
 2 
 
 4642 
 
 4736 
 
 4830 
 
 4924 
 
 5018 
 
 5112 
 
 5206 
 
 5299 
 
 5393 
 
 5487 
 
 94 
 
 3 
 
 5581 
 
 5675 
 
 5769 
 
 5862 
 
 5956 
 
 6050 
 
 6143 
 
 6237 
 
 6331 
 
 6424 
 
 
 4 
 
 6518 
 
 6612 
 
 6705 
 
 6799 
 
 6892 
 
 6986 
 
 7079 
 
 7173 
 
 7266 
 
 7360 
 
 
 5 
 
 7453 
 
 7546 
 
 7640 
 
 7733 
 
 7826 
 
 7920 
 
 8013 
 
 8106 
 
 8199 
 
 8293 
 
 
 6 
 
 8386 
 
 8479 
 
 8572 
 
 8665 
 
 8759 
 
 8852 
 
 8945 
 
 9038 
 
 9131 
 
 9224 
 
 
 7 
 
 9317 
 
 94 1C 
 
 9503 
 
 9596 
 
 9689 
 
 9782 
 
 9875 
 
 9967 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0060 
 
 fil 53 
 
 Ql 
 
 8 
 
 670246 
 
 0339 
 
 0431 
 
 0524 
 
 0617 
 
 0710 
 
 0802 
 
 0895 
 
 0988 
 
 U 1 Jj 
 
 1080 
 
 7J 
 
 9 
 
 1173 
 
 1265 
 
 1358 
 
 1451 
 
 1543 
 
 1636 
 
 1728 
 
 1821 
 
 1913 
 
 2005 
 
 
 470 
 
 2098 
 
 2190 
 
 2283 
 
 2375 
 
 2467 
 
 2560 
 
 2652 
 
 2744 
 
 2836 
 
 2929 
 
 
 1 
 
 3021 
 
 3rl13 
 
 3205 
 
 3297 
 
 3390 
 
 3482 
 
 3574 
 
 3666 
 
 3758 
 
 3850 
 
 
 2 
 
 3942 
 
 4934 
 
 4126 
 
 4218 
 
 4310 
 
 4402 
 
 4494 
 
 4586 
 
 4677 
 
 4769 
 
 92 
 
 3 
 
 4861 
 
 4953 
 
 5045 
 
 5137 
 
 5228 
 
 5320 
 
 5412 
 
 5503 
 
 5595 
 
 5687 
 
 
 4 
 
 5778 
 
 5870 
 
 5962 
 
 6053 
 
 6145 
 
 6236 
 
 6328 
 
 6419 
 
 6511 
 
 6602 
 
 
 5 
 
 6694 
 
 6785 
 
 6876 
 
 6968 
 
 7059 
 
 7151 
 
 7242 
 
 7333 
 
 7424 
 
 7516 
 
 
 6 
 
 7607 
 
 7698 
 
 7789 
 
 7881 
 
 7972 
 
 8063 
 
 8154 
 
 8245 
 
 8336 
 
 8427 
 
 
 7 
 
 8518 
 
 8609 
 
 8700 
 
 8791 
 
 8882 
 
 8973 
 
 9064 
 
 9155 
 
 9246 
 
 9337 
 
 9! 
 
 3 
 
 9428 
 
 9519 
 
 9610 
 
 9700 
 
 9791 
 
 9882 
 
 9973 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0063 
 
 01 54 
 
 0745 
 
 
 9 
 
 680336 
 
 0426 
 
 0517 
 
 0607 
 
 0698 
 
 0789 
 
 0879 
 
 0970 
 
 1060 
 
 \)mj 
 
 1151 
 
 
 480 
 
 1241 
 
 1332 
 
 1422 
 
 1513 
 
 1603 
 
 1693 
 
 1784 
 
 1874 
 
 1964 
 
 2055 
 
 
 1 
 
 2145 
 
 2235 
 
 2326 
 
 2416 
 
 2506 
 
 2596 
 
 2686 
 
 2777 
 
 2867 
 
 2957 
 
 
 2 
 
 3047 
 
 3137 
 
 3227 
 
 3317 
 
 3407 
 
 3497 
 
 3587 
 
 3677 
 
 3767 
 
 3857 
 
 90 
 
 3 
 
 3947 
 
 4037 
 
 4127 
 
 4217 
 
 4307 
 
 4396 
 
 4486 
 
 4576 
 
 4666 
 
 4756 
 
 
 4 
 
 4845 
 
 4935 
 
 5025 
 
 5114 
 
 5204 
 
 5294 
 
 5383 
 
 5473 
 
 5563 
 
 5652 
 
 
 5 
 
 5742 
 
 5831 
 
 5921 
 
 601-0 
 
 6100 
 
 6189 
 
 6279 
 
 6368 
 
 6458 
 
 6547 
 
 
 6 
 
 6636 
 
 6726 
 
 6815 
 
 6904 
 
 6994 
 
 7083 
 
 7172 
 
 7261 
 
 7351 
 
 7440 
 
 
 7 
 
 7529 
 
 7618 
 
 7707 
 
 77% 
 
 7886 
 
 7975 
 
 8064 
 
 8153 
 
 8242 
 
 8331 
 
 
 8 
 
 8420 
 
 8509 
 
 8598 
 
 8687 
 
 8776 
 
 8865 
 
 8953 
 
 9042 
 
 9131 
 
 9220 
 
 89 
 
 9 
 
 9309 
 
 9398 
 
 9486 
 
 9575 
 
 9664 
 
 9753 
 
 9841 
 
 9930 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0019 
 
 01(17 
 
 
 490 
 
 690196 
 
 0285 
 
 0373 
 
 0462 
 
 0550 
 
 0639 
 
 0728 
 
 0816 
 
 0905 
 
 U 1 U/ 
 
 0993 
 
 
 1 
 
 1081 
 
 1170 
 
 1258 
 
 1347 
 
 1435 
 
 1524 
 
 1612 
 
 1700 
 
 1789 
 
 1877 
 
 
 2 
 
 1965 
 
 2053 
 
 2142 
 
 2230 
 
 2318 
 
 2406 
 
 2494 
 
 2583 
 
 2671 
 
 2759 
 
 
 3 
 
 2847 
 
 2935 
 
 3023 
 
 3111 
 
 3199 
 
 3287 
 
 3375 
 
 3463 
 
 3551 
 
 3639 
 
 88 
 
 4 
 
 3727 
 
 3815 
 
 3903 
 
 3991 
 
 4078 
 
 4166 
 
 4254 
 
 4342 
 
 4430 
 
 4517 
 
 
 5 
 
 4605 
 
 4693 
 
 4781 
 
 4868 
 
 4956 
 
 5044 
 
 5131 
 
 5219 
 
 5307 
 
 5394 
 
 
 6 
 
 5482 
 
 5569 
 
 5657 
 
 5744 
 
 5832 
 
 5919 
 
 6007 
 
 6094 
 
 6182 
 
 6269 
 
 
 7 
 
 6356 
 
 6444 
 
 6531 
 
 6618 
 
 6706 
 
 6793 
 
 6880 
 
 6968 
 
 7055 
 
 7142 
 
 
 8 
 
 7229 
 
 7317 
 
 7404 
 
 7491 
 
 7578 
 
 7665 
 
 7752 
 
 7839 
 
 7926 
 
 8014 
 
 87 
 
 9 
 
 8100 
 
 8188 
 
 8275 
 
 8362 
 
 8449 
 
 8535 
 
 8622 
 
 8709 
 
 8796 
 
 8883 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 ^98 
 
 9.8 
 
 19.6 
 
 29 A 
 
 39.2 
 
 49.0 
 
 58.8 
 
 68.6 
 
 78.4 
 
 88.2 
 
 97 
 
 9.7 
 
 19.4 
 
 29.1 
 
 38.8 
 
 48.5 
 
 58.2 
 
 67.9 
 
 77.6 
 
 87.3 
 
 96 
 
 9.6 
 
 19.2 
 
 28.8 
 
 38.4 
 
 48.0 
 
 57.6 
 
 67.2 
 
 76.8 
 
 86.4 
 
 95 
 
 9.5 
 
 19.0 
 
 28.5 
 
 38.0 
 
 47.5 
 
 57.0 
 
 66.5 
 
 76.0 
 
 85.5 
 
 94 
 
 9.4 
 
 18.8 
 
 28.2 
 
 37.6 
 
 47.0 
 
 56.4 
 
 65.8 
 
 75.2 
 
 84.6 
 
 93 
 
 9.3 
 
 18.6 
 
 27.9 
 
 37.2 
 
 46.5 
 
 55.8 
 
 65.1 
 
 74.4 
 
 83.7 
 
 92 
 
 9.2 
 
 18.4 
 
 27.6 
 
 36.8 
 
 46.0 
 
 55.2 
 
 64.4 
 
 73.6 
 
 82.8 
 
 91 
 
 9.1 
 
 18.2 
 
 27.3 
 
 36.4 
 
 45.5 
 
 54.6 
 
 63.7 
 
 72.8 
 
 81.9 
 
 90 
 
 9.0 
 
 18.0 
 
 27.0 
 
 36.0 
 
 45.0 
 
 54.0 
 
 63.0 
 
 72.0 
 
 81.0 
 
 89 
 
 8.9 
 
 17.8 
 
 26.7 
 
 35.6 
 
 44.5 
 
 53.4 
 
 62.3 
 
 71.2 
 
 80.1 
 
 88 
 
 8.8 
 
 17.6 
 
 26.4 
 
 35.2 
 
 44.0 
 
 52.8 
 
 61.6 
 
 70.4 
 
 79.2 
 
 87 
 
 8.7 
 
 17.4 
 
 26.1 
 
 34.8 
 
 43.5 
 
 52.2 
 
 60.9 
 
 69.6 
 
 78.3 
 
 66 
 
 8.6 
 
 17.2 
 
 25.8 
 
 34.4 
 
 43.0 
 
 51.6 
 
 60.2 
 
 68.8 
 
 77.4 
 
LOGARITHMS OF NUMBERS. 
 
 153 
 
 No. 500 L. 698.1 
 
 [No. 544 L. 736 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 DiS. 
 
 500 
 
 698970 
 
 QO-1Q 
 
 9057 
 
 QQ9.4 
 
 9144 
 
 9231 
 
 9317 
 
 9404 
 
 9491 
 
 "9578 
 
 ~9664 
 
 9751 
 
 
 t 
 
 yoJO 
 
 yy^^t 
 
 001 1 
 
 0098 
 
 0184 
 
 0271 
 
 0358 
 
 0444 
 
 0531 
 
 0617 
 
 
 2 
 
 700704 
 
 0790 
 
 0877 
 
 0963 
 
 1050 
 
 1136 
 
 1222 
 
 1309 
 
 1395 
 
 1482 
 
 
 3 
 
 1568 
 
 1654 
 
 1741 
 
 1827 
 
 1913 
 
 1999 
 
 2086 
 
 2172 
 
 2258 
 
 2344 
 
 
 4 
 
 243 1 
 
 2517 
 
 2603 
 
 2689 
 
 2775 
 
 2861 
 
 2947 
 
 3033 
 
 3119 
 
 3205 
 
 
 5 
 
 3291 
 
 3377 
 
 3463 
 
 3549 
 
 3635 
 
 3721 
 
 3807 
 
 3893 
 
 3979 
 
 4065 
 
 86 
 
 6 
 
 4151 
 
 4236 
 
 4322 
 
 4408 
 
 4494 
 
 4579 
 
 4665 
 
 4751 
 
 4837 
 
 4922 
 
 
 7 
 
 5008 
 
 5094 
 
 5179 
 
 5265 
 
 5350 
 
 5436 
 
 5522 
 
 5607 
 
 5693 
 
 5778 
 
 
 8 
 
 5864 
 
 5949 
 
 6035 
 
 6120 
 
 6206 
 
 6291 
 
 6376 
 
 6462 
 
 6547 
 
 6632 
 
 
 9 
 
 6718 
 
 6803 
 
 6888 
 
 6974 
 
 7059 
 
 7144 
 
 7229 
 
 7315 
 
 7400 
 
 7485 
 
 
 510 
 
 7570 
 
 7655 
 
 7740 
 
 7826 
 
 7911 
 
 7996 
 
 8081 
 
 8166 
 
 8251 
 
 8336 
 
 
 1 
 
 8421 
 
 8506 
 
 8591 
 
 8676 
 
 8761 
 
 8846 
 
 8931 
 
 9015 
 
 9100 
 
 9185 
 
 85 
 
 
 O?7fl 
 
 Q-l CC 
 
 Q44O 
 
 QCTX 
 
 9609 
 
 9694 
 
 9779 
 
 9863 
 
 9948 
 
 
 
 
 y^/U 
 
 \TJ JJ 
 
 y^fnU 
 
 y.?<6 i f 
 
 
 
 
 
 
 0033 
 
 
 3 
 
 710117 
 
 0202 
 
 0287 
 
 0371 
 
 0456 
 
 0540 
 
 0625 
 
 0710 
 
 0794 
 
 0879 
 
 
 4 
 
 0963 
 
 1048 
 
 1132 
 
 1217 
 
 1301 
 
 1385 
 
 1470 
 
 1554 
 
 1639 
 
 1723 
 
 
 5 
 
 1807 
 
 1892 
 
 1976 
 
 2060 
 
 2144 
 
 2229 
 
 2313 
 
 2397 
 
 2481 
 
 2566 
 
 
 6 
 
 2650 
 
 2734 
 
 2818 
 
 2902 
 
 2986 
 
 3070 
 
 3154 
 
 3238 
 
 3323 
 
 3407 
 
 
 7 
 
 3491 
 
 3575 
 
 3659 
 
 3742 
 
 3826 
 
 3910 
 
 3994 
 
 4078 
 
 4162 
 
 4246 
 
 84 
 
 8 
 
 4330 
 
 4414 
 
 4497 
 
 4581 
 
 4665 
 
 4749 
 
 4833 
 
 4916 
 
 5000 
 
 5084 
 
 
 9 
 
 5167 
 
 5251 
 
 5335 
 
 5418 
 
 5502 
 
 5586 
 
 5669 
 
 5753 
 
 5836 
 
 5920 
 
 
 520 
 
 6003 
 
 6087 
 
 6170 
 
 6*254 
 
 6337 
 
 6421 
 
 6504 
 
 6588 
 
 6671 
 
 6754 
 
 
 
 6838 
 
 6921 
 
 7004 
 
 7088 
 
 7171 
 
 7254 
 
 7338 
 
 7421 
 
 7504 
 
 7587 
 
 
 2 
 
 7671 
 
 7754 
 
 7837 
 
 7920 
 
 8003 
 
 8086 
 
 8169 
 
 8253 
 
 8336 
 
 8419 
 
 83 
 
 3 
 
 8502 
 
 8585 
 
 8668 
 
 875T 
 
 8834 
 
 8917 
 
 9000 
 
 9083 
 
 9165 
 
 9248 
 
 
 
 Qa-i | 
 
 QA1 / 
 
 Q AQ7 
 
 QCOA 
 
 Qf\f\^ 
 
 Q7 AC* 
 
 QQOQ 
 
 991 1 
 
 9994 
 
 
 
 
 yjJ 1 
 
 y^f 1 f 
 
 y^ty/ 
 
 VDOL 
 
 yOO.7 
 
 y/T-j 
 
 yo^o 
 
 
 
 0077 
 
 
 5 
 
 720159 
 
 0242 
 
 0325 
 
 0407 
 
 0490 
 
 0573 
 
 0655 
 
 0738 
 
 0821 
 
 0903 
 
 
 6 
 
 0986 
 
 1068 
 
 1151 
 
 1233 
 
 1316 
 
 1398 
 
 1481 
 
 1563 
 
 1646 
 
 1728 
 
 
 7 
 
 1811 
 
 1893 
 
 1975 
 
 2058 
 
 2140 
 
 2222 
 
 2305 
 
 2387 
 
 2469 
 
 2552 
 
 
 8 
 
 2634 
 
 2716 
 
 2798 
 
 2881 
 
 2963 
 
 3045 
 
 3UZ7 
 
 3209 
 
 3291 
 
 3374 
 
 
 9 
 
 3456 
 
 3538 
 
 3620 
 
 3702 
 
 3784 
 
 3866 
 
 3948 
 
 4030 
 
 4112 
 
 4194 
 
 82 
 
 530 
 
 4276 
 
 4358 
 
 4440 
 
 4522 
 
 4604 
 
 4685 
 
 4767 
 
 4849 
 
 4931 
 
 5013 
 
 
 1 
 
 5095 
 
 5176 
 
 5258 
 
 5340 
 
 5422 
 
 5503 
 
 5585 
 
 5667 
 
 5748 
 
 5830 
 
 
 
 5912 
 
 5993 
 
 6075 
 
 6156 
 
 6238 
 
 6320 
 
 6401 
 
 6483 
 
 6564 
 
 6646 
 
 
 3 
 
 6727 
 
 6809 
 
 6890 
 
 6972 
 
 7053 
 
 7134 
 
 7216 
 
 7297 
 
 7379 
 
 7460 
 
 
 
 7541 
 
 7623 
 
 7704 
 
 7785 
 
 7866 
 
 7948 
 
 8029 
 
 8110 
 
 8191 
 
 8273 
 
 
 5 
 
 8354 
 
 8435 
 
 8516 
 
 8597 
 
 8678 
 
 8759 
 
 8841 
 
 8922 
 
 9003 
 
 9084 
 
 
 6 
 7 
 
 9165 
 9974 
 
 9246 
 
 9327 
 
 9408 
 
 9489 
 
 9570 
 
 9651 
 
 9732 
 
 9813 
 
 9893 
 
 81 
 
 
 
 005 
 
 0136 
 
 021 7 
 
 029? 
 
 0376 
 
 045 C 
 
 0540 
 
 0621 
 
 0702 
 
 
 8 
 
 730782 
 
 0863 
 
 094^ 
 
 1024 
 
 1105 
 
 1186 
 
 1266 
 
 1347 
 
 1428 
 
 1508 
 
 
 9 
 
 1589 
 
 1669 
 
 1750 
 
 1830 
 
 1911 
 
 1991 
 
 2072 
 
 2152 
 
 2233 
 
 2313 
 
 
 540 
 
 2394 
 
 2474 
 
 2555 
 
 2635 
 
 2715 
 
 2796 
 
 2876 
 
 2956 
 
 3037 
 
 3117 
 
 
 
 3197 
 
 3278 
 
 3358 
 
 3438 
 
 3518 
 
 3598 
 
 3679 
 
 3759 
 
 3839 
 
 3919 
 
 
 2 
 
 3999 
 
 4079 
 
 4160 
 
 4240 
 
 4320 
 
 4400 
 
 4480 
 
 4560 
 
 4640 
 
 4720 
 
 80 
 
 3 
 
 4800 
 
 4880 
 
 4960 
 
 5040 
 
 5120 
 
 5200 
 
 5279 
 
 5359 
 
 5439 
 
 5519 
 
 
 4 
 
 5599 
 
 5679 
 
 5759 
 
 5838 
 
 5918 
 
 5998 
 
 6078 
 
 6157 
 
 6237 
 
 6317 
 
 
 PROPORTIONAL PARTS. 
 
 DIS. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 87 
 86 
 85 
 84 
 
 8.7 
 8.6 
 8.5 
 8.4 
 
 17.4 
 17.2 
 17.0 
 16.8 
 
 26.1 
 25.8 
 25.5 
 25.2 
 
 34.8 
 34.4 
 34.0 
 33.6 
 
 43.5 
 43.0 
 42.5 
 42.0 
 
 52.2 
 51.6 
 51.0 
 50.4 
 
 60.9 
 60.2 
 59.5 
 58.8 
 
 69.6 
 68.8 
 68.0 
 67.2 
 
 78.3 
 77.4 
 76.5 
 75.6 
 
154 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 545 L. 736.] 
 
 [No 584 L. 767 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 $45 
 6 
 
 8 
 9 
 
 736397 
 7193 
 7987 
 8781 
 9572 
 
 6476 
 7272 
 8067 
 8860 
 9651 
 
 6556 
 7352 
 8146 
 8939 
 9731 
 
 6635 
 7431 
 8225 
 9018 
 9810 
 
 6715 
 
 7511 
 8305 
 9097 
 9889 
 
 6795 
 7590 
 8384 
 9177 
 9968 
 
 6874 
 7670 
 8463 
 9256 
 
 6954 
 7749 
 8543 
 9335 
 
 7034 
 7829 
 8622 
 9414 
 
 7113 
 7908 
 8701 
 9493 
 
 
 
 
 
 
 
 
 
 0047 
 
 0126 
 
 07OS 
 
 nooj 
 
 7O 
 
 550 
 
 740363 
 
 0442 
 
 0521 
 
 0600 
 
 0678 
 
 0757 
 
 Uvn/ 
 
 0836 
 
 0915 
 
 U<iUJ 
 
 0994 
 
 v^OH 
 
 1073 
 
 /y 
 
 
 1152 
 
 1230 
 
 1309 
 
 1388 
 
 1467 
 
 1546 
 
 1624 
 
 1703 
 
 1782 
 
 1860 
 
 
 2 
 
 1939 
 
 2018 
 
 2096 
 
 2175 
 
 2254 
 
 2332 
 
 2411 
 
 2489 
 
 2568 
 
 2647 
 
 
 3 
 
 2725 
 
 2804 
 
 2882 
 
 2961 
 
 3039 
 
 3118 
 
 3196 
 
 3275 
 
 3353 
 
 3431 
 
 
 4 
 
 3510 
 
 3588 
 
 3667 
 
 3745 
 
 3823 
 
 3902 
 
 3980 
 
 4058 
 
 4136 
 
 4215 
 
 
 5 
 
 4293 
 
 4371 
 
 4449 
 
 4528 
 
 4606 
 
 4684 
 
 4762 
 
 4840 
 
 4919 
 
 4997 
 
 
 6 
 
 5075 
 
 5153 
 
 5231 
 
 5309 
 
 5387 
 
 5465 
 
 5543 
 
 5621 
 
 5699 
 
 5777 
 
 78 
 
 7 
 
 5855 
 
 5933 
 
 6011 
 
 6089 
 
 6167 
 
 6245 
 
 6323 
 
 6401 
 
 6479 
 
 6556 
 
 
 8 
 
 6634 
 
 6712 
 
 6790 
 
 6868 
 
 6945 
 
 7023 
 
 7101 
 
 7179 
 
 7256 
 
 7334 
 
 
 9 
 
 7412 
 
 7489 
 
 7567 
 
 7645 
 
 7722 
 
 7800 
 
 7878 
 
 7955 
 
 8033 
 
 8110 
 
 
 560 
 
 8188 
 
 8266 
 
 8343 
 
 8421 
 
 8498 
 
 8576 
 
 8653 
 
 8731 
 
 8808 
 
 8885 
 
 
 
 8963 
 
 9040 
 
 9118 
 
 9195 
 
 9272 
 
 9350 
 
 9427 
 
 9504 
 
 9582 
 
 9659 
 
 
 2 
 
 9736 
 
 9814 
 
 9891 
 
 9968 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0045 
 
 0123 
 
 0200 
 
 0277 
 
 0354 
 
 0431 
 
 
 3 
 
 750508 
 
 0586 
 
 0663 
 
 0740 
 
 0817 
 
 0894 
 
 0971 
 
 1048 
 
 1125 
 
 1202 
 
 
 4 
 
 1279 
 
 1356 
 
 1433 
 
 1510 
 
 1587 
 
 1664 
 
 . 1741 
 
 1818 
 
 1895 
 
 1972 
 
 77 
 
 5 
 
 2048 
 
 2125 
 
 2202 
 
 2279 
 
 2356 
 
 2433 
 
 2509 
 
 2586 
 
 2663 
 
 2740 
 
 
 6 
 
 2816 
 
 2893 
 
 2970 
 
 3047 
 
 3123 
 
 3200 
 
 3277 
 
 3353 
 
 3430 
 
 3506 
 
 
 7 
 
 3583 
 
 3660 
 
 3736 
 
 3813 
 
 3889 
 
 3966 
 
 4042 
 
 4119 
 
 4195 
 
 4272 
 
 
 8 
 
 4348 
 
 4425 
 
 4501 
 
 4578 
 
 4654 
 
 4730 
 
 4807 
 
 4883 
 
 4960 
 
 5036 
 
 
 9 
 
 5112 
 
 5189 
 
 5265 
 
 5341 
 
 5417 
 
 5494 
 
 5570 
 
 5646 
 
 5722 
 
 5799 
 
 
 570 
 
 5875 
 
 5951 
 
 6027 
 
 6103 
 
 6180 
 
 6256 
 
 6332 
 
 6408 
 
 6484 
 
 6560 
 
 
 1 
 
 6636 
 
 6712 
 
 6758 
 
 6864 
 
 6940 
 
 7016 
 
 7092 
 
 7168 
 
 7244 
 
 7320 
 
 76 
 
 2 
 
 7396 
 
 7472 
 
 7548 
 
 7624 
 
 7700 
 
 7775 
 
 7851 
 
 7927 
 
 8003 
 
 8079 
 
 
 3 
 
 8155 
 
 8230 
 
 8306 
 
 8382 
 
 8458 
 
 8533 
 
 8609 
 
 8685 
 
 8761 
 
 8836 
 
 
 4 
 
 8912 
 
 8988 
 
 9063 
 
 9139 
 
 9214 
 
 9290 
 
 9366 
 
 9441 
 
 9517 
 
 9592 
 
 
 i 
 
 QAA 
 
 074-1 
 
 9819 
 
 9894 
 
 QQ7O 
 
 
 
 
 
 
 
 9 
 
 7ODO 
 
 7/*1J 
 
 
 
 77/\J 
 
 0045 
 
 0121 
 
 0196 
 
 0272 
 
 0347 
 
 
 6 
 
 760422 
 
 0498 
 
 0573 
 
 0649 
 
 0724 
 
 0799 
 
 0875 
 
 0950 
 
 1025 
 
 1101 
 
 
 7 
 
 1176 
 
 1251 
 
 1326 
 
 1402 
 
 1477 
 
 1552 
 
 1627 
 
 1702 
 
 1778 
 
 1853 
 
 
 8 
 
 1928 
 
 2003 
 
 2078 
 
 2153 
 
 2228 
 
 2303 
 
 2378 
 
 2453 
 
 2529 
 
 2604 
 
 73 
 
 9 
 
 2679 
 
 2754 
 
 2829 
 
 2904 
 
 2978 
 
 3053 
 
 3128 
 
 3203 
 
 3278 
 
 3353 
 
 
 580 
 
 3428 
 
 3503 
 
 3578 
 
 3653 
 
 3727 
 
 3802 
 
 3877 
 
 3952 
 
 4027 
 
 4101 
 
 
 1 
 
 4176 
 
 4251 
 
 4326 
 
 4400 
 
 4475 
 
 4550 
 
 4624 
 
 4699 
 
 4774 
 
 4848 
 
 
 2 
 
 4923 
 
 4998 
 
 5072 
 
 5147 
 
 5221 
 
 5296 
 
 5370 
 
 5445 
 
 5520 
 
 5594 
 
 
 3 
 
 5669 
 
 5743 
 
 5818 
 
 5892 
 
 5966 
 
 6041 
 
 6115 
 
 6190 
 
 6264 
 
 6338 
 
 
 4 
 
 6413 
 
 6487 
 
 6562 
 
 6636 
 
 6710 
 
 6785 
 
 6859 
 
 6933 
 
 7007 
 
 7082 
 
 
 PROPORTIONAL, PARTS. 
 
 Diff. 
 1ST- 
 
 1 
 
 3 
 
 ~T6T 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 8.3 
 
 24.9 
 
 33.2 
 
 41.5 
 
 49.8 
 
 58.1 
 
 66.4 
 
 74.7" 
 
 82 
 
 8.2 
 
 16.4 
 
 24.6 
 
 32.8 
 
 41.0 
 
 49.2 
 
 57.4 
 
 65.6 
 
 73.8 
 
 81 
 
 8.1 
 
 16.2 
 
 24.3 
 
 32.4 
 
 40.5 
 
 48.6 
 
 56.7 
 
 64.8 
 
 72.9 
 
 80 
 
 8.0 
 
 16.0 
 
 24.0 
 
 32.0 
 
 40.0 
 
 48.0 
 
 56.0 
 
 64.0 
 
 72.0 
 
 79 
 
 7.9 
 
 15.8 
 
 23.7 
 
 31.6 
 
 39.5 
 
 47.4 
 
 55.3 
 
 63.2 
 
 71.1 
 
 78 
 
 7.8 
 
 15.6 
 
 23.4 
 
 31.2 
 
 39.0 
 
 46.8 
 
 54.6 
 
 62.4 
 
 70.2 
 
 77 
 
 7.7 
 
 15.4 
 
 23.1 
 
 30.8 
 
 38.5 
 
 46.2 
 
 53.9 
 
 61.6 
 
 69.3 
 
 76 
 
 7.6 
 
 15.2 
 
 22.8 
 
 30.4 
 
 38.0 
 
 45.6 
 
 53.2 
 
 60.8 
 
 68.4 
 
 75 
 
 7.5 
 
 15.0 
 
 22.5 
 
 30.0 
 
 37.5 
 
 45.0 
 
 52.5 
 
 60.0 
 
 67.5 
 
 74 
 
 7.4 
 
 14,8 
 
 22,2 
 
 29.6 
 
 37.0 
 
 44.4 
 
 51.8 
 
 59.3 
 
 66* 
 
LOGARITHMS OF NUMBERS. 
 
 155 
 
 No. 585 L. 767.] 
 
 [No. 629 L. 79ft 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 585 
 
 767156 
 
 7230 
 
 ~730~4 
 
 7379 
 
 7453 
 
 7527 
 
 7601 
 
 7675 
 
 7749 
 
 7823 
 
 
 6 
 
 7898 
 
 7972 
 
 8046 
 
 8120 
 
 8194 
 
 8268 
 
 8342 
 
 8416 
 
 8490 
 
 8564 
 
 74 
 
 7 
 
 8638 
 
 8712 
 
 8786 
 
 8860 
 
 8934 
 
 9008 
 
 9082 
 
 9156 
 
 9230 
 
 9303 
 
 
 
 9377 
 
 945 1 
 
 9525 
 
 9599 
 
 9673 
 
 9746 
 
 9820 
 
 9894 
 
 9968 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0042 
 
 
 9 
 
 770115 
 
 0189 
 
 0263 
 
 0336 
 
 0410 
 
 0484 
 
 0557 
 
 0631 
 
 0705 
 
 0778 
 
 
 590 
 
 0852 
 
 0926 
 
 0999 
 
 1073 
 
 1146 
 
 1220 
 
 1293 
 
 1367 
 
 1440 
 
 1514 
 
 
 1 
 
 1587 
 
 1661 
 
 1734 
 
 1808 
 
 1881 
 
 1955 
 
 2028 
 
 2102 
 
 2175 
 
 2248 
 
 
 2 
 
 2322 
 
 2395 
 
 2468 
 
 2542 
 
 2615 
 
 2688 
 
 2762 
 
 2835 
 
 2908 
 
 2981 
 
 
 3 
 
 3055 
 
 3128 
 
 3201 
 
 3274 
 
 3348 
 
 3421 
 
 3494 
 
 3567 
 
 3640 
 
 3713 
 
 
 4 
 
 3786 
 
 3860 
 
 3933 
 
 4006 
 
 4079 
 
 4152 
 
 4225 
 
 4298 
 
 4371 
 
 4444 
 
 73 
 
 5 
 
 4517 
 
 4590 
 
 4663 
 
 4736 
 
 4809 
 
 4882 
 
 4955 
 
 5028 
 
 5100 
 
 5173 
 
 
 6 
 
 5246 
 
 5319 
 
 5392 
 
 5465 
 
 5538 
 
 5610 
 
 5683 
 
 5756 
 
 5829 
 
 5902 
 
 
 7 
 
 5974 
 
 6047 
 
 6120 
 
 6193 
 
 6265 
 
 6338 
 
 6411 
 
 6483 
 
 6556 
 
 6629 
 
 
 8 
 
 6701 
 
 6774 
 
 6846 
 
 6919 
 
 6992 
 
 7064 
 
 7137 
 
 7209 
 
 7282 
 
 7354 
 
 
 9 
 
 7427 
 
 7499 
 
 7572 
 
 7644 
 
 7717 
 
 7789 
 
 7862 
 
 7934 
 
 8006 
 
 8079 
 
 
 600 
 
 8151 
 
 8224 
 
 8296 
 
 8368 
 
 8441 
 
 8513 
 
 8585 
 
 8658 
 
 8730 
 
 8802 
 
 
 1 
 
 8874 
 
 8947 
 
 9019 
 
 9091 
 
 9163 
 
 9236 
 
 9308 
 
 9380 
 
 9452 
 
 9524 
 
 
 
 9596 
 
 9669 
 
 9741 
 
 9813 
 
 9885 
 
 9957 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0029 
 
 0101 
 
 0173 
 
 0245 
 
 
 3 
 
 780317 
 
 0389 
 
 0461 
 
 0533 
 
 0605 
 
 0677 
 
 0749 
 
 0821 
 
 0893 
 
 0965 
 
 72 
 
 4 
 
 1037 
 
 1109 
 
 1181 
 
 1253 
 
 1324 
 
 1396 
 
 1468 
 
 1540 
 
 1612 
 
 1684 
 
 
 5 
 
 1755 
 
 1827 
 
 1899 
 
 1971 
 
 2042 
 
 2114 
 
 2186 
 
 2258 
 
 2329 
 
 2401 
 
 
 6 
 
 2473 
 
 2544 
 
 2616 
 
 268 T 
 
 2759 
 
 2831 
 
 2902 
 
 2974 
 
 3046 
 
 3117 
 
 
 7 
 
 3189 
 
 3260 
 
 3332 
 
 3403 
 
 3475 
 
 3546 
 
 3618 
 
 3689 
 
 3761 
 
 3832 
 
 
 8 
 
 3904 
 
 3975 
 
 4046 
 
 4118 
 
 4189 
 
 4261 
 
 4332 
 
 4403 
 
 4475 
 
 4546 
 
 
 9 
 
 4617 
 
 4689 
 
 4760 
 
 4831 
 
 4902 
 
 4974 
 
 5045 
 
 5116 
 
 5187 
 
 5259 
 
 
 610 
 
 5330 
 
 5401 
 
 5472 
 
 5543 
 
 5615 
 
 5686 
 
 5757 
 
 5828 
 
 5899 
 
 5970 
 
 
 
 6041 
 
 6112 
 
 6183 
 
 6254 
 
 6325 
 
 6396 
 
 6467 
 
 6538 
 
 6609 
 
 6680 
 
 71 
 
 2 
 
 6751 
 
 6822 
 
 6893 
 
 6964 
 
 7035 
 
 7106 
 
 7177 
 
 7248 
 
 7319 
 
 7390 
 
 
 
 7460 
 
 7531 
 
 7602 
 
 7673 
 
 7744 
 
 7815 
 
 7885 
 
 7956 
 
 8027 
 
 8098 
 
 
 4 
 
 8168 
 
 8239 
 
 8310 
 
 8381 
 
 8451 
 
 8522 
 
 8593 
 
 8663 
 
 8734 
 
 8804 
 
 
 5 
 
 8875 
 
 8946 
 
 9016 
 
 9087 
 
 9157 
 
 9228 
 
 9299 
 
 9369 
 
 9440 
 
 9510 
 
 
 
 9581 
 
 965 1 
 
 9722 
 
 9792 
 
 986- 
 
 9933 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0004 
 
 0074 
 
 0144 
 
 0215 
 
 
 7 
 
 790285 
 
 0356 
 
 0426 
 
 0496 
 
 0567 
 
 0637 
 
 0707 
 
 0778 
 
 0848 
 
 0918 
 
 
 8 
 
 0988 
 
 1059 
 
 1129 
 
 1199 
 
 1269 
 
 1340 
 
 1410 
 
 1480 
 
 1550 
 
 1620 
 
 
 9 
 
 1691 
 
 1761 
 
 1831 
 
 1901 
 
 1971 
 
 2041 
 
 2111 
 
 2181 
 
 2252 
 
 2322 
 
 
 620 
 
 2392 
 
 2462 
 
 2532 
 
 2602 
 
 2672 
 
 2742 
 
 2812 
 
 2882 
 
 2952 
 
 3022 
 
 70 
 
 1 
 
 3092 
 
 3162 
 
 3231 
 
 3301 
 
 3371 
 
 3441 
 
 3511 
 
 3581 
 
 3651 
 
 3721 
 
 
 2 
 
 3790 
 
 3860 
 
 3930 
 
 4000 
 
 4070 
 
 4139 
 
 4209 
 
 4279 
 
 4349 
 
 4418 
 
 
 
 4488 
 
 4558 
 
 4627 
 
 4697 
 
 4767 
 
 4836 
 
 4906 
 
 4976 
 
 5045 
 
 5115 
 
 
 4 
 
 5185 
 
 5254 
 
 5324 
 
 5393 
 
 5463 
 
 5532 
 
 5602 
 
 5672 
 
 5741 
 
 5811 
 
 
 5 
 
 5880 
 
 5949 
 
 6019 
 
 6088 
 
 6158 
 
 6227 
 
 6297 
 
 6366 
 
 6436 
 
 6505 
 
 
 6 
 
 6574 
 
 6644 
 
 6713 
 
 6782 
 
 6852 
 
 6921 
 
 6990 
 
 7060 
 
 7129 
 
 7198 
 
 
 7 
 
 7268 
 
 7337 
 
 7406 
 
 7475 
 
 7545 
 
 7614 
 
 7683 
 
 7752 
 
 7821 
 
 7890 
 
 
 8 
 
 7960 
 
 8029 
 
 8098 
 
 8167 
 
 8236 
 
 8305 
 
 8374 
 
 8443 
 
 8513 
 
 8582 
 
 
 9 
 
 8651 
 
 8720 
 
 8789 
 
 8858 
 
 8927 
 
 8996 
 
 9065 
 
 9134 9203 
 
 9272 
 
 69 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 74 
 73 
 72 
 71 
 70 
 69 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 7.5 
 
 7.4 
 7.3 
 7.2 
 7.1 
 7.0 
 6.9 
 
 15.0 
 
 14.8 
 14.6 
 14.4 
 14.2 
 14.0 
 13.8 
 
 22.5 
 22.2 
 21.9 
 21.6 
 21.3 
 21.0 
 20.7 
 
 30.0 
 29.6 
 29.2 
 28.8 
 28.4 
 28.0 
 27.6 
 
 37.5 
 37.0 
 36.5 
 36.0 
 35.5 
 35.0 
 34.5 
 
 45.0 
 44.4 
 43.8 
 43.2 
 42.6 
 42.0 
 41.4 
 
 52.5 
 
 51.8 
 51.1 
 50.4 
 49.7 
 49.0 
 48.3 . 
 
 60.0 
 59.2 
 58.4 
 57.6 
 56.8 
 56.0 
 55.2 
 
 67.5 
 66.6 
 65.7 
 64.8 
 63.9 
 63.0 
 62.1 
 
156 
 
 LOGAK1THMS OF NUMBERS. 
 
 No. 630 L. 799.1 
 
 lNo.674L.829, 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 "630 
 
 799341 
 
 9409 
 
 9478 
 
 9547 
 
 9616 
 
 9685 
 
 9754 
 
 9823 
 
 9892 
 
 9961 
 
 
 1 
 
 800029 
 
 0098 
 
 0167 
 
 0236 
 
 0305 
 
 0373 
 
 0442 
 
 0511 
 
 0580 
 
 0648 
 
 
 2 
 
 0717 
 
 0786 
 
 0854 
 
 0923 
 
 0992 
 
 1061 
 
 1129 
 
 1198 
 
 1266 
 
 1335 
 
 
 3 
 
 1404 
 
 1472 
 
 1541 
 
 1609 
 
 1678 
 
 1747 
 
 1815 
 
 1884 
 
 1952 
 
 2021 
 
 
 4 
 
 2089 
 
 2158 
 
 2226 
 
 2295 
 
 2363 
 
 2432 
 
 2500 
 
 2568 
 
 2637 
 
 2705 
 
 
 5 
 
 2774 
 
 2842 
 
 2910 
 
 2979 
 
 3047 
 
 3116 
 
 3184 
 
 3252 
 
 3321 
 
 3389 
 
 
 6 
 
 3457 
 
 3525 
 
 3594 
 
 3662 
 
 3730 
 
 3798 
 
 3867 
 
 3935 
 
 4003 
 
 4071 
 
 
 7 
 
 4139 
 
 4208 
 
 4276 
 
 4344 
 
 4412 
 
 4480 
 
 4548 
 
 4616 
 
 4685 
 
 4753 
 
 
 8 
 
 4821 
 
 4889 
 
 4957 
 
 5025 
 
 5093 
 
 5161 
 
 5229 
 
 5297 
 
 5365 
 
 5433 
 
 68 
 
 9 
 
 5501 
 
 5569 
 
 5637 
 
 5705 
 
 5773 
 
 5841 
 
 5908 
 
 5976 
 
 6044 
 
 6112 
 
 
 640 
 
 806180 
 
 6248 
 
 6316 
 
 6384 
 
 6451 
 
 6519 
 
 6587 
 
 6655 
 
 6723 
 
 6790 
 
 
 1 
 
 6858 
 
 6926 
 
 6994 
 
 7061 
 
 7129 
 
 7197 
 
 7264 
 
 7332 
 
 7400 
 
 7467 
 
 
 2 
 
 7535 
 
 7603 
 
 7670 
 
 7738 
 
 7806 
 
 7873 
 
 7941 
 
 8008 
 
 8076 
 
 8143 
 
 
 3 
 
 8211 
 
 8279 
 
 8346 
 
 8414 
 
 8481 
 
 8549 
 
 8616 
 
 8684 
 
 8751 
 
 8818 
 
 
 4 
 
 8886 
 
 8953 
 
 9021 
 
 9088 
 
 9156 
 
 9223 
 
 9290 
 
 9358 
 
 9425 
 
 9492 
 
 
 5 
 
 9560 
 
 9627 
 
 9694 
 
 9762 
 
 9829 
 
 9896 
 
 9964 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0031 
 
 0098 
 
 0165 
 
 
 6 
 
 810233 
 
 0300 
 
 0367 
 
 0434 
 
 0501 
 
 0569 
 
 0636 
 
 0703 
 
 0770 
 
 0837 
 
 
 7 
 
 0904 
 
 0971 
 
 1039 
 
 1106 
 
 1173 
 
 1240 
 
 1307 
 
 1374 
 
 1441 
 
 1508 
 
 6: 
 
 8 
 
 1575 
 
 1642 
 
 1709 
 
 1776 
 
 1843 
 
 1910 
 
 1977 
 
 2044 
 
 2111 
 
 2178 
 
 
 9 
 
 2245 
 
 2312 
 
 2379 
 
 2445 
 
 2512 
 
 2579 
 
 2646 
 
 2713 
 
 2780 
 
 2847 
 
 
 650 
 
 2913 
 
 2980 
 
 3047 
 
 3114 
 
 3181 
 
 3247 
 
 3314 
 
 3381 
 
 3448 
 
 3514 
 
 
 1 
 
 3581 
 
 3648 
 
 3714 
 
 3781 
 
 3848 
 
 3914 
 
 3981 
 
 4048 
 
 4114 
 
 4181 
 
 
 2 
 
 4248 
 
 4314 
 
 4381 
 
 4447 
 
 4514 
 
 4581 
 
 4647 
 
 4714 
 
 4780 
 
 4847 
 
 
 3 
 
 4913 
 
 4980 
 
 5046 
 
 5113 
 
 5179 
 
 5246 
 
 5312 
 
 5378 
 
 5445 
 
 5511 
 
 
 4 
 
 5578 
 
 5644 
 
 5711 
 
 5777 
 
 5843 
 
 5910 
 
 5976 
 
 6042 
 
 6109 
 
 6175 
 
 
 5 
 
 6241 
 
 6308 
 
 6374 
 
 6440 
 
 6506 
 
 6573 
 
 6639 
 
 6705 
 
 6771 
 
 6838 
 
 
 6 
 
 6904 
 
 6970 
 
 7036 
 
 7102 
 
 7169 
 
 7235 
 
 7301 
 
 7367 
 
 7433 
 
 7499 
 
 
 7 
 
 7565 
 
 7631 
 
 7698 
 
 7764 
 
 7830 
 
 7896 
 
 7962 
 
 8028 
 
 8094 
 
 8160 
 
 
 8 
 
 8226 
 
 8292 
 
 8358 
 
 8424 
 
 8490 
 
 8556 
 
 8622 
 
 8688 
 
 8754 
 
 8820 
 
 66 
 
 9 
 
 8885 
 
 8951 
 
 9017 
 
 9083 
 
 9149 
 
 9215 
 
 9281 
 
 9346 
 
 9412 
 
 9478 
 
 
 660 
 
 9544 
 
 9610 
 
 9676 
 
 9741 
 
 9807 
 
 9873 
 
 9939 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0004 
 
 0070 
 
 0136 
 
 
 1 
 
 820201 
 
 0267 
 
 0333 
 
 0399 
 
 0464 
 
 0530 
 
 0595 
 
 0661 
 
 0727 
 
 0792 
 
 
 2 
 
 0858 
 
 0924 
 
 0989 
 
 1055 
 
 1120 
 
 1186 
 
 1251 
 
 1317 
 
 1382 
 
 1448 
 
 
 3 
 
 1514 
 
 -1579 
 
 1645 
 
 1710 
 
 1775 
 
 1841 
 
 1906 
 
 1972 
 
 2037 
 
 2103 
 
 
 4 
 
 2168 
 
 2233 
 
 2299 
 
 2364 
 
 2430 
 
 2495 
 
 2560 
 
 2626 
 
 2691 
 
 2756 
 
 
 5 
 
 2822 
 
 2887 
 
 2952 
 
 3018 
 
 3083 
 
 3148 
 
 3213 
 
 3279 
 
 3344 
 
 3409 
 
 
 6 
 
 3474 
 
 3539 
 
 3605 
 
 3670 
 
 3735 
 
 3800 
 
 3865 
 
 3930 
 
 3996 
 
 4061 
 
 
 7 
 
 4126 
 
 4191 
 
 4256 
 
 4321 
 
 4386 
 
 4451 
 
 4516 
 
 4581 
 
 4646 
 
 4711 
 
 
 8 
 
 4776 
 
 4841 
 
 4906 
 
 4971 
 
 5036 
 
 5101 
 
 5166 
 
 5231 
 
 5296 
 
 5361 
 
 65 
 
 9 
 
 5426 
 
 5491 
 
 5556 
 
 5621 
 
 5686 
 
 5751 
 
 5815 
 
 5880 
 
 5945 
 
 6010 
 
 
 670 
 
 6075 
 
 6140 
 
 6204 
 
 6269 
 
 6334 
 
 6399 
 
 6464 
 
 6528 
 
 6593 
 
 6658 
 
 
 1 
 
 6723 
 
 6787 
 
 6852 
 
 6917 
 
 6981 
 
 7046 
 
 7111 
 
 7175 
 
 7240 
 
 7305 
 
 
 2 
 
 7369 
 
 7434 
 
 7499 
 
 7563 
 
 7628 
 
 7692 
 
 7757 
 
 7821 
 
 7886 
 
 7951 
 
 
 3 
 
 8015 
 
 8080 
 
 8144 
 
 8209 
 
 8273 
 
 8338 
 
 8402 
 
 8467 
 
 8531 
 
 8595 
 
 
 4 
 
 8660 
 
 8724 
 
 8789 
 
 8853 
 
 8918 
 
 8982' 9046 
 
 9111 
 
 9175 
 
 9239 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 9 
 
 68 
 67 
 66 
 65 
 64 
 
 6.8 
 6.7 
 6.6 
 6.5 
 6.4 
 
 13.6 
 13.4 
 13.2 
 13.0 
 12.8 
 
 20.4 
 20.1 
 19.8 
 19.5 
 19.2 
 
 27.2 
 26.8 
 26.4 
 26.0 
 25.6 
 
 34.0 
 33.5 
 33.0 
 32.5 
 32.0 
 
 40.8 
 40.2 
 39.6 
 39.0 
 
 38.4 
 
 47.6 
 46.9 
 46.2 
 45.5 
 44.8 
 
 54.4 
 53.6 
 52.8 
 52.0 
 51.2 
 
 61.2 
 60.3 
 59.4 
 58.5 
 57.6 
 
LOGARITHMS Ofr NtJMSERS. 
 
 15? 
 
 No. 675 L. 829.] 
 
 [No. 719 L. 857. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 ~67T 
 
 829304 
 9947 
 
 9368 
 
 9432 
 
 9497 
 
 9561 
 
 9625 
 
 9690 
 
 9754 
 
 9818 
 
 9882 
 
 
 6 
 
 
 001 1 
 
 0075 
 
 0139 
 
 0204 
 
 0268 
 
 0332 
 
 0396 
 
 0460 
 
 "TTT 
 
 
 7 
 
 830589 
 
 0653 
 
 0717 
 
 0781 
 
 0845 
 
 0909 
 
 0973 
 
 1037 
 
 1102 
 
 1166 
 
 
 3 
 
 1230 
 
 1294 
 
 . 1358 
 
 1422 
 
 1486 
 
 1550 
 
 1614 
 
 1678 
 
 1742 
 
 1806 
 
 64 
 
 9 
 
 1870 
 
 1934 
 
 1998 
 
 2062 
 
 2126 
 
 2189 
 
 2253 
 
 2317 
 
 2381 
 
 2445 
 
 
 680 
 
 2509 
 
 2573 
 
 2637 
 
 2700 
 
 2764 
 
 2828 
 
 2892 
 
 2956 
 
 3020 
 
 3083 
 
 
 1 
 
 3147 
 
 3211 
 
 3275 
 
 3338 
 
 3402 
 
 3466 
 
 3530 
 
 3593 
 
 3657 
 
 3721 
 
 
 2 
 
 3784 
 
 3848 
 
 3912 
 
 3975 
 
 4039 
 
 4103 
 
 4166 
 
 4230 
 
 4294 
 
 4357 
 
 
 3 
 
 4421 
 
 4484 
 
 4548 
 
 4611 
 
 4675 
 
 .4739 
 
 4802 
 
 4866 
 
 4929 
 
 4993 
 
 
 4 
 
 5056 
 
 5120 
 
 5183 
 
 5247 
 
 5310 
 
 5373 
 
 5437 
 
 5500 
 
 5564 
 
 5627 
 
 
 5 
 
 5691 
 
 5754 
 
 5817 
 
 5881 
 
 5944 
 
 6007 
 
 6071 
 
 6134 
 
 6197 
 
 6261 
 
 
 6 
 
 6324 
 
 6387 
 
 6451 
 
 6514 
 
 6577 
 
 6641 
 
 6704 
 
 6767 
 
 6830 
 
 6894 
 
 
 7 
 
 6957 
 
 7020 
 
 7083 
 
 7146 
 
 7210 
 
 7273 
 
 7336 
 
 7399 
 
 7462 
 
 7525 
 
 
 8 
 
 7588 
 
 7652 
 
 7715 
 
 7778 
 
 7841 
 
 7904 
 
 7967 
 
 8030 
 
 8093 
 
 8156 
 
 63 
 
 9 
 
 8219 
 
 8282 
 
 8345 
 
 8408 
 
 8471 
 
 8534 
 
 8597 
 
 8660 
 
 8723 
 
 8786 
 
 
 690 
 
 8849 
 
 8912 
 
 8975 
 
 9038 
 
 9101 
 
 9164 
 
 9227 
 
 9289 
 
 9352 
 
 9415 
 
 
 1 
 
 94/8 
 
 9541 
 
 9604 
 
 9667 
 
 9729 
 
 9792 
 
 9855 
 
 9918 
 
 9981 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0043 
 
 
 2 
 
 840106 
 
 0169 
 
 0232 
 
 0294 
 
 0357 
 
 0420 
 
 0482 
 
 0545 
 
 0608 
 
 0671 
 
 
 3 
 
 0733 
 
 0796 
 
 0859 
 
 0921 
 
 0984 
 
 1046 
 
 1109 
 
 1172 
 
 1234 
 
 1297 
 
 
 4 
 
 1359 
 
 1422 
 
 1485 
 
 1547 
 
 1610 
 
 1672 
 
 1735 
 
 1797 
 
 1860 
 
 1922 
 
 
 5 
 
 1985 
 
 2047 
 
 2110 
 
 2172 
 
 2235 
 
 2297 
 
 2360 
 
 2422 
 
 2484 
 
 2547 
 
 
 6 
 
 2609 
 
 2672 
 
 2734 
 
 2796 
 
 2859 
 
 2921 
 
 2983 
 
 3046 
 
 3108 
 
 3170 
 
 
 7 
 
 3233 
 
 3295 
 
 3357 
 
 3420 
 
 3482 
 
 3544 
 
 3606 
 
 3669 
 
 3731 
 
 3793 
 
 
 8 
 
 3855 
 
 3918 
 
 3980 
 
 4042 
 
 4104 
 
 4166 
 
 4229 
 
 4291 
 
 4353 
 
 4415 
 
 
 9 
 
 4477 
 
 4539 
 
 4601 
 
 4664 
 
 4726 
 
 4788 
 
 4850 
 
 4912 
 
 4974 
 
 5036 
 
 
 700 
 
 5098 
 
 5160 
 
 5222 
 
 5284 
 
 5346 
 
 5408 
 
 5470 
 
 5532 
 
 5594 
 
 5656 
 
 62 
 
 1 
 
 5718 
 
 5780 
 
 5842 
 
 5904 
 
 5966 
 
 6028 
 
 6090 
 
 6151 
 
 6213 
 
 6275 
 
 
 2 
 
 6337 
 
 6399 
 
 6461 
 
 6523 
 
 6585 
 
 6646 
 
 6708 
 
 6770 
 
 6832 
 
 6894 
 
 
 3 
 
 6955 
 
 7017 
 
 7079 
 
 7141 
 
 7202 
 
 7264 
 
 7326 
 
 7388 
 
 7449 
 
 7511 
 
 
 4 
 
 7573 
 
 7634 
 
 7696 
 
 7758 
 
 7819 
 
 7881 
 
 7943 
 
 8004 
 
 8066 
 
 8128 
 
 
 5 
 
 8189 
 
 8251 
 
 8312 
 
 8374 
 
 8435 
 
 8497 
 
 8559 
 
 8620 
 
 8682 
 
 8743 
 
 
 6 
 
 8805 
 
 8366 
 
 8928 
 
 8989 
 
 9051 
 
 9112 
 
 9174 
 
 9235 
 
 9297 
 
 9358 
 
 
 7 
 
 9419 
 
 9431 
 
 9542 
 
 9604 
 
 9665 
 
 9726 
 
 9788 
 
 9849 
 
 9911 
 
 9972 
 
 
 8 
 
 850033 
 
 0095 
 
 0156 
 
 0217 
 
 0279 
 
 0340 
 
 0401 
 
 0462 
 
 0524 
 
 0585 
 
 
 9 
 
 0646 
 
 0707 
 
 0769 
 
 0830 
 
 0891 
 
 0952 
 
 1014 
 
 1075 
 
 1136 
 
 1197 
 
 
 710 
 
 1258 
 
 1320 
 
 1381 
 
 1442 
 
 1503 
 
 1564 
 
 1625 
 
 1686 
 
 1747 
 
 1809 
 
 
 1 
 
 1870 
 
 1931 
 
 1992 
 
 2053 
 
 2114 
 
 2175 
 
 2236 
 
 2297 
 
 2358 
 
 2419 
 
 61 
 
 2 
 
 2480 
 
 2541 
 
 2602 
 
 2663 
 
 2724 
 
 2785 
 
 2846 
 
 2907 
 
 2968 
 
 3029 
 
 
 3 
 
 3090 
 
 3150 
 
 3211 
 
 3272 
 
 3333 
 
 3394 
 
 3455 
 
 3516 
 
 3577 
 
 3637 
 
 
 4 
 
 3698 
 
 3759 
 
 3820 
 
 3881 
 
 3941 
 
 4002 
 
 4063 
 
 4124 
 
 4185 
 
 4245 
 
 
 5 
 
 4306 
 
 4367 
 
 4428 
 
 4488 
 
 4549 
 
 4610 
 
 4670 
 
 4731 
 
 4792 
 
 4852 
 
 
 6 
 
 4913 
 
 4974 
 
 5034 
 
 5095 
 
 5156 
 
 5216 
 
 5277 
 
 5337 
 
 5398 
 
 5459 
 
 
 7 
 
 5519 
 
 5580 
 
 5640 
 
 5701 
 
 5761 
 
 5822 
 
 5882 
 
 5943 
 
 6003 
 
 6064 
 
 
 8 
 
 6124 
 
 6185 
 
 6245 
 
 6306 
 
 6366 
 
 6427 
 
 6487 
 
 6548 
 
 6608 
 
 6668 
 
 
 9 
 
 6729 6789J 6850 
 
 6910 
 
 6970 
 
 7031 
 
 7091 
 
 7152 
 
 7212 
 
 7272 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 65 
 64 
 63 
 62 
 61 
 60 
 
 6.5 
 6.4 
 6.3 
 6.2 
 6.1 
 6.0 1 
 
 13.0 
 12.8 
 12.6 
 12.4 
 12.2 
 12.0 
 
 19.5 
 19.2 
 18.9 
 18.6 
 18.3 
 18.0 
 
 26.0 
 25.6 
 25.2 
 24.8 
 24.4 
 24.0 
 
 32.5 
 32.0 
 31.5 
 31.0 
 30.5 
 30.0 
 
 39.0 
 38:4 
 37.8 
 37.2 
 36.6 
 36.0 
 
 45.5 
 
 44.8 
 44.1 
 43.4 
 42.7 
 42.0 
 
 52.0 
 51.2 
 50.4 
 49.6 
 48.8 
 48.0 
 
 58.5 
 57.6 
 56.7 
 55.8 
 54.9 
 54.0 
 
158 
 
 LOGARITHMS OF NUMBERS. 
 
 Ho. 720 L. 857.] 
 
 (No. 764 L. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 720 
 
 857332 
 
 7393 
 
 7453 
 
 7513 
 
 7574 
 
 7634 
 
 7694 
 
 7755 
 
 7815 
 
 7875 
 
 
 
 7935 
 
 7995 
 
 8056 
 
 8116 
 
 S176 
 
 8236 
 
 8297 
 
 8357 
 
 8417 
 
 8477 
 
 
 2 
 
 8537 
 
 8597 
 
 8657 
 
 8718 
 
 8778 
 
 8838 
 
 8898 
 
 8958 
 
 9018 
 
 9078 
 
 
 3 
 
 9138 
 
 9198 
 
 9258 
 
 9318 
 
 9379 
 
 9439 
 
 9499 
 
 9559 
 
 9619 
 
 9679 
 
 60 
 
 4 
 
 9739 
 
 9799 
 
 9859 
 
 9918 
 
 9978 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0038 
 
 0098 
 
 0158 
 
 021fi 
 
 fl?7fl 
 
 
 5 
 
 860338 
 
 0398 
 
 0458 
 
 0518 
 
 0578 
 
 0637 
 
 0697 
 
 0757 
 
 0817 
 
 U^/O 
 
 0877 
 
 
 6 
 
 0937 
 
 0996 
 
 1056 
 
 1116 
 
 1176 
 
 1236 
 
 1295 
 
 1355 
 
 1415 
 
 1475 
 
 
 7 
 
 1534 
 
 1594 
 
 1654 
 
 1714 
 
 1773 
 
 1833 
 
 1893 
 
 1952 
 
 2012 
 
 2072 
 
 
 8 
 
 2131 
 
 2191 
 
 2251 
 
 2310 
 
 2370 
 
 2430 
 
 2489 
 
 2549 
 
 2608 
 
 2668 
 
 
 9 
 
 2728 
 
 2787 
 
 2847 
 
 2906 
 
 2966 
 
 3025 
 
 3085 
 
 3144 
 
 3204 
 
 3263 
 
 
 730 
 
 3323 
 
 3382 
 
 3442 
 
 3501 
 
 3561 
 
 3620 
 
 3680 
 
 3739 
 
 3799 
 
 3858 
 
 
 1 
 
 3917 
 
 3977 
 
 4036 
 
 4096 
 
 4155 
 
 4214 
 
 4274 
 
 4333 
 
 4392 
 
 4452 
 
 
 2 
 
 4511 
 
 4570 
 
 4630 
 
 4689 
 
 4748 
 
 4808 
 
 4867 
 
 4926 
 
 4985 
 
 5045 
 
 
 3 
 
 5104 
 
 5163 
 
 5222 
 
 5282 
 
 5341 
 
 5400 
 
 5459 
 
 5519 
 
 5578 
 
 5637 
 
 
 4 
 
 5696 
 
 5755 
 
 5814 
 
 5874 
 
 5933 
 
 5992 
 
 6051 
 
 6110 
 
 6169 
 
 6228 
 
 
 5 
 
 6287 
 
 6346 
 
 6405 
 
 6465 
 
 6524 
 
 6583 
 
 6642 
 
 6701 
 
 6760 
 
 6819 
 
 
 6 
 
 6878 
 
 6937 
 
 6996 
 
 7055 
 
 7114 
 
 7173 
 
 7232 
 
 7291 
 
 7350 
 
 7409 
 
 59 
 
 7 
 
 7467 
 
 7526 
 
 7585 
 
 7644 
 
 7703 
 
 7762 
 
 7821 
 
 7880 
 
 7939 
 
 7998 
 
 
 8 
 
 8056 
 
 8115 
 
 8174 
 
 8233 
 
 8292 
 
 8350 
 
 8409 
 
 8468 
 
 8527 
 
 8586 
 
 
 9 
 
 8644 
 
 8703 
 
 8762 
 
 8821 
 
 8879 
 
 8938 
 
 8997 
 
 9056 
 
 9114 
 
 9173 
 
 
 740 
 
 9232 
 
 9290 
 
 9349 
 
 9408 
 
 9466 
 
 9525 
 
 9584 
 
 9642 
 
 9701 
 
 9760 
 
 
 1 
 
 9818 
 
 9877 
 
 9935 
 
 9994 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0053 
 
 01 1 1 
 
 0170 
 
 0228 
 
 0287 
 
 0345 
 
 
 2 
 
 870404 
 
 0462 
 
 0521 
 
 0579 
 
 0638 
 
 0696 
 
 0755 
 
 0813 
 
 0872 
 
 0930 
 
 
 3 
 
 0989 
 
 1047 
 
 1106 
 
 1164 
 
 1223 
 
 1281 
 
 1339 
 
 1398 
 
 1456 
 
 1515 
 
 
 4 
 
 1573 
 
 1631 
 
 1690 
 
 1748 
 
 1806 
 
 1865 
 
 1923 
 
 1981 
 
 2040 
 
 2098 
 
 
 5 
 
 2156 
 
 2215 
 
 2273 
 
 2331 
 
 2389 
 
 2448 
 
 2506 
 
 2564 
 
 2622 
 
 2681 
 
 
 6 
 
 2739 
 
 2797 
 
 2855 
 
 2913 
 
 2972 
 
 3030 
 
 3088 
 
 3146 
 
 3204 
 
 3262 
 
 
 7 
 
 3321 
 
 3379 
 
 3437 
 
 3495 
 
 3553 
 
 3611 
 
 3669 
 
 3727 
 
 3785 
 
 3844 
 
 
 8 
 
 3902 
 
 3960 
 
 4018 
 
 4076 
 
 4134 
 
 4192 
 
 4250 
 
 4308 
 
 4366 
 
 4424 
 
 58 
 
 9 
 
 4482 
 
 4540 
 
 4598 
 
 4656 
 
 4714 
 
 4772 
 
 4830 
 
 4888 
 
 4945 
 
 5003 
 
 
 750 
 
 5061 
 
 5119 
 
 5177 
 
 5235 
 
 5293 
 
 5351 
 
 5409 
 
 5466 
 
 5524 
 
 5582 
 
 
 1 
 
 5640 
 
 5698 
 
 5756 
 
 5813 
 
 5871 
 
 5929 
 
 5987 
 
 6045 
 
 6102 
 
 6160 
 
 
 2 
 
 6218 
 
 6276 
 
 6333 
 
 6391 
 
 6449 
 
 6507 
 
 6564 
 
 6622 
 
 6680 
 
 6737 
 
 
 3 
 
 6795 
 
 6853 
 
 6910 
 
 6968 
 
 7026 
 
 7083 
 
 7141 
 
 7199 
 
 7256 
 
 7314 
 
 - 
 
 4 
 
 7371 
 
 7429 
 
 7487 
 
 7544 
 
 7602 
 
 7659 
 
 7717 
 
 7774 
 
 7832 
 
 7889 
 
 
 5 
 
 7947 
 
 8004 
 
 8062 
 
 8119 
 
 8177 
 
 8234 
 
 8292 
 
 8349 
 
 8407 
 
 8464 
 
 
 6 
 
 8522 
 
 8579 
 
 8637 
 
 8694 
 
 8752 
 
 8809 
 
 8866 
 
 8924 
 
 8981 
 
 9039 
 
 
 7 
 
 9096 
 
 9153 
 
 9211 
 
 9268 
 
 9325 
 
 9383 
 
 9440 
 
 9497 
 
 9555 
 
 9612 
 
 
 
 9669 
 
 9726 
 
 9784 
 
 9841 
 
 9898 
 
 9956 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0013 
 
 0070 
 
 0127 
 
 0185 
 
 
 9 
 
 880242 
 
 0299 
 
 0356 
 
 0413 
 
 0471 
 
 0528 
 
 0585 
 
 0642 
 
 0699 
 
 0756 
 
 
 760 
 
 0814 
 
 0871 
 
 0928 
 
 0985 
 
 1042 
 
 1099 
 
 1156 
 
 1213 
 
 1271 
 
 1328 
 
 
 
 1385 
 
 1442 
 
 1499 
 
 1556 
 
 1613 
 
 1670 
 
 1727 
 
 1784 
 
 1841 
 
 1898 
 
 
 2 
 
 1955 
 
 2012 
 
 2069 
 
 2126 
 
 2183 
 
 2240 
 
 2297 
 
 2354 
 
 2411 
 
 2468 
 
 57 
 
 3 
 
 2525 
 
 2581 
 
 2638 
 
 2695 
 
 2752 
 
 2809 
 
 2866 
 
 2923 
 
 2980 
 
 3037 
 
 
 4 
 
 3093 
 
 3150 
 
 3207 
 
 3264 
 
 3321 
 
 3377 
 
 3434 
 
 3491 
 
 3548 
 
 3605 
 
 
 PROPORTIONAL, PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 59 
 58 
 57 
 56 
 
 5.9 
 5.8 
 5.7 
 5.6 
 
 11.8 
 11.6 
 11.4 
 11.2 
 
 17.7 
 17.4 
 17.1 
 
 16.8 
 
 *23.6 
 23.2 
 22.8 
 22.4 
 
 29.5 
 29.0 
 28.5 
 28.0 
 
 35.4 
 34.8 
 34.2 
 33.6 
 
 41.3 
 40.6 
 39.9 
 39.2 
 
 47.2 
 46.4 
 45.6 
 44.8 
 
 53.1 
 52.2 
 51.3 
 50.4 
 
LOGARITHMS OF NUMBERS. 
 
 159 
 
 No. 765 L. 883.] 
 
 [No. 809 L. 908. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 765 
 
 883661 
 
 3718 
 
 3775 
 
 3832 
 
 3888 
 
 3945 
 
 4002 
 
 4059 
 
 4115 
 
 4172 
 
 
 6 
 
 4229 
 
 4285 
 
 4342 
 
 4399 
 
 4455 
 
 4512 
 
 4569 
 
 4625 
 
 4682 
 
 4739 
 
 
 7 
 
 4795 
 
 4852 
 
 4909 
 
 4965 
 
 5022 
 
 5078 
 
 5135 
 
 5192 
 
 5248 
 
 5305 
 
 
 8 
 
 5361 
 
 5418 
 
 5474 
 
 5531 
 
 5587 
 
 5644 
 
 5700 
 
 5757 
 
 5813 
 
 5870 
 
 
 9 
 
 5926 
 
 5983 
 
 6039 
 
 6096 
 
 6152 
 
 6209 
 
 6265 
 
 6321 
 
 6378 
 
 6434 
 
 
 770 
 
 6491 
 
 6547 
 
 6604 
 
 6660 
 
 6716 
 
 6773 
 
 6829 
 
 6885 
 
 6942 
 
 6998 
 
 
 1 
 
 7054 
 
 7111 
 
 7167 
 
 7223 
 
 7280 
 
 7336 
 
 7392 
 
 7449 
 
 7505 
 
 7561 
 
 
 2 
 
 7617 
 
 7674 
 
 7730 
 
 7786 
 
 7842 
 
 -7898 
 
 7955 
 
 8011 
 
 8067 
 
 8123 
 
 
 3 
 
 8179 
 
 8236 
 
 8292 
 
 8348 
 
 8404 
 
 8460 
 
 8516 
 
 8573 
 
 8629 
 
 8685 
 
 
 A 
 
 8741 
 
 8797 
 
 8853 
 
 8909 
 
 8965 
 
 9021 
 
 9077 
 
 9134 
 
 9190 
 
 9246 
 
 
 
 9302 
 9862 
 
 9358 
 9918 
 
 9414 
 9974 
 
 9470 
 
 9526 
 
 9582 
 
 9638 
 
 9694 
 
 9750 
 
 9806 
 
 56 
 
 
 
 
 
 0030 
 
 0086 
 
 0141 
 
 0197 
 
 0253 
 
 0309 
 
 0365 
 
 
 7 
 
 890421 
 
 0477 
 
 0533 
 
 0589 
 
 0645 
 
 0700 
 
 0756 
 
 0812 
 
 0868 
 
 0924 
 
 
 8 
 
 0980 
 
 1035 
 
 1091 
 
 1147 
 
 1203 
 
 1259 
 
 1314 
 
 1370 
 
 1426 
 
 1482 
 
 
 9 
 
 1537 
 
 1593 
 
 1649 
 
 1705 
 
 1760 
 
 1816 
 
 1872 
 
 1928 
 
 1983 
 
 2039 
 
 
 780 
 
 2095 
 
 2150 
 
 2206 
 
 2262 
 
 2317 
 
 2373 
 
 2429 
 
 2484 
 
 2540 
 
 2595 
 
 
 
 2651 
 
 2707 
 
 2762 
 
 2818 
 
 2873 
 
 2929 
 
 2985 
 
 3040 
 
 3096 
 
 3151 
 
 
 2 
 
 3207 
 
 3262 
 
 3318 
 
 3373 
 
 3429 
 
 3484 
 
 3540 
 
 3595 
 
 3651 
 
 3706 
 
 
 3 
 
 3762 
 
 3817 
 
 3873 
 
 3928 
 
 3984 
 
 4039 
 
 4094 
 
 4150 
 
 4205 
 
 4261 
 
 
 4 
 
 4316 
 
 4371 
 
 4427 
 
 4482 
 
 4538 
 
 4593 
 
 4648 
 
 4704 
 
 4759 
 
 4814 
 
 
 5 
 
 4870 
 
 4925 
 
 4980 
 
 5036 
 
 5091 
 
 5146 
 
 5201 
 
 5257 
 
 5312 
 
 5367 
 
 
 6 
 
 5423 
 
 5478 
 
 5533 
 
 5588 
 
 5644 
 
 5699 
 
 5754 
 
 5809 
 
 5864 
 
 5920 
 
 
 7 
 
 5975 
 
 6030 
 
 6085 
 
 6140 
 
 6195 
 
 6251 
 
 6306 
 
 6361 
 
 6416 
 
 6471 
 
 
 8 
 
 6526 
 
 6581 
 
 6636 
 
 6692 
 
 6747 
 
 6802 
 
 6857 
 
 6912 
 
 6967 
 
 7022 
 
 
 9 
 
 7077 
 
 7132 
 
 7187 
 
 7242 
 
 7297 
 
 7352 
 
 7407 
 
 7462 
 
 7517 
 
 7572 
 
 
 
 
 
 
 
 
 
 
 
 
 
 55 
 
 790 
 
 7627 
 
 7682 
 
 7737 
 
 7792 
 
 7847 
 
 7902 
 
 7957 
 
 8012 
 
 8067 
 
 8122 
 
 
 1 
 
 8176 
 
 8231 
 
 8286 
 
 8341 
 
 8396 
 
 8451 
 
 8506 
 
 8561 
 
 8615 
 
 8670 
 
 
 2 
 
 8725 
 
 8780 
 
 8835 
 
 8890 
 
 8944 
 
 8999 
 
 9054 
 
 9109 
 
 9164 
 
 9218 
 
 
 3 
 
 9273 
 
 9328 
 
 9383 
 
 9437 
 
 9492 
 
 9547 
 
 9602 
 
 9656 
 
 9711 
 
 9766 
 
 
 4 
 
 9821 
 
 9875 
 
 9930 
 
 9985 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0039 
 
 0094 
 
 0149 
 
 0203 
 
 0258 
 
 0312 
 
 
 5 
 
 900367 
 
 0422 
 
 0476 
 
 0531 
 
 0586 
 
 0640 
 
 0695 
 
 0749 
 
 0804 
 
 0859 
 
 
 6 
 
 0913 
 
 0968 
 
 1022 
 
 1077 
 
 1131 
 
 1186 
 
 1240 
 
 1295 
 
 1349 
 
 1404 
 
 
 7 
 
 1458 
 
 1513 
 
 1567 
 
 1622 
 
 1676 
 
 1731 
 
 1785 
 
 1840 
 
 1894 
 
 1948 
 
 
 8 
 
 2003 
 
 2057 
 
 2112 
 
 2166 
 
 2221 
 
 2275 
 
 2329 
 
 2384 
 
 2438 
 
 2492 
 
 
 9 
 
 2547 
 
 2601 
 
 2655 
 
 2710 
 
 2764 
 
 2818 
 
 2873 
 
 2927 
 
 2981 
 
 3036 
 
 
 800 
 
 3090 
 
 3144 
 
 3199 
 
 3253 
 
 3307 
 
 3361 
 
 3416 
 
 3470 
 
 3524 
 
 3578 
 
 
 1 
 
 3633 
 
 3687 
 
 3741 
 
 3795 
 
 3849 
 
 3904 
 
 3958 
 
 4012 
 
 4066 
 
 4120 
 
 
 2 
 
 4174 
 
 4229 
 
 4283 
 
 4337 
 
 4391 
 
 4445 
 
 4499 
 
 4553 
 
 4607 
 
 4661 
 
 
 3 
 
 4716 
 
 4770 
 
 4824 
 
 4878 
 
 4932 
 
 4986 
 
 5040 
 
 5094 
 
 5148 
 
 5202 
 
 
 4 
 
 5256 
 
 5310 
 
 5364 
 
 5418 
 
 5472 
 
 5526 
 
 5580 
 
 5634 
 
 5688 
 
 5742 
 
 54 
 
 5 
 
 5796 
 
 5850 
 
 5904 
 
 5958 
 
 6012 
 
 6066 
 
 6119 
 
 6173 
 
 6227 
 
 6281 
 
 
 6 
 
 6335 
 
 6389 
 
 6443 
 
 6497 
 
 6551 
 
 6604 
 
 6658 
 
 6712 
 
 6766 
 
 6820 
 
 
 7 
 
 6874 
 
 6927 
 
 6981 
 
 7035 
 
 7089 
 
 7143 
 
 7196 
 
 7250 
 
 7304 
 
 7358 
 
 
 8 
 
 7411 
 
 7465 
 
 7519 
 
 7573 
 
 7626 
 
 7680 
 
 7734 
 
 7787 
 
 7841 
 
 7895 
 
 
 9 
 
 7949 
 
 8002 
 
 8056 
 
 8110 
 
 8163 
 
 8217 
 
 8270 
 
 8324 
 
 8378 
 
 8431 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 57 
 56 
 55 
 54 
 
 5.7 
 5.6 
 5.5 
 5.4 
 
 11.4 
 11.2 
 11.0 
 10.8 
 
 17.1 
 16.8 
 16.5 
 16.2 
 
 22.8 
 22.4 
 22.0 
 21.6 
 
 28.5 
 28.0 
 27.5 
 27.0 
 
 34.2 
 33.6 
 33.0 
 32.4 
 
 39.9 
 39.2 
 38.5 
 37.8 
 
 45.6 
 44.8 
 44.0 
 43.2 
 
 51.3 
 50.4 
 49.5 
 48.6 
 
LOGARITHMS OF NUMBERS. 
 
 No. 810 L. 908.) 
 
 [No. 854 L. 93* 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 810 
 
 908485 
 
 8539 
 
 8592 
 
 8646 
 
 8699 
 
 8753 
 
 8807 
 
 8860 
 
 8914 
 
 8967 
 
 
 
 9021 
 
 9074 
 
 9128 
 
 9181 
 
 9235 
 
 9289 
 
 9342 
 
 9396 
 
 9449 
 
 9503 
 
 
 2 
 
 9556 
 
 9610 
 
 9663 
 
 9716 
 
 9770 
 
 9823 
 
 9877 
 
 9930 
 
 9984 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0037 
 
 
 3 
 
 910091 
 
 0144 
 
 0197 
 
 0251 
 
 0304 
 
 0358 
 
 0411 
 
 0464 
 
 0518 
 
 0571 
 
 
 4 
 
 0624 
 
 0678 
 
 0731 
 
 0784 
 
 0838 
 
 0891 
 
 0944 
 
 0998 
 
 1051 
 
 1104 
 
 
 5 
 
 1158 
 
 1211 
 
 1264 
 
 1317 
 
 1371 
 
 1424 
 
 1477 
 
 1530 
 
 1584 
 
 1637 
 
 
 6 
 
 1690 
 
 1743 
 
 1797 
 
 1850 
 
 1903 
 
 1956 
 
 2009 
 
 2063 
 
 2116 
 
 2169 
 
 
 7 
 
 2222 
 
 2275 
 
 2328 
 
 2381 
 
 2435 
 
 2488 
 
 2541 
 
 2594 
 
 2647 
 
 2700 
 
 
 8 
 
 2753 
 
 2806 
 
 2859 
 
 2913 
 
 2966 
 
 3019 
 
 3072 
 
 3125 
 
 3178 
 
 3231 
 
 
 9 
 
 3284 
 
 3337 
 
 3390 
 
 3443 
 
 3496 
 
 3549 
 
 3602 
 
 3655 
 
 3708 
 
 3761 
 
 53 
 
 820 
 
 3814 
 
 3867 
 
 3920 
 
 3973 
 
 4026 
 
 4079 
 
 4132 
 
 4184 
 
 4237 
 
 4290 
 
 
 1 
 
 4343 
 
 4396 
 
 4449 
 
 4502 
 
 4555 
 
 4608 
 
 4660 
 
 4713 
 
 4766 
 
 4819 
 
 
 2 
 
 4872 
 
 4925 
 
 4977 
 
 5030 
 
 5083 
 
 5136 
 
 5189 
 
 5241 
 
 5294 
 
 5347 
 
 
 3 
 
 5400 
 
 5453 
 
 5505 
 
 5558 
 
 5611 
 
 5664 
 
 5716 
 
 5769 
 
 5822 
 
 5875 
 
 
 4 
 
 5927 
 
 5980 
 
 6033 
 
 6085 
 
 6138 
 
 6191 
 
 6243 
 
 6296 
 
 6349 
 
 6401 
 
 
 5 
 
 6454 
 
 6507 
 
 6559 
 
 6612 
 
 6664 
 
 6717 
 
 6770 
 
 6822 
 
 6875 
 
 6927 
 
 
 6 
 
 6980 
 
 7033 
 
 7085 
 
 7138 
 
 7190 
 
 7243 
 
 7295 
 
 7348 
 
 7400 
 
 7453 
 
 
 7 
 
 7506 
 
 7558 
 
 7611 
 
 7663 
 
 7716 
 
 7768 
 
 7820 
 
 7873 
 
 7925 
 
 7978 
 
 
 8 
 
 8030 
 
 8083 
 
 8135 
 
 8188 
 
 8240 
 
 8293 
 
 8345 
 
 8397 
 
 8450 
 
 8502 
 
 
 9 
 
 8555 
 
 8607 
 
 8659 
 
 8712 
 
 8764 
 
 8816 
 
 8869 
 
 8921 
 
 8973 
 
 9026 
 
 
 830 
 
 9078 
 
 9130 
 
 9183 
 
 9235 
 
 9287 
 
 9340 
 
 9392 
 
 9444 
 
 9496 
 
 9549 
 
 
 1 
 
 9601 
 
 9653 
 
 9706 
 
 9758 
 
 9810 
 
 9862 
 
 9914 
 
 9Q67 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0019 
 
 0071 
 
 
 2 
 
 920123 
 
 0176 
 
 0228 
 
 0280 
 
 0332 
 
 0384 
 
 0436 
 
 0489 
 
 0541 
 
 0593 
 
 
 3 
 
 0645 
 
 0697 
 
 0749 
 
 0801 
 
 0853 
 
 0906 
 
 0958 
 
 1010 
 
 1062 
 
 1114 
 
 5*- 
 
 4 
 
 1166 
 
 1218 
 
 1270 
 
 1322 
 
 1374 
 
 1426 
 
 1478 
 
 1530 
 
 1582 
 
 1634 
 
 
 5 
 
 1686 
 
 1738 
 
 1790 
 
 1842 
 
 1894 
 
 1946 
 
 1998 
 
 2050 
 
 2102 
 
 2154 
 
 
 6 
 
 2206 
 
 2258 
 
 2310 
 
 2362 
 
 2414 
 
 2466 
 
 2518 
 
 2570 
 
 2622 
 
 2674 
 
 
 7 
 
 2725 
 
 2777 
 
 2829 
 
 2881 
 
 2933 
 
 2985 
 
 3037 
 
 3089 
 
 3140 
 
 3192 
 
 
 8 
 
 3244 
 
 3296 
 
 3348 
 
 3399 
 
 3451 
 
 3503 
 
 3555 
 
 3607 
 
 3658 
 
 3710 
 
 
 9 
 
 3762 
 
 3814 
 
 3865 
 
 3917 
 
 3969 
 
 4021 
 
 4072 
 
 4124 
 
 4176 
 
 4228 
 
 
 840 
 
 4279 
 
 4331 
 
 4383 
 
 4434 
 
 4486 
 
 4538 
 
 4589 
 
 4641 
 
 4693 
 
 4744 
 
 
 1 
 
 4796 
 
 4848 
 
 4899 
 
 4951 
 
 5003 
 
 5054 
 
 5106 
 
 5157 
 
 5209 
 
 5261 
 
 
 2 
 
 5312 
 
 5364 
 
 5415 
 
 5467 
 
 5518 
 
 5570 
 
 5621 
 
 5673 
 
 5725 
 
 5776 
 
 
 3 
 
 5828 
 
 5879 
 
 5931 
 
 5982 
 
 6034 
 
 6085 
 
 6137 
 
 6188 
 
 6240 
 
 6291 
 
 
 4 
 
 6342 
 
 6394 
 
 6445 
 
 6497 
 
 6548 
 
 6600 
 
 6651 
 
 6702 
 
 6754 
 
 6805 
 
 
 5 
 
 6857 
 
 6908 
 
 6959 
 
 7011 
 
 7062 
 
 7114 
 
 7165 
 
 7216 
 
 7268 
 
 7319 
 
 
 6 
 
 7370 
 
 7422 
 
 7473 
 
 7524 
 
 7576 
 
 7627 
 
 7678 
 
 7730 
 
 7781 
 
 7832 
 
 
 7 
 
 7883 
 
 7935 
 
 7986 
 
 8037 
 
 8088 
 
 8140 
 
 8191 
 
 8242 
 
 8293 
 
 8345 
 
 
 8 
 
 8396 
 
 8447 
 
 8498 
 
 8549 
 
 8601 
 
 8652 
 
 8703 
 
 8754 
 
 8805 
 
 8857 
 
 
 9 
 
 8908 
 
 8959 
 
 9010 
 
 9061 
 
 9112 
 
 9163 
 
 9215 
 
 9266 
 
 9317 
 
 9368 
 
 
 850 
 
 9419 
 
 9470 
 
 9521 
 
 9572 
 
 9623 
 
 9674 
 
 9725 
 
 9776 
 
 9827 
 
 9879 
 
 
 1 
 
 9930 
 
 9981 
 
 
 
 
 
 
 
 
 
 51 
 
 
 
 
 0032 
 
 0083 
 
 0134 
 
 0185 
 
 0236 
 
 0287 
 
 0338 
 
 0389 
 
 
 2 
 
 930440 
 
 0491 
 
 0542 
 
 0592 
 
 0643 
 
 0694 
 
 0745 
 
 0796 
 
 0847 
 
 0898 
 
 
 3 
 
 0949 
 
 1000 
 
 1051 
 
 1102 
 
 1153 
 
 1204 
 
 1254 
 
 1305 
 
 1356 
 
 1407 
 
 
 4 
 
 1458 
 
 1509 
 
 1560 
 
 1610 
 
 1661 
 
 1712 
 
 1763 
 
 1814 
 
 1865 
 
 1915 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 
 9 
 
 53 
 52 
 51 
 50 
 
 5.3 
 5.2 
 5.1 
 5.0 
 
 10.6 
 .10.4 
 10.2 
 10.0 
 
 15.9 
 15.6 
 15.3 
 15.0 
 
 21.2 
 20.8 
 20.4 
 20.0 
 
 26.5 
 26.0 
 25.5 
 25.0 
 
 31.8 
 31.2 
 30.6 
 30.0 
 
 37.1 
 36.4 
 35.7 
 35.0 
 
 42.4 
 41.6 
 40.8 
 40.0 
 
 47.7 
 46.8 
 45.9 
 45.0 
 
LOGARITHMS OF NUMBERS. 
 
 161 
 
 No. 855 L. 931. J 
 
 [No. 899 L. 954, 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 855 
 
 931966 
 
 2017 
 
 2068 
 
 2118 
 
 2169 
 
 2220 
 
 2271 
 
 2322 
 
 2372 
 
 2423 
 
 
 6 
 
 2474 
 
 2524 
 
 2575 
 
 2626 
 
 2677 
 
 2727 
 
 2778 
 
 2829 
 
 2879 
 
 2930 
 
 
 7 
 
 2981 
 
 3031 
 
 3082 
 
 3133 
 
 3183 
 
 3234 
 
 3285 
 
 3335 
 
 3386 
 
 3437 
 
 
 8 
 
 3487 
 
 3538 
 
 3589 
 
 3639 
 
 3690 
 
 3740 
 
 3791 
 
 3841 
 
 3892 
 
 3943 
 
 
 9 
 
 3993 
 
 4044 
 
 4094 
 
 4145 
 
 4195 
 
 4246 
 
 4296 
 
 4347 
 
 4397 
 
 4448 
 
 
 860 
 
 4498 
 
 4549 
 
 4599 
 
 4650 
 
 4700 
 
 4751 
 
 4801 
 
 4852 
 
 4902 
 
 4953 
 
 
 1 
 
 5003 
 
 5054 
 
 5104 
 
 5154 
 
 5205 
 
 5255 
 
 5306 
 
 5356 
 
 5406 
 
 5457 
 
 
 2 
 
 5507 
 
 5558 
 
 5608 
 
 5658 
 
 5709 
 
 5759 
 
 5809 
 
 5860 
 
 5910 
 
 5960 
 
 
 3 
 
 6011 
 
 6061 
 
 6111 
 
 6162 
 
 6212 
 
 6262 
 
 6313 
 
 6363 
 
 6413 
 
 6463 
 
 
 4 
 
 6514 
 
 6564 
 
 6614 
 
 6665 
 
 6715 
 
 6765 
 
 6815 
 
 6865 
 
 6916 
 
 6966 
 
 
 5 
 
 7016 
 
 7066 
 
 7116 
 
 7167 
 
 7217 
 
 7267 
 
 7317 
 
 7367 
 
 7418 
 
 7468 
 
 
 6 
 
 7518 
 
 7568 
 
 7618 
 
 7668 
 
 7718 
 
 7769 
 
 7819 
 
 7869 
 
 7919 
 
 7969 
 
 
 7 
 
 8019 
 
 8069 
 
 8119 
 
 8169 
 
 8219 
 
 8269 
 
 8320 
 
 8370 
 
 8420 
 
 8470 
 
 50 
 
 6 
 
 8520 
 
 8570 
 
 8620 
 
 8670 
 
 8720 
 
 8770 
 
 8820 
 
 8870 
 
 8920 
 
 8970 
 
 
 9 
 
 9020 
 
 9070 
 
 9120 
 
 9170 
 
 9220 
 
 9270 
 
 9320 
 
 9369 
 
 9419 
 
 9469 
 
 
 870 
 
 9519 
 
 9569 
 
 9619 
 
 9669 
 
 9719 
 
 9769 
 
 9819 
 
 9869 
 
 9918 
 
 9968 
 
 
 1 
 
 940018 
 
 0068 
 
 0118 
 
 0168 
 
 0218 
 
 0267 
 
 0317 
 
 0367 
 
 0417 
 
 0467 
 
 
 2 
 
 0516 
 
 0566 
 
 0616 
 
 0666 
 
 0716 
 
 0765 
 
 0815 
 
 0865 
 
 0915 
 
 0964 
 
 
 3 
 
 1014 
 
 1064 
 
 1114 
 
 1163 
 
 1213 
 
 1263 
 
 1313 
 
 1362 
 
 1412 
 
 1462 
 
 
 4 
 
 1511 
 
 1561 
 
 1611 
 
 1660 
 
 1710 
 
 1760 
 
 1809 
 
 1859 
 
 1909 
 
 1958 
 
 
 3 
 
 2003 
 
 2058 
 
 2107 
 
 2157 
 
 2207 
 
 2256 
 
 2306 
 
 2355 
 
 2405 
 
 2455 
 
 
 6 
 
 2504 
 
 2554 
 
 2603 
 
 2653 
 
 2702 
 
 2752 
 
 2801 
 
 2851 
 
 2901 
 
 2950 
 
 
 7 
 
 3000 
 
 3049 
 
 3099 
 
 3148 
 
 3198 
 
 3247 
 
 3297 
 
 3346 
 
 3396 
 
 3445 
 
 
 8 
 
 3495 
 
 3544 
 
 3593 
 
 3643 
 
 3692 
 
 3742 
 
 3791 
 
 3841 
 
 3890 
 
 3939 
 
 
 9 
 
 3989 
 
 4038 
 
 4088 
 
 4137 
 
 4186 
 
 4236 
 
 4285 
 
 4335 
 
 4384 
 
 4433 
 
 
 880 
 
 4483 
 
 4532 
 
 4581 
 
 4631 
 
 4680 
 
 4729 
 
 4779 
 
 4828 
 
 4877 
 
 4927 
 
 
 1 
 
 4976 
 
 5025 
 
 5074 
 
 5124 
 
 5173 
 
 5222 
 
 5272 
 
 5321 
 
 5370 
 
 5419 
 
 
 2 
 
 5469 
 
 5518 
 
 5567 
 
 5616 
 
 5665 
 
 5715 
 
 5764 
 
 5813 
 
 5862 
 
 5912 
 
 
 3 
 
 5961 
 
 6010 
 
 6059 
 
 6108 
 
 6157 
 
 6207 
 
 6256 
 
 6305 
 
 6354 
 
 6403 
 
 
 4 
 
 6452 
 
 6501 
 
 6551 
 
 6600 
 
 6649 
 
 6698 
 
 6747 
 
 6796 
 
 6845 
 
 6894 
 
 
 5 
 
 6943 
 
 6992 
 
 7041 
 
 7090 
 
 7139 
 
 7189 
 
 7238 
 
 7287 
 
 7336 
 
 7385 
 
 
 6 
 
 7434 
 
 7483 
 
 7532 
 
 7581 
 
 7630 
 
 7679 
 
 7728 
 
 7777 
 
 7826 
 
 7875 
 
 49 
 
 7 
 
 7924 
 
 7973 
 
 8022 
 
 8070 
 
 8119 
 
 8168 
 
 8217 
 
 8266 
 
 8315 
 
 8364 
 
 
 8 
 
 8413 
 
 8462 
 
 8511 
 
 8560 
 
 8608 
 
 8657 
 
 8706 
 
 8755 
 
 8804 
 
 8853 
 
 
 9 
 
 8902 
 
 8951 
 
 8999 
 
 9048 
 
 9097 
 
 9146 
 
 9195 
 
 9244 
 
 9292 
 
 9341 
 
 
 690 
 
 9390 
 
 9439 
 
 9488 
 
 9536 
 
 9585 
 
 9634 
 
 9683 
 
 9731 
 
 9780 
 
 9829 
 
 
 1 
 
 9878 
 
 9926 
 
 9975 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0024 
 
 0073 
 
 0121 
 
 0170 
 
 0219 
 
 0267 
 
 0316 
 
 
 2 
 
 950365 
 
 0414 
 
 0462 
 
 0511 
 
 0560 
 
 0608 
 
 0657 
 
 0706 
 
 0754 
 
 0303 
 
 
 3 
 
 0851 
 
 0900 
 
 0949 
 
 0997 
 
 1046 
 
 1095 
 
 1143 
 
 1192 
 
 1240 
 
 1289 
 
 
 4 
 
 1338 
 
 1386 
 
 1435 
 
 1483 
 
 1532 
 
 1580 
 
 1629 
 
 1677 
 
 1726 
 
 1775 
 
 
 5 
 
 1823 
 
 1872 
 
 1920 
 
 1969 
 
 2017 
 
 2066 
 
 2114 
 
 2163 
 
 2211 
 
 2260 
 
 
 6 
 
 2308 
 
 2356 
 
 2405 
 
 2453 
 
 2502 
 
 2550 
 
 2599 
 
 2647 
 
 2696 
 
 2744 
 
 
 7 
 
 2792 
 
 2841 
 
 2889 
 
 2938 
 
 2986 
 
 3034 
 
 3083 
 
 3131 
 
 3180 
 
 3228 
 
 
 8 
 
 3276 
 
 3325 
 
 3373 
 
 3421 
 
 3470 
 
 3518 
 
 3566 
 
 3615 
 
 3663 
 
 3711 
 
 
 9 
 
 3760 
 
 3808 
 
 3856 
 
 3905 
 
 3953 
 
 4001 
 
 4049 
 
 4098 
 
 4146 
 
 4194 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 45.9 
 45.0 
 44.1 
 43.2 
 
 51 
 50 
 49 
 48 
 
 5.1 
 5.0 
 4.9 
 48 
 
 10.2 
 10.0 
 9.8 
 9.6 
 
 15.3 
 15.0 
 14.7 
 14.4 
 
 20.4 
 20.0 
 19.6 
 19.2 
 
 25.5 
 25.0 
 24.5 
 24.0 
 
 30.6 
 30.0 
 29.4 
 28.8 
 
 35.7 
 35.0 
 34.3 
 33.6 
 
 40.8 
 40.0 
 39.2 
 38.4 
 
162 
 
 LOGARITHMS OF NUMBERS. 
 
 Ho. 900 L. 954.J 
 
 [No. 944 L. 975. 
 
 N. 
 
 1 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 900 
 
 954243 
 
 4291 
 
 4339 
 
 4387 
 
 4435 
 
 4484 
 
 4532 
 
 4580 
 
 4628 
 
 4677 
 
 . 
 
 1 
 
 4725 
 
 4773 
 
 4821 
 
 4869 
 
 4918 
 
 4966 
 
 5014 
 
 5062 
 
 5110 
 
 5158 
 
 
 2 
 
 5207 
 
 5255 
 
 5303 
 
 5351 
 
 5399 
 
 5447 
 
 5495 
 
 5543 
 
 5592 
 
 5640 
 
 
 3 
 
 5688 
 
 5736 
 
 5784 
 
 5832 
 
 5880 
 
 5928 
 
 5976 
 
 6024 
 
 6072 
 
 6120 
 
 
 4 
 
 6168 
 
 6216 
 
 6265 
 
 6313 
 
 6361 
 
 6409 
 
 6457 
 
 6505 
 
 6553 
 
 6601 
 
 
 5 
 
 6649 
 
 6697 
 
 6745 
 
 6793 
 
 6840 
 
 6888 
 
 6936 
 
 6984 
 
 7032 
 
 7080 
 
 48 
 
 6 
 
 7128 
 
 7176 
 
 7224 
 
 7272 
 
 7320 
 
 7368 
 
 7416 
 
 7464 
 
 7512 
 
 7559 
 
 
 7 
 
 7607 
 
 7655 
 
 7703 
 
 7751 
 
 7799 
 
 7847 
 
 7894 
 
 7942 
 
 7990 
 
 8038 
 
 
 8 
 
 8086 
 
 8134 
 
 8181 
 
 8229 
 
 8277 
 
 8325 
 
 8373 
 
 8421 
 
 8468 
 
 8516 
 
 
 9 
 
 8564 
 
 8612 
 
 8659 
 
 8707 
 
 8755 
 
 8803 
 
 8850 
 
 8898 
 
 8946 
 
 8994 
 
 
 910 
 
 9041 
 
 9089 
 
 9137 
 
 9185 
 
 9232 
 
 9280 
 
 9328 
 
 9375 
 
 9423 
 
 9471 
 
 
 I 
 
 9518 
 
 9566 
 
 9614 
 
 9661 
 
 9709 
 
 9757 
 
 9804 
 
 9852 
 
 9900 
 
 9947 
 
 
 2 
 
 9995 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0042 
 
 0090 
 
 Atao 
 
 ni oe 
 
 n?^ 
 
 A7Af 
 
 rjaoo 
 
 n^7A 
 
 
 
 3 
 
 960471 
 
 0518 
 
 0566 
 
 V 1 JO 
 
 0613 
 
 U 1 O J 
 
 0661 
 
 \jLjj 
 
 0709 
 
 UZOU 
 
 0756 
 
 \)jZ,c 
 
 0804 
 
 U.3/O 
 
 0851 
 
 0423 
 0899 
 
 
 4 
 
 0946 
 
 0994 
 
 1041 
 
 1089 
 
 1136 
 
 1184 
 
 1231 
 
 1279 
 
 1326 
 
 1374 
 
 
 5 
 
 1421 
 
 1469 
 
 1516 
 
 1563 
 
 1611 
 
 1658 
 
 1706 
 
 1753 
 
 1801 
 
 1848 
 
 
 6 
 
 1895 
 
 1943 
 
 1990 
 
 2038 
 
 2085 
 
 2132 
 
 2180 
 
 2227 
 
 2275 
 
 2322 
 
 
 7 
 
 2369 
 
 2417 
 
 2464 
 
 2511 
 
 2559 
 
 2606 
 
 2653 
 
 2701 
 
 2748 
 
 2795 
 
 
 8 
 
 2843 
 
 2890 
 
 2937 
 
 2985 
 
 3032 
 
 3079 
 
 3126 
 
 3174 
 
 3221 
 
 3268 
 
 
 9 
 
 3316 
 
 3363 
 
 3410 
 
 3457 
 
 3504 
 
 3552 
 
 3599 
 
 3646 
 
 3693 
 
 3741 
 
 
 920 
 
 3788 
 
 3835 
 
 3882 
 
 3929 
 
 3977 
 
 4024 
 
 4071 
 
 4118 
 
 4165 
 
 4212 
 
 
 1 
 
 4260 
 
 4307 
 
 4354 
 
 4401 
 
 4448 
 
 4495 
 
 4542 
 
 4590 
 
 4637 
 
 4684 
 
 
 2 
 
 4731 
 
 4778 
 
 4825 
 
 4872 
 
 4919 
 
 4966 
 
 5013 
 
 5061 
 
 5108 
 
 5155 
 
 
 3 
 
 5202 
 
 5249 
 
 5296 
 
 5343 
 
 5390 
 
 5437 
 
 5484 
 
 5531 
 
 5578 
 
 5625 
 
 
 4 
 
 5672 
 
 5719 
 
 5766 
 
 5813 
 
 5860 
 
 5907 
 
 5954 
 
 6001 
 
 6048 
 
 6095 
 
 47 
 
 5 
 
 6142 
 
 6189 
 
 6236 
 
 6283 
 
 6329 
 
 6376 
 
 6423 
 
 6470 
 
 6517 
 
 6564 
 
 
 6 
 
 6611 
 
 6658 
 
 6705 
 
 6752 
 
 6799 
 
 6845 
 
 6892 
 
 6939 
 
 6986 
 
 7033 
 
 
 7 
 
 7080 
 
 7127 
 
 7173 
 
 7220 
 
 7267 
 
 7314 
 
 7361 
 
 7408 
 
 7454 
 
 7501 
 
 
 8 
 
 7548 
 
 7595 
 
 7642 
 
 7688 
 
 7735 
 
 7782 
 
 7829 
 
 7875 
 
 7922 
 
 7969 
 
 
 9 
 
 8016 
 
 8062 
 
 8109 
 
 8156 
 
 8203 
 
 8249 
 
 8296 
 
 8343 
 
 8390 
 
 8436 
 
 
 930 
 
 8483 
 
 8530 
 
 8576 
 
 8623 
 
 8670 
 
 8716 
 
 8763 
 
 8810 
 
 8856 
 
 8903 
 
 
 1 
 
 8950 
 
 8996 
 
 9043 
 
 9090 
 
 9136 
 
 9183 
 
 9229 
 
 9276 
 
 9323 
 
 9369 
 
 
 2 
 
 9416 
 
 9463 
 
 9509 
 
 9556 
 
 9602 
 
 9649 
 
 9695 
 
 9742 
 
 9789 
 
 9835 
 
 
 3 
 
 9882 
 
 9928 
 
 9975 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0021 
 
 0068 
 
 01 14 
 
 0161 
 
 0207 
 
 0254 
 
 0300 
 
 
 4 
 
 970347 
 
 0393 
 
 0440 
 
 0486 
 
 0533 
 
 0579 
 
 0626 
 
 0672 
 
 0719 
 
 0765 
 
 
 5 
 
 0812 
 
 0858 
 
 0904 
 
 0951 
 
 0997 
 
 1044 
 
 1090 
 
 1137 
 
 1183 
 
 1229 
 
 
 6 
 
 1276 
 
 1322 
 
 1369 
 
 1415 
 
 1461 
 
 1508 
 
 1554 
 
 1601 
 
 1647 
 
 1693 
 
 
 7 
 
 1740 
 
 1786 
 
 1832 
 
 1879 
 
 1925 
 
 1971 
 
 2018 
 
 2064 
 
 2110 
 
 2157 
 
 
 8 
 
 2203 
 
 2249 
 
 2295 
 
 2342 
 
 2388 
 
 2434 
 
 2481 
 
 2527 
 
 2573 
 
 2619 
 
 
 9 
 
 2666 
 
 2712 
 
 2758 
 
 2804 
 
 2851 
 
 2897 
 
 2943 
 
 2989 
 
 3035 
 
 3082 
 
 
 940 
 
 3128 
 
 3174 
 
 3220 
 
 3266 
 
 3313 
 
 3359 
 
 3405 
 
 3451 
 
 3497 
 
 3543 
 
 
 1 
 
 3590 
 
 3636 
 
 3682 
 
 3728 
 
 3774 
 
 3820 
 
 3866 
 
 3913 
 
 3959 
 
 4005 
 
 
 2 
 
 4051 
 
 4097 
 
 4143 
 
 4189 
 
 4235 
 
 4281 
 
 4327 
 
 4374 
 
 4420 
 
 4466 
 
 
 3 
 
 4512 
 
 4558 
 
 4604 
 
 4650 
 
 4696 
 
 4742 
 
 4788 
 
 4834 
 
 4880 
 
 4926 
 
 
 4 
 
 4972 
 
 5018 
 
 5064 
 
 5110 
 
 5156 
 
 5202 
 
 5248 
 
 5294 
 
 5340 
 
 5386 
 
 46 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 47 
 46 
 
 4.7 
 4.6 
 
 9.4 
 9.2 
 
 14.1 
 13.8 
 
 18.8 
 18.4 
 
 23.5 
 23.0 
 
 28.2 
 27.6 
 
 32.9 
 32.2 
 
 37.6 
 36.8 
 
 42.3 
 41.4 
 
LOGARITHMS OF NUMBERS. 
 
 163 
 
 No. 945 L. 975.J 
 
 (No. 989 L. 995. 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 945 
 
 975432 
 
 5478 
 
 5524 
 
 5570 
 
 5616 
 
 5662 
 
 5707 
 
 5753 
 
 5799 
 
 5845 
 
 
 6 
 
 5891 
 
 5937 
 
 5983 
 
 6029 
 
 6075 
 
 6121 
 
 6167 
 
 6212 
 
 6258 
 
 6304 
 
 
 7 
 
 6350 
 
 6396 
 
 6442 
 
 6488 
 
 6533 
 
 6579 
 
 6625 
 
 6671 
 
 6717 
 
 6763 
 
 
 8 
 
 6808 
 
 6854 
 
 6900 
 
 6946 
 
 6992 
 
 7037 
 
 7083 
 
 7129 
 
 7175 
 
 7220 
 
 
 9 
 
 7266 
 
 7312 
 
 7358 
 
 7403 
 
 7449 
 
 7495 
 
 7541 
 
 7586 
 
 7632 
 
 7678 
 
 
 950 
 
 7724 
 
 7769 
 
 7815 
 
 7861 
 
 7906 
 
 7952 
 
 7998 
 
 8043 
 
 8089 
 
 8135 
 
 
 1 
 
 8181 
 
 8226 
 
 8272 
 
 8317 
 
 8363 
 
 8409 
 
 8454 
 
 8500 
 
 8546 
 
 8591 
 
 
 2 
 
 8637 
 
 8683 
 
 8728 
 
 8774 
 
 8819 
 
 8865 
 
 8911 
 
 8956 
 
 9002 
 
 9047 
 
 
 3 
 
 9093 
 
 9138 
 
 9184 
 
 9230 
 
 9275 
 
 9321 
 
 9366 
 
 9412 
 
 9457 
 
 9503 
 
 
 4 
 
 9548 
 
 9594 
 
 9639 
 
 9685 
 
 9730 
 
 9776 
 
 9821 
 
 9867 
 
 9912 
 
 9958 
 
 
 5 
 
 980003 
 
 0049 
 
 0094 
 
 0140 
 
 0185 
 
 0231 
 
 0276 
 
 0322 
 
 0367 
 
 0412 
 
 
 6 
 
 0458 
 
 0503 
 
 0549 
 
 0594 
 
 0640 
 
 0685 
 
 0730 
 
 0776 
 
 0821 
 
 0867 
 
 
 7 
 
 0912 
 
 0957 
 
 1003 
 
 1048 
 
 1093 
 
 1139 
 
 1184 
 
 1229 
 
 1275 
 
 1320 
 
 
 8 
 
 1366 
 
 1411 
 
 1456 
 
 1501 
 
 1547 
 
 1592 
 
 1637 
 
 1683 
 
 1728 
 
 1773 
 
 
 9 
 
 1819 
 
 1864 
 
 1909 
 
 1954 
 
 2000 
 
 2045 
 
 2090 
 
 2135 
 
 2181 
 
 2226 
 
 
 960 
 
 2271 
 
 2316 
 
 2362 
 
 2407 
 
 2452 
 
 2497 
 
 2543 
 
 2588 
 
 2633 
 
 2678 
 
 
 1 
 
 2723 
 
 2769 
 
 2814 
 
 2859 
 
 2904 
 
 2949 
 
 2994 
 
 3040 
 
 3085 
 
 3130 
 
 
 2 
 
 3175 
 
 3220 
 
 3265 
 
 3310 
 
 3356 
 
 3401 
 
 3446 
 
 3491 
 
 3536 
 
 3581 
 
 
 3 
 
 3626 
 
 3671 
 
 3716 
 
 3762 
 
 3807 
 
 3852 
 
 3897 
 
 3942 
 
 3987 
 
 4032 
 
 
 4 
 
 4077 
 
 4122 
 
 4167 
 
 4212 
 
 4257 
 
 4302 
 
 4347 
 
 4392 
 
 4437 
 
 4482 
 
 
 5 
 
 4527 
 
 4572 
 
 4617 
 
 4662 
 
 4707 
 
 4752 
 
 4797 
 
 4842 
 
 4887 
 
 4932 
 
 45 
 
 6 
 
 4977 
 
 5022 
 
 5067 
 
 5112 
 
 5157 
 
 5202 
 
 5247 
 
 5292 
 
 5337 
 
 5382 
 
 
 7 
 
 5426 
 
 5471 
 
 5516 
 
 5561 
 
 5606 
 
 5651 
 
 5696 
 
 5741 
 
 5786 
 
 5830 
 
 
 8 
 
 5875 
 
 5920 
 
 5965 
 
 6010 
 
 6055 
 
 6100 
 
 6144 
 
 6189 
 
 6234 
 
 6279 
 
 
 9 
 
 6324 
 
 6369 
 
 6413 
 
 6458 
 
 6503 
 
 6548 
 
 6593 
 
 6637 
 
 6682 
 
 6727 
 
 
 
 6772 
 
 6817 
 
 6861 
 
 6906 
 
 6951 
 
 6996 
 
 7040 
 
 7085 
 
 7130 
 
 7175 
 
 
 1 
 
 7219 
 
 7264 
 
 7309 
 
 7353 
 
 7398 
 
 7443 
 
 7488 
 
 7532 
 
 7577 
 
 7622 
 
 
 2 
 
 7666 
 
 7711 
 
 7756 
 
 7800 
 
 7845 
 
 7890 
 
 7934 
 
 7979 
 
 8024 
 
 8068 
 
 
 3 
 
 8113 
 
 8157 
 
 8202 
 
 8247 
 
 8291 
 
 8336 
 
 8381 
 
 8425 
 
 8470 
 
 8514 
 
 
 
 8559 
 
 8604 
 
 8648 
 
 8693 
 
 8737 
 
 8782 
 
 8826 
 
 8871 
 
 8916 
 
 8960 
 
 
 5 
 
 9005 
 
 9049 
 
 9094 
 
 9138 
 
 9183 
 
 9227 
 
 9272 
 
 9316 
 
 9361 
 
 9405 
 
 
 
 9450 
 
 9494 
 
 9539 
 
 9583 
 
 9628 
 
 9672 
 
 9717 
 
 9761 
 
 9806 
 
 9850 
 
 
 7 
 7 
 
 9395 
 
 9939 
 
 9983 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0028 
 
 0072 
 
 01 17 
 
 0161 
 
 0206 
 
 025C 
 
 O7O4 
 
 
 8 
 
 990339 
 
 0383 
 
 0428 
 
 0472 
 
 0516 
 
 0561 
 
 0605 
 
 0650 
 
 0694 
 
 U^Vn 
 
 0738 
 
 
 9 
 
 0783 
 
 0827 
 
 0871 
 
 0916 
 
 0960 
 
 1004 
 
 1049 
 
 1093 
 
 1137 
 
 1182 
 
 
 980 
 
 1226 
 
 1270 
 
 1315 
 
 1359 
 
 1403 
 
 1448 
 
 1492 
 
 1536 
 
 1580 
 
 1625 
 
 
 1 
 
 1669 
 
 1713 
 
 1758 
 
 1802 
 
 1846 
 
 1890 
 
 1935 
 
 1979 
 
 2023 
 
 2067 
 
 
 2 
 
 2111 
 
 2156 
 
 2200 
 
 2244 
 
 2288 
 
 2333 
 
 2377 
 
 2421 
 
 2465 
 
 2509 
 
 
 3 
 
 2554 
 
 2598 
 
 2642 
 
 2686 
 
 2730 
 
 2774 
 
 2819 
 
 2863 
 
 2907 
 
 2951 
 
 
 4 
 
 2995 
 
 3039 
 
 3083 
 
 3127 
 
 3172 
 
 3216 
 
 3260 
 
 3304 
 
 3348 
 
 3392 
 
 
 5 
 
 3436 
 
 3480 
 
 3524 
 
 3568 
 
 3613 
 
 3657 
 
 3701 
 
 3745 
 
 3789 
 
 3833 
 
 
 6 
 
 3877 
 
 3921 
 
 3965 
 
 4009 
 
 4053 
 
 4097 
 
 4141 
 
 4185 
 
 4229 
 
 4273 
 
 
 7 
 
 4317 
 
 4361 
 
 4405 
 
 4449 
 
 4493 
 
 4537 
 
 4581 
 
 4625 
 
 4669 
 
 4713 
 
 44 
 
 8 
 
 4757 
 
 4801 
 
 4845 
 
 4889 
 
 4933 
 
 4977 
 
 5021 
 
 5065 
 
 5108 
 
 5152 
 
 
 9 
 
 5196 
 
 5240 
 
 5284 
 
 5328 
 
 5372 
 
 5416 
 
 5460 
 
 5504 
 
 5547 
 
 5591 
 
 
 PROPORTIONAL PARTS. 
 
 Diff. 
 
 46 
 45 
 44 
 43 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 4.6 
 4.5 
 4.4 
 4.3 
 
 9.2 
 9.0 
 8.8 
 8.6 
 
 13.8 
 13.5 
 13.2 
 12.9 
 
 18.4 
 18.0 
 17.6 
 17.2 
 
 23.0 
 22.5 
 22.0 
 21.5 
 
 27.6 
 27.0 
 26.4 
 25.8 
 
 32.2 
 31.5 
 30.8 
 30.1 
 
 36.8 
 36.0 
 35.2 
 34.4 
 
 41.4 
 40.5 
 39.6 
 38.7 
 
164 
 
 HYPERBOLIC LOGARITHMS. 
 
 No. 990 L. 995 J 
 
 [No.999L.999. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 990 
 
 995635 
 
 5679 
 
 5723 
 
 5767 
 
 5811 
 
 5854 
 
 5898 
 
 5942 
 
 5986 
 
 6030 
 
 
 1 
 
 6074 
 
 6117 
 
 6161 
 
 6205 
 
 6249 
 
 6293 
 
 6337 
 
 6380 
 
 6424 
 
 6468 
 
 44 
 
 2 
 
 6512 
 
 6555 
 
 6599 
 
 6643 
 
 6687 
 
 6731 
 
 6774 
 
 6818 
 
 6862 
 
 6906 
 
 
 3 
 
 6949 
 
 6993 
 
 7037 
 
 7080 
 
 7124 
 
 7168 
 
 7212 
 
 7255 
 
 7299 
 
 7343 
 
 
 4 
 
 7386 
 
 7430 
 
 7474 
 
 7517 
 
 7561 
 
 7605 
 
 7648 
 
 7692 
 
 7736 
 
 7779 
 
 
 3 
 
 7823 
 
 7867 
 
 7910 
 
 7954 
 
 7998 
 
 8041 
 
 8085 
 
 8129 
 
 8172 
 
 8216 
 
 
 6 
 
 8259 
 
 8303 
 
 8347 
 
 8390 
 
 8434 
 
 8477 
 
 8521 
 
 8564 
 
 8608 
 
 8652 
 
 
 7 
 
 8695 
 
 8739 
 
 8782 
 
 8826 
 
 8869 
 
 8913 
 
 8956 
 
 9000 
 
 9043 
 
 9087 
 
 
 8 
 
 9131 
 
 9174 
 
 9218 
 
 9261 
 
 9305 
 
 9348 
 
 9392 
 
 9435 
 
 9479 
 
 9522 
 
 
 9 
 
 9565 
 
 9609 
 
 9652 
 
 9696 
 
 9739 
 
 9783 
 
 9826 
 
 9870 
 
 9913 
 
 9957 
 
 
 
 
 
 
 
 
 
 
 
 
 
 43 
 
 HYPERBOLIC LOGARITHMS. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 1.01 
 
 .0099 
 
 1.45 
 
 .3716 
 
 .89 
 
 .6366 
 
 2.33 
 
 .8458 
 
 2.77 
 
 .0188 
 
 1.02 
 
 .0198 
 
 1.46 
 
 .3784 
 
 .90 
 
 .6419 
 
 2.34 
 
 .8502 
 
 2.78 
 
 .0225 
 
 1.03 
 
 .0296 
 
 1.47 
 
 .3853 
 
 .91 
 
 .6471 
 
 2.35 
 
 .8544 
 
 2.79 
 
 .0260 
 
 1.04 
 
 .0392 
 
 1.48 
 
 .3920 
 
 .92 
 
 .6523 
 
 2.36 
 
 .8587 
 
 2.80 
 
 .0296 
 
 1.05 
 
 .0488 
 
 1.49 
 
 .3988 
 
 .93 
 
 .6575 
 
 2.37 
 
 .8629 
 
 2.81 
 
 .0332 
 
 1.06 
 
 .0583 
 
 1.50 
 
 .4055 
 
 .94 
 
 .6627 
 
 2.38 
 
 .8671 
 
 2.82 
 
 .0367 
 
 1.07 
 
 .0677 
 
 1.51 
 
 .4121 
 
 .95 
 
 .6678 
 
 2.39 
 
 .8713 
 
 2.83 
 
 .0403 
 
 1.08 
 
 .0770 
 
 1.52 
 
 .4187 
 
 .96 
 
 .6729 
 
 2.40 
 
 .8755 
 
 2.84 
 
 .0438 
 
 1.09 
 
 .0862 
 
 1.53 
 
 .4253 
 
 .97 
 
 .6780 
 
 2.41 
 
 .8796 
 
 2.85 
 
 .0473 
 
 1.10 
 
 .0953 
 
 1.54 
 
 .4318 
 
 .98 
 
 .6831 
 
 2.42 
 
 .8838 
 
 2.86 
 
 .0508 
 
 1.11 
 
 .1044 
 
 1.55 
 
 .4383 
 
 1.99 
 
 .6881 
 
 2.43 
 
 .8879 
 
 2.87 
 
 .0543 
 
 1.12 
 
 .1133 
 
 1.56 
 
 .4447 
 
 2.00 
 
 .6931 
 
 2.44 
 
 .8920 
 
 2.88 
 
 .0578 
 
 1.13 
 
 .1222 
 
 1.57 
 
 .4511 
 
 2.01 
 
 .6981 
 
 2.45 
 
 .8961 
 
 2.89 
 
 .0613 
 
 1.14 
 
 .1310 
 
 1.58 
 
 .4574 
 
 2.02 
 
 .7031 
 
 2.46 
 
 .9002 
 
 2.90 
 
 .0647 
 
 1.15 
 
 .1398 
 
 1.59 
 
 .4637 
 
 2.03 
 
 .7080 
 
 2.47 
 
 .9042 
 
 2.91 
 
 .0682 
 
 1.16 
 
 .1484 
 
 1.60 
 
 .4700 
 
 2.04 
 
 .7129 
 
 2.48 
 
 .9083 
 
 2.92 
 
 .0716 
 
 1.17 
 
 .1570 
 
 1.61 
 
 .4762 
 
 2.05 
 
 .7178 
 
 2.49 
 
 .9123 
 
 2.93 
 
 .0750 
 
 1.18 
 
 .1655 
 
 1.62 
 
 .4824 
 
 2.06 
 
 .7227 
 
 2.50 
 
 .9163 
 
 2.94 
 
 .0784 
 
 1.19 
 
 .1740 
 
 1.63 
 
 .4886 
 
 2.07 
 
 .7275 
 
 2.51 
 
 .9203 
 
 2.95 
 
 .0818 
 
 1.20 
 
 .1823 
 
 1.64 
 
 .4947 
 
 2.08 
 
 .7324 
 
 2.52 
 
 .9243 
 
 2.96 
 
 .0852 
 
 1.21 
 
 .1906 
 
 1.65 
 
 .5008 
 
 2.09 
 
 .7372 
 
 2.53 
 
 .9282 
 
 2.97 
 
 .0886 
 
 1.22 
 
 .1988 
 
 J.66 
 
 .5068 
 
 2.10 
 
 .7419 
 
 2.54 
 
 .9322 
 
 2.98 
 
 .0919 
 
 1.23 
 
 .2070 
 
 1.67 
 
 .5128 
 
 2.11 
 
 .7467 
 
 2.55 
 
 .9361 
 
 2.99 
 
 .0953 
 
 1.24 
 
 .2151 
 
 1.68 
 
 .5188 
 
 2.12 
 
 .7514 
 
 2.56 
 
 .9400 
 
 3.00 
 
 .0986 
 
 1.25 
 
 .2231 
 
 1.69 
 
 .5247 
 
 2.13 
 
 .7561 
 
 2.57 
 
 .9439 
 
 3.01 
 
 .1019 
 
 1.26 
 
 .2311 
 
 1.70 
 
 .5306 
 
 2.14 
 
 .7608 
 
 2.58 
 
 .9478 
 
 3.02 
 
 .1056 
 
 1.27 
 
 .2390 
 
 1.71 
 
 .5365 
 
 2.15 
 
 .7655 
 
 2.59 
 
 .9517 
 
 3.03 
 
 .1081 
 
 1.28 
 
 .2469 
 
 1.72 
 
 .5423 
 
 2.16 
 
 .7701 
 
 2.60 
 
 .9555 
 
 3.04 
 
 .1113 
 
 1.29 
 
 .2546 
 
 1.73 
 
 .5481 
 
 2.17 
 
 .7747 
 
 2.61 
 
 .9594 
 
 3.05 
 
 .1154 
 
 1.30 
 
 .2624 
 
 1.74 
 
 .5539 
 
 2.18 
 
 .7793 
 
 2.62 
 
 .9632 
 
 3.06 
 
 .1187 
 
 1.31 
 
 .2700 
 
 1.75 
 
 .5596 
 
 2.19 
 
 .7839 
 
 2.63 
 
 .9670 
 
 3.07 
 
 .1219 
 
 1.32 
 
 .2776 
 
 1.76 
 
 .5653 
 
 2.20 
 
 .7885 
 
 2.64 
 
 .9708 
 
 3.08 
 
 .1246 
 
 1.33 
 
 .2852 
 
 1.77 
 
 .5710 
 
 2.21 
 
 .7930 
 
 2.65 
 
 .9746 
 
 3.09 
 
 .1284 
 
 1.34 
 
 .2927 
 
 1.78 
 
 .5766 
 
 2.22 
 
 .7975 
 
 2.66 
 
 .9783 
 
 3.10 
 
 .1312 
 
 1.35 
 
 .3001 
 
 1.79 
 
 .5822 
 
 2.23 
 
 .8020 
 
 2.67 
 
 .9821 
 
 3.11 
 
 .1349 
 
 1.36 
 
 .3075 
 
 1.80 
 
 .5878 
 
 2.24 
 
 .8065 
 
 2.68 
 
 .9858 
 
 3.12 
 
 .1378 
 
 1.37 
 
 .3148 
 
 1.81 
 
 .5933 
 
 2.25 
 
 .8109 
 
 2.69 
 
 .9895 
 
 3.13 
 
 .1410 
 
 1.38 
 
 .3221 
 
 1.82 
 
 .5988 
 
 2.26 
 
 .8154 
 
 2.70 
 
 .9933 
 
 3.14 
 
 .1442 
 
 1.39 
 
 .3293 
 
 1.83 
 
 .6043 
 
 2.27 
 
 .8198 
 
 2.71 
 
 .9969 
 
 3.15 
 
 .1474 
 
 1.40 
 
 .3365 
 
 1.84 
 
 .6098 
 
 2.28 
 
 .8242 
 
 2.72 
 
 1 .0006 
 
 3.16 
 
 .1506 
 
 1.41 
 
 .3436 
 
 1.85 
 
 .6152 
 
 2.29 
 
 .8286 
 
 2.73 
 
 1 .0043 
 
 3.17 
 
 .1537 
 
 1.42 
 
 .3507 
 
 1.86 
 
 .6206 
 
 2.30 
 
 .8329 
 
 2.74 
 
 1 .0080 
 
 3.18 
 
 .1569 
 
 1.43 
 
 .3577 
 
 1.87 
 
 .6259 
 
 2.31 
 
 .8372 
 
 2.75 
 
 1.0116 
 
 3.19 
 
 .1600 
 
 1.44 
 
 .3646 
 
 1.88 
 
 .6313 
 
 2.32 
 
 .8416 
 
 2.76 
 
 1.0152 
 
 3.20 
 
 .1632 
 
HYPERBOLIC LOGARITHMS. 
 
 165 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 3.21 
 
 .1663 
 
 3.87 
 
 .3533 
 
 4.53 
 
 .5107 
 
 5.19 
 
 .6467 
 
 5.85 
 
 .7664 
 
 3.22 
 
 .1694 
 
 3.88 
 
 .3558 
 
 4.54 
 
 .5129 
 
 5.20 
 
 .6487 
 
 5.86 
 
 .7681 
 
 3.23 
 
 .1725 
 
 3.89 
 
 .3584 
 
 4.55 
 
 .5151 
 
 5.21 
 
 .6506 
 
 5.87 
 
 .7699 
 
 3.24 
 
 .1756 
 
 3.90 
 
 .3610 
 
 4.56 
 
 .5173 
 
 5.22 
 
 .6525 
 
 5.88 
 
 .7716 
 
 3.25 
 
 .1787 
 
 3.91 
 
 .3635 
 
 4.57 
 
 .5195 
 
 5.23 
 
 .6544 
 
 5.89 
 
 .7733 
 
 3.26 
 
 .1817 
 
 3.92 
 
 .3661 
 
 4.58 
 
 .5217 
 
 5.24 
 
 .6563 
 
 5.90 
 
 .7750 
 
 3.27 
 
 .1848 
 
 3.93 
 
 .3686 
 
 4.59 
 
 .5239 
 
 5.25 
 
 .6582 
 
 5.91 
 
 .7766 
 
 3.28 
 
 .1878 
 
 3.94 
 
 .3712 
 
 4.60 
 
 .5261 
 
 5.26 
 
 .6601 
 
 5.92 
 
 .7783 
 
 3.29 
 
 .1909 
 
 3.95 
 
 .3737 
 
 4.61 
 
 .5282 
 
 5.27 
 
 .6620 
 
 5.93 
 
 .7800 
 
 3.30 
 
 .1939 
 
 3.96 
 
 .3762 
 
 4.62 
 
 .5304 
 
 5.28 
 
 .6639 
 
 5.94 
 
 .7817 
 
 3.31 
 
 .1969 
 
 3.97 
 
 .3788 
 
 4.63 
 
 .5326 
 
 5.29 
 
 .6658 
 
 5.95 
 
 .7834 
 
 3.32 
 
 .1999 
 
 3.98 
 
 .3813 
 
 4.64 
 
 .5347 
 
 5.30 
 
 .6677 
 
 . 5.96 
 
 .7851 
 
 3.33 
 
 .2030 
 
 3.99 
 
 .3838 
 
 4.65 
 
 .5369 
 
 5.31 
 
 .6696 
 
 5.97 
 
 .7867 
 
 3.34 
 
 .2060 
 
 4.00 
 
 .3863 
 
 4.66 
 
 .5390 
 
 5.32 
 
 .6715 
 
 5.98 
 
 .7884 
 
 3.35 
 
 .2090 
 
 4.01 
 
 .3888 
 
 4.67 
 
 .5412 
 
 5.33 
 
 .6734 
 
 5. 99' 
 
 .7901 
 
 3.36 
 
 .2119 
 
 4.02 
 
 .3913 
 
 4.68 
 
 .5433 
 
 5.34 
 
 .6752 
 
 6.00 
 
 .7918 
 
 3.37 
 
 .2149 
 
 4.03 
 
 .3938 
 
 4.69 
 
 .5454 
 
 5.35 
 
 .6771 
 
 6.01 
 
 .7934 
 
 3.38 
 
 .2179 
 
 4.04 
 
 .3962 
 
 4.70 
 
 .5476 
 
 5.36 
 
 .6790 
 
 6.02 
 
 .7951 
 
 3.39 
 
 .2208 
 
 4.05 
 
 .3987 
 
 4.71 
 
 .5497 
 
 5.37 
 
 .6808 
 
 6.03 
 
 .7967 
 
 3.40 
 
 .2238 
 
 4.06 
 
 .4012 
 
 4.72 
 
 .5518 
 
 5.38 
 
 .6827 
 
 6.04 
 
 .7984 
 
 3.41 
 
 .2267 
 
 4.07 
 
 .4036 
 
 4.73 
 
 .5539 
 
 5.39 
 
 .6845 
 
 6.05 
 
 .8001 
 
 3.42 
 
 .2296 
 
 4.08 
 
 .4061 
 
 4.74 
 
 .5.560 
 
 5.40 
 
 .6864 
 
 606 
 
 .8017 
 
 3.43 
 
 .2326 
 
 4.09 
 
 .4085 
 
 4.75 
 
 .5581 
 
 5.41 
 
 .6882 
 
 6.07 
 
 .8034 
 
 3.44 
 
 .2355 
 
 4.10 
 
 .4110 
 
 4.76 
 
 .5602 
 
 5.42 
 
 .6901 
 
 6.08 
 
 .8050 
 
 3.45 
 
 .2384 
 
 4.11 
 
 .4134 
 
 4.77 
 
 .5623 
 
 5.43 
 
 .6919 
 
 6.09 
 
 .8066 
 
 3.46 
 
 .2413 
 
 4.12 
 
 .4159 
 
 4.78 
 
 .5644 
 
 5.44 
 
 .6938 
 
 6.10 
 
 .8083 
 
 3.47 
 
 .2442 
 
 4.13 
 
 .4183 
 
 4.79 
 
 .5665 
 
 5.45 
 
 .6956 
 
 6.11 
 
 .8099 
 
 3.48 
 
 .2470 
 
 4.14 
 
 .4207 
 
 4.80 
 
 .5686 
 
 5.46 
 
 .6974 
 
 6.12 
 
 .8116 
 
 3.49 
 
 .2499 
 
 4.15 
 
 .4231 
 
 4.81 
 
 .5707 
 
 5.47 
 
 .6993 
 
 6.13 
 
 .8132 
 
 3.50 
 
 .2528 
 
 4.16 
 
 .4255 
 
 4.82 
 
 .5728 
 
 5.48 
 
 .7011 
 
 6.14 
 
 .8148 
 
 3.51 
 
 .2556 
 
 4.17 
 
 .4279 
 
 4.83 
 
 .5748 
 
 5.49 
 
 .7029 
 
 6.15 
 
 .8165 
 
 3.52 
 
 .2585 
 
 4.18 
 
 .4303 
 
 4.84 
 
 .5769 
 
 5.50 
 
 .7047 
 
 6.16 
 
 .8181 
 
 3.53 
 
 .2613 
 
 4.19 
 
 .4327 
 
 4.85 
 
 .5790 
 
 5.51 
 
 .7066 
 
 6.17 
 
 .8197 
 
 3.54 
 
 .2641 
 
 4.20 
 
 .4351 
 
 4.86 
 
 .5810 
 
 5.52 
 
 .7084 
 
 6.18 
 
 .8213 
 
 3.55 
 
 .2669 
 
 4.21 
 
 .4375 
 
 4.87 
 
 .5831 
 
 5.53 
 
 .7102 
 
 6.19 
 
 .8229 
 
 3.56 
 
 .2698 
 
 4.22 
 
 .4398 
 
 4.88 
 
 5851 
 
 5.54 
 
 .7120 
 
 6.20 
 
 .8245 
 
 3.57 
 
 .2726 
 
 4.23 
 
 .4422 
 
 4.89 
 
 .5872 
 
 5.55 
 
 .7138 
 
 6.21 
 
 .8262 
 
 3.58 
 
 .2754 
 
 4.24 
 
 4446 
 
 4.90 
 
 .5892 
 
 5.56 
 
 .7156 
 
 6.22 
 
 .8278 
 
 3.59 
 
 .2782 
 
 4.25 
 
 .4469 
 
 4.91 
 
 .5913 
 
 5.57 
 
 .7174 
 
 6.23 
 
 .8294 
 
 3.60 
 
 .2809 
 
 4.26 
 
 .4493 
 
 4.92 
 
 .5933 
 
 5.58 
 
 .7192 
 
 6.24 
 
 .8310 
 
 3.61 
 
 .2837 
 
 4.27 
 
 .4516 
 
 4.93 
 
 .5953 
 
 5.59 
 
 .7210 
 
 6.25 
 
 .8326 
 
 3.62 
 
 .2865 
 
 4.28 
 
 .4540 
 
 4.94 
 
 .5974 
 
 5.60 
 
 .7228 
 
 6.26 
 
 .8342 
 
 3.63 
 
 .2892 
 
 4.29 
 
 .4563 
 
 4.95 
 
 .5994 
 
 5.61 
 
 .7246 
 
 6.27 
 
 .8358 
 
 3.64 
 
 .2920 
 
 4.30 
 
 .4586 
 
 4.96 
 
 .6014 
 
 5.62 
 
 .7263 
 
 6.28 
 
 .8374 
 
 365 
 
 .2947 
 
 4.31 
 
 .4609 
 
 4.97 
 
 .6034 
 
 5.63 
 
 .7281 
 
 6.29 
 
 .8390 
 
 3.66 
 
 .2975 
 
 4.32 
 
 .4633 
 
 4.98 
 
 .6054 
 
 5.64 
 
 .7299 
 
 6.30 
 
 .8405 
 
 3.67 
 
 .3002 
 
 4.33 
 
 .4656 
 
 4.99 
 
 .6074 
 
 5.65 
 
 .7317 
 
 6.31 
 
 .8421 
 
 3.68 
 
 .3029 
 
 4.34 
 
 .4679 
 
 5.00 
 
 .6094 
 
 5.66 
 
 .7334 
 
 6.32 
 
 .8437 
 
 3.69 
 
 .3056 
 
 4.35 
 
 .4702 
 
 5.01 
 
 .6114 
 
 5.67 
 
 .7352 
 
 6.33 
 
 .8453 
 
 3.70 
 
 .3083 
 
 4.36 
 
 .4725 
 
 5.02 
 
 .6134 
 
 5.68 
 
 .7370 
 
 6.34 
 
 8469 
 
 3.71 
 
 .3110 
 
 4.37 
 
 .4748 
 
 5.03 
 
 .6154 
 
 5.69 
 
 .7387 
 
 6.35 
 
 .8485 
 
 3.72 
 
 .3137 
 
 4.38 
 
 .4770 
 
 5.04 
 
 .6174 
 
 5.70 
 
 .7405 
 
 6.36 
 
 .8500 
 
 3.73 
 
 .3164 
 
 4.39 
 
 .4793 
 
 5.05 
 
 .6194 
 
 5.71 
 
 .7422 
 
 6.37 
 
 .8516 
 
 3.74 
 
 .3191 
 
 4.40 
 
 .4816 
 
 5.06 
 
 .6214 
 
 5.72 
 
 .7440 
 
 6.38 
 
 .8532 
 
 3.75 
 
 .3218 
 
 4.41 
 
 .4839 
 
 5.07 
 
 .6233 
 
 5.73 
 
 .7457 
 
 6.39 
 
 .8547 
 
 3.76 
 
 .3244 
 
 4.42 
 
 .4861 
 
 5.08 
 
 .6253 
 
 5.74 
 
 .7475 
 
 6.40 
 
 .8563 
 
 3.77 
 
 .3271 
 
 4.43 
 
 .4884 
 
 5.09 
 
 .6273 
 
 5.75 
 
 .7492 
 
 6.41 
 
 .8579 
 
 3.78 
 
 .3297 
 
 4.44 
 
 .4907 
 
 5.10 
 
 .6292 
 
 5.76 
 
 .7509 
 
 6.42 
 
 .8594 
 
 3.79 
 
 .3324 
 
 4.45 
 
 .4929 
 
 5.11 
 
 .6312 
 
 5.77 
 
 .7527 
 
 6.43 
 
 .8610 
 
 3.80 
 
 .3350 
 
 4.46 
 
 .4951 
 
 5.12 
 
 .6332 
 
 5.78 
 
 .7544 
 
 6.44 
 
 .8625 
 
 3.81 
 
 .3376 
 
 4.47 
 
 .4974 
 
 5.13 
 
 .6351 
 
 5.79 
 
 .7561 
 
 6.45 
 
 .8641 
 
 3.82 
 
 .3403 
 
 4.48 
 
 .4996 
 
 5.14 
 
 .6371 
 
 5.80 
 
 .7579 
 
 6.46 
 
 .8656 
 
 3.83 
 
 .3429 
 
 4.49 
 
 .5019 
 
 5.15 
 
 .6390 
 
 5.81 
 
 .7596 
 
 6.47 
 
 .8672 
 
 3.84 
 
 .3455 
 
 4.50 
 
 .5041 
 
 5.16 
 
 .6409 
 
 5.82 
 
 .7613 
 
 6.48 
 
 8687 
 
 3.85 
 
 .3481 
 
 4.51 
 
 .5063 
 
 5.17 
 
 .6429 
 
 5.83 
 
 1 .7630 
 
 6.49 
 
 .8703 
 
 3.86 
 
 .3507 
 
 4.52 
 
 .5085 
 
 5.18 
 
 .6448 
 
 5.84 
 
 1.7647 
 
 6.50 
 
 .8718 
 
106 
 
 HYPERBOLIC LOGARITHMS. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No 
 
 Log. 
 
 6.51 
 
 1.8733 
 
 7.15 
 
 .9671 
 
 7.79 
 
 2.0528 
 
 8.66 
 
 2.1587 
 
 9.94 
 
 2.2966 
 
 6.52 
 
 1.8749 
 
 7.16 
 
 .9685 
 
 7.80 
 
 2.0541 
 
 8.68 
 
 2.1610 
 
 9.96 
 
 2.2986 
 
 6.53 
 
 1 .8764 
 
 7.17 
 
 .9699 
 
 7.81 
 
 2.0554 
 
 8.70 
 
 2.1633 
 
 9.98 
 
 2.3006 
 
 6.54 
 
 1.8779 
 
 7.18 
 
 .9713 
 
 7.82 
 
 2.0567 
 
 8.72 
 
 2 1656 
 
 10.00 
 
 2.3026 
 
 6.55 
 
 1.8795 
 
 7.19 
 
 .9727 
 
 7.83 
 
 2.0580 
 
 8.74 
 
 2.1679 
 
 10.25 
 
 2.3279 
 
 6.56 
 
 1.8810 
 
 7.20 
 
 .9741 
 
 7.84 
 
 2.0592 
 
 8.76 
 
 2.1702 
 
 10.50 
 
 2.3513 
 
 6.57 
 
 1.8825 
 
 7.21 
 
 .9754 
 
 7.85 
 
 2.0605 
 
 8.78 
 
 2.1725 
 
 10.75 
 
 2.3749 
 
 6.58 
 
 1 .8840 
 
 7.22 
 
 .9769 
 
 7.86 
 
 2.0618 
 
 8.80 
 
 2.1748 
 
 11.00 
 
 2.3979 
 
 6.59 
 
 1.8856 
 
 7.23 
 
 .9782 
 
 7.87 
 
 2.0631 
 
 8.82 
 
 2.1770 
 
 11.25 
 
 2.4201 
 
 6.60 
 
 1.8871 
 
 7.24 
 
 .9796 
 
 7.88 
 
 2.0643 
 
 8.84 
 
 2.1793 
 
 11.50 
 
 2.4430 
 
 6.61 
 
 1 .8886 
 
 7.25 
 
 .9810 
 
 7.89 
 
 2.0656 
 
 8.86 
 
 2.1815 
 
 11.75 
 
 2.4636 
 
 6.62 
 
 1.8901 
 
 7.26 
 
 .9824 
 
 7.90 
 
 2.0669 
 
 8.88 
 
 2.1838 
 
 12.00 
 
 2.4849 
 
 6.63 
 
 1.8916 
 
 7.27 
 
 .9838 
 
 7.91 
 
 2.0681 
 
 8.90 
 
 2.1861 
 
 12.25 
 
 2.5052 
 
 6.64 
 
 1 .893 1 
 
 7.28 
 
 .9851 
 
 7.92 
 
 2.0694 
 
 8.92 
 
 2.1883 
 
 12.50 
 
 2.5262 
 
 6.65 
 
 1 .8946 
 
 7.29 
 
 .9865 
 
 7.93 
 
 2.0707 
 
 8.94 
 
 2.1905 
 
 12.75 
 
 2.5455 
 
 6.66 
 
 1 8961 
 
 7.30 
 
 .9879 
 
 7.94 
 
 2.0719 
 
 8.96 
 
 2.1928 
 
 13.00 
 
 2.5649 
 
 6.67 
 
 1.8976 
 
 7.31 
 
 .9892 
 
 7.95 
 
 2.0732 
 
 8.98 
 
 2.1950 
 
 13.25 
 
 2.5840 
 
 6.68 
 
 1.8991 
 
 7.32 
 
 .9906 
 
 7.96 
 
 2.0744 
 
 9.00 
 
 2.1972 
 
 13.50 
 
 2.6027 
 
 6.69 
 
 1 .9006 
 
 7.33 
 
 .9920 
 
 7.97 
 
 2.0757 
 
 9.02 
 
 2.1994 
 
 13.75 
 
 2.621 1 
 
 6.70 
 
 1.9021 
 
 7.34 
 
 .9933 
 
 7.98 
 
 2.0769 
 
 9.04 
 
 2.2017 
 
 14.00 
 
 2.6391 
 
 6.71 
 
 1 .9036 
 
 7.35 
 
 .9947 
 
 7.99 
 
 2.0782 
 
 9.06 
 
 2.2039 
 
 14.25 
 
 2.6567 
 
 6.72 
 
 1.9051 
 
 7.36 
 
 .9961 
 
 800 
 
 2.0794 
 
 9.08 
 
 2.2061 
 
 14.50 
 
 2.6740 
 
 6.73 
 
 1 .9066 
 
 7.37 
 
 .9974 
 
 8.01 
 
 2.0807 
 
 9.10 
 
 2.2083 
 
 14.75 
 
 2.6913 
 
 6.74 
 
 1.9081 
 
 7.38 
 
 .9988 
 
 8.02 
 
 2.0819 
 
 9.12 
 
 2.2105 
 
 15.00 
 
 2.7081 
 
 6.75 
 
 1 .9095 
 
 7.39 
 
 2.0001 
 
 8.03 
 
 2.0832 
 
 9.14 
 
 2.2127 
 
 15.50 
 
 2.7408 
 
 6.76 
 
 1.9110 
 
 7.40 
 
 2.0015 
 
 8.04 
 
 2.0844 
 
 9.16 
 
 2.2148 
 
 16.00 
 
 2.7726 
 
 6.77 
 
 1.9125 
 
 7.41 
 
 2.0028 
 
 8.05 
 
 2.0857 
 
 9.18 
 
 2.2170 
 
 16.50 
 
 2.8034 
 
 6.78 
 
 1.9140 
 
 7.42 
 
 2.0041 
 
 8.06 
 
 2.0869 
 
 9.20 
 
 2.2192 
 
 17.00 
 
 2.8332 
 
 6.79 
 
 1.9155 
 
 7.43 
 
 2.0055 
 
 8.07 
 
 2.0882 
 
 9.22 
 
 2.2214 
 
 17.50 
 
 2.8621 
 
 6.80 
 
 1.9169 
 
 7.44 
 
 2.0069 
 
 8.08 
 
 2.0894 
 
 924 
 
 2.2235 
 
 18.00 
 
 2.8904 
 
 6.81 
 
 1.9184 
 
 7.45 
 
 2.0082 
 
 8.09 
 
 2.0906 
 
 9.26 
 
 2.2257 
 
 18.50 
 
 2.9178 
 
 6.82 
 
 1.9199 
 
 7.46 
 
 2.0096 
 
 8.10 
 
 2.0919 
 
 9.28 
 
 2.2279 
 
 19.00 
 
 2.9444 
 
 6.83 
 
 1.9213 
 
 7.47 
 
 2.0108 
 
 8.11 
 
 2.0931 
 
 9.30 
 
 2.2300 
 
 19.50 
 
 2.9703 
 
 6.84 
 
 1 .9228 
 
 7.48 
 
 2.0122 
 
 8.12 
 
 2.0943 
 
 9.32 
 
 2.2322 
 
 20.00 
 
 2.9957 
 
 6.85 
 
 1 .9242 
 
 7.49 
 
 2.0136 
 
 8.13 
 
 2.0956 
 
 9.34 
 
 2.2343 
 
 21 
 
 3.0445 
 
 6.86 
 
 1.9257 
 
 7.50 
 
 2.0149 
 
 8,14 
 
 2.0968 
 
 9.36 
 
 2.2364 
 
 22 
 
 3.0910 
 
 6.87 
 
 1.9272 
 
 7.51 
 
 2.0162 
 
 8.15 
 
 2.0980 
 
 9.38 
 
 2.2386 
 
 23 
 
 3.1355 
 
 6.88 
 
 1 .9286 
 
 7.52 
 
 2.0176 
 
 8.16 
 
 2.0992 
 
 9.40 
 
 2.2407 
 
 24 
 
 3.1781 
 
 6.89 
 
 1.9301 
 
 7.53 
 
 2.0189 
 
 8.17 
 
 2.1005 
 
 9:42 
 
 2.2428 
 
 25 
 
 3.2189 
 
 6.90 
 
 1 .93 1 5 
 
 7.54 
 
 2.0202 
 
 8.18 
 
 2.1017 
 
 9.44 
 
 2.2450 
 
 26 
 
 3.2581 
 
 N 6.91 
 
 1 .9330 
 
 7.55 
 
 2.0215 
 
 8.19 
 
 2.1029 
 
 9.46 
 
 2.2471 
 
 27 
 
 3.2958 
 
 6.92 
 
 1.9344 
 
 7.56 
 
 2.0229 
 
 8.20 
 
 2.1041 
 
 9.48 
 
 2.2492 
 
 28 
 
 3.3322 
 
 6.93 
 
 1.9359 
 
 7.57 
 
 2.0242 
 
 8.22 
 
 2.1066 
 
 9.50 
 
 2.2513 
 
 29 
 
 3.3673 
 
 6.94 
 
 1.9373 
 
 7.58 
 
 2.0255 
 
 8.24 
 
 2.1090 
 
 9.52 
 
 2.2534 
 
 30 
 
 3.4012 
 
 6.95 
 
 1.9387 
 
 7.59 
 
 2.0268 
 
 8.26 
 
 2.1114 
 
 9.54 
 
 2.2555 
 
 31 
 
 3.4340 
 
 6.96 
 
 1 .9402 
 
 7.60 
 
 2.0281 
 
 8.28 
 
 2.1138 
 
 9.56 
 
 2.2576 
 
 32 
 
 3.4657 
 
 6.97 
 
 1.9416 
 
 7.61 
 
 2.0295 
 
 8.30 
 
 2.1163 
 
 9.58 
 
 2.2597 
 
 33 
 
 3.4965 
 
 6.98 
 
 1 .9430 
 
 7.62 
 
 2.0308 
 
 8.32 
 
 2.1187 
 
 9.60 
 
 2.2618 
 
 34 
 
 3.5263 
 
 6.99 
 
 1 .9445 
 
 7.63 
 
 2.0321 
 
 8.34 
 
 2.1211 
 
 9.62 
 
 2.2638 
 
 35 
 
 3.5553 
 
 7.00 
 
 1 .9459 
 
 7.64 
 
 2.0334 
 
 8.36 
 
 2.1235 
 
 9.64 
 
 2.2659 
 
 36 
 
 3.5835 
 
 7.01 
 
 1 .9473 
 
 7.65 
 
 2.0347 
 
 8.38 
 
 2.1258 
 
 9.66 
 
 2.2680 
 
 37 
 
 3.6109 
 
 7.02 
 
 1 .9488 
 
 7.66 
 
 2.0360 
 
 8.40 
 
 2.1282 
 
 9.68 
 
 2.2701 
 
 38 
 
 3.6376 
 
 7.03 
 
 1 .9502 
 
 7.67 
 
 2.0373 
 
 8.42 
 
 2.1306 
 
 9.70 
 
 2.2721 
 
 39 
 
 3.6636 
 
 7.04 
 
 1.9516 
 
 7.68 
 
 2.0386 
 
 8.44 
 
 2.1330 
 
 9.72 
 
 2.2742 
 
 40 
 
 3.6889 
 
 7.05 
 
 1.9530 
 
 7.69 
 
 2.0399 
 
 8.46 
 
 2.1353 
 
 9.74 
 
 2.2762 
 
 41 
 
 3.71J6 
 
 7.06 
 
 1.9544 
 
 7.70 
 
 2.0412 
 
 8.48 
 
 2.1377 
 
 9.76 
 
 2.2783 
 
 42 
 
 3.7377 
 
 7.07 
 
 1.9559 
 
 7.71 
 
 2.0425 
 
 8.50 
 
 2.1401 
 
 9.78 
 
 2.2803 
 
 43 
 
 3.7612 
 
 7.08 
 
 1.9573 
 
 7.72 
 
 2.0438 
 
 8.52 
 
 2.1424 
 
 9.80 
 
 2.2824 
 
 44 
 
 3.7842 
 
 7.09 
 
 1.9587 
 
 7.73 
 
 2.0451 
 
 8.54 
 
 2.1448 
 
 9.82 
 
 2.2844 
 
 45 
 
 3.8067 
 
 7.10 
 
 1.9601 
 
 7.74 
 
 2.0464 
 
 8.56 
 
 2.1471 
 
 9.84 
 
 2.2865 
 
 46 
 
 3.8286 
 
 7.11 
 
 1.9615 
 
 7.75 
 
 2.0477 
 
 8.58 
 
 2.1494 
 
 9.86 
 
 2.2885 
 
 47 
 
 3.8501 
 
 7.12 
 
 1 .9629 
 
 7.76 
 
 2.0490 
 
 8.60 
 
 2.1518 
 
 9.88 
 
 2.2905 
 
 48 
 
 3.8712 
 
 7.13 
 
 1 .9643 
 
 7.77 
 
 2.0503 
 
 8.62 
 
 2.1541 
 
 9.90 
 
 2.2925 
 
 49 
 
 3.8918 
 
 7.14 
 
 1.9657 
 
 7.78 
 
 2.0516 
 
 8.64 
 
 2.1564 
 
 9.92 
 
 2.2946 
 
 50 
 
 3.9120 
 
LOGARITHMIC TRIGONOMETRICAL FUNCTIONS. 
 
 167 
 
 LOGARITHMIC SINES, ETC. 
 
 1 
 
 Sine. 
 
 Cosec. 
 
 Versin. 
 
 Tangent 
 
 Cotan. 
 
 Covers. 
 
 Secant. 
 
 Cosine. 
 
 bb 
 
 0) 
 
 Q 
 
 o 
 
 n.Neg. 
 
 nfinite. 
 
 n.Neg. 
 
 In.Neg. 
 
 Infinite. 
 
 0.00000 
 
 1 0.00000 
 
 0.00000 
 
 90 
 
 1 
 
 .24186 
 
 1.75814 
 
 6.18271 
 
 8.24192 
 
 11.75808 
 
 9.99235 
 
 10.00007 
 
 9.99993 
 
 89 
 
 2 
 
 .54282 
 
 1.43718 
 
 6.78474 
 
 8.54308 
 
 1 1 .45692 
 
 9.98457 
 
 10.00026 
 
 9.99974 
 
 88 
 
 3 
 
 .71880 
 
 1.28120 
 
 7.13687 
 
 8.71940 
 
 1 1 .28060 
 
 9.97665 
 
 10.00060 
 
 9.99940 
 
 87 
 
 4 
 
 .84358 
 
 1.15642 
 
 7.38667 
 
 8.84464 
 
 11.15536 
 
 9.96860 
 
 10.00106 
 
 9.99894 
 
 80 
 
 5 
 
 .94030 
 
 1.05970 
 
 7.58039 
 
 8.94195 
 
 1 1 .05805 
 
 9.96040 
 
 10.00166 
 
 9.99834 
 
 85 
 
 6 
 
 .01923 
 
 0.98077 
 
 7.73863 
 
 9.02162 
 
 10.97838 
 
 9.95205 
 
 10.00239 
 
 999761 
 
 84 
 
 7 
 
 9.08589 
 
 0.91411 
 
 7.87238 
 
 9.08914 
 
 10.91086 
 
 9.94356 
 
 10.00325 
 
 9.99675 
 
 83 
 
 8 
 
 .14356 
 
 0.85644 
 
 7.98820 
 
 9.14780 
 
 10.85220 
 
 9.93492 
 
 10.00425 
 
 9.99575 
 
 82 
 
 9 
 
 .19433 
 
 0.80567 
 
 8.09032 
 
 9.19971 
 
 10.80029 
 
 9.92612 
 
 0.00538 
 
 9.99462 
 
 81 
 
 10 
 
 9.23967 
 
 0.76033 
 
 8.18162 
 
 9.24632 
 
 10.75368 
 
 9.91717 
 
 10.00665 
 
 9.99335 
 
 80 
 
 11 
 
 9.28060 
 
 0.71940 
 
 8.26418 
 
 9.28865 
 
 10.71135 
 
 9.90805 
 
 10.00805 
 
 9.99195 
 
 79 
 
 12 
 
 9.31788 
 
 0.68212 
 
 8.33950 
 
 9.32747 
 
 10.67253 
 
 9.89877 
 
 10.00960 
 
 9.99040 
 
 78 
 
 13 
 
 9.35209 
 
 0.64791 
 
 8.40875 
 
 9.36336 
 
 0.63664 
 
 9.88933 
 
 10.01128 
 
 9.98872 
 
 77 
 
 14 
 
 9.38368 
 
 0.61632 
 
 8.47282 
 
 9.39677 
 
 0.60323 
 
 9.87971 
 
 10.01310 
 
 9.98690 
 
 76 
 
 15 
 
 9.41300 
 
 0.58700 
 
 8.53243 
 
 9.42805 
 
 10.57195 
 
 9.86992 
 
 10.01506 
 
 9.98494 
 
 75 
 
 16 
 
 9.44034 
 
 0.55966 
 
 8.58814 
 
 9.45750 
 
 10.54250 
 
 9.85996 
 
 10.01716 
 
 9.98284 
 
 74 
 
 17 
 
 9.46594 
 
 0.53406 
 
 8.64043 
 
 9 48534 
 
 10.51466 
 
 9.84981 
 
 10.01940 
 
 9.98060 
 
 73 
 
 18 
 
 9 48998 
 
 0.51002 
 
 8.68969 
 
 9.51178 
 
 10.48822 
 
 9.83947 
 
 10.02179 
 
 9.97821 
 
 72 
 
 19 
 
 9.51264 
 
 10.48736 
 
 8.73625 
 
 9.53697 
 
 10.46303 
 
 9.82894 
 
 10.02433 
 
 9.97567 
 
 71 
 
 20 
 
 9.53405 
 
 10.46595 
 
 8.78037 
 
 9.56107 
 
 10.43893 
 
 9.81821 
 
 10.02701 
 
 9.97299 
 
 70 
 
 21 
 
 9.55433 
 
 10.44567 
 
 8.82230 
 
 9.58418 
 
 10.41582 
 
 9.80729 
 
 10.02985 
 
 9.97015 
 
 69 
 
 22 
 
 9.57358 
 
 10.42642 
 
 8.86223 
 
 9.60641 
 
 10.39359 
 
 9.79615 
 
 10.03283 
 
 9.96717 
 
 68 
 
 23 
 
 9.59188 
 
 10.40812 
 
 8.90034 
 
 9.62785 
 
 10.37215 
 
 9.78481 
 
 10.03597 
 
 9.96403 
 
 67 
 
 24 
 
 9.6093 1 
 
 10.39069 
 
 8.93679 
 
 9.64858 
 
 10.35142 
 
 9.77325 
 
 10.03927 
 
 9.96073 
 
 66 
 
 25 
 
 9.62595 
 
 10.37405 
 
 8.97170 
 
 9.66867 
 
 10.33133 
 
 9.76146 
 
 10.04272 
 
 9.95728 
 
 65 
 
 26 
 
 9.64184 
 
 10.35816 
 
 9.00521 
 
 9.68818 
 
 10.31182 
 
 9.74945 
 
 10.04634 
 
 9.95366 
 
 64 
 
 27 
 
 9.65705 
 
 10.34295 
 
 9.03740 
 
 9.70717 
 
 10.29283 
 
 9.73720 
 
 10.05012 
 
 9.94988 
 
 63 
 
 28 
 
 9.67161 
 
 10.32839 
 
 9.06838 
 
 9.72567 
 
 10.27433 
 
 9.72471 
 
 10.05407 
 
 9.94593 
 
 62 
 
 29 
 
 9.68557 
 
 10.31443 
 
 9.09823 
 
 9.74375 
 
 10.25625 
 
 9.71197 
 
 10.05818 
 
 9.94182 
 
 61 
 
 30 
 
 9.69897 
 
 10.30103 
 
 9.12702 
 
 9.76144 
 
 10.23856 
 
 9.69897 
 
 10.06247 
 
 9.93753 
 
 60 
 
 31 
 
 9.71184 
 
 10.28816 
 
 9.15483 
 
 9.77877 
 
 10.22123 
 
 9.68571 
 
 10.06693 
 
 9.93307 
 
 59 
 
 32 
 
 9.72421 
 
 10.27579 
 
 9.18171 
 
 9.79579 
 
 10.20421 
 
 9.67217 
 
 10.07158 
 
 9.92842 
 
 58 
 
 33 
 
 9.73611 
 
 10.26389 
 
 9.20771 
 
 9.81252 
 
 10.18748 
 
 9.65836 
 
 10.07641 
 
 9.92359 
 
 57 
 
 34 
 
 9.74756 
 
 10.25244 
 
 9.23290 
 
 9.82899 
 
 10.17101 
 
 9.64425 
 
 10.08143 
 
 9.91857 
 
 56 
 
 35 
 
 9.75859 
 
 10.24141 
 
 9.25731 
 
 9.84523 
 
 10.15477 
 
 9.62984 
 
 10.08664 
 
 9.91336 
 
 55 
 
 36 
 
 9.76922 
 
 10.23078 
 
 9.28099 
 
 9.86126 
 
 10.13874 
 
 9.61512 
 
 10.09204 
 
 9.90796 
 
 54 
 
 37 
 
 9.77946 
 
 10.22054 
 
 9.30398 
 
 9.87711 
 
 10.12289 
 
 9.60008 
 
 10.09765 
 
 9.90235 
 
 53 
 
 38 
 
 9.78934 
 
 10.21066 
 
 9.32631 
 
 9.89281 
 
 10.10719 
 
 9.58471 
 
 10.10347 
 
 9.89653 
 
 52 
 
 39 
 
 9.79887 
 
 10.20113 
 
 9.34802 
 
 9.90837 
 
 10.09163 
 
 9.56900 
 
 10.10950 
 
 9.89050 
 
 51 
 
 40 
 
 9.80807 
 
 10.19193 
 
 9.36913 
 
 9.92381 
 
 10.07619 
 
 9.55293 
 
 10.11575 
 
 9.88425 
 
 50 
 
 41 
 
 9.81694 
 
 10.18306 
 
 9.38968 
 
 9.93916 
 
 10.06084 
 
 9.53648 
 
 10.12222 
 
 9.87778 
 
 49 
 
 42 
 
 9.82551 
 
 10.17449 
 
 9.40969 
 
 9.95444 
 
 10.04556 
 
 9.51966 
 
 10.12893 
 
 9.87107 
 
 48 
 
 43 
 
 9.83378 
 
 10.16622 
 
 9.42918 
 
 9.96966 
 
 10.03034 
 
 9.50243 
 
 10.13587 
 
 9.86413 
 
 47 
 
 44 
 
 9.84177 
 
 10.15823 
 
 9.44818 
 
 9.98484 
 
 10.01516 
 
 9.48479 
 
 10.14307 
 
 9.85693 
 
 46 
 
 45 
 
 9.84949 
 
 10.15052 
 
 9.4667 
 
 10.00000 
 
 10.00000 
 
 9.46671 
 
 10.15052 
 
 9.84949 
 
 45 
 
 
 Cosine 
 
 Secant. 
 
 Covers 
 
 Cotan. 
 
 Tangent 
 
 Versin. 
 
 Cosec. 
 
 Sine. 
 
 
 From 45 to 90 read from bottom of table upwards. 
 
168 
 
 LOGARITHMS OF NUMBERS. 
 
 Four-place Logarithms of Numbers to 1000. 
 
 For six-place logarithms of numbers to 10,000, see pp. 137 to 164. 
 
 No. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 1 
 
 8 
 
 9 
 
 No. 
 
 
 
 
 0000 
 
 3010 
 
 4771 
 
 6021 
 
 6990 
 
 7782 
 
 8451 
 
 9031 
 
 9542 
 
 
 
 2 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 0000 
 3010 
 4771. 
 6021 
 6990 
 7782 
 8451 
 9031 
 9542 
 
 0414 
 3222 
 4914 
 6128 
 7076 
 7853 
 8513 
 9085 
 9590 
 
 0792 
 3424 
 5052 
 6232 
 7160 
 7924 
 8573 
 9138 
 9638 
 
 1139 
 3617 
 5185 
 6335 
 7243 
 7993 
 8633 
 9191 
 9685 
 
 1461 
 3802 
 5315 
 6435 
 7324 
 8062 
 8692 
 9243 
 9731 
 
 1761 
 3979 
 5441 
 6532 
 7404 
 8129 
 8751 
 9294 
 9777 
 
 2041 
 4150 
 5563 
 6628 
 7482 
 8195 
 8808 
 9345 
 9823 
 
 2304 
 4314 
 5682 
 6721 
 7559 
 8261 
 8865 
 9395 
 9868 
 
 2553 
 4472 
 5798 
 6812 
 7634 
 8325 
 8921 
 9445 
 9912 
 
 2788 
 4624 
 5911 
 6902 
 7709 
 8388 
 8976 
 9494 
 9956 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 10 
 
 0000 
 
 0043 
 
 0086 
 
 0128 
 
 0170 
 
 0212 
 
 0253 
 
 0294 
 
 0334 
 
 0374 
 
 10 
 
 It 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 0414 
 0792 
 1139 
 1461 
 1761 
 2041 
 2304 
 2553 
 2788 
 
 0453 
 0828 
 1173 
 1492 
 1790 
 2068 
 2330 
 2577 
 2810 
 
 0492 
 0864 
 1206 
 1523 
 1818 
 2095 
 
 2355 
 2601 
 2833 
 
 0531 
 0899 
 1239 
 1553 
 1847 
 2122 
 2380 
 2625 
 2856 
 
 0569 
 0934 
 1271 
 1584 
 1875 
 2148 
 2405 
 2648 
 2878 
 
 0607 
 0969 
 1303 
 1614 
 1903 
 2175 
 2430 
 2672 
 2900 
 
 0645 
 1004 
 1335 
 1644 
 1931 
 2201 
 2455 
 2695 
 2923 
 
 0682 
 1038 
 1367 
 1673 
 1959 
 2227 
 2480 
 2718 
 2945 
 
 0719 
 1072 
 1399 
 1703 
 1987 
 2253 
 2504 
 2742 
 2967 
 
 0755 
 1106 
 1430 
 1732 
 2014 
 2279 
 2529 
 2765 
 2989 
 
 11 
 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 20 
 
 3010 
 
 3032 
 
 3054 
 
 3075 
 
 3096 
 
 3118 
 
 3139 
 
 3160 
 
 3181 
 
 3201 
 
 20 
 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 
 3222 
 
 3424 
 3617 
 3802 
 3979 
 4150 
 4314 
 4472 
 4624 
 
 3243 
 3444 
 3636 
 3820 
 3997 
 4166 
 4330 
 4487 
 4639 
 
 3263 
 3464 
 3655 
 3838 
 4014 
 4183 
 4346 
 4502 
 4654 
 
 3284 
 3483 
 3674 
 3856 
 4031 
 4200 
 4362 
 4518 
 4669 
 
 3304 
 3502 
 3692 
 3874 
 4048 
 4216 
 4378 
 4533 
 4683 
 
 3324 
 3522 
 3711 
 3892 
 4065 
 4232 
 4393 
 4548 
 4698 
 
 3345 
 3541 
 3729 
 3909 
 4082 
 4249 
 4409 
 4564 
 4713 
 
 3365 
 3560 
 3747 
 3927 
 4099 
 4265 
 4425 
 4579 
 4728 
 
 3385 
 3579 
 3766 
 3945 
 4116 
 4281 
 4440 
 4594 
 4742 
 
 3404 
 3598 
 3784 
 3962 
 4133 
 4298 
 4456 
 4609 
 4757 
 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 
 30 
 
 4771 
 
 4786 
 
 4800 
 
 4814 
 
 4829 
 
 4843 
 
 4857 
 
 4871 
 
 4886 
 
 4900 
 
 30 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 4914 
 5052 
 5185 
 5315 
 5441 
 5563 
 5682 
 5798 
 5911 
 
 4928 
 5065 
 5198 
 5328 
 5453 
 5575 
 5694 
 5809 
 5922 
 
 4942 
 5079 
 5211 
 5340 
 5465 
 5587 
 5705 
 5821 
 5933 
 
 4955 
 5092 
 5224 
 5353 
 5478 
 5599 
 5717 
 5832 
 5944 
 
 4969 
 5105 
 5237 
 5366 
 5490 
 5611 
 5729 
 5843 
 5955 
 
 4983 
 5119 
 5250 
 5378 
 5502 
 5623 
 5740 
 5855 
 5966 
 
 4997 
 5132 
 5263 
 5391 
 5515 
 5635 
 5752 
 5866 
 5977 
 
 5011 
 5145 
 5276 
 5403 
 5527 
 5647 
 5763 
 5877 
 5988 
 
 5024 
 5159 
 5289 
 5416 
 5539 
 5658 
 5775 
 5888 
 5999 
 
 5038 
 5172 
 5302 
 5428 
 5551 
 5670 
 5786 
 5899 
 6010 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 40 
 
 6021- 
 
 6031 
 
 6042 
 
 6053 
 
 6064 
 
 6075 
 
 6085 
 
 6096 
 
 6107 
 
 6117 
 
 40 
 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 6128 
 6232 
 6335 
 6435 
 6532 
 6628 
 6721 
 6812 
 6902 
 
 6138 
 6243 
 6345 
 6444 
 6542 
 6637 
 6730 
 6821 
 6911 
 
 6149 
 6253 
 6355 
 6454 
 6551 
 6646 
 6739 
 6830 
 6920 
 
 6160 
 6263 
 6365 
 6464 
 6561 
 6656 
 6749 
 6839 
 6928 
 
 6170 
 6274 
 6375 
 6474 
 6571 
 6665 
 6758 
 6848 
 6937 
 
 6180 
 6284 
 6385 
 6484 
 6580 
 6675 
 6767 
 6857 
 6946 
 
 6191 
 6294 
 6395 
 6493 
 6590 
 6684 
 6776 
 6866 
 6955 
 
 6201 
 6304 
 6405 
 6503 
 6599 
 6693 
 6785 
 6875 
 6964 
 
 6212 
 6314 
 6415 
 6513 
 6609 
 6702 
 6794 
 6884 
 6972 
 
 6222 
 6325 
 6425 
 6522 
 6618 
 6712 
 6803 
 6893 
 6981 
 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 50 
 
 6990 
 
 6998 
 
 7007 
 
 7016' 
 
 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 50 
 
LOGARITHMS OP NUMBERS. 
 
 169 
 
 Four-place Logarithms of Numbers to 1000. 
 
 For six-place logarithms of numbers to 10,000, see pp. 137 to 164. 
 
 No. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 No. 
 
 50 
 
 6990 
 
 6998 
 
 7007 
 
 7016 
 
 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 50 
 
 51 
 52 
 53 
 
 7076 
 7160 
 
 7243 
 
 7084 
 7168 
 7251 
 
 7093 
 7177 
 7259 
 
 7101 
 
 7185 
 7267 
 
 7110 
 7193 
 7275 
 
 7118 
 7202 
 7284 
 
 7126 
 7210 
 7292 
 
 7135 
 7218 
 7300 
 
 7143 
 7226 
 7308 
 
 7152 
 7235 
 7316 
 
 51 
 
 52 
 53 
 
 54 
 55 
 56 
 
 7324 
 7404 
 7482 
 
 7332 
 7412 
 7490 
 
 7340 
 7419 
 7497 
 
 7348 
 7427 
 7505 
 
 7356 
 7435 
 7513 
 
 7364 
 7443 
 7520 
 
 7372 
 7451 
 7528 
 
 7380 
 7459 
 7536 
 
 7388 
 7466 
 7543 
 
 7396 
 7474 
 7551 
 
 54 
 55 
 56 
 
 57 
 58 
 59 
 
 7559 
 7634 
 7709 
 
 7566 
 7642 
 7716 
 
 7574 
 7649 
 7723 
 
 7582 
 7657 
 7731 
 
 7589 
 7664 
 7738 
 
 7597 
 7672 
 
 7745 
 
 7604 
 7679 
 7752 
 
 7612 
 7686 
 7760 
 
 7619 
 7694 
 7767 
 
 7627 
 7701 
 7774 
 
 57 
 58 
 59 
 
 60 
 
 7782 
 
 7789 
 
 7796 
 
 7803 
 
 7810 
 
 7818 
 
 7825 
 
 7832 
 
 7839 
 
 7846 
 
 60 
 
 61 
 62 
 63 
 
 7853 
 7924 
 7993 
 
 7860 
 7931 
 8000 
 
 7868 
 7938 
 8007 
 
 7875 
 7945 
 8014 
 
 7882 
 7952 
 8021 
 
 7889 
 7959 
 8028 
 
 7896 
 7966 
 8035 
 
 7903 
 7973 
 8041 
 
 7910 
 7980 
 8048 
 
 7917 
 7987 
 8055 
 
 61 
 62 
 63 
 
 64 
 65 
 66 
 
 8062 
 8129 
 8195 
 
 8069- 
 8136 
 8202 
 
 8075 
 8142 
 8209 
 
 8082 
 8149 
 8215 
 
 8089 
 8156 
 8222 
 
 8096 
 8162 
 8228 
 
 8102 
 8169 
 8235 
 
 8109 
 8176 
 8241 
 
 8116 
 8182 
 8248 
 
 8122 
 8189 
 8254 
 
 64 
 65 
 66 
 
 67 
 68 
 69 
 
 8261 
 8325 
 8388 
 
 8267 
 8331 
 8395 
 
 8274 
 8338 
 8401 
 
 8280 
 8344 
 8407 
 
 8287 
 8351 
 8414 
 
 8293 
 8357 
 8420 
 
 8299 
 8363 
 8426 
 
 8306 
 8370 
 8432 
 
 8312 
 8376 
 8439 
 
 8319 
 
 8382 
 8445 
 
 67 
 68 
 69 
 
 70 
 
 8451 
 
 8457 
 
 8463 
 
 8470 
 
 8476 
 
 8482 
 
 8488 
 
 8494 
 
 8500 
 
 8506 
 
 70 
 
 71 
 72 
 73 
 
 8513 
 8573 
 8633 
 
 8519 
 8579 
 8639 
 
 8525 
 8585 
 8645 
 
 8531 
 8591 
 8651 
 
 8537 
 8597 
 8657 
 
 8543 
 8603 
 8663 
 
 8549 
 8609 
 8669 
 
 8555 
 8615 
 8675 
 
 8561 
 8621 
 8681 
 
 8567 
 8627 
 8686 
 
 71 
 72 
 73 
 
 74 
 75 
 76 
 
 8692 
 8751 
 8808 
 
 8698 
 8756 
 8814 
 
 8704 
 8762 
 8820 
 
 8710 
 8768 
 8825 
 
 8716 
 8774 
 8831 
 
 8722 
 8779 
 8837 
 
 8727 
 8785 
 8842 
 
 8733 
 8791 
 8848 
 
 8739 
 8797 
 8854 
 
 8745 
 8802 
 8859 
 
 74 
 75 
 76 
 
 77 
 78 
 79 
 
 8865 
 8921 
 8976 
 
 8871 
 8927 
 8982 
 
 8876 
 8932 
 8987 
 
 8882 
 8938 
 8993 
 
 8887 
 8943 
 8998 
 
 8893 
 8949 
 9004 
 
 8899 
 8954 
 9009 
 
 8904 
 8960 
 9015 
 
 8910 
 8965 
 9020 
 
 8915 
 8971 
 9025 
 
 77 
 78 
 79 
 
 80 
 
 9031 
 
 9036 
 
 9042 
 
 9047 
 
 9053 
 
 9058 
 
 9063 
 
 9069 
 
 9074 
 
 9079 
 
 80 
 
 81 
 82 
 83 
 
 9085 
 9138 
 9191 
 
 9090 
 9143 
 9196 
 
 9096 
 9149 
 9201 
 
 9101 
 9154 
 9206 
 
 9106 
 9159 
 9212 
 
 9112 
 9165 
 9217 
 
 9117 
 9170 
 9222 
 
 9122 
 9175 
 9227 
 
 9128 
 9180 
 9232 
 
 9133 
 9186 
 9238 
 
 81 
 82 
 83 
 
 84 
 85 
 86 
 
 9243 
 9294 
 9345 
 
 9248 
 9299 
 9350 
 
 9253 
 9304 
 9355 
 
 9258 
 9309 
 9360 
 
 9263 
 9315 
 9365 
 
 9269 
 9320 
 9370 
 
 9274 
 9325 
 9375 
 
 9279 
 9330 
 9380 
 
 9284 
 9335 
 9385 
 
 9289 
 9340 
 9390 
 
 84 
 85 
 86 
 
 87 
 88 
 89 
 
 9395 
 9445 
 9494 
 
 9400 
 9450 
 9499 
 
 9405 
 9455 
 9504 
 
 9410 
 9460 
 9509 
 
 9415 
 9465 
 9513 
 
 9420 
 9469 
 9518 
 
 9425 
 9474 
 9523 
 
 9430 
 9479 
 9528 
 
 9435 
 9484 
 9533 
 
 9440 
 9489 
 9538 
 
 87 
 88 
 89 
 
 90 
 
 9542 
 
 9547 
 
 9552 
 
 9557 
 
 9562 
 
 9566 
 
 9571 
 
 9576 
 
 9581 
 
 9586 
 
 90 
 
 91 
 92 
 93 
 
 9590 
 9638 
 9685 
 
 9595 
 9643 
 9689 
 
 9600 
 9647 
 9694 
 
 9605 
 9652 
 9699 
 
 9609 
 9657 
 9703 
 
 9614 
 9661 
 9708 
 
 9619 
 9666 
 9713 
 
 9624 
 9671 
 9717 
 
 9628 
 9675 
 9722 
 
 9633 
 9680 
 9727 
 
 91 
 92 
 93 
 
 94 
 95 
 96 
 
 9731 
 9777 
 9823 
 
 9736 
 9782 
 9827 
 
 9741 
 9786 
 9832 
 
 9745 
 9791 
 9836 
 
 9750 
 9795 
 9841 
 
 9754 
 9800 
 9845 
 
 9759 
 9805 
 9850 
 
 9764 
 9809 
 9854 
 
 9768 
 9814 
 9859 
 
 9773 
 9818 
 9863 
 
 94 
 95 
 96 
 
 97 
 98 
 99 
 
 9868 
 9912 
 9956 
 
 9872 
 9917 
 9961 
 
 9877 
 9921 
 9965 
 
 9881 
 9926 
 9969 
 
 9886 
 9930 
 9974 
 
 9890 
 9934 
 9978 
 
 9894 
 9939 
 9983 
 
 9899 
 9943 
 9987 
 
 9903 
 9948 
 9991 
 
 9908 
 9952 
 9996 
 
 97 
 98 
 99 
 
 100 
 
 0000 
 
 0004 
 
 0009 
 
 0013 
 
 0017 
 
 0022 
 
 0026 
 
 0030 
 
 0035 
 
 0039 
 
 100 
 
170 NATURAL TRIGONOMETRICAL FUNCTIONS. 
 
 NATURAL TRIGONOMETRICAL, FUNCTIONS. 
 
 
 
 M. 
 
 Sine. 
 
 Co- 
 Vers. 
 
 Cosec. 
 
 Tang. 
 
 Co tan. 
 
 Se- 
 cant. 
 
 Ver. 
 
 Sin. 
 
 Cosine. 
 
 
 
 o 
 
 
 
 .00000 
 
 1 .0000 
 
 Infinite 
 
 .00000 
 
 Infinite 
 
 .0000 
 
 .00000 
 
 1.0000 
 
 1)0 
 
 ^ 
 
 
 15 
 
 .00436 
 
 .99564 
 
 229.18 
 
 .00436 
 
 229.18 
 
 .0000 
 
 .00001 
 
 .99999 
 
 
 45 
 
 
 30 
 
 .00873 
 
 .99127 
 
 114.59 
 
 .00873 
 
 114.59 
 
 .0000 
 
 .00004 
 
 .99996 
 
 
 30 
 
 
 45 
 
 .01309 
 
 .98691 
 
 76.397- 
 
 .01309 
 
 76.390 
 
 .0001 
 
 .00009 
 
 .99991 
 
 
 15 
 
 1 
 
 
 
 .01745 
 
 .98255 
 
 57.299 
 
 .01745 
 
 57.290 
 
 .0001 
 
 .00015 
 
 .99985 
 
 89 
 
 
 
 
 15 
 
 .02181 
 
 .97819 
 
 45.840. 
 
 .02182 
 
 45.829 
 
 .0002 
 
 .00024 
 
 .99976 
 
 
 45 
 
 
 30 
 
 .02618 
 
 .97382 
 
 38.202 
 
 .02618 
 
 38.188 
 
 .0003 
 
 .00034 
 
 .99966 
 
 
 30 
 
 
 45 
 
 .03054 
 
 .96946 
 
 32.746 
 
 .03055 
 
 32.730 
 
 .0005 
 
 .00047 
 
 .99953 
 
 
 15 
 
 2 
 
 
 
 .03490 
 
 .96510 
 
 28.654 
 
 .03492 
 
 28.636 
 
 .0006 
 
 .00061 
 
 .99939 
 
 88 
 
 
 
 
 15 
 
 .03926 
 
 .96074 
 
 25.471 
 
 .03929 
 
 25.452 
 
 .0008 
 
 .00077 
 
 .99923 
 
 
 45 
 
 
 30 
 
 .G4362 
 
 .95638 
 
 22.926 
 
 .04366 
 
 22.904 
 
 .0009 
 
 .00095 
 
 .99905 
 
 
 30 
 
 
 45 
 
 .04798 
 
 .95202 
 
 20.843 
 
 .04803 
 
 20.819 
 
 .0011 
 
 .00115 
 
 .99885 
 
 
 15 
 
 3 
 
 
 
 .05234 
 
 .94766 
 
 19.107 
 
 .05241 
 
 19.081 
 
 .0014 
 
 .00137 
 
 .99863 
 
 87 
 
 
 
 
 15 
 
 .05669 
 
 .9433 1 
 
 17.639 
 
 .05678 
 
 17.611 
 
 .0016 
 
 .00161 
 
 .99839 
 
 
 45 
 
 
 30 
 
 .06105 
 
 .93895 
 
 16.380 
 
 .06116 
 
 16.350 
 
 .0019 
 
 .00187 
 
 .9981.3 
 
 
 30 
 
 
 45 
 
 .06540 
 
 .93460 
 
 15.290 
 
 .06554 
 
 15.257 
 
 .0021 
 
 .00214 
 
 .99786 
 
 
 15 
 
 4 
 
 
 
 .06976 
 
 .93024 
 
 14.336 
 
 .06993 
 
 14.301 
 
 .0024 
 
 .00244 
 
 .99756 
 
 80 
 
 
 
 
 15 
 
 .07411 
 
 .92589 
 
 13.494 
 
 .07431 
 
 13.457 
 
 .0028 
 
 .00275 
 
 .99725 
 
 
 45 
 
 
 30 
 
 .07846 
 
 .92154 
 
 12.745 
 
 .07870 
 
 12.706 
 
 .0031 
 
 .00308 
 
 .99692 
 
 
 30 
 
 
 45 
 
 .08281 
 
 .91719 
 
 12.076 
 
 .08309 
 
 12.035 
 
 .0034 
 
 .00343 
 
 .99656 
 
 
 15 
 
 5 
 
 
 
 .08716 
 
 .91284 
 
 11.474 
 
 .08749 
 
 11.430 
 
 .0038 
 
 .00381 
 
 .99619 
 
 85 
 
 
 
 
 15 
 
 .09150 
 
 .90850 
 
 10.929 
 
 .09189 
 
 10.883 
 
 .0042 
 
 .00420 
 
 .99580 
 
 
 45 
 
 
 30 
 
 .09585 
 
 .90415 
 
 10.433 
 
 .09629 
 
 10.385 
 
 .0046 
 
 .00460 
 
 .99540 
 
 
 30 
 
 
 45 
 
 .10019 
 
 .89981 
 
 9.9812 
 
 .10069 
 
 9.9310 
 
 .0051 
 
 .00503 
 
 .99497 
 
 
 15 
 
 6 
 
 
 
 .10453 
 
 .89547 
 
 9.5668 
 
 .10510 
 
 9.5144 
 
 .0055 
 
 .00548 
 
 .99452 
 
 84 
 
 
 
 
 15 
 
 .10887 
 
 .89113 
 
 9.1855 
 
 .10952 
 
 9.1309 
 
 .0060 
 
 .00594 
 
 .99406 
 
 
 45 
 
 
 30 
 
 .11320 
 
 .88680 
 
 8.8337 
 
 .11393 
 
 8.7769 
 
 .0065 
 
 .00643 
 
 .99357 
 
 
 30 
 
 
 45 
 
 .11754 
 
 .88246 
 
 8.5079 
 
 .11836 
 
 8.4490 
 
 .0070 
 
 .00693 
 
 .99307 
 
 
 15 
 
 7 
 
 
 
 .12187 
 
 .87813 
 
 8.2055 
 
 .12278 
 
 8.1443 
 
 .0075 
 
 .00745 
 
 .99255 
 
 83 
 
 
 
 
 15 
 
 .12620 
 
 .87380 
 
 7.9240 
 
 .12722 
 
 7.8606 
 
 .0081 
 
 .00800 
 
 .99200 
 
 
 45 
 
 
 30 
 
 .13053 
 
 .86947 
 
 7.6613 
 
 .13165 
 
 7.5958 
 
 .0086 
 
 .00856 
 
 .99144 
 
 
 30 
 
 
 45 
 
 .13485 
 
 .86515 
 
 7.4156 
 
 .13609 
 
 7.3479 
 
 .0092 
 
 .00913 
 
 .99086 
 
 
 15 
 
 8 
 
 
 
 .13917 
 
 .86083 
 
 7.1853 
 
 .14054 
 
 7.1154 
 
 .0098 
 
 .00973 
 
 .99027 
 
 82 
 
 
 
 
 15 
 
 .14349 
 
 .85651 
 
 6.9690 
 
 .14499 
 
 6.8969 
 
 .0105 
 
 .01035 
 
 .98965 
 
 
 45 
 
 
 30 
 
 .14781 
 
 .85219 
 
 6.7655 
 
 .14945 
 
 6.6912 
 
 .0111 
 
 .01098 
 
 .98902 
 
 
 30 
 
 
 45 
 
 .15212 
 
 .84788 
 
 6.5736 
 
 .15391 
 
 6.4971 
 
 .0118 
 
 .01164 
 
 .98836 
 
 
 15 
 
 9 
 
 
 
 .15643 
 
 .84357 
 
 6.3924 
 
 .15838 
 
 6.3138 
 
 .0125 
 
 .01231 
 
 .98769 
 
 81 
 
 
 
 
 15 
 
 .16074 
 
 .83926 
 
 6.2211 
 
 .16286 
 
 6.1402 
 
 .0132 
 
 .01300 
 
 .98700 
 
 
 45 
 
 
 30 
 
 .16505 
 
 .83495 
 
 6.0589 
 
 .16734 
 
 5.9758 
 
 .0139 
 
 .01371 
 
 .98629 
 
 
 30 
 
 
 45 
 
 .16935 
 
 .83065 
 
 5.9049 
 
 .17183 
 
 '5.8197 
 
 .0147 
 
 .01444 
 
 .98556 
 
 
 15 
 
 10 
 
 
 
 .17365 
 
 .82635 
 
 5.7588 
 
 .17633 
 
 5.6713 
 
 .0154 
 
 .01519 
 
 .98481 
 
 80 
 
 
 
 
 15 
 
 .17794 
 
 .82206 
 
 5.6198 
 
 .18083 
 
 5.5301 
 
 .0162 
 
 .01596 
 
 .98404 
 
 
 45 
 
 
 30 
 
 .18224 
 
 .81776 
 
 5.4874 
 
 .18534 
 
 5.3955 
 
 .0170 
 
 .01675 
 
 .98325 
 
 
 30 
 
 
 45 
 
 .18652 
 
 .81348 
 
 5.3612 
 
 .18986 
 
 5.2672 
 
 .0179 
 
 .01755 
 
 .98245 
 
 
 15 
 
 11 
 
 
 
 .19081 
 
 .80919 
 
 5.2408 
 
 .19438 
 
 5.1446 
 
 .0187 
 
 .01837 
 
 .98163 
 
 79 
 
 
 
 
 15 
 
 .19509 
 
 .80491 
 
 5.1258 
 
 .19891 
 
 5.0273 
 
 .0196 
 
 ,01921 
 
 .98079 
 
 
 45 
 
 
 30 
 
 .19937 
 
 .80063 
 
 5.0158 
 
 .20345 
 
 4.9152 
 
 .0205 
 
 .02008 
 
 .97992 
 
 
 30 
 
 
 45 
 
 .20364 
 
 .79636 
 
 4.9106 
 
 .20800 
 
 4.8077 
 
 .0214 
 
 .02095 
 
 .97905 
 
 
 15 
 
 13 
 
 
 
 .20791 
 
 .79209 
 
 4.8097 
 
 .21256 
 
 4.7046 
 
 .0223 
 
 .02185 
 
 .97815 
 
 78 
 
 
 
 
 15 
 
 .21218 
 
 .78782 
 
 4.7130 
 
 21712 
 
 4.6057 
 
 .0233 
 
 .02277 
 
 .97723 
 
 
 45 
 
 
 30 
 
 .21644 
 
 .78356 
 
 4.6202 
 
 .22169 
 
 4.5107 
 
 .0243 
 
 .02370 
 
 .97630 
 
 
 30 
 
 
 45 
 
 .22070 
 
 .77930 
 
 4.5311 
 
 .22628 
 
 44194 
 
 .0253 
 
 .02466 
 
 .97534 
 
 
 15 
 
 13 
 
 
 
 .22495 
 
 .77505 
 
 4.4454 
 
 .23087 
 
 4.3315 
 
 .0263 
 
 .02563 
 
 .97437 
 
 77 
 
 
 
 
 15 
 
 .22920 
 
 .77080 
 
 4.3630 
 
 .23547 
 
 4.2468 
 
 .0273 
 
 .02662 
 
 .97338 
 
 
 45 
 
 
 30 
 
 .23345 
 
 .76655 
 
 4.2837 
 
 .24008 
 
 4.1653 
 
 .0284 
 
 .02763 
 
 .97237 
 
 
 30 
 
 
 45 
 
 .23769 
 
 .76231 
 
 4.2072 
 
 .24470 
 
 4.0867 
 
 .0295 
 
 .02866 
 
 .97134 
 
 
 15 
 
 14 
 
 
 
 24192 
 
 .75808 
 
 4.1336 
 
 .24933 
 
 4.0108 
 
 .0306 
 
 .02970 
 
 .97030 
 
 76 
 
 
 
 
 15 
 
 .24615 
 
 .75385 
 
 4.0625 
 
 25397 
 
 3.9375 
 
 .0317 
 
 .03077 
 
 .96923 
 
 
 45 
 
 
 30 
 
 .25038 
 
 .74962 
 
 3.9939 
 
 .25862 
 
 3.8667 
 
 .0329 
 
 .03185 
 
 .96815 
 
 
 30 
 
 
 45 
 
 .25460 
 
 .74540 
 
 3.9277 
 
 .26328 
 
 3.7983 
 
 .0341 
 
 .03295 
 
 .96705 
 
 
 15 
 
 15 
 
 
 
 .25882 
 
 .74118 
 
 3.8637 
 
 .26795 
 
 3.7320 
 
 1.0353 
 
 .03407 
 
 .96593 
 
 !> 
 
 
 
 
 
 Co- 
 sine. 
 
 Ver. 
 
 Sin. 
 
 Secant. 
 
 Cotan 
 
 Tang. 
 
 Cosec. 
 
 Co- 
 Vers. 
 
 Sine. 
 
 
 
 M; 
 
 From 75 to 90 read from bottom of table upwards. 
 
NATURAL TRIGONOMETRICAL FUNCTIONS. 
 
 171 
 
 
 
 M. 
 
 Sine. 
 
 Co- 
 Vers. 
 
 Cosec 
 
 Tang 
 
 Cotan 
 
 Secant 
 
 Ver. 
 
 Sin. 
 
 Cosine 
 
 
 I 
 
 15~ 
 
 ~0~ 
 
 .25882 
 
 .74118 
 
 3.8637 
 
 .26795 
 
 3.7320 
 
 1.0353 
 
 .03407 
 
 .96593 
 
 75 
 
 ~ 
 
 
 15 
 
 .26303 
 
 .73697 
 
 3.8018 
 
 .27263 
 
 3.6680 
 
 1.0365 
 
 .03521 
 
 .96479 
 
 
 45 
 
 
 30 
 
 .26724 
 
 .73276 
 
 3.7420 
 
 .27732 
 
 3.6059 
 
 1.0377 
 
 .03637 
 
 .96363 
 
 
 30 
 
 
 45 
 
 .27144 
 
 .72856 
 
 3.6840 
 
 .28203 
 
 3.5457 
 
 1.C390 
 
 .03754 
 
 .96246 
 
 
 15 
 
 16 
 
 
 
 .27564 
 
 .72436 
 
 3.6280 
 
 .28674 
 
 3.4874 
 
 1 .0403 
 
 .03874 
 
 .96126 
 
 74 
 
 
 
 
 15 
 
 .27983 
 
 .72017 
 
 3.5736 
 
 .29147 
 
 3.4308 
 
 1.0416 
 
 .03995 
 
 .96005 
 
 
 45 
 
 
 30 
 
 .28402 
 
 .71598 
 
 3.5209 
 
 .29621 
 
 3.3759 
 
 1.0429 
 
 .04118 
 
 .95882 
 
 
 30 
 
 
 45 
 
 .28820 
 
 .71180 
 
 3.4699 
 
 .30096 
 
 3.3226 
 
 1 .0443 
 
 .04243 
 
 .95757 
 
 
 15 
 
 17 
 
 
 
 .29237 
 
 .70763 
 
 3.4203 
 
 .30573 
 
 3.2709 
 
 1.0457 
 
 .04370 
 
 .95630 
 
 73 
 
 
 
 
 15 
 
 .29654 
 
 .70346 
 
 3.3722 
 
 .31051 
 
 3.2205 
 
 1.0471 
 
 .04498 
 
 .95502 
 
 
 45 
 
 
 30 
 
 .30070 
 
 .69929 
 
 3.3255 
 
 .31530 
 
 3.1716 
 
 1 .0485 
 
 .04628 
 
 .95372 
 
 
 30 
 
 
 45 
 
 .30486 
 
 69514 
 
 3.2801 
 
 .32010 
 
 3.1240 
 
 1.0500 
 
 .04760 
 
 .95240 
 
 
 15 
 
 18 
 
 
 
 .30902 
 
 69098 
 
 3.2361 
 
 .32492 
 
 3.0777 
 
 1.0515 
 
 .04894 
 
 .95106 
 
 72 
 
 
 
 
 15 
 
 31316 
 
 68684 
 
 3.1932 
 
 .32975 
 
 3.0326 
 
 1.0530 
 
 .05030 
 
 .94970 
 
 
 45 
 
 
 30 
 
 31730 
 
 .68270 
 
 3.1515 
 
 .33459 
 
 2.9887 
 
 1.0545 
 
 .05168 
 
 .94832 
 
 
 30 
 
 
 45 
 
 32144 
 
 67856 
 
 3.1110 
 
 .33945 
 
 2.9459 
 
 1 .0560 
 
 .05307 
 
 .94693 
 
 
 15 
 
 19 
 
 
 
 32557 
 
 67443 
 
 3.0715 
 
 34433 
 
 2.9042 
 
 1.0576 
 
 .05448 
 
 .94552 
 
 71 
 
 
 
 
 15 
 
 32969 
 
 67031 
 
 3.0331 
 
 .34921 
 
 2.8636 
 
 1 .0592 
 
 .05591 
 
 .94409 
 
 
 45 
 
 
 30 
 
 33381 
 
 66619 
 
 2.9957 
 
 35412 
 
 2.8239 
 
 1 .0608 
 
 .05736 
 
 .94264 
 
 
 30 
 
 
 45 
 
 33792 
 
 66208 
 
 2.9593 
 
 35904 
 
 2.7852 
 
 1 .0625 
 
 .05882 
 
 .94118 
 
 
 !5 
 
 20 
 
 
 
 34202 
 
 65798 
 
 2.9238 
 
 36397 
 
 2.7475 
 
 1 .0642 
 
 .0603 1 
 
 .93969 
 
 70 
 
 
 
 
 15 
 
 34612 
 
 65388 
 
 2.8892 
 
 36892 
 
 2.7106 
 
 1 .0659 
 
 .06181 
 
 .93819 
 
 
 45 
 
 
 30 
 
 35021 
 
 64979 
 
 2.8554 
 
 37388 
 
 2.6746 
 
 1.0676 
 
 .06333 
 
 .93667 
 
 
 30 
 
 
 45 
 
 35429 
 
 64571 
 
 2.8225 
 
 37887 
 
 2.6395 
 
 1 .0694 
 
 ,.06486 
 
 .93514 
 
 
 1) 
 
 21 
 
 
 
 35837 
 
 64163 
 
 2.7904 
 
 38386 
 
 2.6051 
 
 1.0711 
 
 .06642 
 
 .93358 
 
 69 
 
 
 
 
 15 
 
 36244 
 
 63756 
 
 2.7591 
 
 38888 
 
 2.5715 
 
 1.0729 
 
 .06799 
 
 .93201 
 
 
 45 
 
 
 30 
 
 36650 
 
 63350 
 
 2.7285 
 
 39391 
 
 2.5386 
 
 1.0748 
 
 .06958 
 
 .93042 
 
 
 30 
 
 
 45 
 
 37056 
 
 62944 
 
 2.6986 
 
 39896 
 
 2.5065 
 
 1.0766 
 
 .07119 
 
 .92881 
 
 
 13 
 
 22 
 
 
 
 37461 
 
 62539 
 
 2.6695 
 
 40403 
 
 2.4751 
 
 1.0785 
 
 .07282 
 
 .92718 
 
 68 
 
 
 
 
 15 
 
 37865 
 
 62135 
 
 2.6410 
 
 40911 
 
 2.4443 
 
 1 .0804 
 
 .07446 
 
 .92554 
 
 
 45 
 
 
 30 
 
 38268 
 
 61732 
 
 2.6131 
 
 41421 
 
 2.4142 
 
 1 .0824 
 
 .07612 
 
 .92388 
 
 
 30 
 
 
 45 
 
 38671 
 
 61329 
 
 2.5859 
 
 41933 
 
 2.3847 
 
 1 .0844 
 
 .07780 
 
 .92220 
 
 
 15 
 
 23 
 
 
 
 39073 
 
 60927 
 
 2.5593 
 
 42447 
 
 2.3559 
 
 1 .0864 
 
 .07950 
 
 .92050 
 
 67 
 
 
 
 
 15 
 
 39474 
 
 60526 
 
 2.5333 
 
 42963 
 
 2.3276 
 
 1 .0884 
 
 .08121 
 
 .91879 
 
 
 45 
 
 
 30 
 
 39875 
 
 60125 
 
 2.5078 
 
 43481 
 
 2.2998 
 
 1 .0904 
 
 .08294 
 
 .91706 
 
 
 30 
 
 
 45 
 
 40275 
 
 59725 
 
 2.4829 
 
 44001 
 
 2.2727 
 
 1 .0925 
 
 .08469 
 
 .91531 
 
 
 15 
 
 24 
 
 
 
 40674 
 
 59326 
 
 2.4586 
 
 44523 
 
 2.2460 
 
 1.0946 
 
 .08645 
 
 .91355 
 
 66 
 
 
 
 
 15 
 
 41072 
 
 58928 
 
 2.4348 
 
 45047 
 
 2.2199 
 
 1.0968 
 
 .08824 
 
 .91176 
 
 
 45 
 
 
 30 
 
 41469 
 
 58531 
 
 2.4114 
 
 45573 
 
 2.1943 
 
 1 .0989 
 
 .09004 
 
 .90996 
 
 
 30 
 
 
 45 
 
 41866 
 
 58134 
 
 2.3886 
 
 46101 
 
 2.1692 
 
 1.1011 
 
 .09186 
 
 .90814 
 
 
 15 
 
 25 
 
 
 
 42262 
 
 57738 
 
 2.3662 
 
 46631 
 
 2.1445 
 
 1.1034 
 
 .09369 
 
 .90631 
 
 65 
 
 
 
 
 15 
 
 42657 
 
 57343 
 
 2.3443 
 
 47163 
 
 2.1203 
 
 1.1056 
 
 .09554 
 
 .90446 
 
 
 45 
 
 
 30 
 
 43051 
 
 56949 
 
 2.3228 
 
 47697 
 
 2.0965 
 
 1.1079 
 
 .09741 
 
 .90259 
 
 
 30 
 
 
 45 
 
 43445 
 
 56555 
 
 2.3018 
 
 48234 
 
 2.0732 
 
 1.1102 
 
 .09930 
 
 .90070 
 
 
 15 
 
 26 
 
 
 
 43837 
 
 56163 
 
 2.2812 
 
 48773 
 
 2.0503 
 
 1.1126 
 
 .10121 
 
 .89879 
 
 64 
 
 
 
 
 15 
 
 44229 
 
 55771 
 
 2.2610 
 
 49314 
 
 2.0278 
 
 1.115.0 
 
 .10313 
 
 .89687 
 
 
 45 
 
 
 30 
 
 44620 
 
 55380 
 
 2.2412 
 
 49858 
 
 2.0057 
 
 1.1174 
 
 .10507 
 
 .89493 
 
 
 30 
 
 
 45 
 
 45010 
 
 54990 
 
 2.2217 
 
 50404 
 
 1 .9840 
 
 1.1198 
 
 .10702 
 
 .89298 
 
 
 15 
 
 27 
 
 
 
 45399 
 
 54601 
 
 2.2027 
 
 50952 
 
 1 .9626 
 
 1.1223 
 
 .10899 
 
 .89101 
 
 63 
 
 
 
 
 15 
 
 45787 
 
 54213 
 
 2.1840 
 
 51503 
 
 1.9416 
 
 1.1248 
 
 .11098 
 
 88902 
 
 
 45 
 
 
 30 
 
 46175 
 
 53825 
 
 2.1657 
 
 52057 
 
 1.9210 
 
 1.1274 
 
 .11299 
 
 .88701 
 
 
 30 
 
 
 45 
 
 46561 
 
 53439 
 
 2.1477 
 
 52612 
 
 1 .9007 
 
 1.1300 
 
 .11501 
 
 .88499 
 
 
 15 
 
 23 
 
 
 
 46947 
 
 53053 
 
 2.1300 
 
 53171 
 
 1 .8807 
 
 1.1326 
 
 .11705 
 
 .88295 
 
 62 
 
 
 
 
 15 
 
 47332 
 
 52668 
 
 2.1127 
 
 53732 
 
 1.8611 
 
 1.1352 
 
 .11911 
 
 .88089 
 
 
 45 
 
 
 30 
 
 47716 
 
 52284 
 
 2.0957 
 
 54295 
 
 1.8418 
 
 1.1379 
 
 .12118 
 
 .87882 
 
 
 30 
 
 
 45 
 
 48099 
 
 51901 
 
 2.0790 
 
 54862 
 
 1.8228 
 
 1.1406 
 
 .12327 
 
 .87673 
 
 
 15 
 
 29 
 
 
 
 48481 
 
 51519 
 
 2.0627 
 
 55431 
 
 1 .8040 
 
 1.1433 
 
 .12538 
 
 .87462 
 
 61 
 
 
 
 
 15 
 
 48862 
 
 51138 
 
 2.0466 
 
 56003 
 
 1.7856 
 
 1.1461 
 
 .12750 
 
 .87250 
 
 
 45 
 
 
 30 
 
 49242 
 
 50758 
 
 2.0308 
 
 56577 
 
 1.7675 
 
 1.1490 
 
 .12964 
 
 .87036 
 
 
 30 
 
 
 45 
 
 49622 
 
 .50378 
 
 2.0152 
 
 57155 
 
 1.7496 
 
 1.1518 
 
 .13180 
 
 .86820 
 
 
 15 
 
 30 
 
 
 
 50000 
 
 .50000 
 
 2.0000 
 
 57735 
 
 1.7320 
 
 1.1547 
 
 .13397 
 
 .86603 
 
 60 
 
 _0 
 
 
 
 Co- 
 sine. 
 
 Ver. 
 Sin. 
 
 Se- 
 cant. 
 
 Co tan. 
 
 Tang.. 
 
 Cosec. 
 
 Co- 
 Vers. 
 
 Sine. 
 
 o 
 
 M. 
 
 From 60 to 75 read from bottom of table upwards. 
 
172 NATUKAL TRIGONOMETRICAL FUNCTIONS. 
 
 o 
 
 M. 
 
 Sine. 
 
 Co- 
 Vers. 
 
 Cosec. 
 
 Tang. 
 
 Co tan. 
 
 Secant. 
 
 Ver. 
 Sin. 
 
 Cosine 
 
 
 
 80~ 
 
 
 
 .50000 
 
 .50000 
 
 2.0000 
 
 .57735 
 
 .7320 
 
 .1547 
 
 .13397 
 
 .86603 
 
 60 
 
 
 
 
 15 
 
 .50377 
 
 .49623 
 
 .9850 
 
 .58318 
 
 .7147 
 
 .1576 
 
 .13616 
 
 .86384 
 
 
 45 
 
 
 30 
 
 .50754 
 
 .49246 
 
 .9703 
 
 .58904 
 
 .6977 
 
 .1606 
 
 .13837 
 
 .86163 
 
 
 30 
 
 
 45 
 
 .51129 
 
 .48871 
 
 .9558 
 
 .59494 
 
 .6808 
 
 .1636 
 
 .14059 
 
 .85941 
 
 
 15 
 
 31 
 
 
 
 .51504 
 
 .48496 
 
 .9416 
 
 .60086 
 
 .6643 
 
 .1666 
 
 .14283 
 
 .85717 
 
 59 
 
 
 
 
 15 
 
 .51877 
 
 .48123 
 
 .9276 
 
 .60681 
 
 .6479 
 
 .1697 
 
 .14509 
 
 .85491 
 
 
 45 
 
 
 30 
 
 .52250 
 
 .47750 
 
 .9139 
 
 .61280 
 
 .6319 
 
 .1728 
 
 .14736 
 
 .85264 
 
 
 30 
 
 
 45 
 
 .52621 
 
 .47379 
 
 .9004 
 
 .61882 
 
 .6160 
 
 .1760 
 
 .14965 
 
 .85035 
 
 
 15 
 
 33 
 
 
 
 .52992 
 
 .47008 
 
 .8871 
 
 .62487 
 
 .6003 
 
 .1792 
 
 .15195 
 
 .84805 
 
 58 
 
 
 
 
 15 
 
 .53361 
 
 .46639 
 
 .8740 
 
 .63095 
 
 .5849 
 
 .1824 
 
 .15427 
 
 .84573 
 
 
 45 
 
 
 30 
 
 .53730 
 
 .46270 
 
 .8612 
 
 .63707 
 
 .5697. 
 
 .1857 
 
 .15661 
 
 .84339 
 
 
 30 
 
 
 45 
 
 .54097 
 
 .45903 
 
 .8485 
 
 .64322 
 
 .5547 
 
 .1890 
 
 .15896 
 
 .84104 
 
 
 15 
 
 33 
 
 
 
 .54464 
 
 .45536 
 
 .8361 
 
 .64941 
 
 5399 
 
 .1924 
 
 .16133 
 
 .83867 
 
 67 
 
 
 
 
 15 
 
 .54829 
 
 .45171 
 
 .8238 
 
 .65563 
 
 .5253 
 
 .1958 
 
 .16371 
 
 .83629 
 
 
 45 
 
 
 30 
 
 .55194 
 
 .44806 
 
 .8118 
 
 .66188 
 
 .5108 
 
 .1992 
 
 .16611 
 
 .83389 
 
 
 30 
 
 
 45 
 
 .55557 
 
 .44443 
 
 .7999 
 
 .66818 
 
 .4966 
 
 .2027 
 
 .16853 
 
 .83147 
 
 
 15 
 
 34 
 
 
 
 .55919 
 
 .44081 
 
 .7883 
 
 .67451 
 
 .4826 
 
 .2062 
 
 .17096 
 
 .82904 
 
 56 
 
 
 
 
 15 
 
 .56280 
 
 .43720 
 
 .7768 
 
 .68087 
 
 .4687 
 
 .2098 
 
 .17341 
 
 .82659 
 
 
 45 
 
 
 30 
 
 .56641 
 
 .43359 
 
 .7655 
 
 .68728 
 
 .4550 
 
 .2134 
 
 .17587 
 
 .82413 
 
 
 30 
 
 
 45 
 
 .57000 
 
 .43000 
 
 .7544 
 
 .69372 
 
 .4415 
 
 .2171 
 
 .17835 
 
 .82165 
 
 
 15 
 
 35 
 
 
 
 .57358 
 
 .42642 
 
 .7434 
 
 .70021 
 
 .4281 
 
 .2208 
 
 .18085 
 
 .81915 
 
 55 
 
 
 
 
 15 
 
 .57715 
 
 .42285 
 
 .7327 
 
 .70673 
 
 .4150 
 
 .2245 
 
 .18336 
 
 .81664 
 
 
 45 
 
 
 30 
 
 .58070 
 
 .41930 
 
 .7220 
 
 .71329 
 
 .4019 
 
 .2283 
 
 .18588 
 
 .81412 
 
 
 30 
 
 
 45 
 
 .58425 
 
 .41575 
 
 .7116 
 
 .71990 
 
 .3891 
 
 .2322 
 
 .18843 
 
 .81157 
 
 
 15 
 
 36 
 
 
 
 .58779 
 
 .41221 
 
 .7013 
 
 .72654 
 
 .3764 
 
 .2361 
 
 .19098 
 
 .80902 
 
 54 
 
 
 
 
 15 
 
 .59131 
 
 .40869 
 
 .6912 
 
 .73323 
 
 .3638 
 
 .2400 
 
 .19356 
 
 .80644 
 
 
 45 
 
 
 30 
 
 .59482 
 
 .40518 
 
 .6812 
 
 .73996 
 
 .3514 
 
 .2440 
 
 .19614 
 
 .80386 
 
 
 30 
 
 
 45 
 
 .59832 
 
 .40168 
 
 .6713 
 
 .74673 
 
 .3392 
 
 .2480 
 
 .19875 
 
 .80125 
 
 
 15 
 
 37 
 
 
 
 .60181 
 
 .39819 
 
 .6616 
 
 .75355 
 
 .3270 
 
 .2521 
 
 .20136 
 
 .79864 
 
 53 
 
 
 
 
 15 
 
 .60529 
 
 .39471 
 
 .6521 
 
 .76042 
 
 .3151 
 
 .2563 
 
 .20400 
 
 .79600 
 
 
 45 
 
 
 30 
 
 .60876 
 
 .39124 
 
 .6427 
 
 .76733 
 
 .3032 
 
 .2605 
 
 .20665 
 
 .79335 
 
 
 30 
 
 
 45 
 
 .61222 
 
 .38778 
 
 .6334 
 
 .77428 
 
 .2915 
 
 .2647 
 
 .20931 
 
 .79069 
 
 
 15 
 
 38 
 
 
 
 .61566 
 
 .38434 
 
 .6243 
 
 .78129 
 
 .2799 
 
 .2690 
 
 .21199 
 
 .78801 
 
 52 
 
 
 
 
 15 
 
 .61909 
 
 .38091 
 
 .6153 
 
 78834 
 
 .2685 
 
 .2734 
 
 .21468 
 
 .78532 
 
 
 45 
 
 
 30 
 
 .62251 
 
 .37749 
 
 .6064 
 
 .79543 
 
 .2572 
 
 .2778 
 
 .21739 
 
 .78261 
 
 
 30 
 
 
 45 
 
 .62592 
 
 .37408 
 
 5976 
 
 .80258 
 
 .2460 
 
 2822 
 
 .22012 
 
 .77988 
 
 
 15 
 
 39 
 
 
 
 .62932 
 
 .37068 
 
 .5890 
 
 .80978 
 
 .2349 
 
 .2868 
 
 .22285 
 
 .77715 
 
 51 
 
 
 
 
 15 
 
 .63271 
 
 .36729 
 
 .5805 
 
 .81703 
 
 .2239 
 
 .2913 
 
 .22561 
 
 .77439 
 
 
 45 
 
 
 30 
 
 .63608 
 
 .36392 
 
 .5721 
 
 .82434 
 
 .2131 
 
 .2960 
 
 .22833 
 
 .77162 
 
 
 30 
 
 
 45 
 
 .63944 
 
 .36056 
 
 .5639 
 
 .83169 
 
 .2024 
 
 .3007 
 
 .23116 
 
 .76884 
 
 
 15 
 
 40 
 
 
 
 .64279 
 
 .35721 
 
 .5557 
 
 .83910 
 
 .1918 
 
 .3054 
 
 .23396 
 
 .76604 
 
 50 
 
 
 
 
 15 
 
 .64612 
 
 .35388 
 
 .5477 
 
 .84656 
 
 .1812 
 
 .3102 
 
 .23677 
 
 .76323 
 
 
 45 
 
 
 30 
 
 .64945 
 
 .35055 
 
 .5398 
 
 .85408 
 
 .1708 
 
 .3151 
 
 .23959 
 
 .76041 
 
 
 30 
 
 
 45 
 
 .65276 
 
 .34724 
 
 .5320 
 
 .86165 
 
 .1606 
 
 .3200 
 
 .24244 
 
 .75756 
 
 
 15 
 
 41 
 
 
 
 .65606 
 
 .34394 
 
 .5242 
 
 .86929 
 
 .1504 
 
 .3250 
 
 .24529 
 
 .75471 
 
 49 
 
 
 
 
 15 
 
 .65935 
 
 .34065 
 
 .5166 
 
 .87698 
 
 .1403 
 
 .3301 
 
 .24816 
 
 .75184 
 
 
 45 
 
 
 30 
 
 .66262 
 
 .33738 
 
 .5092 
 
 .88472 
 
 .1303 
 
 .3352 
 
 .25104 
 
 .74896 
 
 
 30 
 
 
 45 
 
 .66588 
 
 .33412 
 
 .5018 
 
 .89253 
 
 .1204 
 
 .3404 
 
 .25394 
 
 .74606 
 
 
 15 
 
 42 
 
 
 
 .66913 
 
 .33087 
 
 .4945 
 
 .90040 
 
 .1106 
 
 .3456 
 
 .25686 
 
 .74314 
 
 48 
 
 
 
 
 15 
 
 .67237 
 
 .32763 
 
 .4873 
 
 .90834 
 
 .1009 
 
 .3509 
 
 .25978 
 
 .74022 
 
 
 45 
 
 
 30 
 
 .67559 
 
 .32441 
 
 .4802 
 
 .91633 
 
 .0913 
 
 .3563 
 
 .26272 
 
 .73728 
 
 
 30 
 
 
 45 
 
 .67880 
 
 .32120 
 
 .4732 
 
 .92439 
 
 .0818 
 
 .3618 
 
 .26568 
 
 .73432 
 
 
 15 
 
 43 
 
 
 
 .68200 
 
 .31800 
 
 .4663 
 
 .93251 
 
 .0724 
 
 .3673 
 
 .26865 
 
 .73135 
 
 47 
 
 
 
 
 15 
 
 .68518 
 
 .31482 
 
 .4595 
 
 .94071 
 
 .0630 
 
 .3729 
 
 .27163 
 
 .72837 
 
 
 45 
 
 
 30 
 
 .68835 
 
 .31165 
 
 .4527 
 
 .94896 
 
 .0538 
 
 .3786 
 
 .27463 
 
 .72537 
 
 
 30 
 
 
 45 
 
 .69151 
 
 .30849 
 
 .4461 
 
 .95729 
 
 .0446 
 
 .3843 
 
 .27764 
 
 .72236 
 
 
 15 
 
 44 
 
 
 
 .69466 
 
 .30534 
 
 .4396 
 
 .96569 
 
 .0355 
 
 .3902 
 
 .28066 
 
 .71934 
 
 46 
 
 
 
 
 15 
 
 .69779 
 
 .30221 
 
 .4331 
 
 .97416 
 
 .0265 
 
 .3961 
 
 .28370 
 
 .71630 
 
 
 45 
 
 
 30 
 
 .70091 
 
 .29909 
 
 .4267 
 
 .98270 
 
 .0176 
 
 .4020 
 
 .28675 
 
 .71325 
 
 
 30 
 
 
 45 
 
 .70401 
 
 .29599 
 
 .4204 
 
 .99131 
 
 .0088 
 
 .4081 
 
 .28981 
 
 .71019 
 
 
 15 
 
 45 
 
 
 
 .70711 
 
 .29289 
 
 .4142 
 
 1 .0000 
 
 .0000 
 
 .4142 
 
 .29289 
 
 .70711 
 
 45 
 
 
 
 
 
 Cosine 
 
 Ver. 
 Sin. 
 
 Se- 
 cant. 
 
 Cotan. 
 
 Tang. 
 
 Cosec. 
 
 Co- 
 Vers. 
 
 Sine. 
 
 
 
 M. 
 
 From 45 to 60 read from bottom of table upwards. 
 
SPECIFIC GRAVITY. 
 
 173 
 
 MATERIALS. 
 
 THE CHEMICAL ELEMENTS. 
 
 Common Elements (42). 
 
 11 
 
 
 
 
 12 
 
 
 
 
 V 
 
 
 OrC 
 
 
 Name. 
 
 |-s 
 
 IJ 
 
 Name. 
 
 1^ 
 
 fl 
 
 Name. 
 
 J't? 
 
 Al 
 
 Sb 
 
 Aluminum 
 Antimony 
 
 27.1 
 120.2 
 
 F 
 Au 
 
 Fluorine 
 Gold 
 
 19. 
 197.2 
 
 Pd 
 P 
 
 Palladium 
 Phosphorus 
 
 106.7 
 31. 
 
 As 
 
 Arsenic 
 
 75.0 
 
 H 
 
 Hydrogen 
 
 1.01 
 
 Pt 
 
 Platinum 
 
 195.2 
 
 Ba 
 
 Barium 
 
 137.4 
 
 I 
 
 Iodine 
 
 126.9 
 
 K 
 
 Potassium 
 
 39.1 
 
 Bi 
 
 Bismuth 
 
 208.0 
 
 Ir 
 
 Iridium 
 
 193.1 
 
 Si 
 
 Silicon 
 
 28.3 
 
 B 
 
 Boron 
 
 11.0 
 
 Fe 
 
 Iron 
 
 55.84 
 
 Ag 
 
 Silver 
 
 107.9 
 
 Br 
 
 Bromine 
 
 79.9 
 
 Pb 
 
 Lead 
 
 207.2 
 
 Na 
 
 Sodium 
 
 23. 
 
 Cd 
 
 Cadmium 
 
 112.4 
 
 Li 
 
 Lithium 
 
 6.94 
 
 Sr 
 
 Strontium 
 
 87.6 
 
 Ca 
 
 Calcium 
 
 40.1 
 
 Mg 
 
 Magnesium 
 
 24.34 
 
 S 
 
 Sulphur 
 
 32.1 
 
 C 
 
 Carbon 
 
 12. 
 
 Mn 
 
 Manganese 
 
 54.9 
 
 Sn 
 
 Tin 
 
 119. 
 
 Cl 
 
 Chlorine 
 
 35.5 
 
 Hg 
 
 Mercury 
 
 200.6 
 
 Ti 
 
 Titanium 
 
 48.1 
 
 Cr 
 
 Chromium 
 
 52.0 
 
 Ni 
 
 Nickel 
 
 58.7 
 
 W 
 
 Tungsten 
 
 184.0 
 
 Co 
 
 Cobalt 
 
 59. 
 
 N 
 
 Nitrogen 
 
 14.01 
 
 Va 
 
 Vanadium 
 
 51.0 
 
 Cu 
 
 Copper 
 
 63.6 
 
 
 
 Oxygen 
 
 16. 
 
 Zn 1 
 
 Zinc 
 
 65.4 
 
 The atomic weights of many of the elements vary in the decimal 
 place as given by different authorities. The above are the most recent 
 values referred to O = 16 and H = 1.008. When H is taken as 1, 
 O = 15.879, and the other figures are diminished proportionately. 
 
 Rare Elements (37). 
 
 Beryllium, Be. Indium, In. Ruthenium, Ru. Thallium, Tl. 
 
 Caesium, Cs. Lanthanum, La. Samarium, Sm. Thorium, Th. 
 
 Cerium, Ce. Molybdenum, Mo. Scandium, Sc. Uranium, U. 
 
 Erbium, Er. Niobium, Nb. Selenium, Se. Ytterbium, Yr. 
 
 Gallium, Ga. Osmium, Os. Tantalum, Ta. Yttrium, Y. 
 
 Germanium, Ge. Rhodium, R. Tellurium, Te. Zirconium, Zr. 
 
 Glucinum, G. Rubidium, Rb. Terbium, Tb. 
 
 Elements recently discovered (1895-1900): Argon, A, 39.9; Krypton 
 Kr, 81.8; Neon, Ne, 20.0; Xenon, X, 128.0; constituents of the atmos- 
 phere, which contains about 1 per cent by volume of Argon, and very 
 small quantities of the others. Helium, He, 4.0; Radium, Ra, 225.0; 
 Gadolinium, Gd, 156.0; Neodymium. Nd, 143.6; Praesodymium, Pr, 
 110.5; Thulium, Tm, 171.0. 
 
 SPECIFIC GRAVITY. 
 
 The specific gravity of a substance is its weight as compared with the 
 weight of an equal bulk of pure water. In the metric system it is the 
 weight in grammes per cubic centimeter. 
 
 To find the specific gravity of a substance; 
 
 W = weight of body in air ; w = weight of body submerged in water. 
 
 Specific gravity = 
 
 W 
 
 W -w' 
 
 If the substance be lighter than the water, sink it by means of a 
 heavier substance, and deduct the weight of the heavier substance. 
 
 Specific gravity determinations are usually referred to the standard of 
 the weight of water at 62 F., 62.355 Ib. per cubic foot. Some expert- 
 
174 
 
 MATERIALS. 
 
 menters have used 60 F. as the standard, and others 32 and 39.1 F. 
 There is no general agreement. 
 
 Given sp. gr. referred to water at 39.1 F., to reduce it to the standard 
 of 62 F. multiply it by 1.00112. 
 
 Given sp. gr. referred to water at 62 F., to find weight per cubic foot 
 multiply by 62.355. Given weight per cubic foot, to find sp. gr. multiply 
 by 0.016037. Given sp. gr., to find weight per cubic inch multiply by 
 
 Weight and Specific Gravity of Metals. 
 
 
 Specific Gravity. 
 Range accord- 
 ing to 
 several 
 Authorities. 
 
 Specific Grav- 
 ity. Approx. 
 Mean Value, 
 used in 
 . Calculation 
 of Weight. 
 
 Weight 
 per 
 Cubic 
 Foot, 
 Ibs. 
 
 Weight 
 per 
 Cubic 
 Inch, 
 Ibs. 
 
 
 2.56 to 2.71 
 
 2.67 
 
 166.5 
 
 00963 
 
 Antimony 
 
 6.66 to 6.86 
 
 6 76 
 
 421 6 
 
 02439 
 
 Bismuth 
 
 9.74 to 9.90 
 
 9.82 
 
 612.4 
 
 0.3544 
 
 Brass: Copper + Zinc-K 
 80 20 
 70 30L . 
 60 40 
 50 50* 
 
 Cadmium . . 
 
 7.8 to 8.6 
 
 8.52 to 8.96 
 8.6 to 8.7 
 
 {8.60 
 8.40 
 8.36 
 8.20 
 
 8.853 
 865 
 
 536.3 
 523.8 
 521.3 
 511.4 
 
 552. 
 539 
 
 0.3103 
 0.3031 
 0.3017 
 0.2959 
 
 0.3195 
 03121 
 
 Calcium 
 
 1.58 
 
 1.58 
 
 98.5 
 
 0.0570 
 
 Ch rom i um 
 
 50 
 
 5 
 
 311 8 
 
 1804 
 
 Cobalt 
 
 85 to 8 6 
 
 8.55 
 
 533 1 
 
 3085 
 
 
 19.245 to 19.361 
 
 19.258 
 
 1200.9 
 
 06949 
 
 Copper . . . 
 
 8.69 to 8 92 
 
 8853 
 
 552 
 
 03195 
 
 Iridium 
 
 22.38 to 23. 
 
 22.38 
 
 1396 
 
 08076 
 
 Iron Cast 
 
 6 85 to 7 48 
 
 7218 
 
 450 
 
 02604 
 
 Iron Wrought 
 
 7.4 to 7.9 
 
 7 70 
 
 480 
 
 02779 
 
 Lead 
 
 11.07 to 11.44 
 
 11.38 
 
 709.7 
 
 04106 
 
 Manganese ... 
 
 7. to 8. 
 
 8. 
 
 499 
 
 02887 
 
 Magnesium. . , 
 
 1 .69 to 1 .75 
 
 1.75 
 
 109. 
 
 0.0641 
 
 j 32 
 Mercury < 60 
 1212 
 Nickel 
 
 13.61 
 13.58 
 13.37 to 13.38 
 8.279 to 8.93 
 
 13.61 
 13.58 
 13.38 
 8.8 
 
 848.6 
 846.8 
 834.4 
 548 7 
 
 0.4908 
 0.49 1 1 
 0.4828 
 03175 
 
 Platinum 
 
 20.33 to 22.07 
 
 21.5 
 
 1347.0 
 
 07758 
 
 
 0.865 
 
 0.865 
 
 53.9 
 
 0.0312 
 
 Silver 
 
 10.474 to 10.511 
 
 10.505 
 
 655.1 
 
 03791 
 
 Sodium 
 
 0.97 
 
 0.97 
 
 60.5 
 
 0.0350 
 
 Steel... 
 
 7 69* to 7.932t 
 
 7.854 
 
 4896 
 
 02834 
 
 Tin 
 
 7.291 to 7.409 
 
 7.350 
 
 458.3 
 
 0.2652 
 
 Titanium . . 
 
 5.3 
 
 5.3 
 
 330 5 
 
 1913 
 
 
 17. to 17.6 
 
 17.3 
 
 1078.7 
 
 0.6243 
 
 Zinc. . . 
 
 6.86 to 7.20 
 
 7.00 
 
 436.5 
 
 0.2526 
 
 * Hard and burned. 
 
 t Very pure and soft. The sp. gr. decreases as the carbon is increased. 
 
 In the first column of figures the lowest are usually those of cast metals, 
 which are more or less porous; the highest are of metals finely rolled or 
 drawn into wire. 
 
 The weight of 1 cu. cm. of mercury at C. is 13.59545 grams (Thiessen). 
 Taking atmosphere = 29.92 in. of mercury at 32 F. = 14.6963 Ib. per 
 sq. in., 1 cu. im of mercury = 0.49117 Ib. Taking water at 0.036085 Ib. 
 per cu. in. at 62 F., the specific gravity of mercury is at 32 F. 13.611. 
 
SPECIFIC GKAVITY. 
 
 175 
 
 Specific Gravity of Liquids at 60 F. 
 
 A 'r\ AT *' tV 
 
 I 200 
 
 Naphtha 
 
 0.670 to 0.737 
 
 " Nitric 
 
 1.54 
 
 
 0.93 
 
 " Sulphuric 
 
 1 849 
 
 " Olive 
 
 0.92 
 
 Alcohol pure 
 
 0.794 
 
 " Palm 
 
 0.97 
 
 " 95 per cent . . 
 " 50 per cent 
 
 0.816 
 0.934 
 
 ' Petroleum, crude. 
 " Rape 
 
 0.78 to 1.00 
 0.92 
 
 Ammonia 27 9 per ct 
 
 0.891 
 
 * Turpentine 
 
 0.86 
 
 Bromine 
 
 2.97 
 
 " Whale 
 
 0.92 
 
 Carbon disulphide 
 
 1.26 
 
 Tar 
 
 1.0 
 
 Ether Sulphuric 
 
 72 
 
 Vinegar 
 
 1.08 
 
 Gasoline 
 
 660 to 0.670 
 
 Water 
 
 1.0 
 
 Kerosene. . 
 
 0.753 to 0.864 
 
 Water, Sea ... 
 
 1.026 to 1.03 
 
 Compression of the following Fluids under a Pressure of 15 Ib. 
 per Square Inch. 
 
 Water 0.00004663 I Ether 0.00006158 
 
 Alcohol 0.0000216 | Mercury 0.00000265 
 
 The Hydrometer. 
 
 The hydrometer is an instrument for determining the density of 
 liquids. It is usually made of glass, and consists of three parts: (1) 
 the upper part, a graduated stem or fine tube of uniform diameter; 
 (2) a bulb, or enlargement of the tube, containing air, and (3) a small 
 bulb at the bottom, containing shot or mercury which causes the in- 
 strument to float in a vertical position. The graduations are figures 
 representing either specific gravities, or the numbers of an arbitrary scale, 
 as in Baume's, Twaddell's, Beck's, and other hydrometers. 
 
 There is a tendency to discard all hydrometers with arbitrary scales 
 and to use only those which read in terms of the specific gravity 
 directly. 
 
 Baume's Hydrometer and Specific Gravities Compared. 
 
 5 Heavy liquids, Sp. gr. 
 l Light liquids, Sp. gr. 
 
 145 -r (145 -deg. Be.) 
 140 -r (130 + deg. Be.) 
 
 Degrees 
 Baume* 
 
 Liquids 
 Heavier 
 than 
 Water, 
 Sp. Gr. 
 
 Liquids 
 Lighter 
 than 
 Water, 
 Sp. Gr. 
 
 Degrees 
 Baume* 
 
 Liquids 
 Heavier 
 than 
 Water, 
 Sp. Gr 
 
 Liquids 
 Lighter 
 than 
 Water, 
 Sp. Gr. 
 
 Degrees 
 Baume* 
 
 Liquids 
 Heavier 
 than 
 Water, 
 Sp. Gr. 
 
 Liquids 
 
 Htr 
 
 Water, 
 Sp. Gr. 
 
 00 
 
 000 
 
 
 190 
 
 151 
 
 0940 
 
 380 
 
 355 
 
 0833 
 
 1.0 
 
 .007 
 
 
 20.0 
 
 .160 
 
 0.933 
 
 39.0 
 
 .368 
 
 0.828 
 
 2.0 
 3.0 
 
 .014 
 021 
 
 
 21.0 
 22.0 
 
 .169 
 .179 
 
 0.927 
 0.921 
 
 40.0 
 41 
 
 .381 
 394 
 
 0.824 
 819 
 
 4.0 
 
 .028 
 
 
 23.0 
 
 189 
 
 0915 
 
 42 
 
 408 
 
 814 
 
 5.0 
 
 .036 
 
 
 24.0 
 
 .198 
 
 0.909 
 
 44.0 
 
 .436 
 
 0805 
 
 6.0 
 7.0 
 
 .043 
 .051 
 
 
 25.0 
 26.0 
 
 .208 
 .219 
 
 0.903 
 0.897 
 
 46.0 
 48.0 
 
 .465 
 .495 
 
 0.796 
 0.787 
 
 8.0 
 9.0 
 
 .058 
 .066 
 
 
 27.0 
 28.0 
 
 .229 
 .239 
 
 0.892 
 0.886 
 
 50.0 
 52.0 
 
 .526 
 .559 
 
 0.778 
 0.769 
 
 10.0 
 11.0 
 12.0 
 13.0 
 14.0 
 15.0 
 16.0 
 17.0 
 
 .074 
 .082 
 .090 
 .099 
 .107 
 .115 
 .124 
 .133 
 
 1.000 
 0.993 
 0.986 
 0.979 
 0.972 
 0.966 
 0.959 
 0.952 
 
 29.0 
 30.0 
 31.0 
 32.0 
 330 
 34.0 
 35.0 
 36.0 
 
 .250 
 .261 
 .272 
 .283 
 .295 
 .306 
 1.318 
 1.330 
 
 0.881 
 0.875 
 0.870 
 0.864 
 0,859 
 0.854 
 0.849 
 0.843 
 
 54.0 
 56.0 
 58.0 
 60.0 
 65.0 
 70.0 
 75.0 
 
 .593 
 .629 
 .667 
 .706 
 .813 
 .933 
 2.071 
 
 0761 
 0.753 
 0.745 
 0.737 
 0.718 
 0.700 
 0.683 
 
 18.0 
 
 142 
 
 0946 
 
 370 
 
 1 343 
 
 0838 
 
 
 
 
 
 
 
 
 
 
 
 
 
170 
 
 MATERIALS. 
 
 Specific Gravity and Weight of Gases at Atmospheric Pressure 
 and 33 F. 
 
 (For other temperatures and pressures see Physical Properties of Gases.) 
 
 
 Density, 
 Air => 1. 
 
 Density, 
 H = f. 
 
 Grammes 
 per Litre. 
 
 Lbs. per 
 Cu. Ft. 
 
 Cubic Ft. 
 per Lb. 
 
 Air 
 
 1 .0000 
 
 1 4.444 
 
 .2931 
 
 0.080728 
 
 12388 
 
 
 1.1052 
 
 15.963 
 
 .4291 
 
 0.08921 
 
 11 209 
 
 Hydrogen, H 
 
 0.0692 
 
 1 000 
 
 0.0895 
 
 0.00559 
 
 1 78 93 1 
 
 Nitrogen, N 
 
 0.9701 
 
 14.012 
 
 .2544 
 
 0.07831 
 
 12 770 
 
 Carbon monoxide, CO . 
 Carbon dioxide, CO2 . . 
 Metha ne,marsh-gas, CtU 
 Ethyl ene C2EU 
 
 0.9671 
 1.5197 
 0.5530 
 0.9674 
 
 13.968 
 21.950 
 7.987 
 13.973 
 
 .2505 
 .9650 
 0.7150 
 .2510 
 
 0.07807 
 0.12267 
 C.04464 
 07809 
 
 12.810 
 8.152 
 22.429 
 12 805 
 
 
 08982 
 
 12.973 
 
 .1614 
 
 0.07251 
 
 13.792 
 
 
 0.5889 
 
 8.506 
 
 0.7615 
 
 04754 
 
 21 036 
 
 Water vapor, HtO . . , . 
 Sulphur dioxide, SO 2 . . 
 
 0.6218 
 2.213 
 
 8.981 
 31.965 
 
 0.8041 
 2.862 
 
 0.05C20 
 0.1787 
 
 19.922 
 5.597 
 
 Specific Gravity and Weight of Wood. 
 
 
 Specific 
 Gravity. 
 
 rii 
 
 Sl| 
 
 QjOPn 
 
 
 
 Specific 
 Gravity, 
 
 &4 
 %as 
 
 ! 
 
 uoPk 
 
 Alder 
 
 Avge. 
 0.56 to 0.80 0.68 
 0.73 to 0.79 0.76 
 0.60 to 0.84 0.72 
 0.31 to 0.40 0.35 
 0.62 to 0.85 0.73 
 0.56 to 0.74 0.65 
 0.91 to 1.33 1.12 
 0.49 to 0.75 0.62 
 0.61 to 0.72 0.66 
 0.46 to 0.66 0.56 
 0.24 0.24 
 0.41 to 0.66 0.53 
 0.76 0.76 
 1.13 to 1.33 1.23 
 0.55 to 0.78 0.61 
 0.48 to 0.70 0.59 
 0.84 to 1 .00 0.92 
 0.59 0.59 
 0.36 to 0.41 0.38 
 0.69 to 0.94 0.77 
 0.76 0.76 
 
 42 
 47 
 45 
 22 
 46 
 41 
 70 
 39 
 41 
 35 
 15 
 33 
 47 
 76 
 33 
 37 
 57 
 37 
 24 
 48 
 47 
 
 Hornbeam. . 
 Juniper .... 
 Larch 
 Lignum vita? 
 Linden . . . 
 Locust 
 Mahogany. . 
 Maple 
 
 Avge. 
 0.76 0.76 
 0.56 0.56 
 0.56 0.56 
 0.65 to 1.33 1.00 
 0.604 
 0.728 
 0.56 to 1.06 0.81 
 0.57 to 0.79 0.68 
 0.56 to 0.90 0.73 
 0.96 to 1.26 1.11 
 0.69 to 0.86 0.77 
 0.73 to 0.75 0.74 
 0.35 to 0.55 0.45 
 0.46 to 0.76 0.61 
 0.38 to 0.58 0.48 
 0.40 to 0.50 0.45 
 0.59 to 0.62 0.60 
 0.66 to 0.98 0.82 
 0.50 to 0.67 0.58 
 0.49 to 0.59 0.54 
 
 47 
 35 
 35 
 62 
 37 
 46 
 51 
 42 
 46 
 69 
 48 
 46 
 28 
 38 
 30 
 28 
 37 
 51 
 36 
 34 
 
 
 Ash 
 
 Bamboo .... 
 Beech 
 
 Birch 
 Box 
 
 Cedar. 
 
 Cherry 
 Chestnut. . . . 
 Cork 
 
 Mulberry. . . 
 Oak, Live . . 
 Oak, White. 
 Oak, Red . . 
 Pine, White 
 " Yellow 
 Poplar 
 Spruce 
 Sycamore . . 
 Teak 
 
 Cypress 
 Dogwood . . . 
 Ebony. . 
 
 Elm. . . 
 
 Fir 
 
 Gum 
 
 Hackmatack 
 Hemlock. . . . 
 Hickory 
 Holly. . 
 
 Walnut 
 Willow 
 
 
OP THE USEFUL METALS. 
 
 177 
 
 Weight and Specific Gravity of Stones, Brick, Cement, etc. 
 Water = 1.00.) 
 
 (Pure 
 
 
 Lb. per Cu. Ft. 
 
 Sp. Gr. 
 
 Ashes 
 
 43 
 
 
 
 87 
 
 1.39 
 
 Brick, Soft 
 
 100 
 
 1 .6 
 
 
 112 
 
 1.79 
 
 Hard 
 
 125 
 
 2.0 
 
 " Pressed 
 
 135 
 
 2.16 
 
 " Fire 
 
 140 to 150 
 
 2. 24 to 2 4 
 
 Sand-lime 
 
 136 
 
 2.18 
 
 Brickwork in mortar 
 
 100 
 
 1 6 
 
 " cement . . % 
 
 112 
 
 1.79 
 
 Cement, American, natural 
 
 
 28 to 3 2 
 
 " Portland 
 
 
 3 . 05 to 3 15 
 
 loose 
 
 92 
 
 
 " in barrel 
 
 115 
 
 
 Clay 
 
 120 to 150 
 
 ' 1 .92 to 2.4 
 
 Concrete 
 
 120 to 155 
 
 1 92 to 2 48 
 
 Earth, loose . ... 
 
 72 to 80 
 
 1 . 1 5 to 1 28 
 
 rammed 
 
 90 to 110 
 
 1 44 to 1 76 
 
 Emery . 
 
 250 
 
 4. 
 
 Glass 
 
 1 56 to 1 72 
 
 25 to 2 75 
 
 flint 
 
 180 to 196 
 
 2.88 to 3 14 
 
 Gneiss 1 
 
 160 to 170 
 
 2. 56 to 2.72 
 
 Granite f 
 Gravel 
 
 100 to 120 
 
 1.6 to 1.92 
 
 Gypsum 
 
 130 to 150 
 
 2 08 to 2 4 
 
 Hornblende 
 
 200 to 220 
 
 3.2 to 3. 52 
 
 Ice . 
 
 55 to 57 
 
 88 to 92 
 
 Lime, quick, in bulk 
 
 50 to 60 
 
 0.8 to 0.96 
 
 Limestone 
 
 140 to 185 
 
 2 30 to 2 90 
 
 Magnesia, Carbonate 
 
 150 
 
 2.4 
 
 Marble 
 
 160 to 180 
 
 2 56 to 2 88 
 
 Masonry, dry rubble 
 
 140 to 160 
 
 2.24 to 2.56 
 
 " dressed 
 
 140 to 180 
 
 2 24 to 2 88 
 
 Mica 
 
 175 
 
 2.80 
 
 Mortar 
 
 90 to 100 
 
 44 to 1 6 
 
 Mud, soft flowing 
 
 104 to 120 
 
 .67 to 1 .92 
 
 Pitch 
 
 72 
 
 15 
 
 Plaster of Paris 
 
 93 to 113 
 
 .50 to T.81 
 
 Quartz 
 
 165 
 
 2.64 
 
 Sand . . .... 
 
 90 to 110 
 
 44 to 1 76 
 
 " wet 
 
 118 to 129 
 
 .89 to 2. 07 
 
 Sandstone .... 
 
 140 to 150 
 
 2 24 to 2.4 
 
 Slate 
 
 170 to 180 
 
 2.72 to 2.88 
 
 Soapstone ... 
 
 166 to 175 
 
 2 65 to 2.8 
 
 Stone, various 
 
 135 to 200 
 
 2.16to3.4 
 
 " crushed 
 
 100 
 
 
 Tile 
 
 1 10 to 120 
 
 1 76 to 1 92 
 
 Trap Rock 
 
 1 70 to 200 
 
 2.72 to 3. 4 
 
 PROPERTIES OF THE USEFUL METALS. 
 
 Aluminum, AI. Atomic weight 27.1. Specific gravity 2.6 to 2.7. 
 The lightest of all the useful metals except magnesium. A soft, ductile, 
 malleable metal, of a white color, approaching silver, but with a bluish 
 cast. Very non-corrosive. Tenacity about one-third that of wrought 
 iron. Formerly a rare metal, but since 1890 its production and use 
 have greatly increased on account of the discovery of cheap processes 
 for reducing it from the ore. Melts at 1215 F. For further description 
 see Aluminum, under Strength of Materials, page 380. 
 
 Antimony (Stibium), Sb. At. wt. 120.2 Sp. gr. 6.7 to 6.8. A 
 brittle metal of a bluish-white color and highly crystaline or laminated 
 structure. Melts at 842 F. Heated in the open air it burns with a 
 
178 MATERIALS. 
 
 bluish-white flame. Its chief use is for the manufacture of certain alloys, j 
 as type-metal (antimony 1, lead 4), britannia (antimony 1, tin 9), and 4 
 various anti-friction metals (see Alloys). Cubical expansion by heat 3 
 from 32 to 212 F., 0.0070. Specific heat 0.050. 
 
 Bismuth, Bi. At. wt. 208.5. Bismuth is of a peculiar light reddish I 
 color, highly crystalline, and so brittle that it can readily be pulverized, j 
 It melts at 510 F., and boils at about 2300 F. Sp. gr. 9.823 at 54 F., ] 
 and 10.055 just above the melting-point. Specific heat about 0.0301 at j 
 ordinary temperatures. Coefficient of cubical expansion from 32 to i 
 212, 0.0040. Conductivity for heat about 1/56 and for electricity only .] 
 about i/so of that of silver. Its tensile strength is about 6400 IDS. per | 
 square inch. Bismuth expands in cooling, and Tribe has shown that } 
 this expansion does not take place until after solidification. Bismuth is \ 
 the most diamagnetic element known, a sphere of it being repelled by a ; 
 strong magnet. 
 
 Cadmium, Cd. At. wt. 112.4. Sp. gr. 8.6 to 8.7. A bluish-white 
 metal, lustrous, with a fibrous fracture. Melts below 500 F. and vola- 
 tilizes at about 680 F. It is used as an ingredient, in some fusible alloys 
 with lead, tin, and bismuth. Cubical expansion from 32 to 212 F., 
 0.0094. 
 
 Copper, Cu. At. wt. 63.6. Sp. gr. 8.81 to 8.95. Fuses at about ; 
 1930^ F. Distinguished from all other metals by its reddish color. Very 
 ductile and malleable, and its tenacity is next to iron. Tensile strength 
 20,000 to 30,000 Ibs. per square inch. Heat conductivity 73.6% of that i 
 of silver, and superior to that of other metals. Electric conductivity 
 equal to that of gold and silver. Expansion by heat from 32 to 212 F., 
 0.0051 of its volume. Specific heat 0.093. (See Copper under Strength 
 of Materials; also Alloys.) 
 
 Gold (Aurum), Au. At. wt. 197.2. Sp. gr., when pure and pressed 
 in a die, 19.34. Melts at about 1915 F. The most malleable and duc- 
 tile of all metals. One ounce Troy may be beaten so as to cover 160 sq. 
 ft. of surface. The average thickness of gold-leaf is 1/282000 of an inch, i 
 or 100 sq. ft. per ounce. One grain may be drawn into a wire 500 ft. in 
 length. The ductility is destroyed by the presence of 1/2000 part of lead, 
 bismuth, or antimony. Gold is hardened by the addition of silver or of 
 copper. U. S. gold coin is 90 parts gold and 10 parts alloy, which is 
 chiefly copper with a little silver. By jewelers the fineness of gold is 
 expressed in carats, pure gold being 24 carats, three-fourths fine 18 
 carats, etc. 
 
 Iridium, Ir. Iridium is one of the rarer metals. It has a white 
 lustre, resembling that of steel; its hardness is about equal to that of the 
 ruby; in the C9ld it is quite brittle, but at white heat it is somewhat 
 malleable. It is one of the heaviest of metals, having a specific gravity 
 of 22.38. It is extremely infusible and almost absolutely inoxidizable. 
 
 For uses of iridium, methods of manufacturing it, etc., see paper by 
 W. L. Dudley on the "Iridium Industry," Trans. A. I. M. E., 1884. 
 
 Iron (Ferrum),Fe. At. wt. 55.9. Sp. gr.: Cast, 6.85 to 7.48; Wrought, 
 7.4 to 7.9. Pure iron is extremely infusible, its melting point being above 
 3000 F., but its fusibility increases with the addition of carbon, cast 
 iron fusing ab9ut 2500 F. Conductivity for heat 11.9, and for electricity 
 12 to 14.8, silver being 100. Expansion in bulk by heat: cast iron 
 0.0033, and wrought iron 0.0035, from 32 to 212 F. Specific, heat: 
 cast iron 0.1298, wrought iron 0.1138, steel 0.1165. Cast iron exposed 
 to continued heat becomes permanently expanded 1 1/2 to 3 per cent of its 
 length. Grate-bars should therefore be allowed about 4 per cent play. 
 (For other properties see Iron and Steel under Strength of Materials.) 
 
 Lead (Plumbum), Pb. At. wt 206.9. Sp. gr. 11.07 to 11.44 by dif- 
 ferent authorities. Melts at about 625 F., softens and becomes pasty 
 at about 617 F. If broken by a sudden blow when just below the 
 melting-point it is quite brittle and the fracture appears crystalline. 
 Lead is very malleable and ductile, but its tenacity is such that it can 
 be drawn into wire with great difficulty. Tensile strength, 1600 to 
 2400 Ibs. per square inch. Its elasticity is very low, and the metal 
 flows under very slight strain. Lead dissolves to some extent in pure 
 water, but water containing carbonates or sulphates forms over vt 
 film of insoluble salt which prevents further action. 
 
PROPERTIES OF THE USEFUL METALS. 179 
 
 Magnesium, Mg. At. wt. 24.36. Sp. gr. 1.69 to 1.75. Silver-white, 
 brilliant, malleable, and ductile. It is one of the lightest of metals, 
 weighing only about tvyo thirds as much as aluminum. In the form of 
 filings, wire, 9r thin ribbons it is highly combustible, burning with a 
 light of dazzling brilliancy, useful for signal-lights and for flash-lights 
 for photographers. It is nearly non-corrosive, a thin film of carbonate 
 of magnesia forming on exposure to damp air, which protects it from 
 further corrosion. It may be alloyed with aluminum, 5 per cent Mg 
 added to Al giving about as much increase of strength and hardness as 
 10 per cent of copper. Cubical expansion by heat 0.0083, from 32 to 
 212 F. Melts at 1200 F. Specific heat 0.25. 
 
 Manganese, Mn. At. wt. 55. Sp. gr. 7 to 8. The pure metal is not 
 used in the arts, but alloys of manganese and iron, called spiegeleisen 
 when containing below 25 per cent of manganese, and ferro-manganese 
 when containing from 25 to 90 per cent, are used in the manufacture of 
 steel. Metallic manganese, when alloyed with iron, oxidizes rapidly in 
 the air, and its function in steel manufacture is to remove the oxygen 
 from the bath of steel whether it exists as oxide of iron or as occluded 
 gas. 
 
 Mercury (Hydrargyrum), Hg. At. wt. 199.8. A silver-white metal, 
 liquid at temperatures above 39 F., and boils at 680 F. Unchange- 
 able as gold, silver, and platinum in the atmosphere at ordinary tem- 
 peratures, but oxidizes to the red oxide when near its boiling-point. 
 Sp. gr.: when liquid 13.58 to 13.59, when frozen 14.4 to 14.5. Easily 
 tarnished by sulphur fumes, also by dust, from which it may be freed 
 by straining through a cloth. No metal except iron or platinum should 
 be allowed to touch mercury. The smallest portions of tin, lead, zinc, 
 and even copper to a less extent, cause it to tarnish and lose its perfect 
 liquidity. Coefficient of cubical expansion from 32 to 212 F. 0.0182; 
 per deg. 0.000101. 
 
 Nickel, Ni. At. wt. 58.7. Sp. gr. 8.27 to 8.93. A silvery-white 
 metal with a strong lustre, not tarnishing on exposure to the air. Duc- 
 tile, hard, and as tenacious as iron. It is attracted to the magnet and 
 may be made magnetic like iron. Nickel is very difficult of fusion, melt- 
 ing at about 3000 F. Chiefly used in alloys with copper, as german- 
 silver, nickel-silver, etc., and also in the manufacture of steel to increase 
 its hardness and strength, also for nickel-plating. Cubical expansion 
 from 32 to 212 F., 0.0038. Specific heat 0.109. 
 
 Platinum, Pt. At. wt. 194X A whitish steel-gray metal, malleable, 
 very ductile, and as unalterable by ordinary agencies as gold. When 
 fused and refined it is as soft as copper. Sp. gr. 21.15. It is fusible only 
 by the oxyhydrogen blowpipe or in strong electric currents. When com- 
 bined with iridium it forms an alloy of great hardness, which has been 
 used for gun- vents and for standard weights and measures. The most 
 important uses of platinum in the arts are for vessels for chemical labo- 
 ratories and manufactories, and for the connecting wires in incandescent 
 electric lamps and for electrical contact points. Cubical expansion from 
 32 to 212 F., 0.0027, less than that of any other metal except the rare 
 metals, and almost the same as glass. 
 
 Silver (Argentum), Ag. At. wt. 107.9. Sp. gr. 10.1 to 11.1, accord- 
 ing to condition and purity. It is the whitest of the metals, very malle- 
 able and ductile, and in hardness intermediate between gold and copper. 
 Melts at about 1750 F. Specific heat 0.056. Cubical expansion from 
 32 to 212 F., 0.0058. As a conductor of electricity it is equal to copper. 
 As a conductor of heat it is superior to all other metals. 
 
 Tin (Stannum), Sn. At. wt. 119. Sp. gr. 7.293. White, lustrous, 
 soft, malleable, of little strength, tenacity about 3500 Ibs. per square 
 inch. Fuses at 442 F. Not sensibly volatile when melted at ordinary 
 heats. Heat conductivity 14.5, electric conductivity 12.4; silver being 
 100 in each case. Expansion of volume by heat 0.0069 from 32 to 212 F. 
 Specific heat 0.055. Its chief uses are for coating of sheet-iron (called 
 tin plate) and for making alloys with copper and other metals. 
 
 Zinc, Zn. At. wt. 65.4. Sp. gr. 7.14. Melts at 780 F. Volatilizes 
 and burns in the air when melted, with bluish-white fumes of zinc oxide. 
 It is ductile and malleable, but to a much less extent than copper, and 
 
180 
 
 MATERIALS. 
 
 its tenacity, about 5000 to 6000 Ibs. per square inch, is about one tenth 
 that of wrought iron. It is practically non-corrosive in the atmosphere, 
 a thin film of carbonate of zinc forming upon it. Cubical expansion 
 between 32 and 212 F., 0.0088. Specific heat 0.096. Electric conduc- 
 tivity 29, heat conductivity 36, silver being 100. Its principal uses are 
 for coating iron surfaces, called "galvanizing," and for making brass and 
 other alloys. 
 
 Table Showing the Order of 
 
 Tenacity. Infusibility. 
 
 Iron Platinum 
 
 Copper Iron 
 
 Aluminum Copper 
 
 Platinum Gold 
 
 Silver Silver 
 
 Zinc Aluminum 
 
 Gold Zinc 
 
 Tin Lead 
 
 Lead Tin 
 
 MEASURES AND WEIGHTS OF VARIOUS MATERIALS 
 (APPROXIMATE). 
 
 Malleability. 
 
 Ductility. 
 
 Gold 
 
 Platinum 
 
 Silver 
 
 Silver 
 
 Aluminum 
 
 Iron 
 
 Copper 
 Tin 
 
 Copper 
 Gold 
 
 Lead 
 
 Aluminum 
 
 Zinc 
 
 Zinc 
 
 Platinum 
 
 Tin 
 
 Iron 
 
 Lead 
 
 Brickwork. Brickwork is estimated 
 various thicknesses of wall runs as follows: 
 
 by the thousand, and for 
 
 8i/4-in. wall, or 1 brick in thickness, 14 bricks per superficial foot. 
 123/4 " 11/2" 21 " 
 
 17 " " " 9 " " " Oft " " " 
 
 17 
 
 2U/2 
 
 28 
 35 
 
 An ordinary brick measures about 81/4X4 X 2 inches, which is equal 
 to 66 cubic inches, or 26.2 bricks to a cubic foot. The average weight is 
 4 1/2 Ibs. 
 
 Fuel. A bushel of bituminous coal weighs 76 pounds and contains 
 2688 cubic inches = 1.554 cubic feet. 29.47 bushels = 1 gross ton. 
 
 One acre of bituminous coal contains 1600 tons of 2240 pounds per 
 foot of thickness of coal worked. 15 to 25 per cent must be deducted for 
 waste in mining. 
 
 41 to 45 cubic feet bituminous coal when broken down = 1 ton, 2240 Ibs. 
 
 34 t< 
 123 
 70.9 
 1 cu 
 1 
 1 
 
 a 
 
 i 
 i 
 
 3 41 
 
 bic fo 
 
 ' anthracite prepared for market . . 
 ' of charcoal 
 
 . = 1 ton, 2240 Ibs. 
 = 1 ton 2240 Ibs 
 
 " " " coke . 
 
 . = 1 ton, 2240 Ibs 
 
 ot of anthracite coal 
 
 = 55 to 66 Ibs 
 
 " bituminous coal . . . 
 
 = 50 to 55 Ibs 
 
 Cumberland (semi-bituminous) coal. . . . 
 Cannel coal . 
 
 = 53 Ibs. 
 = 50 3 Ibs 
 
 Charcoal (hardwood) 
 
 = 18.5 Ibs. 
 
 " (nine) . . 
 
 = 18 Ibs. 
 
 A bushel of coke weighs 40 pounds (35 to 42 pounds). 
 
 A bushel of charcoal. - In 1881 the American Charcoal-Iron Work- 
 ers' Association adopted for use in its official publications for the stand- 
 ard bushel of charcoal 2748 cubic inches, or 20 pounds. A ton of char- 
 coal is to be taken at 2000 pounds. This figure of 20 pounds to the 
 bushel was taken as a fair average of different bushels used throughout 
 the country, and it has since been established by law in some States. 
 
 Cement. Portland, per bbl. net, 376 Ibs., per bag, net 94 Ibs. 
 
 Natural, per bbl. net, 282 Ibs., per bag net 94 Ibs. 
 
 Lime. A struck bushel 72 to 75 Ibs. 
 
 Grain. A struck bushel of wheat = 60 Ibs.; of corn = 56 Ibs.; of 
 oats = 30 Ibs. 
 
 Salt. A struck bushel of salt, coarse, Syracuse, N. Y. = 56 Ibs.; 
 Turk's Island = 76 to 80 Ibs. 
 
MEASUKES AND WEIGHTS OF VARIOUS MATERIALS. 181 
 
 Ores, Earths, etc. 
 
 13 cubic feet of ordinary gold or silver ore, in mine = 1 ton = 2000 Ibs. 
 
 20 " broken quartz =1 ton = 2000 Ibs. 
 
 18 feet of gravel in bank =1 ton. 
 
 27 cubic feet of gravel when dry =1 ton. 
 
 25 " sand 
 
 18 " earth in bank 
 
 27 " earth when dry 
 
 17 " clay 
 
 Except where otherwise stated, a ton = 2240 Ibs. 
 
 WEIGHTS OF LOGS, LUMBER, ETC. 
 
 Weight of Green Logs to Scale 1000 Feet, Board Measure. 
 
 Yellow pine (Southern) 8,000 to 10,0001bs. 
 
 1 ton. 
 
 1 ton. 
 = 1 ton. 
 = 1 ton. 
 
 , 
 
 Norway pine (Michigan) 7,000 to 8,000 
 
 WhitP ninp nVTirhiffaTi^ I off of stum P 7 ' 000 to 7,000 
 
 (Micnigan) j QUt of water 7 000 to g 000 
 
 White pine (Pennsylvania), bark off 5,000 to 6,000 
 
 Hemlock (Pennsylvania), bark off . 6,000 to 7,000 
 
 Four acres of water are required to store 1,000,000 feet of logs. 
 
 Weight of 1000 Feet of Lumber, Board Measure. 
 
 Yellow or Norway pine Dry, 3,000 Ibs. Green, 5,000 Ibs. 
 
 White pine ' 2,500 " 4,000 " 
 
 Weight of 1 Cord of Seasoned Wood, 128 Cu. Ft. per Cord, Ibs. 
 
 Hickory or sugar maple. . . . 4,500 
 
 White oak 3,850 
 
 Beech, red oak or black oak . 3,250 
 
 Poplar, chestnut or elm. . . 2,350 
 Pine (white or Norway).. . 2,000 
 Hemlock bark, dry 2,200 
 
 WEIGHT OF RODS, BARS, PLATES, TUBES, AND SPHERES 
 OF DIFFERENT MATERIALS. 
 
 Notation: b = breadth, t = thickness, s = side of square, D = ex- 
 ternal diameter, d = internal diameter, all in inches. 
 
 Sectional areas: of square bars = s 2 ; of flat bars = W; of round rods 
 = 0.7854 Z> 2 ; of tubes = 0.7854 (D 2 - rf 2 ) = 3.1416 (Dt -Z 2 ). 
 
 Volume of 1 foot in length: of square bars = 12s 2 ; of flat bars = 12bt; 
 of round bars = 9.4248D 2 ; of tubes = 9.4248 (D 2 - d 2 ) = 37.699 
 (Dt -2 2 ), in cu. in. 
 
 Weight per foot length = volume + weight per cubic inch of mate- 
 rial. Weight of a sphere = diam. 3 X 0.5236 X weight per cubic inch. 
 
 
 
 3 
 
 $& 
 
 
 r .g 
 
 . 
 
 4 
 
 . 
 
 d 
 
 
 
 u . 
 
 *? rX 
 
 [Vj f^.O 
 
 fe PQ 
 
 U . 
 
 j> -fj iH 
 
 JV 'tf 
 
 
 Material. 
 
 P| 
 
 5 > 
 
 
 ^ 
 
 fctrf 
 
 g| 
 
 
 If fa 
 
 y 
 
 "gjj 
 
 
 JJ 
 
 ge 
 
 g-w 
 
 +i*H ^ 
 
 i*s 
 
 i* 
 
 I^-S 
 
 -3 
 
 4J a 
 
 
 
 
 
 8 2 X 
 
 btX 
 
 
 
 D*X 
 
 D*X 
 
 Cast iron 
 
 7.218 
 
 450. 
 
 37.5 
 
 31/8 
 
 31/8 
 
 0.2604 
 
 15-16 
 
 2.454 
 
 0.1363 
 
 Wrought iron. . 
 
 7.7 
 
 480. 
 
 40. 
 
 31/3 
 
 31/3 
 
 .2779 
 
 1. 
 
 2.618 
 
 .1455 
 
 Steel 
 
 7.854 
 
 489.6 
 
 40.8 
 
 3.4 
 
 3.4 
 
 .2833 
 
 1.02 
 
 2.670 
 
 .1484 
 
 Copper & Bronze 
 (copper and tin) 
 
 8.855 
 
 552. 
 
 46. 
 
 3.833 
 
 3.833 
 
 .3195 
 
 1.15 
 
 3.011 
 
 .1673 
 
 Brass ( zm^* 
 
 8.393 
 
 523.2 
 
 43.6 
 
 3.633 
 
 3.633 
 
 3029 
 
 1.09 
 
 2.854 
 
 .1586 
 
 Monel metal, rolled 
 
 8.95 
 
 558. 
 
 46.5 
 
 3.87 
 
 3.87 
 
 .323 
 
 1.16 
 
 3.043 
 
 .1691 
 
 Lead... 
 
 1 1.38 
 
 709.6 
 
 59.1 
 
 493 
 
 493 
 
 .4106 
 
 1 48 
 
 3.870 
 
 .2150 
 
 Aluminum 
 
 2.67 
 
 166.5 
 
 13.9 
 
 1.16 
 
 1.16 
 
 .0963 
 
 0.347 
 
 0.908 
 
 .0504 
 
 Glass. 
 
 2.62 
 
 163.4 
 
 13.6 
 
 1.13 
 
 1 13 
 
 .0945 
 
 0.34 
 
 0.891 
 
 .0495 
 
 Pine wood, dry 
 
 0.481 
 
 30.0 
 
 2.5 
 
 0.21 
 
 0.21 
 
 .0174 
 
 1-16 
 
 0.164 
 
 .0091 
 
 Weight per cylindrical in., 1 in. long, = coefficient of D 2 in next to 
 last column -7- 12. 
 
182 MATERIALS. 
 
 FOP tubes use the coefficient of D 2 in next to last column, as for rods, 
 and multiply it into (D 2 d 2 ) ; or multiply it by 4 (Dt - 2 2 ) . 
 
 For hollow spheres use the coefficient of D 3 in the last column and 
 multiply it into (D 3 - d 3 ). 
 
 For hexagons multiply the weight of square bars by 0.866 (short 
 diam. of hexagon = side of square). For octagons multiply by 0.8284. 
 
 COMMERCIAL SIZES OF MERCHANT IRON AND STEEL 
 
 BARS. 
 
 Steel Bars. 
 
 Flats, Square Edge. s/g to 3 in. wide, by any thickness from 
 1/8 in. up to width; 3 to 5 in. wide by any thickness 1/4 t9 3 in. 
 inclusive; 5 to 7 in. wide, by any thickness, 1/4 to 2 in. inclusive. 
 
 Flats, Band Edge. Thicknesses are in B. W. G., 3/ 8 in. wide by 
 No. 18 to No. 4. 7/i6 in. by No. 19 to No. 4. 1/2 in. by No. 22 to No. 
 4. 9/i6 to 1 in. by No. 23 to No. 4. 1 1/16 to 2 in. by No. 22 to No. 4. 
 2Vi6 to 3 in. by No. 21 to No. 1. 39/16 to 4 in. by No. 19 to No. 1. 
 4Vi6 to 41/2 in. by No. 18 to No. 1. 49/i 6 to 5 Vie in. by No. 17 to No. 1. 
 5 i/s to 6 3/4 in. by No. 16 to No. 1. 7 in., 7 1/4 in., 7 1/2 in., 7 5/8 in., 7 3/ 4 in., 
 7 7/8 in., 8 in., 81/4 in., 81/2 in., 85/8 in., each by No. 14 to No. 1. 95/ 8 
 in. by No. 12 to No. 1. 
 
 Squares. Widths across faces: 3/ie to 2 in., advancing by 1/64 in.; 
 21/32 to 3 1/2 in., advancing by 1/32 in.; 3 9/ie to 51/2 in., advancing by 
 Vie in. 
 
 Round-cornered Squares. 1/4 to 3/4 in., across faces, advancing 
 by 1/64 in. 
 
 Rounds. Diameters: 7/32 to 13/4 in., inclusive, advancing by 1/64 
 in.; 1 25/32 in. to 31/2 in. inclusive, advancing by 1/32; 3 9/ie to 7 in., 
 inclusive, advancing by Vie in. 
 
 Half Rounds. Diameters: 5/16 to 7/s in., inclusive, advancing by 
 1/64 in. ; 15/16 to 1 3/4 in . , advancing by Vie in. ; 2 in. ; 2 1/2 in. ; 3 in. 
 
 .Hexagons. Width across faces: 1/4 to 13/ie in., inclusive, advanc- 
 ing by 1/32 in.; 1 1/4 in. to 3 Vie in., advancing by Vie in. 
 
 Iron Bars. 
 
 Round. 3 /i6 to 1 7 /8 in., advancing by Vs2 in.; 1 15 /i6 to 2 3 /4 in., advancing 
 by Vie in.; 2 7 / 8 to 3 3 /4 in., advancing by Vs in.; 4 to 5 in., advancing by 
 1/4 in. 
 
 Squares. Vie to 5 /s in., advancing by 1/32 in.; n/ie in. to 1 in., advancing 
 by Vie in.; 1 Vg in. to 2 1/2 in., advancing by Vs in.; 2 3 /4 in. to 4 */2 in., ad- 
 vancing by 1/4 in- 
 Half Rounds. -8/g, 7/ 16 , l/ 2 , 5/ 8 , 11/ 16 , 3/ 4 , 7/ 8f 1, 1 l/ g , 1 \j\ 3/ g , 1 l/ 2 , 
 
 1 3/4, 2 in. 
 
 OvalS. V2 X V4, 5/8 X 5/16, 3/4 X 3/8 and 7/ 8 X 7/16 in. 
 
 Half Ovals. 1/2 X Vie, Vs X Vie, 3 /4 X Vie, Vs X Vie, 1 X Vie, 
 3 /4 X V4, Vs X i/4, 1 X i/4, 1 Vs X 1/4. 1 X Vie, 1 Vs X Vie, 1 V 4 X Vie, 
 1 X Vs, 1 Vs X Vs, 1 V 4 X Vs, 1 V2 X Vs, 1 3 /4 X V* 2 X Vs in. 
 
 Flats. 1/2 X Vie to Vs in.; Vs X Vie to 1/2 in.; 3 /4 X Vie to Vs in.; 
 Vs X Vie to 3 /4 in.; 1 X Vie to Vs in.; 1 Vie X i/4 to Vs in-; 1 Vs X Vie to 
 1 in.; 1 1/4 X Vie to 1 in.; 1 3 /s X Vie to 1 Vs in.; 1 1/2 X Vie to 1 1/4 in.; 
 
 1 Vs X V 4 to 1 1/2 in.; 1 3 /4 X Vie to 1 1/2 in.; 1 Vs X I /A to 1 1/2 in.; 2 X Vie 
 to 1 3 / 4 in.; 2 Vs X V 4 to 1 1/4 in.; 2 i/ 4 X Vie to 2 in.; 2 Vs X V 4 to 1 3 /4 in.; 
 2V 2 XVie to 2V4 in.; 2 Vs X V 4 to 2 i/ 4 in.; 2 3 /4 X Vie to 2 1/2 in.; 
 
 2 7/8 X V 8 to 1/2 in.; 2 Vs X Vs to 2 i/ 4 in.; 3 X Vie to 2 3 /4 in.; 3 Vs X 1 V2 
 to 2 Vs in.; 3 1/ 4 X */4 to 2 3 /4 in.; 3 1/2 X Vie to 2 Vs in.; 3 3 / 4 X V 4 to 3 in.; 
 
 4 X V4 to 3 in.; 4 1/4 X V4 to 2 in.; 4 1/2 X J /4 to 2 1/2 in.; 4 3 /4 X V4 to 2 
 in.; 5 X x /4 to 2 3/ 4 in.; 5 1/2 X V4 to 2 in.; 6 X V4 to 2 in.; 6 1/2 X V 4 to 
 1 in.; 7 X !/4 to 2 in.; 7 1/2 X x /4 to 1 in.; 8 X V4 to 2 in. 
 
 Round Edge Flats. 1 to 2 in. wide by V 4 to 1 V 4 in. thick; 2 1/4 to 
 4 1/2 in. wide by 3 /s to 1 1/4 in. thick. 
 
WEIGHT OP IRON AND STEEL SHEETS. 
 
 183 
 
 WEIGHT OF IRON AND STEEI, SHEETS. 
 
 Weights in Pounds per Square Foot. 
 
 (For weights by the Decimal Gauge, see page 33.) 
 
 Thickness by Birmingham Gauge. 
 
 U. S. Standard Gauge, 1893. (See 
 p. 32.) 
 
 No. of 
 Gauge. 
 
 Thick- 
 ness in 
 Inches. 
 
 Iron. 
 
 Steel. 
 
 No. of 
 Gauge. 
 
 Thick- 
 ness, In. 
 (Approx.) 
 
 Iron. 
 
 Steel. 
 
 0000 
 
 0.454 
 
 18.16 
 
 18.52 
 
 0000000 
 
 0.5 
 
 20. 
 
 20.40 
 
 000 
 
 .425 
 
 17.00 
 
 17.34 
 
 000000 
 
 0.4688 
 
 18.75 
 
 19.125 
 
 00 
 
 .38 
 
 15.20 
 
 15.50 
 
 00000 
 
 0.4375 
 
 17.50 
 
 17.85 
 
 
 
 .34 
 
 13.60 
 
 13.87 
 
 0000 
 
 0.4063 
 
 16.25 
 
 16.575 
 
 1 
 
 .3 
 
 12.00 
 
 12.24 
 
 000 
 
 0.375 
 
 15. 
 
 15. 3C 
 
 2 
 
 .284 
 
 11.36 
 
 11.59 
 
 00 
 
 0.3438 
 
 13.75 
 
 14.025 
 
 3 
 
 .259 
 
 10.36 
 
 10.57 
 
 
 
 0.3125 
 
 12.50 
 
 12.75 
 
 4 
 
 .238 
 
 9.52 
 
 9.71 
 
 1 
 
 0.2813 
 
 11.25 
 
 11.475 
 
 5 
 
 .22 
 
 8.80 
 
 8.98 
 
 2 
 
 0.2656 
 
 10.625 
 
 10.837 
 
 6 
 
 .203 
 
 8.12 
 
 8.28 
 
 3 
 
 0.25 
 
 10. 
 
 10.20 
 
 7 
 
 .18 ' 
 
 7.20 
 
 7.34 
 
 4 
 
 0.2344 
 
 9.375 
 
 9.562 
 
 8 
 
 .165 
 
 6.60 
 
 6.73 
 
 5 
 
 0.2188 
 
 8.75 
 
 8.925 
 
 9 
 
 .148 
 
 5.92 
 
 6.04 
 
 6 
 
 0.2031 
 
 8.125 
 
 8.287 
 
 10 
 
 .134 
 
 5.36 
 
 5.47 
 
 7 
 
 0.1875 
 
 7.5 
 
 7.65 
 
 11 
 
 .12 
 
 4.80 
 
 4.90 
 
 8 
 
 0.1719 
 
 6.875 
 
 7.012 
 
 12 
 
 .109 
 
 4.36 
 
 4.45 
 
 9 
 
 0.1563 
 
 6.25 
 
 6.375 
 
 13 
 
 .095 
 
 3.80 
 
 3.88 
 
 10 
 
 0.1405 
 
 5.625 
 
 5.737 
 
 14 
 
 .083 
 
 3.32 
 
 3.39 
 
 11 
 
 0.125 
 
 5. 
 
 5.10 
 
 15 
 
 .072 
 
 2.88 
 
 2.94 
 
 12 
 
 0.1094 
 
 4.375 
 
 4.462 
 
 16 
 
 .065 
 
 2.60 
 
 2.65 
 
 13 
 
 0.0938 
 
 3.75 
 
 3.825 
 
 17 
 
 .058 
 
 2.32 
 
 2.37 
 
 14 
 
 0.0781 
 
 3.125 
 
 3.187 
 
 18 
 
 .049 
 
 .96 
 
 2.00 
 
 15 
 
 0.0703 
 
 2.8125 
 
 2.869 
 
 19 
 
 .042 
 
 .68 
 
 1.71 
 
 16 
 
 0.0625 
 
 2.5 
 
 2.55 
 
 20 
 
 .035 
 
 .40 
 
 1.43 
 
 17 
 
 0.0563 
 
 2.25 
 
 2.295 
 
 21 
 
 .032 
 
 .28 
 
 1.31 
 
 18 
 
 0.05 
 
 2. 
 
 2.04 
 
 22 
 
 .028 
 
 .12 
 
 1.14 
 
 19 
 
 0.0438 
 
 .75 
 
 .785 
 
 23 
 
 .025 
 
 .00 
 
 1.02 
 
 20 
 
 0.0375 
 
 .50 
 
 .53 
 
 24 
 
 .022 
 
 .88 
 
 .898 
 
 21 
 
 0.0344 
 
 .375 
 
 .402 
 
 25 
 
 .02 
 
 .80 
 
 .816 
 
 22 
 
 0.0312 
 
 .25 
 
 .275 
 
 26 
 
 .018 
 
 .72 
 
 .734 
 
 23 
 
 0.0281 
 
 .125 
 
 .147 
 
 27 
 
 .016 
 
 .64 
 
 .653 
 
 24 
 
 0.025 
 
 
 .02 
 
 28 
 
 .014 
 
 .56 
 
 .571 
 
 25 
 
 0.0219 
 
 0^875 
 
 0.892 
 
 29 
 
 .013 
 
 .52 
 
 .530 
 
 26 
 
 0188 
 
 0.75 
 
 0.765 
 
 30 
 
 .012 
 
 .48 
 
 .490 
 
 27 
 
 0.0172 
 
 0.6875 
 
 0.701 
 
 31 
 
 .01 
 
 .40 
 
 .408 
 
 28 
 
 0.0156 
 
 0.625 
 
 0.637 
 
 32 
 
 .009 
 
 .36 
 
 .367 
 
 29 
 
 0.0141 
 
 0.5625 
 
 0.574 
 
 33 
 
 .008 
 
 .32 
 
 .326 
 
 30 
 
 0.0125 
 
 0.5 
 
 0.51 
 
 34 
 
 .007 
 
 .28 
 
 .286 
 
 31 
 
 0.0109 
 
 0.4375 
 
 0.446 
 
 35 
 
 .005 
 
 .20 
 
 .204 
 
 32 
 
 0.0102 
 
 0.40625 
 
 0.414 
 
 36 
 
 .004 
 
 .16 
 
 .163 
 
 33 
 
 0.0094 
 
 0.375 
 
 0.382 
 
 
 
 
 
 34 
 
 0.0086 
 
 0.34375 
 
 0.351 
 
 
 
 
 
 35 
 
 0.0078 
 
 0.3125 
 
 0.319 
 
 
 
 
 
 36 
 
 0.0070 
 
 0.28125 
 
 0.287 
 
 
 
 
 
 37 
 
 0.0066 
 
 0.26562 
 
 0.271 
 
 
 
 
 
 38 
 
 0.0063 
 
 0.25 
 
 0.255 
 
 Iron. Steel. 
 
 Specific gravity . . 7.7 7.854 
 
 489.6 
 Weight per cubic inch 0.2778 0.2833 
 
 As there are many gauges in use differing from each other, and even the 
 thicknesses of a certain specified gauge, as the Birmingham, are not assumed 
 the same by all manufacturers, orders for sheets and wires should always 
 state the weight per square foot, or the thickness in thousandths of an inch. 
 
184 
 
 MATERIALS. 
 
 WEIGHTS OF SQUARE AND ROUND BARS OP WROUGHT 
 IRON IN POUNDS PER LINEAL FOOT. 
 
 Iron weighing 480 Ib. per cubic foot. For steel add 2 per cent. 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 2l? 
 
 Sgj 
 *& 
 
 ii 
 
 !e^ 
 
 J! 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 *H e8 M 
 5 
 
 ajM 
 
 '8 3^ 
 
 *Jt 
 
 Weight of 
 Round Bar 
 1 Ft. Long. 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 !lf 
 I J 
 II! 
 
 Weight of 
 Round Bar I 
 1 Ft. Long. [ 
 
 
 
 
 
 H/16 
 
 24.08 
 
 18.91 
 
 3/8 
 
 96.30 
 
 75.64 
 
 Vl6 
 
 0.013 
 
 0.010 
 
 3/4 
 
 25.21 
 
 19.80 
 
 7/16 
 
 08.55 
 
 77.40 
 
 VS 
 
 .052 
 
 .041 
 
 13/16 
 
 26.37 
 
 20.71 
 
 1/2 
 
 100.8 
 
 79.19 
 
 3/16 
 
 .117 
 
 .092 
 
 7/8 
 
 27.55 
 
 21.64 
 
 /16 
 
 103.1 
 
 81.00 
 
 1/4 
 
 .208 
 
 .164 
 
 15/16 
 
 28.76 
 
 22.59 
 
 5/8 
 
 105.5 
 
 82.83 
 
 5/16 
 
 .326 
 
 .256 
 
 3 
 
 30.00 
 
 23.56 
 
 H/16 
 
 107.8 
 
 84 69 
 
 3/8 
 
 .469 
 
 .368 
 
 1/16 
 
 31.26 
 
 24.55 
 
 3/4 
 
 110.2 
 
 86.56 
 
 7/16 
 
 .638 
 
 .501 
 
 1/8 
 
 32.55 
 
 25.57 
 
 13/16 
 
 112.6 
 
 88.45 
 
 >/2 
 
 .833 
 
 .654 
 
 3/16 
 
 33.87 
 
 26.60 
 
 7/8 
 
 115.1 
 
 9036 
 
 9/16 
 
 1.055 
 
 .828 
 
 1/4 
 
 35.21 
 
 27.65 
 
 15/16 
 
 117.5 
 
 92.29 
 
 5/8 
 
 1.302 
 
 1.023 
 
 5/16 
 
 36.58 
 
 28.73 
 
 6 
 
 120.0 
 
 94.25 
 
 H/16 
 
 1.576 
 
 1.237 
 
 3/8 
 
 37.97 
 
 29.82 
 
 1/8 
 
 125.1 
 
 98.22 
 
 3/4 
 
 1.875 
 
 1.473 
 
 7/16 
 
 39.39 
 
 30.94 
 
 1/4 
 
 130.2 
 
 102.3 
 
 13/16 
 
 2.201 
 
 1.728 
 
 1/2 
 
 40.83 
 
 32.07 
 
 3/8 
 
 135.5 
 
 106.4 
 
 7/8 
 
 2.552 
 
 2.004 
 
 9 /16 
 
 42.30 
 
 33.23 
 
 V2 
 
 140.8 
 
 110.6 
 
 15/16 
 
 2.930 
 
 2.301 
 
 5/8 
 
 43.80 
 
 34.40 
 
 5/8 
 
 146.3 
 
 114.9 
 
 1 
 
 3.333 
 
 2.618 
 
 H/16 
 
 45.33 
 
 35.60 
 
 3/4 
 
 151.9 
 
 119.3 
 
 Vl6 
 
 3.763 
 
 2.955 
 
 3/4 
 
 46.88 
 
 36.82 
 
 7/8 
 
 157*6 
 
 123.7 
 
 1/8 
 
 4.219 
 
 3.313 
 
 13/16 
 
 48.45 
 
 38.05 
 
 
 163.3 
 
 128.3 
 
 3/16 
 
 4.701 
 
 3.692 
 
 7/8 
 
 50.05 
 
 39.31 
 
 1/8 
 
 169.2 
 
 132.9 
 
 1/4 
 
 5.208 
 
 4.091 
 
 15/16 
 
 51.68 
 
 40.59 
 
 1/4 
 
 175.2 
 
 137.6 
 
 5/16 
 
 5.742 
 
 4.510 
 
 4 
 
 53.33 
 
 41.89 
 
 3/8 
 
 181.3 
 
 1424 
 
 3/ 8 
 
 6.302 
 
 4.950 
 
 1/16 
 
 55.01 
 
 43.21 
 
 1/2 
 
 187 5 
 
 147.3 
 
 7/16 
 
 6.888 
 
 5.410 
 
 1/8 
 
 56.72 
 
 44.55 
 
 5/8 
 
 193.8 
 
 152.2 
 
 1/2 
 
 7.500 
 
 5.890 
 
 3/16 
 
 58.45 
 
 45.91 
 
 3/4 
 
 200.2 
 
 157.2 
 
 9/16 
 
 8.138 
 
 6.392 
 
 1/4 
 
 60.21 
 
 47.29 
 
 7/8 
 
 206.7 
 
 162.4 
 
 5/8 
 
 8.802 
 
 6.913 
 
 5/16 
 
 61.99 
 
 48.69 
 
 
 213.3 
 
 167.6 
 
 H/16 
 
 9.492 
 
 7.455 
 
 3/8 
 
 63.80 
 
 50.11 
 
 1/4 
 
 226.9 
 
 178.2 
 
 3/ 4 
 
 10.21 
 
 8.018 
 
 7/16 
 
 65.64 
 
 51.55 
 
 1/2 
 
 240.8 
 
 189.2 
 
 13/16 
 
 10.95 
 
 8.601 
 
 V2 
 
 67.50 
 
 53.01 
 
 3/4 
 
 255.2 
 
 200.4 
 
 7/8 
 
 11.72 
 
 9.204 
 
 9 /16 
 
 69.39 
 
 54.50 
 
 9 
 
 270.0 
 
 212.1 
 
 15 /16 
 
 12.51 
 
 9.828 
 
 5/8 
 
 .71.30 
 
 56.00 
 
 1/4 
 
 285.2 
 
 224.0 
 
 2 
 
 13.33 
 
 10.47 
 
 U/16 
 
 73.24 
 
 57.52 
 
 1/9 
 
 300.8 
 
 236.3 
 
 1/16 
 
 14.18 
 
 11.14 
 
 3/4 
 
 75.21 
 
 59.07 
 
 3/4 
 
 316.9 
 
 248.9 
 
 1/8 
 
 15.05 
 
 11.82 
 
 13/16 
 
 77.20 
 
 60.63 
 
 10 
 
 333.3 
 
 261.8 
 
 3/16 
 
 15.95 
 
 12.53 
 
 7/8 
 
 79.22 
 
 62.22 
 
 1/4 
 
 350.2 
 
 275.1 
 
 1/4 
 
 16.88 
 
 13.25 
 
 15/16 
 
 81.26 
 
 63.82 
 
 1/9 
 
 367.5 
 
 288.6 
 
 5/16 
 
 17.83 
 
 14.00 
 
 5 
 
 83.33 
 
 65.45 
 
 3/4 
 
 385.2 
 
 302.5 
 
 3/8 
 
 18.80 
 
 14.77 
 
 Vl6 
 
 85.43 
 
 67.10 
 
 11 
 
 403 3 
 
 3168 
 
 7/16 
 
 1980 
 
 15.55 
 
 1/8 
 
 87.55 
 
 68.76 
 
 1/4 
 
 421.9 
 
 331.3 
 
 1/2 
 
 20.83 
 
 16.36 
 
 3/16 
 
 89.70 
 
 70.45 
 
 1/2 
 
 440.8 
 
 346.2 
 
 9/16 
 
 21.89 
 
 17.19 
 
 1/4 
 
 91.88 
 
 72.16 
 
 3/4 
 
 460.2 
 
 361.4 
 
 5/8 
 
 22.97 
 
 18.04 
 
 5/16 
 
 94.08 
 
 73.89 
 
 12 
 
 480. 
 
 377. 
 
WEIGHT OF STEEL BARS. 
 
 185 
 
 WEIGHT OP SQUARE AND ROUND STEEL BARS PER LINEAL 
 FOOT. (Steel Weighing 489.6 Ib. per cu. ft.) 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 Weight of 
 Square Bar 
 1 Ft. Long. 
 
 Weight of 
 Round Bar 
 1 Ft. Long. 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 Weight of 
 Square Bar 
 1 Ft. Long. 
 
 *e 
 s s 
 Sl% 
 
 ! 
 ^- 
 
 Thickness or 
 Diameter 
 in Inches. 
 
 Weight of 
 Square Bar 
 1 Ft. Long. 
 
 Weight of 
 Round Bar 
 1 Ft. Long. 
 
 
 
 
 
 H/16 
 
 24.56 
 
 19.29 
 
 3/8 
 
 98.23 
 
 77.15 
 
 1/16 
 
 0.013 
 
 0.010 
 
 3/4 
 
 25.71 
 
 20.20 
 
 7/16 
 
 100.5 
 
 78.95 
 
 1/8 
 
 .053 
 
 .042 
 
 13/16 
 
 26.90 
 
 21.12 
 
 1/2 
 
 102.8 
 
 80.77 
 
 3/16 
 
 .119 
 
 .094 
 
 7/8 
 
 28.10 
 
 22.07 
 
 9/16 
 
 105.2 
 
 82.62 
 
 V4 
 
 .212 
 
 .167 
 
 15/16 
 
 29.34 
 
 23.03 
 
 5/8 
 
 107.6 
 
 84.49 
 
 5/16 
 
 .333 
 
 .261 
 
 3 
 
 30.60 
 
 24.03 
 
 U/ifl 
 
 110.0 
 
 86.38 
 
 3/8 
 
 .478 
 
 .375 
 
 1/16 
 
 31 .89 
 
 25.04 
 
 3/4 
 
 112.4 
 
 88.29 
 
 7/16 
 
 .651 
 
 .511 
 
 1/8 
 
 33.20 
 
 26.08 
 
 13/16 
 
 114.9 
 
 90.22 
 
 1/2 
 
 .850 
 
 .667 
 
 3/16 
 
 34.55 
 
 27.13 
 
 7/8 
 
 117.4 
 
 92.17 
 
 9/16 
 
 1.076 
 
 .845 
 
 1/4 
 
 35.91 
 
 28.20 
 
 15/16 
 
 119.9 
 
 94.14 
 
 5/8 
 
 1.328 
 
 1 .043 
 
 5/16 
 
 37.31 
 
 29.30 
 
 6 
 
 122.4 
 
 96.14 
 
 H/16 
 
 1.608 
 
 1.262 
 
 3/8 
 
 38.73 
 
 30.42 
 
 1/8 
 
 127.6 
 
 100.2 
 
 3/4 
 
 1 .913 
 
 1 .502 
 
 7/16 
 
 40.18 
 
 31 .56 
 
 1/4 
 
 132.8 
 
 104.3 
 
 13/16 
 
 2.245 
 
 1.763 
 
 1/2 
 
 41 .65 
 
 32.71 
 
 3/8 
 
 138.2 
 
 108.5 
 
 7/8 
 
 2.603 
 
 2.044 
 
 9/16 
 
 43.15 
 
 33.89 
 
 1/2 
 
 143.6 
 
 112.8 
 
 15/16 
 
 2.989 
 
 2.347 
 
 5/8 
 
 44.68 
 
 35.09 
 
 5/8 
 
 149.2 
 
 117.2 
 
 1 
 
 3.400 
 
 2.670 
 
 U/16 
 
 46.24 
 
 36.31 
 
 3/4 
 
 154.9 
 
 121.7 
 
 1/16 
 
 3.838 
 
 3.014 
 
 3/4 
 
 47.82 
 
 37.56 
 
 7/8 
 
 160.8 
 
 126.2 
 
 1/8 
 
 4.303 
 
 3.379 
 
 13/16 
 
 49.42 
 
 38.81' 
 
 7 
 
 166.6 
 
 130.9 
 
 3/16 
 
 4.795 
 
 3.766 
 
 7/8 
 
 51 .05 
 
 40.10 
 
 1/8 
 
 172.6 
 
 135.6 
 
 1/4 
 
 5.312 
 
 4.173 
 
 15/16 
 
 52.71 
 
 41 .40 
 
 1/4 
 
 178.7 
 
 140. < 
 
 5/16 
 
 5.857 
 
 4.600 
 
 4 
 
 54.40 
 
 42.73 
 
 3/8 
 
 184.9 
 
 145.1 
 
 3/8 
 
 6.428 
 
 5.049 
 
 1/16 
 
 56.11 
 
 44.07 
 
 1/2 
 
 191.3 
 
 150.2 
 
 7/16 
 
 7.026 
 
 5.518 
 
 1/8 
 
 57.85 
 
 45.44 
 
 5/ 8 
 
 197.7 
 
 155.2 
 
 1/2 
 
 7.650 
 
 6.008 
 
 3/16 
 
 59.62 
 
 46.83 
 
 3/4 
 
 204.2 
 
 159.3 
 
 9/16 
 
 8.301 
 
 6.520 
 
 1/4 
 
 61:41 
 
 48.24 
 
 7/8 
 
 210.8 
 
 165.6 
 
 5/8 
 
 8.978 
 
 7.051 
 
 5/16 
 
 63.23 
 
 49.66 
 
 8 
 
 217.6 
 
 171.0 
 
 H/16 
 
 9.682 
 
 7.604 
 
 3/8 
 
 65.08 
 
 51.11 
 
 1/4 
 
 231.4 
 
 181.8 
 
 3/4 
 
 10.41 
 
 8.178 
 
 7/16 
 
 66.95 
 
 52.58 
 
 1/2 
 
 245.6 
 
 193.0 
 
 13/16 
 
 11 .17 
 
 8.773 
 
 1/2 
 
 68.85 
 
 54.07 
 
 3/4 
 
 260.3 
 
 204 .4 
 
 7/8 
 
 11 .95 
 
 9.388 
 
 9/16 
 
 70.78 
 
 55.59 
 
 9 
 
 275.4 
 
 216.3 
 
 15/16 
 
 12.76 
 
 10.02 
 
 5/8 
 
 72.73 
 
 57.12 
 
 1/4 
 
 290.9 
 
 228.5 
 
 2 
 
 13.60 
 
 10.68 
 
 n/i6 
 
 74.70 
 
 58.67 
 
 1/2 
 
 306.8 
 
 241.0 
 
 1/16 
 
 14.46 
 
 11 .36 
 
 3/4 
 
 76.71 
 
 60.25 
 
 3/4 
 
 323.2 
 
 253.9 
 
 1/8 
 
 15.35 
 
 12.06 
 
 13/16 
 
 78.74 
 
 61.84 
 
 10 
 
 340.0 
 
 267.0 
 
 3/16 
 
 16.27 
 
 12.78 
 
 7/8 
 
 80.80 
 
 63.46 
 
 1/4 
 
 357.2 
 
 280.6 
 
 1/4 
 
 17.22 
 
 13.52 
 
 15/16 
 
 82.89 
 
 65.10 
 
 1/2 
 
 374.9 
 
 294. 4 
 
 5/16 
 
 18.19 
 
 14.28 
 
 5 
 
 85.00 
 
 66.76 
 
 3/4 
 
 392.9 
 
 308.6 
 
 3/8 
 
 19.18 
 
 15.07 
 
 Vl6 
 
 87.14 
 
 68.44 
 
 11 
 
 411.4 
 
 323.1 
 
 7/16 
 
 20.20 
 
 15.86 
 
 ' 1/8 
 
 89.30 
 
 70.14 
 
 1/4 
 
 430.3 
 
 337.9 
 
 1/2 
 
 21.25 
 
 16.69 
 
 3/16 
 
 91 .49 
 
 71.86 
 
 1/2 
 
 449.6 
 
 353.1 
 
 9/16 
 
 22.33 
 
 17.53 
 
 1/4 
 
 93 72 
 
 73.60 
 
 3/4 
 
 469.4 
 
 368.6 
 
 5/8 
 
 23.43 
 
 18.40 
 
 5/16 
 
 95.96 
 
 75.37 
 
 12 
 
 489.6 
 
 384.5 
 
 Weight of Fillets. 
 
 Ra- 
 dius, 
 In. 
 
 Area, 
 Sq. In. 
 
 Weight per In., Lb. 
 
 Ra- 
 dius, 
 In. 
 
 Area, 
 Sq. In. 
 
 Weight per In., Lb. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Brass. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Brass. 
 
 1/4 
 
 0.0134 
 
 0.0035 
 
 0.0038 
 
 0.0040 
 
 13/16 
 
 0.1416 
 
 0.0369 
 
 0.0401 
 
 0.0414 
 
 5/16 
 
 .0209 
 
 .0054 
 
 .0059 
 
 .0061 
 
 7/8 
 
 .1634 
 
 .0428 
 
 .0465 
 
 .0479 
 
 3/8 
 
 .0302 
 
 .0078 
 
 .0085 
 
 .0088 
 
 15/16 
 
 .1886 
 
 .0491 
 
 .0534 
 
 .0550 
 
 7/16 
 
 .0411 
 
 .0107 
 
 .0116 
 
 .0120 
 
 1 
 
 .2146 
 
 .0559 
 
 .0608 
 
 .0626 
 
 1/2 
 
 .0536 
 
 .0140 
 
 .0152 
 
 .0157 
 
 1 1/8 
 
 .2716 
 
 .0709 
 
 .0771 
 
 .0794 
 
 9/1 fi 
 
 .0679 
 
 .0177 
 
 .0192 
 
 .0200 
 
 1 1/4 
 
 .3353 
 
 .0874 
 
 .0950 
 
 .0979 
 
 5/8 
 
 .0834 
 
 .0218 
 
 .0237 
 
 .0244 
 
 1 3/8 
 
 .4057 
 
 .0920 
 
 .1000 
 
 .1030 
 
 H/16 
 
 .1014 
 
 .0264 
 
 .0287 
 
 .0300 
 
 1 1/2 
 
 .4828 
 
 .1259 
 
 .1368 
 
 .1410 
 
 3/4 
 
 .1207 
 
 .0315 
 
 .0342 
 
 .0352 
 
 15/8 
 
 .5668 
 
 .1479 
 
 .1608 
 
 .1657 
 
 Continued on next page. 
 
186 
 
 MATERIALS. 
 
 Weights per Lineal Inch of Bound, Square and Hexagon Steel. 
 
 Weight of 1 cu. in. = 0.2836 Ib. Weight of 1 cu. ft. 490 Ib. 
 
 Thick- 
 ness or 
 Diam- 
 eter. 
 
 Round. 
 
 Square. 
 
 Hexagon 
 
 Thick- 
 ness or 
 Diam- 
 eter. 
 
 Round. 
 
 Square. 
 
 Hexagon. 
 
 V32 
 
 0.0002 
 
 0.0003 
 
 0.0002 
 
 17/8 
 
 . 783 1 
 
 0.9970 
 
 0.8635 
 
 1/16 
 
 .0009 
 
 .0011 
 
 .0010 
 
 115/ 
 
 .8361 
 
 .0646 
 
 .9220 
 
 3/32 
 
 .0020 
 
 .0025 
 
 .0022 
 
 2 
 
 .8910 
 
 .1342 
 
 .9825 
 
 1/8 
 
 .0035 
 
 .0044 
 
 .0038 
 
 21/16 
 
 .9475 
 
 .2064 
 
 .0448 
 
 5/32 
 
 .0054 
 
 .0069 
 
 .0060 
 
 21/8 
 
 .0058 
 
 .2806 
 
 .1091 
 
 3/16 
 
 .0078 
 
 .0101 
 
 .0086 
 
 23/i 6 
 
 .0658 
 
 .3570 
 
 .1753 
 
 7/32 
 
 .0107 
 
 .0136 
 
 .0118 
 
 21/4 
 
 .1276 
 
 .4357 
 
 .2434 
 
 1/4 
 
 .0139 
 
 .0177 
 
 .0154 
 
 25/ie 
 
 .1911 
 
 .5165 
 
 .3135 
 
 9/32 
 
 .0176 
 
 .0224 
 
 .0194 
 
 23/ 8 
 
 .2564 
 
 .6569 
 
 .3854 
 
 5/16 
 
 .0218 
 
 .0277 
 
 .0240 
 
 27/ie 
 
 .3234 
 
 .6849 
 
 .4593 
 
 H/32 
 
 .0263 
 
 .0335 
 
 .0290 
 
 21/2 
 
 .3921 
 
 .7724 
 
 .5351 
 
 3/8 
 
 .0313 
 
 .0405 
 
 .0345 
 
 25/ 8 
 
 .5348 
 
 1.9541 
 
 .6924 
 
 13/32 
 
 .0368 
 
 .0466 
 
 .0405 
 
 23/i 
 
 .6845 
 
 2.1446 
 
 .8574 
 
 7/16 
 
 .0426 
 
 .0543 
 
 .0470 
 
 27/ 8 
 
 .8411 
 
 2.3441 
 
 2.0304 
 
 15/32 
 
 .0489 
 
 .0623 
 
 .0540 
 
 3 
 
 2.0046 
 
 2.5548 
 
 2.2105 
 
 1/2 
 
 .0557 
 
 .0709 
 
 .0614 
 
 31/8 
 
 2.1752 
 
 2.7719 
 
 2.3986 
 
 17/32 
 
 .0629 
 
 .0800 
 
 .0693 
 
 31/4 
 
 2.3527 
 
 2.9954 
 
 2.5918 
 
 9/16 
 
 .0705 
 
 .0897 
 
 .0777 
 
 33/g 
 
 2.5371 
 
 3.2303 
 
 2.7977 
 
 19/32 
 
 .0785 
 
 .1036 
 
 .0866 
 
 31/2 
 
 2.7286 
 
 3.4740 
 
 3.0083 
 
 5/8 
 
 .0870 
 
 .1108 
 
 .0959 
 
 35/8 
 
 2.9269 
 
 3.7265 
 
 3.2275 
 
 21/32 
 
 .0959 
 
 .1221 
 
 .1058 
 
 33/4 
 
 3.1323 
 
 3.9880 
 
 3.4539 
 
 11/16 
 
 .1053 
 
 .1340 
 
 .1161 
 
 37/g 
 
 3.3446 
 
 4.2582 
 
 3.6880 
 
 23/32 
 
 .1151 
 
 .1465 
 
 .1270 
 
 4 
 
 3.5638 
 
 4.5374 
 
 3.9298 
 
 3/4 
 
 .1253 
 
 .1622 
 
 .1382 
 
 41/8 
 
 3.7900 
 
 4.8254 
 
 4.1792 
 
 25/32 
 
 .1359 
 
 .1732 
 
 .1499 
 
 41/4 
 
 4.0232 
 
 5.1223 
 
 4.4364 
 
 13/16 
 
 .1470 
 
 .1872 
 
 .1620 
 
 43/8 
 
 4.2634 
 
 5.4280 
 
 4.7011 
 
 27/32 
 
 .1586 
 
 .2019 
 
 .1749 
 
 41/2 
 
 4.5105 
 
 5.7426 
 
 4.9736 
 
 7/8 
 
 .1705 
 
 .2171 
 
 .1880 
 
 45/8 
 
 4.7645 
 
 6.0662 
 
 5.2538 
 
 29/32 
 
 .1829 
 
 .2329 
 
 .2015 
 
 43/4 
 
 5.0255 
 
 6.6276 
 
 5.5416 
 
 15/16 
 
 .1958 
 
 .2492 
 
 .2159 
 
 47/8 
 
 5.2935 
 
 6.7397 
 
 5.8371 
 
 31/32 
 
 .2090 
 
 .2661 
 
 .2305 
 
 5 
 
 5.5685 
 
 7.0897 
 
 6.1403 
 
 9 
 
 .2227 
 
 .2836 
 
 .2456 
 
 51/8 
 
 5.8504 
 
 7.4496 
 
 6.4511 
 
 1 1/16 
 
 .2515 
 
 .3201 
 
 .2773 
 
 51/4 
 
 6.1392 
 
 7.8164 
 
 6.7697 
 
 1 1/8 
 
 .2819 
 
 .3589 
 
 .3109 
 
 53/8 
 
 6.4351 
 
 8.1930 
 
 7.0959 
 
 1 3/16 
 
 .3141 
 
 .4142 
 
 . .3464 
 
 51/2 
 
 6.7379 
 
 8.5786 
 
 7.4298 
 
 U/4 
 
 .3480 
 
 .4431 
 
 .3838 
 
 55/8 
 
 7.0476 
 
 8.9729 
 
 7.7713 
 
 1 5/16 
 
 .3837 
 
 .4885 
 
 .4231 
 
 53/4 
 
 7.3643 
 
 9.3762 
 
 8.1214 
 
 1 3/8 
 
 .4211 
 
 .5362 
 
 .4643 
 
 57/ 8 
 
 7.6880 
 
 9 . 7883 
 
 8.4774 
 
 1 7/16 
 
 .4603 
 
 .5860 
 
 .5076 
 
 6 
 
 8.0186 
 
 10.2192 
 
 8.8420 
 
 1 V2 
 
 .5012 
 
 .6487 
 
 .5526 
 
 61/4 
 
 8 . 7007 
 
 11.0877 
 
 9.5943 
 
 1 9/16 
 
 .5438 
 
 .6930 
 
 .5996 
 
 6l/ 2 
 
 9.4107 
 
 11.9817 
 
 10.3673 
 
 1 5/8 
 
 .5882 
 
 .7489 
 
 .6480 
 
 63/4 
 
 10.1485 
 
 12.9211 
 
 11.1908 
 
 1 H/16 
 
 .6343 
 
 .8076 
 
 .6994 
 
 7 
 
 10.9142 
 
 13.8960 
 
 12.0351 
 
 1 3/4 
 
 .6821 
 
 .8685 
 
 .7521 
 
 71/2 
 
 12.5291 
 
 15.9520 
 
 13.8158 
 
 1 13/16 
 
 .7317 
 
 .9316 
 
 .8069 
 
 8 
 
 14.2553 
 
 18.1497 
 
 15.7192 
 
 Weight of Fillets. Continued from page 185. . 
 
 Ra- 
 dius, 
 In. 
 
 Area, 
 Sq. In. 
 
 Weight per In., Lb. 
 
 Ra- 
 dius, 
 In. 
 
 Area, 
 Sq. In. 
 
 Weight per In., Lb. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Brass. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Br.ass. 
 
 13/4 
 
 0.6572 
 
 0.1713 
 
 0.1862 
 
 0.1920 
 
 27/8 
 
 1.774 
 
 0.4621 
 
 0.5022 
 
 0.5017 
 
 1 7/8 
 
 .7545 
 
 .1970 
 
 .2137 
 
 .2202 
 
 3 
 
 1.931 
 
 .4950 
 
 .5471 
 
 .5635 
 
 2 
 
 .8585 
 
 .2237 
 
 .2431 
 
 .2504 
 
 31/4 
 
 2.267 
 
 .5903 
 
 .6417 
 
 .6609 
 
 21/8 
 
 .9692 
 
 .2502 
 
 .2743 
 
 .2826 
 
 31/2 
 
 2.629 
 
 .6926 
 
 .7438 
 
 .7661 
 
 US 
 
 1.086 
 
 .2832 
 
 .3079 
 
 .3172 
 
 33/4 
 
 3.018 
 
 .7873 
 
 .8523 
 
 .8817 
 
 23/8 
 
 1.210 
 
 .3155 
 
 .3429 
 
 .3532 
 
 
 3.434 
 
 .8933 
 
 .9709 
 
 1.000 
 
 21/2 
 
 1.341 
 
 .3496 
 
 .3800 
 
 .3914 
 
 41/4 
 
 3.876 
 
 1.008 
 
 1.096 
 
 1.130 
 
 25/ 8 
 
 1.478 
 
 .3857 
 
 .4192 
 
 .4317 
 
 41/2 
 
 4.346 
 
 1.132 
 
 1.231 
 
 1.270 
 
 23/ 4 
 
 1.623 
 
 .4222 
 
 .4589 
 
 .4727 
 
 43/4 
 
 4.842 
 
 1.261 
 
 1.371 
 
 1.421 
 
WEIGHT OF PLATE IKON. 
 
 187 
 
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WEIGHTS OF FLAT WROUGHT IRON. 189 
 
 
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 eNinfxOtsiinr^OeNinhNCfNmhNCincmoinOin 
 
 oienin^Ot^iao eNfen'mot^ooceNinr^Of^jin^N* 
 
 fmr>.o^' enmr^o^ enmtviO^ *n t o> en t> m^en 
 
 ^' en ^* m t^ GO s o en *! m \o i> o^ m O GO en in GO* 
 
 fNCNCMfsjenenenen 
 
 ~ cs en ^T m vd t> oo & es en ^1" m \o r^ o^ ^ \d GO' ' e>i m* 
 
 (S f\j eNi encn^^J'ininin\OvOi>GOO t >' <Sen 
 
 ^ qqt>; 
 g ' o' oo 
 
 H IC>OCO^. 
 
 >> :x 
 
 5! *vo 
 
 o *> .V K 
 
 -o x 'X i 
 
 ea M ;o ^ 
 
 I '^'If 
 
 r4 %$"3 ^ X- 
 
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 K^^E hC 
 
 SX^.S 
 
 $ Jill -*3^^ 
 
 "S X WK~ * 
 
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190 
 
 MATERIALS. 
 
 WEIGHTS OF STEEL BLOOMS. 
 
 Soft steel. 1 cubic inch 0.284 Ib. 1 cubic foot = 490.75 Ibs. 
 
 Size, 
 Inches 
 
 Lengths. 
 
 1" 
 
 6" 
 
 13" 
 
 18" 
 
 24" 
 
 30" 
 
 36" 
 
 42" 
 
 48" 
 
 54" 
 
 60" 
 
 66" 
 
 12 X6 
 X5 
 
 20.45 
 17.04 
 
 123 
 102 
 
 245 
 204 
 
 368 
 307 
 
 491 
 409 
 
 613 
 511 
 
 736 
 613 
 
 ~859 
 716 
 
 982 
 
 818 
 
 1104 
 920 
 
 1227 
 1022 
 
 1350 
 1125 
 
 X4 
 
 13.63 
 
 82 
 
 164 
 
 245 
 
 327 
 
 409 
 
 491 
 
 573 
 
 654 
 
 736 
 
 818 
 
 900 
 
 11 X6 
 
 18.75 
 
 113 
 
 225 
 
 338 
 
 450 
 
 563 
 
 675 
 
 788 
 
 900 
 
 1013 
 
 1 125 
 
 1238 
 
 X5 
 
 15.62 
 
 94 
 
 188 
 
 281 
 
 375 
 
 469 
 
 562 
 
 656 
 
 750 
 
 843 
 
 937 
 
 1031 
 
 X4 
 
 12.50 
 
 75 
 
 150 
 
 225 
 
 300 
 
 375 
 
 450 
 
 525 
 
 600 
 
 675 
 
 750 
 
 825 
 
 10 X8 
 
 22.72 
 
 136 
 
 273 
 
 409 
 
 545 
 
 682 
 
 818 
 
 954 
 
 1091 
 
 1227 
 
 1363 
 
 1500 
 
 X7 
 
 19.88 
 
 120 
 
 239 
 
 358 
 
 477 
 
 596 
 
 715 
 
 835 
 
 955 
 
 1074 
 
 1193 
 
 1312 
 
 X6 
 
 17.04 
 
 102 
 
 204 
 
 307 
 
 409 
 
 511 
 
 613 
 
 716 
 
 818 
 
 920 
 
 1022 
 
 1125 
 
 X5 
 
 14.20 
 
 85 
 
 170 
 
 256 
 
 341 
 
 426 
 
 511 
 
 596 
 
 682 
 
 767 
 
 852 
 
 937 
 
 X4 
 
 11.36 
 
 68 
 
 136 
 
 205 
 
 273 
 
 341 
 
 409 
 
 477 
 
 546 
 
 614 
 
 682 
 
 750 
 
 K3 
 
 8.52 
 
 51 
 
 102 
 
 153 
 
 204 
 
 255 
 
 306 
 
 358 
 
 409 
 
 460 
 
 511 
 
 562 
 
 9 X8 
 
 20.45 
 
 123 
 
 245 
 
 368 
 
 491 
 
 613 
 
 736 
 
 859 
 
 982 
 
 1104 
 
 1227 
 
 1350 
 
 X7 
 
 17.89 
 
 107 
 
 215 
 
 322 
 
 430 
 
 537 
 
 644 
 
 751 
 
 859 
 
 966 
 
 1073 
 
 1181 
 
 X6 
 
 15.34 
 
 92 
 
 184 
 
 276 
 
 368 
 
 460 
 
 552 
 
 644 
 
 736 
 
 828 
 
 920 
 
 1012 
 
 X5 
 
 12.78 
 
 77 
 
 153 
 
 230 
 
 307 
 
 383 
 
 460 
 
 537 
 
 614 
 
 690 
 
 767 
 
 844 
 
 X4 
 
 10.22 
 
 61 
 
 123 
 
 184 
 
 245 
 
 307 
 
 368 
 
 429 
 
 490 
 
 552 
 
 613 
 
 674 
 
 X3 
 
 7.66 
 
 46 
 
 92 
 
 138 
 
 184 
 
 230 
 
 276 
 
 322 
 
 368 
 
 414 
 
 460 
 
 506 
 
 8 X8 
 
 18.18 
 
 109 
 
 218 
 
 327 
 
 436 
 
 545 
 
 655 
 
 764 
 
 873 
 
 982 
 
 1091 
 
 1200 
 
 X7 
 
 15.9 
 
 95 
 
 191 
 
 286 
 
 382 
 
 477 
 
 572 
 
 668 
 
 763 
 
 859 
 
 954 
 
 1049 
 
 X6 
 
 13.63 
 
 82 
 
 164 
 
 245 
 
 327 
 
 409 
 
 491 
 
 573 
 
 654 
 
 736 
 
 818 
 
 900 
 
 X5 
 
 11.36 
 
 68 
 
 136 
 
 205 
 
 273 
 
 341 
 
 409 
 
 477 
 
 546 
 
 614 
 
 682 
 
 750 
 
 X4 
 
 9.09 
 
 55 
 
 109 
 
 164 
 
 218 
 
 273 
 
 327 
 
 382 
 
 436 
 
 491 
 
 545 
 
 600 
 
 X3 
 
 6.82 
 
 41 
 
 82 
 
 123 
 
 164 
 
 204 
 
 245 
 
 286 
 
 327 
 
 368 
 
 409 
 
 450 
 
 7 X7 
 
 13.92 
 
 83 
 
 167 
 
 251 
 
 334 
 
 418 
 
 501 
 
 585 
 
 668 
 
 752 
 
 835 
 
 919 
 
 X6 
 
 11.93 
 
 72 
 
 143 
 
 215 
 
 286 
 
 358 
 
 430 
 
 501 
 
 573 
 
 644 
 
 716 
 
 788 
 
 X5 
 
 9.94 
 
 60 
 
 119 
 
 179 
 
 7,38 
 
 298 
 
 358 
 
 417 
 
 477 
 
 536 
 
 596 
 
 656 
 
 X4 
 
 7.95 
 
 48 
 
 96 
 
 143 
 
 191 
 
 239 
 
 286 
 
 334 
 
 382 
 
 429 
 
 477 
 
 525 
 
 X3 
 
 5.96 
 
 36 
 
 72 
 
 107 
 
 143 
 
 179 
 
 214 
 
 250 
 
 286 
 
 322 
 
 358 
 
 393 
 
 61/2X61/2 
 
 12. 
 
 72 
 
 144 
 
 216 
 
 288 
 
 360 
 
 432 
 
 504 
 
 576 
 
 648 
 
 720 
 
 792 
 
 X4 
 
 7.38 
 
 44 
 
 89 
 
 133 
 
 177 
 
 221 
 
 266 
 
 310 
 
 354 
 
 399 
 
 443 
 
 487 
 
 6 X6 
 
 10.22 
 
 61 
 
 123 
 
 184 
 
 245 
 
 307 
 
 368 
 
 429 
 
 490 
 
 551 
 
 613 
 
 674 
 
 X5 
 
 8.52 
 
 51' 
 
 102 
 
 153 
 
 204 
 
 255 
 
 307 
 
 358 
 
 409 
 
 460 
 
 511 
 
 562 
 
 X4 
 
 6.82 
 
 41 
 
 82 
 
 123 
 
 164 
 
 204 
 
 245 
 
 286 
 
 327 
 
 368 
 
 409 
 
 450 
 
 X3 
 
 5.11 
 
 31 
 
 61 
 
 92 
 
 123 
 
 153 
 
 184 
 
 214 
 
 245 
 
 276 
 
 307 
 
 337 
 
 5i/ 2 X5i/ 2 
 
 8.59 
 
 52 
 
 103 
 
 155 
 
 206 
 
 258 
 
 309 
 
 361 
 
 412 
 
 464 
 
 515 
 
 567 
 
 X4 
 
 6.25 
 
 37 
 
 75 
 
 112 
 
 150 
 
 188 
 
 225 
 
 262 
 
 300 
 
 337 
 
 375 
 
 412 
 
 5 X5 
 
 7.10 
 
 43 
 
 85 
 
 128 
 
 170 
 
 213 
 
 256 
 
 298 
 
 341 
 
 383 
 
 426 
 
 469 
 
 X4 
 
 5.68 
 
 34 
 
 68 
 
 102 
 
 136 
 
 170 
 
 205 
 
 239 
 
 273 
 
 307 
 
 341 
 
 375 
 
 41/2X41/2 
 
 5.75 
 
 35 
 
 69 
 
 104 
 
 138 
 
 173 
 
 207 
 
 242 
 
 276 
 
 311 
 
 345 
 
 380 
 
 X4 
 
 5.11 
 
 31 
 
 61 
 
 92 
 
 123 
 
 153 
 
 184 
 
 215 
 
 246 
 
 276 
 
 307 
 
 338 
 
 4 X4 
 
 4.54 
 
 27 
 
 55 
 
 82 
 
 109 
 
 136 
 
 164 
 
 191 
 
 218 
 
 246 
 
 272 
 
 300 
 
 X31/2 
 
 3.97 
 
 24 
 
 48 
 
 72 
 
 96 
 
 119 
 
 143 
 
 167 
 
 181 
 
 215 
 
 238 
 
 262 
 
 X3 
 
 3.40 
 
 20 
 
 41 
 
 61 
 
 82 
 
 102 
 
 122 
 
 143 
 
 163 
 
 184 
 
 204 
 
 224 
 
 31/2X31/2 
 
 3.48 
 
 21 
 
 42 
 
 63 
 
 84 
 
 104 
 
 125 
 
 146 
 
 167 
 
 188 
 
 209 
 
 230 
 
 X3 
 
 2.98 
 
 18 
 
 36 
 
 54 
 
 72 
 
 89 
 
 107 
 
 ' 125 
 
 143 
 
 161 
 
 179 
 
 197 
 
 3 X3 
 
 2.56 
 
 15 
 
 31 
 
 46 
 
 61 
 
 77 
 
 92 
 
 108 
 
 123 
 
 138 
 
 154 
 
 169 
 
ROOFING MATERIALS AND ROOF CONSTRUCTION. 191 
 
 ROOFING MATERIALS AND ROOF CONSTRUCTION. 
 
 Approximate Weight of Roofing Materials. 
 
 (American Sheet & Tin Plate Co.) 
 
 Material. 
 
 Lb. per 
 
 sq. ft. 
 
 Corrugated galvanized iron, No. 20, unbearded 
 
 Copper, 16 oz. standing seam . . . . , 
 
 Felt and asphalt, without sheathing 
 
 Glass, i/s in. thick 
 
 Hemlock sheathing, 1 in. thick 
 
 Lead, about l/s in. thick 
 
 Lath and plaster ceiling (ordinary) 
 
 Mackite, 1 in. thick, with plaster 
 
 Neponset roofing, felt, 2 layers 
 
 Spruce sheathing, 1 in. thick 
 
 Slate, 3/i6 in. thick, 3 in. double lap 
 
 Slate, l/s in. thick, 3 in. double lap 
 
 Shingles, 6 in. X 18 in., 1/3 to weather 
 
 Skylight of glass, 3/ie to 1/2 in., including frame 
 
 Slag roof, 4-ply 
 
 Terne plate, 1C, without sheathing 
 
 Terne plate, IX, without sheathing 
 
 Tiles (plain), 10 1/2 in. X 6 1/4 in. X 5/8 in. - 5 1/4 in. to weather . 
 
 Tiles (Spanish), 14 1/2 in. X 10 l/ 2 in.- 7 1/4 in. to weather 
 
 White pine sheathing, 1 in. thick 
 
 Yellow pine sheathing, 1 in. thick 
 
 21/4 
 
 ,./< 
 </< 
 
 6 to 8 
 6 to 8 
 10 
 
 1/2 
 21/2 
 63/4 
 
 4l/ 2 
 
 4 to 10 
 4 
 1/2 
 
 5/8 
 18 
 
 81/2 
 21/2 
 
 Snow and Wind Loads on Roofs. 
 
 In designing roofs, in addition to the weight of roofing material to 
 be supported, recognition must be given to possible snow and wind loads. 
 
 In snowy localities the minimum snow load per horizontal sq. ft. of 
 roof should be considered as 25 Ib. for slopes up to 20 degrees. For 
 each degree increase in slope up to 45 degrees, this load may be reduced 
 1 Ib. Above 45-degree slope no snow load need be considered. In 
 especially severe climates these allowances should be increased in ac- 
 cordance with actual conditions. 
 
 The wind load is the pressure normal to the surface of the roof pro- 
 duced by a wind blowing horizontally. The wind pressure against a 
 vertical plane as determined by the U. S. Signal Service at Mt. Wash- 
 ington, N. H., is for various velocities of wind: 
 
 Velocity, miles per hr .. 10 20 30 40 50 60 80 100 
 
 Pressure, Ib. per sq. ft 0.4 1.6 3.6 6.4 10.0 14.4 25.6 40.0 
 
 The pressure on a flat surface is twice that on a cylindrical surface 
 of the same projected area. For further information regarding wind 
 pressure, see page 626. As the slope of the roof increases, the greater 
 becomes the wind pressure on it. The pressure normal to the surface 
 of roofs of different slopes exerted by a wind velocity of 100 miles per 
 hour (40 Ib. per sq. ft. on a vertical plane) is 
 
 Rise, in. per ft. . 4 6 8 12 16 18 24 
 
 Angle with 
 
 horizontal. . 
 Pitch (Rise -j- 
 
 Span) 1/6 1/4 V3 1/2 V3 V4 1 
 
 Wind pressure. . 16.8 23.7 29.1 36.1 38.7 39.3 40.0 
 
 Roof Construction. (N. G. Taylor Co., Philadelphia.) Roofs with 
 less than 1/3 pitch are made with flat seams, and should preferably be 
 covered with 14 X 20 in. sheets, rather than with 20 X 28-in. sheets, as 
 the larger number of seams tend to stiffen the surface and prevent 
 buckles. For a flat seam roof the edges of the sheets are turned 1/2 in., 
 locked together and soldered. The sheets are fastened to the sheath.- 
 
 . 18 26' 26 34' 33 41' 45 0' 53 8' 56 19' 63 26' 
 
192 
 
 MATERIALS, 
 
 ing boards by cleats 8 in. apart and locked in the seams. Two 1-in 
 barbed and tinned nails are driven in each cleat. Steep tin roofs 
 should be made with standing seams and from 28 X 20-in. sheets. The 
 sheets are first single or double seamed and soldered together in a long 
 strip reaching from eave to ridge. The sloping seams are composed 
 of two "upstands" interlocked at the upper edge and held to the sheath- 
 ing boards by cleats. No solder is used in standing seams as a rule 
 In soldering tin roofs, only a good rosin flux should be used. The use 
 of acid must be carefully avoided. 
 
 ttoof Paints. The American Sheet and Tin Plate Co. recommends 
 for painting metal work and tin roofs metallic brown, Venetian red, or 
 red oxide paint, ground in pure linseed oil. The paint should be 
 rubbed well in, and should not be spread thin. See also Preservative 
 Coatings, page 471. 
 
 Tin Plates are made of soft sheet steel coated with tin, and are 
 called in the trade "coke" or "charcoal" plates according to the weight 
 of coating. These terms have survived from the time when the highest 
 quality of plate was made from charcoal-iron, while the lower grades 
 were made from coke-iron. Consequently, plates to-day with the 
 lighter coatings are known as coke-plates, and are used for tin cans, etc. 
 The various grades of charcoal-plates are designated by the letters A to 
 AAAAA, the latter having the heaviest coating and the highest polish. 
 There is one other brand made with a heavier coating than 5A, which is 
 especially adapted for nickel-plating. The unit 9f value and measure- 
 ment of tin plates is the "base-box," which will hold 112 sheets of 
 14 X 20 in. plate, or 31360 sq. in. of any size. Plates lighter than 65 Ib. 
 per base box (No. 36 gage) are known as taggers tin. 
 
 Weights of Standard Galvanized Sheets. 
 
 (American Sheet & Tin Plate Co.) 
 
 1 
 
 o 
 
 M 
 
 $ 
 
 &B 
 
 d* 
 
 | 
 
 d 
 
 O 
 
 1* 
 
 
 
 fc^ 
 
 5 
 
 1 
 O 
 
 & 
 $$ 
 
 I* 
 
 a* 
 
 O 
 
 M 
 
 s 
 
 I* 
 tf 
 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 
 112.5 
 102.5 
 92.5 
 82.5 
 72.5 
 62.5 
 52.5 
 
 7.031 
 6.406 
 5.781 
 5.156 
 4.531 
 3.906 
 3.281 
 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 
 47.5 
 42.5 
 38.5 
 34.5 
 30.5 
 26.5 
 24.5 
 
 2.969 
 2.656 
 2.406 
 2.156 
 1.906 
 1.656 
 1.531 
 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 
 22.5 
 20.5 
 18.5 
 16.5 
 14.5 
 13.5 
 12.5 
 
 1.406 
 1.281 
 1.156 
 1.031 
 0.906 
 .844 
 .781 
 
 29 
 30 
 31 
 32 
 33 
 34 
 
 11.5 
 10.5 
 9.5 
 9.0 
 8.5 
 8.0 
 
 0.719 
 .656 
 .594 
 .563 
 .531 
 .500 
 
 Standard Weights and Gages of Tin Plate. 
 
 (American Sheet & Tin Plate Co., Pittsburgh.) 
 
 II 
 
 Nearest 
 Wire 
 Gage No. 
 
 cr 
 
 O3 
 
 I* 
 ^ 
 
 S.g 
 
 PQo 
 
 ^(N 
 
 x 
 
 F 
 
 <u 
 
 T3 S 
 
 ^ 
 
 Nearest 
 Wire 
 Gage No. 
 
 a 1 
 
 CO 
 
 fe 
 a ... 
 
 ^ 
 
 gfl 
 
 i 
 X 
 
 ^a 
 
 100 
 107 
 118 
 135 
 128 
 139 
 155 
 148 
 175 
 
 
 
 g 
 
 Nearest 
 Wire 
 Gage No. 
 
 O" 
 
 CQ . 
 
 53 
 P. r 
 
 ^ 
 
 Sg 
 
 
 
 F* 
 
 55 Ib. 
 60 
 65 
 70 
 75 
 80 
 85 
 90 
 95 
 
 38 
 37 
 36 
 35 
 34 
 33 
 32 
 31 
 31 
 
 0.252 
 .275 
 .298 
 .321 
 .344 
 .367 
 .390 
 .413 
 .436 
 
 55 
 
 60 
 65 
 70 
 75 
 80 
 85 
 90 
 95 
 
 lOOlb. 
 1C 
 1181b. 
 IX 
 IXL 
 DC 
 2X 
 2XL 
 3X 
 
 30V 2 
 30 
 29 
 28 
 28 
 28 
 27 
 27 
 26 
 
 0.459 
 .491 
 .542 
 .619 
 .588 
 .638 
 .711 
 .679 
 .803 
 
 3XL 
 DX 
 4X 
 4XL 
 D2X 
 D3X 
 D4X 
 
 26 
 26 
 25 
 25 
 24 
 23 
 22 
 
 0.771 
 .826 
 .895 
 .863 
 .964 
 1.102 
 1.239 
 
 168 
 180 
 195 
 188 
 210 
 240 
 270 
 
 
 
 
 
TIN AND TERNE PLATES. 
 
 193 
 
 Sizes and Net Weight per Box of 100 Ib. (0.459 Ib. per sq. ft.) 
 Tin Plates. 
 
 Size of 
 Sheets. 
 
 Sheets 
 per 
 Box. 
 
 Weight 
 per 
 Box. 
 
 Size of 
 Sheets. 
 
 Sheets 
 per 
 Box. 
 
 Weight 
 per 
 Box. 
 
 Size of 
 Sheets. 
 
 Sheets 
 per 
 Box. 
 
 Weight 
 per 
 Box. 
 
 10 X14 
 
 225 
 
 100 
 
 15X15 
 
 225 
 
 161 
 
 14 X31 
 
 112 
 
 155 
 
 14 X20 
 
 112 
 
 100 
 
 16X16 
 
 225 
 
 183 
 
 111/4X223/4 
 
 112 
 
 91 
 
 20 X28 
 
 112 
 
 200 
 
 17X17 
 
 225 
 
 206 
 
 131/4x173/4 
 
 112 
 
 84 
 
 10 X20 
 
 225 
 
 143 
 
 18X18 
 
 112 
 
 116 
 
 131/4X191/4 
 
 112 
 
 91 
 
 11 X22 
 
 225 
 
 172 
 
 19X19 
 
 112 
 
 129 
 
 131/2x191/2 
 
 112 
 
 94 
 
 11i/ 2 'X23 
 
 225 
 
 189 
 
 20X20 
 
 112 
 
 143 
 
 131/2x193/4 
 
 112 
 
 95 
 
 12 X12 
 
 225 
 
 103 
 
 21X21 
 
 112 
 
 158 
 
 14 Xl83/ 4 
 
 124 
 
 103 
 
 12 X24 
 
 112 
 
 103 
 
 22X22 
 
 112 
 
 172 
 
 14 X19V 4 
 
 120 
 
 103 
 
 13 X13 
 
 225 
 
 121 
 
 23X23 
 
 112 
 
 189 
 
 14 X21 
 
 112 
 
 105 
 
 13 X26 
 
 H2 
 
 121 
 
 24X24 
 
 112 
 
 204 
 
 14 X22 
 
 .112 
 
 110 
 
 14 X14 
 
 225 
 
 140 
 
 26X26 
 
 112 
 
 241 
 
 14 X221/4 
 
 112 
 
 111 
 
 14 X28 
 
 112 
 
 140 
 
 16X20 
 
 112 
 
 114 
 
 15V 2 X23 
 
 112 
 
 127 
 
 For weight per box of other than 100-lb. plates multiply by the 
 figures in the column "Weight per Box" in the preceding table, and 
 divide by 100. Thus for IX plates 20 X 28 in., 200 X 135 + 100 = 270. 
 
 Sheets Required for Tin Roofing. 
 
 (American Sheet & Tin Plate Co., 1914.) 
 
 
 Sheets 
 
 
 Sheets 
 
 
 Sheets 
 
 
 Sheets 
 
 
 Sheets 
 
 e 
 
 Required. 
 
 
 
 Required 
 
 .j 
 
 Required. 
 
 +1 
 
 Required. 
 
 42 
 
 Required. 
 
 
 
 S_4 
 
 R 
 
 
 g^_. 
 
 , 
 
 
 _; 
 
 w 
 
 
 g^_. 
 
 H 
 
 
 Is 
 
 CO 
 
 1^ 
 
 s^ 
 
 cr 
 
 CO 
 
 1^ 
 
 2^ 
 
 s 
 
 1 
 
 S&H 
 
 1 
 
 ^ 
 
 s^ 
 
 D* 
 CO 
 
 1^ 
 
 
 *o 
 
 ^X 
 
 ^* 
 
 "o 
 
 ^ V 
 
 T3 V 
 
 *o 
 
 co^ 
 
 'O V 
 
 "o 
 
 ^ V 
 
 3* 
 
 "8 
 
 co 
 
 ^ 
 
 1 
 
 ~ 
 
 CO 
 
 6 
 fc 
 
 "S 
 ST 
 
 S3 * 
 
 CO^ 
 
 6 
 
 I- 
 
 co^ 
 
 6 
 fc 
 
 !- 
 
 Is 
 
 CO 
 
 1 
 
 ICTJ- 
 
 Is 
 
 CO 
 
 100 
 
 59 
 
 31 
 
 280 
 
 164 
 
 86 
 
 460 
 
 269 
 
 141 
 
 640 
 
 374 
 
 197 
 
 820 
 
 479 
 
 252 
 
 110 
 
 65 
 
 34 
 
 290 
 
 170 
 
 89 
 
 470 
 
 275 
 
 144 
 
 650 
 
 379 
 
 200 
 
 830 
 
 484 
 
 255 
 
 120 
 
 70 
 
 37 
 
 300 
 
 175 
 
 92 
 
 480 
 
 280 
 
 148 
 
 660 
 
 385 
 
 203 
 
 840 
 
 490 
 
 258 
 
 130 
 
 76 
 
 40 
 
 310 
 
 181 
 
 95 
 
 490 
 
 286 
 
 151 
 
 670 
 
 391 
 
 206 
 
 850 
 
 496 
 
 26! 
 
 140 
 
 82 
 
 43 
 
 320 
 
 187 
 
 99 
 
 500 
 
 292 
 
 154 
 
 680 
 
 397 
 
 209 
 
 860 
 
 502 
 
 264 
 
 150 
 
 88 
 
 46 
 
 330 
 
 193 
 
 102 
 
 510 
 
 298 
 
 157 
 
 690 
 
 403 
 
 212 
 
 870 
 
 508 
 
 267 
 
 160 
 
 94 
 
 50 
 
 340 
 
 199 
 
 105 
 
 520 
 
 304 
 
 160 
 
 700 
 
 409 
 
 215 
 
 880 
 
 514 
 
 270 
 
 170 
 
 100 
 
 53 
 
 350 
 
 205 
 
 108 
 
 530 
 
 309 
 
 163 
 
 710 
 
 414 
 
 218 
 
 890 
 
 519 
 
 273 
 
 180 
 
 105 
 
 56 
 
 360 
 
 210 
 
 
 540 
 
 315 
 
 166 
 
 720 
 
 420 
 
 221 
 
 900 
 
 525 
 
 276 
 
 190 
 
 111 
 
 59 
 
 370 
 
 216 
 
 114 
 
 550 
 
 321 
 
 169 
 
 730 
 
 426 
 
 224 
 
 910 
 
 531 
 
 279 
 
 200 
 
 117 
 
 62 
 
 380 
 
 222 
 
 '117 
 
 560 
 
 327 
 
 172 
 
 740 
 
 432 
 
 227 
 
 920 
 
 537 
 
 282 
 
 210 
 
 123 
 
 65 
 
 390 
 
 228 
 
 120 
 
 570 
 
 333 
 
 175 
 
 750 
 
 438 
 
 230 
 
 930 
 
 543 
 
 285 
 
 220 
 
 129 
 
 68 
 
 400 
 
 234 
 
 123 
 
 580 
 
 339 
 
 178 
 
 760 
 
 444 
 
 233 
 
 940 
 
 549 
 
 288 
 
 230 
 
 135 
 
 71 
 
 410 
 
 240 
 
 126 
 
 590 
 
 344 
 
 181 
 
 770 
 
 449 
 
 236 
 
 950 
 
 554 
 
 291 
 
 240 
 
 140 
 
 74 
 
 420 
 
 245 
 
 129 
 
 600 
 
 350 
 
 184 
 
 780 
 
 455 
 
 239 
 
 960 
 
 560 
 
 295 
 
 250 
 
 146 
 
 77 
 
 430 
 
 251 
 
 132 
 
 610 
 
 356 
 
 187 
 
 790 
 
 461 
 
 243 
 
 970 
 
 566 
 
 298 
 
 260 
 
 152 
 
 80 
 
 440 
 
 257 
 
 135 
 
 620 
 
 362 
 
 190 
 
 800 
 
 467 
 
 246 
 
 980 
 
 572 
 
 301 
 
 270 
 
 158 
 
 83 
 
 450 
 
 263 
 
 138 
 
 630 
 
 368 
 
 194 
 
 810 
 
 473 
 
 249 
 
 990 
 
 578 
 
 304 
 
 Terne Plates, or Roofing Tin, are coated with an alloy of tin and lead. 
 In the "U. S. Eagle, N.M." brand the alloy is 32% tin, 68% lead. 
 The weight per 112 sheets of this brand before and after coating is as 
 follows: 
 
 1C 14 X 20 1C 20 X 28 IX 14 X 20 IX 20 X 28 
 Black plates ... 95 to 100 Ib. 190 to 200 Ib. 125 to 130 Ib. 250 to 260 Ib. 
 After coating. . . 115 to 120 230 to 240 145 to 150 290 to 300 
 
 Terne plates are made in two thicknesses: 1C, in which the iron body 
 weighs about 50 Ib. per 100 sq. ft., and IX, in which it weighs 62 1/2 Ib. 
 per 1.00 sq. ft. The 1C grade is preferred for roofing, wnile the !?C 
 
194 
 
 MATERIALS. 
 
 grade is used for spouts, valleys, gutters, and flashings. The standard 
 weight of 14 X 20 in. 1C plates is 107 Ib. per base-box, and of 14 x 20- 
 in. IX plate 135 Ib. 
 
 Long terne sheets are made in'gages, Nos. 14 to 32, from 10 to 40 in. 
 wide and up to 120 in. long. They are made in five grades with coat- 
 ings of 8, 12, 15, 20, and 25 Ib. 
 
 A box of 112 sheets 14 X 20 in. will cover approximately 192 sq. ft. 
 of roof, flat seam, or 583 sheets 1000 sq. ft. For standing seam roofing 
 a sheet 20 X 28 in. will cover 475 sq. in., or 303 sheets 1000 sq. ft. A 
 box of 112 sheets 20 X 28 in. will cover approximately 366 sq. ft. 
 
 The common sizes of tin plates are 10 X 14 in. and multiples of that 
 measure. The sizes most generally used are 14 x 20 and 20 X 28 in. 
 
 Specifications for Tin and Terne Plate. (Penna. R.R., 1903.) 
 
 
 Material Desired. 
 
 Rejected if less than 
 
 Tin 
 Plate. 
 
 No. 1 
 Terne. 
 
 No. 2 
 Terne. 
 
 Tin 
 Plate. 
 
 No. 1 
 
 Terne. 
 
 No. 2 
 Terne. 
 
 Coating: 
 Tin, per cent 
 
 100 
 
 0.023 
 
 0.496 
 .625 
 .716 
 .808 
 .900 
 
 26 
 74 
 0.046 
 
 0.519 
 .648 
 .739 
 .831 
 .923 
 
 16 
 84 
 0.023 
 
 0.496 
 .625 
 .716 
 .808 
 .900 
 
 
 
 
 Lead, per cent 
 
 
 
 
 Amount per sq. ft., Ib. . 
 Weight, Ib. per sq. ft. of 
 Grade 1C... 
 
 0.0183 
 
 0.468 
 .590 
 .676 
 .763 
 .850 
 
 0.0413 
 
 0.490 
 .612 
 .699 
 .787 
 .874 
 
 0.083 
 
 0.468 
 .590 
 .676 
 .763 
 .850 
 
 Grade IX ... 
 
 Grade IXX 
 
 Grade IXXX . . 
 
 Grade IXXXX 
 
 Each sheet in a shipment of tin or terne plate must (1) be cut as 
 nearly exact to size ordered as possible; (2) must be rectangular, flat, 
 and free from flaws; (3) must double seam successfully under reason- 
 able treatment; (4) must show a smooth edge with no sign of fracture 
 when bent through an angle of 180 degrees and flattened down with a 
 wooden mallet ; (5) must be so nearly like every other sheet in the ship- 
 ment, both in thickness and in uniformity and amount of coating, that 
 110 difficulty will arise in the shops due to varying thickness of sheets. 
 
 Corrugated Sheets. Weight per 100 Sq. Ft., Lb. 
 
 (American Sheet & Tin Plate Co., Pittsburgh, 1914.) 
 
 Corruga- 
 tions. 
 
 5/8 in. 
 
 1V4 in. 
 
 2 in. 
 
 2 i/ 2 in.* 
 26 in. 
 wide. 
 
 2 1/2 in.f 
 27 i/ 2 in. 
 wide. 
 
 3 in. 
 
 5 in. 
 
 U. S. Std. 
 Sheet 
 Metal 
 Gage. 
 
 "8 
 a 
 
 & 
 
 jh 
 
 eft N 
 
 o 
 
 1 
 
 a 
 '3 
 ft 
 
 i 
 
 11 
 
 o' rt 
 
 ! 
 
 ia 
 
 PH 
 
 li 
 
 O'~ 
 
 I 
 1 
 
 jb 
 
 5* 
 
 1 
 
 & 
 
 ji 
 
 1 
 
 1 
 PH 
 
 li 
 
 0'" 
 
 1 
 '< 
 
 PH 
 
 "68 
 75 
 81 
 95 
 108 
 122 
 135 
 148 
 162 
 215 
 269 
 336 
 470 
 
 h 
 
 73 N 
 
 0'~ 
 
 ~~77 
 
 84 
 91 
 97 
 111 
 124 
 137 
 151 
 164 
 178 
 231 
 285 
 352 
 486 
 
 29 
 28 
 27 
 26 
 25 
 24 
 23 
 22 
 21 
 20 
 18 
 16 
 14 
 12 
 10 
 
 "i\ 
 
 78 
 85 
 99 
 113 
 
 81 
 88 
 95 
 102 
 116 
 130 
 
 "7\ 
 78 
 85 
 99 
 113 
 127 
 141 
 155 
 169 
 
 81 
 88 
 95 
 102 
 116 
 130 
 144 
 158 
 172 
 186 
 
 "68 
 75 
 82 
 95 
 109 
 122 
 136 
 149 
 163 
 216 
 270 
 
 77 
 84 
 91 
 98 
 111 
 125 
 138 
 151 
 165 
 178 
 232 
 286 
 
 "68 
 75 
 82 
 95 
 109 
 122 
 136 
 149 
 163 
 216 
 270 
 338 
 472 
 607 
 
 77 
 84 
 91 
 98 
 111 
 125 
 138 
 151 
 165 
 178 
 232 
 286 
 353 
 488 
 623 
 
 69 
 76 
 83 
 97 
 110 
 124 
 137 
 151 
 165 
 219 
 274 
 342 
 478 
 615 
 
 78 
 85 
 92 
 99 
 113 
 126 
 140 
 153 
 167 
 181 
 235 
 290 
 358 
 494 
 631 
 
 "68 
 75 
 82 
 95 
 109 
 122 
 136 
 149 
 163 
 216 
 270 
 338 
 472 
 
 77 
 84 
 91 
 98 
 111 
 125 
 138 
 151 
 165 
 178 
 232 
 286 
 353 
 488 
 
 
 .... 
 
 .... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * Siding. t Roofing, 
 
SLATE. 
 
 195 
 
 Covering width of plates, lapped one corrugation. 24 in. Standard 
 lengths, 5, 6, 7, 8, 9, and 10 ft.; maximum length, 12 ft. 
 
 Ordinary corrugated sheets should have a lap of 1 1/2 or 2 corrugations 
 side-lap for roofing in order to secure water-tight side seams ; if the roof 
 is rather steep 1 1/2 corrugations will answer. Some manufacturers 
 make a special high-edge corrugation on sides of sheets, and thereby are 
 enabled to secure a water-proof side-lap with one corrugation only, thus 
 saving from 6% to 12% of material to cover a given area. 
 
 No. 28 gage corrugated iron is generally used for applying to wooden 
 buildings; but for applying to iron framework No. 24 gage or heavier 
 should be adopted. 
 
 Galvanizing sheet iron adds about 21/2 oz. to its weight per square 
 foot. 
 
 Slate. 
 
 Slate in roofs is measured by the square, 1 square being equal to 100 
 superficial square feet. In measuring, the width of the eaves is allowed 
 at the widest part. Hips, valleys, and cuttings are measured lineally 
 and 6 in. extra is allowed. The thickness of slate for roofing varies 
 usually from 1/8 to 3/ 16 in. The weight varies, when lapped, from 
 4 1/2 to 63/4 lb. per sq. ft. The laps range from 2 to 4 in., 3 in. being 
 the standard. As" slate is usually laid, the number of square feet of roof 
 covered by one slate is w (I 3) -~ 288, w and I being the width and 
 length respectively of the slate in inches. 
 
 Number and Superficial Area of Slate for One Square of Roof. 
 
 Size, 
 In. 
 
 No. 
 per 
 Sq. 
 
 Area, 
 
 
 
 Size, 
 In. 
 
 No. 
 
 K 
 
 Area, 
 Sq. 
 Ft. 
 
 Size, 
 In. 
 
 No. 
 
 I? 
 
 Area, 
 
 1?: 
 
 Size, 
 In. 
 
 No. 
 
 per 
 Sq. 
 
 Area, 
 Sq. 
 Ft. 
 
 6X12 
 7X12 
 
 533 
 457 
 
 267 
 
 10X14 
 8X16 
 
 261 
 
 277 
 
 246 
 
 10X20 
 11 X20 
 
 169 
 154 
 
 235 
 
 12X24 
 14X24 
 
 114 
 98 
 
 228 
 
 8X12 
 9X12 
 7X14 
 8X14 
 
 400 
 355 
 374 
 327 
 
 '254' 
 
 9X16 
 10X16 
 9X18 
 10X18 
 
 246 
 221 
 213 
 192 
 
 '240' 
 
 12X20 
 14X20 
 16X20 
 12 X22 
 
 141 
 121 
 137 
 126 
 
 23J 
 
 16X24 
 14X26 
 16X26 
 
 86 
 89 
 78 
 
 '225' 
 
 9X14 
 
 291 
 
 
 12X18 
 
 160 
 
 240 
 
 14X22 
 
 108 
 
 
 
 
 
 Weight of Slate, in Pounds, for One Square of Roof. 
 
 (1 cu. ft. slate = 175 lb.) 
 
 Length 
 of 
 Slate, In. 
 
 Thickness of Slate, Inch. 
 
 Vs 
 
 3 /16 
 
 V4 
 
 3 /8 
 
 Va 
 
 5/8 
 
 3 /4 
 
 1 
 
 !>4' 
 
 16 
 18 
 20 
 22 
 24 
 26 
 
 483 
 460 
 445 
 434 
 425 
 418 
 412 
 407 
 
 724 
 688 
 667 
 650 
 637 
 626 
 617 
 610 
 
 967 
 920 
 890 
 869 
 851 
 836 
 825 
 815 
 
 1450 
 1379 
 1336 
 1303 
 1276 
 1254 
 1238 
 1222 
 
 1936 
 1842 
 1784 
 1740 
 1704 
 1675 
 1653 
 1631 
 
 2419 
 2301 
 2229 
 2174 
 2129 
 2093 
 2066 
 2039 
 
 2902 
 2760 
 2670 
 2607 
 2553 
 2508 
 2478 
 2445 
 
 3872 
 3683 
 3567 
 3480 
 3408 
 3350 
 3306 
 3263 
 
 Corrugated Arches. 
 
 For corrugated curved sheets for floor and ceiling construction in 
 fireproof buildings, No. 16, 18, or 20 gage iron is commonly used, and 
 sheets may be curved from 4 to 10 in. rise the higher the rise the 
 stronger the arch. By a series of tests it has been demonstrated that 
 corrugated arches give the most satisfactory results with a base length 
 not exceeding 6 ft., and 5 ft. or even less is preferable where great 
 strength is required. These corrugated arches are made with 1 1/4 X 3 /8, 
 
196 
 
 MATERIALS. 
 
 2 1/2 X 1/2, 3 X 3/4, and 5 X Vs in. corrugations, and in the same width 
 of sheet as above mentioned. 
 
 Terra-Cotta. 
 
 Porous terra-cotta roofing 3 in. thick weighs 16 Ib. per square foot and 
 2 in. thick 12 Ib. per square foot. 
 
 Ceiling made of the same material 2 in. thick weighs 11 Ib. per square 
 foot. 
 
 Tiles. 
 
 Flat tiles 61/4 X 101/2 X 5/8 in. weigh from 1480 to 1850 Ib. per square 
 of roof (100 square feet), the lap being one-half the length of the tile. 
 
 Tiles with grooves and fillets weigh from 740 to 925 Ib. per square of 
 roof. 
 
 Pan-tiles 141/2 X 101/2 laid 10 in. to the weather weigh 850 Ib. per 
 square. 
 
 Pine Shingles. 
 
 The figures below give the weight of shingles required to cover one 
 square of a common gable roof. For hip roofs add 5 per cent. 
 
 Inches exposed to weather. . ............. 4 41/2 5 51/2 6 
 
 No. of shingles per square of roof ......... 900 800 720 655 600 
 
 Weight of shingles per square, Ib ......... 216 192 173 157 144 
 
 Skylight Glass Required for One Square of Roof. 
 
 Dimensions, in ............... 12 X 48 15 X 60 20 X 100 94 X 156 
 
 Thickness, in ........ , ........ 3/ 16 i/ 4 3/ 8 l/ 2 
 
 Area, sq. ft .................. 3.997 6.246 13.880 101.768 
 
 Weight per square, Ib ......... 250 350 500 700 
 
 No allowance has been made in the above figures for lap. If ordinary 
 window-glass is used, single thick glass (about Vie inch) will weigh about 
 82 Ib. per square, and double thick glass (about i/s inch) will weigh 
 about 164 Ib. per square, no allowance being made for lap. A box of 
 ordinary window-glass contains as nearly 50 square feet as the size of 
 the panes will admit. Panes of any size are made to order by the 
 manufacturers, but a great variety of sizes are usually kept in stock, 
 ranging from 6X8 inches to 36 X 60 inches. 
 
 THICKNESS OF CAST-IRON WATER-PIPES. 
 
 P. H. Baermann, in a paper read before the Engineers' Club of Phila- 
 delphia in 1882, gave twenty different formulae for determining the 
 thickness of cast-iron pipes under pressure. The formulae are of three 
 classes: 
 
 1. Depending upon the diameter only. 
 
 2. Those depending upon the diameter and head and which add a 
 constant. 
 
 3. Those depending upon the diameter and head contain an additive 
 or subtractive term depending upon the diameter, and add a constant. 
 
 The more modern formulae are of the third class, and are as follows: 
 
 t = 0.00008/id + O.Old + 0.36 ................ Shedd, No. 1. 
 
 t = 0.00006/id + 0.0133d + 0.296 ............. Warren Foundry, No. 2. 
 
 t = 0.000058M + 0.0152d 4- 0.312 ............ Francis, No. 3. 
 
 t = 0.000048/id 4- 0.013d + 0.32 .............. Dupuit, No. 4. 
 
 t = 0.00004/id 4- 0.1 Vd~4- 0.15 ..... ......... Box, No. 5. 
 
 t = 0.000135/id 4- 0.4 - 0.001 Id .............. Whitman, No. 6. 
 
 t = 0.00006 (h 4- 230) d 4- 0.333 - 0.0033d ...... Fanning, No. 7. 
 
 t = O.OOOlSftd + 0.25 - 0.0052d ............... Meggs, No. 8. 
 
 In which t = thickness in inches, h = head in feet, d = diameter in 
 inches. For h = 100 ft., and d = 10 in., formulas Nos. 1 to 7 inclusive 
 give to from 0.49 to 0.54 in., but No. 8 gives only 0.35 in. Fanning's 
 formula, now (1908) in most common use, gives 0.50 in. 
 
 Rankine (Civil Engineering}, p. 721, says: "Cast-iron pipes should be 
 made of a soft and tough quality of iron. Great attention should be paid 
 
THICKNESS OF CAST-IRON WATEB-HPES. 1Q7 
 
 to molding them C9rrectly, so that the thickness may be exactly uniform 
 all round. Each pipe should be tested for air-bubbles and flaws by ring- 
 ing it with a hammer, and for strength by exposing it to double the 
 intended greatest working pressure." The rule for computing the thick- 
 ness of a pipe to. resist a given working pressure is t = rp/f, where r is 
 the radius in inches, p the pressure in pounds per square inch, and /the 
 tensile strength of the iron per square inch. When / = 18,000, and a 
 factor of safety of 5 is used, the above expressed in terms of d and h 
 becomes t = 0.5d X 0.433/1 -T- 3600 = 0.00006d/i. 
 
 "There are limitations, however, arising from difficulties in casting, 
 and by the strain produced by shocks, which cause the thickness to be 
 made greater than that given by the above formula." (See also Burst- 
 ing Strength of Cast-iron Cylinders, under "Cast Iron.") 
 
 The most common defect of cast-iron pipes is due to the "shifting of 
 the core," which causes one side of the pipe to be thinner than the other. 
 Unless the pipe is made of very soft iron the thin side is apt to be chilled 
 in casting, causing it to become brittle and it may contain blow-holes 
 and " cold-shots." This defect should be guarded against by inspection 
 of every pipe for uniformity of thickness. 
 
 Standard Thicknesses and Weights of Cast-iron Pipe. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1915.) 
 
 : . 
 
 Class A. 
 
 Class B. 
 
 Class C. 
 
 Class D. 
 
 
 100 Ft. Head. 
 
 200 Ft. Head. 
 
 300 Ft. Head. 
 
 400 Ft. Head. 
 
 
 
 43 Lb. Pressure. 
 
 86 Lb. Pressure. 
 
 130 Lb. Pressure. 
 
 1 73 Lb. Pressure 
 
 rt c 
 
 .6 c3 
 
 ** 
 
 Pounds per 
 
 AS 
 
 Pounds per 
 
 %& 
 
 Pounds per 
 
 %* 
 
 Pounds per 
 
 |S 
 
 
 
 S - 
 
 Ft. 
 
 L'gth. 
 
 2 if 
 
 El 
 
 Ft. 
 
 L'gth. 
 
 PH 
 
 Ft. 
 
 L'gth. 
 
 g| 
 
 Ft. 
 
 Lgfch. 
 
 3 
 
 0.39 
 
 14.5 
 
 175 
 
 0.42 
 
 16.2 
 
 194 
 
 0.45 
 
 17.1 
 
 205 
 
 0.48 
 
 18.0 
 
 216 
 
 4 
 
 .42 
 
 20.0 
 
 240 
 
 .45 
 
 21.7 
 
 260 
 
 .48 
 
 23.3 
 
 280 
 
 .52 
 
 25.0 
 
 300 
 
 6 
 
 .44 
 
 30.8 
 
 370 
 
 .48 
 
 33.3 
 
 400 
 
 .51 
 
 35.8 
 
 430 
 
 .55 
 
 38.3 
 
 460 
 
 8 
 
 .46 
 
 42.9 
 
 515 
 
 .51 
 
 47.5 
 
 570 
 
 .56 
 
 52.1 
 
 625 
 
 .60 
 
 55.8 
 
 670 
 
 10 
 
 .50 
 
 57.1 
 
 685 
 
 .57 
 
 63.8 
 
 765 
 
 .62 
 
 70.8 
 
 850 
 
 .68 
 
 76.7 
 
 920 
 
 12 
 
 .54 
 
 72.5 
 
 870 
 
 .62 
 
 82.1 
 
 985 
 
 .68 
 
 91.7 
 
 1100 
 
 .75 
 
 100.0 
 
 1200 
 
 14 
 
 .57 
 
 89.6 
 
 1075 
 
 .66 
 
 102.5 
 
 1230 
 
 .74 
 
 116.7 
 
 1400 
 
 .82 
 
 129.2 
 
 1550 
 
 16 
 
 .60 
 
 108.3 
 
 1300 
 
 .70 
 
 125.0 
 
 1500 
 
 .80 
 
 143.8 
 
 1725 
 
 .89 
 
 158.3 
 
 1900 
 
 18 
 
 .64 
 
 129.2 
 
 1550 
 
 .75! 150.0 
 
 1800 
 
 .87 
 
 175.0 
 
 2100 
 
 .96 
 
 191.7 
 
 2300 
 
 20 
 
 .67 
 
 150.0 
 
 1800 
 
 .80 
 
 175.0 
 
 2100 
 
 .92 
 
 208.3 
 
 2500 
 
 .03 
 
 229.2 
 
 2'/50 
 
 24 
 
 .76 
 
 204.2 
 
 2450 
 
 .89 
 
 233.3 
 
 2800 
 
 .04 
 
 279.2 
 
 3350 
 
 .16 
 
 306.7 
 
 3680 
 
 30 
 
 .88 
 
 291.7 
 
 3500 
 
 .03 
 
 333.3 
 
 4000 
 
 .20 
 
 400.0 
 
 4800 
 
 .37 
 
 450.0 
 
 5400 
 
 36 
 
 .99 391.7 
 
 4700 
 
 .15 
 
 454.2 
 
 5450 
 
 .36 
 
 545.8 
 
 6550 
 
 .58 
 
 625.0 
 
 7500 
 
 42 
 
 .10' 512.5 
 
 6150 
 
 .28 
 
 591.7 
 
 7100 
 
 .54 
 
 716.7 
 
 8600 
 
 .78 
 
 825.0 
 
 9900 
 
 48 
 
 .26! 666.7 
 
 8000 
 
 .42 
 
 750.0 
 
 9000 
 
 .71 
 
 908.3 
 
 10900 
 
 .96 1050.0 
 
 12600 
 
 54 
 
 .35 800.0 
 
 9600 
 
 .55 
 
 933.3 
 
 11200 
 
 .90 
 
 1141.7 
 
 13700 
 
 2.23il341.7 
 
 16100 
 
 60 
 
 .39 916.7 
 
 11000 
 
 .67 
 
 1104.2 
 
 13250 
 
 2.00 
 
 1341.7 
 
 16100 
 
 2.38 
 
 1583.3 
 
 19000 
 
 72 
 
 .62 1281.9 
 
 15380 
 
 .95 
 
 1547.3 
 
 18570 
 
 2.39 
 
 1904.3 
 
 22850 
 
 
 
 . 
 
 84 
 
 .72! 1635.8 
 
 19630 
 
 2.22 
 
 2104.1 
 
 25250 
 
 
 
 
 
 
 The above weights are per length to lay 12 feet, including standard 
 sockets; proportionate allowance to be made for any variation. 
 
 Weight of Underground Pipes. (Adopted by the Natl. Fire Pro- 
 tection Association, 1913.) Weights are not to be less than those 
 specified when the normal pressures do not exceed 125 Ib. per sq. in. 
 When the normal pressures are in excess of 125 Ib. heavier pipes should 
 be used. The weights given include sockets. 
 
 Pipe, in. . , 46 8 10 12 14 16 
 
 Weights per foot, Ib.... 23 35.8 52.1 70.8 91.7 116.7 143.8 
 
198 
 
 MATERIALS. 
 
 Standard Thicknesses and Weights of Cast Iron Pipe. 
 For Fire Lines and High-Pressure Service. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1915.) 
 
 Nominal Inside 
 Diam., In. 
 
 Class E. 
 500 ft. Head. 
 217-lb. Pressure. 
 
 Class F. 
 600 ft. Head. 
 260-lb. Pressure. 
 
 Class G. 
 700 ft. Head. 
 3044b. Pressure. 
 
 Class H. 
 800 ft. Head. 
 347-lb. Pressure. 
 
 ft 
 
 r . O> 
 
 & c 
 
 Lb. per 
 
 A& 
 
 _o - 
 
 Lb. per 
 
 if 
 
 Hg 
 
 Lb. per 
 
 ii 
 
 r. 0> 
 ^ C 
 
 Lb. per 
 
 Ft. 
 
 Lgth. 
 
 Ft. 
 
 Lgth. 
 
 Ft. 
 
 Lgth. 
 
 Ft. 
 
 Lgth. 
 
 6 
 8 
 10 
 12 
 14 
 16 
 18 
 20 
 24 
 30 
 36 
 
 0.58 
 .66 
 .74 
 .82 
 .90 
 .98 
 .07 
 .15 
 .31 
 .55 
 .80 
 
 42.5 
 60.9 
 86.9 
 114.6 
 145.6 
 180.7 
 221.8 
 265.8 
 359.1 
 530.9 
 738.1 
 
 510 
 731 
 
 1043 
 1375 
 1747 
 2168 
 2662 
 3190 
 4309 
 6371 
 8857 
 
 0.61 
 .71 
 .80 
 .89 
 .99 
 1.08 
 1.17 
 1.27 
 1.45 
 1.73 
 2.02 
 
 44.3 
 66.8 
 92.8 
 122.8 
 158.8 
 196.5 
 239.3 
 287.3 
 392.3 
 588.8 
 821.0 
 
 531 
 
 802 
 1114 
 1474 
 1905 
 2358 
 2872 
 3448 
 4707 
 7065 
 9852 
 
 0.65 
 .75 
 .86 
 .97 
 .07 
 .18 
 .28 
 .39 
 .75 
 
 48.1 
 72.3 
 101.4 
 136.2 
 175.1 
 218.0 
 268.2 
 321.8 
 479.8 
 
 577 
 
 868 
 1217 
 1634 
 2101 
 2616 
 3218 
 3862 
 5758 
 
 0.69 
 .80 
 .92 
 .04 
 .16 
 .27 
 .39 
 .51 
 .88 
 
 50.5 
 76.1 
 107.3 
 144.4 
 187.5 
 233.8 
 287.8 
 345.8 
 510.6 
 
 606 
 913 
 1288 
 1733 
 2250 
 2805 
 3453 
 4149 
 6127 
 
 
 
 
 
 
 
 All lengths to lay 12 ft. Weights are approximate; those per foot 
 include allowance for bell; those per length include bell. Propor- 
 tionate allowance is to be made for variations from standard length. 
 
 Standard and Heavy Cast Iron Bell and Spigot Gas Pipe. 
 Weights and Dimensions. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1914.) 
 
 
 Actual Out- 
 
 Thickness, 
 
 Dia. of Sock- 
 
 A 
 
 Weight per 
 
 Weight per 
 
 , fi 
 
 side Dia., In. 
 
 In. 
 
 ets, In. 
 
 *o w" 
 
 Foot, Lb. 
 
 Length, Lb. 
 
 p 
 
 $4 
 
 
 
 'O . 
 
 CT3 
 
 
 
 "O . 
 
 CTJ 
 
 i 
 
 O 4_> 
 
 fl 
 
 ^ . 
 
 fl"rt 
 
 
 
 r o . 
 
 CTJ 
 
 > 
 
 > 
 
 s 
 
 11 
 
 o> 
 
 3a 
 
 8 
 
 la 
 
 0) 
 
 &o 
 
 3s 
 
 8 
 
 OS 
 
 8 
 
 fc 
 
 & 
 
 w 
 
 w rt 
 
 w 
 
 oa* 
 
 w 
 
 pW 
 
 * 
 
 W 
 
 02* 
 
 w 
 
 4 
 
 4.80 
 
 5.00 
 
 0.40 
 
 0.42 
 
 5.80 
 
 5.80 4.00 
 
 19.33 
 
 20.0 
 
 232 
 
 240 
 
 6 
 
 6.90, 7.10 
 
 .43 
 
 .47 
 
 7.90 
 
 7.90 4.00 
 
 30.25 
 
 32.8 
 
 363 
 
 394 
 
 8 
 
 9.05 9.05 
 
 .45 
 
 .49 
 
 10.05 
 
 9.85 4.00 
 
 42.08 
 
 45.3 
 
 505 
 
 544 
 
 10 
 
 11 .10i 11 .10 
 
 .49 
 
 .51 
 
 12.10 
 
 11 .90 4.00 
 
 55.91 
 
 58.7 
 
 671 
 
 703 
 
 12 
 
 13.20 
 
 13.20 
 
 .54 
 
 .57 
 
 14.20 
 
 14.00 4.50 
 
 73.83 
 
 76.1 
 
 886 
 
 913 
 
 16 
 
 17.40 
 
 17.40 
 
 .62 
 
 .65 
 
 18.40 
 
 18.40 4.50 
 
 112.58 
 
 117.2 
 
 1351 
 
 1406 
 
 20 
 
 21.60 
 
 21 .60 
 
 .6G 
 
 .75 
 
 22.85 
 
 22.60 4.50 
 
 153.83 
 
 166.7 1846! 2000 
 
 24 
 
 25.80 
 
 25.80 
 
 .76 
 
 .82 
 
 27.05 
 
 26.80 5.00 
 
 206.41 
 
 224.0 2477; 2688 
 
 30 
 
 31 .74 
 
 32.00 
 
 .85 
 
 1 .00 
 
 32.99 
 
 33.00 5.00 
 
 284.001323.9 
 
 3408 3887 
 
 36 
 
 37.96 
 
 38.30 
 
 .95 
 
 1.05 
 
 39.21 
 
 39.30 5.00 
 
 379.25 442.7 4551 5312 
 
 42 
 
 44.20 44.50 
 
 1 .07 
 
 1 .26 
 
 45.45 
 
 45.50 5.00 
 
 497.66 581 .3 5972 6975 
 
 48 
 
 50.50 50.80 
 
 1.26 
 
 1.38 
 
 51 .75i 51 .80 5.00 
 
 663.50! 739. 6 7962 8875 
 
 The Standard pipe listed above conforms to the standard adopted by 
 the American Gas Institute in 1911. The heavy pipe given is not in- 
 cluded in the A. G. I. standards but is used by many gas engineers for 
 service under paved streets with heavy traffic, or where subsoil condi- 
 tions make the heavier pipe desirable. Pipes are made to lay 12 ft. 
 length. Weights per foot include bell and bead. Length of bead = 
 0.75 in. for 4- and 6-in. pipe; 1.00 in. for 8- to48-in. pipe. Thickness of 
 bead = 0.19 in. for 4- and 6-in. pipe; 0.25-in. for 8- to 48-in. pipe. 
 
LEAD REQUIRED FOR CAST IRON PIPE JOINTS. 199 
 
 Standard Flanged Cast Iron Pipe for Gas. 
 
 (United Cast Iron Pipe & Foundry Co., 1914, Am. Gas. Inst. Std., 1913.) 
 
 Nomi- 
 nal 
 
 Thick- 
 ness, 
 
 Flange 
 Diam., 
 
 Flange 
 Thick- 
 
 Bolt 
 Circle 
 
 Bolts 
 
 Wgt. 
 Single 
 
 Approx. Wgt., 
 Lb. 
 
 Diam., 
 In. 
 
 In. 
 
 In. 
 
 ness, 
 
 In. ' 
 
 No. 
 
 Size, 
 In. 
 
 r lange, 
 Lib. 
 
 Foot. 
 
 Lgth. 
 
 4 
 
 0.40 
 
 9.00 
 
 0.72 
 
 7.125 
 
 ~T~ 
 
 0.625 
 
 8.19 
 
 18.62 
 
 223 
 
 6 
 
 .43 
 
 11.00 
 
 .72 
 
 9.125 
 
 4 
 
 .625 
 
 10.46 
 
 29.01 
 
 348 
 
 8 
 
 .45 
 
 13.00 
 
 .75 
 
 11 .125 
 
 8 
 
 .625 
 
 12.65 
 
 40.05 
 
 481 
 
 10 
 
 .49 
 
 16.00 
 
 .86 
 
 13.75 
 
 8 
 
 .625 
 
 22.53! 54.71 
 
 656 
 
 12 
 
 .54 
 
 18.00 
 
 .875 
 
 15.75 
 
 8 
 
 .625 
 
 25.96 71.34 
 
 856 
 
 16 
 
 .62 
 
 22.50 
 
 .00 
 
 20.00 
 
 12 
 
 .75 
 
 39.68 
 
 108.61 
 
 1303 
 
 20 
 
 .68 
 
 27.00 
 
 .00 
 
 24.50 
 
 16 
 
 .75 
 
 51.10! 147.95 
 
 1775 
 
 24 
 
 .76 
 
 31 .00 
 
 .125 
 
 28.50 
 
 16 
 
 .75 
 
 65.00 
 
 197.38 
 
 2369 
 
 30 
 
 .85 
 
 37.50 
 
 .25 
 
 35.00 
 
 20 
 
 .875 
 
 96.70 
 
 273.45 
 
 3281 
 
 36 
 
 .95 
 
 44.00 
 
 .375 
 
 41 .25 
 
 24 
 
 .875 
 
 132.26 
 
 366.67 
 
 4400 
 
 42 
 
 1.07 
 
 50.75 
 
 .56 
 
 47.75 
 
 28 
 
 1.00 
 
 186.83 483.48 
 
 5802 
 
 48 
 
 1 .26 
 
 57.00 
 
 .75 
 
 54.00 
 
 32 
 
 1 .00 
 
 235.23 
 
 647.36 
 
 7768 
 
 Pipe is made in 12-ft. lengths, and faced Vie in. short for gaskets. 
 Weight per foot includes flanges. Flanges are Am. Gas. Inst., and are 
 different from the "American 1914" standard for water and steam pipe. 
 Pipes heavier than above may be made by reducing internal diameters. 
 
 Threaded Cast Iron Pipe. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1914.) 
 
 Nominal diam., in 
 
 3 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 Actual outside diam., in 
 
 3.96 
 
 5.00 
 
 7.10 
 
 9.30 
 
 11 40 
 
 13.50 
 
 Thickness, in., Class B 
 
 0.42 
 
 0.45 
 
 0.48 
 
 0.51 
 
 0.57 
 
 0.62 
 
 Wt. per foot, Class B . . 
 
 14.6 
 
 20.1 
 
 31 .2 
 
 43.9 
 
 60.5 
 
 78.9 
 
 Thickness in Class D 
 
 48 
 
 52 
 
 55 
 
 60 
 
 68 
 
 75 
 
 Wt. per foot, Class D 
 
 16.4 
 
 22.8 
 
 35.3 
 
 51.2 
 
 71.4 
 
 93.7 
 
 Quantity of Lead Required for Cast Iron Pipe Bell and Spigot Joints. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1914.) 
 
 S 
 
 Depth of Joint 
 
 i 
 
 Depth of Joint 
 
 c 
 
 2 In. 1 2 1/4 In. | 2 1/2 In. | Solid. 
 
 
 
 2 In. 
 
 2 1/4 In. | 2 1/2 In. | Solid. 
 
 p 
 
 Approx. Weight of Lead in Joint. Lb. 
 
 3~ 
 
 Approx. Weight of Lead in Joint. Lb. 
 
 3 
 
 6.00 
 
 6.50 7.00 
 
 10.25 
 
 74 
 
 44.00 48.00 52.50 
 
 95.00 
 
 4 
 
 7.50 
 
 8.00 
 
 8.75 
 
 13.00 
 
 30 
 
 54.25 
 
 59.50 
 
 64.75 
 
 117.50 
 
 6 
 
 10.25 
 
 11.25 
 
 12.25 
 
 18.00 
 
 36 
 
 64.75 
 
 71 .00 
 
 77.25 
 
 140.25 
 
 8 
 
 13.25 
 
 14.50 
 
 15.75 
 
 23.00 
 
 42 
 
 75.25 
 
 78.75 
 
 85.50 
 
 155.25 
 
 10 
 
 16.00 
 
 17.50 
 
 19.00 
 
 31 .00 
 
 48 
 
 85.50 
 
 94.00 
 
 102.25 
 
 202.25 
 
 12 
 
 19.00 
 
 20.50 
 
 22.50 
 
 36.50 
 
 54 
 
 97.60 
 
 107.10 
 
 116.60 
 
 238.60 
 
 14 
 
 22.00 
 
 24.00 
 
 26.00 
 
 38.50 
 
 60 
 
 108.30 
 
 118.80 
 
 129.50 
 
 255.50 
 
 16 
 
 30.00 
 
 33.00 
 
 35.75 
 
 64.75 
 
 72 
 
 128.00 
 
 140.50 
 
 153.00 
 
 302.50 
 
 18 
 
 33.80 
 
 36.90 
 
 40.00 
 
 72.00 
 
 84 
 
 147.00 
 
 161 .50 
 
 175.60 
 
 348.00 
 
 20 
 
 37.00 
 
 40.50 
 
 44.00 
 
 80.00 
 
 
 
 
 
 
 The above table gives the calculated weight of lead required for pipe 
 joints both with and without gasket. Weight of lead taken at 0.41 
 Ib. per cu. in. Allowance has been made for lead to project beyond the 
 face of the bell for calking. Pipe specifications allow lead space to vary 
 from those given in tables, hence the weights of lead may vary ap- 
 proximately 11 to 16 per cent from those given above, 
 
200 
 
 MATERIALS 
 
 Cast-iron Pipe Columns, Weight and Safe Loads, Pounds. 
 
 (U. S. Cast Iron Pipe and Foundry Co., 1914.) 
 
 T onrrfVi 
 
 4-Inch Pipe. 
 
 6-Inch Pipe. 
 
 8-Inch Pipe. 
 
 1 0-Inch Pipe. 
 
 ijGngtn. 
 
 Wgt. 
 
 Load. 
 
 Wgt. 
 
 Load. 
 
 Wgt. 
 
 Load. 
 
 Wgt. 
 
 Load. 
 
 6 ft. in. 
 
 160 
 
 56070 
 
 245 
 
 100100 
 
 359 
 
 164410 
 
 428 
 
 224200 
 
 6 6 
 
 171 
 
 54130 
 
 262 
 
 98310 
 
 385 
 
 162400 
 
 464 
 
 222300 
 
 7 
 
 183 
 
 52190 
 
 280 
 
 96270 
 
 410 
 
 160350 
 
 500 
 
 220300 
 
 7 6 
 
 194 
 
 50250 
 
 298 
 
 94100 
 
 436 
 
 1 58200 
 
 535. 
 
 218300 
 
 8 
 
 206 
 
 48320 
 
 316 
 
 92040 
 
 462 
 
 1 56000 
 
 571 
 
 216200 
 
 8 6 
 
 217 
 
 46440 
 
 333 
 
 89820 
 
 487 
 
 153600 
 
 607 
 
 213900 
 
 9 
 
 229 
 
 44590 
 
 351 
 
 87620 
 
 513 
 
 1 5 1 200 
 
 643 
 
 211600 
 
 9 6 
 
 240 
 
 42800 
 
 368 
 
 85450 
 
 539 
 
 148760 
 
 678 
 
 209300 
 
 10 
 
 251 
 
 41050 
 
 386 
 
 83260 
 
 564 
 
 146260 
 
 714 
 
 206900 
 
 10 6 
 
 262 
 
 39360 
 
 404 
 
 81040 
 
 590 
 
 143700 
 
 750 
 
 204500 
 
 11 
 
 274 
 
 37730 
 
 421 
 
 78840 
 
 615 
 
 141160 
 
 785 
 
 202200 
 
 11 6 
 
 285 
 
 36160 
 
 439 
 
 76700 
 
 642 
 
 138570 
 
 821 
 
 199800 
 
 12 
 
 297 
 
 34670 
 
 457 
 
 74580 
 
 667 
 
 135920 
 
 857 
 
 197400 
 
 12 6 
 
 308 
 
 33220 
 
 474 
 
 71600 
 
 692 
 
 133340 
 
 893 
 
 195000 
 
 Base and Top Castings. 
 
 
 
 
 Ins. square 10 
 
 12 
 
 14 
 
 16 
 
 Wt., Ibs. 65 
 
 100 
 
 145 
 
 200 
 
 Add weight of base and top castings f9r complete weight of column. 
 Loads are based on Gordon's formula, with a factor of safety of 8. 
 
 Weight of Open End Cast-Iron Cylinders. 
 
 Cast iron = 450 Ibs. per cubic foot. 
 Pounds per Lineal Foot. 
 
 
 Thick. 
 
 Wgt. 
 
 
 Thick. 
 
 Wgt. 
 
 
 Thick. 
 
 Wgt. 
 
 
 Thick. 
 
 Wgt. 
 
 Bore. 
 
 of 
 Metal. 
 
 per 
 Foot. 
 
 Bore. 
 
 of 
 Metal. 
 
 per 
 Foot. 
 
 Bore. 
 
 of 
 
 Metal. 
 
 Foot. 
 
 Bore. 
 
 of 
 Metal. 
 
 per 
 Foot. 
 
 In. 
 
 In. 
 
 Lb. 
 
 In. 
 
 "in*. 
 
 Lb. 
 
 In. 
 
 In. 
 
 Lb. 
 
 In. 
 
 In. 
 
 Lb. 
 
 4 
 
 3/8 
 
 16.1 
 
 11 
 
 V2 
 
 56.5 
 
 17 
 
 V8 
 
 153.6 
 
 24 
 
 7/8 
 
 213.7 
 
 
 !/2 
 
 22.1 
 
 
 5/8 
 
 71.3 
 
 18 
 
 5/8 
 
 114.3 
 
 
 1 
 
 245.4 
 
 
 5/8 
 
 28.4 
 
 
 3/4 
 
 86.5 
 
 
 3/4 
 
 138.1 
 
 26 
 
 3/4 
 
 197.0 
 
 5 
 
 3/8 
 
 19.8 
 
 12 
 
 V2 
 
 61.4 
 
 
 7/8 
 
 162.1 
 
 
 7/8 
 
 230.9 
 
 
 1/2 
 
 27.0 
 
 
 5/8 
 
 77.5 
 
 19 
 
 5/8 
 
 120.4 
 
 
 1 
 
 265.1 
 
 
 5/8 
 
 34.4 
 
 
 3/4 
 
 93.9 
 
 
 3/4 
 
 145.4 
 
 28 
 
 3/4 
 
 211.7 
 
 6 
 
 3/8 
 
 23.5 
 
 13 
 
 V2 
 
 66.3 
 
 
 7/8 
 
 170.7 
 
 
 7/8 
 
 248.1 
 
 
 1/2 
 
 31.9 
 
 
 5/8 
 
 83.6 
 
 20 
 
 5/8 
 
 126.6 
 
 
 1 
 
 284.7 
 
 
 5/8 
 
 40.7 
 
 
 3/4 
 
 101.2 
 
 
 3/4 
 
 152.8 
 
 30 
 
 7/8 
 
 265.2 
 
 7 
 
 3/8 
 
 27.2 
 
 14 
 
 V2 
 
 71.2 
 
 
 7/8 
 
 179.3 
 
 
 
 304.3 
 
 
 V2 
 
 36.8 
 
 
 5/8 
 
 89.7 
 
 21 
 
 5/8 
 
 132.7 
 
 
 U/8 
 
 343.7 
 
 
 5/8 
 
 46.8 
 
 
 3/4 
 
 108.6 
 
 
 3/4 
 
 160.1 
 
 32 
 
 7/8 
 
 282.4 
 
 8 
 
 3/8 
 
 30.8 
 
 15 
 
 5/8 
 
 95.9 
 
 
 7/8 
 
 187.9 
 
 
 1 
 
 324.0 
 
 
 1/2 
 
 41.7 
 
 
 3/4 
 
 116.0 
 
 22 
 
 5/8 
 
 138.8 
 
 
 H/8 
 
 365.8 
 
 
 5/8 
 
 52.9 
 
 
 7/8 
 
 136.4 
 
 
 3/4 
 
 167.5 
 
 34 
 
 7/8 
 
 299.6 
 
 9 
 
 V2 
 
 46.6 
 
 16 
 
 5/8 
 
 102.0 
 
 
 7/8 
 
 196.5 
 
 
 1 
 
 343.7 
 
 
 5/8 
 
 59.1 
 
 
 3/4 
 
 123.3 
 
 23 
 
 3/4 
 
 174 9 
 
 
 H/8 
 
 388.0 
 
 
 3/4 
 
 71.8 
 
 
 7/8 
 
 145.0 
 
 
 7/8 
 
 205.1 
 
 36 
 
 7/8 
 
 316.6 
 
 TO 
 
 1/2 
 
 51.5 
 
 17 
 
 5/8 
 
 108.2 
 
 
 
 235.6 
 
 
 ] 
 
 363.1 
 
 
 5/8 
 
 65.2 
 
 
 3/4 
 
 130.7 
 
 24 
 
 8/4 
 
 182.2 
 
 
 H/8 
 
 410.0 
 
 
 3/4 
 
 79.2 
 
 
 
 
 
 
 
 
 
 
 The weight of two flanges may be reckoned = weight of one foot, 
 
WELDED PIPE. 
 
 201 
 
 WROUGHT-IRON (OR STEEL) WELDED PIPE. 
 
 For discussion of the Briggs Standard of Wrought-iron Pipe Dimen- 
 sions, see Report of the Committee of the A. S. M. E. in "Standard 
 Pipe and Pipe Threads," 1886. Trans., Vol. VIII, p. 29. The diameter 
 of the bottom of the thread is derived from the formula D 
 
 (0.05D+ 1.9) x i, in which D = outside diameter of the tubes, and n 
 the number of threads to the inch. The diameter of the top of the 
 thread is derived from the formula 0.8 ^ X 2 + d, or 1.6 i + d, in which 
 
 d is the diameter at the bottom of the thread at the end of the pipe. 
 The sizes for the diameters at the bottom and top of the thread at the 
 end of the pipe are as follows : 
 
 Standard Pipe Threads. 
 
 
 Nom- 
 
 m ^3 
 
 Diam. 
 
 Diam. 
 
 
 Nom- 
 
 OS'S 
 
 Diam. 
 
 Diam. 
 
 
 inal 
 
 ijl 
 
 of Pipe 
 
 of Pipe 
 
 
 inal 
 
 
 6f Pipe 
 
 of Pipe 
 
 Size. 
 
 Ex- 
 
 
 at Root 
 
 at Top 
 
 Size. 
 
 Ex- 
 
 QJ*"" 1 
 
 at Root 
 
 at Top 
 
 
 ternal 
 
 -C ^ 
 
 of 
 
 of 
 
 
 ternal 
 
 S cD 
 
 of 
 
 of 
 
 
 Diam. 
 
 H a 
 
 Thread. 
 
 Thread. 
 
 
 Diam. 
 
 H ft 
 
 Thread. 
 
 Thread. 
 
 
 
 1/8 
 
 0.405 
 
 27 
 
 0.3339 
 
 0.3931 
 
 5 
 
 5.563 
 
 8 
 
 5.2907 
 
 5.4907 
 
 1/4 
 
 .540 
 
 18 
 
 .4329 
 
 .5218 
 
 6 
 
 6.625 
 
 8 
 
 6.3460 
 
 6.5460 
 
 3/8 
 
 .675 
 
 18 
 
 .5676 
 
 .6565 
 
 7 
 
 7.625 
 
 8 
 
 7.3398 
 
 7.5398 
 
 1/2 
 
 .840 
 
 14 
 
 .7013 
 
 .8156 
 
 8 
 
 8.625 
 
 8 
 
 8.3336 
 
 8.5336 
 
 3/4 
 
 1.050 
 
 14 
 
 .9105 
 
 1.0248 
 
 9 
 
 9.625 
 
 8 
 
 9.3273 
 
 9.5273 
 
 1 
 
 1.315 
 
 111/2 
 
 1 . 1 440 
 
 1.2832 
 
 10 
 
 10.750 
 
 8 
 
 10.4453 
 
 10.6453 
 
 H/4 
 
 1.660 111/2 
 
 1 .4876 
 
 1 .6267 
 
 11 
 
 11.750 
 
 8 
 
 11.4390 
 
 11.6390 
 
 H/2 
 
 1.900;i1l/ 2 
 
 1.7265 
 
 1 .8657 
 
 12 
 
 12.750 
 
 8 
 
 12.4328 
 
 12.6328 
 
 2 
 
 2.375I1U/2 
 
 2.1995 
 
 2.3386 
 
 13 
 
 14.000 
 
 8 
 
 13.6750 
 
 13.8750 
 
 21/2 
 
 2.875 8 
 
 2.6195 
 
 2.8195 
 
 14 
 
 15.000 
 
 8 
 
 14.6688 
 
 14.8688 
 
 3 
 
 3.500 8 
 
 3.2406 
 
 3.4406 
 
 15 
 
 16.000 
 
 8 
 
 15.6625 
 
 15.8625 
 
 31/2 
 
 4.000 8 
 
 3.7375 
 
 3.9375 
 
 170.D. 
 
 17.000 
 
 8 
 
 16.6563 
 
 16.8563 
 
 4 
 
 4.500 8 
 
 4.2343 
 
 4. 4343 
 
 18O.D. 
 
 18.000 
 
 8 
 
 17.6500 
 
 17.8500 
 
 4l/ 2 
 
 5.000 8 
 
 4.7313 
 
 4.9313 
 
 20 O.D. 
 
 20.000 
 
 8 
 
 19.6375 
 
 19.8375 
 
 Tap Drills for Pipe Taps (Briggs' Standard) . 
 
 Size of 
 Tap, 
 In. 
 
 Size of 
 Drill, 
 In. 
 
 Size of 
 Tap, . 
 In. 
 
 Size of 
 Drill, 
 In. 
 
 Size of 
 Tap, 
 In. 
 
 Size of 
 Drill, 
 In. 
 
 Size of 
 Tap, 
 In. 
 
 Siz^of 
 Drill, 
 In. 
 
 1/8 
 
 V4 
 3/8 
 1/2 
 
 21/64 
 29/64 
 19/32 
 23/32 
 
 3/4 
 
 1 1/4 
 
 1 V2 
 
 ,% 
 
 1 3/16 
 1 15/32 
 1 23/32 
 
 2 
 
 21/2 
 
 31/2 
 
 2 3/16 
 2H/16 
 3 5/16 
 313/ifi 
 
 4 
 
 41/2 
 
 6 
 
 4 3/16 
 4H/16 
 5 1/4 
 6 5/ii 
 
 Having the taper, length of full-threaded portion, and the sizes at 
 bottom and top of thread at the end of the pipe, as given in the table, 
 taps and dies can be made to secure these points correctly, the length 
 of the imperfect threaded portions on the pipe, and the length the tap 
 is run into the fittings beyond the point at which the size is as given, or, 
 in other words, beyond the end of the pipe, having no effect upon the 
 standard. The angle of the thread is 60, and it is slightly rounded off 
 at top and bottom, so that, instead of its depth being 0.866 its pitch, as 
 is the case with a full V-thread, it is 4/ 5 the pitch, or equal to 0.8 -r- n, n 
 being the number of threads per inch. 
 
 Taper of conical tube ends, 1 in 32 to axis of tube = % inch to the 
 foot total taper. 
 
 The thread is perfect for a distance (L) from the end of the pipe, ex- 
 pressed by the rule, L = (0.8 D + 4.8) -j-n; where D = outside diameter 
 
202 
 
 MATERIALS. 
 
 adtj jo 
 
 urj auQ ui 
 
 D -s *h 
 
 Od 
 
 i 
 
 I 
 
 m- 
 ce 
 
 ^co,fn--moxpvoorsoo'^- a 
 
 gSRS^Js- ^ 
 
 p-v 
 
 fe^c 
 
 
 Ov !>, *X V CO CN CN <S ' O 
 
 . 
 M O <N CO 
 
 >.. 
 !>. fN vO 
 
 cr 
 
 '- > 
 
 o oo oo i-> a 
 
 PUB 
 
 - 
 
 o r>.ooo oo 
 
 spug 
 
 qouj jad 
 
 >i OO OO if- -- OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 
 
 ssau^oiqj, 
 
 SO^CN 
 "\ v/*l OO 
 ^ CS <N 
 
 f in so r>i O"- 
 
 P-HO CN CN en -t- ftrMn so r*N oo oo ON o o o cNcs^inso 
 
 t2^ 
 
 I 
 
 QPQ 
 
 doc 
 :8 
 
WELDED PIPE. 
 
 203 
 
 in inches. Then come two threads, perfect at the root or bottom, 
 but imperfect at the top, and then come three or four threads imperfect 
 at both top and bottom. These last do not enter into the joint at all, 
 but are incident to the process of cutting the threads. The thickness 
 of the pipe under the root of the thread at the end of the pipe = 0.0175 
 D + 0.025 in. 
 
 Briggs' standard gages are made by Pratt & Whitney Co., Hartford, 
 Conn. 
 
 Standard Welded Pipe. The permissible variation in weights is 5% 
 above and 5% below those given in the table on the opposite page. 
 Pipe is furnished with threads and couplings, and in random lengths 
 unless otherwise ordered. Weights are figured on the basis of one 
 cubic inch of steel weighing 0.2833 lb., and the weight per foot with 
 threads and couplings is based on a length of 20 feet, including the 
 coupling, but shipping lengths of small sizes will usually average less 
 than 20 feet. Taper of threads is % inch diameter per foot length for 
 all sizes. The weight of water contained in one lineal foot is based 
 on a weight of 62.425 pounds per cubic foot, which is the weight at its 
 maximum density (39.1 F.) 
 
 The steel used for lap-welded pipe has the following average analysis 
 and physical properties: 
 
 El. Tens. Elong. 
 C Mn "' S P Lim. Str. in 8 in. 
 
 Bessemer 0.07 0.30 0.045 0.100 36,000 58,000 22% 
 
 Open-hearth 0.09 0.40 0.035 0.025 33,000 53,000 25% 
 
 Extra Strong~Plpe. (National Tube Company, 1915) 
 
 
 
 
 . 
 
 
 
 Length of 
 
 * bc-w 
 
 
 Diameter. 
 
 i 
 
 ^J 
 
 Circum- 
 ference. 
 
 Transverse Area. 
 
 Pipe per 
 Sq. Foot. 
 
 sfj 
 
 . 
 
 41 
 
 || 
 
 1 
 
 9 
 
 || 
 
 ll 
 
 t< 
 
 bi 
 
 0) 
 
 J 
 
 J 
 
 sUO 
 
 53 
 
 W 
 
 & 
 
 s 
 
 ^ 
 
 & 
 
 
 
 W 
 
 ^ 
 
 ^ 
 
 H w 
 
 &W 
 
 J 
 
 
 In. 
 
 In. 
 
 In. 
 
 Lb. 
 
 In. 
 
 In. 
 
 Sq.In. 
 
 Sq. In. 
 
 Sq.In 
 
 Ft. 
 
 Ft. 
 
 Ft. 
 
 Va 
 
 0.405 
 
 0.215 
 
 .095 
 
 0.314 
 
 1.272 
 
 0.675 
 
 0.129 
 
 0.036 
 
 0.093 
 
 9.431 
 
 17.766 
 
 3966.393 
 
 1/4 
 
 .540 
 
 .302 
 
 .119 
 
 .535 
 
 1.696 
 
 .949 
 
 .229 
 
 .072 
 
 .157 
 
 7.073 
 
 12.648 
 
 2010.290 
 
 3/8 
 
 .675 
 
 .423 
 
 .126 
 
 .738 
 
 2.121 
 
 1.329 
 
 .358 
 
 .141 
 
 .217 
 
 5.658 
 
 9.030 
 
 1024.689 
 
 1/2 
 
 .840 
 
 .546 
 
 .147 
 
 1.087 
 
 2.639 
 
 1.715 
 
 .554 
 
 .234 
 
 .320 
 
 4.547 
 
 6.995 
 
 615.017 
 
 ' 3/ 4 
 
 1.050 
 
 .742 
 
 .154 
 
 1.473 
 
 3.299 
 
 2.331 
 
 .866 
 
 .433 
 
 .433 
 
 3.637 
 
 5.147 
 
 333.016 
 
 
 1.315 
 
 .957 
 
 .179 
 
 2.171 
 
 4.131 
 
 3.007 
 
 1.358 
 
 .719 
 
 .639 
 
 2.904 
 
 3.991 
 
 200.193 
 
 1 1/4 
 
 1.660 
 
 1.278 
 
 .191 
 
 2.996 
 
 5.215 
 
 4.015 
 
 2.164 
 
 1.283 
 
 .881 
 
 2.301 
 
 2.988 
 
 112.256 
 
 U/2 
 
 1.900 
 
 1.500 
 
 .200 
 
 3.631 
 
 5.969 
 
 4.712 
 
 2.835 
 
 1.767 
 
 1.068 
 
 2.010 
 
 2.546 
 
 81 .487 
 
 2 
 
 2.375 
 
 1.939 
 
 .218 
 
 5.022 
 
 7.461 
 
 6.092 
 
 4.430 
 
 2.953 
 
 1.477 
 
 1.608 
 
 1.969 
 
 48.766 
 
 21/2 
 
 2.875 
 
 2.323 
 
 .276 
 
 7.661 
 
 9.032 
 
 7.298 
 
 6.492 
 
 4.238 
 
 2.254 
 
 1.328 
 
 1.644 
 
 33.976 
 
 3 
 
 3.500 
 
 2.900 
 
 .300 
 
 10.252 
 
 10.996 
 
 9.111 
 
 9.621 
 
 6.605 
 
 3.016 
 
 1.091 
 
 1.317 
 
 21.801 
 
 31/2 
 
 4.000 
 
 3.364 
 
 .318 
 
 12.505 
 
 12.566 
 
 10.568 
 
 12.566 
 
 8.888 
 
 3.678 
 
 0.954 
 
 1.135 
 
 16.202 
 
 4 
 
 4.500 
 
 3.826 
 
 .337 
 
 14.983 
 
 14.137 
 
 12.020 
 
 15.904 
 
 1 1 .497 
 
 4.407 
 
 .848 
 
 0.998 
 
 12.525 
 
 41/2 
 
 5.000 
 
 4.290 
 
 .355 
 
 17.611 
 
 15.708 
 
 13.477 
 
 19.635 
 
 14.455 
 
 5.180 
 
 .763 
 
 .890 
 
 9.962 
 
 5 
 
 5.563 
 
 4.813 
 
 .375 
 
 20.778 
 
 17.477 
 
 15.120 
 
 24.306 
 
 18.194 
 
 6.112 
 
 .686 
 
 .793 
 
 7.915 
 
 6 
 
 6.625 
 
 5.761 
 
 .432 
 
 28.573 
 
 20.813 
 
 18.099 
 
 34.472 
 
 26.067 
 
 8.405 
 
 .576 
 
 .663 
 
 5.524 
 
 7 
 
 7.625 
 
 6.625 
 
 .500 38.048 
 
 23.955 
 
 20.813 
 
 45.664 
 
 34.472 
 
 11.192 
 
 .500 
 
 .576 
 
 4.177 
 
 8 
 9 
 
 8.625 
 9.625 
 
 7.625 
 8.625 
 
 .500 43.388 
 .50048.728 
 
 27.096 
 30.238 
 
 23.955 
 27.096 
 
 58.426 
 72.760 
 
 45.663 
 58.426 
 
 12.763 
 14.334 
 
 .442 
 .396 
 
 .500 
 .442 
 
 3.154 
 2.465 
 
 10 
 
 10.750 
 
 9.750 
 
 .500 54.735 33.772 
 
 30.631 
 
 90.763 
 
 74.662 
 
 16.101 
 
 .355 
 
 .391 
 
 1.929 
 
 11 
 
 11.750 
 
 10.750 
 
 .50060.07536.914 
 
 33.772 
 
 108.434 
 
 90.763 
 
 17.671 
 
 .325 
 
 .355 
 
 1.587 
 
 12 
 
 12.750 11.7*0 
 
 .50065.415 
 
 40.055 
 
 36.914 
 
 127.676 
 
 108.434 
 
 19.242 
 
 .299 
 
 .325 
 
 1.328 
 
 13 
 
 14. 000 Si 3. 000 
 
 .50072.091 
 
 43.982 
 
 40.841 
 
 153.938 
 
 132.732 
 
 21.206 
 
 .272 
 
 .293 
 
 1.085 
 
 14 
 
 15.000' 14.0001 .500 77.431 147.124 
 
 43.982 
 
 176.715 
 
 153.93822.777 
 
 .254 
 
 .272 
 
 0.935 
 
 15 
 
 16.000! 15.0001 .500182.771 50.265 
 
 47.124 
 
 201 .062 
 
 176.715l24.347 
 
 .238 
 
 .254 
 
 .815 
 
 The permissible variation in weight is 5% above and 5% below. 
 Furnished with plain ends! and in random lengths unless otherwise 
 ordered. 
 
204 
 
 MATERIALS, 
 
 Double Extra Strong Pipe. (National Tube Company, 1915.) 
 
 
 Diameter. 
 
 1 
 
 li 
 
 3 
 
 Circum- 
 ference. 
 
 Transverse Area. 
 
 Length of 
 Pipe per 
 Sq. Foot. 
 
 J..& 
 
 *-M 
 
 1 
 
 i* 
 
 H 
 
 i" 
 
 Thickn 
 
 s 
 
 ^ 
 
 & 
 
 11 
 
 h-t 
 
 il 
 
 * a 
 H 
 
 6-d 
 
 * 
 
 HH 
 
 -3 
 % 
 
 % 
 
 -1 
 
 a 
 
 Int. 
 Surface. 
 
 O.SU 
 
 43 C 
 
 |35 
 1 
 
 
 In. 
 
 In. 
 
 In. 
 
 Lb. 
 
 In. 
 
 In. 
 
 Sq.In Sq.In 
 
 Sq.In 
 
 Ft. 
 
 Ft. 
 
 Feet. 
 
 1/2 
 
 0.840 
 
 0.2520.294 
 
 1.714 2.639 
 
 0.792 
 
 0.554 
 
 0.050 
 
 0.504 
 
 4.547 
 
 15.157 
 
 2887.165 
 
 3/4 
 
 1.050 
 
 .4341 .308 
 
 2.440 3.299 
 
 1.363 
 
 .8661 .148 
 
 .718 
 
 3.637 
 
 8.801 
 
 973.404 
 
 
 1.315 
 
 .599 .358 
 
 3.659 4.131 
 
 1.882 
 
 1.358 
 
 .282 
 
 1.076 
 
 2.904 
 
 6.376 
 
 510.998 
 
 U/4 
 
 1.660 
 
 .896 
 
 .382 
 
 5.214 5.215 
 
 2.815 
 
 2.164 .630 
 
 1.534 
 
 2.301 
 
 4.263 
 
 228.379 
 
 H/2 
 
 1.900 
 
 1.100 
 
 .400 6.408; 5.969 
 
 3.456 
 
 2.835 
 
 .950 
 
 1.885 
 
 2.010 
 
 3.472 
 
 151.526 
 
 2 
 
 2.375 
 
 1.503 
 
 .436 9.029 7.461 
 
 4.722 
 
 4.430 
 
 1.774 
 
 2.656 
 
 1.608 
 
 2.541 
 
 81.162 
 
 21/2 
 
 2.875 
 
 1.771 
 
 .552.13.695! 9.032 
 
 5.564 
 
 6.492 2.464 
 
 4.028 
 
 1.328 
 
 2.156 
 
 58.457 
 
 3 
 
 3.500 
 
 2.300 .60018.58310.996 
 
 7.226 
 
 9.621 
 
 4.155 
 
 5.4t>6 
 
 1.091 
 
 1.660 
 
 34.659 
 
 31/2 
 
 4.000 
 
 2.728! .63622.850 12. 5b6 
 
 8.570 
 
 12.566 5.845 
 
 6.721 
 
 0.954 
 
 1.400 
 
 24.637 
 
 4 
 
 4.500 
 
 3.152 .67427.541 14.137 
 
 9.902 
 
 15.904 
 
 7.803 
 
 8.101 
 
 .848 
 
 1.211 
 
 18.454 
 
 41/2 
 
 5.000 
 
 3.580 1 .71032.53015.708 
 
 1 1 .247 
 
 19.635 
 
 10.066 
 
 9.569 
 
 .763 
 
 1.066 
 
 14.306 
 
 5 
 
 5.563 
 
 4.063 .75038.55217.477 
 
 12.764 
 
 24.306 
 
 12.966 
 
 1 1 .340 
 
 .686 
 
 0.940 
 
 11.107 
 
 6 
 
 6.625 
 
 4.897 .86453.16020.813 
 
 15.384 
 
 34.472 
 
 18.835 
 
 15.637 
 
 .576 
 
 .780 
 
 7.646 
 
 7 
 
 7.625 
 
 5.875 
 
 .875 63.079 23.955 
 
 18.457 
 
 45.664 
 
 27.109 
 
 18.555 
 
 .500 
 
 .650 
 
 5.312 
 
 8 
 
 8.625 
 
 6.875 .875 72 424127.096 21 .598 58.426 
 
 37.12221.304 .442 .555 
 
 3.879 
 
 The permissible variation in weight is 10% above and 10% below. 
 Furnished with plain ends and in random lengths unless otherwise 
 ordered. 
 
 Standard Boiler Tubes and Flues Lap- Welded. 
 
 (National Tube Company, 1915.) 
 
 Diameter. 
 
 1 
 
 1 
 
 Circum- 
 ference. 
 
 Transverse Area. 
 
 Length of Tube 
 per Sq. Foot. 
 
 |:K 
 
 jN 
 
 QjlS 
 
 
 z* 
 
 .5? 3 
 
 ii 
 
 JB 
 
 fa 
 
 -3 
 
 3 
 
 8 
 
 
 
 fig 
 
 *O 4J O 
 
 "5 S 
 
 < 
 
 1 
 
 1 
 
 f 
 
 i a 
 
 j 
 
 I a 
 
 3* 
 
 B 
 
 a 
 
 l| 
 
 *l 
 
 J ' 
 
 In. 
 
 In. 
 
 In. 
 
 Lb. 
 
 In. 
 
 In. 
 
 Sq.In. 
 
 Sq. In. 
 
 Sq.In 
 
 Ft. 
 
 Ft. 
 
 Ft. 
 
 Ft. 
 
 13/4 
 
 1.560 
 
 0.095 
 
 1.679 
 
 5.498 
 
 4.901 
 
 2.405 
 
 1.911 
 
 .494 
 
 2.182 
 
 2.448 
 
 2.315 
 
 75.340 
 
 
 1.8.0 
 
 .095 
 
 1.932 
 
 6.283 
 
 5.686 
 
 3.142 
 
 2.573 
 
 .569 
 
 1.90912.110 
 
 2.010 
 
 55.965 
 
 21/4 
 
 2.0oO 
 
 .095 
 
 2.186 
 
 7.0o9 
 
 6.472 
 
 3.976 
 
 3.333 
 
 .643 
 
 1 .697 1 .854 
 
 1.775 
 
 43.205 
 
 21/2 
 
 2.282 
 
 .109 
 
 2.783 
 
 7.854 
 
 7.109 
 
 4.909 
 
 4.090 
 
 .819 
 
 1.527 
 
 1.673 
 
 1.600 
 
 35.208 
 
 23/4 
 
 2.532 
 
 .109 
 
 3.074 
 
 8.639 
 
 7.955 
 
 5.940 
 
 5.036 
 
 .904 
 
 1.388 
 
 1.508 
 
 1.448 
 
 28.599 
 
 3 
 
 2.782 
 
 .109 
 
 3.365 
 
 9.425 
 
 8.740 
 
 7.0b9 
 
 6.079 
 
 .990 
 
 1.273 
 
 1.373 
 
 1.323 
 
 23.690 
 
 31/4 
 
 3.010 
 
 .120 
 
 4.011 
 
 10.210 
 
 9.456 
 
 8.296 
 
 7.116 
 
 1.180 
 
 1.175 
 
 1.269 
 
 1.222 
 
 20.237 
 
 31/2 
 
 3.260 
 
 .120 
 
 4.331 
 
 10.996 
 
 10.242 
 
 9.621 
 
 8.347 
 
 1.274 
 
 1.091 
 
 1.171 
 
 1.131 
 
 17.252 
 
 33/4 
 
 3.510 
 
 .120 
 
 4.652 
 
 1 1 .781 
 
 1 1 .027 
 
 1 1 ,045 
 
 9.677 
 
 1.368 
 
 1.018 
 
 1.088 
 
 1.053 
 
 14.882 
 
 4 
 
 3.732 
 
 .134 
 
 5.532 
 
 12.5o6 
 
 1 1 .724 
 
 12.5ob 
 
 10.939 
 
 1.627 
 
 0.954 
 
 .023 
 
 0.989 
 
 13.164 
 
 4l/ 2 
 
 4.232 
 
 .134 
 
 6.2t8 
 
 14.137 
 
 13.295 
 
 15.904 
 
 14.0b6 
 
 1.838 
 
 .848 
 
 0.902 
 
 .875 
 
 10.237 
 
 5 
 
 4.704 
 
 .148 
 
 7.6o9 
 
 15.708 
 
 14.776 
 
 19.b35 
 
 17.379 
 
 2.256 
 
 .763 
 
 .812 
 
 .787 
 
 8.286 
 
 6 
 
 5.670 
 
 .165 
 
 10.282 
 
 18.850 
 
 17.813 
 
 28.274 
 
 25.249 
 
 3.025 
 
 .636 
 
 .673 
 
 .655 
 
 5.703 
 
 7 
 
 6.670 
 
 .165 
 
 12.044 
 
 21.991 
 
 20.954 
 
 38.485 
 
 34.942 
 
 3.543 
 
 .545 
 
 .572 
 
 .559 
 
 4.12t 
 
 8 
 
 7.670 
 
 165 
 
 13.807 
 
 25.133 
 
 24.096 
 
 50.265 
 
 46.204 
 
 4.061 
 
 .477 
 
 .498 
 
 .487 
 
 3.117 
 
 9 
 
 8.640 
 
 .180 
 
 16.955 
 
 28.274 
 
 27.143 
 
 63.617 
 
 58.629 
 
 4.988 
 
 .424 
 
 .442 
 
 .433 
 
 2.456 
 
 10 
 
 9.594 
 
 .203 
 
 21 .240 
 
 31.416 
 
 30.140 
 
 78.540 
 
 72.292 
 
 6.248 
 
 .381 
 
 .398 
 
 .390 
 
 1.992 
 
 11 
 
 10.560 
 
 .220 
 
 -25.329 34.5^8 
 
 33.175 
 
 95.033 
 
 87.582 
 
 7.451 
 
 .347 
 
 .361 
 
 .354 
 
 1.644 
 
 12 
 
 1 1 .542 
 
 .229 
 
 28.788 37.699 
 
 36.2oO 
 
 113.097 
 
 104.629 
 
 8.468 
 
 .318 
 
 .330 
 
 .324 
 
 1.376 
 
 13 
 
 12.524 
 
 .238 
 
 32.439 40.841 
 
 39.3*5 132.732 
 
 123.190 
 
 9.542 
 
 .293 
 
 .304 
 
 .299 
 
 1.169 
 
 14 
 
 13.504 
 
 .248 
 
 36.424 
 
 43.982 
 
 42.424 
 
 153.938 
 
 143.224 
 
 10.714 
 
 .272 
 
 .282 
 
 .277 
 
 1.005 
 
 15 
 16 
 
 14.482 
 15.460 
 
 .25940.775 
 .270145.359 
 
 47.124 
 50.265 
 
 45.497 
 48.509 
 
 176.715 
 201.062 
 
 164.721 
 187.719 
 
 1 1 .994 
 13.343 
 
 .254 
 .238 
 
 .263 
 .247 
 
 .259 
 .242 
 
 0.874 
 .767 
 
LAP-WELDED STEEL PIPE. 
 
 205 
 
 Weights and Bursting Strength of Lap-Welded Steel Pipe. 
 
 (American Spiral Pipe Works, Chicago, 1911.) 
 
 20-Pt. Lengths, Plain Ends without Connections. Thicknesses in 
 U. S. Standard Gage or Inches. Bursting Strength in Lb. per Sq. Jn. 
 Internal Pressure. 
 
 Inside Dia., 
 Ins. 
 
 Thickness, 
 Ins. 
 
 d 
 
 i< 
 
 r 
 
 Bursting 
 Strength. 
 
 Inside Dia., 
 Ins. 
 
 Thickness, 
 Ins. 
 
 3 
 s*f 
 ft 
 .pfc 
 ^ 
 
 Bursting 
 Strength. 
 
 Inside Dia., 
 Ins. 
 
 Thickness, 
 Ins. 
 
 a 
 
 M 
 
 r 
 
 Bursting 
 Strength. 
 
 12 
 
 10G 
 
 19.3 
 
 1172 
 
 28 
 
 3/4 
 
 244 
 
 2678 
 
 42 
 
 1/4 
 
 119 
 
 595 
 
 " 
 
 3/16 
 
 25.8 
 
 1562 
 
 " 
 
 
 329 
 
 3570 
 
 " 
 
 1/2 
 
 239 
 
 1190 
 
 11 
 
 1/4 
 
 34.6 
 
 2083 
 
 " 
 
 H/4 
 
 416 
 
 4462 
 
 " 
 
 3/4 
 
 362 
 
 1784 
 
 14 
 
 10G 
 
 22.4 
 
 1005 
 
 30 
 
 3/16 
 
 64 
 
 625 
 
 * 
 
 1 
 
 486 
 
 2380 
 
 " 
 
 V4 
 
 40.2 
 
 1785 
 
 " 
 
 1/4 
 
 85 
 
 833 
 
 " 
 
 1 1/4 
 
 612 
 
 2976 
 
 " 
 
 3/8 
 
 61.0 
 
 2678 
 
 " 
 
 1/2 
 
 172 
 
 1666 
 
 44 
 
 1/4 
 
 124 
 
 568 
 
 11 
 
 1/2 
 
 82.0 
 
 3568 
 
 " 
 
 3/4 
 
 261 
 
 2500 
 
 " 
 
 1/2 
 
 250 
 
 1136 
 
 16 
 
 10G 
 
 25.6 
 
 879 
 
 " 
 
 
 352 
 
 3328 
 
 " 
 
 3/4 
 
 378 
 
 1705 
 
 " 
 
 I/I 
 
 45.8 
 
 1562 
 
 " 
 
 H/4 
 
 444 
 
 4160 
 
 " 
 
 1 
 
 508 
 
 2277 
 
 " 
 
 3/8 
 
 69.4 
 
 2344 
 
 32 
 
 3/16 
 
 68 
 
 586 
 
 " 
 
 U/4 
 
 640 
 
 2840 
 
 " 
 
 1/2 
 
 93.5 
 
 3124 
 
 " 
 
 1/4 
 
 91 
 
 781 
 
 48 
 
 V4 
 
 135 
 
 520 
 
 M 
 
 5/8 
 
 118.0 
 
 3904 
 
 " 
 
 V2 
 
 183 
 
 1562 
 
 " 
 
 1/2 
 
 273 
 
 1040 
 
 18 
 
 10G 
 
 28.7 
 
 781 
 
 " 
 
 3/4 
 
 278 
 
 2344 
 
 " 
 
 3/4 
 
 412 
 
 1562 
 
 M 
 
 1/4 
 
 51.4 
 
 1388 
 
 " 
 
 1 
 
 374 
 
 3125 
 
 " 
 
 
 553 
 
 2080 
 
 " 
 
 3/8 
 
 77.8 
 
 2082 
 
 " 
 
 U/4 
 
 472 
 
 3906 
 
 " 
 
 U/4 
 
 696 
 
 2604 
 
 " 
 
 1/2 
 
 104.7 
 
 2776 
 
 34 
 
 3/16 
 
 72 
 
 551 
 
 50 
 
 1/4 
 
 141 
 
 500 
 
 " 
 
 5/8 
 
 132.0 
 
 3472 
 
 " 
 
 1/4 
 
 96 
 
 735 
 
 " 
 
 1/2 
 
 284 
 
 1000 
 
 20 
 
 10G 
 
 31.9 
 
 703 
 
 * 
 
 1/2 
 
 194 
 
 1470 
 
 " 
 
 3/4 
 
 429 
 
 1500 
 
 M 
 
 1/4 
 
 57.0 
 
 1250 
 
 " 
 
 3/4 
 
 294 
 
 2206 
 
 
 
 1 
 
 576 
 
 2000 
 
 " 
 
 1/2 
 
 116.2 
 
 2500 
 
 " 
 
 1 
 
 396 
 
 2942 
 
 " 
 
 11/4 
 
 724 
 
 2500 
 
 * 
 
 3/4 
 
 177.0 
 
 3736 
 
 " 
 
 U/4 
 
 500 
 
 3678 
 
 54 
 
 1/4 
 
 152 
 
 463 
 
 22 
 
 10G 
 
 35.0 
 
 639 
 
 36 
 
 3/16 
 
 76 
 
 520 
 
 
 1/2 
 
 306 
 
 926 
 
 " 
 
 1/4 
 
 62.6 
 
 1136 
 
 " 
 
 1/4 
 
 102 
 
 694 
 
 
 
 3/4 
 
 462 
 
 1390 
 
 " 
 
 1/2 
 
 127.0 
 
 2272 
 
 " 
 
 1/2 
 
 206 
 
 1388 
 
 " 
 
 1 
 
 620 
 
 1852 
 
 " 
 
 3/4 
 
 194.0 
 
 3410 
 
 
 
 3/4 
 
 311 
 
 2080 
 
 " 
 
 U/4 
 
 780 
 
 2315 
 
 " 
 
 1 
 
 262.0 
 
 4555 
 
 ' 
 
 
 419 
 
 2776 
 
 60 
 
 V4 
 
 169 
 
 416 
 
 24 
 
 10G 
 
 38.0 
 
 586 
 
 
 
 U/4 
 
 528 
 
 3472 
 
 
 1/2 
 
 340 
 
 832 
 
 ** 
 
 V4 
 
 68.0 
 
 1041 
 
 38 
 
 s/rt 
 
 80 
 
 493 
 
 ' 
 
 3/4 
 
 513 
 
 1250 
 
 " 
 
 1/2 
 
 138.0 
 
 2082 
 
 
 
 1/4 
 
 107 
 
 658 
 
 
 
 
 688 
 
 1664 
 
 " 
 
 3/4 
 
 210.0 
 
 3124 
 
 " 
 
 1/2 
 
 217 
 
 1316 
 
 " 
 
 U/4 
 
 864 
 
 2080 
 
 M 
 
 1 
 
 284.0 
 
 4160 
 
 *< 
 
 3/4 
 
 328 
 
 1972 
 
 66 
 
 1/4 
 
 186 
 
 379 
 
 26 
 
 3/16 
 
 55.0 
 
 721 
 
 " 
 
 
 441 
 
 2632 
 
 " 
 
 !/2 
 
 374 
 
 758 
 
 
 1/4 
 
 74.0 
 
 961 
 
 
 
 U/4 
 
 556 
 
 3288 
 
 " 
 
 3/4 
 
 563 
 
 1132 
 
 '* 
 
 1/2 
 
 150.0 
 
 1922 
 
 40 
 
 3/16 
 
 84 
 
 467 
 
 " 
 
 1 
 
 755 
 
 1516 
 
 " 
 
 3/4 
 
 227.0 
 
 2885 
 
 " 
 
 1/4 
 
 113 
 
 625 
 
 ' 
 
 U/4 
 
 948 
 
 1892 
 
 " 
 
 
 307.0 
 
 3847 
 
 " 
 
 1/2 
 
 228 
 
 1250 
 
 72 
 
 V4 
 
 203 
 
 347 
 
 " 
 
 H/4 
 
 388.0 
 
 4809 
 
 ' 
 
 3/4 
 
 345 
 
 1868 
 
 
 1/2 
 
 407 
 
 694 
 
 28 
 
 3/16 
 
 60.0 
 
 669 
 
 " 
 
 1 
 
 464 
 
 2500 
 
 * 
 
 3/4 
 
 614 
 
 1040 
 
 " 
 
 V4 
 
 80.0 
 
 892 
 
 " 
 
 U/4 
 
 584 
 
 3124 
 
 < 
 
 
 822 
 
 1388 
 
 " 
 
 1/2 
 
 161 .0 
 
 1784 
 
 42 
 
 3/16 
 
 89 
 
 446 
 
 " 
 
 U/4 
 
 1032 
 
 1736 
 
 For dimensions of extra heavy rolled steel flanges for above pipe, 
 see table page 211. 
 
 Square Pipe, external size, 7/g, 1, H/ 4 , li/ 2 , Hl/ie, 2, 21/2, 3 in. 
 
 Rectangular Pipe, external size, 1 1/4 X 1, 11/2X1 V4, 2X1 1/4, 
 2X1 1/2, 21/2X1 1/2, 3X2. 
 
 Two or more thicknesses of each size. 
 
 Pipe Specialties. Hand railings and their fittings; ladders with flat 
 or round pipe bars and runners; seamless cylinders, with flat, domed, 
 disked, or necked ends; special shapes for automobiles, to replace drop 
 forgings ; tapered tubes, and other specialties are illustrated in National 
 Tube Co.'s Book of Standards. 
 
206 
 
 MATERIALS. 
 
 Special Sizes of Lap-welded Pipe Boston Casing. (National Tube Co.) 
 
 N 
 
 1 
 
 8 
 
 ss 
 
 tfiS 
 
 5. a 
 
 li 
 
 68* 
 
 !'! 
 
 M 
 
 ! 8 
 
 as 
 
 ll 
 
 1 
 
 l a 
 
 I s 
 
 ga 
 
 I s 
 
 S Q 
 
 e" 
 
 l a 
 
 &* 
 
 E-i C 
 
 IJ 
 
 *Q 
 w 
 
 E-< fl 
 
 2 
 
 21/4 
 
 0.100 
 
 4l/ 2 
 
 43/4 
 
 0.145 
 
 55/ 8 
 
 6 
 
 0.224 
 
 81/4 
 
 85/s 
 
 0.217 
 
 21/4 
 
 21/2 
 
 .108 
 
 41/2 
 
 43/4 
 
 .193 
 
 55/8 
 
 6 
 
 .275 
 
 81/4 
 
 85/8 
 
 .264 
 
 21/2 
 
 23/4 
 
 .113 
 
 43/4 
 
 5 
 
 .152 
 
 61/4 
 
 65/8 
 
 .169 
 
 85/8 
 
 9 
 
 .196 
 
 23/4 
 
 3 
 
 .116 
 
 5 
 
 51/4, 
 
 .153 
 
 61/4 
 
 65/s 
 
 .185 
 
 95/8 
 
 10 
 
 .209 
 
 3 
 
 31/4 
 
 .120 
 
 5 
 
 51/4 
 
 .182 
 
 65/8 
 
 7 
 
 .174 
 
 105/8 
 
 11 
 
 .224 
 
 31/4 
 
 31/2 
 
 .125 
 
 5 
 
 51/4 
 
 .182 
 
 65/8 
 
 7 
 
 .231 
 
 115/8 
 
 12 
 
 .243 
 
 31/2 
 
 33/4 
 
 .129 
 
 5 
 
 51/4 
 
 .241 
 
 7V4 
 
 75/8 
 
 .181 
 
 121/2 
 
 13 
 
 .259 
 
 33/4 
 
 4 
 
 .134 
 
 5 
 
 51/4 
 
 .301 
 
 75/8 
 
 8 
 
 .186 
 
 131/2 
 
 14 
 
 .276 
 
 4 
 
 41/4 
 
 .138 
 
 53/18 
 
 5l/ 2 
 
 .154 
 
 75/8 
 
 8 
 
 .236 
 
 141/2 
 
 15 
 
 .291 
 
 41/4 
 
 4l/ 2 
 
 .142 
 
 55/8 
 
 6 
 
 .164 
 
 81/4 
 
 85/8 
 
 .188 
 
 15l/ 2 
 
 16 
 
 .302 
 
 41/4 
 
 4l/ 2 
 
 .205 
 
 55/ 8 
 
 6 
 
 .190 
 
 
 
 
 
 
 
 Other sizes of lap- welded pipe: Inserted Joint Casing, external 
 diameters same as Boston Casing, with the least thickness. The 5 5/g 
 casing is made 0.164 and 0.190 in. thick. California Diamond X Casing, 
 sizes 5 5/ 8 to 15 1/2, all heavier than Boston. Oil Well Tubing, 11/4 to 4 in. ; 
 Bedstead Tubing, 3/ 8 to 3 in.; Flush Joint Tubing, 3 to 18 in.; Allison 
 Vanishing Thread Tubing, 2 to 8 in., ends upset, 11/4 to 8 in., ends not 
 upset; Special Rotary Pipe, 2 1/2 to 6 in.; South Penn Casing, 53/i 6 to 
 12 1/2 in. ; Reamed and Drifted Pipe, 2 to 6 in. ; Air-line Pipe, 1 1/2 to 6 in. ; 
 Drill Pipe, 4 to 6 in. ; Dry-kiln Pipe, 1 and 1 1/4 in. ; Tuyere Pipe, 1 and 
 H/4 in. 
 
 TUBULAR ELECTRIC LINE POLES. 
 
 For railway work the poles most used are 30 ft. long, and are com- 
 posed of 7-in., 6-in., and 5-in. pipe. Anchor poles are usually 8-in., 
 7-in., and 6-in., but often they are made of larger pipe. Full directions 
 for designing such poles are given in the National Tube Co.'s Book of 
 Standards, which contains 38 pages of tables of dimensions, load, de- 
 flection, etc., of poles of different sizes and weights. 
 
 PROTECTIVE COATINGS FOR PIPE. 
 
 (1) Galvanizing The pipe cleaned from scale and rust by pickling 
 in warm dilute sulphuric acid, washed, immersed in an alkaline bath, 
 dried and immersed in molten zinc. (2) Bituminous Coating The 
 cleaned, dried and warmed pipe is dipped in a bath of refined coal tar 
 pitch, free from water and the lighter oils, at a temperature not below 
 212, and then baked. (3) "National Coating." The bituminous 
 coated pipe, after baking is wrapped with a strip of fabric saturated 
 with the hot compound, the edges of the fabric overlapping. 
 
 VALVES AND FITTINGS. 
 
 (From Information Furnished by National Tube Co., 1915.) 
 
 Wrought pipe is usually connected in one of three ways, screwed, 
 flanged or leaded joints. 
 
 Screwed. Pipe in sizes from i/g m. to 15 in. inclusive is regularly 
 threaded on the ends, and is connected by means of threaded couplings. 
 
 Flanged. Pipe in sizes 11/4 inches and larger is frequently connected 
 by drilled flanges bolted together, the joint being made by a gasket 
 between the flange faces. 
 
 Flanges are attached to the pipe in a variety of ways. The most 
 common method for sizes of. pipe from U/4 in. to 15 in. inclusive 
 is by screwing them on the pipe. Many prefer peened flanges for 
 pipe larger than 6 in. The peened flange is shrunk on the end of 
 the pipe, and the latter is then peened over or expanded into a recess 
 in the flange face. Steel flanges are also welded to pipe and loose 
 flanges are used by flanging over the pipe ends. When no method 
 of attaching is stated, screwed flanges are always furnished. 
 
VALVES AND FITTINGS. 207 
 
 Working Pressures. All valves and fittings are classified, as a rule, 
 under five general headings, representing the working pressures for 
 which they are suitable, as follows: Low Pressure, up to 25 pounds 
 per square inch. Standard, up to 125 pounds per square inch. Medium 
 Pressure, from 125 pounds to 175 pounds per square inch. Extra 
 Heavy, from 175 pounds to 250 pounds per square inch. Hydraulic, 
 for high pressure water up to 800 pounds per square inch. 
 
 The following table gives the names of different valves and fittings, 
 the material of which they are made, and the regular sizes manu- 
 factured for the different pressures (L, low; S, standard; M, medium; 
 E, extra heavy ; H , hydraulic) : 
 
 SCREWED FITTINGS. 
 
 Malleable Iron S, E, H, sizes 1/8 to 8 in. 
 
 Cast Iron S, E, 1/4 to 12 in. 
 
 FLANGED FITTINGS. 
 
 Cast Iron L, S, E, H, sizes 2 in. and larger. 
 
 GATE VALVES. 
 
 Brass L S M E If up to 3 in. 
 
 Iron Body, sizes. . 12 to 48 2 to 30 2 to 18 1 1/4 to 24 H/2 to 12 in. 
 
 GLOBE AND ANGLE VALVES. 
 
 Brass S, i/s to 4; M, 1/4 to 3; E, 1/2 to 3; H, 1/2 to 2 
 
 Iron Body S, 2 to 12; E, 2 to 12 
 
 CHECK VALVES. 
 
 Brass S, M, E, H, sizes l/s to 3 in. 
 
 Iron Body L, S, M , E, H, ' 2 to 12 in. 
 
 COCKS, STEAM AND GAS. 
 
 Brass sizes 1/4 to 3 in. 
 
 Iron Body * 1/2 to 3 in. 
 
 Nipples. Nipples are made in all sizes from i/g in. to 12 in. in- 
 clusive, in all lengths, either black or galvanized, and regular right- 
 hand or right- and left-hand threads. (For table of nipples see National 
 Tube Co.'s Book of Standards.) Long screws or tank nipples are made 
 of extra heavy pipe because there is less danger of crushing or splitting 
 them when screwing up. 
 
 Screwed Fittings Malleable Iron. Standard Malleable Iron Fittings 
 are made both plain and beaded. The former are generally used for 
 low pressure gas and water, as in house plumbing and railing work. The 
 beaded is the standard steam, air, gas, or oil fitting. Beaded fittings, 
 in sizes 4 in. and smaller, are made in nearly every useful combination of 
 openings. Sizes larger than 4 in. are not usually made reducing except 
 by means of bushing. Extra heavy and hydraulic malleable iron 
 fittings are flat bead, or banded. 
 
 Screwed Fittings Cast Iron. It is not considered good practice to 
 use screwed cast-iron fittings of any kind in sizes larger than 6 in. 
 
 Flanged Fittings. The flanges of the low pressure and standard are 
 the same with the exception of the flange thickness, which is less on the 
 low pressure. These flanges are known as the American Standard. 
 (See pp. 209, 210.) 
 
 There is no recognized standard for flanges in hydraulic work. 
 
 Unions. Unions are usually classified under two headings, Nut unions 
 and Flange unions. Nut unions are commonly used in sizes 2 in. and 
 smaller, and flange unions in sizes larger than 2 in. However, many 
 manufacturers make nut unions as large as 4 in. and flange unions 
 smaller than 2 in. 
 
 Nut unions are made in malleable iron, brass, and malleable iron, 
 and ail brass. The all malleable iron union (lip union) is the standard 
 malleable iron union of the trade and requires a gasket. The brass 
 and malleable iron union is a better union, because no gasket is re- 
 quired and there is no possibility of the parts rusting together. The 
 pipe end of this union which carries an external thread, called the 
 
208 MATERIALS. 
 
 thread end, upon which the ntit or ring screws, is made of brass, and the 
 other pipe end (called the bottom) and nut ring are made of malleable 
 iron. The seat formed by the brass and iron pipe ends, when brought 
 together, is truly spherical and the harder iron is sure to make a perfect 
 joint with the softer brass. 
 
 All-brass unions are made with a spherical or conical seat, no gaskets 
 being required. The finished all-brass union is often used where showy 
 work is desired, such as oil piping for engines, etc. 
 
 Flange unions are made of malleable iron, malleable iron and brass, 
 cast iron, and cast iron and brass. 
 
 The type of flange union recommended for standard work is made 
 with a brass to iron non-corrosive ball joint seat which requires no 
 gasket to make a tight joint even when the pipe alignment is imperfect. 
 The flange is loose on the collar, so that the bolts match the holes in 
 any position. 
 
 Valves and Cocks. The most common means for regulating the flow 
 of fluids in pipes is by means of valves and cocks, valves being pre- 
 ferred because of the easier operation and greater reliability. The 
 common types of valves are straightway or gate, globe, and angle. A 
 globe valve offers more resistance to the flow of any fluid than the 
 straightway valve. 
 
 Globe and Angle Valves. Many manufacturers make a globe and 
 angle valve known as light standard or competition valve, but it is 
 not recommended for any work except the lowest pressures, or where 
 the valve will not be often opened or closed. 
 
 Cocks. Among the modern types of cocks is one made with iron 
 body and brass plug. This cock has an inverted plug with a spring 
 at the bottom constantly pressing the plug against the seat, which 
 reseats the plug if it should stick. These cocks are tested to 250 Ib. 
 cold-water pressure, and 125 Ib. compressed-air pressure under water, 
 and are recommended for 125 Ib. working pressure. 
 
 Blast Furnace Fittings. Tuyere cocks and tuyere unions used in 
 blast furnace piping are always made of brass on account of ease in 
 disconnecting, greater reliability of metal and resistance to corrosion 
 from the impurities in the water, such as sulphuric acid. 
 
 STANDARD PIPE FLANGES (CAST IRON). 
 
 The following tables showing dimensions of standard pipe flanges 
 were adopted by the American Society of Mechanical Engineers, the 
 Master Steam and Hot Water Fitters' Association, and a committee 
 representing the manufacturers of pipe fittings. They represent a 
 compromise between the standards adopted by the American Society of 
 Mechanical Engineers and the Master Steam and Hot Water Fitters' 
 Association hi 1912, known as the 1912 U. S. Standard, and the stand- 
 ards adopted by a conference of manufacturers in July, 1912, known 
 as the Manufacturers' standard. The new standards, given in the 
 tables, are called the American Standard, and became effective Jan. 1, 
 1914. The table of flanges for extra heavy fittings is for working 
 pressures up to 250 Ib. per sq. in. The table for ordinary fittings is for 
 working pressures up to 125 Ib. per sq. in. In the tables, the values of 
 
 T X T) 
 
 stresses in pipe walls were calculated from the formula S = - . > 
 
 where p = working pressure, Ib. per sq. in., t = thickness of pipe, 
 in., and r = radius of pipe, in. The highest stress was found to be 
 2000 Ib. per sq. in. on the 250-lb., 46- and 48-in. pipe walls, giving a 
 factor of safety of about 10. The desirable thickness of pipe (Col. 2) 
 
 is calculated from the formula T = PA* 3 -P + 0.333/1 - -^ Jl.2. 
 
 where p = pressure, Ib., per sq. in., 5 = 1800, and d = diameter 
 of pipe. The minimum thickness in even fractions of an inch is given 
 in Col. 3. The following approximate formulae were also used for 
 ordinary fittings: Diam. of bolt circles = 1.10 d + 3. Flange thick- 
 ness (for pipe diameters 26 to 100 in. inclusive) = 0.0315 d + 1.25. 
 For extra heavy fittings the formulae are: Bolt circle = 1.171d+3.75; 
 Flange thickness = 0.0546 d + 1.375 (for sizes 10 to 48 in. inclusive). 
 
American Standard Cast Iron Pipe flanges for Pressures Up to 
 
 Lb. per Sq. In. (All Dimensions in Inches.) 
 
 r r Pipe 
 
 
 
 Flanges. 
 
 Bolts. 
 
 
 
 fc 
 
 Thickness 
 
 E 
 
 jj 
 
 i 
 
 o 
 
 Jj 
 
 ^ 
 
 
 
 .S 
 
 a 
 
 f- 
 
 See Fig. 75, 
 p. 210 
 
 S 
 
 & 
 
 |i 
 
 n & 
 
 W OH 
 
 ! 
 
 Q 
 
 IS 
 H 
 
 
 if 
 
 0) 
 
 g 
 
 5 
 
 I! 
 
 CU *M 
 
 g& 
 
 
 
 A 
 
 B 
 
 C 
 
 1 
 
 0.43 
 
 7/16 
 
 143 
 
 4 
 
 7/16 
 
 I 1/2 
 
 3 
 
 ~4 
 
 7/16 
 
 0.093 
 
 264 
 
 9/16 
 
 2.12 
 
 ^9l 
 
 U2T 
 
 1 1/4 
 
 0.44 
 
 7/16 
 
 178 
 
 41/2 
 
 1/2 
 
 15/8 
 
 33/8 
 
 4 
 
 7/16 
 
 0.093 
 
 412 
 
 9/16 
 
 2.38 0.91 
 
 L47 
 
 H/2 
 
 0.45 
 
 7/16 
 
 214 
 
 
 9/16 
 
 13/4 
 
 37/8 
 
 4 
 
 1/2 0.126; 
 
 438 
 
 5/82.731.00 
 
 1.73 
 
 2 
 
 0.46 
 
 7/16 
 
 286 
 
 6 
 
 5/8 
 
 2 
 
 43/4 
 
 4 
 
 5/8 1 
 
 0.202 
 
 486 
 
 3/4 ! 
 
 3.35 
 
 1.21 
 
 2.14 
 
 21/2 
 
 0.48 
 
 7/16 
 
 357 
 
 7 
 
 11/16 
 
 21/4 
 
 51/2 
 
 4 
 
 5/8 0.202 
 
 750 
 
 3/4 3.88 
 
 1.21 
 
 2.67 
 
 '3 
 
 0.50 
 
 7/16 
 
 428 
 
 71/2 
 
 3/4 
 
 21/4 
 
 6 
 
 4 
 
 5/8 i 0.202 
 
 1093 
 
 3/4 
 
 4.23 
 
 1.21 
 
 3.02 
 
 31/2 
 
 0.52 
 
 7/16 
 
 500 
 
 81/2 
 
 13/16 
 
 21/2 
 
 7 
 
 4 
 
 5/8 
 
 0.202 
 
 1488 
 
 3/4 
 
 4.94 
 
 1.21 
 
 3.73 
 
 4 
 
 0.53 
 
 1/2 
 
 500 
 
 9 
 
 15/16 
 
 21/2 
 
 71/2 
 
 8 
 
 5/8 '0.202 
 
 972 
 
 3/4 
 
 2.87 
 
 1.21 
 
 1.56 
 
 41/2 
 
 0.55 
 
 1/2 
 
 562 
 
 91/4 
 
 15/16 
 
 23/8 
 
 73/4 
 
 8 
 
 3/4 
 
 0.302 
 
 823 
 
 7/8^2.96 
 
 1.44 
 
 1.52 
 
 5 
 
 0.56 
 
 1/2 
 
 625 
 
 10 
 
 15/16 
 
 21/2 
 
 81/2 
 
 8 
 
 3/4 
 
 0.302 
 
 1016 
 
 7/8 
 
 3.25 
 
 1.44 
 
 1.81 
 
 6 
 
 0.60 
 
 9/16 
 
 667 
 
 11 
 
 
 21/2 
 
 91/2 
 
 8 
 
 3/4 
 
 0.302 
 
 1463 
 
 7/8 
 
 3.63 
 
 1.44 
 
 2.19 
 
 7 
 
 0.63 
 
 5/8 
 
 700 
 
 12l/ 2 
 
 1/16 
 
 23/4 
 
 103/4 
 
 8 
 
 3/4 '0.302 
 
 1991 
 
 7/84.11 
 
 1.44 
 
 2.67 
 
 8 
 
 0.66 
 
 5/8 
 
 800 
 
 131/2 
 
 1/8 
 
 23/4 
 
 113/4 
 
 8 
 
 3/4! 0.302 2600 
 
 7/8 4.50 
 
 1.44 
 
 3.06 
 
 9 
 
 0.70 
 
 H/16 
 
 818 
 
 15 
 
 1/8 
 
 3 
 
 131/4112 
 
 3/4 0.302 2194 
 
 7/ 8| 3.43 
 
 1 .44 1 .99 
 
 10 
 
 0.73 
 
 3/4 
 
 833 
 
 16 
 
 8/18 
 
 3 
 
 141/4112 
 
 7/8 
 
 0.420 
 
 1948 
 
 
 3.69 
 
 1 .66 2.03 
 
 12 
 
 0.80 
 
 13/16 
 
 923 
 
 19 
 
 1/4 
 
 31/2 
 
 17 
 
 12 
 
 7/8 
 
 0.420 
 
 2805 
 
 
 4.40 
 
 1.66 
 
 2.74 
 
 14 
 
 0.86 
 
 7/8 
 
 1000 
 
 21 
 
 3/8 
 
 31/2 
 
 183/4 
 
 12 
 
 
 0.5502915 
 
 1/8 
 
 4.86 1 .88 
 
 2.98 
 
 15 
 
 0.90 
 
 7/8 1072 
 
 221/4 
 
 3/8 
 
 35/8 
 
 20 
 
 16 
 
 1 
 
 0.5502510 
 
 1/83.90 1.88 
 
 2.02 
 
 16 
 
 0.93 
 
 
 1000 
 
 231/2 
 
 7/16 
 
 33/4 
 
 21 1/4 
 
 16 
 
 1 
 
 0.550 
 
 2856 
 
 1/8 
 
 4.14 
 
 1.88 
 
 2.26 
 
 18 
 
 1.00 
 
 1/16 
 
 1059 
 
 25 
 
 9/16 
 
 31/2 
 
 223/4 
 
 16 
 
 1 l/s 0.694 
 
 2865 
 
 1/44.44 
 
 2.09 
 
 2.35 
 
 20 
 
 1.07 
 
 1/8 
 
 1111 
 
 271/2 
 
 H/16 
 
 33/4 
 
 25 
 
 20 
 
 1 1/8 
 
 0.694 
 
 2829 
 
 1/4 
 
 3.91 
 
 2.09 
 
 1.82 
 
 22 
 24 
 
 1.13 
 1.20 
 
 3/16 
 1/4 
 
 1158 
 1200 
 
 
 13/16 
 7/8 
 
 33/4 
 
 271/4 
 291/2 
 
 20 
 20 
 
 1 1/4 0.893 2660 
 l/iO.8933166 
 
 1 3/8 4.2612.31 
 1 3/ 8 ;4.62l2.31 
 
 1.95 
 2.31 
 
 26 
 
 1.27 
 
 5/16 
 
 1238 
 
 341/4 
 
 2 
 
 41/8 
 
 313/4 
 
 24 
 
 1 1/4 
 
 0.893 
 
 3096 
 
 13/8 
 
 4.14 
 
 2.31 
 
 1.83 
 
 28 
 30 
 
 1.33 
 1.40 
 
 3/8 
 7/16 
 
 1273 
 1304 
 
 361/2 
 
 383/4 
 
 2 1/16 
 2 1/8 
 
 4i/ 4 | 34 ' 
 43/ 8 l 36 
 
 28 
 28 
 
 1 l / 4 10. 893 1 3078 
 13/ 8 1.057 12985 
 
 1 3/8 3.81 
 1/2 4.03 
 
 2.31 
 2.53 
 
 1.50 
 1.50 
 
 32 
 
 1.47 
 
 1/2 
 
 1333 
 
 413/4J2 1/4 
 
 47/8 
 
 381/2 
 
 28 
 
 1 1/2 
 
 1.294 
 
 2775 
 
 5/8 
 
 4.31 
 
 2.75 
 
 1.56 
 
 34 
 
 1.54 
 
 9/16 
 
 1360 
 
 433/42 5/i 6 
 
 47/8 
 
 401/2 
 
 32 
 
 H/2 
 
 .294274 
 
 1 5/8 3.97 
 
 2.75 
 
 1.22 
 
 36 
 
 1.60 
 
 5/8 
 
 1385 
 
 46 
 
 2 3/ 8 
 
 5 
 
 423/4 
 
 32 
 
 1 1/2 
 
 .294 
 
 3073 
 
 15/8 
 
 4.19 
 
 2.75 
 
 1.44 
 
 38 
 
 1.67 
 
 H/16 
 
 1407 
 
 483/4 
 
 2 3/ 8 
 
 53/8 
 
 451/4 
 
 32 
 
 1 5/8 
 
 .515 
 
 2924 
 
 1 3/4 4.43 
 
 2.96 
 
 1.47 
 
 40 
 
 1.73 
 
 3/4 
 
 1428 
 
 503/42 1/2 
 
 53/ 8 471/4 
 
 36 
 
 1 5/8 
 
 .515 
 
 2880 
 
 13/4 
 
 4.11 
 
 2.96 
 
 1.15 
 
 42 
 
 1.82 
 
 13/16 
 
 1448 
 
 53 
 
 2 5/8 
 
 5l/ 2 49i/ 2 
 
 36 
 
 1 5/8 
 
 .5153175 
 
 13/4 
 
 4.31 
 
 2.96 
 
 1.35 
 
 44 
 
 1.87 
 
 7/8 11467 
 
 551/4 
 
 2 5/ 8 
 
 5 5/8 51 3/ 4 
 
 40 
 
 15/8 
 
 .515 
 
 3136 
 
 1 3/ 4 4.06 
 
 2.96 
 
 1.10 
 
 46 
 
 1.94 
 
 115/ie 1484 
 
 571/42H/16 
 
 55/8 533/4 
 
 40 
 
 1 5/8 
 
 .515 
 
 3428 
 
 18/4 
 
 4.22 
 
 2.96 
 
 1.26 
 
 48 
 
 2.00 
 
 2 
 
 1500 
 
 591/212 3/ 4 
 
 53/4 
 
 56 
 
 44 
 
 1 5/8 
 
 .515 
 
 3393 
 
 13/4 
 
 3.98 
 
 2.96 
 
 1.02 
 
 50 
 52 
 
 2.07 
 2.14 
 
 21/16 
 21/8 
 
 1515 
 1530 
 
 SI'" 
 
 2 3/4 
 2 7/8 
 
 57/8 
 6 
 
 581/444 
 60 1/2 44 
 
 13/4J .746)3195 
 1 3/ 4 { .746 3456 
 
 7/8|4.14 
 7/84.30 
 
 3.19 
 3.19 
 
 0.95 
 1.11 
 
 54 
 
 2.20 
 
 23/16 1543 661A3 161/s 
 
 62 3/4 44 
 
 13/4 
 
 .746 
 
 3726 
 
 17/8 
 
 4.45 
 
 3.19 
 
 1.26 
 
 56 
 
 2.27 
 
 21/4 
 
 1555 683/4 
 
 3 163/8 
 
 65 
 
 48 
 
 13/4 
 
 .746 
 
 3674 
 
 1 7/8 4.26 
 
 3.19 
 
 1.07 
 
 58 
 
 2.34 
 
 2 5/16 1567 
 
 71 
 
 3 1/8 61/2 
 
 671/4 
 
 48 
 
 1 3/4 
 
 .746 
 
 394 
 
 17/fi 
 
 4.4013.19 
 
 1.21 
 
 60 
 
 2.41 
 
 27/ie 1538 
 
 73 
 
 3 1/8 61/2 
 
 691/4 
 
 52 
 
 13/4 
 
 .7463892 
 
 1 7/8 4.19 
 
 3.19 
 
 1.00 
 
 62 
 
 2.47 
 
 2 1/2 1550 
 
 753/4 
 
 3 1/4 
 
 67/8 
 
 713/4 
 
 52 
 
 1 7/8 12. 051 3538 
 
 2 
 
 4.34 
 
 3.41 
 
 0.93 
 
 64 
 
 2.54 
 
 2 9/16 
 
 1561 
 
 78 
 
 3 1/4 
 
 7 
 
 74 
 
 52 
 
 7/8 
 
 2.051 
 
 3770 
 
 2 
 
 4.48 
 
 3.41 
 
 1.07 
 
 66 
 
 2.61 
 
 25/ 8 
 
 1572 
 
 80 
 
 3 3/g 
 
 7 
 
 76 
 
 52 
 
 7/ 8 2.051 
 
 4010 
 
 2 
 
 4.60 
 
 3.41 
 
 1.19 
 
 68 
 
 2.68 
 
 2H/16H582 
 
 821/43 3/8 
 
 71/8 
 
 781/4 
 
 56 
 
 7/8 
 
 2.051 
 
 3952 
 
 2 
 
 4.38 
 
 3.41 
 
 0.97 
 
 70 
 
 2.74 
 
 23/4 11591 
 
 84l/ 2 13 1/2 
 
 71/4 
 
 801/2 
 
 56 
 
 7/8 ! 2. 051 
 
 4188 
 
 2 
 
 4.51 
 
 3.41 
 
 1.10 
 
 72 
 
 2.81 
 
 213/ie '1600 86 1/2 3 1/2 
 
 71/4 
 
 821/2 
 
 60 
 
 7/ 8 2.051 
 
 4136 
 
 2 
 
 4.33 
 
 3.41 
 
 0.92 
 
 74 
 
 2.88 
 
 27/ 8 1609 881/213 5/ 8 
 
 71/4 
 
 841/2 
 
 60 
 
 7/8 
 
 2.051 
 
 4368 
 
 2 
 
 4.44 
 
 3.41 
 
 1.03 
 
 76 
 
 2.94 
 
 215/16 
 
 1617 903/43 5/8 
 
 73/8 
 
 861/260 
 
 7/82.051 
 
 4608 
 
 2 
 
 4.54 
 
 3.41 
 
 1.13 
 
 78 
 
 3.01 
 
 3 
 
 1625 93 - 
 
 3 3/4 
 
 71/2 
 
 883/4 
 
 60 
 
 2 
 
 2.302 
 
 432 
 
 21/8 
 
 4.66 
 
 3.63 
 
 1.03 
 
 80 
 
 3.08 
 
 31/16 
 
 1633 951/4 
 
 3 3/ 4 
 
 75/8 
 
 91 
 
 60 
 
 2 
 
 2.302 
 
 4549 
 
 2l/ 8 !4.78 
 
 3.63 
 
 1.15 
 
 82 
 
 3.15 
 
 31/8 
 
 1640 971/23 7/8 
 
 73/4 931/4 
 
 60 
 
 2 
 
 2.302 
 
 4779 
 
 2 l/s 4.90 
 
 3.63 
 
 1.27 
 
 84 
 
 3.21 
 
 33/16 
 
 1647 993/43 7/ 8 
 
 77/8 951/2 
 
 64 
 
 2 
 
 2.302 
 
 4702 
 
 21/8 
 
 4.68 
 
 3.63 
 
 1.05 
 
 86 
 
 3.28 
 
 31/4 
 
 1653 102 
 
 4 
 
 8 973/4 
 
 64 
 
 2 
 
 2.302 
 
 4928 
 
 2 l/8,'4.79 
 
 3.63 
 
 1.16 
 
 88 
 
 3.35 
 
 35/16 
 
 1660 1041/4 
 
 4 
 
 81/8 100 
 
 68 
 
 2 
 
 2.302 
 
 4857 
 
 2 l/s 
 
 4.60 
 
 3.63 
 
 0.97 
 
 90 
 
 3.41 
 
 33/8 
 
 1667 s 106 1/2 4 1/8 
 
 81/411021/4 
 
 6821/s 
 
 2.648 4416 
 
 21/4 
 
 !4.71 
 
 3.83 
 
 0.88 
 
 92 
 
 3.48 
 
 31/2 
 
 16431083/44 l/s 
 
 83/ 8 104 1/2 68 21/8^2.648 4615 
 
 2 1/4 4.81 
 
 3.83 
 
 0.98 
 
 94 
 
 3.55 
 
 39/16 
 
 1649 111 
 
 4 1/4 
 
 8.1/2 1061/468 21/8 
 
 2.648 
 
 4817 
 
 21/4 
 
 4.89 
 
 3.83 
 
 1.06 
 
 96 
 98 
 100 
 
 3.62 
 3.68 
 3.75 
 
 35/8 
 3H/16 
 33/4 
 
 1655 1131/4 
 1661 1151/s 
 1667J1173/4 
 
 41/4 85/81081/216821/43.023440 
 4 S/g Is 3/4 110 3/ 4 |68 2 1/4 3.023 4587 
 4 3/8 |87/ 8 ;113 |68l2 1/413.023 4776 
 
 2 3/8 4.99 4.06 
 23/85.094.06 
 23/ 8 5.20l4.06 
 
 0.93 
 1.03 
 1.14 
 
210 
 
 MATERIALS. 
 
 The last three columns of the table refer to the sketch Fig. 75, and show 
 
 the distances between bolt holes, the maximum 
 
 space occupied by the nuts and the minimum 
 
 t-*-B->j space between adjacent nuts, all measured on 
 
 /-f-\ '/i~\! tne cnor d- Bolt holes are to straddle the center 
 
 /. ; \ !(--} V- une ' ancl are to De Vs in. larger in diameter than 
 
 \ /^ C J\ / the bolts. Standard weight fittings and flanges 
 
 j~ ^ are to be plain faced, but extra heavy fittings and 
 
 flanges are to have a raised surface i/ie in. high 
 
 (On Chord) inside of bolt holes for gaskets. Square head bolts 
 
 with hexagonal nuts are recommended, but for 
 
 Fig. 75. bolts is/g in. diameter and larger, studs with a nut 
 
 on each end may be substituted. Flanges are to 
 
 be spot bored for nuts for sizes 32 in. to 100 in. inclusive. For super- 
 heated steam, steel flanges, fittings and valves are recommended. 
 
 American Standard Extra Heavy Cast Iron Pipe Flanges 
 For Pressures up to 250 Lb. per Sq. In. (All Dimensions in Inches.) 
 
 Pipe | d 
 
 Flanges. 
 
 
 Bolts. 
 
 
 See Fig. 75, 
 p. 210. 
 
 g 
 
 Thickness.^ 
 
 
 i 
 
 "8 
 
 1 
 
 . 
 
 fe 
 
 d 
 
 d 
 
 0) 
 
 o 
 
 8 
 
 ij 
 
 sl 
 
 I 
 
 w P< 
 
 i 
 
 Thickn. 
 
 8 
 
 g 
 
 | Numbe 
 
 IA 
 
 > a 1 
 43 co 
 
 * * 
 
 4J> rt 
 
 55 
 
 PQ 
 
 A 
 
 B 
 
 C 
 
 ~y 
 
 0.45 
 
 1/2 
 
 250 
 
 41/2 
 
 H/16 
 
 13/4 31/4 
 
 4 1/2 
 
 0.126 
 
 389 
 
 5/8 
 
 2.29 
 
 .00 
 
 1.29 
 
 H/4 
 
 0.47 
 
 1/2 
 
 312 
 
 5 
 
 3/4 
 
 17/8 
 
 33/4 4! 1/2 
 
 0.126 
 
 609 
 
 5/8 
 
 2.65 
 
 .00 
 
 1.65 
 
 , U/2 
 
 0.49 
 
 1/2 
 
 375 6 
 
 13/18 
 
 21/4 
 
 41/2 4 5/80.202 
 
 547 
 
 3/43.17 
 
 .21 
 
 1.96 
 
 
 0.51 
 
 1/2 
 
 500 
 
 61/2 
 
 7/8 
 
 21/4 
 
 5 
 
 4 5/ 8 
 
 0.202 
 
 972 
 
 3/4 
 
 3.53 
 
 .21 
 
 2.32 
 
 21/2 
 
 0.53 
 
 9/16 
 
 555 
 
 71/2 
 
 | ' 
 
 21/2 
 
 57/g 
 
 4 
 
 3/4,0.302 
 
 1016 
 
 7/8 
 
 4.15 
 
 .442.71 
 
 3 
 
 0.56 
 
 9/16 
 
 667 
 
 81/4 
 
 1 1/8 
 
 25/8 
 
 65/ 8 ! 8 
 
 3/4 
 
 0.302 
 
 731 
 
 7/8 
 
 2.53 
 
 .44 
 
 .09 
 
 31/2 
 
 0.59 
 
 9/16 
 
 778 
 
 9 
 
 13/16 
 
 23/4| 71/4| 8 
 
 3/40.302 
 
 995 7/ 8 ;2.77 
 
 .44 
 
 .33 
 
 
 0.61 
 
 5/8 
 
 800 
 
 10 
 
 1 1/4 
 
 3 
 
 77/ 8 
 
 
 
 3/4 
 
 0.302 
 
 1300! 7/8 
 
 3.01 
 
 .44 
 
 .57 
 
 41/2 
 
 0.64 
 
 5/8 
 
 900 
 
 101/2 
 
 1 5/16 
 
 3 
 
 81/2 
 
 8 
 
 3/t 0.302 
 
 1646 7/ 8 '3. 25 
 
 .44 
 
 .81 
 
 5 
 
 0.67 
 
 
 909 
 
 11 
 
 13/8 
 
 3 
 
 91/4 
 
 8 
 
 3/4!0.302|2032 
 
 7/8 3.53 
 
 .44 2.09 
 
 6 
 
 0.72 
 
 3/4 
 
 1000 
 
 121/2 
 
 1 7/16 
 
 31/4 
 
 105/8 
 
 12 
 
 3/4 0.302 
 
 1950 7/82.75 
 
 1.44 
 
 .31 
 
 7 
 
 0.78 
 
 13/16 
 
 1077 
 
 14 
 
 
 31/2J 11 7/8 
 
 12 
 
 7/80.420 
 
 1909 
 
 3.07 
 
 1.66 
 
 .41 
 
 8 
 
 0.83 
 
 13/16 
 
 1230 15 
 
 15/8 
 
 31/213 
 
 12 
 
 7/8 0.420 2493 
 
 3.36 
 
 1.66 
 
 .70 
 
 9 
 
 0.89 
 
 7/8 
 
 1285 
 
 161/4 
 
 1 3/4 
 
 35/ 8 :i4 
 
 12 
 
 1 
 
 0.550 
 
 2410 l/s 
 
 3.62 
 
 1.88 
 
 .74 
 
 10 
 
 0.94 
 
 15/16 
 
 1333 
 
 171/2 
 
 17/8 
 
 33/4151/4 
 
 16 
 
 1 
 
 0.5502231 1/8,2.97 
 
 1.88 
 
 .09 
 
 12 
 
 1.05 
 
 | 
 
 1500 
 
 201/2 
 
 2 
 
 41/4 
 
 173/4 
 
 16 
 
 11/80.6942546 1/4 3.46 
 
 2.09 
 
 .37 
 
 14 
 15 
 16 
 
 1.16 
 1.21 
 1.27 
 
 U/8 
 13/16 
 
 HA 
 
 155523 
 1579 24 1/2 
 
 1600:25 1/2 
 
 21/8 
 23/16 
 21/4 
 
 41/ 2 !20l/420 1 i/sO.6942773 1/4 3.17 2.09 
 43/4 21 1/2 20 1 1 A 1 0. 893 1 2473! 3/ 8 3.36 2.31 
 43/4J22 1/2120 1 1/4 10. 893 2814 3/ 8 |3.52 2.31 
 
 .08 
 .05 
 .21 
 
 18 
 
 1.37 
 
 13/8 
 
 1636 
 
 28 
 
 23/8 
 
 5 
 
 243/4 
 
 24 
 
 1 1/4 0.893 j 2968 3/ 8 |3.232.31 
 
 0.92 
 
 20 
 22 
 
 1.48H/2 1666301/2 
 1.5919/16 176033 
 
 21/2 
 25/8 
 
 5 1/4 27 
 
 5 1/4 29 1/4 
 
 24 
 24 
 
 13/8 
 1 1/2 
 
 .057 3096 
 .295 3058 
 
 1/2 3.52 2.53 0.99 
 5/8 3.81 2.75 .06 
 
 24 
 
 1 .70 1 5/8 
 
 1846 
 
 36 
 
 23/4 
 
 5 3/4 32 
 
 24 
 
 1 5/8 
 
 .515 
 
 3110il 3/4 
 
 4.18296 
 
 .22 
 
 26 
 
 1.81 1 13/ie 
 
 1793381/4 
 
 2 13/16 
 
 61/8341/2 
 
 28 
 
 15/8 
 
 .5153126 1 3/4 3.86! 2.96 0.9 J 
 
 28 
 
 1.91 
 
 17/8 
 
 1866 
 
 403/4 
 
 215/1663/8 
 
 37 
 
 28 
 
 15/8 
 
 .515!3629j1 3/44.142.96 
 
 .18 
 
 30 
 
 2.02 
 
 2 
 
 1875 
 
 43 
 
 3 
 
 61/2 
 
 391/4 
 
 28 
 
 1 3/4 
 
 1.7463615 1 7/ 8 ! 4.38 3.19 
 
 .19 
 
 32 
 
 2.1321/s. 1882451/4 
 
 31/8 
 
 65/ 8 41 1/228 
 
 1 7/82.051 
 
 3501 2 
 
 4.64,341 
 
 .26 
 
 34 
 36 
 
 2.2421/4 1 1889 47 1/2 
 2.35123/s 189450 
 
 31/4 
 33/8 
 
 63/4 
 
 43i/ 2 
 46 
 
 28 
 32 
 
 1 7/8 2.051 
 1 7/82.051 
 
 39522 
 
 38772 
 
 4.873.41 
 4.503.41 
 
 .46 
 .09 
 
 38 
 
 2.4627/ 16 1948521/4 
 
 37/ie 71/848 
 
 32 1 7/8 2.051 
 
 43202 
 
 4.703.41 
 
 .29 
 
 40 
 42 
 44 
 46 
 48 
 
 2.562 9/161953541/2 
 2.67 2 n/16 1953 57 
 2.78:213/161955591/1 
 2.8912 7/8 200061 1/2 
 3.003 : 2000 65 
 
 3 9/i 6 7l/4 
 3 11/16 7 1/2 
 33/4 .75/8 
 37/8 73/4 
 4 l81/ 2 
 
 501/4 36 1 7/ 8 ! 2.051 4255 2 4.38 3.41 0.97 
 523/4J36 1 7/8 2.051 4691 2 4.59 3.41 .18 
 55 1362 2.302458721/84.793.63 .16 
 57 1/4 40 2 ; 2.302 4512 2 1/8 4.49 3.63 0.86 
 603/ 4 402 12.302 4913 2 i/s 4.76 3.63 1.13 
 
 * Thickness of flange given in table includes raised face. 
 
FORGED AND ROLLED STEEL FLANGES. 
 
 211 
 
 Forged Steel Flangeslfor Riveted Pipe. 
 
 Riveted Pipe Manufacturers' Standard.* 
 
 ll 
 
 II 
 
 72 
 
 0) 
 T3 g 
 
 3 i 
 5 
 
 Thickness 
 of Flange.* 
 
 83 
 
 |3 
 
 3<2 
 
 IS 
 
 Diam. of 
 Bolt Circle. 
 
 -2 
 
 g 
 11 
 
 W 
 
 Outside 
 Diam. 
 
 Thickness 
 of Flange.* 
 
 o 
 
 & 
 
 0-2 
 
 IS 
 
 Diam. of 
 Bolt Circle. 
 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 j ] 
 
 6 
 
 8 
 9 
 10 
 11 
 13 
 14 
 J5 
 
 5/16 .... 
 5/16 9/16 
 5/16 9/16 
 3/8 9/ 16 
 3/8 9/i 6 
 3/8 5/8 
 3/8 5/ 8 
 3/8 11/16 
 7 /16 
 
 4 
 8 
 8 
 8 
 8 
 8 
 8 
 8 
 12 
 
 V/18 
 
 7/16 
 7/16 
 1/2 
 1/2 
 1/2 
 1/2 
 1/2 
 1/2 
 
 43/4 
 5 15/16 
 6 15/16 
 
 7T,, 
 
 10 
 
 M 1/4 
 121/4 
 13 3/ 8 
 
 16 
 18 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 
 211/4 
 
 %,\ 
 %'< 
 
 32 
 34 
 36 
 38 
 
 V8 3/ 4 
 V8 3/4 
 5/8 V8 
 H/16 7/8 
 11/16 7/ 8 
 
 1 
 
 1 
 
 12 
 16 
 16 
 16 
 16 
 24 
 28 
 28 
 28 
 
 V2 
 5/8 
 5/8 
 5/8 
 
 V8 
 3/4 
 
 3/4 
 3/4 
 3/4 
 
 191/4 
 2H/4 
 
 231/8 
 26 
 273/4 
 293/4 
 313/4 
 333/4 
 353/4 
 
 12 
 13 
 14 
 15 
 
 16 
 17 
 18 
 19 
 
 7/16 3/4 
 7/16 .... 
 7/16 3/ 4 
 9/16 3/4 
 
 12 
 12 
 12 
 12 
 
 1/2 
 1/2 
 1/2 
 1/2 
 
 141/4 
 
 15 1/4 
 
 161/4 
 
 177/ 16 
 
 34 
 36 
 40 
 42 
 
 40 
 42 
 46 
 48 
 
 H/8 
 
 H/8 
 M/8 
 
 28 
 32 
 32 
 36 
 
 3/4 
 3/4 
 3/4 
 
 3/4 
 
 373/4 
 393/4 
 433/4 
 453/4 
 
 * Flanges for riveted pipe are also made with the outside diameter and 
 the drilling dimensions the same as those of the A. S. M. E. standard 
 (page 209) , and with the thickness as given in the second column of fig- 
 ures under "Thickness of Flange" in the above table. 
 
 Curved Forged Steel Flanges are also made for boilers and tanks. 
 See catalogue of American Spiral Pipe Works, Chicago. 
 
 Forged and Rolled Steel Flanges. 
 
 Dimensions in Inches. (American Spiral Pipe Works, 1913.) 
 
 Standard Companion Flanges. 
 
 Standard Shrink Flanges. 
 
 "3 DD 
 
 
 
 
 g 
 
 8 
 
 -. . 
 
 
 
 
 3 
 
 8 
 
 1 .| 
 
 T3 PJ 
 
 a a? 
 
 1 
 
 ^3 
 
 
 S3 8 
 
 -8 a 
 
 a 
 
 i , 
 
 fd 
 
 . . 
 
 
 |l 
 
 O Q 
 
 |i 
 
 p 
 
 |I 
 
 n 
 
 5 w 
 
 III 
 
 l| 
 
 
 iP 
 
 "a^ 
 
 |1 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 2 
 
 6 
 
 21/8 
 
 5/8 
 
 1 
 
 31/8 
 
 4 
 
 9 
 
 43/8 
 
 15/16 
 
 23/i 6 
 
 53/ 4 
 
 21/2 
 
 7 
 
 21/2 
 
 H/16 
 
 1 Vl6 
 
 35/8 
 
 41/2 
 
 91/4 
 
 47/ 8 
 
 15/16 
 
 21/4 
 
 61/8 
 
 ^ 
 
 71/3 
 
 31/8 
 
 3/4 
 
 1 1/8 
 
 45/16 
 
 5 
 
 10 
 
 57/16 
 
 15/16 
 
 25/i 6 
 
 67/ 8 
 
 31/2 
 
 81/2 
 
 35/ 8 
 
 13/16 
 
 13/16 
 
 47/ 8 
 
 6 
 
 It 
 
 61/2 
 
 
 27/ie 
 
 77/8 
 
 4 
 
 9 
 
 41/8 
 
 15/16 
 
 13/16 
 
 53/8 
 
 7 
 
 121/2 
 
 71/2 
 
 1/16 
 
 21/2 
 
 9 
 
 41/2 
 
 91/4 
 
 45/ 8 
 
 15/16 
 
 
 5 13/16 
 
 8 
 
 131/2 
 
 81/2 
 
 1/8 
 
 25/8 
 
 10 
 
 5 
 
 10 
 
 51/8 
 
 15/16 
 
 1 5/16 
 
 67/ie 
 
 9 
 
 15 
 
 91/2 
 
 1/8 
 
 23/4 
 
 11 1/8 
 
 6 
 
 11 
 
 
 
 I 7/16 
 
 7 9/16 
 
 10 
 
 16 
 
 Id 5/8 
 
 3/16 
 
 3 
 
 121/4 
 
 7 
 
 121/2 
 
 7 3/1J 
 
 1/16 
 
 H/2 
 
 85/8 
 
 12 
 
 19 
 
 125/8 
 
 1/4 
 
 33/8 
 
 141/2 
 
 8 
 
 131/2 
 
 
 1/8 
 
 15/8 
 
 9 H/16 
 
 14 
 
 21 
 
 137/s 
 
 3/8 
 
 33/8 
 
 157/s 
 
 9 
 
 15 
 
 9 3/i6 
 
 1/8 
 
 13/4 
 
 105/s 
 
 15 
 
 221/4 
 
 147/ 8 
 
 3/8 
 
 31/2 
 
 167/ 8 
 
 10 
 
 16 
 
 105/18 
 
 3/16 
 
 1 7/8 
 
 1 1 15/16 
 
 16 
 
 231/2 
 
 157/ 8 
 
 7/16 
 
 35/8 
 
 18 
 
 12 
 
 19 
 
 125/i 6 
 
 1/4 
 
 21/16 
 
 141/8 
 
 18 
 
 25 
 
 177/s 
 
 9/16 
 
 37/8 
 
 201/8 
 
 14 
 
 21 
 
 131/2 
 
 13/8 
 
 
 157/ 16 
 
 20 
 
 271/2 
 
 197/s J 
 
 11/16 
 
 41/8 
 
 22 1/4 
 
 
212 
 
 MATERIALS, 
 
 Forged and Rolled Steel Flanges. Continued. 
 Extra Heavy Companion Flanges. 
 
 Is 
 iff 
 
 233 
 
 Outside 
 Diam. 
 
 Js 
 
 Thick- 
 ness. 
 
 *o . 
 
 J3-^5 
 
 s 3 
 
 1* 
 
 *8 . 
 
 c -a 
 
 I* 
 
 Nominal 
 Size, Ins. 
 
 Outside 
 Diam. 
 
 .1 
 
 I Q 
 
 Thick- 
 ness. 
 
 o 
 
 
 1* 
 
 i 
 
 # 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 91/8 
 
 101/8 
 
 113/16 
 129/ia 
 145/ 8 
 1513/w 
 17 3/i 6 
 181/4 
 
 j* 
 
 31/ 2 
 4l/ 2 
 6 
 
 61/2 
 
 71/2 
 81/4 
 
 9 
 10 
 
 ,o./, 
 
 121/2 
 
 21/8 
 21/2 
 31/8 
 35/8 
 41/8 
 45/8 
 51/8 
 63/16 
 
 7/8 
 
 1/8 
 1/8 
 1/4 
 1/4 
 H/4 
 
 3/8 
 7/16 
 9/16 
 5/8 
 3/4 
 13/16 
 
 2 ?/8 
 
 33/8 
 41/16 
 4H/16 
 55/16 
 5 13/16 
 61/4 
 6 13/16 
 77/8 
 
 7 
 
 8 
 9 
 10 
 12 
 14 
 15 
 16 
 
 14 
 15 
 16 
 
 171/2 
 
 20 
 
 221/2 
 
 1/2 
 
 73/16 
 83/i 6 
 93/16 
 105/ie 
 I25/ 16 
 
 131/2 
 141/2 
 151/2 
 
 1 5/16 
 13/8 
 17/16 
 H/2 
 1V8 
 13/4 
 1 13/16 
 17/8 
 
 21/16 
 23/16 
 21/4 
 23/ 8 
 29/16 
 2 H/16 
 2 13/16 
 31/16 
 
 Extra Heavy High Hub Flanges. 
 
 Size. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 Size. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 4 
 
 10 
 
 43/8 
 
 I 1/8 
 
 31/8 
 
 53/4 
 
 18 
 
 27 
 
 177/ 8 
 
 2 
 
 5 
 
 203/4 
 
 " 4 1/2 
 
 101/2 
 
 47/8 
 
 H/4 
 
 31/4 
 
 61/4 
 
 20 
 
 291/2 
 
 197/g 
 
 21/4 
 
 5l/ 2 
 
 22i/ 2 
 
 5 
 
 11 
 
 57/16 
 
 H/4 
 
 31/4 
 
 7 
 
 22 
 
 3H/2 
 
 
 21/4 
 
 51/2 
 
 243/4 
 
 6 
 
 12l/ 2 
 
 61/2 
 
 H/4 
 
 31/4 
 
 7 15/16 
 
 24 
 
 34 
 
 
 27/16 
 
 61/4 
 
 27 
 
 7 
 
 14 
 
 71/2 
 
 15/16 
 
 33/8 
 
 .91/8 
 
 30 
 
 40 
 
 
 27/ W 61/4 
 
 33 
 
 8 
 
 15 
 
 81/2 
 
 13/8 
 
 3l/ 2 
 
 105/i 6 
 
 36 
 
 46 
 
 
 2 7/16 
 
 61/4 
 
 39 
 
 9 
 
 16 
 
 91/2 
 
 17/16 
 
 35/8 
 
 113/8 
 
 42 
 
 52 
 
 
 27/16 61/4 
 
 45 
 
 10 
 
 17V2 
 
 105/g 
 
 H/2 
 
 33/4 
 
 125/s 
 
 48 
 
 581/4 
 
 
 27/16 
 
 61/2 
 
 5H/4 
 
 11 
 
 183/4 
 
 115/8 
 
 19/16 
 
 37/8 
 
 135/ 8 
 
 54 
 
 641/2 
 
 
 27/16 
 
 61/2 
 
 571/4 
 
 12 
 
 20 
 
 125/ 8 
 
 15/8 
 
 4 
 
 143/4 
 
 60 
 
 703/s 
 
 
 27/16 
 
 .61/2 
 
 633/ 8 
 
 14 
 
 221/2 
 
 137/8 
 
 13/4 
 
 43/8 
 
 I63/i 6 
 
 66 
 
 77 
 
 
 27/16 
 
 71/2 
 
 69l/ 2 
 
 15 
 
 23.1/2 
 
 147/ 8 
 
 1 13/16 
 
 41/2 
 
 171/4 
 
 72 
 
 831/s 
 
 
 27/16 
 
 71/2 
 
 755/ 8 
 
 16 
 
 25 
 
 15 7/ 8 j 
 
 17/8 
 
 43/4 
 
 181/2 
 
 
 
 
 
 
 
 The Rockwood Pipe Joint. Tfle system of flanged joints now in 
 common use for high pressures, made by slipping a flange over the pipe, 
 expanding the end of the pipe by rolling or peening, and then facing it in 
 a lathe, so that when the flanges of two pipes are bolted together the 
 bearing of the joint is on the ends of the pipes themselves and not on the 
 flanges, was patented by George I. Rockwood, April 5, 1897, No. 580,058, 
 and first described in Eng. Rec., July 20, 1895. The joint as made by 
 different manufacturers is known by various trade names, as Walmanco, 
 Van Stone, etc. 
 
 Matheson Joint and Converse Lock-joint Pipe. Sizes, external 
 diameters 2 to 20 in., 22, 24, 26, 28, and 30 in. Kimberley Joint Pipe, 
 6 to 30 in. These pipes are considerably lighter than standard pipe. 
 The Converse and Kimberley joints are made with special forms of ex- 
 ternal hubs, filled and calked with lead. The Matheson joint is also 
 a lead-packed joint, but the bell or socket is made by expanding one of 
 the pipes, the end being reinforced by a steel band. The lead required 
 per joint is less than for other lead- joint pipes of the same diameter. 
 
 PIPE FITTINGS. 
 
 Dimensions of Standard Cast-Iron Flanged Pipe Fittings, for Pres- 
 sures up to 125 Lb. per Sq. In. (Adopted March 20, 1914, by a 
 joint committee of manufacturers and of the Am. Soc. M. E.) 
 Dimensions in the tables, pages 213 and 214, refer t9 corresponding 
 letters on the sketches on page 215. For dimensions of flanges 
 and bolts see Table of Standard Flanges, pages 209 and 210. 
 
213 
 Standard Cast Iron Flanged Pipe Fittings for Pressures up to 125 lb. 
 
 per Sq. In. (see sketches p. 215.) 
 
 Size. 
 
 Tees, Crosses 
 and Ells. 
 
 Long 
 Radius 
 Ells. 
 
 45 
 degree 
 Ells. 
 
 Laterals. 
 
 Re- 
 ducers. 
 
 Min. 
 Thick- 
 ness of 
 Metal. 
 
 H/4 
 
 j* 
 
 f>/ 2 
 
 3./ 2 
 
 41/2 
 
 6 
 7 
 
 8 
 9 
 10 
 12 
 14 
 15 
 16 
 18 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 34 
 36 
 38 
 40 
 42 
 44 
 46 
 48 
 50 
 52 
 54 
 56 
 58 
 60 
 62 
 64 
 66 
 68 
 70 
 72 
 74 
 76 
 78 
 80 
 82 
 84 
 86 
 88 
 90 
 92 
 94 
 96 
 98 
 100 
 
 A-A 
 
 fy 
 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 20 
 22 
 24 
 28 
 29 
 30 
 33 
 36 
 40 
 44 
 46 
 48 
 50 
 52 
 54 
 56 
 58 
 60 
 62 
 64 
 66 
 68 
 70 
 74 
 78 
 82 
 84 
 88 
 90 
 94 
 96 
 
 too 
 
 102 
 106 
 108 
 112 
 116 
 118 
 120 
 124 
 126 
 130 
 134 
 136 
 138 
 142 
 146 
 148 
 
 A 
 
 31/2 
 33/4 
 
 4l/ 2 
 
 51/2 
 
 6 
 
 61/2 
 71/2 
 
 8 
 
 81/2 
 
 9 
 10 
 11 
 12 
 
 14 
 
 g.A 
 
 161/2 
 
 18 
 20 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 37 
 39 
 41 
 42 
 44 
 45 
 47 
 48 
 50 
 51 
 53 
 54 
 56 
 58 
 59 
 60 
 62 
 63 
 65 
 67 
 68 
 69 
 71 
 73 
 74 
 
 B 
 5 
 
 51/2 
 61/2 
 
 73/4 
 81/2 
 
 91/2 
 101/4 
 11 V2 
 123/4 
 14 
 151/4 
 161/2 
 
 19 
 
 21 1/2 
 223/4 
 
 261/2 
 
 IV /2 
 36l/ 2 
 39 
 
 4H/2 
 
 44 
 
 '/' 
 5 si I/2 
 
 56* 
 
 61 1/2 
 64 
 
 6 V /2 
 Jl A 
 
 76l/ 2 
 79 
 
 8H/2 
 
 84 
 
 86 1/2 
 89 
 
 9H/2 
 
 94 
 96l/ 2 
 99 
 
 101 1/2 
 
 104 
 1061/2 
 109 . 
 
 !!1 1/2 
 
 1161/2 
 
 119 
 
 !ir /2 
 
 !' /2 
 
 C 
 
 ] 3 /4 
 
 21/4 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 51/2 
 51/2 
 
 6 
 
 61/2 
 
 71/2 
 71/2 
 
 8 
 8 
 
 81/2 
 91/2 
 
 10 
 11 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 50 
 
 D 
 
 JV, 
 }| V , 
 
 13 
 
 Hl/2 
 
 15 
 |5./ 2 
 
 18 
 
 g* 
 
 24 
 251/2 
 30 
 33 
 
 341/2 
 
 *>/, 
 
 43 
 46 
 491/2 
 53 
 56 
 59 
 
 E 
 
 53/4 
 
 61/4 
 
 8 
 
 ,r /2 
 a* 
 
 12i/ 2 
 
 131/2 
 141/2 
 161/2 
 171/2 
 191/2 
 
 201/2 
 2?./, 
 
 281/2 
 30 
 32 
 35 
 371/2 
 401/2 
 44 
 461/ 2 
 49 
 
 F 
 
 13/4 
 13/4 
 
 21/2 
 21/2 
 
 3 
 3 
 3 
 
 31/2 
 31/2 
 
 41/2 
 41/2 
 
 51/2 
 
 6 
 6 
 
 61/2 
 
 8 
 
 81/2 
 
 9 
 9 
 
 91/2 
 
 10 
 
 G 
 "6 " 
 
 61/2 
 
 J. A 
 
 9 
 10 
 11 
 
 M'/ 2 
 
 14 
 16 
 17 
 18 
 19 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 34 
 36 
 38 
 40 
 42 
 44 
 46 
 48 
 50 
 52 
 54 
 56 
 58 
 60 
 62 
 64 
 66 
 68 
 70 
 72 
 74 
 76 
 78 
 80 
 82 
 84 
 86 
 88 
 90 
 92 
 94 
 % 
 98 
 100 
 
 7/16 
 
 l^ 
 7/16 
 
 MM 
 
 7/16 
 
 !/! 
 7/16 
 1/2 
 1/2 
 1/2 
 9/16 
 5/8 
 5/8 
 
 $' 
 
 % 16 
 
 7/8 
 
 1/16 
 1/8 
 3/16 
 
 1/4 
 5/16 
 
 y? 
 
 7 /16 
 1/2 
 9/16 
 5/8 
 
 "/" 
 
 8r 
 
 ' 15/16 
 
 21/16 
 21/8 
 23/16 
 21/4 
 25/ 16 
 27/i 6 
 21/2 
 29/ 16 
 25/8 
 2 H/16 
 23/4 
 2 13/16 
 27/8 
 2 15/16 
 
 31/16 
 31/8 
 33/is 
 31/4 
 35/ia 
 33/8 
 31/2 
 39/16 
 35/ 8 
 3 11/16 
 33/4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
214 
 
 MATERIALS. 
 
 Dimensions of American Standard Flanged Reducing Fittings. Short 
 Body Pattern. (All Dimensions in Inches.) 
 
 Long body patterns are used when outlets are larger than those in 
 table, and have the same dimensions as straight size fittings. All re- 
 ducing fittings from 1 to 16 in. inclusive have same dimensions as 
 straight size fittings. The dimensions of reducing fittings are always 
 regulated by the reduction of the outlet. 
 
 18 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 34 
 56 
 38 
 40 
 42 
 44 
 46 
 48 
 50 
 52 
 54 
 56 
 58 
 
 Tees, Ells, Crosses. 
 
 Laterals. 
 
 i 
 
 w 
 
 ~60~ 
 62 
 64 
 66 
 68 
 70 
 72 
 74 
 76 
 78 
 80 
 82 
 84 
 86 
 88 
 90 
 92 
 94 
 96 
 98 
 100 
 
 Tees, Ells, 
 and Crosses. 
 
 J* 
 
 Cfl+3 
 
 *3 
 
 S-o 
 
 12 
 14 
 15 
 16 
 18 
 18 
 20 
 20 
 22 
 24 
 24 
 26 
 28 
 28 
 30 
 32 
 32 
 34 
 36 
 36 
 38 
 
 AA 
 
 26 
 28 
 28 
 30 
 32 
 32 
 36 
 36 
 38 
 40 
 40 
 44 
 46 
 46 
 48 
 52 
 52 
 54 
 58 
 58 
 62 
 
 A 
 
 13 
 14 
 14 
 15 
 16 
 16 
 18 
 18 
 19 
 20 
 20 
 22 
 23 
 23 
 24 
 26 
 26 
 27 
 29 
 29 
 31 
 
 B 
 
 N " 
 W^ 
 
 So 
 
 a* 
 
 9 
 10 
 10 
 12 
 12 
 14 
 15 
 
 D 
 
 26 
 28 
 29 
 32 
 35 
 37 
 39 
 
 E 
 
 F 
 
 1 
 
 V2 
 
 o' /2 
 
 
 
 
 H 
 
 271/2 
 291/2 
 31 1/2 
 34 i/ 2 
 38 
 40 
 42 
 
 S 4 ^ 
 
 w5 
 
 & 
 
 S-8 
 
 40 
 40 
 42 
 44 
 44 
 46 
 48 
 48 
 50 
 52 
 52 
 54 
 56 
 56 
 58 
 60 
 60 
 62 
 64 
 64 
 66 
 
 AA 
 
 66 
 66 
 68 
 70 
 70 
 74 
 80 
 80 
 84 
 86 
 86 
 88 
 94 
 94 
 96 
 100 
 100 
 104 
 106 
 106 
 110 
 
 A 
 
 ~33 
 33 
 34 
 35 
 35 
 37 
 40 
 40 
 42 
 43 
 43 
 44 
 47 
 47 
 48 
 50 
 50 
 52 
 53 
 53 
 55 
 
 B 
 
 "4? 
 
 42 
 44 
 45 
 46 
 47 
 48 
 49 
 50 
 52 
 53 
 54 
 56 
 57 
 58 
 61 
 62 
 63 
 64 
 65 
 67 
 
 17 l /2 
 
 18 
 19 
 20 
 
 11 
 
 24 
 25 
 26 
 28 
 29 
 30 
 31 
 33 
 34 
 35 
 36 
 37 
 39 
 40 
 
 25 
 27 
 
 281/2 
 
 \V h 
 
 37 
 39 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Extra Heavy American Standard Flanged Reducing Fittings. 
 Body Pattern. (All Dimensions in Inches.) 
 
 Short 
 
 1 
 
 CO 
 
 Tees, Ells and Crosses. 
 
 Laterals. 
 
 | 
 
 c/5 
 
 Tees, Ells and Crosses. 
 
 ti 
 
 05^3 
 
 go 
 
 ^"o 
 
 AA 
 
 A 
 
 K 
 
 S-^ 
 
 .3 Q) 
 C/253 
 
 So 
 
 & 
 
 D 
 
 E 
 
 F 
 
 H 
 
 II 
 
 a* 
 
 3 
 
 AA 
 
 A 
 
 K 
 
 18 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 
 12 
 14 
 15 
 16 
 18 
 18 
 20 
 20 
 
 28 
 31 
 33 
 34 
 38 
 38 
 41 
 41 
 
 14 
 
 151/2 
 161/2 
 
 17 
 19 
 19 
 
 20 l/ 2 
 201/2 
 
 17 
 
 1S V2 
 gv, 
 
 24 
 
 251/2 
 26i/ 2 
 
 9 
 10 
 10 
 12 
 
 34 
 37 
 40 
 44 
 
 31 
 34 
 37 
 41 
 
 3 
 3 
 3 
 3 
 
 8'" 
 
 39 
 
 43 
 
 34 
 36 
 38 
 40 
 42 
 44 
 46 
 48 
 
 22 
 24 
 24 
 26 
 28 
 28 
 30 
 32 
 
 44 
 47 
 47 
 50 
 53 
 53 
 55 
 58 
 
 22 
 
 231/2 
 
 >* 
 
 2$ 
 i 172 
 
 28 
 291/2 
 301/2 
 
 31 1/2 
 331/2 
 
 341/2 
 
 351/2 
 37i/ 2 
 
 Standard Brass Flanges as adopted Sept. 17, 1913, by the Committee 
 of manufacturers on the standardization of Valves and Fittings, to be- 
 come effective Jan. 1, 1914 are listed on page 215. The bolt holes for 
 these flanges are to be drilled i/ie in. greater than the bolt diameter for 
 sizes 2 in. and smaller, and % in. greater than the bolt diameter for 
 sizes 2 l /2 in. and larger. The flanges have smooth, plain faces, and when 
 coupled to extra heavy iron flanges, the latter should have the raised 
 surface faced off. 
 
STANDARD BRASS FLANGES. 
 
 215 
 
 Side Outlet 
 
 Tee 
 STEAIGHT SIZE FITTINGS. 
 
 JH 'M**: 
 
 Laterals 
 REDUCING FITTINGS. 
 
 Jfoducers 
 
 The dimensions on these sketches refer to the corresponding letters 
 in the tables of flanged fittings, pages 213 and 214, and also to the 
 reference letters in the tables of screwed fittings, page 216. 
 
 Standard Brass Flanges. 
 
 
 Standard For Pressures up 
 to 125 Lb. 
 
 Extra Heavy For Pressures 
 up to 250 Lb. 
 
 Size, 
 In. 
 
 Diam., 
 In. 
 
 Thick- 
 ness, 
 In. 
 
 Bolt 
 Circle , 
 In. 
 
 No. 
 of 
 Bolts. 
 
 Size 
 of 
 Bolts, 
 In. 
 
 Diam., 
 In. 
 
 Thick- 
 ness, 
 In. 
 
 Bolt 
 Circle, 
 In. 
 
 No. 
 of 
 Bolts. 
 
 Size 
 of 
 Bolts, 
 In. 
 
 V4& 3 /8 
 
 2V2 
 
 9 /32 
 
 1 n /16 
 
 4 
 
 3 /8 
 
 3 
 
 3/8 
 
 2 
 
 4 
 
 7 /16 
 
 1/2 
 
 3 /4 
 
 3 
 
 3V2 
 
 5 /16 
 H/32 
 
 2V8 
 2V2 
 
 4 
 4 
 
 3 /8 
 3/8 
 
 jv, 
 
 13/32 
 7 /16 
 
 23/ 8 
 
 2 7 / 8 
 
 4 
 4 
 
 ' 
 
 1 
 
 4 
 
 3/8 
 
 3 
 
 4 
 
 7 /16 
 
 41/2 
 
 V2 
 
 3V4 
 
 4 
 
 V2 
 
 H/4 
 
 4V 2 
 
 1V32 
 
 33/ 8 
 
 4 
 
 7 /16 
 
 5 
 
 n/32 
 
 33/ 4 
 
 4 
 
 V2 
 
 H/2 
 
 5 
 
 Vl6 
 
 3 7 /8 
 
 4 
 
 V 2 
 
 6 
 
 9 /16 
 
 4V2 
 
 4 
 
 5 /8 
 
 2 
 
 6 
 
 V 2 
 
 43/ 4 
 
 4 
 
 5 /8 
 
 6V2 
 
 5 /8 
 
 5 
 
 4 
 
 5 /8 
 
 2V 2 
 
 7 
 
 9 /16 
 
 5V2 
 
 4 
 
 5 /8 
 
 7V2 
 
 n /16 
 
 5 7 /8 
 
 4 
 
 3 /4 
 
 3 
 
 ?V2 
 
 5 /8 
 
 6 
 
 4 
 
 ' 5 /8 
 
 8V4 
 
 3/4 
 
 6Vs 
 
 8 
 
 3 /4 
 
 3V2 
 
 81/2 
 
 H/16 
 
 7 
 
 4 
 
 5 /8 
 
 9 
 
 13/16 
 
 7V4 
 
 8 
 
 3/4 
 
 4 
 
 9 
 
 n /16 
 
 7V2 
 
 8 
 
 5 /8 
 
 10 
 
 7 /8 
 
 7V 8 
 
 8 
 
 3/4 
 
 4V2 
 
 9V 4 
 
 23/32 
 
 73/4 
 
 8 
 
 3/4 
 
 10V2 
 
 7 /8 
 
 8V2 
 
 8 
 
 3/4 
 
 5 
 
 10 
 
 3 /4 
 
 8V2 
 
 8 
 
 3/4 
 
 11 
 
 15 /16 
 
 9V4 
 
 8 
 
 3 /4 
 
 6 
 
 11 
 
 . 13 /16 
 
 9i/ 2 
 
 8 
 
 3/4 
 
 12V2 
 
 
 105/ 8 
 
 12 
 
 3/4 
 
 7 
 
 12V2 
 
 7 /8 
 
 10 : V4 
 
 8 
 
 3 /4 
 
 14 
 
 Vl6 
 
 11 7 /8 
 
 12 
 
 7 /8 
 
 8 
 
 131/2 
 
 16 /16 
 
 11 3/ 4 
 
 8 
 
 3/4 
 
 15 
 
 1/8 
 
 13 
 
 12 
 
 7 /8 
 
 9 
 
 15 
 
 15 /16 
 
 131/4 
 
 12 
 
 3/4 
 
 16i/ 4 
 
 1/8 
 
 14 
 
 12 
 
 1 
 
 10 
 
 16 
 
 
 141/4 
 
 12 
 
 7 /8 
 
 17V2 
 
 3/16 
 
 15V4 
 
 16 
 
 1 
 
 12 
 
 19 
 
 1Vl6 
 
 17 
 
 12 
 
 7 /8 
 
 201/2 
 
 V4 
 
 173/4 
 
 16 
 
 IV8 
 
'216 
 
 MATERIALS. 
 
 Dimensions of Screwed Cast Iron and Malleable Pipe Fittings, For 
 Steam and Water. (Crane Co., Chicago, 1914.) 
 
 R = regular fitting; E.H. ~ extra heavy fitting. For meaning of 
 dimensions see sketches p. 215. Dimensions in inches. 
 
 . 
 
 Long 
 
 
 
 
 5 1 *" Tee, Cross, Ell. 
 
 Rad. 
 
 45 Deg. Ell. 
 
 Lateral. 
 
 Reducer.* 
 
 wng. 
 
 Ell. 
 
 
 
 
 Dimension. A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 G 
 
 Size, 
 Ins. 
 
 Cast Iron. 
 
 Mall. 
 
 Mall. 
 
 Cast Iron. 
 
 Mall. 
 
 C.I. 
 
 C.I. 
 
 C.I. 
 
 Mall. 
 
 
 R. 
 
 E. H. 
 
 E.H. 
 
 E. H. 
 
 R. 
 
 E.H. 
 
 E.H. 
 
 R. 
 
 R. 
 
 R. 
 
 E. H. 
 
 1/4 
 
 13/16 
 
 
 1 i/ifi 
 
 
 3/4 
 
 
 3/4 
 
 
 
 
 
 3/8 
 
 15/ie 
 
 
 1 1/4 
 
 
 13/16 
 
 
 7/8 
 
 
 
 
 
 1/2 
 
 1 1/8 
 
 
 1 1/2 
 
 
 7/8 
 
 
 1 ' 
 
 21/2 
 
 1 7/8 
 
 
 
 3/4 
 
 15/16 
 
 
 13/4 
 
 
 1 
 
 
 U/8 
 
 3 
 
 21/4 
 
 
 1 H/16 
 
 1 
 
 1 7/16 
 
 2" 
 
 2 
 
 2 1/2 
 
 U/8 
 
 13/8" 
 
 15/16 
 
 31/2 
 
 23/4 
 
 
 2 
 
 1 1/4 
 
 13/4 
 
 21/4 
 
 21/4 
 
 3 
 
 15/16 
 
 
 H/2 
 
 41/4 
 
 31/4 
 
 21/8 ' 
 
 23/8 
 
 1 V2 
 
 1 15/16 
 
 29/16 
 
 
 31/2 
 
 17/16 
 
 15/8 
 
 1 H/16 
 
 47/8 
 
 313/16 
 
 21/4 
 
 2 H/16 
 
 2 
 
 21/4 
 
 3 
 
 3 
 
 4 
 
 
 1 15/16 
 
 2 
 
 53/4 
 
 41/2 
 
 27/16 
 
 23/16 
 
 2l/ 2 
 
 2 H/16 
 
 31/2 
 
 31/2 
 
 43/4 
 
 1 IS/16 
 
 21/4 
 
 21/4 
 
 61/4 
 
 53/16 
 
 2 H/16 
 
 
 3 
 
 31/8 
 
 41/8 
 
 41/8 
 
 51/2 
 
 2 3/16 
 
 21/2 
 
 21/2 
 
 77/8 
 
 61/8 
 
 2 15/16 
 
 
 3l/ 2 
 
 37/16 
 33/4 
 
 4H/16 
 51/8 
 
 45/8 
 51/8 
 
 61/423/8 
 7 25/8 
 
 "29/ie 
 23/4 
 
 25/8 
 2 13/16 
 
 87/8 
 93/4 
 
 67/ 8 
 75/8 
 
 31/8 
 33/8 
 
 
 41/2 
 
 41/16 
 
 51/2 
 
 55/8 
 
 73/4!213/i 6 3 
 
 
 115/8 
 
 91/4 
 
 35/8 
 
 
 5 
 
 47/16 
 
 61/8 
 
 61/4 
 
 
 31/16 35/ie 
 
 
 115/8 
 
 91/t 
 
 37/8 
 
 
 6 
 
 51/8 
 
 71/4 
 
 71/4 
 
 91/2 
 
 37/16 133/4 
 
 
 137/ 16 
 
 103/4 
 
 43/8 
 
 
 7 
 
 5 13/16 
 
 81/8 
 
 
 
 37/8 
 
 4 
 
 
 151/4 
 
 121/4 
 
 4 13/16 
 
 
 8 
 
 61/2 
 
 91/8 
 
 
 
 41/4 
 
 43/4 
 
 
 1615/i 6 
 
 135/8 
 
 51/4 
 
 
 9 
 10 
 
 73/16 
 77/8 
 
 
 
 
 4H/16 
 53/16 
 
 47/8 ' 
 
 
 20H/16 
 
 163/4 
 163/4 
 
 5 H/16 
 63/ie 
 
 
 12 
 
 91/4 
 
 133/8 
 
 
 
 6 
 
 51/2 
 
 1 
 
 195/s 
 
 71/8 
 
 
 * The reducers are for reducing from the size of pipe given to the 
 next smaller size. In addition, malleable reducers are listed for 1 % X 
 Vi,^ l A X 1, 1 Yi X Vi, 2 x 1, 2 X Vi- The dimension G given in the 
 table is the same for these special fittings as for the regular fittings 
 given above. 
 
 Strength of Pipe Fittings. To determine the actual bursting strength 
 of cast iron fittings, and also to determine the influence of form upon 
 the strength, Crane Co. conducted experiments in which flanged 
 fittings of different sizes and forms were tested to destruction by inter- 
 nal pressure. The experiments showed that the strength of ells is 
 practically the same, regardless of degree, or whether the ell is straight 
 or reducing sizes. Fittings of the same general shape as the tee or 
 cross are of nearly the same strength, and relatively of about two-thirds 
 the strength of an ell. The straight lateral has about one-third the 
 strength of the ell. The following average figures of bursting strength 
 of extra heavy tees and ells are condensed from the company s 1914 
 catalogue: 
 
 12 14 16 18 20 24 
 
 1 H/8 13/16 H/4 15/16 H/2 
 
 Size of fitting, ins., 6 8 10 
 Thickness of metal, in. 3/4 13/ 16 15/ 16 
 
 Tees, Perro-steel: 
 Burst at, Ib. per sq.in.2733 2250 2160 2033 1825 1700 1450 1275 1300 
 
 Tees, Cast Iron: 
 Burst at, lb.persq.in.1687 1350 1306 1380 1100 1025 600 750 700 
 
 Ells, Ferro-steel: 
 Burst at, Ib. per sq.in.3266 2725 2350 2133 
 
 Ells, Cast Iron: 
 Burst at, Ib. per sq. in. 2275 1625 1541 1275 1075 1250 
 
STANDARD STRAIGHT-WAY GATE VALVES. 217 
 
 Length of Thread on Pipe that- should be screwed into fittings to 
 make a tight joint is given by Crane Co. as follows: 
 
 Size of pipe, in 1/8 
 
 Length of thread, in.1/4 
 
 1/4 
 3/8 
 
 3/8 
 
 Size of pipe, in 31/2 4 41/2 
 
 Length of thread, in. 11/16 11/ie IVs 
 
 '2 3/4 1 H/4 H/2 2 21/2 3 
 
 '2 V2 Vl6 5/ 8 5/ 8 11/ 16 15/ 16 1 
 
 5 6 7 8 9 10 12 
 
 13/16 H/4 H/4 15/16 13/8 1 1/2 15/8 
 
 VALVES. 
 
 Dimensions of Standard Globe, Angle and Cross Valves. 
 
 (Crane Co., 1914.) 
 
 Iron Body, Brass Trimmings, with Yoke. 
 
 Dimensions in Inches: B, face to face, flanged; B/2, center to face, 
 flanged (Angle and Cross Valves) ; C, diameter of flanges; D, thickness 
 of flanges; S, center to top of stem, open; O, diameter of wheel. 
 
 Size. 
 2 
 
 21/2 
 31/2 
 41/2 
 
 6 
 
 B 
 
 8 
 
 81/2 
 91/2 
 101/2 
 
 11 
 
 12 
 13 
 14 
 
 B/2 
 
 C 
 
 6 
 
 7 
 
 71/2 
 Bl/2 
 
 9 
 
 91/4 
 
 10 
 11 
 
 D 
 
 S 
 
 O 
 
 Size. 
 
 7 
 8 
 10 
 12 
 14 
 15 
 16 
 
 B 
 
 B/2 
 
 C 
 
 D 
 
 11/16 
 H/8 
 13/16 
 H/4 
 13/8 
 13/8 
 17/16 
 
 S 
 
 4 
 
 41/4 
 43/ 4 
 
 51/4 
 51/2 
 
 6 
 
 61/2 
 
 5/8 
 H/16 
 3/4 
 13/16 
 15/16 
 15/16 
 15/16 
 
 103/4 
 1U/4 
 
 g* 
 
 151/4 
 151/4 
 171/4 
 
 19 
 
 61/2 
 
 6l/ 2 
 
 71/2 
 71/2 
 
 9 
 9 
 10 
 12 
 
 16 
 17 
 20 
 24 
 28 
 30 
 32 
 
 8 
 
 81/2 
 10 
 12 
 14 
 15 
 16 
 
 121/2 
 131/2 
 
 16 
 19 
 21 
 
 221/4 
 231/2 
 
 201/2 
 23 3/4 
 28 
 34 
 38l/ 2 
 381/2 
 41 1/2 
 
 Standard Straight- Way Gate Valves. (Crane Co., 1914.) 
 Iron Body. Brass Trimmings. Wedge Gate. 
 
 Dimensions in Inches: A, nominal size; B, face to face, flanged; C, 
 diam. of flanges; D, thickness of flanges; K, end to end, screwed; N, 
 center to top of non-rising stem; O, diam. of wheel; S, center to top of 
 rising stem, open; Y, center to outside of by-pass; P, size of by-pass; 
 X, number of turns to open. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 K 
 
 N 
 
 O 
 
 S 
 
 Y 
 
 P 
 
 X 
 
 2 
 
 7 
 
 6 
 
 5/8 
 
 57/i 6 
 
 113/4 
 
 61/2 
 
 141/2 
 
 
 
 7 
 
 21/2 
 
 71/2 
 
 7 
 
 H/16 
 
 57/8 
 
 123/4 
 
 61/2 
 
 16 
 
 
 
 8 
 
 3 
 
 8 
 
 71/2 
 
 3/4 
 
 61/8 
 
 141/4 
 
 71/2 
 
 19 
 
 
 
 101/4 
 
 31/2 
 
 81/2 
 
 81/2 
 
 13/16 
 
 61/2 
 
 151/4 
 
 71/2 
 
 2U/4 
 
 
 
 101/8 
 
 4 
 
 9 
 
 9 
 
 15/10 
 
 67/8 
 
 161/t 
 
 9 
 
 24 
 
 
 
 83/4 
 
 41/2 
 
 91/2 
 
 91/4 
 
 15/16 
 
 71/8 
 
 175/s 
 
 9 
 
 251/ 2 
 
 
 
 9 
 
 5 
 
 10 
 
 10 
 
 15/16 
 
 73/8 
 
 19 
 
 10 
 
 28 l/ 2 
 
 
 
 11 
 
 6 
 
 101/2 
 
 11 
 
 1 
 
 73/4 
 
 203/4 
 
 12 
 
 313/4 
 
 
 
 125/ 8 
 
 7 
 
 11 
 
 121/2 
 
 H/16 
 
 81/4 
 
 23 
 
 12 
 
 371/4 
 
 
 
 151/4 
 
 8. 
 
 1H/2 
 
 131/2 
 
 H/8 
 
 83/4 
 
 26 
 
 14 
 
 41 
 
 
 
 16 
 
 9 
 
 12 
 
 15 
 
 H/8 
 
 91/4 
 
 28 
 
 14 
 
 443/4 
 
 
 
 183/4 
 
 10 
 
 13 
 
 16 
 
 13/16 
 
 97/8 
 
 301/4 
 
 16 
 
 50 
 
 
 
 20l/ 2 
 
 12 
 
 14 
 
 19 
 
 H/4 
 
 115/8 
 
 351/4 
 
 18 
 
 571/4 
 
 
 
 241/8 
 
 14 
 
 15 
 
 21 
 
 13/8 
 
 
 391/4 
 
 20 
 
 663/4 
 
 19l/ 2 
 
 2 
 
 281/4 
 
 15 
 
 15 
 
 221/4 
 
 13/8 
 
 
 4U/8 
 
 20 
 
 693/4 
 
 21 
 
 2 
 
 3H/2 
 
 16 
 
 16 
 
 231/2 
 
 17/16 
 
 
 441/4 
 
 22 
 
 751/4 
 
 233/4 
 
 3 
 
 331/4 
 
 18 
 
 17 
 
 25 
 
 19/16 
 
 
 483/t 
 
 24 
 
 86 
 
 243/4 
 
 3 
 
 351/2 
 
 20 
 
 18 
 
 271/2 
 
 1 n/io 
 
 
 521/2 
 
 24 
 
 91 
 
 273/4 
 
 4 
 
 421/4 
 
 22 
 
 19 
 
 291/2 
 
 1 13/16 
 
 
 551/2 
 
 27 
 
 100 
 
 29 
 
 4 
 
 46 
 
 24 
 
 20 
 
 32 
 
 1 V8 
 
 
 62 
 
 30 
 
 109 
 
 301/2 
 
 4 
 
 50 
 
 26 
 
 23 
 
 341/4 
 
 2 
 
 
 657/s 
 
 30 
 
 1171/2 
 
 32 
 
 4 
 
 65 
 
 28 
 
 26 
 
 361/2 
 
 2 1/16 
 
 
 70 
 
 36 
 
 125 
 
 33 
 
 4 
 
 80 
 
 30 
 
 30 
 
 383/4 
 
 2 1/8 
 
 
 75l/ 2 
 
 36 
 
 133 
 
 34 
 
 4 
 
 921/2 
 
 36 
 
 36 
 
 453/4 
 
 2 3/ 8 
 
 
 83 
 
 
 158 l/ 2 
 
 39 
 
 6 
 
 108 
 
218 
 
 MATERIALS. 
 
 Extra Heavy Straight-Way Gate Valves. 
 
 Ferro-steel. Hard Metal Seats. Wedge Gate. (For meaning of letters, see p. 217.) 
 
 A 
 
 B 
 
 K 
 
 C 
 
 D 
 
 N 
 
 s 
 
 
 
 P 
 
 Y 
 
 X 
 
 U/4 
 
 6l/ 2 
 
 51/2 
 
 5 
 
 3/4 
 
 83/4 
 
 105/8 
 
 5 
 
 
 
 12 
 
 1 V2 
 
 . 71/2 
 
 61/4 
 
 6 
 
 13/16 
 
 95/8 
 
 121/4 
 
 51/2 
 
 
 
 11 
 
 2 
 
 81/2 
 
 7 
 
 61/2 
 
 7/8 
 
 101/2 
 
 133/4 
 
 61/2 
 
 
 
 14 
 
 21/2 
 
 91/2 
 
 8 
 
 71/2 
 
 
 127/s 
 
 16 
 
 71/2 
 
 
 
 15 
 
 3 
 
 111/8 
 
 9 
 
 81/4 
 
 H/8 
 
 145/8 
 
 191/2 
 
 9 
 
 
 
 14 
 
 31/2 
 
 11V8 
 
 10 
 
 9 
 
 13/16 
 
 151/2 
 
 22 
 
 10 
 
 
 
 16 
 
 
 12 
 
 11 
 
 10 
 
 H/4 
 
 173/4 
 
 241/2 
 
 12 
 
 
 
 18 
 
 41/2 
 
 131/4 
 
 121/4 
 
 101/2 
 
 15/16 
 
 183/4 
 
 27 
 
 12 
 
 
 
 21 
 
 5 
 
 15 
 
 13l/ 2 
 
 11 
 
 13/8 
 
 201/4 
 
 293/4 
 
 14 
 
 
 
 23 
 
 6 
 
 157/ 8 
 
 l57/ 8 
 
 12l/ 2 
 
 17/16 
 
 23 
 
 341/8 
 
 16 
 
 H/4 
 
 13 
 
 28 
 
 7 
 
 161/4 
 
 161/4 
 
 14 
 
 H/2 
 
 243/4 
 
 38 
 
 18 
 
 H/4 
 
 141/8 
 
 30 
 
 8 
 
 161/2 
 
 161/2 
 
 15 
 
 15/8 
 
 283/4 
 
 423/4 
 
 20 
 
 H/2 
 
 157/8 
 
 34 
 
 9 
 
 17 
 
 17 
 
 161/4 
 
 13/4 
 
 301/2 
 
 47 
 
 20 
 
 H/2 
 
 163/ 8 
 
 40 
 
 10 
 
 18 
 
 18 
 
 171/2 
 
 17/8 
 
 333/4 
 
 523/4 
 
 22 
 
 H/3 
 
 167/8 
 
 39 
 
 12 
 
 193/4 
 
 
 201/2 
 
 2 
 
 371/4 
 
 60 
 
 24 
 
 2 
 
 197/8 
 
 46 
 
 14 
 
 221/2 
 
 
 23 
 
 21/8 
 
 423/4 
 
 673/4 
 
 24 
 
 2 
 
 205/ 8 
 
 52 
 
 15 
 
 221/2 
 
 
 241/2 
 
 23/16 
 
 423/4 
 
 673/4 
 
 24 
 
 2 
 
 205/ 8 
 
 52 
 
 16 
 
 24 
 
 
 251/2 
 
 21/4 
 
 
 751/4 
 
 27 
 
 3 
 
 251/4 
 
 60 
 
 18 
 
 26 
 
 
 28 
 
 23/8 
 
 
 821/4 
 
 30 
 
 3 
 
 26 1/2! 67 
 
 20 
 
 28 
 
 
 301/2 
 
 21/2 
 
 
 91 1/2 
 
 30 
 
 4 
 
 30 1/2 74 
 
 22 
 
 291/2 
 
 
 33 
 
 25/8 
 
 
 101 
 
 36 
 
 4 
 
 32 1/4 
 
 82 
 
 24 
 
 31 
 
 
 36 
 
 23/4 
 
 
 109 
 
 36 
 
 4 
 
 33 
 
 88 
 
 For dimensions of Medium Valves and Extra Heavy Hydraulic 
 Valves, see Crane Company's catalogue. 
 
 NATIONAL STANDARD HOSE COUPLINGS 
 
 Adopted by the National Board of Fire Underwriters, American 
 Waterworks Association, New England Waterworks Association, Na- 
 tional Firemen's Association, National Fire Protection Association. 
 
 Dimensions in Inches. 
 
 2V2 
 
 V4 
 31/1, 
 
 35/ 8 
 
 1 V 
 
 1 
 
 7V 2 
 
 7 /8 
 
 3.0925 3.6550 
 
 1 
 
 3V2 
 l /4 
 
 4V4 
 
 2.87153.37634.00135.3970 
 
 6 
 1 
 4.28 
 
 4V2 
 
 V4 
 5 3 /4 
 
 5.80 
 
 ,' The threads to be of the 60 V. pattern with 0.01 in. cut off the top 
 of thread and 0.01 in. left in the bottom of the 2 y 2 -m., 3-in., and 3 l A-ir\. 
 couplings, and 0.02 in. in like manner for the 4 l / 2 -m. couplings. 
 
 A = inside diameter of hose couplings, N = number of threads per 
 
 WOODEN STAVE PIPE. 
 
 Pipes made of wooden staves, banded with steel hoops, are made by 
 the Excelsior Wooden Pipe Co., San Francisco, in sizes from 10 inches to 
 10 feet in diameter, and are extensively used for long-distance Piping, 
 especially in the Western States. The hoops are made of steel rods witl 
 upset and threaded ends. When buried below the hydraulic grade line 
 and kept full of water, these pipes are practically indestructible. J 
 the economic design and use of stave pipe see paper by A, L, Adams, 
 Trans. 4. S, C, ., vcH, xU, 
 
RIVETED HYDRAULIC PIPE. 
 
 219 
 
 Weight and Strength of Riveted Hydraulic Pipe. 
 
 (Pelton Water Wheel, San Francisco, 1915.) 
 
 Thickness. 
 
 4-in. 
 
 5-in. 
 
 6-in. 
 
 7- 
 
 n. 
 
 8-in. 
 
 Gauge. 
 
 In. 
 
 18 
 16 
 14 
 12 
 10 
 
 0.050 
 .062 
 .078 
 .109 
 .140 
 
 S 
 555 
 693 
 866 
 
 W 
 
 2.8 
 3.7 
 
 4.4 
 
 S 
 444 
 555 
 693 
 
 W 
 3.5 
 4 4 
 5.5 
 
 S 
 370 
 462 
 578 
 .808. 
 
 W 
 4.1 
 5.2 
 6.4 
 8.8 
 
 S 
 317 
 396 
 495 
 693 
 
 W 
 4.7 
 5.9 
 7.3 
 10.0 
 
 5 
 277 
 346 
 433 
 606 
 777 
 
 W 
 5.3 
 6.7 
 
 8.2 
 11.5 
 14.5 
 
 
 
 
 
 
 9-in. 
 
 10-in. 
 
 11 -in. 
 
 12-in. 
 
 14-in. 
 
 " 16 
 14 
 12 
 10 
 8 
 
 0.062 
 .078 
 .109 
 .140 
 .171 
 3 /16 
 
 308 
 385 
 539 
 693 
 
 7.5 
 9.2 
 12.6 
 16.4 
 
 277 
 346 
 485 
 623 
 761 
 832 
 
 8.3 
 10.2 
 14.2 
 18.0 
 21.5 
 23.5 
 
 252 
 314 
 439 
 565 
 693 
 757 
 
 9.0 
 11.0 
 15.2 
 19.3 
 23.5 
 25.5 
 
 231 
 
 289 
 404 
 519 
 635 
 693 
 
 9.9 
 1Z.2 
 16.7 
 21.0 
 25.6 
 27.7 
 
 198 
 
 248 
 346 
 445 
 543 
 594 
 
 11.4 
 14.0 
 19.2 
 24.2 
 29.5 
 31.9 
 
 
 15-in. 
 
 16-in. 
 
 18-in. 
 
 20-in. 
 
 22-in. 
 
 16 
 14 
 12 
 10 
 8 
 
 0.062 
 .078 
 .109 
 .140 
 .171 
 3/16 
 1/4 
 5/16 
 3/8 
 7/16 
 
 185 
 231 
 323 
 415 
 507 
 555 
 739 
 
 12.0 
 14.0 
 20.3 
 25.7 
 30.4 
 34.0 
 45.5 
 
 173 
 217 
 303 
 388 
 475 
 520 
 693 
 866 
 
 12.8 
 16.0 
 21.5 
 27.3 
 33.3 
 36.0 
 48.2 
 60.6 
 
 154 
 193 
 270 
 346 
 422 
 462 
 616 
 770 
 924 
 
 14.5 
 17.8 
 24.4 
 30.7 
 38.4 
 40.5 
 54.1 
 67.7 
 81.3 
 
 139 
 173 
 242 
 311 
 380 
 416 
 555 
 693 
 831 
 970 
 
 16.0 
 19.6 
 27.3 
 34.5 
 41.5 
 45.0 
 59.6 
 74.6 
 89.5 
 105.0 
 
 126 
 157 
 220 
 283 
 346 
 378 
 505 
 631 
 757 
 883 
 
 17.7 
 21.2 
 29.2 
 37.1 
 45.2 
 49.0 
 65.5 
 81.5 
 98.0 
 114.5 
 
 
 
 
 
 
 
 
 
 
 
 
 24-in. 
 
 26-in. 
 
 30-in. 
 
 36-in. 
 
 42-in. 
 
 14 
 12 
 10 
 8 
 
 0.078 
 .109 
 .140 
 .171 
 3/16 
 V4 
 5 /16 
 3/8 
 7/16 
 1/2 
 5/8 
 3/4 
 
 7/8 
 
 144 
 202 
 259 
 317 
 346 
 462 
 578 
 693 
 808 
 924 
 
 23.7 
 32.5 
 40.5 
 49.2 
 53.0 
 71.0 
 88.5 
 106.0 
 124.5 
 142.0 
 
 133 
 
 186 
 239 
 293 
 320 
 427 
 533 
 640 
 747 
 854 
 1066 
 
 25.5 
 34.5 
 43.7 
 53.0 
 57.5 
 76.5 
 95.5 
 114.5 
 134.0 
 153.0 
 191.0 
 
 162 
 
 208 
 254 
 277 
 370 
 462 
 555 
 647 
 739 
 924 
 1108 
 
 39.5 
 50.3 
 60.5 
 65.5 
 87.5 
 109.0 
 130.5 
 151.5 
 174.5 
 220.0 
 264.0 
 
 134 
 173 
 211 
 231 
 308 
 385 
 462 
 539 
 616 
 770 
 924 
 1078 
 
 47.7 
 60.0 
 75.0 
 79.0 
 105.5 
 130.0 
 156.0 
 182.5 
 207.0 
 260.0 
 312.5 
 366.0 
 
 148 
 181 
 198 
 264 
 330 
 396 
 462 
 528 
 660 
 792 
 924 
 
 69.5 
 84.7 
 91.5 
 122.0 
 151.0 
 180.5 
 211.0 
 240.5 
 302.0 
 361.5 
 424.0 
 
 
 
 
 
 
 
 48-in. 
 
 54-in. 
 
 60-in. 
 
 66-in. 
 
 72-in. 
 
 8 
 
 0.171 
 3/16 
 
 V4 
 5/16 
 3/8 
 7/16 
 1/2 
 5/8 
 3/4 
 
 7/8 
 
 158 
 173 
 231 
 289 
 346 
 404 
 462 
 578 
 693 
 808 
 924 
 
 98 
 106.0 
 142.0 
 177.0 
 212.0 
 249.0 
 284.0 
 354.0 
 430.0 
 505.0 
 582.0 
 
 141 
 154 
 205 
 256 
 308 
 359 
 411 
 513 
 616 
 719 
 822 
 
 110.0 
 119.0 
 159.0 
 198.0 
 237.0 
 277.5 
 316.5 
 399.5 
 479.5 
 563.5 
 647.5 
 
 127 
 139 
 185 
 231 
 277 
 323 
 370 
 462 
 555 
 647 
 739 
 
 121.0 
 131.0 
 175.0 
 218.0 
 261.0 
 303.0 
 349.0 
 440.0 
 528.0 
 620.0 
 712.0 
 
 127 
 
 168 
 210 
 252 
 294 
 336 
 420 
 504 
 588 
 672 
 
 144.5 
 193.0 
 239.0 
 286.5 
 334.0 
 382.0 
 480.0 
 577.5 
 677.0 
 777.5 
 
 115 
 
 154 
 193 
 231 
 270 
 308 
 385 
 462 
 539 
 616 
 
 158.0 
 211.0 
 260.0 
 312.0 
 365.0 
 414.0 
 520.0 
 624.0 
 732.0 
 840.0 
 
 
 
 
 
 
 Pipe made of sheet steel plate, ultimate tensile strength 55,000 Ibs. per 
 sq. in., double-riveted longitudinal joints and single-riveted circular joints. 
 Strength of longitudinal joints, 70%. Strain by safe pressure, 1/4 of ulti- 
 mate strength. 
 
220 
 
 MATERIALS. 
 
 Riveted Iron Pipe. 
 (Abendroth & Root Mfg. Co.) 
 
 Sheets punched and rolled, ready for riveting, are packed in con- 
 venient form for shipment. The following table shows the iron and 
 rivets required for punched and formed sheets. 
 
 Number Square Feet of 
 Iron Required to Make 
 100 Lineal Feet Punched 
 
 ^ -i 302 
 
 Number Square Feet of 
 Iron Required to Make 
 100 Lineal Feet Punched 
 
 * u GJ3 
 
 and Formed Sheets 
 
 
 and Formed Sheets 
 
 "O O PH 
 
 when put Together. 
 
 fl || 
 
 when put Together. 
 
 1~ il 
 
 Diam- 
 eter in 
 Inches. 
 
 Width 
 of Lap 
 in 
 Inches. 
 
 Square 
 Feet. 
 
 Q, > ^ C"3 
 
 Diam- 
 eter in 
 Inches. 
 
 Width 
 of Lap 
 in 
 Inches. 
 
 Square 
 Feet. 
 
 allll 
 
 3 
 
 1 
 
 90 
 
 1600 
 
 14 
 
 U/2 
 
 397 
 
 2800 
 
 4 
 
 1 
 
 116 
 
 1700 
 
 15 
 
 U/2 
 
 423 
 
 2900 
 
 5 
 
 11/2 
 
 150 
 
 1800 
 
 16 
 
 U/2 
 
 452 
 
 3000 
 
 6 
 
 U/2 
 
 178 
 
 1900 
 
 18 
 
 U/2 
 
 506 
 
 3200 
 
 7 
 
 U/2 
 
 206 
 
 2000 
 
 20 
 
 U/2 
 
 562 
 
 3500 
 
 8 
 
 U/2 
 
 234 
 
 2200 
 
 22 
 
 U/2 
 
 617 
 
 3700 
 
 9 
 
 U/2 
 
 258 
 
 2300 
 
 24 
 
 U/2 
 
 670 
 
 3900 
 
 10 
 
 H/2 
 
 289 
 
 2400 
 
 26 
 
 U/2 
 
 725 
 
 4100 
 
 11 
 
 11/2 
 
 314 
 
 2500 
 
 28 
 
 U/2 
 
 779 
 
 4400 
 
 12 
 
 1 1/2 
 
 343 
 
 2600 
 
 30 
 
 U/2 
 
 836 
 
 4600 
 
 13 
 
 
 369 
 
 2700 
 
 36 
 
 U/2 
 
 998 
 
 5200 
 
 Spiral Riveted Pipe. 
 
 Approximate Bursting Strength. Pounds per Square Inch. 
 (American Spiral Pipe Works, Chicago, 1915.) 
 
 Inside 
 Diam. 
 Inches. 
 
 iniCKness. \j. &. oiaiiuaru oauge. 
 
 No.20. 
 
 No. 18. 
 
 No. 16. 
 
 No. 14. 
 
 No. 12. 
 
 No. 10. 
 
 No. 8. 
 
 No. 6. 
 
 No. 3 
 
 (V4"). 
 
 3 
 
 1500 
 
 2000 
 
 
 
 
 
 
 
 
 4 
 
 1125 
 
 1500 
 
 1875 
 
 
 
 
 
 
 
 5 
 
 900 
 
 1200 
 
 1500 
 
 
 
 
 
 
 
 6 
 
 
 1000 
 
 1250 
 
 1560 
 
 2170 
 
 
 
 
 
 7 
 
 
 860 
 
 1070 
 
 1340 
 
 1860 
 
 
 
 
 
 8 
 
 
 750 
 
 935 
 
 1170 
 
 1640 
 
 
 
 
 
 9 
 
 
 
 835 
 
 1045 
 
 1460 
 
 
 
 
 
 10 
 
 
 
 750 
 
 935 
 
 1310 
 
 
 
 
 
 11 
 
 
 
 680 
 
 850 
 
 1200 
 
 
 
 
 
 12 
 
 
 
 625 
 
 780 
 
 1080 
 
 1410 
 
 
 
 
 13 
 
 
 
 575 
 
 720 
 
 1010 
 
 1295 
 
 
 
 
 14 
 
 
 
 535 
 
 670 
 
 940 
 
 1210 
 
 
 
 
 15 
 
 
 
 
 625 
 
 875 
 
 1125 
 
 
 
 
 16 
 
 
 
 
 585 
 
 820 
 
 1050 
 
 1290 
 
 1520 
 
 1880 
 
 18 
 
 
 
 
 520 
 
 730 
 
 940 
 
 1140 
 
 1360 
 
 1660 
 
 20 
 
 
 
 
 470 
 
 660 
 
 840 
 
 1030 
 
 1220 
 
 1500 
 
 22 
 
 
 
 
 425 
 
 595 
 
 765 
 
 940 
 
 1108 
 
 1364 
 
 24 
 
 
 
 
 390 
 
 540 
 
 705 
 
 820 
 
 1015 
 
 1250 
 
 26 
 
 
 
 
 
 505 
 
 650 
 
 795 
 
 935 
 
 1154 
 
 28 
 
 
 
 
 
 470 
 
 605 
 
 735 
 
 870 
 
 1071 
 
 30 
 
 
 
 
 
 435 
 
 560 
 
 685 
 
 810 
 
 1000 
 
 32 
 
 
 
 
 
 410 
 
 525 
 
 645 
 
 760 
 
 940 
 
 34 
 
 
 
 
 
 380 
 
 490 
 
 600 
 
 715 
 
 880 
 
 36 
 
 
 
 
 
 365 
 
 470 
 
 570 
 
 680 
 
 830 
 
 40 
 
 
 
 
 
 330 
 
 420 
 
 515 
 
 610 
 
 750 
 
BENT 'AND COILED PIPES. 
 
 221 
 
 Weight per Sq. Ft. of Sheet Steel for Riveted Pipe. 
 
 (American Spiral Pipe Works, Chicago, 1915.) 
 
 Thick- 
 ness 
 B.W.G. 
 
 Thick- 
 ness, 
 In. 
 
 Weight 
 in Lb., 
 Black. 
 
 Weight 
 in Lb., 
 Galvan- 
 ized. 
 
 Thickness 
 B.W.G. 
 
 Thick- 
 ness, 
 In. 
 
 Weight 
 in Lb., 
 Black. 
 
 Weight 
 inLb., 
 Galvan- 
 ized. 
 
 26 
 24 
 22 
 20 
 
 0.018 
 .022 
 .028 
 .035 
 
 0.7344 
 0.8976 
 1.1424 
 1.428 
 
 0.8844 
 1.0476 
 1.2924 
 1.578 
 
 18 
 16 
 14 
 12 
 
 0.049 
 .065 
 .083 
 .109 
 
 1.9992 
 2.652 
 3.3864 
 4.4472 
 
 2.1492 
 2.802 
 3.5364 
 4.5972 
 
 Weights based on steel of 489.6 Ib. per cu. ft. Weights of galvanized 
 sheets based on an addition of 0.075 Ib. per sq. ft. of surface. 
 
 BENT AND COILED PIPES. 
 
 (National Pipe Bending Co., New Haven, Conn.) 
 Coils and Bends of Iron and Steel Pipe. 
 
 Size of pipe Inches 
 
 Vi 
 
 3/ 9 
 
 1/2 
 
 3 /1 
 
 j 
 
 1 If* 
 
 1 lh 
 
 2 
 
 71/? 
 
 1 
 
 Least outside diameter 
 
 7 
 
 ?.ih 
 
 3V-> 
 
 41/2 
 
 6 
 
 8 
 
 12 
 
 16 
 
 74 
 
 37 
 
 
 
 
 
 
 
 
 
 
 
 
 
 31/o 
 
 4 
 
 41 A> 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 17 
 
 Least outside diameter 
 of coil Inches 
 
 40 
 
 48 
 
 52 
 
 58 
 
 66 
 
 80 
 
 9? 
 
 10*5 
 
 HO 
 
 H6 
 
 
 
 
 
 
 
 
 
 
 
 
 Lengths continuous welded up to 3-in. pipe or coupled as desired. 
 
 90* Bends in Iron or Steel Pipe. 
 
 (Whitlock Coil Pipe Co., Hartford, Conn.) 
 
 Size pipe, I.D 
 
 3 
 
 }!/ 
 
 4 
 
 41/o 
 
 5 
 
 6 
 
 
 
 8 
 
 Q 
 
 10 
 
 1? 
 
 Radius of bend . . , 
 
 1? 
 
 13 
 
 15 
 
 17 
 
 ?0 
 
 71 
 
 7f 
 
 
 30 
 
 36 
 
 4"? 
 
 48 
 
 End 
 
 3 
 
 31/2 
 
 31/o 
 
 4 
 
 4 
 
 4 
 
 I 
 
 
 5 
 
 5 
 
 6 
 
 6 
 
 Center to face 
 
 15 
 
 161/2 
 
 181/o 
 
 21 
 
 74 
 
 77 
 
 31 
 
 
 35 
 
 41 
 
 48 
 
 54 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Size pipe, O D 
 
 14 
 
 16 
 
 18 
 
 20 
 
 ?? 
 
 ?< 
 
 | 
 
 
 26 
 
 78 
 
 
 30 
 
 Radius of bend . . . 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 IK 
 
 ) 
 
 
 70 
 
 140 
 
 
 160 
 
 End 
 
 7 
 
 7 
 
 7 
 
 8 
 
 8 
 
 f 
 
 | 
 
 
 10 
 
 10 
 
 
 10 
 
 Center to face 
 
 67 
 
 77 
 
 87 
 
 98 
 
 108 
 
 11* 
 
 ! 
 
 
 30 
 
 150 
 
 
 170 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The radii given are for the center of the pipe. "End" means the 
 length of straight pipe, in addition to the 90 bend, at each end of the 
 pipe. "Center to face" means the perpendicular distance from the 
 center of one end of the bent pipe to a plane passing across the other end. 
 The dimensions given are the minimums recommended. Larger radii 
 than are shown are recommended for flexibility and lesser friction. 
 
 Flexibility of Pipe Bends. (Valve World, Feb., 1906.) So far as 
 can be ascertained, no thorough attempt has ever been made to de- 
 termine the maximum amount of expansion which a U-loop, or quarter 
 bend, would take up in a straight run of pipe having both ends anchored. 
 The Crane Company has adopted five diameters of the pipe as a stand- 
 ard radius, which comes nearer than any other to suiting average re- 
 
222 
 
 MATERIALS. 
 
 quirements, and at the same time produces a symmetrical article. Bends 
 shorter than this can be made, but they are extremely stiff, tend to 
 buckle in bending, and the metal in the outer wall is stretched beyond- 
 a desirable point. 
 
 In 1905 the Crane Company made a few experiments with 8-inch U 
 and quarter bends to ascertain the amount of expansion they would take 
 up. The U-bend was made of steel pipe 0.32 inch thick, weighing 28 
 Ibs. per foot, with extra heavy cast-iron flanges screwed on and refaced. 
 It was connected by elbows to two straight pipes, N, 67 ft., 5. 82 ft., 
 which were firmly anchored at their outer ends. Steam was then let 
 into the pipes with results as follows: 
 80 Ib. Expansion, 
 
 Expansion, N, 7/ 8 , S, U/s . 
 
 Expansion, N, 13/ie, S, 11/2 . 
 
 Expansion, JV, 11/8 , S, 17/ 8 . 
 
 Expansion, N, 11/2 . S, 17/ 8 . 
 
 50 Ib. 
 100 Ib. 
 150 Ib. 
 200 Ib. 
 
 Total 1 7/ 8 in. 
 Total 2 in. 
 Total 2 H/iein. 
 Total 3 in. 
 Total 3 3/8 in. 
 
 Flange broke. 
 
 Flange broke 
 at 208 Ibs. 
 
 Straight pipe 148 ft., one end. 80 
 
 Quarter bend, full weight pipe. 
 Ibs. Total expansion, 1 3/ 8 . Flange leaked. 
 
 Quarter bend, extra heavy pipe. Expanded 7/8 in. when a flange 
 broke. Replaced with a new flange, which broke when the expansion 
 was \y% in. 
 
 Wrought Pipe Bends. (National Tube Co.). The following are 
 given as the advisable (R) and the least allowable (Ri) radii in inches 
 to which pipe should be bent: 
 
 Size. 
 
 R. 
 
 Ri. 
 
 Size. 
 
 R. 
 
 Ri. 
 
 Size. 
 
 R. 
 
 Ri. 
 
 Size. 
 
 R. 
 
 Ri. 
 
 Size. 
 
 R. 
 
 Ri. 
 
 iv. 
 
 3V. 
 
 15 
 
 18 
 21 
 
 24 
 
 10 
 12 
 14 
 16 
 
 4V. 
 
 6 
 7 
 
 27 
 30 
 36 
 42 
 
 18 
 20 
 24 
 28 
 
 8 
 9 
 10 
 11 
 
 48 
 54 
 60 
 66 
 
 32 
 36 
 40 
 44 
 
 12 
 13 
 14 
 15 
 
 72 
 84 
 90 
 100 
 
 48 
 60 
 68 
 76 
 
 180.D. 
 200.D. 
 22O.D. 
 24 0. D. 
 
 125 
 150 
 165 
 180 
 
 90 
 120 
 132 
 144 
 
 Bends of 12-in. pipe and smaller to be of full weight pipe; 14 to 16 
 In. outside diameter, not less than 3/ 8 in. thick; 18 in. and larger, not 
 less than 7/i 6 to 1/2 in. thick. With welded flanges there must be a 
 short straight length of pipe, preferably equal to two diameters of the 
 pipe, between the flange and the bend. 
 
 Coils and Bends of Drawn Brass and Copper Tubing. 
 
 Size of tube, outside diameter. .Inches 
 Least outside diameter of coil . . Inches 
 
 1/4 
 
 3/8 
 H/2 
 
 2 V2 
 
 5/8 
 21/2 
 
 3 3/ 4 
 
 1 
 4 
 
 H/4 
 6 
 
 13/8 
 
 Size of tube, outside diameter.. Inches 
 Least outside diameter of coil. .Inches 
 
 H/2 
 
 9 5/8 
 
 li 3/4 
 
 2 
 12 
 
 ,2* 
 
 P 
 
 21/2 
 18 
 
 23/4 
 20 
 
 Lengths continuous brazed, soldered, or coupled as desired. 
 
 SEAMLESS TUBES. 
 
 Locomotive Boiler Tubes, Seamless. Diameters, external, 11/2, 1 3 A, 
 17/8, 2, 21/4, 21/2, and 3 in. 
 
 Nine thicknesses of 
 
 each size, inch.. .0.095 .109 .110 .120 .125 .134 .135 .148 .150 
 Birmingham wire 
 
 gage 13 12 ... 11 ,.. 10 ... 9 ... 
 
 Shelby Seamless Steel Tubes are made of three classes of open- 
 hearth steel: 0.17 C (0.14 to O'.19%); 0.35 C (0.30 to 0.40%); and 
 31/2% nickel (0.20 to 0.30 C, 3 to 4% nickel). In all, manganese is 
 from 0.40 to 0.60%; sulphur, 0.015 to 0.040; phosphorus, 0.010 to 
 0.035%. Hot finished tubes are not given any heat treatment after 
 
COLD-DRAWN SEAMLESS STEEL TUBES. 223 
 
 NO en tx ! CO in (N O\ NO en 
 
 oo in co CN in co CN n oo | rs <n cb 
 
 _ p p p 
 
 oo in co in co in <N co in es co in <N 
 eNfNfN<N<Ncsenenenen 
 
 enNOOenNoOenNOOenNOOent^Cent^ 
 
 O eNeseviev) 
 
 enNOoO^enNO sO^NO NO NO NO 1 NO NO NO NO 
 
 O ' 
 
 00 
 
 rt > o'---- f 
 
 0^- ~ 
 
 D GO en m vo GO . n oo n oo m co 
 
 fNeNfNfNenen 
 
 ONr^in^fNOONt^vOenO^NOenON 
 
 ' 
 
 enONOenO^NO. ,_ 
 
 CN en en ^r * ; >n NO NO 
 
 
 O rs CN| en en -<r -f m in 
 ^^ I ' 
 
 jsl sSSSa^ 
 
 ^d 
 
 4J O jrt I (M 00 f< 00 OOTPOO 
 
 373 -2 c 
 Q'Q M 
 
224 
 
 MATERIALS. 
 
 leaving the hot mills. Cold-drawn tubes are annealed before and heat- 
 treated after drawing. .The physical properties of finished material are 
 as follows: 
 
 Temper 
 
 Tensile 
 Strength. 
 
 Elastic 
 Limit. 
 
 Elong. in 
 8 In., %. 
 
 0.17 C 
 
 0.35 C 
 
 3l/ 2 %Ni. 
 
 ( S, unannealed . . . 
 1 T, finish anneal . . 
 j W, soft anneal . . . 
 ( Y, retort anneal . 
 !S, unannealed. . . 
 T, finish anneal . . 
 U, med. anneal . . 
 !S, unannealed . . . 
 W, finish anneal . . 
 U, med. anneal . . 
 
 65,000 to 80,000 
 60,000 to 75,000 
 47,000 to 55,000 
 45,000 to 52,000 
 85,000 to 100,000 
 80,000 to 95,000 
 65,000 to 80,000 
 95,000 to 110.000 
 85,000 to 105,000 
 70,000 to 85,000 
 
 60,000 to 70,000 
 50,000 to 65,000 
 27,000 to 35,000 
 22,000 to 28,000 
 75,000 to 90,000 
 70,000 to 85,000 
 50,000 to 60,000 
 85,000 to 100,000 
 75,000 to 90,000 
 45,000 to 60,000 
 
 3 to 7 
 10 to 16 
 28 to 33 
 30 to 40 
 Low 
 12 to 18 
 20 to 30 
 10 to 18 in 2" 
 15 to 25 in 2" 
 40 to 50 in 2" 
 
 The 0.17 C tube is also furnished in intermediate tempers. U, V, 
 and X, between T and Y, and special treatments are given to order. 
 
 In estimating the effective steam-heating or boiler surface of tubes, 
 the surface in contact with air or gases of combustion (whether internal 
 or external to the tubes) is to be taken. 
 
 For heating liquids by steam, superheating steam, or transferring heat 
 from one liquid or gas to another, the mean surface of the tubes is to be 
 taken. 
 
 Outside Area of Tubes. 
 
 To find the square feet of surface, S, in a tube of a given length, L, in 
 ieet, and diameter, d, in inches, multiply the length in feet by the diam- 
 eter in inches and by 0.2618. Or, S = 3 - 141 ^ dL =0.2618 dL. For the 
 
 diameters in the table below, multiply the length in feet by the figures 
 given opposite the diameter. 
 
 Area of Tubes per Lineal Foot. 
 
 Diam. 
 
 Area, 
 
 Dia. 
 
 Area, 
 
 Dia. 
 
 Area, 
 
 Dia. 
 
 Area, 
 
 ,Dia. 
 
 Area, 
 
 Dia. 
 
 Area, 
 
 In. 
 
 Sq. Ft. 
 
 In. 
 
 Sq. Ft. 
 
 In. 
 
 Sq. Ft. 
 
 In. 
 
 Sq. Ft. 
 
 In. 
 
 Sq. Ft. 
 
 In. Sq.Ft. 
 
 1'4 
 
 0.0654 
 
 11/4 
 
 0.3272 
 
 21/4 
 
 0.5890 
 
 31/4 
 
 0.8508 
 
 5 
 
 1 .3090 
 
 9 
 
 2.3562 
 
 1/2 
 
 .1309 
 
 1 1/2 
 
 .3927 
 
 21/3 
 
 .6545 
 
 31 /a 
 
 .9163 
 
 6 
 
 1.5708 
 
 10 
 
 2.6180 
 
 8/4 
 
 .1963 
 
 13 //| 
 
 .4581 
 
 23/4 
 
 .7199 
 
 33/4 
 
 .9817 
 
 7 
 
 1 .8326 
 
 11 
 
 2.8798 
 
 1 
 
 .2618 
 
 2 
 
 .5236 
 
 3 
 
 .7854 
 
 4 
 
 1 .0472 
 
 8 
 
 2.0944 
 
 12 
 
 3.1416 
 
 Seamless Brass and Copper Tube, Iron Pipe Sizes. 
 
 Nominal 
 
 Diam., In. 
 
 Wt. per Ft., 
 Lb. 
 
 Nominal 
 
 Diam., In. 
 
 Wt. per Ft., 
 Lb. 
 
 Size, 
 In. 
 
 Out- 
 side. 
 
 In- 
 side. 
 
 Brass 
 
 Cop- 
 per. 
 
 Size, 
 In. 
 
 Out- 
 side. 
 
 In- 
 side. 
 
 Brass 
 
 Cop- 
 per. 
 
 1/g 
 
 0.405 
 
 0.281 
 
 0.246 
 
 0.259 
 
 3 
 
 3.500 
 
 3.062 8.314 
 
 8.741 
 
 1/4 
 
 .540 
 
 .375 
 
 .437 
 
 .459 
 
 3*/2 
 
 4.000 
 
 3.500 10.85 
 
 11.41 
 
 3/8 
 
 .675 
 
 .494 
 
 .612 
 
 .644 
 
 4 
 
 4.500 
 
 4.000 12.29 
 
 12.93 
 
 1/2 
 
 .840 
 
 .625 
 
 .911 
 
 .958 
 
 *Vi 
 
 5.000 
 
 4.500 13.74 
 
 14.44 
 
 3/4 
 
 1.050 
 
 .822 
 
 1.235 
 
 1.298 
 
 5 
 
 5.563 
 
 5.062 15.40 
 
 16.19 
 
 1 
 
 1.315 
 
 1 .062 
 
 1 .740 
 
 1.829 
 
 6 
 
 6.625 
 
 6.125 18.44 
 
 19.39 
 
 11/4 
 
 1.660 
 
 1 .368 
 
 2.557 
 
 2.698 
 
 7 
 
 7.625 
 
 7.06223.92 
 
 25.15 
 
 U/2 
 
 1.900 
 
 1.600 
 
 3.037 
 
 3.193 
 
 8 
 
 8.625 
 
 8.00030.05 
 
 31 .60 
 
 2 
 
 2.375 
 
 2.062 
 
 4.017 
 
 4.224 
 
 9 
 
 9.625 
 
 8.937 
 
 36.94 
 
 38.84 
 
 2i/ 2 
 
 2.875 
 
 2.500 
 
 5.830 
 
 6.130 
 
 10 
 
 10.750 10.019 
 
 43.91 
 
 46.17 
 
SEAMLESS BRASS TUBES. 
 
 225 
 
 Weight per Foot of Seamless Brass Tubes. 
 
 (Condensed from Manufacturers' Standard Tables, 1915.) 
 
 A.W.G. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 Wall.* 
 
 0.2576 
 
 0.2043 
 
 0.1620 
 
 0.1285 
 
 0.1019 
 
 .0808 
 
 .0641 
 
 .0508 
 
 .0403 
 
 .0320 
 
 .0253 
 
 .0201 
 
 Diam.f 
 
 1/g 
 
 
 
 
 
 
 
 
 0.044 
 
 0.039 
 
 0.034 
 
 0.029 
 
 0.024 
 
 3/i6 
 
 
 
 
 
 
 
 0!692 
 
 .080 
 
 .069 
 
 .058 
 
 .048 
 
 .039 
 
 1/4 
 
 
 
 
 
 0.175 
 
 OJ58 
 
 .138 
 
 .117 
 
 .098 
 
 .081 
 
 .066 
 
 .053 
 
 5/i6 
 
 
 
 
 
 .248 
 
 .217 
 
 .184 
 
 .154 
 
 .127 
 
 .104 
 
 .084 
 
 .068 
 
 3/8 
 
 
 
 
 0.376 
 
 .322 
 
 .275 
 
 .231 
 
 .191 
 
 .156 
 
 .127 
 
 .103 
 
 .083 
 
 1/2 
 
 
 
 6! 634 
 
 .562 
 
 .469 
 
 .392 
 
 .323 
 
 .264 
 
 .214 
 
 .173 
 
 .139 
 
 .112 
 
 5/8 
 
 i'.io 
 
 6! 994 
 
 .868 
 
 .748 
 
 .617 
 
 .509 
 
 .416 
 
 .338 
 
 .273 
 
 .219 
 
 .176 
 
 .141 
 
 3/4 
 
 1.47 
 
 1.29 
 
 1.10 
 
 .934 
 
 .764 
 
 . .626 
 
 .509 
 
 .411 
 
 .331 
 
 .266 
 
 .213 
 
 .170 
 
 7 /8 
 
 1.84 
 
 1.59 
 
 1.34 
 
 .12 
 
 .911 
 
 .743 
 
 .601 
 
 .485 
 
 .389 
 
 .312 
 
 .249 
 
 .199 
 
 
 2.21 
 
 1.88 
 
 1.57 
 
 .31 
 
 .06 
 
 .859 
 
 .694 
 
 .558 
 
 .448 
 
 .358 
 
 .286 
 
 .228 
 
 11/8 
 
 2.59 
 
 2.18 
 
 1.81 
 
 .49 
 
 .21 
 
 .976 
 
 .787 
 
 .632 
 
 .506 
 
 .404 
 
 .322 
 
 .257 
 
 1 V4 
 
 2.96 
 
 2.47 
 
 2.04 
 
 .68 
 
 .35 
 
 .09 
 
 .879 
 
 .705 .564 
 
 .450 
 
 .359 
 
 .286 
 
 13/8 
 
 3.33 
 
 2.77 
 
 2.27 
 
 .86 
 
 .50 
 
 .21 
 
 .972 
 
 .779 
 
 .622 
 
 .497 
 
 .396 
 
 .315 
 
 1 V2 
 
 3.70 
 
 3.06 
 
 2.51 
 
 2.05 
 
 .65 
 
 .33 
 
 .06 
 
 .852 
 
 .681 
 
 .543 
 
 .432 
 
 .344 
 
 13/4 
 
 4.45 
 
 3.65 
 
 2.98 
 
 2.42 
 
 .94 
 
 .56 
 
 .25 
 
 .999 
 
 .797 
 
 .635 
 
 .506 
 
 .402 
 
 2 
 
 5.19 
 
 4.24 
 
 3.45 
 
 2.79 
 
 2.24 
 
 .79 
 
 .44 
 
 .15 
 
 .914 
 
 .728 
 
 .579 
 
 .460 
 
 21/4 
 
 5.94 
 
 4.84 
 
 3.91 
 
 3.16 
 
 2.53 
 
 2.03 
 
 .62 
 
 .29 
 
 .03 
 
 .820 
 
 .652 
 
 .519 
 
 21/2 
 
 6.68 
 
 5.43 
 
 4.38 
 
 3.54 
 
 2.83 
 
 2.26 
 
 .81 
 
 .44 
 
 .15 
 
 .913 
 
 .722 
 
 .577 
 
 23/4 
 
 7.43 
 
 6.02 
 
 4.85 
 
 3.91 
 
 3.12 
 
 2.50 
 
 .99 
 
 .59 
 
 .26 
 
 .01 
 
 .799 
 
 .635 
 
 3 
 
 8.17 
 
 6.61 
 
 5.32 
 
 4.28 
 
 3.42 
 
 2.73 
 
 2.18 
 
 .73 
 
 .38 
 
 .10 
 
 .872 
 
 .693 
 
 31/4 
 
 8.92 
 
 7.20 
 
 5.79 
 
 4.65 
 
 3.71 
 
 2.96 
 
 2.36 
 
 .88 
 
 .50 
 
 .19 
 
 .946 
 
 .751 
 
 31/2 
 
 9.66 
 
 7.79 
 
 6.26 
 
 5.02 
 
 4.01 
 
 3.20 
 
 2.55 
 
 2.03 
 
 .61 
 
 .28 
 
 .02 
 
 .809 
 
 33/4 
 
 10.4 
 
 8.38 
 
 6.73- 
 
 5.39 
 
 4.30 
 
 3.43 
 
 2.73 
 
 2.18 
 
 .73 
 
 .37 
 
 .09 
 
 .867 
 
 4 
 
 11.2 
 
 8.97 
 
 7.19 
 
 5.77 
 
 4.60 
 
 3.66, 
 
 2.92 
 
 2.32 
 
 .85 
 
 .47 
 
 .17 
 
 .926 
 
 41/4 
 
 11.9 
 
 9.56 
 
 7.66 
 
 6.14 
 
 4.89 
 
 3.90 
 
 3.10 
 
 2.47 
 
 .96 
 
 .56 
 
 .24 
 
 .984 
 
 41/2 
 
 12.6 
 
 10.2 
 
 8.13 
 
 6.51 
 
 5.19 
 
 4.13 
 
 3.29 
 
 2.62 
 
 2.08 
 
 .65 
 
 .31 
 
 1.04 
 
 43/4 
 
 13.4 
 
 10.7 
 
 8.60 
 
 6.88 
 
 5.48 
 
 4.37 
 
 3.47 
 
 2.76 2.20 
 
 .74 
 
 .39 
 
 1.10 
 
 
 14.1 
 
 11.3 
 
 9.07 
 
 7.25 
 
 5.78 
 
 4.60 
 
 3.66 
 
 2.91 
 
 2.31 
 
 .84 
 
 .46 
 
 1.16 
 
 51/4 
 
 14.9 
 
 11.9 
 
 9.54 
 
 7.62 
 
 6.07 
 
 4.83 
 
 3.85 
 
 3.06 
 
 2.43 
 
 .93 
 
 
 
 51/2 
 
 15.6 
 
 12.5 
 
 10.0 
 
 8.00 
 
 6.36 (5.07 
 
 4.03 
 
 3.20 
 
 2.55 
 
 2.02 
 
 
 
 53/4 
 
 16.4 
 
 13.1 
 
 10.5 
 
 8.37 
 
 6.66 |5.30 
 
 4.22 
 
 3.35 
 
 2.66 
 
 2.11 
 
 
 
 6 
 
 17.1 
 
 13.7 
 
 10.9 
 
 8.74 
 
 6.95 5.53 
 
 4.40 
 
 3.50 
 
 2.78 2.21 
 
 
 
 61/4 
 
 17.9 
 
 14.3 
 
 11.4 
 
 9.11 
 
 7 25 15.77 
 
 4.59 
 
 3.65 J2.90 
 
 
 
 
 6l/ 2 
 
 18.6 
 
 14.9 
 
 11.9 
 
 9.48 
 
 7.54 16.00 
 
 4.77 
 
 3.79 
 
 3.01 
 
 
 
 
 63/4 
 /4 
 
 19 4 
 
 15 5 
 
 12 3 
 
 9 85 
 
 7 84 !* ?4 
 
 4 96 
 
 3 94 
 
 
 
 
 
 
 20.1 
 
 16 1 
 
 12 8 
 
 10 2 
 
 8.13 
 
 6 47 
 
 5.14 
 
 4.09 
 
 
 
 
 
 71/4 
 
 20 8 
 
 16 7 
 
 13 3 
 
 10 6 
 
 8 43 
 
 6 70 
 
 5 33 
 
 4 23 
 
 
 
 
 
 71/2 
 
 21.6 
 
 17^2 
 
 13.8 
 
 11.0 
 
 S.72 
 
 6.94 
 
 5.51 
 
 4.38 
 
 
 
 
 
 73/4 
 
 22 3 
 
 17 8 
 
 14 2 
 
 11 .3 
 
 9 02 
 
 7 17 
 
 5.70 
 
 4 53 
 
 
 
 
 
 8 
 
 23 1 
 
 18 - 4 
 
 14 - 7 
 
 11 7 
 
 9 31 
 
 7*40 
 
 5 88 
 
 4 67 
 
 
 
 
 
 81/4 
 
 23.8 
 
 19 
 
 15.2 
 
 12.1 
 
 9 61 
 
 7 64 
 
 6 07 
 
 4 82 
 
 
 
 
 
 81/2 
 
 24 6 
 
 19 6 
 
 15 6 
 
 12 5 
 
 9 90 
 
 7 87 
 
 6 25 
 
 4 97 
 
 
 
 
 
 83/4 
 
 25 3 
 
 20 2 
 
 16.1- 
 
 12 8 
 
 10 2 
 
 8.11 
 
 6.44 
 
 5 12 
 
 
 
 
 
 9 
 
 26 1 
 
 20 8 
 
 16 6 
 
 13 2 
 
 10 5 
 
 8 34 
 
 6 63 
 
 5 26 
 
 
 
 
 
 91/4 
 
 26 8 
 
 21 4 
 
 17 
 
 13 6 
 
 10.8 
 
 8.57 
 
 6 81 
 
 5 41 
 
 
 
 
 
 91/2 
 
 27 6 
 
 22 
 
 17 5 
 
 13 9 
 
 11 1 
 
 8 81 
 
 7 00 
 
 5 56 
 
 
 
 
 
 93/4 
 
 28.3 
 
 22.6 
 
 18.0 
 
 14.3 
 
 11.4 
 
 9.04 
 
 7.18 
 
 5.70 
 
 
 
 
 
 10 
 
 29.0 
 
 23.2 
 
 18.4 
 
 14.7 
 
 11.7 
 
 9.27 
 
 7.37 
 
 5.85 
 
 
 
 
 
 * Thickness in inches. t Outside diameter, inches. 
 
 Seamless brass tubes are made from H in. to 1 in. outside diameter, 
 varying by i/ie in., and from 1 H in. to 10 in. outside diameter, varying by 
 K in., and in all gages from No. 2 to No. 24 A. W. G. witnin the limits 
 of the above table. To determine the weight per foot of a tube of a 
 given inside diameter, add to the weights given above the weights given 
 below, under the corresponding gage numbers. 
 
 A.W.G. 2 4 6 8 10 12 14 16 18 20 22 24 26 
 Lb.perft. 1.54 .966 .607 .382 .240 .151 .095 .060 .038 .024 .015 .009 .0059 
 
 For copper tubing add 5 % to the weights given above. 
 
226 
 
 MATERIALS. 
 
 Aluminum Tubing is made in sizes from % to 2 in. diatn., advanc- 
 ing by i/g inch, and from 2 to 6 in. diam., advancing by y in., in 
 practically all thicknesses from No. 24 to No. 1 B.W.G. Aluminum 
 pipe is made in sizes to correspond with iron-pipe fittings, ranging in 
 diameter from i/s to 4 in. Aluminum pipe fittings are made in prac- 
 tically all standard pipe sizes. Details of sizes, weights, strength, 
 etc., of these tubes, pipes, and fittings are given in the pamphlets of 
 the Aluminum Co. of America, Pittsburgh. 
 
 Lead and Tin-Lined Lead Pipe. 
 
 (United Lead Company, New York, 1915.) 
 
 In- 
 
 
 
 8 
 
 In- 
 
 
 
 8 
 
 In- 
 
 
 
 % a 
 
 side 
 Dia., 
 In. 
 
 Let- 
 ter. 
 
 Weight 
 per Ft. 
 
 l| 
 
 side 
 Dia., 
 In. 
 
 Let- 
 ter. 
 
 Weight 
 per Ft. 
 
 j 
 
 H^ 
 
 side 
 Dia., 
 In. 
 
 Let- 
 ter. 
 
 Weight 
 per Ft. 
 
 -1 1 
 3> 
 
 3/8 
 
 D 
 
 10 oz. 
 
 9 
 
 5/8 
 
 AA 
 
 2 3/4 Ib. 
 
 21 
 
 1/4 
 
 AA 
 
 5 3/4 Ib. 
 
 25 
 
 3/8 
 
 C 
 
 12 
 
 10 
 
 5/8 
 
 AAA 
 
 31/2 " t 
 
 26 
 
 1/4 
 
 AAA 
 
 63/4 " 
 
 28 
 
 3/8 
 
 B 
 
 1 Ib. 
 
 13 
 
 3/4 
 
 E 
 
 
 8 
 
 1/2 
 
 E 
 
 3 
 
 12 
 
 3/8 
 
 ' A 
 
 1 1/4 " 
 
 15 
 
 3/4 
 
 D 
 
 1 1/4 " 
 
 9 
 
 1/2 
 
 D 
 
 3 1/2 " 
 
 14 
 
 3/8 
 
 AA 
 
 1 1/2 " 
 
 17 
 
 3/4 
 
 C 
 
 13/4 
 
 13 
 
 1/2 
 
 C 
 
 4 1/4 " 
 
 16 
 
 3/8 
 
 AAA 
 
 1 3/4 " 
 
 20 
 
 3/4 
 
 Spec'l 
 
 
 14 
 
 1/2 
 
 B 
 
 5 
 
 19 
 
 7/16 
 
 
 13 OZ. 
 
 10 
 
 3/4 
 
 B 
 
 21/4 
 
 16 
 
 1/2 
 
 A 
 
 61/2 " 
 
 24 
 
 7/16 
 
 
 1 Ib. 
 
 12 
 
 3/4 
 
 A 
 
 
 20 
 
 1/2 
 
 AA 
 
 7 1/2 " 
 
 27 
 
 1/2 
 
 E 
 
 9 oz. 
 
 6 
 
 3/4 
 
 AA 
 
 31/2 
 
 23 
 
 1/2 
 
 AAA 
 
 81/2 " 
 
 30 
 
 1/2 
 
 D 
 
 12 
 
 8 
 
 3/4 
 
 AAA 
 
 43/4 
 
 29 
 
 3/4 
 
 D 
 
 4 
 
 14 
 
 1/2 
 
 C 
 
 1 Ib. 
 
 11 
 
 
 E 
 
 1 1/2 
 
 9 
 
 3/4 
 
 C 
 
 5 
 
 17 
 
 1/2 
 
 B 
 
 1 1/4 " 
 
 13 
 
 
 D 
 
 2 
 
 12 
 
 3/4 
 
 B 
 
 6 
 
 20 
 
 1/2 
 
 Spec'l 
 
 I V2 " 
 
 15 
 
 
 C 
 
 21/2 
 
 14 
 
 3/ 4 
 
 A 
 
 7 
 
 23 
 
 1/2 
 
 A 
 
 1 3/4 " 
 
 17 
 
 
 B 
 
 31/4 
 
 18 
 
 3/4 
 
 AA 
 
 81/2 '. 
 
 27 
 
 1/2 
 
 AA 
 
 2 " 
 
 19 
 
 
 A 
 
 4 
 
 21 
 
 13/4 
 
 AAA 
 
 10 
 
 31 
 
 1/2 
 
 Spec'l 
 
 2l/ 2 " 
 
 22 
 
 
 AA 
 
 43/4 
 
 25 
 
 2 
 
 D 
 
 43/4 ' 
 
 14 
 
 1/2 
 
 AAA 
 
 3 
 
 26 
 
 
 AAA 
 
 6 
 
 30 
 
 2 
 
 C 
 
 6 
 
 18 
 
 5/8 
 
 E 
 
 3/4 " 
 
 7 
 
 V4 
 
 E 
 
 2 
 
 10 
 
 2 
 
 B 
 
 7 
 
 21 
 
 5/8 
 
 D 
 
 1 " 
 
 9 
 
 V4 
 
 D 
 
 2.1/2 
 
 12 
 
 2 
 
 A 
 
 8 
 
 23 
 
 5/8 
 
 C 
 
 1 V2 " 
 
 13 
 
 1/4 
 
 C 
 
 3 
 
 14 
 
 2 
 
 AA 
 
 9 
 
 26 
 
 5/8 
 
 B 
 
 2 " 
 
 16 
 
 1/4 
 
 B 
 
 33/4 
 
 17 
 
 2 
 
 AAA 
 
 113/4 " 
 
 33 
 
 5/8 
 
 A 
 
 21/2 " 
 
 20 
 
 1/4 J 
 
 A 
 
 43/4 
 
 21 
 
 
 
 
 
 Weight of lead is taken 0.4106 Ib. per cu. in. The safe working 
 strength of lead is about K the elastic limit, or 225 Ib. per sq. in. 
 
 To find the thickness of lead pipe required when the head of 
 water is given. (Chadwick Lead Works.) 
 
 RULE. Multiply the head in feet by size of pipe wanted, expressed 
 decimally, and divide by 750; the quotient will be the thickness re- 
 quired, in one-hundredths of an inch. Thus the thickness of a half-inch 
 pipe for a head of 25 feet will be 25X0. 50-5-750 = 0.016 inch. 
 
 This rule corresponds to a safe working stress of 165 Ibs. per sq.in. 
 It gives thicknesses of small diameter pipes that are much less than 
 those given iii the table below. 
 
 Weight of Lead Pipe Which Should Be Used for a Given 
 Head of Water (United Lead Co., New York, 1915.) 
 
 Head or 
 Number 
 of Feet 
 Fall. 
 
 Pres- 
 sure 
 per sq. 
 inch. 
 
 Caliber and Weight per Foot. 
 
 Letter. 
 
 Vs in. 
 
 1/2 in. 
 
 Vs in. 
 
 3 /4 in. 
 
 1 in. 
 
 11/4 in. 
 
 30ft. 
 50ft. 
 75ft. 
 100ft. 
 ]50 ft. 
 200ft. 
 
 131b. 
 22 Ib. 
 32 Ib. 
 44 Ib. 
 65 Ib. 
 87 Ib. 
 
 D 
 
 C 
 B 
 A 
 AA 
 AAA 
 
 10 oz. 
 12 oz. 
 1 Ib. 
 
 11/4lb. 
 1 1/2 Ib. 
 1 3/4 Ib. 
 
 3/4 Ib. 
 1 Ib. 
 1 1/4 Ib. 
 
 1 3/4 Ib. 
 
 2 Ib. 
 3 Ib. 
 
 1 Ib. 
 
 1 1/2 Ib. 
 2 Ib. 
 2 l/ 2 Ib. 
 23/ 4 lb. 
 3 i/ 2 Ib. 
 
 1 1/4 Ib. 
 1 3/4 Ib. 
 2 1/4 Ib 
 3 Ib. 
 3 l/ 2 Ib. 
 4 3/ 4 Ib. 
 
 2 Ib. 
 
 2 1/2 Ib. 
 3l/ 4 lb. 
 4 Ib. 
 43/ilb. 
 6 Ib- 
 
 2 1/2 Ib. 
 3 Ib. 
 33/ 4 lb. 
 43/ 4 Ib. 
 5 3/4 Ib. 
 63/4lb. 
 
LEAD AND TIN-LINED PIPE. 
 
 227 
 
 1 1/2 in., 2 and 3 pounds per foot. 
 
 " 3 and 4 pounds per foot. 
 
 *' 3 1/2, 5, and 6 pounds per foot. 
 3 1/2 " 4 pounds per foot. 
 
 Lead Waste-Pipe. 
 
 4 in., 5, 6, and 8 pounds per foot. 
 4 1/2 " 6 and 8 pounds per foot. 
 
 5 " 8, 1 0, and 1 2 pounds per foot. 
 
 6 "12 pounds per foot. 
 
 Tin-Lined and Lead-Lined Iron Pipe. 
 
 (United Lead Co., New York, 1915.) 
 
 Size, 
 In. 
 
 Wt. per ft., Ib. 
 
 Size, 
 In. 
 
 Wt.perft.,lb. 
 
 Size, 
 In. 
 
 Wt.perft.,lb. 
 
 Size, 
 In. 
 
 Wt. per 
 ft., Ib. 
 Lead 
 Lined. 
 
 Lead 
 Lined. 
 
 Tin 
 Lined. 
 
 Lead 
 Lined. 
 
 Tin 
 Lined. 
 
 Lead 
 Lined. 
 
 Tin 
 
 Lined. 
 
 1/2- 
 
 A 
 !|g 
 
 , 13/8 
 
 1 V8 
 21/2 
 
 3-1/2 
 
 43/ 8 
 
 1 
 
 13/8 
 
 |U 
 
 33/4 1 
 
 f'A 
 
 31/2 
 
 61/8 
 81/2 
 111/2 
 
 14l/ 2 
 
 152/3 
 
 51/4 
 71/2 
 101/6 
 128/ 10 
 141/6 
 
 41/2 
 
 6 
 7 
 8 
 
 18 
 
 21 l/ 2 
 293/4 
 36 
 47 
 
 16 
 
 26 l/io 
 191/6 
 
 9 
 10 
 12 
 
 66 
 75 
 
 88 
 
 
 
 
 Block Tin Pipe and Tubing. 
 
 Diam., In. 
 
 Thick- 
 
 Wt. 
 
 Diam., In. 
 
 Thick- 
 
 Wt. 
 
 Diam., In. 
 
 Thick- 
 
 Wt. 
 
 In- 
 
 Out- 
 
 ness, 
 i.- 
 
 ftT 
 
 In- 
 
 Out- 
 
 ness, 
 
 ir\ 
 
 per 
 
 ft., 
 
 In- 
 
 Out- 
 
 ness, 
 
 ?^ f 
 
 side. 
 
 side. 
 
 n. 
 
 oz. 
 
 side. 
 
 side. 
 
 in. 
 
 oz. 
 
 side. 
 
 side. 
 
 in. 
 
 oz. 
 
 Tubing. 
 
 
 
 Pipe. 
 
 
 
 Pipe. 
 
 
 
 1/8 
 
 0.25 
 
 0.062 
 
 1.9 
 
 3/8 
 
 0.495 
 
 0.06 
 
 4 
 
 5/8 
 
 0.800 
 
 0.037 
 
 10 
 
 1/8 
 
 .202 
 
 .0385 
 
 | 
 
 3/8 
 
 .503 
 
 .064 
 
 41/2 
 
 5/8 
 
 .831 
 
 .103 
 
 12 
 
 3/16 
 
 .292 
 
 .053 
 
 2 
 
 3/8 
 
 .515 
 
 .07 
 
 5 
 
 3/4 
 
 .901 
 
 .076 
 
 10 
 
 3/16 
 
 .331 
 
 .072 
 
 3 
 
 3/8 
 
 .539 
 
 .082 
 
 6 
 
 3/4 
 
 .928 
 
 .089 
 
 12 
 
 3/16 
 
 .367 
 
 .09 
 
 4 
 
 3/8 
 
 .561 
 
 .093 
 
 7 
 
 
 .172 
 
 .086 
 
 15 
 
 
 .388 
 
 .069 
 
 3.1/2 
 
 3/8 
 
 .584 
 
 .104 
 
 8 
 
 
 .204 
 
 .102 
 
 18 
 
 PirP 
 
 
 
 1/2 
 
 .632 
 
 .066 
 
 6 
 
 1/4 
 
 .436 
 
 .093 
 
 20 
 
 ripe. 
 
 
 
 1/2 
 
 .670 
 
 .085 
 
 8 
 
 !/4 
 
 .471 
 
 .110 
 
 24 
 
 1/4 
 
 .400 
 
 .075 
 
 4 
 
 1/2 
 
 .707 
 
 .103 
 
 10 
 
 1/2 
 
 .746 
 
 .123 
 
 32 
 
 1/4 
 
 .433 
 
 .091 
 
 5 
 
 1/2 
 
 .741 
 
 .120 
 
 12 
 
 1/2 
 
 .802 
 
 .151 
 
 40 
 
 5/16 
 
 .444 
 
 .066 
 
 4 
 
 5/8 
 
 .735 
 
 .055 
 
 6 
 
 2 
 
 2.236 
 
 .118 
 
 40 
 
 Vl6 
 
 .562 
 
 .065 
 
 5 
 
 5/8 
 
 .768 
 
 .071 
 
 8 
 
 2 
 
 2.280 
 
 .140 
 
 48 
 
 Weight of tin taken as 0.2652 Ib. per cubic inch. 
 
 Weight Per Foot of Brass- and Copper-Lined Iron Pipe. 
 
 (United Lead Co., New York, 1915.) 
 
 1/2 
 
 3/4 
 
 1 
 
 13/8 
 
 
 13/8 
 
 H/4 
 H/2 
 
 22/3 22/3 
 
 3 l/4i 3 1/4 
 
 4 1/3! 4 3/8 
 
 21/2 
 
 4 
 
 67/ 10 63/ 4 
 83/4 88/10 
 126/ 10 ! |27/io 
 
 191/ 2 
 
 3 2 i 1A 
 
 Sll 
 
 193/ 4 
 
 25 6/ 10 
 381/2 
 
228 
 
 MATERIALS. 
 
 Lead-Lined pipe is particularly adapted for use in contact with acids, 
 mine water, salt water, or any liquid which has a corrosive action on 
 iron pipe. 
 
 Lead Covered iron pipe for use in bleacheries, etc., where steam 
 passes through the pipe and the exterior is in contact with acid or cor- 
 rosive solutions is made in commercial sizes of H, %, 1, 1%, 1 ^, 2 
 and 3 inches. 
 
 Brass and Copper Pipes, Lined with Tin or Lead, are made in com- 
 mercial sizes of y^, y, 1, 1 1 A, 1^, and 2 inches. 
 
 Sheet Lead is rolled to any weight per sq. ft. from 1 to 7 Ib. in any 
 width up to 11 ft. 6 in., and from 8 Ib. up, 12 ft. wide. A square foot of 
 rolled sheet lead 1 in. thick weighs approximately 59 Y 2 Ib. 
 
 Approximate Weight of Sheet Zinc. 
 
 (Aluminum Co. of America, 1914.) 
 
 o* 
 
 fc 
 
 o 
 
 1| 
 *s 
 
 o" . 
 w -a 
 
 NM 
 
 a> 
 
 ft 4a 
 
 6 
 2 
 
 o 
 
 Is 
 
 11 
 
 w-a 
 
 r 
 
 6 
 
 
 
 Is 
 
 5-S. 
 > g 
 
 1 
 
 d 
 
 1 g 
 If 
 
 a* 
 
 I* 
 
 i 
 
 ^j 1 " 1 
 
 -4-Jfe 
 
 i 
 
 g 
 N 
 
 HH 
 
 H 
 
 ^ 
 
 N 
 
 S 
 
 
 
 _c 
 
 H 
 
 
 
 i 
 
 0.002 
 
 0.075 
 
 8 
 
 0.016 
 
 0.60 
 
 15 
 
 0.040 
 
 1.50 
 
 22 
 
 0.090 
 
 3.37 
 
 2 
 
 .004 
 
 .15 
 
 9 
 
 .018 
 
 .67 
 
 16 
 
 .045 
 
 1.68 
 
 23 
 
 .100 
 
 3.75 
 
 3 
 
 .006 
 
 .225 
 
 10 
 
 .020 
 
 .75 
 
 17 
 
 .050 
 
 1.87 
 
 24 
 
 .125 
 
 4.70 
 
 4 
 
 .008 
 
 .30 
 
 11 
 
 .024 
 
 .90 
 
 18 
 
 .055 
 
 2.06 
 
 25 
 
 .250 
 
 9.41 
 
 5 
 
 .010 
 
 .37 
 
 12 
 
 .028 
 
 1.05 
 
 19 
 
 .060 
 
 2.25 
 
 26 
 
 .375 
 
 14.11 
 
 6 
 
 .012 
 
 .45 
 
 13 
 
 .032 
 
 1.20 
 
 20 
 
 .070 
 
 2.62 
 
 27 
 
 .500 
 
 18. 8( 
 
 7 
 
 .014 
 
 .52 
 
 14 
 
 .034 
 
 1.35 
 
 21 
 
 .080 
 
 3.00 
 
 28 
 
 1.000 
 
 37.60 
 
 Weight of Sheet or Bar Brass. 
 
 (Compiled from Manufacturers' Standard Tables.) 
 
 A 
 
 * 
 
 
 -bi 
 
 oi 
 
 .^ 
 
 bib 
 
 k A 
 
 aa 
 
 i* 
 
 bib 
 
 -A 
 
 *Q 
 
 
 
 08 3 
 
 
 
 
 
 
 
 a 
 
 
 P 
 
 j2 M 
 J* 
 
 ^ 
 
 
 0) t-, 
 
 II 
 
 1 
 
 aJ . 
 
 cr 
 
 OQ 
 
 |S 
 
 1:- 
 m 
 
 11 
 
 CO 
 
 $ 
 
 1 
 
 In. 
 1/16 
 
 2.77 
 
 Lb. 
 0.014 
 
 Lb. 
 0.011 
 
 In. 
 
 3/4 
 
 33.21 
 
 Lb. 
 2.075 
 
 Lb. 
 1.630 
 
 In. 
 
 17/16 
 
 63.66 
 
 Lb. 
 7.623 
 
 Lb. 
 5.987 
 
 1/8 
 
 5.54 
 
 .058 
 
 .045 
 
 13/16 
 
 35.98 
 
 2.435 
 
 1.913 
 
 H/2 
 
 66.42 
 
 8.300 
 
 6.519 
 
 3/16 
 
 8.30 
 
 .130 
 
 .102 
 
 
 38.75 
 
 2.824 
 
 2.218 
 
 19/16 
 
 69.19 
 
 9.006 
 
 7.073 
 
 1/4 
 
 11.07 
 
 .231 
 
 .181 
 
 15/16 
 
 41.51 
 
 3.242 
 
 2.546 
 
 15/8 
 
 71.96 
 
 9.741 
 
 7.651 
 
 5/16 
 
 13.84 
 
 .360 
 
 .283 
 
 
 44.28 
 
 3.689 
 
 2.897 
 
 
 74.73 
 
 10.50 
 
 8.250 
 
 3/8 
 
 16.61 
 
 .519 
 
 .407 
 
 '1/16 
 
 47.05 
 
 4.164 
 
 3.271 
 
 1 3/ 4 16 
 
 77.49 
 
 11.30 
 
 8.873 
 
 7/16 
 
 19.37 
 
 .706 
 
 .555 
 
 11/8 
 
 49.82 
 
 4.669 
 
 3.667 
 
 1 13/16 
 
 80.26 12.12 
 
 9.518 
 
 1/2 
 
 22.14 
 
 .922 
 
 .724 
 
 13/16 
 
 52.59 
 
 5.202 
 
 4.086 
 
 17/8 
 
 83.03 12.97 
 
 10.19 
 
 9/16 
 
 24.91 
 
 1.167 
 
 .917 
 
 U/4 
 
 55.35 
 
 5.764 
 
 4.527 
 
 1 15/16 
 
 85.80 13.85 
 
 10.88 
 
 5/8 
 
 27.68 
 
 1.441 
 
 1.132 
 
 15/16 
 
 58.12 
 
 6.355 
 
 4.991 
 
 2 
 
 88.56 14.76 
 
 11.59 
 
 11/16 
 
 30.44 
 
 1.744 
 
 1.369 
 
 13/8 
 
 60.89 
 
 6.974 
 
 5.478 
 
 
 
 
 
WEIGHT OF COPPER AND BRASS WIRE AND PLATES. 229 
 
 u\ i> O^ vO CO IA O^ co IA <N O -<f CN vO < 
 
 OCNOMOcNiACOC^cOcoiArNroONCO riA^- , 
 
 tJ CN O^ 00 F^ h. sO in T <* CO CO CO CN CN CN CO"" 
 
 r 
 
 bCt/2 ^ OOcOAOoOoot N m ^cooOr^^O^^^Ococoir 
 
 ft j co o O^ oo t> ^O in *n ^ ^ co co CN CN CN CN < 
 5 H ,-^g 
 
 ( ^rN'? 
 
 "SJ 
 
 - fn _. >Tf2oo Cn "" V lAlA ~oin^O^cocs 
 
 ^CN^f^^^cOCOCN OOOOOO 00O 
 
 
 <Nh OOOiA t- 
 
 S^CNCNCNCN oooooooooo "^ 
 
 Soooooooooooooooooooo >>-2 
 
 ^ -M 9 
 
 O '0 
 
 o . x 
 
 fNco-^-mvOt^oOO^O CNco^-iAvOf^oOO^O 'SM 
 CNCNCNCNCNCSCNCNCNCOCOCOCOCOCOCOCOCOCO 1 ^- 
 
 ,Q . "~. *~". 
 
 n 
 
 o| 
 
 it 
 
 i ^- 
 
 u 
 
 x -.-.-.-. . . -. : ~ -. . . . .-.-.-.;-.-.-. .-. 
 
 .ja^coco^-' o i Amc^^^a^cooO'<i-' o^r>.mfcocN 
 on i 'oooooO-^-OMncNO^t^iriTrcocNCN ~- 
 ^ ^ co co CN 
 
 '3 . O^r>.t > *.CN-*\o 
 
 JH-J fe m <^ co oo vO IA o*v <y> T}- NO CN o <N o o 
 
 ^ ^fNiAroco^ AinfomOOvO'<ra;r^ > X) < ^oqoocNa>O^O 
 
 a H^ co co o^ ro <^' \o a <^ co o o> - -<* a^ A CN av t^ vc -^ co co 
 
 Q -jpO tnOvncNOr^NOiAcococN 
 
 ^ -5 ~*SK**-RV*4-a*^' 
 
 5 ^ ? CO CO CN CN CN CN O O O O O O O O O O 
 
 O* 
 
 s 888' 
 
230 
 
 MATERIALS. 
 
 Weight of Aluminum Plates. (Brown & Sharpe Gage.) 
 (Aluminum Co. of America, 1914.) 
 
 Gage. 
 
 Thick- 
 ness, 
 In. 
 
 Wgt., 
 Lb. 
 
 Gage. 
 
 Thick- 
 ness, 
 In. 
 
 '^ 
 
 Gage. 
 
 Thick- 
 ness, 
 In. 
 
 Wgt., 
 Lb. 
 
 0000 
 
 0.46000 
 
 6.406 
 
 12 
 
 0.080808 
 
 1.126 
 
 27 
 
 0.014195 
 
 0.1976 
 
 000 
 
 .40964 
 
 5.704 
 
 13 
 
 .071961 
 
 1.002 
 
 28 
 
 .012641 
 
 .1760 
 
 00 
 
 .36480 
 
 5.080 
 
 14 
 
 .064084 
 
 .8924 
 
 29 
 
 .011257 
 
 .1567 
 
 
 
 .32486 
 
 4.524 
 
 15 
 
 .057068 
 
 .7946 
 
 30 
 
 .010025 
 
 .1396 
 
 1 
 
 .28930 
 
 4.029 
 
 16 
 
 .050820 
 
 .7078 
 
 31 
 
 .008928 
 
 .1244 
 
 2 
 
 .25763 
 
 3.588 
 
 17 
 
 .045257 
 
 .6302 
 
 32 
 
 .007950 
 
 .1107 
 
 3 
 
 .22942 
 
 3.195 
 
 18 
 
 .040303 
 
 .5612 
 
 33 
 
 .007080 
 
 .09854 
 
 4 
 
 .20431 
 
 2.845 
 
 19 
 
 .035890 
 
 .4998 
 
 34 
 
 .006304 
 
 .08778 
 
 5 
 
 .18194 
 
 2.534 
 
 20 
 
 .031961 
 
 .4450 
 
 35 
 
 .005614 
 
 .07817 
 
 6 
 
 .16202 
 
 2.256 
 
 21 
 
 .028462 
 
 .3964 
 
 36 
 
 .005000 
 
 .06962 
 
 7 
 
 .14428 
 
 2.009 
 
 22 
 
 .025347 
 
 .3530 
 
 37 
 
 .004453 
 
 .06201 
 
 8 
 
 .12849 
 
 1.789 
 
 23 
 
 .022571 
 
 .3143 
 
 38 
 
 .003965 
 
 .05521 
 
 9 
 
 .11443 
 
 1.594 
 
 24 
 
 .020100 
 
 .2798 
 
 39 
 
 .003531 
 
 .04917 
 
 10 
 
 .10189 
 
 1.418 
 
 25 
 
 .017900 
 
 .2492 
 
 40 
 
 .003144 
 
 .04378 
 
 11 
 
 .090742 
 
 1.264 
 
 26 
 
 .015940 
 
 .2219 
 
 
 
 
 Weight of Sheet or Bar Aluminum (Sp. Gr. 2.68). 
 (Aluminum Co. of America, 1914.) 
 
 tess, 
 or Dia. 
 
 & 
 
 o* 
 
 bi 
 
 A 
 
 o? ti 
 
 U 
 
 eJ 
 
 g3 
 
 ,+J 
 
 s*. 
 
 O 4 
 
 b 
 
 ts 
 
 t-i be 
 
 wjj 
 
 a 
 
 .-s 
 
 03 j_ 
 
 2 o 
 
 4 
 
 bD 
 
 3 
 
 ti 
 
 J 
 
 II 
 
 ofGQ 
 a t-> 
 
 * 
 
 T3 ,? 
 
 g 
 
 !v>2 
 
 CQ 
 
 $ 
 
 5 . 
 
 
 
 ^^5 
 
 
 c 
 
 l| 
 
 oo M 
 
 J 4 ^ JH 
 O 
 
 3 
 
 S 
 
 1* 
 
 e a 
 
 JB ft 
 
 GO 
 
 CT,-| 
 
 QQ 
 
 & H 
 
 2S 
 
 02 
 
 JSft 
 CQ 
 
 * 
 
 1? 
 
 S 33 
 
 a 
 
 OQ 
 
 c^^ 
 
 1- 
 
 In. 
 
 
 Lb. 
 
 Lb. 
 
 In. 
 
 
 ~LbT 
 
 Lb. 
 
 In. 
 
 
 Lb. 
 
 "EET 
 
 1/16 
 
 0.8690.004 
 
 0.003 
 
 3/4 
 
 10.436 
 
 0.652 
 
 0.516 
 
 1Vl6 
 
 20.002 
 
 2.396 1.882 
 
 1/8 
 
 1.739 
 
 .018 
 
 .014 
 
 IS/IB '11. 306 .766 
 
 .601 
 
 1 1/2 20.872 2.609 2 049 
 
 3/16 
 
 2.609 
 
 .041 
 
 .032 
 
 7/8 12.175 
 
 .888 
 
 .697 
 
 l/16 
 
 21.741 2.831 2.223 
 
 V4 
 
 3.479 
 
 .072 
 
 .057 
 
 15/16' 13. 045 .019 
 
 .800 
 
 1 5/ 8 22.611 3.062 2 405 
 
 8/16 
 
 4.348 
 
 .114 
 
 .089 
 
 1 
 
 13.915 .159 .911 
 
 1 n/16 123.481 3.302 2.593 
 
 3/8 
 
 5.218 .163 
 
 .128 
 
 11/16 14.784 .309 .028 
 
 13/ 4 24.350 3 550 2 79 
 
 Vl6 
 
 6.088 1 .222 
 
 .174 
 
 1 1/8 15.654 .467 .152 
 
 1 13/16 25.250 3.810 2.992 
 
 1/2 
 
 6.958 .290 
 
 .227 
 
 13/15 16.524 .635 .284 
 
 17/8 
 
 26.090 
 
 4.075 3.202 
 
 9/16 
 
 7.827 .367 
 
 .288 
 
 11/4 
 
 17.934 .812 .423 
 
 1 15/16 
 
 26.960 
 
 4.352 3.417 
 
 " 5/8 
 
 8.697| .453 
 
 .356 
 
 15/16 
 
 18.263 .997 .569 
 
 2 
 
 27.829 
 
 4.638 3.642 
 
 H/16 
 
 9.5671 .548 
 
 .430 
 
 13/8 
 
 19.133^2.192 1 .722 
 
 
 
 1 
 
 For further particulars regarding aluminum see pp. 380-383; 396-401. 
 
 Weight Per Foot of Copper Rods, Pounds. 
 
 (From tables of manufacturers, 1914.) 
 
 In. 
 
 Round. 
 
 Square. 
 
 In. 
 
 Round. 
 
 Square. 
 
 In. 
 
 Round. 
 
 Square. 
 
 1/8 
 1/4 
 3/8 
 
 1/2 
 5/8 
 3/4 
 7/8 
 
 0.04735 
 .1894 
 .4261 
 .7576 
 1.184 
 1 .705 
 2.320 
 3.030 
 
 0.06028 
 .2411 
 ' .5424 
 .9644 
 1.507 
 2.170 
 2.953 
 3.857 
 
 1/8 
 1/4 
 3/8 
 1/2 
 5/8 
 3/4 
 
 a 778 
 
 3.835 
 4.735 
 5.729 
 6.818 
 8.002 
 9.281 
 10.65 
 12.12 
 
 4.882 
 6.028 
 7.293 
 8.679 
 10.19 
 11 .81 
 13.56 
 15.53 
 
 2V8 
 21/4 
 23/8 
 21/2 
 25/ 8 
 23/4 
 27/8 
 
 13.68 
 15.34 
 17.09 
 18.94 
 20.88 
 22.92 
 25.05 
 27.27 
 
 17.41 
 19.53 
 21.76 
 24.11 
 26.58 
 29.18 
 31.89 
 34.71 
 
 For weight of octagon rod, multiply the weight of round rod by 1.081. 
 For weight of hexagon rod, multiply the weight of round rod by 1.12. 
 
SCREW THREADS. 
 
 231 
 
 SCREW THREADS. 
 
 Sellers or U. S. Standard. 
 
 The system of screw threads devised by William Sellers and recom- 
 mended for adoption by a committee of the Franklin Institute in 1864 
 is now in general use in the United States and is known as the U. S. 
 standard. The angle of the thread is 60 deg. The thread is flat- 
 tened at the top, the width of flat being one-eighth the pitch. The 
 bottom of the thread is filled in, the width of flat at the bottom also 
 being one-eighth the pitch. The wearing surface of the thread is thus 
 three-quarters the pitch. 
 
 Diana, at root of thread = diam. of bolt- (1.299 -~ No. of threads 
 per in.). Depth of thread = 0.6495 X pitch. 
 
 For a sharp V thread, with an angle of 60 deg. the formula is 
 Diam. at root of thread = diam. of bolt (1.733 -s- No. of threads per in.). 
 
 The rules for dimensioning nuts and heads given in the Franklin 
 Institute report are: 
 
 Let d = diameter of bolt, D = short diameter of rough nut or head, 
 
 (Continued on page 232.) 
 
 Dimensions of Screw-Threads, Sellers or U. S. Standard. 
 
 BOLTS AND THREADS. 
 
 NUTS AND BOLT 
 HEADS. 
 
 
 T3 
 
 ^j 
 
 
 .JJ 
 
 ^j 
 
 a* 
 
 _p g 
 
 * . 
 
 
 
 " 
 
 S 
 
 "o 
 
 PQ 
 
 $ 
 
 OS'S 
 
 A 
 
 
 JS o 
 
 Sea 
 
 Ij 
 
 S 
 
 fc 
 
 w 
 
 
 cv 
 
 
 
 
 ) M 
 
 
 .2 g 
 
 .2 
 
 f. 
 
 8 
 
 "o 
 
 CO 
 
 *sj 
 
 "8 
 
 "* oa 
 
 
 d 
 
 
 Q 
 
 
 
 
 1 
 
 || 
 
 Ctf *-i 
 
 S 
 
 go 
 
 S^ 1 
 
 3 
 
 M| 
 
 if! 
 
 
 1 
 
 5 
 
 H 
 
 3 
 
 | 
 
 ^PQw 
 
 ^ "oca 
 
 w 
 
 ^W 
 
 M 
 
 S 
 
 i 
 
 In. 
 
 
 In. 
 
 In. 
 
 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 1/4 
 
 20 
 
 0.185 
 
 0.0062 
 
 0.049 
 
 0.027 
 
 1/2 
 
 0.578 
 
 0.707 
 
 V4 
 
 V 4 
 
 5/16 
 
 18 
 
 .240 
 
 .0059 
 
 .077 
 
 .045 
 
 19/32 
 
 .686 
 
 .840 
 
 5/16 
 
 19 /64 
 
 3/8 
 
 16 
 
 .294 
 
 .0078 
 
 .110 
 
 .068 
 
 H/16 
 
 .794 
 
 .972 
 
 3/8 
 
 n /32 
 
 7/16 
 
 14 
 
 .345 
 
 .0089 
 
 .150 
 
 .093 
 
 25/32 
 
 .902 
 
 .105 
 
 7/16 
 
 25 /64 
 
 1/2 
 
 13 
 
 .400 
 
 .0096 
 
 .196 
 
 .126 
 
 7/8 
 
 .011 
 
 .237 
 
 V2 
 
 7 /16 
 
 9/16 
 
 12 
 
 .454 
 
 .0104 
 
 .249 
 
 .162 
 
 31/32 
 
 .119 
 
 .370 
 
 9/16 
 
 31 /64 
 
 5/8 
 
 11 
 
 .507 
 
 .0113 
 
 .307 
 
 .202 
 
 1 Vl6 
 
 .227 
 
 .502 
 
 5/8 
 
 17 /32 
 
 3/4 
 
 10 
 
 .620 
 
 .0125 
 
 .442 
 
 .302 1 1/4 
 
 .444 
 
 .768 
 
 3/1 
 
 5 /8 
 
 7/8 
 
 9 
 
 .731 
 
 .0139 
 
 .601 
 
 .420 
 
 1 7/16 
 
 .660 
 
 2.033 
 
 7/8 
 
 23 /32 
 
 
 8 
 
 .837 
 
 .0156 
 
 .785 
 
 .550 
 
 1 5/8 
 
 .877 
 
 2.298 
 
 
 13/16 
 
 1 1/8 
 
 7 
 
 .939 
 
 .0178 
 
 .994 
 
 .694 1 13/1 
 
 2.093 
 
 2.563 
 
 V8 
 
 29/32 
 
 H/4 
 
 7 
 
 .065 .0178 
 
 1.227 
 
 .891 
 
 2 
 
 2.310 
 
 2.828 
 
 1/4 
 
 
 13/8 
 
 6 
 
 .160 
 
 .0208 
 
 1.485 
 
 1.057 
 
 23/16 
 
 2.527 
 
 3.093 3/ 8 i 3/ 3? 
 
 I 1/2 
 
 6 
 
 .284 
 
 .0208 
 
 1.767 
 
 1.295 
 
 23/8 
 
 2.743 
 
 3.358 1/2 3 /, fi 
 
 15/8 
 
 51/2 
 
 .389 
 
 .0227 
 
 2.074 
 
 1.515 
 
 
 2.960 
 
 3.623 
 
 5/8 9 /*2 
 
 13/4 
 
 5 
 
 .491 
 
 .0250 
 
 2.405 
 
 1.746 
 
 23/f 
 
 3.176 
 
 3.889 
 
 13/4 
 
 3 /8 
 
 17/8 
 
 5 
 
 .616 
 
 .0250 
 
 2.761 
 
 2.051 
 
 2 15/16 
 
 3.393 
 
 4.154 
 
 1 7/8 
 
 15/32 
 
 2 
 
 41/2 
 
 .712 
 
 .0278 
 
 3.142 
 
 2.302 
 
 31/8 
 
 3.609 
 
 4.419 
 
 2 
 
 9 /l6 
 
 21/4 
 
 41/2 
 
 .962 
 
 .0278 
 
 3.976 
 
 3.023 
 
 31/2 
 
 4.043 
 
 4.949 
 
 21/4 
 
 3/4 
 
 21/2 
 
 4 ' 
 
 2.176 
 
 .0312 
 
 4.909 
 
 3.719 
 
 37/s 
 
 4.476 
 
 5.479 
 
 21/2 
 
 J 5 /16 
 
 23/4 
 
 4 
 
 2.426 
 
 .0312 
 
 5.940 
 
 4.622 
 
 41/4 
 
 4.909 
 
 6.010 
 
 
 
 3 
 
 31/2 
 
 2.629 
 
 .0357 
 
 7.069 
 
 5.428 
 
 45/8 
 
 5.342 
 
 6.540 
 
 3 
 
 2 5 /16 
 
 31/4 
 
 31/2 
 
 2.879 
 
 .0357 
 
 8.296 
 
 6.510 
 
 5 
 
 5.775 
 
 7.070 31/4 
 
 2 !/2 
 
 31/2 
 
 31/4 
 
 3.100 
 
 .0384 
 
 9.621 
 
 7.548 
 
 53/8 
 
 6.208 
 
 7.600 
 
 31/2 
 
 2 U /16 
 
 33/4 
 
 3 
 
 3.317 
 
 .0417 
 
 11.045 
 
 8.641 
 
 53/4 
 
 6.641 
 
 8.131 
 
 33/4 
 
 27/s 
 
 4 
 
 3 
 
 3.567 
 
 .0417 
 
 12.566 
 
 9.993 
 
 61/8 
 
 7.074 
 
 8.661 
 
 4 
 
 3 VIP 
 
 41/4 
 
 27/8 
 
 3.798 
 
 .0435 
 
 14.186 
 
 11.328 
 
 61/2 
 
 7.508 
 
 9.191 
 
 41/4 
 
 3V4 
 
 41/2 
 
 23/4 
 
 4.028 
 
 .0454 115.904 
 
 12.743 
 
 67/8 
 
 7.941 
 
 9.721 
 
 41/2 
 
 
 43/4 
 
 25/8 
 
 4.256 
 
 .0476 17.721 
 
 14.250 
 
 71/4 
 
 8.374 
 
 10.252 
 
 43/4 
 
 3 5/g 
 
 5 
 
 21/2 
 
 4.480 
 
 .0500 19.635 
 
 15.763 
 
 75/8 
 
 8.807 
 
 10.782 
 
 5 
 
 3 13 /16 
 
 51/4 
 
 21/2 
 
 4.730 
 
 .0500 21.648 
 
 17.572 
 
 8 
 
 9.240 
 
 11.312 
 
 5V4 
 
 4 
 
 51/2 
 
 23/8 
 
 4.953 
 
 .0526 '23.758 
 
 19.267 
 
 83/8 
 
 9.673 
 
 11.842 
 
 51/2 
 
 4Vl6 
 
 53/4 
 
 23/8 
 
 5.203 
 
 .0526 25.967 
 
 21.262 
 
 83/4 
 
 10.106 
 
 12.373 
 
 53/4 
 
 
 6 
 
 21/4 
 
 5.423! .0555 28.274 
 
 23.098 
 
 91/8 
 
 10.539 
 
 12.903 
 
 6 
 
 4 9 /l6 
 
232 
 
 MATERIALS. 
 
 Di = short diameter of finished nut or head ; T thickness of rough 
 nut; Ti = thickness of finished nut; t = thickness of rough head, U 
 thickness of finished head; D = 1.5 d + i/s; A = 1.5 d 4- i/ie; T = d- 
 Ti = d- i/i 6 ; t = y 2 D, ti = 1/2 d - i/ie. 
 
 The dimensions given by the above formulae for nuts and heads are 
 not generally accepted by the makers of nuts and bolts. The general 
 practice is to make the rough and finished nuts of the same dimensions, 
 otherwise different wrenches would be required for the same size of 
 nut. The dimensions of nuts and bolt heads given in the above table 
 are those adopted by the Upson Nut Co., Hoopes and Townsend, and 
 the U. S. Navy, and agree with the formulae D = 1.5 d + 1/3, T = Ti = 
 d,t = ti = 1/2 -D. 
 
 Screw-Threads, Whitworth (English) Standard. 
 
 g' 
 
 ,d 
 
 j 
 
 ,d 
 
 j 
 
 4 
 
 j 
 
 jg 
 
 ^ 
 
 ^ 
 
 
 
 1 
 
 9 
 
 1 
 
 
 
 5 
 
 9 
 
 5 
 
 
 
 ^ 
 
 S 
 
 
 8 
 
 S 
 
 a 
 
 
 S 
 
 S 
 
 Q 
 
 S 
 
 1/4 
 
 20 
 
 5/8 
 
 11 
 
 i 
 
 8 
 
 13/4 
 
 5 
 
 3 
 
 3V? 
 
 5/16 
 
 ft 
 7/16 
 
 1/2 
 
 18 
 16 
 14 
 12 
 
 H/16 
 3/4 
 13/16 
 
 7/8 
 
 11 
 
 10 
 10 
 9 
 
 H/8 
 H/4 
 13/8 
 H/2 
 
 7 
 7 
 6 
 6 
 
 21/4 
 21/2 
 
 4 
 
 3V4 
 33/4 
 
 31/4 
 3V4 
 
 
 '.2 
 
 15/16 
 
 9 
 
 15/8 
 
 5 
 
 23/4 
 
 31/2 
 
 
 
 In the Whitworth or English system the angle of the thread is 55 
 degrees, and the point and root of the thread are rounded to a radius of 
 0.1373 X pitch. The depth of the thread is 0.6403 X pitch. 
 
 International Standard Thread (Metric System). 
 
 The form of thread is the same as the U. S. Standard. P = pitch, 
 in millimetres = 25.4 + no. of threads per in. No. of threads per in. =* 
 25.4 H-P: 
 
 Diam., mm. 67 8 9 10 11 12 14 16 18 20 22 24 27 
 Pitch, mm. 1.0 1.0 1.25 1.25 1.5 1.5 1.75 2. 2. 2.5 2.5 2.5 3. 3. 
 Diam., mm. 30 33 36 39 42 45 48 52 56 60 64 68 72 76 80 
 Pitch, mm. 3.5 3.5 4. 4. 4.5 4.5 5. 5. 5.5 5.5 6. 6. 6.5 6.5 7. 
 
 British Association Standard Thread. 
 
 The angle between the threads is 47 1 A. The depth of the thread is 
 0.6 X the pitch. The tops and bottoms of the threads are rounded with 
 a radius of 2/11 of the pitch. 
 
 Number 0124556 
 
 Diameter, mm 6.0 5.3 4.7 4.1 3.64 3.2 2.8 
 
 Pitch, mm 1.00 0.90 0.81 0.73 0.66 0.590.53 
 
 Number 7 8 9 10 12 14 19 
 
 Diameter, mm 2.5 2.2 1.9 1.7 1.3 1.0 0.79 
 
 Pitch, mm 0.48 0.43 0.39 0.35 0.28 0.23 0.19 
 
 Limit Gages for Iron for Screw-Threads. 
 
 In ad9pting the Sellers, or Franklin Institute, or United States Stand- 
 ard, as it is variously called, a difficulty arose from the fact that it is 
 the habit of iron manufacturers to make iron over-size, and as there are 
 no over-size screws in the Sellers system, if iron is too large it is necessary 
 to cut it away with the dies. So great is this difficulty, that the practice 
 of making taps and dies over-size has become very general. If the 
 Sellers system is adopted it is essential that iron should be obtained of 
 the correct size, or very nearly so. Of course no high degree of precision 
 is possible in rolling iron, and when exact sizes were demanded, the ques- 
 tion arose how much allowable variation there should be from the true 
 size. It was proposed to make limit-gages for inspecting iron with two 
 openings, one larger and the other smaller than the standard size, and 
 
SCREW THREADS. 
 
 233 
 
 then specify that the iron should enter the large end and not enter the 
 small one. The following table of dimensions for the limit-gages was 
 adopted by the Master Car-Builders' Association in 1883. 
 
 "o . 
 
 fl) C 
 
 11 
 a 
 S* 
 
 II 
 
 - _O 
 
 13^ 
 
 1 
 
 Difference. 
 
 1 
 
 1* 
 
 w 
 
 ~5/8 
 3/4 
 
 , 7/8 
 
 H/8 
 
 H/4 
 
 11 
 f 
 
 If 
 
 
 Difference. 
 
 Size of Iron, 
 In. 
 
 11 
 
 QjO 
 
 II 
 
 -- .O 
 
 1 
 
 Difference. 
 
 1/4 
 
 5/16 
 3/8 
 7/16 
 V2 
 9/16 
 
 0.2550 
 0.3180 
 0.3810 
 0.4440 
 0.5070 
 0.5700 
 
 0.2450 
 0.3070 
 0.3690 
 0.4310 
 0.4930 
 0.5550 
 
 0.010 
 0.011 
 0.012 
 0.013 
 0.014 
 0.015 
 
 0.6330 
 0.7585 
 0.8840 
 1 .0095 
 1.1350 
 1 .2605 
 
 0.6170 
 0.7415 
 0.8660 
 0.9905 
 1 .1150 
 1 .2395 
 
 0.016 
 0.017 
 0.018 
 0.019 
 0.020 
 0.021 
 
 13/8 
 H/2 
 15/8 
 13/4 
 17/8 
 
 .3860 
 .5115 
 .6370 
 .7625 
 .8880 
 
 1 .3640 
 1 .4885 
 1 .6130 
 1 .7375 
 1 .8620 
 
 0.022 
 0.023 
 0.024 
 0.025 
 0.026 
 
 Caliper gages with the above dimensions, and standard reference 
 gages for testing them, are made by the Pratt & Whitney Co., Hartford. 
 
 Automobile Screws and Nuts. The Society of Automobile Engi- 
 neers (1912) adopted standard specifications for hexagon head screws, 
 castle and plain nuts known as the A.L.A.M. standard. Material to 
 be steel, elastic limit not less than 60,000 Ibs. per sq. in., tensile strength 
 not less than 100,000 Ibs. per sq. in. U. S. Standard thread is used, the 
 threaded portion of screws being 1 K times the diameter. The castle 
 nut has a boss on the upper surface with six slots for a locking pin 
 through the bolt. 
 
 Standard Automobile Screws, Castle and Plain Nuts. 
 
 All dimensions in inches. P = pitch, or number of threads per inch. 
 d = diam. of cotter pin. P -4- 8 = flat top of thread. The body 
 diam. of screws is 0.001 in. less than nominal diam., with a plus 
 tolerance of zero and a minus tolerance of 0.002 in. The top shall be 
 between 0.003 in. and 0.003 in. large. 
 
 D 
 
 P 
 
 B 
 
 Ai 
 
 H 
 
 K 
 
 I 
 
 A 
 
 c 
 
 E 
 
 d 
 
 1/4 
 
 28 
 
 7/13 
 
 7/32 
 
 3/16 
 
 1/16 
 
 3/32 
 
 9/32 
 
 
 5/64 
 
 1/16 
 
 Vl6 
 
 24 
 
 1/2 
 
 17/64 
 
 15/64 
 
 Vl6 
 
 7/64 
 
 21/64 
 
 3/32 
 
 5/64 
 
 1/16 
 
 3/8 
 
 24 
 
 9/16 
 
 21/61 
 
 9/32 
 
 3/32 
 
 1/8 
 
 13/32 
 
 1/8 
 
 1/8 
 
 3/32 
 
 7/16 
 
 20 
 
 5/8 
 
 3/8 
 
 21/64 
 
 3/32 
 
 1/8 
 
 29/64 
 
 1/8 
 
 1/8 
 
 3/32 
 
 1/2 
 
 20 
 
 3/4 
 
 7/16 
 
 3/8 
 
 3/32 
 
 1/8 
 
 9/16 
 
 3/16 
 
 1/8 
 
 3/32 
 
 9/16 
 
 18 
 
 7/8 
 
 31/64 
 
 27/64 
 
 3/32 
 
 1/8 
 
 39/04 
 
 3/16 
 
 5/32 
 
 1/8 
 
 5/8 
 
 18 
 
 15/16 
 
 35/64 
 
 15/32 
 
 3/32 
 
 1/8 
 
 23/32 
 
 1/4 
 
 5/32 
 
 1/8 
 
 H/16 
 
 16 
 
 1 
 
 19/32 
 
 33/64 
 
 3/32 
 
 1/8 
 
 49/64 
 
 1/4 
 
 5/32 
 
 1/8 
 
 3/1 
 
 16 
 
 H/16 
 
 21/32 
 
 9/16 
 
 3/32 
 
 1/8 
 
 13/16 
 
 Vl 
 
 5/32 
 
 1/8 
 
 7/8 
 
 14 
 
 1 V4 
 
 49/o 
 
 21/32 
 
 3/32 
 
 1/8 
 
 29/32 
 
 1/4 
 
 5/32 
 
 1/8 
 
 1 
 
 14 
 
 17/10 
 
 7/8 
 
 3/4 
 
 3/32 
 
 Vs 
 
 1 
 
 1/4 
 
 5/32 
 
 1/8 
 
 H/8 
 
 12 
 
 15/8 
 
 63/64 
 
 27/32 
 
 5/32 
 
 7/32 
 
 15/32 
 
 5/16 
 
 7/32 
 
 H/04 
 
 M/4 
 
 12 
 
 1 13/16 
 
 1 3/32 
 
 15/16 
 
 5/32 
 
 7/32 
 
 H/4 
 
 5/16 
 
 7/32 
 
 H/64 
 
 13/8 
 U/2 
 
 12 
 12 
 
 2 
 23/16 
 
 1 13/64 
 15/16 
 
 H/32 
 H/8 
 
 3/16 
 3/16 
 
 1/4 
 1/4 
 
 1 13/32 
 H/2 
 
 3/8 
 3/8 
 
 1/4 
 1/4 
 
 13/04 
 13/64 
 
234 
 
 MATERIALS. 
 
 The Acme Screw Thread. 
 
 The Acme Thread is an adaptation of the commonly used style of worm 
 thread and is intended to take the place of the square thread. It is a 
 little shallower than the Worm thread, but the same depth as the square 
 thread and much stronger than the latter. The angle of the thread is 29. 
 
 The various parts of the Acme .Thread are obtained as follows: 
 
 Width of point of tool for screw* or tap thread = 
 (0.3707 -5- No. of Threads per in.) - 0.0052. 
 
 Width of screw or nut thread = 0.3707 *- No. of Threads per in. 
 
 Diam. of Tap = Diam, of Screw + 0.020. 
 
 Diam - of Screw - 
 
 -0.020 
 
 *F F-H - 
 
 No. of Threads per in. 
 
 Depth of Thread = | 1 -5- (2 X No. of Threads per in.) j- + 0.010. 
 The angle of the thread is29 deg. 
 
 MACHINE SCREWS. A. S.M.E. Standard. 
 
 Ther American Society of Mechanical Engineers (1907) received a report 
 on standard machine screws from its committee on that subject. The 
 included angle of the thread is 60 degrees and a flat is made at the top 
 and bottom of the thread of one-eighth of the pitch for the basic diameter. 
 A uniform increment of 0.013 inch exists between all sizes from to 10 
 and 0.026 inch in* the remaining sizes. . The pitches are a function ot the 
 diameter as expressed by the formula 
 
 Threads per inch 
 
 The minimum tap conforms to the basic standard in all respects except 
 diameter. The difference between the minimum tap and the maximum 
 screw provides an allowance for error in pitch and for wear of the tap in 
 service. 
 
 A. S. M. E. Standard Machine Screws. 
 (Corbin Screw Corporation.) 
 
 Size. 
 
 Outside Diameters. 
 
 Pitch Diameters. 
 
 Root Diameters. 
 
 
 Out. 
 
 
 
 
 
 
 
 
 
 
 No. 
 
 Dia. 
 and 
 Thds. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 
 per In. 
 
 
 
 
 
 
 
 
 
 
 
 
 0.060-80 
 
 0.0572 
 
 0.060 
 
 0.0028 
 
 0.0505 
 
 0.0519 
 
 0.0014 
 
 0.0410 
 
 0.0438 
 
 0.0028 
 
 1 
 
 .073-72 
 
 .070 
 
 .073 
 
 .003 
 
 .06251 .064 
 
 .0015 
 
 .052 
 
 .055 
 
 .0030 
 
 2 
 
 .086-64 
 
 .0828 
 
 .086 
 
 .0032 
 
 .0743 
 
 .0759 
 
 .0016 
 
 .0624 
 
 .0657 
 
 .0033 
 
 3 
 
 .099-56 
 
 .0955 
 
 099 
 
 .0035 
 
 .0857 
 
 .0874 
 
 .0017 
 
 .0721 
 
 .0758 
 
 .0037 
 
 4 
 
 .112-48 
 
 .1082 
 
 .112 
 
 .0038 
 
 .0966 
 
 .0985 
 
 .0019 
 
 .0807 
 
 .0849 
 
 .0042 
 
 5 
 
 .125-44 
 
 .1210 
 
 .125 
 
 .0040 
 
 .1082 
 
 .1102 
 
 .0020 
 
 .0910 
 
 .0955 
 
 .0045 
 
 6 
 
 .138-40 
 
 .1338 
 
 .138 
 
 .0042 
 
 .1197 
 
 .1218 
 
 .0021 
 
 .1007 
 
 .1055 
 
 .0048 
 
 7 
 
 .151-36 
 
 .1466 
 
 .151 
 
 .0044 
 
 .1308 
 
 .1330 
 
 .0022 
 
 .1097 
 
 .1149 
 
 .0052 
 
 8 
 
 .164-36 
 
 .1596 
 
 .164 
 
 .0044 
 
 .1438 
 
 .146 
 
 .0022 
 
 .1227 
 
 .1279 
 
 .0052 
 
 9 
 
 .177-32 
 
 .1723 
 
 .177 
 
 .0047 
 
 .1544 
 
 .1567 
 
 .0023 
 
 .1307 
 
 .1364 
 
 .0057 
 
 10 
 
 .190-30 
 
 .1852 
 
 .190 
 
 .0048 
 
 .166 
 
 .1684 
 
 .0024 
 
 .1407 
 
 .1467 
 
 .0060 
 
 12 
 
 .216-28 
 
 .2111 
 
 .216 
 
 .0049 
 
 .1904 
 
 .1928 
 
 .0024 
 
 .1633 
 
 .1696 
 
 .0063 
 
 14 
 
 .242-24 
 
 .2368 
 
 .242 
 
 .0052 
 
 .2123 
 
 .2149 
 
 .0026 
 
 .1808 
 
 .1879 
 
 .0071 
 
 16 
 
 .268-22 
 
 .2626 
 
 .268 
 
 .0054 
 
 .2358 
 
 .2385 
 
 .0027 
 
 .2014 
 
 .209 
 
 .0076 
 
 18 
 
 .294-20 
 
 .2884 
 
 .294 
 
 .0056 
 
 .2587 
 
 .2615 
 
 .0028 
 
 .2208 
 
 .229 
 
 .0082 
 
 20 
 
 .320-20 
 
 .3144 
 
 .320 
 
 .0056 
 
 .2847 
 
 .2875 
 
 .0028 
 
 .2468 
 
 .255 
 
 .0082 
 
 22 
 
 .346-18 
 
 .3402 
 
 .346 
 
 .0058 
 
 .3070 
 
 .3099 
 
 .0029 
 
 .2649 
 
 .2738 
 
 .0089 
 
 24 
 
 .372-16 
 
 .366 
 
 .372 
 
 .0060 
 
 .3284 
 
 .3314 
 
 .0030 
 
 .281 
 
 .2908 
 
 .0098 
 
 26 
 
 .398-16 
 
 .392 
 
 .398 
 
 .0060 
 
 .3544 
 
 .3574 
 
 .0030 
 
 .307 
 
 .3168 
 
 .0098 
 
 28 
 
 .424-14 
 
 .4178 
 
 .424 
 
 .0062 
 
 .3745 
 
 .3776 
 
 .0031 
 
 .3204 
 
 .3312 
 
 .0108 
 
 30 
 
 .450-14 
 
 .4438 
 
 .450 
 
 .0062 
 
 .4005 
 
 .4036 
 
 .0031 
 
 .3464 
 
 .3572 
 
 .0108 
 
A. S. M. E. STANDARD TAPS. 
 
 235 
 
 A. S. M. E. Special Screws. 
 
 (All Dimensions in Inches.) 
 
 Old 
 
 No. 
 
 New. 
 
 Outside Diameters. 
 
 Pitch Diameters. 
 
 Root Diameters. 
 
 Outside 
 Diam. and 
 Threads 
 per In. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 *~j 
 
 0.073-64 
 
 0.0698 
 
 0.073 
 
 0.0032 
 
 0.0613 
 
 0.0629 
 
 0.0016 
 
 0.0494 
 
 0.0527|0.0033 
 
 2 
 
 .086-56 
 
 .0825 
 
 .086 
 
 .0035 
 
 .0727 
 
 .0744 
 
 .0017 
 
 .0591 
 
 .0628 
 
 .0037 
 
 3 
 
 .099-48 
 
 .0952 
 
 .099 
 
 .0038 
 
 .0836 
 
 .0855 
 
 .0019 
 
 .0677 
 
 .0719 
 
 .0042 
 
 4 
 
 .112-40 
 
 .1078 
 
 .112 
 
 .0042 
 
 .0937 
 
 .0958 
 
 .0021 
 
 .0747 
 
 .0795 
 
 .0048 
 
 
 36 
 
 .1076 
 
 .112 
 
 .0044 .0918 
 
 .0940 
 
 .0022 
 
 .0707 
 
 .0759 
 
 .0052 
 
 5 
 
 .125-40 
 
 .1208 
 
 .125 
 
 .0042 .1067 
 
 .1088 
 
 .0021 .0877 
 
 .0925 
 
 .0048 
 
 
 36 
 
 .1206 
 
 .125 .0044 .1048 
 
 .1070 
 
 .0022 .0837 
 
 .0889 
 
 .0052 
 
 6 
 
 .138-36 
 
 .1336 
 
 .138 .0044! .1178 
 
 .1200 
 
 .0022 .0967 
 
 .1019 .0052 
 
 
 32 
 
 .1333 
 
 .138; .0047! .1154 
 
 .1177 
 
 .0023 
 
 .0917 
 
 .0974 .0057 
 
 7 
 
 .151-32 
 
 .1463 
 
 .151 .0047 .1284 
 
 .1307 
 
 .0023 
 
 .1047 
 
 .1104 
 
 .0057 
 
 
 30 
 
 .1462 
 
 .151 .0048 .1270 
 
 .1294 
 
 .0024 
 
 .1017 
 
 .1077 
 
 .0060 
 
 8 
 
 .164-32 
 
 .1593 
 
 .164 .0047 .1414 
 
 .1437 
 
 .0023 
 
 .1177 
 
 .1234 
 
 .0057 
 
 
 30 
 
 .1592 
 
 .164 .0048 .1400 
 
 .1 424 
 
 .0024 
 
 .1147 
 
 .1207 
 
 .0060 
 
 9 
 
 .177-30 
 
 .1722 
 
 .177 .0048 .1529 
 
 .1553 
 
 .0024 
 
 .1277 
 
 .1337 
 
 .0060 
 
 
 24 
 
 .1718 
 
 .177 
 
 .0052 .1473 
 
 .1499 
 
 .0026 
 
 .1158 
 
 .1229 
 
 .0071 
 
 10 
 
 .190-32 
 
 .1853 
 
 .190 .0047 .1674 
 
 .1697 
 
 .0023 
 
 .1437 
 
 .1494 
 
 .0057 
 
 
 24 
 
 .1848 
 
 .190 .0052 .1603 
 
 .1629 
 
 .00261 .1288 
 
 .1359 
 
 .0071 
 
 12 
 
 .216-24 
 
 .21Q8 
 
 .216 
 
 .0052 .1863 
 
 .1889 
 
 .0026 
 
 .1548 
 
 .1619 
 
 .0071 
 
 14 
 
 .242-20 ! .2364 
 
 .242 
 
 .0056 .2067 
 
 .2095 
 
 .0028 
 
 .1688 
 
 .1770 
 
 .0032 
 
 16 
 
 .268-20 
 
 .2624 
 
 .268 
 
 .0056 .2327 
 
 .2355 
 
 .0028 
 
 .1948 
 
 .2030 
 
 .0082 
 
 18 
 
 .294-18 
 
 .2882 
 
 .294 
 
 .0058 .2550 
 
 .2579 
 
 .0029 
 
 .2129 
 
 .2218 
 
 .0089 
 
 20 
 
 .320-18 
 
 .3142 
 
 .320 
 
 .0058 .2810 
 
 .2839 
 
 .0029 
 
 .2389 
 
 .2478 
 
 .0089 
 
 22 
 
 .346-16 
 
 .3400 
 
 .346 
 
 .0060 
 
 .3024 
 
 .3054 
 
 .0030 
 
 .2550 
 
 .2648 
 
 .0098 
 
 24 
 
 .372-18 
 
 .3662 
 
 .372 
 
 .0058 .3330 
 
 .3359 
 
 .0029 
 
 .2909 
 
 .2998 
 
 .0089 
 
 26 
 
 .398-14 
 
 .3918 
 
 .398 
 
 .0062 .3485 
 
 .3516 
 
 .0031 
 
 .2944 
 
 .3052 
 
 .0108 
 
 28 
 
 .424-16 
 
 .4180 
 
 .424] .0060 
 
 .3804 
 
 .3834 
 
 .0030 
 
 .3330 
 
 .3428 .0098 
 
 30 
 
 .450-16 
 
 .4440 
 
 .450! .0060 .4064 
 
 .4094 .0030 
 
 .3590 
 
 .3688 
 
 .0098 
 
 A. S. M. E. Standard Taps. 
 
 (Corbin Screw Corporation.) 
 
 Size. 
 
 Outside Diameters. 
 
 Pitch Diameters. 
 
 Root Diameters. 
 
 Tap Drill 
 . Diameters. 
 
 No. 
 
 Out. Dia. 
 and 
 Thds. 
 per In. 
 
 Mini- 
 mum, 
 In. 
 
 Maxi- 
 mum, 
 In. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum, 
 In. 
 
 Maxi- 
 mum, 
 In. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum, 
 In. 
 
 Maxi- 
 mum, 
 In. 
 
 Dif- 
 fer- 
 ence. 
 
 
 
 0.060-80 
 
 0.0609 
 
 0.0632 
 
 0.0023 
 
 0.0528 
 
 0.0538 
 
 0.0010 
 
 0.0447 
 
 0.0466 
 
 0.0019 
 
 0.0465 
 
 1 
 
 .073-72 
 
 .0740 
 
 .0765 
 
 .0025 
 
 .0650 
 
 .0660 
 
 .0010 
 
 .0560 
 
 .0580 
 
 .0020 
 
 .0595 
 
 2 
 
 .086-64 
 
 .0871 
 
 .0898 
 
 .0027 
 
 .0770 
 
 .0781 
 
 .0011 
 
 .0668 
 
 .Oo89 
 
 .0021 
 
 .0700 
 
 3 
 
 .099-56 
 
 .1002 
 
 .1033 
 
 .0031 
 
 .0886 
 
 .0897 
 
 .0011 
 
 .0770 
 
 .0793 
 
 .0023 
 
 .0785 
 
 4 
 
 .112-48 
 
 .1133 
 
 .1168 
 
 .0035 
 
 .0998 
 
 .1010 
 
 .0012 
 
 .0862 
 
 .0887 
 
 .0025 
 
 .0890 
 
 5 
 
 .125-44 
 
 .1263 
 
 .1301 
 
 .0038 
 
 .1116 
 
 .1129 
 
 .0013 
 
 .0968 
 
 .0995 
 
 .0027 
 
 .0995 
 
 6 
 
 .138-40 
 
 .1394 
 
 .1435 
 
 .0041 
 
 .1232 
 
 .1246 
 
 .0014 
 
 .1069 
 
 .1097 
 
 .0028 
 
 .1100 
 
 7 
 
 .151-36 
 
 .1525 
 
 .1569 
 
 .0044 
 
 .1345 
 
 .1359 
 
 .0014 
 
 .1164 
 
 .1193 
 
 .0029 
 
 .1200 
 
 8 
 
 .164-36 
 
 .1655 
 
 .1699 
 
 .0044 
 
 .1475 
 
 .1489 
 
 .0014 
 
 .1294 
 
 .1323 
 
 .0029 
 
 .1360 
 
 9 
 
 .177-32 
 
 .1786 
 
 .1835 
 
 .0049 
 
 .1583 
 
 .1598 
 
 .0015 
 
 .1380 
 
 .1411 
 
 .0031 
 
 .1405 
 
 10 
 
 . 190-30 
 
 .1916 
 
 .1968 
 
 .0052 
 
 .1700 
 
 .1716 
 
 .0016 
 
 .1483 
 
 .1515 
 
 .0032 
 
 .1520 
 
 12 
 
 .216-28 
 
 .2176 
 
 .2232 
 
 .0056 
 
 .1944 
 
 .1961 
 
 .0017 
 
 .1712 
 
 .1745 
 
 .0033 
 
 .1730 
 
 14 
 
 .242-24 
 
 .2438 
 
 .2500 
 
 .0062 
 
 .2167 
 
 .2184 
 
 .0017 
 
 .1896 
 
 .1931 
 
 .0035 
 
 .1935 
 
 16 
 
 .268-22 
 
 .2698 
 
 .2765 
 
 .0067 
 
 .2403 
 
 .2421 
 
 .0018 
 
 .2108 
 
 .2144 
 
 .0036 
 
 .2130 
 
 18 
 
 .294-20 
 
 .2959 
 
 .3031 
 
 .0072 
 
 .2634 
 
 .2652 
 
 .0018 
 
 .2309 
 
 .2346 
 
 .0037 
 
 .2340 
 
 20 
 
 .320-20 
 
 .3219 
 
 .3291 
 
 .0072 
 
 .2894 
 
 .2912 
 
 .0018 
 
 .2569 
 
 .2606 
 
 .0037 
 
 .2610 
 
 22 
 
 .346-18 
 
 .3479 
 
 .3559 
 
 .0080 
 
 .3118 
 
 .3138 
 
 .0020! .2757 
 
 .27.96 
 
 .0039 
 
 .2810 
 
 24 
 
 .372-16 
 
 .374 
 
 .3828 
 
 .0088 
 
 .3334 
 
 .3354 
 
 .0020 
 
 .2928 
 
 .2968 
 
 .0040 
 
 .2968 
 
 26 
 
 .398-16 
 
 .400 
 
 .4088 
 
 .0088 
 
 .3594 
 
 .3614 
 
 .0020 
 
 .3188 
 
 .3228 
 
 .0040 
 
 .3230 
 
 28 
 
 .424-14 .4261 
 
 .4359 
 
 .0098 
 
 .3797 
 
 .3818 
 
 .00211 .3333 
 
 .3374 
 
 .0041 
 
 .3390 
 
 30 
 
 .450-14 
 
 .4521 
 
 .4619 
 
 -.0098 
 
 .4057 
 
 .4078 
 
 .00211 .3593 
 
 .3634 
 
 .0041 
 
 .3680 
 
236 
 
 MATERIALS. 
 
 A. S. M. E. Special Taps. 
 
 (Corbin Screw Corporation.) 
 
 Size. 
 
 Outside Diameters. 
 
 Pitch Diameters. 
 
 Root Diameters. 
 
 *t 
 
 No. 
 
 Out. Dia. 
 and 
 Thds. 
 
 Min., 
 In. 
 
 Max., 
 In. 
 
 Dif- 
 fer- 
 
 Min., 
 in. 
 
 Max., 
 In. 
 
 Dif- 
 fer- 
 
 Min., 
 In. 
 
 Max., 
 In. 
 
 Dif- 
 fer- 
 
 Q| 
 
 Sg 
 
 
 per In. 
 
 
 
 ence. 
 
 
 
 ence. 
 
 
 
 ence. 
 
 H M 
 
 j~ 
 
 0.073-64 
 
 0.0741 
 
 0.0768 
 
 0.0027 
 
 0.0640 
 
 0.0651 
 
 0.0011 
 
 0.0538 
 
 0.0559 
 
 0.0021 
 
 0550 
 
 2 
 
 .086-56 
 
 .0872 
 
 .09031 .0031 
 
 .0756 
 
 .0767 
 
 .0011 
 
 .0640 
 
 .0663 
 
 .00231 .0670 
 
 3 
 
 .099-48 
 
 .1003 
 
 .1038 
 
 .0035 
 
 .0868 
 
 .0880 
 
 .0012 
 
 .0732 
 
 .0757 
 
 .0025! 0760 
 
 4 
 
 .112-40 
 
 .1134 
 
 .1175 
 
 .0041 
 
 .0972 
 
 .0986 
 
 .0014 
 
 .0809 
 
 .08371 .0028 
 
 .0820 
 
 
 36 
 
 .1135 
 
 .1179 
 
 .0044 
 
 .0955 
 
 .0969 
 
 .0014 
 
 .0774 
 
 .0803! .0029 
 
 .0810 
 
 5 
 
 .125-40 
 
 .1264 
 
 .1305 
 
 .0041 
 
 .1102 
 
 .1116 
 
 .0014 
 
 .0939 
 
 .0967 
 
 .0028 
 
 .0980 
 
 
 36 
 
 . 1 2o5 
 
 .1309 
 
 .0044 
 
 .1085 
 
 .1099 
 
 .0014 
 
 .0904 
 
 .0933 
 
 .0029 
 
 .0935 
 
 6 
 
 .138-36 
 
 .13*> 
 
 .14:>y 
 
 .Ou44 
 
 .1215 
 
 .1229 
 
 .0014 
 
 .1034 
 
 .1003 
 
 .0029 
 
 .1065 
 
 
 32 
 
 .1395 
 
 .14*5 
 
 .00^9 
 
 .1193 
 
 .12u8 
 
 .0015 
 
 .0990 
 
 .1021 
 
 .0031 
 
 .1015 
 
 7 
 
 .151-32 
 
 .1526 
 
 .1575 
 
 .0049 
 
 .1323 
 
 .1338 
 
 .0015 
 
 .1120 
 
 .1151 
 
 .0031! .1160 
 
 
 30 
 
 .1526 
 
 .1578 
 
 .0052 
 
 .1310 
 
 .1326 
 
 .0016 
 
 .1093 
 
 .1125 
 
 .0032 .1130 
 
 8 
 
 .164-32 
 
 .1656 
 
 .1705 
 
 .0049 
 
 .1453 
 
 .1468 
 
 .0015 
 
 .1250 
 
 .1281 
 
 .0031 
 
 .1285 
 
 
 30 
 
 .1656 
 
 .1708 
 
 .0052 
 
 .1440 
 
 .1456 
 
 .0016 
 
 .1223 
 
 .1255 
 
 .0032 
 
 .1285 
 
 9 
 
 . 177-30 
 
 .1786 
 
 .1838 
 
 .0052 
 
 .1569 
 
 .1585 
 
 .0016 
 
 .1353 
 
 .1385 
 
 .0032 
 
 .1405 
 
 
 24 
 
 .1788 
 
 .1850 
 
 .0062 
 
 .1517 
 
 .1534 
 
 .0017 
 
 .1247 
 
 .1282 
 
 .0035 
 
 .1285 
 
 10 
 
 . 190-32 
 
 .1916 
 
 .1965 
 
 .0049 
 
 .1713 
 
 .1728 
 
 .0015 
 
 .1510 
 
 .1541 
 
 .0031 
 
 .1540 
 
 
 24 
 
 .1918 
 
 .1980 
 
 .0062 
 
 .1647 
 
 .1664 
 
 .0017 
 
 .1377 
 
 .1412 
 
 .0035 
 
 .1405 
 
 12 
 
 .216-24 
 
 .2178 
 
 .2240 
 
 .00o2 
 
 .1907 
 
 .1924 
 
 .0017 
 
 .1637 
 
 .1672 
 
 .0035 
 
 .1660 
 
 14 
 
 .242-20 
 
 .2439 
 
 .2511 
 
 .0072 
 
 .2114 
 
 .2132 
 
 .0018 
 
 .1789 
 
 .1826 
 
 .0037 
 
 .1820 
 
 16 
 
 .268-20 
 
 .2699 
 
 .2771 
 
 .0072 
 
 .2374 
 
 .2392 
 
 .0018 
 
 .2049 
 
 .2086 
 
 .0037 
 
 .2093 
 
 18 
 
 .294-18 
 
 .2959 
 
 .3039 
 
 .0080 
 
 .2598 
 
 .2618 
 
 .0020 
 
 .2237 
 
 .2276 
 
 .0039 .2280 
 
 20 
 
 .320-18 
 
 .3219 
 
 .3299 
 
 .0080 
 
 .2858 
 
 .2878 
 
 .0020 
 
 .2497 
 
 .2536 
 
 .0039 .2570 
 
 22 
 
 .346-16 
 
 .3480 
 
 .3568 
 
 .0088 
 
 .3074 
 
 .3094 
 
 .0020 
 
 .2668 
 
 .2708 
 
 .0040 
 
 .2720 
 
 24 
 
 .372-18 
 
 .3739 .3819 
 
 .0080 
 
 .3378 
 
 .3398 
 
 .0020 
 
 .3017 
 
 .3056 
 
 .0039 
 
 .3125 
 
 26 
 
 .398-14 
 
 .4u01 
 
 .4099 
 
 .0098 
 
 .3537 
 
 .3558 
 
 .0021 
 
 .3073 
 
 .3114 
 
 .0041 
 
 .3125 
 
 28 
 
 .424-16 
 
 .42oO 
 
 .4348 
 
 .0088 
 
 .3854 
 
 .3874 
 
 .0020 
 
 .3448 
 
 .3488 
 
 .0040 
 
 .3480 
 
 30 
 
 .450-16 
 
 .4520 
 
 .4dOo 
 
 .00o8 
 
 .4114 
 
 .4134 
 
 .0020 
 
 .3708 
 
 .3748 
 
 .0040 
 
 .3770 
 
 Wood Screws. 
 
 Two systems of wood screw threads are in common use, that of the 
 American Screw Co. and that of the Asa I. Cook Co. They are alike 
 as to diameters but differ in the number of threads per inch. 
 
 
 
 Threads 
 
 
 
 Threads 
 
 
 
 Threads 
 
 
 
 per In. 
 
 
 
 per In. 
 
 
 
 per In. 
 
 No. 
 
 Diam., 
 In. 
 
 po- 
 
 rt O 
 
 No. 
 
 Diam., 
 In. 
 
 llo 
 
 ^1; 
 
 No. 
 
 Diam., 
 In. 
 
 g CU o* 
 
 -i<? 
 
 
 
 <co 
 
 %u 
 
 
 
 <& 
 
 <! u 
 
 
 
 < 
 
 4Jo 
 
 
 
 0.058 
 
 32 
 
 30 
 
 11 
 
 0.203 
 
 12 
 
 12.5 
 
 22 
 
 0.347 
 
 7 
 
 7.5 
 
 1 
 
 .071 
 
 28 
 
 28 
 
 1? 
 
 .216 
 
 11 
 
 12 
 
 7.3 
 
 .361 
 
 7 
 
 
 2 
 
 .084 
 
 26 
 
 26 
 
 13 
 
 .229 
 
 11 
 
 11 
 
 24 
 
 .374 
 
 7 
 
 7 
 
 3 
 
 .097 
 
 24 
 
 24 
 
 14 
 
 .242 
 
 10 
 
 10 
 
 25 
 
 .387 
 
 7 
 
 
 4 
 
 .110 
 
 22 
 
 22 
 
 15 
 
 .255 
 
 10 
 
 9.5 
 
 7.6 
 
 .400 
 
 6 
 
 6.5 
 
 5 
 
 .124 
 
 20 
 
 20 
 
 16 
 
 .268 
 
 9 
 
 9 
 
 27 
 
 .413 
 
 6 
 
 
 6 
 
 .137 
 
 18 
 
 18 
 
 17 
 
 .282 
 
 9 
 
 8.5 
 
 78 
 
 .426 
 
 6 
 
 6.5 
 
 7 
 
 .150 
 
 16 
 
 17 
 
 18 
 
 .295 
 
 8 
 
 8 
 
 29 
 
 .439 
 
 6 
 
 
 8 
 
 .163 
 
 15 
 
 15 
 
 19 
 
 .308 
 
 8 
 
 
 30 
 
 .453 
 
 6 
 
 6 
 
 9 
 
 .176 
 
 14 
 
 14 
 
 ?0 
 
 321 
 
 8 
 
 7 5 
 
 
 
 
 
 10 
 
 .189 
 
 13 
 
 13 
 
 21 
 
 .334 
 
 8 
 
 
 
 
 
 
STANDARD STUDS. 
 
 237 
 
 Dimensions of Machine Screw Heads, A. S. M. E. Standard 
 
 FLAT HEAD. ROUND HEAD.* OVAL FILLISTER FLAT FILLIS- 
 
 (1) (2) HEAD. TER HEAD. 
 
 (3) (4) 
 
 * Form of head is semi-elliptical in axial cross section. 
 
 Dimensions 
 
 A = Diam. of Body. D = 
 B = Diam. of/ (1) 
 Head and rad. V2A -0.008 
 of oval (3J. 
 C = Height of i A -0.008 
 
 = Width of Slot 
 (2) 
 1.85A -0.005 
 
 0.7A 
 
 MC + o.oi 
 
 , = 0.173 A + 
 (3) 
 1.64A -0.009 
 
 0.66A -0.002 
 
 HF 
 0.134B +C 
 
 0.015. 
 (4) 
 1.64A -0.009 
 
 0.66A -0.002 
 
 1 AG 
 
 Head or Side V 1.739 
 of Head (3). I 
 E = Depth of Slot. K C 
 F = Height of ) 
 
 Head (3). I 
 
 
 
 
 H 
 
 B 
 
 B 
 
 C 
 
 C 
 
 C 
 
 
 E 
 
 E 
 
 E 
 
 E 
 
 F 
 
 
 (D 
 
 (2) 
 
 (3,4) 
 
 (D 
 
 (2) 
 
 (3,4) 
 
 D 
 
 (D 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (3) 
 
 0.0600.112 
 
 0.106 
 
 0.0894 
 
 0.030 
 
 0.042 
 
 0.03760.025 
 
 0.010 
 
 031 
 
 025 
 
 019 
 
 0.0496 
 
 .073i .138 
 
 .130 
 
 .1107 
 
 .037 
 
 .051 
 
 .0461 
 
 .028 
 
 .012 
 
 .035 
 
 .030 
 
 .023 
 
 .Oo09 
 
 .0861 .164 
 
 .154 
 
 .1320 
 
 .045 
 
 .060 
 
 ..0548 .030 
 
 .015 
 
 040 
 
 036 
 
 027 
 
 .0725 
 
 099 
 
 190 
 
 ,178 
 
 .1530 
 
 052 
 
 .069 
 
 .0633 .032 
 
 017 
 
 044 
 
 04? 
 
 03? 
 
 .0838 
 
 .112 
 
 .216 
 
 .202 
 
 .1747 
 
 .060 
 
 .078 
 
 .0719 .034 
 
 .020 
 
 .049 
 
 .048 
 
 .036 
 
 .0953 
 
 .125 
 
 .242 
 
 .226 
 
 .1960 
 
 .067 
 
 .087 
 
 .0805 
 
 .037 
 
 .022 
 
 053 
 
 053 
 
 .040 
 
 .1068 
 
 .138 
 
 .268 
 
 .250 
 
 .2170 .075 
 
 .097 
 
 .0890 
 
 .039 
 
 .025 
 
 .058 
 
 .059 
 
 .044 
 
 .1180 
 
 .151 
 
 .294 
 
 .274 
 
 .2386 .082 
 
 .106 
 
 .0976 
 
 .041 
 
 .027 
 
 063 
 
 065 
 
 .049 
 
 .1296 
 
 .164 
 
 .320 
 
 .298 
 
 .2599; .090 
 
 .115 
 
 .1062 
 
 .043 
 
 .030 
 
 .067 
 
 .071 
 
 .053 
 
 .1410 
 
 .177 
 
 .346 
 
 . 322 
 
 . 2813 
 
 .097 
 
 .124 
 
 .1148 .046 
 
 .032 
 
 .072 
 
 .076 
 
 .057 
 
 .1524 
 
 .190 
 
 .372 
 
 .346 
 
 .3026 
 
 .105 
 
 .133 
 
 .1234 .048 
 
 035 
 
 076 
 
 082 
 
 062 
 
 .1639 
 
 .216 
 
 .424 
 
 .394 
 
 .3452 
 
 .120 
 
 .151 
 
 .1405 
 
 .052 
 
 .040 
 
 .085 
 
 .093 
 
 .070 
 
 .1868 
 
 .242 
 
 .476 
 
 .443 
 
 .3879 
 
 135 
 
 .169 
 
 .1577 .057 
 
 045 
 
 094 
 
 105 
 
 079 
 
 .2097 
 
 .268 
 
 .528 
 
 .491 
 
 .4305 .150 
 
 .188 
 
 .17^8 .061 
 
 .050 
 
 .104 
 
 .116 
 
 .087 
 
 .2325 
 
 .294 
 
 .580 
 
 .539 
 
 .4731 .164 
 
 .206 
 
 .1920 
 
 .066 
 
 .055 
 
 .113 
 
 .128 
 
 .0% 
 
 .2554 
 
 .320 
 
 .632 
 
 .587 
 
 .5158 
 
 179 
 
 .224 
 
 .2092 
 
 070 
 
 060 
 
 .122 
 
 .140 
 
 .104 
 
 .2783 
 
 .346 
 
 684 
 
 635 
 
 .5584 .194 
 
 .242 
 
 .2263' .075 
 
 065 
 
 131 
 
 150 
 
 113 
 
 .3011 
 
 .372 
 
 .736 
 
 .683 
 
 .6010 .209 
 
 .260 
 
 .2435S .079 
 
 .070 
 
 .140 
 
 .162 
 
 .122 
 
 .3240 
 
 .398 
 
 .788 
 
 731 
 
 .6437 .224 
 
 .279 
 
 .2606 .084 
 
 075 
 
 149 
 
 ,173 
 
 .130 
 
 .3469 
 
 .424 
 
 .840 
 
 .779 
 
 .6863 .239 
 
 .297 .2778 .088 
 
 .080 
 
 .158 
 
 .185 
 
 .139 
 
 .3698 
 
 .450 .892 
 
 .827 
 
 .7290 .254 
 
 .315 
 
 .2950 .093 .0851 .167 
 
 .196 
 
 .147 
 
 .3927 
 
 Standard Studs. The Ups9n Nut Co., Cleveland, gives (1914) the 
 f9llowing formulae for the dimensions of standard stud bolts with 
 either V or U. S. Standard threads: A = diam. of stud; B = 
 length of short thread ; C = length of unthreaded portion ; D = length 
 of long thread; E = total length of stud, all in inches. B = A -\- 1 A\ 
 C = A; D = E- (B+ C). 
 
238 
 
 MATERIALS. 
 
 Dimensions of Standard Set and Cap-Screws. 
 
 Compiled from tables of leading manufacturers. All dimensions 
 in inches. D = short diam. of head, square and hex. heads, or diam. 
 of round head; L = maximum length, I = minimum length under head; 
 //, r, maximum and minimum length over all; H = length of head. 
 
 Diam. of Screws . . . 
 Threads per In .... 
 
 Vs 
 40 
 
 VlG 
 
 24 
 
 V4 
 
 20 
 
 Vie 
 18 
 
 3 /8 
 
 16 
 
 VlG 
 
 14 
 
 ^ 
 or 13 
 
 VlG 
 
 12 
 
 5 /8 
 11 
 
 3 /4 
 
 10 
 
 Vs 
 9 
 
 1 
 
 8 
 
 IVs 
 7 
 
 V4 
 
 7 
 
 Sq. Head j ? 
 Set-Screws. |j" 
 
 
 
 V 
 
 V 2 
 
 *i. 
 Vs 
 
 Vs 
 
 V2 
 
 ' 
 
 5 /8 
 
 V2 
 
 5 /8 
 
 9 /16 
 
 3 /4 
 
 Vs 
 4V 2 
 
 3 /4 
 
 V 4 
 4 3 / 4 
 
 V 5 s 
 
 1V4 
 
 1 
 5 
 
 IVs 
 
 U/8 
 1 3 /4 
 
 IV, 
 
 
 
 
 
 Sq. Head 
 Cap-Screws. 
 
 D 
 H 
 L 
 
 Z 
 
 
 
 Vs 
 
 * 
 
 3 /4 
 
 7/16 
 VlG 
 
 3 /4 
 
 V 2 
 
 $ 
 
 3 /4 
 
 V2 
 
 ^ 
 
 3 /4 
 
 > 
 3 /8 
 
 3 /4 
 
 Via 
 
 ^ 
 
 3 /4 
 
 5 /8 
 
 Vi 
 
 3 /4 
 3 /4 
 
 
 
 3 /4 
 
 n /16 
 V 4 !G 
 
 1 
 
 13 /16 
 
 $ 
 
 i 
 
 3 /4 
 
 Vs 
 
 4V2 
 
 Vs 
 4% 
 
 IV4 
 
 '/: 
 
 1V 2 
 
 T 
 
 ! 3 /4 
 
 IVs 
 IVs 
 
 2 
 
 1V 2 
 
 T 
 
 
 
 
 
 LL ^ 
 
 1^1 
 
 Hexagon 
 Head 
 Cap-Screws. 
 
 D 
 H 
 L 
 
 I 
 
 VlG 
 
 ^ 
 3 /4 
 
 5 /8 
 
 ' 
 
 3 /4 
 
 Vs 
 Vs 
 4V 2 
 
 1 
 
 3 /4 
 
 tf: 
 
 IVs 
 V 5 s 
 
 IV* 
 
 T 
 1V4 
 
 IVs 
 IVs 
 
 2 
 
 IVs 
 IV, 
 
 2 
 
 
 
 
 
 Round and 
 Filister 
 Head 
 Cap-Screws. 
 
 D 
 H 
 L 
 
 I 
 
 ''? 
 
 3 /4 
 
 V 4 
 
 % 
 
 Vs 
 V 4 
 
 ^ 
 
 5// 16 
 
 $! 
 
 3 /4 
 
 9 /16 
 3 /8 
 
 3 /4 
 
 % 
 4 # 
 
 3 /4 
 
 ' 
 
 3 /4 
 
 w/i, 
 
 
 1 
 
 ? 
 
 n/4 
 
 i< 
 
 iVj 
 
 IVs 
 Vs 
 6 
 
 1V4 
 
 1V4 
 
 6 
 2 
 
 
 
 Flat Head f 9, 
 Cap-Screws. | 
 
 V4 
 1/4 
 
 3 /4 
 
 Vs 
 
 3 /4 
 
 2ft 
 
 3 /4 
 
 6 /8 
 2V4 
 3 /4 
 
 V 
 
 3 /4 
 
 13 /16 
 1 
 
 Vs 
 
 n/4 
 
 1 
 
 3 
 
 U/2 
 
 IVs 
 
 ! 3 /4 
 
 'i 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Button-Head 
 Cap-Screws. 
 
 D 
 L 
 
 I 
 
 7 /32 
 1V4 
 3 /4 
 
 VlG 
 3 /4 
 
 VlG 
 
 % 
 
 Vl6 
 2V2 
 3 /4 
 
 5 /8 
 2 3 /4 
 3 /4 
 
 
 
 3 /4 
 
 13 /16 
 1 
 
 15 /16 
 IV4 
 
 1 
 
 3 
 
 1V 
 
 
 
 1 3 /4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Socket Set-Screws, 
 Length. 
 
 
 
 
 U /32 
 
 Vl6 
 
 Va 
 
 9 /16 
 
 Vs 
 
 n /16 
 
 Vs 
 
 1 
 
 IV4 
 
 
 
 
 
 
 
 
 
 Threads are U. S. Standard. On all cap-screws of 1 in. and less in 
 diam. and 4 in. long and under, threads are cut % of the length of body; 
 longer than 4 in. threads are cut 1 A of the length of body. Lengths 
 advance by y in. from minimum to maximum. 
 
 Oval Head Rivets Approximate Number in One Pound 
 
 (Garland Nut & Rivet Co., Pittsburgh.) 
 
 Diam. 
 
 7/16 
 
 3/8 
 
 Vl6 
 
 V4 
 
 3/16 
 
 1/8 
 
 Diam. 
 
 7/16 
 
 3/8 
 
 5/16 
 
 V4 
 
 3/16 
 
 V8 
 
 Length 
 
 
 
 
 
 
 
 Length 
 
 
 
 
 
 
 
 V4 
 
 
 
 
 123 
 
 262 
 
 630 
 
 15/8 
 
 101/2 
 
 16 
 
 23 
 
 40 
 
 71 
 
 166 
 
 3/8 
 
 
 
 56 
 
 102 
 
 210 
 
 500 
 
 1 3/8 
 
 10 
 
 15 
 
 21 
 
 36 
 
 68 
 
 160 
 
 1/2 
 
 21 " ' 
 
 34" 
 
 49 
 
 9Q 
 
 177 
 
 415 
 
 17/8 
 
 91/2 
 
 141/2 
 
 20 
 
 35 
 
 62 
 
 145 
 
 5/8 
 
 19 
 
 30 
 
 45 
 
 78 
 
 150 
 
 350 
 
 2 
 
 9 
 
 14 
 
 18 
 
 32 
 
 60 
 
 140 
 
 3/4 
 
 17 
 
 27 
 
 39 
 
 70 
 
 132 
 
 300 
 
 21/4 
 
 81/2 
 
 13 
 
 16 
 
 29 
 
 55 
 
 
 V8 
 
 16 
 
 24 
 
 35 
 
 6* 
 
 110 
 
 280 
 
 21/2 
 
 8 
 
 12 
 
 15 
 
 27 
 
 48 
 
 
 1 
 
 15 
 
 22 
 
 33 
 
 56 
 
 100 
 
 250 
 
 23/4 
 
 71/2 
 
 11 
 
 14 
 
 25 
 
 44 
 
 
 1 Vs 
 
 14 
 
 21 
 
 31 
 
 50 
 
 96 
 
 
 3 
 
 
 10 
 
 13 
 
 23 
 
 42 
 
 
 H/4 
 
 13 
 
 20 
 
 27 
 
 46 
 
 88 
 
 205 
 
 31/2 
 
 6 
 
 9 
 
 12 
 
 20 
 
 
 
 '13/8 
 
 12 
 
 18 
 
 26 
 
 44 
 
 80 
 
 
 4 
 
 
 8 
 
 
 18 
 
 ... 
 
 ... 
 
 H/2 
 
 11 
 
 17 
 
 24 
 
 42 
 
 77 
 
 J78 
 
 
 
 
 
 
 
 
 Small rivets are made to fit holes of their rated size; the actual diameter 
 may vary slightly from the decimals given below: 
 
 Size 3/ 32 7/64 l/ 8 9/64 5/33 11/ M 3/ 10 
 
 Approx. diam 094 .109 125 .140 .155 .170 .185 
 
 Size 7/32 1/4 9/32 5/ ie 3/g 7/ ie 
 
 Approx. diam,,., 215 .245 ,275 .305 ,365 .425 
 
WEIGHT OF RIVETS. 
 
 239 
 
 Weight of 100 Cone Head Rivets. 
 
 (Hoopes & Townsend, Philadelphia, 1914.) 
 
 L'gth 
 Under 
 
 Scant Diameter, In. 
 
 Head 
 In. 
 
 Vl 
 
 9 /16 
 
 5 /s 
 
 U/16 
 
 3 /4 
 
 13 /16 
 
 7 /8 
 
 1 
 
 U/8* 
 
 11/4* 
 
 3/4 
 
 8.6 
 
 11 .9 
 
 15.5 
 
 
 
 
 
 
 
 
 7/8 
 
 9.3 
 
 12.7 
 
 16.5 
 
 
 
 
 
 
 
 
 1 
 
 9.9 
 
 13.6 
 
 17.6 
 
 22.4 
 
 28.1 
 
 34 5 
 
 
 
 
 
 1 l/ 8 
 
 10.6 
 
 14.4 
 
 18.6 
 
 23.6 
 
 29.6 
 
 36.3 
 
 
 
 
 
 1 V4 
 
 11 2 
 
 15.2 
 
 19.6 
 
 24.9 
 
 31 1 
 
 38 1 
 
 46 
 
 65 
 
 
 
 13/8 
 
 11 .9 
 
 16.1 
 
 20.7 
 
 26.1 
 
 32.6 
 
 39.8 
 
 48 
 
 68 
 
 93 
 
 
 1 V2 
 
 12.5 
 
 16.9 
 
 21 .7 
 
 27.4 
 
 34. 
 
 41 .6 
 
 50 
 
 70 
 
 96 
 
 J27 
 
 15/8 
 
 13.2 
 
 17.7 
 
 22.7 
 
 28.6 
 
 35.6 
 
 43 .4 
 
 52 
 
 73 
 
 100 
 
 132 
 
 13/4 
 
 13.8 
 
 18.6 
 
 23.8 
 
 29.9 
 
 37.1 
 
 45.1 
 
 54 
 
 76 
 
 103 
 
 136 
 
 17/8 
 
 14.5 
 
 19.4 
 
 24.8 
 
 31.1 
 
 38.6 
 
 46.9 
 
 56 
 
 78 
 
 107 
 
 -140 
 
 2 
 
 15.1 
 
 20.2 
 
 25.8 
 
 32.4 
 
 40.1 
 
 48.7 
 
 58 
 
 81 
 
 110 
 
 145 
 
 21/8 
 
 15.8 
 
 21 :0 
 
 26.9 
 
 33.7 
 
 41.6 
 
 50.5 
 
 60 
 
 84 
 
 114 
 
 149 
 
 21/4 
 
 16.4 
 
 21.9 
 
 27.9 
 
 34.9 
 
 43.1 
 
 52.2 
 
 62 
 
 87 
 
 117 
 
 153 
 
 23/8 
 
 17.1 
 
 22.7 
 
 28.9 
 
 36.2 
 
 44.6 
 
 54.0 
 
 64 
 
 89 
 
 121 
 
 158 
 
 21/2 
 
 17.8 
 
 23.5 
 
 30.0 
 
 37.4 
 
 46.1 
 
 55.8 
 
 66 
 
 92 
 
 124 
 
 162 
 
 25/8 
 
 18.4 
 
 24.4 
 
 31.0 
 
 38.7 
 
 47.6 
 
 57.5 
 
 68 
 
 95 
 
 128 
 
 166 
 
 23/4 
 
 19.1 
 
 25.2 
 
 32.0 
 
 39.9 
 
 49.1 
 
 59.3 
 
 70 
 
 97 
 
 132 
 
 171 
 
 27/8 
 
 19.7 
 
 26.0 
 
 33.1 
 
 41 .2 
 
 50.6 
 
 61.1 
 
 72 
 
 100 
 
 135 
 
 175 
 
 3 
 
 20.4 
 
 26.9 
 
 34.1 
 
 42.5 
 
 52. 
 
 62.8 
 
 74 
 
 103 
 
 139 
 
 179 
 
 31/4 
 
 21.7 
 
 28.5 
 
 36.2 
 
 45.0 
 
 55. 
 
 66.4 
 
 78 
 
 108 
 
 146 
 
 188 
 
 31/2 
 
 22.9 
 
 30.2 
 
 38.2 
 
 47.5 
 
 58. 
 
 69.9 
 
 83 
 
 114 
 
 153 
 
 197 
 
 33/4 
 
 24.3 
 
 31.9 
 
 40.3 
 
 50.0 
 
 61. 
 
 73.4 
 
 87 
 
 119 
 
 160 
 
 205 
 
 4 
 
 25.6 
 
 33.5 
 
 42.4 
 
 52.5 
 
 64. 
 
 77.0 
 
 91 
 
 124 
 
 167 
 
 214 
 
 41/4 
 
 26.9 
 
 35.2 
 
 44.4 
 
 55.0 
 
 67. 
 
 80.5 
 
 95 
 
 130 
 
 174 
 
 223 
 
 41/2 
 
 28.2 
 
 36.9 
 
 46.5 
 
 57.5 
 
 70. 
 
 84.0 
 
 99 
 
 135 
 
 181 
 
 232 
 
 43/4 
 
 29.5 
 
 38.5 
 
 48.6 
 
 60.0 
 
 73. 
 
 87.6 
 
 103 
 
 141 
 
 188 
 
 240 
 
 5 
 
 30.8 
 
 40.2 
 
 50.6 
 
 62.6 
 
 76. 
 
 91 .1 
 
 107 
 
 146 
 
 195 
 
 249 
 
 51/4 
 
 32.1 
 
 41 .9 
 
 52.7 
 
 65.1 
 
 .79. 
 
 94.6 
 
 1 1 1 
 
 151 
 
 202 
 
 258 
 
 51/2 
 
 33.4 
 
 43.5 
 
 54.8 
 
 67.6 
 
 82. 
 
 98.2 
 
 115 
 
 157 
 
 209 
 
 266 
 
 53/4 
 
 34.7 
 
 45.2 
 
 56.8 
 
 70.1 
 
 85. 
 
 101.7 
 
 120 
 
 162 
 
 216 
 
 275 
 
 6 
 
 36.0 
 
 46.8 
 
 58.9 
 
 72.6 
 
 88. 
 
 105.2 
 
 124 
 
 167 
 
 223 
 
 284 
 
 6l/ 2 
 
 38.7 
 
 50.2 
 
 63.0 
 
 77.6 
 
 94. 
 
 112.3 
 
 132 
 
 178 
 
 237 
 
 301 
 
 7 
 
 41.3 
 
 53.5 
 
 67.2 
 
 82.7 
 
 100^ 
 
 119.4 
 
 140 
 
 189 
 
 251 
 
 319 
 
 Wgt. 
 
 
 
 
 
 
 
 
 
 
 
 of 
 
 4.7 
 
 6.9 
 
 9.3 
 
 12.3 
 
 16.1 
 
 20.4 
 
 26 
 
 38 
 
 54 
 
 75 
 
 Hds. 
 
 
 
 
 
 
 
 
 
 
 
 * All Rivets larger than one inch are made to exact diameter. 
 
 Tinners' Rivets. Flat Heads. (Garland Nut & Rivet Co.) 
 
 k 
 
 i 
 
 ! 
 
 b 
 
 j? 2 
 
 | d 
 
 S M 
 
 A 
 
 P 
 
 2 
 
 3 s 
 
 S M 
 
 * 
 
 f* 
 g 2 
 
 31bs. 
 
 31/2 
 
 5 
 6 
 
 7 ' 
 
 Id 
 
 er 
 
 ji 
 
 ~s> . 
 
 p 
 
 l| 
 - 
 
 8 
 9 
 10 
 12 
 14 
 16 
 
 0.070 
 .080 
 .090 
 .094 
 J01 
 .109 
 
 1/8 
 9/64 
 5/32 
 H/64 
 3/16 
 3/16 
 
 4 oz. 
 6 
 8 
 10 
 12 
 14 
 
 0.115 
 .120 
 .125 
 .133 
 .140 
 .147 
 
 13/64 
 
 7/32 
 15/64 
 1/4 
 17/64 
 9/32 
 
 1 lb. 
 
 1 V4 
 1 1/2 
 ,3 /4 
 
 21/2 
 
 0.160 
 .163 
 .173 
 .185 
 .200 
 .215 
 
 5/16 
 21/64 
 H/32 
 3/8 
 25/64 
 13/32 
 
 0.225 
 .230 
 .233 
 .253 
 .275 
 .293 
 
 7/16 
 29/ 6 4 
 15/32 
 1/2 
 33/64 
 17/32 
 
240 
 
 MATERIALS. 
 
 Shearing Value, Area of Rivets, and Bearing Value of Riveted Plates. 
 
 Shearing Value = Area of Rivet X Allowable Shearing Stress Per Sq. In. 
 Bearing Value = Diameter of Rivet X Thickness of Plate X Allowable 
 Bearing Stress Per Square Inch. 
 
 Di- 
 am. 
 of 
 Riv- 
 et. 
 In. 
 
 Area. 
 Sq. 
 In. 
 
 Single 
 Shear 
 6,000 
 Lbs. 
 Sq.In. 
 
 Double 
 Shear 
 6,000 
 Lbs. 
 Sq.In. 
 
 Bearing Value for Different Thicknesses of Plate 
 in Inches at 1 2,000 Lb. per Square Inch. 
 
 i /4 
 
 In. 
 
 Vie 
 In. 
 
 /8 
 In. 
 
 Vl6 
 
 In. 
 
 J/2 
 In. 
 
 Vs 
 In. 
 
 Vl 
 In. 
 
 Vs 
 In. 
 
 1 
 In. 
 
 V2 
 5/8 
 3/4 
 
 Vs 
 
 0.1964 
 0.3068 
 0.4418 
 0.6013 
 0.7854 
 
 1178 
 1841 
 2651 
 3608 
 4712 
 
 2356 
 3682 
 5301 
 7216 
 9425 
 
 1500 
 1875 
 
 1875 
 2344 
 2813 
 
 2250 
 2813 
 3375 
 3938 
 
 2625 
 3281 
 3938 
 4594 
 5250 
 
 3000 
 3750 
 
 
 
 
 4688 
 5625 
 
 
 
 
 2250 
 2625 
 3000 
 
 4500 
 5250 
 6000 
 
 6750 
 7875 
 
 
 
 3281 
 3750 
 
 6563 
 
 9188 
 10500 
 
 12000 
 
 4500 
 
 75001 
 
 900(J| 
 
 Di- 
 am. 
 of 
 Riv- 
 et, 
 In. 
 
 Area, 
 Sq. 
 In. 
 
 Single 
 Shear 
 7,500 
 Lbs. 
 Sq. 
 In. 
 
 Double 
 Shear 
 7,500 
 Lbs. 
 . Sq. 
 In. 
 
 2945 
 4602 
 6627 
 9020 
 11781 
 
 Bearing Value for Different Thicknesses of Plate 
 in Inches at 15,000 Lbs. per Square Inch. 
 
 1/4 
 In. 
 
 Vl6 
 
 In. 
 
 J/8 
 In. 
 
 Vie 
 In. 
 
 y* 
 
 In. 
 
 Vs 
 In. 
 
 J/4 
 In. 
 
 T /8 
 
 In. 
 
 1 
 In. 
 
 V2 
 
 5/8 
 3/4 
 
 ,' /8 
 
 0.1964 
 0.3068 
 0.4418 
 0.6013 
 0.7854 
 
 1473 
 2301 
 3313 
 4510 
 5891 
 
 1875 
 2344 
 
 2344 
 2930 
 3516 
 
 2813 
 3516 
 4219 
 4922 
 5625] 
 
 3781 
 
 3750 
 
 
 
 
 
 4102 
 4922 
 5742 
 6563 
 
 4688 
 
 5859 
 7031 
 
 8438 
 9844 
 
 11484 
 13125 
 
 15000 
 
 2813 
 3281 
 3750 
 
 5625 
 6563 
 7500 
 
 4102 
 4688 
 
 8203 
 9375 
 
 11 250J 
 
 Di- 
 am. 
 of 
 Riv- 
 et, 
 In. 
 
 V2 
 5/8 
 3/4 
 
 V8 
 
 Area, 
 Sq. 
 In. 
 
 Single 
 Shear 
 10,000 
 Lbs. 
 Sq. 
 In. 
 
 Double 
 Shear 
 10,000 
 Lbs. 
 Sq. 
 In. 
 
 Bearing Value for Different Thicknesses of Plate 
 in Inches at 20,000 Lbs. per Square Inch. 
 
 i /4 
 
 In. 
 2500 
 3125 
 
 Vl6 
 In. 
 
 3l25 
 3906 
 
 4688 
 
 Vs 
 In. 
 
 37501 
 4688 
 5625 
 6563 
 7500 
 
 Vl6 
 
 In. 
 
 1/2 
 
 In. 
 
 Vs 
 In. 
 
 V< 
 In. 
 
 T /8 
 
 In. 
 
 1 
 
 In. 
 
 0.1964 
 0.3068 
 0.4418 
 0.6013 
 0.7854 
 
 1964 
 3068 
 4418 
 6013 
 7854 
 
 3927 
 6136 
 8836 
 12026 
 15708 
 
 4375 
 
 5000 
 6250 
 
 
 
 
 
 5469 
 
 7813 
 9375 
 
 11250 
 13125 
 
 
 .... 
 
 3750 
 4375 
 5000 
 
 6563 
 7656 
 8750 
 
 7500 
 8750 
 10000 
 
 5469 
 6256 
 
 10938 
 12500 
 
 15313 
 17500 
 
 20000 
 
 15000| 
 
 Dia. 
 of 
 Riv- 
 et. 
 
 371? 
 
 1/4- 
 5/16 
 11/32 
 3/8 
 Vl6 
 
 Area 
 in 
 Square 
 Inches. 
 
 6,000 Lbs. 
 per Sq. In. 
 
 Bearing Value for Different Thicknesses of Plate 
 in Inches at 1 2,000 Lb. per Square Inch. 
 
 Single 
 Shear 
 
 Double 
 Shear. 
 
 Vs 
 In. 
 
 3 /l 6 
 
 In. 
 
 i /4 
 
 In. 
 
 Vl6 
 
 In. 
 
 n /32 
 
 In. 
 
 ' Vs 
 In. 
 
 Vl6 
 In. 
 
 0.0274 
 0.0491 
 0.0764 
 0.0924 
 0.1104 
 0.1499 
 
 164 
 295 
 458 
 554 
 662 
 899 
 
 328 
 589 
 917 
 1109 
 1325 
 1799 
 
 281 
 375 
 
 468 
 
 42?. 
 
 
 
 
 
 563 
 703 
 
 750 
 938 
 
 
 
 
 
 1172 
 1289 
 1406 
 
 
 
 
 515 
 563 
 656 
 
 773 
 
 844 
 984 
 
 1031 
 1125 
 1313 
 
 1418 
 1547 
 1804 
 
 
 
 1687 
 1969 
 
 2297 
 
 1640 
 
 All bearing values above or to right of zigzag lines are greater than 
 double shear. Values between upper and lower zigzag lines are less 
 than double and greater than single shear. Values below and to left 
 of lower zigzag lines are less than single shear. 
 
WEIGHT OF LAG SCREWS 
 
 241 
 
 LENGTH OF RIVETS REQUIRED FOR VARIOUS GRIPS 
 
 (American Bridge Co. Standard Dimensions in Inches.) 
 
 Grip 
 a 
 
 Diameter, In. 
 
 Grip 
 b 
 
 Diameter, In. 
 
 1/2 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 1/2 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 1/2 
 
 1 1/2 
 
 13/4 
 
 17/8 
 
 2 
 
 21/8 
 
 1/2 
 
 1/8 
 
 "Tl/4 
 
 1 V4 
 
 13/8 
 
 Ts7 8 
 
 5/8 
 
 15/8 
 
 17/8 
 
 2 
 
 21/8 
 
 21/4 
 
 5/8 
 
 1/4 
 
 1 3/8 
 
 1 3/8 
 
 1 V2 
 
 1 1/2 
 
 3/4 
 
 13/4 
 
 2 
 
 21/8 
 
 21/4 
 
 23/g. 
 
 3/4 
 
 3/8 
 
 H/2 
 
 1 V2 
 
 1 5/8 
 
 15/8 
 
 7/8 
 
 17/8 
 
 21/8 
 
 21/4 
 
 23/8 
 
 21/2 
 
 7/8 
 
 1/2 
 
 15/8 
 
 15/8 
 
 13/4 
 
 1 3/4 
 
 1 
 
 2 
 
 21/4 
 
 23/ 8 
 
 21/2 
 
 25/ 8 
 
 1 
 
 5/8 
 
 13/4 
 
 13/4 
 
 1 7/8 
 
 1 7/8 
 
 1/4 
 
 21/4 
 
 21/2 
 
 25/ 8 
 
 23/4 
 
 27/8 
 
 1/4 
 
 7/8 
 
 2 
 
 2 
 
 21/8 
 
 21/8 
 
 1/2 
 
 25/ 8 
 
 27/ 8 
 
 3 
 
 3 1/8 
 
 31/4 
 
 1/2 
 
 21/8 
 
 21/4 
 
 23/8 
 
 23/ 8 
 
 21/2 
 
 3/4 
 
 3 
 
 31/4 
 
 33/ 8 
 
 31/2 
 
 35/ 8 
 
 3/4 
 
 21/2 
 
 2 5/8 
 
 23/4 
 
 23/4 
 
 27/ 8 
 
 2 
 
 31/4 
 
 31/2 
 
 35/ 8 
 
 33/4 
 
 37/ 8 
 
 2 
 
 23/ 4 
 
 27/ 8 
 
 3 
 
 3 
 
 31/8 
 
 1/4 
 
 31/2 
 
 33/4 
 
 37/ 8 
 
 4 
 
 41/8 
 
 1/4 
 
 3 
 
 31/8 
 
 31/4 
 
 31/4 
 
 33/ 8 
 
 1/2 
 
 33/4 
 
 4 
 
 41/8 
 
 4 1/4 
 
 43/8 
 
 1/2 
 
 3 1/4 
 
 33/ 8 
 
 31/2 
 
 31/2 
 
 35/8 
 
 3/4 
 
 4 
 
 41/4 
 
 '43/ 8 
 
 41/2 
 
 45/ 8 
 
 3/4 
 
 31/2 
 
 35/3 
 
 33/4 
 
 33/4 
 
 37/ 8 
 
 3 
 
 43/ 8 
 
 45/8 
 
 43/ 4 
 
 47/ 8 
 
 5 
 
 3 
 
 37/g 
 
 4 
 
 4 
 
 41/8 
 
 41/4 
 
 1/4 
 
 45/g 
 
 47/ 8 ; 5 
 
 51/8 
 
 51/4 
 
 1/4 
 
 41/8 
 
 41/4 
 
 41/4 
 
 43/8 
 
 41/2 
 
 1/2 
 
 47/8 
 
 51/8 
 
 51/4 
 
 53/8 
 
 51/2 
 
 1/2 
 
 43/ 8 
 
 41/2 
 
 41/2 
 
 45/8 
 
 43/4 
 
 3/4 
 
 51/8 
 
 53/ 8 
 
 51/2 
 
 55/8 
 
 53/4 
 
 3/4 
 
 45/ 8 
 
 43/4 
 
 43/4 
 
 47/8 
 
 5 
 
 4 
 
 53/8 
 
 55/8 
 
 53/4 
 
 57/ 8 
 
 6 
 
 4 
 
 47/ 8 
 
 5 
 
 5 
 
 51/8 
 
 51/4 
 
 1/4 
 
 53/ 4 
 
 6 
 
 61/8 
 
 61/4 
 
 63/ 8 
 
 1/4 
 
 51/4 
 
 53/ 8 
 
 53/ 8 
 
 51/2 
 
 55/8 
 
 1/2 
 
 61/8 
 
 6 3/8 
 
 61/2 
 
 65/8 
 
 63/4 
 
 1/2 
 
 55/ 8 
 
 53/4 
 
 53/4 
 
 53/4 
 
 57/8 
 
 3/4 
 
 63/ 8 
 
 65/8 
 
 63/4 
 
 67/ 8 
 
 7 
 
 3/4 
 
 57/ 8 
 
 6 
 
 6 
 
 6 
 
 61/8 
 
 5 
 
 65/8 
 
 67/g 
 
 7 
 
 71/8 
 
 71/4 
 
 5 
 
 61/8 
 
 61/4 
 
 61/4 
 
 61/4 
 
 63/8 
 
 Weight of 100 Lag Screws. 
 
 (Hoopes & Townsend, Philadelphia, 1914.) 
 
 
 Diameter, Inches. 
 
 Vl6 
 
 3 /8 
 
 Vl8 
 
 V 2 
 
 9 /16 
 
 5/8 
 
 3 /4 
 
 7 /8 
 
 1 
 
 H/8 
 
 iV 4 
 
 Length Under Head to Point. 
 
 Ib. 
 4.2 
 4.7 
 5.2 
 5.7 
 6.2 
 7.2 
 8.2 
 9.2 
 10.2 
 11.3 
 12.4 
 13.5 
 
 Ib. 
 6.5 
 7.1 
 7.7 
 8.4 
 9.2 
 10.6 
 12.0 
 13.5 
 15.0 
 16.5 
 18.0 
 19.5 
 
 Ib. 
 9.2 
 10.0 
 10.9 
 11.8 
 12.7 
 14.6 
 16.6 
 18.8 
 20.7 
 22.8 
 24.9 
 27.0 
 31.1 
 35.2 
 
 Ib. 
 13.0 
 13.8 
 14.9 
 16.1 
 17.4 
 19.0 
 21.5 
 24.0 
 26.5 
 29.0 
 31.5 
 34.0 
 39.0 
 44.0 
 49.0 
 54.0 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 
 
 
 
 
 
 
 23.0 
 24.5 
 26.0 
 29.2 
 32.5 
 35.9 
 39.3 
 42.7 
 46.1 
 49.5 
 56.3 
 63.1 
 69.9 
 76.7 
 83.5 
 90.5 
 
 24.8 
 27.3 
 29.0 
 32.9 
 36.9 
 41.0 
 44.9 
 48.8 
 52.7 
 56.6 
 64.5 
 72.5 
 80.5 
 88.5 
 96.5 
 104.5 
 112.5 
 121.0 
 129.5 
 138.0 
 
 
 
 
 
 
 
 
 
 
 
 43.0 
 48.3 
 53.8 
 59.6 
 65.5 
 71.5 
 77.5 
 83.5 
 95.5 
 107.6 
 119.8 
 131.0 
 143.1 
 155.4 
 167.6 
 179.8 
 192.0 
 204.0 
 
 
 
 
 
 75.0 
 78.5 
 82.0 
 86.0 
 90.0 
 98.0 
 106.0 
 122.5 
 139.0 
 155.5 
 172.0 
 188.5 
 205.0 
 221.5 
 238.0 
 255.0 
 272.0 
 
 "96" 
 99 
 108 
 118 
 128 
 138 
 158 
 178 
 198 
 219 
 240 
 261 
 282 
 304 
 326 
 348 
 
 
 
 
 
 150 
 163 
 176 
 203 
 230 
 257 
 284 
 311 
 338 
 365 
 393 
 421 
 449 
 
 '246' 
 270 
 300 
 332 
 365 
 395 
 425 
 459 
 493 
 527 
 562 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Thds. 
 per in. 
 
 10 
 
 7 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4V2 
 
 4V2 
 
 3 
 
 3 
 
 3 
 
242 
 
 MATERIALS 
 
 Approximate Weight of Machine Bolts per 100, Square Heads and 
 Square Nuts. (Hoopes & Townsend, Philadelphia, 1914.) 
 
 Length Under 
 Head to 
 Point, In. 
 
 Diameter. 
 
 In! 
 
 4/8 
 In. 
 
 7/16 
 In. 
 
 1/2 
 In. 
 
 Vie 
 
 In. 
 
 V8 
 In. 
 
 3/4 
 In. 
 
 7/8 
 In. 
 
 In. 
 
 H/4 
 In. 
 
 11/2 
 In. 
 
 13/4 
 In. 
 
 2 
 
 In. 
 
 H/4 
 
 3.1 
 
 8.4 
 
 12.5 
 
 17.7 
 
 24.3 
 
 30.7 
 
 50.4 
 
 
 
 
 
 
 
 
 [1 V2 
 
 3.4 
 
 9.2 
 
 13.6 
 
 19.1 
 
 26.0 
 
 32.8 
 
 53.5 
 
 
 
 
 
 
 
 2 
 
 4.1 
 
 10.8 
 
 15.7 
 
 21.8 
 
 29.5 
 
 37.1 
 
 59.7 
 
 89.4 
 
 125.7 
 
 
 
 
 
 21/2 
 
 4.8 
 
 12.3 
 
 17.8 
 
 24.6 
 
 33.0 
 
 41.4 
 
 65.9 
 
 97.3 
 
 136.8 
 
 246.3 
 
 
 
 
 3 
 
 5.5 
 
 13.8 
 
 19.9 
 
 27.4 
 
 36.5 
 
 45.7 
 
 72.1 
 
 105.7 
 
 147.8 263.5 
 
 '476 
 
 
 
 31/2 
 
 6.2 
 
 15.3 
 
 21.8 
 
 29.8 
 
 40.0 
 
 50.0 
 
 78.3 
 
 114.2 
 
 158.9: 280.8 
 
 495 
 
 
 
 4 
 
 6.9 '16.9 
 
 24.0 
 
 32.6 
 
 43.5 
 
 54.4 
 
 84.5 
 
 122.6 
 
 169.9 298.1 
 
 520 
 
 720 
 
 
 41/2 
 
 7.5! 18.4 
 
 26.1 
 
 35.4 
 
 46.7 
 
 58.3 
 
 90.3 
 
 H0.5 
 
 179.4 314.1 
 
 545 
 
 753 
 
 
 5 
 
 8.2 19.9 
 
 28.2 
 
 38.1 
 
 50.2 
 
 62.6 
 
 96.5 
 
 138.9 
 
 190.4 331.4 
 
 570 
 
 786 
 
 1180 
 
 5l/ 2 
 
 8.9'21.5 
 
 30.3 
 
 40.9 
 
 53.7 
 
 66.9 
 
 102.7 
 
 147.4201.5 348.6 595 
 
 820 
 
 1225 
 
 6 
 
 9.6'23.0 
 
 32.4 
 
 43.7 
 
 57.2 
 
 71.3 
 
 108.9 
 
 155.8 
 
 212.5 365.9 620 
 
 854 
 
 1270 
 
 61/2 
 
 10.3 
 
 24.6 
 
 34.5 
 
 46.4 
 
 60.7 
 
 75.6 
 
 115.1 
 
 164.3223.6 383.1 645 
 
 888 
 
 1315 
 
 7 
 
 11.0 
 
 26.1 
 
 36.6 49.2 
 
 64.2 
 
 79.9 
 
 121.3 
 
 172.7 234.6 400.4 670 
 
 922 
 
 1360 
 
 71/2 
 
 11.7 
 
 27.7 
 
 38.8 51.9 
 
 67.6 
 
 84.2 
 
 127.6 
 
 181.2 
 
 245.6 417.7 
 
 695 
 
 956 
 
 1405 
 
 8 
 
 12.4 
 
 29.2 
 
 40.9 54.7 
 
 71.1 
 
 88.5 
 
 133.8 
 
 189 .6 256.71 434.9 
 
 725 
 
 990 
 
 1450 
 
 9 
 
 13.7 
 
 32.4 
 
 44.9 60.0 
 
 77.8 
 
 96.8 
 
 145.7 
 
 205 .9 278.0 468.2 
 
 775 
 
 1058 
 
 1540 
 
 10 
 
 15.1 
 
 35.5 
 
 49.1 1 65.5 
 
 84.8 
 
 105.4 
 
 158.2 
 
 222.8 
 
 300.0 
 
 502.7 
 
 825 
 
 1126 
 
 1630 
 
 11 
 
 16.5 
 
 38.6 
 
 53.4 71.0 
 
 91.8 
 
 114.1 
 
 170.6 
 
 239.8322.2 
 
 537.3 
 
 875 
 
 1194 
 
 1720 
 
 12 
 
 17.941.7 
 
 57.6 
 
 76.5 
 
 98.8 122.7 
 
 183.0 
 
 256.7 
 
 344.3 
 
 571.8 
 
 925 
 
 1262 
 
 1810 
 
 13 
 14 
 
 19.3144.8 
 20.6547.9 
 
 61.8 82.0 
 66.0 87.6 
 
 105.5 131.0 195.4 
 112.51139.6207.9 
 
 273.6 ( 366.3 
 290.5388.4 
 
 606.3 
 640.8 
 
 975 
 1025 
 
 1330 
 1398 
 
 1900 
 1990 
 
 15 
 
 22.051.0 
 
 70.3 93.1 
 
 119.5J 148 .2 220 .3 
 
 307.4410.5 
 
 675.3 
 
 1075 
 
 1468 2080 
 
 16 
 
 23.454.1 
 
 74.5 98.6 
 
 126.4 
 
 156.9 
 
 232.7 
 
 324.3 
 
 432.6 
 
 709.8 
 
 1125 
 
 1536 
 
 2170 
 
 17 
 
 24.857.2 
 
 78.7 104.1 
 
 133.4 
 
 165.5245.1 
 
 341.2454.7 
 
 744.3 
 
 1175 
 
 1604 2260 
 
 18 
 
 26.260.3 
 
 82.9 109.7 
 
 140.4 174.1 
 
 257 .6 1 358.1 
 
 476.8 
 
 778.9 
 
 1225 
 
 1672 2350 
 
 20 
 
 28.966.5 
 
 91.4 120.7 
 
 154.4 191.4 
 
 282.4 392.0 
 
 521.0 
 
 847.9 1325 
 
 1808 
 
 2530 
 
 22 
 
 31.772.7 
 
 99.9 131.7 
 
 168.4208.6307.3 
 
 425.8565.1 
 
 916.9 1425 
 
 19442710 
 
 24 
 
 34.4 78.9 
 
 108.3 142.8 
 
 182.4 
 
 225.9 
 
 332.1 
 
 459.6 
 
 609.3 
 
 986.01525 
 
 2080 
 
 2890 
 
 26 
 
 37.2 85.2 
 
 116.8 153.8 
 
 196.3 
 
 243.1 
 
 357.0 
 
 493.4653.5 
 
 1055.0 16252216 3070 
 
 28 
 
 40.091.4 
 
 125.2 164.9 
 
 210.3 
 
 260.4381.8 
 
 527 .3 697 .7 1124.0 17252352 
 
 3250 
 
 30 
 
 42.7 97.6 
 
 133.7 175.9 
 
 224.3 
 
 277.7 406.7 
 
 561. 1 741 .9i 1193 .01825 2488 3450 
 
 Weight per 1 00 Nuts. 
 
 Square 
 Hexagon 
 
 Diff. 
 
 0.7 
 0.6 
 
 0.1 
 
 2.5 
 2.1 
 
 ~QA 
 
 3.9 
 3.2 
 
 ~07 
 
 5.7 
 
 4.8 
 
 ~<K9 
 
 8.1 
 6.7 
 
 1.4 
 
 9.9 
 
 8.3 
 
 1.6 
 
 16.8 
 14.0 
 
 26.9 
 22.3 
 
 4.6 
 
 40.1 
 33.4 
 
 ~6.7 
 
 77.8 
 64.0 
 
 162 
 134 
 
 28 
 
 257 
 207 
 
 50 
 
 381 
 307 
 
 74 
 
 2.8 
 
 13.8 
 
 Weight of 100 Heads. 
 
 Square 
 Hexagon 
 
 0.8 
 0.7 
 
 2.4 
 2.2 
 
 4.01 5.9 
 
 3.5 5.3 
 
 8.8 
 7.9 
 
 11.4 
 10.3 
 
 20.0 
 17.0 
 
 31.4 
 28.2 
 
 44.9 
 39.4 
 
 90.9 
 83.9 
 
 144 
 132 
 
 231 
 215 
 
 345 
 302 
 
 Diff. 
 
 0.1 
 
 0.2 
 
 0.5] 0.6 
 
 0.9 
 
 1.1 
 
 3.0 
 
 3.2 
 
 5.5 
 
 7.0 
 
 12 
 
 16 
 
 43 
 
 For Weight of Bolts with Hex. Heads and Hex. Nuts. 
 Subtract | 0.2 | 0.6| 1 .2| 1.5| 2.3| 2.7| 5.81 7.8| 12.2| 20 8[ 40| 66| 117 
 
 Sizes of Cast Washers. (Upson Nut Co., Cleveland, 1914 ) 
 
 Diam. 
 
 Hole. 
 
 Thick. 
 
 Bolt. 
 
 Weight. 
 Lbs. 
 
 Diam. 
 
 Hole. 
 
 Thick. 
 
 Bolt. 
 
 Weight. 
 Lbs. 
 
 In. 
 21/4 
 23/4 
 
 31/2 
 
 In. 
 
 l',l 
 T* 
 
 In. 
 
 11/16 
 3/4 
 
 13/16 
 
 7/8 
 
 In. 
 
 1/2 
 5/8 
 3/4 
 
 7/8 
 
 V2 
 
 5/8 
 3/4 
 
 11/4 
 
 In. 
 
 4 
 41/2 
 
 6 
 
 In. 
 
 U/8 
 H/4 
 13/8 
 13/4 
 
 In. 
 
 15/16 
 
 U/8 
 H/4 
 
 In. 
 1 
 U/8 
 H/4 
 11/2 
 
 15/ 8 
 
 T 
 
WBOUGHT WASHERS. 
 
 243 
 
 Weight and Dimensions of Hanger Bolts. 
 
 (Hoopes & Townsend, Philadelphia, 1914.) 
 
 One end cut with deep wood screw thread, the other fitted with a 
 standard cold punched, chamfered and trimmed square nut. 
 
 Diameter, In. 
 
 Vl 
 
 5/8 
 
 3 /4 
 
 7 /8 
 
 1 
 
 1 1/8 
 
 1 1/4 
 
 13/g 
 
 M/2 
 
 Length Over All, In. 
 
 ~ 
 
 Approximate Weight per 100. 
 
 4 
 6 
 8 
 10 
 12 
 14 
 16 
 
 24 
 34 
 44 
 54 
 
 
 
 
 
 
 
 
 
 53 
 67 
 81 
 95 
 
 80 
 97 
 114 
 134 
 154 
 
 106 
 138 
 166 
 196 
 226 
 256 
 
 
 
 
 
 
 174 
 217 
 259 
 295 
 329 
 
 257 
 299 
 332 
 374 
 417 
 
 301 
 351 
 401 
 451 
 501 
 
 456 
 511 
 566 
 621 
 
 532 
 597 
 677 
 747 
 
 
 
 
 Threads per inch: 
 Nut end 
 
 13 
 6 
 
 11 
 5 
 
 10 
 
 41/2 
 
 9 
 
 41/2 
 
 8 
 3 
 
 7 
 3 
 
 7 
 3 
 
 6 
 
 21/2 
 
 6 
 
 21/2 
 
 Screw end 
 
 Turnbuckles. 
 
 (Cleveland City Forge and Iron Co.) 
 Standard sizes made with right and left threads. D = outside diamete^ 
 
 FIG. 76. 
 
 of screw. A = length in clear between heads = 6 ins. for all sizes, 
 B = length of tapped heads = 1 1/2 D nearly. C = 6 ins. + 3 D nearly- 
 
 Wrought Washers, Manufacturers' Standard. 
 
 (Upson Nut Co., Cleveland, 1914.) 
 
 
 
 |0 
 
 
 
 
 13 
 
 
 
 |0 
 
 
 , 
 
 13 
 
 6 
 
 o> 
 
 1^ 
 
 
 .So 
 
 if 
 
 i 
 
 o> 
 
 _o 
 
 ^ 
 
 S 
 
 If 
 
 .2 
 
 'o 
 
 is w 
 
 'o 
 
 Q 
 
 
 
 
 'o 
 
 
 2 
 
 o~~ 
 
 53 
 
 b 
 
 B 
 
 p 
 
 W 
 
 55 
 
 r 
 
 5 
 
 W 
 
 H 
 
 W 
 
 ^ 
 
 ^ 
 
 In. 
 
 In. 
 
 No. 
 
 In. 
 
 
 
 In. 
 
 In. 
 
 No 
 
 In. 
 
 
 
 9/16 
 
 1/4 
 
 18 
 
 3/16 
 
 39400 
 
 2.53 
 
 21/2 
 
 1 Vl6 
 
 8 
 
 1 
 
 568 
 
 176 
 
 3/4 
 
 5/16 
 
 16 
 
 V4 
 
 15600 
 
 6.4 
 
 23/4 
 
 
 8 
 
 H/8 
 
 473 
 
 211 
 
 7/8 
 
 3/8 
 
 16 
 
 5/16 
 
 11250 
 
 8.8 
 
 3 
 
 13/8 
 
 8 
 
 U/4 
 
 364 
 
 261 
 
 1 
 
 7/16 
 
 14 
 
 3/8 
 
 6800 
 
 14.7 
 
 31/4 
 
 H/2 
 
 7 
 
 13/8 
 
 275 
 
 364 
 
 M/4 
 
 1/2 
 
 14 
 
 7/16 
 
 4300 
 
 21. 
 
 31/2 
 
 1V8 
 
 7 
 
 H/2 
 
 256 
 
 390 
 
 13/8 
 
 9/16 
 
 12 
 
 1/2 
 
 2600 
 
 38.4 
 
 33/4 
 
 13/4 
 
 7 
 
 15/8 
 
 220 
 
 454 
 
 H/2 
 
 5/8 
 
 12 
 
 9/16 
 
 2250 
 
 44.4 
 
 4 
 
 17/8 
 
 7 
 
 13/4 
 
 197 
 
 508 
 
 13/4 
 
 H/16 
 
 10 
 
 5/8 
 
 1300 
 
 77. 
 
 41/4 
 
 2 
 
 7 
 
 17/8 
 
 174 
 
 575 
 
 2 
 
 13/16 
 
 9 
 
 3/4 
 
 900 
 
 111. 
 
 41/2 
 
 21/8 
 
 7 
 
 2 
 
 160 
 
 625 
 
 21/4 
 
 15/16 
 
 8 
 
 7 /8 
 
 782 
 
 153. 
 
 43/4 
 
 23/8 
 
 5 
 
 21/4 
 
 122 
 
 820 
 
 
 
 
 
 
 
 5 
 
 25/8 
 
 4 
 
 21/2 
 
 106 
 
 943 
 
244 
 
 MATERIALS. 
 
 Track Bolts and V. S. Standard Hexagon Nuts, Sizes and Weights for 
 Different Weights of Kail. (Upson Nut Co., Cleveland, 1914.) 
 
 Size of Bolts, In. 
 
 Diam. of Nuts, 
 In. 
 
 .d 
 
 fM W) 
 
 d 
 
 1 
 
 Size of Bolts, In. 
 
 Diam. of Nuts, 
 In. 
 
 i* 
 
 d 
 
 .2 
 
 c 
 
 ~3 
 
 pq 
 
 00 
 
 Diam. of Nuts, 
 In. 
 
 !i 
 
 d 
 
 Kegs per Mile, 
 4-bolt Joint. 
 
 Rails 70 to lOOlb. per Yard. 
 
 Rails-45 to 85 lb. per Yard. 
 
 Rails 20to 301b. per Yard. 
 
 X5 
 
 X43/4 
 
 X 4 1/2 
 X 4 1/4 
 X4 
 
 X33/4 
 
 X31/2 
 X31/4 
 X3 
 
 7/8 X 5 1/2 
 7/8 X 5 1/4 
 7/8X5 
 7/8 X 4 3/4 
 7/8 X 4 1/2 
 7/8 X 4 1/4 
 7/8X4 
 
 15/8 
 15/8 
 15/8 
 15/8 
 15/8 
 15/8 
 15/8 
 15/8 
 15/8 
 1 7/18 
 1 7/15 
 17/13 
 17/16 
 17/16 
 17/16 
 17/16 
 
 110 
 115 
 120 
 125 
 130 
 H5 
 140 
 145 
 150 
 143 
 148 
 153 
 158 
 163 
 168 
 173 
 
 13.0 
 12.3 
 11.8 
 11.2 
 10.8 
 10.4 
 10.0 
 9.7 
 94 
 9.8 
 95 
 9.2 
 89 
 8.6 
 8.4 
 8.1 
 
 XXXXXXXXXXXXXX 
 
 tinue 
 
 1/4 
 
 V4 
 
 1/4 
 
 1/4 
 1/4 
 V4 
 1/4 
 1/4 
 1/4 
 1/4 
 1/4 
 
 d) 
 205 
 210 
 215 
 220 
 225 
 230 
 235 
 240 
 247 
 254 
 257 
 260 
 266 
 283 
 
 6.8 
 6.7 
 6.6 
 6.4 
 6.3 
 6.2 
 6.1 
 6.0 
 5.8 
 5.7 
 5.6 
 55 
 5.3 
 5.0 
 
 5/8 X 2 1/4 
 5/8X2 
 1/2X3 
 
 1/2X23/4 
 1/2 X 2 1/2 
 1/2 X 2 1/4 
 1/2X2 
 
 1/16 
 H/16 
 
 7/8 
 7/8 
 7/8 
 7/8 
 7/8 
 
 495 
 525 
 715 
 737 
 760 
 800 
 820 
 
 2.8 
 2.7 
 
 ^9 
 .8 
 .7 
 
 Rails 12 to 161b. per Yd. 
 
 V2 X 1 3 /4 
 1/2 X 1 V2 
 1/2 X 1 3/8 
 1/2 X 1 V4 
 3/8X2 
 3/8 X 1 3/4 
 3/8 X 1 V2 
 
 7/8 
 7/8 
 7/8 
 7/8 
 H/16 
 H/16 
 H/16 
 
 890 
 980 
 1070 
 1160 
 1590 
 1710 
 1830 
 
 .6 
 .4 
 .2 
 .2 
 .0 
 .0 
 .0 
 
 Rails 30 to 40 lb. per Yard. 
 
 Rails 45 to 85 lb. per Yard. 
 
 3/4 X 2 3/4 
 3/4 X 2 1/2 
 5/8 X 3 1/2 
 5/8 X 3 1/4 
 5/8X3 
 5/8 X 2 3/4 
 5/8 X 2 1/2 
 
 H/4 
 V4 
 1/16 
 1/16 
 1/16 
 1/16 
 1/16 
 
 300 
 317 
 375 
 392 
 410 
 435 
 465 
 
 4.7 
 4.4 
 3.8 
 3.6 
 3.4 
 3.2 
 30 
 
 Rails 8 to 121b. per Yard. 
 
 7/8X37/ 8 
 7/8X33/4 
 7/8 X 3 1/2 
 7/8 X 3 1/4 
 7/8X3 
 3/4 X 5 3/4 
 
 17/16 
 17/16 
 17/16 
 17/16 
 17/16 
 H/4 
 
 178 
 183 
 188 
 193 
 198 
 200 
 
 79 
 7.7 
 7.5 
 7.3 
 7.1 
 7.0 
 
 3/8 X 1 1/4| H/16 
 
 2010 
 
 1.0 
 
 Length and Number of Cut Nails to the Pound. 
 
 Size. 
 
 Length. 
 
 Common. 
 
 Clinch. 
 
 Fence. 
 
 Finishing. 
 
 g 
 
 E 
 
 
 
 M 
 
 1 
 u 
 
 k 
 
 1 
 
 
 Tobacco. 
 
 Cut Spikes. 
 
 3/ 4 
 
 3/ 4 in. 
 
 
 
 
 
 
 800 
 
 
 
 
 
 v 
 
 7/ 8 
 
 
 
 
 
 
 500 
 
 
 
 
 
 2d 
 
 
 800 
 
 
 
 1100 
 
 1000 
 
 376 
 
 
 
 
 
 3d 
 
 1 1/4 
 
 480 
 
 
 
 720 
 
 760 
 
 224 
 
 
 
 
 
 4d 
 
 1 1/2 
 
 288 
 
 
 
 523 
 
 368 
 
 180 
 
 398 
 
 
 
 
 5d 
 
 1 >i 
 
 200 
 
 
 
 410 
 
 
 
 
 
 130 
 
 
 6d 
 7d 
 
 2 '' 
 
 2i/ 4 
 
 168 
 124 
 
 95 
 
 74 
 
 84 
 64 
 
 268 
 188 
 
 
 
 224 
 
 126 
 98 
 
 96 
 82 
 
 
 8d 
 9d 
 
 2V 2 
 
 23/4 
 
 88 
 70 
 
 62 
 53 
 
 48 
 36 
 
 146 
 130 
 
 
 
 128 
 110 
 
 75 
 65 
 
 68 
 
 
 lOd 
 
 ^ '* 
 
 58 
 
 46 
 
 30 
 
 102 
 
 
 
 91 
 
 55 
 
 
 28 
 
 12d 
 
 31/4 
 
 44 
 
 42 
 
 24 
 
 76 
 
 
 
 71 
 
 40 
 
 
 
 16d 
 
 3 I'/o 
 
 34 
 
 38 
 
 20 
 
 62 
 
 
 
 54 
 
 27 
 
 
 22 
 
 20d 
 
 4 
 
 23 
 
 33 
 
 16 
 
 54 
 
 
 
 40 
 
 
 
 14V2 
 
 30d 
 
 4 l /9 
 
 18 
 
 20 
 
 
 
 
 
 33 
 
 
 
 121/2 
 
 40d 
 
 5 " 
 
 14 
 
 
 
 
 
 
 27 
 
 
 
 9V2 
 
 50d 
 
 51/2 
 
 10 
 
 
 
 
 
 
 
 
 
 8 
 
 60d 
 
 6 _ 
 
 8 
 
 
 
 
 
 
 
 
 
 6 
 
EAILROAD MATERIAL. 
 
 245 
 
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 m 
 
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246 
 
 NUMBER OF WIRE NAILS PER POUND. 
 
 APPROXIMATE NUMBER OF WIRE NAILS PER POUND. 
 
 (American Steel and Wire Co., ] 908.) 
 
 
 
 These approximate numbers are an average only, 
 and the figures given may be varied either way by 
 changes in the dimensions of the heads or points 
 Brads and no-head nails will run more to the pound 
 than the table shows, and large or thick-headed 
 nails will run less. 
 
 Length, Inches. 
 
 - 
 
 jj :::::::::::: 
 
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 o ^r^^^ 
 
 rj- ^ 10 NO 1^ ON 
 
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 ^ 
 
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 n*ss-a8=sssg55a||| ; = ; 
 
 5 
 
 sS9S3Kss;sRs$?;aas5^KR| ; : 
 
 !S^ . . 
 
 - 
 
 - 1 ;Rsssi2SH|^=Ss||||g| | 
 
 2 
 
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 10 
 
 ONt-,OMo r> <N oo r>s NO vN 
 
 r<i ON NO o T f 
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STEEL WIRE NAILS. 
 
 247 
 
248 
 
 MATERIALS. 
 
 WROUGHT SPIKES. 
 
 Number of Nails in Keg of 150 Pounds. 
 
 Length, 
 Inches. 
 
 V4 in. 
 
 5 /16 in. 
 
 3/8 in. 
 
 Length, 
 Inches. 
 
 1/4 in. 
 
 5 /i6 in. 
 
 3/8 in. 
 
 7/i6 in. 
 
 1/2 in. 
 
 3 
 
 2250 
 
 
 
 7 
 
 1161 
 
 662 
 
 482 
 
 445 
 
 306 
 
 31/2 
 
 1890 
 
 1208 
 
 
 8 
 
 
 635 
 
 455 
 
 34 
 
 256 
 
 4 
 
 41/9 
 
 1650 
 1464 
 
 1135 
 1064 
 
 
 9 
 10 
 
 
 573 
 
 424 
 391 
 
 300 
 270 
 
 240 
 222 
 
 5 
 
 1380 
 
 930 
 
 "742 
 
 11 
 
 
 
 
 249 
 
 203 
 
 6 
 
 1292 
 
 868 
 
 570 
 
 12 
 
 
 
 
 236 
 
 180 
 
 For sizes and weights of wire spikes see Steel Wire Nails, page 235. 
 
 BOAT SPIKES. 
 
 Number in Keg of 200 Pounds. 
 
 Length. 
 
 1/4 
 
 5/16 
 
 3/8 
 
 V2 
 
 
 2375 
 
 
 
 
 
 2050 
 
 1230 
 
 940 
 
 
 6 * 
 
 1825 
 
 1175 
 
 800 
 
 450 
 
 
 
 990 
 
 650 
 
 375 
 
 8 ' .. . . 
 
 
 880 
 
 600 
 
 333 
 
 9 * . .., 
 
 
 
 525 
 
 300 
 
 10 " 
 
 
 
 475 
 
 275 
 
 WIRES OF DIFFERENT METALS AND ALLOYS. 
 
 (J. Bucknall Smith's Treatise on Wire.) 
 
 Brass Wire is commonly composed of an alloy of 1 % to 2 parts of 
 copper to one part of zinc. The tensile strength ranges from 20 to 40 
 tons per square inch, increasing with the percentage of zinc in the alloy. 
 
 German or Nickel Silver, an alloy of copper, zinc, and nickel, is 
 practically brass whitened by the addition of nickel. It has been 
 drawn into wire as fine as 0.002 inch diameter. 
 
 Platinum wire may be drawn into the finest sizes. On account of its 
 high price its use is practically confined to special scientific instruments 
 and electrical appliances in which resistances to high temperature, 
 oxygen, and acids are essential. It expands less than other metals 
 when heated. Its coefficient of expansion being almost the same as 
 that of glass permits its being sealed in glass \v ithout fear of cracking 
 the latter. It is therefore used in incandescent electric lamps. 
 
 Phosphor-bronze Wire contains from 2 to 6 per cent of tin and 
 from 1/20 to i/s per cent of phosphorus. The presence of phosphorus 
 is detrimental to electric conductivity. 
 
 "Delta-metal" wire is made from an alloy of copper, iron, and zinc, 
 Its strength ranges from 45 to 62 tons per square inch. It is used for 
 some kinds of wire rope, also for wire gauze. It is not subject to 
 deposits of verdigris. It has great toughness, even when its tensile 
 strength is over 60 tons per square inch. 
 
 Aluminum Wire. Specific gravity 2.68. Tensile strength between 
 10 and 15 tons per square inch. It has been drawn as fine as 11,401 
 yards to the ounce, or 0.042 grain per yard. 
 
 Aluminum Bronze, 90 copper, 10 aluminum, has high strength and 
 ductility; is inoxidizable, sonorous. Its electric conductivity is 12.6 
 per cent. See page 396. 
 
 Silicon Bronze, patented in 1882 by L. Weiler of Paris, is made as 
 follows: Fluosilicate of potash, pounded glass, chloride of sodium and 
 calcium, carbonate of soda and lime, are heated in a plumbago crucible, 
 and after the reaction takes place the contents are thrown into the 
 molten bronze to be treated. Silicon-bronze wire has a conductivity 
 of from 40 to 98 per cent of that of copper wire and four times more 
 than that of iron, while its tensile strength is nearly that of steel, or 
 
 (Continued on page 250.) 
 
PROPERTIES OF STEEL WIRE. 
 
 249 
 
 PROPERTIES OF STEEL WIRE. 
 
 (John A. Roebling's Sons Co., 1908.) 
 
 No., 
 Roebling 
 Gauge. 
 
 Diam., 
 in. 
 
 Area, 
 square 
 inches. 
 
 Breaking 
 strain, 100, 
 000 Ib. per 
 sq. inch. 
 
 Weight in pounds. 
 
 Feet in 
 2000 Ib. 
 
 Per 
 1000ft. 
 
 Per 
 
 mile. 
 
 000000 
 
 0.460 
 
 0.166191 
 
 16,619 
 
 558.4 
 
 2,948 
 
 3,582 
 
 00000 
 
 0.430 
 
 0.145221 
 
 14,522 
 
 487.9 
 
 2,576 
 
 4,099 
 
 0000 
 
 393 
 
 0.121304 
 
 12,130 
 
 407.6 
 
 2,152 
 
 4,907 
 
 000 
 
 0.362 
 
 0.102922 
 
 10,292 
 
 345.8 
 
 1,826 
 
 5,783 
 
 00 
 
 0.331 
 
 0.086049 
 
 8,605 
 
 289.1 
 
 1,527 
 
 6,917 
 
 
 
 0.307 
 
 0.074023 
 
 7,402 
 
 248.7 
 
 1,313 
 
 8,041 
 
 1 
 
 0.283 
 
 0.062902 
 
 6,290 
 
 211.4 
 
 1,116 
 
 9,463 
 
 2 
 
 0.263 ' 
 
 0.054325 
 
 5,433 
 
 182.5 
 
 964 
 
 10,957 
 
 3 
 
 0.244 
 
 0.046760 
 
 4,676 
 
 157.1 
 
 830 
 
 12,730 
 
 4 
 
 0.225 
 
 0.039761 
 
 3,976 
 
 133.6 
 
 705 . 
 
 14,970 
 
 5 
 
 0.207 
 
 0.033654 
 
 3,365 
 
 113.1 
 
 597 
 
 17,687 
 
 6 
 
 0.192 
 
 0.028953 
 
 2,895 
 
 97.3 
 
 514 
 
 20,559 
 
 7 
 
 0.177 
 
 0.024606 
 
 2,461 
 
 82.7 
 
 437 
 
 24,191 
 
 v 8 
 
 0.162 
 
 0.020612 
 
 2,061 
 
 69.3 
 
 366 
 
 28,878 
 
 9 
 
 148 
 
 0.017203 
 
 1,720 
 
 57.8 
 
 305 
 
 34,600 
 
 10 
 
 0.135 
 
 0.014314 
 
 1,431 
 
 48.1 
 
 254 
 
 41,584 
 
 11 
 
 0.120 
 
 O.C11310 
 
 1,131 
 
 38.0 
 
 201 
 
 52,631 ' 
 
 12 
 
 0.105 
 
 0.008659 
 
 866 
 
 29.1 
 
 154 
 
 68,752 
 
 13 
 
 0.092 
 
 0.006648 
 
 665 
 
 22.3 
 
 118 
 
 89,525 
 
 14 
 
 0.080 
 
 0.005027 
 
 503 
 
 16.9 
 
 89.2 
 
 118,413 
 
 15 
 
 0.072 
 
 0.004071 
 
 407 
 
 13.7 
 
 72.2 
 
 146,198 
 
 16 
 
 0.063 
 
 0.003117 
 
 312 
 
 10.5 
 
 55.3 
 
 191,022 
 
 17 
 
 0.054 
 
 0.002290 
 
 229 
 
 7.70 
 
 40.6 
 
 259,909 
 
 18 
 
 0.047 
 
 0.001735 
 
 174 
 
 5.83 
 
 30.8 
 
 343,112 
 
 19 
 
 0.041 
 
 0.001320 
 
 132 
 
 4.44 
 
 23.4 
 
 450,856 
 
 20 
 
 0.035 
 
 0.000962 
 
 96 
 
 3.23 
 
 17.1 
 
 618,620 
 
 21 
 
 0.032 
 
 0.000804 
 
 .80 
 
 2.70 
 
 14.3 
 
 740,193 
 
 22 
 
 0.028 
 
 0.000616 
 
 62 
 
 2.07 
 
 10.9 
 
 966,651 
 
 23 
 
 0.025 
 
 000491 
 
 49 
 
 1.65 
 
 8.71 
 
 
 24 
 
 0.023 
 
 0.000415 
 
 42 
 
 1.40 
 
 7.37 
 
 t< 
 
 25 
 
 0.020 
 
 0.000314 
 
 31 
 
 1.06 
 
 5.58 
 
 t 
 
 26 
 
 0.018 
 
 0.000254 
 
 25 
 
 0.855 
 
 4.51 
 
 t 
 
 27 
 
 0.017 
 
 0.000227 
 
 23 
 
 .763 
 
 4.03 
 
 t 
 
 28 
 
 0.016 
 
 0.000201 
 
 20 
 
 .676 
 
 3.57 
 
 u 
 
 29 
 
 0.015 
 
 0.000177 
 
 18 
 
 .594 
 
 3.14 
 
 
 30 
 
 0.014 
 
 0.000154 
 
 15 
 
 .517 
 
 2.73 
 
 
 
 31 
 
 0.0135 
 
 0.000143 
 
 14 
 
 .481 
 
 2.54 
 
 
 32 
 
 0.013 
 
 0.000133 
 
 13 
 
 .446 
 
 2.36 
 
 
 33 
 
 0.011 
 
 0.000095 
 
 9.5 
 
 .319 
 
 1.69 
 
 
 34 
 
 0.010 
 
 0.000079 
 
 7.9 
 
 .264 
 
 1.39 
 
 
 35 
 
 0.0095 
 
 0.000071 
 
 7.1 
 
 .238 
 
 1.26 
 
 
 36 
 
 0.009 
 
 0.000064 
 
 6.4 
 
 .214 
 
 1.13 
 
 
 The above table was calculated on a basis of 483.84 Ib. per cu. ft. for steel 
 wire. Iron wire is a trifle lighter. The breaking strains are calculated for 
 100,000 Ib. per sq. in. throughout, simply for convenience, so that the 
 breaking strains or wires of any strength per sq. in. may be quickly deter- 
 mined by multiplying the values given in the tables by the ratio between 
 the strength per square inch and 100,000. Thus, a No. 15 wire, with a 
 
 strength per sq. in. of 150,000 Ib., ha,? breaking strain of 407 X 
 
 ,,,. 
 Ol 00 
 
250 
 
 MATERIALS. 
 
 28 to 55 tons per square inch of section. The conductivity decreases 
 as the tensile strength increases. Wire whose conductivity equals 95 
 per cent of that of pure copper gives a tensile strength of 28 tons per 
 square inch, but when its conductivity is 34 per cent of pure copper, 
 its strength is 50 tons per square inch. It is being largely used for 
 telegraph wires. It has great resistance to oxidation. 
 
 Ordinary Drawn and Annealed Copper Wire has a strength of from 
 15 to 20 tons per square inch. 
 
 " PLOW "-STEEL WIRE. 
 
 Experiments by Dr. Percy on the English plow-steel (so-called) 
 gave the following results: Specific gravity, 7.814; carbon, 0.828 per 
 cent; manganese! 0.587 per cent; silicon, 0.143 per cent; sulphur, 0.009 
 per cent; phosphorus, nil; copper, 0.030 per cent. No traces of chro- 
 mium, titanium, or tungsten were found. The breaking strains of the 
 wire were as follows: 
 
 Diameter, inch 0.093 0.132 0.159 0.191 
 
 Pounds per sq. inch. 344,960 257,600 224,000 201,600 
 The elongation was only from 0.75 to 1.1 per cent. 
 
 STRENGTH OF PIANO-WIRE. 
 
 The average strength of English piano-wire is given as follows by 
 Webster, Horsfals & Lean: 
 
 Size, 
 Music-wire 
 Gauge. 
 
 Equivalent 
 Diameters, 
 Inch. 
 
 Ultimate 
 Tensile 
 Strength, 
 Pounds. 
 
 Size, 
 Music-wire 
 Gauge. 
 
 Equivalent 
 Diameters, 
 Inch. 
 
 Ultimate 
 Tensile 
 Strength, 
 Pounds. 
 
 12 
 
 0.029 
 
 225 
 
 18 
 
 0.041 
 
 395 
 
 13 
 
 .031 
 
 250 
 
 19 
 
 .043 
 
 425 
 
 14 
 
 .033 
 
 285 
 
 20 
 
 .045 
 
 500 
 
 15 
 
 .035 
 
 305 
 
 21 
 
 .047 
 
 540 
 
 16 
 
 .037 
 
 340 
 
 22 
 
 .052 
 
 650 
 
 17 
 
 .039 
 
 360 
 
 
 
 
 These strength range from 300,000 to 340,000 Ibs. per sq. in. The 
 composition of this wire is as follows: Carbon, 0.570; silicon, 0.090; 
 sulphur, 0.011; phosphorus, 0.018; manganese, 0.425. 
 
 GALVANIZED IRON WIRE FOR TELEGRAPH AND 
 TELEPHONE LINES. 
 
 (Trenton Iron Co.) 
 
 WEIGHT PER MILE-OHM. This term is to be understood as dis- 
 tinguishing the resistance of material only, and means the weight of such 
 material required per mile to give the resistance of one ohm. To ascer- 
 tain the mileage resistance of any wire, divide the " weight per mile- 
 ohm" by the weight of the wire per mile. Thus in a grade of Extra 
 Best Best, of which the weight per mile-ohm is 5000, the mileage ..resist- 
 ance of No. 6 (weight per mile 525 Ibs.) would be about 91/2 ohms; and 
 No. 14 steel wire, 6500 Ibs. weight per mile-ohm (95 Ibs. weight per mile), 
 would show about 69 ohms. 
 
 Sizes of Wire used in Telegraph and Telephone Lines. 
 
 No. 4. Has not been much used until recently; is now used on 
 important lines where the multiplex systems are applied. 
 
 No. 5. Little used in the United States. 
 
 No. 6. Used for important circuits between cities. 
 
 No. 8. Medium size for circuits of 400 miles or less. 
 
 No. 9. For similar locatipns to No. 8, but on somewhat shorter cir- 
 cuits; until lately was the size most largely used in this country. 
 
 Nos. 10, 11. For shorter circuits, railway telegraphs, private lines, 
 police and fire-alarm lines, etc. 
 
 No, 12. For telephone lines, police and fire-alarm lines, etc. 
 
TELEGRAPH AND TELEPHONE WIRE. 
 
 251 
 
 Nos. 13, 14. For telephone lines and short private lines; steel wire is 
 used most generally in these sizes. 
 
 The coating of telegraph wire with zinc as a protection against oxida- 
 tion is now generally admitted to be the most efficacious method. 
 
 The grades of line wire are generally known to the trade as "Extra 
 Best Best ' (E. B. B.), "Best Best" (B. B.), and "Steel." 
 
 "Extra Best Best" is made of the very best iron, as nearly pure as 
 any commercial iron, soft, tough, uniform, and of very high conduc- 
 tivity, its weight per mile-ohm being about 5000 Ibs. 
 
 The "Best Best" is of iron, showing in mechanical tests almost as 
 good results as the E. B. B., but is not quite as soft, and somewhat lower 
 in conductivity; weight per mile-ohm about 5700 Ibs. 
 
 The "Steel" wire is well suited for telephone or short telegraph lines, 
 and the weight per mile-ohm is about 6500 Ibs. 
 
 The following are (approximately) the weights per mile of various 
 sizes of galvanized telegraph wire, drawn by Trenton Iron Co.'s gauge: 
 No. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. 
 
 Lbs. 720, 610, 525, 450, 375, 310, 250, 200, 160, 125, 95. 
 
 Tests of Telegraph Wire. 
 
 The following data are taken from a table given by Mr. Prescott relat- 
 ing to tests of E. B. B. galvanized wire furnished the Western Union 
 Telegraph Go. 
 
 Size 
 of 
 Wire 
 
 Diam., 
 Inch. 
 
 Weight. 
 
 Length. 
 Feet 
 per 
 pound. 
 
 Resistance. 
 Temp. 75.8 Fahr. 
 
 Ratio of 
 Breaking 
 Weight to 
 Weight 
 per mile. 
 
 Grains 
 per foot. 
 
 Pounds 
 per mile. 
 
 Feet 
 per ohm 
 
 Ohms 
 per mile. 
 
 4 
 
 0.238 
 
 1043.2 
 
 886.6 
 
 6.00 
 
 958 
 
 5.51 
 
 
 5 
 
 .220 
 
 891.3 
 
 673.0 
 
 7.85 
 
 727 
 
 7.26 
 
 
 6 
 
 .203 
 
 758.9 
 
 572.2 ' 
 
 9.20 
 
 618 
 
 8.54 
 
 3.05 
 
 7 
 
 .180 
 
 595.7 
 
 449.9 
 
 11.70 
 
 578 
 
 10.86 
 
 3.40 
 
 8 
 
 .165 
 
 501.4 
 
 378.1 
 
 14.00 
 
 409 
 
 12.92 
 
 3.07 
 
 9 
 
 .148 
 
 403.4 
 
 304.2 
 
 17.4 
 
 328 
 
 16.10 
 
 3.38 
 
 10 
 
 .134 
 
 330.7 
 
 249.4 
 
 21.2 
 
 269 
 
 19.60 
 
 3.37 
 
 11 
 
 .120 
 
 265.2 
 
 200.0 
 
 26.4 
 
 216 
 
 24.42 
 
 2.97 
 
 12 
 
 .109 
 
 218.8 
 
 165.0 
 
 32.0 
 
 179 
 
 29.60 
 
 3.43 
 
 14 
 
 083 
 
 126.9 
 
 95.7 
 
 55.2 
 
 104 
 
 51.00 
 
 3.05 
 
 Sizes, Weights and Strengths of Hard-Copper Telegraph and 
 Telephone Wire. 
 
 (J. A. Roebling's Sons Co., 1908.) 
 
 
 
 a 
 
 ^g 
 
 *-! 
 
 g||| 
 
 
 
 K 
 
 _G 
 '3 
 
 d -2 
 
 f||| 
 
 CO 
 g; 
 
 j 
 
 A 
 
 BO 
 
 fafl 
 
 *Jk 
 
 ' a 5fg 
 
 02 
 
 d 
 
 
 40 
 
 m 
 W) 
 
 P"!k 
 
 ^ PS.S Q* 
 
 W) a aj 
 
 t'W o 
 
 C tM fl 
 
 pq| 
 
 r 
 
 
 
 3 . 
 
 c3 s3 GO o 
 
 S SSQ 
 
 g2^ | 
 
 P 
 
 r 
 
 ~ 0) 
 
 13 . 
 
 igpfe 
 
 X -Sp*] O e^ 
 
 NO 
 
 
 
 g 
 
 
 
 15'S'S 
 
 P. o . "^ 
 Q.^ g > a. 
 
 So 
 
 1 
 
 J'g 
 
 ^^ 
 
 i^^^ 
 
 SJS-i'| 
 
 CO 
 
 Q 
 
 ^ 
 
 
 
 H 
 
 
 72 
 
 Q 
 
 K 
 
 
 
 g 
 
 ^Pn * 
 
 9 
 
 0.114 
 
 208 
 
 653 
 
 4.39 
 
 2 
 
 13 
 
 0.072 
 
 83 
 
 274 
 
 11.01 
 
 61/2 
 
 10 
 
 0.102 
 
 166 
 
 540 
 
 5.49 
 
 3 
 
 14 
 
 0.064 
 
 65 
 
 220 
 
 13.94 
 
 8 
 
 11 
 
 0.091 
 
 132 
 
 426 
 
 6.90 
 
 4 
 
 15 
 
 0.057 
 
 52 
 
 174 
 
 17.57 
 
 9 
 
 12 
 
 0.081 
 
 105 
 
 334 
 
 8.70 
 
 6 
 
 16 
 
 0.051 
 
 42 
 
 139 
 
 21.95 
 
 10 
 
 In handling this wire the greatest care should be observed to avoid 
 kinks, bends, scratches or cuts. Joints should be made only with 
 Mclntire connectors. On account of its conductivity being about five 
 
252 
 
 MATERIALS. 
 
 times that of E. B. B. iron wire, and its breaking strength over three 
 times its weight per mile, copper may be used of which the section is 
 smaller and the weight less than an equivalent iron wire, allowing a 
 greater number of wires to be strung on the poles. Besides this advan- 
 tage, the reduction of section materially decreases the electrostatic 
 capacity, while its non-magnetic character lessens the self-induction of 
 the line, both of which features tend to increase the possible speed of 
 signaling in telegraphing, and to give greater clearness of enunciation 
 over telephone lines, especially those of great length. 
 
 Weight of Bare and Insulated Copper Wire* Pounds. 
 
 (John A. Roebling's Sons Co., 1908.) 
 
 
 Weight per 1000 Feet, Solid. 
 
 Weight per Mile, Solid. 
 
 02 
 
 
 Weather- 
 
 
 
 
 Weather- 
 
 
 
 
 proof. 
 
 -a % 
 
 bb 
 
 
 proof. 
 
 ^ 0) 
 
 hb 
 
 sj 
 
 6 
 
 ll 
 
 11 
 
 111 
 
 d 
 
 ll 
 
 g 
 
 o> . 
 
 33 
 
 3 oj 
 
 ll 
 
 g||' 
 
 C 
 I'g 
 
 
 & 
 
 QPQ 
 
 HPQ 
 
 
 
 Spq 
 
 & 
 
 Srt 
 
 Htt 
 
 E 
 
 sta 
 
 0000 
 
 641 
 
 723 
 
 767 
 
 862 
 
 925 
 
 3384 
 
 3817 
 
 4050 
 
 4550 
 
 4890 
 
 000 
 
 509 
 
 587 
 
 629 
 
 710 
 
 760 
 
 2687 
 
 3098 
 
 3320 
 
 3750 
 
 4020 
 
 00 
 
 403 
 
 467 
 
 502 
 
 562 
 
 600 
 
 2127 
 
 2467 
 
 2650 
 
 2970 
 
 3170 
 
 
 
 320 
 
 377 
 
 407 
 
 462 
 
 495 
 
 1689 
 
 1989 
 
 2150 
 
 2440 
 
 2610 
 
 1 
 
 253 
 
 294 
 
 316 
 
 340 
 
 365 
 
 1335 
 
 1553 
 
 1670 
 
 1800 
 
 1930 
 
 2 
 
 202 
 
 239 
 
 260 
 
 280 
 
 300 
 
 1066 
 
 1264 
 
 1370 
 
 1480 
 
 1585 
 
 3 
 
 159 
 
 185 
 
 199 
 
 230 
 
 270 
 
 840 
 
 977 
 
 1050 
 
 1220 
 
 1425 
 
 4 
 
 126 
 
 151 
 
 164 
 
 190 
 
 220 
 
 665 
 
 795 
 
 865 
 
 1000 
 
 1160 
 
 5 
 
 100 
 
 122 
 
 135 
 
 155 
 
 190 
 
 528 
 
 646 
 
 710 
 
 820 
 
 1000 
 
 6 
 
 79 
 
 100 
 
 112 
 
 127 
 
 160 
 
 417 
 
 529 
 
 590 
 
 670 
 
 840 
 
 8 
 
 50 
 
 66 
 
 75 
 
 85 
 
 110 
 
 264 
 
 349 
 
 395 
 
 450 
 
 580 
 
 9 
 
 39 
 
 54 
 
 62 
 
 
 
 ^206 
 
 283 
 
 325 
 
 
 
 10 
 
 32 
 
 46 
 
 53 
 
 60 
 
 "so 
 
 169 
 
 241 
 
 280 
 
 3i5 
 
 420 
 
 12 
 
 20 
 
 30 
 
 35 
 
 42 
 
 55 
 
 106 
 
 158 
 
 185 
 
 220 
 
 290 
 
 14 
 
 12.4 
 
 20 
 
 25 
 
 30 
 
 40 
 
 66 
 
 107 
 
 130 
 
 160 
 
 210 
 
 16 
 
 7.9 
 
 16 
 
 20 
 
 24 
 
 30 
 
 42 
 
 83 
 
 105 
 
 130 
 
 160 
 
 18 
 
 4.8 
 
 12 
 
 16 
 
 19 
 
 24 
 
 25 
 
 64 
 
 85 
 
 100 
 
 130 
 
 20 
 
 3.1 
 
 9 
 
 12 
 
 
 
 16 
 
 48 
 
 65 
 
 
 
 Specifications for Hard-Drawn Copper Wire. 
 
 The British Post Office authorities require that hard-drawn copper 
 wire supplied to them shall be of the lengths, sizes, weights, strengths, 
 and conductivities as set forth in the annexed table. 
 
 Weight per Statute 
 Mile, Ib. 
 
 Approximate Equiv- 
 alent Diameter, mils. 
 
 W) 
 Cj 
 
 13 
 
 | 
 
 ' e8 S 
 
 1! 
 
 
 
 vji 
 
 6^ 
 
 q> .--. _g r; 
 
 i> s 
 
 si 
 
 | 
 
 i 
 
 ^ 
 
 | 
 
 
 
 si 
 
 s-s 
 
 |||^' 
 
 g^j 
 
 sl 
 
 | 
 
 i 
 
 s 
 
 1 
 
 1 
 
 II 
 
 II 
 
 I sis 
 
 i ^.i 
 
 ST -2 
 
 'S 
 
 3 
 
 
 'S 
 
 2 
 
 -a 
 
 .'s ^ 
 
 rt ^ "S 
 
 3 ^g^ 
 
 ti m 
 
 S 
 
 * 
 
 02 
 
 S 
 
 s 
 
 S 
 
 S H 
 
 * 
 
 i 
 
 100 
 
 971/2 
 
 1021/2 
 
 79 
 
 78 
 
 80 
 
 330 
 
 30 
 
 9.10 
 
 50 
 
 150 
 200 
 
 1461/4 
 195 
 
 1533/4 
 205 
 
 97 
 112 
 
 951/2 
 
 1101/2 
 
 98 
 1131/4 
 
 490 
 650 
 
 25 
 20 
 
 6.05 
 4.53 
 
 50 
 50 
 
 400 
 
 390 
 
 410 
 
 158 
 
 1551/ 2 
 
 1601/4 
 
 1300 
 
 10 
 
 2.27 
 
 50 
 
WIRE ROPE. 
 
 253 
 
 Stranded Copper Feed Wire, Weight in Pounds. 
 
 (John A. Roebling's Sons Co., 1908.) 
 
 
 ^ Weight per 1000 Feet. 
 
 Weight per Mile. 
 
 
 
 Weather- 
 
 
 
 
 Weather- 
 
 
 M 
 
 
 
 proof 
 
 
 
 
 proof 
 
 
 1 
 
 U 
 
 oT o o5 
 
 9 
 
 IT 
 
 *s 
 
 !lN 
 
 .2 
 
 i 
 
 
 
 1,3 
 
 lls 
 
 m 
 
 
 
 o 8 
 
 'E 8 
 
 
 o 3 
 
 
 
 
 'E t-i 
 
 
 o 
 
 SoS 
 
 CQ 
 
 
 HPQ 
 
 jfc& 
 
 
 fl 
 
 fi 
 
 Htt 
 
 ^P< 
 
 53 
 
 2,000,000 
 
 6100 
 
 6690 
 
 7008 
 
 
 7540 
 
 2208 
 
 35323 
 
 37000 
 
 
 39800 
 
 1 750,000 
 
 5338 
 
 5894 
 
 6193 
 
 
 6700 
 
 28184 
 
 31119 
 
 32700 
 
 
 35400 
 
 1,500,000 
 
 4375 
 
 5098 
 
 5380 
 
 
 5830 
 
 24156 
 
 26915 
 
 28400 
 
 
 30800 
 
 1,250,000 
 
 3813 
 
 4264 
 
 4508 
 
 
 4940 
 
 20132 
 
 22516 
 
 23800 
 
 
 20000 
 
 1.000.00C 
 
 3050 
 
 3456 
 
 3674 
 
 3860 
 
 3980 
 
 6104 
 
 18246 
 
 19400 
 
 20400 
 
 26100 
 
 900,000 
 
 2745 
 
 3127 
 
 3332 
 
 3520 
 
 3640 
 
 4493 
 
 16513 
 
 17600 
 
 18600 
 
 11000 
 
 800,000 
 
 2440 
 
 2799 
 
 2992 
 
 3180 
 
 3280 
 
 2883 
 
 14779 
 
 15800 
 
 16800 
 
 19200 
 
 750,000 
 
 2288 
 
 2635 
 
 2822 
 
 3000 
 
 3100 
 
 12080 
 
 13913 
 
 14900 
 
 15850 
 
 17300 
 
 700,000 
 
 2135 
 
 2471 
 
 2650 
 
 2820 
 
 2920 
 
 11272 
 
 13045 
 
 14000 
 
 14900 
 
 16300 
 
 600,000 
 
 1830 
 
 2093 
 
 2235 
 
 2350 
 
 2450 
 
 9662 
 
 11052 
 
 11800 
 
 12400 
 
 15400 
 
 500,000 
 
 1525 
 
 1765 
 
 1894 
 
 1990 
 
 2080 
 
 8052 
 
 9318 
 
 10000 
 
 10500 
 
 13100 
 
 450,000 
 
 1373 
 
 1601 
 
 1724 
 
 1820 
 
 1900 
 
 7249 
 
 8452 
 
 9100 
 
 9600 
 
 10000 
 
 400,000 
 
 1220 
 
 1436 
 
 1553 
 
 1650 
 
 1700 
 
 6441 
 
 7584 
 
 8200 
 
 8700 
 
 9000 
 
 350,000 
 
 1068 
 
 1248 
 
 1345 
 
 1440 
 
 1500 
 
 5639 
 
 6589 
 
 7100 
 
 7600 
 
 7900 
 
 300,000 
 
 915 
 
 1083 
 
 1174 
 
 1270 
 
 1310 
 
 4831 
 
 5721 
 
 6200 
 
 6700 
 
 6900 
 
 250,000 
 
 762 
 
 907 
 
 985 
 
 1060 
 
 1120 
 
 4023 
 
 4788 
 
 5200 
 
 5600 
 
 5900 
 
 B.&S. 
 
 
 
 
 
 
 
 
 
 
 
 Gauge. 
 
 
 
 
 
 
 
 
 
 
 
 0000 
 
 645 
 
 745 
 
 800 
 
 900 
 
 960 
 
 3405 
 
 3935 
 
 4220 
 
 4750 
 
 5070 
 
 000 
 
 513 
 
 604 
 
 653 
 
 735 
 
 785 
 
 2708 
 
 3190 
 
 3450 
 
 3880 
 
 4150 
 
 00 
 
 406 
 
 482 
 
 522 
 
 583 
 
 625 
 
 2143 
 
 2544 
 
 2760 
 
 3080 
 
 3300 
 
 
 
 322 
 
 388 
 
 424 
 
 480 
 
 510 
 
 1700 
 
 2051 
 
 2240 
 
 2530 
 
 2700 
 
 1 
 
 255 
 
 303 
 
 328 
 
 355 
 
 380 
 
 1346 
 
 1599 
 
 1735 
 
 1870 
 
 2000 
 
 2 
 
 203 
 
 246 
 
 270 
 
 290 
 
 335 
 
 1071 
 
 1301 
 
 1425 
 
 1540 
 
 1770 
 
 3 
 
 160 
 
 190 
 
 206 
 
 240 
 
 280 
 
 844 
 
 1004 
 
 1090 
 
 1270 
 
 1480 
 
 4 
 
 127 
 
 155 
 
 170 
 
 195 
 
 230 
 
 670 
 
 820 
 
 900 
 
 1030 
 
 1220 
 
 5 
 
 101 
 
 126 
 
 140 
 
 160 
 
 195 
 
 533 
 
 668 
 
 740 
 
 845 
 
 1030 
 
 6 
 
 80 
 
 103 
 
 115 
 
 132 
 
 165 
 
 422 
 
 544 
 
 610 
 
 695 
 
 870 
 
 8 
 
 50 
 
 68 
 
 78 
 
 87 
 
 105 
 
 264 
 
 359 
 
 410 
 
 460 
 
 555 
 
 WIRE ROPE. 
 
 The following notes and tables are compiled from data furnished 
 by the American Steel & Wire Co., Cleveland, 1915. 
 
 Wire ropes, which have almost entirely superseded chains and 
 manila rope for haulage and hoisting purposes, are made with a vary- 
 ing number of wires to the strand, and a varying number of strands 
 to the rope, according to the service in which they are to be used and 
 the degree of flexibility required. Five grades of rope are usually 
 manufactured, as regards the material used, viz.: Iron, crucible 
 cast steel, extra strong crucible cast steel, "plow-steel," and an improved 
 grade of plow-steel called "Monitor." Haulage rope, for mines, 
 docks, etc., usually consists of 6 strands of 7 wires each laid around a 
 hemp core. Hoisting rope, for elevators, mines, coal and ore hoists, 
 conveyors, derricks, steam shovels, dredges, logging, etc., consists of 
 6 strands of 19 wires each, with a single hemp core. A more flexible 
 rope, for crane service, etc., consists of 6 3 7- wire strands wound around 
 a single hemp core. In general, the flexibility of the rope is increased 
 by increasing the number of wires in the strands. The most flexiblo 
 

 254 MATERIALS. 
 
 standard rope made consists of 6 61- wire strands and one hemp core. 
 Other varieties comprise flattened strand ropes for haulage, hoisting, 
 and transmission, non-spinning rope for the suspension of loads at the 
 end of a single line, steel clad rope for severe conditions of service, 
 guy and rigging ropes, and hawsers for towing or mooring. 
 
 Breaking Strength of Wire Rope. The various manufacturers 
 have adopted standard figures for the strength of all sizes and qualities 
 of wire rope. Formerly, it was the custom to test the individual wires 
 and to consider their combined strength as the strength of the rope 
 as a whole. These strengths were greater than the actual strength 
 obtained by breaking the finished rope. The figures given in the 
 tables herewith represent actual breaks of the various ropes, and range 
 from 95 to 80 per cent or less of the combined strength of the single 
 wires, depending on the construction. The figures, which were 
 adopted May 1, 1910, are considerably lower than those given in 
 earlier tables. In general, a factor of safety of five is allowed in giving 
 the working loads. 
 
 Lay of Wire Rope. Lang Lay. The regular lay of wire rope com- 
 prises wires in the strands laid to the left, the strands being laid to 
 the right, known as right-hand rope; or wires laid to the right, and 
 strands laid to the left, known as left-hand rope. In Lang lay rope 
 the wires in the strands and the strands themselves are laid in the 
 rope in the same direction, either right or left. Lang lay rope is some- 
 what more flexible than ordinary rope, and as the wires are laid more 
 axially in the rope, longer surfaces are exposed to wear, and the en- 
 durance is thereby increased. 
 
 Sheaves and Drums. Drums and sheaves of the largest practicable 
 diameter are recommended in all wire rope installations. If possible, 
 drums should be lagged, and where feasible, a grooved drum on hoists 
 is more desirable than a flat drum. The grooves should give ample 
 clearance between successive windings ; thus a drum for %-inch rope 
 should have the grooves at least 7/g-inch apart on centers. The 
 grooves should be made smooth in order not to cut the rope, and they 
 should be of slightly larger radius than the rope in order to avoid wedg- 
 ing or pinching it. Overwinding, that is, the winding, of the rope in 
 more than one layer, is to be avoided if possible, by making the drum 
 large enough to take all the rope in a single layer. Overwinding will 
 rapidly destroy the rope, and the extra cost of the larger drum will be 
 more than compensated by the greater life of the rope. The best 
 possible alignment of sheaves and drums should be made to avoid 
 undue wear on the sides of the sheaves and the rope. In general, the 
 lead sheaves over which the rope runs from the drum should be aligned 
 with the center of the drum, or if the drum is not entirely filled, with 
 the center of the portion on which the rope is wound. The distance 
 between the drum and lead sheave should be such as to cause an angle 
 not exceeding 1 30' between the line from the center of .the sheave to 
 the center of the drum, and the line from the center of the sheave to the 
 outer side of the drum. When the sheaves become worn, they should 
 be replaced or the grooves turned before they are used with a new 
 wire rope, otherwise the rope will not work properly. For many 
 
 Surposes, particularly mine service, the grooves can advantageously 
 e lined with well-seasoned, hardwood blocks set on end, which can 
 be renewed when worn. Large sheaves, running at high velocity, 
 should be lined with leather set on end, or with india-rubber. This 
 is the practice for power transmission between distant points, where 
 the rope frequently runs at a velocity of 4,000 feet per minute. 
 
 Reversed Bending. Reverse bending, that is, bending the wire 
 rope first in one direction over sheaves and then in the opposite direc- 
 tion, is to be avoided wherever possible. This practice will wear out 
 a rope more quickly than any other known method. A little care in 
 design will usually eliminate all situations which call for reversed 
 bending, and it is even desirable to change existing constructions if 
 necessary to remove this condition. .The expense of rope renewals 
 will more than equal the cost of change as a rule. 
 
 Handling Wire Rope. Wire rope must not be coiled or uncoiled 
 like hemp rope. When received in a coil it should be rolled on the - 
 ground like a hoop and straightened out before being put on the 
 sheaves. If on a reel, it should be mounted on a spindle or a flat 
 
GALVANIZED WIRE ROPE. 
 
 255 
 
 Galvanized Iron and Steel Wire Rope. 
 
 For Ship and Yacht Rigging, Guys, etc. 
 
 6 Strands, 7 or 12 Wires per Strand, 1 Hemp Core; 6 Strands, 
 19 Wires per Strand, 1 Hemp Core. 
 
 Diameter, In. 
 
 Approx. Circum., In. 
 
 J 
 
 CM 
 
 
 
 4.85 
 4.42 
 4.15 
 3.55 
 3.24 
 3.00 
 2.45 
 2.21 
 2.00 
 1.77 
 1.58 
 1.20 
 
 7 or 12- Wire 
 Strand, Iron 
 
 19- Wire 
 
 Strand, Steel 
 
 d 
 
 i 
 
 4 
 
 7 or 12- Wire 
 Strand, Iron. 
 
 19- Wire 
 Strand, Steel 
 
 fi 
 
 !tg 
 
 g^-5 
 
 H 
 
 *o 
 
 !s 
 
 i 
 
 ^ i i 
 
 X s "' 
 
 II 
 
 Sp 
 
 0*043 
 
 2S 
 
 a o 
 
 O OJ3 
 
 CD c 
 3 a & 
 
 r* P5 t/} 
 
 rt 
 
 13 
 
 u 
 
 g 
 
 a 
 
 i 
 $ 
 
 ii 
 
 4* 
 
 o 0^3 
 
 6a)| 
 |&| 
 
 ii 
 
 o ox" 
 III 
 
 13/4 
 HI/16 
 5/8 
 1/2 
 7/16 
 3/8 
 1/4 
 3/16 
 1/8 
 1/16 
 
 7/8 
 
 51/2 
 51/4 
 
 43/4 
 41/0 
 4.,, 
 
 33/4 
 
 31/2 
 
 3V, 
 
 23/4 
 
 42.0 
 38.0. 
 35.0 
 30.0 
 28.0 
 26.0 
 23.0 
 19.0 
 18.0 
 16.1 
 14.1 
 11.1 
 
 11.0 
 10.5 
 10.0 
 9.5 
 9.0 
 8.5 
 8.0 
 7.5 
 6.5 
 6.0 
 5.75 
 5.25 
 
 42^0 
 38.0 
 34.0 
 31.0 
 28.0 
 22.0 
 
 J3" 
 12 
 11 
 10 
 9 
 8.5 
 
 13/1G 
 3/4 
 5/8 
 9/16 
 V2 
 7/16 
 3/8 
 5/16 
 9/32 
 1/4 
 7/22 
 3/16 
 
 21/2 
 21/4 
 
 13/4 
 
 H/2 
 H/4 
 H/8 
 
 7/8 
 3/4 
 
 5/8 
 1/2 
 
 1.03 
 0.89 
 0.62 
 50 
 0.39 
 0.30 
 0.22 
 0.15 
 0.125 
 0.09 
 0.063 
 0.04 
 
 9.4 
 7.8 
 5.7 
 4.46 
 3.39 
 2.35 
 1.95 
 1.42 
 1.20 
 0.99 
 0.79 
 0.61 
 
 5 
 
 4.75 
 4.5 
 3.75 
 3 
 2.5 
 2.25 
 2 
 1.75 
 1.5 
 1.25 
 1.125 
 
 19.0 
 16.8 
 11.7 
 9.0 
 7.0 
 5.0 
 4.2 
 3.2 
 
 8.0 
 7.0 
 6.0 
 5.25 
 
 4.75 
 4.25 
 3.75 
 3.0 
 
 
 
 
 
 
 Galvanized Steel Wire Strand. 
 
 7 or 19 Wires Twisted into a Single Strand. 
 
 3/4 
 
 5/8 
 
 2100 
 1610 
 1200 
 800 
 
 9/16 
 
 1/2 
 7/16 
 3/8 
 
 650 
 510 
 415 
 295 
 
 M a 
 
 C m 
 
 11000 
 8500 
 6500 
 5000 
 
 P 
 
 5/16 
 1/4 
 7/32 
 3/16 
 
 210 
 125 
 95 
 75 
 
 3800 
 2300 
 1800 
 1400 
 
 5/32 
 1/8 
 3/32 
 
 900 
 500 
 400 
 
 19-wire strand is made only from 1 to H in. diam., 7- wire strand is 
 made only -from % to 3/ 32 in. diam. 
 
 Galvanized Steel Cables for Suspension Bridges. 
 
 Composed of 6 Strands with Wire Center. 
 
 . 
 
 
 Approx. 
 
 
 
 Appro. 
 
 
 
 Approx. 
 
 Diam., 
 In. 
 
 Wt. per 
 Foot, 
 Lb. 
 
 Breaking 
 Strain, 
 Tons 
 
 Diam., 
 In. 
 
 Wt. per 
 Foot, 
 Lb. 
 
 Break- 
 ing 
 Strain, 
 
 Diam., 
 In. 
 
 Wt. per 
 Foot, 
 Lb 
 
 Break- 
 ing 
 Strain, 
 
 
 
 (2000 Lb.). 
 
 
 
 Tons. 
 
 
 
 Tons. 
 
 73/, 
 
 12.7 
 
 310 
 
 21/4 
 
 8.52 
 
 208 
 
 13/4 
 
 5.10 
 
 124 
 
 25/8 
 
 11.6 
 
 283 
 
 21/8 
 
 7.60 
 
 185 
 
 15/8 
 
 4.34 
 
 106 
 
 21/2 
 
 10.5 
 
 256 
 
 2 
 
 6.73 
 
 164 
 
 1 1/2 
 
 3.70 
 
 90 
 
 23/ 8 
 
 9.50 
 
 232 
 
 17/8 
 
 5 90 
 
 144 
 
 13/8 
 
 3.10 
 
 75 
 
 
256 MATERIALS* 
 
 turntable and properly unwound. Kinking or untwisting must be 
 avoided. 
 
 Protection of Wire Rope. Wire rope should -be protected by a 
 suitable lubricant, both internally and externally, to prevent rust and 
 to keep it pliable. If this is omitted rust will set in and stiffen the 
 rope, resulting in poor service. Raw linseed oil, applied with a piece 
 of sheepskin, the wool inside, is a good preservative; the oil also may 
 be mixed with Spanish brown or lamp-black. Wire rope running 
 under water should be treated with mineral or vegetable tar, one 
 bushel of fresh slacked lime being added to each barrel of tar to 
 neutralize the acid. The tar is well boiled and the rope saturated 
 with it. Wire rope manufacturers furnish special compounds for the 
 treatment of wire ropes. 
 
 Exposure to Heat. Where wire rope is exposed to intense heat, as 
 in foundry or steel mill service, a soft iron core is often substituted for 
 the hemp core. Asbestos also is sometimes used, but it rapidly dis- 
 integrates and is not recommended. The use of the iron core adds 
 from 7 to 10 per cent to the strength of the rope, but the wear on the 
 center is as great as on the outside strands, and the hemp center 
 is to be preferred wherever possible. 
 
 VARIETIES AND USES OF WIRE ROPE. 
 
 Transmission, Haulage or Standing Rope. Usually made of 6 
 7-wire strands and one hemp core, in all five grades noted above. Iron 
 rope is comparatively little used except in the smaller sizes. It is 
 composed of very soft wires of low tensile strength. Crucible cast 
 steel rope is particularly adapted to mine haulage work, including tail 
 rope and endless haulage systems, gravity hoists, and coal and ore dock 
 haulage, roads operating small grip cars. The sizes, 3/ 8 to 5/8 inch 
 inclusive, are used for sand lines in oil wells, and from 5/8 to 1 inch for 
 oil-well drilling. In general it can be used for severe service, and 
 where the flexibility required is a minimum. Extra strong crucible 
 cast steel rope has practically the same applications as the preceding 
 rope, .except that being stronger a smaller rope can be used for the 
 same service. The plow-steel rope is advised for situations similar 
 to those for which the cast steel ropes are used, but where it is neces- 
 sary to secure increased strength, without altering the working con- 
 ditions. The wires are harder and capable of standing greater wear 
 than any of the foregoing ropes. Monitor plow-steel rope is the 
 strongest and stiffest of all and is used for work demanding the greatest 
 strength and lightest rope possible. Sheaves for this rope should, if 
 possible, be somewhat larger than for other grades. For working loads, 
 strength, etc., of these ropes, see table, page 257. 
 
 Standard Hoisting Rope. Composed of 6 19-wire strands and a 
 hemp core; made in the following grades: Iron, mild steel, crucible 
 cast steel, extra strong crucible cast steel, plow-steel, and Monitor 
 plow-steel. The wires are smaller than those in transmission ropes of 
 the same size, and it is more flexible. It will not stand as much 
 abrasion as transmission rope. The iron rope is used for elevator 
 hoisting, where the strength is sufficient, and is almost universally 
 employed for counterweights, except on traction elevators. Where 
 the pulleys are comparatively small it is sometimes used for power 
 transmission. The mild steel rope is made especially for traction 
 elevators, where quick starting and stopping is required. The cru- 
 cible cast steel rope is adapted to mine hoisting, logging, elevators, 
 derricks, hay presses, dredges, cableways, inclined planes, coal hoists, 
 conveyors, ballast unloaders, ship hoists, and similar applications. 
 The extra strong crucible cast steel rope is adapted to the same pur- 
 poses and may be used for heavier loads than the former rope. It is 
 extensively used for oil-well drilling and tubing lines. Plow-steel rope 
 is used for heavy mine work, inclined planes, dredges, cableways, for 
 heavy logging, etc. It is especially desirable for deep mine shafts 
 and long inclines on account of its great strength per unit of weight. 
 It is the most economical rope where the weight of the rope is to be 
 considered or the capacity of the machinery is to be increased without 
 Changing sheaves or drums. Monitor plow-steel rope is somewhat 
 
TRANSMISSION, HAULAGE AND HOISTING ROPE. 257 
 
 Transmission, Haulage, OP Standing Rope. 
 
 6 Strands, 7 Wires per Strand, 1 Hemp Core. 
 
 
 d 
 i i 
 
 -P 
 
 Approximate Breaking 
 Strength, Tons 
 (2000 Ibs.) 
 
 Allowable Working 
 Load, Tons (2000 Ibs.) 
 
 Min. Dia. 
 Drum or 
 Sheave,In. 
 
 
 
 i 
 
 t bfl 
 
 
 1 
 
 to 
 c -: 
 
 
 
 
 
 1 
 
 be 
 
 
 
 
 
 
 f 
 
 
 ^ . 
 
 
 u 
 
 
 "oS 
 
 PM 
 
 
 O 
 
 2 0) $ 
 
 *3 
 
 
 
 OJ 
 
 & 
 
 
 
 s 
 
 K*3 
 
 
 
 MfjpGQ 
 
 -M 
 
 CQ 
 
 o^_. 
 
 
 0) 
 
 35 
 
 ^'wS 
 
 3a 
 
 2-i 
 
 
 
 & 
 
 i 
 
 i 
 
 |e r 
 
 h-l 
 
 %% 
 
 6* 
 
 *" 2 
 
 ^0 
 
 | 
 
 I 
 
 <s jj 
 
 |2J 
 
 1 
 
 
 
 1 
 
 1 
 
 IV? 
 
 43/ 4 
 
 3.55 
 
 32.0 
 
 63.0 
 
 73.0 
 
 82 
 
 90.0 
 
 64 
 
 12 6 
 
 14.6 
 
 16 4 
 
 18 
 
 16 
 
 11 
 
 13/8 
 
 41/4 
 
 3.00 
 
 28.053.0 
 
 63.0 
 
 72.0 
 
 79.0 
 
 5.6 
 
 10.6 
 
 12.6 
 
 14 4 
 
 16 
 
 15 
 
 10 
 
 U/4 
 
 4 
 
 2.45 
 
 23.046.0 
 
 54.0 
 
 60.0 
 
 67.0 
 
 4 6 
 
 9 2 
 
 10.8 
 
 \7 
 
 13 
 
 13 
 
 9 
 
 H/8 
 
 31/2 
 
 2.00 
 
 19.0 
 
 37.0 
 
 43.0 
 
 47.0 
 
 52.0 
 
 3.8 
 
 7.4 
 
 8.6 
 
 9 4 
 
 10 
 
 1 20 
 
 8 
 
 1 
 
 3 
 
 1.58 
 
 15.0 
 
 31.0 
 
 35.0 
 
 38,0 
 
 42.0 
 
 3 
 
 6 2 
 
 7.0 
 
 7 6 
 
 8 4 
 
 10 5 
 
 7 
 
 7/8 
 
 23/4 
 
 1.20 
 
 12.0 
 
 24.0 
 
 28.0 
 
 31.0 
 
 33.0 
 
 2.4 
 
 4.8 
 
 5.6 
 
 6 2 
 
 6 6 
 
 9 
 
 6 
 
 3/4 
 
 2V4 
 
 0.89 
 
 8.8 
 
 18.6 
 
 21.0 
 
 23 
 
 25 
 
 1 7 
 
 3 7 
 
 4.2 
 
 4 6 
 
 5 
 
 7 5 
 
 5 
 
 5/8 
 
 21/8 
 
 0.75 
 
 7.3 
 
 15.4 
 
 16.7 
 
 18.0 
 
 20.0 
 
 1.5 
 
 31 
 
 3.3 
 
 3 6 
 
 4 
 
 7 25 
 
 4 75 
 
 9/16 
 
 
 J.62 
 
 6.0113.0 
 
 14.5 
 
 16 
 
 17 5 
 
 1 2 
 
 2 6 
 
 2.9 
 
 3 ? 
 
 3 5 
 
 7 
 
 4 50 
 
 
 13/ 4 
 
 0.50 
 
 4.8 
 
 10.0 
 
 11.0 
 
 12.0 
 
 13.0 
 
 0.96 
 
 2 
 
 2.2 
 
 2 4 
 
 2 6 
 
 6 
 
 4 00 
 
 1/2 
 
 IV? 
 
 J.39 
 
 3.7 
 
 7.7 
 
 8.85 
 
 10 
 
 11 
 
 74 
 
 1 5 
 
 1.8 
 
 ? 
 
 
 5 5 
 
 3 50 
 
 7/16 
 
 U/4 
 
 0.30 
 
 2.6 
 
 5.5 
 
 6.25 
 
 7.0 
 
 7.75 
 
 0.52 
 
 1 1 
 
 1.25 
 
 1 4 
 
 15 
 
 45 
 
 3.00 
 
 
 H/8 
 
 ).22 
 
 2.2 
 
 4.6 
 
 5.25 
 
 5 9 
 
 65 
 
 44 
 
 9? 
 
 1.05 
 
 1 2 
 
 1 3 
 
 4 
 
 2 75 
 
 5/16 
 
 1 
 
 0.15 
 
 1.7 
 
 3.5 
 
 3.95 
 
 4.4 
 
 
 34 
 
 70 
 
 0.79 
 
 88 
 
 
 3.5 
 
 2.25 
 
 9/32 
 
 7/8 
 
 0.125 
 
 1.2 
 
 2.5 
 
 2.95 
 
 3.4 
 
 
 0.24 
 
 0.50 
 
 0.59 
 
 0.68 
 
 
 3.0 
 
 1.75 
 
 Standard Hoisting Rope. 
 
 6 Strands, 19 Wires per Strand, 1 Hemp Core. 
 
 
 A 
 
 i 
 
 Approximate Breaking 
 Strength, Tons (2000 Lbs). 
 
 Allowable Working Loads 
 Tons (2000 Lbs). 
 
 Min. Dia. 
 Sheave or 
 Drum, Ft. 
 
 1-4 
 
 rcum., ] 
 
 bo 
 
 '3 
 
 
 1 
 
 fis 
 
 
 | 
 
 
 1 
 
 a 
 
 c -p 
 
 
 
 
 
 
 
 O 
 
 ^ 
 
 
 u 
 
 Jl 
 
 "oi 
 
 
 
 
 ^ 
 
 Jl 
 
 "oi 
 
 
 
 <u 
 
 
 1 
 
 g 
 
 g'3 
 
 
 jU 
 
 
 03 
 
 111 
 
 
 3 j 
 
 rt * 
 
 w 
 
 !* 
 
 1 
 
 
 
 
 a 
 
 cL-i-f 
 
 C 
 
 'S $ 
 
 *"3 
 
 j 
 
 1J 
 
 g 
 
 o <u 
 
 S S 
 
 j 
 
 1 
 
 g 
 
 "a> 
 
 .5 
 P 
 
 < 
 
 3* 
 
 2 
 
 M 
 
 o w 
 
 w 
 
 ,2 * 
 
 
 2 
 
 u 75 
 
 
 
 
 00 
 
 2 
 i i 
 
 1 
 
 23/4 
 
 85/8 
 
 11.95 
 
 111.0 
 
 211.0 
 
 243.0 
 
 275.0 
 
 315.0 
 
 22.2 
 
 42.2 
 
 48.6 
 
 55.0 
 
 63.0 
 
 17.0 
 
 11 
 
 21/2 
 
 77/8 
 
 9.85 
 
 92.0 
 
 170.0 
 
 200.0 
 
 229.0 
 
 263.0 
 
 18.4 
 
 34.0 
 
 40.0 
 
 46.0 
 
 53.0 
 
 15.0 
 
 10.0 
 
 21/4 
 
 71/8 
 
 8.00 
 
 72.0 
 
 133.0 
 
 160.0 
 
 186.0 
 
 210.0 
 
 14.4 
 
 26.6 
 
 32.0 
 
 37.0 
 
 42.0 
 
 14.0 
 
 9.0 
 
 2 
 
 61/4 
 
 6.30 
 
 55.0 
 
 106.0 
 
 123.0 
 
 140.0 
 
 166.0 
 
 11.0 
 
 21.2 
 
 24.6 
 
 28.0 
 
 33.0 
 
 12.0 
 
 8.0 
 
 17/8 
 
 53/4 
 
 5.55 
 
 50.0 
 
 96.0 
 
 112.0 
 
 127.0 
 
 150.0 
 
 10.0 
 
 19.0 
 
 22.4 
 
 25.0 
 
 30.0 
 
 12.0 
 
 8.0 
 
 13/4 
 
 51/2 
 
 4.85 
 
 44.0 
 
 85.0 
 
 99.0 
 
 112.0 
 
 133.0 
 
 8.8 
 
 17.0 
 
 19.8 
 
 22.0 
 
 27.0 
 
 11.0 
 
 7-0 
 
 15/8 
 
 5 
 
 4.15 
 
 38.0 
 
 72.0 
 
 83.0 
 
 94.0 
 
 110.0 
 
 7.6 
 
 14.4 
 
 16.6 
 
 19.0 
 
 22.0 
 
 10.9 
 
 6.5 
 
 H/2 
 
 43/4 
 
 3.55 
 
 33.0 
 
 64.0 
 
 73.0 
 
 82.0 
 
 98.0 
 
 6.6 
 
 12.8 
 
 14.6 
 
 16.0 
 
 20.0 
 
 9.0 
 
 6.0 
 
 13/8 
 
 41/4 
 
 3.00 
 
 28.0 
 
 56.0 
 
 64.0 
 
 72.0 
 
 84.0 
 
 5.6 
 
 11.2 
 
 12.8 
 
 14.0 
 
 17.0 
 
 8.5 
 
 5.5 
 
 U/4 
 
 4 
 
 2.45 
 
 22.8 
 
 47.0 
 
 53.0 
 
 58.0 
 
 69.0 
 
 4.56 
 
 9.4 
 
 10.6 
 
 12.0 
 
 14.0 
 
 7.5 
 
 5.0 
 
 H/8 
 
 31/2 
 
 2.00 
 
 18.6 
 
 38.0 
 
 43.0 
 
 47.0 
 
 56.0 
 
 3.72 
 
 7.6 
 
 8.6 
 
 9.4 
 
 11.0 
 
 7.0 
 
 4.5 
 
 
 3 
 
 1.58 
 
 14.5 
 
 30.0 
 
 34.0 
 
 38.0 
 
 45.0 
 
 2.90 
 
 6.0 
 
 6.80 
 
 7.6 
 
 9.0 
 
 6.0 
 
 4.0 
 
 7/8 
 
 23/4 
 
 1.20 
 
 11.8 
 
 23.0 
 
 26.0 
 
 29.0 
 
 35.0 
 
 2.36 
 
 4.6 
 
 5.20 
 
 5.8 
 
 7.0 
 
 55 
 
 3.5 
 
 3/4 
 
 21/4 
 
 0.89 
 
 8.5 
 
 17.5 
 
 20.2 
 
 23.0 
 
 26.3 
 
 1.70 
 
 3.5 
 
 4.04 
 
 4.6 
 
 5.3 
 
 4.5 
 
 3.0 
 
 5/8 
 
 2 
 
 0.62 
 
 6.0 
 
 12.5 
 
 14.0 
 
 15.5 
 
 19.0 
 
 1.20 
 
 2.5 
 
 2.80 
 
 3.1 
 
 3.8 
 
 4.0 
 
 2.5 
 
 9/16 
 
 13/4 
 
 0.50 
 
 4.7 
 
 10.0 
 
 11.2 
 
 12.3 
 
 14.5 
 
 0.94 
 
 2.0 
 
 2.24 
 
 2.4 
 
 2.9 
 
 3.5 
 
 2.25 
 
 V2 
 
 H/2 
 
 0.39 
 
 3.9 
 
 8.4 
 
 9.2 
 
 10.0 
 
 12.1 
 
 0.78 
 
 1.68 
 
 1.84 
 
 2.0 
 
 2.4 
 
 3.0 
 
 2.0 
 
 7/16 
 
 U/4 
 
 0.30 
 
 2.9 
 
 6.5 
 
 7.25 
 
 8.0 
 
 9.4 
 
 0.58 
 
 1.30 
 
 1.45 
 
 1.6 
 
 1.9 
 
 2.75 
 
 1.75 
 
 3/8 
 
 H/8 
 
 0.22 
 
 2.4 
 
 4.8 
 
 5.30 
 
 5.75 
 
 6.75 
 
 0.48 
 
 0.96 
 
 1.06 
 
 1.15 
 
 1.35 
 
 2.25 
 
 1.50 
 
 5/16 
 
 1 
 
 0.15 
 
 1.5 
 
 3.1 
 
 3.50 
 
 3.80 
 
 4.50 
 
 0.30 
 
 0.62 
 
 0.70 
 
 0.76 
 
 0.9 
 
 2.0 
 
 1.25 
 
 V4 
 
 3/4 
 
 0.10 
 
 1.1 
 
 2.2 
 
 2.43 
 
 2.65 
 
 3.15 
 
 0.22 
 
 0.44 
 
 0.49 
 
 0.53 
 
 0.63 
 
 1.5 
 
 1.00 
 
258 MATERIALS. 
 
 stiff er than the same diameter of crucible and plow-steel ropes, but 
 strength for strength, it is equally flexible. A smaller rope of this 
 grade than any of the others can be used for a given service. It is 
 particularly adapted to derricks, dredges, skidders, and stump pullers. 
 The sheaves should be somewhat larger, if possible, than for the other 
 grades. See tables, page 257. 
 
 Extra Flexible Hoisting Rope. Consists of 8 19-wire strands and 
 one hemp core. The greater flexibility permits its use on smaller 
 sheaves and drums, such as are usually found on derricks. It is not 
 advisable to use it where there is much overwinding, as it will flatten 
 much more quickly than the 6 X 19 standard rope. It is made in 
 the five grades of iron, crucible cast steel, extra strong crucible cast 
 steel, plow-steel, and Monitor plow-steel. Its uses are the same as 
 those of standard hoisting rope, noted above. See tables, page 259. 
 
 Special Flexible Hoisting Rope. Consists of 6 37-wire strands and 
 one hemp core. It is extremely flexible, and is especially adapted 
 to service on cranes where the sheaves are rather small. It is made 
 in the grades crucible cast steel, extra strong crucible cast steel, plow- 
 steel, and Monitor plow-steel. It will not stand as much abrasion 
 as the 6 19-wire strand rope, but it is particularly efficient, as over 
 50 per cent of the wires are in the inner layers and are protected from 
 abrasion. The crucible steel ropes are used for general hoisting work 
 where the sheaves are small, while the plow-steel varieties are recom- 
 mended for crane service. The Monitor plow-steel rope is largely 
 used on dredges for both main and spud ropes. See table, page 259. 
 
 Flattened Strand Rope. Flattened strand ropes are used where an 
 increased wearing surface is desired above that obtained with a round 
 strand rope. They are made both for haulage and transmission, 
 and for hoisting, and are always made Lang lay. 
 
 The haulage rope is made in three types, each of which has one 
 hemp core. The first has 5 9-wire strands, the center wire being 
 of elliptical section; the second has 6 8- wire strands, the center wire 
 being of triangular section; the third has 5 11 -wire strands, the three 
 center wires being of smaller diameter than the others and laid along- 
 side of each other in the same plane. These ropes are made in the 
 iron, crucible cast steel, extra strong crucible cast steel, and Monitor 
 plow-steel grades. They are made in diameters ranging from 1 K 
 inch, down to 3/ 8 inch. The 1-inch 6 8-wire strand rope weighs 
 1.80 Ib. per ft. and has an approximate strength of 34 tons, in the 
 crucible cast steel grade. Monitor plow-steel rope of the same diam- 
 eter and weight has an approximate breaking strength of 36 tons. 
 The similar figures for 3/Hnch rope, weighing 0.45 Ib. per ft., are: 
 Crucible cast steel, 9.6 tons; Monitor plow -steel, 11.9 tons. 
 
 Flattened strand hoisting rope is made in two types, each with 
 one hemp core: (A) 5 28-wire strands, the center wire being of ellip- 
 tical section; and (B) 6 25-wire strands, the center wire being of 
 triangular section, and the 12 wires immediately surrounding it being 
 of smaller diameter than the outer wires. These ropes compare in 
 flexibility with the standard hoisting ropes, but have about 150 per 
 cent greater wearing surface. Type A is made in the grades of iron, 
 crucible cast steel, extra strong crucible cast steel, and Monitor plow 
 steel. Type B is made in the grades of crucible cast steel, extra strong 
 crucible cast steel, and Monitor plow steel. They are made in sizes 
 ranging from 21/4 in. diam. down to 3/ 8 inch. Type B rope, 2 in. 
 diam., weighing 7.25 Ib. per ft., has the following breaking strength: 
 Crucible cast steel, 117 tons; Monitor plow steel, 183 tons. The 
 similar figures for H-inch rope of the same type, weighing 0.45 Ib. 
 per ft., are: Crucible cast steel, 9.3 tons; Monitor plow steel, 13.3 
 tons. 
 
 Non-Spinning Hoisting Rope. Comprises 18 7- wire strands and 
 one hemp core, 6 strands, long lay, being laid around the core to the 
 left, and 12 strands, regular lay being laid to the right around them. 
 A free object suspended from the end of a rope of this character will 
 not rotate and endanger the lives of persons below it. Furthermore, 
 the attention required to handle and guide the load is decreased. 
 This rope is recommended for back haul or single-line derricks, and 
 for shaft sinking and mine hoisting, where the bucket swings without 
 guides. This rope works best where it does not overwind on the 
 
FLEXIBLE HOISTING ROPE. 
 
 259^ 
 
 Extra Flexible Steel Hoisting Rope. 
 
 8 Strands, 19 Wires per Strand, 1 Hemp Core. 
 
 
 4 
 1 
 
 ,a 
 
 Approximate Strength, 
 Tons (2000 Lbs.). 
 
 Allowable Working 
 Load, Tons (2000 Lbs.). 
 
 & 
 
 L 
 
 
 
 
 
 
 
 
 
 d 
 
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 A 
 
 11 
 
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 ^ 
 
 H/2 
 
 43/4 
 
 3.19 
 
 58.0 
 
 66.0 
 
 74.0 
 
 80.0 
 
 11.6 
 
 13.0 
 
 14.8 
 
 16.0 
 
 3.75 
 
 13/8 
 
 41/4 
 
 2.70 
 
 51.0 
 
 57.0 
 
 64.0 
 
 68.0 
 
 10.2 
 
 11.0 
 
 12.8 
 
 13.0 
 
 3.50 
 
 11/4 
 
 
 2.20 
 
 42.0 
 
 47.0 
 
 52.0 
 
 56.0 
 
 8.4 
 
 9.4 
 
 10.4 
 
 11.0 
 
 3.20 
 
 U/8 
 
 31/2 
 
 1.80 
 
 34.0 
 
 38.0 
 
 43.0 
 
 46.0 
 
 6.8 
 
 7.6 
 
 8.6 
 
 9.2 
 
 2.83 
 
 1 
 
 3 
 
 1.42 
 
 26.0 
 
 29.7 
 
 33.0 
 
 36.0 
 
 5.2 
 
 5.9 
 
 6.6 
 
 7.2 
 
 2.50 
 
 7/ 8 
 
 23/4 
 
 1.08 
 
 20.0 
 
 23.0 
 
 26.0 
 
 28.0 
 
 4.0 
 
 4.6 
 
 5.2 
 
 5.6 
 
 2.16 
 
 3/4 
 
 21/4 
 
 0.80 
 
 15.3 
 
 17.6 
 
 20.0 
 
 22.0 
 
 3.06 
 
 3.5 
 
 4.0 
 
 4.4 
 
 .83 
 
 5/8 
 
 
 0.56 
 
 10.9 
 
 12.4 
 
 14.0 
 
 15.0 
 
 2.18 
 
 2.5 
 
 2.8 
 
 3.0 
 
 .75 
 
 9/16 
 
 13/4 
 
 0.45 
 
 8.7 
 
 10.1 
 
 11.6 
 
 12.0 
 
 1.74 
 
 20 
 
 2.32 
 
 2.4 
 
 .50 
 
 1/2 
 
 
 0.35 
 
 7.3 
 
 8.0 
 
 8.7 
 
 9.5 
 
 1.46 
 
 1.6 
 
 1.74 
 
 1.9 
 
 .33 
 
 7/16 
 
 1 V4 
 
 0.27 
 
 5.7 
 
 6.30 
 
 6.90 
 
 
 1.14 
 
 1.26 
 
 1.38 
 
 
 .16 
 
 3/8 
 
 1 1/8 
 
 0.20 
 
 4.2 
 
 4.66 
 
 5.12 
 
 
 0.84 
 
 0.93 
 
 1.02 
 
 
 .00 
 
 6/10 
 
 1 
 
 0.13 
 
 2.75 
 
 3.05 
 
 3.35 
 
 
 0.55 
 
 0.61 
 
 0.67 
 
 
 0.83 
 
 
 3/4 
 
 0.09 
 
 1.80 
 
 2.02 
 
 2.25 
 
 
 0.36 
 
 0.40 
 
 0.45 
 
 
 0.75 
 
 Special Flexible Steel Hoisting Rope. 
 
 6 Strands, 37 Wires per Strand, 1 Hemp Core. 
 
 
 C 
 
 ,* 
 
 Breaking Strength, 
 
 Allowable Working Load, 
 
 g 
 
 
 W r 
 
 S 
 
 Tons (2000 Lbs.). 
 
 Tons (2000 Lbs.). 
 
 O _iJ 
 
 
 S 
 
 Q, 
 
 
 ^j 
 
 
 
 
 a 
 
 
 
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 5 
 
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 Monitor 
 Steel R 
 
 Crucible 
 Steel R 
 
 Extra St 
 Crucibl 
 Steel R 
 
 m oJ 
 * 
 & 
 
 Monitor 
 Steel R 
 
 51 
 
 !: 
 
 23/4 
 
 85/8 
 
 11.95 
 
 200 
 
 233.0 
 
 265.0 
 
 278.0 
 
 40.0 
 
 47.0 
 
 53.0 
 
 55.0 
 
 
 21/2 
 
 77/8 
 
 9.85 
 
 160.0 
 
 187.0 
 
 214.0 
 
 225.0 
 
 32.0 
 
 37.0 
 
 43.0 
 
 45.0 
 
 
 21/4 
 
 71/8 
 
 8.00 
 
 125.0 
 
 150.0 
 
 175.0 
 
 184.0 
 
 25.0 
 
 30.0 
 
 35.0 
 
 37.0 
 
 
 2 
 
 61/4 
 
 6.30 
 
 105.0 
 
 117.0 
 
 130.0 
 
 137.0 
 
 21.0 
 
 23.0 
 
 26.0 
 
 27.0 
 
 
 17/8 
 
 53/4 
 
 5.55 
 
 94.0 
 
 106.0 
 
 119.0 
 
 125.0 
 
 18.8 
 
 21.2 
 
 23.8 
 
 25.0 
 
 
 13/4 
 
 51/2 
 
 4.85 
 
 84.0 
 
 95.0 
 
 108.0 
 
 113.0 
 
 17.0 
 
 19.0 
 
 22.0 
 
 23.0 
 
 
 15/8 
 
 5 
 
 4.15 
 
 71.0 
 
 79.0 
 
 90.0 
 
 95.0 
 
 14.0 
 
 16.0 
 
 18.0 
 
 19.0 
 
 
 H/2 
 
 43/4 
 
 3.55 
 
 63.0 
 
 71.0 
 
 80.0 
 
 84.0 
 
 12.0 
 
 14.0 
 
 16.0 
 
 17.0 
 
 3. 75. 
 
 13/8 
 
 41/4 
 
 3.00 
 
 55.0 
 
 61.0 
 
 68.0 
 
 71.0 
 
 11.0 
 
 12.0 
 
 14.0 
 
 14.0 
 
 3.50 
 
 H/4 
 
 4 
 
 2.45 
 
 45.0 
 
 50.0 
 
 55.0 
 
 58.0 
 
 9.0 
 
 10.0 
 
 11.0 
 
 11.0 
 
 3.20 
 
 U/8 
 
 31/2 
 
 2.00 
 
 34.0 
 
 39.0 
 
 44.0 
 
 46.0 
 
 7.0 
 
 8.0 
 
 9.0 
 
 9.2 
 
 2.83 
 
 
 3 
 
 1.58 
 
 29.0 
 
 32.0 
 
 35.0 
 
 37.0 
 
 6.0 
 
 6.4 
 
 7.0 
 
 7.4 
 
 2.50 
 
 7/8 
 
 23/4 
 
 1.20 
 
 23.0 
 
 25.0 
 
 27.0 
 
 29.0 
 
 5.0 
 
 5.0 
 
 5.0 
 
 5.8 
 
 2.16 
 
 3/4 
 
 21/4 
 
 0.89 
 
 17.5 
 
 19.0 
 
 21.0 
 
 23.0 
 
 3.5 
 
 3.8 
 
 4.0 
 
 4.6 
 
 .83 
 
 5/8 
 
 2 
 
 0.62 
 
 11.2 
 
 12.6 
 
 14.0 
 
 16.0 
 
 2.2 
 
 2.5 
 
 3.0 
 
 3.2 
 
 75 
 
 
 13/4 
 
 0.50 
 
 9.5 
 
 10.5 
 
 11.5 
 
 12.5 
 
 1.9 
 
 2.1 
 
 2.3 
 
 2.5 
 
 .50 
 
 1/2 6 
 
 
 0.39 
 
 7.25 
 
 8.25 
 
 9.25 
 
 9.75 
 
 1.45 
 
 1.65 
 
 1.85 
 
 1.9 
 
 .33 
 
 7/16 
 
 1 1/4 
 
 0.30 
 
 5.5 
 
 6.35 
 
 7.2 
 
 7.50 
 
 1.1 
 
 1.27 
 
 1.4 
 
 1.5 
 
 .15 
 
 3/8 
 
 H/8 
 
 0.22 
 
 4.2 
 
 4.65 
 
 5.1 
 
 5.30 
 
 0.84 
 
 0.93 
 
 1.0 
 
 1.06 
 
 .00 
 
260 
 
 MATERIALS. 
 
 drum. The best fastening is an open or closed socket, but the wire 
 rope makers recommend that fastenings be attached at the factory. 
 This rope should not be as heavily loaded as ordinary hoisting rope. 
 It is made in the grades of iron, crucible cast steel, extra strong crucible 
 cast steel, plow steel, and Monitor plow steel. See table, page 261. 
 
 Extra Flexible Iron Hoisting Rope. 
 
 8 Strands, 19 Wires per Strand, 1 Hemp Core. 
 
 Diam. In 1 7/ 8 3/ 4 5/ 8 9/ 16 i/ 2 
 
 Approx. Circum., in 3 2 % 2 M 2 1% H/ 2 
 
 Weight per ft., Ib 1.42 1.08 0.80 0.56 0.45 0.35 
 
 Approximate Strength, tons 
 
 (2000 Ibs.) 16.0 13.0 9.5 7.0 6.0 5.0 
 
 Working Load, tons (2000 Ibs.) 3 . 1 2.6 1.9 l."4 1.2 1.0 
 Min. Diam of Drum, ft 6.0 5.5 4.5 4.0 3.5 3.0 
 
 Steel-Clad Hoisting Rope. The regular grades of hoisting ropes, 
 as well as the special flexible and extra flexible, are furnished, if de- 
 sired, with a flat strip of steel wound spirally around each strand. 
 These give additional wearing surface without sacrificing the flexibility. 
 When the flat winding is worn through, a complete rope remains with 
 unimpaired strength. These ropes are designed for severe conditions 
 of service, and an additional service of 50 to 100 per cent over that of 
 the unprotected rope is frequently obtained. The hoisting rope 
 tables on pages 257 and 259 may be used for the strength of steel- 
 clad rope, by referring to the diameter of the rope, as it would be were 
 no wrapping applied. The steel wrapping is not considered as adding 
 any strength to the rope, but merely serving to increase its life. 
 
 Flat Rope. Flat rope consists of a number of "flat-rope" strands, 
 twisted alternately right and left, placed side by side and served with 
 soft Swedish iron or steel wire, to form a flat rope of the desired width 
 and thickness. The soft sewing wires wear much quicker than the 
 rope wire, and have to be replaced from time to time, at which time 
 worn strands can also be renewed. Flat rope is used principally for 
 hoisting heavy loads out of deep shafts, it requiring a reel but little 
 larger than the width of the rope, whereas round rope necessitates 
 the use of a large drum. Its use is recommended where saving of 
 machinery space is an object. It does not twist or spin in the shaft, 
 It is also used for operating spouts on coal and ore docks, and for raising 
 and lowering emergency gates on canals and similar machinery. For 
 details of methods of fastening it to drums, the manufacturers should 
 be consulted. Drums and sheaves should be as large as possible. A 
 rule for the diameter of the drum is D = c t, where D is diameter of 
 drum at bottom; ft., t = thickness of rope; in. and c = 100 for drums 
 and 160 for sheaves. Sheaves should be crowned at the center and 
 have deep flanges to guide the rope. See table, page 261. 
 
 Track Cable for Aerial Tramways. Composed of several successive 
 layers of wires wrapped around a single wire core, the number of 
 wires varying with the diameter of the cable. The cable is made in 
 plow steel and crucible steel grades 
 
 Track Cable for Aerial Tramways. 
 
 21/2 
 21/4 
 
 Breaking 
 Stress Tons 
 (2000 Lbs.). 
 
 1310 
 1036 
 935 
 840 
 728 
 
 161.0 189.0 
 
 13/4 
 
 1V8 
 H/2 
 13/8 
 U/4 
 
 Breaking 
 Stress Tons 
 (2000 Lbs.). 
 
 145.8 
 124.0 
 108.4 
 88.8 
 .71.8 
 
 171.0 
 146.0 
 127.5 
 105.0 
 84.6 
 
 H/8 
 
 V8 
 3/4 
 
 5/8 
 
 Breaking 
 St'ssTons 
 (2000 Lbs.) 
 
 60.0 
 49.2 
 37.6 
 27.6 
 19.2 
 
STEEL FLAT EOPB. 
 
 261 
 
 Non-Spinning Hoisting Rope. 
 
 18 Strands, 7 Wires per Strand, 1 Hemp Core. 
 
 
 d 
 
 
 Approximate Breaking 
 Strength, Tons (2000 Lb.). 
 
 Allowable Working Load, 
 Tons (2000 Lb.). 
 
 4 
 
 d 
 
 M 
 
 5 . 
 
 \ 
 
 i 
 & 
 
 ;ble Cast 
 ;1 Rope. 
 
 4 
 
 1 
 o5 
 
 tor PlowT 
 ;1 Rope. 
 
 1 
 
 rt 
 
 ible Cast 
 ;1 Rope. 
 
 2^o; o 
 
 L 
 
 tor Plow 
 ;1 Rope. 
 
 Diameter 
 m or Shea A 
 
 1 
 
 a 
 
 
 
 
 P 
 
 Ceo 
 
 lol 
 
 ft 
 
 3 
 
 
 e S 
 
 el 
 
 lul 
 
 11 
 
 | 
 
 ! 
 
 3 
 
 
 p 
 
 >H 
 
 
 
 w 
 
 S 
 
 ^ 
 
 M 
 
 
 
 w 
 
 S 
 
 ^ 
 
 S 
 
 13/4 
 
 51/2 
 
 5.50 
 
 45.80 
 
 85.90 
 
 101.00 
 
 111.10 
 
 122.00 
 
 9.1 
 
 17.1 
 
 20.2 
 
 22.2 
 
 24.04 
 
 7.00 
 
 15/8 
 
 5 
 
 4.90 
 
 39.80 
 
 74.40 
 
 87.60 
 
 96.30 
 
 
 7.9 
 
 14.8 
 
 17.5 
 
 19.2 
 
 
 6.50 
 
 
 43/4 
 
 4.32 
 
 34.00 
 
 63.80 
 
 75.00 
 
 82.50 
 
 90 '.70 
 
 6.8 
 
 12.7 
 
 15.0 
 
 16.5 
 
 18J 
 
 6.00 
 
 13/8 
 
 41/4 
 
 3.60 
 
 28.20 
 
 52.00 
 
 62.40 
 
 68.60 
 
 75.50 
 
 5.6 
 
 10.4 
 
 12.4 
 
 13.7 
 
 15.1 
 
 5.50 
 
 U/4 
 
 4 
 
 2.80 
 
 23.40 
 
 43.80 
 
 51.60 
 
 56.80 
 
 62.50 
 
 4.6 
 
 8.7 
 
 10.3 
 
 11.3 
 
 12.5 
 
 5.00 
 
 H/8 
 
 31/2 
 
 2.34 
 
 19.60 
 
 36.80 
 
 43.20 
 
 47.50 
 
 52.20 
 
 3.9 
 
 7.3 
 
 8.6 
 
 9.5 
 
 10.4 
 
 4.50 
 
 1 
 
 3 
 
 1.73 
 
 14.95 
 
 28.00 
 
 33.00 
 
 36.30 
 
 39.00 
 
 2.9 
 
 5.6 
 
 6.6 
 
 7.2 
 
 7.8 
 
 4.00 
 
 7/8 
 
 23/4 
 
 1.44 
 
 11.95 
 
 22.50 
 
 26.50 
 
 31.80 
 
 35.00 
 
 2.3 
 
 4.5 
 
 5.3 
 
 6.3 
 
 7.0 
 
 3.50 
 
 3/ 4 
 
 21/4 
 
 1.02 
 
 8.85 
 
 16.70 
 
 19.60 
 
 24.60 
 
 27.00 
 
 1.7 
 
 3.3 
 
 3.9 
 
 4.9 
 
 5.4 
 
 3.00 
 
 ! 5/8 
 
 2 
 
 0.70 
 
 5.90 
 
 11.10 
 
 13.10 
 
 15.75 
 
 17.30 
 
 1.1 
 
 2.2 
 
 2.6 
 
 3.1 
 
 3.4 
 
 2.50 
 
 9/16 
 
 13/4 
 
 0.57 
 
 4.85 
 
 9.10 
 
 10.70 
 
 12.80 
 
 
 0.97 
 
 1.8 
 
 2.1 
 
 2.5 
 
 
 2.25 
 
 1/2 
 
 U/2 
 
 0.42 
 
 3.65 
 
 6.90 
 
 8.10 
 
 9.75 
 
 iojo 
 
 0.73 
 
 1.3 
 
 1.6 
 
 1.9 
 
 2.\ 
 
 2.00 
 
 7/16 
 
 U/4 
 
 0.31 
 
 2.63 
 
 4.90 
 
 5.80 
 
 6.85 
 
 
 0.52 
 
 0.98 
 
 1.1 
 
 1.3 
 
 
 1.75 
 
 3/8 
 
 H/8 
 
 0.25 
 
 2.10 
 
 3.90 
 
 4.60 
 
 5.55 
 
 6.16 
 
 0.42 
 
 0.78 
 
 0.92 
 
 1.1 
 
 \'.2 
 
 1.50 
 
 Steel Flat Kope. 
 
 A 
 
 V 
 
 g 
 
 1/4 
 1/4 
 1/4 
 1/4 
 
 JJ/16 
 5/16 
 5/16 
 5/16 
 
 ^ 16 
 5/16 
 
 d 
 4 
 
 1 
 
 U/2 
 
 h 
 
 U/2 
 
 21/2 
 
 31/2 
 
 i 
 
 e r 
 1 
 ^ 
 
 0.65 
 0.82 
 1.06 
 1.23 
 
 Allow- 
 able 
 Working 
 Load, 
 Tons 
 (2000 
 Lbs.). 
 
 d 
 1 
 
 'rS 
 
 3/8 
 3/8 
 3/8 
 3/8 
 
 1/2 
 
 V2 
 1/2 
 V2 
 1/2 
 V 
 1/2 
 1/2 
 1/2 
 
 d 
 
 H- 1 
 
 1 
 
 g 
 
 41/2 
 51/2 
 
 6 
 
 d 
 
 d 
 
 5 
 
 ? 
 
 Allow- 
 able 
 Working 
 Load, 
 Tons 
 (2000 
 Lbs.). 
 
 d 
 
 1 
 
 1 
 1 
 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 
 1/4 
 3/4 
 3/4 
 3/4 
 
 S 
 
 M 
 
 
 3 
 $ 
 
 
 
 1 
 
 
 Allow- 
 able 
 Working 
 Load, 
 Tons 
 (2000 
 Lbs.). 
 
 ll 
 f 
 
 2.6 
 3.4 
 4.4 
 5.2 
 
 |S 
 
 S 
 
 ^4 
 
 rJ2 Q} 
 
 I 1 
 
 O 
 
 |l 
 
 S 
 
 ~ 
 
 11 
 
 5 M 
 
 O 
 
 |oa 
 S 
 
 21.0 
 
 23.8 
 26.4 
 29.0 
 34.2 
 39.4 
 
 3.10 
 4.00 
 5.30 
 6.20 
 
 2.85 
 3.10 
 3.50 
 3.73 
 
 12.6 
 13.6 
 15.4 
 16.2 
 
 6.6 
 16.2 
 18.4 
 19.4 
 
 41/2 
 51/2 
 
 6 
 7 
 8 
 
 4.55 
 5.10 
 5.65 
 6.15 
 7.30 
 8.40 
 
 18.2 
 20.4 
 22.8 
 25.0 
 29.6 
 34.0 
 
 0.79 
 1.10 
 1.35 
 1.60 
 1.88 
 2.15 
 
 3.6 
 4.6 
 6.0 
 7.2 
 8.2 
 9.6 
 
 4.4 
 5.6 
 7.0 
 8.6 
 10.0 
 11.4 
 
 21/2 
 
 31/2 
 
 41/2 
 
 51/2 
 
 6 
 7 
 
 2.20 
 2.50 
 2.80 
 3.15 
 3.85 
 4.20 
 4.55 
 4.90 
 5.90 
 
 9.0 
 10.4 
 12.0 
 13.8 
 16.6 
 18.0 
 19.6 
 21.0 
 25.6 
 
 10.8 
 12.6 
 14.4 
 16.4 
 19.8 
 21.6 
 23.6 
 25.2 
 30.6 
 
 5 
 6 
 7 
 8 
 
 6.85 
 7.50 
 8.25 
 9.75 
 
 27.0 
 30.2 
 33.6 
 40.4 
 
 31.4 
 35.0 
 38.8 
 46.8 
 
 3/8 
 3/8 
 
 3 /8 
 3/8 
 3/8 
 
 2 
 
 21/2 
 31/2 
 
 1.30 
 1.70 
 1.89 
 2.30 
 2.43 
 
 5.4 
 7.2 
 8.2 
 10.0 
 10.8 
 
 6.6 
 8.6 
 9.8 
 12.0 
 13.0 
 
 V8 
 7/8 
 7/8 
 7/8 
 
 5 
 6 
 7 
 8 
 
 7.50 
 9.53 
 9.56 
 10.60 
 
 31.0 
 36.0 
 40.6 
 45.0 
 
 34.4 
 41.8 
 46.6 
 51.6 
 
 5/8 
 5/8 
 
 31/2 
 
 3.50 
 4.00 
 
 13.6 
 15.8 
 
 15.8 
 18.4 
 
 
 
 
 
 
 The allowable working load in the above table is 1/5 of the approxi- 
 mate breaking stress of the rope. 
 
262^ 
 
 MATERIALS. 
 
 Locked Wire Cable. Locked wire cable and locked coil-track 
 cable, of the general form shown in Fig. 77, are used as track cables 
 for aerial tramways. They differ only in the number and size of 
 
 Fig. 77. 
 
 wires used, and both are made of crucible cast steel. The locked 
 wire cable is the more flexible of the two. These cables are smoother 
 than the track cable described on page 260. 
 
 Locked Coil and Locked Wire Cable. 
 
 d 
 
 Wt. per 
 Ft., Lb. 
 
 Break- 
 ing 
 
 Stress, 
 Tons 
 (2000 
 
 Lbs.). 
 
 ^ 
 j 
 
 3 
 
 Wt. 
 Ft., 
 
 per 
 Lb. 
 
 Break- 
 ing 
 Stress, 
 Tons 
 (2000 
 Lbs.). 
 
 d 
 
 3 
 
 Wt. per 
 Ft., Lbs. 
 
 Break- 
 ing 
 Stress 
 Tons 
 (2000 
 Lbs.). 
 
 TJ 
 
 0)_i 
 
 9 
 
 fl 
 
 Id 
 o o 
 oO 
 
 0) OJ 
 
 x.% 
 
 $* 
 
 Ji 
 
 2 
 
 'd 
 o> o> 
 
 ja.SJ 
 
 P 
 
 h 
 
 ^ 
 
 Locked 
 Wire. 
 
 *j 
 
 8? 
 
 J 
 
 82 
 
 3 s 
 
 Ij 
 
 a? 
 
 J 
 
 'O 
 0) 0) 
 -M.S3 
 
 S* 
 
 21/2 
 
 2.A 
 
 13/4 
 15/8 
 
 6.30 
 
 15.60 
 12.50 
 10.00 
 7.65 
 6.60 
 
 J03 
 
 240 
 190 
 160 
 120 
 103 
 
 H/2 
 13/8 
 U/4 
 H/8 
 
 5.30 
 4.40 
 3.70 
 3.00 
 2.35 
 
 5:S 
 
 3.80 
 3.15 
 2.50 
 
 89 
 75 
 62 
 50 
 40 
 
 89 
 75 
 62 
 50 
 40 
 
 7/8 
 3/4 
 5/8 
 9/16 
 V2 
 
 . 1.80 
 
 1.88 
 1.30 
 0.90 
 0.72 
 0.57 
 
 30 
 
 30 
 
 22 
 15.5 
 12.5 
 10 
 
 Galvanized Steel Hawser. 
 
 For Lake and Deep Sea Towing and Mooring Lines. 
 
 fi 
 
 Q 
 
 C 
 
 
 
 Six 3 7- Wire 
 Strands, 1 
 Hemp Core 
 
 Six 24- Wire 
 Strands, 7 
 Hemp Cores. 
 
 d 
 
 B 
 
 3 
 
 Circum., In. 
 
 Six 3 7- Wire 
 Strands, 1 
 Hemp Core. 
 
 Six 24- Wire 
 Strands, 7 
 Hemp Cores 
 
 
 
 i 
 
 jja 
 
 ^^ 
 
 1 
 
 HA 
 
 rg3 
 c M^: 
 S|| 
 
 ^ 
 
 
 
 1. 
 
 4J.fl 
 
 ^^ 
 
 1 
 
 H -A 
 
 1^ 
 
 311 
 
 JcotJ. 
 
 
 
 *. 
 
 4J^5 
 
 ^ 
 
 | 
 
 E?A 
 
 ^ 
 
 ! 
 
 M^^ 
 
 
 
 1 . 
 
 .ij-Q 
 
 pH 
 
 0) 
 
 I. 
 
 9& 
 
 1^1 
 w^^ 
 
 23/8 
 25/16 
 21/4 
 21/8 
 21/16 
 
 1 15/16 
 1 13/16 
 13/4 
 1 H/16 
 15/8 
 
 71/2 
 71/4 
 71/8 
 63/4 
 61/2 
 61/4 
 
 6 
 
 53/4 
 51/2 
 
 jvi 
 
 8.82 
 8.36 
 8.00 
 7.06 
 6.65 
 6.30 
 5.84 
 5.13 
 4.85 
 4.42 
 4.15 
 
 188 
 182 
 171 
 155 
 140 
 132 
 125 
 112 
 104 
 97 
 87 
 
 5^8i 
 5.51 
 5.09 
 4.48 
 4.24 
 3.86 
 3.63 
 
 ii3 
 
 106 
 98 
 88 
 82 
 76 
 74 
 
 H/2 
 17/16 
 13/8 
 H/4 
 13/16 
 H/8 
 H/16 
 
 7/8 
 13/16 
 3/4. 
 
 43/4 
 41/2 
 41/4 
 
 33/4 
 
 31/2 
 
 3. A 
 
 23/ 4 
 
 21/2 
 21/4 
 
 3.55 
 3.24 
 3.00 
 2.45 
 2.21 
 2.00 
 1.77 
 1.58 
 1.20 
 1.03 
 0.89 
 
 76 
 72 
 66 
 54 
 47 
 42 
 38 
 31.5 
 26 
 22 
 20 
 
 3.10 
 2.92 
 2.62 
 2.15 
 .93 
 .75 
 .54 
 .38 
 .05 
 0.90 
 78 
 
 63 
 55 
 50 
 42 
 38 
 34 
 27 
 25 
 20 
 17 
 14 
 
SPLICING WIRE ROPES. 
 
 203 
 
 To Splice a Wire Rope. The tools required will be a email marline 
 spike, nipping cutters, and either clamps or a small hemp-rope sling with 
 which to wrap around and untwist the rope. If a bench-vise is acces- 
 sible it will be found convenient. 
 
 In splicing rope, a certain length is used up in making the splice. An 
 allowance of not less than 16 feet for i/2-mch rope, and proportionately 
 longer for larger sizes, must be added to the length of an endless rope in 
 ordering. 
 
 Having measured, carefully, the length the rope should be after splicing, 
 and marked the points M and M', Fig. 78, unlay the strands from each 
 end E and E' to M and M' and cut off the center at M and M', and then: 
 
 (1). Interlock the six unlaid strands of each end alternately and draw 
 them together so that the points M and M' meet, as in Fig. 79. 
 
 (2). Unlay a strand from one end, and following the unlay closely, lay 
 into the seam or groove it opens, the strand opposite it belonging to the 
 other end of the rope, until within a length equal to three or four times 
 the length of one lay of the rope, and cut the other strand to about the 
 same length from the point of meeting as at A, Fig. 80. 
 
 (3). Unlay the adjacent strand in the opposite direction, and following 
 the unlay closely, lay in its place the corresponding opposite strand, cut- 
 ting the ends as described before at B, Fig. 80. 
 
 There are now four strands laid in place terminating at A and B, with 
 the eight remaining at MM', as in Fig. 80. 
 
 It will be well after laying each pair of strands to tie them temporarily 
 " the points A and B. 
 
 M 
 
 \B 
 
 FIG. 80. 
 
 A A A% 
 
 A A' A" M B B' B" 
 
 FIG. 81. SPLICING WIRE ROPE. FIG. 82. 
 
 Pursue the same course with the remaining four pairs of opposite 
 strands, stopping each pair about eight or ten turns of the rope short of 
 the preceding pair, and cutting the ends as before. 
 
 We now have all the strands laid in their proper places with their re- 
 spective ends passing each other, as in Fig. 81. 
 
 All methods of rope-splidng are identical to this point: their variety 
 consists in the method of tucking the ends. The one given below is the 
 one most generally practiced. 
 
 Clamp the rope either in a vise at a point to the left of A, Fig. 81, and 
 by a hand-clamp applied near A, open up the rope by untwisting suffi- 
 ciently to cut the core at A, and seizing it with the nippers, let an assis- 
 tant draw it out slowly, you following it closely, crowding the strand in 
 its place until it is all laid in. Cut the core where the strand ends, and 
 push the end back into its place. Remove the clamps and let the rope 
 close together around it. Draw out the core in the opposite direction 
 and lay the other strand in the center of the rope, in the same manner. 
 Repeat the operation at the five remaining points, and hammer the rope 
 lightly at the points where the ends pass each other at A, A, B, B, etc., 
 with small wooden mallets, and the splice is complete, as shown in Fig. 82. 
 
 If a clamp and vise are not obtainable, two rope slings and short 
 wooden levers may be used to untwist, and open up the rope. 
 
 A rope spliced as above will .be nearly as strong as the original rope 
 and smooth everywhere. After running a few days, the splice, if well 
 made, cannot be found except by close examination. 
 
 The above instructions have been adopted by the leading rope manu- 
 facturers of America. 
 
264 
 
 MATERIALS. 
 
 CHAINS. 
 
 Weight per Foot, Proof Test and Breaking Weight. 
 
 (Pennsylvania Railroad Specifications, 1903.) 
 
 Nominal 
 Diameter 
 of Wire. 
 Inches. 
 
 Description. 
 
 Maximum 
 Length of 
 100 Links. 
 Inches. 
 
 Weight 
 per 
 Foot. 
 Lbs. 
 
 Proof 
 Test. 
 Lbs. 
 
 Breaking 
 Weight. 
 Lbs. 
 
 5/00 
 
 Twisted chain 
 
 1 03 1/ 8 
 
 020 
 
 
 
 3/ 16 
 
 
 961/4 
 
 0.35 
 
 
 
 3/16 
 
 V4 
 5/16 
 3/8 
 3/s 
 
 Perfection twisted chain 
 Straight-link chain .... 
 
 Crane chain 
 
 151 1* 
 102 
 1143/4 
 1143/4 
 1135/0 
 
 0.27 
 0.70 
 1.10 
 1.60 
 1.60 
 
 1,600 
 2,500 
 3,600 
 4,140 
 
 3,200 
 5,000 
 7,200 
 8,280 
 
 7/16 
 7/16 
 
 Straight-link chain .... 
 Crane chain 
 
 127l/ 2 
 1261/4 
 
 2.07 
 2.07 
 
 4,900 
 5,635 
 
 9,800 
 11,270 
 
 V2 
 1/2 
 
 Straight-link chain .... 
 .Crane chain 
 
 153 /4 
 1511/2 
 
 2.50 
 2.60 
 
 6,400 
 7,360 
 
 12,800 
 14,720 
 
 5/8 
 
 5/0 
 
 Straight-link chain .... 
 Crane chain 
 
 1781/2 
 1763/4 
 
 4.08 
 4.18 
 
 10,000 
 11,500 
 
 20,000 
 23,000 
 
 3/4 
 3/i 
 
 Straight-link chain .... 
 Crane chain 
 
 204 
 202 
 
 5.65 
 5.75 
 
 14,400 
 16,560 
 
 28,800 
 33,120 
 
 7/8 
 
 
 2521/2 
 
 7.70 
 
 22,540 
 
 45,080 
 
 1 
 
 I K 
 
 277 ?/4 
 
 9.80 
 
 29,440 
 
 58,880 
 
 1 
 
 1 I/a 
 
 Straight-Jink chain 
 Crane chain 
 
 280l/ 2 
 303 
 
 9.80 
 12.65 
 
 25,600 
 38,260 
 
 51,200 
 76,520 
 
 1 1/4 
 
 
 3531/2 
 
 15.50 
 
 46,000 
 
 92,000 
 
 1 1/2 
 
 i 
 
 4165/ 8 
 
 22.50 
 
 66 240 
 
 132,480 
 
 1 3/1 
 
 <i 
 
 4793/4 
 
 30.00 
 
 90, 1 60 
 
 180,320 
 
 2 /4 
 
 " " 
 
 5551/2 
 
 39.00 
 
 117,760 
 
 235,520 
 
 Elongation of all sizes, 10 per cent. All chain must stand the proof 
 test without deformation. A piece 2 ft. long out of each 200 ft. is 
 tested to destruction. 
 
 British Admiralty Proving Tests of Chain Cables. Stud-links. 
 Minimum size in inches and 16ths. Proving test in tons of 2240 Ibs. 
 Min. Size: H * H ' it l- l& H JA H 1A II 
 Test, tons: 8 10.1 11.9 13f 15| 18 20.3 22f 25*fe 28.1 31 34 
 Min. Size: 1& 1* l T 9 s if Hi If Hi H Hi 2 2$ 
 Test, tons: 37*fc 40 43.9 474 51* 55.1 59.1 63* 6743 72 81* 
 
 Wrought-iron Chain Cables. The strength of a chain link is less 
 than twice that of a straight bar of a sectional area equal to that of one 
 side of the link. . A weld exists at one end and a bend at the other, each 
 requiring at least one heat, which produces a decrease in the strength. 
 The report of the committee of the U. S. Testing Board (1879), on tests 
 of wrought-iron and chain cables, contains the following conclusions. 
 That beyond doubt, when made of American bar iron, with cast-iron 
 studs, the studded link is inferior in strength to the unstudded one. 
 
 "That when proper care is exercised in the selection of material, a varia- 
 tion of 5 to 17 per cent of the strongest may be expected in the resistance 
 of cables. Without this care, the variation may rise to 25 per cent. 
 
 "That with proper material and construction the ultimate resistance of 
 the chain may be expected to vary from 155 to 170 per cent of that of the 
 bar used in making the links, and show an average of about 163 per cent. 
 
 "That the proof test of a chain cable should be about 50 per cent of 
 the ultimate resistance of the weakest link." 
 
 The decrease of the resistance of the studded below the unstudded 
 cable is probably due to the fact that in the former the sides of the link 
 do not remain parallel to each other up to failure, as they do in the latter. 
 The result is an increase of stress in the studded link over the unstudded 
 in the proportion of unity, to the secant of half the inclination of the 
 sides of the former to each other. 
 
 From a great number of tests of bars and unfinished cables, the commit- 
 tee considered that the average ultimate resistance, and proof tests of 
 chain cables made of the bars, whose diameters are given, should be 
 such as are shown in the accompanying table. 
 
CHAINS. 
 
 265 
 
 ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN CABLES. 
 
 Diam. 
 of 
 Bar. 
 
 Average resist. 
 = 163% of Bar. 
 
 Proof Test. 
 
 Diam. 
 of 
 Bar. 
 
 Average resist. 
 = 163% of Bar. 
 
 Proof Test 
 
 Inches. 
 
 Pounds. 
 
 Pounds. 
 
 Inches. 
 
 Pounds. 
 
 Pounds. 
 
 
 71,172 
 
 33,840 
 
 19/16 
 
 162,283 
 
 77,159 
 
 U/16 
 
 79,544 
 
 37,820 
 
 15/8 
 
 174,475 
 
 82,956 
 
 U/8 
 
 88,445 
 
 42,053 
 
 1 H/16 
 
 187,075 
 
 88,947 
 
 13/16 
 
 97,731 
 
 46,468 
 
 13/4 
 
 200,074 
 
 95,128 
 
 11/4 
 
 107,440- 
 
 51,084 
 
 1 13/16 
 
 213,475 
 
 101,499 
 
 15/16 
 
 117,577 
 
 55,903 
 
 17/8 
 
 227,271 
 
 108,058 
 
 13/8 
 
 128,129 
 
 60,920 
 
 1 15/16 
 
 241,463 
 
 114,806 
 
 17/16 
 
 139,103 
 
 66, 1 38 
 
 2 
 
 256,040 
 
 121,737 
 
 U/2 
 
 150,485 
 
 71,550 
 
 
 
 
 Pitch, Breaking, Proof and Working Strains of Chains. 
 
 (Bradlee & Co., Philadelphia.) 
 
 
 
 JO 
 
 
 D.B.G. Special Crane. 
 
 Crane. 
 
 .2 
 
 
 0> 
 
 ft 
 
 .2 
 
 ^ 
 
 |, 
 
 g 
 
 ,0 
 
 Jt 
 
 !p n 
 
 "i 
 
 .2 
 
 
 
 
 73 
 
 
 t->~* 
 
 *o3 C 
 
 
 (-<* 
 
 CJ5 fl 
 
 3 
 
 . 
 
 f* 
 
 P 
 
 1 
 
 1 
 
 M o 
 
 1 
 
 .s" 
 
 O 
 
 ? 
 
 .rH 
 
 X 
 
 o 
 
 0> 
 
 12 
 
 H 
 
 hc 
 o3C/} 
 
 &^ 
 
 
 OJ S 
 
 W) 
 
 *" ^Q 
 
 S-2" 
 
 V 
 
 O 
 
 ft 
 
 '5 
 
 o 
 
 <3 bfl 
 
 *rt rt * 
 
 O 
 
 (B hO 
 
 ^ m 
 
 N 
 
 
 ft 
 
 
 
 ^.2 
 
 
 
 >a 
 
 ^5p 
 
 w 
 
 K 
 
 A 
 
 O 
 
 P4 
 
 
 o 
 
 OH 
 
 
 
 1/4 
 
 25/32 
 
 3/4 
 
 15/16 
 
 1,932 
 
 3,864 
 
 1,288 
 
 1,680 
 
 3,360 
 
 1,120 
 
 5/16 
 
 27/32 
 
 1 
 
 U/8 
 
 2,898 
 
 5,796 
 
 1,932 
 
 2,520 
 
 5,040 
 
 1,680 
 
 3/8 
 
 31/32 
 
 U/2 
 
 15/16 
 
 4,186 
 
 8,372 
 
 2,790 
 
 3,640 
 
 7,280 
 
 2,427 
 
 7/16 
 
 15/32 
 
 2 
 
 U/2 
 
 5,796 
 
 11,592 
 
 3,864 
 
 5,040 
 
 10,080 
 
 3,360 
 
 1/2 
 
 1 H/32 
 
 21/2 
 
 1 13/16 
 
 7,728 
 
 15,456 
 
 5,152 
 
 6,720 
 
 13,440 
 
 4,480 
 
 9/16 
 
 1 15/32 
 
 33/io 
 
 2 
 
 9,660 
 
 19,320 
 
 6,440 
 
 8,400 
 
 16,800 
 
 5,600 
 
 5/8 
 
 I 23/3> 
 
 41/10 
 
 23/16 
 
 11,914 
 
 23,828 
 
 7,942 
 
 10,360 
 
 20,720 
 
 6,907 
 
 H/16 
 
 1 13/16 
 
 5 
 
 23/8 
 
 14,490 
 
 28,980 
 
 9,660 
 
 12,600 
 
 25,200 
 
 8,400 
 
 3/4 
 
 1 15/16 
 
 62/io 
 
 29/16 
 
 17,388 
 
 34,776 
 
 11,592 
 
 15,120 
 
 30,240 
 
 10,080 
 
 13/16 
 
 21/16 
 
 67/io 
 
 23/4 
 
 20,286 
 
 40,572 
 
 13,524 
 
 17,640 
 
 35,280 
 
 11,760 
 
 7/8 
 
 23/16 
 
 83/8 
 
 215/16 
 
 22,484 
 
 44,968 
 
 14,989 
 
 20,440 
 
 40,880 
 
 13,627 
 
 15/16 
 
 27/ie 
 
 9 
 
 33/16 
 
 25,872 
 
 51,744 
 
 17,248 
 
 23,520 
 
 47,040 
 
 15,680 
 
 
 21/2 
 
 101/2 
 
 33/ 8 
 
 29,568 
 
 59,136 
 
 19,712 
 
 26,880 
 
 53,760 
 
 17,920 
 
 11/16 
 
 25/8 
 
 12 
 
 39/16 
 
 33,264 
 
 66,538 
 
 22,176 
 
 30,240 
 
 60,480 
 
 20,160 
 
 U/8 
 
 23/ 4 
 
 135/g 
 
 313/16 
 
 37,576 
 
 75,152 
 
 25,050 
 
 34,160 
 
 68,320 
 
 22,773 
 
 13/16 
 
 31/16 
 
 137/io 
 
 4 
 
 41,888 
 
 83,776 
 
 27,925 
 
 38,080 
 
 76,160 
 
 25,387 
 
 11/4 
 
 31/8 
 
 16 
 
 43/ie 
 
 46,200 
 
 92,400 
 
 30,800 
 
 42,000 
 
 84,000 
 
 28,000 
 
 
 33/8 
 
 161/9 
 
 43/8 
 
 50,512 
 
 101 024 
 
 33,674 
 
 45,920 
 
 91,840 
 
 30,613 
 
 13/J 6 
 
 39/16 
 
 191/4 
 
 49/i 6 
 
 55,748 
 
 111,496 
 
 37,165 
 
 50,680 
 
 101,360 
 
 33,787 
 
 1 7/16 
 
 311/16 
 
 
 43/4 
 
 60,368 
 
 120,736 
 
 40,245 
 
 54,880 
 
 109,760 
 
 36,587 
 
 U/2 
 
 37/ 8 
 
 23 
 
 51/8 
 
 66,528 
 
 133,056 
 
 44,352 
 
 60,480 
 
 120,960 
 
 40,320 
 
 19/16 
 
 4 
 
 25 
 
 55/ie 
 
 70,762 
 
 141,524 
 
 47,174 
 
 65,520 
 
 131,140 
 
 43,180 
 
 13/4 
 
 43/4 
 
 31 
 
 57/8 
 
 82,320 
 
 164,640 
 
 54,880 
 
 
 
 
 2 
 
 53/4 
 
 40 
 
 63/ 4 
 
 107,520 
 
 215,040 
 
 71,680 
 
 
 
 
 21/4 
 
 63/4 
 
 523/4 
 
 75/8 
 
 136,080 
 
 272,160 
 
 90,720 
 
 
 
 
 2l/ 2 
 
 7 
 
 641/2 
 
 83/8 
 
 168,000 
 
 336,000 
 
 112,000 
 
 
 
 
 23/4 
 
 71/4 
 
 73 
 
 91/8 
 
 193,088 
 
 386, 1 76 
 
 128,725 
 
 
 
 
 3 
 
 73/4 
 
 86 
 
 97/8 
 
 217,728 
 
 435,456 
 
 145,152 
 
 
 
 
 The distance from center of one link to center of next is equal to the 
 inside length of link, but in practice 1/32 in. is allowed for weld. This is 
 approximate, and where exactness is required, chain should be made so. 
 
 FOR CHAIN SHEAVES. The diameter, if possible, should be not less 
 than thirty times the diameter of chain used. 
 
 EXAMPLE. For 1-inch chain use 30-inch sheaves. 
 
T&, 
 
 ~ ^ ' % J 
 
 ^,< 
 
 WTHEBEOOE 
 
 MATERIALS. 
 
 SHAPES AND SIZES OF FIRE-BRICK. 
 
 (Stowe-Fuller Co., Cleveland, 1914.) 
 
 Name of 
 Brick 
 or 
 
 Length, 
 Inches. 
 
 Width, 
 Inches. 
 
 Thick-' 
 ness, 
 Inches. 
 
 _ . 
 
 o| 
 
 0) t< 
 
 n& 
 
 ta 
 
 M0> 
 
 *- be 
 
 ' S 
 
 '? S 
 
 Tile. 
 
 
 j>tj 
 
 >3 
 
 IS 
 
 26 
 
 Ss 
 
 62 
 
 '2u 
 
 
 a 
 
 6 
 
 c 
 
 d 
 
 c 
 
 / 
 
 
 
 HH 
 
 STRAIGHT BRICK. 
 
 9-inch . 
 
 9 
 
 
 4l/o 
 
 
 21/2 
 
 
 
 
 Large 9-inch . . 
 Small 9- " . . 
 
 9 
 9 
 
 
 63/4" 
 
 31/0 
 
 
 21/2 
 
 
 
 
 Checker . . 
 
 9 
 
 
 3 
 
 
 3 
 
 
 
 
 Soap . . ., 
 No. 1 Split 
 
 9 
 9 
 
 
 21/2 
 
 41/0 
 
 
 21/4 
 
 
 
 
 No. 2 " ... 
 
 9 
 
 
 4l'/o 
 
 
 2 
 
 
 
 
 Checker Tile . I 
 
 1820, 
 
 } 
 
 6 
 
 
 3 
 
 
 
 
 Mill 
 
 24 
 1820, 
 
 ) 
 
 (. 
 
 9 
 
 
 3 
 
 
 
 
 Mill Block . 
 
 24 
 
 ' 
 
 9 
 
 
 6 
 
 
 
 
 No. 1 Bridgewall 
 No. 2 
 
 13 
 13 
 
 
 61/2 
 61/2 
 
 
 6 
 3 
 
 
 
 
 WEDGE SHAPE AND TAPER BRICKS. 
 Large 9-in. No 
 
 1 Wedge . . . 
 Large 9-in. No 
 
 2 Wedge... 
 No. 1 Wedge . 
 No. 2 " . 
 No. 1 Key*. . 
 No. 2 " * . . 
 No. 3 " * . . 
 No. 4 " * . . 
 No. 1 Archf. . 
 No. 2 " t- . 
 Side Skew . . . 
 End Skew . . . 
 Skew Back. . . 
 No. 1 Neck . . 
 No. 2 " . . 
 No. 3 " . . 
 Feather Edge . 
 Jamb . 
 
 Edge Arch 
 
 63/4 
 
 63/4 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41/2 
 41A> 
 
 4'" 
 
 31/2 
 21/4 
 
 13/4 
 
 ii/2 
 V" 
 
 21/2 
 
 21/2 
 21/2 
 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 21/2 
 
 21/0 
 
 17/8 
 U/2 
 U/2 
 
 2" 
 
 ../, 
 
 
 
 102 
 
 63 
 102 
 63 
 112 
 65 
 41 
 26 
 72 
 42 
 
 60 
 
 30 
 60 
 30 
 144 
 72 
 36 
 18 
 48 
 24 
 
 
 
 
 
 '5/8 
 
 1/8 
 
 2" 
 
 
 
 
 36 
 
 CIRCLE BRICK, Curved Edges. 
 
 No. 1 . 
 No. 2. 
 
 No! 4 '. 
 No. 5. 
 
 81/2 
 
 9 
 
 9 
 9 
 9 
 
 51/4 4i/ 2 !.. 
 69/1641/2.. 
 
 73/1641/2 .. 
 79/16 41/2 . . 
 75/8 41/ 2 . . 
 
 . 2l/ 2 . 
 
 . 21/2' . 
 
 . 2l/ 2 . 
 
 . 21/2 . 
 
 : 21/2 . 
 
 9 
 II 
 14 
 20 
 
 24 
 
 CUPOLA BLOCKS. 
 
 No. 1 
 No. 2 . . 
 
 9 
 
 63/8 
 
 63/4 
 
 6 
 6 
 
 
 4 
 4 
 
 
 15 
 17 
 
 30 
 36 
 
 No. 3 . 
 
 9 
 
 71/8 
 
 6 
 
 
 4 
 
 
 71 
 
 48 
 
 No. 4 
 
 9 
 
 71/2 
 
 6 
 
 
 4 
 
 
 52 
 
 60 
 
 * Tapers lengthwise, t Tapers breadthwise. 
 
 Other special shapes of brick and tile manufactured are: Locomo- 
 tive tile, 32, 34, and 40 in. X 10 in. X 3 in. ; 34 and 36 in. X 8 in. X 3 in. 
 Blast Furnace Shapes, 13 H X 6 X 2^ in. straight; No. 1, 12 ft. Key 
 
NUMBER OF FIEE BRICK FOR CIRCLES. 
 
 267 
 
 13^X6 X5X2H in. thick, 91 brick to circle; No. 2, 6 ft. Key 
 13 J^ X 6 X 43/8 X 2% in. thick, 53 brick to circle; bottom blocks, 
 18 X 9 X 4 1 A in. straight. Standard Block Linings, 9X9, 12 X 9, 
 15 X 9, 18 X 9, all 4 V in. thick, made straight, and as key-brick 
 for use with straight brick to line any diameter of furnace ; the key- 
 bricks are made for radii of 5, 7 1 A, and 10 ft. Pottery Kiln Brick, 
 flat back, 9X6 X 2 H in. ; flat back arch, 9X6X3^X2^ in.; 
 56 brick to a 32-inch inside diam. circle, No. 2 flat back arch, 9X6 
 X 3 y X 2 in., 31 brick to a 22-inch inside diam. circle. 
 
 A straight 9-inch fire-brick weighs 7 Ibs., a silica brick, 6.2 Ibs.; a 
 magnesia brick, 9 Ibs. ; a chrome brick, 10 Ibs. A silica brick expands 
 about i/s inch per foot when heated to 2,500 F. 
 
 Clay brick expand or shrink, dependent upon the proportion of 
 silica to alumina contained in the brick; but most fire clay brick 
 contain alumina sufficient to show some shrinkage. 
 
 One cubic foot of wall requires 17, 9-inch bricks; one cubic yard, 
 requires 460. Where keys, wedges, and other "shapes" are used, add 
 10 per cent, in estimating the number required. 
 
 To secure the best results, fire-brick should be laid in the same clay 
 from which they are manufactured. One ton of ground clay should 
 be sufficient to lay 3,000 ordinary bricks. It should be used as a 
 thin paste and not as mortar. The thinner the joint the better the 
 furnace wall. In ordering bricks, the service for which they are to be 
 used should be stated. 
 
 Silica brick should be laid in silica cement and with the smallest 
 joint possible. 
 
 Ground fire-brick or old cupola blocks mixed with fire-clay make 
 the best cupola daub known. 
 
 NUMBER OF FIRE-BRICK REQUIRED FOR VARIOUS 
 CIRCLES. 
 
 Diam. 
 of 
 Circle. 
 
 Key Bricks. 
 
 Arch Bricks. 
 
 Wedge Bricks. 
 
 -T 
 
 d 
 
 
 cK 
 
 6 
 
 
 <M 
 
 6 
 fc 
 
 6 
 
 "ttf 
 1 
 
 s 
 
 6 
 
 6 
 
 .s 
 
 Ov 
 
 la 
 "o 
 H 
 
 <s 
 
 6 
 
 d 
 fc 
 
 .s 
 
 0> 
 
 3 
 S 
 
 ft. in. 
 1 6 
 2 
 2 6 
 3 
 3 6 
 4 
 4 6 
 5 
 5 6 
 6 
 6 6 
 7 
 7 6 
 8 
 8 6 
 9 
 9 6 
 10 
 10 6 
 II 
 11 6 
 12 
 12 6 
 
 25 
 17 
 9 
 
 "\3 
 25 
 ^8 
 
 
 
 25 
 30 
 34 
 38 
 42 
 46 
 
 
 
 
 
 
 
 
 
 42 
 31 
 21 
 10 
 
 
 
 42 
 
 
 
 
 
 18 
 36 
 54 
 7? 
 
 
 49 
 57 
 64 
 72 
 80 
 87 
 95 
 102 
 110 
 117 
 125 
 132 
 140 
 147 
 155 
 162 
 170 
 177 
 185 
 193 
 
 60 
 
 48 
 36 
 24 
 12 
 
 '26' 
 40 
 59 
 79 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 
 '"s" 
 
 15 
 
 23 
 30 
 38 
 46 
 53 
 61 
 68 
 76 
 83 
 91 
 98 
 106 
 
 60 
 68 
 76 
 83 
 91 
 98 
 106 
 113 
 121 
 128 
 136 
 144 
 151 
 159 
 166 
 174 
 181 
 189 
 196 
 204 
 
 
 
 
 32 
 25 
 19 
 13 
 6 
 
 10 
 21 
 32 
 42 
 53 
 63 
 
 
 
 51 
 55 
 59 
 63 
 
 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 
 8 
 15 
 23 
 30 
 38 
 45 
 53 
 60 
 68 
 75 
 83 
 90 
 98 
 105 
 113 
 121 
 
 
 
 58 
 52 
 47 
 42 
 37 
 31 
 26 
 21 
 16 
 11 
 5 
 
 9 
 19 
 29 
 38 
 47 
 57 
 66 
 76 
 85 
 94 
 104 
 113 
 113 
 
 67 
 71 
 76 
 80 
 84 
 88 
 92 
 97 
 101 
 105 
 109 
 113 
 117 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch 
 brick as may be needed in addition. 
 
268 
 
 MATERIALS. 
 
 Refractoriness of Some American Fire-Brick. (R. F. Weber, 
 A. I. M. E., 1904.) Prof. Heinrich Ries notes that the fusibility of New 
 Jersey brick is influenced largely by its percentage of silica, but also in 
 part by the texture of the clay. It was found that the fustion-point of 
 almost any of the New Jersey fire-bricks could be reduced four or five 
 Seger cones by grinding the brick sufficiently fine to pass through a 
 700-mesh sieve. 
 
 Mr. Weber draws the conclusion from his tests of 44 bricks that it is 
 evident that the refractoriness of a fire-brick depends on the total quan- 
 tity of fluxes present, the silica percentage and the coarseness of grain; 
 moreover, chemical analysis alone cannot be used as an index of the 
 refractoriness except within rather wide limits. The following table 
 shows the composition, fusion-point, and physical properties of six 
 most refractory and of five least refractory of the 44 bricks. 
 
 J.3 
 
 
 
 
 
 
 1 
 
 
 
 
 Locality. 
 
 Si0 2 . 
 
 A1 2 O 3 . 
 
 Fe.03. 
 
 TiO 2 . 
 
 ill 
 
 J3tJ& 
 
 4 
 
 *-! fl 
 
 6 5? 
 
 
 
 
 
 
 J^ra5 
 
 eg 
 
 ' Cr^ 
 
 55 
 
 
 
 
 
 
 < 
 
 sT 
 
 3 
 
 
 
 Per 
 
 Per 
 
 Per 
 
 Per 
 
 Per 
 
 Per 
 
 No. 
 
 
 
 cent. 
 
 cent. 
 
 cent. 
 
 cent. 
 
 cent. 
 
 cent. 
 
 
 1.... 
 
 Missouri . 
 
 51 59 
 
 38 26 
 
 1 84 
 
 1 97 
 
 6 34 
 
 10 25 
 
 32 to 33 
 
 
 Kentucky 
 
 54.90 
 
 38.19 
 
 2J8 
 
 K55 
 
 3J8 
 
 6.91 
 
 32 to 33 
 
 y'.'.'. 
 
 Pennsylvania 
 
 53.05 
 
 41.16 
 
 2.65 
 
 1.80 
 
 1.34 
 
 5.79 
 
 32 to 33 
 
 4.... 
 
 Colorado 
 
 93.57 
 
 2.53 
 
 0.62 
 
 0.27 
 
 3.01 
 
 3.90 
 
 32 to 33 
 
 5... 
 
 Ken tucky 
 
 44 77 
 
 43 08 
 
 2 78 
 
 2 54 
 
 6 83 
 
 12.15 
 
 31 to 32 
 
 6 
 
 New York 
 
 68 70 
 
 20 75 
 
 1 20 
 
 5 54 
 
 3 81 
 
 10 55 
 
 31 to 32 
 
 40.... 
 
 Pennsylvania 
 
 61.28 
 
 27.13 
 
 2.90 
 
 1.37 
 
 7.31 
 
 11.58 
 
 26 
 
 41.... 
 
 Pennsylvania 
 
 74.83 
 
 16.40 
 
 3.26 
 
 0.77 
 
 4.74 
 
 8.77 
 
 26 
 
 42... 
 
 Alabama 
 
 67 19 
 
 25.05 
 
 2 83 
 
 71 
 
 4.22 
 
 7 76 
 
 26 
 
 43 
 
 Indiana 
 
 60 76 
 
 31 66 
 
 5 67 
 
 1 58 
 
 33 
 
 7 58 
 
 26 
 
 44. ... 
 
 Kentucky 
 
 60.58 
 
 32.49 
 
 2.25 
 
 1.69 
 
 2.99 
 
 6.93 
 
 26 
 
 1 Fairly uniform, angular flint-clay particles, constituting body of 
 brick. Largest pieces 5 to 6 mm. in diameter. White. 
 
 2 Coarse-grained ; angular pieces of flint-clay as large as 9 mm. Aver- 
 age 4 to 5 mm. Light buff. 
 
 3 Coarse, angular flint-clay particles, varying from 1 to 5 mm. in 
 diameter. Average 4 to 5 mm. Buff. 
 
 4 Fine-grained quartz particles. Largest 2 to 3 mm. in diameter. 
 White. 
 
 6 Medium grain; flint-clay particles, fairly uniform in size, 3 to 4 mm. 
 Light buff. 
 
 6 Coarse grain; quartz particles, 4 to 5 mm. in diameter, forming 
 about 50 per cent of brick. White. 
 
 40 Fine grain; small, white flint-clay particles, not over 2 mm. in 
 diameter and not abundant. Buff. 
 
 41 Medium grain; pieces of quartz with pinkish color and angular flint- 
 clay particles. About 3 mm. in diameter. Buff. 
 
 42 Fine grain; even texture. Few coarse particles. Brown. 
 
 tt Fine grain; some particles as large as 1 to 2 mm. in diameter. Buff. 
 44 Angular, dark-colored, flinty-clay particles. Maximum size 5 mm. 
 Throughout a reddish-brown matrix. 
 
 SLAG BRICKS AND SLAG BLOCKS. 
 
 Slag bricks are made by mixing granulated basic slag and slaked lime, 
 molding the mixture in a brick press or by hand, and drying. The silica 
 in the slag ranges from 22.5% to 35%; the alumina andiron oxide together, 
 from 16.1% to 21%; the lime, from 40% to 51.5%. The granulated slag 
 is dried and pulverized. Powdered slaked lime is added in sufficient quan- 
 
ANALYSES OF FIRE CLAYS. 
 
 269 
 
 tity to bring the total calcium oxide in the mixture up to about 55%. 
 Usually a small amount of -water is added. The mixture is then molded 
 into shape, and the bricks are then dried for six to ten days in the open 
 air. Slag bricks weigh less than clay bricks of equal size, require less 
 mortar in laying up, and are at least equal to them in crushing strength. 
 
 Slag blocks are made by running molten slag direct from the furnaces 
 into molds. If properly made, they are stronger than slag bricks. They 
 are, however, impervious to air and moisture; and on that account 
 dwellings constructed of them are apt to be damp. Their chief uses are 
 for foundations or for paving blocks. The properties required in a slag 
 paving block, viz: density, resistance to abrasion, toughness, and rough- 
 ness of surface, vary with the chemical composition of the slag, the 
 rapidity of cooling, .and the character of the molds used. Blocks cast in 
 sand molds, and heavily covered with loose sand, cool slowly, and give 
 much better results than those cast in iron molds. E. C. Eckel, Ena. 
 News, April 30, 1903. 
 
 ANALYSES OF FIRE CLAYS. 
 
 Brand. 
 
 Titanic Acid, 
 TiO 2 
 
 O 
 33 
 
 i 
 
 s 
 
 m 
 
 Alumina, 
 A1 2 3 
 
 B 
 
 p 
 
 O 
 1 
 
 I 
 
 S 
 
 
 oT 
 
 '3 
 
 lo 
 
 !* 
 
 9, 
 W 
 
 
 
 n 
 
 1 
 
 9, 
 
 1 
 
 C8 
 
 1 
 
 Total Im- 
 purities. 
 
 1 
 
 Mt Savage^- 
 
 
 50.46 
 56.80 
 44.40 
 56.15 
 55.87 
 56.80 
 67.84 
 68.01 
 48.35 
 44.80 
 
 51.50 
 63.18 
 44.61 
 45.26 
 67.47 
 65.60 
 73.82 
 65.41 
 53.40 
 55.46 
 
 73.71 
 67.12 
 
 35.90 
 30.08 
 33.56 
 33.30 
 41.39 
 30.08 
 21.83 
 24.09 
 36.37 
 39.00 
 
 44.85 
 23.70 
 38.01 
 37.85 
 19.33 
 20.75 
 15.88 
 30.55 
 26.40 
 31.74 
 
 18.33 
 21.18 
 
 12.744 
 10.50 
 14.575 
 9.68 
 
 ' '7.69 
 5.98 
 3.03 
 10.56 
 14.70 
 
 1.94 
 6.87 
 13.63 
 13.30 
 10.45 
 11.00 
 6.45 
 
 .50 
 .12 
 .08 
 0.59 
 .60 
 .67 
 .57 
 .01 
 2.00 
 0.30 
 
 0.33 
 1.20 
 1.25 
 2.03 
 2.56 
 2.00 
 2.95 
 70 
 
 0.13 
 
 0.02 
 
 Trace 
 0.80 
 
 1.65 
 1 9? 
 
 
 Mt. Savage 2 . . . 
 Mt. Savages. . . 
 Mt. Savage* . . . 
 Strasburg, O. . . 
 Cumberland, Md 
 Woodbridge.NJ 
 Carter Co., Ky . 
 ClearfieldCo.,Pa 
 Clearfield 5 and. 
 Cambria Cos., 
 Pa 6 
 
 1.15 
 1.53 
 
 6.'45 
 1.15 
 
 
 Tr. 
 0.17 
 0.40 
 
 6.'28 
 3.01 
 0.07 
 0.20 
 
 0.23 
 0.17 
 0.08 
 0.08 
 0.41 
 1.65 
 Tr. 
 
 0.11 
 0.12 
 0.30 
 
 6.24 
 
 6! 12 
 1.00 
 
 1.15 
 
 0.47 
 0.41 
 0.02 
 0.07 
 Tr. 
 Tr. 
 
 0.2 
 
 6.'29 
 2.30 
 2.24 
 
 ' 2.5 
 
 47 
 0.20 
 
 4'" 
 
 1.47 
 0.88 
 2.79 
 3.97 
 4.33 
 4.02 
 4.73 
 
 
 
 Clinton Co., Pa. 
 Clarion Co., Pa. 
 FarrandsvillePa 
 St.LouisCo.,Mo 
 Gottwerth, Aus. 
 Stourbridge, En. 
 Glenboig, Scot. 
 La Bouchade,Fr 
 Coblentz, Ger. 
 Diesdorf , Rhine- 
 land . . 
 
 1.46 
 1.02 
 
 \33 
 
 2.52 
 1.74 
 1.26 
 1.07 
 Tr. 
 0.90 
 
 4.55 
 3.47 
 3.59 
 5.14 
 
 3.85 
 3 58 
 
 S0 2 0.19 
 
 0.20 
 
 3.65 
 
 12.00 
 9.37 
 
 5.17 
 6.21 
 
 4.20 
 0.59 
 
 0.89 
 1.85 
 
 0.69 
 0.19 
 
 Tr. 
 0.32 
 
 0.64 
 0.14 
 
 0.10 
 0.84 
 
 0. 
 2.49 
 
 2.12 
 2.02 
 
 >5 
 0.68 
 
 0.24 
 
 4.20 
 4.09 
 
 3.85 
 5.93 
 
 
 0.90 
 
 Dowlair, Wales. 
 
 
 1 Mass. Inst. of Technology, 1871. 2 Report on Clays of New Jersey. 
 Prof. G. H. Cook, 1877. * Second Geological Survey of Penna., 1878. 
 * Dr. Otto Wuth (2 samples), 1885. 5 Flint clay from Clea.rfleld and 
 Cambria counties, Pa., average of hundreds of analyses by Harbison- 
 Walker Refractories Co., Pittsburg, Pa. 6 Same material calcined. 
 All other analyses from catalogue of Stowe-Fuller Co., 1914. 
 
 MAGNESIA BRICKS. 
 
 "Foreign Abstracts" of the Institution of Civil Engineers, 1893, gives a 
 paper by C. Bischof on the production of magnesia bricks. The material 
 most in favor at present is the magnesite of Styria, which, although less 
 pure considered as a source of magnesia than the Greek, has the property 
 of fritting at a high temperature without melting. 
 
 At a red heat magnesium carbonate is decomposed into carbonic acid 
 and caustic magnesia, which resembles lime in becoming hydrated and 
 
270 MATERIALS. 
 
 recarbonated when exposed to the air, and possesses a certain plasticity, 
 
 so that it can be moulded when subjected to a heavy pressure. By long- 
 continued or stronger heating the material becomes dead-burnt, giving a 
 form of magnesia of high density, sp. gr. 3.8, as compared with 3.0 in the 
 plastic form, which is unalterable in the air but devoid of plasticity. A 
 mixture of two volumes of dead-burnt with one of plastic magnesia can 
 be moulded into bricks which contract but little in firing. Other binding 
 materials that have been used are: clay up to 10 or 15 per cent; gas-tar, 
 perfectly freed from water, soda, silica, vinegar as a solution of magnesium 
 acetate which is readily decomposed by heat, and carbolates of alkalies 
 or lime. Among magnesium compounds a weak solution of magnesium 
 chloride may also be used. For setting the bricks lightly burnt, caustic 
 magnesia, with a small proportion of silica to render, it less refractory, is 
 recommended. The strength of the bricks may be increased by adding 
 iron, either as oxide or silicate. If a porous product is required, sawdust 
 or starch may be added to the mixture. When dead-burnt magnesia is 
 used alone, soda is said to be the best binding material. See also papers 
 by A. E. Hunt, Trans. A. I. M. E. t xvi, 720, and by T. Egleston, Trans. 
 A. I. M.E., xiv, 458. 
 
 The average composition of magnesite, crude and calcined, is given as 
 follows by the Harbison-Walker Refractories Co., Pittsburg (1907). 
 
 Gre 
 Crude. 
 Carbonate of magnesia 97.00% 
 Magnesia 
 Silica 1 25 
 
 cian. 
 Calcined. 
 
 94'.66'% 
 2.75 
 0.70 
 0.80 
 1.50 
 0.40 
 
 Styrian. 
 Crude. Calcined. 
 92.50% 
 85.50% 
 1.50 3.00 
 0.50 1.00 
 3.90 8.00 
 1.25 2.50 
 0.50 
 
 Alumina 
 
 0.40 
 
 Iron Oxide 
 
 ... 40 
 
 Lime 
 
 0.75 
 
 Loss ....'. 
 
 
 100.05 100.15 99.65 100.50 
 
 With the calcined Styrian magnesite of the above analysis it is not 
 necessary to use a . binder either for making brick or for forming the 
 bottom of an open-hearth furnace. 
 
 ZIRCONIA. 
 
 Zirconiaore (84.1 ZrO 2 ; 7.74 SiO 2 ; 3.10Fe 2 O 3 ; 1.21 TiO 2 ; 0.66A1 2 O3: 
 loss on ignition 2.72) vitrifies slightly at 1830 C. (3326 F) . Mixed with 
 different percentages of clay and molded into cones it vitrifies at some- 
 what lower temperatures. A zirconia brick containing 5% clay be- 
 came plastic on its face at 1800 C. (3272F;). (H. Conrad Meyer, 
 j\fet. & Chem. Eng., Vol. xii, No. 12, 1914, Vol. xiii, No. 4, 1915; 
 Circular of Foote Mineral Co., Philadelphia.) 
 
 ASBESTOS. 
 
 The following analyses of asbestos aregiven~by J. T. Donald. Eng. and 
 M. Jour., June 27, 1891. 
 
 Canadian. 
 Italian. Broughton. Templeton. 
 
 Silica 40.30% 40.57% 40.52% 
 
 Magnesia 43.37 41.50 42.05 
 
 Ferrous oxide 87 2.81 1.97 
 
 Alumina 2.27 .90 2..10 
 
 Water 13.72 13.55 13.46 
 
 100.53 99.33 100.10 
 
 Chemical analysis throws light upon an important point in connection 
 with asbestos, i.e., the cause of the harshness of the fibre of some varieties. 
 Asbestos is principally a hydrous silicate of magnesia, i.e., silicate of mag- 
 nesia combined with water. When harsh fibre is analyzed it is found to 
 contain less water than the soft fibre. In fibre of very fine quality from 
 Black Lake analysis showed 14.38% of water, while a harsh-fibred sa>mple 
 gave only 11.70%. If soft fibre be heated to a temperature that will drive 
 off a portion of the combined water, there results a substance so brittle 
 that it may be crumbled between thumb and finger. There is evidently 
 some connection between the consistency, of the fibre and the amount of 
 water in its composition, 
 
STANDARD CROSS SECTIONS. 
 
 Recommended by a Committee of the Am. Soc. M. B.; 1912. 
 
 271 
 
 Cast Iron 
 
 Wrought Iron 
 
 Cast Steel 
 
 Wrought Steel 
 
 Aluminum Rubber, Vulcanite 
 
 Rock 
 
 Original Filling 
 
 Earth 
 
 Sand 
 
 Other Materials 
 
 Wrought Steel Nickel Steel 
 
 Chrome Steel Vanadium Steel 
 
 fill 
 
 ; .M : :&V; ; 
 
 
 wws 
 
 
 Concrete Concrete Blocks 
 
 Cyclopean Expanded Wire or 
 
 PonorpfA Metal Rods 
 
 concrete Reinf orced concrete 
 
272 STKENGTH OF MATERIALS. 
 
 STRENGTH OP MATERIALS. 
 
 Stress and Strain. There is much confusion among writers on 
 strength of materials as to the definition of these terms. An external 
 force applied to a body, so as to pull it apart, is resisted by an internal 
 force, or resistance, and the action of these forces causes a displacement 
 of the molecules, or deformation. By some writers the external force is 
 called a stress, and the internal force a strain; 9thers call the external 
 force a strain, and the internal force a stress; this confusi9n of terms is 
 not of importance, as the words stress and strain are quite commonly 
 used synonymously, but the use of the word strain to mean molecular 
 displacement, deformation, or distortion, as is the custom of some, is a 
 corruption of the language. See Engineering News, June 23, 1892. 
 Some authors in order to avoid confusion never use the word strain in 
 their writings. Definitions by leading authorities are given below. 
 
 Stress. A stress is a force which acts in the interior of a body, and 
 resists the external forces which tend to change its shape. A deformation 
 is the amount of change of shape of a body caused by the stress. The 
 word strain is often used as synonymous with stress, and sometimes it is 
 also used to designate the deformation. (Merriman.) 
 
 The force by which the molecules of a body resist a strain at any point 
 is called the stress at that point. 
 
 The summation of the displacements of the molecules of a body for a 
 given point is called the distortion or strain at the point considered. 
 (Burr.) 
 
 Stresses are the forces which are applied to bodies to bring into action 
 their elastic and cohesive properties. These forces cause alterations of 
 the forms of the bodies upon which they act. Strain is a name given to 
 the kind of alteration produced by the stresses. The distinction between 
 stress and strain is not always observed, one being used for the other. 
 (Wood.) 
 
 The use of the word stress as synonymous with " stress per square inch," 
 or with "strength per square inch," should be condemned as lacking in 
 precision. 
 
 Stresses are of different kinds, viz.: tensile, compressive, transverse, tor- 
 sional, and shearing stresses. 
 
 A tensile stress, or pull, is a force tending to elongate a piece. A com- 
 pressive stress, or push, is a force tending to shorten it. A transverse stress 
 tends to bend it. A torsional stress tends to twist it. A shearing stress 
 tends to force one part of it to slide over the adjacent part. 
 
 Tensile, compressive, and shearing stresses are called simple stresses. 
 Transverse stress is compounded of tensile and compressive stresses, and 
 torsional of tensile and shearing stresses. 
 
 To these five varieties of stresses might be added tearing stress, which is 
 either tensile or shearing, but in which the resistance of different portions 
 of the material are brought into play in detail, or one after the other, 
 instead of simultaneously, as in the simple stresses. 
 
 Effects of Stresses. The following general laws for cases of simple 
 tension or compression have been established by experiment (Merriman) : 
 
 1. When a small stress is applied to a body, a small deformation is pro- 
 duced, and on the removal of the stress the body springs back to its original 
 form. For small stresses, then, materials may be regarded as perfectly 
 elastic. 
 
 2. Under small stresses the deformations are approximately proportional 
 to the forces or stresses which produce them, and also approximately pro- 
 portional to the length of the bar or body. 
 
 3. When the stress is great enough a deformatipn is produced which is 
 partly permanent, that is, the body does not spring back entirely to its 
 original form on removal of the stress. This permanent part is termed a 
 set. In such cases the deformations are not proportional to the stress. 
 
 4. When the stress is greater still the deformation rapidly increases and 
 the body finally ruptures. 
 
 5. A sudden stress, or shock, is more injurious than a steady stress or 
 than a stress gradually applied. 
 
ELASTIC LIMIT AND YIELD POINT. 
 
 273 
 
 Elastic Limit. The elastic limit is defined as that load at which 
 the deformations cease to be proportional to the stresses, or at which 
 the rate of stretch (or other deformation) begins to increase. It is also 
 defined as the load at which a permanent set first becomes visible. The 
 last definition is not considered as good as the first, as it is found that with 
 some materials a set occurs with any load, no matter how small, and that 
 with others a set which might be called permanent vanishes with lapse of 
 time, and as it is impossible to get the point of first set without removing 
 the whole load after each increase of load, which is frequently inconven- 
 ient. The elastic limit, defined, however, as that stress at which the 
 extensions begin to increase at a higher rate than the applied stresses, 
 usually corresponds very nearly with the point of first measurable per- 
 manent set. 
 
 Apparent Elastic TJmit. Prof. J. B. Johnson (Materials of Con- 
 struction, p. 19) defines the " apparent elastic limit " as " the point on the 
 stress diagram [a plotted diagram in which the ordinates represent loads 
 and the abscissas the corresponding elongations] at which the rate of 
 deformation is 50% greater than it is at the origin," [the minimum rate]. 
 An equivalent definition, proposed by the author, is that point at which 
 the modulus of extension (length X increment of load per unit of section 
 -=- increment of elongation) is two thirds of the maximum. Fcr steel, 
 with a modulus of elasticity of 30,000,000, this is equivalent to that 
 point at which the increase of elongation in an 8-inch specimen for 1000 
 Ibs. per sq. in. increase of load is 0.0004 in. 
 
 Yield-point. The term yield-point has recently been introduced into 
 the literature of the strength of materials. It is defined as that point at 
 which the rate of stretch suddenly increases rapidly with no increase of 
 the load. The difference between the elastic limit, strictly defined as 
 the point at which the rate of stretch begins to increase, and the yield- 
 point, may in some cases be considerable. This difference, however, will 
 not be discovered in short test-pieces unless the readings of elongations 
 are made by an exceedingly fine instrument, as a micrometer reading to 
 0.0001 inch. In using a coarser instrument, such as calipers reading to 
 1/100 of an inch, the elastic limit and the yield-point will appear to be 
 simultaneous. Unfortunately for precision of language, the term yield- 
 point was not introduced until long after the term elastic limit had been 
 almost universally adopted to signify the same physical fact which is now 
 defined by the term yield-point, that is, not the point at which the first 
 change in rate, observable 9iily by a microscope, occurs, but that later 
 point (more or less indefinite as to its^ precise position) at which the 
 increase is great enough to be seen by the naked eve. A most convenient 
 method of determining the point at which a sudden increase of rate of 
 stretch occurs in short specimens, when a testing-machine in which the 
 pulling is done by screws is used, is to note the weight on the beam at 
 the instant that the beam "drops." During the earlier portion of the 
 test, as the extension is steadily increased by the uniform but slow rota- 
 tion of the screws, the poise is moved steadily along the beam to keep it 
 in equipoise; suddenly a point is reached at which the beam drops, and 
 will not rise until the elongation has been considerably increased by the 
 further rotation of the screws, the advancing of the poise meanwhile 
 being suspended. This point corresponds practically to the point at which 
 the rate of elongation suddenly increases, and to the point at which 
 an appreciable permanent set is first found. It is also the point 
 which has hitherto been called in practice and in text-books the elastic 
 limit, and it will probably continue to be so called, although the use 9f 
 the newer term " yield-point " for it, and the restriction of the term elastic 
 limit to mean the earlier point at which the rate of stretch begins to 
 increase, as determinable only by micrometric measurements, is more 
 precise and scientific. In order to obtain the yield-point by the drop of 
 the beam with approximate accuracy, the screws of the testing machine 
 must be run very slowly as the yield-point is approached, so as to cause 
 an elongation of not more than, say, 0.005 in. per minute. 
 
 In tables of strength of materials hereafter given, the term elastic limit 
 is used in its customary meaning, the point at which the rate of stress has 
 begun to increase as pbservable by ordinary instruments or by the drop of 
 the beam. With this definition it is practically synonymous with yield- 
 point. 
 
274 STRENGTH < >F MATERIALS. 
 
 Coefficient (or Modiilii-0 of Klasticity. --This is a term express- 
 ing the relation between the amount of extension or compression of a mate- 
 rial and the load producing that extension or compression. 
 
 It is defined as the load per unit of section divided bv the extension per 
 unit of length. 
 
 Let P be the applied load, k the sectional area of the piece, I the length 
 of the part extended, A the amount of the extension, and E the coefficient 
 of elasticity. Then P * k = the load on a unit of section; A ~ / = the 
 elongation of a unit of length. 
 
 p A Pl 
 
 The coefficient of elasticity is sometimes denned as the figure ex: 
 
 slant. This definition follows from the formula above given, thus: 
 If k = one square inch. ( and A each = one inch, then E = P. 
 
 Within the elastic limit, when the deformations are proportional to the 
 stresses, the coefficient of elasticity is constant, but beyond the elastic 
 ..imit it decreases rapidly. 
 
 In cast iron there is generally no apparent limit of elasticity, the defor- 
 mations increasing at a faster rate than th .rid a permanent 
 
 set being produced by small loads. The coefficient of elasticity therefore 
 is not constant during any portion of a test, but grows smaller as the load 
 increases. The same is true in the case of timber. In wrought iron and 
 steelj however, there is a well-defined elastic limit, and the coefficient of 
 elasticity within that limit is nearly constant. 
 
 Resilience, or Work of Resistance of a Material. Within the 
 elastic limit, the resistance increasing uniformly from zero stress to the 
 stress at the elastic limit . the work done by a load applied gradually is 
 equal to one half the product of the final stress by the extension or other 
 deformation. Beyond the elastic limit, the extensions increasing more 
 rapidly than the loads, and the strain diagram (a plotted diagram showing 
 the relation of extensions to stresses) approximating a parabolic form, the 
 work is approximately equal to two thirds the product of the maximum 
 stress by the extension. 
 
 The amount of work required to break a bar, measured usually in inch- 
 pounds, is called its resilience: the work required to strain it to the elastic 
 limit is called its elastic resilience. (See below.) 
 
 Under a load applied suddenly the momentary elastic distortion is 
 equal to twice that caused by the same load applied gradually. 
 
 When a solid material is exposed to percussive stress, as when a weight 
 falls upon a beam transversely, the work of resistance is measured by the 
 product of the weight into the total fall. 
 
 Elastic Resilience. In a rectangular beam tested by transverse 
 stressrsupported at the ends and loaded in the middle, 
 
 in which, if P is the load in pounds at the elastic limit. R = the modulus of 
 transverse strength, or the stress on the extreme fibre, at the elastic limit, 
 B = modulus of elasticity, A = deflection, I, 6, and <1 = length, breadth. 
 and depth in inches. Substituting for P ia (2) its value in (1), A= ] 
 + Ed. 
 
 The elastic resilience = half the product of the load and deflection = 
 l /2P A, and the elastic resilience per cubic inch = 1/2 PA -5- Ibd. 
 
 Substituting the values of P and A, this reduces to elastic resilience per 
 
 1 02 
 
 cubic inch = =, w , which is independent of the dimensions; and therefore 
 
 18 bj 
 
 the elastic resilience per cubic inch for transverse strain may be used as a 
 modulus expressing one valuable quality of a material, 
 
ELEVATION OF THE ELASTIC LIMIT. 275 
 
 Similarly for tension: Let P = tensile stress in pounds per square inch 
 at the elastic limit; e = elongation per unit of length at the elastic limit: 
 E = modulus of elasticity = P -*- e\ whence e = P + E 
 
 Then elastic resilience per cubic inch = 1/2 Pe = 5 #~ 
 
 Elevation of Ultimate Resistance and Elastic Limit. It was 
 
 first observed by Prof. R. H. Thurston, and Commander L. A. Beardslee, 
 U.S. N., independently, in 1873, that if wrought iron be subjected to a 
 stress beyond its elastic limit, but not beyond its ultimate resistance, and 
 then allowed to "rest" for a definite interval of time a considerable 
 increase of elastic limit and ultimate resistance may be experienced. In 
 other words, the application of stress and subsequent "rest" increases 
 the resistance of wrought iron. This "rest" may be an entire release 
 from stress or a simple holding the test-piece at a given intensity of 
 stress. 
 
 Commander Beardslee prepared twelve specimens and subjected them 
 to a stress equal to the ultimate resistance of the material, vuthout 
 breaking the specimens. These were then allowed to rest, entirely free 
 from stress, from 24 to 30 hours, after which they were again stressed 
 until broken. The gain in ultimate resistance by the rest was found to 
 vary from 4.4 to 17 per cent. 
 
 This elevation of elastic and ultimate resistance appears to be peculiar 
 to iron and steel; it has not been found in other metals. 
 
 Relation of the Elastic Limit to Endurance under Repeated 
 Stresses (condensed from Engineering, August 7, 1891). When engi- 
 neers first began to test materials, it was soon recognized that if a speci- 
 men was loaded beypnd a certain point it did not recover its original 
 dimensions on removing the load, but took a permanent set; this point 
 was called the elastic limit. Since below this point a bar appeared to 
 recover completely its original form and dimensions on removing the 
 load, it appeared obvious that it had not been injured by the load, and 
 hence the working load might be deduced from the elastic limit by using 
 a small factor of safety. 
 
 Experience showed, however, that in many cases a bar would not carry 
 safely a stress anywhere near the elastic limit of the material as- deter- 
 mined by these experiments, and the whole theory of any connection 
 between the elastic limit of a bar and its working load became almost 
 discredited, and engineers employed the ultimate strength only in deduc- 
 ing the safe working load to which their structures might be subjected. 
 Still, as experience accumulated it was observed that a higher factor of 
 safety was required for a live load than for a dead one. 
 
 In 1871 Wohler published the results of a number of experiments on 
 bars of iron and steel subjected to live loads. In these experiments the 
 stresses were put on and removed from the specimens without impact, 
 but it was, nevertheless, found that the breaking stress of the materials 
 was in every case much below the statical breaking load. Thus, a bar 
 of Krupp's axle steel having a tenacity of 49 tons per square inch broke 
 with a stress of 28.6 tons per square inch, when the load was completely 
 removed and replaced without impact 170,000 times. These expenments 
 were made on a large number of different brands of iron and steel, and 
 the results were concordant in showing that a bar would break with an 
 alternating stress of only, say, one third the statical breaking strength of 
 the material, if the repetitions of stress were sufficiently numerous. At 
 the same time, however, it appeared from the general trend of the experi- 
 ments that a bar would stand an indefinite number of alternations of 
 stress, provided the stress was kept below the limit. 
 
 Prof. Bauschinger defines the elastic limit as the point at which stress 
 ceases to be sensibly proportional to extension, the latter being measured 
 with a mirror apparatus reading to 1/5000 of a millimetre, or about 
 1/100000 in. This limit is always below the yield-point, and may on 
 occasion be zero. On loading a bar above the yield -point, this point 
 rises with the stress, and the rise continues for weeks, months, and 
 possibly for years if the bar is left at rest under its load. On the other 
 hand, when a bar is loaded beyond its true elastic limit, but below its 
 yield-point, this limit rises, but reaches a maximum as the yield-point is 
 approached, and then falls rapidly, reaching even to zero. On leaving 
 the bar at rest under a stress exceeding that of tys primitive 
 
276 
 
 STRENGTH OF MATERIALS. 
 
 down point the elastic limit begins to rise again, and may, if left a sufifl* 
 cient time, rise to a point much exceeding its previous value. 
 
 A bar has two limits of elasticity, one for tension and one for com- 
 pression. Bauschinger loaded a number of bars in tension until stress 
 ceased to be sensibly proportional to deformation. The load was then 
 removed and the bar tested in compression until the elastic limit in this 
 direction had been exceeded. This process raises the elastic limit in 
 compression, as would be found on testing the bar in compression a second 
 time. In place of this, however, it was now again tested in tension, when 
 it was found that the artificial raising of the limit in compression had 
 lowered that in tension below its previous value. By repeating the 
 process of alternately testing in tension and compression, the two limits 
 took up points at equal distances from the line of no load, both in tension 
 and compression. These limits Bauschinger calls natural elastic limits 
 of the bar, which for wrought iron correspond to a stress of about 81/2 tons 
 per square inch, but this is practically the limiting load to which a bar 
 of the same material can be strained alternately in tension and com- 
 pression, without breaking when the loading is repeated sufficiently often, 
 as determined by Wohler's method. 
 
 As received from the rolls the elastic limit of the bar in tension is above 
 the natural elastic limit of the bar as defined by Bauschinger, having been 
 artificially raised by the deformations to which it has been subjected in 
 the process of manufacture. Hence, when subjected to alternating 
 stresses, the limit in tension is immediately lowered, while that in com- 
 pression is raised until they both correspond to equal loads. Hence, in 
 Wohler's experiments, in which the bars broke at loads nominally below 
 the elastic limits of the material, there is every reason for concluding that 
 the loads were really greater than true elastic limits of the material. 
 This is confirmed by tests on the connecting-rods of engines, which work 
 under alternating stresses of equal intensity. Careful experiments on 
 old rods show that the elastic limit in- compression is the same as that in 
 tension, and that both are far below the tension elastic limit of the 
 material as received from the rolls. 
 
 The common opinion that straining a metal beyond its elastic limit 
 injures it appears to be untrue. It is not the mere straining of a metal 
 beyond one elastic limit that injures it, but the straining, many times 
 repeated, beyond its two elastic limits. Sir Benjamin Baker has shown 
 that in bending a shell plate for a boiler the metal is of necessity strained 
 beyond its elastic limit, so that stresses of as much as 7 tons to 15 tons 
 per square inch may obtain in it as it comes from the rolls, and unless the 
 plate is annealed, these stresses will still exist after it has been built into 
 the boiler. In such a case, however, when exposed to the additional - 
 stress due to the pressure inside the boiler, the overstrained portions of 
 the plate will relieve themselves by stretching and taking a permanent 
 set, so that probably after a year's working very little difference could be 
 detected in the stresses in a plate built into the boiler as it came from the 
 bending rolls, and in one which had been annealed, before riveting into 
 lace, and the first, in spite of its having been strained beyond its elastic 
 mits, and not subsequently annealed, would be as strong as the other. 
 
 p 
 li 
 
 Resistance of Metals to Repeated Shocks. 
 
 More than twelve years were spent by Wohler at the instance of the 
 Prussian Government in experimenting upon the resistance of iron and 
 steel to repeated stresses. The results of his experiments are expressed 
 in what is known as Wohler's law, which is given in the following words 
 in Dubois's translation of Weyrauch: 
 
 " Rupture may be caused not only by a steady load which exceeds the 
 carrying strength, but also by repeated applications of stresses, none of 
 which are equal to the carrying strength. The differences of these stresses 
 are measures of the disturbance of continuity, in so far as by their increase 
 the minimum stress which is still necessary for rupture diminishes." 
 
 A practical illustration of the meaning of the first portion of this law 
 may be given thus: If 50,000 pounds once applied will just break a bar 
 of iron or steel, a stress very much less than 50,000 pounds will break it 
 if repeated sufficiently often. 
 
EFFECT OF VIBEATION AND LOAD. 277 
 
 | This is fully confirmed by the experiments of Fairbairn and Spangenberg, 
 as well as those of Wohler; and, as is remarked by Weyrauch, it may be 
 considered as a long-known result of common experience. It partially 
 accounts for what Mr. Holley has called the "intrinsically ridiculous 
 factor of safety of six." 
 
 Another " long-known result of experience" is the fact that rupture may 
 be caused by a succession of shocks or impacts, none of which alone would 
 be sufficient to cause it. Iron axles, the piston-rods of steam hammers, 
 and other pieces of metal subject to continuously repeated shocks, 
 invariably break after a certain length of service. They have a "life" 
 which is limited. 
 
 Several years ago Fairbairn wrote: " We know that in some cases 
 . wrought iron subjected to C9ntinuous vibration assumes a crystalline 
 structure, and that the cohesive powers are much deteriorated, but we 
 j are ignorant of the causes of this change." We are still ignorant, not 
 i only of the causes of this change, but of the conditions under which it 
 i takes place. Who knows whether wrought iron subjected to very slight 
 continuous vibration will endure forever? or whether to insure final 
 i rupture each of the continuous small shocks must amount at least to a 
 f certain percentage of single heavy shock (both measured in foot-ppunds), 
 which would cause rupture with one application? Wohler found in test- 
 ing iron by repeated stresses (not impacts) that in one case 400,000 
 applications of a stress of 500 centners to the square inch caused rupture, 
 ! while a similar bar remained sound after- 48,000,000 applications of a 
 stress of 300 centners to the square inch (1 centner = 110.2 Ibs.). 
 
 Who knows whether or not a similar law holds true in regard to repeated 
 !.. shocks? Suppose that a bar of iron would break under a single impact of 
 f 1000 foot-pounds, how many times would it be likely to bear the repetition 
 I of 100 foot-pounds, or would it be safe to allow it to remain for fifty years 
 subjected to a continual succession of blows of even 10 foot-pounds each? 
 Mr. William Metcalf published in the Metallurgical Review, Dec., 1877, 
 the results of some tests of the life of steel of different percentages of 
 1 carbon under impact. Some small steel pitmans were made, the specifi- 
 cations for which required that the unloaded machine should run 4^ 
 I hours at the rate of 1200 revolutions per minute before breaking. 
 
 The steel was all of uniform quality, except as to carbon. Here are the 
 results. The 
 
 0.30 C. ran 1 h. 21 m. Heated and bent before breaking. 
 
 0.49 C. 1 h. 28 m. 
 
 0.53 C. 4 h. 57 m. Broke without heating. 
 
 0.65 C. 3 h. 50 m. Broke at weld where imperfect. 
 
 0.80 C. 5 h. 40 m. 
 
 0.84 C. 18 h. 
 
 0.87 C. Broke in weld near the end. 
 
 0.96 C. Ran 4.55 m., and the macnine broke down. 
 
 Some other experiments by Mr. Metcalf confirmed his conclusion, viz. 
 that high-carbon steel was better adapted to resist repeated shocks and 
 vibrations than low-carbon steel. 
 
 These results, however, would scarcely be sufficient to induce any 
 engineer to use 0.84 carbon steel in a car-axle or a bridge-rod. Further 
 experiments are needed to confirm or overthrow them. 
 
 (See description of proposed apparatus for such an investigation in the 
 author's paper in Trans. A. /. M. E., vol. viii, p. 76, from which the above 
 extract is taken.) 
 
 Effect of Vibration and Load on Steel. (Prof. P. R. Alger, U. S. 
 Navy, U. S. Naval Inst. Proc., Dec., 1910.) In 1883, or thereabouts, 
 a test of the theory that guns are weakened by the shock and vibration 
 of repeated firing was made at the Washington Navy Yard as follows: 
 Heavy weights, sufficient to strain the wire nearly to its elastic limit, 
 were suspended by pieces of wire, and small hammers were arranged 
 
 that, actuated by the machinery of the shop, they struck the taut 
 wires at regular and frequent intervals. After months of constant 
 vibration, all the time under severe strain, the wires, when tested 
 showed unchanged physical qualities. Moreover, every gun, army 
 and navy, that has suffered accident, since we first began to build 
 
278 STKENGTH OF MATERIALS. 
 
 steel guns, has had the metal of the part that failed tested, and neve* 
 has there been a case when any material difference was found between 
 the physical qualities shown by the last tests and those shown by the 
 original tests for acceptance. One of these guns, a 12-in., had been 
 fired 481 rounds when its muzzle was blown off. (The fact stated in 
 the last sentence tends to confirm the "theory" that guns are weakened 
 by repeated firing, although the weakening may not be discovered by 
 physical tests.) 
 
 Stresses Produced by Suddenly Applied Forces and Shocks. 
 
 (Mansfield Merriman, R. R. & Eng. Jour., Dec., 1889.) 
 
 Let P be the weight which is dropped from a height h upon the end of a 
 bar, and let y be the maximum elongation which is produced. The work 
 performed by the falling weight, then, is W = P(h + y), and this must 
 equal the internal work of the resisting molecular stresses. The stress in 
 the bar, which is at first 0, increases up to a certain limit Q, which is 
 greater than P; and if the elastic limit be not exceeded the elongation 
 increases uniformly with the stress, so that the internal work is equal to 
 the mean stress 1/2 Q multiplied by the total elongation y, or TP=i/2 Qv. 
 Whence, neglecting the work that may be dissipated in heat, 
 
 J /2 Qy = Ph + Py. 
 
 If e be the elongation due to the static load P, within the elastic limit 
 V = -pe; whence Q = P (l + y 1 +2-V which gives the momentary 
 maximum stress. Substituting this value of Q, there results y = e 
 fl + y 1 +2-V which is the value of the momentary maximum elon- 
 gation. 
 
 A shock results when the force P, before its action on the bar, is moving 
 with velocity, as is the case when a weight P falls from a height h. The 
 above formulas show that this height h may be small if e is a small quan- 
 tity, and yet very great stresses and deformations be produced. For 
 Instance, let h = 4e, then Q = 4P and y = 4e; also let h = 12e, then 
 Q = 6P and y = 6e. Or take a wrought-iron bar 1 in. square and 5 ft. 
 long: under a steady load of 5000 Ibs. this will be compressed about 0.012 
 in., supposing that no lateral flexure occurs;, but if a weight of 5000 Ibs. 
 drops upon its end from the small height of 0.048 in. there will be produced 
 the stress of 20,000 Ibs. 
 
 A suddenly applied force is one which acts with the uniform intensity P 
 upon the end of the bar, but which has no velocity before acting upon it. 
 This corresponds to the case of h = in the above formulas, and gives 
 Q = 2P and y = 2e for the maximum stress and maximum deforma- 
 tion. Probably the action of a rapidly moving train upon a bridge 
 produces stresses of this character. For a further discussion of this 
 subject, in which the inertia of the bar is considered, see Merriman's 
 Mechanics of Materials, 10th ed., 1908. 
 
 TENSILE STRENGTH. 
 
 The following data are usually obtained in testing by tension in a testing- 
 machine a sample of a material of construction: 
 
 The load and the amount of extension at the elastic limit. 
 
 The maximum load applied before rupture. 
 
 The elongation of the piece, measured between gauge-marks, placed a 
 stated distance apart before the test; and the reduction of area at the 
 point of fracture. 
 
 The load at the elastic limit and the maximum load are recorded in 
 pounds per square inch of the original area. The elongation is recorded 
 as a percentage of the stated length between the gauge-marks, and the 
 reduction of area as a percentage of the original area. The coefficient of 
 elasticity is calculated from the ratio the extension within the elastic 
 
PRECAUTIONS IN MAKING TENSILE TESTS. 279 
 
 limit per inch of length bears to the load per square inch producing that 
 extension. 
 
 On account of the difficulty of making accurate measurements of the 
 fractured area of a test-piece, and of the fact that elongation is more 
 valuable than reduction of area as a measure of ductility and of resilience 
 or work of resistance before rupture, modern experimenters are abandoning 
 the custom of reporting reduction of area. The data now calculated 
 from th? results of a tensile test for commercial purposes are: 1. Tensile 
 strength in pounds per square inch of original area. 2. Elongation per 
 cent of a stated length between gauge-marks, usually 8 inches. 3. Elastic 
 limit in pounds per square inch of original area. 
 
 The short or grooved test specimen gives with most metals, especially 
 with wrought iron and steel, an apparent tensile strength much higher 
 than the real strength. This form of test-piece is now almost entirely 
 abandoned. Pieces 2 in. in length between marks are used for forgings. 
 
 The following results of the tests of six specimens from the same i/4-in. 
 steel bar illustrate the apparent elevation of elastic limit and the changes 
 in other properties due to change in length of stems which were turned 
 down in each specimen to 0.798 in. diameter. (Jas. E. Howard, Eng. 
 Congress 1893, Section G.) 
 
 Description of Stem. 
 
 Elastic Limit, 
 Lbs. per Sq. In. 
 
 Tensile Strength, 
 Lbs. per Sq. In. 
 
 Contraction of 
 Area, per cent. 
 
 1 .00 in. long 
 
 64,900 
 
 94,400 
 
 49.0 
 
 50 in. long 
 
 65,320 
 
 97,800 
 
 43.4 
 
 
 68,000 
 
 102,420 
 
 39.6 
 
 Semicircular groove, 0.4 
 
 75,000 
 
 116,380 
 
 31.6 
 
 Semicircular groove, 1/8 
 
 86,000, about 
 
 134,960 
 
 23.0 
 
 V-shaped groove 
 
 90,000, about 
 
 117,000 
 
 Indeterminate. 
 
 Test plates made by the author in 1879 of straight and grooved test- 
 pieces of boiler-plate steel cut from the same gave the following results: 
 
 5 straight pieces, 56,605 to 59,012 Ibs. T. S. Aver. 57,566 Ibs. 
 
 4 grooved " 64,341 to 67,400 " " " 65,452 " 
 
 Excess of the short or grooved specimen, 21 per cent, or 12,114 Ibs. 
 
 Measurement of Elongation. In order to be able to compare 
 records of elongation, it is necessary not only to have a uniform length of 
 section between gauge-marks (say 8 inches), but to adopt a uniform 
 method of measuring the elongation to compensate for the difference 
 between the apparent elongation when the piece breaks near one of the 
 gauge-marks, and when it breaks midway between them. The following 
 method is recommended (Trans. A. S. M. E., vol. xi, p. 622): 
 
 Mark on the specimen divisions of 1/2 inch each. After fracture measure 
 from the point of fracture the length of 8 of the marked spaces on each 
 fractured portion (or 7 + on one side and 8 4- on the other if the fracture 
 is not at one of the marks). The sum of these measurements, less 8 
 inches, is the elongation of 8 inches of the original length. If the fracture 
 is so near one end of the specimen that 7 + spaces are not left on the 
 shorter portion, then take the measurement of as many spaces (with the 
 fractional part next to the fracture) as are left, and for the spaces lacking 
 add the measurement of as many corresponding spaces of the longer 
 portion as are necessary to make the 7 -f- spaces. 
 
 Precautions Required in making Tensile Tests. The testing- 
 machine itself should be tested, to determine whether its weighing 
 apparatus is accurate, and whether it is so made and adjusted that 
 in the test of a properly made specimen the line of strain of the testing- 
 machine is absolutely in line with the axis of the specimen. 
 
280 
 
 STRENGTH OF MATERIALS. 
 
 The specimen should be so shaped that it will not give an incorrect 
 record of strength. 
 
 It should be of uniform minimum section for not less than eight inches 
 of its length. Eight inches is the standard length for bars. For forgings 
 and castings and in special cases shorter lengths are used; these show 
 greater percentages of elongation, and the length between gauge marks 
 should therefore always be stated in the record. 
 
 Regard must be had to the time occupied in making tests of certain 
 materials. Wrought iron and soft steel can be made to show a higher 
 than their actual apparent strength by keeping them under strain for a 
 great length of time. 
 
 In testing soft alloys, copper, tin, zinc, and the like, which flow under 
 constant strain, their highest apparent strength is obtained by testing 
 them rapidly. In recording tests of such materials the length of time 
 occupied in the test should be stated. 
 
 For very accurate measurements of elongation, corresponding to incre- 
 ments of load during the tests, the electric contact micrometer, described 
 in Trans. A. S. M. E., vol. vi. p. 479, will be found convenient. When 
 readings of elongation are then taken during the test, a strain diagram 
 may be plotted from the reading, which is useful in comparing the quali- 
 ties of different specimens. Such strain diagrams are made automatically 
 by the new Olsen testing-machine, described in Jour. Frank. Inst. 1891. 
 
 The coefficient of elasticity should be deduced from measurement 
 observed between fixed increments of load per unit section, say between 
 2000 and 12,000 pounds per square inch or between 1000 and 11,000 
 pounds instead of between and 10,000 pounds. 
 
 Shapes of Specimens for Tensile Tests. The shapes shown be- 
 low were recommended by the author in 1882 when he was connected 
 With the Pittsburgh Testing Laboratory. They are now in most general 
 use; the earlier forms, with 5 inches or less in length between shoulders, 
 being almost entirely abandoned. 
 
 No. 1. Square or flat bar. as 
 rolled. 
 
 No. 2. Round bar, as rolled. 
 
 No. 3. Standard shape for 
 flats or squares. Fillets 
 1/2 inch radius. 
 
 No. 4. Standard shape for 
 rounds. Fillets 1/2 inch 
 radius. 
 
 No. 5. Government shape 
 formerly used for marine 
 boiler-plates of iron. Not 
 recommended, as results 
 are generally in error. 
 
 Increasing the Tensile Strength of Iron Bars by Twisting them. 
 
 Ernest L. Ransome of San Francisco obtained a patent, in 1888, for 
 an "improvement in strengthening and testing wrought metal and steel 
 rods or bars, consisting in twisting the same in a cold state. . . . Any 
 defect in the lamination of the metal which would otherwise be concealed 
 is revealed by twisting, and imperfections are shown at once. The 
 treatment may be applied to bolts, suspension-rods or bars subjected to 
 tensile strength of any description." 
 Jesse J. Shuman (Am. Soc. Test. Mat., 1907) describes several series of 
 
COMPKESSIVE STRENGTH. 281 
 
 experiments on the effect of twisting square steel bars. Following are 
 some of the results: 
 
 Soft Bessemer steel bars 1/2 in. square. Tens. Strength, plain bar, 60,400, 
 
 No. of turns per foot 3 43/ 4 5 53/ 4 57/ 8 
 
 Yield point, Ibs. per sq. in 65,600 72,400 84,800 84,000 80,800 
 
 Ult. strength " " " 83,200 89,600 92,000 90,000 88,800 
 
 Elongation in 8 in., % 10 5.75 6.25 7.5 3.75 
 
 Bessemer, 0.25 carbon, 1/2 in. sq. Tens, strength, plain bar, 75,000. 
 
 No. of turns per foot 3 41/2 47/ 8 5 51/2 
 
 Yield point, Ibs. per sq. in 83,600 83,200 88,800 84,200 84,200 
 
 Ult. strength " " 99,600 99,200 104,000 102,000 100,800 
 
 Elongation in 8 in., % 8 4.5 4 5.75 6 
 
 Bars of each grade twisted off when given more turns than stated. 
 Soft Bessemer, square bars, different sizes. 
 
 Size.in.sq 1/4 3/ 8 i/ 2 5/ 8 3/ 4 7/ 8 1 H/ 8 li/ 4 
 
 No. of turns per ft 4 31/23 21/4 1 1/2 1 V4 1 7 /8 3 /4 
 
 Yield rjint, increase %* 11182 6483 85.577 82 64 59 
 
 Ult. strength " %* 37 38.6 41 33.5 34.3 29.7 22.8 20.1 28.9 
 
 * Average of two tests each. 
 
 Mr. Schuman recommends that in twisting bars for reinforced concrete, 
 in order not to be in danger of approaching the breaking point, the num- 
 ber of turns should be about half the number at which the steel is at its 
 maximum strength, which for Bessemer of about 60,000 Ibs. tensile 
 strength means one-complete twist in 8 to 10 times the size of the bar. 
 
 Steel bars strengthened by twisting are largely used in reinforced 
 concrete. 
 
 COMPRESSIVE STRENGTH. 
 
 What is meant by the term "compressive strength" has not yet been 
 settled by the authorities, and there exists more confusion in regard to 
 this term than in regard to any other used by writers on strength of 
 materials. The reason of this may be easily explained. The effect of a 
 compressive stress upon a material varies with the nature of the material, 
 and with the shape and size of the specimen tested. While the effect of a> 
 tensile stress is to produce rupture or separation of particles in the direc- 
 tion of the line of strain, the effect of a C9mpressive stress on a piece of 
 material may be either to cause it to fly into splinters, to separate into 
 two or more wedge-shaped pieces and fly apart, to bulge, buckle, or bend, 
 or to flatten out and utterly resist rupture or separation of particles. A 
 piece of speculum metal (copper 2, tin 1) under compressive stress will 
 exhibit no change of appearance until rupture takes place, and then it 
 will fly to pieces as suddenly as if blown apart by gunpowder. A piece 
 of cast iron or of stone will generally split into wedge-shaped fragments. 
 A piece of wrought iron will buckle or bend. A piece of wood or zinc 
 may bulge, but its action will depend upon its shape and size. A piece 
 of lead will flatten out and resist compression till the last degree; that is, 
 the more it is compressed the greater becomes its resistance. 
 
 Air and other gaseous bodies are compressible to any extent as long as 
 they retain the gaseous condition. Water not confined in a vessel is com- 
 pressed by its own weight to the thickness of a mere film, while when 
 confined in a vessel it is almost incompressible. 
 
 It is probable, although it has not been determined experimentally, 
 that solid bodies when confined are at least asr incompressible as water. 
 When they are not confined, the effect of a compressive stress is not only 
 to shorten them, but also to increase their lateral dimensions or bulge 
 them. Lateral stresses are therefore induced by compressive stresses. 
 
 The weight per square inch of original section required to produce any 
 given amount or percentage of shortening of any material is not a constant 
 quantity, but varies with both the length and the sectional area, with the 
 shape of the sectional area, and with the relation of the area to the length. 
 The "compressive strength" of a material, if this term be supposed to 
 mean the weight in pounds per square inch necessary to cause runture, 
 may vary with every size and shape of specimen experimented upon. 
 
282 STRENGTH OF MATERIALS. 
 
 Still more difficult would it be to state what is the " compressive strength" 
 of a material which does not rupture at all, but flattens out. Suppose we 
 are testing a cylinder of a soft metal like lead, two inches in length and 
 one inch in diameter, a certain weight will shorten it one per cent, another 
 weight ten per cent, another fifty per cent, but no weight that we can 
 place upon it will rupture it, for it will flatten out to a thin sheet. What, 
 then, is its compressive strength? Again, a similar cylinder of soft 
 wrought iron would probably compress a few per cent, bulging evenly 
 all around; it would then commence to bend, but at first the bend would 
 be imperceptilbe to the eye and too small to be measured. Soon this 
 bend would be great enough to be noticed, and finally the piece might be 
 bent nearly double, or otherwise distorted. What is the "compressive 
 strength" of this piece of iron? Is it the weight per square inch which 
 compresses the piece one per cent or five per cent, that which causes th'e 
 first bending (impossible to be discovered), or that which causes a per- 
 ceptible bend? 
 
 As showing the confusion concerning the definitions of compressive 
 strength, the following statements from different authorities on the 
 strength of wrought iron are of interest. 
 
 Wood's Resistance of Materials states, " Comparatively few experiments 
 have been made to determine how much wrought iron will sustain at the 
 point of crushing. Hodgkinson gives 65,000, Rondulet 70,800, Weisbach 
 72,000, Rankine 30,000 to 40,000. It is generally assumed that wrought 
 iron will resist about two thirds as much crushing as to tension, but the 
 experiments fail to give a very definite ratio." 
 
 The following values, said to be deduced from the experiments of Major 
 Wade, Hodgkinson, and Capt. Meigs, are given by Haswell: 
 
 American wrought iron 127,720 Ibs. 
 
 " (mean) 85,500 " 
 
 ,. u ( 65,200 " 
 
 English { 40!000 " 
 
 Stoney states that the strength of short pillars of any given material, 
 all having the same diameter, does not vary much, provided the length of 
 the piece is not less than one and does not exceed four or five diameters, 
 and that the weight which will just crush a short prism whose base equals 
 one square inch, and whose height is not less than 1 to 1V and does not 
 exceed 4 or 5 diameters, is called the crushing strength of the material. 
 It would be well if experimenters would all agree upon some such defi- 
 nition of the term "crushing strength," and insist that all experiments 
 which are made for the purpose of testing the relative values of different 
 materials in compression be made on specimens of exactly the same 
 shape and size. An arbitrary size and shape should be assumed and 
 agreed upon for this purpose. The size mentioned by Stoney is definite 
 as regards area of section, viz., one square inch, but is indefinite as re- 
 gards length, viz., from one to five diameters. In some metals a speci- 
 men five diameters long would bend, and give a much lower apparent 
 strength than a specimen having a length of one diameter. The words 
 "will just crush" are also indefinite for ductile materials, in which the 
 resistance increases without limit if the piece tested does not bend. In 
 such cases the weisht which causes a certain percentage of compression, 
 as five, ten, or fifty per cent, should be assumed as the crushing strength. 
 
 For future experiments on crushing strength three things are desir- 
 able: First, an arbitrary standard shape and size of test specimen for 
 comparison of all materials. Secondly, a standard limit of compression 
 for ductile materials, which shall be considered equivalent to fracture 
 in brittle materials. Thirdly, an accurate knowledge of the relation 
 of the crushing strength of a specimen of standard shape and size to 
 the crushing strength of specimens of all other shapes and sizes. The 
 latter can only be secured by a very extensive and accurate series of 
 experiments upon all kinds of materials, and on specimens of a great 
 number of different shapes and sizes. 
 
 The author proposes, as a standard shape and size, for a compressive 
 
COLUMNS, PILLARS, OH STRUTS. 283 
 
 test specimen for all metals, a cylinder one inch in length, and one half 
 square inch in sectional area, or 0.798 inch diameter; and for the limit 
 of compression equivalent to fracture, ten per cent of the original length. 
 The term " compressive strength," or " compressive strength of standard 
 specimen," would then mean the weight per square inch required to 
 fracture by compressive stress a cylinder one inch long and 0.798 inch 
 diameter, or to reduce its length to 0.9 inch if fracture does not take 
 place before that reduction in length is reached. If such a standard, or 
 any standard size whatever, had been used by the earlier authorities on 
 the strength of materials, we never would have had such discrepancies 
 in their statements in regard to the compressive strength of wrought 
 iron as those given ab9ve. 
 
 The reasons why this particular size is recommended are: that the 
 sectional area, one-half square inch, is as large as can be taken in the 
 ordinary testing-machines of 100,000 pounds capacity, to include all 
 the ordinary metals of construction, cast and wrought iron, and the 
 softer steels; and that the length, one inch, is convenient for calcula- 
 tion of percentage of compression. If the length were made two inches, 
 many materials would bend in testing, and give incorrect results. Even 
 in cast iron Hodgkinson found as the mean of several experiments on 
 various grades, tested in specimens % inch in height, a compressive 
 strength per square inch of 94,730 pounds, while the mean of the same 
 number of specimens of the same irons tested in pieces iy 2 inches in 
 height was only 88., 800 pounds. The best size and shape of standard 
 specimen should, however, be settled upon only after consultation and 
 agreement among several authorities. 
 
 The Committee on Standard Tests of the American Society of Me- 
 chanical Engineers say (vol. xi, p. 624) : 
 
 "Although compression tests have heretofore been made on diminu- 
 tive sample pieces, it is highly desirable that tests be also made on long 
 pieces from 10 to 20 diameters in length, corresponding more nearly with 
 actual practice, in order that elastic strain and change of shape may be 
 determined by using proper measuring apparatus. 
 
 "The elastic limit, modulus or coefficient of elasticity, maximum and 
 ultimate resistances, should be determined, as well as the increase of 
 section at various points, viz., at bearing surfaces and at crippling point. 
 
 " The use of long compression- test pieces is recommended, because the 
 investigation of short cubes or cylinders has led to no direct application 
 of the constants obtained by their use in computation of actual struc- 
 tures, which have always been and are now designed according to em- 
 pirical formulse obtained from a few tests of long columns." 
 
 COLUMNS, PILLARS, OR STRUTS. 
 
 Notation. -^-P = crushing weight in pounds; d = exterior diameter 
 in inches; a = area in square inches; L = length in feet; I = length in 
 inches; S = compressive stress, Ibs. per sq. in.; E = modulus of elasticity 
 in tension or compression; r = least radius of gyration; <, an experimental 
 coefficient. 
 
 For a short column centrally loaded S = P/a, but for a long column 
 which tends to bend under load , the stress on the concave side is greater^ 
 and on the convex side less than P/a. 
 
 Hodgkinson's Formula for Columns. 
 
 Both ends rounded, the Both ends flat, the length 
 
 u- A t n i. length of the column of the column exceed- 
 
 ,olumn. exceeding 15 times its ing 30 times its diam- 
 
 diameter. eter. 
 
 Solid cylindrical col- ) & -- - af . d 3 ' 7 * 
 
 = 
 
 l col- ) 
 
 > 
 
 on . . . J 
 
 . . > f = jJfj . _ 
 
 umns of cast iron . . . J L 1 7 
 
 Solid cylindrical col- | 
 
 p _ ne ocn 
 
 ' 2 
 
 r/3'55 
 
 P = 98,920 j~ 
 P = 299,600 - 
 
 umns of wrought iron J L 2 
 
 These formulae apply only in cases in which the length is so great that 
 
'284 
 
 STRENGTH OF MATERIALS. 
 
 the column breaks by bending and not by simple crushing. Hodgkinson's 
 tests were made on small columns, and his results are not now con- 
 sidered reliable. 
 
 Euler's Formula for Long Columns. 
 
 7T 2 E (r/l) 2 for columns with round or hinged ends. 
 
 with fixed ends, multiply by 4; with one end round and the other fixed, 
 multiply by 21/4; for one end fixed and the other free, as a post set in the 
 ground, divide by 4. P is the load which causes a slight deflection: a 
 
 load greater than P will cause an increase of deflection until the column 
 fails by bending. The formula is now little used. 
 
 Christie's Tests (Trans. A. S. C. E. 1884: Merriman's Mechanics 
 of Materials}. About 300 tests of wrought-iron struts were made, the 
 duality of the iron being about as follows: tensile strength per sq. in., 
 49,600 IDS., elastic limit 32,000 Ibs., elongation 18% in 8 ins. 
 
 The following table gives the average results. 
 
 Ratio I IT 
 Length to 
 Least JJ,a- 
 
 Ultimate Load, P/a, in Pounds per Square Inch. 
 
 
 
 
 
 
 Gyraticra. 
 
 Fixed Ends, 
 
 Flat Ends. 
 
 Hinged Ends. 
 
 Round Ends. 
 
 20 
 
 46,000 
 
 46,000 
 
 46,000 
 
 44,000 
 
 40 
 
 40,000 
 
 40,000 
 
 40,000 
 
 36,500 
 
 eo 
 
 36,000 
 
 36,000 
 
 36,000 
 
 30,500 
 
 80 
 
 32,000 
 
 32,000 
 
 31,500 
 
 25,000 
 
 100 
 
 30,000 
 
 29,800 
 
 28,000 
 
 20,500 
 
 120 
 
 28,000 
 
 26,300 
 
 24,300 
 
 16,500 
 
 140 
 
 25,500 
 
 23,500 
 
 21,000 
 
 12,800 
 
 160 
 
 23,000 
 
 20,000 
 
 16,500 
 
 9,500 
 
 180 
 
 20,000 % 
 
 16,800 
 
 12,800 
 
 7,500 
 
 200 
 
 17,500 
 
 14,500 
 
 10,800 
 
 6,000 
 
 220 
 
 15,000 
 
 12,700 
 
 8,800 
 
 5,000 
 
 240 
 
 13,000 
 
 11,200 
 
 7,500 
 
 4,300 
 
 260 
 
 11,000 
 
 9,800 
 
 6,500 
 
 3,800 
 
 280 
 
 10,000 
 
 8,500 
 
 5,700 
 
 3,200 
 
 300 
 
 9,000 
 
 7,200 
 
 5,000 
 
 2,800 
 
 320 
 
 8,000 
 
 6,000 
 
 4,500 
 
 2,500 
 
 360 
 
 6,500 
 
 4,300 
 
 3,500 
 
 1,900 
 
 400 
 
 5.200 
 
 3,000 
 
 2,500 
 
 1,500 
 
 The results of Christie's tests agree with those computed by Euler's 
 formula for round-end columns with llr between 150 and 400, but 
 differ widely from them in shorter columns, and still more widely in 
 columns with fixed ends. 
 
 Rankine's Formula (sometimes called Gordon's), S = fl +< f-j J 
 
 n rr 
 
 or = . Applying Rankine's formula to the results of 
 
 experiments, wide variations are found in the values of the empirical 
 coefficient <. Merriman gives the following values, which are extensively 
 employed in practice. 
 
 VALUES OF <f> FOR RANKINE'S FORMULA. 
 
 Material. 
 
 Both Ends 
 Fixed. 
 
 Fixed and 
 Round. 
 
 Both Ends 
 Round. 
 
 Timber 
 
 1/3 000 
 
 1 78/3 000 
 
 4/3 000 
 
 
 1 /5.000 
 
 1.78/5 000 
 
 4/5 000 
 
 Wrought Iron . . 
 
 1/36,000 
 
 1.78/36,000 
 
 4/36,000 
 
 Steel !.. 
 
 1 /25.000 
 
 1.78/25,000 
 
 4/25 000 
 
 
 
 
 
 The value to be taken for S is the ultimate compressive strength of the 
 
WORKING FORMULAE FOR STRUTS. 285 
 
 material for cases of rupture, and the allowable compressive unit stress 
 for cases of design. 
 
 Burr gives the following values as commonly taken for S and <f>. 
 
 For solid wrought-iron columns, S = 36,000 to 40,000, tf> = 1/36,000 to 
 1/40,000. 
 
 For solid cast-iron columns, . S = 80,000, <j> = 1/6,400. 
 
 For hollow cast-iron columns, P /a = 80,000 *- 1 + ^Q ^ (d = outside 
 diam. in inches). 
 
 The coefficient of P/d 2 is given by different writers as 1/400, 1/500, 
 1/600 and 1/800. (See Strength of Cast-iron Columns, below.) 
 
 Sir Benjamin Baker gives for mild steel, S = 67,000 Ibs., < = 1/22,400; 
 for strong steel, S = 114,000 Ibs., d> = 1/14,400. Prof. Burr considers 
 these only loose approximations. (See Straight-line Formula, below). 
 
 For dry timber, Rankine gives 8 = 7200 Ibs., </> = 1/3000. 
 
 The Straight-line Formula. The results of computations by Euler's 
 or Rankine's formulas give a curved line when pk)tted on a diagram 
 with values of l/r as abscissas and value of P/a as ordinates. The Average 
 results of experiments on columns within the limits of l/r commonly 
 used in practice, say from 50 to 200, can be represented by a straight line 
 about as accurately as by a curve. Formulas derived from such plotted 
 lines, of the general form P/a = S - C l/r, in which C is an experimental 
 coefficient, are in common use, but Merriman says it is advisable that the 
 use of this formula should be limited to cases in which the specifications 
 require it to be employed, and for rough approximate computations. 
 Values of S and C given by T. H. Johnson are as follows: 
 
 F H R F H R 
 
 Wrought Iron: 
 
 S = 42,000 Ibs., C = 128, 157, 203; limit of l/r = 218, 178,138 
 Structural Steel: 
 
 5=52,500" C = 179, 220, 284; ...... 195,159,123 
 
 Cast Iron: 5=80,000" C = 438, 537, 693; ...... 122, 99, 77 
 
 Oak, flat ends: 
 
 S = 5,400 " C = 28: 128 
 
 F, flat ends; H, hinged ends; R, round ends. 
 
 Merriman says: "The straight-line formula is not suitable for investi- 
 gating a column, that is for determining values of S due to given loads, 
 because S enters the formula in such a manner as to lead to a cubic 
 equation when it is the only unknown quantity. It may be used to find 
 the safe load for a given column to withstand a given unit stress, or to 
 design a column for a given load and unit stress. When so used, it is 
 customary to divide the values of S and C given in the table by an 
 assumed factor of safety. For example, Cooper's specifications require 
 that the sectional area a for a medium-steel post of a through railroad 
 bridge shall be found from P/a = 17,000 - 90 l/r Ibs. per sq. in., in 
 which P is the direct dead-load compression on the post plus twice the 
 live-load compression; the values of S and C here used are a little less 
 than one-third of those given in the table for round ends." 
 
 Working^ Formulae for Wrought-iron and Steel Struts of Various 
 Forms. Burr gives the following practical formulae: 
 
 p. = Ultimate 
 
 Kind of Strut. Ibs? W'in. mate 
 
 of Section. 
 
 Flat and fixed end iron angles and tees 44000 - 140 (1) 8800 -28^ (2) 
 Hinged-end iron angles and tees ...... 46000 -175^ (3) 9200 - 35 ^ (4) 
 
 Flat-end iron channels and I-beams . . . 40000 - 1 10 - (5) 8000 - 22 - (6) 
 
286 
 
 STRENGTH OF MATERIALS. 
 
 Flat-end mild-steel angles ............. 52000 - 180 l - (7) 10400 - 36^ (8) 
 
 Flat-end high-steel angles ........... 76000-290 l - (9) 15200 -58 (10) 
 
 Pin-end solid wrought-iron columns . . .32000 - 80 - 
 
 6400 - 16 - 
 
 32000- 277 
 
 6400-55^1 
 
 Equations (1) to (4) are to be used only between - =40 and - = 200 
 
 11 (5) and (6) " " " " " " = 20 " " = 200 
 
 (7) to (10) " " " " " " = 40 " " = 200 
 
 (11) and (12) " !! !! !! !' " = 20 " " = 200 
 
 or ~ = 6 and - => 65 
 d d 
 
 Comparison of Column Compression Formulae. The Carnegie 
 Steel Co. gives in its Pocket Companion (1913) a table comparing the 
 allowable unit stresses in columns calculated from the formulae of the 
 American Bridge Co., American Railway Engineering Association, 
 Gordon, and the New York, Philadelphia, and Boston Building Laws, 
 for various values of l/r. The table below is condensed from this 
 table and compares the values obtained by the American Bridge Co. 
 formula with the average of all those, except that of the American 
 Bridge Co. for values of l/r up to 120, and with the values obtained 
 by Gordon's formula for values of l/r from 125 to 200. 
 
 Allowable Unit Stresses Pounds per Sq. In. 
 
 l/r 
 
 Am. Bridge 
 Co. 
 
 Average. 
 
 \l/r 
 
 Am. Bridge 
 Co. 
 
 Average. 
 
 l/r 
 
 Am. Bridge 
 Co. 
 
 Gordon. 
 
 
 
 14,000 
 
 14,790 
 
 65 
 
 1 1,450 
 
 11,803 
 
 125 
 
 6,750 
 
 8,715 
 
 5 
 
 14,000 
 
 14,719 
 
 70 
 
 11,100 
 
 11,466 
 
 130 
 
 6,500 
 
 8,510 
 
 10 
 
 14,000 
 
 14,620 
 
 75 
 
 10,750 
 
 11,130 
 
 135 
 
 6,250 
 
 8,300 
 
 15 
 
 14,000 
 
 14,499 
 
 80 
 
 10,400 
 
 10,794 
 
 140 
 
 6,000 
 
 8,095 
 
 20 
 
 14,000 
 
 14,355 
 
 85 
 
 10,050 
 
 10,459 
 
 145 
 
 5,750 
 
 7,890 
 
 25 
 
 14,000 
 
 14,185 
 
 90 
 
 9,700 
 
 10,127 
 
 150 
 
 5,500 
 
 7,690 
 
 30 
 
 13,900 
 
 13,977 
 
 95 
 
 9,350 
 
 9,785 
 
 155 
 
 5,250 
 
 7,495 
 
 35 
 
 13,550 
 
 13,701 
 
 100 
 
 9,000 
 
 9,473 
 
 160 
 
 5,000 
 
 7,305 
 
 40 
 
 13,200 
 
 13,410 
 
 105 
 
 8,650 
 
 9,150 
 
 165 
 
 4,750 
 
 7,120 
 
 45 
 
 12,850 
 
 13,106 
 
 110 
 
 8,300 
 
 8,837 
 
 170 
 
 4,500 
 
 6,935 
 
 50 
 
 12,500 
 
 12,790 
 
 115 
 
 7,950 
 
 8,528 
 
 180 
 
 4,000 
 
 6,580 
 
 55 
 
 12,150 
 
 12,467 
 
 120 
 
 7,600 
 
 8,221 
 
 190 
 
 3,500 
 
 6,240 
 
 60 
 
 11,800 
 
 12,137 
 
 
 
 
 200 
 
 3,000 
 
 5,920 
 
 Built Columns (Burr). Steel columns, properly made, of steel 
 ranging in specimens from 65,000 to 73,000 Ib. per square inch, should 
 give a resistance 25 to 33 per cent in excess of that of wrought-iron 
 columns with the same value of I *- r, provided that ratio does not exceed 
 140. 
 
 The unsupported width of a plate in a compression member should not 
 exceed 30 times its thickness. 
 
 In built columns the transverse distance between center lines of rivets 
 securing plates to angles or channels, etc., should not exceed 35 times the 
 plate thickness. If this width is exceeded, longitudinal buckling of the 
 plate takes place, and the column ceases to fail as a whole, but yields in 
 detail. 
 
 The thickness of the leg of an angle to which latticing is riveted should 
 not be less than 1/9 of the length of that leg or side if the column is purely 
 a compression member. The above limit may be passed somewhat in stiff 
 ties and compression members designed to carry transverse loads. 
 ^ The panel points of latticing should not be separated by a greater clis- 
 
WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 287 
 
 tance than 60 times the thickness of the angle-leg to which the latticing 
 is riveted, if the column is wholly a compression member. 
 
 The rivet pitch should never exceed 16 times the thickness of the 
 thinnest metal pierced by the rivet, and if the plates are very thick it 
 should never nearly equal that value. 
 
 Burr gives the following general principles which govern the resistance 
 of built columns: 
 
 The material should be disposed as far as possible from the neutral axis 
 of the cross-section, thereby increasing r; 
 
 There should be no initial internal stress; 
 
 The individual portions of the column should be mutually supporting; 
 
 The individual portions of the column should be so firmly secured to 
 each other that no relative motion can take place, in order that the 
 column may fail as a whole, thus maintaining the original value of r. 
 
 Stoney says: " When the length of a rectangular wrought-iron tubular 
 column does not exceed 30 times its least breadth, it fails by the bulging or 
 buckling of a short portion of the plates, not by the flexure of the pillar 
 as a whole." 
 
 Tests of Five Large Built Steel Columns. (Proc. A. S. C. E., Feb., 
 1911; Eng. News, Mar. 16, 1911). The lateral dimensions of the 
 columns were -about 20 X 30 in., and their sectional area 90 sq. in. 
 They were made of two ribs 30 in. deep, spaced 207/g in., laced by two 
 lines of 2 1/2 X 3 /8 in. lacing. Each rib was made of an outside plate, 
 30 XH/16 in., and an inside plate, I7 l /z X 5 /8 in., and two inner edging 
 angles, 6 X 6 X 5 /8 in. Transverse plate diaphragms, 6 ft. apart, gave 
 additional lateral rigidity. The test columns were fitted with 10-in. 
 pins set parallel to the plane of the lacing. The columns were tested 
 in the 1,200-ton hydraulic machine at Phcenixville, Pa.; two of them 
 (Nos. 1 and 2) did not reach failure. The results are as below: 
 
 No. 
 1 
 
 Section 
 Area Sq. In. 
 90 73 
 
 Length 
 Ft. In. 
 20 
 
 l/f 
 
 26 2 
 
 Max. Load 
 Lb. 
 2 600 962 
 
 Lb. per 
 Sq. In. 
 
 28 667 
 
 2 
 
 90 33 
 
 36 5 
 
 47.2 
 
 2 600,962 
 
 28,794 
 
 3 
 
 90.78 
 
 36 5 
 
 47.2 
 
 2,675,183 
 
 29,469 
 
 4 . 
 
 90 32 
 
 36 5 
 
 47.2 
 
 2 726 815 
 
 30,191 
 
 5. . 
 
 89.96 
 
 36 5 
 
 47.1 
 
 2,742,950 
 
 30,490 
 
 Nos. 3 and 4 failed by bulging of plates in front of pins; No. 5 by 
 web-plates bulging inward 121/2 in. from one end. The columns de- 
 parted from strictly proportional compression at a load as low as 20,000 
 Ib. per sq. in. Plotted curves of the tests show that all the columns 
 reached their elastic limit at about this figure, and an ultimate strength 
 at about 30,000 Ib. per sq. ill. Eng. News says that it does not appear 
 that the lacing contributed to the failure. It shows that the com- 
 pressive strength of these columns did not exceed 60% of the tensile 
 strength of the metal. 
 
 WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 
 
 Theodore Cooper gives the following in his Bridge Specifications: 
 Compression members shall be so proportioned that the maximum load 
 shall in no case cause a greater strain than that determined by the follow- 
 ing formula: 
 
 8000 * 
 
 P = Tjj for square-end compression members; 
 
 1 + 
 
 40,000 r 2 
 
 8000 
 p = - _ - for compression members with one pin and one square 
 
 30,000r2 en ; 
 8000 
 P = - - for compression members with pin-bearings; 
 
 1 + 
 
 20,000 r* 
 
288 STRENGTH OF MATERIALS. 
 
 (These values may be increased in bridges over 150 ft. span. See 
 Cooper's Specifications.) 
 
 P the allowed compression per square inch of cross-section; 
 I = the length of compression member, in inches; 
 
 r = the least radius of gyration of the section in inches. 
 
 No compression member, however, shall have a length exceeding 25 
 times its least width. 
 
 Tension Members. All parts of the structure shall be so proportioned 
 that the maximum loads shall in no case cause a greater tension than the 
 following (except in spans exceeding 150 feet): 
 
 Pounds per 
 
 sq. in. 
 On lateral bracing ....................... ........ " ........... 15,000 
 
 On solid rolled beams, used as cross floor-beams and stringers .... 9,000 
 
 On bottom chords and main diagonals (forged eye-bars) ......... 10,000 
 
 On bottom chords and main diagonals (plates or shapes), net section 8,000 
 On counter rods and long verticals (forged eye-bars) .... ........ 8,000 
 
 On counter and long verticals (plates or shapes), net section ..... 6,500 
 
 On bottom flange of riveted cross-girders, net section .......... . . 8,000 
 
 On bottom flange of riveted longitudinal plate girders over 20 ft. 
 
 long, net section ........................................... 8,000 
 
 On bottom flange of riveted longitudinal plate girders under 20 ft. 
 
 long, net section .......................................... 7,000 
 
 On floor-beam hangers, and other similar members liable to sudden 
 
 loading (bar iron with forged ends) ......................... 6,000 
 
 On floor-beam hangers, and other similar members liable to sudden 
 
 loading (plates or shapes), net section ....................... 5,000 
 
 Members subject to alternate strains of tension and compression shall be 
 proportioned to resist each kind of strain. Both of the strains shall, how- 
 ever, be considered as increased by an amount equal to 8/ 10 of the least of 
 the two strains, for determining the sectional area by the above allowed 
 strains. 
 
 The Phcenix Bridge Co. (Standard Specifications, 1895) gives the follow- 
 ing: 
 
 The greatest working stresses in pounds per square inch shall be s 
 follows: 
 
 Tension. 
 
 Steel. Iron. 
 
 p Q nno Fi 4. Min ' stress "| For bars p_7 500 f i + Min - Stress 1 
 F-9,000 ^1 + Max stress j forged ends- T*W L 1 t Max. stress] 
 
 P~8 500 Fl 4- Min - Stress 1 Plates or > = 7 000 Fl + Min " Stress 1 
 F-8,500 1 + 7.UUU l + 
 
 8,500 pounds. Floor-beam hangers, forged ends ...... 7,000 pounds. 
 
 7,500 " Floor-beam hangers, plates or shapes, net 
 
 section ............................ 6,000 
 
 10,000 Lower flanges of rolled beams ......... 8,000 
 
 20,000 " Outside fibres of pins ................ 15,000 
 
 30,000 " Pins for wind-bracing ................ 22,500 
 
 20,000 Lateral bracing ............ . ........ 15,000 
 
 Shearing. 
 
 9,000 pounds. Pins and rivets ...................... 7,500 pounds. 
 
 Hand-driven rivets 20% less unit stresses. 
 
 For bracing increase unit stresses 50%. 
 $,000 pounds. Webs of plate girders ................ 5,000 pounds. 
 
 Bearing. 
 
 16 000 pounds. Projection semi-intrados pins and rivets, 12,000 pounds. 
 Hand-driven rivets 20% less unit stresses. For 
 bracing increase unit stresses 50%, 
 
STRENGTH OF CAST-IRON COLUMNS. 289 
 
 Compression. 
 
 Lengths less than forty times the least radius of gyration, P previously 
 found. See Tension. 
 
 Lengths more than forty times the least radius of gyration, P reduced 
 by following formulae: 
 
 P 
 
 For both ends fixed, b = 75 
 
 
 36,000 r 2 
 
 p 
 For one end hinged, b = -^ 
 
 1 
 
 24,000 r 2 
 
 P 
 For both ends hinged, b = 
 
 18,000 r 2 
 
 P = permissible stress previously found (see Tension); b = allowable 
 working stress per square inch; I = length of member in inches; r = least 
 radius of gyration of section in inches. No compression member, how- 
 ever, shall have a length exceeding 45 times its least width. 
 
 Pounds per 
 sq. in. 
 
 In counter web members 10,500 
 
 In long verticals 10,000 
 
 In all main-web and lower-chord eye-bars , 13,200 
 
 In plate hangers (net section} 9,000 
 
 In tension members of lateral and transverse bracing 19,000 
 
 In steel-angle lateral ties (net section) 15,000 
 
 For spans over 200 feet in length the greatest allowed working stresses 
 per square inch, in lower-chord and end main-web eye-bars, shall be taken 
 at 
 
 min. total stressX 
 
 10,000 (l 
 
 max. total stress/ 
 
 whenever this quantity exceeds 13,200. 
 
 The greatest allowable stress in the main-web eye-bars nearest the centre 
 of such spans shall be taken at 13,200 pounds per square inch; and those 
 for the intermediate eye-bars shall be found by direct interpolation 
 between the preceding values. 
 
 The greatest allowable working stresses in steel plate and lattice girders 
 and rolled beams shall be taken as follows: 
 
 Pounds per 
 sq. in. 
 
 Upper flange of plate girders (gross section) 10,000 
 
 Lower flange of plate girders (net section) 10,000 
 
 In counters and long verticals of lattice girders (net section) 9,000 
 In lower chords and main diagonals of lattice girders (net 
 
 section) 10,000 
 
 In bottom flanges of rolled beams 10,000 
 
 In top flanges of rolled beams 10,000 
 
 THE STRENGTH OF OAST-IRON COLUMNS. 
 
 Hodgkinson's experiments (first published in Phil. Trans. Royal Socy., 
 1840, and condensed in Tredgold on Cast Iron, 4th ed., 1846), and Gordon's 
 formula, based upon them, are still used (1898) in designing cast-iron col- 
 umns. They are entirely inadequate as a basis of a practical formula 
 suitable to the present methods of casting columns. 
 
 Hodgkinson's experiments were made on nine "long" pillars, about 71/2 
 ft. long, whose external diameters ranged from 1.74 to 2.23 in., and 
 average thickness from 0.29 to 0.35 in., the thickness of each column also 
 Varying, and on 13 "sljort" pillars, 0.733 fy. to 2,251 ft. long, with exter- 
 
290 
 
 STRENGTH OF MATERIALS. 
 
 nal diameters from 1.08 to 1.26 in., all of them less than 1/4 in. thick. 
 The iron used was Low Moor, Yorkshire, No. 3, said to be a good iron, not 
 very hard, earlier experiments on which had given a tensile strength of 
 14,535 and a crushing strength of 109,801 Ibs. per sq. in. Modern cast- 
 iron columns, such as are used in the construction of buildings, are very 
 different in size, proportions, and quality of iron from the slender "long" 
 pillars used in Hodgkinson's experiments. There is usually no check, by 
 actual tests or by disinterested inspection, upon the quality of the material. 
 The tensile, compressive, and transverse strength of cast iron varies 
 through a great range (the tensile strength ranging from less than 10,000 
 to over 40,000 Ibs. per sq. in.), with variations in the chemical composition 
 of the iron, according to laws which are as yet very imperfectly under- 
 stood, and with variations in the method of melting and of casting. 
 There is also a wide variation in the strength of iron of the same melt 
 when cast into bars of different thicknesses. 
 
 Another difficulty in obtaining a practical formula f9r the strength of 
 cast-iron columns is due to the uncertainty of the quality of the casting, 
 and the danger of hidden defects, such as internal stresses due to unequal 
 cooling, cinder or dirt, blow-holes, "cold-shuts," and cracks on the inner 
 surface, which cannot be discovered by external inspection. Variation 
 in thickness, due to rising of the core during casting, is also a common 
 defect 
 
 In addition to these objections to the use of Gordon's formula, for cast- 
 iron columns, we have the data of experiments on full-sized columns, 
 made by the Building Department of New York City (Eng'g News, Jan. 13 
 and 20, 1898). Ten columns in all were tested, six 15-inch, 1901/4 inches 
 long, two 8-inch, 160 inches long, and two 6-inch, 120 inches long. The 
 tests were made on the large hydraulic machine of the Phoenix Bridge Co., 
 of 2,000,000 pounds capacity, which was calibrated for frictionai error by 
 the repeated testing within the elastic limit of a large Phoenix column, 
 and the comparison of these tests with others made on the government 
 machine at the Watertown Arsenal. The average frictionai error was 
 calculated to be 15.4 per cent, but Engineering News, revising the data, 
 makes it 17.1 per cent, with a variation of 3 per cent either way from the 
 average with different loads. The results of the tests of the columns are 
 given below. 
 
 TESTS OF CAST-IRON COLUMNS. 
 
 
 
 Thickness. 
 
 Breaking Load. 
 
 her. 
 
 Inches. 
 
 Max. 
 
 Min. 
 
 Average. 
 
 Pounds. 
 
 Pounds 
 per Sq. In. 
 
 j 
 
 15 
 
 1 
 
 
 , 
 
 ,356,000 
 
 30,830 
 
 2 
 
 15 
 
 1 5/16 
 
 
 H/8 
 
 ,330,000 
 
 27,700 
 
 3 
 
 15 
 
 H/4 
 
 
 H/8 
 
 ,198,000 
 
 24,900 
 
 4 
 
 151/s 
 
 17/32 
 
 
 H/8 
 
 ,246,000 
 
 25,200 
 
 5 
 
 15 
 
 1 H/16 
 
 
 1 H/64 
 
 ,632,000 
 
 32,100 
 
 6 
 
 15 
 
 H/4 
 
 H/8 
 
 13/16 
 
 2,082,000 + 
 
 40,400 + 
 
 7 
 8 
 
 73/ 4 to81/ 4 
 8 
 
 U/4 
 13/32 
 
 
 1 
 13/64 
 
 651,000 
 612,800 
 
 31,900 
 26,800 
 
 9 
 
 61/16 
 
 15/32 
 
 11/8 . 
 
 19/64 
 
 400,000 
 
 22,700 
 
 10 
 
 63/32 
 
 H/8 
 
 H/16 
 
 17/64 
 
 455,200 
 
 26,300 
 
 Column No. 6 was not broken at the highest load of the testing 
 machine. 
 
 Columns Nos. 3 and 4 were taken from the Ireland Building, which 
 collapsed on August 8, 1895; the other four 15-inch columns were made 
 from drawings prepared by the Building Department, as nearly as possible 
 s of Nos. 3 and 4. Nos. 1 and 2 were made by a foundry in New 
 
 duplicates of . . . 
 
 York with no knowledge of their ultimate use. 
 
 Nos. 5 a.nc} 6 were 
 
SAFE LOADS FOB CAST-IRON COLUMNS. 
 
 291 
 
 by a foundry in Brooklyn with the knowledge that they were to be tested. 
 Nos. 7 to 10 were made from drawings furnished by the Department. 
 Applying Gordon's formula, as used by the Building Department, 
 
 S =-. a , to these columns gives for the breaking strength per square 
 
 1 + 400 eP 
 
 inch of the 15-inch columns 57,143 pounds, for the 8-inch columns 40,000 
 pounds, and for the 6-inch columns 40,000. The strength of columns Nos. 
 3 and 4 as calculated is 128 per cent more than their actual strength; their 
 actual strength is less than 44 per cent of their calculated strength; and 
 the factor of safety, supposed to be 5 in the Building Law, is only 2.2 f9r 
 central loading, no account being taken of the likelihood of eccentric 
 loading. 
 
 Prof. Lanza, Applied Mechanics, p. 372, quotes the records of 14 
 tests of cast-iron mill columns, made on the Watertown testing-machine in 
 1887-88, the breaking strength per square inch ranging from 25,100 to 
 63,310 pounds, and showing no relation between the breaking strength 
 per square inch and the dimensions of the columns. Only 3 of the 14 
 columns had a strength exceeding 33,500 pounds per square inch. The 
 average strength of the other 11 was 29,600 pounds per square inch. Prof. 
 Lanza says that it is evident that in the case of such columns we cannot 
 rely upon a crushing strength of greater than 25,000 or 30,000 pounds 
 per square inch of area of section. 
 
 He recommends a factor of safety of 5 or 6 with these figures for crush- 
 ing strength, or 5000 pounds per square inch of area of section as the 
 highest allowable safe load, and in addition makes the conditions that 
 the length of the column shall not be greatly in excess of 20 times the 
 diameter, that the thickness of the metal shall be such as to insure a good 
 strong casting, and that the sectional area should be increased if necessary 
 to insure that the extreme fibre stress due to probable eccentric loading 
 shall not be greater than 5000 pounds per square inch. 
 
 Prof. W. H. Burr (Eng'g News, June 30, 1898) gives a formula derived 
 from plotting the results of the Watertown and Phoenixville tests, above 
 described, which represents the average strength of the columns in pounds 
 per square inch. It is p = 30,500 - 160 l/d. It is to be noted that this 
 is an average value, and that the actual strength of many of the columns 
 was much lower. Prof. Burr says: "If cast-iron columns are designed 
 with anything like a reasonable and real margin of safety, the amount of 
 metal required dissipates any supposed' economy over columns of mild 
 steel." 
 
 Square Columns. Square cast-iron columns should be abandoned. 
 They are liable to have serious internal strains from difference in con- 
 traction on two adjacent sides. John F. Ward, Eng. News, Apr. 16, 1896. 
 
 Safe Load, in Tons of 2000 Lbs., for Round Cast-iron Columns* 
 with Turned Capitals and Bases. 
 
 Loads being not eccentric, and length of column not exceeding 20 times 
 the diameter. Based on ultimate crushing strength of 25,000 Ibs. per 
 sq. in. and a factor of safety of 5. 
 
 Thick- 
 
 Diameter, Inches. 
 
 ness, 
 Inches. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 5/8 
 3/4 
 7/8 
 
 11/8 
 11/4 
 
 26.4 
 30.9 
 35.2 
 39.2 
 
 31.3 
 36.8 
 42.1 
 47.1 
 
 42.7 
 48.9 
 55.0 
 60.8 
 
 48.6 
 55.8 
 62.8 
 69.6 
 76 1 
 
 54.5 
 62.7 
 70.7 
 78.4 
 85 9 
 
 69.6 
 78.5 
 87.2 
 95.7 
 
 76.5 
 86.4 
 96.1 
 105.5 
 
 94.2 
 104.9 
 115.3 
 
 102.1 
 
 113.8 
 125.2 
 
 110.0 
 122.6 
 135.0 
 
 131.4 
 144.8 
 
 1644 
 
 13/8 
 
 
 
 
 
 93 1 
 
 103.9 
 
 114.7 
 
 125.5 
 
 136.3 
 
 147.1 
 
 157.9 
 
 179.5 
 
 11/2 
 
 
 
 
 
 
 
 123.7 
 
 135.5 
 
 147.3 
 
 159.0 
 
 170.8 
 
 194.4 
 
 13/4 
 
 
 
 
 
 
 
 
 
 168.4 
 
 182.1 
 
 195 8 
 
 223 3 
 
 2 
 
 
 
 
 
 
 
 
 
 
 204.2 
 
 219.9 
 
 251.3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
292 STRENGTH OF MATERIALS. 
 
 For lengths greater than 20 diameters the allowable loads should be 
 decreased. How much they should be decreased is uncertain, since suffi- 
 cient data of experiments on full-sized very long columns, from which a 
 formula for the strength of such columns might be derived, are as yet 
 lacking. There is, however, rarely, if ever, any need of proportioning 
 cast-iron columns with a length exceeding 20 diameters. 
 
 Safe Loads in Tons of 200O Pounds for Cast-iron Columns. 
 
 (By the Building Laws of New York City, Boston, and Chicago, 1897.) 
 
 New York. Boston. Chicago. 
 
 ( 8a 5 a 5 a 
 
 Square columns. ... ) ~ /r~" 12 JT~ 
 
 114- i _L _ la. 
 
 r ' Knn ^/2 * ~ i ncfi^n * 
 
 Round columns 
 
 ) 1 + 
 
 500 cP T 1067cP 800 d 2 
 
 Ba 5a 5a 
 
 ~~ 
 
 400 d* 800 d 2 T 600 & 
 
 a = sectional area in square inches; 1= unsupported length of column 
 in inches; d = side of square column or thickness of round column in 
 inches. 
 
 The safe load of a 15-inch round column iy 2 inches in thickness, 16 
 feet long, according to the laws of these cities would be, in New York, 361 
 tons; in Boston, 264 tons; in Chicago, 250 tons. 
 
 The allowable stress per square inch of area of such a column would be, 
 in New York, 11,350 pounds; in Boston, 8300 pounds; in Chicago, 7850 
 pounds. A safe stress of 5000 pounds per square inch would give for the 
 safe load on the column 159 tons. 
 
 Strength of Brackets on Cast-iron Columns. The columns tested 
 by the New York Building Department referred to above had brackets 
 cast upon them, each bracket consisting of a rectangular shelf sup- 
 ported by one or two triangular ribs. These were tested after the 
 columns had been broken in the principal tests. In 17 out of 22 cases the 
 brackets broke by tearing a hole in the body of the column, instead of by 
 shearing or transverse breaking of the bracket itself. The results were 
 surprisingly low and very irregular. Reducing them to strength per 
 square inch of the total vertical section through the shelf and rib or ribs, 
 they ranged from 2450 to 5600 Ibs., averaging 4200 Ibs., for a load con- 
 centrated at the end of the shelf, and 4100 to 10,900 Ibs., averaging 8000 
 .Ibs., for a distributed load. (Eng'g News, Jan. 20, 1898.) 
 
 Maximum Permissible Stresses in columns used in buildings. 
 (Building Ordinances of City of Chicago, 1893.) 
 
 For riveted or other forms of wrought-iron columns: 
 
 g r= 12000 a ^ i length of column in inches; 
 
 Z 2 r = least radius of gyration in inches; 
 
 36000 r 2 a = area * c l umn in square inches. 
 
 For riveted or other steel columns, if more than 60 r in length: 
 
 s = 17 ,ooo - 521 
 
 If less than 60 r in length: S = 13,500 a. 
 For wooden posts: 
 
 e ac a = area of post in square inches; 
 
 " 72"' d = least side of rectangular post in inches; 
 
 1 + ocn^o I = length of post in inches; 
 
 250 d 2 < 600 for white or Norway pine; 
 
 C = { 800 for oak ; 
 
 (900 for long-leaf yellow pine, 
 
MOMENT OF INERTIA AND RADIUS OF GYRATION. 293 
 
 MOMENT OF INERTIA AND RADIUS OF GYRATION. 
 
 The moment of inertia of a section is the sum of the products of 
 each elementary area of the section into the square of its distance from an 
 assumed axis of rotation, as the neutral axis. 
 
 Assume the section to be divided into a great many equal small areas, 
 a, and that each such area has its own radius, r, or distance from the 
 assumed axis of rotation, then the sum of all the products derived by 
 multiplying each a by the square of its r is the moment of inertia, 7, or 
 7 = 2 ar 2 , in which 2 is the sign of summation. 
 
 For moment of inertia of the weight or mass of a body se Mechanics. 
 
 The radius of gyration of the section equals the square root of the 
 quotient of the moment of inertia divided by the area of the section. If 
 R = radius of gyration, 7 = moment of inertia and A = area 
 
 R =V/7Z II A = R 2 . 
 
 The center of gyration is the point where the entire area might be 
 
 concentrated and have the same moment of inertia as the actual area. 
 
 The distance of this center from the axis of rotation is the radius of 
 
 gyration. 
 
 The moments of inertia of various sections are as follows: 
 
 d = diameter, or outside diameter; d\ = inside diameter; 6 = breadth; 
 
 h = depth; 61, hi,- inside breadth and depth; 
 
 Solid rectangle 7 = Vi2&/i 3 ; Hollow rectangle 7 = Vi2(&& 8 - &i/ti 3 ); 
 
 Solid square 7 = Vi2& 4 ; Hollow square 7 = 1/12(6* 6i 4 ); 
 
 Solid cylinder 7 = i/Qi^d 4 ; Hollow cylinder 7 = i/w^Cd 4 di 4 ). 
 
 Moment of Inertia about any Axis. If b breadth and h = 
 depth of a rectangular section its moment of inertia about its central 
 axis (parallel to the breadth) is 1/12 bh*; and about one side is 1/3 bh z . If 
 a parallel axis exterior to the section is taken, and d = distance of this 
 axis from the farthest side and d\ = its distance from the nearest side, 
 (d di = h}, the moment of inertia about this axis is 1/36 (d 3 di 3 ). 
 
 The moment of inertia of a compound shape about any axis is equal to 
 the sum of the moments of inertia, with reference to the same axis, of all 
 the rectangular portions composing it. 
 
 Moment of Inertia of Compound Shapes. (Pencoyd Iron 
 Works.) The moment of inertia of any section about any axis is equal 
 to the 7 about a parallel axis passing through its centre of gravity 4- (the 
 area of the section X the square of the distance between the axes). 
 
 By this rule, the moments of inertia or radii of gyration of any single 
 sections being known, corresponding values may be obtained for any 
 combination of these sections. 
 
 E. A. Dixon (Am. Mach., Dec. 15, 1898) gives the following formula for 
 the moment of inertia of any rectangular element of a built up beam: 
 7 = 1/3 (h 3 h\ 3 )b, I = moment of inertia about any axis parallel to the 
 neutral axis, h = distance from the assumed axis to the farthest fiber, 
 h\ = distance to nearest fiber, b = breadth of element. The sum of the 
 moments of inertia of ail the elements, taken about the center of gravity 
 or neutral axis of the section, is the moment of inertia of the section. 
 
 The polar moment of inertia of a surface is the sum of the products 
 obtained by multiplying each elementary area by the square of its dis- 
 tance from the center of gravity of the surface; it is equal to the sum of 
 the moments of inertia taken with respect to two axes at right angles to 
 each other passing through the center of gravity. It is represented by 
 J. For a solid shaft J = 1/32 ^d 4 ; for a hollow shaft, J = 1/32 *(d* ofi 4 ), 
 5n which d is the outside andr/i the inside diameter. 
 
 The polar radius of gyration, R p = \/J/A, is defined as the radius of 
 a circumference along which the entire area might be concentrated and 
 have the same polar moment of inertia as the actual area. 
 
 For a solid circular section R p 2 = i/s 7J> 2 ; for a hollow circular sec- 
 tion R p * = l/ 8 (d 2 + di 2 ). 
 
 Moments of Inertia and Radius of Gyration for Various Sec- 
 tions, and their Use in the Formulas for Strength of Girders and 
 Columns. The strength of sections to resist strains, either as 
 girders or as columns, depends not only on the area but also on the 
 form of the section, and the property of the section which forms the 
 
294 STRENGTH OF MATERIALS. 
 
 basis of the constants used in the formulas for strength of girders and 
 columns to express the effect of the form, is its moment of inertia about 
 its neutral axis. The modulus of resistance of any section to transverse 
 bending is its moment of inertia divided by the distance from the neutral 
 axis to the fibres farthest removed from that axis; or 
 
 Section modulus = =- Moment of inertia _ ; z = 7 
 
 Distance of extreme fibre from axis c 
 
 Moment of resistance = section modulus X unit stress on extreme fibre. 
 
 Radius of* Gyration of Compound Shapes. In the case of a 
 pair of any shape without a web the value of R can always be found with- 
 out considering the moment of inertia. 
 
 The radius of gyration for any section around an axis parallel to another 
 axis passing through its centre of gravity is found as follows: 
 
 Let r = radius of gyration around axis through centre of gravity; R = 
 radius of gyration around another axis parallel to above; d = distance 
 between axes: R = Vrf 2 + r 2 . 
 
 When r is small, R may be taken as equal to d without material error. 
 
 Graphical Method for Finding Radius of Gyration. Benj. F. 
 La Rue, Eng. News-, Feb. 2, 1893, gives a short graphical method for 
 finding the radius of gyration of hollow, cylindrical, and rectangular 
 columns, as follows: 
 
 For cylindrical columns: 
 
 Lay off to a scale of 4 (or 40) a right-angled triangle, in which the base 
 equals the outer diameter, and the altitude equals the inner diameter 
 of the column, or vice versa. The hypothenuse, measured to a scale of 
 unity (or 10), will be the radius of gyration sought. 
 
 This depends upon the formula 
 
 G= VMom. of inertia -*- Area = 1/4 
 in which A = area and D = diameter of outer circle, a = area and d =* 
 diameter of inner circle, and G = radius of gyration. V/)2 + ^2 is the 
 expression for the hypothenuse of a right-angled triangle, in which D and 
 d are the base and altitude. 
 
 The sectional area of a hollow round column is 0.7854(Z) 2 d 2 ). By 
 constructing a right-angled triangle in which D equals the hypothenuse 
 and d equals the altitude, the base will equal V)2 _ & Calling the 
 value of this expression for the base B, the area will equal 0.7854.8 2 . 
 
 Value of G for square columns: 
 
 Lay off as before, but using a scale of 10, a right-angled triangle of which 
 the base equals D or the side of the outer square, and the altitude equals d, 
 the side of the inner square. With a scale of 3 measure the hypothenuse, 
 which will be, approximately, the radius of gyration. 
 
 This process for square columns gives an excess of slightly more than 
 4%. By deducting 4% from the result, a close approximation will be 
 obtained. 
 
 A very close result is also obtained by measuring the hypothenuse with 
 the same scale by which the base and altitude were laid off, and multiplying 
 by the decimal 0.29'; more exactly, the decimal is 0.28867. 
 
 The formula is 
 
 VMom. of ii 
 Area 
 
 of inertia 1 . 
 
 D 2 + eJ 2 , = 0.28867 
 
 This may also be applied to any rectangular column by using the lesser 
 diameters of an unsupported column, and the greater diameters if the 
 column is supported in the direction of its least dimensions. 
 
 ELEMENTS OF USUAL SECTIONS. 
 
 Moments refer to horizontal axis through centre of gravity. This table 
 is intended for convenient application where extreme accuracy is not 
 important. Some of the terms are only approximate; those marked * are 
 correct. Values for radius of gyration in flanged beams apply to standard 
 minimum sections only. A = area of section; b = breadth; h = depth: 
 D = diameter. 
 
ELEMENTS OF USUAL SECTIONS. 
 
 295 
 
 Shape 
 
 of Section. 
 
 Moment 
 of Inertia. 
 
 Section 
 Modulus. 
 
 Square of 
 Least 
 Radius of 
 Gyration. 
 
 Least 
 Radius of 
 Gyration. 
 
 4 
 
 Solid Rect- 
 
 6^3* 
 
 6A 2 * 
 
 (Least side) 2 * 
 
 Least side * 
 
 i 
 
 angle. 
 
 12 
 
 6 
 
 12 
 
 3.46 
 
 En t 
 
 Hrllr*OT T? <+ 
 
 
 bW bh** 
 
 h*+h* 
 
 h+h l 
 
 i 
 
 angle. 
 
 12 
 
 6h 
 
 12 
 
 4.89 
 
 
 
 
 
 
 
 
 
 Solid Circle. 
 
 1/64 irZ)** 
 = 0.049 ID* 
 
 = (?U982>3 
 
 ~I6~ 
 
 D* 
 4 
 
 y^Si 
 
 Hollow Circle. 
 A, area of 
 
 AD* -ad** 
 
 AD*-a#* 
 
 D2-f^ 2 * 
 
 D + d 
 
 1JP 
 
 a, area of 
 small section. 
 
 16 
 
 SO 
 
 16 
 
 5.64 
 
 ^ 
 
 Solid Triangle. 
 
 . 6fc3 
 36 
 
 24~ 
 
 The least of 
 the two ; 
 
 T8 2 r l4 
 
 The least 
 of the two; 
 h b 
 4^4 r 4T9 
 
 o 
 
 Even Angle. 
 
 Ah* 
 1 0.2 
 
 7T . 
 
 25" 
 
 6 
 5 
 
 tT 
 
 
 Ah* 
 
 ^^ 
 
 (hb}* 
 
 hb 
 
 J 
 
 Uneven Angle. 
 
 9.5 
 
 6.5 
 
 \3(h*+b*) 
 
 2.6(h + b) 
 
 B 
 
 Even Cross. 
 
 \9 
 
 93 
 
 223 
 
 474 
 
 eP 
 
 Even Tee. 
 
 Ah* 
 U.I 
 
 T" 
 
 b* 
 223 
 
 6 
 4.74 
 
 ^ 
 
 I Beam. 
 
 Ah* 
 6.66 
 
 ^^ 
 3.2 
 
 62 
 
 21 
 
 6 
 438 
 
 TO 
 
 Channel. 
 
 Ah* 
 7.34 
 
 A* 
 
 3.67 
 
 6 2 
 12.5 
 
 6 
 334 
 
 <f|Hq 
 >-ft i 
 
 Deck Beam. 
 
 Ah* 
 6.9 
 
 Ah 
 4 
 
 62 
 363 
 
 6 
 6 
 
 Distance of base from centre of gravity, solid triangle, -; even angle, ^-^. 
 
 o o.o' 
 
 uneven angle, ^-r ; even tee, 77-5 ; deck beam, ; all other shapes 
 
 ' O.O O.O .i.O 
 
 given in the table, - or 
 
296 STRENGTH OF MATERIALS. 
 
 ECCENTRIC LOADING OF COLUMNS. 
 
 In a given rectangular cross-section, such as a masonry joint under 
 pressure, the stress will be distributed uniformly over the section only 
 when the resultant passes through the centre of the section; any deviation 
 from such a central position will bring a maximum unit pressure to one 
 edge and a minimum to the other; when the distance of the resultant 
 from one elge is one third of the entire width of the joint, the pressure at 
 the nearer edge is twice the mean pressure, while that at the farther edge 
 is zero, and that when the resultant approaches still nearer to the edge 
 the pressure at the farther edge becomes less than zero: in fact, becomes 
 a tension, if the material (mortar, etc.) there is capable of resisting tension. 
 Or, if, as usual in masonry joints, the material is practically incapable of 
 resisting tension, the pressure at the nearer edge, when the resultant 
 approaches it nearer than one third of the width, increases very rapidly 
 and dangerously, becoming theoretically infinite when the resultant 
 reaches the edge. 
 
 With a given position of the resultant relatively to one edge of the joint 
 or section, a similar redistribution of the pressures throughout the section 
 may be brought about by simply adding to or diminishing the width of 
 the section. 
 
 Let P = the total pressure on any section of a bar of uniform thickness. 
 
 w =- the width of that section = area of the section, when thickness = 1. 
 p =. p/ w = the mean unit pressure on the section. 
 
 M = the maximum unit pressure on the section. 
 
 m = the minimum unit pressure on the section. 
 d = the eccentricity of the resultant = its distance from the centre of 
 the section 
 
 When d = - w then M = 2p and m = O. 
 6 
 
 When d is greater than 1/6 iff, the resultant in that case being less than 
 one third of the width from one edge, p becomes negative. (J. C. Traut- 
 wine, Jr., Engineering News, Nov. 23, 1893.) 
 
 Eccentric Loading of Cast-iron Columns. Prof. Lanza writes 
 the author as follows: The table on page 276 applies when the result- 
 ant of the loads upon the column acts along its central axis, i.e., passes 
 through the centre of gravity of every section. In buildings and other 
 constructions, however, cases frequently occur when the resultant load 
 does not pass through the centre of gravity of the section: and then the 
 pressure is not evenly distributed over the section, but is greatest on the 
 side where the resultant acts. (Examples occur when the loads on 
 the floors are not uniformly distributed.) In these cases the outside 
 fibre stresses of the column should be computed as follows, viz.: 
 Let P = total pressure on the section; 
 
 d = eccentricity of resultant = its distance from the centre of 
 
 gravity of the section; 
 
 A = area of the section, and / its moment of inertia about an axis in 
 its plane, passing through its centre of gravity, and perpendic- 
 ular to d; 
 ci = distance of most compressed and ci = that of least compressed 
 
 fibre from above stated axis; 
 si =* maximum and sz = minimum pressure oer unit of area. Then 
 
 P , (Pd)ci P (Pd)ca. 
 
 Sl - A + I" and S2 = A ~ -J- 
 
 Having assumed a certain trial section for the column to be designed, si 
 should be computed, and, if it exceed the proper safe value, a different 
 section should be used for which si does not exceed this value. 
 
 The proper safe value, in the case of cast-iron columns whose ratio of 
 length to diameter does not greatly exceed 20, is 5000 pounds per square 
 inch when the eccentricity u^ed in the computation of si is liable to occur 
 frequently in the ordinary uses of the structure; but when it is one which 
 can only occur in rare cases the value 8000 Ibs. per sq. in. may be used. 
 
 A long cap on a column is more conducive to the production of eccen- 
 tricity of loading than a short one, hence a long cap is a source of weakness, 
 
TRANSVERSE STRENGTH. 297 
 
 TRANSVERSE STRENGTH. 
 
 In transverse tests the strength of bars of rectangular section is found to 
 vary directly as the breadth of the specimen tested, as the square of its 
 depth, and inversely as its length. The deflection under any load varies 
 as the cube of the length, and inversely as the breadth and as the cube of 
 the depth. Represented algebraically, if S = the strength and D the 
 deflection, / the length, b the breadth, and d the depth, 
 
 bd 2 I s 
 
 S varies as r- and D varies as , ^- 
 I bd 3 
 
 For the purpose of reducing the strength of pieces of various sizes to 
 a common standard, the term modulus of rupture (represented by R) is 
 used. Its value is obtained by experiment on a bar of rectangular section 
 supported at the ends and loaded in the middle and substituting numerical 
 values in the following formula: 
 
 in which P = the breaking load in pounds, I = the length in inches, b the 
 breadth, and d the depth. 
 
 The modulus of rupture is sometimes defined as the strain at the instant 
 of rupture upon a unit of the section which is most remote from the neu- 
 tral axis on the side which first ruptures. This definition, however, is 
 based upon a theory which is yet in dispute among authorities, and it is 
 better to define it as a numerical value, or experimental constant, found 
 by the application of the formula above given. 
 
 From the above formula, making / 12 inches, and b and d each 1 inch, it 
 follows that the modulus of rupture is 18 times the load required to break 
 a bar one inch square, supported at two points one foot apart, the load 
 being applied in the middle. 
 
 , , span in feet X load at middle in Ibs. 
 
 Coefficient of transverse strength = ^- -77. r 
 
 breadth in inches X (depth in inches) 2 
 
 = th of the modulus of rupture. 
 
 lo 
 
 Fundamental Formulae for Flexure of Beams (Merriman). 
 
 Resisting shear = vertical shear; 
 
 Resisting moment = bending moment; 
 
 Sum of tensile stresses = sum of compressive stresses: 
 
 Resisting shear = algebraic sum of all the vertical components of the 
 internal stresses at any section of the beam. 
 
 If A be the area of the section and S s the shearing unit stress, then 
 resisting shear = AS S ; and if the vertical shear = F, then V= AS S . 
 
 The vertical shear is the algebraic sum of all the external vertical forces 
 on one side of the section considered. It is equal to the reaction of one 
 support, considered as a force acting upward, minus the sum of all the 
 vertical downward forces acting between the support and the section. 
 
 The resisting moment = algebraic sum of all the moments of the inter- 
 nal horizontal stresses at any section with reference to a point in that 
 
 section, = in which S = the horizontal unit stress, tensile or com- 
 
 c 
 
 pressive as the case may be, upon the fibre most remote from the neutral 
 axis, c = the slwrtest distance from that fibre to said axis, and 7 = the 
 moment of inertia of the cross-section with reference to that axis. 
 
 The bending moment M is the algebraic sum of the moment of the 
 external forces on one side of the section with reference to a point in that 
 section = moment of the reaction of one support minus sum of moments 
 of loads between the support and the section considered. 
 
 The bending moment is a compound quantity = product of a force by 
 the distance of its point of application from the section considered, the 
 distance being measured on a line drawn from the section perpendicular 
 to the direction of the action of the force, 
 
298 
 
 STRENGTH OF MATERIALS. 
 
 Concerning the formula, M=*SI/c, p. 297, Prof. Merriman, "710. News, 
 July 21, 1894, says: The formula quoted is true when the unit-stress S on 
 the part of the beam farthest from the neutral axis is within the elastic limit 
 of the material. It is not true when this limit is exceeded, because then 
 the neutral axis does not pass through the center of gravity of the cross- 
 section, and because also the different longitudinal stresses are not pro- 
 portional to their distances from that axis, these two requirements being 
 involved in the deduction of the formula. But in all cases of design the 
 permissible unit-stresses should not exceed the elastic limit, and hence 
 the formula applies rationally, without regarding the ultimate strength 
 of the material or any of the circumstances regarding rupture. Indeed, 
 so great reliance is placed upon this formula that the practice of. testing 
 beams by rupture has been almost entirely abandoned, and the allowable 
 unit-stresses are mainly derived from tensile and compressive tests. 
 
 APPROXIMATE GREATEST SAFE LOADS IN LBS. ON STEEL 
 BEAMS. (Pencoyd Iron Works.) 
 
 Based on fiber strains of 16,000 Ibs. for steel. (For iron the loads should 
 bo one-eighth less, corresponding to a fibre strain of 14,000 Ibs. per square 
 inch.) Beams supported at the ends and uniformly loaded. 
 
 L = length in feet between supports; a = interior area in square 
 A = sectional area of beam in square inches; 
 
 inches; d interior depth in inches. 
 
 D = depth of beam in inches. w = working load in net tons. 
 
 Shape of 
 Section. 
 
 Greatest Safe Load in Pounds. 
 
 Deflection in Inches. 
 
 Load in 
 Middle. 
 
 Load 
 Distributed. 
 
 Load in 
 Middle. 
 
 Load 
 Distributed. 
 
 Solid Rect- 
 angle. 
 
 890 AD 
 
 1780 AD 
 
 wL* 
 
 wL* 
 
 L 
 
 L 
 
 32 AD 2 
 
 52AD 2 
 
 Hollow 
 Rectangle. 
 
 890(AZ)-acO 
 
 1780(AZ>-ad) 
 
 wtf 
 
 wL* 
 
 L 
 
 L 
 
 32(AD' 2 -aa' 2 ) 
 
 52(AD 2 -ad 2 ) 
 
 Solid 
 Cylinder. 
 
 667AD 
 
 \333AD 
 
 wtf 
 
 wL3 
 
 L 
 
 L 
 
 24 AD 2 
 
 38 AD 2 
 
 Hollow 
 Cylinder. 
 
 667(AD-ad) 
 L 
 
 ]333(AD-ad) 
 
 wU 
 
 wL* 
 
 L 
 
 24(AD 2 -ad*) 
 
 38(AD' 2 -ad 2 ) 
 
 Even- 
 legged 
 Angle or 
 Tee. 
 
 885AD 
 
 1770AD 
 
 wL* 
 
 wL 3 
 
 L 
 
 L 
 
 32AD 2 
 
 52AD 2 
 
 Channel or 
 Z bar 
 
 1525AD 
 
 3050AD 
 
 wL* 
 
 wL* 
 
 L 
 
 L 
 
 53 AD 2 
 
 85AD2 
 
 Deck 
 Beam. 
 
 1380AD 
 
 276QAD 
 
 wL s 
 
 wlfi 
 
 L 
 
 L 
 
 50AZ>2 
 
 SOAD 2 
 
 I Beam. 
 
 1695 AD 
 
 3390AD 
 
 wL* 
 
 wU 
 
 L 
 
 L 
 
 58 AD 2 
 
 93AD 2 
 
 I 
 
 11 
 
 III 
 
 IV 
 
 V 
 
 The above formulas for the strength and stiffness 9f rolled beams of 
 various sections are intended for convenient application in cases where 
 gtrict accuracy is not required. 
 
TBANSVERSE STRENGTH OF BEAMS. 
 
 299 
 
 A IS 
 
 -IS 
 
 *>.*_, 3 
 
 ft; v> CkJ ft- 
 
 So 
 
 * a: s: 
 
 IQO | oo ivo , 
 
 + 
 -|T 
 
 %| 
 
 ^s r- 
 
 9S\ 
 
 T|cr 
 
 II 
 
 
 
 
 
 3 
 
 S 
 
 CQ 
 
 t 
 
300 
 
 STRENGTH OF MATERIALS. 
 
 The rules for rectangular and circular sections are correct, while those 
 for the flanged sections are approximate, and limited in their application 
 to the standard shapes as given in the Pencoyd tables. When the section 
 of any beam is increased above the standard minimum dimensions, the 
 flanges remaining unaltered, and the web alone being thickened, the ten- 
 dency will be for the load as found by the rules to be in excess of the 
 actual; but within the limits that it is possible to vary any section in the 
 rolling; the rules will apply without any serious inaccuracy. 
 
 The calculated safe loads will be approximately one half of loads that 
 would injure the elasticity of the materials. 
 
 The rules for deflection apply to any load below the elastic limit, or 
 less than double the greatest safe load by the rules. 
 
 If the beams are long without lateral support, reduce the loads for the 
 ratios of width to span as follows: 
 
 Length of Beam. 
 20 times flange width. 
 30 
 
 40 " 
 50 " 
 60 " 
 70 " 
 
 Proportion of Calculated Load 
 forming Greatest Safe Load. 
 
 Whole calculated load. 
 
 9-10 
 
 8-10 
 
 7-10 
 
 6-10 
 
 5-10 
 
 These rules apply to beams supported at each end. For beams supported 
 otherwise, alter the coefficients of the table as described below, referring 
 to the respective columns indicated by number. 
 
 Changes of Coefficients for Special Forms of Beams. 
 
 Kind of Beam. 
 
 Coefficient for Safe 
 Load, 
 
 Coefficient for Deflec- 
 tion. 
 
 Fixed at one end, loaded 
 at the other. 
 
 One fourth of the coeffi- 
 cient, col. II. 
 
 One sixteenth of the co- 
 efficient of col. IV. 
 
 Fixed at one end, load 
 evenly distributed. 
 
 One fourth of the coeffi- 
 cient of col. III. 
 
 Five forty-eighths of the 
 coefficient of col. V. 
 
 Both ends rigidly fixed, 
 or a continuous beam, 
 with a load in middle. 
 
 Twice the coefficient of 
 col. II. 
 
 Four times the coeffi- 
 cient of col. IV. 
 
 Both ends rigidly fixed, 
 or a continuous beam, 
 with load evenly dis- 
 tributed. 
 
 One and one-half times 
 the coefficient of col. 
 III. 
 
 Five times the coefficient 
 of col. V. 
 
 Formulae for Transverse Strength of Beams. Referring to table 
 on page 299, 
 
 P = load at middle; 
 
 W = total load, distributed uniformly; 
 
 I = length, b = breadth, d depth, in inches; 
 B = modulus of elasticity; 
 R = modulus of rupture, or stress per square inch of extreme fiber; 
 
 7 = moment of inertia; 
 
 c = distance between neutral axis and extreme fibre. 
 For breaking load of circular section, replace bd? by 
 
BEAMS OF UNIFORM STRENGTH. 
 
 301 
 
 The value of R at rupture, or the modulus of rupture (see page 282), 
 is about 60,000 for structural steel, and about 110,000 for strong steel. 
 (Merriman.) 
 
 For cast iron the value of R varies greatly according to quality. Thurs- 
 ton found 45,740 and 67,980 in No. 2 and No. 4 cast iron, respectively. 
 
 For beams fixed at both ends and loaded in the middle, Barlow, by 
 experiment, found the maximum moment of stress = 1/6 PI instead of 
 1/8 PI, the result given by theory. Prof. Wood (Resist. Matls. p. 155) 
 says of this case: The phenomena are of too complex a character to admit 
 of a thorough and exact analysis, and it is probably safer to accept the 
 results of Mr. Barlow in practice than to depend upon theoretical results. 
 
 BEAMS OP UNIFORM STRENGTH THROUGHOUT THEIR 
 LENGTH. 
 
 The section is supposed in all cases to be rectangular throughout. The 
 beams shown in plan are of uniform depth throughout. Those shown in 
 elevation are of uniform breadth throughout. 
 
 B = breadth of beam. D = depth of beam. 
 
 ELEVATION. 
 
 Fixed at one end, loaded at the other* 
 curve parabola, vertex at loaded end ; BD 
 proportional to distance from loaded end- 
 The beam may be reversed, so that the 
 upper edge is parabolic, or both edges may 
 be parabolic. 
 
 Fixed at one end, loaded at tne other; 
 triangle, apex at loaded end ; BD 2 propor- 
 tional to the distance from the loaded end. 
 
 Fixed at one end ; load distributed ; tri- 
 angle, apex at unsupported end ; BD 2 pro- 
 portional to square of distance from unsup- 
 ported end. 
 
 Fixed at one end; load distributed; 
 curves two parabolas, vertices touching 
 each other at unsupported end; BD* 
 proportional to distance from unsupported 
 end. 
 
 Supported at both ends; load at any one 
 point; two parabolas, vertices at the 
 points of support, bases at point loaded; 
 BD 2 proportional to distance from nearest 
 point of support. The upper edge or 
 both edges may also be parabolic. 
 
 Supported at both ends ; load at any one 
 point; two triangles, apices at points of 
 support, bases at point loaded; BD 2 pro- 
 portional to distance from the nearest 
 point of support. 
 
 Supported at both ends; load distri- 
 buted; curves two parabolas, vertices at 
 the middle of the beam; bases centre line 
 of beam; BD 2 proportional to product of 
 distances from points of support. 
 
 Supported at both ends; load distri- 
 buted; curve semi-ellipse: BD 2 propor- 
 tional to the product of the distances 
 from the points of support. 
 
302 
 
 STRENGTH OF MATERIALS. 
 
 DIMENSIONS AND WEIGHTS OF STEUCTUEAL STEEL 
 SECTIONS COMMONLY EOLLED. 
 
 ( Carnegie Steel Co., 1913.) 
 
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WEIGHTS AND DIMENSIONS OF ANGLES. 303 
 
 IF 
 
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304 
 
 STRENGTH OF MATERIALS. 
 
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PROPERTIES Otf ROLLED STRUCTURAL STEEL. 305 
 
 Weights and Dimensions of I-Beams. 
 
 Size, 
 In. 
 
 Wt. 
 
 f 
 
 Lb. 
 
 Size, 
 In. 
 
 Wt. 
 
 ST. 
 
 Lb. 
 
 Size, 
 In. 
 
 Wt. 
 per 
 Ft., 
 Lb. 
 
 Size, 
 In. 
 
 Wt. 
 
 IE 
 
 Lb. 
 
 Size, 
 In. 
 
 Wt. 
 
 f 
 
 Lb. 
 
 Size, 
 In. 
 
 Wt. 
 per 
 Ft., 
 Lb. 
 
 27 
 24 
 
 83.0 
 115.0 
 110.0 
 105.0 
 100.0 
 95.0 
 90.0 
 85.0 
 80.0 
 69 5 
 
 20 
 18 
 
 90.0 
 85.0 
 8D.O 
 75.0 
 70.0 
 65.0 
 90.0 
 85.0 
 80.0 
 75 
 
 18 
 15 
 
 55.0 
 46.0 
 75.0 
 70.0 
 65.0 
 60.0 
 55.0 
 50.0 
 45.0 
 42 
 
 12 
 10 
 
 45.0 
 40.0 
 35.0 
 31.5 
 27.5 
 40.0 
 35.0 
 30.0 
 25.0 
 22 
 
 9 
 8 
 
 7 
 6 
 
 21.0 
 25.5 
 23.0 
 20.5 
 18.0 
 17.5 
 20.0 
 17.5 
 15.0 
 17.25 
 
 5 
 
 4 
 
 3 
 
 12.25 
 9.75 
 10.5 
 9.5 
 8.5 
 7.5 
 7.5 
 6.5 
 5.5 
 
 21 
 
 57 5 
 
 
 70 
 
 
 36 
 
 9 
 
 35 
 
 
 14.75 
 
 
 
 20 
 
 100.0 
 95.0 
 
 
 65.0 
 60.0 
 
 12 
 
 55.0 
 50.0 
 
 
 30.0 
 25.0 
 
 5 
 
 12.25 
 14.75 
 
 
 
 Weights and Dimensions of Channels. 
 
 15 
 
 55.0 
 50.0 
 45.0 
 40.0 
 35 
 
 13 
 12 
 
 37.0 
 35.0 
 32.0 
 40.0 
 35 
 
 10 
 9 
 
 30.0 
 25.0 
 20.0 
 15.0 
 25 
 
 8 
 7 
 
 18.75 
 16.25 
 13.75 
 11.25 
 19 75 
 
 6 
 5 
 
 15.5 
 13.0 
 10.5 
 8.0 
 11 5 
 
 4 
 3 
 
 5.25 
 6.0 
 5.0 
 4.0 
 
 13 
 
 33.0 
 50 
 
 ' 
 
 30.0 
 25 
 
 
 20.0 
 15 
 
 
 17.25 
 14 75 
 
 
 9.0 
 6 5 
 
 
 
 
 45 
 
 
 20 5 
 
 
 13 25 
 
 
 12 25 
 
 4 
 
 7 25 
 
 
 
 
 40.0 
 
 10 
 
 35.0 
 
 8 
 
 21.25 
 
 
 9.75 
 
 
 6.25 
 
 
 
 PROPERTIES OF ROLLED STRUCTURAL STEEL. 
 
 Explanation of Tables of the Properties of I-Beams, Channels, 
 Angles, Z-Bars, Tees, etc. (Carnegie Steel Co.) 
 
 The tables of properties of I-beams and channels, pp. 307 to 313, 
 are calculated for all standard sizes and weights to which each pattern 
 is rolled, excepting for five weights of the 13-in. channel which is omitted 
 in the tables. The table of properties of angles are calculated for the 
 maximum, intermediate, and minimum weights of each size, excepting 
 that only maximum and minimum weights are given for a few of the 
 smaller sizes as noted in the tables. The properties of Z-bars are given 
 for thicknesses differing by Vi6 in. The table of properties of Tee shapes 
 lists the lightest section of each size. In the case of angles there will 
 be two section moduli for each position of the neutral axis, since the 
 distance between the neutral axis and the extreme fiber is different on 
 either side of the axis. With T-sections there are two section moduli 
 where the neutral axis is parallel to the flange. In these cases only 
 the smaller section moduli are given. 
 
 The column headed x, in the table of the properties of standard 
 channels, giving the distance of the center of gravity of channel from 
 the outside of web, is used to obtain the radius of gyration for columns 
 or struts consisting of two channels latticed, for the case of the neutral 
 axis passing through the center of the cross-section parallel to the webs 
 of the channels. This radius of gyration is equal to the distance be- 
 tween the center of gravity of the channel and the center of the section, 
 i.e., neglecting the moments of inertia of the channels around their own 
 axes, thereby introducing a slight error on the side of safety. 
 
 In the tables of safe loads of beams and channels, the safe loads for 
 various lengths of span are given only for the lightest weight of each 
 section rolled in the various sizes. The safe loads of the heavier weights 
 of each section can be calculated from the data given in the tables of 
 properties. The safe loads given in the tables are for a uniform load 
 per running foot on the beam or channel. If the load, instead of being 
 uniform, is concentrated at the center of the span, multiply it by 2 
 and then consider it as a uniform load. The deflection will be 0,8 X 
 
306 
 
 STRENGTH OF MATERIALS* 
 
 the deflection for the uniform load. The safe loads in the tables are 
 calculated solely with reference to the safe unit stresses due to flexure, 
 and the values given will not produce average shearing stresses in the 
 web greater than -10, 000 Ib. per sq. in., the maximum allowed in the 
 American Bridge Co.'s specifications. When the beams carry con- 
 centrated loads, the buckling or shearing stresses in the web, rather 
 than the resistance of the flanges to bending stresses may limit the 
 carrying capacity. 
 
 The tables of safe loads for angles, tees, and Z-bars give the safe loads 
 on a span of 1 ft., from which the safe load for any length of span may 
 be obtained by direct division. They also give the values at which 
 the allowed safe load will produce the maximum allowable deflection 
 of 1/360 of the span length. 
 
 The tables are based on an extreme fiber stress of 16,000 Ib. per sq. in., 
 which is the customary figure for quiescent loads, as in buildings. 
 Where running loads are involved, as in bridges, crane runways, etc., an 
 extreme fiber stress of 12,500 Ib. per sq. in. should be used and the values 
 reduced accordingly. For suddenly applied loads, the extreme fiber 
 stresses should be reduced to 8,000 Ib. per sq. in. 
 
 It is assumed in the tables that the load is applied normal to the 
 neutral axis perpendicular to the web at the center, and that the beam 
 deflects only vertically in the plane of bending. For other conditions 
 of loading, the safe load must be determined by the general theory of 
 flexure (see page 297) in accordance with the mode of application of the 
 load and its character. Under these conditions the safe loads will be 
 considerably lower than those given in the tables. It is also assumed 
 in the tables that the compression flanges of the various sections are 
 secured against lateral deflection by the use of the rods at proper inter- 
 vals. The lateral unsupported length of beams and girders should not 
 exceed forty times the width of the compression flange. When thj 
 unsupported length exceeds ten times this width, the tabular safe loads 
 should be reduced as follows, W being the width of the compression 
 flange: 
 Length of unsupported 
 
 flange 5W WW 15W 20W 25W 'SOW 35W 40W 
 
 Percentage of full safe 
 
 load allowed 100 100 90.6 81.2 71.9 62.5 53.1 43.8 
 
 In addition to the lateral deflection induced by pure bending stresses 
 in the beam, there may be deflection due to the thrust of arches or 
 other loads acting on a line perpendicular to the line of the principal 
 stresses. These should be neutralized by tie rods so that in no case 
 will the unit stresses exceed 16,000 Ib. per sq. in. 
 
 (For much other important information concerning rolled structural 
 shapes, see the "Pocket Companion" of the Carnegie Steel Co., Pitts- 
 burgh, Pa., price $2.) 
 
 Allowable Tension Values in Bars Thousands of Pounds. 
 
 (Carnegie Steel Co., 1913.) 
 
 
 Round Bars. 
 
 Square Bars. 
 
 
 Round Bars. 
 
 Square Bars. 
 
 Size, 
 
 Unit 
 
 Unit 
 
 Unit 
 
 Unit 
 
 Size, 
 
 Unit 
 
 Unit 
 
 Unit 
 
 Unit 
 
 In. 
 
 Stress 
 
 Stress 
 
 Stress 
 
 Stress 
 
 In. 
 
 Stress 
 
 " Stress 
 
 Stress 
 
 Stress 
 
 
 16,000 
 
 20,000 
 
 16,000 
 
 20,000 
 
 
 16,000 
 
 20,000 
 
 16,000 
 
 20,000 
 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 Lb. per 
 Sq. In. 
 
 1/4 
 
 0.8 
 
 1.0 
 
 1 .0 
 
 1.3 
 
 13/ 4 
 
 38.5 
 
 48.1 
 
 49.0 
 
 61.3 
 
 1/fl 
 
 3.1 
 
 3.9 
 
 4.0 
 
 5.0 
 
 2 
 
 50.3 
 
 62.8 
 
 64.0 
 
 80.0 
 
 3/4 
 
 7.1 
 
 8.8 
 
 9.0 
 
 11 .3 
 
 2l/ 4 
 
 63.6 
 
 79.5 
 
 81 .0 
 
 101.3 
 
 
 12.6 
 
 15.7 
 
 16.0 
 
 20.0 
 
 21/2 
 
 78.5 
 
 98.2 
 
 100.0 
 
 125.0 
 
 11/4 
 
 19.6 
 
 24.5 
 
 25.0 
 
 31 .3 
 
 23/ 4 
 
 95.0 
 
 118.8 
 
 121 .0 
 
 151,3 
 
 U/2 
 
 28.3 
 
 35.3 
 
 36.0 
 
 45.0 
 
 3 
 
 113.1 
 
 141.4 
 
 144.0 
 
 180.0 
 
PKOPERTIES OF ROLLED STRUCTURAL STEEL. 307 
 
 Properties of Carnegie Standard I-Beams Steel.* 
 
 
 
 
 
 . 
 
 Neutral Axis Per- 
 
 Neutral Axis Coin- 
 
 
 
 g 
 
 
 Q) 
 
 5 
 
 pendicular to Web 
 
 cident with Center 
 
 1 
 
 1 
 
 a 
 .2 
 
 P? 
 
 
 at Center. 
 
 Line of Web. 
 
 2 
 
 & 
 
 
 E 
 *s 
 
 "o 
 
 "o . 
 
 - 
 
 m 
 
 o . 
 
 - 
 
 1 
 
 o 
 
 1 
 
 ? 
 
 03 
 
 o 
 1 
 
 u 
 
 4J 03 
 
 n 
 
 11 
 
 |f 
 
 ft 
 
 |! 
 
 if 
 
 |1 
 
 Q 
 
 
 
 1 
 
 If 
 
 1 
 
 r 
 
 1 
 
 1^ 
 
 1" 
 
 JjO 
 
 1^ 
 
 in. 
 
 Ib 
 
 sq. in. 
 
 in. 
 
 in. 
 
 in.* 
 
 in. 
 
 in.3 
 
 in.* 
 
 in. 
 
 in.3 
 
 27 
 
 83.0 
 
 24.41 
 
 7.500 
 
 0.424 
 
 2888.6 
 
 10.88 
 
 214.0 
 
 53.1 
 
 1.47 
 
 14.1 
 
 24 
 
 115.0 
 
 33.98 
 
 8.000 
 
 0.750 
 
 2955.5 
 
 9.33 
 
 246.3 
 
 83.2 
 
 1.57 
 
 20.8 
 
 
 110.0 
 
 32.48 
 
 7.938 
 
 0.688 
 
 2883.5 
 
 9.42 
 
 240.3 
 
 81.0 
 
 1.58 
 
 20.4 
 
 
 
 105.0 
 
 30.98 
 
 7.875 
 
 0.625 
 
 2811.5 
 
 9.53 
 
 234.3 
 
 78.9 
 
 1.60 
 
 20.0 
 
 M 
 
 100.0 
 
 29.41 
 
 7.254 
 
 0.754 
 
 2379.6 
 
 9.00 
 
 198.3 
 
 48.6 
 
 1.28 
 
 13.4 
 
 
 
 95.0 
 
 27.94 
 
 7.193 
 
 0.693 
 
 2309.0 
 
 9.09 
 
 192.4 
 
 47.1 
 
 1.30 
 
 13.1 
 
 
 
 90.0 
 
 26.47 
 
 7.131 
 
 0.631 
 
 2238.4 
 
 9.20 
 
 186.5 
 
 45.7 
 
 1.31 
 
 12.8 
 
 
 
 85.0 
 
 25.00 
 
 7.070 
 
 0.570 
 
 2167.8 
 
 9.31 
 
 180.7 
 
 44.4 
 
 1.33 
 
 12.6 
 
 
 
 80.0 
 
 23.32 
 
 7.000 
 
 0.500 
 
 2087.2 
 
 9.46 
 
 173.9 
 
 42.9 
 
 1.36 
 
 12.3 
 
 
 
 69.5 
 
 20.44 
 
 7.000 
 
 0.390 
 
 1928.0 
 
 9.71 
 
 160.7 
 
 39.3 
 
 1.39 
 
 11.2 
 
 2\ 
 
 57.5 
 
 16.85 
 
 6.500 
 
 0.357 
 
 1227.5 
 
 8.54 
 
 116.9 
 
 28.4 
 
 1.30 
 
 8.8 
 
 20 
 
 100.0 
 
 29.41 
 
 7.284 
 
 0.884 
 
 1655.6 
 
 7.50 
 
 165.6 
 
 52.7 
 
 1.34 
 
 14.5 
 
 
 95.0 
 
 27.94 
 
 7.210 
 
 0.810 
 
 1606.6 
 
 7.58 
 
 160.7 
 
 50.8 
 
 1.35 
 
 14.1 
 
 * 
 
 90.0 
 
 26.47 
 
 7.137 
 
 0.737 
 
 1557.6 
 
 7.67 
 
 155.8 
 
 49.0 
 
 1.36 
 
 13.7 
 
 
 
 85.0 
 
 25.00 
 
 7.063 
 
 0.663 
 
 1508.5 
 
 7.77 
 
 150.9 
 
 47.3 
 
 1.37 
 
 13.4 
 
 
 
 80.0 
 
 23.73 
 
 7.000 
 
 0.600 
 
 1466.3 
 
 7.86 
 
 146.6 
 
 45.8 
 
 .39 
 
 13.1 
 
 M 
 
 75.0 
 
 22.06 
 
 6.399 
 
 0.649 
 
 1268.8 
 
 7.58 
 
 126.9 
 
 30.3 
 
 .17 
 
 9.5 
 
 " 
 
 70.0 
 
 20.59 
 
 6.325 
 
 0.575 
 
 1219.8 
 
 7.70 
 
 122.0 
 
 29.0 
 
 .19 
 
 9.2 
 
 
 
 65.0 
 
 19.08 
 
 6.250 
 
 0.500 
 
 1169.5 
 
 7.83 
 
 117.0 
 
 27.9 
 
 .21 
 
 8.9 
 
 18 
 
 90.0 
 
 26.47 
 
 7.245 
 
 0.807 
 
 1260.4 
 
 6.90 
 
 140.0 
 
 52.0 
 
 .40 
 
 14.4 
 
 
 85.0 
 
 25.00 
 
 7.163 
 
 0.725 
 
 1220.7 
 
 6.99 
 
 135.6 
 
 50.0 
 
 .42 
 
 14.0 
 
 
 
 80.0 
 
 23.53 
 
 7.082 
 
 0.644 
 
 1181.0 
 
 7.09 
 
 131.2 
 
 48.1 
 
 .43 
 
 13.6 
 
 
 
 75.0 
 
 22.05 
 
 7.000 
 
 0.562 
 
 1141.3 
 
 7.19 
 
 126.8 
 
 46.2 
 
 .45 
 
 13.2 
 
 < 
 
 70.0 
 
 20.59 
 
 6.259 
 
 0.719 
 
 921.2 
 
 6.69 
 
 102.4 
 
 24.6 
 
 .09 
 
 7.9 
 
 < 
 
 65.0 
 
 19.12 
 
 6.177 
 
 0.637 
 
 881.5 
 
 6.79 
 
 97.9 
 
 23.5 
 
 .11 
 
 7.6 
 
 
 
 60.0 
 
 17.65 
 
 6.095 
 
 0.555 
 
 841.8 
 
 6.91 
 
 93.5 
 
 22.4 
 
 .13 
 
 7.3 
 
 
 
 55.0 
 
 15.93 
 
 6.000 
 
 0.460 
 
 795.6 
 
 7.07 
 
 88.4 
 
 21.2 
 
 .15 
 
 7.1 
 
 
 
 46.0 
 
 13.53 
 
 6.000 
 
 0.322 
 
 733.2 
 
 7.36 
 
 81.5 
 
 19.9 
 
 .21 
 
 6.6 
 
 15 
 
 75.0 
 
 22.06 
 
 6.292 
 
 0.882 
 
 691.2 
 
 5.60 
 
 92.2 
 
 30.7 
 
 .18 
 
 9.8 
 
 
 70.0 
 
 20.59 
 
 6.194 
 
 0.784 
 
 663.7 
 
 5.68 
 
 88.5 
 
 29.0 
 
 .19 
 
 9.4 
 
 
 
 65.0 
 
 19.12 
 
 6.096 
 
 0.686 
 
 636.1 
 
 5.77 
 
 84.8 
 
 27.4 
 
 .20 
 
 9.0 
 
 M 
 
 60.0 
 
 17.67 
 
 6.000 
 
 0.590 
 
 609.0 
 
 5.87 
 
 81.2 
 
 26.0 
 
 .21 
 
 8.7 
 
 " 
 
 55.0 
 
 16.18 
 
 5.746 
 
 0.656 
 
 511.0 
 
 5.62 
 
 68.1 
 
 17.1 
 
 .02 
 
 5.9 
 
 M 
 
 50.0 
 
 14.71 
 
 5.648 
 
 0.558 
 
 483.4 
 
 5.73 
 
 64.5 
 
 16.0 
 
 .04 
 
 5.7 
 
 
 
 45.0 
 
 13.24 
 
 5.550 
 
 0.460 
 
 455.9 
 
 5.87 
 
 60.8 
 
 15.1 
 
 .07 
 
 5.4 
 
 
 
 42.0 
 
 12.48 
 
 5.500 
 
 0.410 
 
 441.8 
 
 5.95 
 
 58.9 
 
 14.6 
 
 .08 
 
 5.3 
 
 
 
 36.0 
 
 10.63 
 
 5.500 
 
 0.289 
 
 405.1 
 
 6.17 
 
 54.0 
 
 13.5 
 
 .13 
 
 4.9 
 
 12 
 
 55.0 
 
 16.18 
 
 5.611 
 
 0.821 
 
 321.0 
 
 4.45 
 
 53.5 
 
 17.5 
 
 .04 
 
 6.2 
 
 
 50.0 
 
 14.71 
 
 5.489 
 
 0.699 
 
 303.4 
 
 4.54 
 
 50.6 
 
 16.1 
 
 .05 
 
 5.9 
 
 
 
 45.0 
 
 13.24 
 
 5.366 
 
 0.576 
 
 285.7 
 
 4.65 
 
 47.6 
 
 14.9 
 
 .06 
 
 5.6 
 
 
 
 40.0 
 
 11.84 
 
 5.250 
 
 0.460 
 
 269.0 
 
 4.77 
 
 44.8 
 
 13.8 
 
 .08 
 
 5.3 
 
 
 
 35.0 
 
 10.29 
 
 5.086 
 
 0.436 
 
 228.3 
 
 4.71 
 
 38.0 
 
 10.1 
 
 0.99 
 
 4.0 
 
 
 
 31.5 
 
 9.26 
 
 5.000 
 
 0.350 
 
 215.8 
 
 4.83 
 
 36.0 
 
 9.5 
 
 .01 
 
 3.8 
 
 
 
 27.5 
 
 8.04 
 
 5.000 
 
 0.255 
 
 199.6 
 
 4.98 
 
 33.3 
 
 8.7 
 
 .04 
 
 3.5 
 
 10 
 
 40.0 
 
 11.76 
 
 5.099 
 
 0.749 
 
 158.7 
 
 3.67 
 
 31.7 
 
 9.5 
 
 0.90 
 
 3.7 
 
 
 
 35.0 
 
 10.29 
 
 4.952 
 
 0.602 
 
 146.4 
 
 3.77 
 
 29.3 
 
 8.5 
 
 0.91 
 
 3.4 
 
 
 
 30.0 
 
 8.82 
 
 4.805 
 
 0.455 
 
 134.2 
 
 3.90 
 
 26.8 
 
 7.7 
 
 0.93 
 
 3.2 
 
 
 
 25.0 
 
 7.37 
 
 4.660 
 
 0310 
 
 122.1 
 
 4.07 
 
 24.4 
 
 6.9 
 
 0.97 
 
 3.0 
 
 " 
 
 22.0 
 
 6.52 
 
 4.670 
 
 0.232 
 
 113.9 
 
 4.18 
 
 22.8 
 
 6.4 
 
 0.99 
 
 2.7 
 
 * See notes on next page. 
 
 (Table continued on next page.') 
 
308 
 
 STRENGTH OF MATERIALS, 
 
 Properties of Carnegie Standard I-Beams Steel. Continued. 
 
 
 
 
 
 
 Neutral Axis Per- 
 
 Neutral Axis Coin- 
 
 
 . 
 
 
 o3 
 
 1 
 
 pendicular to Web 
 
 cident with Center 
 
 i 
 
 
 
 g 
 
 i 
 
 p 
 
 at Centeix 
 
 Line of Web. 
 
 1 
 
 
 
 E 
 
 o 
 
 o . 
 
 _ fl 
 
 . 
 
 o 
 
 d 
 
 . 
 
 s 
 
 p, 
 
 J 
 
 s 
 
 S 
 
 
 ^~ 
 
 3 
 
 -u.rt 
 
 8-S 
 
 g 
 
 f 
 
 "M 
 
 "* 
 
 
 1 
 
 11 
 
 $ 8 
 
 |1. 
 
 <u "E 
 S o> 
 
 ss 
 
 ll 
 
 M 
 
 S 
 
 'S 
 
 <u 
 
 25 
 
 
 P 
 
 55 
 
 
 P 
 
 lo 
 
 t5^ 
 
 Q 
 
 
 
 < 
 
 ^ 
 
 H 
 
 
 
 PH 
 
 |! 
 
 S 
 
 
 $ 
 
 "m7 
 
 Ib. 
 
 sq. in. 
 
 in. 
 
 in. 
 
 in.* 
 
 in. 
 
 in. 3 
 
 in.* 
 
 in i 
 
 in.3 
 
 9 
 
 35.0 
 
 10.29 
 
 4.772 
 
 0.732 
 
 111.8 
 
 3.29 
 
 24.8 
 
 7.3 
 
 0.84 
 
 3.1 
 
 " 
 
 30.0 
 
 8.82 
 
 4.609 
 
 0.569 
 
 101.9 
 
 3.40 
 
 22.6 
 
 6.4 
 
 0.85 
 
 2.8 
 
 " 
 
 25.0 
 
 7.35 
 
 4.446 
 
 0.406 
 
 91.9 
 
 3.54 
 
 20.4 
 
 5.7 
 
 0.88 
 
 2.5 
 
 " 
 
 21.0 
 
 6.31 
 
 4.330 
 
 0.290 
 
 84.9 
 
 3.67 
 
 18.9 
 
 5.2 
 
 0.90 
 
 2.4 
 
 8 
 
 25.5 
 
 7.50 
 
 4.271 
 
 0.541 
 
 68.4 
 
 3.02 
 
 17.1 
 
 4.8 
 
 0.80 
 
 2.2 
 
 *' 
 
 23.0 
 
 6.76 
 
 4.179 
 
 0.449 
 
 64.5 
 
 3.09 
 
 16.1 
 
 4.4 
 
 0.81 
 
 2.1 
 
 " 
 
 20.5 
 
 6.03 
 
 4.087 
 
 0.357 
 
 60.6 
 
 3.17 
 
 15.2 
 
 4.1 
 
 0.82 
 
 2.0 
 
 ' 
 
 18.0 
 
 5.33 
 
 4.000 
 
 0.270 
 
 56.9 
 
 3.27 
 
 14.2 
 
 3.8 
 
 0.84 
 
 1.9 
 
 " 
 
 17.5 
 
 5.15 
 
 4.330 
 
 0.210 
 
 58.3 
 
 3.37 
 
 14.6 
 
 4.5 
 
 .0.93 
 
 2.1 
 
 7 
 
 20.0 
 
 5.88 
 
 3.868 
 
 0.458 
 
 42.2 
 
 2.68 
 
 12.1 
 
 3.2 
 
 0.74 
 
 .7 
 
 
 
 17.5 
 
 5.15 
 
 3.763 
 
 0.353 
 
 39.2 
 
 2.76 
 
 11.2 
 
 2.9 
 
 0.76 
 
 .6 
 
 " 
 
 15.0 
 
 4.42 
 
 3.660 
 
 0.250 
 
 36.2 
 
 2.86 
 
 10.4 
 
 2.7 
 
 0.78 
 
 .5 
 
 6 
 
 17.25 
 
 5.07 
 
 3.575 
 
 0.475 
 
 26.2 
 
 2.27 
 
 8.7 
 
 2.4 
 
 0.68 
 
 .3 
 
 * 
 
 14.75 
 
 4.34 
 
 3.452 
 
 0.352 
 
 24.0 
 
 2.35 
 
 8.0 
 
 2.1 
 
 0.69 
 
 .2 
 
 
 
 12.25 
 
 3.61 
 
 3.330 
 
 0.230 
 
 21.8 
 
 2.46 
 
 7.3 
 
 .9 
 
 0.72 
 
 
 5 
 
 14.75 
 
 4.34 
 
 3.294 
 
 0.504 
 
 15.2 
 
 1.87 
 
 6.1 
 
 .7 
 
 0.63 
 
 !o 
 
 " 
 
 12.25 
 
 3.60 
 
 3.147 
 
 0.357 
 
 13.6 
 
 1.94 
 
 5.5 
 
 .5 
 
 0.63 
 
 0.92 
 
 
 
 9.75 
 
 2.87 
 
 3.000 
 
 0.210 
 
 12.1 
 
 2.05 
 
 4.8 
 
 .2 
 
 0.65 
 
 0.82 
 
 4 
 
 10.5 
 
 3.09 
 
 2.880 
 
 0.410 
 
 7.1 
 
 .52 
 
 3.6 
 
 .0 
 
 0.57 
 
 0.70 
 
 
 
 9.5 
 
 2.79 
 
 2.807 
 
 0.337 
 
 6.8 
 
 .55 
 
 3.4 
 
 0.93 
 
 0.58 
 
 0.66 
 
 * 
 
 8.5 
 
 2.50 
 
 2.733 
 
 0.263 
 
 6.4 
 
 .59 
 
 3.2 
 
 0.85 
 
 0.58 
 
 0.62 
 
 f 
 
 7.5 
 
 2.21 
 
 2.660 
 
 0.190 
 
 6.0 
 
 .64 
 
 3.0 
 
 0.77 
 
 0.59 
 
 0.58 
 
 3 
 
 7.5 
 
 2.21 
 
 2.521 
 
 0.361 
 
 2.9 
 
 .15 
 
 1.9 
 
 0.60 
 
 0.52 
 
 0.48 
 
 < 
 
 6.5 
 
 1.91 
 
 2.423 
 
 0.263 
 
 2.7 
 
 .19 
 
 1.8 
 
 0.53 
 
 0.52 
 
 0.44 
 
 " 
 
 5.5 
 
 1.63 
 
 2.330 
 
 0.170 
 
 2.5 
 
 .23 
 
 1.7 
 
 0.46 
 
 0.53 
 
 0.40 
 
 L = safe loads in pounds, uniformly distributed ; I = span in feet; 
 M = moments of forces in foot-pounds ; / = fiber stress. 
 S section modulus. 
 
 = S?; L = ~ f~; for/= 16,0001b.per sq. in. (for build- 
 
 J.& O I 
 
 ings) L = 32) ^ 7 3 for/ = 12,500 Ib. per sq. in. (for bridges) ; L = 25 ^ 7 3 
 
 pi o I 
 
 Properties of Carnegie Trough Plates Steel. 
 
 
 
 
 
 
 Moment of 
 
 
 
 Sec- 
 tion 
 Index. 
 
 Size, in 
 Inches. 
 
 Weight 
 per 
 Foot. 
 
 Area 
 of Sec- 
 tion. 
 
 Thick- 
 ness in 
 Inches. 
 
 Inertia, 
 Neutral 
 Axis 
 Parallel to 
 
 Section 
 Modulus, 
 Axis as 
 before. 
 
 Radius 
 of Gy- 
 ration, 
 Axis as 
 
 
 
 
 
 
 Length. 
 
 
 before. 
 
 
 
 Ib. 
 
 sq. in. 
 
 
 / 
 
 S 
 
 r 
 
 M 10 
 
 91/2X33/ 4 
 
 16.3 
 
 4.78 
 
 V2 
 
 3.7 
 
 1.4 
 
 0.91 
 
 M 11 
 
 91/2X3 3/4 
 
 18.0 
 
 5.28 
 
 9/16 
 
 4.1 
 
 1.6 
 
 0.91 
 
 M 12 
 
 91/2X33/4 
 
 19.7 
 
 5.79 
 
 5/8 
 
 4.6 
 
 1.8 
 
 0,90 
 
 M 13 
 
 91/2X33/4 
 
 21.4 
 
 6.30 
 
 H/16 
 
 5.0 
 
 2.0 
 
 0.90 
 
 M 14 
 
 91/2X33/4 
 
 23.2 
 
 6.97 
 
 3/4 
 
 5.5 
 
 2.2 
 
 0.90 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 309 
 
 Safe Loads, in Thousands of Pounds, Uniformly Distributed for 
 Carnegie Steel I-Beams. 
 
 e 
 I 
 
 27 in. 
 
 83 
 Ib. 
 
 24-inch. 
 
 21 in. 
 
 57^ 
 Ib. 
 
 20-inch. 
 
 18-inch. 
 
 1 5-inch. 
 
 105 
 
 Ib. 
 
 80 Ib. 
 
 69K 
 
 )b. 
 
 80 Ib. 
 
 65 Ib. 
 
 75 Ib. 
 
 46 Ib. 
 
 60 Ib: 
 
 42 Ib. 
 
 36 
 
 Ib. 
 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 50 
 
 
 
 
 
 
 
 
 
 
 177 
 
 
 
 
 
 
 
 
 
 
 
 
 173.2 
 144.4 
 123.7 
 108.3 
 96.2 
 86.6 
 78.7 
 72.2 
 66.6 
 61.9 
 57.7 
 54.1 
 50.9 
 48.1 
 45.6 
 43.3 
 41.2 
 39.4 
 37.7 
 36.1 
 34.6 
 33.3 
 32.1 
 30.9 
 29.9 
 28.9 
 
 123.0 
 104.8 
 89.8 
 78.5 
 69.8 
 62.8 
 57.1 
 52.4 
 48.3 
 44.9 
 41.9 
 39.3 
 37.0 
 34.9 
 33.1 
 31.4 
 29.9 
 28.6 
 27.3 
 26.2 
 25.1 
 24.2 
 23.3 
 22.4 
 21.7 
 20.9 
 
 86.7 
 823 
 72.0 
 64.0 
 57.6 
 52.4 
 48.0 
 44.3 
 41.2 
 38.4 
 36.0 
 33.9 
 32.0 
 30.3 
 28.8 
 27.4 
 26.2 
 25.1 
 24.0 
 23.0 
 22.2 
 21.3 
 20.6 
 19.9 
 19.2 
 18.6 
 18.0 
 
 
 
 
 
 
 240.0 
 223.4 
 195.5 
 173.8 
 156.4 
 142.2 
 130.3 
 120.3 
 111.7 
 104.3 
 97.7 
 92.0 
 86.9 
 82.3 
 78.2 
 74.5 
 71.1 
 68.0 
 65.2 
 62.6 
 60.2 
 57.9 
 55.9 
 53.9 
 52.1 
 50.5 
 48.9 
 47.4 
 46.0 
 44.7 
 43.4 
 42.3 
 41.2 
 40.1 
 39.1 
 
 200.0 
 
 202.3 
 
 115.9 
 
 229.0 
 228.2 
 207.5 
 190.2 
 175.6 
 163.0 
 152.2 
 142.6 
 134.3 
 126.8 
 120.1 
 114.1 
 108.7 
 103.7 
 99.2 
 95.1 
 91.3 
 87.8 
 84.5 
 81.5 
 78.7 
 76.1 
 73.6 
 71.3 
 69.2 
 67.1 
 65.2 
 63.4 
 61.7 
 60.1 
 58.5 
 57.1 
 55.7 
 54.3 
 53.1 
 51.9 
 50.7 
 49.6 
 48.6 
 47.5 
 46.6 
 45.6 
 
 300.0 
 
 240.0 
 
 187.2 
 171.4 
 155.8 
 142.8 
 131.8 
 122.4 
 114.3 
 107.1 
 100.8 
 95.2 
 90.2 
 85.7 
 81.6 
 77.9 
 74.5 
 71.4 
 68.6 
 65.9 
 63.5 
 61.2 
 59.1 
 57.1 
 55.3 
 53.6 
 51.9 
 50.4 
 49.0 
 47.6 
 46.3 
 45.1 
 43.9 
 42.8 
 41.8 
 40.8 
 39.9 
 38.9 
 38.1 
 37.3 
 36.5 
 35.7 
 35.0 
 34.3 
 
 150.0 
 
 178.2 
 155.9 
 138.6 
 124.7 
 113.4 
 104.0 
 96.0 
 89. 
 83.2 
 78.0 
 73.4 
 69.3 
 65.7 
 62.4 
 59.4 
 56.7 
 54.2 
 52.0 
 49.9 
 48.0 
 46.2 
 44.6 
 43.0 
 41.6 
 40.2 
 39.0 
 37.8 
 36.7 
 35.6 
 34.7 
 33.7 
 32.8 
 32.0 
 31.2 
 30.4 
 29.7 
 
 193.2 
 169.1 
 150.3 
 135.3 
 123.0 
 112.7 
 104.1 
 96.6 
 90.2 
 845 
 79.6 
 75.1 
 71.2 
 67.6 
 64.4 
 61.5 
 58.8 
 56.4 
 54.1 
 52.0 
 50.1 
 48.3 
 46.6 
 45.1 
 43.6 
 42.3 
 41.0 
 39.8 
 38.6 
 37.6 
 
 231.9 
 206.1 
 185.5 
 168.7 
 154.6 
 142.7 
 132.5 
 123.7 
 116.0 
 10X1 
 103.1 
 97.6 
 92.8 
 88.3 
 84.3 
 80.7 
 77.3 
 74.2 
 71.4 
 68.7 
 66.3 
 64.0 
 61.8 
 59.8 
 58.0 
 56.2 
 54.6 
 53.0 
 51.5 
 50.1 
 48.8 
 47.6 
 46.4 
 45.3 
 44.2 
 43.1 
 42.2 
 41.2 
 40.3 
 39.5 
 387 
 
 108.6 
 96.6 
 86.9 
 79.0 
 72.4 
 66.8 
 62.1 
 57.9 
 54.3 
 51.1 
 48.3 
 45.7 
 43.4 
 41.4 
 39.5 
 37.8 
 3&.2 
 34.8 
 33.4 
 32.2 
 31.0 
 30.0 
 29.0 
 28.0 
 27.2 
 26.3 
 25.6 
 24.8 
 24.1 
 
 277.7 
 249.9 
 227.2 
 208.3 
 192.2 
 178.5 
 166.6 
 156.2 
 147.0 
 138.8 
 131.5 
 125.0 
 119.0 
 113.6 
 108.7 
 104.1 
 100.0 
 96.1 
 92.6 
 89.3 
 86.2 
 83.3 
 80.6 
 78.1 
 75.7 
 73.5 
 71.4 
 69.4 
 67.5 
 65.8 
 64.1 
 62.5 
 61.0 
 59.5 
 58.1 
 56.8 
 55.5 
 54.3 
 53.2 
 52.1 
 
 138.6 
 124.7 
 113.4 
 103.9 
 95.9 
 89.1 
 83.1 
 77.9 
 73.4 
 69.3 
 65.6 
 62.4 
 59.4 
 56.7 
 54.2 
 52.0 
 49.9 
 48.0 
 46.2 
 44.5 
 43.0 
 41.6 
 .40.2 
 39.0 
 37.8 
 36.7 
 35.6 
 34.6 
 33.7 
 32.8 
 32.0 
 31.2 
 30.4 
 29.7 
 
 27.9 
 27.1 
 
 20.3 
 19.6 
 
 
 
 
 
 
 
 
 
 
 36.6 
 35.6 
 
 23.5 
 22.9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 38.1 
 37.2 
 
 
 
 
 
 
 
 
 
 
 
 29.0 
 28.3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Table con- 
 tinued on 
 next page. 
 
 51.0 
 50.0 
 
 37.9 
 37.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Loads above upper horizontal lines will produce maximum allow- 
 able shear in webs. Loads below lower horizontal lines will produce 
 excessive deflections and must not be used with plastered ceilings. 
 Maximum fiber stress, 16,000 Ib. per sq. in. Safe loads given include 
 the weight of beam, which should be deducted to give net load. 
 
310 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads, in Thousands of Pounds, Uniformly Distributed for 
 Carnegie Steel I-Beams. Continued. 
 
 i 
 
 a 
 ^ 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 r j 
 J2 
 13 
 14 
 15 
 16 
 
 r 
 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 
 12-inch. 
 
 1 0-inch. 
 
 9-in. 
 
 8-inch. 
 
 7-in. 
 
 6-in. 
 
 5-in. 
 
 4-in. 
 
 3-in. 
 
 40 Ib. 
 
 31^ 
 Ib. 
 
 27y 2 
 
 Ib. 
 
 25 
 
 Ib. 
 
 22 
 Ib. 
 
 21 
 Ib. 
 
 18 
 
 Ib. 
 
 17^ 
 Ib. 
 
 15 
 
 Ib. 
 
 12M 
 Ib. 
 
 9M 
 Ib. 
 
 7Yz 
 Ib. 
 
 5^ 
 Ib. 
 
 10.2 
 
 5.9 
 4.4 
 3.5 
 2.9 
 
 2.2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 27.6 
 25.8 
 19.4 
 15.5 
 12.9 
 11.1 
 9.7 
 8.6 
 7.7 
 
 7.0 
 6.5 
 
 21.0 
 17.2 
 12.9 
 10.3 
 8.6 
 7.4 
 6.4 
 5.7 
 5.2 
 4.7 
 4.3 
 
 15.2 
 10.6 
 8.0 
 6.4 
 5.3 
 4.5 
 4.0 
 3.5 
 3.2 
 
 
 
 
 
 
 52.2 
 50.3 
 40.3 
 33.6 
 28.8 
 25.2 
 22.4 
 20.1 
 18.3 
 16.8 
 15.5 
 14.4 
 13.4 
 12.6 
 11.8 
 11.2 
 
 43.2 
 37.9 
 30.3 
 25.3 
 21.7 
 19.0 
 16.9 
 15.2 
 13.8 
 12.6 
 11.7 
 10.8 
 10.1 
 9.5 
 8.9 
 8.4 
 
 33.6 
 
 35.0 
 27.6 
 22.1 
 18.4 
 15.8 
 13.8 
 12.3 
 11.0 
 10.0 
 9.2 
 
 8.5 
 7.9 
 
 110.4 
 
 84.0 
 
 61.2 
 59.1 
 50.7 
 44.4 
 39.4 
 35.5 
 32.3 
 29.6 
 27.3 
 25.3 
 23.7 
 22.2 
 20.9 
 19.7 
 18.7 
 17.7 
 16.9 
 16.1 
 15.4 
 14.8 
 
 62.0 
 
 46.4 
 
 "4U3 
 
 34.7 
 30.4 
 27.0 
 24.3 
 22.1 
 20.2 
 18.7 
 17.4 
 16.2 
 15.2 
 14.3 
 13.5 
 12.8 
 12.1 
 11.6 
 11.0 
 
 95.6 
 79.7 
 68.3 
 59.8 
 53.1 
 47.8 
 43.5 
 39.8 
 36.8 
 34.2 
 31.9 
 29.9 
 28.1 
 26.6 
 25.2 
 23.9 
 22.8 
 21.7 
 20.8 
 19.9 
 
 76.7 
 63.9 
 54.8 
 48.0 
 42.6 
 38.4 
 34.9 
 32.0 
 29.5 
 27.4 
 25.6 
 24.0 
 22.6 
 21.3 
 20.2 
 19.2 
 18.3 
 17.4 
 16.7 
 16.0 
 
 52.1 
 43.4 
 37.2 
 32.6 
 28.9 
 26.0 
 23.7 
 21.7 
 20.0 
 18.6 
 17.4 
 16.3 
 15.3 
 14.5 
 13.7 
 13.0 
 
 12.4 
 11.8 
 
 31.1 
 25.9 
 22.2 
 19.4 
 17.3 
 15.6 
 14.1 
 13.0 
 12.0 
 11.1 
 10.4 
 9.7 
 9.2 
 8.6 
 
 6.0 
 5.5 
 
 Loads above 
 the upper 
 zontal lines 
 produce maxi- 
 Q allowable 
 ar in webs, 
 is below lower 
 I produce ex- 
 and should 
 stered ceilings. 
 ?ss, 16,000 Ib. 
 > given include 
 which should 
 net load. 
 
 7.4 
 6.9 
 
 hor 
 will 
 mur 
 she 
 Loa 
 
 5S Wil 
 
 tions, 
 hplaj 
 r stn 
 loads 
 )eam, 
 ) give 
 
 10.6 
 10.1 
 
 horizontal line 
 cessive deflec 
 not be used wit 
 Maximum flbe 
 persq. in. Safe 
 the weight of t 
 be deducted tc 
 
 
 
 
 19.1 
 18.4 
 
 15.3 
 14.8 
 
 14.2 
 13.6 
 
 Properties of Carnegie Corrugated Plates Steel. 
 
 
 
 
 
 
 Moment of 
 
 
 
 Sec- 
 tion 
 Index. 
 
 Size, in 
 Inches. 
 
 Weight 
 Foot. 
 
 Area 
 of Sec- 
 tion. 
 
 Thick- 
 ness in 
 Inches. 
 
 Inertia, 
 Neutral 
 Axis 
 Parallel to 
 
 Section 
 Modulus, 
 Axis as 
 before. 
 
 Radius 
 of Gy- 
 ration, 
 Axis as 
 
 
 
 
 
 
 Length. 
 
 
 before. 
 
 M30 
 
 83/i XI 1/2 
 
 Ib. 
 8.1 
 
 sq. in. 
 2.38 
 
 1/4 
 
 0.64 
 
 S 
 0.8 
 
 O. r 52 
 
 M31 
 
 83/4 XI 9/16 
 
 10.1 
 
 2.96 
 
 5/16 
 
 0.95 
 
 1.1 
 
 0.57 
 
 M32 
 
 83/4 XI 5/8 
 
 12.0 
 
 3.53 
 
 3/8 
 
 1.3 
 
 1.4 
 
 0.62 
 
 M33 
 
 123/i 6 X23/4 
 
 17.8 
 
 5.22 
 
 V8 
 
 4.8 
 
 3.3 
 
 0.96 
 
 M34 
 
 123/ 16 X2l3/i6 
 
 20.8 
 
 6.10 
 
 7/16 
 
 5.8 
 
 3.9 
 
 0.98 
 
 M35 
 
 123/16X27/8 
 
 23.7 
 
 6.97 
 
 1/2 
 
 6.8 
 
 4.5 
 
 0.99 
 
SPACING OF I-BEAMS FOR UNIFORM LOAD. 311 
 
 Spacing of Carnegie Steel I-Beams for Uniform Load of 100 Lbs. 
 per Square Foot. 
 
 (Figures in table give the proper distance, feet, center to center of beams.) 
 
 Ill 
 
 Ft. 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 
 27-in. 
 83 Ib. 
 
 228.2 
 188.6 
 158.5 
 135.0 
 116.4 
 101.4 
 89.2 
 79.0 
 70.4 
 63.2 
 57.1 
 51.8 
 47.2 
 43.1 
 39.6 
 36.5 
 33.8 
 31.3 
 29.1 
 
 24-inch. 
 
 21 -in. 
 
 20-inch. 
 
 18-inch. 
 
 1 5-inch. 
 
 105 
 
 Ib. 
 
 249.9 
 206.5 
 173.6 
 147.9 
 127.5 
 111.1 
 97.6 
 86.5 
 77.1 
 69.2 
 62.5 
 56.7 
 51.6 
 47.2 
 43.4 
 40.0 
 37.0 
 34.3 
 31 9 
 
 80 
 Ib. 
 
 185.5 
 153.3 
 128.8 
 109.8 
 94.7 
 82.5 
 72.5 
 64.2 
 57.3 
 51.4 
 46.4 
 42.1 
 38.3 
 35.1 
 32.2 
 29.7 
 27.5 
 25.5 
 23.7 
 
 69^ 
 
 Ib. 
 
 171.4 
 141.6 
 119.0 
 101.4 
 87.4 
 76.2 
 66.9 
 53.3 
 52.9 
 47.5 
 42.8 
 38.9 
 35.4 
 32.4 
 29.8 
 27.4 
 25.4 
 23.5 
 21.9 
 
 57^ 
 Ib. 
 
 80 
 Ib. 
 
 65 
 
 Ib. 
 
 75 
 
 Ib. 
 
 46 
 
 Ib. 
 
 60 
 
 Ib. 
 
 42 
 Ib. 
 
 36 
 
 Ib. 
 
 57.6 
 47.6 
 40.0 
 34.1 
 29.4 
 25.6 
 22.5 
 19.9 
 17.8 
 16.0 
 14.4 
 13.1 
 11.9 
 10.9 
 10.0 
 9.2 
 8.5 
 
 124.7 
 103.1 
 86.6 
 73.8 
 63.6 
 55.4 
 48.7 
 43.2 
 38.5 
 34.5 
 31.2 
 28.3 
 25.8 
 23.6 
 21.7 
 20.0 
 18.5 
 17.1 
 15.9 
 
 156.4 
 129.3 
 108.6 
 92.6 
 79.8 
 69.5 
 61.1 
 54.1 
 48.3 
 43.3 
 39.1 
 35.5 
 32.3 
 29.6 
 27.2 
 25.0 
 23.1 
 21.5 
 700 
 
 124.8 
 103.1 
 86.6 
 73.8 
 63.7 
 54.4 
 48.7 
 43.2 
 38.5 
 34.6 
 31.2 
 28.3 
 25.8 
 23.6 
 21.7 
 20.0 
 18.5 
 17.1 
 159 
 
 135.3 
 111.8 
 93.9 
 80.0 
 69.0 
 60.1 
 52.8 
 46.8 
 41.8 
 37.5 
 33.8 
 30.7 
 28.0 
 25.6 
 23.5 
 21.6 
 20.0 
 18.6 
 17.3 
 
 e 
 
 7 
 6 
 5 
 4 
 3 
 3 
 3 
 2 
 2 
 2 
 1 
 1 
 1 
 1 
 1 
 1 
 1 
 1 
 
 6.9 
 1.8 
 0.4 
 1.4 
 4.3 
 8.6 
 3.9 
 0.1 
 6.8 
 4.1 
 1.7 
 9.7 
 8.0 
 6.4 
 5.1 
 3.9 
 2.9 
 1 9 
 
 86.6 
 71.6 
 60.1 
 51.3 
 44.2 
 38.5 
 33.8 
 30.0 
 26.7 
 24.0 
 21.7 
 19.6 
 17.9 
 16.4 
 15.0 
 13.9 
 12.8 
 
 62.8 
 51.9 
 43.6 
 37.2 
 32.1 
 27.9 
 24.5 
 21.7 
 19.4 
 17.4 
 15.7 
 14.3 
 13.0 
 11.9 
 10.9 
 10.1 
 9.3 
 
 1 1 
 
 
 
 
 Distance f 
 between 
 supports. 
 
 12-inch. 
 
 10-inch. 
 
 9-in 
 
 8-inch. 
 
 7-in. 
 
 6-in. 
 
 5-in. 
 
 4-in 
 
 3-in 
 
 40 
 Ib. 
 
 ^ 
 
 27^ 
 Ib. 
 
 25 
 Ib. 
 
 22 
 Ib. 
 
 21 
 
 Ib. 
 
 18 
 Ib. 
 
 17^ 
 Ib. 
 
 15 
 
 Ib. 
 
 W 
 
 ft 
 
 7H 
 Ib. 
 
 5^ 
 Ib. 
 
 Ft. 
 
 !" 
 
 61/2 
 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 
 
 
 
 
 
 
 
 60.7 
 5%1 
 42.1 
 35.9 
 31.0 
 23.7 
 18.7 
 15.2 
 12.5 
 10.5 
 9.0 
 7.7 
 6.7 
 5.9 
 
 '"53 
 
 4.7 
 
 62 
 51 
 43 
 36 
 
 l\ 
 
 19 
 15 
 12 
 10 
 9 
 7 
 6 
 6 
 -5 
 
 4 
 
 .2 
 .4 
 .2 
 .8 
 .8 
 .3 
 .2 
 .6 
 .9 
 .8 
 .2 
 9 
 .9 
 .1 
 
 "4 
 
 44.2 
 36.5 
 30.7 
 26.1 
 22.5 
 17.3 
 13.6 
 11.0 
 9.1 
 7.7 
 6.5. 
 5.6: 
 
 31.0 
 25.6 
 21.5 
 18.3 
 15.8 
 12.1 
 9.6 
 7.8 
 6.4 
 5.4 
 '"4.6 
 40 
 
 20.6 
 17.1 
 14.3 
 12.2 
 10.5 
 8.1 
 6.4 
 5.2 
 ""4.3 
 3.6 
 
 12.7 
 10.5 
 8.8 
 7.5 
 6.5 
 5.0 
 
 "3.9 
 
 3.2 
 
 .. 
 
 7.1 
 5.8 
 4.9 
 
 JT.2 
 : 3.6 
 
 
 
 
 
 
 
 
 132.8 
 
 97i6 
 74.7 
 59.0 
 47.8 
 39.5 
 33.2 
 28.3 
 24.4 
 21.3 
 18.7 
 165 
 14.8 
 13.2 
 12.0 
 10.8 
 9.9 
 9.0 
 8.3 
 
 106.6 
 
 783 
 60.0 
 47.4 
 38.4 
 31.7 
 26.6 
 22.7 
 19.6 
 17.1 
 15.0 
 13.3 
 11.8 
 10.6 
 9.6 
 8.7 
 7.9 
 7.3 
 6.7 
 
 98.6 
 
 72^4 
 55.4 
 43.8 
 35.5 
 29.3 
 24.6 
 21.0 
 18.1 
 15.8 
 13.9 
 12.3 
 11.0 
 9.8 
 8.9 
 8.1 
 7.3 
 6.7 
 6.2 
 
 
 72.4 
 
 532 
 40.7 
 32.2 
 26.1 
 21.5 
 18.1 
 15.4 
 13.3 
 11.6 
 10.2 
 9.0 
 8.0 
 7.2 
 6.5 
 "5."9 
 5.4 
 
 67.5 
 
 49^6 
 38.0 
 30.0 
 24.3 
 20.1 
 16.9 
 14.4 
 12.4 
 10.8 
 9.5 
 8.4 
 7.5 
 6.7 
 6.1 
 "T.5 
 5.0 
 
 55.9 
 
 4l!l 
 31.5 
 24.9 
 20.1 
 16.6 
 14.0 
 11.9 
 10.3 
 9.0 
 7.9 
 7.0 
 6.2 
 5.6 
 5.0 
 
 4.9 
 4.3 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For any other load than 100 Ib. per sq. ft., divide the spacing given 
 by the ratio the given load per sq. ft. bears to 100. Thus for a load 
 of 150 Ib. per sq. ft. divide by 1.5. Maximum fiber stress 16,000 Ib. 
 per sq. in. 
 
 Spacings given below the dotted horizontal lines will produce exces- 
 sive deflection, and should not be used with plastered ceilings. 
 
312 
 
 STRENGTH OP MATERIALS. 
 
 Properties of Carnegie Standard Channels Steel. 
 
 
 
 
 
 
 1 s 
 
 a si 
 
 0) 
 
 gJ5 
 
 gH 
 
 ?s 
 
 11 
 
 -8 
 
 
 
 
 
 
 
 
 
 
 3 ^ 
 
 
 
 
 
 
 
 
 c3 
 
 0) 
 
 'I 
 
 ^ 
 
 
 5 
 
 w 
 
 
 
 
 
 
 ""3 
 
 ^4J 
 
 c" c ^ 
 
 c" JH t> 
 
 3 
 
 ^+3 
 
 *o*o 
 
 1 
 
 !ij 
 
 ^ 
 
 i 
 
 & 
 
 3 |s 
 
 1*1 
 
 111 
 
 |1! 
 
 "!: 
 
 ill 
 
 (D^d 
 
 4J - 
 
 e 2 
 
 
 
 
 *o 
 
 
 
 ! 
 
 (73 
 *O 
 
 I 
 
 i of Flan; 
 
 III 
 
 of^+a 
 -u 03 
 
 Is 
 
 .aj 
 
 -"jp 
 
 if! 
 
 a 
 
 I|| 
 
 a) 
 
 si 
 
 o. 
 
 bo 
 | 
 
 
 1 
 
 is 
 
 |4j| 
 
 III 
 
 Is &** 
 
 1 23 
 
 '%% 
 
 ill 
 
 & 
 
 Q 
 
 
 < 
 
 H 
 
 
 s 
 
 S 
 
 5 
 
 PH 
 
 w 
 
 $ 
 
 5 
 
 in. 
 
 Ibs. 
 
 sq. in. 
 
 in. 
 
 in. 
 
 j 
 
 /' 
 
 r 
 
 r' 
 
 S 
 
 S' 
 
 X 
 
 15 
 
 55. 
 
 16.18 
 
 0.82 
 
 3.82 
 
 430.2 
 
 12.2 
 
 5.16 
 
 0.868 
 
 57.4 
 
 4.1 
 
 0.82 
 
 '* 
 
 50. 
 
 14.71 
 
 0.72 
 
 3.72 
 
 402.7 
 
 11.2 
 
 5.23 
 
 0.873 
 
 53.7 
 
 3.8 
 
 0.80 
 
 " 
 
 45. 
 
 13.24 
 
 0.62 
 
 3.62 
 
 375.1 
 
 10.3 
 
 5.32 
 
 0.882 
 
 50.0 
 
 3.6 
 
 0.79 
 
 
 
 40. 
 
 11.76 
 
 0.52 
 
 3.52 
 
 347.5 
 
 9.4 
 
 5.43 
 
 0.893 
 
 46.3 
 
 3.4 
 
 0.78 
 
 * 
 
 35. 
 
 10.29 
 
 0.43 
 
 3.43 
 
 319.9 
 
 8.5 
 
 5.58 
 
 0.908 
 
 42.7 
 
 3.2 
 
 0.79 
 
 " 
 
 33. 
 
 9.90 
 
 0.40 
 
 3.40 
 
 312.6 
 
 8.2 
 
 5.62 
 
 0.912 
 
 41.7 
 
 3.2 
 
 0.79 
 
 12 
 
 40. 
 
 11.76 
 
 0.76 
 
 3.42 
 
 196.9 
 
 6.6 
 
 4.09 
 
 0.751 
 
 32.8 
 
 2.5 
 
 0.72 
 
 " 
 
 35. 
 
 10.29 
 
 0.64 
 
 3.30 
 
 179.3 
 
 5.9 
 
 4.17 
 
 0.757 
 
 29.9 
 
 2.3 
 
 0.69 
 
 " 
 
 30. 
 
 8.82 
 
 0.51 
 
 3.17 
 
 161.7 
 
 5.2 
 
 4.28 
 
 0.768 
 
 26.9 
 
 2.1 
 
 0.68 
 
 . 
 
 25. 
 
 7.35 
 
 0.39 
 
 3.05 
 
 144.0 
 
 4.5 
 
 4.43 
 
 0.785 
 
 24.0 
 
 .9 
 
 0.68 
 
 " 
 
 201/2 
 
 6.03 
 
 0.28 
 
 2.94 
 
 128.1 
 
 3.9 
 
 4.61 
 
 0.805 
 
 21.4 
 
 .7 
 
 0.70 
 
 10 
 
 35. 
 
 10.29 
 
 0.82 
 
 3.18 
 
 115.5 
 
 4.7 
 
 3.35 
 
 0.672 
 
 23.1 
 
 .9 
 
 0.70 
 
 
 30. 
 
 8.82 
 
 0.68 
 
 3.04 
 
 103.2 
 
 4.0 
 
 3.42 
 
 0.672 
 
 20.7 
 
 .7 
 
 0.65 
 
 " 
 
 25. 
 
 7.35 
 
 0.53 
 
 2.89 
 
 91.0 
 
 3.4 
 
 3.52 
 
 0.680 
 
 18.2 
 
 .5 
 
 0.62 
 
 " 
 
 20. 
 
 5.88 
 
 0.38 
 
 2.74 
 
 78.7 
 
 2.9 
 
 3.66 
 
 0.696 
 
 15.7 
 
 .3 
 
 0.61 
 
 * 
 
 15. 
 
 4.46 
 
 0.24 
 
 2.60 
 
 66.9 
 
 2.3 
 
 3.87 
 
 0.718 
 
 13.4 
 
 .2 
 
 0.64 
 
 9 
 
 25. 
 
 7.35 
 
 0.62 
 
 2.82 
 
 70.7 
 
 3.0 
 
 3.10 
 
 0.637 
 
 15.7 
 
 .4 
 
 0.62 
 
 " 
 
 20. 
 
 5.88 
 
 0.45 
 
 2.65 
 
 60.8 
 
 2.5 
 
 3.21 
 
 0.646 
 
 13.5 
 
 .2 
 
 0.59 
 
 " 
 
 15. 
 
 4.41 
 
 0.29 
 
 2.49 
 
 50.9 
 
 2.0 
 
 3.40 
 
 0.665 
 
 11.3 
 
 .0 
 
 0.59 
 
 " 
 
 131/4 
 
 3.89 
 
 0.23 
 
 2.43 
 
 47.3 
 
 1.8 
 
 3.49 
 
 0.674 
 
 10.5 
 
 0.97 
 
 0.61 
 
 8 
 
 2H/4 
 183/4 
 
 6.25 
 5.51 
 
 0.58 
 0.49 
 
 2.62 
 2.53 
 
 as 
 
 2.3 
 2.0 
 
 2.77 
 2.82 
 
 0.600 
 0.603 
 
 11.9 
 11.0 
 
 .1 
 .0 
 
 0.59 
 0.57 
 
 " 
 
 161/4 
 
 4.78 
 
 0.40 
 
 2.44 
 
 39.9 
 
 .8 
 
 2.89 
 
 0.610 
 
 10.0 
 
 0.95 
 
 0.56 
 
 " 
 
 133/4 
 
 4.04 
 
 0.31 
 
 2.35 
 
 36.0 
 
 .6 
 
 2.98 
 
 0.619 
 
 9.0 
 
 0.87 
 
 0.56 
 
 " 
 
 1H/4 
 
 3.35 
 
 0.22 
 
 2.26 
 
 32.3 
 
 .3 
 
 3.11 
 
 0.630 
 
 8.1 
 
 0.79 
 
 0.58 
 
 7 
 
 193/4 
 
 5.81 
 
 0.63 
 
 2.51 
 
 33.2 
 
 .9 
 
 2.39 
 
 0.565 
 
 9.5 
 
 0.96 
 
 0.58 
 
 ** 
 
 171/4 
 
 5.07 
 
 0.53 
 
 2.41 
 
 30.2 
 
 .6 
 
 2.44 
 
 0.564 
 
 8.6 
 
 0.87 
 
 0.56 
 
 *< 
 
 143/4 
 
 4.34 
 
 0.42 
 
 2.30 
 
 27.2 
 
 .4 
 
 2.50 
 
 0.568 
 
 7.8 
 
 0.79 
 
 0.54 
 
 " 
 
 121/4 
 
 3.60 
 
 0.32 
 
 2.20 
 
 24.2 
 
 .2 
 
 2.59 
 
 0.575 
 
 6.9 
 
 0.71 
 
 0.53 
 
 " 
 
 93/4 
 
 2.85 
 
 0.21 
 
 2.09 
 
 21.1 
 
 0.98 
 
 2.72 
 
 0.586 
 
 6.0 
 
 0.63 
 
 0.55 
 
 6 
 
 151/2 
 
 4.56 
 
 0.56 
 
 2.28 
 
 19.5 
 
 .3 
 
 2.07 
 
 0.529 - 
 
 6.5 
 
 0.74 
 
 0.55 
 
 " 
 
 13. 
 
 3.82 
 
 0.44 
 
 2.16 
 
 17.3 
 
 .1 
 
 2.13 
 
 0.529 
 
 5.8 
 
 0.65 
 
 0.52 
 
 " 
 
 101/2 
 
 3.09 
 
 0.32 
 
 2.04 
 
 15.1 
 
 0.88 
 
 2.21 
 
 0.534 
 
 5.0 
 
 0.57 
 
 0.50 
 
 " 
 
 8. 
 
 2.38 
 
 0.20 
 
 1.92 
 
 13.0 
 
 0.70 
 
 2.34 
 
 0.542 
 
 4.3 
 
 0.50 
 
 0.52 
 
 5 
 
 111/2 
 
 3.38 
 
 0.48 
 
 2.04 
 
 10.4 
 
 0.82 
 
 .75 
 
 0.493 
 
 4.2 
 
 0.54 
 
 0.51 
 
 " 
 
 9. 
 
 2.65 
 
 0.33 
 
 .89 
 
 8.9 
 
 0.64 
 
 .83 
 
 0.493 
 
 3.6 
 
 0.45 
 
 0.48 
 
 " 
 
 61/2 
 
 1.95 
 
 0.19 
 
 .75 
 
 7.4 
 
 0.48 
 
 .95 
 
 0.498 
 
 3.0 
 
 0.38 
 
 0.49 
 
 4 
 
 71/4 
 
 2.13 
 
 0.33 
 
 .73 
 
 4.6 
 
 0.44 
 
 .46 
 
 0.455 
 
 2.3 
 
 0.35 
 
 0.46 
 
 " 
 
 61/4 
 
 1.84 
 
 0.25 
 
 .65 
 
 4.2 
 
 0.38 
 
 .51 
 
 0.454 
 
 2.1 
 
 0.32 
 
 0.46 
 
 " 
 
 51/4 
 
 1.55 
 
 0.18 
 
 .58 
 
 3.8 
 
 0.32 
 
 .56 
 
 0.453 
 
 1.9 
 
 0.29 
 
 0.46 
 
 3 
 
 6. 
 
 1.76 
 
 0.36 
 
 .60 
 
 2.1 
 
 0.31 
 
 .08 
 
 0.421 
 
 1.4 
 
 0.27 
 
 0.46 
 
 f* 
 
 5. 
 
 1.47 
 
 0.26 
 
 .50 
 
 IJS- 
 
 0.25 
 
 .12 
 
 0.415 
 
 1.2 
 
 0.24 
 
 0.44 
 
 " 
 
 4. 
 
 1.19 
 
 0.17 
 
 .41 
 
 1.6 
 
 0.20 
 
 .17 
 
 0.409 
 
 1.1 
 
 0.21 
 
 0.44 
 
 I/ = safe load in pounds, uniformly distributed; Z = span in feet; 
 
 M= moment of forces in foot-pounds; / = fiber stress; S = section 
 
 modulus. 
 
 ~^ - , ^, ; for/ = 16,000 Ibs. per sq. in. (for buildings); 
 
 14 O I 
 
 = 32 ^ 7 0>S fo r / = 12,500 Ib. per sq. in. (fo* bridges), L = ^OpOS 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 313 
 Maximum Safe Load for Carnegie Channels in thousands of Pounds. 
 
 Span, 
 Ft. 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 
 31 
 32 
 
 Depth and Weight of Sections. 
 
 3 in. 
 41b. 
 
 15 in. 
 33 Ib. 
 
 13 in. 
 
 32 Ib. 
 
 12 in. 
 
 20^ 
 Ib. 
 
 10 in. 
 151b. 
 
 9 in. 
 
 13M 
 Ib. 
 
 8 in. 
 
 1IM 
 Ib. 
 
 7 in. 
 9M 
 Ib. 
 
 6 in. 
 81b. 
 
 5 in. 
 
 ft 
 
 4 in. 
 5M 
 Ib. 
 
 
 
 
 
 
 
 
 24.0 
 
 19.0 
 
 14.4 
 
 10.2 
 
 
 
 
 4S.O 
 
 41.4 
 
 35.2 
 
 29.4 
 
 23.1 
 15.4 
 11.6 
 9.2 
 7.7 
 6.6 
 5.8 
 5.1 
 4.6 
 4.2 
 3.9 
 
 15.8 
 10.5 
 7.9 
 6.3 
 5.3 
 4.5 
 4.0 
 3.5 
 3.2 
 2.9 
 2.6 
 
 10.1 
 6.7 
 5.1 
 4.1 
 3.4 
 2.9 
 2.5 
 
 5.8 
 3.9 
 2.9 
 2.3 
 1.9 
 
 L5 
 
 120.0 
 
 97.5 
 
 67.2 
 
 47.6 
 35.7 
 28.5 
 23.8 
 20.4 
 17.8 
 15.9 
 14.3 
 13.0 
 11.9 
 11.0 
 10.2 
 9.5 
 8.9 
 8.4 
 7.9 
 7.5 
 7 1 
 
 37.4 
 28.0 
 22.4 
 18.7 
 16.0 
 14.0 
 12.5 
 11.2 
 10.2 
 9.3 
 8.6 
 8.0 
 7.5 
 7.0 
 6.6 
 62 
 
 28.7 
 21.5 
 17.2 
 14.4 
 12.3 
 10.8 
 9.6 
 8.6 
 7.8 
 7.2 
 6.6 
 6.2 
 5.7 
 5.4 
 
 21.4 
 16.1 
 12.9 
 10.7 
 9.2 
 8.0 
 7.1 
 6.4 
 5.8 
 5.4 
 4.9 
 4.6 
 
 111.1 
 88.9 
 74.1 
 63.5 
 55.6 
 49.4 
 44.5 
 40.4 
 37.0 
 34.2 
 31.8 
 29.6 
 27.8 
 26.1 
 24.7 
 23.4 
 22.3 
 21.2 
 20.2 
 19.3 
 18.5 
 17.8 
 17.1 
 16.5 
 15.9 
 15.3 
 14.8 
 
 97.5 
 78.0 
 65.0 
 55.7 
 48.7 
 43.3 
 39.0 
 35.4 
 32.5 
 30.0 
 27.9 
 26.0 
 24.4 
 22.9 
 21.7 
 20.5 
 19.5 
 18.6 
 17.7 
 17.0 
 16.2 
 15.6 
 15.0 
 
 56.9 
 45.5 
 38.0 
 32.5 
 28.5 
 25.3 
 22.8 
 20.7 
 19.0 
 17.5 
 16.3 
 .15.2 
 14.2 
 13.4 
 12.7 
 12.0 
 11.4 
 10.8 
 10.4 
 9.9 
 9.5 
 
 2.2 
 2.0 
 
 3.6 
 3.3 
 
 
 
 
 4.3 
 4.0 
 
 
 
 
 
 
 
 
 5.1 
 4.8 
 
 
 
 
 
 
 
 
 
 
 5.9 
 5.6 
 
 
 
 
 
 
 
 
 
 
 
 
 6.8 
 6.5 
 
 
 
 
 
 
 
 
 .... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 9.1 
 8.8 
 
 
 
 
 
 
 
 
 
 
 Loads above upper horizontal lines 
 will produce maximum allowable shear 
 in webs. Loads below lower horizontal 
 lines will produce excessive deflections. 
 Maximum bending stress, 16,000 Ib. 
 per sq. in. 
 
 14.4 
 13.9 
 
 
 
 
 
 
 
 
 14.3 
 13 9 
 
 
 
 
 
 
 
 Properties of Carnegie T-Shapes Steel. 
 
 Size, 
 
 Mini- 
 mum 
 Thick- 
 ness, In. 
 
 
 CA 
 
 Neutral Axis through C. 
 of G. Parallel to Flange. 
 
 Neutral Axis Co- 
 incident with Cen- 
 ter Line of Stem. 
 
 
 
 
 
 
 i p. 
 
 
 
 
 Flange 
 by 
 
 
 
 
 *3 
 
 
 H-l 
 
 . 
 
 
 
 
 m 
 
 Stem. 
 
 
 
 O.^ 
 
 
 o . 
 
 ** 
 
 3 
 
 5 <jT 
 
 cfl 
 
 HI 
 
 1 
 
 
 i 
 
 | 
 
 ll 
 
 og 
 e cr 
 
 S+3 
 
 81 
 
 i'f 
 
 n3 >> 
 
 el 
 
 .2 
 
 PI 
 
 " 
 
 n 
 
 It 
 
 ll 
 
 In. 
 
 1 
 
 00 
 
 'j* 
 
 
 OH 
 % 
 
 
 
 1 
 
 3^ 
 
 S 
 
 5 
 
 &* 
 
 5 >< 3 
 
 1/2 
 
 13/3* 
 
 13.4 
 
 3.93 
 
 2.4 
 
 0.78 
 
 1.1 
 
 0.73 
 
 5.4 
 
 .17 
 
 2.2 
 
 5 X 21/2 
 
 3/8 
 
 7/16 
 
 10.9 
 
 3.18 
 
 1.5 
 
 0.68 
 
 0.78 
 
 0.63 
 
 4.1 
 
 .14 
 
 .6 
 
 41 / 2 X 31/2 
 
 7/16 
 
 H/16 
 
 15.7 
 
 4.60 
 
 5.1 
 
 1.05 
 
 2.1 
 
 1.11 
 
 3.7 
 
 0.90 
 
 .7 
 
 41/2X3 
 
 3/8 
 
 3/8 
 
 9.8 
 
 2.88 
 
 2.1 
 
 0.84 
 
 0.91 
 
 0.74 
 
 3.0 
 
 .02 
 
 .3 
 
 41/2X3 
 
 5/16 
 
 5/16 
 
 8.4 
 
 2.46 
 
 1.8 
 
 0.85 
 
 0.78 
 
 0.71 
 
 2.5 
 
 .01 
 
 .1 
 
 41/2 X 2l/ 2 
 
 3/8 
 
 3/8 
 
 9.2 
 
 2.68 
 
 1.2 
 
 0.67 
 
 0.63 
 
 0.59 
 
 3.0 
 
 .05 
 
 .3 
 
 41/2X21/2 
 
 5/16 
 
 5/16 
 
 7.8 
 
 2.29 
 
 1.0 
 
 0.68 
 
 0.54 
 
 0.57 
 
 2.5 
 
 .05 
 
 ' 
 
 (Table continued on next page.) 
 
314 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie T-Shapes Steel. Continued. 
 
 Q;_ 
 
 Mini- 
 mum 
 Thick- 
 ness, In. 
 
 
 at 
 
 Neutral Axis through C. 
 of G. Parallel to Flange. 
 
 Neutral Axis Co- 
 incident with Cen- 
 ter Line of Stem. 
 
 bize, 
 Flange 
 
 
 
 
 l-s 
 
 
 d 
 
 H- | 
 
 
 *l 
 
 
 d 
 
 
 by 
 
 St)61Tl 
 
 
 
 &3 
 
 1 
 
 o . 
 
 
 ri 
 
 *^~ 
 
 g 
 
 
 w 
 
 
 & 
 
 
 tf 
 
 M 
 
 *! 
 
 -p c3 
 
 I'-d 
 
 I- 
 
 5 0) 
 
 '3 
 
 S 
 
 J1 
 
 S.s& 
 fl * 2 
 %< 
 
 4* 
 
 il 
 
 c & 
 
 
 32 
 
 II 
 
 
 
 
 | 
 
 'S fe 
 
 CUC/2 
 
 5 
 
 to 
 
 $% 
 
 S-3* 
 
 o 
 
 lio* 
 
 J^ 
 
 In. 
 
 E 
 
 C/2 
 
 
 
 i 
 
 2 
 
 K 
 
 t 
 
 Qis-S 
 
 s 
 
 K 
 
 
 4 X5 
 
 1/2 
 
 1/2 
 
 15.3 
 
 4.50 
 
 10.8 
 
 1.55 
 
 3.1 
 
 .56 
 
 2.8 
 
 0.79 
 
 .4 
 
 4 X5 
 
 3/8 
 
 3/8 
 
 11.9 
 
 3.49 
 
 8.5 
 
 1.56 
 
 2.4 
 
 .51 
 
 2.1 
 
 0.78 
 
 .1 
 
 4 X 41/2 
 
 1/2 
 
 1/2 
 
 14.4 
 
 4.23 
 
 7.9 
 
 1.37 
 
 2.5 
 
 .37 
 
 2.8 
 
 0.81 
 
 .4 
 
 4 X41/2 
 
 3/8 
 
 3/8 
 
 11.2 
 
 3.29 
 
 6.3 
 
 1.39 
 
 2.0 
 
 .31 
 
 2.1 
 
 0.80 
 
 .1 
 
 4 X 4 
 
 1/2 
 
 1/2 
 
 13.5 
 
 3.97 
 
 5.7 
 
 1.20 
 
 2.0 
 
 .18 
 
 2.8 
 
 0.84 
 
 .4 
 
 4 X4 
 
 3/8 
 
 3/8 
 
 10.5 
 
 3.09 
 
 4.5 
 
 1.21 
 
 1.6 
 
 .13 
 
 2.1 
 
 0.83 
 
 .1 
 
 4 X3 
 
 3/8 
 
 3/8 
 
 9.2 
 
 2.68 
 
 2.0 
 
 0.86 
 
 0.90 
 
 0.78 
 
 2.1 
 
 0.89 
 
 .1 
 
 4 X 3 
 
 5/16 
 
 5/16 
 
 7.8 
 
 2.29 
 
 1.7 
 
 0.87 
 
 0.77 
 
 0.75 
 
 1.8 
 
 0.88 
 
 0.88 
 
 4 X 21/2 
 
 3/8 
 
 3/8 
 
 8.5 
 
 2.48 
 
 1.2 
 
 0.69 
 
 0.62 
 
 0.62 
 
 2.1 
 
 0.92 
 
 1.0 
 
 4 X 21/2 
 
 5/16 
 
 5/16 
 
 7.2 
 
 2.12 
 
 1.0 
 
 0.69 
 
 0.53 
 
 0.60 
 
 1.8 
 
 0.91 
 
 0.88 
 
 4 X 2 
 
 3/8 
 
 3/8 
 
 7.8 
 
 2.27 
 
 0.60 
 
 0.52 
 
 0.40 
 
 0.48 
 
 2.1 
 
 0.96 
 
 
 4 X2 
 
 5/16 
 
 5/16 
 
 6.7 
 
 1.95 
 
 0.53 
 
 0.52 
 
 0.34 
 
 0.46 
 
 .8 
 
 0.95 
 
 0^88 
 
 31/2X4 
 
 1/2 
 
 1/2 
 
 12.6 
 
 3.70 
 
 5.5 
 
 1.21 
 
 2.0 
 
 .24 
 
 .9 
 
 0.72 
 
 1.1 
 
 31/2 X 4 
 
 3/8 
 
 3/8 
 
 9.8 
 
 2.88 
 
 4.3 
 
 1.23 
 
 .5 
 
 .19 
 
 .4 
 
 0.70 
 
 0.81 
 
 31/2 X 31/2 
 
 1/2 
 
 1/2 
 
 11.7 
 
 3.44 
 
 3.7 
 
 1.04 
 
 .5 
 
 .05 
 
 .9 
 
 0.74 
 
 1.1 
 
 3i/ 2 X 31/2 
 
 3/8 
 
 3/8 
 
 9.2 
 
 2.68 
 
 3.0 
 
 1.05 
 
 .2 
 
 .01 
 
 .4 
 
 0.73 
 
 0.81 
 
 3l/ 2 X3 
 
 1/2 
 
 1/2 
 
 10.8 
 
 3.17 
 
 2.4 
 
 0.87 
 
 ] 
 
 0.88 
 
 .9 
 
 0.77 
 
 1.1 
 
 31/2X3 
 
 3/8 
 
 3/8 
 
 8.5 
 
 2.48 
 
 1.9 
 
 0.88 
 
 0'.89 
 
 0.83 
 
 .4 
 
 0.75 
 
 0.81 
 
 31/2 X 3 
 
 5/16 
 
 3/8 
 
 7.5 
 
 2.20 
 
 1.8 
 
 0.91 
 
 0.85 
 
 0.85 
 
 .2 
 
 0.74 
 
 0.68 
 
 3 X4 
 
 1/2 
 
 1/2 
 
 11.7 
 
 3.44 
 
 5.2 
 
 1.23 
 
 1.9 
 
 .32 
 
 .2 
 
 0.59 
 
 0.81 
 
 3 X4 
 
 7/16 
 
 7/16 
 
 10.5 
 
 3.06 
 
 4.7 
 
 1.23 
 
 .7 
 
 .29 
 
 .1 
 
 0.59 
 
 0.70 
 
 3 X4 
 
 3/8 
 
 3/8 
 
 9.2 
 
 2.68 
 
 4.1 
 
 1.24 
 
 .5 
 
 .27 
 
 0.90 
 
 0.58 
 
 0.60 
 
 3 X 3i/ 2 
 
 1/2 
 
 1/2 
 
 10.8 
 
 3.17 
 
 3.5 
 
 1.06 
 
 .5 
 
 .12 
 
 .2 
 
 0.62 
 
 0.80 
 
 3 X 3i/ 2 
 
 7/16 
 
 7/16 
 
 9.7 
 
 2.83 
 
 3.2 
 
 1.06 
 
 .3 
 
 .10 
 
 .0 
 
 0.60 
 
 0.69 
 
 3 X 3i/ 2 
 
 3/8 
 
 3/8 
 
 8.5 
 
 2.48 
 
 2.8 
 
 1.07 
 
 .2 
 
 .07 
 
 0.93 
 
 0.61 
 
 0.62 
 
 3 X 3 
 
 1/2 
 
 1/2 
 
 9.9 
 
 2.91 
 
 2.3 
 
 0.88 
 
 .1 
 
 0.93 
 
 .2 
 
 0.64 
 
 0.80 
 
 3 X3 
 
 7/16 
 
 7/16 
 
 8.9 
 
 2.59 
 
 2.1 
 
 0.89 
 
 0.98 
 
 0.91 
 
 .0 
 
 0.63 
 
 0.70 
 
 3 X3 
 
 3/8 
 
 3/8 
 
 7.8 
 
 2.27 
 
 1.8 
 
 0.90 
 
 0.86 
 
 0.88 
 
 0.90 
 
 0.63 
 
 0.60 
 
 3 X3 
 
 5/16 
 
 5/16 
 
 6.7 
 
 1.95 
 
 1.6 
 
 0.90 
 
 0.74 
 
 0.86 
 
 0.75 
 
 0.62 
 
 0.50 
 
 3 X 21/2 
 
 3/8 
 
 3/8- 
 
 7.1 
 
 2.07 
 
 1.1 
 
 0.72 
 
 0.60 
 
 0.71 
 
 0.89 
 
 0.66 
 
 0.59 
 
 3 X 21/2 
 
 5/16 
 
 5/16 
 
 6.1 
 
 1.77 
 
 0.94 
 
 0.73 
 
 0.52 
 
 0.68 
 
 0.75 
 
 0.65 
 
 0.50 
 
 3 X 2i/ 2 
 
 1/4 
 
 1/4 
 
 5.0 
 
 1.47 
 
 0.78 
 
 0.73 
 
 0.43 
 
 0.66 
 
 0.61 
 
 0.64 
 
 0.40 
 
 21/2X3 
 
 3/8 
 
 3/8 
 
 7.1 
 
 2.07 
 
 1.7 
 
 0.91 
 
 0.84 
 
 0.95 
 
 0.53 
 
 0.51 
 
 0.42 
 
 21/2 X 3 
 
 5/16 
 
 5/16 
 
 6.1 
 
 1.77 
 
 1.5 
 
 0.92 
 
 0.72 
 
 0.92 
 
 0.44 
 
 0.50 
 
 0.35 
 
 21/2 X 21/2 
 
 3/8 
 
 3/8 
 
 6.4 
 
 1.87 
 
 1.0 
 
 0.74 
 
 0.59 
 
 0.76 
 
 0.52 
 
 0.53 
 
 0.42 
 
 21/2 X H/4 
 
 3/16 
 
 3/16 
 
 2.87 
 
 0.84 
 
 0.08 
 
 0.31 
 
 0.09 
 
 0.32 
 
 0.29 
 
 0.58 
 
 0.23 
 
 21/4X21/4 
 
 5/16 
 
 5/16 
 
 4.9 
 
 1.43 
 
 0.65 
 
 0.67 
 
 0.41 
 
 0.68 
 
 0.33 
 
 0.48 
 
 0.29 
 
 2 X 2 
 
 5/16 
 
 5/16 
 
 4.3 
 
 1.26 
 
 0.44 
 
 0.59 
 
 0.31 
 
 0.61 
 
 0.23 
 
 0.43 
 
 0.23 
 
 2 X U/2 
 
 1/4 
 
 1/4 
 
 3.09 
 
 0.91 
 
 0.16 
 
 0.42 
 
 0.15 
 
 0.42 
 
 0.18 
 
 0.45 
 
 0.18 
 
 13/4 X 13/4 
 
 1/4 
 
 1/4 
 
 3.09 
 
 0.91 
 
 0.23 
 
 0.51 
 
 0.19 
 
 0.54 
 
 0.12 
 
 0.37 
 
 0.14 
 
 U/2X U/2 
 
 1/4 
 
 1/4 
 
 2.47 
 
 0.73 
 
 0.15 
 
 0.45 
 
 0.14 
 
 0.47 
 
 0.08 
 
 0.32 6.JO 
 
 H/4 X 11/4 
 
 1/4 
 
 1/4 
 
 2.02 
 
 0.59 
 
 0.08 
 
 0.37 
 
 0.10 
 
 0.40 
 
 0.05 
 
 0.28 
 
 0.07 
 
 1 X 1 3/18 
 
 3/ieJ 
 
 1.25 
 
 0.37 
 
 0.03 
 
 0.29 
 
 0.05 
 
 0.32 
 
 0.02 
 
 0.22 
 
 0.04 
 
 Ten light-weight T's of sizes under 2K X 2K in, are omitted. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 315 
 
 Maximum Safe Loads on Carnegie T-Shapes. 
 
 Allowable Uniform Load in Thousands of Pounds. Neutral Axis Parallel 
 to Flange. Maximum Bending Stress, 16,000 Pounds Per Square Inch. 
 
 
 
 
 Maximum 
 
 
 
 
 Maximum 
 
 Size. 
 
 Wgt. 
 
 IFt. 
 
 Span 
 
 Span. 
 360 X De- 
 flection. 
 
 Size. 
 
 Wgt. 
 
 1 Ft. 
 Span 
 
 Span. 
 360 X De- 
 flection. 
 
 
 Foot, 
 
 
 
 
 Foot, 
 
 
 
 n 
 
 
 
 1 
 
 oT 
 
 
 
 
 
 |d 
 
 Stem, 
 Tn. 
 
 Lb. 
 
 Safe 
 Load. 
 
 Safe iLgth., 
 Load.! Feet. 
 
 S . 
 
 Stem, 
 Tn. 
 
 Lb. 
 
 Safe 
 Load. 
 
 Safe 
 Load. 
 
 Lgth., 
 Feet. 
 
 E 
 
 
 
 1 
 
 fe 
 
 
 
 
 
 
 
 3 
 
 13.4 
 
 II .41 
 
 .25 9.1 
 
 
 3 1/2 
 
 9.7 
 
 14.19 
 
 .46 
 
 9.7 
 
 5 
 
 21/2 
 
 10.9 
 
 8.96 
 
 1.20 
 
 7.5 
 
 
 31/2 
 
 2-5 
 
 12.37 
 
 .26 
 
 9.8 
 
 
 31/2 
 
 15.7 
 9.8 
 
 22.72 
 9.71 
 
 2.37 
 .07 
 
 ~9.6 
 9.1 
 
 
 3 
 3 
 
 9.9 
 8.9 
 
 11 .73 
 10.45 
 
 .41 
 .24 
 
 8.3 
 8.4 
 
 41/2 
 
 3 
 
 21/2 
 
 21/2 
 
 8.4 
 9.2 
 7.8 
 
 8.32 
 6.72 
 5.76 
 
 0.90 
 0.87 
 0.74 
 
 9.2 
 
 7.7 
 7.8 
 
 3 
 
 3 
 3 
 
 21/2 
 21/2 
 21/2 
 
 7.8 
 6.7 
 7.1 
 6.1 
 5.0 
 
 9.17 
 7.89 
 6.40 
 5.55 
 4.59 
 
 .08 
 0.92 
 0.89 
 0.76 
 0.62 
 
 8.5 
 8.6 
 7.2 
 7.3 
 7.4 
 
 
 5 
 5 
 
 15.3 
 1 1 9 
 
 33.39 2.40 13.9 
 25 92 RA. \A \ 
 
 4 
 
 41/2 
 
 41/2 
 
 4 
 3 
 
 14.4 
 11.2 
 13.5 
 10.5 
 9.2 
 
 27.09 
 21.12 
 21 .55 
 '6.85 
 9.60 
 
 2.15 
 .65 
 1 .89 
 .45 
 1 .08 
 
 12.6 
 12.8 
 11.4 
 11.6 
 8.9 
 
 2 1/2 
 
 3 
 3 
 
 21/2 
 21/2 
 1 1/4 
 
 7.1 
 6.1 
 6.4 
 5.5 
 
 2.87 
 
 8.96 
 7.63 
 6.29 
 5.33 
 0.93 
 
 1.08 
 0.91 
 0.90 
 0.75 
 0.25 
 
 8 '.4 
 7.0 
 7.1 
 3.7 
 
 
 3 
 
 7 8 
 
 8.21 
 
 0.90 
 
 9.1 
 
 9 i / , 
 
 21/.1 
 
 49 
 
 4.37 
 
 0.69 
 
 6.3 
 
 
 21/2 
 
 8.5 
 
 6.61 
 
 0.87 
 
 7.6 
 
 L 1/4 
 
 21/4 
 
 4.1 
 
 3.41 
 
 0.53 
 
 6.4 
 
 
 21/2 
 
 7.2 
 
 5.65 
 
 0.73 
 
 7.7 
 
 2 
 
 4.3 
 
 3 31 
 
 0.59 
 
 5.6 
 
 
 2 
 
 7.8 
 
 4.27 
 
 0.70 
 
 6. 1 
 
 2 2 
 
 3.56 
 
 2.77 
 
 0.49 
 
 5.7 
 
 
 2 
 
 6.7 
 
 3.63 
 
 0.59 
 
 6.2 
 
 
 IV, 
 
 3.09 
 
 1 .60 
 
 0.36 
 
 4.4 
 
 ,, 
 
 4 
 4 
 
 31/2 
 
 31/2 
 
 3 
 
 12.6 
 9.8 
 11.7 
 9.2 
 10.8 
 85 
 
 21 .12 
 16.53 
 16.32 
 12.69 
 12.05 
 9.49 
 
 .90 
 .46 
 .65 
 .27 
 
 .42 
 09 
 
 11.1 
 11.3 
 9.9 
 10.0 
 8.5 
 8.7 
 
 1 3/4 
 
 13/4 
 
 3.09 
 
 ~T:Q3 
 ^703 
 1 .49 
 1.17 
 0.57 
 
 ~OT41 
 07 
 0.36 
 0.27 
 0.15 
 
 4.9 
 
 4ll 
 4.3 
 3.7 
 
 1 1/2 
 
 2 
 
 1 1/4 2 
 
 2.45 
 2.47 
 1 .94 
 1.25 
 
 
 3 
 
 7.5 
 
 9.07 
 
 .04 
 
 8.7 
 
 1 1/4 
 
 2.02 
 
 1 .01 
 
 0.30 
 
 3.4 
 
 
 4 
 4 
 
 11.7 
 10.5 
 
 20.69 
 18 35 
 
 .92 10.8 
 68 10 9 
 
 1 1/4 
 
 5/8 
 
 1 .59 
 0.88 
 
 0.78 
 0.14 
 
 0.22 
 0.07 
 
 3.5 
 
 1.9 
 
 3 
 
 4 
 
 9,2 
 
 16.11 
 
 .47 
 
 11.0 
 
 
 1 
 
 T~25 
 
 "0749 
 
 ins 
 
 27T 
 
 
 31/2 
 
 10.8 
 
 15.89 
 
 .66 
 
 9.6 
 
 
 1 
 
 0.89 
 
 0.35 
 
 0.12 
 
 2.9 
 
316 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Z-fiars. 
 
 
 
 
 
 
 
 .2 i 
 
 2-g 
 
 .2 A 
 
 .a* 
 
 <J| 
 
 . . 
 
 ^bi 
 
 
 
 
 
 
 J$ ~ 
 
 x g 
 
 <-2 
 
 <!! 
 
 
 i<s 
 
 II 
 
 
 
 
 
 
 fl 
 
 '3 
 
 J3 
 
 ^.'3 
 
 /5 nj 
 
 XH 
 
 MH 
 
 
 
 
 
 
 tj * 
 
 3-S 
 
 ~3 rv 
 
 
 fl| 
 
 "o . 
 
 m 
 
 
 
 
 
 
 
 
 0> 
 
 *& 
 
 11 
 
 is 
 
 Sol 
 
 g^ 
 
 
 
 3 
 
 
 
 
 
 
 
 53 
 
 '-p 
 
 4J 
 
 1 
 
 I 
 
 V 
 
 *o 
 
 1 
 
 1 
 
 .* ^ 
 
 hi 
 
 .SO 
 
 Jo 
 
 fH 
 
 l 
 
 S 
 
 111 
 
 J-U 
 D 
 
 11 
 
 "8 
 
 1 
 
 "o 
 
 
 
 J>. 
 
 hickness 
 
 1 
 
 1 
 
 '*o 
 t 
 
 III 
 
 3 
 
 1*2: 
 1^5 
 
 111 
 
 111 
 
 1 
 
 M '3 
 |.2| 
 
 i 
 
 t3 c* 
 
 M 
 
 1? 
 
 H 
 
 & 
 
 < 
 
 % 
 
 
 
 CO 
 
 CO 
 
 K 
 
 
 
 tf 
 
 in. 
 
 in. 
 
 in. 
 
 lb. 
 
 sq. in. 
 
 / 
 
 / 
 
 S 
 
 S 
 
 r 
 
 r 
 
 r 
 
 6 
 
 31/2 
 
 3/8 
 
 15.7 
 
 4.59 
 
 25.32 
 
 9.11 
 
 8.44 
 
 2.75 
 
 2.35 
 
 .41 
 
 0.83 
 
 61/1639/ie 
 
 7/16 
 
 18.4 
 
 5.39 
 
 29.80 
 
 10.95 
 
 9.83 
 
 3.27 
 
 2.35 
 
 .43 
 
 0.83 
 
 61/8 
 
 35/8 
 
 1/2 
 
 21.1 
 
 6.19 
 
 34.36 
 
 12.87 
 
 11.22 
 
 3.81 
 
 2.36 
 
 .44 
 
 0.84 
 
 6 
 
 31/2 
 
 9/16 
 
 22.8 
 
 6.68 
 
 34.64 
 
 12.59 
 
 11.52 
 
 3.91 
 
 2.28 
 
 .37 
 
 0.81 
 
 61/16 
 
 39/16 
 
 5/8 
 
 25.4 
 
 7.46 
 
 38.86 
 
 14.42 
 
 12.82 
 
 4.43 
 
 2.28 
 
 .39 
 
 0.82 
 
 61/8 
 
 35/8 
 
 H/16 
 
 28.1 
 
 8.25 
 
 43.18 
 
 16.34 
 
 14.10 
 
 4.98 
 
 2.29 
 
 .41 
 
 0.84 
 
 6 
 
 31/2 
 
 3/4 
 
 29.4 
 
 8.63 
 
 42.12 
 
 15.44 
 
 14.04 
 
 4.94 
 
 2.21 
 
 .34 
 
 0.81 
 
 6i/i639/i 6 
 
 13/16 
 
 32.0 9.40 
 
 46.13 
 
 17.27 
 
 15.22 
 
 5.47 
 
 2.22 
 
 .36 
 
 0.82 
 
 61/8 
 
 35/8 
 
 7/8 
 
 34.6 
 
 10.17 
 
 50.22 
 
 19.18 
 
 16.40 
 
 6.02 
 
 2.22 
 
 .37 
 
 0.83 
 
 5 
 
 31/4 
 
 5/16 
 
 11.6 
 
 3.40 
 
 13.36 
 
 6.18 
 
 5.34 
 
 2.00 
 
 .98 
 
 .35 
 
 0.75 
 
 5 1/16 
 
 35/16 
 
 3/8 
 
 14.0 
 
 4.10 
 
 16.18 
 
 7.65 
 
 6.39 
 
 2.45 
 
 .99 
 
 .37 
 
 0.76 
 
 51/8 
 
 33/8 
 
 7/16 
 
 16.4 
 
 4.81 
 
 19.07 
 
 9.20 
 
 7.44 
 
 2.92 
 
 .99 .38 
 
 0.77 
 
 5 
 
 31/4 
 
 1/2 
 
 17.9 
 
 5.25 
 
 19.19 
 
 9.05 
 
 7.68 
 
 3.02 
 
 .91 .31 
 
 0.74 
 
 5'1/ie 
 
 35/16 
 
 9/16 
 
 20.2 
 
 5.94 
 
 21.83 
 
 10.51 
 
 8.62 
 
 3.47 
 
 .91 .33 
 
 0.75 
 
 51/8 
 
 33/8 
 
 5/8 
 
 22.6 
 
 6.64 
 
 24.53 
 
 12.06 
 
 9.57 
 
 3.94 
 
 .92 
 
 .35 
 
 0.76 
 
 5 
 
 31/4 
 
 H/16 
 
 23.7 
 
 6.96 
 
 23.68 
 
 11.37 
 
 9.47 
 
 3.91 
 
 .84 
 
 .28 
 
 0.73 
 
 51/16 
 
 3 5/16 
 
 3/4 
 
 26.0 
 
 7.64 
 
 26.16 
 
 12.83 
 
 10.34 
 
 4.37 
 
 .85 
 
 .30 
 
 0.74 
 
 51/8 
 
 33/8 
 
 13/16 
 
 28.4 
 
 8.33 
 
 28.70 
 
 14.36 
 
 11.20 
 
 4.84 
 
 .86 
 
 .31 
 
 0.76 
 
 4 
 
 31/16 
 
 1/4 
 
 8.2 
 
 2.41 
 
 6.28 
 
 4.23 
 
 3.14 
 
 1.44 
 
 .62 
 
 .33 
 
 0.67 
 
 41/16 
 
 31/8 
 
 5/16 
 
 10.3 
 
 3.03 
 
 7.94 
 
 5.46 
 
 3.91 
 
 1.84 
 
 .62 
 
 .34 
 
 0.68 
 
 41/8 
 
 33/16 
 
 3/8 
 
 12.5 
 
 3.66 
 
 9.63 
 
 6.77 
 
 4.67 
 
 2.26 
 
 .62 
 
 .36 
 
 0.69 
 
 4 
 
 31/16 
 
 7/16 
 
 13.8 
 
 4.05 
 
 9.66 
 
 6.73 
 
 4.83 
 
 2.37 
 
 .55 
 
 .29 
 
 0.66 
 
 41/16 
 
 31/8 
 
 1/2 
 
 15.9 
 
 4.66 
 
 11.18 
 
 7.96 
 
 5.50 
 
 2.77 
 
 .55 
 
 .31 
 
 0.67 
 
 41/8 
 
 33/16 
 
 Vl6 
 
 18.0 
 
 5.27 
 
 12.74 
 
 9.26 
 
 6.18 
 
 3.19 
 
 .55 
 
 .33 
 
 0.68 
 
 4 
 
 31/16 
 
 5/8 
 
 18.9 
 
 5.55 
 
 12.11 
 
 8.73 
 
 6.05 
 
 3.18 
 
 .48 
 
 .25 
 
 0.66 
 
 41/16 
 
 31/8 
 
 H/16 
 
 20.9 
 
 6.14 
 
 13.52 
 
 9.95 
 
 6.65 
 
 3.58 
 
 .48 
 
 .27 
 
 0.67 
 
 41/8 
 
 33/16 
 
 3/4 
 
 23.0 
 
 6.75 
 
 14.97 
 
 11.24 
 
 7.26 
 
 4.00 
 
 .49 
 
 .29 
 
 0.68 
 
 3 
 
 2H/16 
 
 1/4 
 
 6.7 
 
 1.97 
 
 2.87 
 
 2.81 
 
 1.92 
 
 1.10 
 
 .21 
 
 .19 
 
 0.55 
 
 31/16 
 
 23/4 
 
 5/16 
 
 8.5 
 
 2.48 
 
 3.64 
 
 3.64 
 
 2.38 
 
 1.40 
 
 .21 
 
 .21 
 
 0.56 
 
 3 
 
 2 H/16 
 
 3/8 
 
 9.8 
 
 2.86 
 
 3.85 
 
 3.92 
 
 2.57 
 
 1.57 
 
 .16 
 
 .17 
 
 0.54 
 
 31/16 
 
 23/4 
 
 7/16 
 
 11.5 
 
 3.36 
 
 4.57 
 
 4.75 
 
 2.98 
 
 1.88 
 
 .17 
 
 .19 
 
 0.55 
 
 3 
 
 2 H/16 
 
 1/2 
 
 12.6 
 
 3.69 
 
 4.59 
 
 4.85 
 
 3.06 
 
 1.99 
 
 .12 
 
 15 
 
 0.53 
 
 31/16 
 
 23/4 
 
 9/16 
 
 14.3 
 
 4.18 
 
 5.26 
 
 5.70 
 
 3.43 
 
 2.31 
 
 .12 
 
 17 
 
 0.54 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 317 
 
 Properties of Carnegie Unequal Angles; Minimum, Intermediate, 
 and Maximum Thicknesses and Weights. 
 
 
 J 
 
 
 
 Moment of 
 
 Section 
 
 Radius of Gyra- 
 
 
 ,fj 
 
 . 
 
 s 
 
 Inertia. /. 
 
 Modulusl-S. 
 
 tion. r. 
 
 Size, 
 In. 
 
 Q 
 
 
 
 If 
 
 w v 
 
 85"! 
 
 <! ^s 
 
 !;! 
 
 rt 
 
 35 fc 
 
 OB g, 
 
 '8 ** c? 
 *** 
 
 5S 8 
 
 *r| 
 
 ^J rt 
 "oJfe 
 
 || 
 
 
 1 
 
 1)1 
 
 ^ 1 
 
 if* 
 
 Ill 
 
 III 
 
 I'gt 
 
 Hi 
 
 2~ 
 
 ^Q 
 
 
 o 
 
 IS 
 
 |* 
 
 S^ 
 
 i" 
 
 
 
 |&g 
 
 
 1*1 
 
 II 
 
 8 X6 
 
 1 
 
 44.2 
 
 13.00 
 
 38.8 
 
 80.8 
 
 8.9 
 
 15.1 
 
 1.73 
 
 2.49 
 
 1.28 
 
 
 3/4 
 
 33.8 
 
 9.94 
 
 30.7 
 
 63.4 
 
 6.9 
 
 11.7 
 
 1.76 
 
 2.53 
 
 1.29 
 
 
 7/16 
 
 20.2 
 
 5.93 
 
 19.3 
 
 39.2 
 
 4.2 
 
 7.1 
 
 1.80 
 
 2.57 
 
 1.30 
 
 8 X 3 1/2 
 
 
 35.7 
 
 10.50 
 
 7.8 
 
 66.2 
 
 3.0 
 
 13.7 
 
 0.86 
 
 2.51 
 
 0.73 
 
 
 3/4 
 
 27.5 
 
 8.06 
 
 6.3 
 
 52.3 
 
 2.3 
 
 10.6 
 
 0.88 
 
 2.55 
 
 0.73 
 
 
 7/16 
 
 16.5 
 
 4.84 
 
 4.1 
 
 32.5 
 
 1.5 
 
 6.4 
 
 0.92 
 
 2.59 
 
 0.74 
 
 7 X31/2 
 
 
 32.3 
 
 9.50 
 
 7.5 
 
 45.4 
 
 3.0 
 
 10.6 
 
 0.89 
 
 2.19 
 
 0.74 
 
 
 H/16 
 
 23.0 
 
 6.75 
 
 5.7 
 
 33.5 
 
 2.1 
 
 7.6 
 
 0.92 
 
 2.23 
 
 0.74 
 
 
 3/8 
 
 13.0 
 
 3.80 
 
 3.5 
 
 19.6 
 
 1.3 
 
 4.3 
 
 0.96 
 
 2.27 
 
 0.76 
 
 6 X4 
 
 
 30.6 
 
 9.00 
 
 10.8 
 
 30.8 
 
 3.8 
 
 8.0 
 
 .09 
 
 1.85 
 
 0.85 
 
 
 H/16 
 
 21.8 
 
 6.40 
 
 8.1 
 
 22.8 
 
 2.8 
 
 5.8 
 
 .13 
 
 .89 
 
 0.86 
 
 
 3/8 
 
 12.3 
 
 3.61 
 
 4.9 
 
 13.5 
 
 1.6 
 
 3.3 
 
 .17 
 
 .93 
 
 0.88 
 
 6 X31/2 
 
 
 28.9 
 
 8.50 
 
 7.2 
 
 29.2 
 
 2.9 
 
 7.8 
 
 0.92 
 
 .85 
 
 0.74 
 
 
 H/16 
 
 20.6 
 
 6.06 
 
 5.5 
 
 21.7 
 
 2.1 
 
 5.6 
 
 0.95 
 
 .89 
 
 0.75 
 
 
 
 9.8 
 
 2.87 
 
 2.9 
 
 10.9 
 
 1.0 
 
 2.7 
 
 .00 
 
 .95 
 
 0.77 
 
 5 X4 
 
 7/8 6 
 
 24.2 
 
 7.11 
 
 9.2 
 
 16.4 
 
 3.3 
 
 5.0 
 
 .14 
 
 .52 
 
 0.84 
 
 
 5/8 
 
 17.8 
 
 5.23 
 
 7.1 
 
 12.6 
 
 2.5 
 
 3.7 
 
 .17 
 
 .55 
 
 0.84 
 
 
 3/8 
 
 11.0 
 
 3.23 
 
 4.7 
 
 8.1 
 
 1.6 
 
 2.3 
 
 .20 
 
 .59 
 
 0.86 
 
 5 X31/2 
 
 7/8 
 
 22.7 
 
 6.67 
 
 6.2 
 
 15.7 
 
 2.5 
 
 4.9 
 
 0.96 
 
 .53 
 
 0.75 
 
 
 5/8 
 
 16.8 
 
 4.92 
 
 4.8 
 
 12.0 
 
 .9 
 
 3.7 
 
 0.99 
 
 .56 
 
 0.75 
 
 
 5/16 
 
 8.7 
 
 2.56 
 
 2.7 
 
 6.6 
 
 .0 
 
 1.9 
 
 1.03 
 
 .61 
 
 0.76 
 
 5 X3 
 
 13/16 
 
 19.9 
 
 5.84 
 
 3.7 
 
 14.0 
 
 .7 
 
 4.5 
 
 0.80 
 
 .55 
 
 0.64 
 
 
 9/16 
 
 14.3 
 
 4.18 
 
 2.8 
 
 10.4 
 
 .3 
 
 3.2 
 
 0.82 
 
 .58 
 
 0.65 
 
 
 5/16 
 
 8.2 
 
 2.40 
 
 1.8 
 
 6.3 
 
 0.75 
 
 1.9 
 
 0.85 
 
 .61 
 
 0.66 
 
 2 X3 
 
 13/16 
 
 18.5 
 
 5.43 
 
 3.6 
 
 10.3 
 
 .7 
 
 3.6 
 
 0.81 
 
 .38 
 
 0.61 
 
 
 9/16 
 
 13.3 
 
 3.90 
 
 2.8 
 
 7.8 
 
 .3 
 
 2.6 
 
 0.85 
 
 .41 
 
 0.6* 
 
 
 5/16 
 
 7.7 
 
 2.25 
 
 1.7 
 
 4.7 
 
 0.75 
 
 1.5 
 
 0.87 
 
 .44 
 
 0.65 
 
 X31/2 
 
 13/16 
 
 18.5 
 
 5.43 
 
 5.5 
 
 7.8 
 
 2.3 
 
 2.9 
 
 1.01 
 
 .19 
 
 0.72 
 
 
 
 13.3 
 
 3.90 
 
 4.2 
 
 5.9 
 
 .7 
 
 2.1 
 
 1.03 
 
 .23 
 
 0.72 
 
 
 5/16 
 
 7.7 
 
 2.25 
 
 2.6 
 
 3.6 
 
 .0 
 
 1.3 
 
 1.07 
 
 .26 
 
 0.73 
 
 X3 
 
 13/16 
 
 17.1 
 
 5.03 
 
 3.5 
 
 7.3 
 
 .7 
 
 2.9 
 
 0.83 
 
 .21 
 
 0.64 
 
 
 9/16 
 
 12.4 i 
 
 3.62 
 
 2.7 
 
 5.6 
 
 .2 
 
 2.1 
 
 0.86 
 
 .24 
 
 0.64 
 
 
 1/4 
 
 5.8 
 
 1.69 
 
 1.4 
 
 2.8 
 
 0.60 
 
 1.0 
 
 0.89 
 
 .28 
 
 0.65 
 
 3V2X3 
 
 13/16 
 
 15.8 
 
 4.62 
 
 3.3 
 
 5.0 
 
 .7 
 
 2.2 
 
 0.85 
 
 .04 
 
 0.62 
 
 
 9/16 
 
 11.4 
 
 3.34 
 
 2.5 
 
 3.8 
 
 .2 
 
 1.6 
 
 0.87 
 
 .07 
 
 0.62 
 
 
 1/4 
 
 5.4 
 
 1.56 
 
 .3 
 
 .9 
 
 0.58 
 
 0.78 
 
 0.91 
 
 .11 
 
 0.63 
 
 12X21/2 
 
 H/16 
 
 1/2 
 
 12.5 
 9.4 
 
 3.65 
 2.75 
 
 .7 
 .4 
 
 4.1 
 3.2 
 
 0.99 
 0.76 
 
 1.9 
 1.4 
 
 0.69 
 0.70 
 
 .06 
 .09 
 
 0.53 
 0.53 
 
 
 1/4 
 
 4.9 
 
 1.44 
 
 0.78 
 
 1.8 
 
 0.41 
 
 0.75 
 
 0.74 
 
 .12 
 
 0.54 
 
 X2i/ 2 
 
 9/16 
 
 9.5 
 
 2.78 
 
 .4 
 
 2.3 
 
 0.82 
 
 1.2 
 
 0.72 
 
 0.91 
 
 0.52 
 
 
 7/16 
 
 7.6 
 
 2.21 
 
 .2 
 
 .9 
 
 0.66 
 
 0.93 
 
 0.73 
 
 0.92 
 
 0.52 
 
 
 
 4.5 
 
 1.31 
 
 0.74 
 
 .2 
 
 0.40 
 
 0.56 
 
 0.75 
 
 0.95 
 
 0.53 
 
 X2 
 
 1/2 
 
 7.7 
 
 2.25 
 
 0.67 
 
 .9 
 
 0.47 
 
 1.0 
 
 0.55 
 
 0.92 
 
 0.43 
 
 
 3/8 
 
 5.9 
 
 1.73 
 
 0.54 
 
 .5 
 
 0.37 
 
 0.78 
 
 0.56 
 
 0.94 
 
 0.43 
 
 
 1/4 
 
 4.1 
 
 1.19 
 
 0.39 
 
 .1 
 
 0.25 
 
 0.54 
 
 0.57 
 
 0.95 
 
 0.43 
 
 2 X2 
 
 1/2 
 
 6.8 
 
 2.00 
 
 0.64* 
 
 
 0.46 
 
 0.70 
 
 0.56 
 
 0.75 
 
 0.42 
 
 
 5/16 
 
 4.5 
 
 1.31 
 
 0.45 
 
 0^79 
 
 0.31 
 
 0.47 
 
 0.58 
 
 0.78 
 
 0.42 
 
 
 1/8 
 
 1.86 
 
 0.55 
 
 0.20 
 
 0.35 
 
 0.13 
 
 0.20 
 
 0.61 
 
 0.89 
 
 0.43 
 
 21/2XH/2 
 
 5/16 
 
 3.92 
 
 1.15 
 
 0.19 
 
 0.71 
 
 0.17 
 
 0.44 
 
 0.41 
 
 0.79 
 
 0.32 
 
 
 3/16 
 
 2.44 
 
 0.72 
 
 0.13 
 
 0.46 
 
 0.11 
 
 0.28 
 
 0.42 
 
 0.80 
 
 0.33 
 
 2V 4 X U/2 
 
 1/2 
 
 5.6 
 
 1.63 
 
 0.26 
 
 0.75 
 
 0.26 
 
 0.54 
 
 0.40 
 
 0.68 
 
 0.32 
 
 
 3/16 
 
 2.28 
 
 0.67 
 
 0.12 
 
 0.34 
 
 0.11 
 
 0.23 
 
 0.43 
 
 0.72 
 
 0.33 
 
 (Table continued on next page.) 
 
318 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Unequal Angles. Continued. 
 
 Size, 
 In. 
 
 Thickness, Inches. 
 
 "o 
 
 & 
 
 b 
 
 P.J 
 
 *! 
 g 
 
 Area of Section, 
 Square Inches. 
 
 Moment of 
 Inertia. /. 
 
 Section 
 Modulus.-/!?. 
 
 Radius of Gyra- 
 tion. r. 
 
 w ft*. 
 
 .3| 
 
 <J 
 
 "sS 
 
 llg 
 J&s 
 
 3*1 
 
 <5 ^ 
 
 sS 
 111 
 
 3f*-JC 
 
 o;P-tGQ 
 
 flj| 
 
 %! 
 
 -^^ 
 
 2*3 M 
 
 ,3 C C 
 
 S(>3 
 
 S5 
 
 w o ft, 
 3^c 
 
 <J cd 
 
 Sfe 
 
 git 
 
 i 
 3 tf,c 
 
 gHHGG 
 
 w o ft. 
 
 3"*" 
 
 <5 rt 
 2^ 
 
 *? 
 
 3 efl o 
 ajpLiJ 
 
 gs| 
 
 M 
 SP 
 
 3 * J3 
 EPkCQ 
 
 oa'-j 
 3 w 
 
 'S 
 
 oJ tsa 
 
 .2 
 ^Q 
 
 hJ ^ 
 
 032 
 0.33 
 0.27 
 0.27 
 0.27 
 0.27 
 0.26 
 0.26 
 
 2 X 1 1/2 
 2 X 1 1/4 
 
 1 3 / 4 Xll/4 
 
 1V2XU/4 
 
 3/8 
 1/8 
 1/4 
 3/16 
 1/4 
 1/8 
 Vl6 
 3/16 
 
 3.99 
 1.44 
 2.55 
 1.96 
 2.34 
 1.23 
 2.59 
 1.64 
 
 1.17 
 0.42 
 0.75 
 0.57 
 0.69 
 0.36 
 0.76 
 0.48 
 
 0.21 
 0.09 
 0.09 
 0.07 
 0.09 
 0.05 
 0.10 
 0.07 
 
 0.43 
 0.17 
 0.30 
 0.23 
 0.20 
 0.11 
 0.16 
 0.10 
 
 0.20 
 0.08 
 0.10 
 0.08 
 0.10 
 0.05 
 0.11 
 0.07 
 
 0.34 
 0.13 
 0.23 
 0.18 
 0.18 
 0.09 
 0.!6 
 0.10 
 
 0.42 
 0.45 
 0.34 
 0.35 
 0.35 
 0.37 
 0.35 
 0.37 
 
 0.61 
 0.64 
 0.63 
 0.64 
 0.54 
 0.56 
 0.45 
 0.46 
 
 Maximum and minimum sizes only are given for angles less than 
 
 Safe Loads, in Thousands of Pounds, for Carnegie Unequal Angles 
 Used as Beams. Minimum, Intermediate, and Maximum Thick- 
 ness and Weights. 
 
 
 Neutral Axis Parallel 
 
 Neutral Axis Parallel 
 
 
 to Shorter Leg. 
 
 to Longer Leg. 
 
 Size of Angle, 
 
 Safe 
 
 Maximum Span, 
 360 X Deflec- 
 
 Safe 
 
 Maximum Span, 
 360 X Deflec- 
 
 Inches. 
 
 Load, 
 1 Foot 
 
 tion. 
 
 Load, 
 1 Foot 
 
 tion. 
 
 
 Span. 
 
 Safe 
 
 Lgth., 
 
 Span. 
 
 Safe 
 
 Lgth.; 
 
 
 
 Load. 
 
 Feet. 
 
 
 Load. 
 
 Feet. 
 
 8X6X1 
 
 161.17 
 
 7.49 
 
 21.5 
 
 95.15 
 
 5.44 
 
 17.5 
 
 8 X6 X 3/4 
 
 124.48 
 
 5.68 
 
 21.9 
 
 73.92 
 
 4.13 
 
 17.9 
 
 8 X6 X 7/16 
 
 75.41 
 
 3.37 
 
 22.4 
 
 45.12 
 
 2.47 
 
 18.3 
 
 8 X 3 l/ 2 X 1 
 
 146.03 
 
 7.53 
 
 19.4 
 
 32.21 
 
 3.10 
 
 10.4 
 
 X3i/ 2 x 3/4 
 
 113.17 
 
 5.72 
 
 19.8 
 
 25.07 
 
 2.33 
 
 10.8 
 
 8 X31/2X Vl6 
 
 68.80 
 
 3.39 
 
 20.3 
 
 15.57 
 
 1.38 
 
 11.3 
 
 7 X 3 i/ 2 X 1 
 
 112.85 
 
 6.52 
 
 17.3* 
 
 31.57 
 
 3,10 
 
 10.2 
 
 7 X3i/ 2 X n/16 
 
 81.07 
 
 4.58 
 
 17.7 
 
 22.83 
 
 2.14 
 
 10.7 
 
 7 X31/2X 3/ 8 
 
 46.19 
 
 2.54 
 
 18.2 
 
 13.44 
 
 1.19 
 
 11.2 
 
 6 X4 XI 
 
 85.55 
 
 5.56 
 
 15.4 
 
 40.43 
 
 3.55 
 
 11.4 
 
 6 X4 X n/16 
 
 61.65 
 
 3.88 
 
 15.9 
 
 29.44 
 
 2.47 
 
 11.9 
 
 6 X4 X 3/ 8 
 
 35.41 
 
 2.16 
 
 16.4 
 
 17.07 
 
 1.39 
 
 12.3 
 
 6 X 3 1/2 X 1 
 
 83.52 
 
 5.57 
 
 15.0 
 
 30.93 
 
 3.09 
 
 10.0 
 
 6 X31/2X 11/16 
 
 60.27 
 
 3.89 
 
 15.5 
 
 22.51 
 
 2:14 
 
 10.5 
 
 6 X31/2X Vl6 
 
 29.23 
 
 1.83 
 
 16.0 
 
 11.09 
 
 1.00 
 
 11.1 
 
 5 X4 X 7/ 8 
 
 53.23 
 
 4.00 
 
 13.3 
 
 35.31 
 
 3.15 
 
 11.2 
 
 5 X 4 X V8 
 
 39.79 
 
 2.92 
 
 13.6 
 
 26.45 
 
 2.28 
 
 11.6 
 
 5 X4 X 3/ 8 
 
 24.96 
 
 1.78 
 
 14.0 
 
 16.75 
 
 1.40 
 
 12.0 
 
 5 X3l/ 2 X 7/ 8 
 
 52.05 
 
 4.04 
 
 12.9 
 
 26.88 
 
 2.71 
 
 99 
 
 5 X31/2X 5/s 
 
 38.93 
 
 2.93 
 
 13.3 
 
 20.27 
 
 1.97 
 
 10.3 
 
 5 X31/2X 5/16 
 
 20.69 
 
 1.51 
 
 13.7 
 
 10.88 
 
 1.02 
 
 10.7 
 
 (Table continued on next page.} 
 
 Maximum bending stress, 16,000 Ib. per sq. in. Safe loads for other 
 spans - 
 the \\ _ 
 "Which can be carried." 
 
 ns are inversely proportional to the span in feet. Safe loads include 
 weight of the angle, which should be deducted to give net load 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 319 
 
 Safe Loads, in Thousands of Pounds, for Carnegie Unequal Angles 
 Used as Beams. Continued. 
 
 
 Neutral Axis Parallel 
 
 Neutral Axis Parallel 
 
 
 to Shorter Leg. 
 
 to Longer Leg. 
 
 Size of Angle, 
 
 Safe 
 
 Maximum Span, 
 360 X Deflec- 
 
 Safe 
 
 Maximum Span, 
 360 X Deflec- 
 
 Inches. 
 
 Load, 
 1 Foot 
 
 tion. 
 
 Load 
 1 Foot 
 
 tion. 
 
 
 Span. 
 
 Safe 
 
 Lgth., 
 
 Span. 
 
 Safe 
 
 Lgth., 
 
 
 
 Load. 
 
 Feet. 
 
 
 Load. 
 
 Feet. 
 
 5 X3 X lVl6 
 
 47.47 
 
 3.77 
 
 12.6 
 
 18.56 
 
 2.16 
 
 8.6 
 
 5 X 3 X 9 /i6 
 
 34.45 
 
 2.65 
 
 13 
 
 13.55 
 
 1.51 
 
 9.0 
 
 5 X3 X 5/16 
 
 20.16 
 
 1.51 
 
 13.4 
 
 8.00 
 
 0.85 
 
 9.4 
 
 41/2X3 X 13/18 
 
 38.61 
 
 3.36 
 
 11.5 
 
 18.24 
 
 2.15 
 
 8.5 
 
 4 1/2 X 3 X 9 /l6 
 
 28.16 
 
 2.38 
 
 11.8 
 
 13.33 
 
 1.51 
 
 8.8 
 
 41/2X3 X Vie 
 
 16.43 
 
 1.35 
 
 12.2 
 
 8.00 
 
 0.87 
 
 9.2 
 
 4 X31/2X 13/16 
 
 31.15 
 
 2.94 
 
 10.6 
 
 24.53 
 
 2.56 
 
 9.6 
 
 4 X31/2X 9/iG . 
 
 22.93 
 
 2.08 
 
 11.0 
 
 17.92 
 
 1.79 
 
 10.0 
 
 4 X 3 1/2 X 5/ 16 
 
 13.44 
 
 1.18 
 
 11.4 
 
 10.67 
 
 1.03 
 
 10.4 
 
 4 X 3 X i3/i 6 
 
 30.61 
 
 2.97 
 
 10.3 
 
 17.92 
 
 2.15 
 
 8.3 
 
 4 X 3 X 9/iii 
 
 22.40 
 
 2.09 
 
 10.7 
 
 13.12 
 
 1.51 
 
 8.7 
 
 4 X 3 X 1/4 
 
 10.67 
 
 0.96 
 
 11.1 
 
 6.40 
 
 0.70 
 
 9.1 
 
 31/2X3 X 13/16 
 
 23.47 
 
 2.57 
 
 9.1 
 
 17.60 
 
 2.17 
 
 8.1 
 
 31/2X3 X 9/16 
 
 17.17 
 
 1.81 
 
 9.5 
 
 12.91 
 
 1.52 
 
 8.5 
 
 31/2X3 X V4 
 
 8.32 
 
 0.84 
 
 9.9 
 
 6.19 
 
 0.70 
 
 8.9 
 
 3 1/2 X 2 1/2 X n/16 
 
 19.73 
 
 2.19 
 
 9.0 
 
 10.56 
 
 1.51 
 
 7.0 
 
 31/2X2 1/2 X 1/2 
 
 15.04 
 
 1.63 
 
 92 
 
 8.11 
 
 1.13 
 
 7.2 
 
 3 1/2 X 2 1/2 X 1/4 
 3 X 2 1/2 X 9/i6 
 
 3 X21/2X 7 /16 
 
 3 X 2 1/2 X 1/4 
 
 3 X2 X 1/2 
 3 X2 X 3/ 8 
 3 X2 X V4 
 
 21/2X2 X 1/2 
 21/2X2 X 5/i 6 
 
 8.00 
 
 12.27 
 9.92 
 5.97 
 
 10.67 
 8.32 
 5.76 
 
 7.47 
 5.01 
 
 0.83 
 
 1.53 
 
 1.22 
 0.71 
 
 1.39 
 1.05 
 0.71 
 
 1.15 
 0.74 
 
 9.6 
 
 8.0 
 8.1 
 8.4 
 
 7.7 
 7.9 
 8.1 
 
 6.5 
 6.8 
 
 4.37 
 
 8.75 
 7.04 
 4.27 
 
 5.01 
 3.95 
 2.77 
 
 4.91 
 3.31 
 
 0.58 
 
 1.25 
 0.99 
 0.58 
 
 0.88 
 0.67 
 0.46 
 
 0.89 
 0.57 
 
 7.6 
 
 7.0 
 7.1 
 
 7.4- 
 
 5.7 
 5.9 
 6.1 
 
 5.5 
 5.8 
 
 21/2X2 X 1/8 
 
 2.13 
 
 0.30 
 
 7.1 
 
 1.49 
 
 0.23 
 
 6.1 
 
 *21/2XH/2X 5 /16 
 
 4.69 
 
 0.73 
 
 6.4 
 
 1.81 
 
 0.41 
 
 4.4 
 
 *21/2XH/2X 3/ 16 
 
 2.99 
 
 0.45 
 
 6.6 
 
 1.17 
 
 0.25 
 
 4.6 
 
 *21/4XH/2X 1/2 
 
 5.76 
 
 1.02 
 
 5.6 
 
 2.77 
 
 0.67 
 
 4.1 
 
 *2 1/4 X 1 1/2 X 3 /16 
 
 2.45 
 
 0.40 
 
 6.0 
 
 1.17 
 
 0.25 
 
 4.6 
 
 *2 X 1 1/2 X 3/ 8 
 
 3.63 
 
 0.70 
 
 5.2 
 
 2.13 
 
 0.51 
 
 4.2 
 
 *2 X 1 V2 X 1/8 
 
 1.39 
 
 0.24 
 
 5.6 
 
 0.80 
 
 0.17 
 
 4.6 
 
 *2 X 1 1/4 X 1/4 
 
 2.45 
 
 0.47 
 
 5.2 
 
 1.04 
 
 0.28 
 
 3.7 
 
 *2 X 1 1/4 X 3/ 16 
 
 1.92 
 
 0.36 
 
 5.3 
 
 0,.80 
 
 0.21 
 
 3.8 
 
 *13/4XH/4X 1/4 
 
 1.92 
 
 0.42 
 
 4.6 
 
 1.01 
 
 0.28 
 
 3.6 
 
 *13/iXH/4X 1/8 
 
 1.00 
 
 0.21 
 
 4.8 
 
 0.56 
 
 0.15 
 
 3.8 
 
 *H/2X11/4X 5/ie 
 
 1.71 
 
 0.44 
 
 3.9 
 
 1.17 
 
 0.34 
 
 3.4 
 
 *l V2 X 1 V4 X 3/ 16 
 
 1.07 
 
 0.26 
 
 4.1 
 
 0.78 
 
 0.22 
 
 3.6 
 
 Maximum bending stress, 16,000 Ib. per sq. in. Safe loads for other 
 spans are inversely proportional to the span in feet. Safe loads include 
 the weight of the angle, which should be deducted to give net load 
 which can be carried. 
 
 * Only maximum and minimum sizes are given for angles smaller 
 than 2^x2 in. 
 
320 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Angles with Equal Legs. Minimum, Inter* 
 mediate and Maximum Thicknesses and Weights. 
 
 
 
 
 
 o o 
 
 i S* 
 
 3 G~ 
 
 3 fi"* 
 
 e-^ta 
 
 t 
 
 
 .0 
 
 
 
 o1 
 
 o1 
 
 & O>J=5 
 
 02 
 
 f Ifel 
 
 *! 
 
 3 
 
 I 
 
 I 
 
 CPO oa 
 
 .315)5 
 
 P*PH 
 
 ^')PH 
 
 y|l 
 
 *T 
 
 
 
 
 
 o5 
 
 o g| 
 
 1 g 
 
 111 
 
 '!& 
 
 2.2O-2 
 
 I 
 
 7 
 
 2 
 
 2 p 
 
 "- 1 SHH 
 
 >&'> 
 
 
 >>'> 
 
 m<ri ^ 
 
 
 l. 
 
 A 
 
 ^2 
 
 s& 
 
 5|5| 
 
 *jjl| 
 
 2-|o| 
 
 _3 o^ 
 
 
 In 
 
 
 
 o 
 
 s 
 
 B E 
 
 o S 
 
 6 
 
 ^ a "i 
 
 
 .2 
 
 % 
 
 d 
 
 PE 
 
 o||o 
 
 I'S o> o 
 
 5 -U +J -p 
 
 |!ss 
 
 1^11 
 
 Q 
 
 EH 
 
 f* 
 
 <i 
 
 Q 
 
 * 
 
 ft 
 
 
 3 
 
 8 X8 
 
 U/8 
 
 56.9 
 
 16.73 
 
 2.41 
 
 98.0 
 
 17.5 
 
 2.42 
 
 .55 
 
 8 X8 
 
 13/16 
 
 42.0 
 
 12.34 
 
 2.30 
 
 74.7 
 
 13.1 
 
 2.46 
 
 .57 
 
 8 X8 
 
 1/2 
 
 26.4 
 
 7.75 
 
 2.19 
 
 48.6 
 
 8.4 
 
 2.51 
 
 .58 
 
 6 X6 
 
 1 
 
 37.4 
 
 11.00 
 
 .86 
 
 35.5 
 
 8.6 
 
 .80 
 
 .16 
 
 6 X6 
 
 11/16 
 
 26.5 
 
 7.78 
 
 .75 
 
 26.2 
 
 6.2 
 
 .83 
 
 .17 
 
 6 X6 
 
 3/8 
 
 14.9 
 
 4.36 
 
 .64 
 
 15.4 
 
 3.5 
 
 .88 
 
 .19 
 
 5 X5 
 
 1 
 
 30.6 
 
 9.00 
 
 .61 
 
 19.6 
 
 5.8 
 
 .48 
 
 0.96 
 
 
 LI/16 
 
 21.8 
 
 6.40 
 
 .50 
 
 14.7 
 
 4.2 
 
 .51 
 
 0.97 
 
 5 X5 
 
 3/8 
 
 12.3 
 
 3.61 
 
 .39 
 
 8.7 
 
 2.4 
 
 .56 
 
 0.99 
 
 4 X4 
 
 13/16 
 
 19.9 
 
 5.84 
 
 .29 
 
 8.1 
 
 3.0 
 
 .18 
 
 0.77 
 
 4 X4 
 
 9/16 
 
 14.3 
 
 4.18 
 
 .21 
 
 6.1 
 
 2.2 
 
 .21 
 
 0.78 
 
 4 X4 
 
 
 6.6 
 
 1.94 
 
 .09 
 
 3.0 
 
 1.0 
 
 .25 
 
 0.79 
 
 31/2X31/2 
 
 13/16 
 
 17.1 
 
 5.03 
 
 .17 
 
 5.3 
 
 2.3 
 
 .02 
 
 0.67 
 
 31/2X31/2 
 
 9/16 
 
 12.4 
 
 3.62 
 
 .08 
 
 4.0 
 
 1.6 
 
 .05 
 
 0.68 
 
 31/2X31/2 
 
 V4 
 
 5.8 
 
 1.69 
 
 0.97 
 
 2.0 
 
 0.79 
 
 .09 
 
 0.69 
 
 3 X3 
 
 5/8 
 
 11.5 
 
 3.36 
 
 0.98 
 
 2.6 
 
 1.3 
 
 0.88 
 
 0.57 
 
 3 X3 
 
 7/16 
 
 8.3 
 
 2.43 
 
 0.91 
 
 2.0 
 
 0.95 
 
 0.91 
 
 0.58 
 
 3 X3 
 
 1/4 
 
 4.9 
 
 1.44 
 
 0.84 
 
 1.2 
 
 0.58 
 
 0.93 
 
 0.59 
 
 21/2X21/2 
 
 1/2 
 
 7.7 
 
 2.25 
 
 0.81 
 
 1.2 
 
 0.73 
 
 0.74 
 
 0.47 
 
 2l/2X2i/ 2 
 
 5/16 
 
 5.0 
 
 1.47 
 
 0.74 
 
 0.85 
 
 0.48 
 
 0.76 
 
 0.49 
 
 21/2X21/2 
 
 1/8 
 
 2.08 
 
 0.61 
 
 0.67 
 
 0.38 
 
 0.20 
 
 0.79 
 
 0.50 
 
 2 X2 
 
 7/16 
 
 5.3 
 
 1.56 
 
 0.66 
 
 0.54 
 
 0.40 
 
 0.59 
 
 0.39 
 
 2 X2 
 
 1/1 
 
 3.19 
 
 0.94 
 
 0.59 
 
 0.35 
 
 0.25 
 
 0.61 
 
 0.39 
 
 2 X2 
 
 1/8 
 
 1.65 
 
 0.48 
 
 0.55 
 
 0.19 
 
 0.13 
 
 0.63 
 
 0.40 
 
 13/4X13/4 
 
 7/16 
 
 4.6 
 
 1.34 
 
 0.59 
 
 0.35 
 
 0.30 
 
 0.51 
 
 0.33 
 
 13/4X1 3 /4 
 
 5/16 
 
 3.39 
 
 1.00 
 
 0.55 
 
 0.27 
 
 0.23 
 
 0.52 
 
 0.34 
 
 13/4X13/4 
 
 1/8 
 
 1.44 
 
 0.42 
 
 0.48 
 
 0.13 
 
 0.10 
 
 0.55 
 
 0.35 
 
 11/2XH/2 
 
 3/8 
 
 3.35 
 
 0.98 
 
 0.51 
 
 0.19 
 
 0.19 
 
 0.44 
 
 0.29 
 
 11/2XU/2 
 
 1/4 
 
 2.34 
 
 0.69 
 
 0.47 
 
 0.14 
 
 0.13 
 
 0.45 
 
 0.29 
 
 11/2XU/2 
 
 1/8 
 
 1.23 
 
 0.36 
 
 0.42 
 
 0.08 
 
 0.07 
 
 0.46 
 
 0.30 
 
 U/4X1V4 
 
 5/16 
 
 2.33 
 
 0.68 
 
 0.42 
 
 0.09 
 
 0.11 
 
 0.36 
 
 0.24 
 
 H/4XH/4 
 
 3/16 
 
 1.48 
 
 0.43 
 
 0.38 
 
 0.06 
 
 0.07 
 
 0.38 
 
 0.24 
 
 11/4XH/4 
 
 1/8 
 
 1.01 
 
 0.30 
 
 0.35 
 
 0.04 
 
 0.05 
 
 0.38 
 
 0.25 
 
 1 XI 
 
 1/4 
 
 1.49 
 
 0.44 
 
 0.34 
 
 0.04 
 
 0.06 
 
 0.29 
 
 0.19 
 
 1 XI 
 
 3/16 
 
 1.16 
 
 0.34 
 
 0.32 
 
 0.03 
 
 0.04 
 
 0.30 
 
 0.19 
 
 1 XI 
 
 1/8 
 
 0.80 
 
 0.23 
 
 0.30 
 
 0.02 
 
 0.03 
 
 0.31 
 
 0.19 
 
RIVET SPACING FOR STRUCTURAL WORK. 321 
 
 Safe Loads, in Thousands of Pounds, Uniformly Distributed for 
 Carnegie Equal Angles Used as Beams. 
 
 (Maximum, Intermediate and Minimum Thicknesses and Weights.) 
 
 
 
 Maximum 
 
 
 
 Maximum 
 
 
 Safe 
 
 Span, 
 
 
 Safe 
 
 Span, 
 
 Size of Angle, 
 Inches. 
 
 Load 
 One- 
 Foot 
 
 360 X De- 
 flection. 
 
 Size of Angle, 
 Inches. 
 
 Load 
 One- 
 Foot 
 
 360 XDe- 
 flection. 
 
 
 Span. 
 
 Safe 
 
 Lgth. 
 
 
 Span. 
 
 Safe 
 
 Lgth. 
 
 + 
 
 
 Load 
 
 Feet. 
 
 
 
 Load 
 
 Feet. 
 
 8 X 8 X 1 1/8 
 
 186.99 
 
 8.31 
 
 22.5 
 
 21/2X21/2X1/2 
 
 7.79 
 
 1.15 
 
 6.8 
 
 113/16 
 
 139.84 
 
 6.08 
 
 23.0 
 
 5/16 
 
 5.12 
 
 0.72 
 
 7.1 
 
 X6 XI 
 
 11/16 
 
 X4 X 13/16 
 
 89.28 
 91.41 
 65.81 
 37.65 
 61.87 
 44.80 
 25.81 
 32.11 
 
 3.82 
 5.48 
 3.85 
 2.14 
 4.55 
 3. IS 
 1.78 
 2.95 
 
 23.4 
 16.7 
 17.1 
 17.6 
 13.6 
 14.1 
 14.5 
 10.9 
 
 1/8 
 
 2 X2 X7/16 
 1/4 
 1/8 
 13/4X13/4XV16 
 5/16 
 1/8 
 11/2XH/2X3/8 
 
 2.13 
 4.27 
 2.67 
 1.39 
 3.20 
 2.45 
 1.07 
 2.03 
 
 0.29 
 0.79 
 0.46 
 0.24 
 0.68 
 0.51 
 0.21 
 0.51 
 
 7.4 
 5.4 
 5.7 
 5.8 
 4.7 
 4.8 
 5.1 
 4.0 
 
 9/16 
 
 23.36 
 
 2.07 
 
 11.3 
 
 V4 
 
 1.39 
 
 0.33 
 
 4.2 
 
 1/4 
 
 11.20 
 
 0.96 
 
 11.7 
 
 1/8 
 
 0.77 
 
 0.17 
 
 4.4 
 
 31/2X31/2X13/16 
 
 24.00 
 
 2.55 
 
 9.4 
 
 H/4X1 1/4XV16 
 
 1.17 
 
 0.36 
 
 3.3 
 
 3 X3 X 5/8 
 
 7 /16 
 V4 
 
 17.60 
 8.43 
 13.87 
 10.13 
 6.19 
 
 1.81 
 0.83 
 1.69 
 1.21 
 0.71 
 
 9.7 
 10.2 
 8.2 
 8.4 
 8.7 
 
 3/16 
 
 1/8 
 
 1 XI X 1/4 
 
 3/16 
 1/8 
 
 0.76 
 0.52 
 0.60 
 0.47 
 0.33 
 
 0.22 
 0.14 
 0.22 
 0.17 
 0.12 
 
 3.5 
 3.6 
 2.6 
 2.7 
 2.8 
 
 Maximum bending stress, 16,000 Ib. per sq. in. Safe loads for 
 
 other spans are inversely proportional to the span in feet. Safe loads 
 
 given include weight of angle which should be deducted to give net 
 
 load that can be carried. 
 
 Rivet Spacing for Structural Work. The following rules are con- 
 densed from those of the Cambria Steel Co. The minimum pitch of 
 rivets should be at least three times the diameter, and in bridge work 
 should not exceed 6 in., or 16 times the thickness of the thinnest outside 
 plate. The minimum distance between edge of any piece and the 
 center of the rivet is 11/4 in. for 3/4 and 7/g in. rivets except in bars 
 less than 21/2 in. wide. If possible this distance should be at least 
 two rivet diameters for all sizes, and should not exceed eight times the 
 thickness of the plate. The maximum pitch for flanges of girders and 
 chords carrying floors is 4 in. Where plates are in compression, the 
 maximum pitch in the lines of stress is sixteen times the plate thickness, 
 and in the line at right angles to the line of stress, thirty-two times the 
 plate thickness, except in the case of cover plates, top chords, and 
 end posts, where the maximum pitch may be forty times the plate 
 thickness. The minimum space between the rivet center and the ad- 
 jacent leg when rivets are adjacent to the corners of angles is 1/2 the 
 diameter of the head, plus 3/g in. clearance. When there is a row of 
 rivets in the adjacent leg, the 3/g in. clearance should be measured from 
 the rivet heads. 
 
 The table below, and those on page 322, give the standards adopted 
 by the American Bridge Co. for rivet spacing in structural and bridge 
 work: 
 
 Gages for Angles, Inches. 
 
 i*Pr*i 
 
 Leg 
 
 gi 
 
 g2 
 
 Max. 
 Rivet 
 
 8 
 
 41/2 
 
 3 
 
 1 1/8 
 
 7 
 
 4 
 
 21/2 
 
 1 
 
 6 
 
 31/2 
 
 21/2 
 21/4 
 
 7/8 
 
 5 
 3 
 
 2 
 
 13/4 
 
 7/8 
 
 4 
 
 21/2 
 
 31/2 
 
 3 
 
 1V4 
 
 21/2 
 13/8 
 
 2 
 
 H/8 
 
 13/4 
 
 'ft 
 
 '% 
 
 1 
 
 5/8 
 
 3/4 
 
 V2 
 
 4- 
 1 
 
 - 
 
 
 
 
 
 
 
 
 
 
 7/8 
 
 7/8 
 
 7 /8 
 
 3/4 
 
 5/8 
 
 V2 
 
 3/8 
 
 3/8 
 
 l/l 
 
 V4 
 
322 
 
 STRENGTH OF MATERIALS. 
 
 Minimum Spacing, Clearance and Stagger for Rivets. 
 
 Distance c, Inches. 
 
 
 
 CN 
 
 ~co 
 
 CN 
 
 CS 
 
 ~co 
 
 _W J 
 
 T3 
 rt 
 
 s 
 
 I 
 
 1 
 
 $ 
 S 
 
 rs 
 
 o 
 
 J 
 
 CO CO 
 
 CN CN CN en 
 
 <o a 
 
 00 2 * 
 
 en en en 
 
 Values below and to right of upper zigzag line are large enough for %-inch rivets. Values below and to right of lower 
 zigzag line are large enough for %-inch rivets. 
 
 Minimum Staeger. d. Inches. U OJ *. 
 
 k% ^ 
 $-tii } _1 
 
 i-^. %!I 
 
 l^-jjj^-2^^ 
 
 -o 
 
 rs 
 
 CO CO 
 
 CN CN CN CN 
 
 < ' 00 % 
 
 M< 00 S 
 H CO t 
 
 
 
 M 
 
 CO - 
 
 CS CS CN CN 
 
 
 
 CO 
 
 en 
 
 co 
 
 en 
 
 ^ 
 
 h en 
 
 \ 
 
 : : : : : ^ 
 
 CS 
 
 CN 
 
 CN CN CN CN 
 
 CN 
 
 CD 
 
 co 
 CS 
 
 en 
 
 cc, 
 
 en 
 
 co 
 
 en 
 
 m 
 
 o 
 
 CO 
 
 ..... CO 
 
 
 oc 
 
 CO CO CC 
 
 oo 
 
 * 
 
 2 
 
 co 
 
 
 00 
 
 CC 
 
 _ 
 
 : : : : :^^ 
 
 CS 
 
 CN CN CN CN 
 
 rs 
 
 CS 
 
 CN 
 
 CN 
 
 en en en 
 
 "" 
 
 CC 
 
 CO 
 
 - 
 
 00 
 
 ,* 
 
 S 
 
 2 
 
 en 
 
 00 
 
 en 
 
 CD 
 
 rt JO CO 
 
 
 
 rs 
 
 CN CN CN CN 
 
 CS 
 
 CN CN CN 
 
 CN 
 
 CO 
 
 
 < 
 
 CO 
 
 00 * 00 2 
 
 cc 
 
 CO ^ 
 
 
 
 Center to Center Distance (a*) of Staggered Rivets 
 
 Distance a, In 
 
 - 
 
 Values of x, In 
 
 CS 
 
 CS CN CS CN 
 
 CN 
 
 CN 
 
 N 
 
 CN 
 
 CN 
 
 CN en 
 
 ov 
 
 -C ^^" 
 
 oc 
 
 CS 
 
 co co ce 
 CN CN CS CN 
 
 CO 
 
 CN 
 
 CN 
 
 CO 
 CS 
 
 CO 
 
 CN 
 
 CN 
 
 CN en 
 
 ]H 
 
 CO 
 
 - 
 
 00< 00 2 
 
 CN CN CN 
 
 CO 
 CN 
 
 CN 
 
 CS 
 
 CS 
 
 co 
 CN 
 
 CO 
 CN 
 
 CO 
 CN 
 
 
 
 ^><>l 
 
 << ^.2 oo 
 
 CO 
 CO 
 
 <:^ ^ 
 
 cc 
 
 22. 
 
 00 ^ 00 
 
 - 
 
 CN CN 
 
 CN 
 
 CN 
 
 CN 
 
 CS 
 
 CN 
 
 CN 
 
 CS 
 
 ><J^ 
 
 1 
 
 js ^ ^js M 
 
 CS 
 
 CN 
 
 CO 
 
 CN 
 
 CC 
 
 CN 
 
 O CO 
 
 CN CN 
 
 " CO 
 
 %ff 
 
 CC 
 
 1 
 
 -5 ^ oo 
 
 2 
 
 2 
 
 CO 
 
 oo * 
 
 ^f M 
 
 
 CS 
 
 CS 
 
 CS 
 
 CN 
 
 CN 
 
 CS 
 
 CS 
 
 > 
 
 co co 
 
 CS 
 
 
 CO CO 
 
 CC 
 
 cc 
 CS 
 
 1 
 
 CO CO 
 
 10 \\co~~^ 
 
 CS 
 
 CS 
 
 CN 
 
 CS 
 
 CS 
 
 aouBJBa^ 
 uinuiiuiT\ 
 
 ;^iin 
 
 
 CO CO ^ ^ ^ ^S CO 
 
 CO 
 
 CO CO 
 
 CS 
 
 l ^ 
 
 
 - 
 
 
 
 - 
 
 CS 
 
 CS 
 
 CN 
 
 CS 
 
 CS 
 
 "UT '(X* 
 
 umuiiuij) 
 
 ^^^c^m 
 
 Distance 
 b, In. 
 
 ^ 
 
 ^^^^ 
 
 PS"" 
 
 ^ 
 
 CS 
 
 00 
 
 CS 
 
 CS 
 
 CN 
 
 CN 
 
 ' U I"^JC 
 
 [s?SS?_f 
 
 
 
 
 
PLATE AND ANGLE COLUMNS. 323 
 
 Notes on Tables of Channel and Plate and Angle Columns. 
 
 (Carnegie Steel Co.) 
 
 The tables on pages 324 to 330 give the safe loads in thousands of 
 pounds which can be imposed on channel and plate and angle columns 
 of the form and dimensions shown in the illustrations, which experience 
 has shown to be desirable for ordinary bridges and buildings. They 
 also give the moments of inertia and radii of gyration about both axes 
 of symmetry, areas of section and weights per foot without allowances 
 for rivet heads, or other details. The tables have been computed for 
 the least radius of gyration in accordance with the American Bridge Co. 
 formula for ratios of l/r up to 120, S = 19,000 - 100 l/r, in which S is 
 the axial compressive strength, Ib. per sq. in., I is the length, in., and 
 r is the radius of gyration, in. The maximum value of S is not to 
 exceed 13,000. For ratios of l/r up to 120 and for greater ratios up 
 to 200 the maximum values of S allowed are as follows : 
 
 l/r 
 
 S 
 
 l/r 
 
 S 
 
 l/r 
 
 S 
 
 l/r 
 
 S 
 
 60 
 70. 
 80 
 90 
 
 13,000 
 12,000 
 1 1 ,000 
 10,000 
 
 100 
 110 
 120 
 130 
 
 9,000 
 8,000 
 7,000 
 6.500 
 
 140 
 150 
 160 
 170 
 
 6,000 
 5,500 
 5,000 
 4,500 
 
 180 
 190 
 
 4,000 
 3,500 
 
 The values given in the table may be compared with the values given 
 by other formulae by means of the comparative table on page 286. 
 It is assumed in the tables that the loads are direct and equally dis- 
 tributed over the cross section of the column or balanced on opposite 
 sides of it. In the case of unbalanced loads bending stresses are pro- 
 duced, and the column must be so proportioned that the combined fiber 
 stresses do not exceed the allowable axial compression. (See page 296.) 
 
 The ratio l/r =120 should not be exceeded for main members under 
 heavy stress. For secondary members such as wind bracing, under 
 higher ratios, which, however, must not exceed 200, may be used. 
 
 Fig. 84 
 
 Fig. 85 
 
 Fig. 86 
 
 * ^>>> 
 
 
 (*3 
 
 [ 
 
 11'^ 
 
 
 S 
 
 
 
 
 
 
 
 Fig. 87 
 
 18-' --H 
 
 Fig. 88 
 
 ) C 
 
 Fig. 89 
 
 DIMENSIONS OF CHANNEL COLUMNS. 
 (See tables, pages 324327.) 
 
324 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads on Carnegie 10-Inch Channel Columns in Thousands 
 of Pounds. (See Figs. 83 and 84, page 323.) 
 
 k 
 
 *g 0> 
 
 d 
 
 !_ 
 
 15 
 
 20 
 
 25 
 30 
 35 
 
 15 
 20 
 
 !:;; 
 
 M c 
 
 a 
 
 ep^ 
 5 
 
 Thickness of 
 Side Plate, Ib. 
 
 Effective Length of Column, Feet. 
 
 .&..&.-&. *<jv4t| Radius of Gyr. 
 'vj'o^ui In bo Axis Parallel to 
 -UK* oj^| Side Plate. 
 
 fl'S 
 
 O Sj5 
 
 |S 
 
 ffl a 
 
 <3 
 
 1T72" 
 3.60 
 3.59 
 3.58 
 3.58 
 
 Weight per Ft. 
 Ib. 
 
 18 
 TT6 
 
 20 
 TT2 
 
 22 
 
 24 
 
 Too 
 
 181 
 
 197 
 213 
 229 
 
 26 
 
 ~95 
 170 
 
 185 
 200 
 215 
 
 28 
 
 ~89 
 159 
 
 173 
 187 
 201 
 
 30 
 
 -83 
 148 
 
 161 
 174 
 187 
 
 32 
 ~77 
 
 34 
 
 Lat. 
 
 106 
 192 
 209 
 226 
 243 
 
 72 
 
 37.8 
 
 12 
 12 
 
 5/16 
 3/8 
 
 7/16 
 1/2 
 
 213 
 
 m 
 
 252 
 271 
 152 
 286 
 305 
 324 
 343 
 
 203 
 221 
 239 
 257 
 T44 
 
 137 
 149 
 161 
 173 
 96 
 179 
 191 
 203 
 215 
 114 
 
 126 
 137 
 148 
 159 
 
 55.5 
 60.6 
 65.7 
 70.8 
 47.8 
 
 Lat. 
 
 136 128 
 
 120 112 
 
 104 
 195 
 207 
 220 
 233 
 124 
 
 88 
 164 
 174 
 185 
 196 
 103 
 
 3.66 
 
 3.55 
 
 Vl6 
 
 i/a 
 
 9/16 
 
 5/8 
 
 271 
 289 
 307 
 325 
 
 256 
 
 272 
 289 
 307 
 165 
 
 240225210 
 256240223 
 272 255 237 
 288 270 252 
 
 4.46 
 4.53 
 4.60 
 4.66 
 
 3.51 
 3.50 
 3.50 
 3.50 
 
 75.7 
 80.8 
 85.9 
 91.0 
 
 Lat. 
 
 186 
 
 176 
 
 155 
 
 145 
 
 134 
 260 
 274 
 
 3.52 
 
 3.41 
 
 57.8 
 
 12 
 12 
 12 
 
 14 
 14 
 
 9/15 
 5/8 
 
 359 
 378 
 
 339 
 357 
 
 319 
 336 
 
 300280 
 316295 
 
 241 
 253 
 
 221 
 233 
 
 201 
 212 
 
 4.45 
 4.52 
 
 3.44 
 3.44 
 
 95.9 
 101.0 
 
 9/16 
 
 5/8 
 
 392 
 411 
 
 424 
 444 
 
 370 
 388 
 
 348 
 364 
 
 326 303 
 341 318 
 
 281 
 295 
 
 259 
 271 
 276 
 289 
 87 
 
 237J 216 
 248 227 
 251 "232 
 263 243 
 
 4.33 
 4.39 
 4.22 
 4.29 
 
 3.37 
 3.37 
 
 105.9 
 111.0 
 
 9/16 
 5/8 
 
 400 
 418 
 
 375 
 392 
 
 350 
 366 
 
 325 
 341 
 ~98 
 230 
 250 
 270 
 
 301 
 315 
 "92 
 
 3.30 
 3.31 
 
 115.9 
 121.0 
 
 Lat. 
 
 116 
 
 114 
 ^252 
 275 
 298 
 |I46 
 312 
 335 
 358 
 380 
 
 109 
 251 
 273 
 295 
 
 103 
 241 
 261 
 282 
 
 81 
 T98 
 214 
 231 
 100 
 
 75 
 187 
 203 
 219 
 ~92 
 
 3.87 
 
 4.70 
 
 39.3 
 
 3/8 
 7/16 
 
 1/2 
 
 252 
 275 
 298 
 
 219 
 238 
 257 
 115 
 
 209 
 226 
 244 
 ~T08 
 255 
 272 
 290 
 308 
 ~T29 
 
 4.63 
 4.70 
 4.76 
 
 4.36 
 4.33 
 4.31 
 4.53 
 
 65.7 
 71.7 
 77.6 
 
 Lat. 
 
 153 
 
 139 
 
 131 
 
 123 
 
 3.66 
 
 49.4 
 
 7/16 
 1/2 
 9/16 
 5/8 
 
 312 
 335 
 358 
 380 
 
 308 
 330 
 352 
 374 
 
 295 
 316 
 337 
 357 
 
 282 268 
 301 287 
 321 306 
 341 324 
 
 241 
 258 
 275 
 291 
 
 228 
 243 
 259 
 274 
 
 4.52 
 4.59 
 4.66 
 4.72 
 
 4.29 
 4.27 
 4.26 
 4.24 
 
 81.7 
 87.6 
 93.6 
 99.5 
 
 25 
 
 
 Lat. 
 
 189J179 
 
 169 
 
 159 
 
 149 
 
 139 
 
 119 
 
 109 
 
 3.52 
 
 4.39 
 
 59.4 
 
 14 
 
 9/16 
 5/8 
 H/16 
 3/4 
 
 396 
 
 419 
 441 
 464 
 
 396 
 419 
 441 
 464 
 
 388 
 410 
 
 432 
 453 
 
 371 
 392 
 412 
 433 
 
 353 
 373 
 393 
 412 
 
 336 
 355 
 373 
 392 
 
 319 
 336 
 354 
 372 
 
 301 284 
 318 300 
 3351 315 
 35l| 331 
 
 4.52 
 4.58 
 4.64 
 4.70 
 
 4.22 
 4.21 
 4.20 
 4.19 
 
 103.6 
 109.5 
 115.5 
 121.4 
 
 30 
 35 
 
 
 Lat. 
 
 224J21I 
 
 199 
 
 187 
 
 174 
 
 162 
 
 149 
 
 137 
 
 125 
 
 3.42 
 
 4.28 
 
 69.4 
 "7253 
 131.4 
 137.4 
 143.3 
 149.3 
 155.2 
 
 14 
 14 
 
 H/16 
 
 3/4 
 
 13/16 
 7/8 
 15/16 
 
 480 
 
 502 
 525 
 548 
 571 
 593 
 
 480 
 502 
 525 
 548 
 571 
 593 
 
 467 446 
 488 466 
 510487 
 532; 508 
 554 529 
 575:549 
 
 424 403 
 444 421 
 464 440 
 483 459 
 503 478 
 522 496 
 
 382 
 399 
 417 
 434 
 452 
 469 
 ~479 
 496 
 514 
 532 
 549 
 567 
 
 360 
 377 
 394 
 410 
 427 
 443 
 ~45T 
 468 
 485 
 502 
 517 
 534 
 
 339 
 354 
 370 
 385 
 401 
 416 
 424 
 440 
 455 
 471 
 486 
 502 
 
 4.53 
 4.59 
 4.65 
 4.70 
 4.76 
 4.81 
 4.66 
 4.72 
 4.77 
 4.82 
 4.87 
 4.92 
 
 4.16 
 4.15 
 4.15 
 4.14 
 4.14 
 4.13 
 
 15/16 
 
 U/16 
 
 H/8 
 13/16 
 
 U/4 
 
 609 
 632 
 654 
 677 
 700 
 723 
 
 609 
 632 
 654 
 677 
 700 
 723 
 
 588 561 533 506 
 610 582 553 525 
 632 603 573 544 
 654624 593 '563 
 675 644612 581 
 697 665i 63 2 '599 
 
 4.10 
 4.10 
 4.10 
 4. IP 
 4.09 
 4.09 
 
 159.3 
 165.2 
 171.2 
 177.1 
 183.1 
 189.0 
 
 Safe loads enclosed between heavy lines are for ratios of l/r riot over 
 60; between the dotted lines are for ratios of l/r not over 200; all 
 other safe loads are for ratios l/r up to 120. Allowable fiber stress 
 13,000 Ib. for lengths of 60 radii or over. Weights do not include rivet 
 heads or other details. 
 
SAFE LOADS ON CHANNEL COLUMNS. 
 
 325 
 
 Safe Loads for Carnegie 12-Inch Channel Columns in Thousands 
 of Pounds. (See Figs. 85 and 86, page 323.) 
 
 Weight of Channel, 
 Ib. per ft. 
 
 Width of Side Plate. 
 
 Thickness of Side 
 Plate, in. 
 
 Effective Length of Column, Feet. 
 
 Radius of Gyration, 
 Axis Parallel to 
 Side Plate. 
 
 Radius of Gyration, 
 Perpendicular to 
 Side Plate. 
 
 Weight per Ft., Ib. 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 2<>y 2 
 
 25 
 30 
 
 30 
 
 - 
 
 ' 
 
 In. 
 
 Lat. 
 
 157 
 
 157| 157 
 
 152 
 
 146 
 
 139 
 
 133 
 
 126 
 
 120 
 
 4.61 
 
 4.50 
 
 50.4 
 
 14 
 
 3/8 
 7/16 
 1/2 
 9/16 
 
 5/8 
 
 Tat: 
 
 293; 293 
 316 ! 316 
 339 339 
 362 362 
 384 384 
 191 191 
 
 290 
 312 
 334 
 355 
 377 
 190 
 
 277 
 298 
 319 
 339 
 360 
 182 
 370 
 390 
 411 
 432 
 453 
 215 
 465 
 486 
 506 
 527 
 548 
 
 265 
 
 284 
 304 
 324 
 344 
 174 
 
 252 
 271 
 290 
 308 
 327 
 166 
 
 239 
 257 
 275 
 292 
 310 
 158 
 
 227 
 243 
 260 
 277 
 293 
 150 
 
 214 
 230 
 246 
 261 
 277 
 142 
 
 5.40 
 5.48 
 5.55 
 5.62 
 5.68 
 4.43 
 5.47 
 5.53 
 5.60 
 5.66 
 5.71' 
 
 4.29 
 4.27 
 4.26 
 4.24 
 4.23 
 ~4~36 
 
 76.7 
 82.7 
 88.6 
 94.6 
 100.5 
 59.4 
 
 14 
 14 
 
 9/16 
 
 5/8 
 H/16 
 
 3/4 
 
 13/16 
 
 396 
 
 419 
 441 
 464 
 487 
 
 396 
 
 419 
 441 
 464 
 487 
 
 387 
 409 
 431 
 .453 
 474 
 ^25 
 
 352 
 372 
 392 
 412 
 431 
 
 335 
 354 
 372 
 391 
 410 
 195 
 
 318 
 335 
 353 
 371 
 388 
 
 300 
 317 
 333 
 350 
 367 
 175 
 375 
 392 
 408 
 425 
 442 
 
 283 
 298 
 314 
 330 
 345 
 165 
 352 
 368 
 383 
 399 
 415 
 
 4.20 
 4.19 
 4.18 
 4.18 
 4.17 
 ~T.23~ 
 4.13 
 4.13 
 4.12 
 4.12 
 4.12 
 
 103.6 
 109.5 
 115.5 
 121.4 
 127.4 
 69.4 
 131.4 
 137.4 
 143.3 
 149.3 
 155.2 
 "7974 
 
 Lat. 
 
 ~3/T 
 13/16 
 7/8 
 15/16 
 
 229| 229 
 
 205 
 
 185 
 
 4.28 
 
 502 
 525 
 
 548 
 571 
 593 
 268 
 
 502 
 525 
 548 
 571 
 593 
 
 487 
 509 
 531 
 553 
 575 
 
 442 
 462 
 482 
 502 
 522 
 
 420 
 439 
 457 
 476 
 495 
 
 397 
 415 
 432 
 450 
 468 
 
 5.52 
 5.58 
 5.64 
 5.70 
 5.75 
 4.17 
 
 Lat. 
 
 268 
 609 
 632 
 654 
 677 
 700 
 723 
 745 
 768 
 791 
 814 
 
 259 
 587 
 609 
 631 
 653 
 674 
 695 
 717 
 739 
 761 
 783 
 
 248 
 
 236 
 
 224 
 
 212 
 477 
 494 
 512 
 530 
 547 
 564 
 582 
 600 
 618 
 635 
 
 200 
 
 188 
 
 4.13 
 
 H 
 
 15/16 
 
 1/16 
 
 1/8 
 3/16 
 1/4 
 5/16 
 3/8 
 7/16 
 1/2 
 
 609 
 632 
 654 
 677 
 700 
 723 
 745 
 768 
 791 
 814 
 
 559 
 580 
 601 
 622 
 642 
 663 
 684 
 704 
 725 
 746 
 
 532 
 552 
 571 
 591 
 610 
 630 
 650 
 670 
 689 
 709 
 
 504 
 523 
 542 
 561 
 578 
 597 
 616 
 635 
 654 
 672 
 
 599 
 622 
 646 
 669 
 693 
 703 
 726 
 750 
 773 
 797 
 820 
 844 
 867 
 891 
 914 
 937 
 961 
 985 
 1007 
 
 449 
 466 
 483 
 499 
 515 
 532 
 548 
 565 
 582 
 599 
 
 421 
 437 
 453 
 469 
 483 
 499 
 515 
 530 
 546 
 562 
 
 5.50 
 5.64 
 5.69 
 5.74 
 5.80 
 5.85 
 5.89 
 5.94 
 5.99 
 6.04 
 
 4.03 
 4.08 
 4.08 
 4.08 
 4.07 
 4.07 
 4.07 
 4.07 
 4,07 
 4.07 
 
 159.3 
 165.2 
 171.2 
 177.1 
 183.1 
 189.0 
 195.0 
 200.9 
 206.9 
 212.8 
 
 16 
 
 15/16 
 
 1/16 
 
 1/8 
 3/16 
 
 1/4 
 
 619 
 645 
 671 
 697 
 723 
 749 
 
 619 
 645 
 671 
 697 
 723 
 749 
 762 
 788 
 814 
 840 
 866 
 892 
 918 
 944 
 970 
 996 
 1022 
 1048 
 1074 
 1100 
 
 619 
 645 
 671 
 697 
 723 
 749 
 ~762 
 788 
 814 
 840 
 866 
 892 
 918 
 944 
 970 
 996 
 1022 
 1048 
 1074 
 |I100 
 
 619 
 645 
 671 
 697 
 723 
 749 
 762 
 
 599 
 623 
 648 
 673 
 697 
 721 
 ~732 
 756 
 781 
 805 
 830 
 854 
 879 
 903 
 928 
 953 
 977 
 1002 
 1027 
 1050 
 
 552 
 574 
 596 
 619 
 642 
 664 
 674 
 696 
 719 
 741 
 764 
 785 
 808 
 830 
 853 
 876 
 897 
 920 
 943 
 965 
 
 528 
 549 
 571 
 593 
 614 
 635 
 644 
 665 
 687 
 708 
 730 
 751 
 773 
 794 
 815 
 837 
 858 
 880 
 901 
 922 
 
 504 
 525 
 545 
 566 
 56 
 606 
 
 5.76 
 5.81 
 5.87 
 5.92 
 5.97 
 6.01 
 ~5~.~87~ 
 5.91 
 5.96 
 6.01 
 6.06 
 6.10 
 6.15 
 6.19 
 6.24 
 6.28 
 6.32 
 6.36 
 6.41 
 6.45 
 
 4.85 
 4.84 
 4.83 
 4.83 
 4.82 
 4.81 
 
 162.0 
 168.8 
 175.6 
 182.4 
 189.2 
 196.0 
 199.2 
 206.0 
 212.8 
 219.6 
 226.4 
 233.2 
 240.0 
 246.8 
 253.6 
 260.4 
 267.2 
 274.0 
 280.8 
 287.6 
 
 16 
 
 3/16 
 1/4 
 
 5/16 
 3/8 
 7/16 
 1/2 
 9/16 
 5/8 
 111/16 
 1 3/4 
 113/16 
 7/8 
 H5/16 
 
 762 
 788 
 814 
 840 
 866 
 892 
 918 
 944 
 970 
 996 
 1022 
 1048 
 1074 
 HOC 
 
 615 
 635 
 656 
 676 
 697 
 716 
 737 
 757 
 778 
 799 
 818 
 839 
 860 
 879 
 
 4.80 
 4.79 
 4.79 
 4.78 
 4.78 
 4.77 
 4.77 
 4.76 
 4.76 
 4.76 
 4.75 
 4.75 
 4.75 
 4.74 
 
 787 
 813 
 838 
 864 
 889 
 915 
 940 
 966 
 992 
 1017 
 1042 
 1068 
 1093 
 
 Safe loads enclosed between heavy lines are for ratios of l/r not 
 over 60; all others are for ratios l/r not over 120. Allowable fiber stress 
 13,000 Ib. for lengths of 60 radii or over. Weights do not include rivet 
 head or other details. 
 
326 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads on 15-Inch Carnegie Channel Columns in .Thousands 
 of Pounds.* (See Figs. 87 and 88, page 323.) 
 
 si 
 
 I 
 
 
 
 u 
 
 *o 
 
 +9 
 
 S 
 
 
 Width of Side Plate, in. 
 
 Thickness of Side 
 Plate, in. 
 
 Effective Length of Column, Feet. 
 
 Radius of Gyration, Axis 
 Parallel to Side Plate. 
 
 Radius of Gyration, 
 Axis Perpendicular to 
 Side Plate. 
 
 
 
 
 
 & 
 
 a 
 
 ! 
 1 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 33 
 
 16 
 
 Lat. 
 
 257 
 413 
 439 
 465 
 491 
 517 
 
 257 
 
 257 
 
 257 
 
 252 
 "400 
 424 
 448 
 473 
 498 
 
 243 
 384 
 407 
 431 
 454 
 478 
 
 251 
 
 233 
 368 
 390 
 413 
 435 
 458 
 
 224 
 352 
 3/3 
 395 
 416 
 438 
 
 231 
 
 214 
 
 5.62 
 6.48 
 6.57 
 6.66 
 6.74 
 6.81 
 
 4.98 
 4.85 
 4.83 
 4.82 
 4.81 
 4.80 
 
 80.2 
 106.8 
 113.6 
 120.4 
 127.2 
 134.0 
 
 3/8 
 7/16 
 1/2 
 9/16 
 
 V8 
 
 413 
 439 
 465 
 491 
 517 
 
 413 
 439 
 465 
 491 
 
 1 
 
 268 
 528 
 554 
 580 
 606 
 632 
 
 306 
 
 413 
 439 
 465 
 491 
 517 
 
 337 
 357 
 
 377 
 398 
 
 418 
 
 ~22? 
 
 35 
 
 40 
 
 45 
 
 16 
 
 Lat. 
 
 268 
 "328 
 554 
 580 
 606 
 632 
 
 268 
 528 
 554 
 580 
 606 
 632 
 
 268 
 [517 
 552 
 578 
 604 
 629 
 
 "306 
 
 261 
 
 241 
 
 5.58 
 
 4.95 
 
 84.2 
 
 5/8 
 H/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 LaT 
 
 507 
 531 
 555 
 580 
 605 
 
 295 
 
 486 
 510 
 533 
 557 
 580 
 
 466 
 488 
 511 
 533 
 556 
 
 272 
 
 446 
 467 
 488 
 510 
 531 
 
 260 
 
 425 
 446 
 466 
 487 
 507 
 
 ~249 
 
 6.77 
 6.84 
 6.91 
 6.98 
 7.04 
 
 5743 
 
 4.79 
 4.78 
 4.77 
 4.77 
 4.76 
 
 138.0 
 144.8 
 151.6 
 158.4 
 165.2 
 
 306 
 
 306 
 
 284 
 
 4.84 
 
 92.1 
 
 16 
 
 13/16 
 
 V8 
 15/13 
 
 11/16 
 
 H/8 
 
 644 
 670 
 696 
 722 
 748 
 774 
 
 644 
 670 
 696 
 722 
 748 
 774 
 
 644 
 670 
 696 
 722 
 748 
 774 
 
 344 
 
 639 
 665 
 690 
 715 
 741 
 767 
 
 614 
 638 
 663 
 687 
 712 
 737 
 
 589 
 612 
 636 
 659 
 683 
 706 
 
 316 
 715 
 738 
 761 
 785 
 808 
 832 
 856 
 879 
 
 564 
 586 
 609 
 631 
 653 
 676 
 
 ^302 
 -684 
 705 
 728 
 751 
 773 
 796 
 818 
 841 
 
 539 
 560 
 581 
 602 
 624 
 646 
 
 5146.85 
 5346.91 
 5546.97 
 57417.03 
 595 7.09 
 615 7.15 
 
 4.73 
 4.72 
 4.72 
 4.71 
 4.71 
 4.71 
 
 168.4 
 175.2 
 182.0 
 188.8 
 195.6 
 202.4 
 
 16 
 
 Lat. 
 
 344| 344 
 
 343 
 
 329 
 
 289 
 "653 
 673 
 695 
 716 
 738 
 760 
 781 
 803 
 
 276 
 
 5.32 
 
 4.75 
 
 102.2 
 
 H/16 
 
 H/8 
 13/15 
 H/4 
 15/16 
 13/8 
 17/16 
 H/2 
 
 786 
 812 
 838 
 864 
 890 
 916 
 942 
 968 
 
 786 
 812 
 838 
 864 
 890 
 916 
 942 
 968 
 
 786 
 812 
 838 
 864 
 890 
 916 
 942 
 968 
 
 777 
 802 
 827 
 853 
 879 
 904 
 930 
 956 
 
 746 
 770 
 794 
 819 
 844 
 868 
 893 
 918 
 
 622 
 641 
 662 
 682 
 703 
 723 
 744 
 764 
 
 6.98 
 7.04 
 7.09 
 7.15 
 7.20 
 7.25 
 7.30 
 7.35 
 
 4.68 
 4.67 
 4.67 
 4.67 
 4.67 
 4.67 
 4.67 
 4.67 
 
 205.6 
 212.4 
 219.2 
 226.0 
 232.8 
 239.6 
 246.4 
 253.2 
 
 33 
 
 18 
 
 3/8 
 7/16 
 1/2 
 9/16 
 
 5/8 
 
 433 
 462 
 491 
 521 
 550 
 
 433 
 462 
 491 
 521 
 550 
 
 433' 
 462 
 491 
 521 
 550 
 
 433 
 462 
 491 
 521 
 550 
 
 433 433 
 462 462 
 491 491 
 
 421 
 449 
 476 
 503 
 530 
 
 407 
 433 
 459 
 486 
 512 
 
 3936.54 
 4186.63 
 4436.72 
 46916.80 
 4946.87 
 
 5.67 
 5.64 
 5.61 
 5.59 
 5.57 
 
 111.9 
 119.6 
 127.2 
 134.9 
 142.5 
 
 521 
 550 
 
 520 
 549 
 
 35 
 
 18 
 
 5/8 
 H/16 
 3/4 
 13/16 
 7/8 
 
 560 
 589 
 619 
 648 
 677 
 
 560 
 589 
 619 
 648 
 677 
 
 560 
 589 
 619 
 648 
 677 
 
 560 
 589 
 619 
 648 
 677 
 
 560 
 589 
 619 
 648 
 677 
 
 558 
 586 
 615 
 643 
 671 
 
 680 
 708 
 736 
 764 
 793 
 821 
 
 540 
 567 
 594 
 621 
 649 
 
 521 
 
 547 
 574 
 599 
 626 
 
 502 
 527 
 553 
 578 
 603 
 
 6.84 
 6.91 
 6.98 
 7.04 
 7.10 
 
 5.56 
 5.54 
 5.53 
 5.51 
 5.50 
 
 146.5 
 154.2 
 161.8 
 169.5 
 177.1 
 
 40 
 
 18 
 
 13/16 
 
 7/8 
 15/16 
 
 1 1/16 
 1 1/8 
 
 686 
 715 
 745 
 774 
 803 
 832 
 
 686 
 715 
 745 
 774 
 803 
 832 
 
 686 
 715 
 745 
 774 
 803 
 832 
 
 686 
 715 
 745 
 774 
 803 
 832 
 
 686 
 715 
 
 745 
 774 
 803 
 832 
 
 657 
 684 
 711 
 738 
 766 
 793 
 
 634 
 660 
 685 
 712 
 738 
 764 
 
 6106.92 
 6366.98 
 660 7.04 
 685 7.10 
 711 7.16 
 73617.21 
 
 5.49 
 5.48 
 5.46 
 5.45 
 5.45 
 5.44 
 
 179.5 
 187.1 
 194.8 
 202.4 
 210.1 
 1217.7 
 
 * Table continued on next page. See' note at foot of page. 
 
SAFE LOADS ON CHANNEL COLUMNS. 
 
 327 
 
 Safe Loads on 15-Inch Carnegie Channel Columns in Thousands 
 of Pounds.* (See Figs. 87 and 88, page 323 . ) 
 
 1 
 
 . 
 
 3 
 
 
 Effective Length of Column, Feet. 
 
 .2 
 
 S 
 
 
 
 
 
 
 
 
 
 
 ;2 
 
 
 
 r 
 
 
 
 
 
 
 
 
 
 
 .2 & 
 
 .2 3 
 
 j2 
 
 g 
 
 s 
 
 0) 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 II 
 
 si . 
 
 J 
 
 & 
 
 T3 
 
 *o . 
 
 
 
 
 
 
 
 
 
 
 r*? ^ 
 
 O Cn 4 -* 
 
 >*4 
 
 u 
 
 W 
 
 $- s 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 'S'S 
 
 
 
 a 
 
 IL 
 
 O 
 
 3 
 
 Is 
 
 
 
 
 
 
 
 
 
 
 ll 
 
 ||| 
 
 ta 
 '3 
 
 
 
 
 
 H 
 
 
 
 
 
 
 
 
 
 
 & 
 
 
 
 
 
 
 1/16 
 
 841 
 
 841 
 
 841 
 
 841 
 
 841 
 
 829 
 
 800 
 
 771 
 
 743 7.05 
 
 5.42 
 
 220.1 
 
 
 
 1/8 
 
 871 
 
 871 
 
 871 
 
 871 
 
 871 
 
 857 
 
 828 
 
 798 
 
 7687.11 
 
 5.42 
 
 227.7 
 
 
 
 3/16 
 
 900 
 
 900 
 
 900 
 
 900 
 
 900 
 
 885 
 
 855 
 
 824 
 
 793 7.17 
 
 5.41 
 
 235.4 
 
 
 
 1/4 
 
 929 
 
 929 
 
 929 
 
 929 
 
 929 
 
 913 
 
 882 
 
 850 
 
 8187.22 
 
 5.40 
 
 243.0 
 
 
 
 5/16 
 
 958 
 
 958 
 
 958 
 
 958 
 
 958 
 
 942 
 
 909 
 
 877 
 
 844 7.27 
 
 5.40 
 
 250.0 
 
 
 
 3/8 
 
 988 
 
 988 
 
 988 
 
 988 
 
 988 
 
 970 
 
 936 
 
 902 
 
 86817.32 
 
 5.39 
 
 258.3 
 
 45 
 
 18 
 
 7/16 
 
 1017 
 
 1017 
 
 1017 
 
 1017 
 
 1017 
 
 998 
 
 963 
 
 928 
 
 893 
 
 7.37 
 
 5.38 
 
 266.0 
 
 
 
 1/2 
 
 1046 
 
 1046 
 
 1046 
 
 1046 
 
 1046 
 
 1026 
 
 991 
 
 955 
 
 919 
 
 7.42 
 
 5.38 
 
 273.6 
 
 
 
 9/16 
 
 1075 
 
 1075 
 
 1075 
 
 1075 
 
 1075 
 
 1054 
 
 1017 
 
 980 
 
 943 7.47 
 
 5.37 
 
 281.3 
 
 
 
 5/8 
 
 1105 
 
 1105 
 
 1105 1105 
 
 1105 
 
 1083 1045 
 
 1007 
 
 969:7.52 
 
 5.37 
 
 288.9 
 
 
 
 H/16 
 
 1134 
 
 1134 
 
 1134 1134 
 
 1134 
 
 1112 1073 
 
 1034 
 
 995 7.57 
 
 5.37 
 
 296.6 
 
 
 
 3/4 
 
 1163 
 
 1163 1163 
 
 1163 
 
 1163 
 
 1139 
 
 1099 1059 
 
 101917.61 
 
 5.36 
 
 304.2 
 
 
 
 7 /8 
 
 1222 
 
 1222 1222 
 
 1222 
 
 1222 
 
 1195 
 
 1153 1111 106917.70 
 
 5.35 
 
 319.5 
 
 
 
 2 
 
 1280 1280 1280 
 
 1280 
 
 1280 
 
 1253 
 
 1208 1164 112017.79 
 
 5.35 
 
 334.8 
 
 Safe 
 
 Loads on 15-Inch Carnegie Channel Columns with Flange Plates 
 in Thousands of Pounds.* (See Fig. 89, page 323.) 
 
 Weight of Chan., Ib. per ft. 
 
 Width of Side Plate, in. 
 
 Thickness of Side Plate, in. 
 
 Width of Web Plate, in. 
 
 Thickness of Web Plate, in. 
 
 Effective Length of Column, Feet. 
 
 Radius of Gyration, Axis 
 Parallel to Side Plate. 
 
 Radius of Gyration, Axis 
 Perpendicular to Side Plate 
 
 Weight per Ft., Ib. 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 -34 
 
 35 
 45 
 
 18 
 
 2 
 
 14 
 
 3/8 
 9/16 
 
 1340 
 1408 
 
 1340 
 1408 
 
 1340 
 1408 
 
 1340 
 1408 
 
 1340 
 1408 
 
 1307 
 1369 
 
 1261 
 1320 
 
 1214 
 1270 
 
 1168 
 1221 
 
 7.65 
 7.52 
 
 5.32350.5 
 5.28368.4 
 
 18 
 
 2 
 
 14 
 
 9/16 
 
 1485 
 
 1485 
 
 1485 
 
 1485 
 
 1485 
 
 1439 
 
 1387 
 
 1335 
 
 1283 
 
 7.39 
 
 5.25 
 
 388.4 
 
 20 
 
 17/8 
 
 21/8 
 21/4 
 23/8 
 21/2 
 25/8 
 23/4 
 27/8 
 
 14 
 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 5/8 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1547 
 1612 
 1677 
 1742 
 1807 
 1872 
 1937 
 2002 
 2067 
 2132 
 
 1543 
 1607 
 1670 
 1735 
 1798 
 1863 
 1926 
 1991 
 2054 
 2118 
 
 1495 
 1557 
 1618 
 1681 
 1742 
 1805 
 1866 
 1929 
 1989 
 2052 
 
 1447 
 1507 
 1566 
 1627 
 1686 
 1747 
 1806 
 1866 
 1925 
 1985 
 
 7.33 
 7.43 
 7.52 
 7.61 
 7.70 
 7.79 
 7.88 
 7.97 
 8.05 
 8.13 
 
 5.97 
 5.96 
 5.95 
 5.95 
 5.94 
 5.94 
 5.93 
 5.93 
 5.92 
 5.92 
 
 404.5 
 421.5 
 438.5 
 455.5 
 472.5 
 489.5 
 506.5 
 523.5 
 540.5 
 557.5 
 
 *Safe load values enclosed within the heavy lines are for ratios of 
 l/r not over 60; all others are for ratios of l/r not over 120. Allowable 
 fiber stress per sq. in., 13,000 Ib. for lengths of 60 radii or over. Weights 
 do not include rivet heads OP other details, 
 
328 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads on Carnegie Plate and Angle Columns In 
 Thousands of Pounds.* 
 
 Web + ) for 
 |2'kngle Leg; 
 
 *|~\ 
 
 + 3 
 
 22 / 
 
 sy 
 
 Angle 
 
 r 
 
 }=> 
 
 s. 
 
 Web 
 Plate. 
 
 Effective Length in Feet. 
 
 Radius of Gyration, 
 Axis Perpendicular 
 to Web Plate. 
 
 13 
 || 
 
 P-IP 
 
 | 23-C 
 ^'<$ 
 
 I Weight, Pounds 
 
 per Foot. j 
 
 a 
 
 
 
 ii 
 
 s 
 
 H 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 2 V2X2 X 1/4 
 3 X2 X V4 
 3 X2 1/2XV4 
 
 6 
 8 
 
 8 
 
 69 
 
 1/4 flf 
 ! 88 
 
 56 
 
 72 
 76 
 
 43 
 60 
 63 
 
 |J3, 
 
 49 
 50 
 
 El 
 
 62 
 70 
 85 
 
 28 
 40 
 42 
 "43 
 52 
 57 
 70 
 
 22 
 34 
 
 I 
 I 
 
 60 
 
 
 
 
 
 2.45 
 2.50 
 2.51 
 
 .04 
 .28 
 .24 
 .19 
 .23 
 .44 
 .49 
 
 19.6 
 21.5 
 
 23.1 
 24.5 
 29.2 
 26.4 
 31.2 
 32. S 
 37.2 
 37.3 
 42. f 
 
 29 
 29 
 28 
 36 
 43 
 52 
 
 23 
 
 22 
 
 28 
 36 
 45 
 47 
 55 
 63 
 74 
 
 "77 
 
 88 
 100 
 
 
 
 
 
 3 X2 1/2X 1/4 
 3 X2 1/2XV16 
 3 1/2X2 1/2X 1/4 
 
 31/2X21/2XV16 
 
 rJRJ 79 65 
 l /4 p70| 95 78 
 101 1 96 83 
 j 1191115 100 
 1 125J120 104 
 6/1B l H2J138 121 
 j WlllfifZB 
 161 16l!l49 
 
 
 
 3.35 
 3.38 
 3.41 
 3.43 
 
 30 
 _38 
 39 
 47 
 55 
 66 
 
 1! 
 
 89 
 
 23 
 30 
 31 
 38 
 48 
 57 
 
 "59 
 
 68 
 78 
 
 31/2X21/2X 5/16 
 3 1/2X2 V2X 3 /8 
 
 4 X3 X 5/i6 
 4 X3 X 3/8 
 
 89 
 104 
 113 
 131 
 
 73 
 86 
 97 
 114 
 
 62 
 73 
 81 
 97 
 
 54 
 
 64 
 
 71 
 83 
 
 3.38 
 3.40 
 3.35 
 
 3.36 
 
 .47 
 .51 
 .67 
 .71 
 
 4 
 4 
 4 
 
 X3 
 X3 
 X3 
 
 X3/8 
 X7/16 
 XV2 
 
 8 
 
 168 168 
 3/8 188 188 
 '208208 
 
 154 
 175 
 196 
 
 136 118 
 155 135 
 174 152 
 
 100 
 114 
 130 
 
 86 
 98 
 110 
 
 3.33 
 3.34 
 3.33 
 
 .70 
 1.73 
 1.77 
 
 44.2 
 49.4 
 54.6 
 
 3 X2 1/2X1/4 
 
 31/2X31/2XV4 
 31/2X21/2X5/16 
 "3 1/2X2 1/2X 5/16 
 
 4 X3 X 5/16 
 4 X3 X 3/s 
 
 10 
 10 
 
 10 
 
 V4 
 5/16 
 
 
 Effective Length in Feet. 
 
 
 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 82 
 100 
 119 
 125 
 
 749 
 |J70 
 1 178 
 1198 
 '207 
 232 
 [236 
 1266 
 1296 
 
 66 
 86 
 103 
 108 
 133 
 154 
 160 
 181 
 
 '207 
 
 232 
 
 236 
 '266 
 296 
 312 
 341 
 
 ! 386 
 89 
 106 
 J131 
 
 52 
 71 
 87 
 91 
 116 
 135 
 140 
 160 
 194 
 220 
 23b 
 266 
 296 
 312 
 341 
 37C 
 386 
 
 44 
 
 57 
 
 TT 
 
 73 
 99 
 117 
 121 
 138 
 175 
 200 
 226 
 |257 
 |288 
 1302 
 1333 
 363 
 
 36 
 50 
 61 
 
 M 
 
 82 
 98 
 101 
 116 
 157 
 180 
 209 
 238 
 267 
 -280 
 309 
 337 
 351 
 
 28 
 43 
 53 
 55 
 
 73 
 85 
 88 
 101 
 
 36 
 45 
 
 47 
 64 
 76 
 78 
 90 
 
 29 
 37 
 ~38 
 56 
 67 
 68 
 79 
 107 
 123 
 
 
 
 4.16 
 4.23 
 4.28 
 4.20 
 4.18 
 4.22 
 
 1.15 
 
 .39 
 .45 
 .42 
 .62 
 .67 
 
 26.5 
 28.1 
 32. S 
 35.1 
 39.4 
 44.6 
 46 .f 
 52. ( 
 54.4 
 60. 
 62. C 
 70. ( 
 77. t 
 
 30 
 
 47 
 57 
 
 39 
 48 
 48 
 57 
 
 ,S 
 
 126 
 144 
 164 
 
 4 
 4 
 5 
 5 
 6 
 .6 
 6 
 
 X3 X 3/8 
 X3 X Vie 
 X3 1/2X 3/8 
 X3 1/2X Vl6 
 
 X4 X 3 /8 
 X4 X 7/16 
 X4 X V2 
 
 3/8 
 
 58 
 68 
 98 
 113 
 
 4.17 
 4.19 
 4.18 
 4.20 
 4.19 
 4.20 
 4.20 
 
 .65 
 .69 
 2.10 
 2.15 
 2.56 
 2.61 
 2.65 
 
 139 
 160 
 192 
 220 
 247 
 258 
 285 
 312 
 
 121 
 140 
 175 
 201 
 226 
 
 158 
 182 
 206 
 
 141 
 163 
 185 
 ~T92 
 214 
 236 
 "245 
 
 6 
 6 
 6 
 
 X4 
 X4 
 X4 
 
 XV2 
 X/16 
 X5/8 
 
 10 
 
 [312 
 1/2 341 
 
 370 
 
 236 
 262 
 287 
 
 214 
 238 
 261 
 "272 
 
 170 
 191 
 210 
 
 4.14 
 4.15 
 4.15 
 
 2.62 
 2.66 
 2.69 
 
 81. t 
 89.4 
 97. C 
 
 6 
 
 X4 
 
 X5/8 
 
 10 5/8 
 
 1336 
 
 J7ol 
 
 Ls 
 
 I 148 
 Tl"7 
 
 UZ2 
 
 |378 
 
 3251298 
 
 218 
 
 4.10 
 
 2.68 
 
 101.: 
 
 "29. 1 
 34.6 
 
 39. ( 
 
 31/2X21/2X 1/4 
 3 1/2X2 1/2X 5/16 
 4 X3 X 5/i6 
 
 12 
 12 
 
 1/4 
 5/1(3 
 
 73 
 89 
 114 
 
 ]59j 52 
 72(63 
 97J80 
 
 44 
 54 
 
 3 71 
 
 T5 
 j 87 
 
 36 
 45 
 63 
 
 28 
 37 
 55 
 "56 
 67 
 
 
 
 5.04 
 5.11 
 5.09 
 
 .35 
 
 .41 
 .61 
 
 46 
 ~47 
 57 
 
 38 
 
 ~38 
 47 
 
 4 
 4 
 
 X3 
 X3 
 
 X Vl6 
 X3/8 
 
 |138 
 (159 
 
 120 
 139 
 
 101Q4 
 119199 
 
 65 
 77 
 
 5.01 
 5.06 
 
 .58 
 .63 
 
 41. t 
 46.6 
 
 *Safe loads enclosed within dotted lines are for ratios of l/r of not 
 over 60. Those enclosed within heavy lines are for ratios of l/r not 
 over 200. All others are for ratios of l/r up to 120. Allowable fiber 
 stress 13,000 Ib. per sq. in. for lengths of 60 radii or less. Eack column 
 consists of four angles and one web plate. AVeights given do not 
 include rivet heads or other details, 
 
SAFE LOADS ON PLATE AND ANGLE COLUMNS. 329 
 
 Safe Loads on Carnegie Plate and Angle Columns in 
 Thousands of Pounds. Continued. 
 
 &$' 
 **1 
 
 ^" C TlT 
 *J ^ 
 
 lii 
 
 i .jt~~~^ 
 
 Angle 
 
 r 
 u 
 
 Web 
 Plate. 
 
 Effective Length in Feet. 
 
 Radius of Gyration, 
 Axis Perpendicular 
 to Web Plate. 
 
 1- 
 
 *%* 
 
 1 
 
 51 
 
 Is. 
 
 
 + To 
 
 .0 5 
 
 &** 
 
 P a*_\ 
 
 A 
 TJ 
 g 
 
 & 18 
 
 O <p 
 
 3 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 |ia 
 
 |n 
 
 s. 
 
 4 
 5 
 
 5 
 6 
 6 
 
 X3 X 3/8 
 X3 1/2X 3/8 
 X31/2X Vl6 
 X3 1/2XV2 
 
 X4 X Vl6 
 X4 X 1/2 
 
 12 
 
 J 187 
 
 217 
 
 3/8 I |g 
 1276 
 j 305 
 
 167 
 
 145 
 201 
 226 
 252 
 2/6 
 305 
 
 124 
 181 
 205 
 229 
 264 
 295 
 
 102] 
 162 
 184 
 206 
 
 244 
 274 
 
 -9i|~5o 
 
 69 
 110 
 125 
 141 
 
 58 
 100 
 114 
 129 
 
 "IS 
 91 
 104 
 118 
 147 
 166 
 173 
 "797 
 213 
 234 
 254 
 162 
 172 
 
 4.99 
 5.02 
 5.05 
 5.07 
 5.06 
 5.07 
 
 1.61 
 2.06 
 2.10 
 2.15 
 2.56 
 2.61 
 
 49.3 
 56.9 
 63.3 
 69.7 
 72.5 
 80.1 
 
 217 
 242 
 266 
 276 
 305 
 
 142 
 162 
 
 184 
 224 
 252 
 
 123 
 141 
 161 
 204 
 230 
 
 184 
 209 
 118 
 242 
 266 
 290 
 314 
 ~325 
 
 164 
 187 
 
 6 
 6 
 6 
 6 
 6 
 
 X4 
 X4 
 X4 
 X4 
 X4 
 
 X V2 
 X 9 /16 
 X5/8 
 X/16 
 X3/4 
 
 12 
 
 V2 
 
 325 
 354 
 383 
 
 43_9 
 458 
 
 325 
 354 
 383 
 411 
 439 
 
 325 
 354 
 383 
 411 
 439 
 
 312 
 342 
 373 
 403 
 43_3 
 451 
 
 288 
 317 
 346 
 375 
 403 
 419 
 
 265 
 
 292 
 319 
 347 
 373 
 
 388 
 
 242 
 
 267 
 293 
 318 
 344 
 
 195 
 217 
 239 
 262 
 284 
 194 
 ~305 
 
 !4.99 
 5.01 
 5.02 
 5.01 
 5.01 
 
 2.57 
 2.61 
 2.65 
 2.69 
 2.72 
 
 85.2 
 92 R 
 100 \ 
 107.6 
 114.8 
 
 6 
 
 X4 
 
 X3/4 
 
 12 
 12 
 
 5/8 
 3/4 
 
 458 
 
 458 
 
 357 
 
 4.96 
 
 2.70 
 
 119 ^ 
 
 6 
 
 X4 
 
 X3/4 
 
 1478 
 
 478 
 
 478|469 436 
 
 403 
 
 370 338 
 
 4.91 
 
 2.69 
 
 125 3 
 
 Safe loads enclosed within dotted lines are for ratios of l/r of not over 
 60. Those enclosed within heavy lines are for ratios of l/r not over 200. 
 All others are for ratios of l/r up to 120. Allowable fiber 
 
 stress 13,000 Ib. per sq. in. for lengths of 60 radii or less. t-r-T^ ^~ 
 
 Each column consists of four angles and one web plate. 3Sr 
 Weights given do not include rivet heads or other details. + 
 
 Safe Loads on Carnegie Plate and Angle Columns 
 with Side Plates in Thousands of Pounds. 
 
 Angles. 
 
 Web 
 Plate. 
 
 Side 
 Plates. 
 
 Effective Length in Feet. 
 
 RadiusofGyration, 
 Axis Perpendic- 
 ular to Web Plate. 
 
 RadiusofGyration, 
 Axis Parallel to 
 Web Plate. 
 
 Weight, Pounds 
 per Foot. 
 
 
 d 
 
 P 
 
 -^ 
 
 13 
 H 
 
 JS 
 
 S 
 
 iS 
 
 1 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 ~289 
 334 
 355 
 377 
 
 26 
 
 28 
 
 30 
 
 6X4X 3/8 
 6X4X 3/8 
 6X4X 7/16 
 6X4X 1/2 
 
 12 
 12 
 12 
 
 3/8 
 
 1/2 
 
 5/8 
 
 14 
 
 3/8 
 1/2 
 V2 
 1/2 
 
 379 
 
 "428 
 458 
 487 
 
 I ! 
 553 
 582 
 610 
 '630 
 675 
 721 
 766 
 
 357 
 
 407 
 434 
 461 
 
 334 
 383 
 407 
 433 
 447 
 495 
 520 
 544 
 
 312 
 358 
 381 
 405 
 417 
 463 
 487 
 509 
 
 267 
 310 
 329 
 349 
 
 244 
 285 
 303 
 321 
 329 
 369 
 388 
 405 
 
 222 
 261 
 277 
 293 
 
 5.58 
 5.71 
 5.68 
 5.65 
 
 3.14 
 3.25 
 3.23 
 3.22 
 
 100.2 
 112.1 
 120.1 
 127 7 
 132.8 
 144.7 
 152.3 
 159 9 
 
 6X4X V2 
 6X4X V2 
 6X4X 9 /J6 
 6X4X 5/8 
 
 14 
 
 V2 
 5/8 
 5 /8 
 5 /S 
 
 ft 
 
 , 7/8 
 
 476 
 526 
 553 
 579 
 
 388 
 432 
 454 
 475 
 
 358 
 401 
 421 
 440 
 
 299 
 338 
 354 
 370 
 
 5.58 
 5.69 
 5.67 
 
 5.64 
 
 3.18 
 3.26 
 3.25 
 3.24 
 
 6X4X Vs 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 
 14 
 
 594 
 644 
 694 
 742 
 
 558 
 606 
 654 
 700 
 
 522 
 568 
 614 
 658 
 
 486 
 529 
 574 
 616 
 
 450 
 491 
 534 
 574 
 
 413 
 453 
 494 
 532 
 
 377 
 415 
 454 
 490 
 
 5.59 
 5.69 
 5.79 
 5.88 
 
 3.21 
 3.27 
 3.33 
 3.37 
 
 165 
 176.9 
 188.8 
 209.7 
 
 Safe loads enclosed in dotted lines are for ratios of l/r not over 60. 
 Those enclosed in -heavy lines are for ratios of l/r not over 200. All 
 others are for ratios of l/r up to 120. Allowable fiber stress, 13,000 Ib. 
 per sq. in. for length of 60 radii and under. Each column consists of 
 four angles, two side plates, and one web plate except those marked *, 
 which have tw9 web plates. Weights given do not include rivet heads 
 and other details. Table continued on next page. 
 
330 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads on Carnegie Plate and Angle Columns with 
 Side Plates in Thousands of Pounds. * Continued. 
 
 Angles. 
 
 Web 
 Plate. 
 
 Side 
 Plates. 
 
 Effective Length in Feet. 
 
 RadiusofGyration 
 Axis Perpendic- 
 ular to Web Plate 
 
 Radius of Gyration 
 Axis Parallel to 
 Web Plate. 
 
 Weight, Pounds | 
 per Foot. 
 
 ,19 
 
 73 
 g 
 
 J2 
 
 g 
 
 3 
 
 T3 
 
 
 
 1 
 H 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 6X4X Vs 
 6X4X 5/s 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/s 
 6X4X 5/8 
 6X4X 5/8 
 
 12 
 
 5/8 
 
 14 
 
 11/8 
 H/4 
 
 13/8 
 11/2 
 15/8 
 13/4 
 17/8 
 
 2 
 
 719 
 840 
 888 
 937 
 986 
 1034 
 1082 
 1l30 
 "353 
 390 
 417 
 442 
 468 
 
 747 
 794 
 840 
 887 
 934 
 980 
 1026 
 ! 1072 
 
 703 
 748 
 793 
 837 
 882 
 926 
 970 
 1014 
 
 659 
 702 
 745 
 787 
 830 
 872 
 914 
 956 
 
 615 
 657 
 697 
 738 
 779 
 818 
 858 
 898 
 
 571 
 611 
 649 
 688 
 727 
 764 
 802 
 840 
 
 527 
 565 
 601 
 638 
 675 
 710 
 746 
 782 
 
 483 
 519 
 553 
 588 
 623 
 657 
 690 
 725 
 
 5.97 
 6.06 
 6.14 
 6.22 
 6.30 
 6.38 
 6.46 
 6.54 
 
 3.14 
 3.45 
 3.48 
 3.51 
 3.54 
 3.56 
 3.58 
 3.60 
 
 212.6 
 224.5 
 236.4 
 248.3 
 260.2 
 272 1 
 284.0 
 295.9 
 
 6X4X V8 
 6X4X Vie 
 6X4X Va 
 6X4X V2 
 6X4X 1/2 
 
 14 
 
 3/8 
 
 14 
 
 3/8 
 3/8 
 3/8 
 7/16 
 1/2 
 
 340 
 365 
 390 
 415 
 439 
 
 317 
 340 
 363 
 387 
 410 
 
 293 
 314 
 336 
 359 
 381 
 
 270 
 289 
 309 
 .331 
 353 
 
 246 
 264 
 282 
 303 
 324 
 
 223 
 239 
 255 
 275 
 295 
 
 205 
 220 
 236 
 251 
 267 
 -284 
 303 
 
 6.46 
 6.45 
 6.43 
 6.49 
 6.55 
 
 3.10 
 3.09 
 3.09 
 3.14 
 3.19 
 
 102.8 
 110.8 
 118 4 
 124.3 
 130.3 
 
 6X4X V2 
 6X4X V2 
 
 14 
 
 3/8 
 
 14 
 
 9/16 
 5/8 
 
 493| 453 
 517| 487 
 
 433 
 456 
 
 403 1 374 
 426 395 
 
 344 
 364 
 
 314 
 
 334 
 
 6.61 
 
 6.67 
 
 3.23 
 3.27 
 
 136.2 
 142.2 
 
 6X4X V2 
 6X4X 9 /l6 
 6X4X 5/g 
 
 14 
 
 1/2 
 
 5/8 
 
 5/8 
 
 14 
 14 
 
 14 
 
 5/8 
 5/8 
 5/8 
 
 535 502 
 561 527 
 587 551 
 
 470 
 493 
 515 
 530 
 576 
 622 
 668 
 713 
 758 
 802 
 847 
 892 
 935 
 981 
 1025 
 
 437 
 459 
 479 
 
 405 
 424 
 443 
 455 
 497 
 540 
 581 
 622 
 664 
 704 
 
 373 
 390 
 407 
 
 340 
 356 
 372 
 
 308 
 322 
 336 
 
 f345 
 378 
 415 
 452 
 487 
 522 
 556 
 591 
 626 
 659 
 696 
 730 
 
 6.58 
 6.56 
 6.54 
 
 3.22 
 3.21 
 3.20 
 
 148.1 
 155.7 
 163.3 
 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/s 
 
 14 
 14 
 
 5/8 
 3/4 
 
 1 7/8 
 H/8 
 H/4 
 
 13/8 
 
 606 
 655 
 705 
 754 
 803 
 852 
 901 
 949 
 998 
 1046 
 1095 
 1144 
 Tl98" 
 1250 
 1315 
 1367 
 1419 
 1471 
 1523 
 
 568 
 615 
 664 
 711 
 758 
 805 
 851 
 
 493 
 536 
 581 
 625 
 667 
 711 
 753 
 
 417 
 457 
 493 
 538 
 577 
 617 
 655 
 
 380 
 418 
 457 
 495 
 532 
 569 
 605 
 642 
 679 
 715 
 753 
 789 
 
 6.47 
 6.58 
 6.68 
 6.78 
 6.87 
 6.96 
 7.05 
 
 3.17 
 3.23 
 3.29 
 3.34 
 3.38 
 3.42 
 3.45 
 
 169.3 
 181.2 
 193.1 
 205.0 
 216.9 
 228.8 
 240.7 
 
 6X4X 5/s 
 6X4X 5/8 
 6X4X 5/s 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X4X 5/8 
 6X6X 5/8 
 6X6X 5/8 
 6X6X 5/8 
 6X6X 5/8 
 6X6X Vs 
 
 H/2 
 15/8 
 13/4 
 17/8 
 
 898 
 945 
 991 
 1038 
 1084 
 "1198 
 
 !S2 
 
 1308 
 1364 
 
 HI 9" 
 1471 
 1523 
 "590 
 T6"57" 
 1728 
 1787 
 1845 
 1904 
 
 796 
 839 
 880 
 924 
 966 
 
 744 
 786 
 825 
 867 
 907 
 
 693 
 732 
 770 
 810 
 848 
 
 7.13 
 7.22 
 7.30 
 7.38 
 7.46 
 
 3.48 
 3.51 
 3.53 
 3.56 
 
 3.58 
 
 252.6 
 264.5 
 276.4 
 288.3 
 300.2 
 
 16 
 
 JV.J 
 
 2 
 
 21/8| 
 21/41 
 23/8| 
 21/2 1 
 
 1146 1091 1036 
 1201 1144 1087 
 1246 1185 1123 
 1301 1237 1174 
 1356 1290 1225 
 1 409| 1 342 , 1274 
 1463 139311324 
 
 981 926 
 1030 973 
 1062 1000 
 1111 1047 
 1160 1094 
 1207 1139 
 1254 1185 
 
 871 
 916 
 939 
 984 
 1029 
 1072 
 1115 
 
 7.45 
 7.53 
 7.36 
 7.44 
 7.53 
 7.61 
 7.69 
 
 4.02 
 4.05 
 3.95 
 3.98 
 4.01 
 4.03 
 4.05 
 
 313.8 
 327.4 
 344.2 
 357.8 
 371.4 
 385.0 
 398.6 
 
 6X6X 5/8 
 8X6X 5 /8 
 8X6X 5/8 
 8X6X 5/8 
 8X6X 5/8 
 8X6X 5/s 
 
 *14 
 
 1/2 
 
 ]6 
 18 
 
 21/2*1592 
 21/2 ,1657 
 23/ 8 M728 
 21/2 11787 
 25/ 8 M845 
 23/4 11904 
 
 1516 1443 1369 1295 
 1616 1543 1470 1397 
 
 1222 
 1324 
 
 1148 
 1251 
 
 7.57 
 7.54 
 
 3.99 416.4 
 4.18 433.6 
 
 172811695 1626 1557 1488 1419 
 1787 1756 1685 1614 1543 1471 
 1845 1818 1744 16711598 1525 
 1904 1879 1804! 1729 1653 1578 
 
 7.54 
 7.62 
 7.70 
 7.78 
 
 4.61 452.3 
 4.63 467.6 
 4.65 482.9 
 4.67 498,2 
 
 8X6X 5/8 
 8X6X 5/s 
 8X6X 5/s 
 8X6X 5/s 
 8X6X 5/8 
 8X6X 5/s 
 
 *14 
 
 5/8 
 
 18 
 
 23/4 J1949 
 
 1949 1949H918 
 
 1841 1763 1686 1608 
 
 7.71 
 
 4.64 510.1 
 
 20 
 
 25/ 8 20272027,2027 
 23/4 2092: 2092 12092 
 27/ 8 21572157 2157 
 3 2222;22222222 
 3 l/s 2287 2287 2287 
 
 2027|2009 1935 1862 
 2092)2077 2002 1926 
 21571214620681991 
 2222|2214 2135 2055 
 2287)2283 2202 2120 
 
 1789 
 1851 
 1913 
 1976 
 2039 
 
 7.70 
 7.78 
 7.86 
 7.94 
 8.01 
 
 5.10 
 5.12 
 5.14 
 5.16 
 
 5.18 
 
 530.5 
 547.5 
 564.5 
 581.5 
 598.5 
 
 *See note at foot of page 329. 
 
PROPERTIES OF BETHLEHEM GIRDER BEAMS. 331 
 
 Bethlehem, Girder and I-Beams, and H- Columns. The tables of 
 special and girder beams give the sections and weights usually rolled. 
 Intermediate and heavier weights may be obtained by special arrange- 
 ment. The table of H-columns gives only the minimum and maximum 
 weights for each section number. Many intermediate weights are 
 regularly made. 
 
 The coefficients of strength given n the tables are based on a maxi- 
 mum fiber stress of 16,000 Ib. per sq. in., which is allowable for quies- 
 cent loads, as in buildings. For moving loads the fiber stress of 12,500 
 Ib. per sq. in. should be used, and the coefficients reduced proportion- 
 ately. For suddenly applied loads, as in railroad bridges, they should 
 be still further reduced. For a fiber stress of 8000 Ib. per sq. in. the 
 coefficients would be one-half those given in the tables. The quotient 
 obtained by d viding the coefficient given for the beam by the span in 
 feet will give the uniformly distributed safe load in pounds, including 
 the weight of the beam. If the load is concentrated at the middle of the 
 span the safe load is one half the uniformly distributed load. 
 
 For further information see handbook of Structural Steel Shapes, 
 Bethlehem Steel Co., South Bethlehem, Pa., 1911. 
 
 Properties of Bethlehem Girder Beams. 
 
 
 
 
 
 
 
 3 
 
 rt'S 
 
 Neutral 
 
 
 
 
 * . 
 
 
 Neutral Axis 
 
 C? D" S) 
 
 Ja ra 
 
 Axis Coin- 
 
 * 
 
 o 
 
 s & 
 
 0> 
 
 oT 
 
 Perpendicular to 
 
 g wCO.S 
 
 CQ fl 
 
 cident with 
 
 93 
 
 
 
 I| 
 
 P 
 
 c 
 
 Web at Center. 
 
 ^ *" oj2 
 
 0>^-( 
 
 Center Line 
 
 | 
 
 
 11 
 
 -s 
 
 E| 
 
 
 ^ * 
 
 1 
 
 of Web. 
 
 "o c 
 
 0,3 
 
 ^ 
 
 11 
 
 *-. 
 
 4J 
 
 
 
 P ^ ( J 
 
 s^^ 
 
 +a 
 
 
 i 
 
 
 
 Kg- 
 
 J300 
 
 gM 
 
 plxj 
 
 ." 
 
 is 
 
 S .3 
 
 IPS 
 
 3 >> c 
 
 121 
 
 II sS 
 
 I'^ld 
 
 'S so 
 
 fl rt 
 I" 8 "S 
 
 fel 
 
 Q 
 
 p 
 
 <1 
 
 H 
 
 f 
 
 S 3 
 
 M " 
 
 w^"^ 
 
 6' 2 " h ~ 1 
 
 rt g;tN 
 
 
 *i'r 
 
 p>og 
 
 
 
 
 
 
 7 
 
 T 
 
 s 
 
 c 
 
 
 
 r' 
 
 30 
 
 200.0 
 
 58.71 
 
 0.75 
 
 15.00 
 
 9150.6 
 
 12.48 
 
 610.0 
 
 6,507,100 
 
 94.65 
 
 630.2 
 
 3.28 
 
 30 
 
 180.0 
 
 53.00 
 
 .69 
 
 13.00 
 
 8194.5 
 
 12.43 
 
 546.3 
 
 5,827,200 
 
 82.60 
 
 433.3 
 
 2.86. 
 
 28 
 
 180.0 
 
 52.86 .69 
 
 14.35 
 
 7264.7 
 
 11.72 
 
 518.9 
 
 5,535,000 
 
 80.75 
 
 533.3 
 
 3.18 
 
 28 
 
 165.0 
 
 48.47 
 
 .66 
 
 12.50 
 
 6562.7 
 
 11.64 
 
 468.8 
 
 5,000,100 
 
 75.15 
 
 371.9 
 
 2.77 
 
 26 
 
 160.0 
 
 46.91 
 
 .63 
 
 13.60 
 
 5620.8 
 
 10.95 
 
 432.4 
 
 4,611,900 
 
 67.95 
 
 435.7 
 
 3.05 
 
 26 
 
 150.0 
 
 43.94 
 
 .63 
 
 12.00 
 
 5153.9 
 
 10.83 
 
 396.5 
 
 4,228,800 
 
 67.95 
 
 314.6 
 
 2.68 
 
 24 
 
 140.0 
 
 41.16 
 
 .60 
 
 13.00 
 
 4201.4 
 
 10.10 
 
 350.1 
 
 3,734,600 
 
 60.85 
 
 346.9 
 
 2.90 
 
 24 
 
 120.0 
 
 35.38 
 
 .53 
 
 12.00 
 
 3607.3 
 
 10.10 
 
 300.6 
 
 3,206,500 
 
 49.25 
 
 249.4 
 
 2.66 
 
 20 
 
 140.0 
 
 41.19 
 
 .64 
 
 12.50 
 
 2934.7 
 
 8.44 
 
 293.5 
 
 3,130,300 
 
 62.10 
 
 348.9 
 
 2.91 
 
 20 
 
 112.0 
 
 32.81 
 
 .55 
 
 12.00 
 
 2342.1 
 
 8.45 
 
 234.2 
 
 2,498,300 
 
 49.25 
 
 239.3 
 
 2.70 
 
 18 
 
 92.0 
 
 27.12 
 
 .48 
 
 11.50 
 
 1591.4 
 
 7.66 
 
 176.8 
 
 1,886,100 
 
 38.05 
 
 182.6 
 
 2.59 
 
 15 
 15 
 
 140. Q! 41.27 
 104.0 30.50 
 
 .80 
 .60 
 
 11.75 
 11.25 
 
 1592.7 
 1220.1 
 
 6.21 
 6.32 
 
 212.4 
 162.7 
 
 2,265,200 
 1,735,300 
 
 67.10 
 47.15 
 
 331.0 
 213.0 
 
 2.83 
 2.64 
 
 15 
 
 73.0 
 
 21.49 
 
 .43 
 
 10.50 
 
 883.4 
 
 6.41 
 
 117.8 
 
 1,256,600 
 
 29.60 
 
 123.2 
 
 2.39 
 
 12 
 
 70.0 
 
 20.58 
 
 .46 
 
 10.00 
 
 538.8 
 
 5.12 
 
 89.8 
 
 957,800 
 
 28.60 
 
 114.7 
 
 2.36 
 
 12 
 
 55.0 
 
 16.18 
 
 .37 
 
 9.75 
 
 432.0 
 
 5.17 
 
 72.0 
 
 768,000 
 
 21.15 
 
 81.1 
 
 2.24 
 
 10 
 
 44.0 
 
 12.95 
 
 .31 
 
 9.00 
 
 244.2 
 
 4.34 
 
 48.8 
 
 521,000 
 
 14.90 
 
 57.3 
 
 2.10 
 
 9 
 
 38.0 
 
 11.22 
 
 .30 
 
 8.50 
 
 170.9 
 
 3.90 
 
 38.0 
 
 405,000 
 
 13.35 
 
 44.1 
 
 1.98 
 
 8 
 
 32.5 
 
 9.54 
 
 .29 
 
 8.00 
 
 114.4 
 
 3.46 
 
 28.6 
 
 305,100 
 
 11.80 
 
 32.9 
 
 1.86 
 
 W=Safe load in pounds uniformly distributed, including weight of beam. 
 L = Span in feet. M Moment of forces in foot-pounds. /= fiber stress, . 
 W=C/L; M=C/8; C= WL = 
 
332 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Bethlehem I-Beams. 
 
 
 
 
 
 
 
 f - o5 
 
 
 
 Neutral 
 
 
 ^ 
 
 
 * 
 
 
 Neutral Axis 
 
 o 1 w> 
 
 J3<S 
 
 Axis Coin- 
 
 I 
 
 
 
 g 
 
 o> 
 
 & 
 
 Perpendicular to 
 
 g w^-S 
 
 *O 
 
 cident with 
 
 8 
 
 ' 
 
 O v 
 
 *s 
 
 ^ 
 
 
 Web at Center. 
 
 ^ O> j^ 
 
 QJ 
 
 Center Line 
 
 
 
 
 
 
 t/3 ^ 
 
 o| 
 
 1* 
 
 
 "8 x 
 
 w o 
 
 of Web. 
 
 v- 
 
 o a 
 
 -M O 
 
 
 1^ 
 
 . 
 
 o a 
 
 fl ,j 
 
 ( . 
 
 C 3 
 
 |.-2o o 
 
 l^r 
 
 43 
 
 >> ' 
 
 X^ 
 
 a 
 
 '33 
 
 c) 3 
 
 I 
 
 .2 
 
 T3 
 
 53 ^ 
 
 JoJ 
 
 '43 O 02 
 
 ^feSfl 
 
 ^. 
 
 .5 
 
 3O O 
 
 0) 
 
 
 
 '3. 
 
 
 
 
 
 OJ^O^O S . 
 
 ca c "^ 
 
 
 
 iS 
 
 * 
 
 
 H 
 
 ^ 
 
 / M 
 
 r 
 
 M *f 
 
 C 
 
 |gH> 
 
 I~ 
 
 *r/* 
 
 30 
 
 120.0 
 
 35.30 
 
 0.540 
 
 io.5oe 
 
 5239.6 
 
 12.18 
 
 349.3 
 
 3,726,000 
 
 51.90 
 
 165.0 
 
 2.16 
 
 28 
 
 105.0 
 
 30.88 
 
 .500 
 
 10.000 
 
 4014.1 
 
 11.40 
 
 286.7 
 
 3,058,400 
 
 44.50 
 
 131.5 
 
 2.06 
 
 26 
 
 90.0 
 
 26.49 
 
 .460 
 
 9.500 
 
 2977.2 
 
 10.60 
 
 229.0 
 
 2,442,800 
 
 37.65 
 
 101.2 
 
 .95 
 
 24 
 
 84.0 
 
 24.80 
 
 .460 
 
 9.250 
 
 2381.9 
 
 9.80 
 
 198.5 
 
 2,117,300 
 
 37.55 
 
 91.1 
 
 .92 
 
 24 
 
 83.0 
 
 24.59 
 
 .520 
 
 9.130 
 
 2240.9 
 
 9.55 
 
 186.7 
 
 1,991,900 
 
 46.55 
 
 78.0 
 
 .78 
 
 24 
 
 73.0 
 
 21.47 
 
 .390 
 
 9.000 
 
 2091.0 
 
 9.87 
 
 174.3 
 
 1,858,700 
 
 27.00 
 
 74.4 
 
 .86 
 
 20 
 
 82.0 
 
 24.17 
 
 .570 
 
 8.890 
 
 1559.8 
 
 8.03 
 
 156.0 
 
 1,663,800 
 
 51.20 
 
 79.9 
 
 .82 
 
 20 
 
 72.0 
 
 21.37 
 
 .430 
 
 8.750 
 
 1466.5 
 
 8.28 
 
 146.7 
 
 1,564,300 
 
 32.45 
 
 75.9 
 
 .88 
 
 20 
 20 
 
 69.0 
 64.0 
 
 20.26 
 18.86 
 
 .520 
 .450 
 
 8.145 
 8.075 
 
 1268.9 
 1222.1 
 
 7.91 
 8.05 
 
 126.9 
 122.2 
 
 1,353,500 
 1,303,600 
 
 44.10 
 34.70 
 
 51.2 
 49.8 
 
 .59 
 .62 
 
 23 
 
 59.0 
 
 17.36 
 
 .375 
 
 8.000 
 
 1172.2 
 
 8.22 
 
 117.2 
 
 1,250,300 
 
 25.00 
 
 48.3 
 
 .66 
 
 18 
 
 59.0 
 
 17.40 
 
 .495 
 
 7.675 
 
 883.3 
 
 7.12 
 
 98.1 
 
 1,046,900 
 
 39.00 
 
 39.1 
 
 .50 
 
 18 
 
 54.0 
 
 15.87 
 
 .410 
 
 7.590 
 
 842.0 
 
 7.28 
 
 93.6 
 
 997,900 
 
 28.75 
 
 37.7 
 
 .54 
 
 18 
 
 52.0 
 
 15.24 
 
 V375 
 
 7.555 
 
 825.0 
 
 7.36 
 
 91.7 
 
 977,700 
 
 24.60 
 
 37.1 
 
 .56 
 
 18 
 
 48.5 
 
 14.25 
 
 .320 
 
 7.500 
 
 798.3 
 
 7.48 
 
 88.7 
 
 946,100 
 
 18.35 
 
 36.2 
 
 .59 
 
 15 
 
 71.0 
 
 20.95 
 
 .520 
 
 7.500 
 
 796.2 
 
 6.16 
 
 106.2 
 
 1,132,400 
 
 38.95 
 
 61.3 
 
 .71 
 
 15 
 
 64.0 
 
 18.81 
 
 .605 
 
 7.195 
 
 664.9 
 
 5.95 
 
 88.6 
 
 945,600 
 
 46.95 
 
 41.9 
 
 .49 
 
 15 
 
 54.0 
 
 15.88 
 
 .410 
 
 7.000 
 
 610.0 
 
 6.20 
 
 81.3 
 
 867,600 
 
 27.40 
 
 38.3 
 
 .55 
 
 15 
 
 45.0 
 
 13.52 
 
 .440 
 
 6.810 
 
 484.8 
 
 5.99 
 
 64.6 
 
 689,500 
 
 30.00 
 
 25.2 
 
 .36 
 
 15 
 
 41.0 
 
 12.02 
 
 .340 
 
 6.710 
 
 456.7 
 
 6.16 
 
 60.9 
 
 649,400 
 
 19.95 
 
 24.0 
 
 .41 
 
 15 
 
 38.0 
 
 11.27 
 
 .290 
 
 6.660 
 
 442.6 
 
 6.27 
 
 59.0 
 
 629,500 
 
 15.05 
 
 23.4 
 
 .44 
 
 12 
 
 36.0 
 
 10.61 
 
 .310 
 
 6.300 
 
 269.2 
 
 5.04 
 
 44.9 
 
 478,600 
 
 16.10 
 
 21.3 
 
 .42 
 
 12 
 
 32.0 
 
 9.44 
 
 .335 
 
 6.205 
 
 228.5 
 
 4.92 
 
 38.1 
 
 406,200 
 
 17.90 
 
 16.0 
 
 .30 
 
 12 
 
 28.5 
 
 8.42 
 
 .250 
 
 6.120 
 
 216.2 
 
 5.07 
 
 36.0 
 
 384,400 
 
 11.10 
 
 15.3 
 
 .35 
 
 10 
 
 28.5 
 
 8.34 
 
 .390 
 
 5.990 
 
 134.6 
 
 4.02 
 
 26.9' 
 
 287,100 
 
 19.90 
 
 12.1 
 
 .21 
 
 10 
 
 23.5 
 
 6.94 
 
 .250 
 
 5.850 
 
 122.9 
 
 4.21 
 
 24.6 
 
 262,200 
 
 10.50 
 
 11.2 
 
 .27 
 
 9 
 
 24.0 
 
 7.04 
 
 .365 
 
 5.555 
 
 92.1 
 
 3.62 
 
 20.5 
 
 218,300 
 
 16.95 
 
 8.8 
 
 .12 
 
 9 
 
 20.0 
 
 6.01 
 
 .250 
 
 5.440 
 
 85.1 
 
 3.76 
 
 18.9 
 
 201,800 
 
 10.05 
 
 8.2 
 
 .17 
 
 8 
 
 19.5 
 
 5.78 
 
 .325 
 
 5.325 
 
 60.6 
 
 3.24 
 
 15.1 
 
 161,600 
 
 13.45 
 
 6.7 
 
 .08 
 
 8 
 
 17.5 
 
 5.18 
 
 .250 
 
 5.250 
 
 57.4 
 
 3.33 
 
 14.3 
 
 153,000 
 
 9.45 
 
 6.4 
 
 .11 
 
 W = Safe load in pounds uniformly distributed, including weight of beam. 
 L = Span in feet. M= Moment of forces in foot-pounds. / = fiber stress. 
 C = Coefficients given in the table. 
 W = C/L; M = C/8; C= WL = 8M 
 
PROPERTIES OF BETHLEHEM H-COLUMNS. 
 
 333 
 
 Dimensions and Properties of Bethlehem Boiled Steel H-Columns.* 
 
 o 
 
 Dimensions, in Inches. 
 
 cj 
 
 Neutral Axis 
 Perpen. to Web. 
 
 Neutral Axis on 
 Center Line of Web. 
 
 & 
 
 
 A & 
 
 
 -i 
 
 i -g 
 
 T3 t> 
 
 
 
 
 
 
 
 -MO, 
 
 ! 
 
 Mean Thic 
 ness of Flan} 
 
 Breadth of 
 Flange. 
 
 Thickness c 
 Web 
 
 & 
 
 J~l 
 
 |3S 
 
 fi 
 
 O OS 
 
 OJ CP 
 
 S-Oi 
 
 Moment of 
 Inertia. 
 
 Section 
 Modulus. 
 
 Radius of 
 Gyration. 
 
 Moment of 
 Inertia. 
 
 Section 
 Modulus. 
 
 Radius of 
 Gyration 
 
 14-Inch H-Columns 
 
 83.5 
 91.0 
 
 133/4 
 
 137/ 8 
 
 H/16 
 
 3/4 
 
 13.92 
 13.96 
 
 0.43 
 .-47 
 
 11.06 
 11.06 
 
 24.46 
 26.76 
 
 884.9 
 976.8 
 
 128.7 
 140.8 
 
 6.01 
 6.04 
 
 294.5 
 325.4 
 
 42.3 
 46.6 
 
 3.47 
 3.49 
 
 99.0 
 162.0 
 
 14 
 15 
 
 13/16 
 15/16 
 
 14.00 
 14.31 
 
 .51 
 
 .82 
 
 11.06 
 11.06 
 
 29.06 
 47.71 
 
 1070.6 
 1894.0 
 
 153.0 
 
 252.5 
 
 6.07 
 6.30 
 
 356.9 
 626.1 
 
 51.0 
 87.5 
 
 3.50 
 3.62 
 
 170.5 
 227.5 
 
 151/8 
 
 16 
 
 13/ 8 
 1 13/16 
 
 14.35 
 14.62 
 
 .86 
 1.13 
 
 11.06 
 11.06 
 
 50.11 
 66.98 
 
 2007.0 
 2859.6 
 
 265.4 
 357.5 
 
 6.33 
 6.53 
 
 662.3 
 929.4 
 
 92.3 
 127.1 
 
 3.64 
 3.72 
 
 236.0 
 287.5 
 
 161/8 
 167/s 
 
 17/8 
 21/4 
 
 14.66 
 14.90 
 
 1.17 
 1.41 
 
 11.06 
 11.06 
 
 69.45 
 84.50 
 
 2991.5 
 3836.1 
 
 371.0 
 454.7 
 
 6.56 
 6.74 
 
 970.0 
 1226.7 
 
 132.3 
 164.7 
 
 3.74 
 3.81 
 
 12-Inch H-Columns 
 
 64.5 
 71.5 
 
 M 3/4 
 
 117/ 8 
 
 5/8 
 H/16 
 
 11.92 
 11.96 
 
 0.39 
 .43 
 
 9.21 
 9.21 
 
 19.00 
 20.96 
 
 499.0 
 556.6 
 
 84.9 
 93.7 
 
 5.13 
 5.15 
 
 168.6 
 188.2 
 
 28.3 
 31.5 
 
 2.98 
 3.00 
 
 78.0 
 132.5 
 
 12 
 13 
 
 3/4 
 U/4 
 
 12.00 
 12.31 
 
 .47 
 .78 
 
 9.21 
 9.21 
 
 22.94 
 38.97 
 
 615.6 
 1141.3 
 
 102.6 
 175.6 
 
 5.18 
 5.41 
 
 208.1 
 380.7 
 
 34.7 
 61.9 
 
 3.01 
 3.13 
 
 139.5 
 161.0 
 
 131/8 
 131/2 
 
 15/16 
 
 11/2 
 
 12.35 
 12.47 
 
 .82 
 .94 
 
 9.21 
 9.21 
 
 41.03 
 47.28 
 
 1214.5 
 1444.3 
 
 185.0 
 214.0 
 
 5.44 
 5.53 
 
 404.1 
 477.0 
 
 65.4 
 76.5 
 
 3.14 
 3.18 
 
 10-Inch H-Columns 
 
 49.0 
 
 97/ 8 
 
 9/16 
 
 9.97 
 
 0.36 
 
 7.67 
 
 14.37 
 
 263.5 
 
 53.4 
 
 4.28 
 
 89.1 
 
 17.9 
 
 2.49 
 
 54.0 
 99.5 
 
 10 
 11 
 
 5/8 
 H/8 
 
 10.00 
 10.31 
 
 .39 
 .70 
 
 7.67 
 7.67 
 
 15.91 
 29.32 
 
 296.8 
 607.0 
 
 59.4 
 110.4 
 
 4.32 
 4.55 
 
 100.4 
 201.7 
 
 20.1 
 39.1 
 
 2.51 
 2.62 
 
 105.5 
 123.5 
 
 111/8 
 
 11 1/2 
 
 13/16 
 1 3/8 
 
 10.35 
 10.47 
 
 .74 
 .86 
 
 7.67 
 7.67 
 
 31.06 
 36.32 
 
 651.0 
 790.4 
 
 117.0 
 137.5 
 
 4.58 
 4.67 
 
 215.6 
 259.3 
 
 41.7 
 49.5 
 
 2.64 
 2.67 
 
 8-Inch H-Columns 
 
 32.0 
 
 77/8 
 
 7/16 
 
 8.00 
 
 0.31 
 
 6.14 
 
 9.17 
 
 105.7 
 
 26.9 
 
 3.40 
 
 35.8 
 
 8.9 
 
 1.98 
 
 34.5 
 71.5 
 
 8 
 9 
 
 , V2 
 
 8.00 
 8.32 
 
 .31 
 .63 
 
 6.14 
 6.14 
 
 10.17 
 21.05 
 
 121.5 
 285.6 
 
 30.4 
 63.5 
 
 3.46 
 3.68 
 
 41.1 
 94.4 
 
 10.3 
 22.7 
 
 2.01 
 2.12 
 
 76.5 
 90.5 
 
 91/8 
 91/2 
 
 H/16 
 H/4 
 
 8.36 
 8.47 
 
 .67 
 .78 
 
 6.14 
 6.14 
 
 22.46 
 26.64 
 
 309.5 
 385.3 
 
 67.8 
 81.1 
 
 3.71 
 3.80 
 
 101.9 
 125.1 
 
 24.4 
 29.6 
 
 2.13 
 2.17 
 
 * The tables are greatly condensed from the original. The depth 
 of section regularly rolled in each size advances by l /% inch from the 
 smallest to the largest section shown in each table. The increased 
 depth of each section in a given size is obtained by adding metal to 
 the flanges, the depth of web remaining constant in each size, 
 
334 STRENGTH OF MATERIALS. 
 
 TORSIONAL STRENGTH. 
 
 Let a horizontal shaft of diameter = d be fixed at one end, and at the 
 other or free end, at a distance = I from the fixed end, let there be fixed 
 a horizontal lever arm with a weight = P acting at a distance = a from 
 the axis of the shaft so as to twist it; then Pa = moment of the applied 
 force. 
 
 Resisting moment = twisting moment = SJ/c, in which S = unit 
 shearing resistance, J = polar -moment of inertia of the section with 
 respect to the axis, and c = distance of the most remote fiber from the 
 axis, in a cross-section. For a circle with diameter d 
 
 For hollow shafts of external diameter d and internal diameter (&, 
 
 Pa = 0.1963 S; d = 5.1 
 
 1 ~^)S 
 
 In solving the last equation the ratio di/d is first assumed. 
 
 For a rectangular bar in which b and d are the long and short sides of 
 the rectangle, Pa = 0.2222 bd z S; and for a square bar with side d, Pa = 
 0.2222 d s S. (Merriman, "Mechanics of Materials," 10th ed.) 
 
 The above formulae are based on the supposition that the shearing 
 resistance at any point of the cross-section is proportional to its distance 
 from the axis; but this is true only within the elastic limit. In mate- 
 rials capable of flow, while the particles near the axis are strained within 
 the elastic limit those at some distance within the circumference may be 
 strained nearly to the ultimate resistance, so that the total resistance is 
 something greater than that calculated by the formulae. For working 
 strength, however, the formulae may be used, with S taken at the safe 
 working unit resistance. 
 
 The ultimate torsional shearing resistance 5 is about the same as the 
 direct shearing resistance, and may be taken at 20,000 to 25,000 Ibs. per 
 square inch for cast iron, 45,000 Ibs. for wrought iron, and 50,000 to 
 150,000 Ibs. for steel, according to its carbon and temper. Large factors 
 of safety should be taken, especially when the direction of stress is re- 
 versed, as in reversing engines, and when the torsional stress is com- 
 bined with other stresses, as is usual in shafting. (See "Shafting.") 
 
 Elastic Resistance to Torsion. Let I = length of bar being 
 twisted, d = diameter, P = force applied at the extremity of a lever arm 
 of length = a, Pa = twisting moment, G = torsional modulus of elas- 
 ticity, 9 = angle through which the free end of the shaft is twisted, 
 measured in arc of radius == 1. 
 
 For a cylindrical shaft, 
 
 P^ ** gd4 A 32PaE 32 Pal. 32 
 
 P = -32T ; * = -^G- ; (? = -^oT* T = 10.186. 
 
 If a = angle of torsion in degrees, 
 
 4__^L- 1 80 9 180X32PaZ 583.6 Pal 
 
 ""180' * * 2 d<G d*G 
 
 The value of G is given by different authorities as from 1/8 to 2/5 of E, 
 the modulus of elasticity for tension. For steel it is generally taken a* 
 12,000,000 Ibs. per sq. in. 
 
COMBINED STRESSES. 335 
 
 COMBINED STRESSES. 
 
 Combined Tension and Flexure. Let A = the area of a bar 
 subjected to both tension and flexure, P = tensile stress applied at the 
 ends, P -* A = unit tensile stress, S = unit stress at the fiber on the 
 tensile side most remote from the neutral axis, due to flexure alone, then 
 maximum tensile unit stress = (P -T- A) + S. A beam to resist com- 
 bined tension and flexure should be designed so that (P * A) + S shall 
 not exceed the proper allowable working unit stress. 
 
 Combined Compression and Flexure. If P * A = unit stress 
 due to compression alone, and S = unit compressive stress at fiber most 
 remote from neutral axis, due to flexure alone, then maximum compres- 
 sive unit stress = (P -*- A) + S. 
 
 Combined Tension (or Compression) and Cross Shear. If 
 applied tension (or compression) unit stress = p, applied shearing unit 
 stress = v, then from the combined action of the two forces 
 
 Max. S = Vp 2 + V4P 2 , Maximum shearing unit stress; 
 Max. t = 1/2 P +vV 4- 1/4P 2 , Maximum tensile (or compressive) unit stress. 
 Combined Flexure and Torsion. If S = greatest unit stress due 
 to flexure alone, and S s = greatest torsional shearing unit stress due to 
 torsion alone, then for the combined stresses 
 
 Max. tension or compression unit stress t = 1/28 + 
 
 Max. shear s = *Ss s * + V4S 2 . 
 
 Equivalent bending moment = 1/2 M + 1/2 ^M 2 + T 2 , where M= bending 
 noment and T = torsional moment. 
 
 Formula f9r diameter of a round shaft subjected to transverse load 
 while transmitting a given horse-power (see also Shafts of Engines): 
 
 ,73 _ 16 M 16 J5ff 402,500,000 H* 
 xt t V n 2 * H 2 
 
 where M = maximum bending moment of the transverse forces in 
 pound-inches,// = horse-power transmitted, n = No. of revs, per minute, 
 and t = the safe allowable tensile or compressive working strength of 
 the material. 
 
 Guest's Formula for maximum tension or compression unit stress is 
 <=\/4<S s 2 + S 9 (Phil. Afa0.,July, 1900). It is claimed by many writers to 
 be more accurate than Rankine's formula, given above. Equivalent 
 bending moment = V^P + T 2 . (Eng'g., Sept. 13 and 27, 1907; July 10, 
 1908; April 23, 1909.) 
 
 Combined Compression and Torsion. For a vertical round shaft 
 carrying a load and also transmitting a given horse-power, the result- 
 ant maximum compressive unit stress 
 
 2P I J72 4P2 
 
 .^+y 321.000.^ + ^, 
 
 in which P is the load. From this the diameter d may be found when t 
 and the other data are given. 
 
 Stress due to Temperature. Let I = length of a bar, A = its sec- 
 tional area, c coefficient of linear expansion for one degree, t = rise or 
 fall in temperature in degrees, E modulus of elasticity, A the change 
 of length due to the rise or fall t: if the bar is free to expand or contract. 
 A = ca. 
 
 If the bar is held so as to prevent its expansion or contraction the 
 stress produced by the change of temperature = -S = ActE. The fol- 
 lowing are average values of the coefficients of linear expansion for a 
 change in temperature of one degree Fahrenheit: 
 
 For brick and stone a = 0.0000050, 
 
 For cast iron a = 0. 0000056, 
 
 For wrought iron and steel.... a= 0.0000065. 
 
336 STRENGTH OF MATERIALS. 
 
 The stress due to temperature should be added to or subtracted from 
 the stress caused by other external forces according as it acts to increase 
 or to relieve the existing stress. 
 
 What stress will be caused in a steel bar 1 inch square in area by a 
 change of temperature of 100 F.? S = ActE = IX 0.0000065 X 100 X 
 30,000,000 = 19,500 Ibs. Suppose the bar is under tension of 19,500 
 Ibs. between rigid abutments before the change in temperature takes 
 place, a cooling of 100 F. will double the tension, and a heating of 100 
 will reduce the tension to zero. 
 
 STRENGTH OF FLAT PLATES. 
 
 For a circular plate supported at the edge, uniformly loaded, according 
 to Grashof, , 
 
 _ 
 6 / ' ~~5rt' 
 
 For a circular plate fixed at the edge, uniformly loaded, 
 2r 2 A /2 r 2 p 3ft 2 
 
 f _ _ v)' f V 71 ' 
 
 f- 3t2 P, < - y 3 / , P - 2r2 > 
 
 in which / denotes the working stress; r, the radius in inches; t, the thick- 
 ness in inches; and p, the pressure in pounds per square inch. 
 For mathematical discussion, see Lanza, " Applied Mechanics." 
 Lanza gives the following table, using a factor of safety of 8, with ten- 
 sile strength of cast iron 20,000, of wrought iron 40,000, and of steel 80,000: 
 
 Supported. Fixed. 
 
 Cast iron ............ t = 0.0182570 r v/p t = 0.0163300 r V" 
 
 Wrought iron ........ t = 0.0117850 r ^p__ t = 0.0105410 r V 
 
 Steel ................ t = 0.0091287 rV p t = 0.0081649 r Vp 
 
 For a circular plate supported at the edge, and loaded with a concen- 
 trated load P applied at a circumference the radius of which is TO: 
 
 for - = 10 20 so 40 
 
 TO 
 c = 4.07 5.00 5.53 5.92 
 
 7T/ C 
 
 The above formulae are deduced from theoretical considerations, and 
 give thicknesses much greater than are generally used in steam-engine 
 cylinder-heads. (See empirical formulae under Dimensions of Parts of 
 Engines.) The theoretical formulae seem to be based on incorrect or 
 incomplete hypotheses, but they err in the direction of safety. 
 
 Thickness of Flat Cast-iron Plates to resist Bursting Pressures. 
 Capt. John Ericsson (Church's Life of Ericsson) gave the following 
 rules: The proper thickness of a square cast-iron plate will be obtained 
 by the following: Multiply the side in feet (or decimals pf a foot) by 
 1/4 of the pressure in pounds and divide by 850 times the side in inches; 
 the quotient is the square of the thickness in inches. 
 
 For a circular plate, multiply 11-14 of the diameter in feet by 1/4 of 
 the pressure on the plate in pounds. Divide by 850 times 11-14 of the 
 diameter in inches. [Extract the square root.] 
 
STRENGTH OF FLAT SURFACES. 337 
 
 Prof. Wm. Harkness; Eng'g News, Sept. 5, 1895, shows that these rules 
 can be put in a more convenient form, thus: For square plates T = 
 0.00495 S ^p, and for circular plates T = 0.00439 D^p, where T = 
 thickness of plate, S = side of the square, D = diameter of the circle v 
 and p = pressure in Ibs. per sq. in. Professor Harkness, however, 
 doubts the value of the rules, and says that MO satisfactory theoretical 
 solution has yet been obtained. 
 
 The Strength of Unstayed Flat Surfaces. Robert Wilson 
 (Bng'g, Sept. 24, 1877) draws attention to the apparent discrepancy 
 between the results of theoretical investigations and of actual experi- 
 ments on the strength of unstayed flat surfaces of boiler-plate, such as 
 the unstayed flat crowns of domes and of vertical boilers. 
 
 On trying to make the rules given by the authorities agree with the 
 results of his experience of the strength of unstayed flat ends of cylin- 
 drical boilers and domes that had given way after Ions use, Mr. Wilson 
 was led to believe that the rules give the breaking strength much lower 
 than it actually is. He describes a number of experiments made by 
 Mr. Nichols of Kirkstall, which gave results varying widely from each 
 Other, as the method of supporting the edges of the plate was varied, 
 and also varying widely from the calculated bursting pressures, the 
 actual results being in all cases very much the higher. Some conclusions 
 drawn from these results are: 
 
 1. Although the bursting pressure has been found to be so high, boiler- 
 makers must be warned against attaching any importance to this, since 
 the plates deflected almost as soon as any pressure was put upon them 
 and sprang back again on the pressure being taken off. This springing 
 of the plate in the course of time inevitably results in grooving or chan- 
 neling, which, especially when aided by the action of the corrosive acids 
 in the water or steam, will in time reduce the thickness of the plate, and 
 bring about the destruction of an unstayed surface at a very low pressure. 
 
 2. Since flat plates commence to deflect at very low pressures, they 
 should never be used without stays; but it is better to dish the plates 
 when they are not stayed by flues, tubes, etc. 
 
 3. Against the commonly accepted opinion that the limit of elasticity 
 should never be reached in testing a boiler or other structure, these ex- 
 periments show that an exception should be made in the case of an un- 
 stayed flat end-plate of a boiler, which will be safer when it has assumed 
 a permanent set that will prevent its becoming grooved by the continual 
 variation of pressure in working. The hydraulic pressure in this case 
 simply does what should have been done before the plate was fixed, 
 that is, dishes it. 
 
 4. These experiments appear to show that the mode of attaching by 
 flange or by an inside or outside angle-iron exerts an important influence 
 on the manner in which the plate is strained by the pressure. 
 
 When the plate is secured to an angle-iron, the stretching under pres- 
 sure is, to a certain extent, concentrated at the line of rivet-holes, and 
 the plate partakes rather of a beam supported than fixed round the edge. 
 Instead of the strength increasing as the square of the thickness, when 
 the plate is attached by an angle-iron, it is probable that the strength 
 does not increase even directly as the thickness, since the plate gives 
 way simply by stretching at the rivet-holes, and the thicker the plate, 
 the less uniformly is the strain borne by the different layers of which the 
 plate may be considered to be made up. When the plate is flanged, the 
 flange becomes compressed by the pressure against the body of the plate, 
 and near the rim, as shown by the contrary flexure, the inside of the plate 
 is stretched more than the outside, and it may be by a kind of shearing 
 action that the plate gives way along the line where the crushing and 
 stretching meet. 
 
 5. These tests appear to show that the rules deduced from the theo- 
 retical investigations of Lame", Rankine, and Grashof are not confirmed 
 by experiment, and are therefore not trustworthy. 
 
 The rules of Lame", etc., apply only within the elastic limit. (Eng'g, 
 Dec. 13, 1895.) 
 
 Unbraced Wrought-iron Heads of Boilers, etc. (The Locomo- 
 tive, Feb., 1890). Few experiments have been made on the strength 
 of flat heads, and our knowledge of them comas largely from theory. 
 Experiments have been made on small plates Vie of an inch thick, 
 
338 STRENGTH OF MATERIALS. 
 
 yet the data so obtained cannot be considered satisfactory when we 
 consider the far thicker heads that are used in practice, although the 
 results agreed weli with Rankine's formula. Mr. Nichols has made ex- 
 periments on larger heads, and from them he has deduced the following 
 rule: "To find the proper thickness for a flat unstayed head, multiply 
 the area of the head by the pressure per square inch that it is to bear 
 safely, and multiply this by the desired factor of safety (say 8): then 
 divide the product by ten times the tensile strength of the material 
 used for the head." His rule for finding the bursting pressure when the 
 dimensions of the head are given is: "Multiply the thickness of the end- 
 plate in inches by ten times the tensile strength of the material used, 
 and divide the product by the area of the head in inches." 
 
 In Mr. Nichols's experiments the average tensile strength of the iron 
 used for the heads was 44,800 pounds. The results he obtained are 
 giren below, with the calculated pressure, by his rule, for comparison. 
 
 1. An unstayed flat boiler-head is 341/2 inches in diameter and 9/io 
 inch thick. What is its bursting pressure? The area of a circle 341/2 
 inches in diameter is 935 square inches; then 9/ie X 44,800 X 10 = 
 252,000, and 252,000 -f- 935 = 270 pounds, the calculated bursting 
 pressure. The head actually burst at 280 pounds. 
 
 2. Head 341/2 inches in diameter and 3/ 8 inch thick. The area = 935 
 square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 -f- 935 
 = 180 pounds, calculated bursting pressure. This head actually burst 
 at 200 pounds. 
 
 3. Head 261/4 inches in diameter, and 3/ 8 inch thick. The area 541 
 square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 *- 541 
 = 311 pounds. This head burst at 370 pounds. 
 
 4. Head 281/2 inches in diameter and 3/ 8 inch thick. The area = 638 
 square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 -* 638 
 = 263 pounds. The actual bursting pressure was 300 pounds. 
 
 In the third experiment, the amount the plate bulged under different 
 pressures was as follows: 
 
 At pounds per sq. in 10 20 40 80 120 140 170 200 
 
 Plate bulged 1/32 Vie Vs J /4 3 /8 V2 5 /8 3 /4 
 
 The pressure was now reduced to zero, and the end sprang back 3/ 18 
 inch, leaving it with a permanent set of 9/ 16 inch. The pressure of 
 200 Ibs. was again applied on 36 separate occasions during an interval of 
 five days, the bulging and permanent set being noted on each occasion, 
 but without any appreciable difference from that noted above. 
 
 The experiments described were confined to plates not widely different 
 in their dimensions, so that Mr. Nichols's rule cannot be relied upon for 
 heads that depart much from the proportions given in the examples. 
 
 Strength of Stayed Surfaces. A flat plate of thickness t is sup- 
 ported uniformly by stays whose distance from center to center is a, 
 uniform load p IDS. per square inch. Each stay supports pa 2 Ibs. The 
 greatest stress on the plate is 
 
 / = f|V (Unwin.) 
 
 For additional matter on this subject see strength of Steam Boilers. 
 
 Stresses in Steel Plating due to Water-pressure, as in plating of 
 vessels and bulkheads (Engineering, May 22, 1891, page 629). 
 
 Mr. J. A. Yates has made calculations of the stresses to which steel 
 plates are subjected by external water-pressure, and arrives at the 
 following conclusions: 
 
 Assume 2a inches to be the distance betvyeen the frames or other 
 rigid supports, and let d represent the depth in feet, below the surface 
 of the water, of the plate under consideration, t = thickness of plate in 
 inches, D the deflection from a straight line under pressure in inches, 
 and P = stress per square inch of section. 
 
 For outer bottom and ballast-tank plating, a = 420 t/d, D should not 
 be greater than 0.05 X 2 a/12, and P/2 not greater than 2 to 3 tons; 
 while for bulkheads, etc., a = 2352 //d, D should not be greater than 
 
THICK HOLLOW CYLINDERS UNDER TENSION. 339 
 
 0.1 X 2 a/ 12, and P/2 not greater than 7 tons. To illustrate the appli- 
 cation of these formulae the following cases have been taken: 
 
 For Outer Bottom, etc. 
 
 For Bulkheads, etc. 
 
 Thick- 
 ness of 
 Plating. 
 
 Depth 
 below 
 Water. 
 
 Spacing of 
 Frames should 
 not exceed 
 
 Thick- 
 ness of 
 Plating. 
 
 Depth of 
 Water. 
 
 Maximum Spac- 
 ing of Rigid 
 Stiff en ers. 
 
 in. 
 
 ft. 
 
 in. 
 
 in. 
 
 ft. 
 
 ft. in. 
 
 1/2 
 
 20 
 
 About 2 1 
 
 1/2 
 
 20 
 
 9 10 
 
 1/2 
 
 10 
 
 42 
 
 3 /8 
 
 20 
 
 7 4 
 
 3/8 
 
 18 
 
 18 
 
 3/8 
 
 10 
 
 14 8 
 
 3/8 
 
 9 
 
 36 
 
 1/4 
 
 20 
 
 4 10 
 
 V4 
 
 10 
 
 20 
 
 1/4 
 
 10 
 
 9 8 
 
 1/4 
 
 5 
 
 40 
 
 V8 
 
 10 
 
 4 10 
 
 It would appear that the course which should be followed in stiffening 
 bulkheads is to fit substantially rigid stiffening frames at comparatively 
 wide intervals, and only work such light angles between as are necessary 
 for making a" fair job of the bulkhead. 
 
 SPHERICAL, SHELLS AND DOMED BOILER-HEADS. 
 
 To find the Thickness of a Spherical Shell to resist a given 
 Pressure. Let d = diameter in inches, and p the internal pressure 
 per square inch. The total pressure which tends to produce rupture 
 around the great circle will be i/4rcd 2 p. Let 5 = safe tensile stress per 
 square inch, and t the thickness of metal in inches; then the resistance 
 to the pressure will be n d t S. Since the resistance must be equal to the 
 pressure, 
 
 iUnd*p = *dtS. Whence* = ^. 
 
 4o 
 
 The same rule is used for finding the thickness of a hemispherical head 
 to a cylinder, as of a cylindrical boiler. 
 
 Thickness of a Domed Head of a Boiler. If S = safe tensile 
 stress per square inch, d = diameter of the shell in inches, and t = thick- 
 ness of the shell, t = pd -s- 2/S; but the thickness of a hemispherical 
 head of the same diameter is t = pd + 4. Hence if we make the 
 radius of curvature of a domed head equal to the diameter of the boiler, 
 
 we shall have i = -f^ = ? , or the thickness of such a domed head 
 
 4o zo 
 
 will be equal to the thickness of the shell. 
 
 THICK HOLLOW CYLINDERS UNDER TENSION. 
 
 Lamg's formula, which is generally used, gives 
 
 t = thickness; n= inside and r2 = outside radius; 
 ^ = maximum allowable hoop tension at the 
 
 interior of the cylinder ; 
 p = intensity of interior pressure; 
 s =* tension at the exterior of the cylinder. 
 
 t _ r J ( h+ P \^ i 1 
 " 1 1 W^p/ 5 
 
340 STRENGTH OF MATERIALS. 
 
 EXAMPLE: Let maximum unit stress at the inner edge of the annulus 
 = 8000 lbs. per square inch, radius of cylinder = 4 inches, interior 
 pressure = 4000 lbs. per square inch. Required the thickness and the 
 tension at the exterior surface. 
 
 ^{{^^'-il-^-i)-.^ 
 
 2n2 2X16 4000 lbs. 
 
 For short cast-iron cylinders, such as are used in- hydraulic presses, it is 
 doubtful if the above formulae hold true, since the strength of the cylindri- 
 cal portion is reinforced by the end. In. that case the strength would be 
 higher than that calculated by the formula. A rule used in practice 
 for such presses is to make the thickness = Vio of the inner circum- 
 ference, for pressures of 3000 to 4000 lbs. per square inch. 
 
 Hooped Cylinders. For very high pressures, as in large guns, hoops 
 or outer tubes of forged steel are shrunk on inner tubes, thus bringing a 
 compressive stress on the latter which assists in resisting the tension due 
 to the internal pressure. For discussion of Lame"s, and other formulae 
 lor built-up guns, see Merriman's "Mechanics of Materials." 
 
 THIN CYLINDERS UNDER TENSION. 
 
 Let p = safe working pressure in lbs. per sq. in.; 
 d = diameter in inches; 
 
 T = tensile strength of the material, lbs. per sq. in.; 
 t = thickness in inches; 
 / = factor of safety; 
 c = ratio of strength of riveted joint to strength of solid plate. 
 
 If T = 50,000, / = 5, and c = 0.7; then 
 
 _ 1 4.0001 dp 
 d ; \ ~ 14^000* 
 
 The above represents the strength resisting rupture along a longitudinal 
 seam. For resistance to rupture in a circumferential seam, due to 
 
 pressure on the ends of the cylinder, we have ^ = ^ - ; 
 
 4 Tt c 
 whence p = . 
 
 Or the strength to resist rupture around a circumference is twice as great 
 as that to resist rupture longitudinally; hence boilers are commonly 
 single-riveted in the circumferential seams and double-riveted in the 
 longitudinal seams. 
 
 CARRYING CAPACITY OF STEEL ROLLERS AND BALLS. 
 
 Carrying Capacity of a Steel Roller between Flat Plates. (Mem- 
 man, Mech. of Mails.) Let S = maximum safe unit stress of the mate- 
 rial, I = length of the roller in inches, d = diameter, E = modulus of 
 
 elasticity, W = load, then W = 2/3 idS (2 S/E)*. Taking w = W/l, 
 and S = 15,000 and E = 30,000,000 lbs. per sq. in. for steel the formula 
 reduces to w = 316 d. Cooper's specifications for bridges, 1901, gives 
 w = 300 d. (The rule given in some earlier specifications, w = 1200 v'd, 
 Is erroneous.) The formula assumes that only the roller is deformed by 
 the load, but experiments show that the plates also are deformed, and 
 that the formula errs on the side of safety. Experiments by CrandaU 
 
RESISTANCE OF HOLLOW CYLINDERS. 341 
 
 and Marston on steel rollers of diameters from 1 to 16 in. show that 
 their crushing loads are closely given by the formula W = 880 Id. (See 
 Holler Bearings.) 
 
 Spherical Rollers. With the same notation as above, d being the 
 diameter of the sphere, S = VWE+i/tndZ', W = 1/4 nd2S2 + E. The 
 diameter of a sphere to carry a given load with an allowable unit- 
 stress S is d ='2 \/WE+irS2. This rule assumes that there is no de- 
 formation of the plates between which the sphere acts, hence it errs on 
 the side of safety. (See Ball Bearings.) 
 
 RESISTANCE OF HOLLOW CYLINDERS TO COLLAPSE. 
 
 Fairbairn's empirical formula (Phil. Trans., 1858) is 
 
 p = 9,675,600 ^. (1) 
 
 where p = pressure in Ib. per square inch, t = thickness of cylinder, 
 d = diameter, and / = length, all in inches. 
 He recommends the simpler formula 
 
 p = 9,675,600 1| (2) 
 
 as sufficiently accurate for practical purposes, for tubes of considerable 
 diameter and length. 
 
 The diameters of Fairbairn's experimental tubes were 4, 6, 8, 10, and 
 12 inches, and their lengths ranged between 19 and 60 inches. 
 
 His formula (2) was until about 1908 generally accepted as the basis of 
 rules for strength of boiler-flues. In some cases, however, limits were 
 fixed to its application by a supplementary formula. 
 
 Lloyd's Register contains the following formula for the strength of 
 circular boiler-flues, viz., 
 
 _ 89.600 V 
 
 Ld 
 
 The English Board of Trade prescribes the following formula for cir- 
 cular flues, when the longitudinal joints are welded, or made with riveted 
 butt-straps, viz., 
 
 90,000 t2 
 (L + Vd * 
 
 For lap-joints and for inferior workmanship the numerical factor may 
 be reduced as low as 60,000. 
 
 The rules of Lloyd's Register, and those of the Board of Trade, pre- 
 scribe further, that in no case the value of P must exceed 800 t/d. (5) 
 
 In formulae (3), (4), (5) P is the highest working pressure in pounds 
 per square inch, t and d are the thickness and diameter in inches, L is 
 the length of the flue in feet measured between the strengthening rings, 
 in case it is fitted with such. Formula (3) is the same as formula (2), 
 with a factor of safety of 9. 
 
 Nystrom has deduced from Fairbairn's experiments the following 
 formula for the collapsing strength of flues : 
 
 p =692,800 ~ . . . (6) 
 
 d v I 
 
 where p, t, I, and d have the same meaning as in formula (1), Nystrom 
 considers a factor of safety of 4 sufficient in applying his formula. (See 
 "A New Treatise on Steam Engineering," by J. W. Nystrom, p. 106.) 
 
 Formulse (1), (3), and (6) have the common defect that they make 
 the collapsing pressure decrease indefinitely with Increase of length, and 
 vice versa. 
 
 D. K. Clark, in his "Manual of Rules," etc., p. 696, gives the dimen- 
 sions of six flues, selected from the reports of the Manchester Steam- 
 users' Association, 1862-69. which collapsed while in actual use in boil- 
 ers. These flues varied from 24 to 60 inches in diameter, and from 
 3/16 to 3/ 8 inch in thickness. They consisted of rings of plates riveted 
 together, with one or two longitudinal seams, but all of them unfortified 
 by intermediate flanges or strengthening rings. From the data Clark 
 
342 STRENGTH OF MATERIALS. 
 
 deduced the following formula "for the average resisting force of 
 common boiler-flues," viz., 
 
 
 where p is the collapsing pressure in pounds per square inch, and d and t 
 are the diameter and thickness expressed in inches. 
 
 Instances of collapsed flues of Cornish and Lancashire boilers collated 
 by Clark (S. E., vol. i, p. 643), showed that the resistance to collapse 
 of flues of 3/g-in. plates, 18 to 43 ft. long, and 30 to 50 in. diameter varied 
 as the 1.75 power of the diameter. Thus, 
 
 For diameters of .............. 30 35 40 45 50 in. 
 
 The collapsing pressures were ... 76 58 45 37 30 Ib. per sq. in. 
 For 7/ 16 -in. plates the collapsing 
 
 pressures were ........ .......... 60 49 42 Ib. per sq. in. 
 
 C. R. Roelker, in Van Nostrand's Magazine, March, 1881, says that 
 Nystrom's formula, (6) , gives a closer agreement of the calculated with 
 the actual collapsing pressures in experiments on flues of every descrip- 
 tion than any of the other formulae. 
 
 Formula for Corrugated Furnaces (Eng'g, July 24, 1891, p. 102). 
 As the result of a series of experiments on the resistance to collapse 
 of Fox's corrugated furnaces, the Board of Trade and Lloyd's Register 
 altered their formulae for these furnaces in 1891 as follows: 
 
 Board of Trade formula is altered from 
 
 T = thickness in inches; D = mean diameter of furnace; W P = work- 
 ing pressure, Ib. per sq. in. 
 
 Lloyd's formula is altered from 
 
 looo xcr - 2) _ wp to i234 Xj (r-2) = wpf 
 
 T = thickness in sixteenths of an inch; 
 D = greatest diameter of furnace; 
 WP working pressure in pounds per square inch. 
 
 Stewart's Experiments. Prof . Reid T. Stewart (Trans. A.S.M.E,, 
 
 5, 10, 15 and 20 ft. between transverse joints tending to hold the tube in 
 a circular form. A second series was made on single lengths of 20 ft. 
 Seven sizes, from 3 to 10 in. outside diam., in all the commercial thick- 
 nesses obtainable, were tested. The tests showed that all the old for- 
 mulae were inapplicable to the wide range of conditions found in modern 
 practice. The principal conclusions drawn from the research are as 
 follows: 
 
 1. The length of tube, between transverse joints tending to hold it 
 in circular form, has no practical influence upon the collapsing pressure 
 of a commercial lap-welded tube so long as this length is npt less than 
 about six diameters of tube. 
 
 2. The formulas, based upon this research, for the collapsing pres- 
 sures of modern lap-welded Bessemer steel tubes, for aii lengths greater 
 than six diameters, are as follows: 
 
 P= 
 
 l,00o(l - y/1 -1600^) ........ (A) 
 
 P = 86,670 t - 1386 ............ (B) 
 
 Where P - collapsing pressure, pounds per sq. inch, d =* outside 
 diameter of tube in inches, t. = thickness of wall in inches* 
 
 Formula A is for values of P less than 581 pounds, or for values of 
 
RESISTANCE OF HOLLOW CYLINDERS. 343 
 
 less than 0.023, while formula B is for values greater than these. When 
 applying .these formulae, to practice, a suitable factor of safety must be 
 applied. 
 
 3. The apparent fibre stress under which the different tubes failed 
 varied from about 7000 Ibs. for the relatively thinnest to 35,000 Ibs. 
 pep sq. ?n. for the relatively thickest walls. Since the average yield 
 point of the material was 37,000 and the tensile strength 58,000 Ibs. 
 per sq. in., it would appear that the strength of a tube subjected to a 
 fluid collapsing pressure is not dependent alone upon either the elastic 
 limit or ultimate strength of the material constituting it. The element 
 of greatest weakness in a tube is its departure from roundness, even 
 when this departure is relatively small. 
 
 The table on the following page is a condensed statement of the principal 
 results of the tests. 
 
 Rational Formulae for Collapse of Tubes. (S. E. Slocum, Eng'g, 
 Jan. 8, 1909.) 
 
 Heretofore designers have been forced to rely either upon the anti- 
 quated experiments of Fairbairn, which were known to be in error bv 
 as much as 100% in many cases, or else to apply the theoretical formu- 
 lae of Love and others, without knowing how far the assumptions on 
 which these formulae are based are actually realized. 
 
 A rational formula for thin tubes under external pressure, due to A. E. H. 
 Love, is 
 
 P = [2 E/(l - m 2 )] (*/D), ....... (1) 
 
 in which P = collapsing pressure in Ibs. per sq. in. 
 
 E = modulus of elasticity in Ibs. per sq. in. 
 
 Nm = Poisson's ratio of lateral to transverse deformation. 
 t = thickness of tube wall in ins. 
 D = external tube diameter in ins. 
 or thick tubes a special case of Lame"s general formula is 
 P = 2u[(t/D) - (/D)2J, ......... (2) 
 
 in which u = ultimate compressive strength in Ibs. per sq. in. 
 
 The average values of the elastic constants are for steel, E = 30,000,000, 
 m = 0.295, u = 40,000; and for brass, E = 14,000,000, m = 0.357, 
 u = 11,000. 
 
 Hence, for thin steel tubes, P = 65,720,000 (f/Z>) ..... (3) 
 
 For thick steel tubes, P = 80,000 [(t/D) - (t/D)*] .... (4) 
 
 For thin brass tubes, P = 32,090,000 (t/D) 3. . .... (5) 
 
 For thick brass tubes, P = 22,000 [(t/D) - (t/D)*] .... (6) 
 
 It is desirable to introduce a correction factor C in (1) which shall 
 allow for the average ellipticity and variation in thickness. The cor- 
 rection for ellipticity = d (I>min/>max) 3 , and that for variation in 
 thickness = C 2 = (tmin/kver.) 3 . From Stewart's twenty-five experiments 
 Ci = 0.967 and Cz = 0.712. The correction factor C = Ci Cz = 0.69; 
 and (1) becomes 
 
 P = C[2Y(1 - m 2 )](i/D)3 ...... (7) 
 
 in which C = 0.69 for Stewart's lap-welded steel flues, t = average 
 thickness in ins., and D = maximum diameter in ins. 
 
 The empirical formulas obtained by Carman (Univ. of Illinois, Bull. 
 No. 17, 1906), are for thin cold-drawn seamless steel tubes, 
 
 P = 50,200,000 (t/D) 3 , 
 and for thin seamless brass tubes, 
 
 P = 25,150,000 (/D)3. 
 
 Carman assigns 0.025 as the upper limit of t/D for thin tubes and 0.03 
 as the lower limit of t/D for thick tubes. Stewart assigns 0.023 as the 
 limit of t/D between thin and thick tubes. 
 
 Comparing these with (3) and (5), it is evident that they correspond 
 to a correction factor of 0.76 for the steel tubes and 0.78 for the brass 
 tubes. Since Carman's experiments were performed on seamless drawn 
 tubes, while Stewart used lap-welded tubes, it might have been antici- 
 
344 
 
 STRENGTH OF MATERIALS. 
 
 COLLAPSING PRESSURE OF LAP- WELDED STEEL TUBES. 
 Outside Diameter, 85/ 8 In.; Length of Pipe, 20 Ft. 
 
 Thick- 
 ness, 
 In. 
 
 Length, 
 Ft. 
 
 Bursting 
 Pressure, 
 Lbs. per 
 Sq. In. 
 
 Aver- 
 age. 
 
 Outside 
 Diam. 
 In. 
 
 Thick- 
 ness. 
 
 Bursting 
 Pressure. 
 
 Aver- 
 age. 
 
 0.176 
 
 2.21 
 
 815-1085 
 
 977 
 
 3 
 
 0.112 
 
 1550-2175 
 
 1860 
 
 0.180 
 
 4.70 
 
 525-705 
 
 792 
 
 3 
 
 O.H3 
 
 2575-3350 
 
 2962 
 
 0.181 
 
 10.03 
 
 455-650 
 
 565 
 
 3 
 
 0.188 
 
 3700-4200 
 
 4095 
 
 0.184 
 
 14.71 
 
 425-610 
 
 548 
 
 4 
 
 0.119 
 
 860-1030 
 
 964 
 
 0.185 
 
 19.72 
 
 450-625 
 
 536 
 
 4 
 
 0.175 
 
 2050-2540 
 
 2280 
 
 0.212 
 
 2.21 
 
 1240-1353 
 
 1314 
 
 4 
 
 0.212 
 
 3075-3375 
 
 3170 
 
 0.212 
 
 4.70 
 
 805-975 
 
 907 
 
 4 
 
 0.327 
 
 5425-5625 
 
 5560 
 
 0.217 
 
 10.50 
 
 700-960 
 
 841 
 
 6 
 
 0.130 
 
 450-640 
 
 524 
 
 0.219 
 
 12.79 
 
 750-1115 
 
 905 
 
 6 
 
 0.167 
 
 715-1110 
 
 928 
 
 0.268 
 
 2.14 
 
 1475-2200 
 
 ' 1872 
 
 6 
 
 0.222 
 
 1200-2075 
 
 1797 
 
 0.274 
 
 4.64 
 
 1345-2030 
 
 1684 
 
 6 
 
 0.266 
 
 1750-2890 
 
 2441 
 
 0.272 
 
 9.64 
 
 1150-1908 
 
 1583 
 
 7 
 
 0.160 
 
 515-675 
 
 592 
 
 0.273 
 
 14.64 
 
 1250-1725 
 
 1485 
 
 7 
 
 0.242 
 
 1525-1850 
 
 1680 
 
 0.268 
 
 19.64 
 
 1250-1520 
 
 1419 
 
 7 
 
 0.279 
 
 1835-2445 
 
 2147 
 
 0.311 
 
 2.16 
 
 2290-2490. 
 
 2397 
 
 8.64 
 
 0.185 
 
 450-625 
 
 536 
 
 0.306 
 
 4 64 
 
 1795-2325 
 
 2073 
 
 8.66 
 
 0.268 
 
 1250-1520 
 
 1419 
 
 0.306 
 
 9.64 
 
 1585-2055 
 
 1807 
 
 8.67 
 
 0.354 
 
 1830-2180 
 
 2028 
 
 0.309 
 
 14.64 
 
 1520-2025 
 
 1781 
 
 10 
 
 0.165 
 
 210-240 
 
 225 
 
 0.302 
 
 19.75 
 
 1575-1960 
 
 1762 
 
 10 
 
 0.194 
 
 305-425 
 
 383 
 
 
 
 
 
 10 
 
 0.316 
 
 1275-1385 
 
 1319 
 
 
 
 
 
 
 
 
 
 COLLAPSING PRESSURE OF LAP- WELDED STEEL TUBES <,LBS. PER SQ. IN.) 
 Calculated by Stewart's Formulae. 
 
 Outside Diameters, Inches. 
 
 ickness. 
 
 2 In. 
 
 21/2 
 In. 
 
 3 In. 
 
 4 In. 
 
 5 In. 
 
 6 In. 
 
 7 In. 
 
 8 In. 
 
 9 In. 
 
 10 In. 
 
 11 In 
 
 H 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 2947 
 
 2081 
 
 1503 
 
 781 
 
 
 
 
 
 
 
 
 12 
 
 3814 
 
 2774 
 
 2081 
 
 1214 
 
 694 
 
 400 
 
 
 
 
 
 
 0.14 
 
 4671 
 
 3468 
 
 2659 
 
 1647 
 
 1041 
 
 636 
 
 400 
 
 286 
 
 217 
 
 
 
 0.16 
 
 5548 
 
 4161 
 
 3236 
 
 2081 
 
 1387 
 
 925 
 
 595 
 
 400 
 
 297 
 
 232 
 
 J87 
 
 0.18 
 
 6414 
 
 4854 
 
 3814 
 
 3514 
 
 1734 
 
 1214 
 
 843 
 
 564 
 
 400 
 
 306 
 
 244 
 
 0.20 
 
 7281 
 
 5548 
 
 4392 
 
 2947 
 
 2081 
 
 1503 
 
 1090 
 
 781 
 
 542 
 
 400 
 
 314 
 
 0.22 
 
 8148 
 
 6241 
 
 4970 
 
 3381 
 
 2427 
 
 1792 
 
 1338 
 
 997 
 
 733 
 
 525 
 
 400 
 
 0.24 
 
 9014 
 
 6934 
 
 5548 
 
 3814 
 
 2774 
 
 2081 
 
 1586 
 
 1214 
 
 935 
 
 694 
 
 512 
 
 0.26 
 
 9881 
 
 7628 
 
 6125 
 
 4248 
 
 3121 
 
 2370 
 
 1833 
 
 1431 
 
 1118 
 
 867 
 
 633 
 
 0.28 
 
 
 8321 
 
 6703 
 
 4681 
 
 3468 
 
 2669 
 
 2081 
 
 1647 
 
 1310 
 
 1041 
 
 820 
 
 0.30 
 
 
 9014 
 
 7281 
 
 5114 
 
 3814 
 
 2947 
 
 2328 
 
 1864 
 
 1503 
 
 1214 
 
 978 
 
 0.32 
 
 
 9708 
 
 7859 
 
 5548 
 
 4161 
 
 3236 
 
 2576 
 
 2081 
 
 1696 
 
 1387 
 
 1135 
 
 34 
 
 
 
 8437 
 
 5981 
 
 4508 
 
 3525 
 
 2824 
 
 2297 
 
 1888 
 
 1561 
 
 1293 
 
 36 
 
 
 
 9014 
 
 6414 
 
 4854 
 
 3814 
 
 3071 
 
 2514 
 
 2081 
 
 1734 
 
 1450 
 
 38 
 
 
 
 9592 
 
 6848 
 
 5201 
 
 4103 
 
 3319 
 
 2731 
 
 2273 
 
 1907 
 
 1608 
 
 0.40 
 
 
 
 
 7281 
 
 5548 
 
 4392 
 
 3567 
 
 2947 
 
 2466 
 
 2081 
 
 1766 
 
 0.42 
 
 
 
 
 7714 
 
 5894 
 
 4681 
 
 3814 
 
 3164 
 
 2659 
 
 2254 
 
 1923 
 
 44 
 
 
 
 
 8148 
 
 6241 
 
 4970 
 
 4062 
 
 3381 
 
 2851 
 
 2427 
 
 2081 
 
 46 
 
 
 
 
 8581 
 
 6588 
 
 5259 
 
 4309 
 
 3598 
 
 3044 
 
 2601 
 
 2238 
 
 48 
 
 
 
 
 9014 
 
 6934 
 
 5548 
 
 4557 
 
 3814 
 
 3236 
 
 2774 
 
 2396 
 
 0.50 
 
 
 
 
 9448 
 
 7281 
 
 5887 
 
 4805 
 
 4031 
 
 3429 
 
 2947 
 
 2554 
 
 
 
 
 
 
 
 
 
 
 
 
 
HOLLOW COPPER BALLS. 345 
 
 pated that the latter would develop a smaller percentage of the theo- 
 retical strength for perfect tubes than the former. 
 
 Formula (2) for thick tubes when corrected for ellipticity and varia^ 
 tion in thickness reads 
 
 P = 2u c C (t/D) [1 - C (t/D)] (8) 
 
 in which t = average thickness, and C = C it Cz, Ci being equal to 
 
 Pminx-OmaxI Cz = ^average/train- 
 
 From Stewart's experiments, average ellipticity C\ = 0.9874, and 
 average variation in thickness Ci = 0.9022; .'. C = 0.9874 X 0.9022 
 = 0.89. 
 
 We have then, for thick lap-welded steel flues, 
 
 P = 2w c 0.89 (t/D) [I - 
 knd for thin lap-welded steel flues, 
 
 P = 0.69 [2 E/(l - m*) 
 in which E = 30,000,000, m = 0.295, and u c = 38,500 Ibs. per sq. in. 
 
 The experimental data of Stewart and Carman have made it possible 
 to correct the rational formulas of Love and Lam6 to conform to actual 
 conditions; and the result is a pair of supplementary formulas (7) and 
 (8), which cover the entire range of materials, diameters, and thicknesses 
 for long tubes of circular section. All that now remains to be done is 
 the experimental . determination of the correction constants for other 
 types of commercial tubes than those already tested. 
 
 HOLLOW COPPER BALLS. 
 
 Hollow copper balls are used as floats in boilers or tanks, to control 
 feed and discharge valves, and regulate the water-level. 
 
 They are spun up in halves from sheet copper, and a rib is formed on 
 one half. Into this rib the other half fits, and the two are then soldered 
 or brazed together. In order to facilitate the brazing, a hole is left on 
 one side of the ball, to allow air to pass freely in or out; and this hole is 
 made use of afterwards to secure the float to its stem. The original 
 thickness of the metal may be anything up to about Vie of an inch, if 
 the spinning is done on a hand lathe, though thicker metal may be used 
 when special machinery is provided for forming it. In the process of 
 spinning, the metal is thinned down in places by stretching; but the 
 thinnest place is neither at the equator of the ball (i.e., along the rib) 
 nor at the poles. The thinnest points lie along two circles, passing 
 around the ball parallel to the rib, one on each side of it, from a third 
 to a half of the way to the poles. Along these lines the thickness may 
 be 10, 15, or 20 per cent less than elsewhere, the reduction depending 
 somewhat on the skill of the workman. 
 
 The Locomotive for October, 1891, gives two empirical rules for deter- 
 mining the thickness of a copper ball which is to work under an external 
 pressure, as follows: 
 
 ,_,, . diameter in inches X pressure in pounds per sq. in. 
 
 16.000 
 2. Thickness - diameter xVpressure. 
 
 These rules give the same result for a pressure of 166 Ibs. only. EX- 
 AMPLE: Required the thickness of a 5-inch copper ball to sustain 
 
 Pressures of 50 100 150 166 200 250 lbs.persq.in. 
 
 Answer by first rule 0156 .0312 .0469 .0519 .0625 .0781 inch. 
 
 Answer by second rule .0285 .0403 .0494 .0518 .0570 ,0637 " 
 
346 STRENGTH OF MATERIALS. 
 
 HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 
 
 (A. W. Wright, Western Society of Engineers, 1881.) 
 Spikes. Spikes driven into dry cedar (cut 18 months): 
 
 Size of spikes 5 X V4in. sq. 6 X 1/4 6 X 1/2 5 X3/S 
 
 Length driven in 41/4 in. 5 in. 5 in. 4i/4in. 
 
 Pounds resistance to drawing. Av'ge. Ibs. 857 821 1691 1202 
 
 Frnm fi tn Q tptq Pflrh I Max - " 1159 923 2129 1556 
 
 I rom 6 to 9 tests each { Min ?66 766 U20 68? 
 
 A. M. Wellington found the force required to draw spikes 9/ig X 9 /i6 in., 
 driven 41/4 inches into seasoned oak, to be 4281 Ibs.; same spikes, etc., 
 in unseasoned oak, 6523 Ibs. 
 
 "Professor W. R. Johnson found that a plain spike 3/ 8 inch square 
 driven 33/g inches into seasoned Jersey yellow pine or unseasoned chest- 
 nut required about 2000 Ibs. force to extract it; from seasoned white 
 oak about 4000 and from well-seasoned locust 6000 Ibs." 
 
 Experiments in Germany, by Funk, give from 2465 to 3940 Ibs. (mean 
 of many experiments about 3000 Ibs.) as the force necessary to extract a 
 plain i/2-inch square iron spike 6 inches long, wedge-pointed for one inch 
 and driven 41/2 inches into white or yellow pine. When driven 5 inches 
 the force required was about Vio part greater. Similar spikes 9/ 16 inches 
 square } 7 inches long, driven 6 inches deep, required from 3700 to 6745 
 Ibs. to extract them from pine; the mean of the results being 4873 Ibs. 
 In ail cases about twice as much force was required to extract them 
 from oak. The spikes were all driven across the grain of the wood. 
 When driven with the grain, spikes or nails do not hold with more than 
 half as much force. 
 
 Boards of oak or pine nailed together by from 4 to 16 tenpenny com- 
 mon cut nails and then pulled apart in a direction lengthwise of the 
 boards, and across the nails, tending to break the latter in two by a 
 shearing action, averaged ab9ut 300 to 400 Ibs. per nail to separate 
 them, as the result of many trials. 
 
 Resistance of Drift-bolts in Timber. Tests made by Rust and 
 Coolidge, in 1878. 
 
 White Norway 
 Pine. Pine. 
 
 1 in. square iron drove 30 in. in 15/ie-in. hole, Ibs 26,400 19,200 
 
 1 in. round " " 34 " " !3/i 6 -in. " 16,800 18,720 
 
 1 in. square " " 18 " " i5/ 16 _i n . " 14,600 15,600 
 
 1 in. round 22 " " i3/i 6 -in. " 13,200 14,400 
 
 Holding-power of Bolts in White Pine. (Eng'g News, Sept. 26, 1891.) 
 
 Round. Square. 
 Lbs. Lbs. 
 
 Average of all plain 1-in. bolts 8224 8200 
 
 Average of all plain bolts, 5/ 8 to 1 ifo in 7805 8110 
 
 Average of all bolts 8383 8598 
 
 Round drift-bolts should be driven in holes i3/ie of their diameter, and 
 square drift-bolts in holes whose diameter is 14/16 of the side of the square. 
 
 Force required to draw Screws out of Norway Pine. 
 
 1/2" diam. drive screw 4 in. in wood. Power required, average 2424 Ibs. 
 
 4 threads per in. 5 in. in wood. " 2743 
 
 1 D'blethr'd,3perin., 4in. in " 2730 
 
 Lag-screw, 7 per in., 1 1/2 " 1465 
 
 6 " " 21/2 "" " " 2026 
 
 1/2 inch R.R. spike 5 2191 
 
 Force required to draw Wood Screws out of Dry Wood. Tests 
 made by Mr. Bevan. The screws were about two inches in length, 0.22 
 diameter at the exterior of the threads, 0.15 diameter at the bottom, the 
 depth of the worm or thread being 0.035 and the number of threads in one 
 inch equal 12. They were passed through pieces of wood half an inch 
 in thickness and drawn-out by the weights stated: Beech, 460 Ibs.; ash, 
 
STRENGTH OF BOLTS. 347 
 
 790 Ibs.; oak, 760 Ibs.; mahogany, 770 Ibs.; elm, 665 Ibs.; sycamore, 
 830 Ibs. 
 
 Tests of Lag-screws in Various Woods were made by A. J. Cox, 
 University of Iowa, 1891: 
 
 Kind of Wood. |V jg St. 
 
 Seasoned white oak . ... 5/8 in. 1/2 in. 4 1/2 in. 8037 3 
 
 7/i6 " 3 6480 1 
 
 1/2 " 3 /8 ' 41/2 " 8780 2 
 
 5/8 
 
 Yellow-pine stick 5/ 8 " l/ 2 ' 4 3800 2 
 
 White cedar, unseasoned 5/s " J /2 ' 4 3405 2 
 
 Cut versus Wire Nails. Experiments were made at the Watertown 
 Arsenal in 1893 on the comparative direct tensile adhesion, in pine and 
 spruce, of cut and wire nails. The results are stated by Prof. W. H. Burr 
 as follows: 
 
 There were 58 series of tests, ten pairs of nails (a cut and a wire nail 
 in each) being used. The tests were made in spruce wood in most in- 
 stances. The nails were of all sizes, from li/s to 6 in. in length. In 
 every case the cut nails showed the superior holding strength by a large 
 percentage. In spruce, in nine different sizes of nails, b9th standard 
 and light weight, the ratio of tenacity of cut to wire nail was about 
 3 to 2. With the" finishing" nails the ratio was roughly 3.5 to 2. With 
 box nails (l\ to 4 inches long) the ratio was roughly 3 to 2. The mean 
 superiority in spruce wood was 61%. In white pine, cut nails, driven 
 with taper along the grain, showed a superiority of 100%, and with 
 taper across the grain of 135%. Also when the nails were driven in the 
 end of the stick, i.e., along the grain, the superiority of cut nails was 
 100%, or the ratio of cut to wire was 2 to 1. Thfc total of the results 
 showed the ratio of tenacity to be about 3.2 to 2 for the harder wood, 
 and about 2 to 1 for the softer, and for the whole taken together the 
 ratio was 3.5 to 2. 
 
 Nail-holding Power of Various Woods. Tests at the Watertown 
 Arsenal on different sizes of nails from 8d. to 60d., reduced to holding 
 power per sq. in. of surface in wood, gave average results, in pounds, 
 as follows: white pine, wire, 167; cut, 405. Yellow pine, wire, 318; cut, 
 662. White oak, wire, 940; cut, 1216. Chestnut, cut, 683. Laurel, 
 wire, 651; cut, 1200. 
 
 Experiments by F. W. Clay. (Eng'g News, Jan. 11, 1894.) 
 
 t Tenacity of 6d nails \ 
 
 Plain. Barbed. Blued. Mean. 
 
 White pine 106 94 135 111 
 
 Yellow pine 190 130 270 196 
 
 Basswood 78 132 219 143 
 
 White oak .-226 300 555 360 
 
 Hemlock 141 201 319 220 
 
 STRENGTH OF BOLTS. 
 
 Effect of Initial Strain in Bolts. Suppose that bolts are used to 
 connect two parts of a machine and that they are screwed up tightly 
 before the effective load comes on the connected parts. Let Pi = the 
 initial tension on a bolt due to screwing up, and Pz the load after- 
 wards added. The greatest load may vary but little from Pi or Pz, 
 according as the former or the latter is greater, or it may approach the 
 value Pi + Pz, depending upon the relative rigidity of the bolts and of 
 the parts connected. Where rigid flanges are bolted together, metal to 
 metal, it is probable that the extension of the bolts with any additional 
 tension relieves the initial tension, and that the total tension is Pi or Pz, 
 but in cases where elastic packing, as india rubber, is interposed, the 
 extension of the bolts may very little affect the -initial tension, and the 
 total strain may be nearly Pi + Pz. Since the latter assumption is 
 more unfavorable to the resistance of the bolt, this contingency should 
 usually be provided for. (See Unwin, "Elements of Machine Design," 
 for demonstration.) 
 
348 
 
 STRENGTH OF MATERIALS. 
 
 Forrest E. Cardullo (Machinery's Reference Series No. 22, 1908) states 
 the effect of initial stress in bolts due to screwing them tight as follows: 
 
 1. When the bolt is more elastic than the material it compresses, the 
 stress in the bolt is either the initial stress or the force applied, whichever 
 is greater. 
 
 2. When the material compressed is more elastic than the bolt, the 
 stress in the bolt is the sum of the initial stress and the force applied. 
 
 Experiments on screwing up 1/2, 8/4, 1 and 1 1/4 in. bolts showed that the 
 stress produced is often sufficient to break a i/2-in...bolt, and that the stress 
 varies about as the square of the diameter. From these experiments 
 Prof. Cardullo calculates what he calls the "working section" of a bolt as 
 equal to its area at the root of the thread, less the area of a i/2-in. bolt 
 at the root of the thread times twice the diameter of the bolt, and gives 
 the following table based on this rule. 
 
 Working Strength of Bolts. U. S. Standard Threads. 
 
 
 
 tat 
 
 a 
 
 V 
 
 . 
 
 . 
 
 , 
 
 
 
 
 "o 
 
 n 
 
 st 
 
 .2 
 
 "o 
 
 I 
 
 1. 
 
 1- 
 
 1-3 
 
 ! 
 
 Q 
 
 1". 
 
 to| 
 
 "oil 
 
 *8la 
 
 'o'S 
 
 *! 
 
 *s 1 
 
 'o 
 
 Si . 
 
 a'Ss 
 
 bc'o 
 
 ri O 
 
 rd O ' 
 
 ^ , 
 
 sL 
 
 5 ft 
 
 ^ * m 
 
 2-2 
 
 o 
 
 Mij 
 
 II 
 
 w> g 
 
 ||| 
 
 ||| 
 
 fcj[l o 
 
 c 1 
 
 c 
 
 11 
 
 H.S 
 
 o S* 
 
 to 
 
 
 H^to 
 
 ^to 
 
 ^2"to 
 
 ^^Tto 
 
 p 
 
 < 
 
 ^ 
 
 ro 
 
 ^ 
 
 
 to 
 
 to 
 
 to 
 
 1/2 
 
 0.126 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5/8 
 
 0.202 
 
 0.044 
 
 220 
 
 264 
 
 308 
 
 352 
 
 440 
 
 528 
 
 3/4 
 
 0.302 
 
 0.113 
 
 565 
 
 678 
 
 791 
 
 904 
 
 1,130 
 
 1,356 
 
 7/8 
 
 0.420 
 
 0.200 
 
 1,000 
 
 1,200 
 
 1,400 
 
 1,600 
 
 2,000 
 
 2,400 
 
 1 
 
 0.550 
 
 0.298 
 
 1,490 
 
 1,788 
 
 2,086 
 
 2,384 
 
 2,980 
 
 3,476 
 
 U/8 
 
 0.694 
 
 0.411 
 
 2,055 
 
 2,466 
 
 2,877 
 
 3,288 
 
 4,110 
 
 4,932 
 
 11/4 
 
 0.893 
 
 0.578 
 
 2,890 
 
 3,468 
 
 4,046 
 
 4,624 
 
 5,780 
 
 6,936 
 
 
 1.057 
 
 0.710 
 
 3,550 
 
 4,260 
 
 4,970 
 
 5,680 
 
 7,100 
 
 8,520 
 
 H/2 
 
 1.295 
 
 0.917 
 
 4,585 
 
 5,502 
 
 6,419 
 
 7,336 
 
 9,170 
 
 10,504 
 
 15/8 . 
 
 1.515 
 
 1.105 
 
 5,525 
 
 6,630 
 
 7,735 
 
 8,840 
 
 11,050 
 
 13,2oO 
 
 
 1.746 
 
 1.305 
 
 6,525 
 
 7,830 
 
 9,135 
 
 10,440 
 
 13,050 
 
 15,660 
 
 17/8 
 
 2.051 
 
 1.578 
 
 7,890 
 
 9,468 
 
 11,046 
 
 12,624 
 
 15,780 
 
 18,936 
 
 2 
 
 2.302 
 
 1.798 
 
 8,990 
 
 10,788 
 
 12,586 
 
 14,384 
 
 17,980 
 
 21,576 
 
 21/4 
 
 3.023 
 
 2.456 
 
 12,280 
 
 14,736 
 
 17,192 
 
 19,648 
 
 24,560 
 
 29,472 
 
 21/2 
 
 3.719 
 
 3.089 
 
 15,445 
 
 18,534 
 
 21,623 
 
 24,712 
 
 30,890 
 
 37,068 
 
 23/4 
 
 4.620 
 
 3.927 
 
 19,635 
 
 23,562 
 
 27,489 
 
 31,416 
 
 39,270 
 
 47,124 
 
 3 
 
 5.428 
 
 4.672 
 
 23,360 
 
 28,032 
 
 32,704 
 
 37,376 
 
 46,720 
 
 56,064 
 
 31/4 
 
 6.510 
 
 5.690 
 
 28,450 
 
 34,140 
 
 39,830 
 
 45,520 
 
 56,900 
 
 68,280 
 
 31/2 
 
 7.548 
 
 6.666 
 
 33,330 
 
 39,996 
 
 46,664 
 
 53,328 
 
 66,660 
 
 79,992 
 
 The stresses on bolts caused by tightening the nuts by a wrench may 
 be calculated as follows: Let L = the effective length of the wrench in 
 inches, P = the force in pounds applied at the distance L, n = no. of 
 threads per inch of the bolt, T = total tension on the bolt if there were 
 no friction, then T = 2 nnLP. Wilfred Lewis, Trans. A. S. M. E., gives 
 for the efficiency of a bolt E = 1 -f- (1 + nd), where d = external diameter 
 of the screw. T X E = 2nnLP -4- (1 + nd) is the tension corrected 
 for friction. It also expresses the load that can be lifted by screwing a 
 nut on a bolt or a bolt into a nut. 
 
 STRENGTH OF CHAINS. 
 
 Formulas for Safe Load on Chains. Writing the formula for the safe 
 lead on chains P Kd 2 , P in pounds, d in inches, the following figures for 
 K are given by the authorities named. 
 
 Open link Stud link 
 
 Unwin ' 13,440; 11,200* 20,160. 
 
 Weisbach 13,350 17,800 
 
 Bach 13,750; 11,000* 16,500; 13,200* 
 
 * The lower figures are for much used chain, subject frequently to the 
 maximum load. G. A Goodenough and L. E. Moore, Univ. of Illinois 
 
STAND-PIPES AND THEIR DESIGN. 349 
 
 STAND-PIPES AND THEIR DESIGN. 
 
 (Freeman C. Coffin, New England Water Works Assoc., Eng. News, 
 March 16, 1893.) See also papers by A. H. Rowland, Eng. Club of Phil., 
 1887; B. F. Stephens, Amer. Water Works Assoc., Eng. News, Oct. 6 
 and 13, 1888; W. Kiersted, Rensselaer Soc. of Civil Eng., Eng'g Record, 
 April 25 and May 2, 1891, and W. D. Pence, Eng. News, April and May, 
 1894- also, J. N. Hazlehurst's " Towers and Tanks for Water Works." 
 
 The question of diameter is almost entirely independent of that of 
 height. The efficient capacity must be measured by the length from the 
 high- water line to a point below which it is undesirable to draw the 
 water on account of loss of pressure for fire-supply, whether that point 
 is the actual bottom of the stand-pipe or above it. This allowable 
 fluctuation ought not to exceed 50 ft., in most cases. This makes the 
 diameter dependent upon two conditions, the first of which is the amount 
 of the consumption during the ordinary interval between the stopping and 
 starting of the pumps. This should never draw the water below a point that 
 will give a good fire stream and leave a margin for still further draught 
 for fires. The second condition is the maximum number of fire streams 
 and their size which it is considered necessary to provide for, and the 
 maximum length of time which they are liable to have to run before the 
 pumps can be relied upon to reinforce them. 
 
 Another reason for making the diameter large is to provide for stability 
 against wind-Dressiire when empty. 
 
 The following table gives the height of stand-pipes beyond which they 
 are not safe against wind-pressures of 40 and 50 Ibs. per square foot. 
 The area of surface taken is the height multiplied by one half the 
 diameter. 
 
 Diameter, feet 20 25 30 35 
 
 Max. height, wind 40 Ibs 45 70 150 
 
 1 50 " 35 55 80 160 
 
 Any form of anchorage that depends upon connections with the side 
 plates near the bottom is unsafe. By suitable guys the wind-pressure is 
 resisted by tension in the guys, and the stand-pipe is relieved from 
 wind strains that tend to overthrow it. The guys should be attached to 
 a band of angle or other shaped iron that completely encircles the tank, 
 and rests upon some sort of bracket or projection, and not be riveted to 
 the tank. They should be anchored at a distance from the base equal 
 to the height of the point at which they are attached, if possible. 
 
 The best plan is to build the stand-pipe of such diameter that it will 
 resist the wind by its own stability. 
 
 Thickness of the Side Plates. 
 
 The pressure on the sides tending to rupture the plates by tension, due 
 to the weight of the water, increases in direct ratio to the height, and 
 also to the diameter. The strain upon a section 1 inch in height at any 
 point is the total strain at that point divided by two for each side is 
 supposed to bear the strain equally. The total pressure at any point is 
 equal to the diameter in inches, multiplied by the pressure per square 
 inch, due to the height at that point. It may be expressed as follows: 
 
 H height in feet, and / = factor of safety; 
 d = diameter in inches; 
 p = pressure in Ibs. per square inch; 
 0.434 = p for 1 ft. in height; 
 
 s = tensile strength of material per square.inch; 
 T = thickness of plate. 
 
 Bulletin, No. 18, 1907, after an extensive theoretical and experimental 
 Investigation, find that these values give maximum stresses in the external 
 fibers of from 26,400 to 40,320 Ibs. per sq. in., which they consider much 
 too high for safety. Taking 20,000 as a permissible maximum stress, 
 they give the formulae for safe load P = 8000 d 2 for open links and 
 P = 10,000 d z for stud links. They say that the stud link will within 
 the elastic limit bear from 20 to 25% more load than the open link, but 
 that the ultimate strength of the stud'link is probably less than that of the 
 open link. See also tables of Size and Strength of Chains, page 264. 
 
350 STRENGTH OF MATERIALS. 
 
 Then the total strain on each side per vertical inch 
 
 = 0.434 Hd = pd , T = OA34Hdf = pdf 
 2 2 ' 2s ~ 2s' 
 
 Mr. Coffin takes / = 5, not counting reduction of strength of joint, 
 equivalent to an actual factor of safety of 3 if the strength of the riveted 
 joint is taken as 60 per cent of that of the plate. 
 
 The amount of the wind strain per square inch of metal at any joint 
 can be found by the following formula, in which 
 
 H = height of stand-pipe in feet above joint; 
 T = thickness of plate in inches; 
 p = wind-pressure per square foot; 
 W = wind-pressure per foot in height above joint; 
 W Dp where D is the diameter in feet; 
 m = average leverage or movement about neutral axis 
 
 or central points in the circumference; or, 
 m = sine of 45, or 0.707 times the radius in feet. 
 
 Then the strain per square inch of plate 
 (Hw) f 
 
 circ. in ft. X mT 
 
 Mr. Coffin gives a number of diagrams useful in the design of stand- 
 pipes, together with a number of instances of failures, with discussion 
 of their probable causes. 
 
 Mr. Kiersted's paper contains the following: Among the most promi- 
 nent strains a stand-pipe has to bear are: that due to the static pressure 
 of the water, that due to the overturning effect of the wind on an empty 
 stand-pipe, and that due to the collapsing effect, on the upper rings, of 
 violent wind storms. 
 
 For the thickness of metal to withstand safely the static pressure of 
 water, let t = thickness of the plate iron in inches; H = height of stand- 
 pipe in feet; D = diameter of stand-pipe in feet. 
 
 Then, assuming a tensile strength of 48,000 Ibs. per square inch, a 
 factor of safety of 4, and .efficiency of double-riveted lap-joint equaling 
 0.6 of the strength of the solid plate, t = 0.00036 H X D; H = 10,000 t 
 -+-3.6D; which will give safe heights for thicknesses up to 5/ 8 to 3/ 4 of an 
 inch. The same formula may also apply for greater heights and thick- 
 nesses within practical limits, if the joint efficiency be increased by triple 
 riveting. 
 
 The conditions for the severest overturning wind strains exist when 
 the stand-pipe is empty. 
 
 Formula for wind-pressure of 50 pounds per square foot, whend = 
 diameter of stand-pipe in inches; x = any. unknown height of stand- 
 pipe; x = VsOTrctf = 15.85 V(#. 
 
 Failures of Stand-pipes. A list showing 23 important failures 
 inside of nine years is given in a paper by Prof. W. D. Pence, Eng'g 
 News, April 5, 12, 19 and 26, May 3, 10 and 24, and June 7, 1894. His 
 discussion of the probable causes of the failures is most valuable. 
 
 Water Tower at Yonkers, N.Y. This tower, with a pipe 122 feet 
 high and 20 feet diameter, is described in Engineering News, May 18, 1892. 
 
 The thickness of the lower rings is u/16 of an inch, based on a tensile 
 strength of 60,000 Ibs. per square inch of metal, allowing 65% for the 
 strength of riveted joints, using a factor of safety of 31/2 and adding a 
 constant of l/g inch. The plates diminish in thickness by Vie inch to 
 the last four plates at the top, which are 1/4 inch thick. 
 
 The contract for steel requires an elastic limit of at least 33,000 Ibs. 
 per square inch; an ultimate tensile strength of from 56,000 to 66,000 Ibs. 
 per square inch; an elongation in 8 inches of at least 20%, and a reduc- 
 tion of area of at least 45%. The inspection of the work was made by the 
 Pittsburgh Testing Laboratory. According to their report the actual 
 conditions developed were as follows: Elastic limit from 34,020 to 39,420; 
 
WROUGHT-IRON AND STEEL WATER PIPES. 
 
 351 
 
 the tensile strength from 58,330 to 65,390; the elongation in 8 inches 
 from 221/2 to 32%; reduction in area from 52.72 to 71.32%; 17 plates 
 out of 141 were rejected in the inspection. 
 
 The following table is calculated by Mr. Kiersted's formulae. The 
 stand-pipe is intended to be self-sustaining; that is, without guys or 
 stiff eners. 
 
 Heights of Stand-pipes for Various Diameters and Thicknesses of 
 Plates. 
 
 Thickness 
 of Plate 
 in Frac- 
 tions of 
 an Inch. 
 
 Diameters in Feet. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 25 
 
 3/16 
 7/32 
 
 50 
 55 
 
 55 
 
 60 
 
 65 
 
 55 
 65 
 75 
 90 
 100 
 110 
 115 
 125 
 130 
 
 50 
 60 
 70 
 85 
 100 
 115 
 120 
 130 
 135 
 145 
 150 
 
 35 
 50 
 55 
 70 
 85 
 100 
 115 
 130 
 145 
 155 
 165 
 
 
 
 
 
 
 
 40 
 50 
 60 
 75 
 85 
 100 
 110 
 120 
 135 
 145 
 160 
 
 40 
 
 45 
 55 
 70 
 80 
 90 
 100 
 115 
 125 
 135 
 150 
 160 
 
 
 
 
 
 1/4 . . - 
 5/16- .. . 
 3/8- .. 
 7/16- .- 
 V2 .... 
 9 /16 
 
 60 
 70 
 75 
 80 
 85 
 
 65 
 75 
 80 
 90 
 95 
 
 70 
 80 
 90 
 95 
 100 
 
 75 
 
 85 
 95 
 100 
 110 
 115 
 
 40 
 50 
 65 
 75 
 85 
 95 
 105 
 120 
 130 
 140 
 150 
 160 
 
 35 
 45 
 55 
 65 
 75 
 85 
 95 
 105 
 115 
 125 
 135 
 145 
 155 
 
 35 
 40 
 50 
 60 
 70 
 80 
 85 
 95 
 105 
 110 
 120 
 130 
 140 
 
 25 
 35 
 40 
 45 
 55 
 60 
 65 
 75 
 80 
 90 
 95 
 105 
 110 
 
 5/ 8 
 
 
 
 
 11/16 
 
 
 
 
 
 3/4 
 
 
 
 
 
 
 13/ 16 
 
 
 
 
 
 
 7/8. ..., 
 
 
 
 
 
 
 
 
 15/ 16 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Heights to nearest 5 feet. Rings are to build 5 feet vertically. 
 
 WROUGHT-IRON AND STEEL WATER-PDPES. 
 
 Riveted Steel Water-pipes (Engineering News, Oct. 11, 1890, and 
 Aug. 1, 1891). The use of riveted wrought-iron pipe has been common 
 in the Pacific States for many years, the largest being a 44-inch conduit 
 in connection with the works of the Spring Valley Water Co., which 
 supplies^San Francisco. The use of wrought iron and steel pipe has been 
 necessary in the West, owing to the extremely high pressures to be with- 
 stood and the difficulties of transportation. As an example: In connec- 
 tion with the water supply of Virginia City and Gold Hill, Nev., there 
 was laid in 1872 an lli/2-inch riveted wrought-iron pipe, a part of which 
 is under a head of 1720 feet. 
 
 In the East, an important example of the use of riveted steel water 
 pipe is that of the East Jersey Water Co., which supplies the city of 
 Newark. The contract provided for a maximum high service supply of 
 25,000,000 gallons daily. In this case 21 miles of 48-inch pipe was laid, 
 some of it under 340 feet head. The plates from which the pipe is made 
 are about 13 feet long by 7 feet wide, open-hearth steel. Four plates 
 are used to make one section of pipe about 27 feet long. The pipe is 
 riveted longitudinally with a double row, and at the end joints with a 
 single row of rivets. Before being rolled into the trench, two of the 
 27-feet lengths are riveted together, thus diminishing the number of 
 joints to be made in the trench and the extra excavation to give room 
 for joining. 
 
 The thickness of the plates varies with the pressure, but only three 
 thicknesses are used, 1/4 , 5/ 16 , and 3/ 8 inches, the pipe made of these 
 thicknesses having a weight of 160, 185, and 225 IDS. per foot, respec- 
 tively. At the works all the pipe was tested to pressure 11/2 times that 
 to which it is to be subjected when in place. 
 
 An important discussion of the design of large riveted steel pipes t< 
 
352 STRENGTH OF MATERIALS. 
 
 resist not only the internal pressure but also the external pressure from 
 moist earth in which they are laid, together with notes on the design of a 
 pipe 18ft. diam. 6000 ft. long for the Ontario Water Power Co., Niagara 
 Falls, by Joseph Mayer, will be found in Eng. News, April 26, 1906. 
 
 STRENGTH OF VARIOUS MATERIALS. EXTRACTS FROM 
 KIRKALDY'S TESTS. 
 
 The publication, in a book by W. G. Kirkaldy, of the results of many 
 thousand tests made during a quarter of a century by his father, David 
 Kirkaldy, has made an important contribution to our knowledge con- 
 cerning the range of variation in strength of numerous materials. A 
 condensed abstract of these results was published in the American Ma- 
 chinist, May 11 and 18, 1893, from which the following still further con- 
 densed extracts are taken: 
 
 The figures for tensile and compressive strength, or, as Kirkaldy calls 
 them, pulling and thrusting stress, are given in pounds per square inch of 
 original section, and for bending strength in pounds of actual stress or 
 pounds per BD 2 (breadth X square of depth) for length of 36 inches 
 between supports. The contraction of area is given as a percentage of 
 the original area, and the extension as a percentage in a length of 10 
 inches, except when otherwise stated. The abbreviations T. S., E. L., 
 Contr., and Ext. are used for the sake of brevity, to represent tensile 
 strength, elastic limit, and percentages of contraction of area, and elon- 
 gation, respectively. 
 
 Cast Iron. 44 tests: T. S. 15,468 to 28,740 pounds; 17 of these 
 were unsound, the strength ranging from 15,468 to 24,357 pounds. 
 Average of all, 23,805 pounds. 
 
 Thrusting stress, specimens 2 inches long, 1.34 to 1.5 in. diameter; 
 43 tests, all sound, 94,352 to 131,912; one, unsound, 93,759; average of 
 all, 113,825. 
 
 Bending stress, bars about 1 in. wide by 2 in. deep, cast on edge. 
 Ultimate stress 2876 to 3854; stress per BD* = 725 to 892; average, 
 820. Average modulus of rupture, R, = 3/2 stress per BD 2 X length, 
 = 44,280. Ultimate deflection, 0.29 to 0.40 in.; average, 0.34 inch. 
 
 Other tests of cast iron, 460 tests, 16 lots from various sources, gave 
 results with total range as follows: Pulling stress, 12,688 to 33,616 
 pounds; thrusting stress, 66,363 to 175,950 pounds; bending stress, per 
 BD 2 , 505 to 1128 pounds; modulus of rupture, R, 27,270 to 61,912. 
 Ultimate deflection, 0.21 to 0.45 inch. 
 
 The specimen which was the highest in thrusting stress was also the 
 highest in bending, and showed the greatest deflection, but its tensile 
 Strength was only 26,502. 
 
 The specimen with the highest tensile strength had a thrusting stress of 
 143,939 and a bending strength, per BD 2 , of 979 pounds with 0.41 de- 
 flection. The specimen lowest in T. S. was also lowest in thrusting and 
 bending, but gave 0.38 deflection. The specimen which gave 0.21 deflec- 
 tion had T. S., 19,188: thrusting, 104,281; and bending, 561. 
 
 Iron Castings. 69 tests; tensile strength, 10,416 to 31,652; thrust- 
 Ing stress, ultimate per square inch, 53,502 to 132,031. 
 
 Channel Irons. Tests of 18 pieces cut from channel irons. T. S. 
 40,693 to 53,141 pounds per square inch; contr. of area from 3.9 to 
 32.5%. Ext. in 10 in. from 2.1 to 22.5%. The fractures ranged all the 
 way from 100% fibrous to 100% crystalline. The highest T. S., 53,141, 
 with 8.1% contr. and 5.3% ext., was 100% crystalline;' the lowest T. S., 
 iO, 693, with 3.9 contr. and 2.1% ext., was 75% crystalline. All the 
 fibrous irons showed from 12.2 to 22.5% ext., 17.3 to 32.5 contr., and 
 T. S. from 43,426 to 49,615. The fibrous irons are therefore of medium 
 tensile strength and high ductility. The crystalline irons are of variable 
 T. S., highest to lowest, and low ductility. 
 
 Lowmoor Iron Bars. Three rolled bars 21/2 inches diameter; ten- 
 Bile tests: elastic, 23,200 to 24,200; ultimate, 50,875 to 51,905; contrac- 
 tion, 44.4 to 42.5; extension, 29.2 to 24.3. Three hammered bars, 41/2 
 Inches diameter, elastic 25,100 to 24,200; ultimate, 46,810 to 49,223; 
 contraction, 20.7 to 46.5; extension, 10.8 to 31.6. Fractures of all, 100 
 per cent fibrous. In the hammered bars the lowest T. S, was accom- 
 panied by lowest ductility. 
 
KIRKALDY'S TESTS. 
 
 353 
 
 Iron Bars, Various. Of a lot of 80 bars of various sizes, some 
 rolled and some hammered (the above Lowmoor bars included), the 
 lowest T. S. (except one) 40,808 pounds per square inch, was shown by 
 the Swedish "hoop L" bar 31/4 inches diameter, rolled. Its elastic limit 
 was 19,150 pounds; contraction 68.7% and extension 37.7% in 10 
 inches. It was also the most ductile of all the bars tested, and was 100% 
 fibrous. The highest T. S., 60,780 pounds, with elastic limit, 29,400; 
 contr., 36.6; and ext., 24.3%, was shown by a " Farnley " 2-inch bar, 
 rolled. It was also 100% fibrous. The lowest ductility 2.6% contr., 
 and 4.1% ext., was shown by a 33/4-inch hammered bar, without brand. 
 It also had the lowest T. S., 40,278 pounds, but rather high elastic limit, 
 25,700 pounds. Its fracture was 95% crystalline. Thus of the two bars 
 showing the lowest T. S., one. was the most ductile and the other the 
 least ductile in the whole series of 80 bars. 
 
 Generally, high ductility is accompanied by low tensile strength, as in 
 the Swedish bars, but the Farnley bars showed a combination of high 
 ductility and high tensile strength. 
 
 Locomotive Forgings, Iron. -17 tests average, E. L., 30,420; 
 T. S., 50,521; contr., 36.5: ext. in 10 inches, 23.8. 
 
 Broken Anchor Forcings, Iron. 4 tests: average, E. L., 23,825; 
 T. S., 40,083; contr., 3.0; ext. in 10 inches, 3.8. 
 
 Kirkaldy places these two irons in contrast to show the difference 
 between good and bad work. The broken anchor material, he says, is 
 of a most treacherous character, and a disgrace to any manufacturer. 
 
 Iron Plate Girder. Tensile tests of pieces cut from a riveted iron 
 girder after twenty years' service in a railway bridge. Top plate, aver- 
 age of 3 tests, E. L., 26,600; T. S., 40,806; contr., 16.1; ext. in 10 inches, 
 7.8. Bottom plate, average of 3 tests, E. L., 31,200; T. S., 44,288; 
 contr., 13.3; ext. in 10 inches, 6.3. Web-plate, average of 3 tests, E. L., 
 28,000; T. S., 45,902; contr., 15.9; ext. in 10 inches, 8.9. Fractures 
 all fibrous. The results of 30 tests from different parts of the girder 
 prove that the iron has undergone no change during twenty years of use. 
 
 Steel Plates. Six plates 100 inches long, 2 inches wide, thickness 
 various, 0.36 to 0.97 inch. T. S., 55,485 to 60,805; E. L., 29,600 to 33,200; 
 contr., 52.9 to 59.5; ext., 17.05 to 18.57. 
 
 Steel Bridge Links. 40 links from Hammersmith Bridge, 1886. 
 
 
 Fracture. 
 
 
 T.S. 
 
 E. L. 
 
 Contr. 
 
 Ext. in 
 100 in. 
 
 Silky. 
 
 Gran- 
 ular. 
 
 70 
 
 65 
 100 
 
 Average of all 
 
 67,294 
 60,753 
 75,936 
 64,044 
 63,745 
 65,980 
 63,980 
 
 38,294 
 36,030 
 44, 1 66 
 32,441 
 38,118 
 36,792 
 39,017 
 
 34.5% 
 30.1 
 31.2 
 34.7 
 52.8 
 40.8 
 6.0 
 
 14.11% 
 15.51 
 12.42 
 13.43 
 15.46 
 17.78 
 6.62 
 
 30% 
 
 30 
 100 
 35 
 
 
 Lowest T. S 
 
 Highest T.S. and 'E. L.. . . 
 Lowest E . L 
 
 Greatest Contraction 
 
 Greatest Extension 
 Least Contr. and Ext 
 
 The ratio of elastic to ultimate strength ranged from 50.6 to 65.2 per 
 cent; average, 56.9 per cent. 
 
 Extension in lengths of 100 inches. At 10,000 Ibs. per sq. in., 0.018 to 
 0.024; mean, 0.020 inch; at 20,000 Ibs. per sq. in., 0.049 to 0.063- mean, 
 0.055 inch; at 30,000 Ibs. per sq. in., 0.083 to 0.100; mean, 0.090; set at 
 30,000 pounds per sq. in., to 0.002; mean, 0. 
 
 The mean extension between 10,000 to 30,000 Ibs. per sq. in. increased 
 regularly at the rate of 0.007 inch for each 2000 Ibs. per sq. in. increment 
 of strain. This corresponds to a modulus of elasticity of 28,571,429. 
 The least increase of extension for an increase of load of 20,000 Ibs. per 
 sq. in., 0.065 inch, corresponds to a modulus of elasticity of 30,769,231, 
 and the greatest, 0.076 inch, to a modulus of 26,315,789. 
 
 Steel Rails. Bending tests, 5 feet between supports, 11 tests of flange 
 rails 72 pounds per yard, 4.63 inches high, 
 
354 STRENGTH OF MATERIALS. 
 
 Elastic stress. Ultimate stress. Deflection at 50,000 Ultimate 
 
 Pounds. Pounds. Pounds. Deflection i 
 
 Hardest... 34,200 60,960 3.24 ins. Sins. 
 
 Softest 32,000 56,740 3.76 " 8 " 
 
 Mean 32,763 59,209 3.53 " 8 " 
 
 All uncracked at 8 inches deflection. 
 
 Pulling tests of pieces cut from same rails. Mean results. 
 
 Elastic Ultimate Contraction of 
 
 Stress. Pounds. area of frac- Extension | 
 
 per sq. in. per sq. in. ture. in 10 ins. 
 
 Top of rails 44,200 83,110 19.9% 13.5% 
 
 Bottom of rails 40,900 77,820 30.9% 22.8% 
 
 Steel Tires. Tensile tests of specimens cut from steel tires. 
 
 KRUPP STEEL. 262 Tests. 
 
 Ext. in 
 
 E. L. T. S. Contr. 5 inches. 
 
 Highest 69,250 119,079 319 18.1 
 
 Mean 52,869 104,112 29.5 19.7 
 
 Lowest 41,700 90,523 45.5 23.7 
 
 VICKERS, SONS & Co. 70 Tests. 
 
 Ext. in 
 
 E. L. T. S. Contr. 5 inches. 
 
 Highest 58,600 120,789 11.8 8.4 
 
 Mean 51,066 101,264 17.6 12.4 
 
 Lowest 43,700 87,697 24.7 16.0 
 
 Note the correspondence between Krupp's and yickers' steels as to 
 tensile strength and elastic limit, and their great difference in contrac- 
 tion and elongation. The fractures of the Krupp steel averaged 22 per 
 cent silky, 78 per cent granular; of the Vicker steel, 7 per cent silky, 
 93 per cent granular. 
 
 Steel Axles. Tensile tests of specimens cut from steel axles. 
 
 PATENT SHAFT AND AXLE TREE Co. 157 Tests. 
 
 Ext. in 
 E. L. T. S. Contr. 5 inches. 
 
 Highest 49,800 99,009 21.1 16.0 
 
 Mean 36,267 72,099 33.0 23.6 
 
 Lowest 31,800 61,382 34.8 25.3 
 
 VICKERS, SONS & Co. 125 Tests. 
 
 Ext. in 
 E. L. T. S. Contr. 5 inches. 
 
 Highest 42,600 83,701 18.9 13.2. 
 
 Mean 37,618 70,572 41.6 27.5 
 
 Lowest. , 30,250 56,388 49.0 37.2 
 
 The average fracture of Patent Shaft and Axle Tree Co. steel was 33 
 per cent silky, 67 per cent granular. 
 
 The average fracture of Vickers' steel was 88 per cent silky, 12 per 
 cent granular. 
 
 Steel Propeller Shafts. Tensile tests of pieces cut from two shafts, 
 mean of four tests each. Hallow shaft, Whitworth, T. S., 61,290: E. L., 
 30,575; contr., 52.8; ext. in 10 inches, 28.6. Solid shaft, VickersT, T. S., 
 46,870; E. L., 20,425; contr., 44.4; ext. in 10 inches, 30.7. 
 
 Thrusting tests, Whitworth, ultimate, 56,201; elastic, 29,300; set at 
 30,000 IDS., 0.18 per cent; set at 40,000 IDS., 2.04 per cent; set at 50,000 
 IDS., 3.82 per cent. 
 
 Thrusting tests, Vickers', ultimate, 44,602; elastic, 22,250; set at 
 30,000 Ibs., 2.29 per cent; set at 40,000 Ibs., 4.69 per cent. 
 
. .. 
 
 115,668;" contr., 37.8; ext. in' 10 inches, 16.6.' Spring steel untem- 
 pered, 15 tests, average, E. L., 38,785; T. S., 69,496; contr., 19.1; ext. 
 in 10 inches, 29.8. These two lots were shipped for the same purpose, 
 viz., railway carriage leaf springs. 
 
 Steel Castings. 44 tests, E. L., 31,816 to 35,567: T. S., 54,928 to 
 63,840; contr., 1.67 to 15.8; ext., 1.45 to 15.1. Note the great varia- 
 tion in ductility. The steel of the highest strength was also the most 
 ductile. 
 
 Riveted Joints, Pulling Tests of Riveted Steel Plates, Triple Riv- 
 eted Lap Joints, Machine Riveted, Holes Drilled. 
 
 Plates, width and thickness, inches: 
 13.50X0.25 13.00X0.51 11.75X0.78 
 Plates, gross sectional area square inches: 
 
 3.375 6.63 9.165 
 
 Stress, total, pounds: 
 
 199,320 332,640 423,180 
 
 Stress per square inch of gross area, joint: 
 
 59,058 50,172 46,173 
 
 Stress per square inch of plates, solid: 
 
 70,765 65,300 64,050 
 
 Ratio of strength of joint to solid plate: 
 
 83.46 76.83 72.09 
 
 Ratio net area of plate to gross: 
 
 73.4 65.5 
 
 Where fractured: 
 
 plate at plate at 
 
 holes. holes. 
 
 12.25 X 1.01 14.00X0.77 
 
 62.7 
 
 plate at 
 holes. 
 
 Rivets, diameter, area and number: 
 
 0.45, 0.159, 24 0.64, 0.321, 21 0.95,0.708, 12 
 
 Rivets, total area: 
 
 3.816 6.741 8.496 
 
 12.372 
 528,000 
 42,696 
 62,280 
 68.55 
 64.7 
 
 plate at 
 holes. 
 
 10.780 
 455,210 
 42,227 
 68,045 
 62.06 
 72.9 
 
 rivets 
 sheared 
 
 1.08, 0.916, 12 0.95,0.708, 12 
 10.992 8.496 
 
 Strength of Welds. Tensile tests to determine ratio of strength of 
 weld to solid bar. 
 
 IRON TIE BARS. 28 Tests. 
 
 Strength of solid bars varied from 43,201 to 57,065 Ibs. 
 
 Strength of welded bars varied from 17,816 to 44,586 Ibs. 
 
 Ratio of weld to solid varied from 37.0 to 79.1% 
 
 IRON PLATES. 7 Tests. 
 
 Strength of solid plate from 44,851 to 47,481 Ibs. 
 
 Strength of welded plate from 26,442 to 38,931 Ibs. 
 
 Ratio of weld to solid 57.7 to 83.9% 
 
 CHAIN LINKS. 216 Tests. 
 
 Strength of solid bar from 49,122 to 57,875 Ibs. 
 
 Strength of welded bar from 39,575 to 48,824 Ibs. 
 
 Ratio of weld to solid 72.1 to 95.4% 
 
 IRON BARS. Hand and Electric Machine Welded. 
 
 32 tests, solid iron, average 52,444 
 
 17 electric welded, average 46,836 ratio 89.1% 
 
 19 ' hand 46,899 ' 89.3% 
 
 STEEL BARS AND PLATES. 14 Tests. 
 
 Strength of solid 54,226 to 64,580 
 
 Strength of weld 28,553 to 46,019 
 
 Ratio weld to solid 52.6 to 8.2.1% 
 
 The ratio of weld to solid in all the tests ranging from 37.0 to 95.4 is 
 proof of the great variation of workmanship in welding. 
 
356 
 
 STRENGTH OF MATERIALS. 
 
 Cast Copper. 4 tests, average, E. L. 9 5900; T. S., 24,781; contr., 
 24.5; ext., 21.8. 
 
 Copper Plates. As rolled. 22 tests, 0.26 to 0.75 in. thick; E. L., 9766 
 to 18,650; T. S., 30,993 to 34,281; contr., 31.1 to 57.6; ext., 39.9 to 
 52.2. The variation in elastic limit is due to difference in the heat at 
 which the plates were finished. Annealing reduces the T. S. only about 
 1000 pounds, but the E. L. from 3000 to 7000 pounds. 
 
 Another series, 0.38 to 0.52 in. thick; 148 tests, T. S., 29,099 to 31,924; 
 contr., 28.7 to 56.7; ext. in 10 inches, 28.1 to 41.8. Note the uniformity 
 in tensile strength. 
 
 Drawn Copper. 74 tests (0.88 to 1.08 inch diameter); T. S., 31,634 
 to 40,557; contr., 37.5 to 64.1; ext. in 10 inches, 5.8 to 48.2. 
 
 Bronze from a Propeller Blade. Means of two tests each from 
 center and edge. Central portion (sp. gr. 8.320), E. L., 7550; T. S., 
 26,312; contr., 25.4; ext. in 10 inches, 32.8. Edge portion (sp. gr. 
 8.550). E. L., 8950; T. S., 35,960; contr., 37.8; ext. in 10 inches, 47.9. 
 
 Cast German Silver. 10 tests: E. L., 13,400 to 29,100; T. S., 
 23,714 to 46,540; contr., 3.2 to 21.5; ext. in 10 inches, 0.6 to 10.2. 
 
 Thin Sheet Metal. Tensile Strength. 
 
 German silver, 2 lots 75,816 to 87,129 
 
 Bronze, 4 lots 73,380 to 92,086 
 
 Brass, 2 lots 44,398 to 58,188 
 
 Copper, 9 lots 30,470 to 48,450 
 
 Iron, 13 lots, lengthway 44,331 to 59,484 
 
 Iron, 13 lots, crossway 39,838 to 57,350 
 
 Steel, 6 lots 49,253 to 78,251 
 
 Steel, 6 lots, crossway 55,948 to 80,799 
 
 Wire Ropes. 
 
 Selected Tests Showing Range of Variation. 
 
 
 I 
 
 t_i 
 
 Strands. 
 
 si 
 
 
 
 
 % 
 
 a s 
 
 
 
 i 
 
 5 
 
 
 M 
 
 a "& . 
 
 Description. 
 
 f-s 
 
 1.S 
 
 II 
 
 . c 
 
 Is 
 
 >"* 
 
 SJ 
 
 Hemp Core. 
 
 ||5 
 
 
 o'" 1 
 
 K^&H 
 
 o g 
 
 OK. 
 
 rt 
 
 
 PM 
 
 
 
 
 r 
 
 
 
 
 fig 
 
 
 
 Galvanized . . . 
 
 7.70 
 
 53.00 
 
 6 
 
 19 
 
 0.1563 
 
 Main 
 
 339,780 
 
 Ungalvanized 
 
 7.00 
 
 53.10 
 
 7 
 
 19 
 
 0.1495 
 
 Main and Strands 
 
 314,860 
 
 Ungalvanized 
 Galvanized 
 
 6.38 
 7.10 
 
 42.50 
 37.57 
 
 7 
 6 
 
 19 
 30 
 
 0.1347 
 0.1004 
 
 Wire Core 
 Main and Strands 
 
 295,920 
 272,750 
 
 Ungalvanized 
 
 6.18 
 
 40.46 
 
 7 
 
 19 
 
 0.1302 
 
 Wire Core 
 
 268,470 
 
 Ungalvanized 
 Galvanized 
 
 6.19 
 4.92 
 
 40.33 
 20.86 
 
 7 
 6 
 
 19 
 30 
 
 0.1316 
 0.0728 
 
 Wire Core 
 Main and Strands 
 
 22 1 ,820 
 1 90,890 
 
 Galvanized 
 
 5.36 
 
 18.94 
 
 6 
 
 12 
 
 0.1104 
 
 Main and Strands 
 
 136,550 
 
 Galvanized 
 
 4.82 
 
 21.50 
 
 6 
 
 7 
 
 0. 1 693 
 
 Main 
 
 129,710 
 
 Ungalvanized 
 
 3.65 
 
 12.21 
 
 6 
 
 19 
 
 0.0755 
 
 Main 
 
 1 1 0, 1 80 
 
 Ungalvanized 
 
 3.50 
 
 12.65 
 
 7 
 
 7 
 
 0.122 
 
 Wire Core 
 
 101,440 
 
 Ungalvanized 
 
 3.82 
 
 14.12 
 
 6 
 
 7 
 
 0.135 
 
 Main 
 
 98,670 
 
 Galvanized 
 
 4.1 1 
 
 11.35 
 
 6 
 
 12 
 
 0.080 
 
 Main and Strands 
 
 75,110 
 
 Galvanized 
 
 3 31 
 
 727 
 
 6 
 
 12 
 
 0.068 
 
 Main and Strands 
 
 55,095 
 
 Ungalvanized 
 
 3.02 
 
 8.62 
 
 6 
 
 7 
 
 0.105 
 
 Main 
 
 49,555 
 
 Ungalvanized 
 
 2.68 
 
 6.26 
 
 6 
 
 6 
 
 0.0963 
 
 Main and Strands 
 
 41,205 
 
 Galvanized 
 
 2 87 
 
 5.43 
 
 6 
 
 12 
 
 0.0560 
 
 Main and Strands 
 
 38,555 
 
 Galvanized 
 
 2 46 
 
 3 85 
 
 6 
 
 12 
 
 00472 
 
 Main and Strands 
 
 28,075 
 
 Ungalvanized 
 Galvanized 
 
 V.75 
 2.04 
 
 2.80 
 . 2.72 
 
 6 
 6 
 
 7 
 12 
 
 0.0619 
 0.0378 
 
 Main 
 Main and Strands 
 
 24,552 
 20,415 
 
 Galvanized 
 
 1.76 
 
 1.85 
 
 6 
 
 12 
 
 0.0305 
 
 Main 
 
 14,634 
 
 
KIRKALDY'S TESTS. 357 
 
 Wire. Tensile Strength. 
 
 German silver, 5 lots < 81,735 to 92,224 
 
 Bronze, 1 lot 78,049 
 
 Brass, as drawn, 4 lots 81,114 to 98,578 
 
 Copper, as drawn, 3 lots 37,607 to 46,494 
 
 Copper annealed, 3 lots 34,936 to 45,210 
 
 Copper (another lot), 4 lots 35,052 to 62,190 
 
 Copper (extension 36.4 to 0.6%). 
 
 Iron, 8 lots 59,246 to 97,908 
 
 Iron (extension 15.1 to 0.7%). 
 
 Steel, 8 lots ; 103,272 to 318.823 
 
 The steel of 318,823 T. S. was 0.047 inch diam., and had an extension of 
 only 3 per cent; that of 103,272 T. S. was 0.107 inch diam., and had an 
 extension of 2.2 per cent. One lot_of_0.044 inch diam. had 267,114 T. S., 
 and 5.2 per cent extension. 
 
 Hemp Ropes, Tin tarred. 15 tests of ropes from 1.53 to 6.90 inches 
 circumference, weighing 0.42 to 7.77 pounds per fathom, showed an 
 ultimate strength of from 1670 to 33,808 pounds, the strength per fathom 
 weight varying from 2872 to 5534 pounds. 
 
 Hemp Ropes,' Tarred. 15 tests of ropes .from 1.44 to 7.12 inches 
 circumference, weighing from 0.38 to 10.39 pounds per fathom, showed 
 an ultimate strength of from 1046 to 31,549 pounds, the strength per 
 fathom weight varying from 1767 to 5149 pounds. 
 
 Cotton Ropes. 5 ropes, 2.48 to 6.51 inches circumference, 1.08 to 
 8.17 pounds per fathom. Strength 3089 to 23,258 pounds, or 2474 to 
 3346 pounds per fathom weight. 
 
 Manila Ropes. 35 tests: 1.19 to 8.90 inches circumference, 0.20 to 
 11.40 pounds per fathom. Strength 1280 to 65,550 pounds, or 3003 to 
 7394 pounds per fathom weight. 
 
 Belting. 
 
 No. of Tensile strength 
 
 lots. per square inch. 
 
 11 Leather, single, ordinary tanned 3248 to 4824 
 
 4 Leather, single, Helvetia 5631 to 5944 
 
 7 Leather, double, ordinary tanned 2160 to 3572 
 
 8 Leather, double Helvetia 4078 to 5412 
 
 6 Cotton, solid woven 5648 to 8869 
 
 14 Cotton, folded, stitched 4570 to 7750 
 
 1 Flax, solid, woven 9946 
 
 1 Flax, folded, stitched 6389 
 
 6 Hair, solid, woven 3852 to 5159 
 
 2 Rubber, solid, woven 4271 to 4343 
 
 Canvas. 35 lots: Strength, lengthwise, 113 to 408 pounds per inch; 
 cross ways, 191 to 468 pounds per inch. 
 
 The grades are numbered 1 to 6, but the weights are not given. The 
 strengths vary considerably, even in the same number. 
 
 Marbles. Crushing strength of various marbles. 38 tests, 8 kinds. 
 Specimens were 6-inch cubes, or columns 4 to 6 inches diameter, and 6 
 and 12 inches high. Range 7542 to 13,720 pounds per square inch. 
 
 Granite. Crushing strength, 17 tests; square columns 4X4 and 
 6 X 4, 4 to 24 inches high, 3 kinds. Crushing strength ranges 10,026 to 
 13,271 pounds per square inch. (Very uniform.) 
 
 Stones. (Probably sandstone, local names only given.) 11 kinds, 42 
 tests, 6X6, columns 12, 18 and 24 inches high. Crushing strength 
 ranges from 2105 to 12,122. The strength of the column 24 inches long 
 is generally from 10 to 20 per cent less than that of the 6-inch cube. 
 
 Stones. (Probably sandstone) tested for London & Northwestern 
 Railway. 16 lots, 3 to 6 tests in a lot. Mean results of each lot ranged 
 from 3785 to 11,956 pounds. The variation is chiefly due to the stones 
 baing from different lots. The different specimens in each lot gav 
 results which generally agreed within 30 per cent. 
 
358 
 
 STRENGTH OF MATERIALS. 
 
 Bricks. Crushing strength, 8 lots; 6 tests in each lot: mean results 
 ranged from 1835 to 9209 pounds per square inch. The maximum 
 variation in the specimens of one lot was over 100 per cent of the 
 lowest. In the most uniform lot the variation was less than 20 per 
 cent. 
 
 Wood. Transverse and Thrusting Tests. 
 
 
 
 
 
 
 5- 
 
 Thrust- 
 
 
 3 
 
 1 
 
 Sizes abt. in 
 . square. 
 
 Span, 
 inches. 
 
 Ultimate 
 
 Stress. 
 
 LW 
 4BD 2 ' 
 
 ing 
 
 Stress 
 
 
 
 
 
 
 
 per sq. 
 
 
 
 
 
 
 
 in. 
 
 
 
 
 
 45,856 
 
 1096 
 
 3586 
 
 
 10 
 
 lU/2to 121/2 
 
 144 
 
 to 
 
 to 
 
 to 
 
 
 
 
 
 80,520 
 
 1403 
 
 5438 
 
 
 
 
 
 37,948 
 
 657 
 
 2478 
 
 Dantzic fir 
 
 12 
 
 12 to 13 
 
 144 
 
 to 
 
 to 
 
 to 
 
 
 
 
 
 54,152 
 
 790 
 
 3423 
 
 
 
 
 
 32,856 
 
 1505 
 
 2473 
 
 English oak 
 
 $ 
 
 41/2 X 12 
 
 120 
 
 to' 
 
 to 
 
 to 
 
 
 
 
 
 39,084 
 
 1779 
 
 4437 
 
 
 
 
 
 23,624 
 
 1190 
 
 2656 
 
 American white oak . . . 
 
 5 
 
 41/2 X 12 
 
 120 
 
 to 
 
 to 
 
 to 
 
 
 
 
 
 26,952 
 
 1372 
 
 3899 
 
 Demerara greenheart, 9 tests (thrusting) 8169 to 10,785 
 
 Oregon pine, 2 tests 5888 and 7284 
 
 Honduras mahogany, 1 test 6769 
 
 Tobasco mahogany, 1 test 5978 
 
 Norway spruce, 2 tests 5259 and 5494 
 
 American yellow pine, 2 tests 3875 and 3993 
 
 English ash, 1 test 3025 
 
 Portland Cement. (Austrian.) Cross-sections of specimens 2 X 21/2 
 inches for pulling tests only; cubes, 3X3 inches for thrusting tests; 
 weight, 98.8 pounds per imperial bushel; residue, 0.7 per cent with 
 sieve 2500 meshes per square inch; 38.8 per cent by volume of water 
 required for mixing; time of setting, 7 days; 10 tests to each lot. The 
 mean results in Ibs. per sq. in. were as follows: 
 
 Age. 
 10 days 
 20 days 
 30 days 
 
 Portland Cement. 
 
 Cement 
 alone, 
 Pulling. 
 
 376 
 
 420 
 
 451 
 
 Cement 
 alone, 
 Thrusting. 
 2910 
 3342 
 3724 
 
 1 Cement, 
 
 2 Sand, 
 
 Thrusting. 
 
 893 
 
 1023 
 
 1172 
 
 1 Cement, 1 Cement, 
 3 Sand, 4 Sand, 
 
 Thrusting. Thrusting. 
 407 228 
 
 494 275 
 
 594 338 
 
 ________ _________ 
 
 cross-section, all aged 10 days, 180 tests; 
 square inch. 
 
 Various samples pulling tests, 2 X 21/2 inches 
 
 , 
 ranges 87 to 643 pounds per 
 
 TENSILE STRENGTH OF WIRE. 
 
 (From J. Bucknall Smith's Treatise on Wire.) 
 Tons per i 
 
 Black or annealed iron wire 
 
 Bright hard drawn 
 
 Bessemer, steel wire 
 
 Mild Siemens-Martin steel wire 
 
 High carbon ditto (or "improved") 
 
 Crucible cast-steel "improved" wire 100 
 
 " Improved " cast-steel " plough " 120 
 
 Special qualities of tempered and improved 
 
 cast steel wire may attain 150 to 170 336,000 to 380,800 
 
 in. sectiona 
 area. 
 25 
 35 
 40 
 60 
 80 
 
 Pounds per 
 sq. in. sec- 
 tional area. 
 
 56,000 
 
 78,400 
 
 89,600 
 134,000 
 179,200 
 224,000 
 268,800 
 
MISCELLANEOUS TESTS OF MATERIALS. 
 
 359 
 
 MISCELLANEOUS TESTS OF MATERIALS. 
 
 Reports of Work of the Watertown Testing-machine in 1883. 
 TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES. 
 
 ''i 
 
 w 
 
 
 
 
 
 I\J 
 
 ^2 . 
 
 a 
 
 "5 
 5 
 
 Is 
 
 A 
 
 fc . 
 
 **3n 03 
 
 o> <j 
 
 "S-g 
 PM 2 
 
 9 
 
 1 
 ~ SR 
 
 jUttg 
 
 fl-3 
 
 1*1 
 
 
 
 lickness 
 
 Is 
 
 0> 
 
 c3 
 
 111 
 
 | s 
 
 is* 
 
 s 
 
 1 
 
 tfj 
 |I 
 
 5 
 
 il'P 
 
 fca 
 
 ^ ft j 
 III 
 
 1 
 
 H 
 
 2 
 
 
 
 
 
 
 H^-2 
 
 HS 
 
 1 
 
 3/8 
 
 H/16 
 
 3/4 
 
 101/2 
 
 6 
 
 13/4 
 
 39,300 
 
 47,180 
 
 47.0 t 
 
 3/8 
 
 H/16 
 
 3/4 
 
 101/2 
 
 6 
 
 13/4 
 
 41,000 
 
 47,180 
 
 49.0 J 
 
 1/2 
 
 3/4 
 
 13/16 
 
 10 
 
 5 
 
 
 35,650 
 
 44,615 
 
 45.6 t 
 
 1/2 
 
 3/1 
 
 13/16 
 
 10 
 
 5 
 
 2 
 
 35,150 
 
 44,615 
 
 44.9 J 
 
 3/8 
 
 H/I6 
 
 3/ 4 
 
 10 
 
 5 
 
 2 
 
 46,360 
 
 47,180 
 
 59.9 
 
 3/8 
 
 H/16 
 
 3/4 
 
 10 
 
 5 
 
 2 
 
 46,875 
 
 47,180 
 
 60.5 
 
 
 3/4 
 
 ' 13/16 
 
 10 
 
 5 
 
 2 
 
 46,400 
 
 44,615 
 
 59.4 | 
 
 1/2 
 
 3/4 
 
 13/16 
 
 10 
 
 5 
 
 2 
 
 46,140 
 
 44,615 
 
 59.2 
 
 5/8 
 
 
 H/16 
 
 101/2 
 
 4 
 
 25/8 
 
 44,260 
 
 44,635 
 
 57.2 
 
 5/8 
 
 1 
 
 
 101/2 
 
 4 
 
 25/8 
 
 42,350 
 
 44,635 
 
 54.9 | 
 
 3/4 
 
 H/8 
 
 13/11! 
 
 11.9 
 
 4 
 
 2.9 
 
 42,310 
 
 46,590 
 
 52.1 
 
 3/4 
 
 H/8 
 
 13/16 
 
 11.9 
 
 4 
 
 2.9 
 
 41,920 
 
 46,590 
 
 51.7 
 
 3'8 
 
 3/4 
 
 13/16 
 
 101/2 
 
 6 
 
 13/4 
 
 61,270 
 
 53,330 
 
 59.5 $ 
 
 3/8 
 
 3/4 
 
 13/16 
 
 10l/ 2 
 
 6 
 
 13/4 
 
 60,830 
 
 53,330 
 
 59.1 I 
 
 1/2 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 47,530 
 
 57,215 
 
 40.2 J 
 
 1/2 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 49,840 
 
 57,215 
 
 42.3 1 
 
 3/8 
 
 H/16 
 
 3/4 
 
 10 
 
 5 
 
 2 
 
 62,770 
 
 53,330 
 
 71.7 | 
 
 3/8 
 
 H/16 
 
 3/4 
 
 10 
 
 5 
 
 2 
 
 61,210 
 
 53,330 
 
 69.8 | 
 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 68,920 
 
 57,215 
 
 57.1 | 
 
 1/2 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 66,710 
 
 57,215 
 
 55.0 
 
 5/8 
 
 1 
 
 H/16 
 
 91/2 
 
 4 
 
 23/8 
 
 62,180 
 
 52,445 
 
 63.4 | 
 
 5/8 
 
 1 
 
 11/16 
 
 91/2 
 
 4 
 
 23/g 
 
 62,590 
 
 52,445 
 
 63.8 
 
 3/4 
 
 H/8 
 
 13/16 
 
 10 
 
 4 
 
 21/2 
 
 54,650 
 
 51,545 
 
 54.0 
 
 3/4 
 
 H/8 
 
 13/16 
 
 10 
 
 4 
 
 21/2 
 
 54,200 
 
 51,545 
 
 53.4 
 
 * Iron. 
 
 t Steel. 
 
 Lap-joint. 
 
 Butt-joint. 
 
 The efficiency of the joints is found by dividing the maximum tensile 
 stress on the gross sectional area of plate by the tensile strength of the 
 material. 
 
 COMPRESSION TESTS OF 3 X 3 INCH WROUGHT-IRON BARS. 
 
 Length, inches. 
 
 Teste 
 Pin Er 
 in. Di 
 pressi 
 Ibs. 
 
 d with Two 
 ds, Pins U/2 
 am. Corn- 
 ve Strength, 
 per sq. in. 
 
 Tested with Two 
 Flat Ends. Com- 
 pressive Strength, 
 Ibs. per sq. in. 
 
 Tested with One 
 Flat and One Pin 
 End. Compressive 
 Strength, Ibs. per 
 sq. in. 
 
 30 ;... 
 
 
 28,260 
 
 
 
 ^ 
 
 
 3 1 ,990 
 26310 
 
 
 
 60 
 
 
 26640 
 
 
 
 90 
 
 
 24,030 
 
 ( 26,780 
 
 (25,120 
 
 120 
 
 
 25,380 
 20,660 
 
 | 25,580 
 1 23,010 
 
 1 25,190 
 ( 22,450 
 
 150 . 
 
 
 20,200 
 16,520 
 
 ( 22,450 
 
 1 21,870 
 
 180 
 
 . 
 
 1 7,840 
 13,010 
 
 
 
 
 
 15,700 
 
 
 
 
360 
 
 STRENGTH OF MATERIALS, 
 
 Tested with Two Pin 
 Ends. Length of Bars 
 120 inches. 
 
 Diameter 
 of Pins. 
 7/8 inch 
 
 Comp. Str., 
 per sq. in., Ibs. 
 16,250 
 
 1 1/8 inches . . 
 
 .... 17 740 
 
 17/8 
 
 "... 21,400 
 
 21/4 " 
 
 22.210 
 
 COMPRESSION OF WROUGHT-IRON COLUMNS, 
 BOX AND SOLID WEB. 
 
 ALL TESTED WITH PIN ENDS. 
 
 LATTICED 
 
 Columns made of 
 
 1 
 H 
 1 
 
 Sectional Area, 
 square inch. 
 
 if 
 il 
 
 t>"o^ 
 
 & 
 
 Ultimate 
 Strength, per 
 square inch, 
 pounds . 
 
 6-inch channel solid web 
 
 100 
 
 9831 
 
 432 
 
 30,220 
 
 6 " 
 
 15.0 
 20.0 
 
 9.977 
 9.762 
 
 592 
 755 
 
 21,050 
 16,220 
 
 8-inch channels, with 5/iQ-in. continuous 
 plates 
 
 20.0 
 26.8 
 
 26.8 
 
 16.281 
 16.141 
 
 19.417 
 
 1,290 
 ,645 
 
 1 940 
 
 22,540 
 17,570 
 
 25,290 
 
 5 /16-inch continuous plates and angles.. 
 Width of plates, 12 in., 1 in. and 7.35 in. 
 7/i6-inch continuous plates and angles.. 
 
 26.8 
 26.8 
 
 16.168 
 20.954 
 
 1,765 
 2,242 
 
 28,020 
 25,770 
 
 8-inch channels latticed ... . . . . 
 
 13 3 
 
 7.628 
 
 679 
 
 33,910 
 
 8 " " 
 
 20.0 
 
 7.621 
 
 924 
 
 34,120 
 
 8 " " 
 
 268 
 
 7 673 
 
 1 255 
 
 29,870 
 
 8-inch channels, latticed, swelled sides . . 
 8 . . 
 8 " " " " .. 
 10-inch channels, latticed, swelled sides. 
 10 " 
 
 13.4 
 20.0 
 26.8 
 16.8 
 25.0 
 
 7.624 
 7.517 
 7.702 
 1 1 .944 
 12.175 
 
 . 684 
 921 
 ,280 
 ,470 
 ,926 
 
 33,530 
 33,390 
 30,770 
 33,740 
 32,440 
 
 10 " " 
 
 16.7 
 
 12.366 
 
 ,549 
 
 31,130 ' 
 
 * 10-inch channels, latticed one side; con- 
 tinuous plate one side . 
 
 25.0 
 25.0 
 
 11.932 
 1 7.622 
 
 ,962 
 1,848 
 
 32,740 
 26,190 
 
 t 10-inch channels, latticed one side; con- 
 tinuous plate one side 
 
 25 
 
 17.721 
 
 1,827 
 
 17,270 
 
 
 
 
 
 
 * Pins in center of gravity of channel bars and continuous plate, 1.63 
 inches from center line of channel bars. 
 
 t Pins placed in center of gravity of channel bars. 
 
 TENSILE TEST OF SIX STEEL EYE-BARS. 
 
 COMPARED WITH SMALL TEST INGOTS. 
 
 The steel was made by the Cambria Iron Company, and the eye-bar 
 heads made by Keystone Bridge Company by upsetting and hammering. 
 All the bars were made from one ingot. Two test pieces, 3/ 4 -inch round, 
 rolled from a test-ingot, gave elastic limit 48,040 and 42,210 pounds; 
 tensile strength, 73,150 and 69,470 pounds, and elongation in 8 inches, 
 22.4 and 25.6 per cent respectively. The ingot from which the eye-bars 
 were made was 14 inches square, rolled to billet, 7X6 inches. The 
 eye-bars were rolled to 61/2 X 1 inch. Chemical tests gave carbon 0.27 
 to 0.30; manganese, 0.64 to 0.73; phosphorus, 0.074 to 0.098. 
 
MISCELLANEOUS TESTS OF IRON AND STEEL. 361 
 
 Gauged Elastic Tensile Elongation 
 
 Length, limit, Ibs. strength per per cent, in 
 
 inches. per sq. in. sq. in., Ibs.. Gauged Length. 
 
 160 37,480 67,800 15.8 
 
 160 36,650 64,000 6.96 
 
 160 71,560 8.6 
 
 200 37,600 68,720 12.3 
 
 200 35,810 65,850 12.0 
 
 200 33,230 64,410 16.4 
 
 200 37,640 68,290 13.9 
 
 The average tensile strength of the 3/4-inch test pieces was 71,310 lbs. f 
 that of the eye-bars 67,230 Ibs., a decrease of 5.7%. The average elastic 
 limit of the test pieces was 45,150 Ibs., that of the eye-bars 36,402 Ibs., a 
 decrease of 19.4%. The elastic limit of the test pieces was 63.3% of 
 the ultimate strength, that of the eye-bars 54.2% of the ultimate strength. 
 
 Tests of 11 full-sized eye bars, 15 X 1V4 to 21/iein., 20.5 to 21.4 ft. long 
 between centers of pins, made by the Phoenix Iron Co., are reported in 
 Eng. News, Feb. 2, 1905. The average T.S. of the bars was 58,300 Ibs. 
 per sq. in.-, E.L., 32,800. The average T.S. of small specimens was 
 63,900, E.L., 37,000. The T.S. of the full-sized bars averaged 8.8% 
 and the E.L. 12.1% lower than the small specimens. 
 
 EFFECT OF COLD-DRAWING ON STEEL. 
 
 Three pieces cut from the same bar of hot-rolled steel: 
 
 1. Original bar, 2.03 in. diam., gauged length 30 in., tensile strength 
 
 55,400 Ibs. per square in.; elongation 23.9%. 
 
 2. Diameter reduced in compression dies (one pass) .094 in.; T. S. 70,420- 
 
 el. 2.7% in 20 in. 
 
 3. " " 0.222 in.; T.S. 81,890; 
 
 el. 0.075% in 20 in. 
 
 Compression test of cold-drawn bar (same as No. 3), length 4 in., diam. 
 1.808 in.: Compressive strength per sq. in., 75,000 Ibs.; amount of com- 
 pression 0.057 in.; set 0.04 in. Diameter increased by compression to 
 1.821 in. in the middle; to 1.813 in. at the ends. 
 
 MISCELLANEOUS TESTS OF IRON AND STEEL. 
 
 Tests of Cold-rolled and Cold-drawn Steel, made by the Cambria 
 Iron Co. in 1897, gave the following results (averages of 12 tests of each): 
 
 E. L. T. S. El. in 8 in. Red. 
 
 Before cold-rolling 35,390 59,980 28.3% 58.5% 
 
 After cold-rolling 72,530 79,830 9.6% 34.9% 
 
 After cold-drawing 76,350 83,860 8.9% 34.2% 
 
 The original bars were 2 in. and 7/ 8 in. diameter. The test pieces cut 
 from the bars were 3/ 4 in. diam., 18 in. long. The reduction in diameter 
 from the hot-rolled to the cold-rolled or cold-drawn bar was Vie in. in 
 each case. 
 
 Cold Rolled Steel Shafting (Jones & Laughlins) in/iein. diam. 
 Torsion tests of 12 samples gave apparent outside fiber stress, calculated 
 from maximum twisting moment, 70,700 to 82,900 Ibs. per sq.in.; fiber 
 stress at elastic limit, 32,500 to 38,800 Ibs. per sq. in.; shearing modulus 
 of elasticity, 11,800,000 to 12,100,000; number of turns per foot before 
 fracture, 1.60 to 2.06. Tech. Quar., vol. xii, Sept., 1899. 
 
 Torsion Tests on Cold Rolled Shafting. (Tech. Quar. XIII, No. 3, 
 1900, p. 229.) 14 tests. Diameter about 1.69 in. Gauged length, 40 to 
 50 in. Outside fiber stress at elastic limit, 28,610 to 33,590 Ibs. per sq. 
 in.; apparent outside fiber stress at maximum load, 67,980 to 77,290. 
 Shearing modulus of elasticity, 11,400,000 to 12,030,000 Ibs. per sq. in. 
 Turns per foot between jaws at fracture, 0.413 to 2.49. 
 
 Torsion Tests on Refined Iron. 13/4 in. diam. 14 tests. Gauged 
 length, 40 ins. Outside fiber stress at elastic limit, 12,790 to 19,140 Ibs. 
 per sq. in.; apparent outside fiber stress at maximum load, 45,350 to 
 58,340. Shearing modulus of elasticity, 10,220,0001011,700,000. Turns 
 per foot between jaws at fracture, 1.08 to 1.42. 
 
362 
 
 STRENGTH OF MATERIALS. 
 
 Tests of Steel Angles with Riveted End Connections. (F. P. 
 
 McKibbin, Proc. A.S.T.M., 1907.) The angles broke through the rivet 
 holes in all cases. The strength developed ranged from 62.5 to 79.1% 
 of the ultimate strength of the gross area, or from 73.9 to 92% of the 
 calculated strength of the net section at the rivet holes. 
 
 SHEARING STRENGTH. 
 
 H. V. Loss in American Engineer and Railroad Journal, March and 
 April, 1893, describes an extensive series of experiments on the shearing 
 of iron and steel bars in shearing machines. Some of his results are: 
 
 Depth of penetration at point of maximum resistance for soft steel 
 bars is independent of the width, but varies with the thickness. If 
 d = depth of penetration and t = thickness, d_= 0.3t for a flat knife, 
 d = 0.25* for a 4 bevel knife, and d = 0.16 v^a f or an 8 bevel knife. 
 The ultimate pressure per inch of width in flat steel bars is approxi- 
 mately 50,000 Ibs. X t. The energy consumed in foot-pounds per inch 
 width of steel bars is, approximately: 1" thick, 1300 ft.-lbs.; 11/2", 
 2500; 13/4", 3700; 17/g", 4500; the energy increasing at a slower rate than 
 the square of the thickness. Iron angles require more energy than steel 
 angles of the same size; steel breaks while iron has to be cut off. For 
 hot-rolled steel the resistance per square inch for rectangular sections 
 varies from 4400 Ibs. to 20,500 Ibs., depending partly upon its hardness 
 and partly upon the size of its cross-area, which latter element indirectly 
 but greatly indicates the temperature, as the smaller dimensions require 
 a considerably longer time to reduce them down to size, which time 
 again means loss of heat. 
 
 It is not probable that the resistance in practice can be brought very 
 much below the lowest figures here given viz., 4400 Ibs. per square 
 inch as a decrease of 1000 Ibs. will henceforth mean a considerable 
 increase in cross-section and temperature. 
 
 Relation of Shearing to Tensile Strength of Different Metals. 
 E. G. Izod, in a paper presented to the British Institution of Mechanical 
 Engrs. (Jan., 1906), describes a series of tests on bars and plates of 
 different metals. The specimens were firmly clamped on two steel 
 plates with opposed shearing edges 4 ins. apart, and a shearing block, 
 which was a sliding fit between these edges-, was brought down upon 
 the specimen, so as to cut it in double shear, by a testing machine. 
 
 
 a 
 
 b 
 
 c 
 
 
 a 
 
 6 
 
 c 
 
 Cast iron. A 
 Cast iron. B 
 
 9.7 
 13.4 
 
 
 152 
 
 Rolled phosphor- 
 bronze 
 
 39.5 
 
 11.7 
 
 61 
 
 Cast iron. C 
 Cast aluminum- 
 bronze. . . . 
 
 11.3 
 33 1 
 
 12 5 
 
 122 
 60 
 
 Aluminum 
 Aluminum alloy 
 Wrough t-iron bar 
 
 6.4 
 12.7 
 26.0 
 
 25.5 
 9.6 
 22 5 
 
 70 
 59 
 
 75 
 
 Cast phosphor- 
 bronze. 
 
 13 4 
 
 2 2 
 
 178 
 
 Mild-steel.0.14 car- 
 bon 
 
 26 9 
 
 34 7 
 
 78 
 
 Cast phosphor- 
 bronze 
 
 19 7 
 
 8 
 
 9^ 
 
 Crucible steel, 0.12 C 
 0.48 C. 
 
 24.9 
 42 1 
 
 43.0 
 26 
 
 74 
 
 68 
 
 Gun metal 
 
 12.1 
 
 7.8 
 
 1(K 
 
 0.71 C.... 
 
 56.3 
 
 15.0 
 
 65 
 
 Yellow brass 
 
 7 5 
 
 6 5 
 
 1?6 
 
 0.77 C 
 
 61 3 
 
 11 
 
 6? 
 
 Yellow brass 
 
 16.0 
 
 35.0 
 
 74 
 
 
 
 
 
 a. Tensile strength of the metal, gross tons per sq. in.; 6. elongation 
 in 2 in.%; c. ratio shearing * tensile strength. The results seem to 
 point to the fact that there is no common law connecting the ultimate 
 shearing stress with the ultimate tensile stress, the ratio varying greatly 
 with different materials. The test figures from crystalline materials, 
 such as cast iron or those with very little or no elongation, seem to indicate 
 that the ultimate shear stress exceeds the ultimate tensile stress by as 
 much as 20 or 25%, while from' those with a fairly high measure of 
 ductility, the ultimate shear stress may be anything from to 50% less 
 than the ultimate tensile stress. 
 
 For shearing strength of rivets, see pages 240, 430 and 435. 
 
STRENGTH OP IRON AND STEEL PIPE. 
 
 363 
 
 STRENGTH OF IRON AND STEEL PIPE. 
 
 Tests of Strength and Threading of Wrought-Iron and Steel 
 Pipe. T. N. Thomson, in Proc. Am. Soc. Heat and Vent. Engineers, 
 vol. xii., p. 80, describes some experiments on welded wrought iron and 
 steel pipes. Short rings of 6-in. pipe were pulled in the direction of a 
 diameter so as to elongate the ring. Four wrought iron rings broke at 
 2400, 3000, 3100 and 4100 Ibs. and four steel rings at 5300 (defective 
 weld) 18,000, 29,000 and 35,000 Ibs. Another series of 9 tests each 
 were tested so as to show the tensile strength of the metal and of the 
 weld. The average strength of the metal was, iron, 34,520, steel, 61,850 
 Ibs. The strength of the weld in iron ranged from 49 to 84, averaging 
 71 per cent of the strength of the metal, and in steel from 50 to 93, 
 averaging 72%. 
 
 A large number of iron and steel pipes of different sizes were tested by 
 twisting, the force being applied at the end of a three-foot lever. The 
 average pull on the steel pipes was: 1/2 in. pipe, 109 Ibs.; 1 in., 172 Ibs.; 
 11/2 in., 300 Ibs.; number of turns in 6 ft. length, respectively, 15, 8 and 
 51/2. Per cent failed in weld, 0, 13 and 13 respectively. For different 
 lots of iron pipe the average pull was: 1/2 in., 68, 81 and 65 Ibs.; 1 in., 
 154, 136, 107 Ibs.; 1 1/ 2 in. 256, 250, 258 Ibs. The number of turns in 
 6 feet for the nine lots were respectively, 41/2, 53/ 4 , 21/2; 61/4, 31/2, 21/2; 
 41/2, 31/2, 21/4. ' The failures in the weld ranged from 33 to 100% in the 
 different lots. 
 
 The force required to thread li/4-in. pipe with two forms of die was 
 tested by pulling on a lever 21 ins. long. The results were as follows: 
 
 Old form of die, iron pipe. . 83 to 87 Ibs. pull, steel pipe 100 to 111 Ibs. 
 Improved die, iron pipe 58 to 62 Ibs. pull, steel pipe, 60 to 65 Ibs. 
 
 Mr. Thomson gives the following table showing approximately the 
 steady pull in pounds required at the end of a 16-in. lever to thread 
 twist and split iron and steel pipe of small sizes: 
 
 
 To Thread with Oiled 
 Dies. 
 
 To 
 Twist 
 Lbs. 
 
 To 
 
 Split 
 Lbs. 
 
 Safety 
 Margin 
 Lbs. 
 
 New 
 Rake 
 Dies. 
 
 New 
 Com- 
 mon 
 Dies. 
 
 Old 
 Com- 
 mon 
 Dies. 
 
 1/2 in. steel 
 
 34 
 27 
 44 
 44 
 69 
 62 
 
 56 
 33 
 60 
 51 
 111 
 106 
 
 60 
 49 
 91 
 73 
 124 
 116 
 
 122 
 102 
 150 
 140 
 286 
 273 
 
 152 
 110 
 240 
 176 
 420 
 327 
 
 74 
 46 
 112 
 81 
 259 
 173 
 
 1/2 in. iron 
 
 3/4 in. steel 
 
 3/4 in. iron 
 
 1 in. steel. ... 
 
 1 in. iron 
 
 
 The margin of safety is computed by adding 30% to the pull required 
 to thread with the old dies and subtracting the sum from the pull re- 
 quired to split the pipe. If the mechanic pulls on the dies beyond the 
 limit, due to imperfect dies, or to a hard spot in the pipe, he will split 
 the pipe. 
 
 Old Boiler Tubes used as Columns. (Tech. Quar. XIII, No. 3, 
 1900, p. 225.) Thirteen tests were made of old 4-in. tubes taken from 
 worn-out boilers. The lengths were from 6 to 8 ft., ratio l/r 53 to 71, 
 and thickness of metal 0.13 to 0.18 in. It is not stated whether the tubes 
 were iron or steel. The maximum load ranged from 34,600 to 50,000 
 Ibs., and the maximum load per sq. in. from 17,100 to 27,500 Ibs. Six 
 new tubes also were tested, with maximum loads 55,600 to 64,800 Ibs., 
 and maximum loads per sq. in. 31,600 to 38,100 Ibs. The relati9n of 
 the strength per sq. in. of the old tubes to the ratio l/r was very variable, 
 being expressed approximately by the formula S = 41,000 300 l/r 
 5000. That of the new tubes is approximately 8 = 52,000 - 300 l/r 
 i 2000. 
 
364 STRENGTH OF MATERIALS. 
 
 HOLDING-POWER OF BOILER-TUBES EXPANDED INTO 
 TUBE-SHEETS. 
 
 Experiments by Chief Engineer W. H. Shock, U. S. N., on brass tubes, 
 21/2 inches diameter, expanded into plates s/ 4 inch thick, gave results 
 ranging from 5850 to 46,000 Ibs. Out of 48 tests 5 gave figures under 
 10,000 Ibs., 12 between 10,000 and 20,000 Ibs., 18 between 20,000 and 
 30.000 Ibs., 10 between 30,000 and 40,000 Ibs., and 3 over 40,000 Ibs. 
 
 Experiments by Yarrow & Co., on steel tubes, 2 to 21/4 inches diameter, 
 gave results similarly varying, ranging from 7900 to 41,715 Ibs., the 
 majority ranging from 20,000 to 30,000 Ibs. In 15 experiments on 
 4 and 5 inch tubes the strain ranged from 20,720 to 68,040 Ibs. Beading 
 the tube does not necessarily give increased resistance, as some of the 
 lower figures were obtained with beaded tubes. (See paper on Rules 
 Governing the Construction of Steam Boilers, Trans. Engineering Con- 
 gress, Section G, Chicago, 1893.) 
 
 The Slipping Point of Rolled Boiler-Tube Joints. 
 
 (O. P. Hood and G. L. Christensen, Trans. A. S. M. E., 1908). 
 
 When a tube has started from its original seat, the fit may be no longer 
 continuous at all points and a leak may result, although the ultimate 
 holding power of the tube may not be impaired. A small movement 9f 
 the tube under stress is then the preliminary to a possible leak, and it 
 is of interest to know at what stress this slipping begins. 
 
 As results of a series of experiments with tube sheets of from 1/2 in. 
 to 1 in. in thickness and with straight and tapered tube seats, the authors 
 found that the slipping point of a 3-in. 12-gage Shelby cold-drawn tube 
 rolled into a straight, smooth machined hole in a 1-in. sheet occurs with 
 a pull of about 7,000 Ibs. The frictional resistance of such tubes is about 
 750 Ibs. per sq. in. of tube-bearing area in sheets 5/3 in. and 1 in. thick. 
 
 Various degrees of rolling do not greatly affect the point of initial slip, 
 and for higher resistances to initial slip other resistance than friction must 
 be depended upon. Cutting a 10-pitch square thread in the seat, about 
 0.01 in. deep will raise the slipping point to three or four times that in a 
 smooth hole. In one test this thread was made 0.015 in. deep in a sheet 
 1 in. thick, giving an abutting area of about 1.4 sq. in., and a resistance 
 to initial slip of 45,000 Ibs. The elastic limit of the tube was reached at 
 about 34,000 Ibs. 
 
 Where tubes give trouble from slipping and are required to carry an 
 unusual load, the slipping point can be easily raised by serrating the tube 
 seat by rolling with an ordinary flue expander, the rolls of which are 
 grooved about 0.007 in. deep and 10 grooves to the inch. One tube 
 thus serrated had its slipping point raised between three and four times 
 its usual value. 
 
 METHODS OF TESTING THE HARDNESS OF METALS. 
 
 BrinelPs Method. J. A. Brinell, a Swedish engineer, ia 1900 pub- 
 lished a method for determining the relative hardness of steel which has 
 come into somewhat extensive use. A hardened steel ball, 10 mm. 
 (0.3937 in.), is forced with a pressure of 3000 kg. (6614 Ibs.) into a flat 
 surface on the sample to be tested, so as to make a slight spherical in- 
 dentation, the diameter of which may be measured by a microscope or 
 the depth by a micrometer. The hardness is defined as the quotient 
 of the pressure by the area of the indentation. From the measurement 
 the "hardness number" is calculated by one of the following formulae: 
 
 H = K (r + Vr? -&)* 2 x rR\ or H = K + 2 n rd. 
 
 K = load, = 3000 kg., r radius of ball, = 5 mm., R = radius and 
 d = depth of indentation. 
 
 The following table gives the hardness number corresponding to 
 different values of Li and d. 
 
STRENGTH OP GLASS. 
 
 365 
 
 R 
 
 H 
 
 tR 
 
 H 
 
 R 
 
 H 
 
 a 
 
 H 
 
 d 
 
 H 
 
 d 
 
 H 
 
 no 
 
 945 
 
 2.40 
 
 156 
 
 3.80 
 
 54.6 
 
 .00 
 
 95.5 
 
 2.20 
 
 43.4 
 
 3.60 
 
 26.5 
 
 20 
 
 654 
 
 2.60 
 
 131 
 
 4.00 
 
 47.8 
 
 .10 
 
 86.8 
 
 2.40 
 
 39.8 
 
 3.80 
 
 25.1 
 
 40 
 
 477 
 
 2.80 
 
 
 4.20 
 
 41.7 
 
 .20 
 
 79.6 
 
 2.60 
 
 36.7 
 
 4.00 
 
 23.9 
 
 60 
 
 363 
 
 3.00 
 
 95.5 
 
 4.40 
 
 36.4 
 
 40 
 
 68 2 
 
 2.80 
 
 34.1 
 
 4.50 
 
 21.2 
 
 80 
 
 285 
 
 3.20 
 
 82.5 
 
 4.60 
 
 31.4 
 
 .60 
 
 59.7 
 
 3.00 
 
 31.8 
 
 5.00 
 
 19.1 
 
 2 00 
 
 229 
 
 3 40 
 
 71.6 
 
 4.80 
 
 26.5 
 
 .80 
 
 53 
 
 3.20 
 
 29.8 
 
 5.50 
 
 17.4 
 
 3.20 
 
 187 
 
 3.60 
 
 62.4 
 
 4.95 
 
 22.2 
 
 2.00 
 
 48.0 
 
 3.40 
 
 28.1 
 
 6.00 
 
 15.9 
 
 The hardness of steel, as determined by the Brinell method, has a 
 uirect relation to the tensile strength, and is equal to the product of a 
 coefficient, C, into the hardness number. Experiments made in Sweden 
 with annealed steel showed that when the impression was made trans- 
 versely to the rolling direction, with H below 175, C = 0.362; with H 
 above 175, C = 0.344. When the impression was made in the rolling 
 direction, with // below 175, C = 0.354; with H above 175, C = 0.324. 
 The product, C X H, or the tensile strength, is expressed in kilograms 
 per square millimeter. 
 
 Electro-magnetic Method. Several instruments have been de- 
 vised for testing the hardness of steel by electrical methods. According 
 to Prof. D. E. Hughes (Cass. Mag., Sept., 1908), the magnetic capacity 
 of iron and steel is directly proportional to the softness, and the resist- 
 ance to a feeble external magnetic force is directly as the hardness. The 
 electric conductivity of steel decreases with the increase of hardness. 
 (See Electric Conductivity of Steel, p. 477.) 
 
 The Scleroscope. This is the name of an instrument invented by 
 A. F. Shore for determining the hardness of metals. It consists chiefly 
 of a vertical glass tube in which slides freely a small cylinder of very 
 hard steel, pointed on the lower end, called the hammer. This hammer 
 is allowed to fall about 10 inches on to the sample to be tested, and the 
 distance it rebounds is taken as a measure of the hardness of the sample. 
 A scale on the tube is divided into 140 equal parts, and the hardness is 
 expressed as the number on the scale to which the hammer rebounds. 
 Measured in this way the hardness of different substances is as follows: 
 Glass, 130; porcelain, 120; hardest steel, 110; tool steel, 1% C., may be 
 as low as 31; mild steel, 0.5 C, 26 to 30; gray castings, 39; wrought 
 iron, 18; babbitt metal, 4 to 10; soft brass, 12; zinc, 8; copper, 6; 
 lead, 2. (Cass. Mag., Sept., 1908.) 
 
 STRENGTH OF GLASS. 
 
 (Fairbairn's "Useful Information for Engineers," Second Series.) 
 
 Best Common Extra 
 
 Flint 
 Glass. 
 
 Mean specific gravity 3.078 
 
 Mean tensile strength, Ibs. per sq. in., bars 2,413 
 
 do. thin plates 4,200 
 
 Mean crush'g strength, Ibs. p. sq. in., cyl'drs 27,582 
 
 do. cubes 13,130 
 
 Green White Crown 
 
 Glass. 
 
 2.528 
 
 2,896 
 
 4,800 
 
 39,876 
 
 20,206 
 
 Glass. 
 2.450 
 2,546 
 6,000 
 31,003 
 21,867 
 
 The bars in tensile tests were about 1/2 inch diameter. The crushing 
 tests were made on cylinders about 3/ 4 inch diameter and from 1 to 2 
 inches high, and on cubes approximately 1 inch on a side. The mean 
 transverse strength of glass, as calculated by Fairbairn from a mean 
 tensile strength of 2560 Ibs. and a mean compressive strength of 30,150 
 Ibs. per sq. in., is, for a bar supported at the ends and loaded in the 
 middle, w = 3140 bd 2 /l, in which w = breaking weight in Ibs., b =- 
 breadth, d = depth, and I = length, in inches. Actual tests will prob- 
 ably show wide variations in both directions from the mean calculated 
 itrength. 
 
366 
 
 STRENGTH OF MATERIALS. 
 
 STRENGTH OF ICE. 
 
 Experiments at the University of Illinois in 1895 (The Technograph, 
 vol. ix) gave 620 IDS. per sq. in. as the average crushing strength of cubes i 
 of manufactured ice tested at 23 F., and 906 IDS. for cubes tested at I 
 14 F. Natural ice, at 12 F., tested with the direction of pressure parallel I 
 to the original water surface, gave a mean of 1070 Ibs., and tested with I 
 the pressure perpendicular to this surface 1845 Ibs. The range of varia- 1 
 tion in strength of individual pieces is about 50% above and below the } 
 mean figures, the lowest and highest figures being respectively 318 and 
 2818 Ibs. per sq. in. The tensile strength of 34 samples tested at 19 to 
 23 F. was from 102 to 256 Ibs. per sq. in. 
 
 STRENGTH OF TIMBER. 
 
 Strength of Long-leaf Pine (Yellow Pine, Pinus Palustris) from 
 Alabama (Bulletin No. 8, Forestry Div., Dept. of Agriculture, 1893. 
 Tests by Prof. J. B. Johnson). 
 
 The following is a condensed table of the range of results of mechani- 
 cal tests of over 2000 specimens, from 26 trees from four different sites 
 in Alabama; reduced to 15 per cent moisture: 
 
 
 Butt Logs. 
 
 Middle Logs. 
 
 Top Logs. 
 
 Av'g 
 of all 
 Butt 
 Logs. 
 0.767 
 
 12,614 
 
 9,460 
 1,926 
 
 2.98 
 7,452 
 1,598 
 17,359 
 866 
 
 Specific gravity 
 
 0.449 to 1 .039 
 4,762 to 16,200 
 
 4,930 to 13,110 
 1,119to 3,117 
 
 0.23 to 4.69 
 4,781 to 9,850 
 675 to 2,094 
 8,600 to 3 1,890 
 464 to 1,299 
 
 0.575 to 0.859 
 7, 640 to 17,128 
 
 5,540 to 11,790 
 1,136 to 2,982 
 
 1.34 to 4.21 
 5,030 to 9,300 
 656 to 1,445 
 6,330 to 29,500 
 539 to 1,230 
 
 0.484 to 0.907 
 4,268 to 15,554 
 
 2,553 to 11,950 
 842 to 2,697 
 
 0.09 to 4.65 
 4, 587 to 9,100 
 584 to 1,766 
 4, 170 to 23,280 
 484 to 1,156 
 
 Transverse strength, rrp- 
 
 do. do. at elast. limit 
 Mod. of elast., thous. Ibs. 
 Relative elast. resilience, 
 inch-pounds per cub. in. 
 Crushing endwise, str. 
 per sq. in .-Ibs 
 
 Crushing across grain, 
 strength per sq. in., Ibs. 
 Tensile strength per sq. 
 in 
 
 Shearing strength (with 
 grain), mean persq. in. 
 
 Some of the deductions from the tests were as follows: 
 
 1. With the exception of tensile strength a reduction of moisture is 
 accompanied by an increase in strength, stiffness, and toughness. 
 
 2. Variation in strength goes generally hand-in-hand with specific 
 gravity. 
 
 3. In the first 20 or 30 feet in height the values remain constant; then 
 occurs a decrease of strength which amounts at 70 feet to 20 to 40 per 
 cent of that of the butt-log. 
 
 4. In shearing parallel with the grain and crushing across and par- 
 allel with the grain, practically no difference was found. 
 
 5. Large beams appear 10 to 20 per cent weaker than small pieces. 
 
 6. Compression tests endwise seem to furnish the best average state- 
 ment of the value of wood, and if one test only can be made, this is the 
 safest, as was also recognized by Bauschinger. 
 
 7. Bled timber is in no respect inferior to unbled timber. 1 
 
 The figures for crushing across the grain represent the load required to 
 cause a compression of 15 per cent. The relative elastic resilience, in 
 inch-pounds per cubic inch of the material, is obtained by measuring 
 the area of the plotted strain-diagram of the transverse test from the 
 origin to the point in the curve at which the rate of deflection is 50 per 
 cent greater than the rate in the earlier part of the test where the dia- 
 gram is a straight line. This point is arbitrarily chosen since there is 
 no definite "elastic limit" in timber as there is in iron. The "strength 
 at the elastic limit" is the strength taken at this same point. Timber 
 is not perfectly elastiq for any load if left. on any great. length of time, 
 
 The long-leaf pine is found in all the Southern coast states from North 
 
STRENGTH OF TIMBER. 
 
 367 
 
 I Carolina to Texas. Prof. Johnson says it is probably the strongest timber 
 I in large sizes to be had in the United States. In small selected speci- 
 i mens, other species, as oak and hickory, may exceed it in strength and 
 (toughness. The other Southern yellow pines, viz., the Cuban, short- 
 f leaf and the loblolly pines are inferior to the long-leaf about in the ratios 
 ( of their specific gravities; the long-leaf being the heaviest of all the 
 r pines. It averages (kiln-dried) 48 pounds per cubic foot, the Cuban 47, 
 [ the short-leaf 40, and the loblolly 34 pounds. 
 
 Strength of Spruce Timber. The modulus of rupture of spruce 
 f is given as follows by different authors: Hatfield, 9900 Ibs. per square 
 i inch; Rankine, 11,100; Laslett, 9045; Trautwine, 8100; Rodman, 6168. 
 I Trautwine advises for use to deduct one-third in the case of knotty and 
 \ poor timber. 
 
 Prof. Lanza, in 25 tests of large spruce beams, found a modulus of 
 
 Lrupture from 2995 to 5666 Ibs.; the average being 4613 Ibs. These 
 
 were average beams, ordered from dealers of good repute. Two beams 
 
 ! of selected stock, seasoned four years, gave 7562 and 8748 Ibs. The 
 
 modulus of elasticity ranged from 897,000 to 1,588,000, averaging 
 
 1 1,294,000. 
 
 Time tests show much smaller values for both modulus of rupture and 
 modulus of elasticity. A beam tested to 5800 Ibs. in a screw machine 
 was left over night, and the resistance was found next morning to have 
 dropped to about 3000, and it broke at 3500. 
 
 Prof. Lanza remarks that while it was necessary to use larger factprs 
 ' of safety, when the moduli of rupture were determined from tests with 
 smaller pieces, it will be sufficient for most timber constructions, except 
 in factories, to use a factor of four. For breaking strains of beams, he 
 states that it is better engineering to determine as the safe load of a 
 timber beam the load that will not deflect it more than a certain fractior? 
 of its span, say about Vsoo to 1/400 of its length. 
 
 Expansion of Timber Due to the Absorption of Water. 
 
 (De Volson Wood, A. S. M. E., vol. x.) 
 
 Pieces 36 X 5 in., of pine, oak, and chestnut, were dried thoroughly^ 
 *nd then immersed in water for 37 days. 
 
 The mean per cent of elongation and lateral expansion were: 
 
 Pine. Oak. Chestnut. 
 
 Elongation, per cent 0.065 0.085 0.165 
 
 Lateral expansion, per cent 2.6 3.5 3.65 
 
 Expansion of Wood by Heat. Trautwine gives for the expansion, 
 of white pine for 1 degree Fahr. 1 part in 440,530, or for 180 degrees 
 1 part in 2447, or about one-third of the expansion of iron. 
 
 Shearing Strength of American Woods, adapted for Pins or 
 Tree-nails. 
 
 J. C. Trautwine (Jour. Franklin Inst.). (Shearing across the grain.) 
 
 per sq. in. 
 
 Ash 6280 
 
 Beech 5223 
 
 Birch 5595 
 
 Cedar (white) 1 372 
 
 "edar (white) 1519 
 
 Cedar (Central American). ... 3410 
 
 Cherry 2945 
 
 Chestnut 1536 
 
 Dogwood 6510 
 
 Ebony 7750 
 
 Gum 5890 
 
 Hemlock 2750 
 
 Locust .7176 
 
 per. sq. in. 
 
 Hickory f 6045 
 
 Hickory 7285 
 
 Maple 6355 
 
 Oak 4425 
 
 Oak (live) 8480 
 
 Pine (white) 2480 
 
 Pine (Northern yellow) 4340 
 
 Pine (Southern yellow) 5735 
 
 Pine (very resinous yellow) . . . 5053 
 
 Poplar 4418 
 
 Spruce 3255 
 
 Walnut (black) 4728 
 
 Walnut (common) 2830 
 
 Transverse Tests of Pine and Spruce Beams. (Tech. Quar. XIII, 
 No. 3, 1900, p. 226.) Tests of 37 hard pine beams, 4 to 10 ins. wide, 6 to 
 12 ins. deep, and 8 to 1C ft. length between supports, showed great varia- 
 
368 STRENGTH OF MATERIALS. 
 
 tions in strength. The modulus of rupture of different beams was as 
 follows: 1, 2970; 4, 4000 to 5000; 1, 5510; 1, 6220; 9, 7000 to 8000- 8 : 
 8000 to 9000; 4, 9000 to 10,000; 5, 10,000 to 11,000; 3, 11,000 to 12,000; 
 1, 13,600. 
 
 Six tests of white pine beams gave moduli of rupture ranging from 
 1840 to 7810; and eighteen tests of spruce beams from 2750 to 7970 Ibs. 
 per sq. in. 
 
 .Drying of Wood. Circular 111, U. S. Forest Service, 1907. Sticks 
 of Southern loblolly pine 11 to 13 inches diameter, 9 to 10 ft. long, were 
 weighed every two weeks until seasoned, to find the weight of water 
 evaporated. The loss, per cent of weight, was as follows: 
 
 Weeks 2 4 6 8 10 12 14 16 
 
 Loss per cent of green wood 16 21 26 31 32 34 35 35 
 
 Preservation of Timber. U. S. Forest Service, Circular 111, 1907, 
 discusses preservative treatment of timber by different methods, namely, 
 brush treatment with creosote and with carbolinium; open tank treat- 
 ment with salt solution, zinc chloride solution; and cylinder treatment 
 with zinc chloride solution and creosote. 
 
 The increased life necessary to pay the cost of these several preserva- 
 tive treatments is respectively: 6, 16, 7, 13, 41, 27, and 55%. The 
 results of the experiments prove that it will pay mining companies to 
 peel their timber, to season it for several months and to treat it with a 
 
 good preservative. Loblolly and pitch pine have been most success- 
 fully preserved by treatment with creosote in an open tank. 
 
 Circular No. 151 of the Forest Service describes experiments on the 
 
 best method of treating loblolly pine cross-arms of telegraph poles. The 
 arms after being seasoned in air are placed in a closed air-tight cylinder, 
 a vacuum is applied sufficient to draw the oil (creosote, dead oil of coal 
 tar) from the storage tank into the treating cylinder. Sufficient pres- 
 sure is then applied to force the oil into the heartwood portion of the 
 timber, and continued until the desired amount of oil is absorbed, then a 
 vacuum is maintained until the surplus oil is drawn from the sap wood. 
 It is recommended that heartwood should finally contain about 6 Ibs. 
 of oil per cubic foot, and sapwood about 10 Ibs. The preliminary bath 
 of live steam, formerly used, has been found unnecessary. Much valu- 
 able information concerning timber treatment and its benefits is con- 
 tained in the several circulars on the subject issued by the Forest 
 Service. 
 
 STRENGTH OF COPPER AT HIGH TEMPERATURES. 
 
 The British Admiralty conducted some experiments at Portsmouth 
 Dockyard in 1877, on the effect of increase of temperature on the tensile 
 strength of copper and various bronzes. The copper experimented upon 
 was in rods 0.72 in. diameter. 
 
 The following table shows some of the results: 
 
 Temperature, 
 Fahr. 
 
 Tensile Strength 
 in Ibs. per sq. in. 
 
 Temperature, 
 Fahr. 
 
 Tensile Strength 
 in Ibs. per sq. in. 
 
 Atmospheric 
 100 
 200 
 
 23,115 
 23,366 
 22,110 
 
 300 
 400 
 500 
 
 21,607 
 21,105 
 19,597 
 
 Up to a temperature of 400 F. the loss of strength was only about 
 10 per cent, and at 500 F. the loss was 16 per cent. The temperature of 
 steam at 200 Ibs. pressure is 382 F., so that according to these experi- 
 ments the loss of strength at this point would not be a serious matter. 
 Above a temperature of 500 the strength is seriously affected. 
 
 COPPER CASTINGS OF HIGH CONDUCTIVITY. 
 
 A method of making copper castings of high electric conductivity is 
 described in The Foundry, Sept., 1910. The copper is melted under 
 a coyer of charcoal and common salt. When thoroughly liquid, 2 oz. 
 of stick magnesium is added per 100 Ib. of copper, being plunged below 
 the surface of the copper and held there until reaction ceases. The 
 metal should be stirred for five minutes with a plumbago stirrer, and 
 reheated before pouring. The castings have a conductivity of about 
 85 % if high grade ingot copper is used. 
 
TESTS OF AMERICAN WOODS. 
 
 369 
 
 TESTS OF AMERICAN WOODS. (Watertown Arsenal Tests, 1883.) 
 
 In all cases a large number of tests were made of each wood. Mini- 
 mum and maximum results only are given. All of the test specimens 
 had a sectional area of 1.575 X 1.575 inches. The transverse test speci- 
 mens were 39.37 inches, between supports, and the compressive test 
 specimens were 12.60 inches long. Modulus of rupture calculated from 
 
 3 PI 
 formula R = ^-rj 2 P = l ac * * n P oun ds at the middle, I = length, in 
 
 Inches, b = breadth, d = depth: 
 
 Name of Wood. 
 
 Transverse Tests. 
 Modulus of 
 Rupture. 
 
 Compression 
 Parallel to 
 Grain, pounds 
 per square inch. 
 
 Min. 
 
 Max. 
 
 Min. 
 
 Max. 
 
 Cucumber tree (Magnolia acuminata) . 
 Yellow poplar white wood (Lirioden- 
 
 7,440 
 6,560 
 6,720 
 
 9,680 
 8,610 
 12,200 
 8,310 
 7,470 
 10,190 
 9,830 
 10,290 
 5,950 
 5,180 
 10,220 
 8,250 
 
 6,720 
 
 4,700 
 8,400 
 14,870 
 11,560 
 7,010 
 9,760 
 7,900 
 5,950 
 13,850 
 
 11,710 
 8,390 
 6,310 
 5,640 
 9,530 
 5,610 
 3,780 
 
 9,220 
 9,900 
 7,590 
 
 8,220 
 10,080 
 
 12,050 
 11,756 
 11,530 
 
 20,130 
 13,450 
 21,730 
 16,800 
 11,130 
 14,560 
 14,300 
 18,500 
 15,800 
 10,150 
 13,952 
 15,070 
 
 11,360 
 
 11,740 
 16,320 
 20,710 
 19,430 
 18,360 
 18,370 
 18,420 
 12,870 
 18,840 
 
 17,610 
 13,430 
 9,530 
 15,100 
 10,030 
 11,530 
 10,980 
 
 21,060 
 11,650 
 14,680 
 
 17,920 
 16,770 
 
 4,560 
 4,150 
 3,810 
 
 7,460 
 6,010 
 8,330 
 5,830 
 5,630 
 6,250 
 6,240 
 6,650 
 4,520 
 4,050 
 6,980 
 4,960 
 
 4,960 
 
 5,480 
 6,940 
 7,650 
 7,460 
 5,810 
 4,960 
 4,540 
 3,680 
 5,770 
 
 5,770 
 3,790 
 2,660 
 4,400 
 5,060 
 3,750 
 2,580 
 
 4,010 
 4,150 
 4,500 
 
 4,880 
 6,810 
 
 7,410 
 5,790 
 6,480 
 
 9,940 
 7,500 
 11,940 
 9,120 
 7,620 
 9,400 
 7,480 
 8,080 
 8,830 
 5,970 
 8,790 
 8,040 
 
 7,340 
 
 6,810 
 8,850 
 10,280 
 8,470 
 9,070 
 8,970 
 8,550 
 6,650 
 7,840 
 
 8,590 
 6,510 
 5,810 
 7,040 
 7,140 
 5,600 
 4,680 
 
 10,600 
 5,300 
 7,420 
 
 9,800 
 10,700 
 
 White wood, Basswood (Tilia Ameri- 
 
 Sugar-maple, Rock-maple (Acer sac- 
 
 Red maple (Acer rubrum) 
 
 
 Wild cherry (Prunus serotina) 
 Sweet gum (Liquidambar styraciflua) . 
 Dogwood (Cornus florida) . 
 
 Sour gum, Pepperidge\(Nyssasyli;atica) 
 Persimmon (Diospyros Virginiana) . . 
 White ash (Fraxunis Americana) .... 
 Sassafras (Sassafras officinale) 
 
 Slippery elm (Ulmus fulva) 
 
 \\hite elm (Ulmus Americana) 
 
 Sycamore; Buttonwood (Platanus 
 occidentalis) .... . 
 
 Butternut; white walnut (Juglans 
 
 Black walnut (Juglans nigrd) 
 
 
 
 White oak (Quercus alba] 
 
 
 
 
 Beech (Fagus ferruginea) 
 
 Canoe-birch, paper-birch (Betula pa- 
 
 Cottonwood (Populus monilifera) 
 White cedar (Thuja occidentalis} 
 Red cedar (Junipcrus Virginiana) . . . 
 Cypress (Saxodium Distichum) 
 White pine (Pinus strobus} 
 
 
 Long-leaved pine, Southern pine 
 
 White spruce (Picea alba} 
 
 Hemlock ( Tsuga Canadensis) 
 Red fir, yellow fir (Pseudotsuga Doug- 
 Jasii) 
 
 Tamarack (Larix Americana) 
 
370 STRENGTH OF MATERIALS. 
 
 TENSILE STRENGTH OF ROLLED ZINC PLATES. 
 
 Herbert F. Moore, in Univ. of III Bulletin, No. 9, 1911, gives a 
 table from which the following averages are taken: 
 Thickness, Tensile Strength, Elongation 
 
 In. Lb. per Sq. In. in 8 In., %. 
 
 with across with across 
 
 rain. grain. grain. grain. 
 
 1340 23050 4.85 0.31 
 
 0.6 21490 23550 1G.63 3.33 
 0.25 23770 22260 11.90 0.27 
 0.10 23580 33620 20.4 14.3 
 0.018 24660 32380 
 
 THE STRENGTH OF BRICK, STONE, ETC. 
 
 A great advance has recently (1895) been made in the manufacture 
 of brick, in the direction of increasing their strength. Chas. P. Chase, in 
 Engineering News, says: "Taking the tests as given in standard engi- 
 neering books eight or ten years ago, we find in Trautwine the strength of 
 brick given as 500 to 4200 Ibs. per sq. in. Now, taking recent tests in 
 experiments made at Watertown Arsenal, the strength ran from 5000 to 
 22,000 Ibs. per sq. in. In the tests on Illinois paving-brick, by Prof. 
 I. O. Baker, we find an average strength in hard paving brick of over 
 5000 Ibs. per square inch. The average crushing strength of ten varie- 
 ties of paving-brick much used in the West, I find to be 7150 Ibs. to the 
 square inch." 
 
 A test of brick made by the dry-clay process at Watertown Arsenal, 
 according to Paving, showed an average compressive strength of 3972 Ibs. 
 per sq. in. In one instance it reached 4973 Ibs. per sq. in. A test was 
 made at the same place on a "fancy pressed brick." The first crack 
 developed at a pressure of 305,000 Ibs., and the brick crushed at 364,300 
 Ibs., or 11,130 Ibs. per sq. in. This indicates almost as great compressive 
 strength as granite paving-blocks, which is from 12,000 to 20,000 Ibs. 
 per sq. in. 
 
 The three following notes on bricks are from Trautwine's Engineer's 
 Pocket-book: 
 
 Strength of Brick. 40 to 300 tons per sq. ft., 622 to 4668 Ibs. per 
 sq. in. A soft brick will crush under 450 to 600 Ibs. per sq. in., or 30 to 
 40 tons per square foot, but a first-rate machine-pressed brick will stand 
 200 to 400 tons per sq. ft. (3112 to 6224 Ibs. per sq. in.). 
 
 Weight of Bricks. Per cubic foot, best pressed brick, 150 Ibs.; 
 good pressed brick, 131 Ibs.; common hard brick, 125 Ibs.; good common 
 brick, 118 Ibs.; soft inferior brick, 100 Ibs. 
 
 Absorption of Water. A brick will in a few minutes absorb 1/2 to 
 3/4 Ib. of water, the last being 1/7 of the weight of a hand-molded one, 
 or Vs of its bulk. 
 
 Strength of Common Red Brick. Tests of 67 samples of Hudson 
 River machine-molded brick were made by I. H. Woolson, Eng. News, 
 April 13, 1905. The crushing strength, in Ibs. per sq. in., of 15 pale brick 
 ranged from 1607 to 4546, average 3010; 44 medium, 2080 to 8944, av. 
 4080; 8 hard brick, 2396 to 6420, av. 4960. Five Philadelphia pressed 
 brick gave from 3524 to 9425, av. 6361. The absorption ranged from 
 8.7 to 21.4% by weight. The relation of absorption to strength varied 
 greatly, but on the average there was an increase of absorption up to 
 3000 Ibs. per sq. in. crushing strength, and beyond that a decrease. 
 
 The Strongest Brick ever tested at the Watertown Arsenal was a 
 paving brick from St. Louis, Mo., which showed a compressive strength 
 of 38,446 Ibs. per sq. in. The absorption was 0.21% by weight and 
 0.5% by volume. The sample was set on end, and measured 2.45 X 3.06 
 ins. in cross section. Eng. News, Mar. 14, 1907. 
 
 Tests of Bricks, full size, on flat side. (Tests made at Watertown, 
 Arsenal in 1883.) The bricks were tested between flat steel buttresses. 
 Compressed surfaces (the largest surface) ground approximately flat. 
 The bricks were all about 2 to 2.1 inches thick, 7.5 to 8.1 inches long, 
 and 3.5 to 3.76 inches wide. Crushing strength per square inch: One 
 lot ranged from 11.056 to 16,734 Ips,; a second, 12,995 to 22,351; a 
 
STRENGTH OF BRICK, STONE, ETC. 
 
 371 
 
 third, 10,390 to 12,709. Other tests gave results from 5960 to 10,250 
 Ibs. per sq. in. 
 
 Tests of Brick. (Tech. Quar., 1900.) Different brands of brick tested 
 on the broad surfaces, and on edge.^gave results as follows, Ibs. per sq. in. 
 
 (Tech. Quar. XII, No. 3, 1899.) 38 tests. ' 
 
 - 
 
 No. 
 Test. 
 
 Aver- 
 age. 
 
 Maxi- 
 mum. 
 
 Mini- 
 mum. 
 
 Per cent Water 
 
 Absorbed. 
 
 On broad surface 
 Bay State, light hard 
 Same, tested on edge . . 
 On broad surface 
 Dover River, soft 
 burned 
 
 71 
 
 67 
 
 38 
 
 7039 
 6241 
 
 5350 
 
 11,240 
 10,840 
 
 8630 
 
 3587 
 3325 
 
 3930 
 
 15. 15 to 19.3 av. 7.5 
 13. 67 to 18.2 " 7.4 
 
 14.0 to 18.6 " 11.6 
 
 Dover River, hard 
 burned 
 
 36 
 
 8070 
 
 10,940 
 
 5850 
 
 4.7 to 10.1 " 7.0 
 
 Central N. Y., soft 
 burned 
 
 36 
 
 2190 
 
 3060 
 
 1370 
 
 17.8 to 22.0 " 19.9 
 
 Central N. Y., me- 
 dium burned 
 Central N. Y., hard 
 burned 
 
 36 
 36 
 
 3600 
 5360 
 
 4950 
 8810 
 
 2080 
 3310 
 
 16.6 to 23. 4 " 18.6 
 8.3 to 16.7 " 12.5 
 
 Another lot,* hard 
 burned 
 
 16 
 
 7940 
 
 9770 
 
 6570 
 
 7.6 to 12.9 " 10.6 
 
 Same,* tested on edge 
 
 16 
 
 6430 
 
 10,230 
 
 3830 
 
 6.2 to 18.7 " 11.4 
 
 * Brand not named. 
 
 The per cent water absorbed in general seemed to have a relation to 
 the strength, the greatest absorption corresponding to the lowest strength, 
 and vice versa, but there were many exceptions to the rule. 
 
 Crushing Strength of Masonry Materials. (From Howe's "Re- 
 taining- Walls.") 
 
 tons per sq. ft. tons per sq. ft. 
 
 Brick, best pressed . 40 to 300 Limestones and marbles 250 to 1000 
 
 Chal'c 20 to 30 Sandstone 150 to 550 
 
 Gran te 300 to 1200 Soapstone 400 to 800 
 
 Strength of Granite. The crushing strength of granite is commonly 
 rated at 12,000 to 15,000 Ibs. per sq. in. when tested in two-inch cubes, 
 and only the hardest and toughest of the commonly used varieties reach 
 a strength above 20,000 Ibs. Samples of granite from a quarry on the 
 Connecticut River, tested at the Watertown Arsenal, have shown a 
 strength of 35,965 Ibs. per sq. in. (Engineering News, Jan. 12, 1893). 
 
 Ordinary granite ranges from 20,000 to 30,000 Ibs. compressive strength 
 per sq. in. A granite from Asheville, N.C., tested at the Watertown 
 Arsenal, gave 51,900 Ibs. Eng. News, Mar. 14, 1907. 
 
 Strength of Avondale, Pa., Limestone. (Engineering News, 
 Feb. 9, 1893.) Crushing strength of 2-in. cubes: light stone 12,112, 
 gray stone 18,040, Ibs. per sq. in. 
 
 Transverse test of lintels, tool-dressed, 42 in. between knife-edge bear- 
 ings, load with knife-edge brought upon the middle between bearings: 
 
 Gray stone, section 6 in. wide X 10 in. high, broke under a load of 20,950 Ibs. 
 
 Modulus of rupture 2,200 " 
 
 Light stone, section 81/4 in. wide X10 in. high, broke under. . . 14,720 " 
 
 Modulus of rupture 1,170 " 
 
 Absorption. Gray stone 0.051 of 1 % 
 
 Light stone 0.052 of 1% 
 
 Tests of Sand-lime Brick. (I. H. Woolson, Eng. News, June 14, 
 1906). Eight varieties of brick in lots of 300 to 800 were received from 
 different manufacturers. They were testeq* for transverse strength, on 
 supports 7 in. apart, loaded in the middle: and half bricks were tested by 
 
372 
 
 STRENGTH OF MATERIALS. 
 
 compression, sheets of heavy fibrous paper being inserted between the 
 specimen and the plates of the testing machine to insure an even bearing. 
 Tests were made on the brick as received, and on other samples after 
 drying at about 150 F. to constant weight, requiring from four to six 
 days. The moisture in two bricks of each series was determined, and 
 found to range from 1 to 10%, average 5.9%. The figures of results 
 given below are the averages of 10 tests in each case. Other bricks of 
 each lot were tested for absorption by being immersed 1/2 in. in water for 
 48 hours, for resistance to 20 repeated freezings and thawings, and for 
 resistance to fire by heating them in a fire testing room, the bricks being 
 built in as 8-in. walls, to 1700 F. and maintaining that temperature 
 three hours, then cooling them with a 1 Vs-in. stream of cold water from 
 a hydrant. Transverse and compressive tests were made after these 
 treatments. The results given below are averages of five tests, except in 
 the case of the bricks tested after firing, in which two samples are averaged. 
 
 EFFECT OF THE FIRE TEST. Several large cracks developed in both 
 the sand-lime and the clay brick walls during the test. These were no 
 worse in one wall than in the other. With the exception of surface 
 deterioration the walls were solid and in good condition. After they 
 were cooled the inside course of each wall was cut through and specimens 
 of each series secured for examination and test. It was difficult to 
 secure whole bricks, owing to the extreme brittleness. 
 
 In general the bricks were affected by fire about half way through. 
 They were all brittle and many of them tender when removed from the 
 wall. With the sand-lime brick, if a brick broke the remainder had t9 be 
 chiseled out like concrete, whereas a clay brick under like conditions 
 would chip out easily. The clay brick were so brittle and full of cracks 
 that the wall could be broken down without trouble. The sand-lime 
 bricks adhered to the mortar better, were cracked less, and were not so 
 brittle. 
 
 Designation of Brick. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 Modulus of ) 
 Rupture ) 
 
 As received 
 
 272 
 
 424 
 
 377 
 
 262 
 
 190 
 
 301 
 
 365 
 
 
 Dried 
 
 320 
 
 505 
 
 406 
 
 334 
 
 197 
 
 570 
 
 494 
 
 11 
 
 Increase, % 
 
 15.0 
 
 16.0 
 
 7.1 
 
 21.5 
 
 3.5 
 
 47.2 
 
 26.2 
 
 
 
 Wet 
 
 248 
 
 349 
 
 345 
 
 241 
 
 243 
 
 250 
 
 485 
 
 41 
 
 After fire 
 
 17 
 
 57 
 
 20 
 
 32 
 
 24 
 
 27 
 
 37 
 
 Compressive ) 
 
 As received 
 
 1875 
 
 2300 
 
 2871 
 
 1923 
 
 1610 
 
 2460 
 
 2669 
 
 Strength, 
 
 Dried 
 
 2604 
 
 2772 
 
 3240 
 
 2476 
 
 1870 
 
 3273 
 
 3190 
 
 Ibs. per sq. in. ) 
 
 Increase, % 
 Wet 
 
 30.2 
 1611 
 
 17.1 
 
 2174 
 
 20.7 
 2097 
 
 22.3 
 1923 
 
 13.5 
 1108 
 
 24.8 
 2063 
 
 16.3 
 2183 
 
 14 
 
 After freez- 
 
 
 
 
 
 
 
 
 
 ing 
 
 1596 
 
 1619 
 
 2265 
 
 1174 
 
 1167 
 
 1851 
 
 1739 
 
 14 
 
 After fire 
 
 1807 
 
 2814 
 
 2573 
 
 2069 
 
 1089 
 
 2051 
 
 4885 
 
 % of lime in brick 
 
 6 
 
 10 
 
 5 
 
 41/9 
 
 41/9 
 
 5 
 
 8 
 
 Pressure for hare 
 Hours in hardeni 
 
 ening, Ibs.. . . 
 ng, Ibs 
 
 120 
 10 
 
 135 
 8 
 
 150 
 
 7 
 
 125 
 10 
 
 10 
 
 150 
 
 7 
 
 125 
 10 
 
 
 STRENGTH OF LIME AND CEMENT MORTAR. 
 
 (Engineering. October 2, 1891.) 
 
 Tests made at the University of Illinois on the effects of adding cement 
 to lime mortar. In all the tests a good quality of ordinary fat lime was 
 used, slaked for two days in an earthenware jar, adding two parts by 
 weight of water to one of lime, the loss by evaporation being made up 
 by fresh additions of water. The cements used were a German Port- 
 land, Black Diamond (Louisville), and Rosendale. As regards fineness 
 of grinding, 85 per cent of the Portland passed through a No. 100 sieve, 
 as did 72 per cent of the Rosendale. A fairly sharp sand, thoroughly 
 washed and dried, passing through a No. 18 sieve and caught on a No. 30. 
 
CEMENT AND FLAGGING. 
 
 373 
 
 was used. The mortar in all cases consisted of two volumes of sand to 
 one of lime paste. The following results were obtained on adding 
 various percentages of cement to the mortar: 
 
 Tensile Strength, pounds per square inch. 
 
 Age . { 
 
 4 
 
 7 
 
 14 
 
 21 
 
 28 
 
 50 
 
 84 
 
 
 Days. 
 
 Days. 
 
 Days. 
 
 Days. 
 
 Days. 
 
 Days. 
 
 Days. 
 
 Lime mortar. . 
 
 4 
 
 8 
 
 10 
 
 13 
 
 18 
 
 21 
 
 26 
 
 20 per cent Rosendale 
 
 5 
 
 81/2 
 
 9l/ 2 
 
 12 
 
 17 
 
 17 
 
 18 
 
 20 Portland . 
 
 5 
 
 81/2 
 
 14 
 
 20 
 
 25 
 
 24 
 
 26 
 
 30 Rosendale 
 
 7 
 
 11 
 
 13 
 
 181/2 
 
 21 
 
 221/2 
 
 23 
 
 30 Portland . 
 
 8 
 
 16 
 
 18 
 
 22 
 
 25 
 
 28 
 
 27 
 
 40 Rosendale 
 
 10 
 
 12 
 
 161/2 
 
 2H/-> 
 
 221/2 
 
 24 
 
 36 
 
 40 Portland . 
 
 27 
 
 39 
 
 38 
 
 43 
 
 47 
 
 59 
 
 57 
 
 60 Rosendale 
 
 9 
 
 13 
 
 20 
 
 16 
 
 22 
 
 221/2 
 
 23 
 
 60 Portland . 
 
 45 
 
 58 
 
 55 
 
 68 
 
 67 
 
 102 
 
 78 
 
 80 Rosendale 
 
 12 
 
 181/2 
 
 22l/ 2 
 
 27 
 
 29 
 
 3U/2 
 
 33 
 
 80 Portland . 
 
 87 
 
 91 
 
 103 
 
 124 
 
 94 
 
 210 
 
 145 
 
 1 00 Rosendale 
 
 18 
 
 23 
 
 26 
 
 31 
 
 34 
 
 46 
 
 48 
 
 1 00 Portland . 
 
 90 
 
 120 
 
 146 
 
 152 
 
 181 
 
 205 
 
 202 
 
 Tests of Portland Cement. 
 
 (Tech. Quar. XIII. No. 3, 1900, p. 236.) 
 
 
 IDay. 
 
 2 Days. 
 
 14 Days 
 
 1 Mo. 
 
 2Mos. 
 
 6Mos. 
 
 1 Year. 
 
 Neat cement: 
 Tension, Ibs. 
 
 
 
 
 
 
 
 
 per sq. in... 
 
 268-312 
 
 454-532 
 
 780-820 
 
 915-920 
 
 950-1100 
 
 1036- 11 90 
 
 996-1248 
 
 Compression, 
 Ibs. per sq. in 
 
 ( 8650 
 to 
 ( 10,250 
 
 13,080 
 to 
 14,860 
 
 23,640 
 to 
 34,820 
 
 
 34,000 
 to 
 38,500 
 
 
 36,150 
 to 
 50,000 
 
 3 sand, 1 cem. 
 
 
 
 
 
 
 
 
 Tens 
 
 56-75 
 
 79-92 
 
 185-211 
 
 211-230 
 
 217-240 
 
 300-382 
 
 280-383 
 
 3 sand, 1 cem. 
 Comp 
 
 ( 1200 
 to 
 ( 1585 
 
 1750 
 to 
 1885 
 
 3780 
 to 
 4420 
 
 
 7850 
 to 
 8250 
 
 
 8000 
 to 
 10,000 
 
 
 
 
 
 TEANSVERSE STRENGTH OF FLAGGING. 
 
 (N. J. Steel & Iron Co.'s Book.) 
 EXPERIMENTS MADE BY R. G. HATFIELD AND OTHERS. 
 
 dis- 
 
 6 = width of the stone in inches; d = its thickness in inches; I 
 tance between bearings in inches. 
 
 The breaking loads in tons of 2000 Ibs., for a weight placed at the center 
 of the space; will be as follows: 
 
 I I 
 
 Bluestone flagging 0.744 Dorchester freestone 0.264 
 
 Quincy granite 0.624 Aubigny freestone 0.216 
 
 Little Falls freestone 0.576 Caen freestone 0.144 
 
 Belleville, N. J., freestone. . 0.480 Glass 1.000 
 
 Granite (another quarry). . . 0.432 Slate 1.2 to 2.7 
 
 Connecticut freestone 0.312 
 
 Thus a block of Quincy granite 80 inches wide and 6 inches thick, 
 resting on beams 36 inches in the clear, would be broken by a load resting 
 
 midway between the beams = 80 * 36 X 0.624 = 49.92 tons. 
 
 oo 
 
374 STRENGTH OF MATERIALS, 
 
 MODULI OF ELASTICITY OF VARIOUS MATERIALS. 
 
 The modulus of elasticity determined from a tensile test of a bar of any 
 material is the quotient obtained by dividing the tensile stress in pounds 
 per square inch at any point of the test by the elongation per inch of 
 length produced by that stress; or if P = pounds of stress applied, 
 K = the sectional area, I = length of the P9rtion of the bar in which the 
 measurement is made, and A = the elongation in that length, the modu- 
 
 p \ nj 
 
 lus of elasticity E = j? * - = ~. The modulus is generally measured 
 
 within the elastic limit only, in materials that have a well-defined elastic 
 limit, such as iron and steel, and when not otherwise stated the modulus 
 Is understood to be the modulus within the elastic limit. Within this 
 limit, for such materials the modulus is practically constant for any 
 given bar, the elongation being directly proportional to the stress. In 
 other materials, such as cast iron, which have no well-defined elastic 
 limit, the elongations from the beginning of a test increase in a greater 
 ratio than the stresses, and the modulus is therefore at its maximum neaf 
 the beginning of the test, and continually decreases. The moduli of 
 elasticity of various materials have already been given above in treating 
 of these materials, but the following table gives some additional values 
 selected from different sources: 
 
 Brass, cast 9,170,000 
 
 Brass wire 14,230,000 
 
 Copper 15,000,000 to 18,000,000 
 
 Lead 1,000,000 
 
 Tin, cast 4,600,000 
 
 Iron, cast 12,000,000 to 27,000,000 (?) 
 
 Iron, wrought 22,000,000 to 29,000,000 (?) 
 
 Steel . ... 28,000,000 to 32,000,000 (see below) 
 
 Marble . . ... 25,000,000 
 
 Slate 14,500,000 
 
 Glass 8,000,000 
 
 Ash. . 1,600,000 
 
 Beech 1,300,000 
 
 Birch.. 1,250,000 to 1,500,000 
 
 Fir. . 869,000 to 2,191,000 
 
 Oak. . 974,000 to 2,283,000 
 
 Teak 2,414,000 
 
 Walnut 306,000 
 
 Pine, long-leaf (butt-logs) . 1,119,000 to 3,117,000 Avge. 1,926,000 
 
 The maximum figures given by some early writers for iron and steel, 
 viz., 40,000,000 and 42,000,000, are und9ubtedly erroneous. The modulus 
 of elasticity of steel (within the elastic limit) is remarkably constant, 
 4 notwithstanding great variations in chemical analysis, temper, etc. It 
 rarely is found below 29,000,000 or above 31,000,000. It is generally 
 taken at 30,000,000 in engineering calculations. Prof. J. B. Johns9n, 
 in his report on Long-leaf Pine, 1893, says: "The modulus of elasticity 
 is the most constant and reliable property of all engineering materials. 
 The wide range of value of the modulus of elasticity of the various metals 
 found in public records must be explained by erroneous methods of 
 
 In a' tensile test of cast iron by the author (Van Nostrand's Science 
 Series, No. 41, page 45), in which the ultimate strength was 23,285 Ibs. 
 per sq. in., the measurements of elongation were made to 0.0001 inch, 
 and the modulus of elasticity was found to decrease from the beginning 
 of the test, as follows: At 1000 Ibs. per sq. in., 25,000,000; at 2000 Ibs., 
 16,666,000; at 4000 Ibs., 15,384,000; at 6000 Ibs., 13,636,000; at 8000 
 Ibs., 12,500,000; at 12,000 Ibs., 11,250,000; at 15,000 Ibs., 10,000,000; 
 at 20,000 Ibs., 8,000 000; at 23,000 Ibs., 6,140,000. 
 
 FACTORS OF SAFETY. 
 
 A factor of safety is the ratio in which the load that is just sufficient to 
 overcome instantly the strength of a piece of material is greater than the 
 greatest safe ordinary working load. (Rankine.) 
 
 Rankine gives the following "examples of the values of those factors 
 which occur in machines": 
 
FACTOR OF SAFETY 375 
 
 Dead Load. Live Load, Live Load, 
 
 Greatest. Mean. 
 
 Iron and steel 3 6 from 6 to 40 
 
 Timber 4 to 5 8 to 10 
 
 Masonry 4 8 
 
 The great factor of safety, 40, is for shafts in millwork which transmit 
 very variable efforts. 
 
 TJnwin gives the following " factors of safety which have been adopted 
 In certain cases for different materials." They "include an^allowance 
 for ordinary contingencies." 
 
 , A Varying Load Producing % 
 
 Stress of Equal Alternate In Structures 
 
 Actual One Kind Stresses of subj. to vary- 
 
 Material. Load only. different kinds, ing Loads and 
 
 Shocks 
 
 Cast iron 4 6 10 15 
 
 Wrought iron and steel 3 5 8 12 
 
 Timber 7 10 15 20 
 
 Brickwork and Masonry 20 30 
 
 In cast iron the factors are high to allow for unknown internal stresses. 
 
 Prof. Wood in his "Resistance of Materials" says: "In regard to the 
 margin that should be left for safety, much depends upon the character 
 of the loading. If the load is simply a dead weight, the margin may be 
 comparatively small; but if the structure is to be subjected to percus- 
 sive forces or shocks, the margin should be comparatively large on account 
 of the indeterminate effect produced by the force. In machines which 
 are subjected to a constant jar while in use, it is very difficult to deter- 
 mine the proper margin which is consistent with economy and safety. 
 Indeed, in such cases, economy as well as safety generally consists in 
 making them excessively strong, as a single breakage may cost much 
 more than the extra material necessary to fully insure safety." 
 
 For discussion of the resistance of materials to repeated stresses and 
 shocks, see pages 275 to 285. 
 
 Instead of using factors of safety, it is becoming customary in designing 
 to fix a certain number 'of pounds per square inch as the maximum stress 
 which will be allowed on a piece. Thus, in designing a boiler, instead of 
 naming a factor of safety of 6 for the plates and 10 for .the stay-bolts, the 
 ultimate tensile strength 9f the steel being from 50,000 t9 60,000 Ibs. per 
 sq. in., an allowable working stress of 10,000 Ibs. per sq. in. on the plates 
 and 6000 Ibs. per sq. in. on the stay-bolts may be specified instead. So 
 also in the use of formulae for columns (see page 285) the dimensions of a 
 column are calculated after assuming a maximum allowable compressive 
 stress per square inch on the concave side of the column. 
 
 The factors for masonry under dead load as given by Rankine and by 
 Unwin, viz., 4 and 20, show a remarkable difference, which may possibly 
 be explained as follows: If the actual crushing strength of a pier of 
 masonry is known from direct experiment, then a factor of safety of 4 is 
 sufficient for a pier of the same size and quality under a steady load; 
 but if the crushing strength is merely assumed from figures given by the 
 authorities (such as the crushing strength of pressed brick, quoted above 
 from Howe's Retaining Walls, 40 to 300 tons per square foot, average 
 170 tons), then a factor of safety of 20 may be none too great. In this 
 case the factor of safety is really a "factor of ignorance." 
 
 The selection of the proper factor of safety or the proper maximum unit 
 stress for any given case is a matter to be largely determined by the 
 judgment of the engineer and by experience. No definite rules can be 
 given. The customary or advisable factors in many particular cases will 
 be found where these cases are considered throughout this book. In 
 general the following circumstances are to be taken into account m the 
 selection of a factor: 
 
 1. When the ultimate strength of the material is known within narrow 
 limits, as in the case of structural steel when tests of samples have been 
 made, when the load is entirely a steady one of a known amount, and 
 there is no reason to fear the deterioration of the metal by corrosion, the 
 lowest factor that should be adopted is 3. 
 
 2. When the circumstances of 1 are modified by a portion of the load 
 being variable, as in floors of warehouses, the factor should be not less 
 than 4. 
 
376 STRENGTH OF MATERIALS. 
 
 3. When the whole load, or nearly the whole, is apt to be alternately 
 put on and taken off, as in suspension rods of floors of bridges, the factor 
 should be 5 or 6. 
 
 4. When the stresses are reversed in direction from tension to com- 
 pression, as in some bridge diagonals and parts of machines, the factor 
 should be not less than 6. 
 
 5. When the piece is subjected to repeated shocks, the factor-should be 
 not less than 10. 
 
 6. When the piece is subject to deterioration from corrosion the section 
 should be sufficiently increased to allow for a definite amount of corrosion 
 before the piece be so far weakened by it as to require removal. 
 
 7. When the strength of the material, or the amount of the load, or 
 both are uncertain, the factor should be increased by an allowance suffi- 
 cient to cover the amount of the uncertainty. 
 
 8. When the strains are of a complex character and of uncertain 
 amount, such as those in the crank-shaft of a reversing engine, a very 
 high factor is necessary, possibly even as high as 40, the figure given by 
 Rankine for shafts in millwork. 
 
 Formulas for Factor of Safety. (F. E. Cardullo, Mach'y, Jan,. 
 1906.) The apparent factor of safety is the product of four factors, or, 
 F = aXbXcXd. 
 
 a is the ratio of the ultimate strength of the material to its elastic limit, 
 not the yield point, but the true elastic limit within which the material is, 
 in so far as we can discover, perfectly elastic, and takes no permanent set. 
 Two reasons for keeping the working stress within this limit are: (1) that 
 the material will rupture if strained repeatedly beyond this limit; and 
 (2) that the form and dimensions of the piece would be destroyed under 
 the same circumstances. 
 
 The second factor, 6, is one depending upon the character of the stress 
 produced within the material. The experiments of Wohler proved that 
 the repeated application of a stress less than the ultimate strength of a 
 material would rupture it. Prof. J. B. Johnson's formula for the relation 
 between the ultimate strength and the "carrying strength" under con- 
 ditions of variable loads is as follows: 
 
 / = U - (2 - Pl /p), 
 
 where / is the "carrying strength" when the load varies repeatedly 
 between a maximnm value, p, and a minimum value, pi, and U is the 
 ultimate strength of the material. The quantities p and p\ have plus 
 signs when they represent loads producing tension, and minus signs when 
 they represent loads producing compression. 
 
 If the load is variable the factor b must then have a value, 
 6 = U/f = 2 - p t /p. 
 
 Taking a load varying between zero and a maximum, 
 Pi/p = 0, and 6 = 2- pi/p = 2. 
 
 Taking a load that produces alternately a tension and a compression 
 equal in amount, 
 
 p' = - p and pi/p = - 1, and 6 = 2- pi/p = 2 - (- 1) = 3. 
 
 The third factor, c, depends upon the manner in which the load is applied 
 to the piece. When the load is suddenly applied c = 2. When not all 
 of the load is applied suddenly, the factor 2 is reduced accordingly. . 
 a certain fraction of the load, n/m, is suddenly applied, the factor is 
 1 + n/m. 
 
 The last factor, d, we may call the "factor of ignorance." All the 
 other factors have provided against known contingencies; this provides 
 against the unknown. It commonly varies in value between 1 1/2 and 3, 
 although occasionally it becomes as great as 10. It provides against 
 excessive or accidental overload, unexpectedly severe service, unreliable 
 or imperfect materials, and all unforeseen contingencies of manufacture 
 or operation. When we know that the load will not be likely to be 
 Increased, that the material is reliable, that failure will not result dis- 
 astrously or even that the piece for some reason must be small or light, 
 this factor will be reduced to its lowest limit, 1 1/2. When life or property 
 would be endangered by thefailureof the piece, this factor must be made 
 
THE MECHANICAL PROPERTIES OF CORK. 377 
 
 larger. Thus, while it is 1 1/2 to 2 in most ordinary steel constructions, 
 it is rarely less than 21/2 for steel in a boiler. 
 
 The reliability of the material in a great measure determines the value 
 of this factor. For instance, in all cases where it would be 1 1/2 for mild 
 steel, it is made 2 for cast iron. It will be larger for those materials 
 subject to internal strains, for instance for complicated castings, heavy 
 forgings, hardened steel, and the like, also lor materials subject to hidden 
 defects, such as internal flaws in lorgings, spongy places in castings, etc. 
 It will be smaller for ductile and larger lor brittle materials. It will be 
 smaller as we are sure that the piece has received uniform treatment, and 
 as the tests we have give more uniform results and more accurate indi- 
 cations of the real strength and quality of the piece itself. In fixing the 
 factor d, the designer must depend on his judgment, guided by the general 
 rules laid down. 
 
 Table of Factors of Safety. 
 
 The following table may assist in a proper choice of the factor of safety 
 It shows the value of the four factors for various materials and conditions 
 of service. 
 
 CLASS OF SERVICE OR MATERIALS. ' 
 
 Bpilers 
 
 Piston and connecting rods for double- 
 acting engines 1 1/2-2 
 
 Piston and connecting rod for single-acting 
 engines 1 1/2-2 
 
 Shaft carrying bandwheel, fly-wheel, or 
 armature I 1/2-2 
 
 Lathe spindles , 
 
 Mill shafting 
 
 Steel work in buildings , 
 
 Steel work in bridges 
 
 Steel work for small work 
 
 Cast iron wheel rims 
 
 Steel wheel" rims 
 
 MATERIALS. 
 
 Cast iron and other castings 
 
 Wrought iron or mild steel 
 
 Oil tempered or nickel steel 
 
 Hardened steel 
 
 Bronze and brass, rolled or forged . 
 
 i bed 
 
 P 
 
 2 1 1 21/4-3 
 
 41/2- 6 
 
 r2 3 2 11/2 
 
 131/2-18 
 
 r2 2 2 11/2 
 
 9 -12 
 
 -2 3 1 11/2 
 
 63/ 4 - 9 
 
 2 2 2 11/2 
 
 12 
 
 2322 
 
 24 
 
 2 
 
 
 2 
 
 4 
 
 2 
 
 
 21/2 
 
 5 
 
 2 
 
 ; 
 
 * H/2 
 
 6 
 
 2 
 
 
 10 
 
 20 
 
 2 
 
 
 4 
 
 8 
 
 M 
 
 nin 
 
 lum Values. 
 
 2 
 
 
 2 
 
 4 
 
 2 
 
 
 H/2 
 
 3 
 
 H/2 
 
 
 H/2 
 
 21/4 
 
 H/2 
 
 
 2 
 
 3 
 
 2 
 
 
 1V2 
 
 3 
 
 THE MECHANICAL PROPERTIES OF CORK. 
 
 Cork possesses qualities which distinguish it from all other solid or 
 liquid bodies, namely, its power of altering its volume in a very marked 
 degree in consequence of change of pressure. It consists, practically, 
 of an aggregation of minute air-vessels, having thin, water-tight, and 
 very strong walls, and hence, if compressed, the resistance to compression 
 rises in a manner more like the resistance of gases than the resistance of 
 an elastic solid such as a spring. In a spring the pressure increases in 
 proportion to the distance to which the spring is compressed, but with 
 gases the pressure increases in a much more rapid manner; that is, in- 
 versely as the volume which the gas is made to occupy. But from the 
 permeability of cork to air, it is evident that, if subjected to pressure in 
 one direction only, it will gradually part with its occluded air by effusion, 
 that is, by its passage through the porous walls of the cells in which it is 
 contained. The gaseous part of cork constitutes 53 %_ of its bulk. Its 
 elasticity has not only a very considerable range, but it is very persistent. 
 Thus in the better kind of corks used in bottling the corks expand the 
 instant they escape from the bottles. This expansion may amount to 
 an increase of volume of 75%, even after the corks have been kept in a 
 state of compression in the bottles for ten years. If the cork be steeped 
 in hot water, the volume continues to increase till it attains nearly three 
 times that which it occupied in the neck of the bottle. 
 
 When cork is subjected to pressure a certain amount of permanent 
 
378 STRENGTH OF MATERIALS. 
 
 deformation or "permanent set" takes place very quickly. This prop* 
 erty is common to all solid elastic substances when strained beyond theii 
 elastic limits, but with cork the limits are comparatively low. Besides 
 the permanent set, there is a certain amount of sluggish elasticity that 
 is, cork on being released from pressure springs back a certain amount 
 at once, but the complete recovery takes an appreciable time. 
 
 Cork which had been compressed and released in water many thousand 
 times had not changed its molecular structure in the least, and had con- 
 tinued perfectly serviceable. Cork which has been kept under a pressure 
 of three atmospheres for many weeks appears to have shrunk to from 
 80% to 85% of its original volume. Van Nostrand's Eng'g Mag., 1886. 
 xxxv. 307. 
 
 VULCANIZED INDIA-RUBBER. 
 
 The specific gravity of a rubber compound, or the number of cubic 
 inches to the pound, is generally taken oy buyers as a correct index of 
 the value, though in reality such is often very far from being the case. 
 In the rubber works the qualities of the rubber made vary from floating, 
 the best quality, to densities corresponding to 11 or 12 cu. in. to the 
 pound, the latter densities being in demand by consumers with whom 
 price appears to be the main consideration. Such densities as these can 
 only be obtained by utilizing to the utmost the quality that rubber 
 exhibits of taking up a large bulk of added matters. Eng'g, 1897. 
 
 Lieutenant X? Vladomiroff, a Russian naval officer, has recently carried 
 out a series of tests at the St. Petersburg Technical Institute with view 
 to establishing rules for estimating the quality of vulcanized india- 
 rubber. The followng, in brief, are the conclusions arrived at, recourse 
 being had to physical properties, since chemical analysis did not give 
 any reliable result: 1. India-rubber should not give the least sign of 
 superficial cracking when bent to an angle of 180 degrees after five hours 
 of exposure in a closed air-bath to a temperature of 125 C. The 
 test-pieces should be 2.4 inches thick. 2. Rubber that does not contain 
 more than half its weight of metallic oxides should stretch to five times 
 its length without breaking. 3. Rubber free from all foreign matter, 
 except the sulphur used in vulcanizing it, should stretch to at least seven 
 times its length without rupture. 4. The extension measured immedi- 
 ately after rupture should not exceed 12% of the original length, with 
 given dimensions. 5. Suppleness may be determined by measuring the 
 percentage of ash formed in incineration. This may form the basis for 
 deciding between different grades of rubber for certain purposes. 6. Vul- 
 canized rubber should not harden under cold. These rules have been 
 adopted for the Russian navy. Iron Age, June 15, 1893. 
 
 Singular Action of India Rubber under Tension. R. H. Thurston, 
 Am. Mack., Mar. 17, 1898, gives a diagram showing the stretch at dif- 
 ferent loads of a piece of partially vulcanized rubber. The results trans- 
 lated into figures are: 
 
 Load, Ibs 30 50 80 1 20 150 200 320 430 
 
 Stretch per in. of 
 
 lengthen 0.5 1. 2.2 4 56 7 7.5 
 
 Stretch per 10 Ibs. in- 
 crease of load 0.17 0.25 0.4 0.45 0.33 0.20 0.08 0.04 
 
 Up to about 30% of the breaking load the rubber behaves like a soft 
 metal in showing an increasing rate of stretch with increase of load, 
 then the rate of stretch becomes constant for a while and later decreases 
 steadily until before rupture it is less than one-tenth of the maximum. 
 Even when stretched almost to rupture it restores itself very nearly to 
 its original dimensions on removing the load, and gradually recovers a 
 part of the loss of form at that instant observable. So far as known, 
 no other substance shows this curious relation of stretch to load. 
 
 Rubber Goods Analysis. Randolph Boiling. (Iron Age, Jan. 28, 1909.) 
 
 The loading of rubber goods used in manufacturing establishments 
 with zinc oxide, lead sulphate, calcium sulphate, etc., and the employ- 
 ment of the so-called " rubber substitutes " mixed with good rubber call for 
 close inspection of the works chemist in order to determine the value of 
 the samples and materials received. The following method of analysis is 
 recommended: 
 
 Thin strips of the rubber must be cut into small bits about the size of 
 
PROPERTIES OF NICKEL. 379 
 
 No. 7 shot.^ A half gram is heated in a 200 c.c. flask with red fuming 
 nitric acid on the hot plate until all organic matter has been decomposed, 
 and the total sulphur is determined by precipitation as barium sulphate. 
 The difference between the total and combined sulphur gives the per 
 cent that has been used for vulcanization. Free sulphur indicates either 
 that improper methods were used in vulcanizing or that an excessive 
 per cent of substitutes was employed. Following is a scheme for the 
 analysis of india-rubber articles: 
 
 1. Extraction with acetone: A. Solution: Resinous constituents of 
 india-rubber, fatty oils, mineral oils, resin oils, solid hydrocarbons, 
 resins, free sulphur. B. Residue. 
 
 2. Extraction with pyridine: C. Extract: Tar, pitch, bituminous 
 bodies, sulphur in above. D. Residue. 
 
 3. Extraction with alcoholic potash: E. Extract: Chlorosulphide 
 substitutes, sulphide substitutes, oxidized (blown) oils, sulphur in 
 substitutes, chlorine in substitutes. F. Residue. 
 
 4. Extraction with nitre-naphthalene: G. Extract: India-rubber, sul- 
 phur in india-rubber, chlorine in india-rubber, the total of the above 
 three estimated by loss. H. Residue. 
 
 5. Extraction with boiling water: I. Extract: Starch (farina), 
 dextrine. K. Residue: Mineral matter, free carbon, fibrous materials, 
 sulphur in inorganic compounds. 
 
 6. Separate estimations: Total sulphur, chlorine in rubber. 
 
 SPECIFICATIONS FOR AIR HOSE. 
 
 The Bureau of Construction and Repair of the U. S. Navy, in 1910, 
 adopted the following specifications for air hose: 
 
 1. The hose to be made up of an inner rubber tube, three or more 
 canvas or braided layers, and an outer rubber cover; to be of the in- 
 ternal diameter required. 2. The tube and cover shall be free from 
 pitting or other irregularities; the tube shall not be less than I/IQ in., 
 and the cover not less than 1/32 in. in thickness. The hose to be of 
 the best quality rubber, duck and friction, and to be capable of stand- 
 ing a hydrostatic pressure of 600 Ib. 3. Samples will be submitted to 
 the mechanical kinking test. The samples should stand the test for 
 the following length of time without leakage at 90 Ib. air pressure 
 3/g in 45 hours. 
 
 7/i6 in 40 hours. 
 
 5/8 in 30 hours. 
 
 3/4 in 25 hours. 
 
 1 1/4 in 3 hours. 
 
 The kinking test is conducted as follows: The test piece, 20 in. in 
 length, is fastened to couplings made up on 45 elbows, the stationary 
 end turned up and the moving end turned down. The ends of the 
 couplings when level are 7 in. apart. The moving end travels vertically 
 through a distance of 14 in., and the speed is such that the hose is 
 kinked about 80 times a minute, the kinking occurring in two places 
 about 4 in. from each end. During this test an air pressure of about 
 90 Ib. per sq. in. is maintained in the hose. The kinking is done on a 
 special machine designed to kink the hose at the speed specified. 
 
 NICKEL. 
 
 Properties of Nickel. (F. L. Sperry, Tran. A.I.M.E., 1895). Nickel 
 has similar physical properties to those of iron and copper. It is less 
 malleable and ductile than iron, and less malleable and more ductile 
 than copper. It alloys with these metals in all proportions. It has 
 nearly the same specific gravity as copper, and is slightly heavier than 
 iron. It melts at a temperature of about 2900 to 3200 F. A small 
 percentage of carbon in metallic nickel lowers its melting-point per- 
 ceptibly. Nickel is harder than either iron or copper; is magnetic, but 
 will not take a temper. It has a grayish-white color, takes a fine polish, 
 and may be rolled easily into thin plates or drawn into wire. It is 
 unappreciably affected by atmospheric action, or by salt water. Com- 
 mercial nickel is from 98 to 99 per cent pure. The impurities are iron, 
 copper, silicon, sulphur, arsenic, carbon, and (in some nickel) a kernel 
 of unreduced oxide. It is not difficult to cast, and acts like some irons 
 
380 
 
 STRENGTH OF MATERIALS. 
 
 in being cold-short. Cast bars are likely to be porous or spongy, 
 but, after hammering or rolling, are compact and tough. 
 
 The average results of several tests are as follows: Castings, tensile 
 strength, 85,000 Ibs. per sq. in., elongation, 12% ; wrought nickel, T. S., 
 96,000, EL, 14%; wrought nickel, annealed, T. S., 95,000, EL, 23%; 
 hard rolled, T. S., 78,000, EL, 10%. (Bee also page 473.) 
 
 Nickel readily takes up carbon, and the porous nature of the metaJ 
 is undoubtedly due to occluded gases. According to Dr. Wedding, 
 nickel may take up as much as 9 % of carbon, which may exist either 
 as amorphous or as graphitic carbon. 
 
 Dr. Fleitmann, of Germany, discovered that a small quantity of pure 
 magnesium would free nickel from occluded gases and give a metal 
 capable of being drawn or rolled perfectly free from blow-holes, to such 
 an extent that the metal may be rolled into thin sheets 3 feet in width. 
 Aluminum or manganese may be used equally as well as a purifying 
 agent; but either, if used in excess, serves to make the nickel very 
 much harder. Nickel will alloy with most of the useful metals, and 
 generally adds the qualities of hardness, toughness, and ductility. 
 
 ALUMINUM ITS PROPERTIES AND USES. 
 
 (Compiled from notes by Alfred E. Hunt, and from publications 
 of the Aluminum Co. of America, 1914.) 
 
 The specific gravity of aluminum varies according to its treatment, 
 as follows: Pure cast, 2.56; sheets, wire, etc., rolled and unannealed, 
 2.68; ditto, annealed, 2.66. The casting alloys range in specific 
 gravity from 2.82 to 2.91. Based on these values, an ingot of cast 
 aluminum 12 in. square, 1 in. thick, weighs 13.3024 Ib. ; a rolled sheet 
 12 in. square, 1 in. thick, weighs 13.9259 Ib.; a 1-in. cast round bar, 
 12 in. long, weighs 0.8706 Ib.; a 1-in. rolled bar, 12 in. long, weighs 
 0.9114 Ib.; a cubic foot of cast aluminum, 159.6288 Ib.; and a cubic 
 foot of rolled aluminum, 167.1114 Ib. Taking the weight of rolled 
 aluminum as 1, the weight of rolled wrought iron is 2.8742; of rolled 
 steel, 2.9322; of rolled copper, 3.3321; of rolled brass, 3.19. Wood 
 for structures can be taken as about one-third the weight of aluminum. 
 
 Chemically, aluminum is readily soluble in hydrochloric acid, and 
 in strong solutions of caustic alkalies. Hot dilute sulphuric acid 
 stowly dissolves it, but concentrated sulphuric acid acts very slowly. 
 Nitric acid, cold, either dilute or concentrated, has but little effect; 
 hot, it acts very slowly. Sulphur has no action at less than a red 
 heat. Chlorine, fluorine, bromine, iodine, and fluohydric acid rapidly 
 corrode it. Salt water has little effect on it, and it resists sea water 
 better than does iron, steel, or copper. Aluminum strips on the sides 
 of a wooden vessel in sea water corroded less than 0.005 inch in six 
 months, about half the corrosion of copper strips. Ammonium solu- 
 tions gradually attack the surface of aluminum, forming a coating 
 ' which is more resistant than the metal, and which while rapidly attacked 
 by concentrated acid or alkali solutions, resists dilute mineral and 
 organic acids, and dry or moist air. It is not attacked by CO2, CO, or 
 HaS, but will absorb these gases when heated. 
 
 The presence of a considerable quantity of aluminum decreases its 
 resistance to corrosion. Commercial aluminum, such as is used for 
 rolling or casting alloys, contains, however, only a negligible quantity 
 of impurities. Occluded gases in molten aluminum cause blow-holes 
 in the ingots, which form laminated plates when the metal is rolled 
 or hammered, which are more liable to corrode than sound metal. 
 Silicon and iron are the impurities usually found, the former ranging 
 in commercial aluminum from 0.30 to 2.0 per cent, and the latter 
 from 0.15 to 2.0 per cent. Other metals are frequently alloyed with 
 aluminum to increase the hardness, rigidity, and strength. See 
 Alloys of Aluminum, page 396. 
 
 Aluminum is electro positive as regards the common metals, and forms 
 a galvanic couple when in contact with them. In service it should be 
 insulated from them by rubber gaskets, or washers, or by a liberal coat 
 of heavy paint. 
 
 In malleability pure aluminum is exceeded only by gold and silver. 
 It is exceeded in ductility only by gold, silver, platinum, iron, and 
 
ALUMINUM ITS PROPERTIES AND USES. 381 
 
 copper. Sheets of aluminum have been rolled down to 0.0005 in. 
 thick and beaten into leaf nearly as thin as gold leaf. The metal is 
 most malleable at a temperature of between 400 and 600 F., and at 
 this temperature it can be drawn down between rolls with nearly as 
 much draught upon it as with heated steel. It has also been drawn 
 into the finest wire. By the Mannesmann process aluminum tubes 
 have been made in Germany. 
 
 The electrical conductivity of aluminum is 61.67, silver being taken 
 as 100. On the same scale, the conductivity of copper is 97.62; of 
 gold, 76.61; of zinc, 29.57; of iron, 14.57; of platinum, 14.42. Alumi- 
 num wire, weight for weight, has a conductivity of 206, taking copper 
 as 100 and aluminum as 62, the aluminum wire having an area 3.33 
 that of the copper wire. Pure aluminum is practically non-magnetic. 
 
 Aluminum melts at 1215 F. It does not volatilize at any tem- 
 perature produced by the combustion of carbon, but it is inadvisable 
 to heat it much beyond th3 melting point or to allow it to remain 
 molten for a great length of time, on account of its capacity to absorb 
 gases. It may be cast in dry or green sand molds or in metal chills, 
 and should be melted in plumbago crucible. Cores should be as soft 
 as will permit safe manipulation. A good core mixture is 15 parts 
 core sand, 1 part rosin. The core should be sprayed with molasses 
 water, baked and washed in plumbago water. 
 
 The mean specific heat of aluminum is 0.2185 (water = 1), being 
 higher than any other metal except magnesium and the alkali metals. 
 Its latent heat of fusion is 51.4 B.T.U. per Ib. The coefficient of 
 linear expansion of aluminum is 0.0000130 per degree F. The thermal 
 conductivity, according to Roberts- Austen, is 31.33 (silver = 100) , 
 copper being the only baser metal which exceeds it. Wiederman 
 and Franz give the thermal conductivity for the metal unannealed as 
 38.87, and annealed as 37.96. Its shrinkage in cooling is 0.2031 in. 
 per foot, slightly more than ordinary brass. The shrinkage varies 
 somewhat with the thickness thicker castings shrinking more than 
 thinner ones. The hardness of aluminum varies with the purity, the 
 purest metal being the softest. In the Bottone scale the hardness of 
 the diamond is 3010, while that of aluminum is 821. 
 
 Aluminum under tension, and section for section, is about as strong 
 as cast iron. Its tensile strength is increased by cold rolling or cold 
 forging, and there are alloys which add considerably to the tensile 
 strength without increasing the specific gravity to over 3 or 3.25. 
 
 The strength of commercial aluminum is given in the following 
 table as the result of many tests : 
 
 Elastic Limit Ultimate Strength Percentage 
 
 per sq. in. in per sq. in. in of Reduction 
 
 Form. Tension, Tension, of Area in 
 
 Ibs. Ibs. Tension. 
 
 Castings 8^500 12,000-14,000 15 
 
 Sheet 12,500-25,000 24,000-40,000 20-30 
 
 Wire 16,000-33,000 25,000-65,000 40^-60 
 
 Bars 14,000-33,000 28,000-40,000 30-40 
 
 The elastic limit per square inch under compression in cast cylin- 
 dric columns of length twice the diameter is 3500 Ib. The ultimate 
 strength per square inch imder compression in cylinders of the same 
 form is 12,000. The modulus of elasticity of cast aluminum is about 
 9,000,000. It is rather an open metal in its texture, and for cylinders 
 to stand pressure an increase in thickness must be given to allow for 
 tMs porosity. Its maximum shearing stress in castings is about 
 12,000, and in forgings about 16,000, or about that of pure copper. 
 Its texture and strength are improved by forging or pressing at a 
 temperature of about 600 F. 
 
 Pure aluminum is too soft and lacking in tensile strength and rigidity 
 for many purposes. Valuable alloys are now being made which seem 
 to give great promise for the future. They are alloys containing from 
 2 % to 7 % or 8 % of copper, manganese, iron, and nickel. See alloys 
 of aluminum, page 396. 
 
 Aluminum can be worked by any of the common mechanical proc- 
 esses, as rolling, stamping, drawing, tapping, spinning, forging, ex- 
 
382 STRENGTH OF MATERIALS. 
 
 truding or machining. Owing to the ductility of the metal, sheet 
 aluminum can be given a deeper stamp or heavier draw than most 
 metals. A draw of over one-quarter to one-third more in depth than 
 can be taken with copper, brass or steel can be made on aluminum 
 sheet of 20 B. & S. gauge or heavier. The same sort of tools and proc- 
 esses are used for stamping as are used for other metal. The tools 
 should be lubricated with vaseline or any greasy oil which is free from 
 grit. It is practically unnecessary to anneal the work between re- 
 draws. 
 
 In spinning it is also unnecessary to anneal the shells after they come 
 from the press, when the first operation is done in the drawing press. 
 The speed of the lathe should range from 2,000 to 3,000 r. p. m., and the 
 best results in spinning will be obtained by the use of hard wood 
 spinning stocks and metal chucks. For finishing and burnishing, steel 
 tools should be used. The best lubricant is soap, tallow, or paraffin 
 candles. In drop forging aluminum, the castings to be forged should 
 be made a little smaller in their horizontal diameter and a little greater 
 in the vertical diameter than is desired for the finished forging. They 
 slKRild be heated to the annealing temperature, about 700 P., before 
 being placed in the die. 
 
 Aluminum can be extruded into shapes which can be obtained in no 
 other way. In these shapes, the metal has a continuity of structure 
 which renders it easier in machining than fabricated shapes made by 
 other methods. It is difficult at the present time (1914), to extrude a 
 shape of greater diameter than 6 inches or one having a thickness of 
 wall of less than 1/g inch. 
 
 In machining, the tools should have a highly whetted edge, such as 
 would be used in wood working, and they should also have a large 
 clearance. That is, the thickness of the blades should increase very 
 slowly from its edge. The tools should operate somewhat faster than 
 for brass, and the feed should be slightly slower in proportion. A good 
 lubricant should be freely used: No. 1 grade lard oil, or lard oil or 
 carbon oil mixed with 25 per cent of some animal oil, give satisfactory 
 results. Another satisfactory lubricant is a mixture of lard oil 25 per 
 cent by volume with benzine 75 per cent. 
 
 In sawing, an ordinary circular saw on a table may be used. The 
 teeth should have no " set," the saw should be thinner at the center than 
 at the periphery, and should run at a peripheral speed of 3,500 to 4,000 
 feet per minute. 
 
 For drilling, an ordinary twist drill may be used, but it should be 
 exceedingly sharp. The drill should rotate about 50 per cent faster, 
 with a feed about 25 per cent slower, than would be used for brass. In 
 tapping, a sharp tap only should be used and a hole drilled with a drill 
 from one to three sizes larger than for brass. The best tap is one having 
 a single spiral flute with a lead of about one turn in every three inches. 
 The best tapping lubricant is the lard oil benzine mixture noted 
 above. 
 
 Aluminum may be finished by caustic dipping and scratch brushing. 
 In caustic dipping, the article is first dipped into the benzine and then 
 into a strong solution of caustic alkali, which is kept at the boiling 
 point, after which it should be placed in a strong hot solution of nitric 
 acid. After draining the acid, the aluminum should be dipped in 
 boiling hot water, which should be constantly drained off and renewed 
 by an addition of fresh water. On removal from the water, it should 
 be rapidly dried over a steam coil. In scratch brushing, the metal is 
 carefully cleaned and then applied to the scratch brush wheel, which 
 rotates at from 1500 to 2000 r. p. m. 
 
 Soldering and Welding Aluminum. Aluminum can be readily 
 electrically welded, but soldering is not altogether satisfactory. The 
 high heat conductivity of the aluminum withdraws the heat of the 
 molten solder so rapidly that it "freezes" before it can flow sufficiently. 
 A German solder said to give good results is made of 80% tin to 20% 
 zinc, using a flux composed of 80 parts stearic acid, 10 parts chloride of 
 zinc, and 10 parts of chloride of tin. Pure tin, fusing at 250 C., 
 has also been used as a solder. The use of chloride of silver as a flux has 
 been patented, and used with ordinary soft solder has given some suc- 
 cess. A pure nickel soldering-bit should be used, as it does not dis- 
 color aluminum as copper bits do. 
 
ALUMINUM ITS PROPERTIES AND USES. 
 
 383 
 
 The following table of aluminum solders which have been successfully 
 used appeared in Machinery, Dec., 1914. See also page 410. 
 
 Tin. 
 
 Alum- 
 inum. 
 
 Zinc. 
 
 Cop- 
 per. 
 
 Bis- 
 muth. 
 
 Lead. 
 
 Phos- 
 phor- 
 Tin*. 
 
 Silver 
 
 Anti- 
 mony 
 
 Cad- 
 mium. 
 
 Mag- 
 nes- 
 ium. 
 
 95.00 
 
 
 
 
 5.00 
 
 
 
 
 
 
 
 78 50 
 
 2 00 
 
 19.00 
 
 
 
 
 0.50 
 
 
 
 
 
 
 66.70 
 
 
 
 
 
 
 33.30 
 
 
 
 
 20 00 
 
 70 00 
 
 
 
 
 
 
 10 00 
 
 
 
 
 97.00 
 
 
 
 
 3.00 
 
 
 
 
 
 
 
 
 6.00 
 
 89.50 
 
 4.50 
 
 
 
 
 
 
 
 
 71 .25 
 
 2 25 
 
 26.00 
 
 
 
 
 0.50 
 
 
 
 
 
 60.00 
 37.50 
 
 4.00 
 
 8.00 
 25 00 
 
 4.00 
 37 50 
 
 
 12.00 
 
 
 12.00 
 
 
 
 
 
 
 8.00 
 
 92.00 
 
 
 
 
 
 
 
 
 
 30 00 
 
 
 20 00 
 
 
 
 
 
 
 
 50 00 
 
 
 80.00 
 
 2.25 
 
 17.00 
 
 
 
 
 0.75 
 
 
 
 
 
 66 00 
 
 15 50 
 
 
 
 9 00 
 
 
 
 
 7 00 
 
 -j- 
 
 2 25 
 
 15.50 
 
 2.50 
 
 78.25 
 
 
 
 2.50 
 
 1 .25 
 
 
 
 
 
 49.05 
 
 20.00 
 
 65.00 
 20 '31 
 
 15.00 
 1 15 
 
 
 26.06 
 
 
 
 3 43 
 
 
 
 30.00 
 
 70.00 
 
 
 
 
 
 
 
 
 
 
 
 4 00 
 
 94 00 
 
 2 00 
 
 
 
 
 
 
 
 
 85.10 
 
 10.80 
 
 
 
 
 
 
 
 
 1.35 
 
 2.75 
 
 60.00 
 86.00 
 
 
 15.00 
 
 
 5.00 
 14 00 
 
 10.00 
 
 
 
 5.00 
 
 
 .4.. 
 
 98 00 
 
 1 00 
 
 
 
 1 00 
 
 
 
 
 
 
 
 20.00 
 
 70.00 
 
 
 10 00 
 
 
 
 
 
 
 
 
 48.00 
 
 2.00 
 
 27.00 
 
 
 
 23.00 
 
 
 
 
 
 
 90.00 
 
 5.00 
 
 
 
 5.00 
 
 
 
 
 
 
 
 84.95 
 
 
 
 .... 
 
 15.05 
 
 
 
 
 
 
 
 ' 10% phosphorus. t This solder also contains 0.25% vanadium. 
 
 $ This solder also contains 5 % chromium. 
 
 Aluminum Wire. Tension tests. Diam. 0.128 in. 14 tests. E.L. 
 12,500 to 19,100; T. S. 25,800 to 26,900 Ibs. per sq. in.; el. 0.30 to 1.02% 
 in 48 ins.; Red. of area, 75.0 to 83.4%. Mod. of el. 8,800,000 to 
 10,700,000. Tech. Quar., xii, 1899. 
 
 Aluminum Rod. Torsion tests. 10 samples, 0.257 in. diam. Appar- 
 ent outside fiber stress, Ibs. per sq. in. 15,900 to 18,300 Ibs. per sq. in. 
 11 samples, 0.367 in. diam. Apparent outside fiber stress, 18,400 to 
 19,200. 10 samples, 0.459 in. diam. Apparent outside ftber stress, 
 20,700 to 21,500 Ibs. per sq. in. The average number of turns per inch 
 for the three series were respectively, 1.58 to 3.65; 1.20 to 2.64; 0.87 to 
 1.06. Ibid. 
 
384 
 
 ALLOYS. 
 
 ALLOYS. 
 
 ALLOYS OF COPPER AND TIN. 
 
 (Extract from Report of U. S. Test Board.*) 
 
 
 Mean Com- 
 
 - 
 
 . 
 
 
 - 
 
 ? 
 
 .S 
 
 Torsion 
 
 . 
 
 position by 
 
 M.S 
 
 .'"! 
 
 n 
 
 H< 
 
 V JO 
 
 
 Tests. 
 
 1 
 
 Analysis. 
 
 Is 1 
 
 . 
 
 O "g 
 
 pi' 
 
 %s 
 
 5? 
 
 gil 
 
 - . 
 
 1 
 
 
 
 * . 
 
 ft 
 
 ' g J 
 
 
 '^sj 
 
 .5 S^ 
 
 ^d 
 
 "c-i 1 
 
 fc 
 
 Cop- 
 
 Tin. 
 
 lfj 
 
 11 
 
 cfjf| 
 
 fl O 3 
 
 03 O 
 
 "1$^ 
 
 'fl**^ 
 
 OJ ** WI 
 
 
 per. 
 
 
 EH~ 
 
 5 
 
 S 
 
 1 
 
 |.! 
 
 5 
 
 1^1 
 
 |HT! 
 
 ' \ 
 
 100. 
 
 
 27,800 
 
 14,000 
 
 6.47 
 
 29,848 
 
 bent. 
 
 42,000 
 
 143 
 
 153 
 
 la 
 
 100. 
 
 
 12,760 
 
 11,000 
 
 0.47 
 
 21,251 
 
 2.31 
 
 39,000 
 
 65 
 
 40 
 
 2 
 
 97.89 
 
 1 .90 
 
 24,580 
 
 10,000 
 
 13.33 
 
 
 
 34,000 
 
 150 
 
 317 
 
 3 
 
 96.06 
 
 3.76 
 
 32,000 
 
 16,000 
 
 14.29 
 
 33',232 
 
 bent. 
 
 42,048 
 
 157 
 
 247 
 
 4 
 
 94.11 
 
 5.43 
 
 
 
 
 38,659 
 
 " 
 
 
 
 
 5 
 
 92.11 
 
 7.80 
 
 28,540 
 
 19,000 
 
 '5*53 
 
 43,731 
 
 " 
 
 42,000 
 
 J60 
 
 126* 
 
 6 
 
 90.27 
 
 9.58 
 
 26,860 
 
 15,750 
 
 3.66 
 
 49,400 
 
 " 
 
 38,000 
 
 175 
 
 114 
 
 7 
 
 88.41 
 
 11.59 
 
 
 
 
 60,403 
 
 " 
 
 
 
 
 8 
 
 87.15 
 
 12.73 
 
 29,430 
 
 20,000 
 
 3'.33 
 
 34,531 
 
 4.00 
 
 53,000 
 
 182 
 
 100* 
 
 9 
 
 82.70 
 
 17.34 
 
 
 
 
 67,930 
 
 0.63 
 
 
 
 
 10 
 
 80.95 
 
 18.84 
 
 32,980 
 
 
 * b'.04 
 
 56,715 
 
 0.49 
 
 78,000 
 
 1'90 
 
 16 " 
 
 11 
 
 77.56 
 
 22.25 
 
 
 
 0. 
 
 29,926 
 
 0.16 
 
 
 
 
 12 
 
 76.63 
 
 23.24 
 
 22',6io 
 
 22,6 JO 
 
 0. 
 
 32,210 
 
 0.19 
 
 114,000 
 
 \22 
 
 '3'.4 
 
 13 
 
 72.89 
 
 26.85 
 
 
 
 0. 
 
 9,512 
 
 0.05 
 
 
 
 
 14 
 
 69.84 
 
 29.88 
 
 5,585 
 
 5,585 
 
 0. 
 
 12,076 
 
 0.06 
 
 147,000 
 
 18 
 
 1.5 
 
 15 
 
 68.58 
 
 31.26 
 
 
 
 0. 
 
 9,152 
 
 0.04 
 
 
 
 
 16 
 
 67.87 
 
 32.10 
 
 
 
 0. 
 
 9,477 
 
 0.05 
 
 
 
 
 17 
 
 65.34 
 
 34.47 
 
 2,201 
 
 2,201 
 
 0. 
 
 4,776 
 
 0.02 
 
 84,700 
 
 16 
 
 | 
 
 18 
 
 56.70 
 
 43.17 
 
 1,455 
 
 1,455 
 
 0. 
 
 2,126 
 
 0.02 
 
 
 
 
 19 
 
 44.52 
 
 55.28 
 
 3,010 
 
 3,010 
 
 0. 
 
 4,776 
 
 0.03 
 
 35,800 
 
 *23 
 
 1 
 
 20 
 
 34.22 
 
 65.80 
 
 3,371 
 
 3,371 
 
 0. 
 
 5,384 
 
 0.04 
 
 19,600 
 
 17 
 
 2 
 
 21 
 
 23.35 
 
 76.29 
 
 6,775 
 
 6,775 
 
 0. 
 
 12,408 
 
 0.27 
 
 
 
 
 22 
 
 15.08 
 
 84.62 
 
 
 
 
 9,063 
 
 0.86 
 
 6,'500 
 
 *23 
 
 25" 
 
 23 
 
 11.49 
 
 88.47 
 
 6,380 
 
 3, 500 
 
 4.io 
 
 10,706 
 
 5.85 
 
 10,100 
 
 23 
 
 62 
 
 24 
 
 8.57 
 
 91.39 
 
 6,450 
 
 3,500 
 
 6.87 
 
 5,305 
 
 bent. 
 
 9,800 
 
 23 
 
 132 
 
 25 
 
 3.72 
 
 96.31 
 
 4,780 
 
 2,750 
 
 12.32 
 
 6,925 
 
 " 
 
 9,800 
 
 23 
 
 220 
 
 26 
 
 0. 
 
 100. 
 
 3,505 
 
 
 35.51 
 
 3,740 
 
 " 
 
 6400 
 
 12 
 
 557 
 
 * The tests of the alloys of copper and tin and of copper and zinc, the 
 results of which are published in the Report of the U. S. Board appointed 
 to test Iron, Steel, and other Metals, Vols. I and II, 1879 and 1881, were 
 made by the author under direction of Prof. R. H. Thurston, chairman of 
 the Committee on Alloys. See preface to the report of the Committee, 
 in Vol. I. 
 
 Nos. la and 2 were full of blow-holes. 
 
 Tests Nos. 1 and la show the variation in cast copper due to varying 
 conditions of casting. In the crushing tests Nos. 12 to 20, inclusive, 
 crushed and broke under the strain, but all the others bulged and flattened 
 out. In these cases the crushing strength is taken to be that which 
 caused a decrease of 10% in the length. The test-pieces were 2 in. long 
 and 5'g in. diameter. The torsional tests were made in Thurston's torsion- 
 machine, on pieces 5/8 in. diameter and 1 in. long between heads. 
 
 Specific Gravity of the Copper-tin Alloys. The specific gravity 
 of copper, as found in these tests, is 8.874 (tested in turnings from the 
 Ingot, and reduced to 39.1 F.). The alloy of maximum sp. gr. 8.956 
 contained 62.42 copper. 37,48 tin, md all tUe alloys containing less taa.a 
 
ALLOYS OF COPPER AND TIN. 385 
 
 37% tin varied irregularly in sp. gr. between 8.65 and 8.93, the density 
 depending not on the composition, but on the porosity of the casting. It 
 is probable that the actual sp. gr. of all these alloys containing less than 
 37% tin is about 8.95, and any smaller figure indicates porosity in the 
 specimen. 
 
 From 37% to 100% tin, the sp. gr. decreases regularly from the maxi- 
 mum of 8.956 to that of pure tin, 7.293. 
 
 Note on the Strength of the Copper-tin Alloys. 
 
 The bars containing from 2% to 24% tin, inclusive, have considerable 
 strength, and all the rest are practically worthless for purposes in which 
 strength is required. The dividing line between the strong and brittle 
 alloys is precisely that at which the color changes from golden yellow to 
 silver-white, viz., at a composition containing between 24% and 30% of 
 tin. 
 
 It appears that the tensile and compressive strengths of these alloys are 
 in no way related to each other, that the torsional strength is closely pro- 
 portional to the tensile strength, and that the transverse strength may de- 
 pend in some degree upon the compressive strength, but it is much more 
 nearly related to the tensile strength. The modulus of rupture, as ob- 
 tained by the transverse tests, is, in general, a figure between those of 
 tensile and compressive strengths per square inch, but there are a few 
 exceptions in which it is larger than either. 
 
 The strengths of the alloys at the copper end of the series increase 
 rapidly with the addition of tin till about 4%, of tin is reached. The 
 transverse strength continues regularly to increase to the maximum, till 
 the alloy containing about 17|% of tin is reached, while the tensile and 
 torsional strengths also increase, but irregularly, to the same point. This 
 irregularity is probably due to porosity of the metal, and might possiWv 
 be removed by any means which would make the castings more compact. 
 The maximum is reached at the alloy containing 82.70 copper, 17.34 tin, 
 the transverse strength, however, being very much greater at this point 
 than the tensile or torsional strength. From the point of maximum 
 strength the figures drop rapidly to the alloys containing about 27.5% of 
 tin, and then more slowly to 37.5%, at which point the minimum (or 
 nearly the minimum) strength, by all three methods of test, is reached. 
 The alloys of minimum strength are found from 37.5% tin to 52.5% tin. 
 The absolute minimum is probably about 45% of tin. 
 
 From 52.5% of tin to about 77.5% tin there is a rather slow and irregu- 
 lar increase in strength. From 77.5% tin to the end of the series, or all 
 tin, the strengths slowly and somewhat irregularly decrease. 
 
 The results of these tests do not seem to corroborate the theory given 
 by some writers, that peculiar properties are possessed by the alloys 
 which are compounded of simple multiples of their atomic weights or 
 chemical equivalents, and that these properties are lost as the com- 
 positions 'vary more or less from this definite constitution. It does 
 appear that a certain percentage composition gives a maximum strength 
 and another certain percentage a minimum, but neither of these com- 
 positions is represented by simple multiples of the atomic weights. 
 
 There appears to be a regular law of decrease from the maximum to 
 the minimum strength which does not seem to have any relation to the 
 atomic proportions, but only to the percentage compositions. 
 
 Hardness. The pieces containing less than 24 % of tin were turned in 
 the lathe without difficulty, a gradually increasing hardness being noticed, 
 the last named giving a very short chip, and requiring frequent sharpening 
 of the tool. 
 
 With the most brittle alloys it was found impossible to turn the test- 
 pieces in the lathe to a smooth surface. No. 13 to No. 17 (26.85 to 34.47 
 tin) could not be cut with a tool at all. Chips would fly off in advance 
 of the tool and beneath it, leaving a rough surface; or the tool would 
 sometimes, apparently, crush off portions of the metal, grinding it to 
 powder. Beyond 40% tin the hardness decreased so that the bars could 
 be easily turned. 
 
386 
 
 ALLOYS. 
 
 ALLOTS OF COPPER AND ZINC. (U. S. Test Board.) 
 
 
 Mean Com- 
 
 
 Elastic 
 Limit 
 
 * : i ; 
 
 Trans- 
 verse 
 
 "~r^ 
 
 Crush- 
 
 Torsional 
 Tests. 
 
 No. 
 
 position by 
 Analysis. 
 
 Tensile 
 Str'gth, 
 Ibs. per 
 sq. in. 
 
 % of 
 Break- 
 
 T ing , 
 Load, 
 
 Ibs. per 
 sq. in. 
 
 Elongation 
 in 5 inch< 
 
 Test 
 Modu- 
 lus of 
 Rup- 
 ture. 
 
 I7- S . 
 
 1^l c 
 
 <Sd-2 
 
 Q w 
 
 ing 
 Str'gth 
 per sq. 
 in., Ibs. 
 
 E-a 
 
 g_g 
 
 H Sr 
 
 ^ 
 
 Angle of 1 
 Tors. deg. | 
 
 Cop- 
 per. 
 
 Zinc. 
 
 j 
 
 97.83 
 
 1.88 
 
 27,240 
 
 
 
 
 
 
 130 
 
 357 
 
 2 
 
 82.93 
 
 16.98 
 
 32,600 
 
 26.1 
 
 26.7 
 
 23,197 
 
 Bent 
 
 
 155 
 
 329 
 
 3 
 
 81.91 
 
 17.99 
 
 32,670 
 
 30.6 
 
 31.4 
 
 21,193 
 
 
 
 166 
 
 345 
 
 4 
 
 77.39 
 
 22.45 
 
 35,630 
 
 20.0 
 
 35.5 
 
 25,374 
 
 
 
 
 169 
 
 311 
 
 5 
 
 76.65 
 
 23.08 
 
 30,520 
 
 24.6 
 
 35.8 
 
 22,325 
 
 
 
 42,000 
 
 165 
 
 267 
 
 6 
 
 73.20 
 
 26.47 
 
 31,580 
 
 23.7 
 
 38.5 
 
 25,894 
 
 " 
 
 
 168 
 
 293 
 
 7 
 
 71.20 
 
 28.54 
 
 30,510 
 
 29.5 
 
 29.2 
 
 24,468 
 
 
 
 
 164 
 
 269 
 
 8 
 
 69.74 
 
 30.06 
 
 28,120 
 
 28.7 
 
 20.7 
 
 26,930 
 
 " 
 
 
 143 
 
 202 
 
 9 
 
 66.27 
 
 33.50 
 
 37,800 
 
 25.1 
 
 37.7 
 
 28,459 
 
 
 
 
 176 
 
 257 
 
 10 
 
 63.44 
 
 36.36 
 
 48,300 
 
 32.8 
 
 31.7 
 
 43,216 
 
 41 
 
 
 202 
 
 230 
 
 11 
 
 60.94 
 
 38.65 
 
 41,065 
 
 40.1 
 
 20.7 
 
 38,968 
 
 
 
 75,000 
 
 194 
 
 202 
 
 12 
 
 58.49 
 
 41.10 
 
 50,450 
 
 54.4 
 
 10.1 
 
 63,304 
 
 
 
 
 227 
 
 93 
 
 13 
 
 55.15 
 
 44.44 
 
 44,280 
 
 44.0 
 
 15.3 
 
 42,463 
 
 " 
 
 78,000 
 
 209 
 
 109 
 
 14 
 
 54.86 
 
 44.78 
 
 46,400 
 
 53.9 
 
 8.0 
 
 47,955 
 
 ' 
 
 
 223 
 
 72 
 
 15 
 
 49.66 
 
 50.14 
 
 30,990 
 
 54.5 
 
 5.0 
 
 33,467 
 
 1.26 
 
 1*17,400 
 
 172 
 
 38 
 
 16 
 
 48.99 
 
 50.82 
 
 26,050 
 
 100 
 
 0.8 
 
 40,189 
 
 0.61 
 
 
 176 
 
 16 
 
 17 
 
 47.56 
 
 52.28 
 
 24,150 
 
 100 
 
 0.8 
 
 48,471 
 
 1.17 
 
 12i,000 
 
 155 
 
 13 
 
 18 
 
 4336 
 
 56.22 
 
 9,170 
 
 100 
 
 
 17,691 
 
 0.10 
 
 
 
 88 
 
 2 
 
 \9 
 
 41.30 
 
 58.12 
 
 3,727 
 
 100 
 
 
 7,761 
 
 0.04 
 
 
 18 
 
 2 
 
 20 
 
 32.94 
 
 66.23 
 
 1,774 
 
 100 
 
 
 8,296 
 
 0.04 
 
 . * 
 
 29 
 
 1 
 
 21 
 
 29.20 
 
 70.17 
 
 6,414 
 
 100 
 
 
 16,579 
 
 0.04 
 
 
 40 
 
 2 
 
 22 
 
 20.81 
 
 77.63 
 
 9,000 
 
 100 
 
 *0.2 
 
 22,972 
 
 0.13 
 
 52J52 
 
 65 
 
 1 
 
 23 
 
 12.12 
 
 86.67 
 
 12,413 
 
 100 
 
 0.4 
 
 35,026 
 
 0.31 
 
 
 82 
 
 3 
 
 24 
 
 4.35 
 
 94.59 
 
 18,065 
 
 100 
 
 0.5 
 
 26,162 
 
 0.46 
 
 
 81 
 
 22 
 
 25 
 
 Cast. 
 
 Zinc. 
 
 5,400 
 
 75 
 
 0.7 
 
 7,539 
 
 0.12 
 
 22,000 
 
 37 
 
 142 
 
 Variation in Strength of Gun-bronze, and Means of Improving 
 the Strength. The figures obtained for alloys of from 7.8% to 12.7% 
 tin, viz., from 26,860 to 29,430 pounds, are much less than are usually 
 given as the strength of gun-metal. Bronze guns are usually cast under 
 the pressure of a head of metal, which tends to increase the strength and 
 density. The strength of the upper part of a gun casting, or sinking 
 head, is not greater than that of the small bars which have been tested 
 in these experiments. The following is an extract from the report of 
 Major Wade concerning the strength and density of gun-bronze (1850): 
 Extreme variation of six samples from different parts of the same 
 gun (a 32-pounder howitzer): Specific gravity, 8.487 to 8.835: tenacity, 
 26,428 to 52,192. Extreme variation of all the samples tested: Specific 
 gravity, 8.308 to 8.850: tenacity 23,108 to 54,531. Extreme variation of 
 all the samples from the gun heads: Specific gravity, 8.308 to 8,756; 
 tenacity, 23,529 to 35,484. 
 
 Major Wade says: The general results on the quality of bronze as it 
 found in guns are mostly of a negative character. They expose delects 
 in density and strength, develop the heterogeneous texture of the metal 
 in different parts of the same gun, and show the irregularity and un- 
 certainty of quality which attend the casting of all guns, although made 
 from similar materials, treated in like manner. 
 
 Navy ordnance bronze containing 9 parts copper and 1 part tin, test" 
 at Washington, D.C., in 1875-6. showed a variation in tensile strength 
 from 29 800 to 51 400 Ibs. per square inch, in elongation from 3% to 
 58%, and in specific gravity from 8.39 to 8.88. 
 
 That a great improvement may be made in the density and tenacity 
 of gun-bronze by compression has been shown by the experiments 
 Mr. S. B. Dean in Boston, Mass., in 1869, and by those of General 
 Uchatius in Austria in 1873. The former increased the density of toe 
 
ALLOYS OF COPPER, TIN AND ZINC. 
 
 387 
 
 metal next the bore of the gun from 8.321 to 8.875, and the tenacity 
 from 27,238 to 41,471 pounds per square inch. The latter, by a similar 
 process, obtained the following figures for tenacity: 
 
 Pounds per sq. in. 
 
 Bronze with 10% tin 72,053 
 
 Bronze with 8% tin 73,958 
 
 Bronze with 6% tin 77,656 
 
 ALLOYS OF COPPER, TIN, AND ZINC. 
 
 (Report of U. S. Test Board, Vol. II, 1881.) 
 
 No. 
 in 
 
 Analysis, 
 Original Mixture. 
 
 Transverse 
 Strength. 
 
 Tensile 
 Strength per 
 square inch. 
 
 Elongation 
 per cent in 
 5 inches. 
 
 Re- 
 
 
 
 
 Mcdulus 
 
 f 
 
 Deflec- 
 
 
 
 
 
 port. 
 
 Cu. 
 
 Sn. 
 
 Zn. 
 
 Ol 
 
 Rup- 
 ture. 
 
 tion, 
 . ins. 
 
 A. 
 
 B. 
 
 A. 
 
 B. 
 
 72 
 
 90 
 
 5 
 
 5 
 
 41,334 
 
 2.63 
 
 23,660 
 
 30,740 
 
 2.34 
 
 9.68 
 
 5 
 
 88.14 
 
 1.86 
 
 10 
 
 31,986 
 
 3.67 
 
 32,000 
 
 33,000 
 
 17.6 
 
 19.5 
 
 70 
 
 85 
 
 5 
 
 10 
 
 44,457 
 
 2.85 
 
 28,840 
 
 28,560 
 
 6.80 
 
 5.28 
 
 71 
 
 85 
 
 10 
 
 5 
 
 62,470 
 
 2.56 
 
 35,680 
 
 36,000 
 
 2.51 
 
 2.25 
 
 89 
 
 85 
 
 12.5 
 
 2.5 
 
 62,405 
 
 2.83 
 
 34,500 
 
 32,800 
 
 1.29 
 
 2.79 
 
 88 
 
 82.5 
 
 12.5 
 
 5 
 
 69,960 
 
 1.61 
 
 36,000 
 
 34,000 
 
 0.86 
 
 0.92 
 
 77 
 
 82.5 
 
 15 
 
 2.5 
 
 69,045 
 
 1.09 
 
 33,600 
 
 33,800 
 
 
 0.68 
 
 67 
 
 80 
 
 5 
 
 15 
 
 42,618 
 
 3.88 
 
 37,560 
 
 32,300 
 
 11.6' 
 
 3.59 
 
 68 
 
 80 
 
 10 
 
 10 
 
 67,117 
 
 2.45 
 
 32,830 
 
 31,950 
 
 1.57 
 
 1.67 
 
 69 
 
 80 
 
 15 
 
 5 
 
 54,476 
 
 0.44 
 
 32,350 
 
 30,760 
 
 0.55 
 
 0.44 
 
 86 
 
 77.5 
 
 10 
 
 12.5 
 
 63,849 
 
 1.19 
 
 35,500 
 
 36,000 
 
 1.00 
 
 1.00 
 
 87 
 
 77.5 
 
 12.5 
 
 10 
 
 61,705 
 
 0.71 
 
 36,000 
 
 32,500 
 
 0.72 
 
 0.59 
 
 63 
 
 75 
 
 5 
 
 20 
 
 55,355 
 
 2.91 
 
 33,140 
 
 34,960 
 
 2.50 
 
 3.19 
 
 85 
 
 75 
 
 7.5 
 
 17.5 
 
 62,607 
 
 1.39 
 
 33,700 
 
 39,300 
 
 1.56 
 
 1.33 
 
 64 
 
 75 
 
 10 
 
 15 
 
 58,345 
 
 0.73 
 
 35,320 
 
 34,000 
 
 1.13 
 
 1.25 
 
 65 
 
 75 
 
 15 
 
 10 
 
 51,109 
 
 0.31 
 
 35,440 
 
 28,000 
 
 0.59 
 
 0.54 
 
 66 
 
 75 
 
 20 
 
 5 
 
 40,235 
 
 0.21 
 
 23,140 
 
 27,660 
 
 0.43 
 
 
 83 
 
 72.5 
 
 7.5 
 
 20 
 
 51,839 
 
 2.86 
 
 32,700 
 
 34,800 
 
 3.73 
 
 3.78 
 
 84 
 
 72.5 
 
 10 
 
 17.5 
 
 53,230 
 
 0.74 
 
 30,000 
 
 30,000 
 
 0.48 
 
 0.49 
 
 59 
 
 70 
 
 5 
 
 25 
 
 57,349 
 
 1.37 
 
 38,000 
 
 32,940 
 
 2.06 
 
 0.99 
 
 82 
 
 70 
 
 7.5 
 
 22.5 
 
 48,836 
 
 0.36 
 
 38,000 
 
 32,400 
 
 0.84 
 
 0.40 
 
 60 
 
 70 
 
 10 
 
 20 
 
 36,520 
 
 0.18 
 
 33,140 
 
 26,300 
 
 0.31 
 
 
 61 
 
 70 
 
 15 
 
 15 
 
 37,924 
 
 0.20 
 
 33,440 
 
 27,800 
 
 0.25 
 
 
 62 
 
 70 
 
 20 
 
 10 
 
 15 126 
 
 0.08 
 
 17,000 
 
 12,900 
 
 0.03 
 
 
 81 
 
 67.5 
 
 2.5 
 
 30 
 
 58,343 
 
 2.91 
 
 34,720 
 
 45,850 
 
 7.27 
 
 3.09 
 
 74 
 
 67.5 
 
 5 
 
 27.5 
 
 55,976 
 
 0.49 
 
 34,000 
 
 34,460 
 
 1.06 
 
 0.43 
 
 75 
 
 67.5 
 
 7.5 
 
 25 
 
 46,875 
 
 0.32 
 
 29,500 
 
 30,000 
 
 0.36 
 
 0.26 
 
 80 
 
 65 
 
 2.5 
 
 32.5 
 
 56,949 
 
 2.36 
 
 41,350 
 
 38,300 
 
 3.26 
 
 3.02 
 
 55 
 
 65 
 
 5 
 
 30 
 
 51,369 
 
 0.56 
 
 37,140 
 
 36,000 
 
 1.21 
 
 0.61 
 
 56 
 
 65 
 
 10 
 
 25 
 
 27,075 
 
 0.14 
 
 25,720 
 
 22,500 
 
 0.15 
 
 0.19 
 
 57 
 
 65 
 
 15 
 
 20 
 
 13,591 
 
 0.07 
 
 6820 
 
 7,231 
 
 
 
 58 
 
 65 
 
 20 
 
 15 
 
 11,932 
 
 0.05 
 
 3,765 
 
 2,665 
 
 
 
 79 
 
 62.5 
 
 2.5 
 
 35 
 
 69,255 
 
 2.34 
 
 44,400 
 
 45,000 
 
 2. J5 
 
 2J9 
 
 78 
 
 60 
 
 2.5 
 
 37.5 
 
 69,508 
 
 1.46 
 
 57,400 
 
 52,900 
 
 4.87 
 
 3.02 
 
 52 
 
 60 
 
 5 
 
 35 
 
 46,076 
 
 0.28 
 
 41,160 
 
 38,330 
 
 0.39 
 
 0.40 
 
 53 
 
 60 
 
 10 
 
 30 
 
 24,699 
 
 0.13 
 
 21,780 
 
 21,240 
 
 0.15 
 
 
 54 
 
 60 
 
 15 
 
 25 
 
 18,248 
 
 0.09 
 
 18,020 
 
 12,400 
 
 
 
 12 
 
 58.22 
 
 2.30 
 
 39.48 
 
 95,623 
 
 1.99 
 
 66,500 
 
 67,600 
 
 3.1 3 
 
 3J5 
 
 3 
 
 58.75 
 
 8.75 
 
 32.5 
 
 35,752 
 
 0.18 
 
 Broke 
 
 before te 
 
 st; very 
 
 brittle 
 
 4 
 
 57.5 
 
 21.25 
 
 21.25 
 
 2,752 
 
 0.02 
 
 725 
 
 1 300 
 
 
 
 73 
 
 55 
 
 0.5 
 
 44.5 
 
 72,308 
 
 3.05 
 
 68,900 
 
 68,900 
 
 9.43 
 
 2.88 
 
 50 
 
 55 
 
 5 
 
 40 
 
 38,174 
 
 0.22 
 
 27,400 
 
 30,500 
 
 0.46 
 
 0.43 
 
 51 
 
 55 
 
 10 
 
 35 
 
 28,258 
 
 0.14 
 
 25,460 
 
 18,500 
 
 0.29 
 
 0.10 
 
 49 
 
 50 
 
 5 
 
 45 
 
 20,814 
 
 0.11 
 
 23,000 
 
 31,300 
 
 0.66 
 
 0.45 
 
388 ALLOYS. 
 
 The transverse tests were made in bars 1 in. square; 22 in. between 
 supports. The tensile tests were made on bars 0.798 in. diam. turned 
 from the two halves of the trans verse- test bar, one half being marked A 
 and the other B. 
 
 Ancient Bronzes. The usual composition of ancient bronze was 
 the same as that of modern gun-metal 90 copper, 10 tin; but the 
 proportion of tin varies from 5% to 15%, and in some cases lead has 
 been found. Some ancient -Egyptian tools contained 88 copper, 12 tin. 
 
 Strength of the Copper-zinc Alloys. The alloys containing less 
 than 15% of zinc by original mixture were generally defective. The 
 bars were full of blow-holes, and the metal showed signs of oxidation. 
 To insure good castings it appears that copper-zinc alloys should con- 
 tain more than 15% of zinc. 
 
 From No. 2 to No. 8 inclusive, 16.98 to 30.06% zinc the bars show a 
 remarkable similarity in all their properties. They have all nearly the 
 same strength and ductility, the latter decreasing slightly as zinc 
 increases, and are nearly alike in color and appearance. Between Nos. 8 
 and 10, 30.06 and 36.36% zinc, the strength by all methods of test 
 rapidly increases. Between No. 10 and No. 15, 36.36 and 50.14% zinc, 
 there is another group, distinguished by high strength and diminished 
 ductility. The alloy of maximum tensile, transverse and torsional 
 strength contains about 41% of zinc. 
 
 The alloys containing less than 55% of zinc are all yellow metals. 
 Beyond 55% the color changes to white, and the alloy becomes weak and 
 brittle. Between 70% and pure zinc the color is bluish gray, the brit- 
 tleness decreases and the strength increases, but not to such a degree as 
 to make them useful for constructive purposes. 
 
 Difference between Composition by Mixture and by Analysis. 
 There is in every case a smaller percentage of zinc in the average analy- 
 sis than in the original mixture, and a larger .percentage of copper. The 
 loss of zinc is variable, but in general averages from 1 to 2%. 
 
 Liquation or Separation of the Metals. In several of the bars a 
 considerable amount of liquation took place, analysis showing a differ- 
 ence in composition of the two ends of the bar. In such cases the 
 change in composition was gradual from one end of the bar to the other, 
 the upper end in general containing the higher percentage of copper. 
 A notable instance was bar No. 13, in the above table, turnings from the 
 upper end containing 40.36% of zinc, and from the lower end 48.52%. 
 
 Specific Gravity. The specific gravity follows a definite law, vary- 
 ing with the composition, and decreasing with the addition of zinc. 
 From the plotted curve of specific gravities the following mean values 
 are taken: 
 
 xer cent zinc 10 20 30 40 50 60 70 80 90 100 
 
 Specific gravity . . . 8.80 8.72 8.60 8.40 8.36 8.20 8.00 7.72 7.40 7.20 7.14 
 
 Graphic Representation of the Law of Variation of Strength of 
 Copper-Tin-Zinc Alloys. In an equilateral triangle the sum of the 
 perpendicular distances from any point within it to the three sides is 
 equal to the altitude. Such a triangle can therefore be used to show 
 graphically the percentage composition of any compound of three parts, 
 such as a triple alloy. Let one side represent copper, a second tin, 
 and the third zinc, the vertex opposite each of these sides representing 
 100 of each element respectively. On points in a triangle of wood rep- 
 resenting different alloys tested, wires were erected of lengths propor- 
 tional to the tensile strengths, and the triangle then built up with plaster 
 to the height of the wires. The surface thus formed has a characteristic 
 topography representing the variations ,of strength with variations of 
 composition. The cut shows the surface thus made. The vertical 
 section to the left represents the law of tensile strength of the copper-tin 
 alloys, the one to the right that of tin-zinc alloys, and the one at the 
 rear that of the copper-zinc alloys. The high point represents the 
 strongest possible alloys of the three metals. Its composition is copper 
 55, zinc 43, tin 2, and its strength about 70,000 Ibs. The high ridge from 
 this point to the point of maximum height of the section on the left is 
 the line of the strongest alloys, represented by the formula zinc + (3 X tin) 
 = 55. 
 
 All alloys lying to the rear of the ridge, containing more copper and 
 less tin or zinc are alloys of greater ductility than those on the line of 
 
ALLOYS OF COPPER, TIN AND ZINC. 
 
 389 
 
 maximum strength, and are the valuable commercial alloys; those in 
 front on the declivity toward the central valley are brittle, and those in 
 the valley are both brittle and weak. Passing from the valley toward the 
 section at the right the alloys lose their brittleness and become soft, the 
 maximum softness being at tin=100, but they remain weak, as is shown 
 by the low elevation of the surface. This model was planned and con- 
 structed by Prof. Thurston in 1877. (See Trans. A S C E., 1881. 
 Report of the U. S. Board appointed to test Iron, Steel etc., vol. ii. 
 Washington, 1881, and Thurston 's Materials of Engineering vol iii.) 
 
 FIG. 90. 
 
 The best alloy obtained in Thurston's research for the U. S. Testing 
 Board has the composition, copper 55, tin 0.5, zinc 44.5. The tensile 
 strength in a cast bar was 68,900 Ibs. per sq. in., two specimens giving 
 the same result; the elongation was 47 to 51 per cent in 5 inches. 
 Thurston's formula for copper-tin-zinc alloys of maximum strength 
 (Trans. A.S.C.E., 1881) is z + 3 t = 55, in which z is the percentage of 
 zinc and t that of tin. Alloys proportioned according to this formula 
 should have a strength of about 40,000 Ibs. per sq. in. + 500 z. The 
 formula fails with alloys containing less than 1 per cent of tin. 
 The following would be the percentage composition of a number of 
 alloys made according to this formula, and their corresponding tensile 
 strength in castings: 
 
 
 
 
 Tensile 
 
 
 
 
 Tensile 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength, 
 Ibs. per 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength 
 Ibs. per 
 
 
 
 
 sq. in. 
 
 
 
 
 sq. in. 
 
 1 
 
 52 
 
 47 
 
 66,000 
 
 8 
 
 31 
 
 61 
 
 55,500 
 
 2 
 
 49 
 
 49 
 
 64,500 
 
 9 
 
 28 
 
 63 
 
 54,000 
 
 3 
 
 46 
 
 5! 
 
 63,000 
 
 10 
 
 25 
 
 65 
 
 52,500 
 
 4 
 
 43 
 
 53 
 
 61,500 
 
 12 
 
 19 
 
 69 
 
 49,500 
 
 5 
 
 40 
 
 55 
 
 60,000 
 
 14 
 
 13 
 
 73 
 
 46,500 
 
 6 
 
 37 
 
 57 
 
 58,500 
 
 16 
 
 7 
 
 77 
 
 43,500 
 
 7 
 
 34 
 
 59 
 
 57,000 
 
 18 
 
 1 
 
 81 
 
 40,500 
 
390 
 
 ALLOYS. 
 
 These alloys, while possessing maximum tensile strength, would In 
 general be too hard for easy working by machine tools. Another series 
 made on the formula z + It = 50 would have greater ductility, together 
 With considerable strength, as follows, the strength being calculated as 
 before, tensile strength in Ibs. per sq. in. = 40,000 + 5000. 
 
 
 
 
 Tensile 
 
 
 
 
 Tensile 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength, 
 Ibs. per 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength, 
 Ibs. per 
 
 
 
 
 sq. in. 
 
 
 
 
 sq. in. 
 
 1 
 
 46 
 
 53 
 
 63,000 
 
 7 
 
 22 
 
 71 
 
 51,000 
 
 2 
 
 42 
 
 56 
 
 61,000 
 
 8 
 
 18 
 
 74 
 
 49,000 
 
 3 
 
 38 
 
 59 
 
 59,000 
 
 9 
 
 14 
 
 77 
 
 47,000 
 
 4 
 
 34 
 
 62 
 
 57,000 
 
 10 
 
 10 
 
 80 
 
 45,000 
 
 5 
 
 30 
 
 65 
 
 55,000 
 
 11 
 
 6 
 
 83 
 
 43,000 
 
 6 
 
 26 
 
 68 
 
 53,000 
 
 12 
 
 2 
 
 86 
 
 41,000 
 
 Composition of Alloys in E very-day Use in Brass Foundries. 
 
 (American Machinist.) 
 
 
 Cop- 
 per. 
 
 Zinc. 
 
 Tin. 
 
 Lead . 
 
 
 Admiralty metal . . 
 Bell metal 
 
 Ibs. 
 87 
 
 16 
 
 Ibs. 
 
 Ibs. 
 8 
 
 4 
 
 Ibs. 
 
 For parts of engines on 
 board naval vessels. 
 Bells for ships and factories 
 
 Brass (yellow) 
 Bush metal 
 
 16 
 
 64 
 
 8 
 8 
 
 4 
 
 1/2 
 4 
 
 For plumbers, ship and house 
 brass work. 
 For bearing bushes for shaft- 
 
 Gun metal 
 
 32 
 
 
 3 
 
 
 ing. 
 For pumps and other hydrau** 
 
 Steam metal 
 
 Hard gun metal. . . 
 Muntz metal 
 
 20 
 
 16 
 60 
 
 1 
 
 '40' 
 
 U/2 
 2V2 
 
 1 
 
 lie purposes. 
 Castings subjected to steam 
 pressure. 
 For heavy bearings. 
 Metal from which bolts and 
 
 Phosphor bronze . . 
 Brazing metal 
 
 92 
 90 
 
 16 
 
 3 
 
 8pho 
 10 
 
 s. tin 
 
 nuts are forged, valve spin- 
 dles, etc. 
 For valves, pumps and gen- 
 eral work. 
 For cog and worm wheels, 
 bushes, axle bearings, slide 
 valves, etc. 
 Flanges for copper pipes. 
 
 solder 
 
 50 
 
 50 
 
 
 
 Solder for the above flanges'. 
 
 Admiralty Metal, for surface condenser tubes where sea water is used 
 for cooling, Cu, 70 ; Zn, 29; Sn, 1. Power, June 1, 1909. 
 
 Gurley's Bronze. 16 parts copper, 1 tin, 1 zinc, 1/2 lead, used by 
 W & L. E. Gurley of Troy for the framework of their engineer's transits. 
 Tensile strength 41,114 Ibs. per sq. in., elongation 27% in 1 inch, sp. gr. 
 $.696. (W. J. Keep, Trans. A, I. M. E., 1890.) 
 
ALLOYS OF COPPER, TIN, AND ZINC. 
 
 391 
 
 Composition of Various Grades of Rolled Brass, Etc. 
 
 Trade Name. 
 
 Copper. 
 
 Zinc. 
 
 Tin. 
 
 Lead. 
 
 Nickel. 
 
 Common high, brass 
 
 61 5 
 
 38 5 
 
 
 
 
 
 60 
 
 40 
 
 
 
 
 Cartridge brass 
 
 662/Q 
 
 331/s 
 
 
 
 
 
 80 3 
 
 20 
 
 
 
 
 Clock brass . 
 
 60 
 
 40 
 
 
 1 1/2 
 
 
 Drill rod 
 
 60 
 
 40 
 
 
 1 1/2 to 2 
 
 
 Sprin " brass 
 
 662/3 
 
 331/3 
 
 11/2 
 
 
 
 18 per cent German silver . 
 
 61 1/2 
 
 20l/-> 
 
 
 
 18 
 
 
 
 
 
 
 
 The above table was furnished by the superintendent of a mill in Connec- 
 ticut in 1894. He says: While each mill has its own proportions for various 
 mixtures, depending upon the purposes for which the product is intended, 
 the figures given are about the average standard. Thus, between cartridge 
 brass with 881/3 per cent zinc and common high brass with 381/2 per cent 
 zinc, there are any number of different mixtures known generally as "high 
 brass," or specifically as. "spinning brass," "drawing brass," etc., wherein 
 the amount of zinc is dependent upon the amount of scrap used in the 
 mixture, the degree of working to which the metal is to be subjected, etc. 
 
 Useful Alloys of Copper, Tin, and Zinc. 
 
 (Selected from numerous sources.) 
 
 
 Copper. 
 
 Tin. 
 
 Zinc. 
 
 U. S. Navy Dept. journal boxes ) _ 
 and guide-gibs . ) 
 
 J 6 
 (82.8 
 58.22 
 62 
 88 
 (64 
 (87.7 
 92.5 
 91 
 87.75 
 85 
 83 
 (13 
 (76.5 
 82 
 83 
 20 
 87 
 88 
 84 
 80 
 81 
 97 
 89.5 
 89 
 89 
 86 
 
 ^ 
 
 79 
 74 
 64 
 
 1 
 
 13.8 
 2.30 
 1 
 10 
 8 
 11.0 
 5 
 7 
 9.75 
 5 
 2 
 2 
 11.8 
 16 
 15 
 1 
 4.4 
 10 
 14 
 18 
 17 
 2 
 2.1 
 8 
 
 ,?* 
 
 \i aft 
 
 18 
 91/2 
 
 1/4 parts. 
 3.4 per cent. 
 39.48 ' 
 37 " 
 2 
 1 parts 
 1 .3 per cent 
 
 2 " 
 
 2.5 " 
 10 
 15 ** 
 2 parts. 
 11.7 percent. 
 2 slightly malleable. 
 1.50 0.50 lead. 
 
 4.3 4.3 M 
 2 
 2 
 .. 2.0 antimony. 
 ..2.0 " 
 1 
 5.6 2.8 lead. 
 3 
 8V2 
 .... 
 
 2 
 21/2 1/2 lead. 
 91/ 2 7 lead. 
 291/2 3 1/2 lead. 
 
 Tobin bronze 
 
 Naval brass 
 
 Composition, U. S. Navy 
 
 
 Gun metal . . 
 
 
 
 
 i i> 
 
 (C II 
 
 Tough brass for engines 
 
 Bronze for rod-boxes (Lafond) 
 " pieces subject to shock. . 
 Red brass parts 
 
 * per cent 
 
 Bronze for pump casings (Lafond).. 
 " eccentric straps. 
 *' shrill whistles . . 
 
 " low-toned whistles 
 
 Art bronze, dull red fracture 
 
 Gold bronze 
 
 Bearing metal 
 
 
 
 
 < 
 
 4 
 
 It 
 
 II 
 
 English brass of A.D. J504 
 
 
392 
 
 ALLOYS. 
 
 "Steam Metal." Alloys of copper and zinc are unsuitable for steam 
 valves and other like purposes, since their strength is greatly reduced at 
 high temperatures, and they appear to undergo a deterioration by con- 
 tinued heating. Alloys of copper with from 10 to 12% of tin, when cast 
 without oxidation, are good steam metals, and a favorite alloy is what 
 is known as "government mixture," 88 Cu, 10 Sn, 2 Zn. It has a 
 tensile strength of about 33,000 Ib. per sq. in., when cold, and about 
 30,600 Ib. when heated to 407 F., corresponding to steam of 250 Ib. 
 pressure. 
 
 Analyses of Tobin bronze by Dr. Chas. B. Dudley gave the following: 
 
 Pig metal Cu, 59.00; Zn, 38.40; Sn, 2.16; Fe, 0.11; Pb, 0.31 
 
 Boiled bar Cu, 61.20; Zn, 37.14; Sn, 0.90; Fe, 0.18; Pb, 0.35 
 
 The rolled bar gave 78,500 Ib. tensile strength, 40% elongation in 
 2 in. and 15% in 8 in. 
 
 The' original Tobin bronze in 1875, as described by Thurston, Trans. 
 A. S. C. E., 1881, had copper 58.22, tin 2.30, zinc 39.48. As cast it 
 had a tenacity of 66,000 Ib. per sq. in., and as rolled 79,000 Ib.; cold 
 rolled it gave 104,000 Ib. 
 
 At a cherry-red heat Tobin bronze can be forged and stamped as 
 readily as steel. Its great tensile strength and its resistance to the 
 corrosive action of sea water make it a suitable metal for condenser 
 plates and other marine purposes. 
 
 Miscellaneous Alloys. (From a circular of the Titanium Alloy Mfg. 
 Co., Niagara Falls, N. Y., 1915.) 
 
 ANALYSES (Approximate). PHYSICAL QUALITIES (Averages). 
 
 No. 
 
 Cu. 
 
 Al. 
 
 Sn. 
 
 Zn. 
 
 Pb. 
 
 T.S. 
 
 .S 
 
 '$* 
 
 s~ 
 
 | 
 
 <S > 
 
 'ga 
 
 aO 
 
 GG 
 
 Brinell 
 Hardness. 
 
 Shrinkage, 
 In. per Ft. 
 
 I. 
 
 -P & 
 
 3* 
 & 
 
 S3 . 
 |s"! 
 
 f 
 
 1 
 3 
 
 90 
 89 
 90 
 
 10 
 10 
 
 "n 
 
 
 
 70,000 
 37,500 
 77,000 
 
 20 
 8 
 24.5 
 
 7.5 
 8,5 
 7.5 
 
 95 
 75 
 
 94 
 
 0.22 
 .125 
 .22 
 
 0.27 
 .31 
 .27 
 
 19,500 
 21,600 
 25,000 
 
 9 
 10 
 11 
 14 
 15 
 
 90 
 88 
 90 
 88 
 80 
 
 
 10 
 10 
 6.5 
 10 
 10 
 
 "2" 
 2 
 
 Y.5 
 2 
 10 
 
 37,500 
 35,000 
 37,000 
 32,500 
 30,000 
 
 17.5 
 16 
 29 
 6.5 
 6 
 
 8.6 
 8.7 
 8.8 
 8.8 
 9.0 
 
 67 
 72 
 55 
 67 
 57 
 
 .125 
 .125 
 .14 
 .125 
 .125 
 
 .31 
 .32 
 .32 
 .32 
 .33 
 
 'jg,50b' 
 
 16 
 
 18 
 
 81 
 85 
 
 
 7 
 5 
 
 3 
 5 
 
 9 
 
 5 
 
 32,500 
 30,000 
 
 17 
 18 
 
 8.9 
 8.5 
 
 52 
 55 
 
 .125 
 .14 
 
 .33 
 .31 
 
 
 19 
 74 
 
 83 
 70 
 
 
 4 
 | 
 
 7 
 77 
 
 6 
 2 
 
 30,500 
 29,500 
 
 17.5 
 25 
 
 8.5 
 8.4 
 
 57 
 52 
 
 .125 
 .186 
 
 .31 
 .30 
 
 
 78 
 
 99.75 
 
 
 
 
 
 18,500 
 
 10 
 
 8.8 
 
 35 
 
 .25 
 
 .32 
 
 
 29 
 3? 
 
 56 
 8 
 
 0.5 
 Q? 
 
 
 43.5 
 
 
 70,000 
 18,000 
 
 28.5 
 1.5 
 
 8.4 
 2.8 
 
 111 
 52 
 
 .25 
 .186 
 
 .30 
 .10 
 
 30,000 
 
 33 
 
 3 
 
 82 
 
 
 15 
 
 
 23,000 
 
 2 
 
 3.1 
 
 62 
 
 .186 
 
 .11 
 
 
 Qualities and Uses: 
 
 No. 1. Strength, toughness, resists corrosion. 
 
 No. 3. Gear bronze; serviceable for worm wheels running against 
 highly finished steel. 
 
 No. 5. Similar to No. 1, but more easily machined. For large, heavy 
 work. 
 
 No. 9. Acid resisting; for mine-pump bodies, and for thrust collars 
 or disks. 
 
 No. 10. "Gun metal"; for heavy pressures and high speeds; for high- 
 grade bearings. 
 
 No. 11. Medium soft bronze; for small bearings lined with babbitt; for 
 steam work. 
 
 No. 14. Gear bronze, softer than No. 3; machines more easily. 
 
 No. 15. Phosphor bronze; for high speed and heavy pressure; for bear- 
 ings subject to shock. 
 
 No. 16. Similar to No. 15, but somewhat softer and lower in price. 
 
 No. 18. High grade red brass: a good steam metal. 
 
COPPER-ZINC-IRON ALLOYS. 
 
 393 
 
 No. 10. Commercial red brass. 
 
 No. 24. A good yellow brass; casts well; takes a high polish. 
 
 No. 28. Pure copper, deoxidized ; high electrical conductivity. 
 
 No. 29. "Manganese bronze"; for propeller blades, valve stems and 
 
 other parts requiring high strength; not good for bearings. 
 No. 32. Standard aluminum alloy; for crank cases, automobile castings, 
 
 No. 33. Tougher than No. 32; takes an extra high polish, can be bent 
 slightly without breaking. 
 
 Special Alloys. (Engineering, March 24, 1893.) 
 JAPANESE ALLOYS for art work: 
 
 
 Copper. 
 
 Silver. 
 
 Gold. 
 
 Lead, 
 
 Zinc. 
 
 Iron. 
 
 Shaku-do 
 
 94.50 
 
 1.55 
 
 3.73 
 
 0.11 
 
 trace. 
 
 trace. 
 
 Shibu-ichi 
 
 67.31 
 
 32.07 
 
 traces. 
 
 0.52 
 
 
 
 GILBERT'S ALLOY for cera-pcrduta process, for casting in plaster of 
 paris. 
 
 Copper 91.4 Tin 5.7 Lead 2.9 Very fusible. 
 
 COPPER-ZINC-IKON ALLOYS.* 
 
 (F. L. Garrison, Jour. Frank. Inst., June and July, 1891.) 
 
 Delta Metal. This alloy, which was formerly known as sterro-metal, 
 is composed of about 60 copper, from 34 to 44 zinc, 2 to 4 iron, and 1 to 2 
 tin. 
 
 The peculiarity of all these alloys is, the content of iron, which appears 
 to have the property of increasing their strength to an unusual degree. 
 In making delta metal the iron is previously alloyed with zinc in known 
 and definite proportions. When ordinary wrought-iron is introduced 
 into molten zinc, the latter readily dissolves or absorbs the former, and 
 will take it up to the extent of about 5% or more. By adding the zinc- 
 iron alloy thus obtained to the requisite amount of copper, it is possi- 
 ble to introduce any definite quantity of iron up to 5% into the copper 
 alloy. Garrison gives the following as the range of composition ot 
 copper-zinc-iron, and copper-zinc-tin-iroa alloys: 
 
 I. II. 
 
 Per cent. Per cent. 
 
 Iron 0.1 to 5 Iron 0.1 to 5 
 
 Copper 50 to 65 Tin 0.1 to 10 
 
 Zinc -.49. 9 to 30 Zinc 1.8 to 45 
 
 Copper 98 to 40 
 
 The advantages claimed for delta metal are great strength and tough- 
 ness. It produces sound castings of close grain. It can be rolled and 
 forged hot, and can stand a certain amount of drawing and hammering 
 when cold. It takes a high polish, and when exposed to the atmosphere 
 tarnishes less than brass. 
 
 When cast in sand delta metal has a tensile strength of about 45,000 
 pounds per square inch, and about 10% elongation; when rolled, ten- 
 sile strength of 60,000 to 75,000 pounds per square inch, elongation 
 from 9% to 17% on bars 1.128 inch in diameter and 1 inch area. 
 
 Wallace gives the ultimate tensile strength 33,600 to 51,520 pounds 
 per square inch, with from 10% to 20% elongation. 
 
 Delta metal can be forged, stamped and rolled hot. It must be forged 
 at a dark cherry-red heat, and care taken to avoid striking when at a 
 black heat. 
 
 According to Lloyd's Proving House tests, made at Cardiff, December 
 20, 1887, a half-inch delta metal-rolled bar gave a tensile strength of 
 88,400 pounds per square inch, with an elongation of 30% in three 
 inches. 
 
394 
 
 ALLOYS. 
 
 ALLOYS OF COPPER, TIN, AND LEAD. 
 
 G. H. Clamer, in Castings, July, 1908, describes some experiments on 
 the use of lead in copper alloys. A copper and lead alloy does not make 
 what would be called good castings; by the introduction of tin a more 
 homogeneous product is secured. By the addition of nickel it was found 
 that more than 15% of lead could be used, while maintaining tin at 8 to 
 10%, and also that the tin could be dispensed with. A good alloy for 
 bearings was then made without nickel, containing Cu 65, Sn 5, Pb 30. 
 This alloy is largely sold under the name of "plastic bronze." If the 
 matrix of tin and copper were so proportioned that the tin remained 
 below 9% then more than 20% of lead could be added with satisfactory 
 results. As the tin is decreased more lead may be added. (See Bear- 
 ing Metal Alloys, below.) 
 
 The Influence of Lead on Brass. E. S. Sperry, Trans. A.I.M.E., 
 1897. As a rule, the lower the brass (that is, the lower in zinc) the 
 more difficult it is to cut. If the alloy is made from pure copper and 
 zinc, the chips are long and tenacious, and a slow speed "must be em- 
 ployed in cutting. For some classes of work, such as spinning or car- 
 tridge brass, these qualities are essential, but for others, such as clock 
 brass or screw rod, they are almost prohibitory. To make an alloy 
 which will cut easily, giving short chips, the best method is the addition 
 of a small percentage of lead. Experiments were made on alloys con- 
 taining different percentages of lead. The following is a condensed 
 statement of the chief results: 
 
 Cu, 60; Zn, 30; Pb, 10. Difficult to obtain a homogeneous alloy. 
 Cracked badly on rolling. 
 
 Cu, 60; Zn, 35; Pb, 5. Good cutting qualities but cracked on rolling. 
 
 Cu, 60; Zn, 37.5: Pb, 2.5. Cutting qualities excellent, but could 
 only be hot-rolled or forged with difficulty. 
 
 Cu, 60; Zn, 38.75; Pb, 1.25. Cutting qualities inferor to those of 
 the alloy containing 2.5% of lead, but superior to those of pure brass. 
 
 Cu, 60; Zn, 40. Perfectly homogeneous. Rolls easily at a cherry 
 red heat, and cracks but slightly in cold rolling. Chips long and tena- 
 cious, necessitating a slow speed in cutting. 
 
 Tensile tests of these alloys gave the following results: 
 
 Copper, % 
 
 60.0 
 
 60.0 
 
 60.0 
 
 60.0 
 
 Zinc, % 
 
 40 
 
 37.5 
 
 35.0 
 
 30.0 
 
 Lead, % r..;. 
 
 None. 
 
 2.5 
 
 5.0 
 
 10.0 
 
 
 C 
 
 A 
 
 H 
 
 C 
 
 A 
 
 H 
 
 C 
 
 A 
 
 H 
 
 C 
 
 A 
 
 H 
 
 T.S. per sq. in.* 
 Elong. in 1 in., %. . . . 
 
 16 
 48 
 
 60 
 51 
 
 107 
 
 39 
 28 
 
 51 
 27 
 
 88 
 
 
 33 
 
 28 
 
 42 
 
 26 
 
 61 
 1 
 
 36 
 36 
 
 35 
 20 
 
 63 
 2 
 
 Elong. in 8 in., % 
 
 27 
 
 33 
 
 
 
 27 
 
 23 
 
 
 
 27 
 
 22 
 
 
 
 30 
 
 16 
 
 3 
 
 Red. of area, % 
 
 61 
 
 44 
 
 13 
 
 30 
 
 33 
 
 
 
 26 
 
 33 
 
 
 
 29 
 
 25 
 
 4 
 
 P.R 
 
 92% 
 
 65% 
 
 61% 
 
 38% 
 
 * Thousands of pounds. C, casting; A, annealed sheet; 
 rolled sheet; P. R., possible reduction in rolling. 
 
 H, hard 
 
 The use of tin, even in small amounts, hardens and increases the ten- 
 sile strength of brass, which is detrimental to free turning. Mr. Sperry 
 gives analyses of several brasses which have given excellent results in 
 turning, all included within the following range: Cu, 60 to 66%, Zn, 38 
 to 32%, Pb, 1.5 to 2.5%. For cartridge-brass sheet, anything over 
 0.10% of lead increases the liability of cracking in drawing. 
 
 PHOSPHOR-BRONZE AND OTHER SPECIAL BRONZES. 
 
 Phosphor-bronze. In the year 1868, Montefiore & Kunzel of Liege. 
 Belgium, found by adding small proportions of phosphorus or "phos- 
 phoret of tin or copper" to copper that the oxides of that metal, nearly 
 always present as an impurity, more or less, were deoxidized and the 
 copper much improved in strength and ductility, the grain of the frac- 
 ture became finer, the color brighter, and a greater fluidity was attained. 
 
ALLOYS FOB CASTING UNDER PRESSURE. 
 
 395 
 
 Three samples of phosphor-bronze, tested by Kirkaldy, gave 
 
 Elastic limit, Ibs. per sq. in 23,800 24,700 16,100 
 
 Tensile strength, IDS. per sq. in. . 
 Elongation, per cent 
 
 52,625 
 8.40 
 
 46,100 
 1.50 
 
 44,448 
 33.40 
 
 The strength of phosphor-bronze varies like that of ordinary bronze 
 according to the percentages of copper, tin, zinc, lead, etc., in the alloy. 
 
 Phosphor-bronze Rod. Torsion tests of 20 samples, 1/4 m. diam. 
 Apparent outside fiber stress, 77,500 to 86,700 Ibs. per sq. in.; average 
 number of turns per inch of length, 0.76 to 1.50. Tech. Quar., vol. xh, 
 Sept., 1899. 
 
 Penn. R. R. Co.'s Specifications for Phosphor-bronze (1902). 
 The metal desired is a homogeneous alloy of copper, 79.70; tin, 10.00; 
 lead, 9.50- phosphorus, 0.80. Lots will not be accepted if samples do 
 not show tin, between 9 and 11%; lead, between 8 and 11%; phos- 
 phorus, between 0.7 and 1%; nor if the metal contains a sum total of 
 other substances than copper, tin, lead, and phosphorus in greater quan- 
 tity than 0.50 per cent. (See also p. 406.) 
 
 Deoxidized Bronze. This alloy resembles phosphor bronze spme- 
 what in composition and also delta metal, in containing zinc and iron. 
 The following analysis gives its average composition: Cu, 82.67; Sn, 12.40; 
 Zn, 3.23; Pb, 2.14; Fe, 0.10; Ag, 0.07; P, 0.005. 
 
 Comparison of Copper, Silicon-bronze, and Phosphor-bronze 
 Wires. (Engineering, Nov. 23, 1883.) 
 
 Description of Wire. 
 
 Tensile Strength. 
 
 Relative Conductivity. 
 
 Pure copper . 
 
 39,827 Ibs. per sq. in. 
 41,6% " 
 108,080 " " " " 
 
 100 per cent. 
 96 " 
 34 " - 
 26 " " 
 
 Silicon bronze (telegraph) 
 (telephone) 
 Phosphor bronze (telephone) . . 
 
 
 Silicon Bronze. (Aluminum World, May, 1897.) 
 
 The most useful of the silicon bronzes are the 3% (97% copper, 3% 
 silicon) and the 5% (95% copper, 5% silicon), although the hardness 
 and strength of the alloy can be increased or decreased at will by 
 increasing or decreasing silicon. A 3% silicon bronze has a tensile 
 strength, in a casting, of about 55,000 Ibs. per sq. in., and from 50% to 
 60% elongation. The 5% bronze has a tensile strength of about 75,000 
 Ibs. and about 8% elongation. More than 5% or 51/2% of silicon in cop- 
 per makes a brittle alloy. In using silicon, either as a flux or for making 
 silicon bronze, the rich alloy of silicon and copper which is now on the 
 market should be used. It should be free from iron and other metals if 
 the best results are to be obtained. Ferro-silicon is not suitable for use 
 in copper or bronze mixtures. 
 
 Copper and Vanadium Alloys. The Vanadium Sales Co. of America 
 reports (1908) that the addition of vanadium to copper has given a tensile 
 strength of 83,000 Ibs. per sq. in.; with an elongation of over 60%. 
 
 ALLOYS FOR CASTING UNDER PRESSURE IN METAL 
 MOLDS. E. L. Lake, Am. Mach., Feb. 13, 1908. 
 
 No. 
 
 Tin. 
 
 Copper. 
 
 Alumi- 
 num. 
 
 Zinc. 
 
 Lead. 
 
 Anti- 
 mony. 
 
 Iron 
 
 j 
 
 14.75 
 
 5.25 
 
 6.25 
 
 73.75 
 
 
 
 
 2 
 3 
 
 19 
 12 
 
 5 
 10.6 
 
 1. 
 3.4 
 
 72.7 - 
 73.8 
 
 2 
 
 0.3 
 
 6!i" 
 
 4 
 
 30.8 
 
 20.4 
 
 2.6 
 
 46.2 
 
 
 
 
 
 
 
 
 
 
 
 
 Nos. 1 and 2 suitable for ordinary work, such as could be performed by 
 average brass castings. No. 3 and 4 are harder. 
 
396 
 
 ALLOYS. 
 
 ALUMINUM ALLOTS. 
 
 The useful alloys of aluminum so far found have been chiefly In two 
 groups, the one of aluminum with not more than 35% of other metals, and 
 the other of metals containing not over 15% of aluminum; in the one case 
 the metals impart hardness and other useful qualities to the aluminum, 
 and in the other the aluminum gives useful qualities to the metal with 
 which it is alloyed. 
 
 Aluminum-Copper Alloys. The useful aluminum-copper alloys can 
 be divided into two classes, the one containing less than 11% of 
 aluminum, and the other containing less than 15% of copper. The first 
 class is best known as Aluminum Bronze. 
 
 Aluminum Bronze. (Cowles Electric Smelting and Al. Co.'s circular.) 
 The standard A No. 2 grade of aluminum bronze, containing 10% of 
 aluminum and 90% of copper, has many remarkable characteristics 
 which distinguish it from all other metals. 
 
 The tenacity of castings of A No. 2 grade metal varies between 75,000 
 and 90,000 Ibs. to the square inch, with from 4 % to 14 % elongation. 
 
 Increasing the proportion of aluminum in bronze beyond 11% pro- 
 duces a brittle alloy; therefore nothing higher than the A No. 1, which 
 contains 11%, is made. 
 
 The B, C, D, and E grades, containing 7 H%, 5%, 2 H%, and 1 1 A% 
 of aluminum, respectively, decrease in tenacity in the order named, that 
 of the former being about 65,000 pounds, while the latter is 25,000 
 pounds. While there is also a proportionate decrease in transverse and 
 torsional strengths, elastic limit, and resistance to compression as the 
 percentage of aluminum is lowered and that of copper raised, the ductil- 
 ity, on the other hand, increases in the same proportion. The specific 
 gravity of the A No. 1 grade is 7.56. 
 
 Bell Bros., Newcastle, gave the specific gravity of the aluminum 
 bronzes as follows: 
 
 3%, 8.691; 4%, 8.621; 5%, 8.369; 10%, 7.689. 
 
 In manufacturing aluminum bronze, only the purest metals should 
 be used. The copper should be melted over a gas or oil fire in a plum- 
 bago crucible, being covered with charcoal to prevent oxidation and 
 the absorption of gases. If a coal fire is used, the copper will absorb 
 gases from the coal and produce an unsatisfactory alloy. The alumi- 
 num is dropped through the charcoal into the molten copper. The alu- 
 minum combines with the copper as soon as its melting point is reached, 
 setting free latent heat and raising the temperature of the mass. The 
 copper becomes brighter and more liquid when the union takes place, 
 and the crucible then should be instantly removed from the fire, 
 skimmed, and poured into ingot molds of convenient size. The liquid 
 should be stirred until poured. The alloy may then be remelted for 
 casting. Each remelting improves the quality of the aluminum bronze 
 up to about four remeltings. (Aluminum Co. of America, 1909.) 
 
 Tests of Aluminum Bronzes. 
 
 (John H. J. Dagger, British Association, 1889.) 
 
 Per cent 
 of 
 Aluminum. 
 
 Tensile Strength. 
 
 Elonga- 
 tion, 
 per cent. 
 
 Specific- 
 Gravity. 
 
 Tons per 
 square inch. 
 
 Pounds per 
 square inch. 
 
 11... 
 
 40 to 45 
 33 " 40 
 25 " 30 
 15 " 18 
 13 15 
 11 " 13 
 
 89,600 to 100,800 
 73,920 " 89,600 
 56,000 " 67,200 
 33,600 " 40,320 
 29,120 " 33,600 
 24,640 " 29,120 
 
 8 
 14 
 40 
 40 
 50 
 55 
 
 7.23 
 7.69 
 6.00 
 8.37 
 8.69 
 
 10.. 
 
 71/2 
 
 5-&/ 2 : ...... 
 
 21/2 
 
 11/4 
 
 Casting. The melting point of aluminum bronze varies slightly with 
 the amount of aluminum contained, the higher grades melting at a 
 lower temperature than the lower grades. The A No. 1 grades melt 
 at about 1700 F M a little higher than ordinary bronze or brass. 
 
ALUMINUM ALLOYS. 
 
 397 
 
 Aluminum bronze shrinks more than ordinary brass. As the metal 
 solidifies rapidly it is necessary to pour it quickly and to make the 
 feeders amply large, so that there will be no "freezing" in them before 
 the casting is properly fed. Baked-sand molds are preferable to green 
 sand, except for small castings, and when fine skin colors are desired in 
 the castings. (Thos. D. West, Trans. A. S. M. E., 1886, vol. viii.) 
 
 All grades of aluminum bronze can be rolled, s wedged, spun, or drawn 
 cold except A 1 and A 2. They can all be worked at a bright red heat. 
 
 In rolling, swedging, or spinning cold, it should be annealed very often 
 and at a brighter red heat than is used for annealing brass. 
 
 Seamless Tubes. Leonard Waldo, Trans. A. S. M. E., vol. xviii, 
 describes the manufacture of aluminum bronze seamless tubing. Many 
 difficulties were met in all stages of the process. A cold drawn bar, 1.49 
 in. outside diameter, 0.05 in. thick, showed a yield point of 68.700, and 
 a tensile strength of 96,000 Ib. per sq. in. with an elongation of 4.9% in 
 10 in. ; heated to bright red and plunged in water, the yield point re- 
 duced to 24,200 and the T. S. to 47,600 Ib. per sq. in., and the elonga- 
 tion in 10 in. increased to 64.9%. 
 
 Brazing. Aluminum bronze will braze as well as any other metal, 
 using one-quarter brass solder (zinc 500, copper 500) and three-quarters 
 borax, or, better, three-quarters cryolite. 
 
 Soldering. Aluminum bronze can be soldered by using a solder of 
 pure block tin .with a flux of zinc filings and muriatic acid. It is advis- 
 able to "tin" the two surfaces before putting them together. 
 
 Aluminum Brass. (E. H. Cowles, Trans. A. I. M. E., vol. xviii.) 
 Cowles aluminum brass is made by fusing together equal weights of A 1 
 aluminum bronze, copper, and zinc. The copper and bronze are first 
 thoroughly melted and mixed, and the zinc is finally added. The 
 material is left in the furnace until small test-bars are taken from it and 
 broken. When these bars show a tensile strength of 80,000 pounds or 
 over, with 2 or 3 per cent ductility, the metal is ready to be poured. 
 Tests of this brass, on small bars, have at times shown as high as 
 100,000 pounds tensile strength. 
 
 The Aluminum Co. of America says (1909) that aluminum brass has 
 an elastic limit of about 30,000 Ib. per sq. in., an ultimate strength of 
 40,000 to 50,000 Ib. per sq. in., and an elongation of 3% to 10% in 8 in. 
 Aluminum brass is used with aluminum ranging from 0.1% to 10%. 
 The best results are obtained by introducing the aluminum in the form 
 of aluminized zinc, a 5 % aluminized zinc being used where less than 1 % 
 of aluminum is required and a 10 % aluminized zinc for aluminum per- 
 centages of over 1 %. The effect of aluminum in brass in quantities of 
 less than 1 % is to make the brass flow freely and to insure a sounder 
 casting, and it enables from one-half to one-third more castings to be 
 made on a gate than is possible where aluminum is not used. In quan- 
 tities over 1 % up to 10% the aluminum increases the strength of brass, 
 enabling a cheaper grade of brass to be used v than wo*uld otherwise be 
 possible. Inasmuch as aluminum lowers the melting point of brass, 
 great care must be taken not to overheat it in melting. 
 
 Tests of Aluminum Brass. 
 
 (Cowles E. S. & Al. Co.) 
 
 Specimen (Castings) 
 
 Diameter 
 of Piece, 
 Inch. 
 
 Area 
 sq. in. 
 
 Tensile 
 Strength, 
 Ibs. per 
 sq. in. 
 
 Elastic 
 Limit, 
 Ibs. per 
 sq. in. 
 
 Elonga- 
 tion, 
 per et. 
 
 Remarks. 
 
 15%AgradeBronze ) 
 
 
 
 
 
 
 M g 
 
 1 7% Zinc [ 
 
 0.465 
 
 0.1698 
 
 41,225 
 
 1 7,668 
 
 41 1/2 
 
 S'S $ M 
 
 68% Copper. ) 
 
 
 
 
 
 
 2Jvo & 
 
 part A Bronze . . ) 
 
 
 
 
 
 
 p-3 $ 
 
 part Zinc > 
 part Copper ) 
 
 0.465 
 
 0.1698 
 
 78,327 
 
 
 2V2 
 
 I" 1 
 
 part A Bronze. . ) 
 part Zinc [ 
 
 0.460 
 
 0.1661 
 
 72,246 
 
 
 2i/ 2 
 
 111! 
 
 part Copper ) 
 
 
 
 
 
 
 H 
 
 
 The first brass on the above list is an extremely tough metal with low 
 
398 
 
 ALLOYS. 
 
 elastic limit, made purposely so as to "upset" easily. The other, which 
 is called Aluminum brass No. 2, is very hard. 
 
 Caution as to Reported Strength of Alloys. The same variation in 
 strength which has been found in tests of gun-metal (copper and 
 tin) noted above, must be expected in tests of aluminum bronze and in 
 fact, of all alloys. They are exceedingly subject to variation in density 
 and in grain, caused by differences hi method of molding and casting 
 temperature of pouring, size of and shape casting, depth of "sinking 
 head," etc. Chill-castings give higher results than sand-castings, and 
 bars cast by themselves purposely for testing almost invariably run 
 higher than test bars attached to castings. Bars cut out from castings 
 are generally weaker than bars cast alone. 
 
 Effect of Copper on Aluminum. Tests of rolled sheets of aluminum, 
 0.04 in. thick, with" varying percentages of copper are reported in The 
 Engineer, Jan. 2, 1891, as follows: 
 
 Aluminum, per cent. ........ 100 98 96 94 92 
 
 Copper, per cent 2 4 6 8 
 
 Specific gravity, calculated 2.78 2.90 3.02 314 
 
 Specific gravity, determined.. 2.67 2.71 2.77 2.82 2.85 
 
 Tensile strength, Ib. per sq.in. 25,535 43,563 44,130 54,773 50,374 
 
 Tests of Aluminum Alloys. 
 
 (Engineer Harris, U. S. N., Trans. A. I. M. E., vol. xviii.) 
 
 Composition. 
 
 Tensile 
 Strength 
 per sq. 
 in., Ib. 
 
 Elastic 
 Limit, 
 Ib. per 
 sq. in. 
 
 Elonga- 
 tion, 
 per ct. 
 
 Reduc- 
 tion of 
 Area, 
 per ct. 
 
 Copper. 
 
 Alumi- 
 num. 
 
 Silicon. 
 
 Zinc. 
 
 Iron. 
 
 91.50% 
 88.50 
 91.50 
 90.00 
 63.00 
 63.00 
 91.50 
 93.00 
 88.50 
 92.00 
 
 6.50% 
 9.33 
 6.50 
 9.00 
 3.33 
 3.33 
 6.50 
 6.50 
 9.33 
 6.50 
 
 \: 7 d % 
 
 1.75 
 1.00 
 0.33 
 0.33 
 1.75 
 0.50 
 1 .66 
 0.50 
 
 
 0.25% 
 0.50 
 0.25 
 
 60,700 
 66,000 
 67,600 
 72,830 
 82,200 
 70,400 
 59,100 
 53,000 
 69,930 
 46,530 
 
 18,000 
 27,000 
 24,000 
 33,000 
 60,000 
 55,000 
 19,000 
 19,000 
 33,000 
 1 7,000 
 
 23.2 
 3.8 
 13 
 2.40 
 2.33 
 0.4 
 15.1 
 6.2 
 1 .33 
 7.8 
 
 30.7 
 7.8 
 21.62 
 5.78 
 9.88 
 4.33 
 23.59 
 15.5 
 3.30 
 19.19 
 
 
 
 33.'33% 
 33.33 
 
 0.25 
 
 
 0.50 
 
 For comparison with the above 6 tests of "Navy Yard Bronze," 
 Cu 88, Sn 10, Zn 2, are given in which the T. S. ranges from 18,000 to 
 24,590, E. L. from 10,000 to 13,000, El. 2.5 to 5.8%, Red. 4.7 to 10.89. 
 
 Alloys of Aluminum, Silicon and Iron. 
 
 M. and E. Bernard have succeeded in obtaining through electrolysis, 
 by treating directly and without previous purification, the aluminum 
 earths (red and white bauxites), the following: 
 
 Alloys such as ferro-aluminum, ferro-silicon-aluminum, and silicon- 
 aluminum, where the proportion of silicon may exceed 10%, which are 
 employed in the metallurgy of iron for refining steel and cast-iron. 
 
 Also silicon-aluminum, where the proportion of silicon does not exceed 
 10%, which may % be employed in mechanical constructions in a rolled or 
 hammered condition, in place of steel, on account of their great resist- 
 ance, especially where the lightness of the piece in construction consti- 
 tutes one of the main conditions of success. 
 
 The following analyses are given: 
 
 1. Alloys applied to the metallurgy of iron, the refining of steel and 
 cast iron: No. 1, Al, 70%; Fe, 25%; Si, 5%. No. 2, Al, 70; Fe, 20; 
 Si, 10. No. 3, Al, 70; Fe, 15; Si, 15. No. 4, Al. 70; Fe, 10; Si, 20. 
 No. 5, Al, 70; Fe, 10; Si, 10; Mn, 10. No. 6, Al. 70; Fe, trace; Si, 20; 
 Mn, 10. 
 
 2. Mechanical alloys: No. 1, Al, 92; Si, 6.75; Fe, 1.25. No. 2, Al, 
 90; Si, 9.25; Fe, 0.75. No. 3, Al, 90; Si, 10; Fe, trace. The best results 
 were with alloys where the proportion of iron was very low, and the 
 proportion of silicon in the neighborhood of 10%. Above that pro- 
 portion the alloy becomes crystalline and can no longer be employed. 
 
ALUMINUM ALLOYS. 399 
 
 The density of the alloys of silicon is approximately the same as that of 
 aluminum. La Metallurgie, 1392. 
 
 Aluminum -Tungsten Alloys have been somewhat used in Europe 
 in the form of rolled sheets under the trade name of Wolfranium. An 
 aluminum-tungsten alloy used in France (1898) for motor-car bodies 
 has the following properties: Cast, sp. gr. 2.86; T.S., 17,000 to 24,000; 
 elong., 12 to 6%. Rolled, sp. gr., 3.09; T.S., 45,500 to 53,600; elong., 
 8 to 6%. 
 
 Aluminum-Antimony alloys have been produced, but have a scien- 
 tific rather than a commercial interest. The alloy whose composition 
 is Sb Al has a higher melting point than either of its constituents. 
 
 Aluminum and Manganese. Manganese is one of the best harden- 
 ers of aluminum. Professor Carpenter found that it increased the 
 strength when added in quantities up to 10%. 
 
 Undesirable Aluminum Alloys. While aluminum will combine 
 with all the metalloids and gaseous elements, such as oxygen, nitrogen, 
 sulphur, selenium, chlorine, iodine, boron, silicon, and carbon, no useful 
 result has been recorded from the combination of metallic aluminum 
 with any of these elements. The prevention of the occlusion of gaseous 
 metalloids in molten aluminum and the prevention of the union of car- 
 bon and aluminum are among the chief precautions to be observed in 
 the metallurgy of aluminum. The effect of sodium and potassium on 
 aluminum is as undesirable as the effect of phosphorus and sulphur on 
 steel. (Aluminum Co. of America.) 
 
 Aluminum-Magnesium. Magnalium. A patented alloy of alumi- 
 num and magnesium, containing 90 to 98% Al has the trade name 
 "magnalium." It is lighter than aluminum (sp. gr. 2.5), and is whiter, 
 harder, and stronger. It can be forged, rolled, drawn, machined, and 
 filed. It resists oxidation better than other light metals or alloys. 
 Tensile strength: cast, 18,400 to 21,300 Ib. per sq. in., with a reduction 
 of area-3.75%; rolled, 52,200 Ib. per sq. in., with a reduction of area 
 of 3.7%; annealed, 42,200 Ib. per sq. in., reduction, 17.8%. Al Mg 
 alloys are said by the Aluminum Co. of America to be as strong as Al 
 Cu alloys. 
 
 Aluminum and Iron. Aluminum alloys with cast-iron up to 15% 
 Al, but the metal decreases in strength as the Al increases. Above 15 % 
 Al the alloys are granular and have practically no coherence. (Trans. 
 A. I. M. E., vol. xviii, A. S. M. E., vol. xix.) It is doubtful if aluminum 
 has much effect on soft gray No. 1 foundry iron, except to keep the 
 metal molten a longer time. With difficult castings, where loss is 
 occasioned by defective castings or where the iron does not flow freely, 
 the addition of aluminum will improve the quality of the casting, and 
 give a closer grained iron. The addition of 2% or more of Al will de- 
 crease the shrinkag'e of cast iron. In wrought iron,.l% Al makes the 
 metal more fluid at 2200 F. than it would be at 3500 F. without Al. 
 An addition of 0.25% Al to the bath causes the charge to stiffen more 
 quickly. (Aluminum Co. of America, 1909.) 
 
 Aluminum, Copper, and Tin. Prof. R. C. Carpenter, Trans. 
 A. S. M. E., vol. xix., finds the following alloys of maximum strength in 
 a series in which two of the three metals are in equal proportions: 
 
 Al, 85; Cu, 7.5; Sn, 7.5; tensile strength, 30,000 Ib. per sq. in.; 
 elongation in 6 in., 4%; sp. gr., 3.02. Al, 6.25; Cu, 87.5; Sn, 6.25; 
 T. S., 63,000; EL, 3.8; sp. gr., 7.35. Al, 5; Cu, 5; Sn, 90; T. S:, 11,000; 
 EL, 10.1; sp. gr., 6.82. 
 
 From 85 to 95% Cu the bars have considerable strength, are close 
 grained and of a golden color. Between 78 and 80 % the color changes 
 to silver white and the bars become brittle. From 78 to 20% Cu the 
 alloys are very hard and brittle, and worthless for practical purposes. 
 Aluminum is strengthened by the addition of equal parts of copper and 
 tin up to 7.5% of each, beyond which the strength decreases. All the 
 alloys that contain between 20 and 60 % of either one of the three metals 
 are very weak. 
 
 Aluminum and Zinc. (Aluminum Co. of America, 1909.) Like the 
 copper alloys, the zinc alloys can be divided into two classes, (1) those 
 containing a relatively small amount of aluminum, and (2) those con- 
 taining less than 35 % of zinc. The first class is known as " aluminized 
 zinc," and the second comprises the zinc casting alloys. Zinc produces 
 tl e g-trongest alloy of aluminum, which strength can be increased by the 
 
400 
 
 ALLOYS. 
 
 addition of other metals. The strongest zinc-aluminum alloy may be 
 as nigh as 35,000 Ib. per sq. in. The high zinc alloys are brittle and 
 more liable to "draw" in heavy parts or lugs than are copper alloys. 
 This can often be overcome by suitable gating, chills, and risers. There 
 is also danger of burning out the zinc and producing a weaker casting. 
 For forging, a zinc-aluminum alloy of 10 to 15% zinc gives excellent 
 results. It is tough, flows well in the dies, is easily machined and is 
 remarkably strong per unit of area. 
 
 Aluminized zinc is used in the bath for galvanizing and in aluminum 
 brass. It is made by melting aluminum in the crucible and then grad- 
 ually stirring in the zinc, after which it is cast into ingots. The 5% 
 alloy is used in the galvanizing bath and for low grade aluminum 
 brass, and the 10 % alloy for lu'gh-grade brass castings. It is introduced 
 in the molten metal the same as pure zinc. In galvanizing it is added 
 in such proportions that the total amount of aluminum in the bath 
 will be about 1 Ib. of aluminum per ton of bath, or about 20 Ib. of 5% 
 alloy per ton of bath. It should be added gradually, and as the bath is 
 consumed fresh 5 % alloy should be added about 1 Ib. at a time for a 
 5- ton bath. When aluminized zinc is used it is unnecessary to use 
 sal ammoniac to clear the bath of oxide. In starting a new bath, how- 
 ever, after adding the aluminized zinc, it is stirred well until the alumi- 
 num combines with the impurities, which rise to the surface as a scum. 
 This is removed, some sal ammoniac is added to counteract the effects 
 of the aluminum, and the proportion of alloy added is reduced. 
 
 Aluminum and Tin. (Aluminum Co. of America, 1909.) Tin, al- 
 loyed with aluminum in proportions of from 1 to 15%, gives added 
 strength and rigidity to heavy castings, increases the sharpness of 
 outline and decreases shrinkage. The aluminum-tin alloys are rather 
 brittle, and although small proportions of tin in certain casting alloys 
 have been advantageously used to decrease shrinkage, they are com- 
 paratively little used on account of the relative cost and brittleness. 
 
 Aluminum and Nickel. (Aluminum Co. of America, 1909.) Al- 
 uminum-nickel alloys with 2 to 5 % of the combined alloying metals are 
 satisfactory for rolling or hammering. A 7 to 9 % alloy produces good 
 results in casting. 
 
 Other Aluminum Alloys. Al 75.7, Cu. 3, Zn 20, Mn 1.3 is an 
 excellent casting metal, having a tensile strength of over 35,000 Ib. 
 per sq. in., and a sp. gr. slightly above 3. It has very little ductility 
 
 Al 96.5, Cu 2, and chromium 1.5 is a little heavier than pure alumi- 
 num and has a tensile strength of 26,300 Ib. per sq. in. A. S. M. E. t 
 vol. xix. 
 
 With the exception of lead and mercury, aluminum unites with all 
 metals, though it unites with antimony with great difficulty. A small 
 percentage of silver whitens and hardens the metal, and gives it added 
 strength; and this alloy is especially applicable to the manufacture of 
 fine instruments and apparatus. The following alloys have been found 
 recently to be useful in the arts: Nickel-aluminum, composed of 20 parts 
 nickel to 80 of aluminum; rosine, made of 40 parts nickel, 10 parts silver, 
 30 parts aluminum, and 20 parts tin, for jewellers' work; mettaline, made 
 of 35 parts cobalt, 25 parts aluminum, 10 parts iron, and 30 parts copper. 
 The aluminum-bourbouze metal, shown at the Paris Exposition of 1889, 
 has a specific gravity of 2.9 to 2.96, and can be cast in very solid shapes, 
 as it has very little shrinkage. From analysis the following composi- 
 tion is deduced: Aluminum, 85.74%; tin, 12.94%; silicon, 1.32%; iron, 
 none. 
 
 Aluminum Alloys used in Automobile Construction (Am. Mach., 
 Aug. 22, 1907.) 
 
 (1) Al 2, Zn, 1, T.S. 35,000; Sp. gr. 3.1 
 
 (2) Al 92, Cu, 8, T.S. 18,000; Sp. gr. 2.84 Ni, trace 
 
 (3) Al 83, Zn, 15, Cu, 2, T.S. 23,000; Sp. gr. 3.1 
 
 (1) Unsatisfactory on account of failures under repeated vibration. 
 (2) Generally used. Resists vibrations well. (3) Used to some extent. 
 Many motor-car makers decline to use it because of uncertainty of its 
 behavior under vibration. 
 
 The Thermit Process. When finely divided aluminum is mixed 
 with a metallic oxide and ignited the aluminum burns with great rapid- 
 ity and intense heat, the chemical reaction being Al + Fe2Oa = A^Os 
 
ALLOYS OP MANGANESE AND COPPER. 
 
 401 
 
 + Fe. The heat thus generated may be used to fuse or weld iron and 
 other metals. See the Thermit Process, under Welding of Steel, page 
 488. 
 
 Resistance of Aluminum Alloys to Corrosion. J. W. Richards, 
 Jour. Frank. Inst., 1895, gives the following table showing the relative 
 resistance to corrosion of aluminum (99 % pure) and alloys of aluminum 
 with different metals, when immersed in the liquids named. The 
 figures are losses per day in milligrams per square centimeter of surface: 
 
 
 3% 
 Caustic 
 Potash. 
 Cold. 
 
 3% 
 Hydro- 
 chloric 
 Acid. 
 Cold. 
 
 Strong 
 Nitric 
 Acid. 
 Cold. 
 
 Strong 
 Salt 
 Solu- 
 tion. 
 150F. 
 
 Strong 
 Acetic 
 Acid. 
 140 F. 
 
 Car- 
 bonic 
 Acid. 
 Water. 
 77 F. 
 
 3 per cent copper 
 
 265.0 
 
 53.3 
 
 36.1 
 
 0.1 
 
 0.4 
 
 0.0 
 
 3 per cent German silver . 
 3 per cent nickel 
 
 1534.4 
 580.3 
 
 130.6 
 180.0 
 
 97.7 
 83.0 
 
 0.05 
 0.13 
 
 0.6 
 0.75 
 
 0.01 
 0.04 
 
 2 per cent titanium . . . 
 
 73.4 
 
 4.3 
 
 18.6 
 
 06 
 
 20 
 
 0.0 
 
 99 per cent aluminum .... 
 
 35.6 
 
 5.8 
 
 9.6 
 
 0.04 
 
 0.15 
 
 0.01 
 
 ALLOYS OF MANGANESE AND COPPER. 
 
 Various Manganese Alloys. E. H. Cowles, in Trans. A. I. M. E., 
 vol. xviii, p. 495, states that as the result of numerous experiments on 
 mixtures of the several metals, copper, zinc, tin, lead, aluminum, iron, 
 and manganese, and the metalloid silicon, and experiments upon th 
 same in ascertaining tensile strength, ductility, color, etc., the most 
 important determinations appear to be about as follows: 
 
 1. That pure metallic manganese exerts a bleaching effect upon cop- 
 per more radical in its action even than nickel. In other words, it was 
 found that 18 H % of manganese present in copper produces as white a 
 color in the resulting alloy as 25% of nickel would do, this being the 
 amount of each required to remove the last trace of red. 
 
 2. That upwards of 20 % or 25 % of manganese may be added to cop- 
 per without reducing its ductility, although doubling its tensile strength 
 and changing its color. 
 
 3. That manganese, copper, and zinc, when melted together and 
 poured into molds behave very much like the most "yeasty" German 
 silver, producing an ingot which is a mass of blow-holes, and which 
 swells up above the mold before cooling. 
 
 4. That the alloy of manganese and copper by itself is very easily 
 oxidized. 
 
 5. That the addition of 1.25% of aluminum to a manganese-copper 
 alloy converts it from one of the most refractory of metals in the casting 
 
 Erocess into a metal of superior casting qualities, and the non-corrodi- 
 ility of which is in many instances greater than that of either German 
 or nickel silver. 
 
 A "silver-bronze" alloy especially designed for rods, sheets, and wire 
 has the following composition: Mn, 18; Al, 1.20; Si, 0.5; Zn, 13; and Cu, 
 67.5%. It has a tensile strength of about 57,000 Ibs. on small bars, and 
 20% elongation. It has been rolled into thin plate and drawn into wire 
 0.008 inch in diameter. A test of the electrical conductivity of this 
 wire (of size No. 32) shows its resistance to be 41.44 times that of pure 
 copper. This is far lower conductivity than that of German silver. 
 
 Manganese Bronze. (F. L. Garrison, Jour. F. /., 1891.) This 
 alloy has been used extensively for casting propeller-blades. Tests of 
 some made by B. H. Cramp & Co., of Philadelphia, gave an average 
 elastic limit of 30,000 Ibs. per sq, in., tensile strength of about 60,000 Ibs. 
 per sq. in. with an elongation of 8% to 10% in sand castings. When 
 rolled, the E. L. is about 80,000 Ibs. per sq. in., tensile strength 95,000 to 
 106,000 Ibs. per sq. in., with an elongation of 12% to 15%. 
 
 Compression tests made at United States Na'vy Department from the 
 metal in the pouring-gate of propeller-hub of U. S. S. Maine gave in 
 two tests a crushing stress of 126,450 and 135,750 Ib. per sq. in. The 
 specimens were 1 inch high by 0.7 x 0.7 inch in cross-section = 0.49 
 square inch. Both specimens gave way by shearing, on a plane making 
 an angle of nearly 45 6 with the direction of stress. 
 
 A test on a specimen 1 X 1 X 1 inch was made from a piece of the 
 
402 
 
 ALLOYS. 
 
 same pouring-gate. " Under stress of 150,000 pounds it was "flattened to 
 0.72 inch high by about 11/4 x 11/4 inches, but without rupture or any 
 sign of distress. 
 
 One of the great objections to the use of manganese bronze, or in fact 
 any alloy except iron or steel, for the propellers of iron ships is on 
 account of the galvanic action set up between the propeller and the 
 stern-posts. This difficulty has in great measure been overcome by 
 putting strips of rolled zinc around the propeller apertures in the stern- 
 frames. 
 
 The following analysis of Parsons' manganese bronze No. 2 was made 
 from a chip from the propeller of Mr. W. K. Vanderbilt's yacht Alva. 
 Cu, 88.64; Zn, 1.57; Sn, 8.70; Fe, 0.72; Pb, 0.30; P, trace. 
 
 It will be observed there is no manganese present and the amount of 
 zinc is very small. 
 
 E. H. Cowles, Trans. A. I. M. E., vol. xviii, says: Manganese bronze, 
 so called, is in reality a manganese brass, for zinc instead of tin is the 
 chief element added to the C9pper. Mr. P. M. Parsons, the proprietor of 
 this brand of metal, has claimed for it a tensile strength of from 24 to 
 28 tons per sq. in. in small bars when cast in sand. 
 
 E. S. Sperry, Am. Mach., Feb. 1, 1906, gives the following analyses of 
 manganese bronze: 
 
 
 Cu. 
 
 Zn. 
 
 Fe. 
 
 Sn. 
 
 Al. 
 
 Mn. 
 
 Pb. 
 
 No. 1 . 
 
 60.27 
 
 37.52 
 
 1.41 
 
 0.75 
 
 
 0.01 
 
 0.01 
 
 " 2 
 
 56.11 
 
 41.34 
 
 1.30 
 
 0.75 
 
 0.47 
 
 0.01 
 
 0.02 
 
 3.::: 
 
 60.00 
 
 38.00 
 
 1.25 
 
 0.65 
 
 
 0.10 
 
 
 ' 4 
 
 56.00 
 
 42.38 
 
 1.25 
 
 0.75 
 
 6.50 
 
 0.12 
 
 
 No. 1 is Parsons' alloy for sheet, No. 2 for sand casting. No. 3 is Mr. 
 Sperry's formula for sheet, and No. 4 his formula for sand castings. 
 
 alloy is made by melting wrought iron, 18 Ibs.; ferro-manganese 
 (80 Fe, 20 Mn), 4 Ibs.; tin, 10 Ibs. The iron and ferro-manganese are 
 first melted and .then the tin is added. In making the bronzes about 
 15 Ibs. of the copper is first melted under charcoal, the steel alloy is 
 added, melted and stirred, then the aluminum is added, melted and 
 stirred, then the rest of the copper is added, and finally the zinc. The 
 only function of the manganese is to act as a carrier to the i?on, which 
 is difficult to alloy with copper without such carrier. The iron is 
 needed to give a high elastic limit. Green sand castings of No. 4 fre- 
 quently give results as high as the following: T. S., 70,000; E. L., 
 30,000 Ibs. per sq. in.; elongation in 6 ins., 18%; reduction of area, 
 26%. 
 
 Magnetic Alloys of Non-Magnetic Metals. (El. World, April 15, 
 1905; Electrot.-Zeit. Mar. 2, 1905.) Dr. Heusler has discovered that 
 alloys of manganese, aluminum, and copper are strongly magnetic. The 
 best results have been obtained when the Mn and Al are in the proportions 
 of their respective atomic weights, 55 and 27.1. Two such alloys are 
 described (1) Mn, 26.8; Al, 13.2; Cu, 60. (2) Mn, 20.1; Al, 9.9: Cu, 70, 
 with 1% Pb added. The first was too brittle to be workable. The 
 second was machined without difficulty. These alloys have as yet no 
 commercial importance, as they are far inferior magnetically (at most 
 1 to 4) to iron. 
 
 GERMAN-SILVER AND OTHER NICKEL ALLOYS. 
 
 German Silver. The composition of German silver is a very un- 
 certain thing and depends largely, on the honesty of the manufacturer 
 and the price the purchaser is willing to pay. It is composed of copper, 
 zinc, and nickel in varying proportions. The best varieties contain 
 from 18% to 25% of nickel and from 20% to 30% of zinc, the remainder 
 being copper. The more expensive nickel silver contains from 25% to 
 33% of nickel and from 75% to 66% of copper. The nickel is used as a 
 whitening element; it also strengthens the alloy and renders it harder 
 and more non-corrodible than the brass made without it, of copper and 
 
ALLOYS OF NICKEL. 
 
 403 
 
 zinc. Of all troublesome alloys to handle in the foundry or rolling-mill, 
 German silver is the worst. It is unmanageable and refractory at every 
 step in its transition from the crude elements into rods, sheets, or wire. 
 (E. H. Cowles, Trans. A. I. M. E., xviii, p. 494.) 
 The following list of copper-nickel alloys is from various sources: 
 
 | Copper. | Nickel. | Tin. | Zinc. 
 
 German silver 
 
 51 6 
 
 25 8 
 
 22.6 
 
 
 
 50.2 
 
 14.8 
 
 3.1 
 
 31.9 
 
 it 
 
 51 1 
 
 13 8 
 
 3.2 
 
 31.9 
 
 it it 
 
 52 to 55 
 
 18 to 25 
 
 
 20 to 30 
 
 Nickel " 
 
 75 to 66 
 
 25 to 33 
 
 
 
 Chinese packfong 
 
 40 4 
 
 31 6 
 
 
 6 5 parts 
 
 tutenag 
 
 8 
 
 3 
 
 
 6.5 " 
 
 German silver 
 
 2 
 
 1 
 
 
 1 
 
 " (cheaper) 
 
 8 
 8 
 
 2 
 3 
 
 
 3.5 " 
 3.5 " 
 
 Nickel-copper Alloys. (F. L. Sperry, A. I. M. E., 1895.) 
 
 Copper. | Nickel. | Zinc. ] Iron. | Cobalt. 
 
 Berlin : 
 
 52 to 63 
 
 22 to 6 
 
 26 to 31 
 
 
 
 French, tableware 
 
 50 
 
 18. 7 to 20 
 
 31.3 to 30 
 
 
 
 
 65.4 
 
 16.8 
 
 13.4 
 
 3.4 
 
 
 Christofle 
 
 50 
 
 50 
 
 
 
 
 Austrian, tableware 
 
 50 to 60 
 
 25 to 20 
 
 25 to 20 
 
 
 
 English, Sheffield 
 
 45.7 to 60 
 
 31 6 to 15 
 
 25.4 to 17 
 
 to 2 6 
 
 to 3 4 
 
 American, castings 
 
 52.5 
 
 17.7 
 
 28 8 
 
 
 
 bearings 
 
 50 
 
 25 
 
 25 
 
 
 
 " one-cent coin 
 
 88 
 
 12 
 
 
 
 
 Nickel coins 
 
 75 
 
 25 
 
 
 
 
 A refined copper-nickel alloy containing 50% copper and 49% nickel, 
 with very small amounts of iron, silicon and carbon, is produced direct 
 from Bessemer matte in the Sudbury (Canada) Nickel Works. German- 
 silver manufacturers purchase a ready-made alloy, which melts at a 
 low heat and requires only the addition of zinc, instead of buying the 
 nickel and copper separately. This alloy, "50-50" as it is called, is 
 almost indistinguishable from pure nickel. Its cost is less than nickel, 
 its melting-point much lower, it can be cast solid in any form desired, 
 and furnishes a casting which works easily in the lathe or planer, yield- 
 ing a silvery- white surface unchanged by air or moisture. For bullet 
 casings now used in various British and Continental rifles, a special alloy 
 of 80% copper and 20% nickel is made. 
 
 Monel Metal. An alloy of about 72% Ni, 1.5 Fe, 26.5 Cu, made from 
 the Canadian copper-nickel ores, is described in the Metal Worker, Oct. 10, 
 1908. It has many valuable properties when rolled into sheets, making 
 it especially suitable for rooting. It is ductile and flexible, is easily 
 soldered, has a high resistance to corrosion, and a relatively small expan- 
 sion and contraction under temperature changes. The tensile strength 
 in castings is from 70,000 to 80,000 Ibs. per sq. in., and in rolled sheets as 
 high as 108,000 Ibs. 
 
 The Supplee-Biddle Hardware Co.'s Bulletin, Jan., 1915, gives the 
 following results of tests of bars of monel metal. The test pieces were 
 0.505 in. diarn. 
 
 Tensile 
 Strength 
 
 Bar from 1 in. sq. casting 79,600 
 
 Hot rolled 1-in. rod 88,150 
 
 Elong. Red. o 
 
 in 2 in. Area 
 
 49.2% 39.3% 
 
 36.0 67.9 
 
 El. 
 
 Limit. 
 31,800 
 58,000 
 
 The strength of monel metal wire, used for window screen cloth, is 
 given as 90,000 Ib. per sq. in., and its analysis 68% Ni, 28% Cu., 2.5% 
 Fe, 1.5% Mn. 
 
 Constantan is an alloy containing about 60% copper and 40% nickel, 
 which is much used for resistance wire in electrical instruments. Its 
 electrical resistance is about twenty-eight to thirty times that of copper, 
 and it possesses a very low temperature coefficient, --^approximately 
 
404 
 
 ALLOYS. 
 
 .00003. This same material is also much used to form one element of 
 base-metal thermo-couples. 
 
 Manganin, Cu Mn Ni, high resistance alloy. See Electrical Resist- 
 ance under Electrical Engineering. 
 
 ALLOYS OF BISMUTH. 
 
 By adding a small amount of bismuth to lead the latter may be 
 hardened and toughened. An alloy consisting of three parts of lead 
 and two of bismuth has ten times the hardness and twenty times the 
 tenacity of lead. The alloys of bismuth with both tin and lead are 
 extremely fusible, and take fine impressions of casts and molds. An 
 alloy of one part Bi, two parts Sn, and one part Pb is used by pewter- 
 workers as a soft solder, and by soap-makers for molds. An alloy of five 
 parts Bi, two parts Sn, and three parts Pb imelts at 199 F., and is 
 S9mewhat used for stereotyping, and for metallic writing-pencils. Thorpe 
 gives the following proportions for the better-known fusible metals: 
 
 Name of Alloy. 
 
 Bis- 
 muth. 
 
 Lead. 
 
 Tin. 
 
 Cad- 
 mium. 
 
 Mer- 
 cury. 
 
 Melting- 
 point. 
 
 Newton's 
 
 50 
 
 31.25 
 
 18.75 
 
 
 
 202 F 
 
 Rose's 
 
 50 
 
 28.10 
 
 24 10 
 
 
 
 203 ' 
 
 D'Arcet's . . 
 
 50 
 
 25.00 
 
 25.00 
 
 
 
 201 ' 
 
 D' Arcet's with mercury 
 
 50 
 
 25.00 
 
 25.00 
 
 
 250.0 
 
 113 ' 
 
 Wood's 
 
 50 
 
 25 00 
 
 12 50 
 
 12 50 
 
 
 149 ' 
 
 Lipowitz's 
 
 50 
 
 26 90 
 
 12 78 
 
 10 40 
 
 
 149 ' 
 
 Guthrie's " Eutectic ". 
 
 50 
 
 20.55 
 
 21.10 
 
 14.03 
 
 
 "Very low.'* 
 
 The action of heat upon some of these alloys is remarkable. Thus, 
 Lipowitz's alloy, which solidifies at 149 F., cpntracts very rapidly at 
 first, as it cools from this point. As the cooling goes on the contrac- 
 tion becomes slower and slower, until the temperature falls to 101.3 
 F. From this point the alloy expands as it cools, until the temperature 
 falls to about 77 F., after which it again contracts, so that at 32 F. 
 a bar of the alloy has the same length as at 115 F. 
 
 Alloys of bismuth have been used for making fusible plugs for boilers, 
 but it is found that they are altered by the continued action of heat, 
 so that one cannot rely upon them to melt at the proper temperature. 
 Pure Banca tin is used by the U. S. Government for fusible plugs. 
 
 FUSIBLE ALLOYS. 
 
 (From various sources. Many of the figures are probably very 
 inaccurate.) 
 
 Sir Isaac Newton's, bismuth 5, lead 3, tin 2, melts at 212 F. 
 
 Rose's, bismuth 2, lead 1, tin 1, melts at 200 " 
 
 Wood's, cadmium 1, bismuth 4, lead 2, tin 1, melts at 165 '* 
 
 Guthrie's, cadmium 13.29, bismuth 47.38, lead 19.36, tin 19.97, 
 
 melts at 160 " 
 
 Lead 1, tin 1, bismuth 1, cadmium 1, melts at 155 '* 
 
 Lead 3, tin 5, bismuth 8, melts at 208 " 
 
 Lead 1, tin 3, bismuth 5, melts at 212 " 
 
 Lead 1, tin 4, bismuth 5, melts at 240 " 
 
 Tin 1, bismuth 1, melts at 286 " 
 
 Lead 2, tin 3, melts at 334 to 367 " 
 
 Tin 2, bismuth 1, melts at 336 " 
 
 Lead 1, tin 2, melts at 340 to 360 " 
 
 Tin 8, bismuth 1, melts at 392 " 
 
 Lead 2, tin 1, melts at 440 to 475 " 
 
 Lead 1, tin 1, melts at 370 to 400 " 
 
 Lead 1 , tin 3, melts at 356 to 383 " 
 
 Tin 3, bismuth 1, melts at 392 " 
 
 Lead 1, bismuth 1, melts at 257 " 
 
 Lead 1, tin 1, bismuth 4, melts at 201 " 
 
 Lead 5, tin 3, bismuth 8, melts at 202 " 
 
 Tin 3, Dismuth 5, melts at 202 M 
 
BEARING METAL ALLOYS. 
 
 405 
 
 BEARING-METAL ALLOYS. 
 
 (C. B. Dudley, Jour. F. /., Feb. and March, 1892.) 
 Alloys are used as bearings in place of wrought iron, cast Iron, or 
 steel, partly because wear and friction are believed to be more rapid 
 when two metals of the same kind work together, partly because the 
 soft metals are more easily worked and got into proper shape, and partly 
 because it is desirable to use a soft metal which will take the wear 
 rather than a hard metal, which will wear the journal more rapidly. 
 
 A good bearing-metal must have five characteristics: (1) It must be 
 strong enough to carry the load without distortion. Pressures on car- 
 journals are frequently as high as 350 to 400 Ib. per square inch. 
 
 (2) A good bearing-metal should not heat readily. The old copper- 
 tin bearing, made of seven parts copper to one part tin, is more apt to 
 heat than some other alloys. In general, research seems to show that 
 the harder the bearing-metal, the more likely it is to heat. 
 
 (3) Good bearing-metal should work well in the foundry. Oxidation 
 while melting causes spongy castings. It can be prevented by a liberal 
 use of powdered charcoal while melting. The addition of 1% to 2% of 
 zinc or a small amount of phosphorus greatly aids in the production of 
 sound castings. This is a principal element of value in phosphor- 
 bronze. 
 
 (4) Good bearing-metals should show small friction. It is true that 
 friction is almost wholly a question of the lubricant used ; but the metal 
 of the bearing has certainly some influence. 
 
 (5) Other things being equal, the best bearing-metal is that which 
 wears slowest. 
 
 The principal constituents of bearing-metal alloys are copper, tin, 
 lead, zinc, antimony, iron, and aluminum. The following table gives 
 the constituents of most of the prominent bearing-metals as analyzed at 
 the Pennsylvania Railroad laboratory at Altoona. 
 
 Analyses of Bearing- metal Alloys. 
 
 Metal. 
 
 Copper. 
 
 Tin. 
 
 Lead. 
 
 Zinc. 
 
 Anti- 
 mony. 
 
 Iron. 
 
 Camelia metal 
 
 70.20 
 1.60 
 
 4.25 
 98.13 
 
 14.75 
 
 10.20 
 
 
 0.55 
 trace 
 
 Anti-friction metal 
 
 
 White metal 
 
 87.92 
 84.87 
 1.15 
 67.73 
 80.69 
 
 
 12 Of 
 
 Car-brass linin tr 
 
 
 trace 
 9.91 
 14.38 
 
 "85J7 
 
 15.10 
 
 
 Salgee anti-friction 
 Graphite bearing-metal . . . 
 
 4.01 
 
 16.73 
 18 83 
 
 ? (I) 
 
 Antimonial lead 
 
 
 
 75.47 
 77.83 
 92.39 
 trace 
 
 9.72 
 9.60 
 2.37 
 
 14.57 
 12.40 
 5.10 
 83.55 
 
 78.44 
 0.31 
 15.06 
 12.52 
 
 
 
 (2) 
 
 Cornish bronze 
 
 trace 
 
 
 trace(3) 
 0.07 
 trace(4> 
 
 0.65 
 0.11 
 
 Delta metal 
 
 * Magnolia, metal 
 
 trace 
 
 0.98 
 38.40 
 
 16.45 
 19.60 
 
 American anti-friction 
 metal 
 
 I'obin bronze 
 
 59.66 
 75.80 
 76.41 
 90.52 
 81.24 
 
 2.16 
 9.20 
 10.60 
 9.58 
 10.98 
 
 Granev bronze 
 
 
 Damascus bronze 
 
 
 
 
 Manganese bronze 
 
 
 
 .. (5) 
 
 Ajax metal 
 
 7.27 
 88 32 
 
 
 
 (6) 
 
 Anti-friction metal 
 
 
 11.93 
 
 
 Harrington bronze 
 
 55.73 
 
 0.97 
 
 
 42.67 
 trace 
 
 "J4J8" 
 6.03 
 
 0.68 
 0.61 
 
 Car-box metal 
 
 84.33 
 94.40 
 
 Hard lead 
 
 
 
 Phosphor-bronze 
 
 79.17 
 76.80 
 
 10.22 
 8.00 
 
 9.61 
 15.00 
 
 
 
 ...(7) 
 
 Ex. B. metal 
 
 
 
 <e{ 
 
 Other constituents: 
 
 (1) No graphite. 
 
 (2) Possible trace of carbon. 
 
 (3) Trace of phosphorus. 
 
 (4) Possible trace of bismuth. 
 
 * Dr. H. C. Torrey says this analy; 
 metal always contains tin. 
 
 (5) No manganese. 
 
 [6) Phosphorus or arsenic, 0.37. 
 7) Phosphorus, 0.94. 
 
 Phosphorus, 0.20. 
 is erroneous and that Magnolia 
 
406 ALLOYS. 
 
 As an example of the influence of minute changes in an alloy, the Har- 
 rington bronze, which consists of a minute proportion of iron in a cop- 
 per-zinc alloy, showed after rolling a tensile strength of 75,000 Ib. and 
 20% elongation in 2 inches. 
 
 In experimenting on this subject on the Pennsylvania Railroad, a 
 certain number of the bearings were made of a standard bearing-metal, 
 and the same number were made of the metal to be tested. These 
 bearings were placed on opposite ends of the same axle, one side of the 
 car haying the standard bearings, the other the experimental. Before 
 going into service the bearings were carefully weighed, and after a 
 sufficient time they were again weighed. The standard bearing-metal 
 used is the "S bearing-metal" of the Phosphor-Bronze Smelting Co. 
 It contains about 79.70% copper, 9.50% lead, 10% tin, and 0.80% phos- 
 phorus. A large number of experiments have shown that the. loss of 
 weight of a bearing of this metal is 1 Jb. to each 18,000 to 25,000 miles 
 traveled. Besides the measurement of wear, observations were made 
 on the frequency of "hot boxes" with the different metals. 
 
 The results of the tests for wear, so far as given, are condensed into 
 the following table: 
 
 Composition. Rate 
 
 Metal. , * x of 
 
 Copper. Tin. Lead. Phos. Arsenic. Wear. 
 
 Standard 79.70 10.00 9.50 0.80 100 
 
 Copper-tin 87.50 12.50 148 
 
 Same, second experiment 
 
 Same, third experiment 147 
 
 Arsenic-bronze 89.20 10.00 0.80 142 
 
 Arsenic-bronze 79.20 10.00 7.00 0.80 115 
 
 Arsenic-bronze 79.70 10.00 9.50 0.80 101 
 
 "K" bronze 77.00 10.50 12.50 92 
 
 Same, second experiment 92.7 
 
 Alloy "B" 77.00 8.00 15.00 86.5 
 
 The old copper-tin alloy of 7 to 1 has repeatedly proved its inferiority 
 to the phospnor-bronze metal. Many more of the copper-tin bearings 
 heated than of the phosphor-bronze. The showing of these tests was so 
 satisfactory that phosphor-bronze was adopted as the standard bearing- 
 metal of the Pennsylvania R.R., and was used for a long time. 
 
 The experiments, however, were continued. It was found that arsenic 
 practically takes the place of phosphorus in a copper-tin alloy, and three 
 tests were made with arsenic-bronzes as noted above. As the propor- 
 tion to lead is increased to correspond with the standard, the durability 
 increases as well. In view of these results the "K" bronze was tried, in 
 which neither phosphorus nor arsenic were used, and in which the lead 
 was increased above the proportion in the standard phosphor-bronze. 
 The result was that the metal wore 7.30% slower than the phosphor- 
 bronze. No trouble from heating was experienced .with the "K" bronze 
 more than with the standard. Dr. Dudley continues: 
 
 At about this time we began to find evidences that wear of bearing- 
 metal alloys variel in accordance with the following law: "That alloy 
 which has the greatest power of distortion without rupture (resilience), 
 will best resist wear." It was now attempted to design an alloy in 
 accordance with this law, taking first the proportions of copper and tin. 
 01/2 parts copper to 1 of in was settled on by experiment as the standard, 
 although some evidence since that time tends to show that 12 or possi- 
 bly 15 parts copper to 1 of tin might have been better. The influence of 
 lead on this copper-tin alloy seems to be much the same as a still further 
 diminution of tin. However, the tendency 9f the metal to yield under 
 pressure increases as the amount of tin is diminished, and the amount 
 of the lead increased, so a limit is set to the use of lead. A certain 
 amount of ti i is also necessary to keep the lead alloyed with the copper. 
 
 Bearings were cast of the metal noted in the table as alloy "B," and it 
 wore 13.5% slower than the standard phosphor-bronze. This metal is 
 now the standard bearing-metal of the Pennsylvania Railroad, being 
 slightly changed in composition to allow tne use of phosphor-bronze 
 scrap. The formula adopted is: Copper, 105 Ibs.: phosphor-bronze, 
 60 Ibs.: tin. 92/4 Ibs.: lead, 251/4 Ibs. By using ordinary care in the 
 foundry, keeping the metal well covered with charcoal during the meltr 
 
ALLOYS CONTAINING ANTIMONY. 
 
 407 
 
 Ing, no trouble Is found in casting good bearings with this metal. The 
 copper and the phosphor-bronze can be put in the pot before putting it 
 in the melting-hole. The tin and lead should be added after the pot is 
 taken from the fire. 
 
 It is not known whether the use of a little zinc, or possibly some other 
 combination, might not give still better results. For the present, how- 
 ever, this alloy is considered to fulfill the various conditions required for 
 good bearing-metal better than any other alloy. The phosphor-bronze 
 had an ultimate tensile strength of 30,000 lb., with 6% elongation, 
 whereas the alloy "B" had 24,000 lb. T. S. and 11% elongation. 
 
 Bearing Metal Practice, 1907. (G. H. Clamer, Proc. A. S. T. M., vii, 
 302, discusses the history of bearing metal practice since the date o! 
 Dr. Dudley's paper quoted above. It was found that tin could be dimin- 
 ished and lead inceased far beyond the figures formerly used, and a satis- 
 factory bearing metal was made with 65% copper, 5% tin and 30% lead. 
 This alloy is largely sold under the name of "plastic bronze." It has a 
 compressiye strength of about 15,000 Ibs. per sq. in., and is found to 
 operate without distortion in the bearings of the heaviest Ioc9motives, 
 not only for driving brasses, but also for rod brasses and bushings, and 
 for bearings of cars of 100,000 Ibs. capacity, the heaviest cars now in 
 service. Specifications of different railroads cover bearing alloys with 
 tin from 8 to 10-% and lead from 10 to 15%. There is also used a vast 
 quantity of bearings made from scrap. These contain copper, 65 to 75%, 
 tin, 2 to 8%, lead, 10 to 18%, zinc, 5 to 20%, and they constitute from 
 50 to 75 per cent of the car bearings now in use. 
 
 White Metal for Engine Bearings. (Report of a British Naval 
 Committee, Eng'g, July 18, 1902.) For lining bearings, crankpin 
 bushes, and other parts exclusive of cross-head bushes: Tin 12, copper 1, 
 antimony 1. Melt 6 tin 1 copper, and 6 tin 1 antimony separately and 
 mix the two together. For cross-head bushes a harder alloy, viz., 85% 
 tin, 5% copper, 10% antimony, has given good results. 
 
 (For other bearing-metals, see "Alloys containing Antimony," below.) 
 
 ALLOYS CONTAINING ANTIMONY. 
 
 VARIOUS ANALYSES OF BABBITT METAL AND OTHER ALLOYS CONTAIN- 
 ING ANTIMONY. 
 
 Tin. 
 
 [Copper.[ Antimony. ,| Zinc. | Lead. | Bismuth. 
 
 Babbitt metal 
 for light duty 
 Harder Babbitt 
 for bearings * 
 Britannia, . 
 
 50 
 -89.3 
 96 
 = 88.9 
 85 7 
 
 1.8 
 4 
 3.7 
 1.0 
 
 5 parts 
 8.9 perct. 
 8 parts 
 7.4per ct. 
 10.1 
 16. 2 
 16 
 25.5 
 62 
 13 
 7.1 
 10 
 
 
 
 
 
 
 
 
 
 
 2.9 
 1.9 
 
 
 
 
 . 81 9 
 
 e 
 
 ...81.0 
 
 2 
 4 
 10 
 1.5 
 1.8 
 5 
 
 
 
 
 
 
 70 5 
 
 4 ' 
 
 22 
 
 6 
 
 '"46!6" 
 
 ........ 
 omotives. 
 
 " Babbitt " 
 
 ...45.5 
 
 Plate pewter 
 
 89.3 
 
 White metal 
 
 ...85 
 
 Bearings on Ger. loc 
 
 * It is mixed as follows: Twelve parts of copper are first melted and 
 then 36 parts of tin are added; 24 parts of antimony are put in, and 
 then 36 parts of tin, the temperature being lowered as soon as the 
 copper is melted in order not to oxidize the tin and antimony, the sur- 
 face of the bath being protected from contact with the air. The alloy 
 thus made is subsequently remelted in the proportion of 50 parts of 
 alloy to 100 tin. (Joshua Rose.) 
 
 White-metal Alloys. The following alloys are used as lining metals 
 by the Eastern Railroad of France (1890): 
 
 Number. 
 
 Lead. 
 
 Antimony. 
 
 Tin. 
 
 Copper. 
 
 1 
 
 65 
 
 25 
 
 ,0 
 
 10 
 
 2 
 
 
 
 11.12 
 
 83.33 
 
 5.55 
 
 3 
 
 70 
 
 20 
 
 10 
 
 
 
 4 
 
 80 
 
 8 
 
 12 
 
 
 
 No. 1 is used for lining cross-head slides, rod-brasses and axle-bear- 
 ings; No. 2 for lining axle-bearings and connecting-rod brasses of heavy 
 
408 
 
 ALLOYS. 
 
 engines; No. 3 for lining eccentric straps and for bronze slide- valves'; 
 and No. 4 for metallic rod-packing. 
 
 Some of the best-known white-metal alloys are the following (Circular 
 of Hoveler & Dieckhaus, London, 1893): 
 
 
 Tin. 
 
 Anti- 
 mony. 
 
 Lead. 
 
 Copper. 
 
 Zinc. 
 
 1. Parsons' 
 
 86 
 
 1 
 
 2 
 
 2 
 
 27 
 
 2. Richards' 
 
 70 
 
 15 
 
 101/2 
 
 41/2 
 
 
 
 3. Babbitt's . . 
 
 55 
 
 18 
 
 231/2 
 
 31/2 
 
 
 
 4. Fenton's 
 
 16 
 
 
 
 
 
 
 79 
 
 5. French Navy 
 6. German Navy 
 
 ^ 
 
 
 
 7V2 
 
 7 
 
 
 7 
 
 7V2 
 
 871/3 
 
 
 "There are engineers who object to white metal containing lead or 
 zinc. This is, however, a prejudice quite unfounded, inasmuch as lead 
 and zinc often have properties of great use in white alloys. 
 
 It is a further fact that an "easy liquid" alloy must not contain more 
 than 18% of antimony, which is an invaluable ingredient of white metal 
 for improving its hardness; but in no case must it exceed that margin, 
 as this would reduce the plasticity of the compound and make it 
 brittle. 
 
 Hardest tin-lead alloy: 6 tin, 4 lead. Hardest of all tin alloys (?) : 74 
 tin, 18 antimony, 8 copper. 
 
 Alloy for thin open-work, ornamental castings: Lead 2, antimony 1. 
 White metal for patterns: Lead 10, bismuth 6, antimony 2, common 
 brass 8, tin 10. 
 
 Type-metal is made of various proportions of lead and antimony, 
 from 17% to 20% antimony according to the hardness desired. 
 
 Babbitt Metals. (C. R. Tompkins, Mechanical News, Jan., 1891.) 
 
 The practice of lining journal-boxes with a metal that is sufficiently 
 fusible to be melted in a common ladle is not always so much for the 
 purpose ot securing anti-friction properties as for the convenience and 
 cheapness of forming a perfect bearing in line with the shaft without 
 the necessity of boring them. Itoxes that are bored, no matter how 
 accurate, require great care in fitting and attaching them to the frame 
 or other parts of a machine. 
 
 It is not good practice, however, to use the shaft for the purpose of 
 casting the bearings, especially if the shaft be steel, for the reason that 
 the hot metal is apt to spring it; the better plan i 
 of the same size or a trifle larger for this purpose. 
 
 , , 
 
 the hot metal is apt to spring it; the better plan is to use a mandrel 
 of the same size or a trifle larger for this purpose. For slow-running 
 journals where the load is moderate, almost any metal that may be 
 ' 
 
 conveniently 'melted and will run free will answer the purpose. For 
 wearing properties, with a moderate speed, there is probably nothing 
 superior to pure zinc, but when not combined with some other metal it 
 shrinks so much in cooling that it cannot be held firmly in the recess, 
 and soon works loose; and it lacks those anti-friction properties which 
 are necessary in order to stand high speed. 
 
 For line-shafting, and all work where the speed is not over 300 or 400 
 r p m an alloy of 8 parts zinc and 2 parts block-tin will not only wear 
 longer 'than any composition of this class, but will successfully resist a 
 heavy load The tin counteracts the shrinkage, so that the metal, if not 
 overheated, will firmly adhere to the box until it is worn out. But this 
 mixture does not possess sufficient anti-friction properties to warrant its 
 use in fast-running journals. 
 
 Among all the soft metals in use there are none that possess greater 
 anti-friction properties than pure lead; but lead alone is impracticable, 
 for it is so soft that it cannot be retained in the recess. But when by 
 any process lead can be sufficiently hardened to be retained in the boxes 
 without materially injuring its anti-friction properties, there is no metal 
 that will wear longer in light fast-running journals. With most of the 
 best and most popular anti-friction metals in use and sold under the 
 name of the Babbitt metal, the basis is lead. 
 
 Lead and antimony have the property of combining with each other 
 in all proportions without impairing the anti-fnction properties of either. 
 The antimony hardens the lead, and when mixed in the proportion of 80 
 
SOLDERS. 
 
 409 
 
 parts lead by weight with 20 parts antimony, no other known compo- 
 sition of metals possesses greater anti-friction or wearing properties, or 
 will stand a higher speed without heat or abrasion. It runs free in its 
 melted state, has no shrinkage, and is better adapted to light high- 
 speed machinery than any other known metal. Care, however, should be 
 manifested in using it, and it should never be heated beyond a temper- 
 ature that will scorch a dry pine stick. 
 
 Many different compositions are sold under the name of Babbitt 
 metal. Some are good, but more are worthless; while but very little 
 genuine Babbitt metal is sold that is made strictly according to the 
 original formula. Most of the metals sold under that name are the 
 refuse of type-foundries and other smelting- works, melted and cast into 
 fancy ingots with special brands, and sold under the name of Babbitt 
 metal. 
 
 I It is difficult at the present time to determine the exact formulae 
 used by the original Babbitt the inventor of the recessed box, as a num- 
 ber of different formulae are given for that composition. Tin, copper, 
 and antimony were the ingredients, and from the best sources of in- 
 formation the original proportions were as follows : 
 
 Another writer gives: 
 83.3% 
 8.3% 
 8.3% 
 
 50 parts tin = 89.3% 
 
 2 parts copper = 3.6% 
 
 4 parts antimony = 7.1 % 
 
 The copper was first melted, and the antimony added first and then 
 about ten or fifteen pounds of tin, the whole kept at a dull-red heat and 
 constantly stirred until the metals were thoroughly incorporated, after 
 which the balance of the tin was added, and after being thoroughly 
 stirred again it was then cast into ingots. When the copper is thoroughly 
 melted, and before the antimony is added, a handful of powdered char- 
 coal should be thrown into the crucible to form a flux, in order to exclude 
 the air and prevent the antimony from vaporizing; otherwise much of it 
 will escape in the form of a vapor and consequently be wasted. This 
 metal, when carefully prepared, is probably one of the best metals in use 
 for lining boxes that are subjected to a heavy weight and wear; but for 
 light fast-running journals the copper renders it more susceptible to 
 friction, and it is more liable to heat than the metal composed of lead and 
 antimony in the proportions just given. 
 
 SOLDERS. 
 
 Common solders, equal parts tin and lead; fine solder, 2 tin to 1 lead; 
 cheap solder, 2 lead, 1 tin. 
 
 Fusing-point of tin-lead alloys (many figures probably inaccurate). 
 
 Tin 1 to lead 25 558 F. 
 
 10. 
 5. 
 3. 
 2. 
 1. 
 
 .541 
 .511 
 .482 
 .441 
 .370 
 
 Tin H/2 to lead 1 334 F. 
 
 .340 
 .356 
 .365 
 .378 
 .381 
 
 The melting point of the tin-lead alloys decreases almost proportionately 
 to the increase of tin, from 619F, the melting point of pure lead, to 356F 
 * when the alloy contains 68% of tin, and then increases to 448F., the melt- 
 ing point of pure tin. Alloys on either side of the 68% mixture begin to 
 soften materially at 356F, because at that temperature the eutectic alloy 
 melts and permits the whole alloy to soften. (Dr. J. A. Mathews.) 
 
 Common pewter contains 4 lead to 1 tin. 
 
 The relative hardness of the various tin and lead solders has been 
 determined by BrineU's method. The results are as follows: 
 
 % Tin 10 20 30 40 
 
 Hardness 3.90 10.10 12.16 14.46 15.76 
 
 7 Tin 66 
 
 iardness 16,66 
 
 67 
 15.40 
 
 14,58 
 
 70 
 15.84 
 
 80 
 15.20 
 
 50 
 14.90 
 
 90 
 13.25 
 
 60 
 14.58 
 
 100 
 4.14 
 
410 
 
 ROPES AND CABLES. 
 
 The hardest solder is the one composed of 2 parts of tin and 1 part of 
 lead. It is the eutectic alloy, or the one with the lowest melting point c* 
 all the mixtures. Mechanical World. 
 
 Gold solder: 14 parts gold, 6 silver, 4 copper. Gold solder for 14-carat 
 gold; 25 parts gold, 25 silver, 121/2 brass, 1 zinc. 
 
 Silver solder: Yellow brass 70 parts, zinc 7, tin 111/2. Another: Silver 
 145 parts, brass (3 copper, 1 zinc) 73, zinc 4. 
 
 German-silver solder: Copper 38, zinc 54, nickel 8. 
 
 Novel's solders for aluminum: 
 
 Tin 100 parts, lead 5; 
 100 " zinc 5; 
 
 1000 
 1000 
 
 copper 10 to 15; 
 nickel 10 to 15; 
 
 melts at 536 to 572 F. 
 
 536 to 612 
 
 662 to 842 
 
 662 to 842 
 
 See also p. 383. 
 
 Novel's solder for aluminum bronze: Tin, 900 parts, copper 100. bis- 
 muth 2 to 3. It is claimed that this solder is also suitable for joining 
 aluminum to copper, brass, zinc, iron or nickel. 
 
 (A. S, 
 
 ROPES AND CABLES. 
 
 STRENGTH OF ROPES. 
 
 Newell & Co., Birkenhead. Klein's Translation of Welsbach, 
 vol. iii, part 1, sec. 2.) 
 
 Hemp. 
 
 Iron. 
 
 Steel. 
 
 TensiiG 
 
 Girth. 
 
 Weight 
 per 
 
 Girth. 
 
 Weight 
 per 
 
 Girth. 
 
 Weight 
 per 
 
 Strength, 
 Gross tons. 
 
 Inches. 
 
 Fathom. 
 
 Inches. 
 
 Fathom. 
 
 Inches. 
 
 Fathom. 
 
 
 
 Pounds. 
 
 
 Pounds. 
 
 
 Pounds. 
 
 
 23/4 
 
 2 
 
 1 
 
 1 
 
 
 
 2 
 
 
 
 11/2 
 
 H/2 
 
 ] 
 
 1 
 
 3 
 
 33/4 
 
 4 
 
 l-Vs 
 
 2 
 
 
 
 4 
 
 
 
 l3/ 4 
 
 21/2 
 
 H/2 
 
 H/2 
 
 5 
 
 41/2 
 
 5 
 
 17/8 
 
 3 
 
 
 
 6 
 
 
 
 2 
 
 31/2 
 
 1 5/8 
 
 2 
 
 7 
 
 5V2 
 
 7 
 
 2V8 
 
 4 
 
 13/4 
 
 21/ 2 
 
 8 
 
 
 
 21/4 
 
 41/2 
 
 
 
 9 
 
 6 
 
 9 
 
 23/8 
 
 5 
 
 17/8 
 
 3 
 
 10 
 
 
 
 21/2 
 
 51/2 
 
 
 
 11 
 
 61/2 
 
 10 
 
 25/8 
 
 6 
 
 2 
 
 31/2 
 
 12 
 
 
 
 23/4 
 
 61/2 
 
 2V8 
 
 4 
 
 13 
 
 7 
 
 12 
 
 27/8 
 
 7 
 
 21/4 
 
 41/2 
 
 14 
 
 
 
 3 
 
 71/2 
 
 
 
 15 
 
 7V2 
 
 14 
 
 3V8 
 
 8 
 
 23/8 
 
 5 
 
 16 
 
 
 
 3V4 
 
 81/2 
 
 
 
 17 
 
 8 
 
 16 
 
 33/8 
 
 9 
 
 2V2 
 
 5V2 
 
 18 
 
 
 
 31/2 
 
 10 
 
 23/8 
 
 6 
 
 20 
 
 81/2 
 
 18 
 
 33/8 
 
 11 
 
 23/4 
 
 61/2 
 
 22 
 
 
 
 33/4 
 
 12 
 
 
 
 24 
 
 91/2 
 
 22 
 
 37/8 
 
 13 
 
 31/4 
 
 8 
 
 26 
 
 10 
 
 26 
 
 4 
 
 14 
 
 
 
 28 
 
 11 
 
 30 
 
 41/4 
 
 15 
 
 33/8 
 
 9 
 
 30 
 
 
 
 43/8 
 
 16 
 
 
 
 32 
 
 
 
 41/2 
 
 18 
 
 31/2 
 
 10 
 
 36 
 
 12 
 
 34 
 
 45/ 8 
 
 20 
 
 33/4 
 
 12 
 
 40 
 
STRENGTH OF ROPES. 411 
 
 ength Sufficient to Cause the Maximum Working Stress. 
 
 (Weisbach.) 
 
 Hempen rope, dry and uritarred 2855 feet. 
 
 Hempen rope, wet or tarred 1975 " " 
 
 Wire rope 4590 " 
 
 Open-link chain 1360 " 
 
 Stud chain 1660 " 
 
 Sometimes, when the depths are very great, ropes are given approxi- 
 mately the form of a body of uniform strength, by making them of separ- 
 ate pieces, whose diameters diminish towards the lower end. It is evi- 
 dent, that by this means the tensions in the fibres caused by the rope's 
 own weight can be considerably diminished. 
 
 Rope for Hoisting or Transmission. Manila Rope. (C. W. Hunt 
 Company, New York.) Rope used for hoisting or for transmission of 
 power is subjected to a. very severe test. Ordinary rope chafes and grinds 
 to powder in the center, while the exterior may look as though it was little 
 worn. 
 
 In bending a rope over a sheave, the strands and the yarns of these 
 strands slide a small distance upon each other, causing friction, and wear 
 the rooe internally. 
 
 The " Stevedore" rope used by the C. W. Hunt Company is made by lubri- 
 cating the fibres with plumbago, mixed with sufficient tallow to hold it in 
 position. This lubricates the yarns of the rope, and prevents internal 
 chafing and wear. After running a short time the exterior of the rope 
 gets compressed and coated with the lubricant. 
 
 In manufacturing rope, the fibres are first spun into a yarn, this yam 
 being twisted in a direction called "right hand." From 20 to 80 of these 
 yarns, depending on the size of the rope, are then put together and 
 twisted in the opposite direction, or "left hand," into a strand. Three of 
 these strands, for a 3-strand, or four for a 4-strand rope, are then twisted 
 together, the twist being again in the "right hand" direction. When the 
 strand is twisted, it untwists each of the threads, and when the three 
 strands are twisted together into rope, it untwists the strands, but again 
 twists up the threads. It is this opposite twist that keeps the rope in its 
 proper form. When a weight is hung on the end of a rope, the tendency 
 is for the rope to untwist, and become longer. In untwisting the rope, it 
 would twist the threads up, and the weight will revolve until the strain of 
 the untwisting strands just equals the strain of the threads being twisted 
 tighter. In making a rope it is impossible to make these strains exactly 
 balance each other. It is this fact that makes it necessary to take out the 
 "turns" in a new rope, that is, untwist it when it is put at work. The 
 proper twist that should be put in the threads has been ascertained approx- 
 imately by experience. 
 
 The amount of work that the rope will do varies greatly. It depends 
 not only on the quality of the fibre and the method of laying up the rope, 
 but also on the kind of weather when the rope is used, the blocks or 
 sheaves over which it is run, and the strain in proportion to the strain put 
 upon the rope. The principal wear comes in practice from defective or 
 badly set sheaves, from excess of load and exposure to storms. 
 
 The loads put upon the rope should not exceed those given in the 
 tables, for the most economical wear. The indications of excessive load 
 will be the twist coming out of the rope, or one of the strands slipping out 
 of its proper position. A certain amount of twist comes out in using it 
 the first day or two, but after that the rope should remain substantially 
 the same. If it does not, the load is too great for the durability of the 
 rope. If the rope wears on the outside, and is good on the inside, it 
 shows that it has been chafed in running over the pulleys or sheaves. If 
 the blocks are very small, it will increase the sliding of the strands and 
 threads, and result in a more rapid internal wear. Rope made for hoist- 
 ing and for rope transmission is usually made with four strands, as expe- 
 rience has shown this to be the most serviceable. 
 
 The strength and weight of "Stevedore" rope is estimated as follows: 
 Breaking strength in pounds = 720 (circumference in inches) 2 ; 
 Weight in pounds per foot = 0.032 (circumference in inches) 8 . 
 
 The Technical Words relating to Cordage most frequently heard 
 are: 
 
 YARN. Fibres twisted together. 
 
412 ROPES AND CABLES/ 
 
 THREAD. Two or more small yarns twisted together. 
 
 STRING. The same as a thread but a little larger yarns. 
 
 STRAND. Two or more large yarns twisted together* 
 
 CORD. Several threads twisted together. 
 
 ROPE. Several strands twisted together. 
 
 HAWSER. A rope of three strands. 
 
 SHROUD-LAID. A rope of four strands. 
 
 CABLE. Three hawsers twisted together. 
 
 YARNS are laid up left-handed into strands. 
 
 STRANDS are laid up right-handed into rope. 
 
 HAWSERS are laid up left-handed into a cable. 
 
 A rope is: 
 
 LAID by twisting strands together in making the rope. 
 
 SPLICED by joining to another rope by interweaving the strands. 
 
 WHIPPED. By winding a string around the end to prevent untwisting. 
 
 SERVED. When covered by winding a yarn continuously and tightly 
 around it. 
 
 PARCELED. By wrapping with canvas. 
 
 SEIZED. When two parts are bound together by a yarn, thread or 
 string. 
 
 PAYED. When painted, tarred or greased to resist wet. 
 
 HAUL. To pull on a rope. 
 
 TAUT. Drawn tight or strained. 
 
 Splicing of Rope. The splice in a transmission rope is not only the 
 weakest part of the rope but is the first part to fail when the rope is worn 
 out. If the rope is larger at the splice, the projecting part will wear on 
 the pulleys and the rope fail from the cutting off of the strands. The fol- 
 lowing directions are given for splicing a 4-strand rope. 
 
 The engravings show each successive operation in splicing a 13/4-inch 
 manila rope. Each engraving was made from a full-size specimen. 
 
 Tie a piece of twine, 9 and 10, around the rope to be spliced, about 
 6 feet from each end. Then unlay the strands of each end back to the 
 twine. 
 
 Butt the ropes together and twist each corresponding pair of strands 
 loosely, to keep them from being tangled, as shown in Fig. 91. 
 
 The twine 10 is now cut, and the strand 8 unlaid and strand 7 carefully 
 laid in its place for a distance of four and a half feet from the junction. 
 
 The strand 6 is next unlaid about one and a half feet and strand 5 laid 
 in Its place. 
 
 The ends of the cores are now cut off so they just meet. 
 
 Unlay strand 1 four and a half feet, laying strand 2 in its place. 
 
 Unlay strand 3 one and a half feet, laying in strand 4. 
 
 Cut all the strands off to a length of about twenty inches for convenience 
 in manipulation. 
 
 The rope now assumes the form shown in Fig. 92 with the meeting 
 points of the strands three feet apart. 
 
 Each pair of strands is successively subjected to the following operation: 
 
 From the point of meeting of the strands 8 and 7, unlay each one three 
 turns; split both the strand 8 and the strand 7 in halves as far back as 
 they are now unlaid and "whip" the end of each half strand with a small 
 piece of twine. 
 
 The half of the strand 7 is now laid in three turns and the half of 8 also 
 laid in three turns. The half strands now meet and are tied in a simple 
 knot, 11, Fig. 93, making the rope at this point its original size. 
 
 The rope is now opened with a marlin spike and the half strand of 7 
 worked around the half strand of 8 by passing the end of the half strand 7 
 through the rope, as shown in the engraving, drawn taut, and again 
 worked around this half strand until it reaches the half strand 13 that was 
 not laid in. This half strand 13 is now split, and the half strand 7 drawn 
 through the opening thus made, and then tucked under the two adjacent 
 strands, as shown in Fig. 94. The other half of the strand 8 is now 
 wound around the other half strand 7 in the same manner. After each 
 pair of strands has been treated in this manner, the ends are cut off at 12, 
 leaving them about four inches long. After a few days wear they will 
 draw into the body of the rope or wear off, so that the locality of the 
 splice can scarcely be detected. 
 
FIG. 94. 
 SPLICING OF ROPES. 
 
414 
 
 ROPES AND CABLES. 
 
 Cargo Hoisting. (C. W. Hunt Company.) The amount of coal that 
 can be hoisted with a rope varies greatly. Under the ordinary conditions 
 of use a rope hoists from 5000 to 8000 tons. Where the circumstances are 
 more ^ favorable, the amounts run up frequently to 12,000 or 15,000 tons 
 occasionally to 20,000 and in one case 32,400 tons to a single fall 
 
 When a hoisting rope is first put in use, it is likely from the strain put 
 upon it to twist up when the block is loosened from the load. This occurs 
 in the first day or two only. The rope should then be taken down and 
 the * turns' taken out of the rope. When put up again the rope should 
 give no further trouble until worn out. 
 
 It is necessary that the rope should be much larger than is needed to 
 bear the strain from the load. 
 
 Practical experience for many years has substantially settled the most 
 economical size of rope to be used which is given in the table below 
 
 Hoisting ropes are not spliced, as it is difficult to make a splice that will 
 not pull out while running over the sheaves, and the increased wear to be 
 obtained in this way is very small. 
 
 Coal is usually hoisted with what is commonly called a "double whip- " 
 that is, with a running block that is attached to the tub which reduces the 
 strain on the rope to approximately one-half the weight of the load 
 hoisted. 
 
 Hoisting rope is ordered by circumference, transmission rope by 
 diameter. 
 
 Working Loads for Manila Eope (C. W. Hunt, Trans.] A. S. M. E., 
 xxiii, 125.) 
 
 Diameter 
 of Rope, 
 Inches. 
 
 Ultimate 
 Strength, 
 Pounds. 
 
 Working Load in Pounds. 
 
 Minimum Diameter of 
 Sheaves in Inches. 
 
 Rapid. 
 
 Medium. 
 
 Slow. 
 
 Rapid. 
 
 Medium. 
 
 Slow. 
 
 1 
 
 H/8 
 U/4 
 13/8 
 H/2 
 15/8 
 13/4 
 
 7,100 
 9,000 
 11,000 
 13,400 
 15,800 
 18,800 
 21.800 
 
 200 
 250 
 300 
 380 
 450 
 530 
 620 
 
 400 
 500 
 600 
 750 
 900 
 1100 
 1250 
 
 1000 
 1250 
 1500 
 1900 
 2200 
 2600 
 3000 
 
 40 
 45 
 50 
 55 
 60 
 65 
 70 
 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 
 8 
 9 
 iO 
 11 
 12 
 13 
 14 
 
 In this table the work'required of the rope is, for convenience, divided 
 into three classes "rapid," "medium," and "slow," these terms being 
 used in the following sense: "Slow" Derrick, crane and quarry work; 
 speed from 50 to 100 feet per minute. "Medium" Wharf and cargo, 
 hoisting 150 to 300 feet per minute. "Rapid" 400 to 800 feet per 
 minute. 
 
 The ultimate strength given in the table is materially affected by the 
 age and condition of a rope in active service, and also it is said to be 
 weaker when it is wet. Trautwine states that a few months of exposed 
 work weakens rope 20 to 50 per cent. The ultimate strength of a new 
 rope given in the table is the result of tests of full sized specimens of 
 manila rope, purchased in the open market, and made by three inde- 
 pendent rope walks. 
 
 The proper 'diameter of pulley-block sheaves for different classes of 
 work given in the table is a compromise of the various factors affecting 
 the case. An increase in the diameter of sheave will materially increase 
 the life of a rope. The advantage, however, is gained by increased 
 difficulty of installation, a clumsiness in handling, and an increase in 
 first cost. The best size is one that considers the advantages and the 
 drawbacks as they are found in practical use, and makes a fair balance 
 between the conflicting elements of the problem. 
 
 Records covering many years have been kept by various coal dealers, 
 of the diameter and cost of their rope per tpn of coal hoisted from ves- 
 sels, using sheaves of from 12 to 16 inches in diameter. These records 
 show conclusively that, in hoisting a bucket that produces 900 pounds 
 stress upon the rope, a li/4-inch diameter rope is too small and a 13/4- 
 inch rope is too large for economy. The Pennsylvania Railroad Company 
 uses iy 2 inch rope, running over 14-inch diameter sheaves for hoisting 
 
STRENGTH OF ROPES. 415 
 
 freight on lighters in New York harbor, and handles on a single part of 
 the rope loads up to 3,000 pounds as a maximum. Greater weights are 
 handled on a 6-part tackle. 
 
 Life of Hoisting and Transmission Rope. A rope 1 V6-in. diam. usu- 
 ally hoists from a vessel from 7000 to 10,000 tons of coal, running with a 
 working stress of 850 to 950 Ibs. over three sheaves, one 12 in., and two 
 16 in. diam. In hoisting 10,000 tons it makes 20,000 trips, bending in 
 that time from a straight line to the curve of the sheave 120,000 times, 
 when it is worn out. A 1000 ft. transmission in a tin-plate mill, with 1^ 
 in. rope, sheaves 5 ft., 17 ft., and 36 ft. apart, center to center, runs 5000 
 ft. per minute making 13,900 bends per hour, or more bends in 9 hours 
 than the hoisting rope made in its entire life, yet the life of a transmission 
 rope is measured in years, not hours. This enormous difference in the 
 life of ropes of the same size and quality is wholly gained by reducing the 
 stresses on the rope and increasing the diameter of the sheaves. 
 
 Efficiency of Knots as a percentage of the full strength of the rope, 
 and the factor of safety when used with the stresses given in the 5th col" 
 umn of the table of working loads. 
 
 Kind of Knot. Effy. Fact. 9 
 
 Eye splice over an iron thimble 90 6.3 
 
 Short splice in the rope 80 5.6 
 
 Timber hitch, round turn, half-hitch 65 4.5 
 
 Bowline slip knot, clove hitch 60 4.2 
 
 Square knot, weaver's knot sheet bend 50 3.5 
 
 Flemish loop, overhand knot 45 3.1 
 
 Full strength of dry rope, average of four tests 100 7.0 
 
 Efficiency of Rope Tackles. Robert Grimshawin 1893 tested a 33/4-in., 
 3-strand ordinary dry manila rope on a "cat and fish" tackle with a 
 6-fold purchase. The sheaves were 8-in. diam., the three upper ones hav- 
 ing roller bearings and the three lower ones solid bushings. The results 
 were as below: 
 
 Net load on tackle, weight raised, Ibs 600 800 1000 1200 
 
 Theoretical force required to raise the weight 100 1333.3 166.7 200 
 
 Actual force required 158 198 243 288 
 
 Percentage above the theoretical 58 48 45.8 44 
 
 Weight and Strength of Manila Rope. Spencer Miller (Eng'g News, 
 Dec. 6, 1890) gives a table of breaking strength of manila rope, which he 
 considers more reliable than the strength computed by Mr. Hunt's formula: 
 Breaking strength = 720 X (circumference in inches) . 2 Mr. Miller's formula 
 is: Breaking weight Ibs. = circumference 2 X a coefficient which varies 
 from 900 for 1/2" to 700 for 2" diameter rope, as below: 
 
 Circumference ..11/2 2 21/2 2 3 /4 3 3l/ 2 33/ 4 41/4 4l/ 2 5 51/2 6 
 Coefficient 900 845 820 790 780 765 760 745 735 725 712 700 
 
 Knots. ' The principle of a knot is that no two parts, which would 
 move in the same direction if the rope were to slip, should lay along side 
 of and touching each other. (See illustrations on the next page.) 
 
 The bowline is one of the most useful knots, it will not slip, and after 
 being strained is easily untied. Commence by making a bight in the 
 rope, then put the end through the bight and under the standing part as 
 shown in G, then pass the end again through the bight, and haul tight. 
 
 The square or reef knot must not be mistaken for the "granny" knot 
 that slips under a strain. Knots H, K and M are easily untied after 
 being under strain. The knot M is useful when the rope passes through 
 an eye and is held by the knot, as it will not slip and is easily untied 
 after being strained. 
 
 The timber hitch S looks as though it would give way, but it will not; 
 the greater the strain the tighter it will hold. The wall knot looks com- 
 plicated, but is easily made by proceeding as follows: Form a bight with 
 strand 1 and pass the strand 2 around the end of it, and the strand 3 
 round the end of 2 and then through the bight of 1 as shown in the cut Z. 
 Haul the ends taut when the appearance is as shown in A A. The end of 
 the strand 1 is now laid over the center of the knot, strand 2 laid over 1 
 and 3 over 2, when the end of 3 is passed through the bight of 1 as shown 
 in BB, Haul all the strands taut as shown in CC. 
 
416 
 
 ROPES AND CABLES. 
 
 Varieties of Knots. A great number of knots have been devised of 
 which a few only are illustrated, but those selected are the most frequently 
 used. In the cut, Fig. 95, they are shown open, or before being drawn 
 taut, in order to show the position of the parts. The names usually 
 given to them are: 
 
 Bight of a rope. 
 
 Simple or Overhand knot. 
 
 Figure 8 knot. 
 
 Double knot. 
 
 Boat knot. 
 
 Bowline, first step. 
 
 Bowline, second step. 
 
 Bowline completed. 
 
 Square or reef knot. 
 
 Sheet bend or weaver's knot. 
 
 Sheet bend with a toggle. 
 
 Carrick bend. 
 
 Stevedore knot completed. 
 
 A. 
 
 B. 
 
 C. 
 
 D. 
 
 E. 
 
 F. 
 
 G. 
 
 H. 
 
 I. 
 
 J. 
 
 K. 
 
 L. 
 
 M. 
 
 N. 
 
 O. 
 
 Stevedore knot commenced. 
 Slip knot. 
 
 P. 
 
 : 
 
 S. 
 
 T. 
 
 U. 
 
 Y. 
 
 W. 
 
 X. 
 
 Y. 
 
 Z. 
 
 AA. 
 BB. 
 CO. 
 
 Flemish loop. 
 
 Chain knot with toggle. 
 
 Half-hitch. 
 
 Timber-hitch. 
 
 Clove- hitch. 
 
 Rolling-hitch. 
 
 Timber-hitch and half-hitch. 
 
 Black wall-hitch. 
 
 Fisherman's bend. 
 
 Round turn and half-hitch 
 
 Wall knot commenced. 
 
 Wall knot completed. 
 
 Wall knot crown commenced. 
 
 Wall knot crown completed. 
 
 Fia. 95. KNOTS. 
 
SPRINGS. 417 
 
 SPRINGS. 
 
 Definitions. A spiral spring is one which is wound around a fixed 
 point or center, and continually receding from it, like a watch spring. A 
 helical spring is one which is wound around an arbor, and at the same time 
 advancing like the thread of a screw. . An elliptical or laminated spring is 
 made of nat bars, plaies, or " leaves," of regularly varying lengths, super- 
 posed one upon the other. 
 
 JL imiir.ited Steel Springs. Clark (Rules, Tables and Data) gives 
 the following from his work on Railway Machinery, 1855: 
 
 __ 1.66 LS. U-n . __ 1.66 L. 
 
 _ 
 11.3 L' AW ' 
 
 A = elasticity, or deflection, in sixteenths of an inch per ton of load; 
 s = working strength, or load, in tons (2240 Ibs.); 
 L span, when loaded in inches- 
 b = breadth of p ates, in inches, taken as uniform; 
 t = thickness of plates, in sixteenths of an inch; 
 n number o'f plates. 
 
 NOTE. 1 The span and the elasticity are those due to the spring 
 when weighted. 
 
 2. When extra thick back and short plates are used, they must be 
 replaced by an equivalent number of plates of the ruling thickness, prior 
 to the employment of the first two formulae. This ,s found by multiply- 
 ing the number of extra thick plates by the cube of their thickness, and 
 dividing by the cube of the ruling thickness. Conversely, the number 
 of plates of the ruling thickness given by the third formula, required to 
 be deducted and replaced by a given number of extra thick plates, are 
 found by the same calculation. 
 
 3. It is assumed that the plates are similarly and regularly formed, 
 and that they are of uniform breadth, and but slightly taper at the ends. 
 
 Reuleaux's Constructor gives for semi-elliptic springs: 
 
 and . f 
 
 6 1 
 
 S = max. direct fiber-strain in plate; b = width of plates: 
 
 n number of plates in spring; h = thickness of plates: 
 
 I one-half length of spring; / = deflection of end of spring; 
 
 P = load on one end of spring; E = modulus of direct elasticity 
 
 The above formula for deflection can be relied upon where all the plates 
 of the spring are regularly shortened; but in semi-elliptic springs, as 
 used, there are generally several plates extending the full length of the 
 spring, and the proportion of these long plates to the whole number is 
 
 usually about one-fourth. * In such cases/ = ^rr-rp' (G. R. Henderson, 
 
 Trans A. S. M. E., vol. xvi.) 
 
 In order to compare the formulae of Reuleaux and Clark we may make 
 the following substitutions in the latter: s in tons = P in Ibs. -f- 1120; 
 As = 16/; L = 21; t = 16/i; then 
 
 A, = i fi _ _ 1 .66 X 8 P X P P/8 
 
 "" 4096 X 1120 X nW ' ~ 5,527, l~33nWi" 
 
 which corresponds with Reuleaux's formula for deflection if in the latter 
 we take E = 33,162,800. 
 
 which corresponds with Reuleaux's formula for working load when S ia 
 the latter is taken at 76,120. 
 
418 
 
 SPRINGS. 
 
 The value of E is usually taken at 30,000,000 and S at 80,000, in which 
 case Reuleaux's formulse become 
 
 13,333 nbh* 
 I 
 
 and / = 
 
 PI* 
 
 5,000,OOOn&/*3 
 
 G. R. Henderson, in Trans. A. S. M. E., vol. xvii, gives a series of 
 tables for use in designing both elliptical and helical springs. 
 
 Helical Steel Springs. 
 
 NOTATION. Let d = diam. of wire or rod of which the spring is made. 
 D = outside diameter of coil, inches. 
 R = mean radius 9f coil, = 1/2 (D d). 
 n = number of coils. 
 P = load applied to the spring, Ibs. 
 G = modulus of torsional elasticity. 
 S stress on extreme fiber caused by load P. 
 F = extension or compression of one coil, in., for load P. 
 Fn = total extension or compressi9n, for load P. 
 W = safe carrying capacity of spring, Ibs. 
 
 Gd* 
 
 64 PR*n , 
 Gd* ' 
 
 W = 
 
 0.1 963 Sd* 
 R 
 
 16 R' 
 
 Values of G according to different authorities range from 10,000,000 to 
 14,000,000. 
 
 The safe working value commonly taken for S = 60,000 Ibs. per sq. in. 
 Taking G at 12,000,000 and S at 60,000 the above formula become 
 
 PR* 
 187,500 d 4 ' 
 
 W 
 
 ^- If P = W, then F = 0.06285^-- 
 
 For square steel the values fpund for F and W are to be multiplied by 
 0.59 and 1.2 respectively, d being the side of the square. 
 
 The stress in a helical spring is almost wholly one of torsion. For 
 method of deriving the formulae for springs from torsional formulae see 
 
 rper by J. W. Cloud, Trans. A. S. M. E., vol. 173. Mr. Cloud takes 
 = 80,000 and G = 12,600,000. 
 
 Taking from the Pennsylvania Railroad Specifications (1891) the 
 capacity when closed, Wi; of the following springs, and the total com- 
 pression when closed H h, in which H = height when free and h 
 when closed, and assuming n = h * d, we have the following compari- 
 son of the specified values of capacity and compression with those ob- 
 tained from the formulse. 
 
 No. 
 
 d.in. 
 
 D 
 
 D-d 
 
 TFi 
 
 W 
 
 H 
 
 h 
 
 H-h 
 
 Fn 
 
 n 
 
 T. 
 
 1/4 
 
 U/2 
 
 11/4 
 
 400 
 
 295 
 
 9 
 
 6 
 
 3 
 
 3.20 
 
 24 
 
 S. 
 
 1/2 
 
 3 
 
 2V2 
 
 1900 
 
 1178 
 
 8 
 
 5 
 
 3 
 
 3.16 
 
 10 
 
 K. 
 
 3/4 
 
 53/4 
 
 5 
 
 2100 
 
 1988 
 
 7 
 
 41/4 
 
 23/4 
 
 3.15 
 
 52/s 
 
 D. 
 
 
 5 
 
 4 
 
 8100 
 
 5890 
 
 101/ 2 
 
 8 
 
 21/2 
 
 2.76 
 
 8 
 
 I. 
 
 H/4 
 
 8 
 
 63/4 
 
 10000 
 
 6788 
 
 9 
 
 53/4 
 
 31/4 
 
 3.86 
 
 43/g 
 
 C. 
 
 U/8 
 
 47/ 8 
 
 33/4 
 
 16000 
 
 8946 
 
 43/ 8 
 
 33/ 8 
 
 1 
 
 1.05 
 
 3 
 
 The value of Fn in the table is calculated from the formula with P= W t 
 Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a 
 spiral spring may be calculated from the formula on page 304 of " Rank- 
 ine's Useful Rules and Tables;" but the experience with Salter's springs 
 has shown that the safe limit of stress is more than twice as great as there 
 given, namely 60,000 to 70,000 Ibs. per square inch of section with 3/ 8 -inch 
 wire, and about 50,000 with i/2-inch wire. Hence the work that can b 
 done by springs of wire is four or five times as great as Rankine allows. 
 
SPRINGS. 419 
 
 For 3/ 8 -inch wire and under, 
 
 12,000 X (diam. of wire) 8 , 
 Maximum load in Ibs. = =' 
 
 Weight in Ibs. to deflect spring 1 in. = 
 
 Mean radius of springs 
 
 180,000 X (diam.) 4 
 
 Number of coils X (rad.) 3 
 The work in foot-pounds that can be stored up in a spiral spring would 
 
 lift it above 50 ft. 
 
 In a few rough experiments made with Salter's springs the coefficient of 
 
 rigidity was noticed to be 12,600,000 to 13,700,000 with i/ 4 -inch wire; 
 
 11,000,000 for 11/32 inch; and 10,600,000 to 10,900,000 for 3/ 8 _inch wire. 
 Helical Springs. J. Begtrup, in the American Machinist of Aug. 
 
 18, 1892, gives formulas for the deflection and carrying capacity of helical 
 
 springs of round and square steel, as follow: 
 
 0.3927 ' F = 8 P (D ~ d)3 . for round steel. 
 
 = 0.471 FT^ F = 4.712 ^ ,. ' , for square steel. 
 L) a Hid* 
 
 W = carrying capacity in pounds, 
 
 S = greatest shearing stress per square inch of material, 
 d = diameter of steel, 
 D = outside diameter of coil, 
 F = deflection of one coil, 
 E = torsional modulus of elasticity, 
 P = load in pounds. 
 
 From these formulas the following table has been calculated by Mr 
 Begtrup. A spring being made of an elastic material, and of such shape 
 as lo allow a great amount of deflection, will not be affected by sudder. 
 shocks or blows to the same extent as a rigid body, and a factor of safety 
 very much less than for rigid constructions may be used. 
 
 HOW TO USE THE TABLE. 
 
 When designing a spring for continuous work, as a car spring, use a 
 greater factor of safety than in the table; for intermittent working, as in 
 a steam-engine governor or safety valve, use figures given in table; for 
 square steel multiply line W by 1.2 and line F by 0.59. 
 
 Example 1. How much will a spring of 3/ 8 " round steel and 3" outside 
 diameter carry with safety? In the line headed D we find 3, and right 
 underneath 473, which is the weight it will carry with safety. How many 
 coils must this spring have so as to deflect 3" with a load of 400 pounds? 
 Assuming a modulus of elasticity of 12 millions we find in the line headed 
 F the figure 0.0610; this is deflection of one coil for a load of 100 pounds; 
 therefore 0.061 X 4 = 0.244" is deflection of one coil for 400 pounds load, 
 and 3 *- 0.244 = 121/2 is the number of coils wanted. This spring will 
 therefore be 43/4" long when closed, counting working coils only, and 
 stretch to 73/4". 
 
 Example 2. A spring 31/4" outside diameter of if\^ steel is wound close; 
 how much can it be extended without exceeding the limit of safety? We 
 find maximum safe load for this spring to be 702 pounds, and deflection of 
 one coil for 100 pounds load 0.0405 inches; therefore 7. 02 X 0.0405 = 0.284" 
 is the greatest admissible opening between coils. We may thus, without 
 knowing the load, ascertain whether a spring is overloaded or not. 
 
 Carrying Capacity and Deflection of Helical Springs of 
 Round Steel. 
 
 d = diameter of steel. D = outside diameter of coil. W= safe, work- 
 ing load in pounds tensile stress not exceeding 60,000 pounds per 
 square inch. F = deflection by a load of 100 pounds of one coil, with a 
 modulus of elasticity of 12 millions. The ultimate carrying capacity 
 will be about twice the safe load. (The original table gives three values 
 
420 
 
 SPRINGS. 
 
 of F, corresponding respectively to a modulus of elasticity of 10, 12 and 
 14 millions. To find values of F for 10 million modulus increase the fig- 
 ures here given by one-fifth; for 14 million subtract one-seventh.) 
 
 d 
 in. 
 .065 
 
 D 
 W 
 F 
 
 0.25 
 35 
 0.0236 
 
 0.50 
 15 
 0.3075 
 
 0.75 
 
 1.00 
 
 1.25 
 
 1.50 
 
 1.75 
 
 2.00 
 
 
 
 
 1.228 
 
 3.053 
 
 6.214 
 
 11.04 
 
 17.87 
 
 27.06 
 
 .120 
 
 D' 
 W 
 F 
 
 0.50 
 107 
 0.0176 
 
 0.75 
 65 
 0.0804 
 
 1.00 
 46 
 0.2191 
 
 1.25 
 36 
 0.4639 
 
 1.50 
 29 
 
 0.8448 
 
 1.75 
 25 
 1.392 
 
 2.00 
 22 
 2.136 
 
 2.25 
 19 
 3.107 
 
 2.50 
 17 
 4.334 
 
 
 
 .180 
 
 D 
 W 
 F 
 
 0.75 
 241 
 0.0118 
 
 1.00 
 167 
 0.0350 
 
 1.25 
 128 
 0.0778 
 
 1.50 
 104 
 
 0.1460 
 
 1.75 
 
 88 
 0.2457 
 
 2.00 
 75 
 
 0.3828 
 
 2.25 
 66 
 0.5632 
 
 2.50 
 59 
 0.7928 
 
 2.75 
 53 
 1.077 
 
 3.00 
 
 49 
 1.423 
 
 
 V4 
 
 D 
 W 
 F 
 
 1.25 
 368 
 0.0171 
 
 1.50 
 294 
 0.0333 
 
 1.75 
 245 
 0.0576 
 
 2.00 
 210 
 0.0914 
 
 2.25 
 184 
 0.1365 
 
 2.50 
 164 
 0. 1944 
 
 2.75 
 147 
 0.2665 
 
 3.00 
 134 
 3.3548 
 
 3.25 
 123 
 0.4607 
 
 3.50 
 113 
 
 0.5859 
 
 
 5/16 
 
 3/8 
 
 D 
 W 
 F 
 
 D 
 W 
 F 
 
 1.50 
 605 
 0117 
 
 1.75 
 500 
 0.0207 
 
 2.00 
 426 
 0.0336 
 
 2.25 
 371 
 0508 
 
 2.50 
 329 
 0732 
 
 2.75 
 295 
 1012 
 
 3.00 
 
 267 
 1357 
 
 3.25 
 245 
 1771 
 
 3.50 
 226 
 2263 
 
 3.75 
 209 
 2839 
 
 4.00 
 195 
 3505 
 
 2.00 
 765 
 0.0145 
 
 2.25 
 663 
 0.0222 
 
 2.50 
 589 
 0.0323 
 
 2.75 
 523 
 0.0452 
 
 3.00 
 
 473 
 0.0610 
 
 3.25 
 433 
 0.0801 
 
 3.50 
 398 
 0.1029 
 
 3.75 
 368 
 0.1297 
 
 4.00 
 343 
 0. 1606 
 
 4.25 
 321 
 0.1963 
 
 4.50 
 301 
 0.2367 
 
 7/16 
 
 1/2 
 
 D 
 W 
 F 
 
 D 
 W 
 F 
 
 2.00 
 1263 
 0069 
 
 2.25 
 1089 
 0108 
 
 2.50 
 
 957 
 0.0160 
 
 2.75 
 853 
 0225 
 
 3.00 
 770 
 0306 
 
 3.25 
 702 
 0405 
 
 3.50 
 
 644 
 0529 
 
 3.75 
 596 
 0661 
 
 4.00 
 544 
 0823 
 
 4.50 
 486 
 1220 
 
 5.00 
 
 432 
 1728 
 
 2.00 
 1963 
 0.0036 
 
 2.25 
 1683 
 0.0057 
 
 2.50 
 
 1472 
 0.0085 
 
 2.75 
 1309 
 0.0121 
 
 3.00 
 1178 
 0.0167 
 
 3.25 
 1071 
 0.0222 
 
 3.50 
 982 
 0.0288 
 
 3.75 
 906 
 0.0366 
 
 4.00 
 841 
 0.0457 
 
 4.50 
 736 
 0.0683 
 
 5 00 
 
 654 
 0.0972 
 
 8/18 
 
 D 
 W 
 F 
 
 2.50 
 2163 
 0.0048 
 
 2.75 
 1916 
 O.Q070 
 
 3 00 
 
 1720 
 0.0096 
 
 3.25 
 1560 
 0.0129 
 
 3.50 
 1427 
 0.0169 
 
 3.75 
 1315 
 0.0216 
 
 4.00 
 1220 
 0.0271 
 
 4.25 
 1137 
 0.0334 
 
 4.50 
 1065 
 0.0406 
 
 5 00 
 945 
 
 0.0582 
 
 5.50 
 849 
 0.0801 
 
 5/8 
 
 D 
 W 
 F 
 
 2.50 
 3068 
 0.0029 
 
 2.75 
 2707 
 0.0042 
 
 3.00 
 
 2422 
 0.0058 
 
 3.25 
 2191 
 0.0079 
 
 3.50 
 2001 
 0.0104 
 
 3.75 
 1841 
 0.0133 
 
 4.00 
 1704 
 0.0168 
 
 4.25 
 1587 
 0.0208 
 
 4.50 
 
 1484 
 0.0254 
 
 5.00 
 1313 
 0.0366 
 
 5.50 
 1180 
 0.0506 
 
 "/16 
 
 D 
 
 W 
 
 F 
 
 3.00 
 3311 
 0.0037 
 
 3.25 
 29S8 
 0.0050 
 
 3.50 
 
 2723 
 0.0066 
 
 3.75 
 2500 
 0.0086 
 
 4.00 
 2311 
 0.0108 
 
 4.25 
 2151 
 0.0135 
 
 4.50 
 2009 
 0.0165 
 
 4.75 
 1885 
 0.0200 
 
 5.00 
 1776 
 0.0239 
 
 5.50 
 1591 
 0.0333 
 
 6.00 
 1441 
 0.0447 
 
 8/4 
 
 D 
 W 
 F 
 
 3.00 
 4418 
 0.0024 
 
 3.25 
 3976 
 0.0033 
 
 3.50 
 3615 
 0.0044 
 
 3.75 
 3313 
 0.0057 
 
 4.00 
 3058 
 0.0072 
 
 4.25 
 2840 
 0.0090 
 
 4.50 
 2651 
 0.0111 
 
 4.75 
 2485 
 0.0135 
 
 5.00 
 2339 
 0.0162 
 
 5.50 
 2093 
 0.0226 
 
 6.003 
 1893 
 0.005 
 
 7/8 
 
 D 
 W 
 F 
 
 3.50 
 6013 
 0.0018 
 
 3.75 
 
 5490 
 0.0024 
 
 4.00 
 5051 
 0.0030 
 
 4.25 
 4676 
 0.0038 
 
 4.50 
 
 4354 
 0.0047 
 
 4.75 
 4073 
 0.0058 
 
 5.00 
 3826 
 0.0070 
 
 5.25 
 3607 
 0.0083 
 
 5.50 
 3413 
 0.0098 
 
 6.00 
 3080 
 0.0134 
 
 6.50 
 2806 
 0.0177 
 
 1 
 
 D 
 W 
 F 
 
 3.50 
 9425 
 0.0010 
 
 3.75 
 8568 
 0.0014 
 
 4.00 
 7854 
 0.0018 
 
 4.25 
 7250 
 0.0023 
 
 4.50 
 6732 
 0.0028 
 
 4.75 
 6283 
 0.0035 
 
 5.00 
 5890 
 0.0043 
 
 5.25 
 5544 
 0.0051 
 
 5.50 
 
 5236 
 0.0061 
 
 6.00 
 
 4712 
 0.0083 
 
 6.50 
 4284 
 0.0111 
 
 F. D. Howe, Am. Mach. Dec. 20, 1906, using Begtrup's formulae com- 
 putes a table for springs made from wire of Roebling's or Washburn and 
 Moen ga-iges, Nos. 28 to 000. It is here given somewhat abridged, 
 values of F corresponding to a torsional modulus of elasticity of 12,000,000 
 only being used. 
 
SPRINGS. 
 
 421 
 
 No. 28 
 0.016" 
 
 D 
 W 
 F 
 
 0.20 
 0.524 
 6.32 
 
 0.25 
 0.41 
 13.02 
 
 0.3125 
 0.31 
 30.2 
 
 0.375 
 0.27 
 47.0 
 
 0.4375 
 0.23 
 76.0 
 
 0.500 
 0.20 
 115 
 
 0.5625 
 0.175 
 166 
 
 0.625 
 0.16 
 230 
 
 0.75 
 0.13 
 402 
 
 0.875 
 0.11 
 695 
 
 No. 24 
 0.0225" 
 
 D 
 W 
 F 
 
 0.25 
 1.18 
 2.78 
 
 0.3125 
 0.92 
 6.31 
 
 0.375 
 0.76 
 11.35 
 
 0.4375 
 0.45 
 18.57 
 
 0.500 
 0.56 
 28.2 
 
 0.5625 
 0.50 
 40.8 
 
 625 
 0.45 
 56.9 
 
 0.75 
 0.37 
 97.5 
 
 0.875 
 0.31 
 166 
 
 0.100 
 0.28 
 242 
 
 No. 22 
 0.028" 
 
 D 
 W 
 F 
 
 0.25 
 2.35 
 1.19 
 
 0.3125 
 1.84 
 2.50 
 
 0.375 
 1 49 
 4.53 
 
 0.4375 
 1.26 
 7.42 
 
 0.50 
 1.095 
 11.40 
 
 0.5625 
 0.96 
 16.5 
 
 0.625 
 0.865 
 23.1 
 
 0.75 
 0.715 
 40.8 
 
 0.875 
 0.61 
 66.0 
 
 1.00 
 0.53 
 99.5 
 
 No. 20 
 0.035" 
 
 D 
 
 W 
 F 
 
 0.25 
 4.7 
 0.451 
 
 0.3125 
 3.64 
 0.952 
 
 0.375 
 2.97 
 1.75 
 
 0.4375 
 2.5 
 2.90 
 
 0.50 
 2.18 
 4.47 
 
 0.5625 
 1.92 
 6.51 
 
 0.625 
 1.72 
 9.14 
 
 0.75 
 1.42 
 16.3 
 
 0.875 
 1.20 
 26.4 
 
 1.00 
 1.05 
 40.0 
 
 No. 18 
 0.047" 
 
 D 
 
 W 
 F 
 
 0.25 
 12.05 
 0.1158 
 
 0.3125 
 9.2 
 0.294 
 
 0.375 
 7.45 
 0.488 
 
 0.4375 
 6.57 
 0.824 
 
 0.50 
 5.40 
 1.320 
 
 0.625 
 4.23 
 1.870 
 
 0.75 
 3.48 
 3.96 
 
 0.875 
 2.95 
 7.85 
 
 1.00 
 
 2.85 
 12.60 
 
 1.125 
 2.27 
 17.5 
 
 No. 14 
 0.08" 
 
 D 
 W 
 F 
 
 0.375 
 41 
 0.0418 
 
 0.5 
 28.8 
 0.121 
 
 0.625 
 
 22.2 
 0.342 
 
 0.75 
 18.1 
 0.572 
 
 0.875 
 15.2 
 0.82 
 
 1.00 
 13.15 
 1.27 
 
 1.125 
 11.6 
 1.86 
 
 1.25 
 10.35 
 2.60 
 
 1.50 
 8.52 
 5.48 
 
 1.75 
 7.25 
 7.57 
 
 No. 12 
 0.105" 
 
 D 
 W 
 F 
 
 0.625 
 52.5 
 0.069 
 
 0.75 
 42.25 
 0.1480 
 
 0.875 
 35.4 
 0.262 
 
 1.00 
 30.4 
 0.395 
 
 1.25 
 23.8 
 0.830 
 
 1.50 
 19.5 
 1.49 
 
 1.75 
 16.6 
 2.45 
 
 2.00 
 
 14.4 
 3.74 
 
 2.25 
 12.7 
 5.45 
 
 2.50 
 11.4 
 7.34 
 
 No. 10 
 0.135" 
 
 D 
 
 W 
 
 F 
 
 0.875 
 77 
 0.081 
 
 1.00 
 67 
 0.135 
 
 1.25 
 52 
 0.276 
 
 1.50 
 42.5 
 0.512 
 
 1.75 
 36 
 
 0.846 
 
 2.00 
 31 
 1.295 
 
 2.25 
 27 
 1.910 
 
 2.50 
 24 
 2.660 
 
 2.75 
 22 
 3.58 
 
 3.00 
 20 
 
 4.75 
 
 No. 8 
 0.162" 
 
 D 
 W 
 F 
 
 1.00 
 120 
 0.0570 
 
 1.25 
 98.5 
 0.124 
 
 1.50 
 76 
 0.199 
 
 1.75 
 64 
 0.554 
 
 2.00 
 55.5 
 0.597 
 
 2.25 
 
 48.8 
 0.880 
 
 2.50 
 43.5 
 1.26 
 
 2.75 
 39 
 1.68 
 
 3.00 
 36 
 2.20 
 
 3.25 
 33 
 
 2.85 
 
 No. 7 
 0.177" 
 
 D 
 W 
 F 
 
 1.00 
 159 
 0.0382 
 
 1.25 
 122 
 0.0828 
 
 1.50 
 99 
 0.156 
 
 1.75 
 
 83.5 
 0.265 
 
 2.00 
 72 
 0.416 
 
 2.25 
 63 
 0.603 
 
 2.50 
 56.4 
 0.830 
 
 2.75 
 51 
 1.15 
 
 3.00 
 46.5 
 1.54 
 
 3.25 
 42.5 
 1.96 
 
 No. 6 
 0.192" 
 
 D 
 
 W 
 F 
 
 1.25 
 158 
 0.0572 
 
 1.50 
 128 
 0.108 
 
 1.75 
 107 
 0.185 
 
 2.00 
 92.5 
 0.284 
 
 2.25 
 81 
 0.420 
 
 2.50 
 72 
 0.590 
 
 2.75 
 65 
 0.802 
 
 3.00 
 
 59.5 
 1.07 
 
 3.25 
 55.5 
 1.38 
 
 3.50 
 50 
 1.74 
 
 No. 3 
 0.205" 
 
 D 
 W 
 
 F 
 
 1.50 
 155 
 0.0820 
 
 1.75 
 131 
 0.139 
 
 2.00 
 113 
 0.218 
 
 2.25 
 99 
 0.321 
 
 2.50 
 
 88.5 
 0.412 
 
 2.75 
 80 
 0.6175 
 
 3.00 
 70 
 0.82 
 
 3.25 
 67 
 1.60 
 
 3.50 
 61.5 
 1.34 
 
 4.00 
 53.5 
 2.22 
 
 No. 4 
 0.225" 
 
 D 
 W 
 F 
 
 1.50 
 210 
 0.0536 
 
 1.75 
 175 
 0.093 
 
 2.00 
 150 
 0.147 
 
 2.25 
 132 
 0.220 
 
 2.50 
 118 
 0.303 
 
 2.75 
 106 
 0.412 
 
 3.00 
 97 
 0.652 
 
 3.25 
 89 
 0.715 
 
 3.50 
 82 
 0.91 
 
 4.00 
 71 
 1.30 
 
 No. 2 
 0.263" 
 
 D 
 W 
 F 
 
 1.50 
 345 
 0.0264 
 
 1.75 
 290 
 0.0458 
 
 2.00 
 250 
 0.0730 
 
 2.25 
 215 
 0.109 
 
 2.50 
 192 
 0.154 
 
 2.75 
 175 
 0.214 
 
 3.00 
 156 
 0.274 
 
 3.25 
 146 
 0.371 
 
 3.50 
 134 
 0.469 
 
 4.00 
 115 
 0.720 
 
 No. 1 
 0.283" 
 
 D 
 
 W 
 F 
 
 1.75 
 360 
 0.0328 
 
 2.00 
 310 
 0.0550 
 
 2.25 
 270 
 0.0778 
 
 2.50 
 240 
 0.112 
 
 2.75 
 215 
 0.155 
 
 3.00 
 195 < 
 0.208 
 
 3.25 
 
 , 180 
 0.270 
 
 3.50 
 165 
 0.344 
 
 4.00 
 145 
 0.530 
 
 4.50 
 127 
 0.775 
 
 No. 
 0.307" 
 
 D 
 
 W 
 F 
 
 1.75 
 470 
 0.0308 
 
 2.00 
 400 
 0.0380 
 
 2.25 
 350 
 0.0548 
 
 2.50 
 310 
 0.0788 
 
 2.75 
 280 
 0.109 
 
 3.00 
 250 
 0.149 
 
 3.25 
 230 
 0.199 
 
 3.50 
 212 
 0.244 
 
 4.00 
 185 
 0.327 
 
 4.50 
 162 
 0.550 
 
 No. 00 
 0.331" 
 
 D 
 W 
 F 
 
 2.00 
 510 
 0.0289 
 
 2.25 
 445 
 0.0388 
 
 2.50 
 390 
 0.0564 
 
 2.75 
 350 
 0.0780 
 
 3.00 
 320 
 0.105 
 
 3.25 
 290 
 0.137 
 
 3.50 
 270 
 0.176 
 
 4.00 
 230 
 0.273 
 
 4.50 
 205 
 0.414 
 
 5.00 
 183 
 0.562 
 
 To find deflection of one coil by one pound, divide the values of F by 100. 
 
422 
 
 SPRINGS. 
 
 ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. 
 
 Pennsylvania Railroad Specifications, 1896. 
 
 
 a 
 
 0> 
 01 
 
 t 
 
 m. 
 
 
 Test 
 
 3. 
 
 
 Class. 
 
 u 
 
 XJ 
 
 *t 
 
 *3 
 
 S a) 
 
 0Q 
 1-1 
 
 * 
 
 ii 
 
 Plates, 
 No. Size, In 
 
 Ins. high. Ibs. 
 (a) (6) 
 
 Ins. Ibs. 
 
 (a) 
 
 J 
 
 oS, 
 aj 
 
 E 1 Triple . 
 
 40 
 
 113/4 
 
 5 3 x ll/3-> 
 
 3 3/4 9 3/8 4 800 
 
 3 5 500 
 
 ? 
 
 E 2, Quadruple . . 
 E 3 Triple .... 
 
 40 
 36 
 
 151/ 2 
 113/4 
 
 5 3 x3/ 8 
 6 3 X 11/32 
 
 33/4 93/ 4 6,650 
 4 95/8 6 000 
 
 3 8,000 
 3 8000 
 
 2 
 
 E 4, Singlet--. 
 
 40 
 
 
 8 3 X 11/32 
 
 5* ffee 
 
 3 2350 
 
 
 E5, " t 
 
 E 6 " |.. 
 
 40 
 
 4? 
 
 
 7 3x3/ 8 
 8 31/2X3/ 8 
 
 1 5/16* .... 3,000 
 1 1/8* 4 375 
 
 4,970 
 6350 
 
 
 E 7. Triple 
 
 36 
 
 i i 3/4 
 
 8 3 X 11/30 
 
 21/2 91/2 11 800 
 
 
 
 E 8, Double 
 E 9, ' 
 E 10, Quadruple.. 
 E 11, 
 E 12, 
 E 13, Double 
 E 14, " 
 E 15, Quadruple.. 
 E 16, 
 E 17, Double 
 E 18, Singlet.... 
 E 19, Double 
 E 20 
 
 32 
 36 
 40 
 40 
 34 
 30 
 40 
 36 
 30 
 36 
 42 
 22 
 ?? 
 
 71/2 
 91/2 
 15V 2 
 151/2 
 151/2 
 91/2 
 91/2 
 151/2 
 151/2 
 91/2 
 
 "ioi/2 
 
 101/2 
 
 6 3 x3/ 8 
 5 4x11/32 
 5 3 x3/ 8 
 5 3X3/8 
 5 3x3/8 
 5 4x3/8 
 6 4X11/32 
 6 3xll/3 2 
 6 3x11/32 
 5 4x3/8 
 9 31/ 2 x3/ 8 
 6 41/2X11/32 
 7 41/2x11/32 
 
 3 9 8,000 
 31/ 2 87/ 16 5,400 
 4 10 8,000 
 33/4 93/4 10,600 
 33/4 93/4 .13,100 
 33/4 9 5,600 
 33/8 9 6,840 
 37/16 93/4 11,820 
 41/2 101/s 8,000 
 23/4 8 8,070 
 1* 5,250 
 13/16 67/ 16 13,800 
 13/16 71/8 I 5 60 
 
 3" 6', 666 
 
 3 10,000 
 3 12,200 
 3 15,780 
 2 10,600 
 2 8,600 
 21/ 2 14,370 
 23/ 4 15,500 
 2 9,540 
 7,300 
 
 "2 
 2 
 2 
 
 2 
 
 E2li 
 E 22, 
 E 23, 
 
 E 24, .... 
 
 24 
 24 
 36 
 36 
 
 101/ 2 
 JO* 
 
 10 
 
 7 41/ 2 X3 8 
 8 41/ 2 X3/8 
 5 4x3/ 8 
 5 4x3/8 
 
 1 71/4 15>50 
 1 81/ 2 18,000 
 21/4 8 8,750 
 21/4 8 7.500 
 
 28,800 
 32,930 
 11 '4 10,750 
 11/4 9,500 
 
 
 (a) Between bands; (&) over all; a.p.t., auxiliary plates touching. 
 * Between bottom of eye and top of leaf, t Semi-elliptical. 
 Tracings are furnished for each class of spring. 
 
 SPRINGS TO RESIST TORSIONAL FORCE. 
 
 (Reuleaux's Constructor.) 
 
 Flat spiral or helical spring P = 
 
 o H 
 
 = 12 
 
 Round helical spring P 
 
 32 R' 
 
 PIR* 
 
 Ebh*' 
 
 PI 
 
 E 
 
 Round bar, in torsion F = =-= ^* 
 
 <* lu /t 
 
 Flat bar, in torsion. 
 
 ' 3RV& 
 
 P = force applied at end of radius or lever-arm R\ & = angular motion 
 at end of radius R; S = permissible maximum stress, = 4/ 5O f permissible 
 stress in flexure: E = modulus of elasticity in tension; G = torsionaJ 
 modulus, = 2/5 E; I = developed length of spiral, or length of bar; d = 
 diameter of wire; b = breadth of flat bar; h = thickness. 
 (Compare Elastic Resistance to Torsion, p. 334.) 
 
HELICAL SPRINGS. 
 
 423 
 
 HELICAL SPRINGS SIZES AND CAPACITIES. 
 
 (Selected from Specifications of Penna. R. R. Co., 1899.) 
 
 
 
 
 
 
 +H 
 
 Test. Height and 
 
 0) 
 
 "M 
 
 
 00 
 
 a 
 
 ^T 
 
 co 
 
 ^ 
 
 O 
 
 Loads. 
 
 .S 
 
 3 
 
 f_T 
 
 & 
 
 .S 
 
 8 
 
 a 
 
 
 25 
 
 
 
 
 o 
 
 <& 
 
 
 Q 
 
 
 
 
 
 
 GO 
 
 
 Q 
 
 
 
 s 
 
 
 ^ 
 
 Qg 
 
 GO 
 
 GO 
 
 
 ,0 
 
 >j 01 
 
 
 
 * 
 
 .d 
 
 i 
 
 | 
 
 "S'Z r 
 
 .S 
 
 .s 
 
 1 
 
 ? 
 
 'S""* 
 
 e3 " 
 
 fc 
 
 5 
 
 "M oi 
 
 i 
 
 E 
 
 1 
 
 J2 o 
 
 "So 
 o 
 
 of 
 
 1 
 
 GO 
 
 c 
 
 i i 
 
 I 
 
 o/o 
 
 6 s 
 
 
 
 
 
 Ibs. oz 
 
 
 
 
 
 
 
 H 26 
 
 9/64 
 
 571/2 
 
 59 
 
 4 
 
 i 
 
 53/4 
 
 3 
 
 31/4 
 
 no 
 
 130 
 
 H 18 
 
 H/64 
 
 75 
 
 761/4 
 
 8 
 
 i 
 
 8 
 
 5 
 
 6 
 
 170 
 
 270 
 
 H 55 
 
 3/16 
 
 451/8 
 
 465/ 16 
 
 55/ 8 
 
 i 
 
 41/2 
 
 35/16 
 
 4 
 
 103 
 
 245 
 
 H 73 
 
 3/16 
 
 426 
 
 4273/4 
 
 3 51/2 
 
 15/16 
 
 39 
 
 221/2 
 
 35 
 
 45 
 
 185 
 
 H 29 
 
 7/32 
 
 20 !/> 
 
 227/ 16 
 
 31/2 
 
 115/32 
 
 HI/16 
 
 19/64 
 
 13/8 
 
 110 
 
 200 
 
 H 1 
 
 1/4 
 
 451/2 
 
 47 
 
 10 
 
 U/4 
 
 51/8 
 
 35/8 
 
 43/ 8 
 
 250 
 
 500 
 
 H 5 
 
 V4 
 
 251/4 
 
 281/4 
 
 6 
 
 2V4 
 
 21/4 
 
 H/8 
 
 U/2 
 
 164 
 
 240 
 
 H 58 
 
 5/16 
 
 2531/2 
 
 2561/2 
 
 5 7 
 
 21/4 
 
 23 
 
 13 
 
 18 
 
 248 
 
 495 
 
 H 74 
 
 5/16 
 
 180 
 
 1821/s 
 
 3 141/2 
 
 IU/16 
 
 191/ 8 
 
 13 
 
 141/ 8 
 
 587 
 
 700 
 
 H 681* 
 
 3/8 
 
 991/2 
 
 1031/4 
 
 3 U/2 
 
 23/4 
 
 9 
 
 5 
 
 7 
 
 350 
 
 700 
 
 H 79 
 
 3/8 
 
 88 
 
 903/4 
 
 2 12 
 
 21/8 
 
 85/ 8 
 
 6 
 
 63/4 
 
 676 
 
 946 
 
 H 802 
 
 13/32 
 
 1923/g 
 
 1953/4 
 
 7 '1/2 
 
 29/16 
 
 18 
 
 119/16 
 
 151/2 
 
 380 
 
 975 
 
 H 43 
 
 7/16 
 
 96 
 
 1025/i 6 
 
 4 1 
 
 47/16 
 
 815/ie 
 
 33/8 
 
 51/8 
 
 450 
 
 660 
 
 H 64 
 
 7/16 
 
 755/8 
 
 781/2 
 
 3 3 
 
 29/32 
 
 75/8 
 
 55/8 
 
 53/4 
 
 1350 
 
 1440 
 
 H 53 2 
 
 15/32 
 
 1695/iQ 
 
 1729/16 
 
 8 4 
 
 217/32 
 
 61/ 2 
 
 21/4 
 
 51/2 
 
 330 
 
 1410 
 
 H 27 2 
 
 1/2 
 
 903/4 
 
 951/8 
 
 5 
 
 31/4 
 
 81/2 
 
 51/4 
 
 63/4 
 
 810 
 
 1500 
 
 H 61 
 
 1/2 
 
 151/2 
 
 213/s 
 
 133/4 
 
 41/4 
 
 13/8 
 
 05/8 
 
 1 
 
 532 
 
 1050 
 
 H 19 
 
 17/32 
 
 8U/2 
 
 851/2 
 
 5 2 
 
 31/32 
 
 8 
 
 59/ie 
 
 67/16 
 
 1200 
 
 1900 
 
 H 86 3 
 
 17/32 
 
 1535/8 
 
 159 
 
 9 10 
 
 4 
 
 33/4 
 
 71/2 
 
 87/ 16 
 
 1156 
 
 1360 
 
 H 63 
 
 9/16 
 
 98 
 
 103 
 
 6 15 
 
 33/4 
 
 91/8 
 
 51/2 
 
 7 
 
 1050 
 
 1800 
 
 H 33 3 
 
 9/16 
 
 801/4 
 
 847/s 
 
 5 101/9 
 
 31/4 
 
 8 
 
 53/8 
 
 613/ie 
 
 1000 
 
 2200 
 
 H 59 2 
 
 5/8 
 
 741/4 
 
 773/4 
 
 67" 
 
 27/8 
 
 81/4 
 
 69/ie 
 
 71/4 
 
 2100 
 
 3500 
 
 H 8(h 
 
 5/8 
 
 1921/2 
 
 1973/4 
 
 16 11 
 
 315/ie 
 
 8 
 
 19/16 
 
 51/2 
 
 900 
 
 2315 
 
 H 72 2 
 H 15 2 
 
 21/32 
 U/16 
 
 601/8 
 
 557/ 8 
 
 631/2 
 593/ 4 
 
 \ !i 7/8 
 
 23/4 
 31/ 2 
 
 75/16 
 53/4 
 
 6 
 
 45/ 16 
 
 63/8 
 53/i 6 
 
 3260 
 1400 
 
 4240 
 3500 
 
 H 41 
 H 40 
 
 U/16 
 
 3/4 
 
 1171/2 
 1771/2 
 
 1231/ 2 
 1865/8 
 
 12 10 
 
 22 21/2 
 
 41/2 
 6V 2 
 
 07/8 
 6 
 
 63/4 
 
 73/8 
 
 85/8 
 87/8 
 
 1500 
 1900 
 
 2720 
 2300 
 
 H 70 
 
 3/4 
 
 62 
 
 66 
 
 7 12 
 
 33/ 8 
 
 7 
 
 55/8 
 
 61/4 
 
 2750 
 
 5050 
 
 H 17 2 
 
 13/16 
 
 100 
 
 1063/4 
 
 14 12 
 
 51/8 
 
 91/8 
 
 6 
 
 75/8 
 
 1700 
 
 3700 
 
 H 662 
 
 13/16 
 
 1051/4 
 
 1103/8 
 
 15 7 
 
 45/32 
 
 07/8 
 
 81/8 
 
 87/8 
 
 3670 
 
 5040 
 
 H 37 
 
 27/32 
 
 77 
 
 817/8 
 
 12 21/2 
 
 315/16 
 
 81/2 
 
 6U/16 
 
 71/2 
 
 3300 
 
 6250 
 
 H 87 2 
 
 27/32 
 
 3013/J6 
 
 13715/ie 
 
 20 9 
 
 53/8 
 
 21/4 
 
 73/4 
 
 87/16 
 
 3540 
 
 4165 
 
 H 12 2 
 
 7/8 
 
 85 
 
 9U/2 
 
 14 7 
 
 5 
 
 81/2 
 
 53/ : 
 
 73/ 8 
 
 2000 
 
 5200 
 
 H 33. 
 
 7/8 
 
 82 
 
 8811/i 6 
 
 13 15 
 
 51/8 
 
 8 
 
 53/8 
 
 613/16 
 
 2250 
 
 5000 
 
 H 2 
 
 15/16 
 
 46 
 
 523/ 8 
 
 8 151/ 4 
 
 5 
 
 45/ 8 
 
 33/8 
 
 4 
 
 3250 
 
 7000 
 
 H 16 
 
 15/16 
 
 85 
 
 927/s 
 
 16 10 
 
 > 
 
 8 
 
 5 
 
 6 
 
 3600 
 
 5100 
 
 H 10 
 
 
 85 
 
 92 
 
 18 14 
 
 51/2 
 
 81/2 
 
 6 
 
 7 
 
 4500 
 
 7000 
 
 H 42! 
 
 
 36 
 
 427/ 8 
 
 8 
 
 53/8 
 
 35/8 
 
 25/8 
 
 33/ 8 
 
 1795 
 
 7180 
 
 H 4 
 
 1 1/16 
 
 987/s 
 
 105 
 
 24 12 
 
 | 
 
 07/8 
 
 81/2 
 
 93/8 
 
 6000 
 
 9570 
 
 H 861 
 
 U/16 
 
 535/s 
 
 1641/2 
 
 38 9 
 
 8 
 
 33/4 
 
 71/2 
 
 87/i 6 
 
 4624 
 
 5440 
 
 H 3 
 
 U/8 
 
 353/ 8 
 
 4U/4 
 
 9 15 
 
 47/8 
 
 41/8 
 
 33/8 
 
 33/4 
 
 6000 
 
 12000 
 
 H 14! 
 
 H/8 
 
 51 
 
 587/s 
 
 14 4 
 
 61/8 
 
 51/8 
 
 3H/16 
 
 43/16 
 
 5000 
 
 8950 
 
 H6! 
 
 3/16 
 
 991/s 
 
 1093/ 4 
 
 31 1 
 
 8 
 
 91/8. 
 
 51/2 
 
 7 
 
 4550 
 
 7750 
 
 H47 
 
 3/16 
 
 731/2 
 
 791/ 2 
 
 23 
 
 57/ie 
 
 81/4 
 
 69/ie 
 
 71/4 
 
 7400 
 
 12500 
 
 H 9 
 
 1/4 
 
 971/2 
 
 108 
 
 33 12 
 
 8 
 
 9 
 
 53/4 
 
 71/2 
 
 4000 
 
 9100 
 
 H 72i 
 
 1/4 
 
 621/8 
 
 683/4 
 
 21 81/2 
 
 53/8 
 
 75/16 
 
 6 
 
 63/8 
 
 0700 
 
 14875 
 
 H 8 
 
 5/ie 
 
 96 
 
 1061/2 
 
 36 12 
 
 8 
 
 91/8 
 
 6 
 
 71/4 
 
 6350 
 
 10600 
 
 H 62 
 
 5/16 
 
 70 
 
 771/ie 
 
 26 12 
 
 513/16 
 
 8 
 
 6V 2 
 
 71/4 
 
 7900 
 
 15800 
 
 H 12! 
 
 3/8 
 
 87 
 
 973/ 8 
 
 36 7 
 
 8 
 
 81/2 
 
 53/4 
 
 73/ 8 
 
 5000 
 
 12200 
 
 H 39i 
 
 3/8 
 
 755/ 8 
 
 831/2 
 
 31 11 
 
 63/8 
 
 83/8 
 
 65/ 8 
 
 71/2 
 
 8150 
 
 16300 
 
 H 28i 
 
 13/32 
 
 8411/ie 
 
 95 
 
 37 3 
 
 8 
 
 81/4 
 
 53/4 
 
 67/8 
 
 7325 
 
 13250 
 
 * The subscript 1 means the outside coil of a concentric group or 
 cluster; 2 and 3 are inner coils. 
 
424 EIVETED JOINTS. 
 
 Phosphor-Bronze Springs. Wilfred Lewis (Engs'. Club, Phila., 1887) 
 
 made some tests of a helical spring of phosphor-bronze wire, 0.12 in. 
 diameter, 11/4 in. diameter from center to center, making 52 coils. 
 
 Such a spring of steel, according to the practice of the P. R. R., might 
 be used for 40 Ibs. A load of 30 Ibs. gradually applied gave a permanent 
 set. With a load of 21 Ibs. in 30 hours the spring lengthened from 20 5/ 8 
 inches to 21 1/8 inches, and in 200 hours to 21 1/4 inches. It was concluded 
 that 21 Ibs. was too great for durability. For a given load the extension 
 of the bronze spring was just double the extension of a similar steel 
 spring, that is, for the same extension the steel spring is twice as strong. 
 Chromium- Vanadium Spring Steel. (Proc. Inst. M. E., 1904, pp 
 1263, 1305.) A spring steel containing C, 0.44; Si, 0.173; Mn, 0.837; Cr, 
 1.044; Va, 0.188 was made into a spring with dimensions as follows: length 
 unstretched 9.6 in. s mean diam. of coils (D) 5.22; No. of coils (n) 4; diam. 
 of wire, (d) 0.561. It was tempered in the usual way. When stretched 
 it showed signs of permanent set at about 1900 Ibs. Compared with two 
 springs of ordinary steels the following formulae are obtained: 
 
 Load at which Permanent Set begins. Extension for a load W. 
 
 Chrome- Vanadium Spring. . .56,300 d*/D Ibs. WnD* + 1,468,000 d* 
 
 West Bromwich Spring 28,400 d*/D " WnD* -^- 1,575,000 d* 
 
 Turton & Platt Spring 44,200 d*/D " WnD* + 1,331,600 d* 
 
 Test of a Vanadium-steel Spring. (Circular of the American Vana- 
 dium Co., 1908). Comparative tests of an ordinary carbon-steel loco- 
 motive flat spring and of a vanadium-steel spring, made by the American 
 Locomotive Co., showed the following: The vanadium spring, on 36-in. 
 centers tested to 94,000 Ibs., reached its elastic limit at 85,000 Ibs., or 
 234,000 Ibs. per sq. in. fiber stress, and a permanent set of 0.48 in. The 
 test was repeated three times without change in the deflection. The 
 carbon spring was tested to 89,280 Ibs. and reached an elastic limit at 
 65,000 Ibs., or 180,000 Ibs. fiber stress, with a permanent set of 1.12 in. 
 On repeating the test it took an additional set of 0.25 in., and on the next 
 test several of the plates failed. 
 
 RIVETED JOINTS. 
 
 Fairbairn's Experiments. The earliest published experiments on 
 riveted joints are contained in the memoir by Sir W. Fairbairn in the 
 Transactions of the Royal Society. Making certain empirical allow- 
 ances, he adopted the following ratios as expressing the relative strength 
 
 of riveted joints: Solid plate 100 
 
 Double-riveted joint 70 
 
 Single-riveted joint 56 
 
 These celebrated ratios appear to rest on a very unsatisfactory analysis 
 of the experiments on which they were based. 
 
 Loss of Strength in Punched Plates. (Proc. Inst. M. E. t 1881.) 
 A report by Mr. W. Parker and Mr. John, made in 1878 to Lloyd's Com- 
 mittee, on the effect of punching and drilling, showed that thin steel 
 plates lost comparatively little from punching, but that in thick plates 
 the loss was very considerable. The following table gives the results for 
 plates punched and not annealed or reamed: 
 
 Thickness of plates A'4 3 /8 1/2 3 /4 
 
 Loss of tenacity, per cent 8 18 26 33 
 
 When 7/8-in. punched holes were reamed out to IVsin. diameter, the loss 
 of tenacity disappeared, and the plates carried as high a stress as drilled 
 plates. Annealing also restores to punched plates their original tenacity. 
 
 The Report of the Research Committee of the Instituti9n of Mechanical 
 Engineers, on Riveted Joints (1881), and records of investigations by Prof. 
 A. B. W. Kennedy (1881, 1882, and 1885), summarize the existing in- 
 formation regarding the comparative effects of punching and drilling 
 upon iron and steel plates. An examination of the voluminous tables 
 given in Professor Unwin's Report, of the experiments made on iron and 
 - steel plates leads to the general conclusion that, while thin plates, even 
 of steel, do not suffer very much from punching, yet in those of 1/2 inch 
 thickness and upwards the loss of tenacity due to punching ranges from 
 10% to 23% in iron plates, and from 11% to 33% in the case of mild 
 steel. In drilled plates there is no appreciable loss of strength, It is 
 
RIVETED JOINTS. 
 
 425 
 
 possible to remove the bad effects of punching by subsequent reaming or 
 annealing. The introduction of a practicable method of drilling the 
 plating of ships and other structures, after it has been bent and shaped, 
 is a matter of great importance. In the modern English practice (1887) 
 of the construction of steam-boilers with steel plates punching is almost 
 entirely abolished, and all rivet-holes are drilled after the plates have 
 been bent to the desired form. 
 
 Strength of Perforated Plates. (P. D. Bennett, Eng'g, Feb. 12, 
 1886. p. 155.) Tests were made to determine the relative effect pro- 
 duced upon tensile strength of a flat bar of iron or steel: 1. By a s/4-inch 
 hole drilled to the required size; 2. By a hole punched Vs inch smaller 
 
 and then drilled to the size of the first hole; and, 3. By a hole punched in 
 the bar to the size of the drilled hole. The relative results in strength 
 per square inch of original area were as follows: 
 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 
 Iron 
 1.000 
 1.029 
 1.030 
 0.795 
 
 Iron. 
 1.000 
 1.012 
 1.008 
 0.894 
 
 Steel. 
 1 000 
 1.068 
 1.059 
 0.935 
 
 Steel. 
 1.000 
 1.103 
 1.110 
 927 
 
 Perforated by drilling . 
 
 Perforated by punching and drilling 
 Perforated by punching only 
 
 
 In tests 2 and 4 the holes were filled with rivets driven by hydraulic 
 pressure. The increase of strength per square inch caused by drilling is 
 a phenomenon of similar nature to that of the increased strength of a 
 grooved bar over that of a straight bar of sectional area equal to the 
 smallest section of the grooved bar. Mr. Bennett's tests on an iron bar 
 0.84 in. diameter, 10 in. long, and a similar bar turned to 0.84 in. diam- 
 eter at one point only, showed that the relative strength 01 the latter to 
 the former was 1.323 to 1.000. 
 
 Comparative Efficiency of Riveting done by Different Methods. 
 
 The Reports of Professors Unwin and Kennedy to the Institution of 
 Mechanical Engineers (Proc. 1881, 1882, and 1885) tend to establish the 
 four following points: 
 
 1. That the shearing resistance of rivets is not highest in joints riveted 
 by means of the greatest pressure; 
 
 2. That the ultimate strength of joints is not affected to an appre- 
 ciable extent by the mode of riveting; and, therefore, 
 
 3. That very great pressure upon the rivets in riveting is not the in- 
 dispensable requirement that it has been sometimes supposed to be; 
 
 4. That the most serious defect of hand-riveted as compared with 
 machine-riveted work consists in the fact that in hand-riveted joints 
 visible slip commences at a comparatively small load, thus giving such 
 joints a low value as regards tightness, and possibly also rendering them 
 liable to failure under sudden strains after slip has once commenced. 
 
 The following figures of mean results give a comparative view of hand 
 and hydraulic riveting, as regards their ultimate strengths in joints, and 
 the periods at which in both cases visible slip commenced. 
 
 
 Hand 
 
 86 01 
 
 82 16 
 
 149 2 
 
 193 6 
 
 Total breaking load. Tons . . . . | 
 
 Hydraulic 
 
 85 75 
 
 82 70 
 
 145 5 
 
 183 1 
 
 
 Hand 
 
 21.7 
 
 25.0 
 
 31 7 
 
 25 
 
 
 Hydraulic 
 
 47.5 
 
 53.7 
 
 49.7 
 
 56.0 
 
 Some of the Conclusions of the Committee of Research on Riveted 
 Joints. 
 
 (Proc. Inst. M. E., April, 1885.) 
 
 The conclusions refer to joints made in soft steel plate with steel rivets, 
 the holes drilled, and the plates in their natural state (unannealed). 
 The rivet or shearing area has been assumed to be that of the holes, not 
 the area of the rivets themselves. The strength of the metal in the joint 
 has been compared with that of strips cut from the same plates. 
 
426 
 
 RIVETED JOINTS. 
 
 The metal between the rivet-holes has a considerably greater tensile 
 resistance per square inch than the unperf orated metal. This excess 
 tenacity amounted to more than 20%, both in 3/ 8 -inch and 3/ 4 -inch plates, 
 when the pitch of the rivet was about 1.9 diameters. In other cases 3/g-inch 
 plate gave an excess of 15% at fracture with a pitch of 2 diameters, of 
 10% with a pitch of 3.6 diameters, and of 6.6%, with a pitch of 3.9 
 diameters; and 3/ 4 -inch plate gave 7.8% excess with a pitch of 2.8 
 diameters. 
 
 In single-riveted joints it may be taken that about 22 tons per square 
 inch is the shearing resistance of rivet steel, when the pressure on the 
 rivets does not exceed about 40 tons per square inch. In double-riveted 
 joints, with rivets of about 3/4-inch diameter, most of the experiments 
 gave about 24 tons per square inch as the shearing resistance, but the 
 joints in one series went at 22 tons. [Tons of 2240 Ibs.] 
 
 The ratio of shearing resistance to tenacity is not constant, but dimin- 
 ishes very markedly and not very irregularly as the tenacity increases. 
 ' The size of the rivet heads and ends plays- a most important part in the 
 strength of the joints at any rate in the case of single-riveted joints. 
 An increase of about one-third in the weight of the rivets (all this increase, 
 of course, going to the heads and ends) was found to add about 81/2% to 
 the resistance of the joint, the plates remaining unbroken at the full 
 shearing resistance of 22 tons per square inch, instead of tearing at a 
 shearing stress of only a little over 20 tons. The additional strength is 
 probably due to the prevention of the distortion of the plates by the 
 great tensile stress in the rivets. 
 
 The intensity of bearing pressure on the rivet exercises, with joints 
 proportioned in the ordinary way, a very important influence on their 
 strength. So long as it does not exceed 40 tons per square inch (meas- 
 ured on the projected area of the rivets), it does not seem to affect their 
 strength; but pressures of 50 to 55 tons per square inch seem to cause 
 the rivets to shear in most cases at stresses varying from 16 to 18 tons 
 per square inch. For ordinary joints, which are to be made equally 
 strong in plate and in rivets, the bearing pressure should therefore prob- 
 ably not exceed 42 or 43 tons per square inch. For double-riveted butt- 
 joints perhaps, as will be noted later, a higher pressure may be allowed, 
 as the shearing stress may probably not be more than 16 or 18 tons per 
 square inch when the plate tears. 
 
 A margin (or net distance from outside of holes to edge of plate) equal 
 to the diameter of the drilled hole has been found sufficient in all cases 
 hitherto tried. 
 
 To attain the maximum strength of a joint, the breadth of lap must be 
 such as to prevent it from breaking zigzag. It has been found that the 
 net metal measured zigzag should be from 30% to 35% in excess of that 
 measured straight across, in order to insure a straight fracture. This 
 corresponds to a diagonal pitch of 2/3 p + d/3, if p be the straight pitch 
 and d the diameter of the rivet-hole. 
 
 Visible slip or "give" occurs always in a riveted joint at a point very 
 much below its breaking load, and by no means proportional to that load. 
 A collation of the results obtained in measuring the slip indicates that it 
 depends up9n the number and size of the rivets in the joint, rather than 
 upon anything else; and that it is tolerably constant for a given size of 
 rivet in a given type of joint. The loads per rivet at which a joint will 
 commence to slip visibly are approximately as follows: 
 
 Diameter of Rivet. 
 
 Type of Joint. 
 
 Riveting. 
 
 Slipping Load per 
 Rivet. 
 
 3/4 inch 
 8/4 
 8/4 
 linch 
 1 " 
 1 " 
 
 Single-riveted 
 Double- riveted 
 Double-riveted 
 Single- riveted 
 Double- riveted 
 Double- riveted 
 
 Hand 
 Hand 
 Machine 
 Hand 
 Hand 
 Machine 
 
 2.5 tons 
 3.0 to 3.5 tons 
 7 tons 
 3.2 tons 
 4.3 tons 
 8 to 10 tons 
 
RIVETED JOINTS. 
 
 427 
 
 
 To find the probable load at which a joint of any breadth will commence 
 to slip, multiply the number of rivets in the given breadth by the proper 
 figure taken from the last column of the table above. The above figures 
 are not given as exact; but they represent the results of the experiments. 
 
 The experiments point to simple rules for the proportioning of joints of 
 maximum strength. Assuming that a bearing pressure of 43 tons per 
 square inch may be allowed on the rivet, and that the excess tenacity of 
 the plate is 10% of its original strength, the following table gives the 
 values of the ratios of diameter d of hole to thickness t of plate (d *- 0, 
 and of pitch p to diameter of hole (p -5- d) in joints of maximum strength 
 in 3/ 8 -inch plate. 
 
 For Single-riveted Plates. 
 
 Original Tenacity of 
 Plate. 
 
 Shearing Resistance 
 of Rivets. 
 
 Ratio. 
 d-r-t 
 
 Ratio. 
 
 Ratio. 
 Plate Area 
 
 
 
 
 
 Tons per 
 Sq. In. 
 
 Lbs. per 
 Sq. In. 
 
 Tons per 
 Sq. In. 
 
 Lbs. per 
 Sq. In. 
 
 
 
 Rivet Area 
 
 30 
 
 67,200 
 
 22 
 
 49,200 
 
 2.48 
 
 2.30 
 
 0.667 
 
 28 
 
 62,720 
 
 22 
 
 49,200 
 
 2.48 
 
 2.40 
 
 0.785 
 
 30 
 
 67,200 
 
 24 
 
 53,760 
 
 2.28 
 
 2.27 
 
 0.713 
 
 28 
 
 62,720 
 
 24 
 
 53,760 
 
 2.28 
 
 2.36 
 
 0.690 
 
 This table shows that the diameter of the hole should be 2Vs times the 
 thickness of the plate, and the pitch of the rivets 23/g times the diameter 
 of the hole. Also, it makes the mean plate area 71% of the rivet area. 
 If a smaller rivet be used than that here specified, the joint will not be of 
 uniform, and therefore not of maximum, strength; but with any other 
 size of rivet the t>est result will be got by use of the pitch obtained from the 
 simple formula p = ad 2 /t + d, where, as before, d is the diameter of the 
 hole. 
 
 The value of the constant a in this equation is as follows: 
 For 30-ton plate and 22-ton rivets, a = 0.524 
 
 " 28 " " " 22 " " " 0.558 
 ,. 3Q , 24 .. 05?0 
 
 " 28 " " " 24 " " " 0.606 
 
 Or, in the mean, the pitch p 
 
 0.56 - + d. 
 
 With too small rivets this 
 
 gives pitches often considerably smaller in proportion than 23/s times the 
 diameter. 
 
 For double-riveted lap-joints a similar calculation to that given 
 above, but with a somewhat smaller allowance for excess tenacity, on 
 account of the large distance between the rivet-holes, shows that for joints 
 of maximum strength the ratio of diameter to thickness should remain 
 precisely as in single-riveted joints; while the ratio of pitch to diameter 
 of hole should be 3.64 for 30-ton plates and 22 or 24 ton rivets, and 3.82 
 for 28-ton plates with the same rivets. 
 
 Here, still more than in the former case, it is likely that the prescribed 
 size of rivet may often be inconveniently large. In this case the diameter 
 of rivet should be taken as large as possible; and the strongest joint for 
 a given thickness of plate and diameter of hole can then be obtained by 
 using the pitch given by the equation p = ad 2 /t + d, where the values of 
 the constant a for different strengths of plates and rivets may be taken 
 as follows, for any thickness of plate from 3/ 8 to 3/ 4 -inch: 
 
 For 30-ton plate and 24-ton rivets ) 
 
 28 " " " 22 " " j 
 
 30 " " 
 
 = 1.16 
 
 t 
 
 1.06 
 
 " 24 
 
 p ~ 1.24 
 
428 
 
 RIVETED JOINTS. 
 
 In double-riveted butt-joints it is impossible to develop the full 
 shearing resistance of the joint without getting excessive bearing pressure, 
 because the shearing area is doubled without increasing the area on which 
 the pressure acts. Considering only the plate resistance and the bearing 
 pressure, and taking this latter as 45 tons per square inch, the best pitch 
 would be about 4 times the diameter of the hole. We may probably say 
 with some certainty that a pressure of from 45 to 50 tons per square inch on 
 the rivets will cause shearing to take place at from 16 to 18 tons per square 
 inch. Working out the equations as before, but allowing excess strength 
 of only 5% on account of the large pitch, we find that the proportions of 
 double-riveted butt-joints of maximum strength, under given conditions, 
 are those of the following table: 
 
 Double-riveted Butt-joints. 
 
 Original Ten- 
 acity of Plate, 
 Tons per Sq. 
 In. 
 
 Shearing Re- 
 sistance of 
 Rivets, Tons 
 per Sq. In. 
 
 Bearing Pres- 
 sure, Tons per 
 Sq. In. 
 
 Ratio 
 d 
 t 
 
 Ratio 
 P 
 d 
 
 30 
 
 16 
 
 45 
 
 1.80 
 
 3.85 
 
 28 
 
 16 
 
 45 
 
 1.80 
 
 4.06 
 
 30 
 
 18 
 
 48 
 
 1.70 
 
 4.03 
 
 28 
 
 18 
 
 48 
 
 1.70 
 
 4.27 
 
 30 
 
 16 
 
 50 
 
 2.00 
 
 4.20 
 
 28 
 
 16 
 
 50 
 
 2.00 
 
 4.42 
 
 Practically, therefore, it may be said that we get a double-riveted butt- 
 joint of maximum strength by making the diameter of hole about 1.8 
 times the thickness of the plate, and making the pitch 4.1 times the 
 diameter of the hole. 
 
 The proportions just given betong to joints ot maximum strength. 
 But in a boiler the one part of the joint, the plate, is much more affected 
 by time, than the other part, the rivets. It is therefore not unreasonable 
 to estimate the percentage by which the iplates might be weakened 'by 
 corrosion, etc., before the boiler would be unfit for use at its proper 
 steam-pressure, and to add correspondingly to the plate area. Probably 
 the best thing to do in this case is to proportion the joint, not for the 
 actual thickness of plate, but for a nominal thickness less than the actual 
 by the assumed percentage. In this case the joint will be approximately 
 one of uniform strength by the time it has reached its final workable 
 condition; up to which time the joint as a whole will not really have been 
 weakened, the corrosion only gradually bringing the strength of the plates 
 down to that of rivets. 
 
 Efficiencies of Joints. 
 
 The average results of experiments by the committee gave: For double- 
 riveted lap-joints in 3 8 -inch plates, efficiencies ranging from 67.1% to 
 81.2%. For double-riveted butt-joints (in double shear) 61.4% to 71.3%. 
 These low results. were probably due to the use of very soft steel in the 
 rivets. For single-riveted lap-joints of various dimensions the efficiencies 
 varied from 54.8% to 60.8%. The shearing resistance of steel did not in- 
 crease nearly so fast as its tensile resistance. With very soft' steel, for 
 instance, of only 26 tons tenacity, the shearing resistance was about 80% 
 of the tensile resistance, whereas with very hard steel of 52 tons tenacity 
 the shearing resistance was only somewhere about 65% of the tensile 
 resistance. 
 
 Proportions of Pitch and Overlap of Plates to Diameter of Rivet- 
 Hole and Thickness of Plate. 
 
 (Prof. A. B. W. Kennedy, Proc. Inst. M. E., April, 1885.) 
 
 t = thickness of plate: 
 
 d = diameter of rivet (actual) in parallel hole; 
 
 p = pitch of rivets, center to center- 
 
 s = space between lines of rivets; 
 
 i overlap of plate. 
 
RIVETED JOINTS. 
 
 429 
 
 The pitch is as wide as is allowable without impairing the tightness ol 
 the joint under steam. 
 
 For single-riveted lap-joints in the circular seams of boilers wnich have 
 double-riveted longitudinal lap-joints, 
 
 d = t X 2.25; p = d X 2.25 = t X 5 (nearly); I = t X 6. 
 
 For double-riveted lap-joints: 
 
 d = 2.25J; p = 8t; s = 4.5J; I = 10.5J. 
 
 Single- riveted Joints. 
 
 Double-riveted Joints. 
 
 t 
 
 d 
 
 P 
 
 I 
 
 t 
 
 d 
 
 P 
 
 s 
 
 I 
 
 3/16 
 
 1/4 
 5/16 
 3/8 
 7/16 
 
 V 2 
 
 9/16 
 
 7/16 
 9/16 
 H/16 
 13/16 
 
 H/8 
 U/4 - 
 
 15/16 
 U/4 
 1 9/i 6 
 17/ 8 
 23/ie 
 21/ 2 
 213/16 
 
 H/8 
 H/2 
 
 17/8 
 21/4 
 25/8 
 
 33/8 
 
 3/16 
 1/4 
 5/16 
 
 $k 
 & 
 
 ' 7/ie 
 9/16 
 H/16 
 13/16 
 
 U'8 
 U/4 
 
 U/2 
 
 2 
 
 21/2 
 
 31/2 
 4 
 41/2 
 
 7/8 
 13/16 
 U/2 
 13/4 
 
 21/4 
 21/2 
 
 2 
 23/4 
 33/8 
 
 45/8 
 
 51/4 
 57/8 
 
 With these proportions and good workmanship there need be no fear of 
 leakage of steam through the riveted joint. 
 
 The net diagonal area, or area of plate, along a zigzag line of fracture 
 should not be less than 30% in excess of the net area straight across the 
 joint, and 35% is better. 
 
 Mr. Theodore Cooper (R. R. Gazette, Aug. 22, 1890), referring to Prof. 
 Kennedy's statement quoted above, gives as a sufficiently approximate 
 rule for the proper pitch between the rows in staggered riveting, one-half 
 of the pitch of the rivets in a row plus one-quarter the diameter of a 
 rivet-hole. 
 
 Test of Double-riveted Lap and Butt Joints. 
 
 (Proc. Inst. M. E., October, 1888.) 
 
 Steel plates of 25 to 26 tons per square inch T. S., steel rivets of 24.6 
 tons shearing strength per square inch. 
 
 Kind of Joint. 
 
 Thickness of 
 Plate. 
 
 Diameter of 
 Rivet-holes. 
 
 Ratio of 
 Pitch to 
 Diameter. 
 
 Comparative 
 Efficiency of 
 Joint. 
 
 Lap 
 
 3/8" 
 
 0.8" 
 
 3.62 
 
 75.2 
 
 Butt 
 
 3/8 
 
 0.7 
 
 3.93 
 
 76.5 
 
 Lap 
 
 3/4 
 
 I 
 
 2 82 
 
 68.0 
 
 Lap 
 
 3/4 
 
 .6 
 
 3.41 
 
 73.6 
 
 Butt 
 
 3/4 
 
 1 
 
 4 00 
 
 72.4 
 
 Butt 
 
 3/4 
 
 .6 
 
 3.94 
 
 76.1 
 
 Lap 
 
 
 3 
 
 2.42 
 
 63.0 
 
 Lap 
 
 | 
 
 .75 
 
 3.00 
 
 70.2 
 
 Butt 
 
 1 
 
 .3 
 
 3.92 
 
 76.1 
 
 
 
 
 
 
 Diameter of Rivets for Different Thicknesses of Plates. 
 
 Thickness 
 of Plate. 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 H/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 15/16 
 
 1 
 
 Diam. (1).. 
 Diam. (2)1. 
 Diam. (3).. 
 Diam. (4).. 
 
 5/8 
 
 5/8 
 1/2 
 
 5/8 
 5/8 
 5/8 
 5/8 
 
 5/8 
 3/4 
 3/4 
 '5/8 
 
 3/4 
 13/16 
 
 3/4 
 
 3/4 
 13/16 
 7/8 
 3/4 
 
 3/4 
 7/8 
 
 7/8 
 
 7/8 
 7/8 
 13/1 
 
 7/8 
 15/16 
 
 7/8 
 
 r/s 
 
 1 
 
 1 
 U/8 
 U/8 
 
 1 
 13/16 
 U/8 
 
 1 
 U/4 
 U/8 
 
 Diam (5) 
 
 3/4 
 
 7/8 
 
 15/16 
 
 | 
 
 
 
 
 
 
 
 
 
 Diam (6) 
 
 11/16 
 
 3/4 
 
 
 l r Vl6 
 
 I 
 
 1 
 
 
 
 
 
 
 
 Diam'. (7) .' 1 
 
 3/8 
 
 1/2 
 
 9 /16 
 
 11/16 
 
 3/4 
 
 13/16 
 
 
 
 
 
 
 
430 
 
 RIVETED JOINTS. 
 
 (1) Lloyd's Rules. (2) Liverpool Rules. 
 
 (4) French Veritas" " (syHartford'Stearn^Boiler'lnsirection and In 
 
 (3) English 
 . ,_, ___________________ iler Inspection and Insur- 
 
 ance Co., double riveted lap-joints. (6) Ditto, triple-riveted butt-joints. 
 (7) F. E. Cardullo. (Vie less than diam. of hole.) 
 
 Calculated Efficiencies Steel Plates and Steel Rivets. The 
 following table has been calculated by the author on the assumptions that 
 the excess strength of the perforated plate is 10%, and that the shearing 
 strength of the rivets per square inch is four-fifths of the tensile strength 
 of the plate (or, if no allowance is made for excess strength of the perfo- 
 rated plate that the shearing strength is 72.7% of the tensile strength). 
 If t = thickness of plate, d = diameter of rivet-hole, p = pitch, and T = 
 tensile strength per square inch, then for single-riveted plates 
 
 (P - d)tX I.IOT 
 
 T, whence p 
 
 0. 57 ly + d. 
 -- 
 
 For double-riveted lap-joints, p = 1.142-7- + d. 
 
 The coefficients 0.571 and 1.142 agree closely with the averages of those 
 given in the report of the committee of the Institution of Mechanical En- 
 gineers, quoted on page 427, ante. 
 
 
 ! 
 
 Pitch. 
 
 Efficiency. 
 
 
 1 
 
 Pitch. 
 
 Efficiency. 
 
 1 
 
 PH 
 JB 
 
 bib 
 
 . 
 
 bio 
 
 .s 
 
 bio 
 
 bi 
 
 
 
 w 
 4) 
 
 PH 
 * 
 
 bio 
 
 a 
 
 bio 
 C 
 
 bio 
 
 .2 
 
 bii 
 
 _g 
 
 1 
 
 sjj 
 
 -1 
 
 1| 
 
 a! 
 
 11 
 
 1 
 
 
 >! 
 
 v' 
 
 1" 
 
 -I 
 
 If 
 
 H 
 
 |S 
 
 g 
 
 Q* 
 
 I s 
 
 |5 
 
 is 
 
 Q* 
 
 I s 
 
 Q 2 
 
 I* 
 
 1^ 
 
 in. 
 3/16 
 
 in. 
 
 7/16 
 
 in. 
 .020 
 
 in. 
 1.603 
 
 fa 
 
 7?7 
 
 in. 
 
 1/2 
 
 in. 
 
 3/4 
 
 in. 
 1.392 
 
 in. 
 2.035 
 
 461 
 
 65 1 
 
 3/16 
 
 1/2 
 
 .261 
 
 2.023 
 
 60.'5 
 
 75.3 
 
 1/2 
 
 7/8 
 
 1.749 
 
 2.624 
 
 50^0 
 
 66.6 
 
 1/4 
 
 1/2 
 
 .071 
 
 1.642 
 
 53.3 
 
 69.6 
 
 1/2 
 
 
 2.142 
 
 3.284 
 
 53.3 
 
 70.0 
 
 1/4 
 
 9/16 
 
 .285 
 
 2.008 
 
 56.2 
 
 72.0 
 
 1/2 
 
 U/8 
 
 2.570 
 
 4.016 
 
 56.2 
 
 72.0 
 
 5/16 
 
 9/16 
 
 .137 
 
 1.712 
 
 50.5 
 
 67.1 
 
 9/16 
 
 3/4 
 
 1.321 
 
 1.892 
 
 43.2 
 
 60.3 
 
 5 /16 
 
 5/8 
 
 .339 
 
 2.053 
 
 53.3 
 
 69.5 
 
 9/16 
 
 7/8 
 
 1.652 
 
 2.429 
 
 47.0 
 
 64.0 
 
 5/16 
 
 H/16 
 
 .551 
 
 2.415 
 
 55.7 
 
 71.5 
 
 9/16 
 
 1 
 
 2.015 
 
 3.030 
 
 50.4 
 
 67.0 
 
 3/8 
 
 5/8 
 
 .218 
 
 1.810 
 
 48.7 
 
 65.5 
 
 9/16 
 
 U/8 
 
 2.410 
 
 3.694 
 
 53.3 
 
 69.5 
 
 3 /8 
 
 3/4 
 
 .607 
 
 2.463 
 
 53.3 
 
 69.5 
 
 9/16 
 
 H/4 
 
 2.836 
 
 4.422 
 
 55.9 
 
 71.5 
 
 3/8 
 
 7/8 
 
 .041 
 
 3.206 
 
 57.1 
 
 72.7 
 
 5/8 
 
 3/4 
 
 1.264 
 
 1.778 
 
 40.7 
 
 57.8 
 
 7/16 
 
 5/8 
 
 .136 
 
 1.647 
 
 45.0 
 
 62.0 
 
 5/8 
 
 7/8 
 
 1.575 
 
 2.274 
 
 44.4 
 
 61.5 
 
 7/16 
 
 3/4 
 
 .484 
 
 2.218 
 
 49.5 
 
 66.2 
 
 5/8 
 
 1 
 
 1.914 
 
 2.827 
 
 47.7 
 
 64.6 
 
 7/16- 
 
 7/8 
 
 .869 
 
 2.864 
 
 53.2 
 
 69.4 
 
 5/8 
 
 U/8 
 
 2.281 
 
 3.438 
 
 50.7 
 
 67.3 
 
 7/16 
 
 1 
 
 2.305 
 
 3.610 
 
 56.6 
 
 72.3 
 
 5/8 
 
 H/4 
 
 2.678 
 
 4.105 
 
 53.3 
 
 69.5 
 
 Apparent Shearing Resistance of Rivet Iron and Steel. 
 
 (Proc. Inst. M. E., 1879, Engineering, Feb. 20, 1880.) 
 
 The true shearing resistance of the rivets cannot be ascertained from 
 experiments on riveted joints (1) because the uniform distribution of the 
 load to all the rivets cannot be insured; (2) because of the friction of the 
 plates, which has the effect of increasing the apparent resistance to shear- 
 ing in an element uncertain in amount. Probably in the case of single- 
 riveted joints the shearing resistance is not much affected by the friction. 
 
 Fairbairn's experiments show that a rivet is 6 1/2% weaker in a drilled 
 fian in a punched hole. By rounding the edge of the rivet-hole, the 
 apparent shearing resistance is increased 12%. Messrs. Greig and Eyth's 
 experiments indicate a greater resistance of the rivets in punched holes 
 than in drilled holes. 
 
 If the apparent shearing resistance is less for double than for single 
 shear, it is probably due to unequal distribution of the stress on the two- 
 rivet sections. 
 
THE STRENGTH OF RIVETED JOINTS. 
 
 431 
 
 ; 
 
 The shearing resistance of a bar, when sheared in circumstances which 
 prevent .friction, is usually less than the tenacity of the bar. The fol- 
 lowing results show the decrease: 
 
 Harkort, iron Tenacity, 26.4 Shearing, 16.5 Ratio, 0.62 
 
 Lavalley, iron 25.4 20.2 0.79 
 
 Greig and Eyth, iron. " 22.2 19.0 0.85 
 
 Greig and Eyth, steel 28.8 22.1 0.77 
 
 In Wohler's researches (in 1870) the shearing strength of iron was found 
 to be four-fifths of the tenacity. Later researches of Bauschinger con- 
 firm this result generally, but they show that for iron the ratio of the 
 shearing resistance and tenacity depends on the direction of the stress 
 relatively to the direction of rolling. The above ratio is valid only if the 
 shear is in a plane perpendicular to the direction of rolling, and if the 
 tension is applied parallel to the direction of rolling. If the plane of shear 
 is parallel to the breadth of the bar, the resistance is only half as great 
 as in a plane perpendicular to the fibers. 
 
 THE STRENGTH OF RIVETED JOINTS. 
 
 Joint of Maximum Efficiency. (F. E. Cardullo.) If a riveted joint 
 is made with sufficient lap, and a proper distance between the rows of 
 rivets, it will break in one of the three following ways: 
 
 1. By tearing the plate along a line, through the outer row of rivets. 
 
 2. By shearing the rivets 
 
 3. By crushing the plate or the rivets. 
 Let t = the thickness of the main plates. 
 
 d the diameter of the rivet-holes. 
 
 f = the tensile strength of the plate in pounds per sq. in. 
 
 5 = the shearing strength of the rivets in pounds per sq. in. when 
 in single shear. 
 
 p = the distance between the centers of rivets of the outer row 
 (see Figs. 96 and 97) = the pitch in single and double lap riveting = twice 
 
 FIG. 96. 
 TRIPLE RIVETING. 
 
 FIG. 97. 
 QUADRUPLE RIVETING. 
 
 the pitch of the inner rows in triple butt strap riveting, in which alter- 
 nate rivets in the outer row are omitted, = four times the pitch in quad- 
 ruple butt strap riveting, in which the outer row has one-fourth of the 
 number of rivets of the two inner rows. 
 
 c = the crushing strength of the rivets or plates in pounds per 
 sq. in. 
 
 n = the number of rivets in each group in single shear. (A group 
 is the number of rivets on one side of a joint corresponding to the dis- 
 tance p; = 1 rivet in single riveting, 2 in double riveting, 5 in triple 
 butt strap riveting, and 11 in quadruple butt strap riveting.) 
 
 m = the number of rivets in each group in double shear, 
 s" = the shearing strength of rivets in double shear, in pounds per 
 sq. in., the rivet section being counted once. 
 
 T the strength of the plate at the weakest section. = ft (p d).' 
 
 S = the strength of the rivets against shearing, = 0.7854d 2 (ns + 
 ms"). 
 
 C = the strength of the rivets or the plates against crushing, = 
 
432 RIVETED JOINTS. 
 
 In order that the joint shall have the greatest strength possible, the 
 tearing, snearing, and crushing strength must all be equal. In order to 
 make it so, 
 
 1. Substitute the known numerical values, equate the expressions for 
 shearing and crushing strength, and find the value of d, taking it to the 
 nearest Viem. 
 
 2. Next find the value of S in the second equation, and substitute it 
 for T in the first equation. Substitute numerical values for the other 
 factors in the first equation, and solve for p. 
 
 The efficiency of a riveted joint in tearing, shearing and crushing, is 
 equal to the tearing, shearing or crushing strength, divided by the quan- 
 tity ftp, or the strength of the solid plate. 
 
 The efficiency in tearing is also equal to (p d) -5- p. 
 
 The maximum possible efficiency for a well-designed joint is 
 
 - m+n 
 
 m + n 4- (/ -H c) 
 
 Empirical formula for the diameter of the rivet-hole when the crush- 
 ing strength is unknown. Assuming that c = 1.4/, and s"= 1.75s, we have 
 by equating C and S, and substituting, 
 
 f(n 4- m) 
 
 1.7821 
 
 s(n+ 1.75m) 
 
 Margin. The distance from the center of any rivet-hole to the edge of 
 the plate should be not less than 11/2(1 The distance between two adja- 
 cent rivet centers should be not less than 2d. It is better to increase 
 each of these dimensions by 1/8 in. 
 
 The distance between the rows of rivets should be such that the net 
 section of plate material along any broken diagonal through the rivet- 
 holes should be not less than 30 per cent greater than the plate section 
 along the outer line of rivets. 
 
 The thickness of the inner cover strap of a butt joint should be s/ 4 of 
 the thickness of the main plate or more. The thickness of the outer strap 
 should be 5/ 8 of the thickness of the main plate or more. 
 
 Steam Tightness. It is of great importance in boiler riveting that 
 the joint be steam tight. It is therefore necessary that the pitch of the 
 rivets nearest to the calked edge be limited to a certain function of the 
 thickness of the plate. The Board of Trade rule for steam tightness is 
 
 p = Ct + 15/ 8 in. 
 
 where p = the maximum allowable pitch in inches. 
 t = the thickness of main plate in inches. 
 C = a constant from the following table. 
 
 No. of Rivets per Group... 12345 
 
 Lap Joints .................. C=1.31 2.62 3.47 4.14 
 
 Double-strapped Joints.... C= 1.75 3.50 4.63 5.52 6.00 
 
 The pitch should not exceed ten inches under any circumstances. 
 
 When the joint has been designed for strength, it should be checked by 
 the above formula. Should the pitch for strength exceed the pitch for 
 steam tightness, take the latter, substitute it in the formula 
 
 ft (p-d) =0.7854 d 2 (ns + ms"), 
 
 and solve for d. If the value of d so obtained is not the diameter of some 
 standard size rivet, take the next larger Vie in. 
 
 Calculation of Triple-riveted Butt and Strap Joints. Formulae: 
 T = ft (p-d), = 0.7854d 2 (ns + ms"), C = dtc (m + n) (notation on 
 
 = W,= 44,000; f = 1.75, = 77,000, c . 1.4 / 
 = 77,000. 
 Then T = 55,000 t{p-d) t S - 276,460^, C - 385,000 d*. 
 
THE STRENGTH OF RIVETED JOINTS 
 
 433 
 
 For maximum strength, T = S = C; dividing by 55,000 t, (p - d) 
 5.027 d*/t = 7d; whence d = 1.3925 t; p = Sd. 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 17/32 
 
 5/8 
 
 H/16 
 
 25/32 
 
 7/8 
 
 Thickness of plate t = 5/ie 
 Diana, rivet hole, 
 
 d= 1.3925 t 7/ 16 
 
 Pitch of outer row, 
 
 v = 8d. . 3.4816 4.1776 4.8736 5.5696 6.2664 6.9624 
 
 T = 55,000 1 (p-d).. 52,360 75,390 102,610 134,020 169,630 209,420 
 
 S = 276,460 d 2 52,330 75,360 102,570 133,970 169,560 209,330 
 
 C = 385,000 dt 52,350 75,390 102,620 134,030 169,630 209,420 
 
 Calculations by logarithms, to nearest 10 pounds. 
 
 Efficiency of all joints (p - d) -* p = 87.5 per cent. 
 
 Maximum efficiency by Cardullo's formula, 
 
 139,860 178,750 207,850 229,880 
 
 194,300 207,300 220,-200 220,200 
 
 1171300 157,900 192,500 230,000 255,500 
 
 .107,360 134,060 162,420 206,250 239,770 266,400 
 
 = 87.5 per cent. 
 
 Diameter of rivet, i/ie in. less than hole 3/ 8 1/2 9/ 16 n/ 16 3/ 4 13/ 16 
 
 Diameter of rivet-hole, next largest 16th, 7/ 16 9/ 16 5/ 8 s/ 4 13/ 16 7/9 
 For the same thickness of plates the Hartford Steam Boiler Inspection 
 and Insurance Co. gives the following proportions: 
 
 Thickness, f, ' 5/ 16 3/ 8 7/ 16 i/ 2 9/ 16 5/ 8 
 
 Diam. rivet-hole, d, 3/ 4 13/ 16 15/ 16 1 1 1/ 16 ll/ 16 
 
 Pitch of outer row, p, 6 1/4 61/2 63/4 71/2 73/4 73/ 4 
 
 Using the same values for f, s, s" and c, we obtain: 
 
 T = 94,530 117,300 ' 
 
 S = 155,400 168,400 
 
 C = 90,030 - 
 
 Strength of solid 
 
 plate, f pt = . . . . 
 
 Efficiency T, S or 
 
 C, lowest * fpt, . 
 
 per cent 83.9 87.5 86.1 86.7 86.7 82.6 
 
 The 5/i6 in. plate fails by crushing, the 5/ 8 by shearing, the others by 
 tearing. 
 
 Calculation of Quadruple Riveting. In this case there are 11 rivets 
 In the group. If the upper strap plate contains all the rivets except the 
 outer row, then n = 1, m = 10. Using the same values for/, s, s" and 
 c as above, we have ns + ms" = 814,000; T = 55,000 (p - d); S =* 
 639,315 d 2 ; C = 847,000 dt. 
 
 For maximum strength, t (p d) = 11.624d 2 = 15. 4dt; whence d = 
 1. 32485 1, p = 16.4 d. Efficiency (p - d)+p = 93.9 per cent. Check by 
 
 Cardullo's formula rrr = 93.9 per cent. 
 
 n 4- m + f/c 114- 10 /ii 
 British Board of Trade and Lloyd's Rules for Riveted Joints. 
 
 Board of Trade. Tensile strength of rivet bars between 26 and 30 tons, 
 el. in 10" not less than 25%, and contr. of area not less than 50%. 
 
 The shearing resistance of the rivet steel to be taken at 23 tons per 
 square inch, 5 to be used for the factor of safety independently of any 
 addition to this factor for the plating. Rivets in double shear to have 
 only 1.75 times the single section taken in the calculation instead of 2. 
 The diameter must not be less than the thickness of the plate and the 
 pitch never greater than 81/2". The thickness of double butt-straps 
 (each) not to be less than 5/ 8 the thickness of the plate; single butt-straps 
 not less than 9/ 8 . 
 
 Distance from center of rivet to edge of hole = diameter of rivet X 1V2. 
 
 Distance between rows of rivets 
 
 = 2 X diam. of rivet or = [(diam. X 4) 4- 1] -* 2, if chain, and 
 
 V[(pitch X 11) 4- (diam. X 4)] X (pitch + diam. X 4) 
 10 
 
 if zigzag. 
 
 Diagonal pitch = (pitch X 6 4- diam. X 4) 4- 10. 
 
 Lloyd's. T. S. of rivet bars, 26 to 30 tons; el. not less than 20% in 8*. 
 The material must stand bending to a curve, the inner radius of which is 
 
434 
 
 RIVETED JOINTS. 
 
 not greater than 11/2 times the thickness of the plate, after having been 
 uniformly heated to a low cherry-red, and quenched in water at 82 F. 
 
 Rivets in double shear to have only 1.75 times the single section taken 
 in the calculation instead of 2. The shearing strength of rivet steel to 
 be taken at 85% of the T. S. of the material of shell plates. In any case 
 where the strength of the longitudinal joint is satisfactorily shown by 
 experiment to be greater than given by the formula, the actual strength 
 may be taken in the calculation. 
 
 Proportions of Riveted Joints. (Hartford S. B. Insp. and Ins. Co.) 
 Single-riveted Girth Seams of Boilers. 
 
 Thickness. 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 Diam. rivet-hole. 
 Pitch 
 
 3/4 H/16 
 21/i 6 21/i 6 
 
 13/16 3/ 4 
 21/8 21/8 
 
 15/16 W16 
 
 23/8 21/8 
 
 1 1V16 
 
 27/16 23/ 8 
 
 1 VIC 1 
 21/- 21/2 
 
 Center to edge . . 
 
 H/8 H/32 
 
 17/32 U/8 
 
 1 13/32 1 7/32 
 
 U/2 H3/32 
 
 19/32 U/2 
 
 Double-riveted Lap Joints. 
 
 Thickness of plate 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/10 
 
 1/2 
 
 
 
 
 
 
 
 Diam. rivet-hole 
 
 3 /4 
 
 13/16 
 
 15/16 
 
 , 
 
 H/16 
 
 Pitch t 
 
 27/8 
 
 27/8 
 
 31/4 
 
 31/4 
 
 3 32 
 
 Dist. bet. rows ... ...... 
 
 1 15/16 
 
 1 15/16 
 
 23/i 6 
 
 23/16 
 
 2 2 
 
 Dist. inner row to edge : . 
 
 H/8 
 
 17/32 
 
 1 13/32 
 
 U/2 
 
 119/32 
 
 Efficiency . . 
 
 74 
 
 72 
 
 70 
 
 70 
 
 68 
 
 
 
 
 
 
 
 Triple-riveted Lap Joints. 
 
 Thickness 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1 2 
 
 
 
 
 
 
 
 Diam. rivet-hole 
 
 H/16 
 
 3/4 
 
 13/16 
 
 15/16 
 
 1 
 
 Pitch 
 
 3 
 
 31/8 
 
 31/4 
 
 33/4 
 
 315/16 
 
 Dist. bet rows 
 
 2 
 
 2Vl6 
 
 23/18 
 
 21/2 
 
 25/8 
 
 Inner row to edge 
 
 11/32 
 
 H/8 
 
 17/32 
 
 113/32 
 
 H/2 
 
 Efficiency 
 
 Ti 
 
 76 
 
 75 
 
 0.75 
 
 0.75 
 
 
 
 
 
 
 
 Triple-riveted Bull-strap Joints. 
 
 Thickness 
 
 5/i 6 
 
 3/ 8 
 
 7/16 
 
 V2 
 
 9 /16 
 
 5/8 
 
 
 
 
 
 
 
 
 Diam. rivet-hole 
 
 3/4 
 
 13/16 
 
 15/16 
 
 1 
 
 H/16 
 
 11/16 
 
 Pitch, inner rows 
 
 31/8 
 
 31/4 
 
 33/8 
 
 33/4 
 
 37/ 8 
 
 37/8 
 
 Dist. bet. inner rows 
 Dist. outer to 2d row. ..... 
 Edge to nearest row 
 Efficiency % ... 
 
 21/8 
 23/ 8 
 U/4 
 
 88 (?) 
 
 ^ 
 ^ 
 
 21/4 
 23/4 
 
 T /32 
 
 23/8 
 
 U/2 
 86.6 
 
 25/8 
 33/16 
 1 19/32 
 85.4 
 
 25/8 
 33/16 
 119/32 
 84(?) 
 
 
 
 
 
 
 
 
 The distance to the edge of the plate is from the center of rivet-holes. 
 
THE STRENGTH OF RIVETED JOINTS. 
 
 435 
 
 
 Pressure Required to Drive Hot Rivets. R. D. Wood ft Co. 
 Philadelphia, give the following table (1897): 
 
 POWER TO DRIVE RIVETS HOT. 
 
 Size. 
 
 Girder- 
 work. 
 
 Tank- 
 work. 
 
 Boiler- 
 work. 
 
 Size. 
 
 Girder- 
 work. 
 
 Tank- 
 work. 
 
 Boiler- 
 work. 
 
 in. 
 
 tons. 
 
 tons. 
 
 tons. 
 
 in. 
 
 tons. 
 
 tons. 
 
 tons. 
 
 1/2 
 
 9 
 
 15 
 
 20 
 
 U/8 
 
 38 
 
 60 
 
 75 
 
 5/8 
 
 12 
 
 18 
 
 25 
 
 U/4 
 
 45 
 
 70 
 
 100 
 
 3/4 
 
 15 
 
 22 
 
 33 
 
 U/2 
 
 60 
 
 85 
 
 125 
 
 7/8 
 
 22 
 
 30 
 
 45 
 
 13/4 
 
 75 
 
 100 
 
 150 
 
 1 
 
 30 
 
 45 
 
 60 
 
 
 
 
 
 The above is based on the rivet passing through only two thicknesses of 
 plate which together exceed the diameter of the rivet but little, if any. 
 
 As the plate thickness increases the power required increases approxi- 
 mately in proportion to the square root of the increase of thickness. Thus, 
 if the total thickness of plate is four times the diameter of the rivet, we 
 should require twice the power given above in order to thoroughly fill the 
 rivet-holes and do good work. Double the thickness of plate would 
 increase the necessary power about 40%. 
 
 It takes about four or five times as much power to drive rivets cold as 
 to drive them hot. Thus, a machine that will drive 3/4-in. rivets hot will 
 usually drive 3/ 8 -in. rivets cold (steel). Baldwin Locomotive Worka 
 drive 1/2 -in. soft-iron rivets cold with 15 tons. 
 
 Riveting Pressure Required for Bridge and Boiler Work. 
 
 (Wilfred Lewis, Engineers' Club of Philadelphia, Nov., 1893.) 
 
 A number of 3' 8 -inch rivets were subjected to pressures between 10,000 
 and 60,000 Ibs. At 10,000 Ibs. the rivet swelled and filled the hole with- 
 out forming a head. At 20,000 Ibs. the head was formed and the plates 
 were slightly pinched. At 30,000 Ibs. the rivet was well set. At 40,000 
 Ibs. the metal in the plate surrounding the rivet began to stretch, and the 
 stretching became more and more apparent as the pressure was increased 
 to 50,000 and 60,000 Ibs. From these experiments the conclusion might 
 be drawn that the pressure required for cold riveting was about 300,000 
 Ibs. per square inch of rivet section. In hot riveting, until recently there 
 was never any call for a 'pressure exceeding 60,000 Ibs.. but now pressures 
 as high as 150,000 Ibs. are not uncommon, and even 300,000 Ibs. have been 
 contemplated as desirable. 
 
 Pressure Required for Heading Cold Rivets. Experiments made 
 by the author in 1906 on 1/2 and 5/8 in. soft steel rivets showed that the 
 pressure required to head a rivet cold, with a hemispherical heading die, 
 was a function of the final or maximum diameter of the head. The 
 metal began to flow and fill the hole at about 50,000 Ibs. per sq. in. press- 
 ure, but it hardened and increased its resistance as it flowed until it reached 
 a maximum of about 100,000 Ibs. per sq. in. of the maximum area of the 
 head. 
 
 Chemical and Physical Tests of Soft Steel Rivets. Ten rivet 
 bars and ten rivets selected from stock of the Champion Rivet Co., Cleve- 
 land, O., were analyzed by Oscar Textor, with results as follows: 
 
 P. 0.008 to 0.027, av. 0.015: Mn, 0.31 to 0.69, av. 0.46: S, 0.023 to 
 0.044, av. 0.033: Si, 0.001 to 0.008, av. 0.005- C, 0.06 to 0.19, av. 0.11. 
 Only four of the 20 samples were over 0.14 C, and these were made for 
 hi?h strength. Ten bars and two rivets Rave tensile strength . 46.735 to 
 55.380, av. 52.195 Ibs. per sq. in.- elastic limit, 31,350 to 43,150. av. 
 35,954- elongation, bars only, 28 to 35, av. 31.9% in 8 ins.: reduction ot 
 area. 65.6%. Eight bars in single shear gave shearing strength 35,660 
 to 50 190 av. 44478 Ibs. per sq. in.; seven bars in double shear eave 
 39,170 to 53,900, av. 45,720 Ibs. The shearing strength averaged 86.3% 
 of the tensile strength. 
 
436 IRON AND STEEL. 
 
 
 
 
 
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CAST IRON. 
 
 CAST IRON. 
 
 437 
 
 The Manufacture of Cast Iron. Pig iron is the name given to the 
 crude form of iron as it is produced in the blast furnace. This furnace 
 is a tall shaft, lined with fire brick, often as large as 100 ft. high and 20 ft. 
 in diameter at its widest part, called the "bosh." The furnace is kept 
 filled with alternate layers of fuel (coke, anthracite or charcoal), while a 
 melting temperature is maintained at the bottom by a strong blast. 
 The iron ore as it travels down the furnace is decarbonized by the carbon 
 monoxide gas produced by the incomplete combustion of the fuel, and as 
 it. travels farther, into a zone of higher temperature, it absorbs carbon 
 and silicon. The phosphorus originally in the ore remains in the iron. 
 The sulphur present in the ore and in the fuel may go into combination 
 with the lime in the slag, or into the iron, depending on the constitution 
 of the slag and on the temperature. The silica and alumina in the ore 
 unite with the lime to form a fusible slag, which rests on the melted iron 
 in the hearth. The iron is tapped from the furnace several times a day, 
 while in large furnaces the slag is usually run off continuously. 
 
 Grading of Pig Iron. Pig iron is approximately graded according 
 to its fracture, the number of grades varying in different districts. In 
 Eastern Pennsylvania the principal grades recognized are known as No. 
 1 and 2 foundry, gray forge or No. 3, mottled or No. 4, and white or No. 
 5. Intermediate grades are sometimes made, as No. 2 X, between No. 1 
 and No. 2, and special names are given to irons more highly silidzed than 
 No. 1, as No. 1 X, silver-gray, and soft. Charcoal foundry pig iron is 
 graded by numbers 1 to 5, but the quality is very different from the 
 corresponding numbers in anthracite and coke pig. Southern coke pig 
 -Iron is graded into ten or more grades. Grading by fracture is a fairly 
 satisfactory method of grading irons made from uniform ore mixtures 
 and fuel, but is unreliable as a means of determining quality of irons 
 produced in different sections or from different ores Grading by chemi- 
 cal analysis, in the latter case, is the only satisfactory method. The 
 following analyses of the five standard grades of northern foundry and 
 mill pig irons are given by J. M. Hartman (Bull. 1. & S. A., Feb., 1892): 
 
 
 No. 1. 
 
 No. 2. 
 
 No'. 3. 
 
 No. 4. 
 
 No. 4B. 
 
 No. 5. 
 
 Iron 
 
 92.37 
 
 92.31 
 
 94.66 
 
 94 48 
 
 94.08 
 
 94 68 
 
 Graphitic ca/rbon 
 
 3 52 
 
 2 99 
 
 2 50 
 
 2 02 
 
 2 02 
 
 
 Combined carbon 
 
 0.13 
 
 0.37 
 
 1.52 
 
 1.98 
 
 1.43 
 
 3 83 
 
 
 2.44 
 
 2.52 
 
 0.72 
 
 0.56 
 
 0.92 
 
 0.41 
 
 Phosphorus 
 
 1.25 
 
 1.08 
 
 26 
 
 0.19 
 
 0.04 
 
 04 
 
 
 0.02 
 
 0.02 
 
 trace 
 
 0.08 
 
 0.04 
 
 0.02 
 
 Manganese 
 
 0.28 
 
 0.72 
 
 0.34 
 
 0.67 
 
 2.02 
 
 0.98 
 
 
 
 
 
 
 
 
 CHARACTERISTICS OF THESE IRONS. 
 
 No. 1. Gray. A large, dark, open-grain iron, softest of all the num- 
 bers and used exclusively in the foundry. Tensile strength low. Elastic 
 limit low. Fracture rough. Turns soft and tough. 
 
 No. 2. Gray. A mixed large and small dark grain, harder than No. 
 1 iron, and used exclusively in the foundry. Tensile strength and elastic 
 limit higher than No. 1. Fracture less rough than No. 1. Turns harder, 
 less tough, and more brittle than No. 1. 
 
 No. 3. Gray. Small, gray, close grain, harder than No. 2 iron, used 
 either in the rolling-mill or foundry. Tensile strength and elastic limit 
 higher than No. 2. Turns hard, less tough, and more brittle than No. 2. 
 
 No. 4. Mottled. White background, dotted closely with small black 
 spots of graphitic carbon: little or no grain. Used exclusively in the 
 rolling-mill. Tensile strength and elastic limit lower than No. 3. Turns 
 with difficulty; less tough and more brittle than No. 3. The manganese 
 In the B pig iron replaces part of the combined carbon, making the iron 
 harder and closing the grain, notwithstanding the lower combined carbon. 
 
438 IRON AND STEEL. 
 
 No. 5. White. Smooth, white fracture, no grain, used exclusively in 
 the rolling mill. Tensile strength and elastic limit much lower than No. 4. 
 Too hard to turn and more brittle than No. 4. 
 
 Southern pig irons are graded as follows, beginning with the highest in 
 silicon: Nos. 1 and 2 silvery, Nos. 1 and 2 solt, all containing over 3% 
 of silicon; Nos. 1, 2, and 3 foundry, respectively about 2.75%, 2.5% and 
 2% silicon; No. 1 mill, or " foundry forge;" No. 2 mill, or gray forge; 
 mottled; white. 
 
 Chemistry of Cast Iron. Abbreviations, TC, total carbon; GC, 
 graphitic carbon; CC, combined carbon. Numerous researches have been 
 made and many papers written, especially between the years 1895 and 
 1908, on the relation of the physical properties to the chemical constitu- 
 tion of cast iron. Much remains to be learned on the subject, but the 
 following is a brief summary of prevailing opinions. 
 
 CARBON. Carbon exists in three states in cast iron: 1, Combined 
 carbon, which has the property of making iron white and hard ; 2, Graphi- 
 tic carbon or graphite, which is not alloyed with the iron, but exists in it 
 as a separate body, since it may be removed from the fractured surface 
 of pig iron by a brush; 3, a third form, called by Ledebur "tempering 
 graphite carbon," into which combined carbon may be changed by pro- 
 longed heating. The relative percentages in which GC and CC may 
 be found in cast iron differ with the rate of cooling from the liquid 
 state, so that in a large casting, cooled slowly, nearly all the C may 
 be GC, while in a small casting from the same ladle cooled quickly, 
 it may be nearly all CC. Tne total C in cast iron usuallv is between 
 3 and 4%. 
 
 COMBINED CARBON. CC increases hardness, brittleness and shrink- 
 age. Up to about 1% it increases strength, then decreases it. The 
 presence of S tends to increase the CC in a casting, while Si tends to 
 change CC to GC. 
 
 GRAPHITE. GC in a casting causes softness and weakness when 
 above 3%; softness and strength when added to irons low in GC and over 
 1% in CC. It increases with the size of the casting, with slow cooling, 
 or rather with holding a long time in the mold at a high temperature. 
 
 SILICON. Si acts as a softener by counteracting the hardening effect 
 of S, and by changing CC into GC, changes white iron to gray, increases 
 fluidity and lessens shrinkage. When added to hard brittle iron, high in 
 CC, it may increase strength by removing hard brittleness, but when it 
 reduces the CC to 1% and less it weakens the iron. Above 3.5 or 4% it 
 changes the fracture to silvery gray, and the iron becomes brittle and 
 weak. The softening effect of Si is modified by S and Mn. 
 
 SULPHUR. S causes the C to take the form of CC, increases hardness, 
 brittleness, and shrinkage, and also has a weakening effect of its own. 
 Above about 0.1% it makes iron very weak and brittle. When Si is 
 below 1%, even 0.06 S makes the iron dangerously brittle. 
 
 MANGANESE. Mnin small amount, less than 0.5%, counteracts the 
 hardening influence of S; in larger amounts it changes GC into CC, and 
 acts as a hardener. Above 2% it makes the iron very hard. Mn com- 
 bines with iron in almost all proportions. When it is from 10 to 30% 
 the'alloyis called spiegeleisen, from the German word for mirror, and has 
 large, bright crystalline faces. Above 50% it is known as ferro-man- 
 ganese. Mn has the property of increasing the solubility of iron for 
 carbon; ordinary pig iron containing rarely over 4.2% C, while spiegel- 
 eisen may have 5%, and ferro-manganese as high as 6%. Cast iron with 
 1% Mn is used in making chilled rolls, in which a hard chill is desired. 
 When softness is required in castings, Mn over 0.4% has to be avoided. 
 Mn increases shrinkage. It also decreases the magnetism of iron. Iron 
 with 25% Mn loses all its magnetism. It therefore has to be avoided in 
 castings for dynamo fields and other pieces of electrical machinery. 
 
 PHOSPHORUS. P increases fluidity, and is therefore valuable for thin 
 and ornamental castings in which strength is not needed. It increases 
 softness and decreases shrinkage. Below 0.7% it does not appear to 
 decrease strength, but above 1% it is a weakener. 
 
 COPPER. Cu is found in pig irons made from ores containing Cu. 
 From 0.1 to 1% it closes the grain of cast iron, but does not appreciably 
 cause brittleness. 
 
g 
 d 
 
 CAST IRON. . 439 
 
 LUMINUM. Al from 0.2 to 1.0% (added to the ladle in the form of 
 a FeAl alloy) increases the softness and strength of white iron ; added to 
 ray iron it softens and weakens it. Where loss is occasioned by 
 efective castings, or where iron does not flow well, the addition of Al 
 will give sounder, closer grained castings. In proportions of 2% and 
 over Al will decrease the shrinkage of cast iron. 
 
 TITANIUM. An addition of 2 to 3% of a TiFe alloy containing 10% 
 Ti caused an increase of 20 to 30% in strength of cast iron. A. J. Rossi, 
 A.I.M.E., xxxiii, 194. Ti reacts with any O or N present in the metal 
 and thus purifies it, and does not remain in the metal. After enough 
 Ti for deoxidation has been added, further additions have no effect. 
 R. Moldenke, A.I.M.E., xxxv, 153. 
 
 VANADIUM. Va to the extent of 0.15% added to the ladle in the form 
 of a ground FeVa alloy greatly increases the strength of cast iron. It 
 acts as a deoxidizer and also by alloying. 
 
 OXIDE OF IRON. The cause of the difference in strength of charcoal 
 and coke irons of identical composition is believed by Dr. Moldenke 
 (A.I.M.E., xxxi, 988) to be the degree of oxidation to which they have 
 been subjected in making or temelting. Since Mn, Ti, and Va all act as 
 deoxidizers, it should be possible by additions to the ladle of alloys of 
 FeMn, FeVa, or IfeTi, to make the two irons of equal strength. 
 
 Temper Carbon. The main part of the C in white cast iron is the carbide 
 Fe 3 C. This breaks down under annealing to what Ledebur calls " temper 
 carbon," and in annealing in oxides, as in making malleable iron, 'it is 
 oxidized to CO. The C remaining in the casting at the end of the process 
 is nearly all GC, since the latter is very slowly oxidized. 
 
 Influence of Various Elements on Cast Iron. W. S. Anderson, 
 Castings, Sept., 1908, gives the following: 
 
 Fluidity, increased by Si, P, G.C. Reduced by S, C.C. 
 Shrinkage, increased by S, Mn, C.C. Reduced by Si, P, G.C. 
 Strength, increased by Mn, C.C. Reduced by Si, S, P, G.C. 
 Hardness, inci eased by S, Mn, C.C. Reduced by Si, G.C. 
 Chill, increased by S, Mn, C.C. Reduced by Si, P, G.C. 
 
 Microscopic Constituents. (See also Metaltographyj under Steel.) 
 
 Ferrite, iron free from carbon. It is found in mild steel in small amounts 
 in gray cast iron, and in malleable cast iron. 
 
 Cementite, FesC. Fe with 6.67% C. Harder than hardened steel. 
 Hardness U on the mineralogical scale. Found in high C steel, and in 
 white and mottled pig. 
 
 Pearlite, a compound made up of alternate laminae of ferrite and cemen- 
 tite, in the ratio of 7 ferrite to 1 cementite, and containing therefore 
 0.83% C. Found in iron and steel cooled very slowly from a high temper- 
 ature. In steel of 0.83 C it composes the entire mass. Steels lower or 
 higher than 0.83 C contain pearlite mixed with ferrite or with cementite. 
 
 Mariensite, the hardening component of steel. Found in iron and 
 steel quenched above the recalescence point, and in tempered steel. It 
 forms the entire structure of 0.83 C steel quenched. 
 
 Analyses of Cast Iron. (Notes of the table on page 440.) 
 
 1 to 7. R. Moldenke, Pittsbg. F'drymen's Assn., 1898; 1 to 5, pig irons; 
 6, white iron cast in chills; 7, gray iron cast in sand from the same ladle. 
 The temperatures were taken with a Le Chatelier pyrometer. For 
 comparison, steel, 1.18 C, melted at 2450 F.; silico-spiegel, 12.30 Si, 
 16.98 Mn, at 2190; ferro-silicon, 12.01 Si, 2.17 CC, at 2040; ferro- 
 tungsten, 39.02 W, at 2280; ferro-manganese, 81.4 Mn, at 2255; ferro- 
 chrome, 62.7 Cr, at 2400; ditto, 5.4 Cr., at 2180. 
 
 8. Gray foundry Swedish pig, very strong. 9. Pig to be used in mix- 
 tures of gray pig and scrap, for castings requiring a hard close grain, 
 machining to a fine surface, and resisting wear. 8 to 15, from paper by 
 F. M. Thomas, Castings, July, 1908. 
 
 16. Specification by J. E. Johnston, Jr., Am. Mach., Oct. 15, 1903. 
 The results were excellent. Si might have been 0.75 to 1.25 if S had 
 been kept below 0.035. 
 
 17 to 22. G. R. Henderson, Trans. A.S.M.E., vol. xx. The chill is to 
 be measured in a test bar 2 X 2 X 24 in., the chill piece being so placed 
 as to form part of one side of the mold. The actual depth of white iron 
 will be measured, 
 
440 
 
 IRON AND STEEL. 
 
 Analyses of Cast Iron. 
 
 (Abbreviations, TC, total carbon; GC, graphitic carbon; CC, combined 
 irbon.) 
 
 TC 
 
 GC 
 
 CC 
 
 Silicon. 
 
 Man- 
 ganese. 
 
 Phos- 
 phorus. 
 
 Sul- 
 phur. 
 
 
 3.98 
 3.78 
 3.88 
 4.03 
 3.56 
 4.39 
 4.45 
 3.30 
 
 0.39 
 1.76 
 2.60 
 3.47 
 3.43 
 0.13 
 2.99 
 2.80 
 
 2 25-2 5 
 
 3.59 
 2.01 
 1.28 
 0.56 
 0.13 
 4.26 
 1.46 
 0.50 
 
 06-08 
 
 0.38 
 0.69 
 1.52 
 2.01 
 2.40 
 0.65 
 0.67 
 2.00 
 
 8-1 2 
 
 0.13 
 0.44 
 0.49 
 0.49 
 0.90 
 0.40 
 0.41 
 0.60 
 
 04-08 
 
 0.20 
 0.53 
 0.46 
 0.39 
 0.08 
 0.25 
 0.26 
 0.08 
 
 15-0 4 
 
 0.038 
 0.031 
 0.035 
 0.034 
 0.032 
 0.038 
 0.039 
 0.03 
 
 Melts at 2048 F. 
 Melts at 2156 F. 
 Mel1sat221lF. 
 M eh sat 2248 F. 
 M el Is at 2280 F. 
 Melts at 2000 F. 
 Melts at 2237 F. 
 Swedish char- 
 coal pig. 
 For engine cylin- 
 
 3.40 
 3.40 
 
 3.40 
 3.20 
 3.2-3.6 
 3 0-3 2 
 
 trace 
 0.20 
 0.1-0.15 
 04-05 
 
 2.90 
 2.60 
 2.5-2.8 
 2-2 3 
 
 0.50 
 0.50 
 
 up to 
 1.0 
 up to 
 
 1.65 
 1.58 
 1.3-1.5 
 1-1.3 
 
 0.04' 
 0.04 
 .03-. 04 
 .06-. 08 
 
 ders. 
 English, high P. 
 No. 1. 
 English, high P. 
 
 For thin orna- 
 mental work. 
 For medium size 
 
 
 2 8-3 
 
 04-06 
 
 1 2-1 5 
 
 1.0 
 06-09 
 
 04-06 
 
 .06-. 08 
 
 castings. 
 Heavy machin- 
 
 
 2.5-2.8 
 
 0.6-0.8 
 
 1.0-1.3 
 1.2-1 8 
 
 0.5-0.7 
 4-1 
 
 0.4-0.7 
 0.4-0.7 
 
 .08-. 12 
 to .06 
 
 ery castings. 
 Cylinders end 
 hydraulic \vork. 
 For hydraulic 
 
 
 2.7-3.0 
 2.6-3.1 
 2 5-3 
 
 0.5-0.8 
 0.6-1.0 
 04-09 
 
 0.5-0.7 
 0.6-0.7 
 1 3-1 7 
 
 0.3-0.5 
 0.1-0.3 
 5-1 
 
 0.3-0.5 
 0.3-0.5 
 03-04 
 
 .05-. 07 
 .05-. 08 
 03 max 
 
 cylinders. 
 For car wheels. 
 For car wheels. 
 Charcoal pig. 1/4 
 
 l'.87 
 
 3.82 
 3.84 
 
 2.3-2.7 
 2.0-2.5 
 1.8-2.2 
 3.44 
 
 3.23 
 3.52 
 2.8-3.2 
 
 2.3-2.4 
 2 4-2 6 
 
 0.5-1.0 
 0.8-1.2 
 0.9-1.4 
 0.43 
 
 0.59 
 0.32 
 0.5-0.7 
 
 0.8-1.0 
 08-1 
 
 1.0-1.5 
 0.8-1.2 
 0.5-1.0 
 1.67 
 
 1.95 
 2.04 
 1.3-1.5 
 
 1.8-2.0 
 9-1 
 
 0.5-1.0 
 0.5-1.0 
 0.3-0.7 
 0.29 
 
 0.39 
 0.39 
 0.3-0.6 
 
 0.8-1.0 
 06-07 
 
 0.3-0.4 
 0.3-0.4 
 0.3-0.4 
 0.095 
 
 0.405 
 0.578 
 0.5-0.8 
 
 0.6-0.8 
 01-03 
 
 .03 " 
 .035 " 
 .035 " 
 0.032 
 
 0.042 
 0.044 
 .06-. 10 
 
 .06-. 10 
 .04-. 06 
 
 in. chill. 
 Ditto 1/2 in. chill. 
 Ditto 3/ 4 in. chill. 
 Ditto 1 in. chill. 
 Series A. Am. 
 F'dmen's Assn. 
 Series B. ditto. 
 Series C. ditto. 
 For locomotive 
 cylinders. 
 " Semi-steel." 
 " Semi-steel." 
 
 4.33 
 3.17 
 
 3.34 
 3.5 
 3.55 
 
 3.08 
 
 J.72 
 
 2.57 
 2.9 
 3.0 
 
 1.25 
 0.45 
 
 0.77 
 0.6 
 0.55 
 
 0.73 
 1.99 
 
 1.89 
 0.7 
 2.75 
 3.10 
 
 0.44 
 0.39 
 
 0.39 
 0.4 
 2.39 
 1.80 
 
 0.43 
 0.65 
 
 0.70 
 0.5 
 86 
 0.90 
 
 0.08 
 0.13 
 
 0,09 
 0.08 
 0.014 
 
 A strong car 
 wheel, Cu, 0.03. 
 Automobile cyl- 
 inders. 
 Ditto. 
 Good car wheel. 
 Scotch irons. 
 " Am. Scotch ** 
 
 
 
 
 0.75-1.5 
 
 to 06 
 
 to 0.22 
 
 to 0.04 
 
 Ohio irons. 
 Pig for malle- 
 
 
 
 
 2-25 
 1 2-1 5 
 
 to 0.7 
 5-0 8 
 
 to 0.7 
 35-0.6 
 
 to 0.15 
 to 0.09 
 
 able castings. 
 Brake-shoes. 
 Hard iron for 
 
 
 
 
 1 5-2 
 
 5-0 8 
 
 35-0.6 
 
 to 0.08 
 
 heavy work. 
 Medium iron for 
 
 
 
 
 2 2-2 8 
 
 to 7 
 
 to 7 
 
 to 0.085 
 
 general work. 
 Soft iron cast'ga 
 
 
 
 
 
 
 
 
 
23 to 25. 
 
 CAST IRON. 441 
 
 ._ 25. Series of bars tested by a committee of the association. 
 See results of tests on page 419. Series A, soft Bessemer mixture; B, 
 dynamo-frame iron; C, light machinery iron. Samples for analysis were 
 taken from the 1-in. square dry sand bars. 
 
 26. Specifications by a committee of the Am. Ry. Mast. Mechs. Assn., 
 1906. T.S., 25,000; transverse test, 3000 Ib. on H/4-in. round bar, 12 in. 
 bet ween supports; deflection, 0.1 in. minimum; shrinkage, 1/8 in. max. 
 27, soft "semi-steel;" 28, harder do. They approach air-furnace iron 
 In most respects, and excel it in strength; test bars 2 X 1 X 24 in. of the 
 low Si semi-steel showing 2800 to 3000 Ib. transverse strength, with 
 7/i6 in. deflection. M. B. Smith, Eng. Digest, Aug., 1908. 29. J. M. 
 Hartman, Bull. I. & S. Assn., Feb., 1892. The chill was very hard, 1/4 in. 
 deep at root of flange, 1/2 in. deep on tread. 30, 31. Strong and shock- 
 resisting. T.S., 38,000. Castings, June, 1908. 32. Com. of A.S.T.M., 
 1905, Proc., v. 65. Successful wheels varying quite considerably from 
 these figures may be made. 33, 34. C. A. Meissner, Iron Age, 1890. 
 Average of several. 35. R. Moldenke, A.S.M.E., 1908. 36-39. J. W 
 Keep, A.S.M.E., 1907. 
 
 A Chilling Iron is one which when copied slowly has a gray fracture, 
 but when cast in a mold one side of which is a thick mass of cast-iron, 
 called a chill, the fractured surface shows white iron for some depth on 
 the side that was rapidly cooled by the chill. See Table Nos. 19-22. 
 
 Specifications for Castings, recommended by a committee of the 
 A.S.T.M., 1908. S in gray iron castings, light, not over 0.08; medium, 
 not over 0.10; heavy, not over 0.12. Alight casting is one having no 
 section over 1/2 in. thick, a heavy casting one having no section less than 
 2 in. thick, and a medium casting one not included in the classification of 
 light or heavy. The transverse strength of the arbitration bar shall not 
 be under 2500 Ib. for light, 2900 Ib. for medium, and 3300 Ib. for heavy 
 castings; in no case shall the deflection be under 0.10 in. When a ten- 
 sile test is specified this shall run not less than 18,000 Ib. per sq. in. for 
 light, 21,000 Ib. for medium, and 24,000 Ib. for heavy castings. 
 
 The " arbitration bar" is 1 1/4 in. diam., 15 in. long, cast in a thoroughly 
 dried and cold sand mold. The transverse test is made with supports 
 12 in. apart. The moduli of rupture corresponding to the figures for 
 transverse strength are respectively 39115, 45373, and 51632, being the 
 product of the figures given and the coastant 15.646, the factor for R/P 
 for a H/4-in. round bar 12 in. between supports.* The standard form of 
 tensile test piece is 0.8 in. diam., 1 in. long between shoulders, with a 
 fillet 7/32 in. radius, and ends 1 in. long, 11/4 in. diam., cut with standard 
 thread, to fit the holders of the testing machine. 
 
 Specifications bv J. W. Keep, A.S.M.E., 1907. See Table of Analyses, 
 Nos. 37-39, page 417. Transverse test, 1x1 x 12-in. bar, hard iron castings. 
 No. 37, 2400 to 2600 Ib.; tensile test of same bar, 22,000 to 25,000 Ib. 
 No. 38, medium, transverse, 2200 to 2400; tensile, 20,000 to 23,000. 
 No. 39, soft, transverse, 2000 to 2200; tensile, 18,000 to 20,000. 
 
 Specifications for Metal for Cast-iron Pipe. Proc. A.S.T.M., 1905, 
 A.L.M.K., xxxv, 166. Specimen bars 2 in. wide x 1 in. thick x 24 in. 
 between supports, loaded in the center, for pipes 12 in. or less in diam. 
 shall support 1900 Ib. and show a deflection of not less than 0.30 in, 
 before breaking. For pipes larger than 12 in., 2000 Ib. and 0.32 in. 
 The corresponding moduli of rupture are respectively 34,200 and 36,000 
 Ib. Four grades of pig are specified: No. 1, Si, 2.75; S, 0.035. No 2. 
 8i, 2.25; S, 0.045. No. 3, Si, 1.75; S, 0.055. No. 4, Si, 1.25; S, 0.065. A 
 variation of 10% of the Si either way, and of 0.01 in the S above the 
 standard, is allowed. 
 
 Chemical Standards for Iron Castings. The following analyses are 
 tentative standards, or probable best analyses, suggested by the 
 Committee on Standards for Iron Castings, American Foundry men's 
 Association, June, 1910. "Heavy" castings are those in which no 
 section is less than 2 in. thick; "light" castings are those having any 
 section less than i/2-in. thick; "medium" castings are those not in- 
 cluded in the definition of light and heavy castings. The desirable 
 
 * Formula, y^Pl = fll/c; see page 299. I = Vstird*; c = *Ad\ d = 
 In.;? =12 in. / = 0.11983; R/P = MX 12 X % * 0.11983 = 15.646. 
 
442 
 
 IRON AND STEEL. 
 
 percentage of silicon depends largely on the thickness of the casting 
 and the practice followed in shaking out. These factors, being in 
 many cases undetermined, are allowed for by giving fairly wide limits 
 to this element. The effect of purifying alloys and the use of steel 
 scrap have not been taken into account. In many cases a wide range 
 of composition is compatible with the best results, and in such cases 
 the question of cost will be the first element to be considered. 
 
 
 Si. 
 
 S. 
 
 P. 
 
 Mn. 
 
 C. 
 
 (Comb.) 
 
 c. 
 
 (Total) 
 
 Acid - resisting castings 
 (stills, eggs, etc.) . . . 
 
 1.00-2.00 
 2.00-2.50 
 
 2.25-2.75 
 1.40-1.60 
 1 .75-2.25 
 
 0.05-* 
 0.06-0.08 
 
 0.06-0.08 
 0.06- 
 0.08- 
 
 0.40-* 
 0.60-0.80 
 
 0.70-0.90 
 0.20- 
 0.40-0.50 
 
 1.00-1.50 
 0.60-0.80 
 
 0.50-0.70 
 0.60-1.00 
 0.60-0.80 
 
 
 3.00-3.50 
 
 Agricultural machinery, 
 ordinary 
 
 
 Agricultural machinery, 
 very thin 
 Annealing boxes, etc 
 Automobile castings. 
 
 
 
 
 
 Balls for ball mills 
 Boiler castings . 
 
 1.00-1.25 
 2.00-2.50 
 1.50-2.25 
 0.75-1.25 
 1.75-2.25 
 0.80-1.00 
 
 0.08- 
 0.06- 
 0.08- 
 0.08-0.10 
 0.07- 
 0.08-0.10 
 
 0.20- 
 0.20- 
 0.40-0.60 
 0.20-0.40 
 0.20-0.40 
 0.20-0.40 
 
 0.60-1.00 
 0.60-1.00 
 0.60-1.00 
 0.80-1.20 
 0.60-1.00 
 0.80-1.20 
 
 
 
 
 
 Car castings, gray iron. . . 
 Chilled castings 
 Chills 
 
 
 
 
 
 Crusher jaws 
 
 
 
 Cutting-tools, chilled .... 
 Cylinders: 
 Air and ammonia 
 Automobile 
 
 1.00-1.25 
 
 1.00-1.75 
 1.75-2.00 
 1.00-1.75 
 0.80-1.20 
 1.20-1.60 
 
 0.08- 
 
 0.09- 
 0.08- 
 0.08- 
 0.10- 
 0.09- 
 
 0.20-0.40 
 
 0.30-0.50 
 0.40-0.50 
 0.20-0.40 
 0.20-0.40 
 0.30-0.50 
 
 0.60-0.80 
 
 0.70-0.90 
 0.60-0.80 
 0.70-0.90 
 0.80-1.00 
 0.70-0.90 
 
 6.55-0.65 
 
 3.00-3.30 
 3.00-3.25 
 3.00-3.30 
 low 
 low 
 
 low 
 low 
 2.97 
 
 low 
 low 
 
 Gas engine . 
 
 Hydraulic, heavy 
 Hydraulic, medium 
 
 
 Locomotive 
 
 1.00-1.50 
 1.00-1.25 
 1.25-1.75 
 1.25-1.50 
 
 2.70 ' 
 
 2.00-2.50 
 2.50-3.00 
 
 1.25-1.75 
 1.50-2.25 
 2.25-2.50 
 1.25-2.00 
 
 0.08-0.10 
 0.10- 
 0.09- 
 0.07- 
 
 0.063 
 
 0.08- 
 0.08- 
 
 0.10- 
 0.08- 
 0.07- 
 0.09- 
 
 0.30-0.50 
 0.20-0.40 
 0.30-0.50 
 0.20- 
 
 0.30 
 
 0.50-0.80 
 0.50-0.80 
 
 0.30-0.50 
 0.40-0.60 
 0.40-0.50 
 0.30-0.50 
 
 0.80-1.00 
 0.80-1.00 
 0.70-0.90 
 0.60-0.80 
 
 0.44 
 
 0.30-0.40 
 0.30-0.40 
 
 0.60-0.80 
 0.50-0.70 
 0.50-0.70 
 0.60-1.00 
 
 1.60 
 
 0.20-0.30 
 0.20-0.30 
 
 Steam engine, heavy. . . 
 Steam engine, medium. 
 Dies, drop-hammer 
 Diamond polishing 
 wheelsf 
 Electrical machinery 
 (frames, bases, spiders), 
 large 
 
 Electrical machinery, 
 small 
 Engine castings: 
 Bedplates 
 Flywheels 
 Do., automobile ..... 
 Frames 
 
 Pillow blocks 
 Piston rings 
 Fire pots and furnace 
 castings .... 
 
 1.50-1.75 
 1.50-2.00 
 
 2.00-2.50 
 2.00-2.50 
 
 0.50-0.75 
 1.00-1.25 
 1.00-1.25 
 
 0.08- 
 0.08- 
 
 0.06- 
 0.06- 
 
 0.15-0.20 
 0.06- 
 0.06- 
 
 0.40-0.50 
 0.30-0.50 
 
 0.20- 
 0.20- 
 
 0.20-0.40 
 0.20-0.30 
 0.20-0.30 
 
 0.60-0.80 
 0.40-0.60 
 
 0.60-1.00 
 0.60-1.00 
 
 1.50-2.00 
 0.80-1.00 
 
 ' b'.30-' ' 
 O.WM.OO 
 
 low 
 
 low 
 low 
 
 low 
 low 
 
 Grate bars 
 
 Grinding machinery, 
 chilled Castings for .... 
 Gun carriages 
 
 Gun iron . . . 
 
 Hardware (light) and 
 hollow ware 
 
 2.25-2.75 
 
 1.25-2.50 
 1.25-1.50 
 
 1.25-1.50 
 
 0.08- 
 
 0.06- 
 0.06- 
 
 0.08- 
 
 0.50-0.80 
 
 0.20- 
 0.20- 
 
 0.30-0.50 
 
 0.50-0.70 
 
 0.60-1.00 
 0.60-1.00 
 
 0.70-0.90 
 
 Heat re^stant iron (re- 
 torts) . . 
 
 0.30- 
 
 low 
 
 Ingot molds and stools. . 
 Locomotive castings, 
 heavy 
 
 
 
 * Affixed hyphens indicate that the percentages present should be 
 under those given. 
 
= 
 
 CAST IKON. 
 
 443 
 
 
 Si. 
 
 S. 
 
 P. 
 
 Mn. 
 
 C. 
 
 (Comb.) 
 
 C. 
 
 (Total) 
 
 Loco. Castings, light. . . . 
 Machinery castings, 
 heavy 
 Do., medium 
 
 1.50-2.00 
 
 1.00-1.50 
 1.50-2.00 
 2.00-2.50 
 1.75-2.00 
 1.00-1.50 
 1.50-2.00 
 2.00-2.50 
 1.75-2.25 
 2.25-2.75 
 
 0.08-* 
 
 0.10- 
 0.09- 
 0.08- 
 0.08-0.10 
 0.08-0.10 
 0.09- 
 0.08- 
 0.09- 
 0.08- 
 
 0.40-0.60 
 
 0.30-0.50 
 0.40-0.60 
 0.50-0.70 
 0.30- 
 0.30-0.50 
 0.40-0.60 
 0.50-0.70 
 0.50-0.70 
 0.60-0.80 
 
 0.60-0.80 
 
 0.80-1.00 
 0.60-0.80 
 0.50-0.70 
 0.50-0.70 
 0.80-1.00 
 0.70-0.90 
 0.60-0.80 
 0.60-0.80 
 0.50-0.70 
 
 . 
 
 
 
 low 
 
 Do., light 
 Friction clutches 
 
 
 low 
 low 
 
 Gears, heavy 
 Do., medium 
 
 
 Do., small 
 Pulleys, heavy 
 Do., light 
 
 Shaft colla s and 
 couplings 
 Shaft hangers 
 
 1.75-2.00 
 1.50-2.00 
 
 0.08- 
 0.08- 
 
 0.40-0.50 
 0.40-0.50 
 
 0.60-0.80 
 0.60-0.80 
 
 
 
 
 
 Ornamental work 
 Permanent molds . . . 
 
 2.25-2.75 
 2.00-2.25 
 
 0.08- 
 0.07- 
 
 0.60-1.00 
 0.20-0.40 
 
 0.50-0.70 
 0.60-1.00 
 
 
 
 
 
 Permanent mold castings. 
 Piano plates . . 
 
 1.50-3.00 
 2.00-2.25 
 
 0.06- 
 0.07- 
 
 
 0.40- 
 
 
 
 0.40-0.60 
 
 0.60-0.80 
 
 
 
 Pipe 
 Pipe fittings. . 
 
 1.50-2.00 
 1.75-2.50 
 
 1.50-1.75 
 0.75-1.25 
 
 0.10- 
 0.08- 
 
 0.08- 
 0.08- 
 
 0.50-0.80 
 0.50-0.80 
 
 0.20-0.40 
 0.20-0.30 
 
 0.60-0.80 
 0.60-0.80 
 
 0.70-0.90 
 0.80-1.00 
 
 
 
 Do., for superheated 
 steam lines. 
 Plow points, chilled . . . 
 
 
 low 
 
 Propeller wheels 
 Pumps, hand .... 
 
 1.00-1.75 
 2.00-2.25 
 2.00-2.25 
 
 0.10- 
 0.08- 
 O.OS- 
 
 0.20-0.40 
 0.60-0.80 
 0.60-0.80 
 
 0.60-1.00 
 0.50-0.70 
 0.50-0.70 
 
 
 low 
 
 Radiators 
 
 0.50-0.60 
 
 
 Railroad castings 
 Rolling mill machinery: 
 Housings 
 Rolls, chilled . . 
 
 1.50-2.25 
 
 1.00-1.25 
 0.60-0.80 
 
 0.75 
 2.00-2.30 
 1.75-2.00 
 1.75-2.25 
 2.25-2.75 
 1.25-1.75 
 1.75-2.25 
 
 0.08- 
 
 0.08- 
 0.06-0.08 
 
 0.03 
 0.08- 
 0.07- 
 0.09- 
 0.08- 
 0.09- 
 0.08- 
 
 0.40-0.60 
 
 0.20-0.30 
 0.20-0.40 
 
 0.25 
 0.60-1.00 
 0.3(V 
 0.50-0.80 
 0.60-0.90 
 0.20-0.40 
 0.30-0.50 
 
 0.60-0.80 
 
 0.80-1.00 
 1.00-1.20 
 
 0.66 
 0.50-0.70 
 0.70-0.90 
 0.60-0.80 
 0.60-0.80 
 0.80-1.00 
 0.60-0.80 
 
 
 low 
 3.00-3.25 
 
 4.10 
 
 Rolls, unchilled (sand- 
 cast) f . . . 
 
 1.20 
 
 Scales 
 
 Slag car castings 
 Soil pipe and fittings .... 
 Stove plate 
 Valves, large 
 
 
 
 
 
 Do., small 
 
 
 low 
 
 ' '2.56' ' 
 
 Water heaters 
 Wheels, large 
 Do., small 
 White iron castings! 
 
 2.00-2.25 
 1.50-2.00 
 1.75-2.00 
 0.50-0.90 
 
 0.08- 
 0.09- 
 0.08- 
 0.15-0.25 
 
 0.30-0.50 
 0.30-0.40 
 0.40-0.50 
 0.20-0.70 
 
 0.60-0.80 
 0.60-0.80 
 0.50-0.70 
 0.17-0.50 
 
 ' '2.96' ' 
 
 * Affixed hyphens indicate that the percentages present should be 
 under those given. 
 
 t But one or two analyses available no suggestion made. 
 
 Standard Specifications for Foundry Pig Iron. 
 
 (American Foundry men's Association, May, 1909.) 
 
 ANALYSIS. It is recommended that foundry pig be bought by analysis. 
 
 SAMPLING. Each carload or its equivalent shall be considered as a 
 unit. One pig of machine-cast, or one-half pig of sand-cast iron shall be 
 taken to every four tons in the car, and shall be so chosen from different 
 parts 9f the car as to represent as nearly as P9.ssible the average quality 
 of the iron. Drillings shall be taken so as to fairly represent the composi- 
 tion of the pig as cast. An equal quantity of the drillings from each pig 
 shall be thoroughly mixed to make up the sample for analysis. 
 
 PERCENTAGE OF ELEMENTS. When the elements are specified the fol- 
 lowing percentages and variations shall be used. Opposite each percent- 
 age of the different elements a syllable has been affixed so that buyers, 
 by combining these syllables, can form a code word to be used in 
 telegraphing. 
 
444 
 
 SILICON 
 
 IRON AND STEEL. 
 SULPHUR TOTAL CARBON MANGANESE 
 
 PHOSPHORUS 
 
 % 
 1.00 
 1.50 
 2.00 
 2.50 
 3.00 
 
 Code 
 La 
 Le 
 Li 
 Lo 
 Lu 
 
 (max.) Code 
 0.04 Sa 
 0.05 Se 
 0.06 Si 
 0.07 So 
 0.08 Su 
 0.09 Sy 
 0.10 Sh 
 
 (min.) 
 3.00 
 3.20 
 3.40 
 3.60 
 3.80 
 
 Code 
 Ca 
 
 8f 
 
 Co 
 
 Cu 
 
 
 
 
 
 
 1 
 1 
 1 
 
 % 
 
 .20 
 .40 
 .60 
 .80 
 .00 
 .25 
 .50 
 
 Code 
 Ma 
 Me 
 Mi 
 Mo 
 Mu 
 My 
 Mh 
 
 
 
 
 
 
 1 
 1 
 1 
 
 % 
 
 .20 
 .40 
 .60 
 .80 
 .00 
 .25 
 .50 
 
 Code 
 Pa 
 Pe 
 Pi 
 Po 
 Pu 
 Py 
 Ph 
 
 Percentages of any element specified one-half way between the above 
 shall be designated by the addition of the letter x to the next lower symbol, 
 thus Lex means 1.75 Si. 
 
 Allowed variation: Si, 0.25; P, 0.20; Mn, 0.20. The percentages of P 
 and Mn may be used as maximum or minimum figures when so specified. 
 
 Example: Le-sa-pi-me represents 1.50 Si, 0.04 S, 0.60 P, 0.40 Mn. 
 
 BASE OR QUOTING PRICE. For market quotations an iron of 2.00 Si 
 (with variation 0.25 either way) and S 0.05 (max.) shall be taken as the 
 base. The following table may be filled out, and become a part of a 
 contract; "B," or Base, represents the price agreed upon for a pig of 
 2.00 Si and under 0.05 S. "C" is a constant differential to be deter- 
 mined at the time the contract is made. 
 
 Sill-, Silicon > 
 
 phur 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 
 0.04 B + 6C B+5C B+4C B+3C B + 2C B + C B B-1C B-2C B-3C 
 0.05 B + 5C B+4C B+3C B + 2C B + 1C B B-1C B-2C B-3C B-4C 
 0.03 B + 4C B + 3C B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C 
 
 0.07 B + 3C B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C B-CC 
 
 0.08 B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C B-CC B-7C 
 0.09 B + 1C B B-1C B--2C B-3C B-4C B-5C B-6C B-7C B-8C 
 0.10 B B-1C B-2C B-3C B-4C B-5C B-6C B-7C B-8C B-9C 
 
 Tensile Tests of Cast-iron Bars. 
 
 (American Foundrymen's Association, 1899.) 
 
 Square Bars. 
 
 Size, in... 
 (A)<7.c.. 
 o m 
 
 0.5x0.5 
 15,900 
 
 1x1 
 13,900 
 15 400 
 
 1.5x1.5 
 12,100 
 12900 
 
 2x2 
 10,600 
 10900 
 
 0.56 
 16,000 
 
 1.13 
 
 13,800 
 13 800 
 
 1.69 
 12,000 
 13 500 
 
 2.15 
 11,000 
 12 200 
 
 " d. s.. 
 
 ** d 771. 
 
 14,600 
 
 12,900 
 13,800 
 
 12,300 
 13,400 
 
 9,800 
 12,100 
 
 14,300 
 
 13,700 
 13,600 
 
 11,700 
 13,200 
 
 10,500 
 10,600 
 
 (B)flr.c.. 
 am. 
 
 17,100 
 
 15,200 
 17,600 
 
 12,900 
 15,000 
 
 11,500 
 11,800 
 
 16,500 
 
 15,900 
 19000 
 
 13,100 
 15 400 
 
 11,400 
 12500 
 
 " d. c. . 
 *' d m. 
 
 16,300 
 
 15,100 
 18,400 
 
 13,300 
 15 000 
 
 11,100 
 12 100 
 
 16,700 
 
 16,200 
 16900 
 
 13,200 
 15 100 
 
 11,000 
 13 100 
 
 (C) ff.c.. 
 " a m. 
 
 17,700 
 
 16,000 
 18 500 
 
 12,500 
 15 100 
 
 11,100 
 11 700 
 
 17,800 
 
 15^00 
 17 400 
 
 14,200 
 15 000 
 
 12,000 
 11 600 
 
 " d.c.. 
 '* d. m. 
 
 16,400 
 
 16,000 
 17,100 
 
 12,200 
 14,100 
 
 11,300 
 9,800 
 
 16,400 
 
 15,900 
 17,700 
 
 14,000 
 15,900 
 
 11 1600 
 10,400 
 
 av. (7. ... 
 av. d. . . . 
 
 av. c. . . . 
 
 13,600 
 15,800 
 14,700 
 
 16,100 
 15,500 
 14,800 
 16,800 
 
 13,400 
 13,400 
 12,500 
 14,200 
 
 11,300 
 11,000 
 10,900 
 11,400 
 
 13,400 
 15,800 
 16,300 
 
 16,000 
 15,700 
 15,200 
 16,400 
 
 13,900 
 13,800 
 13,000 
 f4,600 
 
 11,600 
 11,200 
 11,200 
 11,700 
 
 Round Bars. 
 
 Compression Tests of Cast-iron Bars. 
 
 Size, i 
 
 (A) 
 
 n.. . 
 )... 
 
 0.5x0.5 
 29,570 
 
 Ixl 
 20,010 
 21,990 
 
 1.5x1.5 
 17,180 
 17,920 
 
 2x2 
 13,810 
 13,750 
 
 2.5x2.5 
 10,950 
 12,040 
 
 3x3 
 9,830 
 11,200 
 
 3.5x3.5 
 9,350 
 10,770 
 
 4x4 
 9,100 
 10,340 
 
 
 * 
 
 
 
 17,180 
 
 13,880 
 
 11,430 
 
 10,270 
 
 9,830 
 
 9,950 
 
 
 
 4 
 
 
 
 
 
 10,950 
 
 10,430 
 
 9,540 
 
 9,570 
 
 (B) 
 
 1 ... 
 ? 
 
 38,360 
 
 23,000 
 12,440 
 
 20,980 
 24,820 
 
 18,130 
 21,640 
 
 15,060 
 18,270 
 
 13,790 
 17,000 
 
 13,160 
 15,970 
 
 12,430 
 16,140 
 
 < 
 
 1 
 
 
 
 20,980 
 
 18,740 
 
 15,940 
 
 14,410 
 
 15,200 
 
 13,950 
 
 
 4 
 
 
 
 
 15,060 
 
 
 13,900 
 
 13,560 
 
 13,760 
 
 (C) 
 
 ... 
 ? 
 
 38,360 
 
 24,890 
 27,900 
 
 20,750 
 22,060 
 
 18,010 
 21,750 
 
 17,840 
 19,800 
 
 15,950 
 18,170 
 
 15,880 
 17,100 
 
 14,220 
 16,410 
 
 
 ^ 
 
 
 
 20 750 
 
 19340 
 
 18,050 
 
 16,850 
 
 16,510 
 
 15,250 
 
 " ( 
 
 4... 
 
 
 , , , 
 
 
 17,840 
 
 
 16,040 
 
 16,080 
 
 14,880 
 
CAST IRON. 
 
 445 
 
 Transverse Tests of Cast-iron Bars. Modulus of Rupture. 
 
 Bize *... 
 Diam. f 
 (A)r.d.c.... 
 
 0.5x0.5 
 0.56 
 31,100 
 
 1x1 
 1.13 
 33,400 
 27800 
 
 1.5x1.5 
 1.69 
 33,900 
 38,000 
 
 2x2 
 2.15 
 31,700 
 32,300 
 
 2.5x2.5 
 2.82 
 27,000 
 28,000 
 
 3x3 
 
 3.38 
 26,600 
 28600 
 
 3.5x3.5 
 3.95 
 23,400 
 22400 
 
 4x4 
 4.51 
 
 22,600 
 22900 
 
 (B) s. g. c. . . . 
 
 44,400 
 
 39,100 
 37,400 
 
 39,500 
 40,300 
 
 33,900 
 34,700 
 
 31,900 
 35,800 
 
 29,700 
 33,500 
 
 27,200 
 30 100 
 
 27,600 
 27,100 
 
 " s.d.c 
 " s.d.m. 
 
 35,500 
 
 38,300 
 30200 
 
 34,000 
 36,200 
 
 32,900 
 33,300 
 
 31,900 
 35,200 
 
 30,200 
 30900 
 
 29,300 
 28 100 
 
 25,900 
 25,800 
 
 " r.g.c 
 M r. g.m. .. 
 
 " r. d. m. . . 
 (C) s.g.c 
 
 ' s. g m. 
 
 36,400 
 '37', 800 ' 
 'Si', 800 ' 
 
 46,200 
 40,000 
 49,000 
 39,100 
 39,200 
 
 41,200 
 44,800 
 44,300 
 37,800 
 33,600 
 40,200 
 
 41,400 
 38,800 
 39,200 
 37,700 
 37,900 
 37,000 
 
 41,300 
 37,100 
 40,700 
 33,000 
 32,200 
 33,700 
 
 36,300 
 32,900 
 31,800 
 32,800 
 31,100 
 33,300 
 
 34,800 
 32,700 
 35,300 
 32,000 
 31,300 
 32300 
 
 31,000 
 32,300 
 31,100 
 31,200 
 29,200 
 27,900 
 
 s. d, c. ... 
 
 48,000 
 
 39,100 
 
 38,800 
 38,900 
 
 35,100 
 35,400 
 
 31,200 
 33,500 
 
 29,300 
 32 700 
 
 29,300 
 29 100 
 
 27,800 
 25,500 
 
 r.g.c 
 r g. m. . 
 
 62,800 
 
 48,500 
 55,700 
 
 39,000 
 49,200 
 
 44,500 
 42900 
 
 41,400 
 41,500 
 
 41,200 
 36 500 
 
 35,000 
 34 100 
 
 32,300 
 36,000 
 
 r. d. c. . . . 
 r. d. m. . . 
 Av. (B) s 
 
 (C) s.'. '.'.'. 
 
 (B)& r (CJ^. 
 ** d. 
 Gen'l av 
 Equiv. load. . 
 
 53,000 
 
 '39; 900 
 37,100 
 49,900 
 57,900 
 48,800 
 43,300 
 46,100 
 320 
 
 50,400 
 47,900 
 36,200 
 43,600 
 39,100 
 50,600 
 43,100 
 41,600 
 42,400 
 2356 
 
 44,000 
 51,300 
 37,500 
 42,000 
 37,900 
 45,900 
 41,000 
 40,700 
 40,800 
 7650 
 
 40,200 
 38,000 
 33,700 
 39,300 
 36,300 
 41,400 
 38,800 
 36,500 
 37,700 
 16,756 
 
 39,500 
 38,900 
 33,700 
 38,200 
 32,600 
 40,400 
 36,800 
 35,600 
 36,200 
 31,424 
 
 37,800 
 36,300 
 31,100 
 33,400 
 31,600 
 37,900 
 33,900 
 32,700 
 33,400 
 50,100 
 
 35,200 
 32,200 
 28,700 
 33,700 
 30,500 
 34,100 
 32,200 
 31,300 
 31,700 
 75,516 
 
 32,100 
 33,500 
 26,600 
 31,400 
 27,600 
 33,200 
 30,400 
 30,400 
 29,900 
 106,311 
 
 * Size of sauare bars as cast, in. t Diam. of round bars as cast. in. 
 
 NOTES ON THE TABLES OP TESTS. The machined bars were cut to 
 the next size smaller than the size they were cast. The transverse bars 
 were 12 in. long between supports. (A), (B), (C), three qualities of iron; 
 for analyses see page 417; r t round bars; s, square bars; d, cast in dry sand; 
 g, cast in green sand; r, bar tested as cast; m, bar machined to size. The 
 general average (next to last line of the first table) is the average of the six 
 lines preceding. The equivalent load (last line) is the calculated total 
 load that would break a square bar whose modulus of rupture is that 
 of the general average. 
 
 COMPRESSION TESTS. The figures given are the crushing strengths, in 
 pounds, of in. cubes cut from the bars. Multiply by 4 to obtain Ibs. 
 per sq. in. (1) Cube cut from the middle of the bar; (2) first in. from 
 edge; (3) second in. from edge; (4) third ^ in from edge. 
 
 Some Tests of Cast Iron. (G. Lanza, Trans. A.S.M.E., x, 187.) 
 The chemical analyses were as follows: Gun iron: TC, 3.51; GC, 2.80; 
 S, 0.133; P, 0.155; Si, 1.140. Common iron: S, 0.173; P, 0.413; Si, 1.89. 
 
 The test specimens were 26 in. long: those tested with the skin on being 
 very nearly 1 in. square, and those" tested with the skin removed being 
 cast nearly 1 1/4 in. square, and afterwards planed down to 1 in. square. 
 
 Tensile Elastic Modulus 
 Strength. Limit. ' of 
 
 Elasticity. 
 
 Unplaned common. . 20,200 to 23,000 T.S. Av. = 22,066 6,500 13,194,233 
 Planed common. .. .20,300 to 20,800 " " =20,520 5,833 11,943,953 
 
 Unplaned gun 27,000 to 28,775 " " =28,17511,000 16,130,300 
 
 Planed gun 29,500 to 31,000 " . " =30,500 8,500 15,932,880 
 
 The elastic limit is not clearly defined in cast iron, the elongations increas- 
 ing faster than the increase of the loads from the beginning of the test. 
 The modulus of elasticity is therefore variable, decreasing as the loads 
 increase. 
 
 The Strength of Cast Iron depends on many other things besides 
 its chemical composition. Among them are the size and shape of the 
 casting, the temperature at which the metal is poured, and the rapidity of 
 cooling. Internal stresses are apt to be induced by rapid cooling, and 
 Blow cooling tends to cause segregation of the chemical constituents and 
 
446 IRON AND STEEL. 
 
 opening of the grain of the metal, making it weak. The author recom- 
 mends that in making experiments on the strength of cast iron, bars of 
 several different sizes, such as 1/2, 1, 11/2, and 2 in. square (or round), 
 should be taken, and the results compared. Tests of bars of one size 
 only do not furnish a satisfactory criterion of the quality of the iron of 
 which they are made. Trans. A.T.M.E., xxvi, 1017. 
 
 Theory of the Relation of Strength to Chemical Constitution. 
 J. E. Johnston, Jr. (Am. Mack., April 5 and 12, 1900), and H. M. Howe 
 (Trans. A.I.M.E., 1901) have presented a theory to explain the variation 
 in strength of cast iron with the variation in combined carbon. It is 
 that cast iron is steel of CC ranging from to 4%, with particles of graph- 
 ite, which have no strength, enmeshed with it. The strength of the cast 
 iron therefore is that of the' steel or graphiteless iron containing the same 
 percentage of CC, weakened in some proportion to the percentage of GC. 
 The tensile strength of steel ranges approximately from 40,000 lb. per 
 sq. in. with C to 125,000 lb. with 1 .20 C. With higher C it rapidly becomes 
 weak and brittle. White cast iron with 3% CC is about 30,000 T.S., 
 and with 4% about 18,000. The amount of weakening due to GC is not 
 known, but by making a few assumptions we may construct a table of 
 hypothetical strengths of different compositions, with which results of 
 actual tests may be compared. Suppose the strength of the steel-white 
 cast-iron series is as given below for different percentages of CC, that 
 6.25% GC entirely destroys the strength, and that the weakening effect 
 of other percentages is proportional to the ratio of the square root of that 
 percentage to the square root of 6.25, that the TC. in two irons is respec- 
 tively 3% and 4%, then we have the following: 
 Per cent CC.. 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.02.5 3 3.5 4 
 
 Steel, T.S 40 60 80 100 110 120 125 110 60 40 30 22 18 
 
 Cast iron, 4% 
 
 TC 8 13.2 19.2 26 31.2 37 41.5 40.5 26 20.7 18 15-8 18 
 
 Cast iron, 3% 
 
 TC 15.419.928.5 3842.952.1 5856.1 3628.730 
 
 The figures for strength are in thousands of pounds per sq. in. The 
 table is calculated as follows: Take 0.6 CC; with 4% TC., this leaves 
 3.4 GC, and with 3% TC, 2.4 GO_The sq. root of 3.4 is 1.9, and of 2.4 is 
 1.55. The ratio of these to ^6.25 is respectively 74 and 62%, which 
 subtracted from 100 leave 26 and 38% as the percentage of strength of 
 the 0.6 C steel remaining after the effect of the GC is deducted. The 
 table indicates that strength is increased as total C is diminished, and this 
 agrees with general experience. 
 
 Relation of Strength to Size of Bar as Cast. If it is desired that a 
 test bar shall fairly represent a casting made from the same iron, then 
 the dimensions of the bar as cast should correspond to the dimensions of 
 the casting, so as to have about the same ratio of cooling surface to 
 volume that the casting has. If the test bar is to represent the strength 
 of a plate, it should be cut from the plate itself if possible or else cut 
 from a cylindrical shell made of considerable diameter and of a thickness 
 equal to that of the casting. If the test is for distinguishing the quality 
 of the iron, then at least two test bars should be cast, one say 1/2 or 5/g in. 
 and one say 2 or 21/2 in. diameter, in order to show the effect of rapid 
 and slow cooling. 
 
 In 1904 the author made some tests of four bars of " semi-steel " adver- 
 tised to have a strength of over 30,000 lb. per sq. in. The bars were cast 
 1/2, 1, 2, and 3 in. diam., and turned to 0.46, 0.69, 1.6, and 1.85 in. respec- 
 tively. The results of transverse and tensile tests were: 
 
 Mod. of rupture. .1/2 in., 100.000; 1 in., 61,613; 2 in., 67,619; 3 in., 58,543 
 T.S. per sq. in... 38,510; ' 37,005; 25,685; ' 20,375 
 
 The i/2-in. piece was so hard that it could not be turned in a lathe and 
 had to be ground. 
 
 Influence of Length of Bar upon the Modulus of Rupture. 
 
 (R. Moldenke, Jour. Am. Foundrymen's Assn., Sept., 1899.) Seven 
 sets, each of five 2-in. square bars, made of a heavy machinery mixture, 
 and cast on end, were broken transversely, the distance between sup- 
 ports ranging from 6 to 16 ins. The average results were: 
 Dist. bet. supports, ins.... 6 8 10 12 14 16 
 
 Modulus of rupture 40,000 39,000 35,600 37,000 36,000 34,400 
 
CAST IRON. 
 
 447 
 
 The 10-in. bar in six out of seven cases gave a lower result than the 
 12-in. It appears that the ordinary formulas used in calculating the 
 cross breaking" strength of beams are not only incorrect for cast iron, on 
 account of the chemical differences in the iron itself when in different 
 cross sections, but that with the cross sections identical the distance 
 between the supports must be specially provided for by suitable con- 
 stants in whatever formulae may be developed. As seen from the above 
 results, the doubling of the distance between supports means a drop in 
 the modulus of rupture in the same sized bar of nearly 10 per cent. 
 
 Strength in Relation to Silicon and Cross-section. In castings 
 one half-inch square in section the strength increases as silicon increases 
 from 1.00 to 3.50: in castings 1 in. square in section the strength is practi- 
 cally independent of silicon, while in larger castings the strength decreases 
 as silicon increases. 
 
 The following table shows values taken from Mr. Keep's curves of the 
 approximate transverse strength of cast bars of different sizes reduced to 
 the equivalent strength of a i/2-in. x 12-in. bar. 
 
 Size of Square Cast Bars. 
 1/2 in. 1 1 'in~TTin. | 3 in. j 4 in, 
 
 Strength of a Va-in. X 12-in. 
 ' section, Ib. 
 
 Size of Square Cast Bars. 
 
 1/2 in. | 1 in. | 2 in. | 3 in. | 4 in. 
 
 "^Strength of"a~ V^in. X 12-in." " 
 
 section, Ib. 
 
 290 
 324 
 358 
 
 260 
 272 
 278 
 
 232 
 228 
 220 
 
 222 
 212 
 202 
 
 220 
 208 
 196 
 
 2.50 
 3.00 
 3.50 
 
 392 
 426 
 446 
 
 278 
 276 
 264 
 
 212 
 202 
 192 
 
 190 
 180 
 168 
 
 184 
 172 
 160 
 
 1.00 SI. 
 2.0081} 
 3.50 Hfc 
 
 Inches Square 
 
 FIG. 98. 
 
 Fig. 98 shows the relation of the strength to the size of the cast-iron bar 
 and to Si, according to the figures in the above table. Comparing the 
 2-in. bars with the l/2-in. bars, we find 
 
 Si, per cent 1 1.5 2 2.5 3 3.5 
 
 2-in. weaker than l/2-in., per cent. . 20 30 35 46 53 57 
 
 The fact that with the 1-in. bar the strength is nearly independent of 
 Si, shows that it is the worst size of bar to use to distinguish the quality 
 of the metal. If two bars were used, say l/2-in. and 2-in., the drop in 
 strength would be a better index to the quality than the test of any 
 single bar could be. 
 
 Shrinkage of Cast Iron. W. J. Keep (A. S. M. E. xvi., 1082) gives a 
 series of curves showing that shrinkage depends on silicon and on the 
 cross-section of the casting, decreasing as the silicon and the section 
 increase. The following figures are obtained by inspection of the curves: 
 
 ij 
 
 Size of Square Bars. 
 
 Silicon, 
 Per cent. 
 
 Size of Square Bars. 
 
 l /2 in. 
 
 1 in. 
 
 2 in. 
 
 3 in. | 4 in. 
 
 l /z in.| 1 in. | 2 in. 
 
 3 in. 
 
 4 in. 
 
 Shrinkage, In. per Foot. 
 
 Shrinkage, In. per Foot. 
 
 1.00 
 1.50 
 2.00 
 
 0.178 
 .166 
 .154 
 
 0.158 
 .145 
 .133 
 
 0.129 
 .116 
 .104 
 
 0.112 
 .099 
 .086 
 
 0.102 
 .088 
 .074 
 
 2.50 
 3.00 
 3.50 
 
 0.1421 0.121 
 .130| .109 
 .118| .097 
 
 0.091 
 .078 
 .065 
 
 0.072 
 .058 
 .045 
 
 0.060 
 .046 
 .032 
 
 Mr. Keep says: " The measure of shrinkage is practically equivalent to 
 a chemical analysis of silicon. It tells whether more or less silicon is 
 
448 IRON AND STEEL. 
 
 needed to bring the quality of the casting to an accepted standard of 
 excellence." 
 
 A shrinkage of l/g in. per ft. is commonly allowed by pattern makers. 
 According to the table, this shrinkage will be obtained by varying the Si 
 in relation to the size of the bar as follows: 1/2 in., 3.25 Si; 1 in., 2.4 Si; 
 2 in., 1.1 Si; 3 and 4, less than 1.0 Si. 
 
 Shrinkage and Expansion of Cast Iron in Cooling. (T. Turner, 
 Proc. I. & S. /., 1906.) Some irons show the phenomenon of expanding 
 immediately after pouring, and then contracting. Four irons were 
 tested,, analyzing as follows: (1) " Washed " white iron, CC 2.73; Si, 
 0.01; P, 0.01; Mn and S, traces. (2) Gray hematite, GC, 2.53; CC, 0.86; 
 Si, 3.47; Mn, 0.55; P, 0.04; S, 0.03. (3) Northampton, GC, 2.60; CC, 
 0.15; Si, 3.98; Mn, 0.50; P, 1.25; S, 0.03. (4) Cast iron, GC, 2.73; CC, 
 0.79; Si, 1.41; Mn, 0.43; P, 0.96; S, 0.07. No. 1 was stationary for 5 sec- 
 onds after pouring, shrunk 125 sec., stationary 10 sec., then shrunk till 
 cold. No. 2 expanded 15 sec., shrunk 20 sec. to original size, continued 
 shrinking 90 sec. longer, stationary 10 sec., expanded 30 sec., then shrunk 
 till cold. No. 3 expanded irregularly with three expansions and two 
 shrinkages, until 125 sec. after pouring the total expansion was 0.019 in. 
 in 12 in., then shrunk till cold. No. 4 expanded 0.08 in. in 50 sec., then 
 shrunk till cold. 
 
 Shrinkage Strains Relieved by Uniform Cooling. (F. Schumann, 
 A.S.M.E., xvii, 433.) Mr. Jackson in 1873 cast a flywheel with a very 
 large rim and extremely small straight arms. Cast in the ordinary way, 
 the arms broke either at the rim or at the hub. Then the same pattern 
 was molded so that large chunks of iron were cast between the arms, a 
 thickness of sand separating them. Cast in this way, all the arms re- 
 mained unbroken. 
 
 Deformation of Castings from Unequal Shrinkage. (F. Schu- 
 mann, A. S. M. E., vol. xvii.) A prism cast in a sand mold will main- 
 tain its alignment, after cooling in the mold, provided all parts around 
 its center of gravity of cross section cool at the same rate as to time and 
 temperature. Deformation is due to unequal contraction, and this is 
 due chiefly to unequal cooling. 
 
 Modifying causes that effect contraction are: Imperfect alloying of 
 two or more different irons having different rates of contraction; varia- 
 tions in the thickness of sand forming the mold; unequal dissipation of 
 heat, the upper surface dissipating the greater amount of heat: position 
 and form of cores, which tend to resist the action of contraction, also 
 the difference in conducting power between moist sand and dry-baked 
 cores; differences in the degree of moisture of the sand; unequal expos- 
 ure by the removal of the sand while yet in the act of contracting: 
 flanges, ribs, or gussets that project from the side of the prism, of suffi- 
 cient area to cause the sand to act as a buttress, and thus prevent the 
 natural longitudinal adjustment due to contraction; in light castings of 
 sufficient length the unyielding sand between the flanges, etc., may 
 cause rupture. 
 
 Irregular Distribution of Silicon in Pig Iron. J. W. Thomas 
 (Iron Age, Nov. 12, 1891) finds in analyzing samples taken from every 
 other bed of a cast of pig iron that the silicon varies considerably, the iron 
 coming first from the furnace having generally the highest percentage. In 
 one series of tests the silicon decreased from 2.040 to 1.713 from the first 
 bed to the eleventh. In another case the third bed had 1.260 Si, the 
 seventh 1.718, and the eleventh 1.101. He also finds that the silicon 
 varies in each pig, being higher at the point than at the putt. Some. of 
 his figures are: Point of pig, 2.328 Si; butt of pig, 2.157; point of pig, 
 1.831; butt of pig, 1.787. 
 
 White Iron Converted into Gray by Heating. (A. E. Outerbridge. 
 Jr., Proc. Am. Socy. for Testing MaVls, 1902, p. 229.) When white chilled 
 iron containing a considerable amount of Si and low in GC is heated to 
 about 1850 F. from 31/2 to 10 hours the CC is changed into C, which 
 differs materially from graphite, and a metal is formed which has prop- 
 erties midway between those of steel and cast iron. The specific gravity 
 is raised from 7.2 to about 7.8; the fracture is of finer grain than normal 
 gray iron; and the metal is capable of being forged, hardened, and taking 
 a sharp cutting edge, so that it may be used for axes, hatchets, etc. It 
 differs from malleable cast iron, since the latter has iis carbon removed 
 by oxidation, while the converted cast iron retains its .original total 
 
CAST -IRON. 449 
 
 carbon, although in a changed form. The tensile strength of the new 
 metal is high, 40,000 to 50,000 Ib. per sq. in., with very small elongation. 
 The peculiar change from white to gray iron does not take place if Si 
 is low The analysis of the original castings should be about TO, 3.4 to 
 3.8; Si, 0.9 to 1.2; Mn, 0.35 to 0.20; S, 0.05 to 0.04; P, 0.04 to 0.03. The 
 following shows the change effected by the heat treatment: 
 Before annealing, GO, 0.72; CO, 2.60; Si, 0.71; Mn, 0.11; S, 0.045; P, 0.04 
 After annealing. GO, 2.75; CC, 0.82; Si, 0.73; Mn, 0.11; S, 0.040; P, 0.04 
 
 The GC after annealing is, however, not ordinary graphite, but an 
 allotropic form, evidently identical with what Ledebur calls " tempering 
 graphite carbon." 
 
 Change of Combined to Graphitic Carbon by Heating. (H. M. 
 Howe, Trans. A. I. M. E., 1908, p. 483.) On heating white cast iron to dif- 
 ferent temperatures for some hours, the carbon changes from the com- 
 bined to the graphitic state to a degree which increases in general with 
 the temperature and with the silicon-content. With 0.05 Si, a little 
 graphite formed at 1832 F.; with 0.13 Si, at 1652 F. ; with 2.12 Si, graphite 
 formed at a moderate rate at 1112, and with 3.15 Si, it formed rapidly 
 at 1112 F. In iron free from Si, with 4.271 comb. C. and 0.255 graphitic, 
 none of the C. was changed to graphite on long heating to from 1680 to 
 2349 F., but in iron with 0.75 Si the graphite, originally 0.938%, rose 
 to 1.69% on heating to 1787, and to 2.795% on heating to 2057 F. On 
 the other hand, when carbon enters iron, as in the cementation process 
 in making blister-steel, it appears chiefly as cementite (combined carbon). 
 Also on heating iron containing graphit: to high temperatures and cooling 
 quickly, some of the graphite is changed to cementite. 
 
 Mobility of Molecules of Cast Iron. (A. E. Outerbridge, Jr., 
 A.I.M.E., xxvi, 176; xxxv, 223.) Within limits, cast iron is materially 
 strengthened by being subjected to repeated shocks or blows. Six bars 
 1 in. sq., 15 in. long, subjected for about 4 hours to incessant blows in a 
 tumbling barrel, were 10 to 15% stronger than companion bars not 
 thus treated. Six bars were struck 1000 blows on one end only with a 
 hand hammer, and they showed a like gain in strength. The increase is 
 greater in hard mixtures, or strong iron, than in soft mixtures, or weak 
 iron; greater in 1-in. bars than in l/2-in., and somewhat greater in 2-in. 
 than in 1-in. bars. Bars were treated in a machine by dropping a 14-lb. 
 weight on the middle of a 1-in. bar, supports 12 in. apart. Six bars 
 were first broken by having the weight fall a sufficient distance to break 
 them at the first blow, then six companion bars were subjected to from 
 10 to 50 blows of the same weight falling one-half the former distance, 
 and then the weight was allowed to fall from the height at- which the first 
 bars broke. Not one of the bars broke at the first blow; and from 2 to 
 10, and in one case 15 blows from the extreme height were required to 
 break them. Mr. Outerbridge believes that every casting when first 
 made is under a condition of strain, due to the difference in the rate of 
 cooling at the surface and near the center, and that it is practicable to 
 relieve these strains by repeatedly tapping the casting, allowing the parti- 
 cles to rearrange themselves and assume a new condition of molecular 
 equilibrium. The results, first reported in 1896, were corroborated by 
 other experimenters. A report in Jour. Frank. Inst., 1898, gave tests of 
 82 bars, in which the maximum gain in strength compared with untreated 
 bars was 40%, and the maximum increase , in deflection was 41%. 
 
 In his second paper, 1904, Mr. Outerbridge describes another series of 
 tests which showed that 1-in. sq. bars 15 in. long subjected to repeated 
 heating and cooling grew longer and thicker with each successive oper- 
 ation. One bar heated about an hour each day to about 1450 F. in a 
 gas furnace for 27 times increased its length 1 H/ie in. and its cross-section 
 Vs in. Soft iron expands more rapidly than hard iron. White iron does 
 not expand sufficiently to cover the original shrinkage. Wrought iron and 
 steel bars similarly treated in a closed tube all contracted slightly, the 
 average contraction after 60 heatings being 1/8 in. per foot. The strength 
 and deflection of the cast-iron bars was greatly decreased by the treatment, 
 1250 as compared with 2150 Ib., and 0.1 in. deflection as compared with 
 0.15 in. The specific gravity of the expanded bars was 5.49 to 6.01, as 
 compared with 7.13 for the untreated bars. 
 
 (irate bars of boiler furnaces grow larger in use, as do also cast-iron 
 pipes in ovens for heating air. 
 
450 IRON AND STEEL. 
 
 Castings from Blast Furnace Metal. Castings are frequently made 
 from iron run directly from the blast furnace, or from a ladle filled with 
 furnace metal. Such metal, if high in Si, is more apt to throw out " kish " 
 or loose particles of graphite than cupola metal. With the same percen- 
 tage of Si, it is softer than cupola metal, which is due to two causes: 1, 
 lower S; 2, higher temperature. T. D. West, A.I.M.E., xxxv, 211, 
 reports an example of furnace metal containing Si, 0.51; S, 0.045; Mn, 
 0.75; P, 0.094; which was easily planed, whereas if it had been cupola 
 metal it would have been quite hard. J. E. Johnson, Jr., ibid., p 213, 
 says that furnace metal with S, 0.03, and Si, 0.7, makes good castings, not 
 too hard to be machined. Should the metal contain over 0.9 Si, diffi- 
 culty is experienced in preventing holes and soft places in the castings, 
 caused by the deposition of kish or graphite during or after pouring. 
 The best way to prevent this is to pour the iron very hot when making 
 castings of small or moderate size. 
 
 Effect of Cupola Melting. (G. R. Henderson, A.S.M.E., xx, 621.) 
 27 car-wheels were analyzed in the pig and also after remelting. The 
 P remains constant, as does Si when under 1%. Some of the Mn always 
 disappears. The total C remains the same, but the GO and CC vary in 
 an erratic manner. The metal charged into the cupola should contain 
 more GO, Si and Mn than are desired in the castings. Fairbairn (Manu- 
 facture of Iron, 1865) found that remelting up to 12 times increased tho 
 strength and the deflection, but after 18 remeltings the strength was only 
 s/s and the deflection 1/3 of the original. The increase of strength in the 
 first remeltings was probably due to the change .of GC into. CC, and the 
 subsequent weakening to the increase of S absorbed from the fuel. 
 
 Hard Castings from Soft Pig. (B. F. Fackenthal, Jr., A.I.M.E., 
 xxxv, 993.) Samples from a car load of pig gave Si, 2.61 ; S, 0.023. Cast- 
 ings from the same iron gave 2.33 and 2.26 Si, and 0.26 and 0.25 S, or 
 12 times the S in the original pig; probably due to fuel too high in S, but 
 more probably to the use of too little fuel in remelting. 
 
 The loss of Si in remelting, and the consequent hardening, is affected 
 by the amount of Mn, as shown below: 
 
 Mn, per cent 0.04 0.20 0.43 0.53 
 
 Si lost in remelting, per cent 34 23 12 4 
 
 Difficult Drilling due to LowMn. H. Souther, A.S.T.M., v, 219, 
 reports a case where thin castings drilled easily while thick parts on the 
 same castings rapidly dulled 1/2 and 3/4-in. drills. The chemical constitu- 
 tion was normal except Mn; Si, 2.5; P, 0.7; S about 0.08; C, 3.5; Mn, 0.16. 
 When the Mn was raised to 0.5 the trouble disappeared. 
 
 Addition of Ferro-silicon in the Ladle. (A. E. Outerbridge, Proc. 
 A.S.T.M., vi, 263.) Half a pound of FeSi, containing 50% Si, added to a 
 200-lb. ladle of soft cast iron used for making pulleys with rims 1/4 in. 
 thick, prevented the chilling of the surface of the casting, and enabled 
 the pulleys to be turned more rapidly. Analysis showed that the actual 
 increase of the Si in the casting was less than the calculated increase. 
 Tests of the metal treated with FeSi as compared with untreated metal 
 showed a gain in strength of from 2 to 26%, and a gain in deflection of 2 
 to 3%. The reason assigned for the increase of strength with increase of 
 softness is that cupola iron contains a small amount of iron oxide, which 
 reacts with the Si added in the ladle, forming SiO2, which goes into the 
 slag. 
 
 Additions of Vanadium and Manganese. R. Moldenke, Am. 
 * Fdrymen's Assn., 1908, Am. Mach., Feb. 20, '08. Experiments were 
 made by adding to melted cast iron in the ladle a ground alloy of ferro- 
 vanadium, containing 14.67 Va, 6.36 C, and 0.18 Si. In other experi- 
 ments ferro-manganese (80% Mn) was added, together with the vana- 
 dium. Four kinds of iron were used: burnt gray iron (gratebars, stove 
 iron, etc.), burnt white iron, gray machinery iron (Si, 2.72, S, 0.065, 
 P, 0.068, Mn, 0.54) and remelted car wheels (white, two samples anal- 
 yzed: Si, 0.60 and 0.53, S, 0.122, 0.138; P. 0.399. 0.374; Mn, 0.38, 
 0.44). The bars were 11/4 in. diam., 12 in. between supports. The 
 burnt gray iron was increased in breaking strength from 1310 to 2220 
 Ib. by the addition of 0.05% Va, and the burnt white iron from 144O 
 to 19*10 Ib. by the addition of 0.05 Va and 0.50 Mn. The following are 
 average results; 
 
CAST IRON. 
 
 451 
 
 Gray Machinery Iron. 
 
 Remelted Car Wheels. 
 
 Added Per cent. 
 
 Breaking 
 Strength, 
 Lb. 
 
 Deflec- 
 tion, In. 
 
 Added Per cent. 
 
 Breaking 
 Strength, 
 Lb. 
 
 Deflec- 
 tion, In. 
 
 Va. 
 
 Mn. 
 
 Va. 
 
 Mn. 
 
 0.0 
 0.0 
 0.05 
 0.05 
 0.10 
 0.10 
 0.15 
 
 Averag 
 
 0.0 
 0.50 
 
 1980 
 1970 
 1980 
 2130 
 2372 
 2530 
 2360 
 
 0.105 
 0.100 
 0.100 
 0.100 
 0.090 
 0.120 
 0.100 
 
 0.0 
 
 0.0 
 0.50 
 
 1470 
 2790 
 3020 
 2970 
 2800 
 3030 
 2950 
 3920 
 3069 
 
 0.050 
 0.070 
 0.060 
 0.090 
 0.055 
 0.090 
 0.070 
 0.095 
 
 0.05 
 0.05 
 0.10 
 0.10 
 0.15 
 0.15 
 
 0.50 
 
 0.50 
 
 0.50 
 
 0.50 
 
 bars 
 p e treated 
 
 0.50 
 
 2224 
 
 
 Mod. of rupture. . .35,800 
 
 48,020 
 
 Experiments with Titanium added to cast iron in the ladle are 
 reported by R, Moldenke, Proc. Am. Fdrymeris Assn., 1908. Two 
 irons were used: gray, with 2.58 Si, 0.042 S, 0.54 P, 0.74 Mn; and white, 
 with 0.85 Si, 0.07 S, 0.42 P, 0.6 Mn. Two Fe Ti alloys with 10% Ti 
 were used, one containing no C, and the other 5% C. The latter has 
 the lower melting point. The results were as below: 
 
 
 Gray Iron. 
 
 
 White Iron. Lb. 
 
 Original iron 
 
 9 tests 
 4 tests 
 3 tests 
 6 tests 
 6 tests 
 4 tests 
 ted iron, 
 riginal. . 
 
 1 720-2260 av. 2020 
 2750-3140 ' 3100 
 2880-3150 ' 3030 
 2850-3230 ' 3070 
 2850-3150 ' 2990 
 3030-3270 ' 3190 
 . 3070 
 
 8 tests 
 1 1 tests 
 
 1 920-21 lOav. 2050 
 2210-2660 " 2400 
 
 Plus 0.05 Ti 
 
 Plus 0.10 Ti.. 
 
 Plus 0.05 Ti and C 
 Plus O.lOTi and C 
 Plus 0.1 5 Ti and C 
 Average of trea 
 Increase over o 
 
 9 tests 
 10 tests 
 10 tests 
 
 2230-2720 " 2420 
 2320-2460 " 2400 
 2280-2620 " 2520 
 2430 
 
 18% 
 
 52% 
 
 Modulus of rupture, treated iron 48,030 
 
 38.020 
 
 The test bars were 11/4 in. diam. 12 in. between supports. The im- 
 provement is as marked whether 0.05, 0.10, or 0.15% Ti is used, which 
 indicates that if sufficient Ti is used for deoxidation of the iron, any 
 additional Ti is practically wasted. 
 
 Ti lessens the chilling action, yet whatever chill remains shows much 
 harder iron. Test pieces made with iron which chilled 11/2 in. deep 
 gave but 1 in. chill when the iron was treated in the ladle. The original 
 iron crushed at 173,000 Ibs. per sq. in. and stood 445 in Brinel's test 
 for hardness, soft steel running about 105. The treated piece ran 
 298,000 Ibs. per sq, in. and showed a hardness of 557. Testing the soft 
 metal below the chilled portion lor hardness gave 332 for the original 
 and 322 for the treated piece. 
 
 Strength of Cast-iron Beams. C. H. Benjamin, Mach'y, May, 
 1906. Numerous tests were made of beams of different sections includ- 
 ing hollow rectangles and cylinders, I and T-shapes, etc. All the sec- 
 tions were made approximately the same area, about 4.4 sq. in., and all 
 were tested by transverse loading, with supports 18 in. apart. The 
 results, when reduced by the ordinary formula for stress on the extreme 
 fiber, S = My /I, showed an extraordinary variation, some of the values 
 being as follows: Square bar, 23,300; Round bar, 25,000. Hollow round, 
 3.4 in. outside and 2.5 in. inside diam., 26,450, and 35,800. Hollow 
 ellipse, 3 in. wide, 3.9 in. high, 0.9 in. thick, 36,000. /-beam, 4 in. high, 
 web 0.44 in. thick, 17,700. The holtow cylindrical and elliptical sec- 
 tions are much stronger than the solid sections. This is due to the 
 thinner metal, the greater surface of hard skin, and freedom from 
 shrinkage strains. Professor Benjamin's conclusions from these tests are: 
 
 (1) The commonly accepted formulas for the strength and stiffness 
 of beams do not apply well to cored and ribbed sections 9f cast iron. 
 
 (2) Neither the strength nor the stiffness of a section increases in pro- 
 portion to the increase in the section modulus or the moment of inertia. 
 
 (3) The best way to determine these qualities for a cast-iron beam is 
 by experiment with the particular section desired and not by reasoning 
 from any other section. 
 
452 
 
 IRON AND STEEL. 
 
 Bursting Strength of Cast-Iron Cylinders. C. IJ. Benjamin, 
 A. S. M. E., XIX, 597; Mach'y, Nov., 1905. Four cylinders, 20 in. long, 
 10 1/8 in. int. diam., 3/ 4 in. thick, with flanged ends and bolted covers, 
 burst at 1350, 1400, 1350, and 1200 Ibs. per sq. in. hydraulic pressure, 
 the corresponding fiber stress, from the formula S = pd/2 t, being 9040, 
 10,200, 9735 and 9080. Pieces cut from the shell had an average tensile 
 strength of 14,000 Ibs. per sq. in., and a modulus of rupture in trans- 
 verse tests of 30,000. 
 
 Transverse Strength of Cast-iron Water-pipe. (Technology Quar- 
 terly, Sept., 1897.) Tests of 31 cast-iron pipes by transverse stress gave 
 a maximum outside fibre stress, calculated from maximum load, as- 
 suming each half of pipe as a beam fixed at the ends, ranging from 
 12,800 Ib. to 26,300 Ib. per sq. in. 
 
 Bars 2 in. wide cut from the pipes gave moduli of rupture ranging from 
 28,400 to 51,400 Ib. per sq. in. Four of the tests, bars and pipes: 
 Moduli of rupture of bar... . 28,400 34,400 40,000 51,400 
 Fibre stress of pipe 18,300 12,800 14,500 26,300 
 
 These figures show a great variation in the strength of both bars and 
 pipes, and also that the strength of the bar does not bear any definite 
 relation to the strength of the pipe. 
 
 Bursting Strength of Flanged Fittings. Power, Feb. 4, 1908. 
 The Crane Company, Chicago, published in the Valve World records cf 
 tests of tees and ells, standard and extra heavy, which show that the 
 bursting strength of such fittings is far less than is given by the standard 
 formulae for thick cylinders. As a result of the tests they give the 
 following empirical formula: B = TS/D, in which B = bursting pres- 
 sures, Ibs. per sq. in., T thickness of metal, D = inside diam., and 
 S = 65% of the tensile strength of the metal for pipes up to 12 in. diam., 
 for larger sizes use 60%. The pipes were made of " ferro-steel " of 
 33,000 Ibs. T. S., and of cast iron of 22,000 Ibs. as tested in bars. The 
 following are the principal results of tests of extra heavy tees and ells 
 compared with results of calculation by the Crane Company's formula: 
 
 BUESTINQ STEENGTH OF PIPE-FITTINGS. POUNDS PER SQUARE INCH. 
 
 Inside Diam. 
 Thickness. 
 
 6 
 
 3/4 
 
 8 
 
 13/16 
 
 10 
 
 15/16 
 
 12 
 I 
 
 14 
 
 1 1/8 
 
 16 
 
 13/16 
 
 18 
 
 1 1/4 
 
 20 
 
 15/16 
 
 24 
 
 1 1/2 
 
 B, Ferro-steel 
 calculated .... 
 
 2733 
 2680 
 
 2250 
 2180 
 
 2160 
 2010 
 
 2033 
 1870 
 
 1825 
 1570 
 
 1700 
 1450 
 
 1450 
 1350 
 
 1275 
 1280 
 
 1300 
 1220 
 
 B, Cast iron 
 
 1687 
 
 1350 
 
 1306 
 
 1380 
 
 1100 
 
 1025 
 
 600 
 
 750 
 
 700 
 
 calculated 
 Ells, ferro steel 
 
 1790 
 3266 
 
 1450 
 2725 
 
 1340 
 2350 
 
 1190 
 2133 
 
 1060 
 
 980 
 
 920 
 
 870 
 
 820 
 
 " cast-iron 
 
 2275 
 
 1625 
 
 1541 
 
 1275 
 
 1075 
 
 1250 
 
 
 
 
 Specific Gravity and Strength. (Major Wade, 1856.) 
 
 Third-class guns: Sp. Gr. 7.087, T. S. 20,148. Another lot: least Sp. 
 Gr. 7.163, T. S. 22,402. 
 
 Second-class guns: Sp. Gr. 7.154, T. S. 24,767. Another lot: mean 
 Sp. Gr. 7.302, T. S. 27,232. 
 
 First-class guns: Sp. Gr. 7.204, T. S. 28,805. Another lot: greatest 
 Sp. Gr. 7.402, T. S. 31,027. 
 
 Strength of Charcoal Pig Iron. Pig iron made from Salisbury 
 ores, in furnaces at Wassaic and Millerton, N. Y., has shown over 40,000 
 Ibs. T. S. per square inch, one sample giving 42,281 Ibs. Muirkirk, Md. T 
 iron tested at the Washington Navy Yard showed: average for No. 2' 
 iron, 21,601 Ibs.; No. 3, 23,959 Ibs.; No. 4, 41,329 Ibs.; average den- 
 sity of No. 4, 7.336 (J. C. I. W., v. p. 44). 
 
 Nos. 3 and 4 charcoal pig iron from Chapinville, Conn., showed a 
 tensile strength per square inch of from 34,761 Ibs. to 41,882 Ibs. Char- 
 coal pig iron from Shelby, Ala. (tests made in August, 1891), showed a. 
 strength of 34,800 Ibs. for No. 3; No. 4, 39,675 Ibs.; No. 5, 46,450 Ibs.; 
 and a mixture of equal parts of Nos. 2, 3, 4, and 5, 41,470 Ibs. (Bull.. 
 L & S. A.) 
 
 Variation of Density and Tenacity of Gun-Irons. An increase of 
 density invariably follows the rapid cooling of cast iron, and as a general 
 rule the tenacity is increased by the same means. The tenacity gener- 
 ally increases quite uniformly with the density, until the latter ascends 
 
CAST IRON. 
 
 453 
 
 to some given point; after which an increased density is accompanied 
 by a diminished tenacity. 
 
 The turning-point of density at which the best qualities of gun-iron 
 attain their maximum tenacity; appears to be about 7.30. At this point 
 of density, or near it, whether in proof-bars or gun-heads, the tenacity is 
 greatest. 
 
 As the density of iron is increased its liquidity when melted is dimin- 
 ished. This causes it to congeal quickly, and to form cavities in the 
 interior of the casting. (Pamphlet of Builders' Iron Foundry, 1893.) 
 
 " Semi-steel " is a trade name given by some founders to castings made 
 from pig iron melted in the cupola with additions of from 20 to 30 per 
 cent of steel scrap. Ferro-manganese is also added either in the cupola or 
 in the ladle. The addition of the steel dilutes the Si of the pig iron, and 
 changes some of the C from GO to CC, but the TC is unchanged, for any 
 reduction made by the steel is balanced by absorption of C from the fuel. 
 Semi-steel therefore is nothing more than a strong cast iron, low in Si 
 and containing some Mn, and the name given it is a misnomer. 
 
 Mixture of Cast Iron with Steel. Car wheels are sometimes made 
 from a mixture of charcoal iron, anthracite iron, and Bessemer steel. 
 The following shows the tensile strength of a number of tests of wheel 
 mixtures, the average tensile strength of the charcoal iron used being 
 22,000 Ibs. (Jour. C. I. W., iii, p. 184): 
 
 Ibs. per sq. in. 
 
 Charcoal iron with 2 1/2% steel 22,467 
 
 33/ 4 % steel 26,733 
 
 61/4% steel and 6 1/4% anthracite 24,400 
 
 7V3% steel and 71/2% anthracite 28,150 
 
 21/2% steel, 21/2% wro't iron, and 61/4% anth. 25,550 
 5 % steel, 5% wro't iron, and 10% anth 26,500 
 
 Cast Iron Partially Bessemerized. Car wheels made of partially 
 Bessemerized iron (blown in a Bessemer converter for 3V2 minutes), 
 chilled in a chill test mold over an inch deep, just as a test of C9ld blast 
 charcoal iron for car wheels would chill. Car wheels made of this blown 
 iron have run 250,000 miles. (Jour. C. I. W., vi, p. 77.) 
 
 Bad Cast Iron. On October 15, 1891, the cast-iron fly-wheel of a 
 large pair of Corliss engines belonging to the Amoskeag Mfg. Co., of Man- 
 chester, N.H., exploded from centrifugal force. The fly-wheel was 30 
 feet diameter and 110 inches face, with one set of 12 arms, and weighed 
 116,000 Ibs. After the accident, the rim castings, as well as the ends of 
 the arms, were found to be full of flaws, caused chiefly by the drawing 
 and shrinking of the metal. Specimens of the metal were tested for 
 tensile strength, and varied from 15,000 Ibs. per square inch in sound 
 pieces to 1000 Ibs. in spongy ones. None of these flaws showed on the 
 surface, and a rigid examination of the parts before they were erected 
 failed to give any cause to suspect their true nature. Experiments were 
 carried on for some time after the accident in the Amoskeag Company's 
 foundry in attempting to duplicate the flaws, but with no success in 
 approaching the badness of these castings. 
 
 Permanent Expansion of Cast Iron by Heating. (Valve World, 
 Sept., 1908.) Cast iron subjected to continued temperatures of approx- 
 imately 500 to 600 took a permanent expansion and did not return to 
 its original volume when cooled. 
 
 As steam is being superheated quite commonly to temperatures above 
 575, this fact is of great interest inasmuch as it modifies our ideas about 
 the proper material to be used in the construction of valves and fittings 
 foT service under high temperatures. A permanent volumetric expan- 
 sion is followed by a loss of strength, the loss in cast iron being fully 40 
 per cent in four years. 
 
 Crane Co. made an attempt to determine whether cast steel was affected 
 in the same manner as cast iron. Three flanges were taken, one of cast 
 iron, one of ferrosteel, and the third of cast steel. These flanges were 
 exposed for a total period of 130 hours to temperatures ranging as follows: 
 
 Less than 500, 18 hours; 500 to 700, 97 hours; 710 to 800, 12 hours- 
 over 800, 3 hours. Average temp., 583. 
 
 The Outside diameter in each case was 121/2 in. and the bore 6 29/ 6 4 in. 
 
 The results were: Cast-steel flange, no change. Cast-iron flange, out- 
 side diam. increased 0.019 in., inside diam. increased 0.007 in. Ferro-steel 
 flange, outside diam. increased 0.033 in., inside diam. increased 0.017 in. 
 
454 IRON AND STEEL. 
 
 If the permanent expansion of cast iron stopped at the figures given 
 above, it would not be a serious matter; but all evidence points toward a 
 steady increase as time goes on, as was shown by one of Crane Co.'s 
 14-in. valves, which originally was 221/2 in. face to face, and increased 
 5/16 in. in length in four years under an average temperature of about 
 590. 
 
 MALLEABLE CAST IRON.* 
 
 There are four great classes of work for whose requirements malleable 
 cast iron (commonly called "malleable iron" in America) is especially 
 adapted. These are agricultural implements, railway supplies, carriage 
 and harness castings and pipe fittings. Besides these main classes there 
 are innumerable other unclassified uses. The malleable casting is sel- 
 dom over 175 Ib. in weight, or 3 ft. in length, or % m . thick. The 
 great majority of even the heavier castings do not exceed 10 Ib. 
 
 When properly made, malleable cast iron should have a tensile 
 strength of 42,000 to 48,000 Ib. per sq. in., with an elongation of 5% in 
 2 in. Bars 1 in. square and on supports 12 in. apart should show a 
 transverse strength of 2500 to 3500 Ib., with a deflection of at least K in. 
 
 While the strength of malleable iron should be as stated, much of it 
 will fall as low as 35,000 Ib. per sq. in., and this will still be good for such 
 work as pipe fittings, hardware castings and the like. On the other 
 hand, even 63,000 Ib. per sq. in. has been reached, with a load of 5000 
 Ib. and a deflection of 2 y^ in. in the transverse test. This high strength 
 is not desirable, as the softness of the casting is sacrificed, and its resist- 
 ance to continued shock is lessened. For the repeated stresses of severe 
 service the malleable casting ranks ahead of steel, and only where a high 
 tensile strength is essential must it be replaced by that material. 
 
 The process of making malleable iron may be summarized as follows: 
 The proper cast irons are melted in either the crucible, the air furnace, 
 the open-hearth furnace, or the cupola. The metal when cast into the 
 sand molds must chill white or not more than just a little mottled. After 
 removing the sand from the hard castings they are packed in iron scale, 
 or other materials containing iron oxide, and subjected to a red heat 
 (1250 to 1350 F.) for over 60 hours. They are then cooled slowly, 
 cleaned from scale, chipped or ground, and straightened. Much of the 
 malleable iron made to-day (1915) is annealed for a shorter time and at 
 higher temperatures. The safe method , however, is the one given above. 
 
 When hard, or just from the sand, the composition of the iron should 
 be about as follows: Si, from 0.35 up to 1.00, depending upon the thick- 
 ness and the purpose the casting is to be used for; P not over 0.225, Mn 
 not over 0.20, S not over 0.08. The total carbon can be from 2.75 up- 
 ward, 4.15 being about the highest that can be carried. The lower the 
 carbon the stronger the casting subsequently. Below 2.75 there is apt to 
 be trouble in the anneal, the black-heart structure may not appear, and 
 the castings remain weak. A casting 1 in. thick would necessitate silicon 
 at 0.35, and the use of chills in the mold in addition, to get the iron white. 
 For a casting % in. thick, Si about 0.60 is the proper limit, except where 
 great strength is desired, when it can be dropped to 0.45. Above 0.60 
 there is danger of getting heavily-mottled if not gray iron from the sand 
 molds, and this material, when annealed the long time required for the 
 white castings, would be ruined. For very thin castings, Si can run up 
 to 1.25 and still leave the metal white in fracture. 
 
 Pig Iron for Malleable Castings. The specifications run as follows: 
 Si, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00%, as required; Mn, not over 0.60; 
 P, not over 0.225 ; S, not over 0.05. 
 
 Works making heavy castings almost exclusively specify Si to include 
 0.75 up to 1.50%. Makers of very light work take 1.25 to 2.00%. 
 
 The Melting Furnace. Malleable iron is melted in the reverbera- 
 tory furnace, the open-hearth furnace, and the cupola, the reverberatory 
 being the most extensively used. About 85 per cent of the entire output 
 of the United States is melted by this process. Prior to about 1885, 
 the standard furnace was one of 5 tons capacity. At present (1915) we 
 
 * References. R. Moldenke, Cass Mag., 1907, and Iron Trade 
 Review, 1908; E. C. Wheeler, Iron Age, Nov. 9, 1899; C. H. Gale, Indust. 
 World, April 13, 1908; W. H. Hatfield, ibid. G. A. Akerlund, Iron Tr. 
 Rev., Aug. 23, J906; C. H. Day, Am. Mach., April 5, 1906. 
 
MALLEABLE CAST IRON. 
 
 455 
 
 have furnaces of 25 and 30 tons capacity, though furnaces of from 10 to 
 15 tons are the most popular and give more uniform results than those 
 of larger capacity. 
 
 The adoption of the open-hearth furnace for malleable iron dates 
 back to about 1893. It is used largely in the Pittsburg district. 
 
 Cupola-melted iron does not possess the tensile strength nor ductility 
 of iron melted in the reverberatory or open-hearth furnace, due partly to 
 the higher carbon and sulphur caused by the metal being in contact 
 with the fuel. This feature is rather an advantage than otherwise, as 
 most of the product of cupola-melted iron consists of pipe fittings, cast- 
 ings that are not subjected to any great stress or shock. The castings 
 are threaded, and a strong, tough malleable iron does not cut a clean, . 
 smooth thread, but rather will rough up under the cutting tool. 
 
 In the reverberatory and open-hearth furnaces the metal may be 
 partly desiliconized at will, by an oxidizing flame or by additions of 
 scrap or other low-silicon material, while the total carbon can be lowered 
 by scrap steel additions. Manganese is also oxidized in the furnace. 
 
 The composition of good castings in American practice is : Si, from 0.45 
 to 1.00%; Mn up to 0.30%; P, up to 0.225%; S, up to 0.08%; total 
 carbon in the hard casting, above 2.75%. 
 
 In special cases, especially for very small castings, the silicon may go 
 up as high as 1.25%, while for very heavy work it may drop down to 
 0.35% with very good results. In the case of charcoal iron this figure 
 gives the strongest castings. With coke irons, however, especially when 
 steel scrap additions are the rule, 0.45 should be the lower limit, and 0.65 
 is the best silicon for all-around medium and heavy work, such as rail- 
 road castings. 
 
 In American practice phosphorus is required not to exceed 0.225%, 
 and is preferred lower. In European practice it is required as low as 
 0.10%, but castings have been made successfully with P as high as 
 0.40%. 
 
 The heat treatment of metal during melting has an important bearing 
 upon its tensile strength, elongation, etc. Excessive temperatures pro- 
 mote the chances of burning. Iron is burnt mainly through the genera- 
 tion in melting furnaces of higher temperatures than those prevailing 
 during the initial casting at blast furnaces and an excess of air in the 
 flame. The choicest irons may thus turn out poor material. 
 
 Shrinkage of the Casting. The shrinkage of the hard casting Is 
 about 1/4 in. to the foot, or double that of gray iron. In annealing about 
 half of this is recovered, and hence the net result is the same a*s in prdi- 
 nary foundry pattern practice. The effect of this great shrinkage is to 
 cause shrinkage cracks or sponginess in the interior of the casting. As 
 soon as the liquid metal sets against the surface of the mold and the 
 source of supply is cut off, the contraction of the metal in the interior 
 as it cools causes the particles to be torn apart and to form minute 
 cracks or cavities. " Every test bar, and for that matter every casting 
 may be regarded as a shell of fairly continuous metal with an interior of 
 slight planes of separation at right angles to the surface. This charac- 
 teristic of malleable iron forms the basis of many a mysterious failure." 
 (Moldenke.) 
 
 Packing for Annealing. After the castings have been chipped and 
 sorted they are packed in iron annealing pots, holding about 800 pounds 
 of iron, together with a packing composed of iron ore, hammer and 
 rolling mill scale, turnings, borings, etc. The turnings, etc., were form- 
 erly treated with a solution of salammoniac or muriatic acid to form a 
 heavy coating of oxide, but such treatment is now considered unnec- 
 essary. Blast furnace slag, coke, sand, and fire clay have also been used 
 for packing. The changes in chemical composition of the_castings when 
 annealed in slag and in coke are given as follows by C. H. Gale: 
 
 
 Si. 
 
 S. 
 
 P. 
 
 Mn. 
 
 C. C. 
 
 G. C. 
 
 Hard iron 
 
 63 
 
 043 
 
 147 
 
 21 
 
 2 54 
 
 Trace 
 
 Annealed in slag . . 
 
 61 
 
 049 
 
 145 
 
 21 
 
 24 
 
 1 65 
 
 Annealed in coke 
 
 0.61 
 
 0.065 
 
 0.150 
 
 0.21 
 
 0.25 
 
 2.00 
 
 The Annealing Process. The effect of the annealing is to oxidize 
 and remove the carbon from the surface of the casting, to remove it 
 to a greater or less degree below the surface, and to convert the remain- 
 
456 IRON AND STEEL. 
 
 ing carbon from the combined form into the amorphous form called a 
 "temper carbon" by Professor Ledebur, the German metallurgist. It 
 differs from the graphite found in pig iron, but is usually reported as 
 graphitic carbon by the chemists. In the original malleable process, 
 invented by Reaumur, in 1722, the castings were packed in iron ore and 
 annealed thoroughly, so that most of the carbon was probably oxidized, 
 but in American practice the annealing process is rather a heat treat- 
 ment than an oxidizing process, and its effect is to precipitate the carbon 
 rather than to eliminate it. According to the analysis quoted above, the 
 metal annealed in slag lost 0.65% of its total C, while that annealed in 
 coke lost only 0.29%. In the former, S increased 0.006% and in the 
 latter 0.022%. The Si decreased 0.02% in both cases, while the P and 
 Mn remained constant. 
 
 As to the distribution of carbon in an annealed casting, Dr. Moldenke 
 says: "Take a flat piece of malleable and plane off the skin, say Vie in. 
 deep and gather the chips for analysis. The carbon will be found, say, 
 O.lo% perhaps even less. Cut in another Viein. and the total C will be 
 nearer 0.60%. Now go down successively by sixteenths and the total 
 C will range from, say, 1.70 to 3.65% and will then remain constant until 
 the center is reached." "The malleable casting is for practical purposes 
 a poor steel casting with a lot of graphite, not crystallized, between the 
 crystals or groups of crystals of the steel." 
 
 The heat in the annealing process must be maintained for from two to 
 four days., depending upon the thickness of sections of the castings and 
 the compactness with which the castings or annealing boxes are placed 
 in the furnace. An annealing temperature 1550 to 1600 Fahr. is often 
 used, but it is not essential, as the annealing can be accomplished at 
 1300, but the time required will be longer than that at the higher tem- 
 perature. Burnt iron in the anneal is no uncommon feature, and, gen- 
 erally speaking, it is the result of carelessness. The most carefully pre- 
 pared metal from melting furnaces can here be turned into worthless 
 castings by some slight inattention of detail. The highest temperature 
 for annealing should be registered in each foundry, and kept there by the 
 daily and frequent use of a thermometer constructed for that sole pur- 
 pose. Steady, continued heat insures soft castings, while unequal tem- 
 peratures destroy all chances for successful work, although the initial 
 metal was of the most excellent quality. 
 
 After annealing, the castings are cleaned by tumblers or the sand 
 blast; they are carefully examined for cracks or other defects, and if 
 sprung out of shape are hammered or forced by hydraulic power to the 
 correct shape. Such parts as are produced in great quantities are placed 
 in a drop hammer and one or two blows will insure a correct form. They 
 may be drop-forged or even welded when the iron has been made for that 
 purpose. Castings are sometimes dipped into asphaltum diluted with 
 benzine to give them a better finish. 
 
 Malleable castings must never be straightened hot, especially when 
 thick. In the case of very thin castings there is some latitude, as the 
 material is so decarbonized that it is nearer a steel than genuine mal- 
 leable cast iron. In heating portions of castings that were badly warped, 
 it seems that the amorphous carbon in them was combined again, and 
 while the balance of the casting remained black and sound, the heated 
 parts became white and brittle, as in the original hard casting. Hence 
 the advice to straighten the castings cold, preferably with a drop ham- 
 mer and suitable dies, or still better in the hydraulic press. (R. Moldenke. 
 Proc. A.S.T.M., vi, 244.) 
 
 Physical Characteristics. The characteristic that gives malleable 
 iron its greatest value as compared with gray iron is its ability to resist 
 shocks. Malleability in a light casting 1/4 in. thick and less means a 
 soft, pliable condition and the ability to withstand considerable distor- 
 tion without fracture, while in the heavy sections, 1/2 in. and over, it 
 means the ability to resist shocks without bending or breaking. 
 
 For general purposes it is not altogether desirable to have a metal 
 very high in tensile strength, but rather one which has a high transverse 
 strength, and especially a good deflection. It is not always that a strong 
 and at the same time soft material can be produced in a foundry operat- 
 ing on the lighter grades of castings. The purchaser, therefore, unless he 
 requires very .stiff material, should rather look upon the deflection of 
 
MALLEABLE CAST 1UON. 457 
 
 the metal coupled with the weight it took to do this bending before 
 failure, than for a high tensile strength. 
 
 The ductility of the malleable casting permits the driving of rivets, 
 which cannot so readily be done with gray cast iron; and for certain 
 parts of cars, like the journal boxes, malleable cast iron may be con- 
 sideied supreme, leaving cast iron and "semi-steel " far behind. 
 
 It was formerly the general belief that the strength of malleable iron 
 was largely in the white skin always found on this material, but it has 
 been demonstrated that the removal of the skin does not proportionately 
 lessen the strength of the casting. 
 
 Test Bars. The rectangular shape is used for test bars in preference 
 to the round section, because the latter is more apt to have serious cracks 
 in the center, due to shrinkage, especially if the diameter is large. A 
 round section, unless in very light hardware, is to be avoided, as the 
 shrinkage crack in the center may have an outlet to the skin, and cause 
 failure in service. 
 
 It is customary to provide for two sizes of test bars, the heavy and 
 the light. Thus the 1-in. square bar represents work 1/2 an inch thick 
 and over, and a 1 X V2-in. section bar cares for the lighter castings. 
 Both are 14 inches long. They should be cast at the beginning and at 
 the end of each heat. 
 
 Design of Malleable Castings. As white cast iron shrinks a great 
 deal more than gray iron, and as the sections of malleable castings are 
 lighter than those of similar castings of gray iron, fractures are very 
 common. It is therefore the designer's aim to distribute the metal so 
 as to meet these conditions. In long pieces the stiffening ribs should 
 extend lengthways so as to produce as little resistance as possible to the 
 contraction of the metal at the time of solidification. If this be not 
 possible, the molder provides a "crush core" whose interior is filled with 
 crushed coke. When the metal solidifies in the flask the core is crushed 
 by the casting and thus prevents shrinkage cracks. At other times a 
 certain corner or juncture of ribs in the casting will be found cracked. 
 In order to prevent this a small piece of cast iron (chill) is embedded in 
 the sand at this critical point, and the metal will cool here more quickly 
 than elsewhere, and thus fortify this point, although it may happen that 
 some other part of the casting will be found fractured instead, and in 
 many cases the locations and the shape of strengthening ribs in the 
 casting must be altered until a casting is procured free from shrinkage 
 cracks. In designing of malleable cast-iron details the following rules 
 should be observed: 
 
 Jl) Endeavor to keep the metal in different parts of the casting at a 
 form thickness. In a small casting, of, say, 10 Ibs. weight, l/4-in. 
 metal is about the practical thickness, s/ 16 in. for a casting of 15 to 20 
 Ibs., and 3/ 8 to 1/2 in. for castings of 40 Ibs. and over. (2) Endeavor to 
 avoid sharp junctions of ribs or parts, and if the casting is long, say 24 
 inches or more, the ends should be made of such shape as to offer as 
 little resistance as possible to the contraction of metal when cooling in 
 the mold. 
 
 Specifications for Malleable Iron. The tensile strength of malle- 
 able iron varies with the thickness of the metal, the lighter sections hav- 
 ing a greater strength per square inch than the heavier sections. An 
 Eastern railroad designates the tensile strength desired as follows: Sec- 
 tions 3/ 8 in. thick or less should have a tensile strength of not less than 
 40,000 Ibs. per sq. in.; 3/ 8 to 3/ 4 in. thick, not less than 38,000; and over 
 3/4 in., not less than 36,000 Ibs. per sq. in. Test bars 5/ 8 and 7/ 8 in. diam. 
 were made in the same mold and poured from the same ladle, and an- 
 nealed together. The average tensile strength of five pairs of bars so 
 treated, representing five heats, was, 5/ 8 -in. bars, 45,095; 7/g-in. bars, 
 41,316 Ibs. per sq. in. Average elongation in 6 in.: 5/ 8 -in. bars 5.3%; 
 7/8-in. bars 4.2%. 
 
 A very high tensile strength can be obtained approaching that of 
 cast steel but at the expense of the malleability of the product. Malle- 
 able test bars have been made with a tensile strength of between 60,000 
 and 70,000 Ibs. per sq. in., but the ductility and ability to resist shocks 
 of these bars was not equal to that of bars breaking at 40,000 to 45,000 
 pounds per sq. in. 
 
 The British Admiralty specification is 18 tons (40,320 Ibs.) per 
 square inch, a minimum elongation of 4Vfc% in three inches and a 
 
458 
 
 IRON AND STEEL. 
 
 bending angle of at least 90 over a 1-in. radius, the bar being 1 X % 
 in. in section. 
 
 A committee of the American Society for Testing Materials re- 
 ported, in 1915, a set of specifications for malleable castings which in- 
 cludes the following: The specimen for tensile strength is a round 
 bar 12 in. long, 3/ 4 in. diam. at the ends, tapering to a middle portion 
 4 in. long, 5/8 in. diam. The transverse test specimen is 14 in. long, 
 
 1 in. wide, and 1/2, 5/8, or 3/4 hi. thick, according to the thickness of 
 the casting it represents. Specimens are to be cast without chills, with 
 the ends free in the mold. The tensile strength shall be not less than 
 38,000 Ib. per sq. in. with an elongation not less than 5% in 2 in. The 
 transverse strength, the bar being tested with cope side up, on sup- 
 ports 12 in. apart, pressure being applied at the center shall be respec- 
 tively 900, 1400, and 2000 Ib. with deflections 1.25, -1.00, and 0.75 in 
 the 1/2, 5/8, and 8/4 in. test specimens. The specifications are intended 
 to cover railroad malleable irons and the softer grades only. They in- 
 clude directions as to the casting of the test specimens and as to 
 inspection. 
 
 Improvement in Quality of Castings. (Moldenke.) The history 
 of improvement in the malleable casting is admirably reflected in the 
 test records of any works that has them. Going back to the early 90's, 
 the average tensile strength 9f malleable cast iron was about 35,000 Ibs. 
 per sq. in., with an elongation of about 2% in 2 in. The transverse 
 strength was perhaps 2800 Ibs., with a deflection of 1/2 in. Toward the 
 close of the 90's a fair average of the castings then made would run 
 about 44,000 Ibs. per sq. in., with an elongation of 5% in 2 in., and the 
 transverse strength, about 3500 Ibs., with a deflection of 1/2 inch. These 
 average figures were greatly exceeded in establishments where special 
 attention was given to the niceties 9f the process. The tensile strength 
 here would run 52,000 Ibs. per sq. in. regularly, with 7% elongation in 
 
 2 in., and the transverse strength, 50CO and over, with 11/2 in. deflection. 
 Further Progress Desirable. (Moldenke.) We do not know at 
 
 the present time why cupola malleables require an annealing heat sev- 
 eral hundred degrees higher than air or open-hearth furnace iron. The 
 underlying principles of the oxidation of the bath, which is a frequent 
 cause of defective iron, is practically unknown to the majority of those 
 engaged in this industry. Heats are frequently made that will not 
 pour nor anneal properly, but the causes are still being sought. To 
 produce castings from successive heats, so that with the same composi- 
 tion they will have the same physical strength regardless of how they 
 are tested, is a problem partially solved for steel, but not yet approached 
 for malleable cast iron. 
 
 Sufficient progress in the study of iron with the microscope has been 
 made to warrant the belief that in the not distant future we may be 
 able to distinguish the constituents of the material by means of etching 
 with various chemicals. When the sulphides and phosphides of iron, 
 or the manganese-sulphur compounds, can be seen directly under the 
 microscope, it is probable that a method may be found by which the 
 dangerous ingredients may be so scattered or arranged that they will 
 do the least harm. 
 
 The high sulphur- in European malleable accounts to some extent for 
 the comparatively low strength when contrasted with our product. 
 Their castings being all very light, so long as they bend and twist prop- 
 erly, the purpose is served, and hence until heavier castings become the 
 rule instead of the exception, "white heart" and steely-looking frac- 
 tures will remain the characteristic feature of European work. 
 
 STRENGTH OF MALLEABLE CAST IRON. 
 
 Tests of Square Bars, 1/2 in. and 1 in., by tension, compression and 
 transverse stress, by M. H. Miner and F. E. Blake (Railway Age, Jan. 25, 
 1901). 
 
 TENSION. Six 1/2-in. and six 1-in. round bars, also two 1-in. bars 
 turned to remove the skin, from each of four makers. Average results: 
 
 T. S., l/2-in. bars, 37,470-42,950, av. 40,960; E. L., 16,500-21,100, av. 
 19,176. 
 
 T. S., 1-in. bars, 35,750-40,530, av. 38,300; E. L., 14,860-19,900, av. 
 17,181. 
 
 Tensile strength, turned bars. av. 35.090: Elastic limit, av. 15.660. 
 
WROUGHT IRON. 
 
 459 
 
 Elong. inSin.., y 2 -'m. bars, 4.75 % ; 1-in. bars, 4.32 % ; turned bars, 3.73 %. 
 
 Modulus of elasticity, y 2 -in. bars, 22,289,000; 1-in. bars, 21,677,000. 
 
 COMPRESSION. 16 short blocks, 2 in. long, 1 in. and 1/2 in. square 
 respectively. 
 
 8 long columns, 15 in. long, 1 in. sq., and 7.5 in. long, 1/2 in/sq. respec- 
 tively. 
 
 Averages of blocks from each of four makers: 
 
 Short blocks, l/2-in. sq., 93,000 to 114,500 Ibs. per sq. in. Mean, 
 101,900 Ibs. per sq. in. 
 
 Short blocks, 1 in. sq., 137,600 to 165,300 Ibs. per sq. in. Mean, 
 152,800 Ibs. per sq. in. 
 
 Ratio of final to original length, 1/2 in., 61.7%; 1 in., 52.6%. A small 
 part of the shortening was due to sliding on the 45 plane of fracture. 
 
 Long columns: 1/2 in. X 7.5 in. Mean, 29,400 Ibs. per sq. in.: 1 in. 
 X 15 in., 27,500 Ibs. per sq. in. Ratio of final to original length, 1/2 in., 
 98.5%; 1 in., 98.8%. The long columns did not rupture, but reached 
 the maximum stress after bending into a permanent curve. 
 
 TRANSVERSE TESTS. Maximum fiber stress, mean of 8 tests, l/2-in. 
 bars, 34,163 Ibs. per sq. in. 1-in. bars, 36,125 Ibs. per sq. in. Length 
 between supports, 20 in. The bars did not break, but failed by bending. 
 The l/2-in. bars could be bent nearlv double. 
 
 Malleable Bars cast by Buhl Malleable Co., Detroit, Mich., tested as 
 follows. The tests were reported by Chas. H. Day, Am. Mach., April 5, 
 1906. The castings were all made at the same time. The rectangular 
 sections were approximately 1/4 X 3 /4 in. The star sections were square 
 crosses, 1 in. wide, with arms about 1/4 in. thick. The figures here given 
 are the maximum and minimum results from three bars of each section. 
 TENSILE TESTS. COMPRESSION TESTS. 
 
 Section. 
 
 Area, 
 sq. in. 
 
 Tensile 
 St'gth, 
 Ibs. per 
 
 Elong. 
 in 8 in., 
 
 Red. of 
 Area, 
 
 Area, 
 sq. in. 
 
 L'gth, 
 in. 
 
 Comp. 
 Str., 
 Ibs. per 
 
 Final 
 Area, 
 sq. in. 
 
 
 
 sq. in. 
 
 * 
 
 
 
 
 sq. in. 
 
 
 Round 
 
 0.817 
 
 43,000 
 
 5.87 
 
 4.76 
 
 0.847 
 
 15 
 
 31,700 
 
 0.901 
 
 
 0.801 
 
 43,400 
 
 6.21 
 
 3.98 
 
 0.801 
 
 15 
 
 33,240 
 
 0.886 
 
 
 0.219 
 
 41,130 
 
 7.70 
 
 3.40 
 
 0.209 
 
 7.5 
 
 32,600 
 
 0.221 
 
 ' 
 
 0.202 
 
 44,700 
 
 13.00 
 
 3.63 
 
 0.204 
 
 7.5 
 
 34,600 
 
 0.215 
 
 Square 
 
 0.277 
 
 36,700 
 
 4.70 
 
 2.20 
 
 0.263 
 
 7.5 
 
 33,200 
 
 0.272 
 
 
 0.277 
 
 38,100 
 
 3.72 
 
 3.00 
 
 0.254 
 
 7.5 
 
 31,870 
 
 0.278 
 
 
 
 1.040 
 
 38,460 
 
 4.10 
 
 3.30 
 
 1.051 
 
 15 
 
 29,650 
 
 1.070 
 
 M 
 
 1.Q50 
 
 37,860 
 
 2.38 
 
 2.94 
 
 1.040 
 
 15 
 
 30,450 
 
 1.066 
 
 Rect. 
 
 0.239 
 
 31,200* 
 
 5.19 
 
 1.50 
 
 0.436 
 
 15 
 
 32,200 
 
 0.448 
 
 
 0.244 
 
 37,600 
 
 3.87 
 
 3.80 
 
 0.457 
 
 15 
 
 30,400 
 
 0.467 
 
 Star 
 
 0.584 
 
 34,600 
 
 4.20 
 
 3.10 
 
 
 
 
 
 
 0.575 
 
 37,200 
 
 4.80 
 
 3.50 
 
 
 
 
 
 * Broke in flaw. 
 
 Tests of Rectangular Cast Bars, made by a committee of the Mas- 
 ter Car-builders' Assn. in 1891 and 1892, gave the following results 
 (selected to show range of variation) : 
 
 Size of 
 Section, 
 in. 
 
 Tensile 
 St'gth, 
 Ibs. per 
 sq. in. 
 
 Elastic 
 Limit, 
 Ibs. per 
 sq. in. 
 
 Elonga- 
 tion, % 
 in 4 in. 
 
 Size of 
 Section, 
 in. 
 
 Tensile 
 St'gth, 
 Ibs. per 
 sq. in. 
 
 Elastic 
 Limit, 
 Ibs. per 
 sq. in. 
 
 Elong. 
 in 8 in.. 
 
 %. 
 
 0.25x1.52 
 0.5 xl.53 
 0.78x2 
 0.88x1.54 
 1.52x1.54 
 
 34,700 
 32,800 
 25,100 
 33,600 
 28,200 
 
 21,100 
 17,000 
 15,400 
 19,300 
 
 2 
 2 
 1.5 
 1.5 
 1.5 
 
 0.29x2.78 
 0.39x2.82 
 0.53x2.76 
 0.8 X2.76 
 1.03x2.82 
 
 28,160 
 32,060 
 27,875 
 25,120 
 28,720 
 
 22,650 
 20,595 
 19,520 
 18,390 
 18,220 
 
 06 
 1 3 
 
 1 1 
 
 1 5 
 
 WROUGHT IRON. 
 
 The Manufacture of Wrought Iron. When iron ore, which is an 
 oxide of iron, Fe2Os or FesCU, containing silica, phosphorus, sulphur, 
 etc., as impurities, is heated to a yellow heat in contact with charcoal or 
 other fuel, the oxygen of the ore combines with the carbon of the fuel, 
 part of the iron combines with silica to form a fusible cinder or slag, and 
 the remainder of the iron agglutinates into a pasty mass which is inter- 
 mingled with the cinder. Depending upon the time and the tempera- 
 
460 IRON AND STEEL. 
 
 ture of the operation, and on the kind and quality of the impurities 
 present in the ore and the fuel, more or less of the sulphur and phos- 
 phorus may remain in the iron or may pass into the slag ; a small amount 
 of carbon may also be absorbed by the iron. By squeezing, hammering, 
 or rolling the lump of iron while it is highly heated, the cinder may be 
 nearly all expelled from it, but generally enough remains to give a bar 
 after being rolled, cooled and broken across, the appearance of a fibrous 
 structure. The quality of the finished bar depends upon the extent to 
 which the chemical impurities and the intermingled slag have been 
 removed from the iron. 
 
 The process above described is known as the direct process. It is 
 now but little used, having been replaced by the indirect process known 
 as puddling or boiling. In this process pig iron which has been melted 
 in a reverb eratory furnace is desilicomzed and decarbonized by the 
 oxygen derived from iron ore or iron scale in the bottom of the furnace, 
 and from the oxidizing flame of the furnace. The temperature being too 
 low to maintain the iron, when low in carbon, in a melted C9ndition, it 
 gradually " comes to nature" by the formation of pasty particles in the 
 bath, which adhere to each other, until at length all the iron is decarbon- 
 ized and beco Ties of a pasty condition, and the lumps so formed when 
 gathered together make the "puddle-ball" which is consolidated int9 a 
 bloom by the squeezer and then rolled into "muck-bar." By cutting 
 the muck-bar into short lengths and making a "pile" of them, heating 
 the pile to a welding heat and rerolling, a bar is made which is freer 
 from cinder and more homogeneous than the original bar, and it may 
 be further "refined" by another piling and rerolling. The quality of 
 the iron depends on the quality of the pig-iron, on the extent of the 
 decarbonization, on the extent of dephosphorization which has been 
 effected in the furnace, on the greater or less contamination of the iron 
 by sulphur derived from the fuel, and on the amount of work done on 
 the piles to free the iron from slag. Iron insufficiently decarbonized is 
 irregular, and hard or "steely." Iron thoroughly freed from impurities 
 is soft ani of low tensile strength. Iron high in sulphur is "hot-short," 
 liable to break when being forged. Iron high in phosphorus is "cold- 
 short," of low ductility when cold, and breaking with an apparently 
 crystalline fracture. 
 
 See papers on Manufacture and Characteristics of Wrought Iron, by 
 J. P. Roe, Trans. A. I. M. E., xxxiii, p. 551; xxxvi, pp. 203, 807. 
 
 Electrolytic Iron. (L. Guillet, Proc. Iron & Steel Inst., 1914, Eng'g, 
 Oct. 2, 1914.) Using any pig iron in solution an iron can be obtained 
 of the following average composition, after removal of the gases by 
 annealing: C, 0.004; Si, 0.007; S, 0.006; P, 0.008. The metal de- 
 posited from the solution is extremely brittle and hard, due to occluded 
 hydrogen. The deposition of the iron takes place on a revolving metal 
 mandrel, making tubes of from 4 to 8 in. diam., 12.8 ft. long, 0.004 to 
 0.24 in. thick. After annealing, the metal becomes soft and ductile, with 
 a tensile strength of from 44,000 to 47,000 Ib. per sq. in. The in- 
 dustrial uses of electrolytic iron include the direct manufacture of 
 tubes, sheets, rods for autogenous welding, and the preparation of raw 
 material for the manufacture of steel. In localities where cheap electric 
 current can be obtained the cost is estimated to be as low as $30 to $38 
 per gross ton. Patents on the process are owned by Compagnie Le Fer, 
 Grenoble, France. 
 
 Influence of Reduction in Rolling from Pile to Bar on the 
 Strength of Wrought Iron. The tensile strength of the irons used 
 in Beardslee's tests ranged from 46,000 to 62,700 Ibs. per sq. in., brand 
 L, which was really a steel, not being considered. Some specimens of L 
 gave figures as high as 70,000 Ibs. The amount of reduction of sectional 
 area in rolling the bars has a notable influence on the strength and elastic 
 limit; the greater the reduction from pile to bar, the higher the strength. 
 
 The following are a few figures from tests of one of the brands: 
 Size of bar, in. diam.: 4 3 2 1 1/2 l; 4 
 Area of pile, sq. in.: 80 80 72 25 9 3 
 Bar per cent of pile: 15.7 8.83 4.36 3.14 2.17 1.6 
 Tensile strength, Ib.: 46,322 47,761 48,280 51,128 52,275 59,585 
 Elastic limit. Ib.: 23.430 26,400 31,892 36,467 39,126 
 
 Influence of Chemical Composition on the Properties of Wrought 
 Iron* (Beardslee on Wrought Iron and Chain Cables. Abridgment by 
 
WROUGHT IRON. 
 
 461 
 
 W. Kent. Wiley & Sons, 1879.) A series of 2000 tests of specimens 
 from 14 brands of wrought iron, most of them of high repute, was made 
 in 1877 by Capt. L. A. Beardslee, U.S.N., of the United States Testing 
 Board. Forty-two chemical analyses were made of these irons, with a 
 view to determine what influence the chemical composition had upon the 
 strength, ductility, and welding power. From the report of these testa 
 by A. L. Holley the following figures are taken: 
 
 Brand. 
 
 Average 
 Tensile 
 Strength. 
 
 Chemical Composition. 
 
 S. 
 
 P. 
 
 Si. 
 
 C. 
 
 Mn. 
 
 Slag. 
 
 L 
 
 66,598 
 
 trace 
 
 j 0.065 
 I 0.084 
 
 0.080 
 0.105 
 
 0.212 
 0.512 
 
 0.005 
 0.029 
 
 0.192 
 0.45? 
 
 P 
 
 54,363 
 
 (0.009 
 \ 0.001 
 
 0.250 
 0.095 
 
 0.182 
 0.028 
 
 0.033 
 0.066 
 
 0.033 
 0.009 
 
 0.848 
 1.214 
 
 B 
 
 52 764 
 
 008 
 
 231 
 
 156 
 
 015 
 
 017 
 
 
 !J 
 
 51,754 
 
 j 0.003 
 1 0.005 
 
 0.140 
 0.291 
 
 0.182 
 0.321 
 
 0.027 
 0.051 
 
 trace 
 0.053 
 
 0.678 
 1.724 
 
 
 
 51,134 
 
 ( 0.004 
 \ 0.005 
 
 0.067 
 0.078 
 
 0.065 
 0.073 
 
 0.045 
 0.042 
 
 0.007 
 0.005 
 
 1.168 . 
 0.974 
 
 C 
 
 50,765 
 
 0.007 
 
 0.169 
 
 0.154 
 
 0.042 
 
 0.021 
 
 
 Where two analyses are given, they are the extremes of two or more 
 analyses of the brand. Where one is given, it is the only analysis. 
 Brand L should be classed as a puddled steel. 
 
 ORDER OF QUALITIES GRADED FROM No. 1 TO No. 19. 
 
 Brand. 
 
 Tensile 
 Strength. 
 
 Reduction of 
 Area. 
 
 Elongation. 
 
 Welding Power. 
 
 L 
 P 
 B 
 J 
 
 C 
 
 1 
 
 6 
 12 
 16 
 18 
 19 
 
 18 
 6 
 16 
 19 
 1 
 12 
 
 19 
 3 
 15 
 18 
 4 
 16 
 
 most imperfect, 
 badly, 
 best, 
 rather badly, 
 very- good. 
 
 The reduction of area varied from 54.2 to 25.9 per cent, and the elonga* 
 tion from 29.9 to 8.3 per cent. 
 
 Brand O, the purest iron of the series, ranked No. 18 in tensile strength 
 but was one of the most ductile; brand B, quite impure, was below tho 
 average both in strength and ductility, but was the best in welding 
 power; P, also quite impure, was 'one of the best in every respect except 
 welding, while L, the highest in strength, was not the most pure, it ha(f 
 the least ductility, and its welding power was most imperfect. The 
 evidence of the influence of chemical composition upon quality, there^ 
 fore, is quite contradictory and C9nfusing. The irons differing remark- 
 ably in their mechanical properties, it was found that a much more 
 marked influence upon their qualities was caused by different treatment 
 in rolling than by differences in composition. 
 
 In regard to slag Mr. Holley says: "It appears that the smallest and 
 most worked iron often has the most slag. It is hence reasonable to 
 conclude that an iron may be dirty and yet thoroughly condensed." 
 
 In his summary of "What is learned from chemical analysis, "' he says: 
 " So far, it may appear that little of use to the makers or users of wrought 
 iron has been learned. . . . The character of steel can be surely pred- 
 icated on the analyses of the materials ; that of wrought iron is altered 
 by subtle and unobserved causes." 
 
 Specifications for Wrought Iron. (F. H. Lewis, Engineers' Club of 
 Philadelphia, 1891.) 1. All wrought, iron must be tough, ductile, 
 fibrous, and of uniform quality for each class, straight, smooth, free from 
 cinder-pockets, flaws, buckles, blisters, and injurious cracks along the 
 edges, and must have a workmanlike finish. No specific process or 
 provision of manufacture will be demanded, provided the material fulfills 
 the requirements of these specifications. 
 
 2. The tensile strength, limit of elasticity, and ductility shall be deter- 
 mined from a standard test-piece not less than 1/4 inch thick cut from 
 the full-sized bar, and planed or turned, parallel. The area of cross- 
 
462 IRON AND STEEL. 
 
 section shall not bo less than 1/2 sq. in. The elongation shall be 
 measured after breaking on an original length of 8 in. 
 
 3. The tests shall show not less than the following results: El. in 
 
 8 in. 
 
 For bar iron in tension T. S. = 50,000; E. L. = 26,000; 18% 
 
 For shape iron in tension = 48,000; = 26,000; 15% 
 
 For plates under 36 in. wide = 48,000; = 26,000; 12% 
 
 For plates over 36 in. wide = 46,000; = 25,000; 10% 
 
 4. When full-sized tension members are tested to prove the strength of 
 their connections, a reduction in their ultimate strength of (500 X width 
 of bar) p9unds per square inch will be allowed. 
 
 5. All iron shall bend, cpld, 180 degrees around a curve whose diameter 
 is twice the thickness of piece for bar iron, and three times the thickness 
 for plates and shapes. 
 
 6. Iron which is to be worked hot in the manufacture must be capable 
 Df bending sharply to a right angle at a working heat without sign of 
 fracture. 
 
 7. Specimens of tensile iron upon being nicked on one side and bent 
 shall show a fracture nearly all fibrous. 
 
 8. All rivet iron must be tough and soft, and be capable of bending 
 cold until the sides are in close contact without sign of fracture on the 
 convex side of the curve. 
 
 Penna. B. B. Co.'s Specifications for Merchant-bar Iron (1904). 
 One bar will be selected for test from each 100 bars in a pile. 
 
 All the iron of one size in the shipment will be rejected if the average 
 tensile strength of the specimens tested full size as rolled falls below 
 47,000 Ibs. or exceeds 53,000 Ibs. per sq. in., or if a single specimen falls 
 below 45,000 Ibs. per sq. in.; or when the test specimen has been reduced 
 by machining if the average tensile strength exceeds 53,000 or falls below 
 46,000, or if a single specimen falls below 44,000 Ibs. per sq. in. 
 
 All the iron of one size in the shipment will be rejected if the average 
 elongation in 8 in. falls below the following limits: Flats and rounds, 
 tested as rolled, 1/2 in. and over, 20%; less than 1/2 in., 16%. Flats and 
 rounds reduced by machining 16%. 
 
 Nicking and Bending Tests. When necessary to make nicking and 
 bending tests, the iron will be nicked lightly on one side and then broken 
 by holding one end in a vise, or steam hammer, and breaking the iron by 
 successive blows. It must when thus broken show a generally fibrous 
 structure, not more than 25% crystalline, and must be free from admix- 
 , ture of steel. 
 
 Stay-bolt Iron. (Penna. R. R. Co.'s specifications, 1902). Sample 
 bars must show a tensile strength of not less than 48,000 Ibs. per sq. in. 
 and an elongation of not less than 25% in 8 in. One piece from each lot 
 will be threaded in dies with a sharp V thread, 12 to 1 in. and firmly 
 screwed through two holders having a clear space between them of 5 in. 
 One holder will be rigidly secured to the bed of a suitable machine, and the 
 other vibrated at right angles to the axis over a space of 1/4 in. or i/s in. 
 -each side of the center line. Acceptable iron should stand 2800 double 
 vibrations before breakage. 
 
 Mr. Vauclain, of the Baldwin Locomotive Works, at a meeting of the 
 American Railway Master Mechanics' Association, in 1892, says: Many 
 advocate the softest iron in the market as the best for stay-bolts. He 
 believed in an iron as hard as was consistent with heading the bolt nicely. 
 The higher the tensile strength of the iron, the more vibrations it will 
 stand, for it is not so easily strained beyond the yield-point. The Baldwin 
 specifications for stay-bolt iron call for a tensile strength of 50,000 to 
 52,000 Ibs. per square inch, the upper figure being preferred, and the 
 lower being insisted upon as the minimum. 
 
 Specifications for Wrought Iron for the World's Fair Buildings. 
 (Eng'g News, March 26, 1892.) All iron to be used in the tensile mem- 
 bers of open trusses, laterals, pins and bolts, except plate iron over 
 8 inches wide, and shaped iron, must show by the standard test-pieces 
 a tensile strength in Ibs. per square inch of: 
 
 52 000 7000 X area of original bar in sq. in. 
 circumference of original bar in inches * 
 
 with an elastic limit not less than half the strength given by this formula, 
 and au elongation of 20% in 8 in. 
 
- 
 
 METALS AT VARIOUS TEMPERATURES. d63 
 
 Plate iron 8 to 24 inches wide, T. S. 48,000, E. L. 26,000 Ibs. per sq. in., 
 elong. 12%. Plates over 24 inches wide, T. S. 46,000, E. L. 26,000 Ibs. 
 per sq. in. Plates 24 4o 36 in. wide, elong. 10%; 36 to 48 in., 8%; over 
 48 in., 5%. 
 
 All shaped iron, flanges of beams and channels, and other iron not 
 hereinbefore specified, must show a T. S. in Ibs. per sq. in. of: 
 _ 7000 X area of original bar 
 
 circumference of original bar* 
 
 yith an elastic limit of not less than half the strength given by this formula, 
 and an elongation of 15% for bars 5/8 inch and less in thickness, and of 
 12% for bars of greater thickness. For webs of beams and channels, 
 specifications for plates will apply. 
 
 All rivet iron must be tough and soft, and pieces of the full diameter of 
 the rivet must be capable of bending cold, until the sides are in close con- 
 tact, without sign of fracture on the convex side of the curve. 
 
 TENACITY OF METALS AT VARIOUS TEMPERATURES. 
 
 The British Admiralty made a series of experiments to ascertain what 
 loss of strength and ductility takes place in gun-metal compositions when 
 raised to high temperatures. It was found that all the varieties of gun 
 metal suffer a gradual but not serious 1933 of strength and ductility up to 
 a certain temperature, at which, within a few degrees, a great change 
 takes place, the strength falls to about- one-half the original,. and the 
 ductility is wholly gone. At temperatures above this point, up to 500 F., 
 there is little, if any, further loss of strength; the temperature at which 
 th ; s great change and loss of strength takes place, although uniform in 
 the specimens cast from the same pot, varies about 100 in the same 
 comp9sition cast at different temperatures, or with some varying condi- 
 tions in the foundry process. The temperature at which the change took 
 T, lace in No. 1 series was ascertained to be about 370, and in that of 
 No. 2, at a little over 250. Rolled Muntz metal and copper are satis- 
 factory up to 500, and may be used as securing-bolts with safety. 
 Wrought iron increases in strength up to 500, but loses slightly in duc- 
 tility up to 300, where an increase begins and continues up to 500, 
 where it is still less than at the ordinary temperature of the atmosphere. 
 The strength of Land ore steel is not affected by temperature up to 500, 
 but its ductility is reduced more than one-half. (Iron, Oct. 6, 1877.) 
 
 Strength of Iron and Steel Boiler-plate at High Temperatures. 
 
 (Chas. Huston, Jour. F. I., 1877.) 
 
 AVERAGE OF THREE TESTS OF EACH. 
 
 Temperature F. 68 575 925 
 
 Charcoal iron plate, tensile strength, Ibs 55,366 63,080 65,343 
 
 contr. of area % 26 23 21 
 
 Soft open-hearth steel, tensile strength, Ibs 54,600 66,083 64,350 
 
 contr. % 47 38 33 
 
 1 Crucible steel, tensile strength, Ibs 64,000 69,266 68,600 
 
 contr. % 36 30 21 
 
 Tensile Strength of Iron and Steel at High Temperatures. 
 
 James E. Howard's tests (Iron Age, April 10, 1890) show that the tensile 
 strength of steel diminishes as the temperature increases from until a 
 minimum is reached between 200 and 300 F., the total decrease being 
 about 4000 Ibs. per square inch in the softer steels, and from 6000 to 
 8000 Ibs. in steels of over 80,000 Ibs. tensile strength. From this mini- 
 mum point the strength increases up t9 a temperature of 400 to 650 F., 
 the maximum being reached earlier in the harder steels, the increase 
 amounting to from 10,000 to 20,000 Ibs. per square inch above the mini- 
 mum strength at from 200 to 300. From this maximum, the strength 
 of all the steel decreases steadily at a rate approximating 10,000 Ibs. 
 decrease per 100 increase of temperature. A strength of 20,000 Ibs. 
 per square inch is still shown by 0.10 C. steel at about 1000 F., and by 
 0.60 to 1.00 C. steel at about 1600 F. 
 
 The strength of wrought iron increases with temperature from up 
 to a maximum at from 400 to 600 F., the increase being from 8000 to 
 10,000 Ibs. per square inch, and then decreases steadily till a strength .of 
 only 6000 Ibs. per square inch is shown at 1500 F. 
 
464 
 
 IKON AND STEEL. 
 
 Cast iron appears to maintain its strength, with a tendency to In- 
 crease, until 900 is reached, beyond which temperature the strength 
 gradually diminishes. Under the highest temperatures, 1500 to 1600 F., 
 numerous cracks on the cylindrical surface of the specimen were devel- 
 oped prior to rupture. It is remarkable that cast iron, so much inferior 
 in strength to the steels at atmospheric temperature, under the highest 
 temperatures has nearly the same strength the high-temper steels then 
 have. 
 
 Strength of Wrought Iron and Steel at High Temperatures. 
 (Jour. F. I., cxii, 1881, p. 241.) Kollmann's experiments at Oberhausen 
 included tests of the tensile strength of iron and steel at temperatures 
 ranging between 70 and 2000 F. Three kinds of metal were tested, 
 viz., fibrous iron of 52,464 Ibs. T. S., 38,280 Ibs. E. L., and 17.5% 
 elong.; fine-grained iron of 56,892 Ibs. T. S., 39,113 Ibs. E. L., and 20% 
 elong.; and Bessemer steel of 84,826 Ibs. T. S., 55,029 Ibs. E. L., and 
 14.5% elong. The mean ultimate tensile strength of each material 
 expressed in per cent of that at ordinary atmospheric temperature is 
 given in the following table, the fifth column of which exhibits, for pur- 
 poses of comparison, the results of experiments by a committee of the 
 Franklin Institute in the years 1832-36. 
 
 Temperature 
 Degrees F. 
 
 Fibrous 
 Iron, %. 
 
 Fine-grained 
 Iron, %. 
 
 Bessemer 
 Steel, %. 
 
 Franklin In- 
 stitute, %. 
 
 
 
 100.0 
 
 100.0 
 
 100.0 
 
 96.0 
 
 100 
 
 100.0 
 
 100.0 
 
 100.0 
 
 102.0 
 
 200 
 
 100.0 
 
 100.0 
 
 100.0 
 
 105.0 
 
 300 
 
 97.0 
 
 100.0 
 
 100.0 
 
 106.0 
 
 400 
 
 95.5 
 
 100.0 
 
 100.0 
 
 106.0 
 
 500 
 
 92.5 
 
 98.5 
 
 98.5 
 
 104.0 
 
 600 
 
 88.5 
 
 95.5 
 
 92.0 
 
 99.5 
 
 700 
 
 81.5 
 
 90.0 
 
 68.0 
 
 92.5 
 
 800 
 
 67.5 
 
 77.5 
 
 44.0 
 
 75.5 
 
 900 
 
 44.5 
 
 51.5 
 
 36.5 
 
 53.5 
 
 1000 
 
 26.0 
 
 36.0 
 
 31.0 
 
 36.0 
 
 1100 
 
 20.0 
 
 30 5 
 
 26 5 
 
 
 1200 
 
 18 
 
 28 
 
 22 
 
 
 1400 
 
 13 5 
 
 19 
 
 15 
 
 
 1600 
 
 7.0 
 
 12.5 
 
 10.0 
 
 
 1800 
 
 4 5 
 
 8 5 
 
 7 5 
 
 
 2000 
 
 3.5 
 
 5'.0 
 
 5.0 
 
 
 Effect of Cold on the Strength of Iron and Steel. The following 
 conclusions were arrived at by Mr. Styffe in 1865: 
 
 (1) The absolute strength of iron and steel is not diminished by cold, 
 even at the lowest temperature which ever occurs in Sweden. 
 
 (2) Neither in steel nor in iron is the extensibility less in severe cold 
 than at the ordinary temperature. 
 
 (3) The limit of elasticity in both steel and iron lies higher in severe 
 cold. 
 
 (4) The modulus of elasticity in both steel and iron is increased on 
 reduction of temperature, and diminished on elevation of temperature; 
 but that these variations never exceed 0.05% f9r a change of 1.8 F. 
 
 W. H. Barlow (Proc. Inst. C. E.) made experiments on bars of wrought 
 iron, "cast iron, malleable cast iron, Bessemer steel, and tool steel. The 
 bars were tested with tensile and transverse strains, and also by im- 
 pact: one-half of them at a temperature of 50 F., and the other half at 
 5 F. 
 
 The results of the experiments were summarized as follows: 
 
 1. When bars of wrought iron or steel were submitted to a tensile 
 strain and broken, their strength was not affected by severe cold (5 F.), 
 but their ductility was increased about 1% in iron and 3% m steel. 
 
 2. Whsn bars of cast iron were submitted to a transverse strain at a 
 low temperature, their strength was diminished about 3% and their 
 flexibility about 16%. 
 
 3. When bars of wrought iron, malleable cast iron, steel, and ordinary 
 cast iron were subjected to impact at 5 F., the force required to break 
 them, and their flexibility, were reduced as follows: 
 
' 
 
 DURABILITY OF IKON, COKROSION, ETC. 465 
 
 
 Reduction of 
 Force of Im- 
 pact, %. 
 
 Reduction of 
 Flexibility, 
 
 % 
 
 Wrought iron, about 
 
 3 
 
 18 
 
 Steel (best cast tool), about 
 
 3 1/2 
 
 17 
 
 Malleable cast iron, about 
 
 41/2 
 
 15 
 
 Cast iron, about 
 
 21 
 
 not taken 
 
 The experience of railways in Russia, Canada, and other countries 
 where the winter is severe, ie that the breakages of rails and tires are far 
 more numerous in the cold weather than in the summer. On this 
 account a softer class of steel is employed in Russia for rails than is usual 
 in more temperate climates. 
 
 The evidence extant in relation to this matter leaves no doubt that the 
 capability of wrought iron or steel to resist impact is reduced by cold. On 
 the other hand, its static strength is not impaired by low temperatures. 
 
 Increased Strength of Steel at very Low Temperature. Steel of 
 72,300 Ib. T. S. and 62,800 Ib. elastic limit when tested at 76 F. gave 
 97,600 T. S. and 80,000 E. L. when tested at. the temperature of liquid 
 air. Watertown Arsenal Tests, Eng. Rec., July 21, 1906. 
 
 Prof. R. C. Carpenter (Proc. A. A. A. S. 1897) found that the strength 
 of wrought iron at 70 F. was 20% greater than at 70 F. 
 
 Effect of Low Temperatures on Strength of Railroad Axles. 
 (Thos. Andrews, Proc. Inst. C. E., 1891.) Axles 6 ft. 6 in. long be- 
 tween centers of journals, total length 7 ft. 3V2 in., diameter at middle 
 41/2 in., at wheel-sets 5Vs in., journals 3 3 /4 X 7 in., were tested by impact 
 at temperatures of and 100 F. Between the blows each axle was 
 half turned over, and w r as also replaced for 15 minutes in the water-bath. 
 
 The mean force of concussion resulting from each impact was ascer- 
 tained as follows: 
 
 Let h = height of free fall in feet, w = weight of test ball, hw = W = 
 " energy," or work in foot-tons, x = extent of deflections between bearings 
 
 then F (mean force) = W/x Jiw/x . 
 
 The results of these experiments show that whereas at F. a total 
 average mean force of 179 tons was sufficient to cause the breaking of the 
 axles, at 100 F. a total average mean force of 428 tons was required. 
 In other words, the resistance to concussion of the axles at F. was only 
 about 42% of what it was at 100 F. 
 
 The average total deflection at F. was 6.48 in., as against 15.06 in. 
 with the axles at 100 F. under the conditions stated; this represents an 
 ultimate reduction of flexibility, under the test of impact, of about 57% 
 for the cold axles at F., compared with the warm axles at 100 F. 
 
 EXPANSION OF IEON AND STEEL BY HEAT. 
 
 James E. Howard, engineer in charge of the U. S. test ing- machine at 
 Watertown, Mass., gives the following results of tests made on bars 
 35 in. long (Iron Age, April 10, 1890) : 
 
 
 
 
 
 Coeffi. of 
 
 
 
 
 
 Coeffi. of 
 
 
 C. 
 
 Mn. 
 
 Si. 
 
 Expansion 
 per degree 
 
 
 C. 
 
 Mn 
 
 Si. 
 
 Expansion 
 per degree 
 
 
 
 
 
 F. 
 
 
 
 
 
 F. 
 
 Wrought iron 
 
 
 
 
 0.0000067302 
 
 Steel 
 
 57 
 
 93 
 
 07 
 
 0.0000063891 
 
 Steel. 
 
 09 
 
 11 
 
 
 0000067561 
 
 
 71 
 
 58 
 
 08 
 
 0000064716 
 
 
 70 
 
 45 
 
 
 .0000066259 
 
 , 
 
 81 
 
 56 
 
 17 
 
 .0000062167 
 
 
 
 31 
 
 *7 
 
 
 0000065149 
 
 
 
 89 
 
 57 
 
 19 
 
 0000062335 
 
 it 
 
 W 
 
 70 
 
 
 .0000066597 
 
 
 97 
 
 80 
 
 78 
 
 .0000061700 
 
 
 
 .51 
 
 .58 
 
 02 
 
 .0000066202 
 
 Cast (gun) 
 
 
 
 
 
 
 
 
 
 
 iron 
 
 
 
 
 .0000059261 
 
 DURABILITY OF IRON, CORROSION, ETC. 
 
 Crystallization of Iron by Fatigue. Wrought iron of the best 
 quality is very tough, and breaks, on being pulled in a testing machine or 
 bent after nicking, with a fibrous fracture. Cold-short iron, however, is 
 more brittle, and breaks square across the fibers with a fracture which is 
 
466 
 
 IRON AND STEEL. 
 
 commonly called crystalline although no real crystals are present. Iron 
 which has been repeatedly overstrained, and especially iron subjected 
 to repeated vibrations and shocks, also becomes brittle, and breaks with 
 an apparently crystalline fracture. See " Resistance of Metals to Repeated 
 Shocks, " p. 276. 
 
 Walter H. Finley (Am. Mach., April 27, 1905) relates a case of fail- 
 ures of li/g-in. wrought-iron coupling pins on a train of 1-ton mine cars, 
 apparently due to crystallization. After two pins were broken after a 
 year's hard service, "several hitchings were laid on an anvil and the pin 
 broken by a single blow from a sledge. Pieces of the broken pins were 
 then heated to a bright red, and, after cooling slowly, were again put 
 under the hammer, which failed entiiely to break them. After cutting 
 with a cleaver, the pins were broken, and the fracture showed a complete 
 restoration of the fibrous structure. This annealing process was then 
 applied to the whole supply of hitchings. Piles of twenty-five or thirty 
 were covered by a hot wood fire, which was allowed to die down and go 
 out, leaving the hitchings in a bed of .ashes to cool off slowly.. By 
 repeating this every six months the danger of brittle pins was avoided. 
 
 Durability of Cast Iron. Frederick Gratf, in an article on the 
 Philadelphia water-supply, says that the first cast-iron pipe used there 
 was laid in 1820. These pipes were made of charcoal iron, and were in 
 constant use for 53 years. They were uncoated, and the inside was well 
 filled with tubercles. In salt water good cast iron, even uncoated, will 
 last for a century at least; but; it often becomes soft enough to be cut by 
 a knife, as is shown in iron cannon taken up from the bottom of harbors 
 after long submersion. Close-grained, hard white metal lasts the longest 
 in sea water. (Eng j g News, April 23, 1887, and March 26, 1892.) 
 
 Tests of Iron after Forty Years' Service. A square link 12 inchei 
 broad, 1 inch thick and about 12 feet long was taken from the Kieff 
 bridge, then 40 years old, and tested in comparison with a similar link 
 which had been preserved in the stock-house since the bridge was built. 
 The following is the record of a mean of four longitudinal test-pieces, 
 1 X IVsX 8 inches, taken from each link (Stahl und Eisen. 1890): 
 Old Link . .T. S., 21.8 tons; E. L., 11.1 tons; Elong., 14.05% 
 New Link.' " 22.2 11.9 
 
 Durability of Iron in Bridges. (G. Lindenthal, Eng'g, Ma Y 2, 1884, 
 
 E139.) The Old Monongahela suspension bridge in Pittsburg, built 
 1 1845, was taken down in 1882. The wires of the cables were frequently 
 strained to half of their ultimate strength, yet on testing them after 37 
 years' use they showed a tensile strength of from 72,700 to 100,000 Ibs. 
 per sq in. The elastic limit was from 67,100 to 78,600 Ibs. per sq in. 
 Reduction at point of fracture, 35% to 75%. Their diameter was 0.13 in. 
 
 A new ordinary telegraph wire of same gauge tested for comparison 
 showed: T. S., of 100.000 Ibs.; E. L., 81,550 Ibs.; reduction, 57%. Iron 
 rods used as stays or suspenders showed: T. S., 43,770 to 49,720 Ibs. E. 
 L., 26,380 to 29,200. Mr. Lindenthal draws these conclusions: 
 
 " The above tests indicate that iron highly strained for a long number 
 of years, but still within the elastic limit, and exposed to slight vibration, 
 will not deteriorate in quality. 
 
 "That if subjected to only one kind of strain it will not change its 
 texture, even if strained beyond its elastic limit, for many years. It will 
 stretch and behave much as in a testing-machine during a long test. 
 
 "That iron will change its texture only when exposed to alternate 
 severe straining, as in bending in different directions. If the bending is 
 slight but very rapid, as in violent vibrations, the effect is the same." 
 
 Durability of Iron in Concrete. In Paris a sewer of reinforced con- 
 crete 40 years old was removed and the metal was found in a perfect state 
 of preservation. In excavating for the foundations of the new General 
 Post Office in London some old Roman brickwork had to be removed, 
 and the hoop-iron bonds were still perfectly bright and good. (Eng'g, 
 Aug. 16, 1907, p. 227.) 
 
 Corrosion of Iron Bolts. On bridges over the Thames in London, 
 bolts exposed to the action of the atmosphere and rain-water were eaten 
 away in 25 years from a diameter of 7/g in. to 1/3 in., and from 5/ 8 in. diam- 
 eter to 5/ 16 inch. 
 
 Wire ropes exposed to drip in colliery shafts are very liable to corrosion. 
 
 Corrosive Agents in the Atmosphere. The experiments of F. 
 Grace Calvert (Chemical News, March 3, 1871) show that carbonic acid. 
 
DURABILITY OF IRON, CORROSION, ETC. 467 
 
 in the presence of moisture, is the agent which determines the oxidation 
 of iron in the atmosphere. He subjected perfectly cleaned blades of 
 iron and steel to the action of different gases for a period of four months, 
 with results as follows: 
 
 Dry oxygen, dry carbonic acid, a mixture of both gases, dry and damp 
 oxygen and ammonia: no oxidation. Damp oxygen: in three experi- 
 ments one blade only was slightly oxidized. 
 
 Damp carbonic acid : slight appearance of a white precipitate upon the 
 iron, found to be carbonate of iron. Damp carbonic acid and oxygen: 
 oxidation very rapid. Iron immersed in water containing carbonic acid 
 oxidized rapidly. 
 
 Iron immersed in distilled water deprived of its gases by boiling rusted 
 the iron in spots that were found to contain impurities. 
 
 Sulphurous acid (the product of the combustion of the sulphur in coal) 
 is an exceedingly active corrosive agent, especially when the exposed iron 
 is coated with soot. This accounts for the rapid corrosion of iron in 
 railway bridges exposed to the smoke from locomotives. (See account of 
 experiments by the author on action of sulphurous acid in Jour. Frank. 
 Inst., June, 1875, p. 437.) An analysis of sooty iron rust from a railway 
 bridge showed the presence of sulphurous, sulphuric, and carbonic acids, 
 chlorine, and ammonia. Bloxam states that ammonia is formed from 
 the nitrogen of the air during the process of rusting. 
 
 Galvanic Action is a most active agent of corrosion. It takes place 
 when two metals, one electro-negative to the other, are placed in contact 
 and exposed to dampness. 
 
 Corrosion in Steam-boilers. Internal corrosion may be due either 
 to the use of water containing free acid, or water containing sulphate 
 or cnloride of magnesium, which decompose when heated, liberating the 
 acid, or to water containing air or carbonic acid in solution. External 
 corrosion rarely takes place when a boiler is kept hot, but when cold it 
 is apt to corrode rapidly in those portions where it adjoins the brick- 
 work or where it may be covered by dust or ashes, or wherever damp- 
 ness may lodge. (See Impurities of Water, p. 720, and Incrustation and 
 Corrosion, p. 927 .) 
 
 Corrosion of Iron and Steel. Experiments made at the Riverside 
 Iron Works, Wheeling, W. Va., on the comparative liability to rust of 
 iron and soft Bessemer steel: A piece of iron plate and a similar piece of 
 steel, both clean and bright, were placed in a mixture of yellow loam and 
 sand, with which had been thoroughly incorporated some carbonate of 
 soda, nitrate of soda, ammonium chloride, and chloride of magnesium. 
 The earth as prepared was kept moist. At the end of 33 days the pieces 
 of metal were taken out, cleaned, and weighed, when the iron was found 
 to have lost 0.84% of its weight and the steel 0.72%. The pieces were 
 replaced and after 28 days weighed again, when the iron was found to 
 have lost 2.06% of its original weight and the steel 1.79%. (Eng'g, June 
 26, 1891.) 
 
 Internal Corrosion of Iron and Steel Pipes by Warm Water. 
 (T. N. Thomson, Proc. A. S. H. V. E., 1908.) Three short pieces of iron 
 and three of steel pipes, 2 in. diam., were connected together by nipples 
 and made part of a pipe line conveying water at a temperature varying 
 from 160 to 212 F. In one year 9 13/33 Ibs. of wrought iron lost 203/4 oz., 
 and 913/32 Ibs. of steel 247/g oz. The pipes were sawed in two lengthwise, 
 and the deepest pittings were measured by a micrometer. Assuming that 
 the pitting would have Continued at a uniform rate the wrought-iron pipes 
 would have been corroded through in from 686 to 780 days, and the steel 
 pipes from 760 to 850 days, the average being 742 days for iron and 797 
 days for steel. Two samples each of galvanized iron and steel pipe were 
 also included in the pipe line, and their calculated life was: iron 770 and 
 1163 days; steel 619 and 1163 days. Of numerous samples of corroded 
 pipe received from heating engineers ten had given out within four years 
 of service, and of these six were steel and four were iron. 
 
 To ascertain whether Pipe is made of Wrought Iron or Steel, cut 
 off a short piece of the pipe and suspend it in a solution of 9 parts of water, 
 3 of sulphuric acid, and 1 of hydrochloric acid in a porcelain or glass dish 
 in such a way^ that the end will not touch the bottom of the dish. After 
 2 to 3 hours' immersion remove the pipe and wash off the acid. If the 
 pipe is steel the end will present a bright, solid, unbroken surface, while 
 If made of iron it will show faint ridges or rings, like the year rings in a 
 
468 IRON AND STEEL. 
 
 tree, showing the different layers of iron and streaks of cinder. In order 
 that the scratches made by the cutting-off tool may not be mistaken for 
 the cinder marks, file the end of the pipe straight across or grind on an 
 emery wheel until the marks of the cutting-off tool have disappeared 
 before putting it in the acid. 
 
 Relative Corrosion of Wrought Iron and Steel. (H. M. Howe, 
 Proc. A. S. T. M., 1906.) On one hand we have the very general 
 opinion that steel corrodes very much faster than wrought iron, an opinion 
 held so widely and so strongly that it cannot be ignored. On the other 
 hand we have the results of direct experiments by a great many observers, 
 in different countries and under widely differing conditions; and these 
 results tend to show that there is no very great difference between the 
 corrosion of steel and wrought iron. Under certain conditions steel seems 
 to rust a little faster than wrought iron, and under others wrought iron 
 seems to rust a little faster than steel. Taking the tests in unconfin<ed 
 sea water as a whole wrought iron does constantly a little better than 
 steel, and its advantage seems to be still greater in the case of boiling sea 
 water. In the few tests in alkaline water wrought iron seems to have the 
 advantage over steel, whereas in acidulated water steel seems to rust more 
 slowly than wrought iron. 
 
 Steel which in the first few months may rust faster than wrought iron 
 may, on greatly prolonging the experiments, or pushing them to destruc- 
 tion, actually rust more slowly, and vice versa. 
 
 Carelessly made steel, containing blowholes, may rust faster than 
 wrought iron, yet carefully made steel, free from blowholes, may rust 
 more slowly. Any difference between the two may be due not to the 
 inherent and intrinsic nature of the material, but to defects to which it 
 is subject if carelessly made. Care in manufacture, and special steps to 
 lessen the tendency to rust, might well make steel less corrodible than 
 wrought iron, even if steel carelessly made should really prove more 
 corrodible than wrought iron. 
 
 For extensive discussions on this subject see Trans. A. I. M. E.. 1905. 
 Proc. A. S. T. M., 1906 and 1908, and Bulletins of National Tube Co. 
 
 Corrosion of Fence Wire. (A. S. Cushman, Farmers' Bulletin, No. 
 239, U. 8. Dept. of Agriculture, 1905.) "A large number of letters were 
 received from all over the C9untry in response to official inquiry, and 
 all pointed in the same direction. As far as human testimony is capable 
 of establishing a fact, there need be not the slightest question that modern 
 eteel does not serve the purpose as well as the older metal manufactured 
 twenty or more years ago." 
 
 Electrolytic Theory, and Prevention of Corrosion. (A. S. dish- 
 man, Bulletin No. 30, U. S. Dept. of Agriculture, Office of Public Roads, 
 1907. The Corrosion of Iron.) The various kinds of merchantable iron 
 and steel differ, within wide limits, in their resistance, not only to the 
 ordinary processes of oxidation known as rusting, but also in other corro- 
 sive influences. Different specimens of one and the same kind of iron or 
 steel will show great variability in resistance to corrosion under the con- 
 ditions of use and service. The causes of this variability are numerous 
 and complex, and the subject is not nearly so well understood at the 
 present time as it should be. All investigators are agreed that iron can- 
 not rust in air or oxygen unless water is present, and on the other hand 
 it cannot rust in water unless oxygen is present. 
 
 From the standpoint of the modern theory of solutions, all reactions 
 which take place in the wet way. are attended with certain readjustments 
 of the electrical states of the reacting ions. The electrolytic theory of 
 rusting assumes that before iron can oxidize in the wet way it must first 
 pass into solution as a ferrous ion. 
 
 Dr. Cushman then gives an account of his experiments which he con- 
 siders demonstrate that iron goes into solution up to a certain maximum 
 concentration in pure water, without the aid of oxygen, carbonic acid or 
 other reacting substances. It is apparent that the rusting of iron la 
 primarily due, not to attack by oxygen, but by hydrogen ions. 
 
 Solutions of chromic acid and potassium bichromate inhibit the rusting 
 of iron. If a rod or strip of bright iron or steel is immersed for a few 
 hours in a 5 to 10 per cent solution of potassium bichromate, and is then 
 removed and thoroughly washed, a certain change has been produced 
 on the surface of the metal. The surface may be thoroughly washed 
 
DURABILITY OF IRON, CORROSION, ETC. 469 
 
 and wiped with a clean cloth without disturbing this new surface condi- 
 tion. No visible change has been effected, for the polished surfaces 
 examined under the microscope appear to be untouched. If, however, 
 the polished strips are immersed in water it will be found that rusting is 
 inhibited. An ordinary untreated polished specimen of steel will show 
 rusting in a few minutes when immersed in the ordinary distilled water of 
 the laboratory. Chromated specimens will stand immersion for varying 
 lengths of time before rust appears. In some cases it is a matter of 
 hours, in others of days or weeks before the inhibiting effect is overcome. 
 
 It would follow from the electrolytic theory that in order to have the 
 highest resistance to corrosion a metal should either be as free as possible 
 from certain impurities, such as manganese, or should be so homogene- 
 ous as not to retain localized positive and negative nodes for a long time 
 without change. Under the first condition iron would seem to have the 
 advantage over steel, but under the second much would depend upon 
 care exercised in manufacture, whatever process was used. 
 
 There are two lines of advance by which we may hope to meet the 
 difficulties attendant upon rapid corrosion. One is by the manufacture 
 of better metal, and the other is by the use of inhibitors and protective 
 coverings. Although it is true that laboratory tests are frequently 
 unsuccessful in imitating the conditions in service, it nevertheless appears 
 that chromic acid and its salts should under certain circumstances come 
 into use to inhibit extremely rapid corrosion by electrolysis. 
 
 Chrome Paints. G. B. Heckel (Jour. F. /., Eng. Dig., Sept., 1908) 
 quotes a letter from Mr. Cushman as follows: "My observation that 
 chromic acid and certain of its compounds act as inhibitives has led to 
 many experiments by other workers along the same line. I have found 
 that the chrome compounds on the market vary very much in their action. 
 Some of them show up as strong inhibitors, while others go to the op- 
 posite extreme and stimulate corrosion. Referring only to the labeled 
 names of the pigments, I find among the good ones, in the order cited: 
 Zinc chromate, American vermilion, chrome yellow orange, chrome 
 yellow dd. Among the bad ones, also in the order given, I find: Chrome 
 yellow medium, chrome green, chrome red. Much the worst of all is 
 chrome yellow lemon. I presume that the difference is due to impurities 
 that are present in the bad pigments." 
 
 Mr. Heckel suggests the following formula for a protective paint: 40 
 IDS. American vermilion, 10 Ibs. red lead, 5 Ibs. Venetian red. Zinc 
 oxide and lamp-black to produce the required tint or shade. Grind in 
 1 Va gal. of raw linseed oil increasing the quantity as required for added 
 zinc oxide or lamp-black and 1/8 gal. crusher's drier. For use, thin 
 with raw oil and very little turpentine or benzine. 
 
 He states that the substitution of zinc chrome for the American ver- 
 milion; of any high-grade finely ground iron oxide for the Venetian red; 
 and of American vermilion for the red lead, would probably improve the 
 protective value of the formula; that the addition of a very little kauri 
 gum varnish, if zinc oxide is used, might be found advantageous; and 
 that the substitution of a certain proportion of China wood oil for some 
 of the linseed oil might improve the wearing qualities of the paint. 
 
 Dr. Cushman points out two dangers confronting us when we attempt 
 to base an inhibitive formula on commercial products. The first is that 
 all carbon pigments, excepting pure graphite, may contain sulphur com- 
 pounds easily oxidizable to sulphuric acid when spread out as in a paint 
 film. The second is the probability of variation in the composition of 
 basic lead chromate or American vermilion. Because of these facts, it 
 is necessary, before selecting any particular pigment for its inhibitive 
 quality, to ascertain that it is free from acids or acid-forming impurities. 
 As a result of his experiments he recommends the substitution of Prus- 
 sian blue for the lamp-black in Mr. Heckel's formula, and lays down as a 
 safe rule in the formulation of inhibitive paints, a careful avoidance of 
 all potential stimulators of the hydrogen ions and consequently of any 
 substance which might develop acid; preference being given to chromate 
 pigments which are to some extent soluble in water, and to other pig- 
 ments which in undergoing change tend to develop an alkaline rather 
 than an acid reaction. Calcium sulphate, for example, in any form (as 
 a constituent of Venetian red, for example), he deems dangerous to use 
 because of the possibility of its developing acid. Barium sulphate, on 
 the other hand, he regards as safe, because of its chemical stability.. 
 
470 IRON AND STEEL. 
 
 Corrosion caused by Stray Electric Currents. (W. W- Churchill, 
 Science, Sept. 28, 1906). Surface condensers in electric lighting and 
 other plants were abandoned on account of electrolytic corrosion. The 
 voltage of the rails in the freight yard of the Long Island railroad at the 
 peak of the load was 9 volts above the potential of the river, decreasing 
 to 2 volts or less at light loads. This caused a destruction of water pipes 
 and other things in the railroad yards. Experiments with various metal 
 plates immersed in samples of East River water showed that it gave a 
 more violent action than ordinary sea water. It was further observed 
 that there was a local galvanic action going on, and that the amount of 
 stray currents had something to do with the polarization of the surfaces, 
 making the galvanic action exceedingly violent and destroying thin cop- 
 per tubes at a very rapid rate. There was a violent local action between 
 the zinc and the copper of the brass tubes which were in contact with the 
 electrolyte, and this increased in the reaction as it progressed in stagnant 
 conditions. By interposing a counter electromotive force against the 
 galvanic couple which should exceed in pressure the voltage of the couple, 
 the actions of the electrolytic corrosion ceased. When unconnected, or 
 electrically separated, plates were placed in the electrolyte, if they were 
 of composite construction and had sharp projections into the fluid, raised 
 by cutting and prying up with a knife, they would have these projections 
 promptly destroyed, and if an electric battery having a pressure exceed- 
 ing that of the couple in the East River water was caused to act to pro- 
 duce a counter current, and having a pressure exceeding that of the 
 galvanic couple (0.42 volt), the capacity of this electrolyte to drive off 
 atoms of the mechanically combined metals in the alloys used was ove/- 
 come and corrosion was arrested. 
 
 It, therefore, became desirable not only to carefully provide the bal- 
 ancing quantity of current to equal the stray traction currents arising 
 from the ground returns of railway and other service, but to add to this 
 the necessary voltage through a cathode placed in the circulating water 
 in such a way as to bring to bear electrolytic action which would pre- 
 vent the galvanic action due to this current coming into contact with 
 alloys of mechanically combined metals such as the brass tubes (60% 
 copper, 40% zinc). 
 
 In order to accomplish these two things, it was first necessary to so 
 install the condensers as to prevent undue amounts of stray currents 
 flowing through them, thus tending to reduce the amount of power 
 required to prevent injurious action of these currents and otherwise to 
 neutralize them. This was done by insulating the joints in the piping 
 and from ground connections, and even lining the large water connec- 
 tions with glass melted on to the surface. 
 
 To furnish electromotive force, a 3-K.W. motor generator was pro- 
 vided. By means of a system of wiring, with ammeters and voltmeters, 
 and a connection to an outlying anode in the condensing supply intake 
 at its harbor end, this generator was planned to provide current to neu- 
 tralize the stray currents in the condenser structure to any extent that 
 they had passed the insulated joints in the supports and connections, as 
 well as through the columns of water in the pipe connections, and then 
 to adjust the additional voltage needed to counteract and prevent the 
 galvanic action. All connections were made in a manner to insure a 
 uniform voltage of the various parts of the condenser to prevent local 
 action, each connection being so made and provided with such measuring 
 instruments as to insure ready adjustment to effect this. The apparatus 
 was designed in accordance with the above statements. Its operation 
 has extended over fourteen months (to date, 1906), and with the excep- 
 tion of about ten tubes which have become pitted, the results have been 
 satisfactory. The efficiency of the apparatus amply justifies the ex- 
 pense of its installation, while its operation is not expensive, and the 
 plant described will be followed by other protecting plants of the same 
 character. 
 
 Electrolytic Corrosion due to Overstrain. (C. F. Burgess, El. Rev., 
 Sept. 19, 1908.) Mild steel bars overstrained in their middle portion 
 were subjected to corrosion by suspension in dilute hydrochloric acid 
 solutions, and others by making them the anode in neutral solutions of 
 ammonium chloride and causing current to flow under low current den- 
 sity. In all cases a marked difference was noted in the rate at which the 
 strained portions corroded as compared with the unstrained. 
 
Differences 
 
 PRESERVATIVE COATINGS. 471 
 
 
 Differences of potential of from five to nine millivolts were noted 
 between two electrodes, one of which constituted the strained portion 
 and one the unstrained. 
 
 The more rapid electrolytic corrosion of the strained portion appears 
 to be due to the fact that the strained metal is electropositive to the 
 unstrained, the current finding the easier path through the surface of 
 the electropositive metal. That the strained metal is the more electro- 
 positive is also shown by a liberation of hydrogen bubbles on the un- 
 
 rained portion. 
 
 PRESERVATIVE COATINGS. 
 
 The following notes have been furnished to the author by Prof. A. H. 
 Sabin. (Revised, 1908.) 
 
 Cement. Iron-work is often bedded in concrete; if free from cracks 
 and voids it is an efficient protection; The metal should be cleaned and 
 then washed with neat cement before embedding. 
 
 Asphaltum. This is applied either by dipping (as water-pipe) or 
 by pouring it 9n (as bridge floors). The asphalt should be slightly elastic 
 when cold, with a high melting-point, not softening much at 100 F., 
 applied at 300 to 400; the surface must be dry and should be hot; the 
 coating should be of considerable thickness. 
 
 Paint. Composed of a vehicle or binder, usually linseed oil or some 
 inferior substitute, or varnish (enamel paints); and a pigment, which is a 
 more or less inert solid in the form of a powder, either mixed or ground 
 together. Nearly all paint contains paint drier or japan, which is a lead 
 or (and) manganese compound soluble in oil, and acts as a carrier of 
 oxygen; as little should be used as possible. Boiled oil contains drier; 
 no additional drier is needed. None should be used with varnish paints, 
 nor with '* ready-mixed paints " in general. 
 
 The principal pigments are white lead (carbonate or oxy-sulphate) and 
 white zinc (oxide), red lead (peroxide), oxides of iron, hydrated and 
 anhydrous, graphite, lampblack, bone black, chrome yellow, chrome 
 green, ultramarine and Prussian blue, and various tinting colors. White 
 lead has the greatest body or opacity of white pigments; three coats of it 
 equal five of white zinc; zinc is more brilliant and. permanent, but it is 
 liable to peel, and it is customary to mix the two. These are the standard 
 white paints for all uses, and the basis of all light-colored paints. Anhy- 
 drous iron oxides are brown and purplish brown, hydrated oxides are 
 yellowish red to reddish yellow, with more or less brown; most iron 
 oxides are mixtures of both sorts, and often contain a little manganese 
 and much clay. They are cheap, and are serviceable paints on wood and 
 are often used on iron, but for the latter use are falling into disrepute. 
 Graphite used for painting iron contains from 10 to 90% foreign matter, 
 usually silicates. It is very opaque, hence has great covering power and 
 may be applied in a very thin coat, which is to be avoided. The best 
 raphite paints give very good results. There are many grades of lamp- 
 lack; the cheaper sorts contain oily matter and are especially hard to 
 dry; all lampblack is slow to dry in oil. In a less degree this is true of all 
 paints containing carbon, including graphite. Lampblack is used with 
 advantage with red lead; it is also an ingredient of many '* carbon " 
 paints, the base of which is either bone black or artificial graphite. Red 
 lead dries by uniting chemically with the oil to form a cement; it is heavy, 
 ard makes an expensive paint, and is often highly adulterated. Pure red 
 lead has long had a high reputation as a paint for iron and steel, and is 
 still used extensively, especially as a first coat ; but of late years some of 
 the new paints and varnish-like preparations have displaced it toacon* 
 siderable extent even, on the most important work. 
 
 Varnishes. These are made by melting fossil resin, to which is then 
 added from half its weight to three times its weight of refined linseed oil, 
 and the compound is thinned with turpentine; they usually contain a 
 little drier. They are chiefly used on wood, being more durable and 
 more brilliant than oil, and are often used over ptunt to preserve it. 
 Asphaltum is sometimes substituted in part or in whole for the fossil 
 resm, and in this way are made black varnishes which have been used on 
 iron and steel with good results. Asphaltum and substances like it have 
 
 g 
 bl 
 
472 IKON AND STEEL. 
 
 also been simply dissolved in solvents, as benzine or carbon disulphidft, 
 and used for the same purpose. 
 
 All these preservative coatings are supposed to form impervious films, 
 keeping out air and moisture; but in fact all are somewhat porous. On 
 this account it is necessary to have a film of appreciable thickness, best 
 formed by successive coats, so that the pores of one will be closed by the 
 next. The pigment is used to give an agreeable color, to help fill the 
 tiores of the oil film, to make the paint harder, so that it will resist abra- 
 sion, and to make a thicker film. In varnishes these results are sought to 
 be attained by the resin which is dissolved in the oil. There is no sort of 
 agreement among practical men as to which coating is best for any par- 
 ticular case; this is probably because so much depends on the preparation 
 of the surface and the care with which the coating is applied, and also 
 because the conditions of exposure vary so greatly. 
 
 Methods of Application. From the surface of the rretal mud and 
 dirt must be first removed, then any rusty spots must be cleaned thor- 
 oughly; loose scale may be removed with wire brushes, but thick and 
 closely adherent rust must be removed with steel scrapers, or with hammer 
 and chisel if necessary. The sand-blast is used largely and increasingly 
 to clean before painting, and is the best method known. Pickling is 
 usually done with 10% sulphuric acid; the solution is made more active 
 by heating. All traces of acid must be removed by washing, and the 
 metal must be immediately dried and painted. Less than two coats of 
 paint should never be used, and three or four are better. The first paint- 
 ing of metal is the most important. Paint is always thin on angles and 
 edges, also on bolt and rivet heads; after the first full coat apply a partial 
 or striping coat, covering the angles and edges for at least an inch back 
 from the edge, also all bolt and rivet heads. After this is dry apply the 
 second full coat. At least a week should elapse between coats. 
 
 Cast-iron water pipes are usually coated by dipping in a hot mixture of 
 coal-tar and coal-tar pitch; riveted steel pipes by dipping in hot asphalt 
 or by a japan enamel which is baked on at about 400 F. Ships' bottoms 
 are coated with a varnish paint to prevent rusting, over which is a similar 
 paint containing a poison, as mercury chloride, or a copper compound, 
 or else for this second coat a greasy copper soap is applied hot; this 
 prevents the accumulation of marine growths. Galvanized iron and tin 
 surfaces should be thoroughly cleaned with benzine and scrubbed before 
 painting. When new they are partly covered with grease and chemicals 
 used in coating the plates, and these must be removed or the paint will 
 not adhere. 
 
 Quantity of Paint for a Given Surface. One gallon of paint will 
 cover 250 to 400 sq. ft. as a first coat, depending on the character of the 
 surface, and from 350 to 500 sq. ft. as a second coat. 
 
 Qualities of Paints. The Railroad and Engineering Journal, vols. 
 liv. and lv., 1890 and 1891, has a series of articles on paint as applied to 
 wooden structures, its chemical nature, application, adulteration, etc., by 
 Dr. C. B. Dudley, chemist, and F. N. Pease, assistant chemist, of the 
 Penna. R. R. They give the results of a long series of experiments on 
 paints as applied to railway purposes. 
 
 Inoxydation Processes. (Contributed by Alfred Sang, Pittsburg, 
 Pa., 1908.) The black oxide of iron (FesO^ as a continuous coating 
 affords excellent protection against corrosion. Lavoisier (1781) noted its 
 artificial production and its stable qualities. Faraday (1858) observed 
 the protective properties of the coating formed by the action of steam 
 in superheating tubes. Berthier discovered its formation by the action 
 of highly heated air. 
 
 Bower-Barff Process. Dr. Barff s method was to heat articles to be 
 coated to about 1800 F. and inject steam heated to 1000 F. into the 
 muffle. George and A. S. Bower used air instead of steam, then carbon 
 monoxide (producer gas) to reduce the red oxide. In the combined 
 process, the articles are heated to 1600 F. in a closed retort; super- 
 heated steam is injected for 20 min., then producer gas for 15 to 25 min.; 
 the treatment can be repeated to increase the depth of oxidation. Less 
 heat is required for wrought than for cast iron or steel. By a later 
 improvement, steam heated above the temperature of the articles was 
 injected during the last 1 to 2 hours. By a further improvement known 
 as the " Wells Process," the work is finished in one operation, the steam 
 
PKESERVATIVE COATINGS 473 
 
 and producer-gas being injected together. Articles are slightly in- 
 creased in size by the treatment. The surface is gray, changing to 
 black when oiled; it will chip off if too thin; it will take paint or enamel 
 and may be polished, but can not be either bent or machined; the 
 coating itself is incorrodible and resists sea- water, mine- water and acid 
 fumes; the strength of the metal is slightly reduced. The process is 
 extensively used for small hardware. (See F. S. Barff, Jour. I. & S. 
 Inst., 1877, p. 356; A. S. Bower, Trans. A. I. M. E., 1882, p. 329; B. H. 
 Thwaite, Proc. Inst. C. E., 1883, p. 255; George W. Maynard, Trans. 
 A. S. M. E., iv, 351.) 
 
 Gesner Process. Dr. George W. Gesner's process is in commercial 
 operation since 1890. The coating retort is kept at 1200 F. for 20 
 minutes after charging, then steam, partially decomposed by passing 
 through a red-hot pipe, is allowed to act at intervals during 35 min.; 
 finally, a small quantity of naphtha, or other hydrocarbon, is intro- 
 duced and allowed to act for 15 min. The work is withdrawn when the 
 heat has fallen to 800 F. The articles are neither increased in size nor 
 distorted; the loss of strength and reduction of elongation are only 
 slight. Large pieces can be treated. (See Jour. I. cfe S. Inst., 1890 (ii), 
 p. 850; Iron Age, 1890, p. 544.) 
 
 Hydraesfer Process.- -An improvement of the Gesner process pat- 
 ented by J. J. Bradley and in commercial operation. As its name im- 
 plies, the coating is thought to be an alloy of hydrogen, copper, and iron. 
 The sulphides and phosphides are claimed to be burned out of the sur- 
 face of the metal by the action of hydrogen at a high temperature 
 giving additional rust-proof qualities. The appearance of the finished 
 work is that of genuine Bower-Barffing. 
 
 Russia and Planished Iron. Russia iron is made by cementation 
 and slight oxidation. W. Dewees Wood (U. S. Pat. No. 252,166 of 
 1882) treated planished sheets with hydrocarbon vapors or gas and 
 superheated steam within an air-tight and heated chamber. 
 
 Niter Process. An old process improved by Col. A. R. Bufflngton in 
 1884. The articles are stirred about in a mixture of fused potassium 
 nitrate (saltpeter) and manganese dioxide, then suspended in the vapors 
 and finally dipped and washed in boiling water. Pure chemicals are 
 essential. Used for small arms and pieces which cannot stand the high 
 heat of other processes. (Trans. A. S. M. E., vol. vi, p. 628.) 
 
 Electric Process. A. de Meritens connected polished articles as 
 anodes in a bath of warm distilled water and used a current as weak as 
 Could be conducted. A black film of oxide was formed; too strong a 
 current produced rust. It being essential that hydrogen be occluded in 
 the surface of the metal, it was found necessary, as a rule, to connect 
 the articles as cathodes for a short time previous to inoxidation. (Bull. 
 Soc. Intle. des Electr., 1886, p. 230.) 
 
 Aluminum Coatings. Aluminum can be deposited electrically, the 
 main difficulties being the high voltage required and the readiness of the 
 coating to redissolve. The metal-work of the tower of City Hall, Phila- 
 delphia, was coated by the Tacony Iron & Metal Co., Tacony, Pa., with 
 14 oz. per sq. ft. of copper, on which was deposited 2 Y 2 oz. of an alloy of 
 tin and aluminum. The Reeves Mfg. Co., Canal Dover, Ohio, makes 
 aluminum-coated conductor pipes, etc., said to be as durable as copper 
 and as rust-proof as aluminum. 
 
 Galvanizing is a method of coating articles, usually of iron or steel, 
 with zinc. Galvanized iron resists ordinary corroding agencies, the 
 zinc becoming covered with a film of zinc carbonate, which protects the 
 metal from further chemical action. The coating is, however, quickly 
 destroyed by mine- water, tunnel gases, sea- water and conditions that 
 commonly exist in tropical countries. If the work is badly done and the 
 coating does not adhere properly, and if any acid from the pickle or any 
 chloride from the flux remains on the iron, corrosion takes place under 
 the zinc coating. (See M. P. Wood: Trans. A. S. M. E., xvi. 350. Al- 
 fred Sang: Trans. Am. Foundry men's Assoc., 1907, Iron Age, May 23 
 and 30, 1907, and Proc. Eng. Soc. of W. Penna., Nov., 1907.) 
 
 The Penna, R. R, Specifications for galvanized sheets for car roofs 
 
474 IRON AND STEEL. 
 
 (1907) prescribe that the black sheets before galvanizing should weigh 
 16 oz. per sq. ft., the galvanized sheet 18 oz. Sheets will not be accepted 
 if a chemical determination shows less than 1.5 oz. of zinc per sq. ft. 
 
 Hot Galvanizing. The articles to be galvanized are first cleaned by 
 pickling and then dipped in a solution of hydrochloric acid and immersed 
 in a bath of molten zinc at a temperature of from 800 to 900 F.; when 
 they have reached the temperature of the bath, they are withdrawn and 
 the coating is set in water; sal-ammoniac is used on the pot as a flux, 
 either alone or as an emulsion with glycerine or some other fatty medium. 
 Wire, bands and similar articles are drawn continuously through the 
 bath, and may be passed through asbestos wipers to remove the surplus 
 metal; in this case it is advisable to use a very soft spelter free from iron. 
 If wire is treated slowly and passed through charcoal dust instead of 
 wipers the product is known as "double-galvanized." Tin can be added 
 to the bath to help bring out the spangles, but it gives a less durable 
 coating. Aluminum is added as a Zn-Al alloy, with about 20% Al, to 
 give fluidity. Sheets are galvanized continuously, and except in the 
 case of so-called "flux sheets," are put through rolls as they emerge 
 from the bath, to squeeze off the excess of zinc and improve the adherence. 
 
 Test for Galvanized Wire. Sir W. Preece devised the following 
 standard test for the British Post Office: dip for one minute in a saturated 
 neutral, solution of sulphate of copper, wash and wipe; to pass, the 
 material must stand 3 dips. 
 
 The American standard test is as follows: prepare a neutral solution of 
 sulphate of copper of sp. gr. 1.185, dip for one minute, wash and wipe dry; 
 the wire must stand 4 dips without a permanent coating of copper show- 
 ing on any part of the wire. 
 
 Galvanizing by Cementation; Sherardizing. The alloying of metals 
 at temperatures below their melting points has been known since 1820 
 or earlier. Berry (1838) invented a process of depositing zinc, in which 
 the objects to be coated were placed in a closed retort and covered with 
 a mixture of charcoal and powder of zinc; the retort was heated to cherry- 
 red for a longer or shorter period, according to the bulk of the article and 
 to the desired thickness of the coating. Dumas gave iron articles a slight 
 coating of copper by dipping them in a solution of sulphate of copper and 
 then heated them in a closed retort with oxide of zinc and charcoal dust. 
 Sheet steel cowbells are coated with brass by placing them in a mixture 
 of finely divided brass and charcoal dust and heating them to redness in 
 an air-tight crucible. 
 
 S. Cowper-Coles's process, known as Sherardizing, patented in 1902, 
 consists in packing the objects which are to be coated in zinc dust or 
 pulverized zinc to which zinc oxide with a small percentage of charcoal 
 dust is added, and heating in a closed retort to a temperature below the 
 melting point of zinc. A large proportion of sand can be used to reduce 
 the amount of zinc dust carried in the retort, to prevent caking and give 
 a brighter finish; motion of the retort is in most cases necessary to obtain 
 an even coating. The operation lasts from 30 minutes to saveral hours, 
 depending on the size of the drum. Tempered steel is not affected by 
 the process, but surfaces are hardened, there being a zinc-iron alloy 
 formed to a depth varying with the time of treatment. This process is 
 suitable for small work, giving a superior quality of zinc coating. (See 
 Cowper-Coles, " Preservation and Ornamentatio'n of Iron and Steel Sur- 
 faces," Trans. Soc. Engrs. 1905, p. 183; "Sherardizing," Iron Age, 
 1904, p. 12. Alfred Sang, "Theory and Practice of Sherardizing," 
 El. Chem. and Metall. Ind., May, 1907.) 
 
 Lead Coatings. Lead is a good protection for iron and steel pro- 
 vided it is perfectly gas-tight. Electrically deposited lead does not 
 bond well and the coating is porous. Sheets having a light coating of 
 lead, produced by dipping in the molten metal, are known as terne 
 plates; they have no lasting qualities. Lead-lined wrought pipe, fittings 
 and valves are made for conveying acids and Qtber corroding liquids. 
 
STEEL. 475 
 
 STEEL. 
 
 The Manufacture of Steel. (See Classification of Iron and Steel, 
 p. 436.) Cast steel is a malleable alloy of iron, cast from a fluid mass. 
 It is distinguished from cast iron, which is not malleable, by being much 
 lower in carbon, and from wrought iron, which is welded from a pasty 
 mass, by being free from intermingled slag. Blister steel is a highly 
 carbonized wrought iron, made by the "cementation" process, which 
 consists in keeping wrought-iron bars at a red heat for some days in 
 contact with charcoal. Not oyer 2% of C is usually absorbed.' The 
 surface of the iron is covered with small blisters, supposedly due to the 
 action of carbon on slag. Other wrought steels were formerly made by 
 direct processes from iron ore, and by the puddling process from wrought 
 iron, but these steels are now replaced by cast steels. Blister steel is, 
 however, still used as a raw material in the manufacture of crucible steel. 
 Case-hardening is a process of surface cementation. 
 
 Crucible Steel is commonly made in pots or crucibles holding about 
 . 80 pounds of metal. The raw material may be steel scrap; blister steel 
 bars; wrought iron with charcoal; cast iron with wrought iron or with 
 iron 9re; or any mixture that will produce a metal having the desired 
 chemical constitution. Manganese in some form is usually added to 
 prevent oxidation of the iron. Some silicon is usually absorbed from the 
 crucible, and carbon also if the crucible is made of graphite and clay. 
 The crucible being covered, the steel is not affected by the oxygen or 
 sulphur in the flame. The quality of crucible steel depends on the free- 
 
 elements which are added in the mixture, or after melting, to give par- 
 ticular qualities to the steel, such as carbon, manganese, chromium, 
 tungsten and vanadium. 
 
 Bessemer Steel is made by blowing air through a bath of melted pig 
 iron. The oxygen of the air first burns away the silicon, then the carbon, 
 and before the carbon is entirely burned away, begins to burn the iron. 
 Spiegeleisen or ferro-manganese is then added to deoxidize the metal 
 and to give it the amount of carbon desired in the finished steel. In the 
 ordinary or "acid" Bessemer process the lining of the converter is a, 
 silicious material, which has no effect on phosphorus, and all the phos- 
 phorus in the pig iron remains in the steel. In the "basic" or Thomas 
 and Gilchrist process the lining is of magnesian limestone, and limestone- 
 additions are made to the bath, so as to keep the slag basic, and the phos- 
 phorus enters the slag. By this process ores that were formerly unsuited 
 to the manufacture of steel have been made available. 
 
 Open-hearth Steel. Any mixture that may be used for making 
 steel in a crucible may also be melted on the open hearth of a Siemens 
 regenerative furnace, and may be desiliconized and decarbonized by the 
 action of the flame and by additions of iron ore, deoxidized by the addi- 
 tion of spiegeleisen or ferro-manganese, and recarbonized by the same 
 additions or by pig iron. In the most common form of the process pig 
 iron and scrap steel are melted together on the hearth, and after the 
 manganese has been added to the bath it is tapped into the ladle. In the 
 Talbot process a large bath of melted material is kept in the furnace, 
 melted pig iron, taken from a blast furnace, is added to it, and iron ore 
 is added which contributes its iron to the melted metal while its oxygen 
 decarbonizes the pig iron. When the decarbonization has proceeded far 
 enough, ferro-manganese is added to destroy iron oxide, and a portion 
 of the metal is tapped out, leaving the remainder to receive another 
 charge of pig iron, and thus the process is continued indefinitely. In 
 the Duplex Process melted cast iron is desiliconized in a Bessemer con- 
 verter, and then run into an open hearth, where the steel-making opera- 
 tion is finished. 
 
 The open -hearth process, like the Bessemer, may be either acid or 
 basic, according to the character of the lining. The basic process is a 
 dephosphorizing one, and is the one most generally available, as it can 
 use pig irons that are either low or high in phosphorus. 
 
476 
 
 STEEL, 
 
 Belatioh between the Chemical Composition and Physical 
 Character of Steel. 
 
 W. R. Webster (Trans. A. L M. #., vols. xxi and xxii, 1893-4) gives re* 
 suits of several hundred analyses and tensile tests of basic Bessemer steel 
 plates, and from a study of them draws conclusions as to the relation of 
 chemical composition to strength, the chief of which are condensed as 
 follows : 
 
 The indications are that a pure iron, without carbon, phosphorus, man- 
 ganese, silicon, or sulphur, if it could be obtained, would have a tensile 
 fltrength of 34,750 Ibs. per sq. in., if tested in a 3/ 8 -in. plate. With this as a 
 base, a table is constructed by adding the following hardening effects, as 
 shown by increase of tensile strength, for the several elements named. 
 Carbon, a constant effect of 800 Ibs. for each 0.01%. 
 Sulphur, " 500 " " " 0.01%. 
 Phosphorus, the effect is higher in high-carbon than in low-carbon steels. 
 With carbon hun- 
 dred ths % 9 10 11 12 13 14 15 16 17 
 
 Each 0.01% Phas 
 
 an effect of Ibs.. 900 1000 1100 1200 1300.1400 1500 1500 1500 
 Manganese, the effect decreases as the per cent of manganese increases. 
 
 .00 .15 .20 . .25 .30 .35 .40 .45 .50 .55 
 
 to to to to to to to to to to 
 
 ,.15 .20 .25 .30 .35 .40 .45 .50 .55 .65 
 Strength incr. 
 
 forO.01%... 240 240 220 200 180 160 140 120 100 100 Ibs. 
 Total increase 
 
 from Mn. . .3600 4800 5900 6900 7800 8600 9300 9900 10,400 11,400 
 
 Silicon is so low in this steel that its hardening effect has not been con- 
 sidered. 
 
 With the above additions for carbon and phosphorus the following table 
 has been constructed (abridged from the original by Mr. Webster). To 
 the figures given the additions for sulphur and manganese should be made 
 as above. 
 
 Estimated Ultimate Strengths of Basic Bessemer-steel Plates. 
 
 For Carbon, 0.06 to 0.24; Phosphorus, .00 to .10; Manganese and Sulphur, 
 .00 in all cases. 
 
 Mn being per 
 cent 
 
 Carbon. 
 
 0.06 
 
 .08 
 
 .10 
 
 .12 
 
 .14 
 
 .16 
 
 .18 
 
 .20 
 
 .22 
 
 .24 
 
 Phos. .005 
 
 39,950 
 
 41,550 
 
 43,250 
 
 44,950 
 
 46,650 
 
 48,300 
 
 49,900 
 
 51,500 
 
 53,100 
 
 54,700 
 
 .01 
 
 40,350 
 
 41,950 
 
 43,750 
 
 .5,550 
 
 47,350 
 
 49,050 
 
 50,650 
 
 52,250 
 
 53,850 
 
 55,450 
 
 .02 
 
 41,150 
 
 42,750 
 
 44,750 
 
 46,750 
 
 48,750 
 
 50,550 
 
 52,150 
 
 53,750 
 
 55,350 
 
 56,950 
 
 .03 
 
 41,950 
 
 43,550 
 
 45,750 
 
 47,950 
 
 50,150 
 
 52,050 
 
 53,650 
 
 55,250 
 
 56,850 
 
 58,450 
 
 .04 
 
 42,750 
 
 41,350 
 
 46,750 
 
 49,150 
 
 51,550 
 
 53,550 
 
 55,150 
 
 56,750 
 
 58,350 
 
 59,950 
 
 .05 
 
 43,550 
 
 45,150 
 
 47,750 
 
 50,350 
 
 52,950 
 
 55,050 
 
 56,650 
 
 58,250 
 
 59,850 
 
 61,450 
 
 .06 
 
 44,350 
 
 45,950 
 
 48,750 
 
 51,550 
 
 54,350 
 
 56,550 
 
 58,150 
 
 59,750 
 
 61,350 
 
 62,950 
 
 .07 
 
 45,150 
 
 46,750 
 
 49,750 
 
 52,750 
 
 55,750 
 
 58,050 
 
 59,650 
 
 61,250 
 
 62,850 
 
 64,450 
 
 .08 
 
 45,950 
 
 47,550 
 
 50,750 
 
 53,950 
 
 57,150 
 
 59,550 
 
 61,150 
 
 62,750 
 
 64,350 
 
 65,950 
 
 .09 
 
 46,750 
 
 48,350 
 
 51,750 
 
 55,150 
 
 58,550 
 
 61,050 
 
 62,650 
 
 64,250 
 
 65,850 
 
 67,450 
 
 .10 
 0.001 P. = 
 
 47,550 
 80 Ibs. 
 
 49,150 
 80 Ibs. 
 
 52,750 
 100 Ib. 
 
 56,350 
 I201b. 
 
 59,950 
 1401b. 
 
 62,550 
 1501b. 
 
 64,150 
 1501b. 
 
 65,750 
 1501b. 
 
 67,350 
 1501b. 
 
 68,950 
 1501b. 
 
 In all rolled steel the quality depends on the size of the bloom or ingot 
 from which it is rolled, the work put on it, and the temperature at which 
 it is finished, as well as the chemical composition. 
 
 The above table is based on tests of plates 3/ 8 inch thick and under 70 
 inches wide; for other plates Mr. Webster gives the following corrections 
 for thickness and width. They are made necessary only by the effect of 
 thickness and width on the finishing temperature in ordinary practice. 
 Steel is frequently spoiled by being finished at too high a temperature. 
 
STEEL. 477 
 
 Thickness, in . . 
 
 3/4* 
 
 ll/ 16 
 
 5/g 
 
 9/i 6 
 
 1/2 
 
 7/i 6 [ 3/s 
 
 5/i 6 
 
 
 -2000 
 
 -1750 
 
 -1500 
 
 -1250 
 
 -1000 
 
 -500 
 
 4-3000 
 
 Correction (2) 
 
 -1000 
 
 - 750 
 
 - 500 
 
 - 250 
 
 
 
 500|-HOOO 
 
 +5000 
 
 * And over. (1) Plates up to 70 in. wide. (2) Over 70 in. wide. 
 
 Comparing the actual result of tests of 408 plates with the calculated 
 results, Mr. Webster found the variation to range as below. 
 
 Within Ibs. 1000 2000 3000 4000 5000 
 
 Per cent.. .28.4 55.1 74.7 89.9 94.9 
 
 The last figure would indicate that if specifications were drawn calling 
 for steel plates not to vary more than 5000 Ibs. T. S. from a specified 
 figure (equal to a total range of 10,000 Ibs.), there would be a probability 
 of the rejection of 5% of the blooms rolled, even if the whole lot was made 
 from steel of identical chemical analysis. 
 
 Campbell's Formulae. (H. H. Campbell, The Manufacture and Prop- 
 erties of Iron and Steel, p. 387.) 
 
 Acid steel, 40,000 + 1000 C 4- 1000 P 4- xMn = Ultimate strength. 
 Basic steel, 41,500 4- 770 C 4- 1000 P 4- yMn = Ultimate strength. 
 
 The values of xMn and yMn are given by Mr. Campbell in a table, 
 but they may be found from the formulas xMn = 8 CMn 320 C and 
 yMn = 90 Mn 4- 4 CMn - 2700 - 120 C, or, combining the formulae 
 we have: 
 
 Ult. strength, acid steel, 40,000 4- 680 C 4- 1000 P 4- 8 CMn. 
 
 basic " 38,800 4- 650 C 4- 1000 P + 90 Mn + 4 CMn, 
 
 In these formulae the unit of each chemical element is 0.01%. 
 
 Examples. Required the tensile strength of two steels containing 
 respectively C, 0.10, P, 0.10, Mn, 0.30, and C, 0.20, P, 0.10, Mn, 0.65. 
 
 Answers, by Webster, 59,650 and 77,150; by Campbell, 57,700 and 72,850. 
 
 Low Tensile Strength of Very Pure Steel . Swedish nail-rod 
 open-hearth steel, tested by the author in 1881, showed a tensile strength of 
 only 42,591 Ibs. per sq. in. A piece of American nail-rod steel showed 
 45,021 Ibs. per sq. in. Both steels contained about 0.10 C and 0.015 P, 
 and were very low in S, Mn, and Si. The pieces tested were bars about 
 2 x 3/ 8 in. section. 
 
 R. A. Hadfield (Jour. Iron and Steel Inst., 1894) gives the strength of 
 very pure Swedish iron, remelted and tested as cast, 45,024 Ibs. per sq. 
 in.; remelted and forged, 47,040 Ibs. The analysis of the cast bar was: 
 C, 0.08; Si, 0.04; S, 0.02; P, 0.02; Mn, 0.01; Fe, 99.82. 
 
 " Arinco Ingot Iron." A very pure variety of open-hearth steel, 
 made by the American Rolling Mill Co., Middletown, Ohio, has been 
 given the trade name of Armco-American Ingot Iron. It is claimed 
 for this product that it resists corrosion better than any other grade of 
 wrought iron or steel. It is used chiefly in sheets. The tensile strength 
 is given as 38,000 to 44,000 Ib. per square inch; elastic limit one half 
 the ultimate strength; elongation in 8 inches, 22%. The following 
 analyses are given to show how Armco compares in composition with 
 other iron products: 
 
 S P C Mn Si Cu O H N Fe 
 
 Armco 020 .003 .011 .019 .002 .025 .022 .001 .004 99.893 
 
 Puddled Iron. . .024 .155 .040 .040 .050 .025 .150 .001 .005 99.510 
 
 ^ Mild Steel 050 .070 .115 .500 .005 .055 .023 .002 .009 99.171 
 
 High Carb. Steel .030 .030 1.000 .450 .150 .055 .025 .001 .006 98.253 
 
 Effect of Oxygen upon Strength of Steel. A. Lantz, of the 
 Peine works, Germany, in a letter to Mr. Webster, says that oxygen plays 
 an important role such that, given a like content of C, P, and Mn, a 
 blow with greater oxygen content gives a greater hardness and less ductility 
 than a blow with less oxygen content. The method used for determin- 
 ing oxygen is that 9f Prof. Ledebur, given in Stahl und Eisen, May, 1892, 
 p. 193. The variation in O may make a difference in strength 01 nearly 
 1/2 ton per sq. in. (Jour. I. and S. /., 1894.) 
 
 Electric Conductivity of Steel. Louis Campredon reports in Le 
 Genie Civil [prior to 1895] the results of experiments on the electric resist- 
 ance of steel wires of different composition, ranging from 0.09 to 0.14 C; 
 0.21 to 0.54 Mn; Si, S, and P low. The figures show that the purer and 
 
478 
 
 STEEL. 
 
 softer the steel the better is its electric conductivity, and, furthermore, that 
 manganese is the element which most influences the conductivity. The 
 results may be expressed by the formula R = 5.2 + 6.2S 0.3; in which 
 R = relative resistance, copper being taken as 1 , and S = the sum of the 
 percentages of C, P, S, Si, and Mn. The conclusions are confirmed by 
 J. A. Capp, in 1903, Trans. A. I. M. E., vol. xxxiv, who made forty-five 
 experiments on steel of a wide range of composition. His results may be 
 expressed by the formula R = 5.5 + 4>S> 1. High manganese increases 
 the resistance at an increasing rate. Mr. Capp proposes the following 
 specification for steel to make a satisfactory third rail, having a resistance 
 eight times that of copper: 0,0.15; Mn, 0.30; P, 0.06; S, 0.06; Si, 0.05; 
 none of these figures to De exceeded. 
 
 Range of Variation in Strength of Bessemer and Open-Hearth 
 Steels. 
 
 The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bes- 
 semer and open-hearth steel from which the following figures are selected 
 
 Kind of Steel. 
 
 $ 
 
 Elastic Limit. 
 
 Ultimate 
 Strength. 
 
 Elongation, 
 Per cent 
 in 8 In. 
 
 High't. 
 
 Lowest. 
 
 High't. 
 
 Lowest. 
 
 High't. 
 
 Lowest. 
 
 (a) Bess, structural . 
 (&) " 
 (c) angles .... 
 (d) O. H. firebox . . . 
 (e) O. H. bridge... . 
 
 100 
 170 
 72 
 25 
 20 
 
 46,570 
 47,690 
 41.890 
 
 39,230 
 39,970 
 32,630 
 
 71,300 
 73,540 
 63,450 
 62,790 
 69,940 
 
 61,450 
 65,200 
 56,130 
 50,350 
 63,970 
 
 33.00 
 3.0.25 
 34.30 
 36.00 
 30.00 
 
 23.75 
 23.15 
 26.25 
 25.62 
 22.75 
 
 
 
 REQUIREMENTS OF SPECIFICATIONS. 
 
 a) E. L., 35,000; T. S., 62,000 to 70,000; elong., 22% in Sin. 
 
 b) E. L., 40,000; T. S., 67,000 to 75,000. 
 
 c) E. L., 30,000; T. S., 56,000 to 64,000; elong., 20% in 8 in. 
 
 d) T. S., 50,000 to 62,000; elong., 26% in 4 in. 
 
 e) T. S., 64,000 to 70,000; elong., 20% in 8 in. 
 
 Bending Tests of Steel. (Pencoyd Iron Works.) Steel below 0.10 C 
 should be capable of doubling flat without fracture, after being chilled 
 from a red heat in cold water. Steel of 0.15 C will occasionally submit 
 to the same treatment, but will usually bend around a curve whose radius 
 is equal to the thickness of the specimen; about 90% of specimens stand 
 the latter bending test without fracture. As the steel becomes harder its 
 ability to endure this bending test becomes more exceptional, and when 
 the carbon becomes 0.20 little over 25% of specimens will stand the last- 
 described bending test. Steel having about 0.40% C will usually harden 
 sufficiently to cut soft iron and maintain an edge. 
 
 EFFECT OF HEAT TREATMENT AND OF WORK ON STEEL. 
 
 Low Strength Due to Insufficient Work. (A. E. Hunt, Trans. 
 A. I. M. E., 1886.) Soft steel ingots, made in the ordinary way for 
 boiler plates, have only from 10,000 to 20,000 Ibs. tensile strength per sq. 
 in., an elongation of only about 10% in 8 in., and a reduction of area of 
 less than 20%. Such ingots, properly heated and rolled down from 10 in. 
 to 1/2 in. thickness, will give from 55,000 to 65,000 Ibs. tensile strength, an 
 elongation in 8 in. of from 23% to 33%, and a reduction of area of from 
 55% to 70%. Any work stopping short of the above reduction in thick- 
 ness ordinarily yields intermediate results in tensile tests. 
 
 Effect of Finishing Temperature in Rolling. The strength and 
 ductility of steel depend to a high degree upon fineness of grain, and 
 this may be obtained by having the temperature of the steel rather low, 
 say at a dull red heat, 1300 to 1400 F., during the finishing stage of 
 rolling. In the manufacture of steel rails a great improvement in quality 
 has been obtained by finishing at a low temperature. An indication of 
 the finishing temperature is the amount of shrinkage by cooling after 
 leaving the rolls. The Phila. & Reading Railway Co.'s specification for 
 rails (1902) says, "The temperature of the ingot or bloom shall be such 
 that with rapid rolling and without holding before or in the finishing 
 passes or subsequently, and without artificial cooling after leaving the 
 
EFFECT OF HEAT TREATMENT ON STEEL. 
 
 479 
 
 last pass, the distance between the hot saws shall not exceed 30 ft. 6 in. 
 for a 30-ft. rail." 
 
 Fining the Grain by Annealing. Steel which is coarse-grained 
 on account of leaving the rolls at too high a temperature may be made 
 fine-grained and have its ductility greatly increased without lowering its 
 tensile strength by reheating to a cherry-red and cooling at once in air. 
 (See paper on "Steel Rails," by Robert Job, Trans. A. I. M. E. t 1902.) 
 
 Effect of Cold Rolling. Cold rolling of iron and steel increases the 
 elastic limit and the ultimate strength, and decreases the ductility. 
 Major Wade's experiments on bars rolled and polished cold by Lauth's 
 process showed an average increase of load required to give a slight per- 
 manent set as follows: Transverse, 162%; torsion, 130%; compression, 
 161% on short columns 11/2 in. long, and 64% on columns 8 in. long; 
 tension, 95%. The hardness, as measured by the weight required to 
 produce equal indentations, was increased 50%; and it was found that 
 the hardness was as great in the center of the bars as elsewhere. Sir 
 W. Fairbairn's experiments showed an increase in ultimate tensile 
 strength of 50%, and a reduct on in the elongation in 10 in. from 2 in. 
 or 20 % to 0.79 in. or 7.9 % . 
 
 Effect of Heat Treatment of a Motor-truck Axle. (John Younger, 
 Trans., A. S. M. E., 1915.) Shafts 21/4 in. diam. whose analysis was 
 approximately C,.0.20; Cr, 1.5; Mn, 0.30; Ni, 4.00; Si, 0.20; P and S 
 below 0.04; elastic limit, 90,000; tensile strength, 105,000; reduction in 
 area, 66%; elongation in 2 in., 25%, were found to break in service. 
 The maximum power transmittted was about 33 H.P. at 27 r.p.m 
 Experiments were made with heat treatment to raise the elastic limit. 
 The material selected had C, 0.30; Mn, 0.50; Cr, 1.5; Ni, 3.5. After 
 heat treatment the elastic limit was 175,000 Ib. per sq. in.; tensile 
 strength, 185,000; elongation in 2 in., 14 % ; reduction of area, 53 %. The 
 shafts are machined from hot-rolled bars already heat-treated to show 
 an elastic limit of about 100,000. They are then heated to between 
 1450 and 1500 F. and quenched in oil, then reheated to a little over 
 700 F. and cooled slowly in air. They warped slightly, but were 
 straightened when hot under a press. The Brinell hardness after 
 treatment was 402 to 444. Not one of the shafts thus treated has 
 broken in service. Other steels, such as 5% nickel steels, chrome- 
 vanadium steels, and air-hardening steels have been tried, and all have 
 been standing up to service. The success seems to be due entirely to 
 the high elastic limit. The Brinell hardness test is an unfailing indication 
 of the success or non-success of the heat treatment. 
 
 Effect of Annealing on Rolled Bars. (Campbell, Mfr. of Iron and 
 Steel, 'p. 275.) 
 
 Ultimate 
 Strength. 
 
 Elastic 
 Limit 
 
 Elong. in 
 8 in., %. 
 
 Red. Area, 
 
 Elas. 
 Ratio. 
 
 Natural. 
 
 An- 
 nealed. 
 
 Nat- 
 ural. 
 
 An- 
 nealed. 
 
 Nat- 
 ural. 
 
 An- 
 nealed. 
 
 Nat- 
 ural. 
 
 An- 
 nealed. 
 
 Nat- 
 ural. 
 
 An- 
 nealed* 
 
 d ^ T58.568 
 HI I 62,187 
 -^0} 70,530 
 M 176,616 
 co.5 ( 58,130 
 J J 62,089 
 X 1 69,420 
 <N.S ( 75,865 
 
 54,098 
 58,364 
 65,500 
 69,402 
 51,418 
 55,021 
 60,850 
 67,618 
 
 40,300 
 42,606 
 49,000 
 51,108 
 40,400 
 42,441 
 45,090 
 49,691 
 
 31,823 
 35,120 
 37,685 
 40,505 
 30,393 
 31,576- 
 34,000 
 39,403 
 
 29.7 
 28.0 
 26.9 
 24.5 
 30.1 
 30.1 
 25.6 
 24.7 
 
 28.8 
 28.6 
 23.4 
 23.0 
 31.1 
 30.4 
 26.5 
 26.3 
 
 60.8 
 62.2 
 61.1 
 53.7 
 61.8 
 60.9 
 59.3 
 54.4 
 
 62.7 
 63.5 
 55.3 
 56.5 
 60.5 
 60.0 
 52. 1 
 51.4 
 
 68.8 
 68.5 
 69.5 
 66.7 
 69.5 
 68.4 
 65.0 
 65.5 
 
 58.8 
 60.2 
 57.5 
 58.4 
 59.1 
 57.4 
 55.9 
 58.3 
 
 The bars were rolled from 4 X 4-in. billets of open-hearth steel. The 
 figures are averages of from 2 to 12 tests of each heat. In annealing the 
 bars were heated in a muffle and withdrawn when they had reached a 
 dull yellow heat. 
 
 Hardening of Soft Steel. A. E. Hunt (Trans. A. I. M. E., 1883, vol. 
 xii) says that soft steel, no matter how low in carbon, will harden to a cer- 
 tain extent upon being heated red-hot and plunged into water, and that it 
 hardens more when plunged into brine and less when quenched in oil. 
 
 A heat of open-hearth steel of 0.15% C and 0.29% Mn gave the follow- 
 ing results upon test-pieces from the same 14 in. thick plate. 
 
480 STEEL. 
 
 Unhardened T. S. 55,000 El. in 8 in. 27% Red. of Area 62% 
 
 Hardened in water 74,000 25% 50% 
 
 Hardened in brine " 84,000 " 22% 43% 
 
 Hardened in oil ' 67,000 26% 49% 
 
 The greatly increased tenacity after hardening indicates that there must 
 be a considerable molecular change in the steel thus hardened, and that 
 if such a hardening should be created locally in a steel plate, there must 
 be very dangerous internal strains caused thereby. 
 
 Comparative Tests of Full-sized Eye-bars and Small Samples. 
 (G. G. S. Morison, A. S. C. E., 1893.) 17 full-sized eye-bars, of the steel 
 used in the Memphis bridge, sections 10 in. wide X 1 to 23/iQ in. thick, and 
 sample bars from the same melts. Average results: 
 
 Eye-bars: E. L., 32,350; T. S., 63,330; El. in full length, 13.7%; Red. 
 of area, 36.3%. 
 
 Small bars: E. L., 40,650; T. S., 71,640; El. in 8 ins., 26.2%; Red. 
 of area, 46.7%. 
 
 " Kecalescence " of Steel. If we heat a bar of copper by a flame 
 of constant strength, and note carefully the interval of time occupied in 
 passing from each degree to the next higher degree, we find that these in- 
 tervals increase regularly, i.e., that the bar heats more and more slowly, 
 as its temperature approaches that of the flame. If we substitute a bar of 
 steel for one of copper, we find that these intervals increase regularly up 
 to a certain point, when the rise of temperature is suddenly and in most 
 cases greatly retarded or even completely arrested. After this the regular 
 rise of temperature is resumed, though other like retardations may recur 
 as the temperature rises farther. So if we cooi a bar of steel slowly the 
 fall of temperature is greatly retarded when it reaches a certain point in 
 dull redness. If the steel contains much carbon, and if certain favoring 
 conditions be maintained, the temperature, after descending regularly, 
 suddenly rises spontaneously very abruptly, remains stationary a while 
 and then redescends. This spontaneous reheating is known as " recales- 
 cence." 
 
 These retardations indicate that some change which absorbs or evolves 
 heat occurs within the metal. A retardation while the temperature is 
 rising points to a change which absorbs heat; a retardation during cooling 
 points to some change which evolves heat. (Henry M. Howe, on "Heat 
 Treatment of Steel," Trans. A. L M. E., vol. xxii.) 
 
 Critical Point. (Campbell, p. 287.) If a piece of steel containing over 
 0.50 C be allowed to cool slowly from a high temperature the cooling at 
 first proceeds at a uniformly retarded rate, but when about 700 C. is 
 reached there is an interruption of this regularity. In some cases the 
 rate of cooling may be very slow, in other cases the bar may not decrease 
 in temperature at all, while in still other cases the bar may actually grow 
 hotter for a moment. When this " critical point " is passed, the bar cools 
 as before until it reaches the temperature of the atmosphere. 
 
 In metallography such a critical point is denoted by the letter A, and 
 the particular one just described is known as Ar. In heating a piece of 
 steel an opposite phenomenon is observed, there being an absorption of 
 heat by internal molecular actipn, with a consequent retardation in the 
 rise of temperature, and this point, which is some 30 C. higher than Ar, 
 is called Ac. 
 
 In soft steels, below 0.30 C, three critical points are found in cooling a 
 bar from a high temperature, called Ar 3 , Ar 2 , Ari, Ar t being the lowest, 
 and in heating the bar there are also three points, Aci, Ac 2 , Ac 3 , the first 
 named being the lowest. At each of the points there is a change in the 
 micro-structure of the steel. 
 
 Metallography. This is a name given to a study of the micro-structure 
 of metals. The steel metallographist designates the different structures 
 that are found in a polished and etched section by the names austenite, 
 martensite, pearlite, cementite, ferrite, troostite, and sorbite. Austenite 
 is produced by quenching steel of over 1.40 C in ice water from above 
 1050 C. Martensite is produced by quenching this steel from tempera- 
 tures between 1050 C. and Ari. It is also found together with cementite 
 or ferrite in carbon steels below 1.30 C quenched at any point above Ar^ 
 It is the constituent which confers hardness on steel. In steels cooled 
 slowly to below Ari the structure is composed entirely of ferrite, or 
 entirely of pearlite, or of pearlite mixed with ferrite or cementite. Ferrite 
 
EFFECT OF HEAT TREATMENT ON STEEL. 
 
 481 
 
 Is iron free from carbon and forms almost the whole of a low-carboiT steel, 
 while cementite is considered to be a compound of iron and carbon, FesC, 
 the C of this form being known as cement carbon. Pearlite is an inti- 
 mate mixture of definite proportions of ferrite and cementite, corre- 
 sponding to a pure steel of about 0.80 C, which, unhardened, consists of 
 pearlite alone. Steels lower in C contain pearlite with ferrite, and steels 
 higher in C contain pearlite and cementite. Troostite is a structure found 
 when steel is quenched while cooling through the critical range, and 
 sorbite when it is quenched at the end of the critical range. Quenching 
 in lead or reheating quenched steel to a purple tint may also produce 
 sorbite. (Campbell, p. 296.) 
 
 Effect of Work on the Structure of Soft and Medium Steel. Steel 
 as usually cast, cooling slowly, forms in crystals or grains. Rolling tends 
 to break up this grain, but immediately after the cessation of work the 
 formation of grains begins and continues until the metal has copied to 
 the lower critical point. Hence the lower the temperature to which the 
 steel is worked, the more broken up the structure will be, but on the 
 other hand if the rolling be continued below the critical point, the effect 
 of cold work will be shown and strains will be set up which will make the 
 piece unfit for use without annealing. 
 
 Effect of Heat Treatment. In heating steel through the lowest 
 critical point the crystalline structure is obliterated, the metal assuming the 
 finest condition of which it is capable. Above this point the size of grain 
 increases with the temperature. 
 
 Effect of Heating on Crucible Steel. (W. Campbell, Proc. A.S.T. M., 
 vi, 213.) Six steels, containing carbon as follows: (1) 2.04, (2) 1.94, 
 (3) 1.72, (4) 1.61, (5) 1.04, and (6) 0.70, were heated in a small gas 
 furnace to the temperatures given in the table and allowed to cool 
 slowly in the furnace, and were then tested, with results as below. 
 
 
 As 
 Rolled 
 
 650 
 C 
 
 715 
 C 
 
 760 
 C 
 
 800 
 C 
 
 855 
 C 
 
 905 
 C 
 
 950 
 C 
 
 1070 
 C 
 
 1200 
 C 
 
 (1) T.S.. 
 
 144000 
 
 115400 
 
 114500 
 
 98800 
 
 95650 
 
 93800 
 
 95250 
 
 95200 
 
 99000 
 
 57400 
 
 E.L 
 
 104200 
 
 84600 
 
 83900 
 
 57700 
 
 57800 
 
 55500 
 
 55350 
 
 49350 
 
 49600 
 
 56000 
 
 El. in 2 in 
 
 4.0 
 
 6.0 
 
 7.0 
 
 11.5 
 
 12.5 
 
 12.0 
 
 11.5 
 
 6.0 
 
 4.5 
 
 1.0 
 
 (2) T.S.. 
 
 146400 
 
 115200 
 
 104100 
 
 95000 
 
 92000 
 
 89000 
 
 95350 
 
 91800 
 
 97000 
 
 61350 
 
 E.L 
 
 91000 
 
 91500 
 
 72600 
 
 68650 
 
 50500 
 
 51000 
 
 49450 
 
 49800 
 
 41750 
 
 47000 
 
 El. in 2 in 
 
 6.3 
 
 8.0 
 
 9.5 
 
 15.0 
 
 17.0 
 
 12.5 
 
 7.0 
 
 9.5 
 
 8.5 
 
 2.0 
 
 (3) T.S.. 
 
 153100 
 
 126000 
 
 114100 
 
 100300 
 
 98000 
 
 94000 
 
 94350 
 
 95000 
 
 92350 
 
 65300 
 
 E.L 
 
 98100 
 
 78300 
 
 75700 
 
 50500 
 
 48750 
 
 47900 
 
 48600 
 
 45200 
 
 43100 
 
 50600 
 
 El. in 2 in 
 
 7.2 
 
 8.0 
 
 11.5 
 
 16.5 
 
 10.0 
 
 13.5 
 
 11.0 
 
 7.5 
 
 6.0 
 
 2.0 
 
 (4) T. S. . 
 
 157700 
 
 128100 
 
 117000 
 
 98650 
 
 97700 
 
 95000 
 
 97350 
 
 96350 
 
 94400 
 
 69800 
 
 E.L 
 
 105200 
 
 85300 
 
 81300 
 
 52300 
 
 53350 
 
 51350 
 
 51350 
 
 48500 
 
 51400 
 
 
 El. in 2 in 
 
 6 5 
 
 
 14 5 
 
 
 18 5 
 
 15 
 
 11 5 
 
 7 5 
 
 3 5 
 
 30 
 
 (5) T.S.. 
 
 141100 
 
 105400 
 
 97800 
 
 86800 
 
 96600 
 
 111800 
 
 115900 
 
 111500 
 
 106100 
 
 112600 
 
 EL 
 
 75800 
 
 57700 
 
 55200 
 
 44850 
 
 46600 
 
 47200 
 
 50600 
 
 46800 
 
 56500 
 
 89600 
 
 El. in 2 in. 
 
 12.8 
 
 18.0 
 
 22.0 
 
 26.5 
 
 19.0 
 
 13.0 
 
 13.0 
 
 10.5 
 
 11.0 
 
 11.5 
 
 (6) T.S... 
 
 117000 
 
 95200 
 
 88700 
 
 85600 
 
 94300 
 
 91350 
 
 90300 
 
 90500 
 
 89500 
 
 90000 
 
 E. L 
 
 64700 
 
 53250 
 
 49700 
 
 40200 
 
 42150 
 
 42100 
 
 41400 
 
 39700 
 
 57350 
 
 58500 
 
 El. in 2 in. 
 
 17.0 
 
 23.0 
 
 27.5 
 
 27.0 
 
 19.0 
 
 18.5 
 
 18.0 
 
 16.5 
 
 18.0 
 
 16.0 
 
 The critical points Ari and Aci were determined, and the six steels gave 
 practically identical results; thus Ar t ranged from 696 to 708, averaging 
 704 C., and Ac t ranged from 730 to 737, averaging 733 C. 
 
 The temperatures at which the finest-grained and a very coarse-grained 
 fracture were found are as follows: 
 
 Steel No 123 456 
 
 Finest fracture 800 760 715-760 760 715 715 C 
 
 Very coarse fracture 1070 1070 1070 1070 855 800 O 
 
 Mr. Campbell's paper gives a list of fourteen papers by different authori- 
 ties on the micro-structure and the heat treatment of steel. 
 
 Burning, Overheating, and Restoring Steel. (G. B. Waterhouse, 
 A. S. T, M., vi, 247.) Burnt metal is defined as coarsely crystalline and 
 exceedingly brittle iron or steel, in consequence of excessive heating, 
 often with some layers of oxide of iron. It cannot be effectively restored 
 by heat treatment or mechanical work. Overheated metal is coarsely 
 crystalline from excessive heating, but with, no inter-crystalline spaces. 
 It oan be restored by heat treatment or mechanical worfc. Seven lots of 
 
'482 
 
 STEEL: 
 
 nickel steel bars, containing 3.8% Ni, and C as in the table, 
 to various temperatures in a muffle furnace, with results as 
 
 were heated 
 below. 
 
 %c. 
 
 Heated to. . , 
 
 lOOOa 
 
 lOOOb 
 
 llOOb 
 
 1200b 
 
 13COb 
 
 1200c 
 
 1200d 
 
 41 
 
 T. S. . . . 
 
 90245 
 
 71800 
 
 71700 
 
 74000 
 
 71320 
 
 71487 
 
 74989 
 
 
 El. % in 2 in... 
 
 26 
 
 26 
 
 25 5 
 
 11 
 
 7 
 
 10 5 
 
 25 
 
 0.51 
 
 T.S 
 
 99109 
 
 78600 
 
 78800 
 
 84900 
 
 79600 
 
 81487 
 
 80795 
 
 
 El. % in 2 in... 
 
 21 
 
 25 
 
 24 
 
 11 5 
 
 5 
 
 15 5 
 
 22 5 
 
 0.63 
 
 
 11542! 
 
 89000 
 
 89400 
 
 99600 
 
 85200 
 
 96040 
 
 89842 
 
 
 El. % in 2 in 
 
 16 5 
 
 20 5 
 
 19 
 
 7 
 
 2 
 
 10 
 
 21 
 
 0,79 
 
 
 135194 
 
 108960 
 
 111840 
 
 109600 
 
 66800 
 
 102705 
 
 90214 
 
 
 El. % in 2 in... 
 
 14 
 
 15 
 
 14 
 
 3 
 
 5 
 
 6 
 
 21 
 
 0.97 
 
 T.S.... 
 
 156827 
 
 130336 
 
 138112 
 
 83117 
 
 46648 
 
 114107 
 
 103476 
 
 
 El. % in 2 in.... 
 
 7 5 
 
 
 3 5 
 
 5 
 
 
 
 5 5 
 
 18 
 
 1,24 
 
 T.S..... 
 
 168697 
 
 97510 
 
 98183 
 
 90729 
 
 60600 
 
 95103 
 
 106304 
 
 
 El. in 2 in... 
 
 3 5 
 
 15 
 
 1 
 
 5 
 
 
 
 1 5 
 
 3 5 
 
 f 48 
 
 T. S... 
 
 145642 
 
 63950 
 
 66640 
 
 97894 
 
 35480 
 
 89045 
 
 74592 
 
 
 El. in 2 in 
 
 10.5 
 
 23.6 
 
 25.0 
 
 8.0 
 
 1.0 
 
 17.5 
 
 24.0 
 
 a. Heated to 1000 C., which took 1 hr. 25 min., held tnere 25 mm. and 
 cooled in air. b. The time required to heat to the temperatures named 
 was respectively 1 h. 10 m., 1 h. 45 m., 2 h. 35 m., and 2 h. 35 m. The 
 bars were kept at the desired temperature for an hour and then cooled 
 slowly in place, c. Reheated to 700 C. d. Reheated to 775 C. 
 
 In the steels below 1% C heating to 1200 is accompanied by an increase 
 in ultimate strength and a drop in ductility. Heating above 1200 pro- 
 duces a very coarse crystallization and a great loss in strength and 
 ductility. Reheating the overheated bars to 700 does not materially 
 affect their structure, but reheating to 775 restores the structure nearly 
 to that found before overheating, and completely restores the ductility. 
 Similar results are found with carbon steel. 
 
 Working Steel at a Blue Heat. Not only are wrought iron and 
 Bteelmuch more brittle at a blue heat (i.e., the heat that would produce an 
 oxide coating ranging from light straw to blue on bright steel, 430 to 
 600 F.), but while they are probably not seriously affected by simple 
 exposure to blueness, even if prolonged, yet if they be worked in this range 
 of temperature they remain extremely brittle after cooling, and may 
 Indeed be more brittle than when at blueness; this last point, however, 
 is not certain. (Howe, Metallurgy of Steel, p. 534.) 
 
 Tests by Prof. Krohn, for the German State Railways, show that wprk- 
 ing at blue heat has a decided influence on all materials tested, the injury 
 done being greater on wrought iron and harder steel than on the softer 
 Bteel. The fact that wrought iron is injured by working at a blue heat 
 was reported by Stromeyer. (Engineering News, Jan. 9, 1892.) 
 
 A practice among boiler-makers for guarding against failures due to 
 working at a blue heat consists in the cessation of work as soon as a plate 
 which had been red-hot becomes so cool that the mark produced by 
 rubbing a hammer-handle or other piece of wood will not glow. A plate 
 which is not hot enough to produce this effect, yet too hot to be touched 
 by the hand, is most probably blue hot, and should under no circumstances 
 be hammered or bent. (C. E. Stromeyer, Proc. Inst. C. E., 1886.) 
 
 Oil-tempering and Annealing of Steel Forcings. H. F. J. Porter 
 says (1897) that all steel forgings above 0.1% carbon should be annealed, 
 to relieve them of forging and annealing strains, and that the process 
 of annealing reduces the elastic limit to 47% of the ultimate strength. 
 Oil-tempering should only be practiced on thin sections, and large forgings 
 should be hollow for the purpose. This process raises the elastic limit 
 above 50% of the ultimate tensile strength, and in some alloys of steel, 
 notably nickel steel, will bring it up to 60% of the ultimate. 
 
 Heat Treatment of Armor Plates. (Hadfleld Process, Iron Tr. 
 Rev., Dec. 7, 1905.) A cast armor plate of nickel-chromium steel is 
 heated to from 950 C. to 1100 C., then cooled, preferably in air, then 
 reheated to about 700 and cooled slowly, preferably in the furnace m 
 which the heating was previously effected, again heated to about 700 
 and allowed to cool slowly to 640 C., whereupon it is suddenly cooled by 
 spraying with water or by an air blast, but preferably in water. It is 
 then reheated to about 600 and again suddenly cooled, preferably by 
 quenching in water. Steel treated as described is suitable for armor 
 plates and other articles including parts of safes, Satisfactory results 
 
TKEATMENT OF STRUCTURAL STEEL. 483 
 
 have been obtained by thus treating cast 6-in. armor plates containing 
 about 0.3 to 0.4 C, 0.25 Mn, 1.8 Cr, and 3.3 Ni cast in a sand mold. 
 Such a 6-in. plate attacked by armor-piercing projectiles of 4.7-in. and 
 6-in. calibers, stood over 15,000 foot-tons of energy without showing a 
 crack. Also a 4-in. plate treated as described and having a carbonized 
 or cemented face has withstood the attack of a 5.7-in. armor-piercing shell. 
 
 Brittleness Due to Long-continued Heating. If low-carbon steel, 
 (say under 0.15%) is held for a very long time at temperatures between 
 500 and 750 C. (930 and 1380 F.), the crystals become enormous and 
 the steel loses a large part of its strength and ductility. It takes a long time, 
 in fact days, to produce this effect to any alarming degree, so that it is 
 not liable to occur during manufacture or mechanical treatment, but 
 steel is sometimes placed in positions where it may suffer this injury, for 
 example, in the case of the tie-rods of furnaces, supports of boilers, etc., 
 so that the danger should be borne in mind by all engineers and users of 
 steel. A wrought-iron chain that supported one side of a 50-ton open- 
 hearth ladle, which was heated many times to a temperature above 500 C., 
 finally reached a condition of coarse crystallization, so that it was unable 
 to bear the strain upon it. This phenomenon ol coarse crystallization in 
 low-carbon steel is known as "Stead's Brittleness," after J. E. Stead, who 
 has explained its cause. The effect seems to begin at a temperature of 
 about 500 C. and proceeds more rapidly with. an increase in temperature 
 until we reach 750 C. The damage may be repaired completely by heat- 
 ing the steel to a temperature between 800 and 900 C. The remedy is 
 the same as that for coarse crystallization, due to overheating, and all 
 steel which is placed in positions where it is liable to reach these tempera- 
 tures frequently should be restored at intervals of a week or a month, or 
 as often as may be necessary. (Stoughton.) 
 
 Surface Decarburization of Steel Heated in Melted Salts. A. M. 
 Portevin (Proc. Iron & Steel Inst., 1914. Eng'g, Oct. 9, 1914) shows 
 that the surface layer of steel, to a depth which varies with time and 
 temperature, is greatly reduced in carbon when the steel is heated in 
 a bath of molten alkaline salts. In a steel containing 0.78 % C heated 
 in melted potassium chloride at 900 C., the C at the surface was re- 
 duced in 1/4 hour to 0.5, in 2 hours to 0.3, and in 5 hours to 0.15, the 
 thickness of the decarburized layer being for 1/4, 2, and 5 hours heating, 
 respectively, 0.1, 0.2, and 0.3 mm. When cyanide and cyanate of 
 potassium were added to the chloride decarburization and recarburiza- 
 tion took place simultaneously, the percentage of carbon at the surface 
 being 0.25 at the end of both 1/4 hour and 5 hours, the thickness of the 
 decarburized layer increasing from 0.06 mm. to 0.69 mm. 
 
 Influence of Annealing upon Magnetic Capacity. 
 
 Prof. D. E. Hughes (Eng'g, Feb. 8, 1884, p. 130) has invented a "Mag- 
 netic Balance," for testing the condition of iron and steel, which consists 
 chiefly of a delicate magnetic needle suspended over a graduated circular 
 index, and a magnet coil for magnetizing the bar to be tested. He nnda 
 that the following laws hold with every variety of iron and steel: 
 
 1. The magnetic capacity is directly proportional to the softness, or 
 molecular freedom. 
 
 2. The resistance to a feeble external magnetizing force is directly as 
 the hardness, or molecular rigidity. 
 
 The magnetic balance shows that annealing not only produces softness 
 in iron, and consequent molecular freedom, but it entirely frees it from 
 all strains previously introduced by drawing or hammering. Thus a bar 
 of iron drawn or hammered has a peculiar structure, say a fibrous one, 
 which gives a greater mechanical strength in one direction than another. 
 This bar, if thoroughly annealed at high temperatures, becomes homo- 
 geneous in all directions, and has no longer even traces of its previous 
 strains, provided that there has been no actual separation into a distinct 
 series of fibers. 
 
 TREATMENT OF STRUCTURAL STEEL. 
 (James Christie, Trans. A. S. C. E., 1893.) 
 
 Effect of Punching and Shearing. The physical effects of punching 
 and shearing as denoted by tensile test are for iron or steel: 
 
 Reduction of ductility; elevation of tensile strength at elastic limit; 
 reduction of ultimate tensile strength. 
 * In very thin material the disturbance described is less than in thick; 
 
484 STEEL. 
 
 In fact, a degree of thinness is reached where this disturbance practi- 
 cally ceases. On the contrary, as thickness is increased the injury becomes 
 more evident. 
 
 The effects described do not invariably ensue; for unknown reasons there 
 are sometimes marked deviations from what seems to be a general result. 
 
 By thoroughly annealing sheared or punched steels the ductility is to a 
 large extent restored and the exaggerated elastic limit reduced, the change 
 being modified by the temperature of reheating and the method of cooling. 
 
 It is probable that the best results combined with least expenditure can 
 be obtained by punching all holes where vital strains are not transferred by 
 the rivets, and by reaming for important joints where strains on riveted 
 joints are vital, or wherever perforation may reduce sections to a mini- 
 mum. The reaming should be sufficient to thoroughly remove the mate- 
 .rial disturbed by punching; to accomplish this it is best to enlarge punched 
 holes at least 1/8 m. diameter with the reamer. 
 
 Riveting. It is the current practice to perforate holes Vie in. larger 
 than the rivet diameter. For work to be reamed it is also a usual require- 
 ment to punch the holes from l/g to 3/ 16 in. less than the finished diameter, 
 the holes being reamed to the proper size after the various parts are 
 assembled. 
 
 It is also excellent practice to remove the sharp corner at both ends of 
 the reamed holes, so that a fillet will be formed at the junction of the body 
 and head of the finished rivets. 
 
 The rivets of either iron or mild steel should be heated to a bright red or 
 yellow heat and subjected to a pressure of not less than 50 tons per square 
 inch of sectional area. 
 
 For rivets of ordinary length this pressure has been found sufficient to 
 completely fill the hole. If, however, the holes and the rivets are excep- 
 tionally long, a greater pressure and a slower movement of the closing tool 
 than is used for shorter rivets has been found advantageous. 
 
 Welding. No welding should be allowed on any steel that enters into 
 structures. [See page 487.] 
 
 Upsetting. Enlarged ends on tension bars for screw-threads, eye- 
 bars, etc., are formed by upsetting the material. With proper treatment 
 and a sufficient increment of enlarged sectional area over the body of 
 the bar the result is entirely satisfactory. The upsetting process should 
 be performed so that the properly heated metal is compelled to flow 
 without folding or lapping. 
 
 Annealing. The object of annealing structural steel is for the pur- 
 
 Eose of securing homogeneity of structure that is supposed to be impaired 
 y unequal heating, or by the manipulation necessarily attendant on 
 certain processes. The objects to be annealed should be heated through- 
 out to a uniform temperature and uniformly cooled. 
 
 The physical effects of annealing, as indicated by tensile tests, depend 
 on the grade of steel, or the amount of hardening elements associated with 
 it; also on the temperature to which the steel is raised, and the method 
 or rate of cooling the heated material. 
 
 The physical effects of annealing medium-grade steel, as indicated by 
 tensile test, are reported very differently by different observers, some 
 claiming directly opposite results from others. It is evident, when all the 
 attendant conditions are considered, that the obtained results must vary 
 both in kind and degree. 
 
 The temperatures employed will vary from 1000 to 1500 F. In 
 some cases the heated steel is withdrawn at full temperature from the 
 furnace and allowed to cool in the atmosphere; in others the mass is 
 removed from the furnace, but covered under a muffle, to lessen the free 
 radiation; or, again, the charge is retained in the furnace, and the whole 
 mass cooled with the furnace, and more slowly than by either of the other 
 methods. 
 
 The best general results from annealing will probably be obtained by 
 introducing the material into a uniformly heated oven in which the tem- 
 perature is not so high as to cause a possibility of cracking by sudden and 
 unequal changing of temperature, then gradually raising the temperature 
 of the material until it is uniformly about 1200 F., then withdrawing the 
 material after the temperature is somewhat reduced and cooling under 
 shelter of a muffle sufficiently to prevent too free and unequal cooling on 
 the one hand or excessively slow cooling on the other. 
 
 G.G.Mehrtens, Trans. A. S. C. E., 1893, says: " Anuealing is of advan- 
 
MISCELLANEOUS NOTES ON STEEL. 485 
 
 tage to all steel above 64,000 Ibs. strength per square inch, but it is ques- 
 tionable whether it is necessary in softer steels. The distortions due to 
 heating cause trouble in subsequent straightening, especially of thin plates. 
 "In a general way all unannealed mild steel for a strength of 56.000 to 
 64,000 Ibs. may be worked in the same way as wrought iron. Rough 
 treatment or working at a blue heat must, however, be prohibited. Shear- 
 ing is to be avoided, except to prepare rough plates, which should after- 
 wards be smoothed by machine tools or files before using. Drifting is also 
 
 sinking of the edges of drilled holes is all that is necessary. Working the 
 material while heated should be avoided as far. as possible, and the 
 engineer should bear this in mind when designing structures. Upsetting, 
 cranking, and bending ought to be avoided, but when necessary the 
 material should be annealed after completion. 
 
 "The riveting of a mild-steel rivet should be finished as quickly as pos- 
 sible, before it cools to the dangerous heat. For this reason machine work 
 is the best. There is a special advantage in machine work from the fact 
 that the pressure can be retained upon the rivet until it has cooled suffi- 
 ciently to prevent elongation and the consequent loosening of the rivet." 
 
 Punching and Drilling of Steel Plates. (Proc. Inst. M. E. t Aug., 
 1887, p. 326.) In Prof. Unwin's report the results of the greater number 
 of the experiments made on iron and steel p'ates lead to the general con- 
 clusion that while thin plates, even of steel, do not suffer very much from 
 punching, yet in those of 1/2 in. thickness and upwards the loss of tenacity 
 due to punching ranges from 10% to 23% iniron plates and from 11% to 
 33% in the case of mild steel. 
 
 MISCELLANEOUS NOTES ON STEEL. 
 
 May Carbon be Burned Out of Steel ? Experiments made at the 
 Laboratory of the Penna. Railroad Co. (Specifications for Springs, 1888) 
 with the steel of spiral springs, show that the place from which the borings 
 are taken for analysis has a very important influence on the amount of 
 carbon found. If_the sample is a piece of the round bar, and the borings 
 are taken from the'end of this piece, the carbon is always higher than if the 
 borings are taken from the side of the piece. It is common to find a 
 difference of 0.10% between the center and side of the bar, and in some 
 cases the difference is as high as 0.23%. Apparently during the process 
 of reducing the metal from the ingots to the round oar, with successive 
 heatings, the carbon in the outside of the bar is burned out. 
 
 Effect of Nicking a Steel Bar. The statement is sometimes made 
 that, owing to the homogeneity of steel, a bar with a surface crack or nick 
 in one of its edges is liable to fail by the gradual spreading of the nick, and 
 thus break under a very much smaller load than a sound bar. With iron 
 it is contended this does not occur, as this metal has a fibrous structure. 
 Sir Benjamin Baker has, however, shown that this theory, at least so far 
 as statical stress is concerned, is opposed to the facts, as 'he purposely 
 made nicks in specimens of the mild steel used at the Forth Bridge, but 
 found that the tensile strength of the whole was thus reduced by only 
 about one ton per square inch of section. In an experiment by the Union 
 Bridge Company a full-sized steel counter-bar, with a screw-turned 
 buckle connection, was tested under a heavy statical stress, and at the 
 same time a weight weighing 1040 Ibs. was allowed to drop on it from 
 various heights. The bar was first broken by ordinary statical strain, 
 and showed a breaking stress of 66,800 Ibs. per square inch. The longer 
 of the broken parts was then placed in the machine and put under the 
 following loads, whilst a weight, as already mentioned, was dropped on it 
 from various heights at a distance of five feet from the sleeve-nut of the 
 turn-buckle, as shown below: 
 
 Stress in pounds per sq. in 50,000 55,000 60,000 63,000 65,000 
 
 ft. in. ft. in. ft. in. ft. in. ft. in. 
 
 The weight was then shifted so as to fall directly on the sleeve-nut, and 
 the test proceeded as follows: 
 
 Stress on specimen in Ibs. per square inch 65,350 65,350 68,800 
 
 Height of fall, feet 3 6 d 
 
486 STEEL. 
 
 It will be seen that under this trial the bar carried more than when 
 originally tested statically, showing that the nicking of the bar by screw- 
 ing had not appreciably weakened its power of resisting shocks. Eng'g 
 News. 
 
 Specific Gravity of Soft Steel. (W. Kent, Trans. A. I. M. E., xiv, 
 585.) Five specimens of boiler-plate of C 0.14, P 0.03 gave an average 
 sp. gr. of 7.932, maximum variation 0.008. The pieces were first planed 
 to remove all possible scale indentations, then filed smooth, then cleaned 
 in dilute sulphuric acid, and then boiled in distilled water, to remove all 
 traces of air from the surface. 
 
 The figures of specific gravity thus obtained by careful experiment on 
 bright, smooth pieces of steel are, however, too high for use in determining 
 the weights of rolled plates for commercial purposes. The actual average 
 thickness of these plates is always a little less than is shown by the calipers, 
 on account of the oxide of iron on the surface, and because the surface is 
 not perfectly smooth and regular. A number of experiments on com- 
 mercial plates, and comparison of other authorities, led to the figure 
 7.854 as the average specific gravity of open-hearth boiler-plate steel. 
 This figure is easily remembered as being the same figure with change of 
 position of the decimal point (.7854) which expresses the relation of the 
 area of a circle to that of its circumscribed square. Taking the weight 
 of a cubic foot of water at 62 F. as 62.36 Ibs. (average of several authori- 
 ties), this figure gives 489.775 Ibs. as the weight of a cubic foot of steel, 
 or the even figure, 490 Ibs., may be taken as a convenient figure, and 
 accurate within the limits of the error of observation. 
 
 A common method of approximating the weight of iron plates is to con- 
 sider them to weigh 40 Ibs. per square foot one inch thick. Taking this 
 weight and adding 2% gives almost exactly the weight of steel boiler- 
 plate given above (40 X 12 X 1.02 = 489.6 Ibs. per cubic foot). 
 
 Occasional Failures of Bessemer Steel. G. H. Clapp and A. 
 E. Hunt, in their paper on " The Inspection of Materials of Construction in 
 the United States " (Trans. A. I. M. E., vol. xix), say: Numerous instances 
 could be cited to show the unreliability of Bessemer steel for structural 
 
 ?urposes. One of the most marked, however, was the following: A 
 2-in. I-beam weighing 30 Ibs. to the foot, 20 feet long, on being unloaded 
 from a car broke in two about 6 feet from one end. 
 
 The analyses and tensile tests made do not show any cause for the failure. 
 
 The cold and quench bending tests of both the original 3/4-in. round test- 
 pieces, and of pieces cut from the finished material, gave satisfactory re- 
 sults; the cold-bending tests closing down on themselves without sign of 
 fracture. 
 
 Numerous other cases of angles and plates that were so hard in places as 
 to break off short in punching, or, what was worse, to break the punches, 
 have come under our observation, and although makers of Bessemer steel 
 claim that this is just as likely to occur in open-hearth as in Bessemer steel, 
 we have as yet never seen an instance of failure of this kind in open- 
 hearth steel having a composition such as C 0.25%, Mn 0.70%, P 0.08%. 
 
 J. W. Wailes, in a paper read 'before the Chemical Section of the British 
 Association for the Advancement of Science, in speaking of mysterious 
 failures of steel, states that investigation shows that " these failures occur 
 in steel of one class, viz., soft steel made by the Bessemer process." 
 
 Dangerous Low Carbon Steel. A remarkable failure of ship-plate 
 steel is described in Jour. A. S. M. E., Jan., 1915 (from Trans. North 
 East Coast Institution of Engineers and Shipbuilders). In punching 
 the plates several of them cracked, and on riveting many of them 
 cracked between the Civets; they also cracked on being struck with 
 an ordinary hammer. The plates had passed all the usual chemical 
 and physical tests of Lloyd's. A chemical analysis gave C. 0.05; Si. 
 0.08; Mn. 0.86; S. 0.08; P. 0.06. A micrographic examination showed 
 numerous dove-gray areas of sulphide of manganese. Alternating 
 stress tests on bars 3/ 8 in. diameter, bent 3/g in. each way at 3 in. 
 from the plane of maximum stress, gave only 100 alternations of stress 
 before fracture, as compared with 300 for good steel. Prof. J. O. 
 Arnold, of Sheffield, says the material appears to have been overheated 
 in manufacturing the plates from the slab ingots, and that slow cooling 
 from a high temperature after rolling, the plates being stacked in piles 
 to cool, would make crystallization more perfect and hence more 
 dangerous. 
 
CstlVMSI 
 
 MISCELLANEOUS NOTES ON STEEL. 
 
 487 
 
 Segregation in Steel Ingots. (A. Pourcel, Trans. A.J. M. E., 1893.) 
 H. M. Howe, in his " Metallurgy of Steel," gives a resume of observations, 
 with the results of numerous analyses, bearing upon the phenomena of 
 
 A test-piece taken 24 inches from the head of an ingot 7.5 feet in length 
 gave by analysis very different results from those of a test-piece taken 
 30 inches from the bottom. ' Q p 
 
 Top . 0.92 0.535 0.043 0.161 0.261 
 Bottom 0.37 0.498 0.006 0.025 0.096 
 
 Segregation is less marked in ingots of extra-soft metal cast in cast-iron 
 molds of considerable thickness. It is, however, still important, and ex- 
 plains the difference often shown by the results of tests on pieces taken 
 from different portions of a plate. Two samples, taken from the sound 
 part of a flat ingot, one on the outside and the other in the center, 7.9 
 inches from the upper edge, gave; 
 
 C. S. P. Mn. 
 
 Center 0.14 0.053 0.072 0.576 
 
 Exterior 0.11 0.036 0.027 0.610 
 
 Manganese is the element most uniformly disseminated in hard or soft 
 steel. 
 
 For cannon of large caliber, if we reject, in addition to the part cast in 
 sand and called the masselotte (sinking-head), one-third of the upper part 
 of the ingot, we can obtain a tube practically homogeneous in composition, 
 because the central part is naturally removed by the boring of the tube. 
 With extra-soft steels, destined for ship- or boiler-plates, the solution for 
 practically perfect homogeneity lies in the obtaining of a metal more 
 closely deserving its name of extra-soft metal. 
 
 The injurious consequences of segregation must be suppressed by redu- 
 cing, as far as possible, the elements subject to liquation. 
 
 Segregation in Steel Plates. (C. L. Huston, Proc. A. S. T. M., vi, 182.) 
 
 A plate 370 X 76 X /i 6 in. was rolled from a 16 X 18-in. ingot, weighing 
 2800 Ibs., the ladle test of which showed 0.18 C. Test pieces from the 
 plate gave the Allowing: 
 Top of Ingot: 
 
 Tensile Strength 56,730 67,420 67,050 66,980 
 
 Carbon 0.13 0.25 0.27 0.25 
 
 Bottom of Ingot: 
 
 Tensile Strength 56,120 
 
 Carbon 0.13 
 
 1 
 
 67,420 
 0.25 
 
 57,720 
 
 0.13 
 
 2 
 
 58,400 
 
 0.16 
 
 3 
 
 58,140 
 
 0.16 
 
 4 
 
 56,440 
 0.13 
 
 56,900 
 
 0.14 
 
 5 
 
 Columns 1 and 5, edge of plate; 3, middle; 2 and 4, half way between 
 middle and edge. 
 
 Other tests of low-carbon steel showed a lower degree of segregation. 
 A plate from an ingot of 0.23 C gave minimum 0.18 C T. S., 64,580: 
 maximum 0.38 C, T. S., 70,340. One from an ingot of 0.26 C gave 
 maximum 0.20 C, T. S., 59,600; maximum 0.50 C, T. S., 78,600. (See 
 also paper on this subject by H. M. Howe in vol. vii, p. 75.) 
 
 Endurance of Steel under Repeated Alternate Stresses. (J. E. 
 Howard, A. S. T .M., 1907, p. 252.) Small bars were rapidly rotated in a 
 machine while being subjected to a transverse strain. Two steels gave 
 
 Red. of area, 33.5%. (2) 0.82 C, T. S., 142,000; E. L., 64,000 
 7%; Red. of area, 11.8%. 
 
 Elong., 
 
 Fiber stress 
 No. of rotations be- 
 fore rupture. 
 
 60,000 
 j (1) 12,490 
 1 (2) 37,250 
 
 50,000 
 33,160 
 213,150 
 
 45,000 
 166,240 
 605,640 
 
 40,000 
 455,000 
 202,000,000 
 
 35,000 
 900.000 
 Notb 
 
 30,000 
 76,326,240 
 roken. 
 
 Welding of Steel. H. H. Campbell (Manuf. of Iron and Steel, 
 p. 402) had numerous bars of steel welded by different skilled blacksmiths. 
 The record of results, he says, "is extremely unsatisfactory." The 
 worst weld by each of four workmen showed respectively 70, 54, 58, and 
 44% of the strength of the original bar. Forging steel showed one weld 
 with only 48%, common soft steel 44%, and pure basic steel 59%. In 
 a series of tests by the Royal Prussian Testing Institute, the average 
 strength of welded bars of medium steel was 58% of the natural the 
 poorest bar showing only 23%. In softer steel the average was 71%. 
 
488 STEEL. 
 
 and the poorest 33 %, while in puddled iron the average was 81 % and the 
 poorest 62%. Mr. Campbell concludes: "A weld as performed by 
 ordinary blacksmiths, whether on iron or steel, is not nearly as good as 
 the rest of the bar; and it is still more certain that welds of large rods of 
 common forging steel are unreliable and should not be employed in 
 structural work. Electric methods d9 not offer a solution of the problem, 
 for the metal is heated beyond the critical temperature of crystallization, 
 and only by heavy reductions under the hammer or press can much be 
 done towards restoring the ductility of the piece." 
 
 Welding of Steel. A. E. Hunt (A- /- M. E., 1892) says: "I have never 
 seen so-called ' welded ' pieces of steel pulled apart in a testing-machine 
 or otherwise broken at the joint which have not shown a smooth cleavage 
 plane, as it were, such as in iron would be condemned as an imperfect 
 weld. My experience in this matter leads me to agree with the position 
 taken by Mr. William Metcalf in his paper upon Steel (Trans. A.S.C.E., 
 vol. xvi, p. 301). Mr. Metcalf says, 'I do not believe steel can be welded 
 
 The Thermit Welding Process. (Goldschmidt Thermit Co., New 
 York.) When powdered or finely divided aluminum is mixed with a 
 metallic oxide and ignited, the aluminum burns with great rapidity and 
 intense heat, reducing the oxide to a metal and fusing it. It is said that 
 iron oxide and aluminum will make a temperature of 5400 F., producing 
 fused iron which will melt any iron or steel with which it comes in con- 
 tact. The process is largely used for repairing breaks of large castings 
 or forgings, such as the stern post of a steamship, a locomotive frame, 
 etc. In the operation of welding a large fractured piece, the fracture 
 is drilled out with a series of 3/4-in. holes close together, making a clear 
 opening. A mold of fire-clay and sand is then made to fit all around 
 the fracture, leaving a collar or ring surrounding it, baked in a furnace 
 and then placed in position. The fractured section is then heated by a 
 blow-torch inserted in the riser of the mold. A conical sheet iron cru- 
 cible, lined with magnesia tar, is then inserted in the riser, and thermit 
 (the mixture of aluminum and oxide of iron) poured into it. An ignition 
 powder is placed on top of the thermit, and lighted with a storm match. 
 The mixture begins to burn with great agitation; when this ceases the 
 crucible is tapped, and white-hot fused iron or steel runs into the mold 
 and thoroughly fuses with the pieces to be joined. 
 
 Oxy-acetylene Welding and Cutting of Metals. Autogenous 
 Welding. By means of acetylene gas and oxygen, stored in tanks 
 under pressure, and a properly constructed nozzle or torch in which the 
 two gases are united and fired, an intense temperature said to be 6000 F., 
 is generated, and it may be used to weld or fuse together iron, steel, alumi- 
 num, brass, copper, or other metals. The process of uniting metals by heat 
 without using either flux or compression is called autogenous welding. 
 The oxy-acetylene torch may also be used for cutting metals, such as 
 steel plates, beams and large forgings, and for repairing flaws or defects, 
 or filling cavities by melting a strip of metal and flowing it into place. 
 The apparatus, with instruction in its use, is furnished by the Davis- 
 Bournonville Co., Jersey City, N. J. 
 
 Electric Welding. For description see Electrical Engineering. 
 
 Hydraulic Forging. In the production of heavy forgings from 
 cast ingots of mild steel it is essential that the mass of metal should be 
 operated on as equally as possible throughout its entire thickness. When 
 employing a steam-hammer for this purpose it has been found that the ex- 
 ternal surface of the ingot absorbs a large proportion of the sudden impact 
 of the blow, and that a comparatively small effect only is produced on the 
 central portions of the ingot, owing to the resistance offered by the inertia 
 of the mass to the rapid motion of the falling hammer a disadvantage 
 that is entirely overcome by the slow, though powerful, compression of the 
 hydraulic forging-press, which appears destined to supersede the steam- 
 hammer for the production of massive steel forgings. 
 
 Fluid-compressed Steel by the " Whitworth Process." (Proc. 
 Inst. M. E., May, 1887, p. 167.) In this system a gradually increasing 
 pressure up to 6 or 8 tons per square inch is applied to the fluid ingot, and 
 within half an hour or less after the application of the pressure the column 
 of fluid steel is shortened 1 1/2 inches per foot or one-eighth of its length; the 
 pressure is then kept on for several hours, the result being that the metal 
 is compressed into a perfectly solid and homogeneous material free from 
 blow holes. 
 
STEEL CASTINGS. 489 
 
 In large gun-ring ingots during cooling the carbon is driven to the center, 
 the center containing 0.8 carbon and the outer ring 0.3. The center is 
 bored out until a test shows that the inside of the ring contains the same 
 percentage of carbon as the outside. 
 
 Fluid-compressed steel is made by the Bethlehem Steel Co. for gun and 
 other heavy forcings. 
 
 Putting sufficient pressure upon the outside of the ingot when the walls 
 are solid but the interior is still liquid will prevent the formation of a 
 pipe. In Whitworth's system the ingot is raised and compressed length- 
 wise against a solid ram situated above it, during and shortly after solidifi- 
 cation. In Harmet's method the ingot is forced upward during solidifi- 
 cation into its tapered mold. This causes a large radial pressure on its 
 sides, in Lilienbergls method the ingots are stripped and then run on 
 their cars between a solid and movable wall. The movable wall is then 
 pressed against one side of the ingots. (Stoughton's Metallurgy of Iron 
 and Steel.) 
 
 For other methods of compressing ingots see paper by A. J. Capron in 
 Jour. I. & S. /., 1906, Iron Tr. Rev., May 24, 1906. 
 
 STEEL CASTINGS. 
 
 (E. S. Cramp, Proc. Eng'g Congress, Dept. of Marine Eng'g, Chicago, 1893.) 
 
 In 1891 American steel-founders had successfully produced a consider- 
 able variety of heavy and difficult castings, of which the following are the 
 most noteworthy specimens: 
 
 Bed-plates up to 24,000 Ibs.; stern-posts up to 54,000 Ibs.; stems up to 
 21,000 Ibs.; hydraulic cylinders up to 11,000 IDS.; shaft-struts up to 32,000 
 ibs.; hawse-pipes up to 7500 Ibs.; stern-pipes up to 8000 Ibs. 
 
 The percentage of success in these classes of castings since 1890 has 
 ranged from 65% in the more difficult forms to 90% in the simpler ones; 
 the tensile strength has been from 62,000 to 78,000 Ibs., elongation from 
 15% to 25%. 
 
 The first steel castings of which anything is generally known were 
 crossing-frogs made for the Philadelphia & Reading R. R. in July, 1867, by 
 the William Butcher Steel Works, now the Midvale Steel Co. The molds 
 were made of a mixture of ground fire-brick, black-lead crucible-pots 
 ground fine, and fire-clay, and washed with a black-lead wash. The steel 
 was melted in crucibles, and was about as hard as tool steel. The surface 
 of these castings was very smooth, but the interior was very much honey- 
 combed. This was before the days when the use of silicon was known for 
 solidifying steel. The sponginess, which was almost universal, was a great 
 obstacle to their general adoption. 
 
 The next step was to leave the ground pots out of the molding mixture 
 and to wash the mold with finely ground fire-brick. This was a great im- 
 provement especially in very heavy castings; but this mixture still clung so 
 strongly to the casting that only comparatively simple shapes could be 
 made with certainty. A mold made of such a mixture became almost as 
 hard as fire-brick, and was such an obstacle to the proper shrinkage of 
 castings that, when at all complicated in shape, they had so great a 
 tendency to crack as to make their successful manufacture almost impos- 
 sible. By this time the use of silicon had been discovered, and the only 
 obstacle in the way of making good castings was a suitable molding 
 mixture. This was ultimately found in mixtures having the various kinds 
 of silica sand as the principal constituent. 
 
 One of the most fertile sources of defects in castings is a bad design. 
 Very intricate shapes can be cast successfully if they are so designed as to 
 cool uniformly. Mr. Cramp says while he is not yet prepared to state that 
 Anything that can be cast successfully in iron can be cast in steel, indica- 
 tions seem to point that way in all cases where it is possible to put on suit- 
 able sinking-heads for feeding the casting. 
 
 H. L. Gantt (Trans. A. S. M. #.,xii, 710) says: Steel castings not only 
 shrink much more than iron ones, but with less regularity. The amount of 
 shrinkage varies with the composition and the heat of the metal; the hotter 
 the metal the greater the shrinkage; and, as we get smpother castings from 
 hot metal, it is better to make allowance for large shrinkage and pour the 
 metal as hot as possible. Allow 3/ 16 or 1/4 in. per ft. in length for shrinkage, 
 and 1/4 in. for finish on machined surfaces, except such as are cast "up. 
 Cope surfaces which are to be machined should, in large or hard castings, 
 have an allowance of from %toy 2 in. for finish, as a large mass of metal 
 
490 
 
 STEEL. 
 
 slowly rising in a mold is apt to become crusty on the surface, and such a 
 crust is sure to be full of imperfections. On small, soft castings 1/8 in. on 
 drag side and 1/4 in. on cope side will be sufficient. No core should have 
 less than 1/4 in. finish on aside and very large ones should have as much as 
 1/2 in. on a side. Blow-holes can be entirely prevented in castings by the 
 addition of manganese and silicon in sufficient quantities; but both of 
 these cause brittleness, and it is the object of the conscientious steel- 
 maker to put no more manganese and silicon in his steel than is just suffi- 
 cient to make it solid. The best results are arrived at when all portions of 
 the castings are of a uniform thickness, or very nearly so. 
 
 The following table will illustrate the effect of annealing on tensile 
 strength and elongation of steel castings: 
 
 Carbon. 
 
 Tensile Strength. 
 
 Elongation. 
 
 Unannealed. 
 
 Annealed. 
 
 Unannealed. 
 
 Annealed. 
 
 0.23% 
 0.37 
 0.53 
 
 68,738 
 85,540 
 90,121 
 
 67,210 
 82,228 
 106,415 
 
 22.40% 
 8.20 
 2.35 
 
 31.40% 
 21.80% 
 9.80 
 
 The proper annealing of large castings takes nearly a week. 
 
 The proper steel for roll pinions, hammer dies, etc., seems to be that 
 containing about 0.60 % of carbon. Such castings, properly annealed, have 
 worn weil and seldom broken. Miscellaneous gearing should contain 
 carbon 0.40% to 0.60%, gears larger in diameter being softest. General 
 machinery castings should, as a rule, contain less than 0.40% of carbon, 
 those exposed to great shocks containing as low as 0.20% of carbon. Such 
 castings will give a tensile strength of from 60,000 to 80,000 Ibs. per sq. 
 in and at least 15% extension in 2 in. Machinery and hull castings for 
 war-vessels for the United States Navy, as well as carriages for naval 
 guns, contain from 0.20% to 0.30% of carbon. 
 
 For description of methods of manufacture of steel castings by the Besse- 
 mer, open-hearth, and crucible processes, see paper by P. G. Salom, Trans. 
 A. I. M. E., xiv. 118. 
 
 CRUCIBLE STEEL. 
 
 Selection of Grades by the Eye, and Effect of Heat Treatment. 
 
 (J W. Langley, Amer. Chemist, Nov., 1876.) In the early days of steel 
 making the grades were determined by inspection of the fractured surfaces 
 of the cast ingots. The method of selection is described as follows: 
 
 The steel when thoroughly fluid is poured into cast-iron molds, and 
 when cold the top of the ingot is broken off, exposing a freshly fractured 
 surface. The appearance presented is that of confused groups of crystals, 
 all appearing to have started from the outside and to have met in the 
 center; this general form is common to all ingots of whatever composition, 
 but to the trained eye, and only to one long and critically exercised, a 
 minute but indescribable difference is perceived between varying samples 
 of steel, and this difference is now known to be owing alirmst wholly to 
 variations in the amount of combined carbon, as the following table will 
 show. Twelve samples selected by the eye alone, and analyses of drillings 
 taken direct from the ingot before it had been heated or hammered, gave 
 results as below: 
 
 Ingot Nos. 1 2 3'45678 9 10 11 12 
 C 0.302 .490 -.529 .649 .801 .841 .867 .871 .955 1.0051.0581.079 
 
 Diff. of C 0.188 .039 .120 .152 .040 .026 .004 .084 .050 .053 .021 
 
 The C is seen to increase in quantity in the order of the numbers. The 
 other elements, with the exception of total iron, bear no relation to the 
 number on the samples. The mean difference of Cis 0.071. 
 
 In mild steels the discrimination is less perfect. 
 
 The appearance of the fracture by which the above twelve selections 
 were made can only be seen in the cold ingot before any operation, except 
 the original one of casting, has been performed upon it. As soon as it is 
 hammered, the structure changes, so that all trace of the primitive con- 
 dition appears to be lost. 
 
 The specific gravity of steel is influenced not only by its chemical analy- 
 sis but by the heat to which it is subjected. 
 The sp.gr. of the ingots in the above list ranged from 7.855 for No. 1 
 
CRUCIBLE STEEL. 491 
 
 down to 7.803 for No. 12. Rolling into bars produced a very slight dif- 
 ference, 0.005 in Nos. 5 and 6 and +0.020 in No. 12, but overheating 
 reducedthesp.gr. of the bar 0.023 in No. 3 to 0.135 in No. 12, the sp. gr. of 
 the burnt sample of No. 12 being only 7.690. 
 
 Effect of Heat on the Grain of Steel. (W. Metcalf, Jeans on 
 Steel, p. 642.) A simple experiment will show the alteration produced 
 in a high-carbon steel by different methods of hardening. If a bar of such 
 steel be nicked at about 9 or 10 places, and about half an inch apart, a 
 suitable specimen is obtained for the experiment. Place one end of the 
 bar in a good fire, so that the first nicked piece is heated to whiteness, 
 while the rest of the bar, being out of the fire, is heated up less and less 
 as we approach the other end. As soon as the first piece is at a good 
 white heat, which of course burns a high-carbon steel, and the temperature 
 of the rest of the bar gradually passes down to a very dull red, the metal 
 should be taken out of the fire and suddenly plunged in cold water, in 
 which it should be left till quite cold. It should then be taken out and 
 carefully dried. An examination with a file will show that the first piece 
 has the greatest hardness, while the last piece is the softest, the inter- 
 mediate pieces gradually passing from one condition to the other. On 
 now breaking off the pieces at each nick it will be seen that very consider- 
 able and characteristic changes have been produced in the appearance of 
 the metal. The first burnt piece is very open or crystalline in fracture; 
 the succeeding pieces become closer and closer in the grain until one piece 
 is found to possess that perfectly even grain and velvet-like appearance 
 which is so much prized by experienced steel users. The first pieces also, 
 which have been too much hardened, will probably be cracked; those at 
 the other end will not be hardened, through. Hence if it be desired to 
 make the steel hard and strong, the temperature used must be high 
 enough to harden the metal through, but not sufficient to open the grain. 
 
 Heating Tool Steel. .(Crescent Steel Co., Pittsburg, Pa.) - There are 
 three distinct stages or times of heating: First, for forging; second, for 
 hardening; third, for tempering. 
 
 The first requisite for a good heat for forging is a clean fire and plenty of 
 fuel, so that jets of hot air will not strike the corners of the piece; next, 
 the fire should be regular, and give a good uniform heat to the whole part 
 to be forged. It should be keen enough to heat. the piece as rapidly as 
 may be, and allow it to be thoroughly heated through, without being 
 so fierce as to overheat the corners. Steel should not be left in the fire 
 any longer than is necessary to heat it clear through, as "soaking" in 
 fire is injurious; on the other hand, it is necessary that it should be hot 
 through, to prevent surface cracks. By observing these precautions a 
 piece of steel may always be heated safely, up to even a bright yellow 
 heat, when there is much forging to be done on it. 
 
 The best and most economical of welding fluxes is clean, crude borax, 
 which should be first thoroughly melted and then ground to fine powder. 
 
 After the steel is properly heated, it should be forged to shape as quickly 
 as possible; and just as the red heat is leaving the parts intended for cutting 
 edges, these parts should be refined by rapid, light blows, continued until 
 the red disappears. 
 
 For the second stage of heating, for hardening, great care should be used: 
 first, to protect the cutting edges and working parts from heating more 
 rapidly than the body of the piece; next, that the whole part to be hardened 
 be heated uniformly through, without any part becoming visibly hotter 
 than the other. A uniform heat, as low as will give the required hardness, 
 is the best for hardening. 
 
 For every variation of heat which is great enough to be seen there will 
 result a variation in grain, which may be seen by breaking the piece; and 
 for every such variation in temperature there is a very g9od chance for a 
 crack to be seen. Many a costly tool is ruined by inattention to this point. 
 
 The effect of tpo high heat is to open the grain; to make the steel coarse. 
 The effect of an irregular heat is to cause irregular grain, irregular strains, 
 and cracks. 
 
 As soon as the piece is properly heated for hardening, it should be 
 promptly and thoroughly quenched in plenty of the cooling medium, water, 
 brine, or oil, as the case may be. An abundance of cooling bath, to do 
 the work quickly and uniformly all over, is necessary to good and safe 
 work. 
 
 To harden a large piece safely a running stream should be used. 
 Much uneven hardening is caused_by the.use of too small baths. 
 
492 STEEL. 
 
 For the third stage of heating, to temper, the first important requisite is 
 again uniformity. The next is time; the more slowly a piece is Drought 
 down to its temper, the better and safer is the operation. 
 
 When expensive tools are to be made it is a wise precaution to try small 
 pieces of the steel at different temperatures, so as to find out how low a 
 heat will give the necessary hardness. The lowest heat is the best for any 
 steel. [This is true of carbon steel but not of " high speed " alloy steels.] 
 
 Heating in a Lead Bath. A good method of heating steel to a 
 uniform temperature is by means of a bath of lead kept at a red heat by 
 a gas furnace. See Heat Treatment by the Taylor-White Process, under 
 Machine Shop. 
 
 Heating Steel in Melted Salts by Electric Current. L. M. Cohn 
 (Electrot. z., Aug., 1906, Mach'y, Dec., 1906) describes a furnace pat- 
 ented by Gebr. Korting, Berlin, in which steel may be heated uniformly 
 to any desired temperature up to 1300 C. (2372 F.) without danger of 
 oxidizing. 
 
 The furnace consists mainly of a cast-iron box, lined inside with fire- 
 clay, a second lining of fire-bricks, lined again with asbestos, and 
 inclosing the crucible made of one piece of fireproof material. Two 
 electrodes lead into the crucible, through which alternating current is 
 sent. The crucible is filled with metal salts. For temperatures above 
 1000 C. pure chloride of barium is used, the melting-point of which is 
 at about 950 C. (1742 F.) : for lower temperatures a mixture of chloride 
 of barium and chloride of potassium, 2 to 1, is used, melting at about 
 670 C. (1238 F.). Any other suitable salts may be used. A regulating 
 transformer regulates the current, and thus also the temperature. 
 
 A test was made with a furnace, the bath of which was 61/2 X 61/2 X 7 
 in. A 50-period alternating current of 190-volt primary tension was 
 used. This tension had to be reduced to from 50 to 55 volts by the 
 regulating transformer for starting the furnace, and lowered later on. 
 The heating lasted about half an hour. For temperatures from 750 to 
 1300 C., the secondary tension amounted to from 13 to 18 volts. The 
 consumption of energy was as follows: 880 C., 5.4 Kw.; 1140 C., 8.5 
 Kw. ; 1300 C., 12.25 Kw. A milling cutter 5 in. diam., 11/4 in. bore, 1 in. 
 thick, was heated in 62 seconds to 1300 C. A bushing of tool steel 23/4 
 in. diam., 23/4 in. long, 5/g in. bore, was heated in 243 seconds to 850C. 
 
 Heating to Forge. (Crescent Steel Co.) The trouble in the forge 
 fire is usually uneven heat, and not too high heat. Suppose the piece to 
 be forged has been put into a very hot fire, and forced as quickly as possible 
 to a high yellow heat, so that it is almost up to the scintillating point. If 
 this be done, in a few minutes the outside will be quite soft and in a nice 
 condition for forging, while the middle parts will not be more than red-hot. 
 Now let the piece be placed under the hammer and forged, and the soft 
 outside will yield so much more readily than the hard inside, that the 
 outer particles will be torn asunder, while the inside will remain sound. 
 
 Suppose the case to be reversed and the inside to be much letter than the 
 outside; that is, that the inside shall be in a state of semi-fusion, while the 
 outside is hard and firm. Now ISt the piece be forged, and the outside will 
 be all sound and the whole piece will appear perfectly good until it is 
 cropped, and then it is found to be hollow inside. 
 
 In either case, if the piece had been heated soft all through, or if it had 
 been only red-hot all through, it would have forged perfectly sound. 
 
 In some cases a high heat is more desirable to save heavy labor, but in 
 every case where a fine steel is to be used for cutting purposes it must be 
 borne in mind that very heavy forging refines the bars as they slowly cool, 
 and if the smith heats such refined bars until they are soft, he raises the 
 grain, makes them coarse, and he cannot get them fine again unless he has 
 a very heavy steam-hammer at command and knows how to use it well. 
 
 Annealing. (Crescent Steel Co.) Annealing or softening is accom- 
 plished by heating steel to a red heat and then cooling it very slowly, 
 to prevent it from getting -hard again. 
 
 The higher the degree of heat, the more will steel be softened, until the 
 limit of softness is reached, when the steel is melted. 
 
 It does not follow that the higher a piece of steel is heated the softer it 
 will be when cooled, no matter how slowly it may be cooled; this is proved 
 by the fact that an ingot is always harder than a rolled or hammered bar 
 made from it. 
 
 Therefore there is nothing gained by heating a piece of steel hotter than. 
 
CRUCIBLE STEEL. 
 
 493 
 
 a good bright, cherry-red; on the contrary, a higher heat has several dis- 
 advantages: First. If carried too far, it may leave the steel actually 
 harder than a good red heat would leave it. Second. If a scale is raised 
 on the steel this scale will be harsh, granular oxide of iron, and will spoil 
 the tools used to cut it. Third. A high scaling heat continued for a little 
 time changes the structure of the steel, makes it brittle, liable to crack m 
 hardening, and impossible to refine. 
 
 To anneal any piece of steel, heat it red-hot; heat it uniformly and heat it 
 through, taking care not to let the ends and corners get too hot. As 
 soon as it is hot, take it out of the fire, the sooner the better, and cool it 
 as slowly as possible. A good rule for heating is to heat it at so low a red 
 that when the piece is cold it will still show the blue gloss of the oxide 
 that was put there by the hammer or the rolls. Steel annealed in this 
 way will cut very soft; it will harden very hard, without cracking, and 
 when tempered it will be strong, nicely refined, and will hold a keen, 
 
 Tempering. Tempering steel is the act of giving it, after it has been 
 shaped, the hardness necessary for the work it has to do. This is done by 
 first hardening the piece, generally a good deal harder than is necessary, 
 and then toughening it by -slow heating and gradual softening until it is 
 just right for work. 
 
 A piece of steel properly tempered should always be finer in grain than 
 the bar from which it is made. If it is necessary, in order to make the 
 piece as hard as is required, to heat it so hot that after being hardened the 
 grain will be as coarse as or coarser than the grain in the original bar, then 
 the steel itself is of too low carbon for the desired work. 
 
 If a great degree of hardness is n9t desired, as in the case of tap? and 
 most tools of complicated form, and it is found that at a moderate heat the 
 tools are too hard and are liable to crack, the smith should first use a lower 
 heat in order to save the tools already made, and then notify the bteel- 
 maker that his steel is too high, so as to prevent a recurrence of the 
 trouble. 
 
 )ering 
 also, 
 
 . these 
 
 works Mr. Rose gives a "color scale," lithographed in colors, by which the 
 following is a list of the tools in their order on the color scale, together 
 with the approximate color and the temperature at which the color 
 appears on brightened steel when heated in the air: 
 
 Scrapers for brass; very pale yellow, Hand-plane irons. 
 430 F. Twist-drills. 
 
 Steel-engraving tools, 
 
 Slight turning tools. 
 
 Hammer faces. 
 
 Planer tools for steel. 
 
 Ivory-cutting tools. 
 
 Planer tools for iron. 
 
 Paper-cutters. 
 
 Wood-engraving tools. 
 
 Bone-cutting tools. 
 
 Milling-cutters; straw yellow, 460 F. 
 
 Wire-drawing dies. 
 
 Boring-cutters. 
 
 Leather-cutting dies. 
 
 Screw-cutting dies. 
 
 Inserted saw-teeth. 
 
 Taps. 
 
 Rock-drills. 
 
 Chasers. 
 
 Punches and dies. 
 
 Penknives. 
 
 Reamers. 
 
 Half-round bits. 
 
 Planing and molding cutters. 
 
 Stone-cutting tools; brown yellow, 
 
 500 D F. 
 Gouges, 
 
 Flat drills for brass. 
 
 Wood-boring cutters. 
 
 Drifts. 
 
 Coopers' tools. 
 
 Edging cutters; light purple, 530 F. 
 
 Augers. 
 
 Dental and surgical instruments 
 
 Cold chisels for steel. 
 
 Axes; dark purple, 550 F. 
 
 Gimlets. 
 
 Cold chisels for cast iron. 
 
 Saws for bone and ivory. 
 
 Needles. 
 
 Firmer-chisels. 
 
 Hack-saws. 
 
 Framing-chisels. 
 
 Cold chisels for wrought iron. 
 
 Molding and planing cutters to be 
 
 filed. 
 
 Circular saws for metal. 
 Screw-drivers. 
 
 'F. 
 
 Saws for wood. 
 
 Dark blue, 570 
 Pale blue. 610. 
 Blue, tinged with green, 630. 
 
494 
 
 STEEL. 
 
 Uses of Crucible Steel of Different Carbons. (Metcalf on Steel.) 
 0.50 to 0.60 C, for hot work and for battering tools. 
 0.60 to 0.70 C, ditto, and for tools of dull edge. 
 0.70 to 0.80 C, battering tools, cold-sets, and some forms of reamers and 
 
 taps. 
 
 0.80 to 0.90 C, cold-sets, hand-chisels, drills, taps, reamers and dies. 
 0.90 to 1.00 C, chisels, drills, dies, axes, knives, etc. 
 1.00 to 1.10 C, axes, hatchets, knives, large lathe-tools, and many kinds 
 
 of dies and drills if care be used in tempering them. 
 1.10 to 1.50 C, lathe-tools, graving tools, scribers, scrapers, little drills, 
 
 and many similar purposes. 
 
 The best all-around tool steel is found between 0.90 and 1.10 C; steel 
 that can be adapted safely and successfully to more uses than any 
 other. 
 
 High-speed Tool Steel. (A. L. Valentine, Am. Mach., July 2, 1908.) 
 Eight brands of high-speed steel were analyzed with the following 
 results: 
 
 Steel. I 
 
 | W. | Cr. 
 
 Mn. | Si. | Mo. 
 
 P. 
 
 S. 
 
 & 
 
 * 70 
 
 14 91 
 
 2 95 
 
 01 
 
 
 
 013 
 
 0.008 
 
 b 
 
 C 
 
 d 
 
 0.25 
 0.75 
 49 
 
 17.27 
 14.83 
 17 60 
 
 2.69 
 2.90 
 5 11 
 
 Trace 
 0.08 
 
 0.179 
 
 "5J9' 
 
 0.035 
 0.02 
 0.01 
 
 Trace 
 0.01 
 0.007 
 
 
 
 - 65 
 
 
 
 0.19 
 
 0.039 
 
 9.60 
 
 0.016 
 
 0.005 
 
 f 
 
 60 
 
 13 00 
 
 2 88 
 
 
 
 
 019 
 
 0.01 
 
 
 55 
 
 17 81 
 
 2 48 
 
 11 
 
 090 
 
 
 
 
 fc 
 
 66 
 
 19 03 
 
 
 
 036 
 
 
 0.015 
 
 
 
 
 
 
 
 
 
 
 
 W, Wolfram, symbol for tungsten. 
 
 Where blanks appear in the table, the steel was not analyzed for these 
 ingredients. 
 
 Many different brands of high-speed steel are being made. Some that 
 have been marketed are almost worthless. From some of these steels a 
 tool can be made from one end of a bar that is easily forged, machined 
 and hardened, while the other end of the bar would resist almost any 
 cutting tool and would invariably crack in hardening. Different bars of 
 the same make also give very different results. These faults are some- 
 times caused by non-uniform annealing in the steels which are sent out as 
 thoroughly annealed, and in many cases they are caused by the use of 
 impure ingredients. A good high-speed steel will stand a temperature 
 as high as 1200 F., or over double that of carbon steel, without losing its 
 hardness, and experience has proven that the higher the temperature is 
 raised over the white-heat point, the higher a temperature caused by 
 friction the tool will withstand, before losing its intense hardness. The 
 higher the percentage of carbon is, the more brittle and hard to work the 
 steel will be, especially to forge. The steel which has given the best all- 
 around results has contained about 0.40 C. The analysis of this same 
 steel showed nearly 3% of chromium. The higher the percentage of 
 tungsten in the steel, the better has been its cutting qualities. (See Best 
 High-Speed Tool Steel, and description of the Taylor- White process of 
 heat treatment, under "The Machine-Shop. " 
 
 MANGANESE, NICKEL, AND OTHER "ALLOY" STEELS. 
 
 Manganese Steel. (H. M. Howe, Trans. A. S. M. E., vol. xii.) 
 Manganese steel is an alloy of iron and manganese, incidentally, and 
 probably unavoidably, containing a considerable proportion of carbon. 
 
 The effect of small proportions of manganese on the hardness, strength, 
 and ductility of iron is probably slight. The point at which manganese 
 begins to have a predominant effect is not known; it may be somewhere 
 about 2.5%. 
 
 Manganese steel is very free from blow-holes; it welds with great diffi- 
 culty; its toughness is increased by quenching from a yellpw heat; its elec- 
 tric resistance is enormous, and very constant with changing temperature; 
 it is low in thermal conductivity. Its remarkable combination of great 
 hardness, which cannot be materially lessened by annealing, and great 
 tensile strength, with astonishing toughness and ductility, at once creates 
 and limits its usefulness. 
 
tl ALLOY " STEELS. 495 
 
 The hardness of manganese steel seems to be of an anomalous kind. 
 The alloy is hard, but under some conditions not rigid. It is very hard in 
 its resistance to abrasion; it is not always hard in its resistance to impact. 
 
 Manganese steel forges readily at a yellow heat, though at a bright white 
 heat it crumbles under the hammer. But it offers greater resistance to 
 deformation, i.e., it is harder when hot, than carbon steel. 
 
 The most important single use for manganese steel is for the pins which 
 hold the buckets of elevator dredges. Here abrasion chiefly is to be 
 resisted. Another important use is for the links of common chain- 
 elevators. As a material for stamp-shoes, for horse-shoes, for the knuckles 
 of an automatic car-coupler, it has not met expectations. 
 
 Manganese steel has been regularly adopted for the blades of the Cyclone 
 pulverizer. Some manganese-steel wheels are reported to have run over 
 300,000 miles each without turning, on a New England railroad. 
 
 Manganese Steel and its Uses. (E. F. Lake, Am. Mach., May 16, 
 1907.) When more than 2% and less than 6% of Mn is added, with C 
 less than 0.5%, it makes steel very brittle, so that it can be powdered 
 under a hand hammer. From 6 % Mn up, this brittleness gradually dis- 
 appears until 12% is reached, when the former strength returns and 
 reaches its maximum at 15%. After this, a decrease in toughness, but 
 not in transverse strength, takes place until 20% is reached, after which 
 a rapid decrease in strength again takes place. 
 
 Steel with from 12 to 15% Mn and less than 0.5% of C is very hard 
 and cannot be machined or drilled in the ordinary way ; yet it is so tough 
 that it can be twisted and bent into peculiar shapes without breaking. 
 It is malleable enough to be used for rivets that are to be headed cold. 
 
 This hardness, toughness and malleability make manganese steel the 
 most durable metal known, in its ability to resist wear, for such parts 
 as the teeth on steam-shovel dippers, \vhere they will outwear about three 
 teeth made of the best tool steel ; for plow points on road-building work ; 
 for frogs, switches and crossings in railroad construction; for fluted or 
 toothed crushing rolls used on ore, coal and stone crushers; for gears, 
 sprockets, link belts, etc., when used in places where they are subjected 
 to the grinding wear of gritty particles of dust. 
 
 The higher the percentage of C in the steel, the less percentage of Mn 
 will be required to produce brittleness. Si, however, neutralizes the 
 injurious tendencies of Mn, and in Europe the Si-Mn alloy is used for 
 automobile springs and gears. This steel is not high in Mn and can be 
 rolled, while the peculiar properties given to steel by the addition of from 
 12 to 15% of manganese make such steel impossible to roll; therefore all 
 parts made of this steel have to be cast, after which it can be forged and 
 rendered tougher by quenching from a white heat. 
 
 One of its peculiarities is that it is softened by rapid cooling and can be 
 restored to its former hardness by heating to a bright red. 
 
 It is more difficult to mold in the foundry than the ordinary cast steel, 
 as it must be poured at a very high temperature, and in cooling it shrinks 
 nearly twice as much. The shrinkage allowed for patterns to be cast of 
 the ordinary cast steel is 3/ 16 in. per foot, and for manganese-steel cast- 
 ings 5/i6 in. per foot. 
 
 This enormous shrinkage makes it impossible to cast in any intricate 
 or delicate shapes, and as it is too hard to machine or drill successfully, 
 all holes must be cored in the casting. If a close fit is desired in these 
 they must be ground out with an emery wheel. These properties limit 
 its use to a large extent. 
 
 The composition that seems to give the best results is: Mn, from 12 
 to 15 % ; C, not over 0.5 % ; P, not over 0.04 % ; S, not over 0.04 %. 
 
 Manganese-steel castings should be annealed in order to remove any 
 internal strains which may be caused by its high shrinkage and the fact 
 that the outer surface cools so much quicker than the core, which leaves 
 the center of the casting strained. This can be done by heating to 1500 
 . F. and quenching in water, after which it can be hardened by heating to 
 900 and allowed to cool slowly. Manganese-steel castings, when 
 tested in a 7/ 8 -inch round bar, should show: 
 
 T. S. per sq. in., not less than 140,000 lb.; E. L., not less than 90,000 
 Ib. ; Red. of area, not less than 50% ; Elong. in 2 in., not less than 20%,. 
 
 A new manganeses steel containing between 5 and 9 % of manganese, 
 with carbon ranging from about 0.7 to about 1.3%, is described in U. S. 
 Patent 1,113,539, Oct. 13, 1914, assigned to Taylor-Wharton Iron & 
 
496 
 
 STEEL. 
 
 Steel Co. It is said to possess the characteristic hardness of regular 
 manganese steel, while being cheaper. 
 
 Chrome Steel. (F. L. Garrison, Jour. F. I., Sept., 1891.) Chromium 
 increases the hardness of iron, perhaps also the tensile strength and 
 elastic limit, but it lessens its weldability. 
 
 Chromium does not appear to give steel the power of becoming harder 
 when quenched or chilled. Howe states that chrome steels forge more 
 readily than tungsten steels, and when not containing over 0.5 of chro- 
 mium nearly as well as ordinary carbon steels of like percentage of carbon. 
 On the whole, the status of chrome steel is not satisfactory. There are 
 other steel alloys coming into use, which are so much better that it would 
 seem to be only a question of time when it will drop entirely out of the 
 race. Howe states that many experienced chemists have found no 
 chromium, or but the merest traces, in chrome steel sold in the markets. 
 
 J.W. Langley (Trans. A.S.C.E., 1892) says: Chromium, like manganese, 
 is a true hardener of iron even in the absence of carbon. The addition of 
 1 % or 2 % of chromium to a carbon steel will make a metal which gets 
 excessively hard. Hitherto its principal employment has been in the 
 production of chilled shot and shell. Powerful molecular stresses result 
 during cooling, and the shells frequently break spontaneously months 
 after they are made. 
 
 Tungsten Steel Mushet Steel. (J. B. Nau, Iron Age, Feb. 11, 
 1892.) By incorporating simultaneously carbon and tungsten in iron, 
 it is possible to obtain a much harder steel than with carbon alone, with- 
 out danger of an extraordinary brittleness in the cold metal or an in- 
 creased difficulty in the working of the heated metal. 
 
 When a special grade of hardness is required, it is frequently the 
 custom to use a high tungsten steel, known in England as special steel. 
 A specimen from Sheffield, used for chisels, contained 9.3 % of tungsten, 
 0.7% of silver, and 0.6% of carbon. This steel, though used with ad- 
 vantage in its untempered state to turn chilled rolls, was not brittle; 
 nevertheless it was hard enough to scratch glass. 
 
 A sample of Mushet's special steel contained 8.3 % of tungsten and 
 1.73 % of manganese. 
 
 According to analyses made by the Due de Luynes of ten specimens 
 of the celebrated Oriental damasked steel, eight contained tungsten, two 
 of them in notable quantities (0.518 % to 1 %) , while in all of the samples 
 analyzed nickel was discovered ranging from traces to nearly 4%. 
 
 Stein & Schwartz, of Philadelphia, in a circular say: It is stated that 
 tungsten steel is suitable for the manufacture of steel magnets, since it 
 retains its magnetism longer than ordinary steel. Cast steel to which 
 tungsten has been added needs a higher temperature for tempering than 
 ordinary steel, and should be hardened only between yellow, red, and 
 white. Chisels made of tungsten steel should be drawn between cherry- 
 red and blue, and stand well on iron and steel. Tempering is best done 
 in a mixture of 5 parts of yellow rosin, 3 parts of tar, and 2 parts of 
 tallow, and then the article is once more heated and then tempered as 
 usual in water of about 15 C. 
 
 Aluminum Steel. (Aluminum Co. of America, 1909.) Aluminum is 
 added to steel: To increase the soundness of tops of ingots, and conse- 
 quently decrease the scrap losses; to quiet the ebullition in molten 
 steel, permitting the successful pouring of "wild" steel; to prevent 
 oxidation and increase the homogeneity of the steel ; to increase tensile 
 strength without decreasing ductility; to remove oxygen or oxides, the 
 aluminum acting as a deoxidizer; to reduce the liability of the steel to 
 oxidation; to produce smoother surfaced castings and ingots than is 
 possible without the use of aluminum. 
 
 Aluminum is not a hardener of steel, and none of its alloys with steel 
 have proved advantageous. Strictly speaking, there is no aluminum- 
 steel in the sense that there is nickel-steel or chromium-steel. Alumi- 
 num is the principal deoxidizer of steel ; 100 parts by weight of oxygen 
 will combine with 114 parts of aluminum, 140 parts of silicon or 350 parts 
 of manganese. The aluminum wiU entirely disappear if there is any 
 oxygen present, and it only appears in completely deoxidized steel. J 
 too much aluminum be added, the metal is liable to form deep pipes in 
 the ingots. To add the correct quantity requires experience, but suc- 
 cessful results have been obtained by adding from one-eighth to three- 
 fourth pound of aluminum to the ton of steel. Steel ingots which are 
 
"ALLOY" STEELS. 
 
 497 
 
 to be hammered or rolled have been improved by the addition of 
 two to four ounces of aluminum per ton of steel. For steel castings, to 
 insure soundness and absence of blowholes, 16 to 32 ounces per ton may 
 be advantageously added. The aluminum may be added by throwing 
 the metal in small pieces into the ladle as the metal is poured into it, or 
 by the use of ferro-aluminum placed in the ladle before pouring the steel. 
 The metal is more commonly used in America, and the alloy in England. 
 
 Nickel Steel. The remarkable tensile strength and ductility of nickel 
 steel, as shown by the test-bars and the behavior of nickel-steel armor- 
 plate under shot tests, are witness of the valuable qualities conferred 
 upon steel by the addition of a few per cent of nickel. 
 
 Nickel steel has shown itself to be possessed of some exceedingly valuable 
 properties; these are, resistance to cracking, high elastic limit, and homo- 
 geneity. Resistance to cracking, a property to which the name of non-fissi- 
 bility has been given is shown more remarkably as the percentage of nickel 
 increases. Bars of 27 % nickel illustrate this property. A 1 J-in. square 
 bar was nicked 1/4 in. deep and bent double on itself without further fracture 
 than the splintering off, as it were, of the nicked portion. Sudden failure 
 or rupture of this steel would be impossible; it seems to possess the tough- 
 ness of rawhide with the strength of steel. With this percentage of nickel 
 the steel is practically non-corrodible and non-magnetic. The resistance 
 to cracking shown by the lower percentages of nickel is best illustrated in 
 the many trials of nickel-steel armor. 
 
 In such places (shafts, axles, etc.) where failure is the result of the fatigue 
 of the metal this higher elastic limit of nickel steel will tend to prolong in- 
 definitely the life of the piece, and at the same time, through its superior 
 toughness, offer greater resistance to the sudden strains of shock. 
 
 Howe states that the hardness of nickel steel depends on the proportion 
 of nickel and carbon jointly, nickel up to a certain percentage increasing 
 the hardness, beyond this lessening it. Thus while steel with 2% of nickel 
 and 0.90% of carbon cannot be machined, with less than 5% nickel it can 
 be worked cold readily, provided the proportion of carbon be low. As the 
 proportion of nickel rises higher, cold-working becomes less easy. It forges 
 easily whether it contain much 9r little nickel. 
 
 The presence of manganese in nickel steel is most important, as it 
 appears that without the aid of manganese in proper proportions the 
 conditions of treatment would not be successful. 
 
 Properties of Nickel Steel. D. H. Browne, in Proc. A. I. M. E., 
 1899, gives a paper of 79 pages, entitled "Nickel Steel: a synopsis of 
 experiment and opinion," including a bibliography containing 50 titles. 
 Some extracts from this paper are here given. 
 
 Commercially pure nickel, containing 98.13 Ni, 1.15 Co, 0.43 Fe, 
 0.08 Si, 0.11 Mn, showed the following physical properties: 
 
 
 L. P.* 
 
 E. L. 
 
 T. S. 
 
 M. E.* 
 
 El., % 
 in 2 in. 
 
 CEst bars 
 
 5,119 
 
 12,557 
 
 40,669 
 
 23,989,140 
 
 18.2 
 
 T3 ( Raw 
 
 9,243 
 
 21,045 
 
 72,522 
 
 29,506,500 
 
 43.9 
 
 ~ < Annealed 
 
 17,064 
 
 18,059 
 
 72,806 
 
 26,870,800 
 
 48.6 
 
 f ( Quenched 
 
 
 16,921 
 
 71,860 
 
 
 45.0 
 
 Limit of Proportionality. * Modulus of Elasticity. 
 ANNEALED CAST BARS OF NICKEL STEEL WITH C 0.15 to 0.20. 
 
 (Had- 
 
 field.) The proportion of Ni used in soft steels for armor and for engine- 
 forcings is from 3 to 3.5%. With 0.25 C this produces an E. L. and T. 
 S. equal to open-hearth steel of 0.45 C without Ni, with a ductility 
 equal to that of the lower-carbon steel. 
 
 NICKEL STEEL, 3.25 Ni, AND SIMPLE STEEL PORGINGS COMPARED. 
 (Bethlehem Steel Co.) 
 
 C. 
 
 Ni. 
 
 T. S. 
 
 E.L. 
 
 El., 
 
 % 
 
 Red. 
 Area, 
 
 % 
 
 C. 
 
 Ni. 
 
 T.S. 
 
 E.L. 
 
 EL, 
 
 % 
 
 Red. 
 Area, 
 
 % 
 
 0.20 
 0.30 
 0.40 
 0.50 
 
 
 
 
 
 
 55000 
 75000 
 85000 
 95000 
 
 28000 
 37000 
 43000 
 48000 
 
 34 
 30 
 25 
 21 
 
 60 
 50 
 45 
 40 
 
 0.20 
 0.30 
 0.40 
 0.50 
 
 3.5 
 3.5 
 3.5 
 3.5 
 
 85000 
 95000 
 110000 
 125COO 
 
 48000 
 60000 
 72000 
 5000 
 
 26 
 22 
 18 
 13 
 
 55 
 
 48 
 40 
 32 
 
498 STEEL, 
 
 .As compared with simple steels of the same tensile strength a 3% 
 nickel steel will have from 10 to 20% higher E. L. and from 20 to 30% 
 greater elongation, while as compared with simple steels of the same 
 carbon, the nickel steel, up to 5% Ni, will have about 40% greater tensile 
 strength, with practically the same elongation and reduction of area 
 
 Cholat and Harmet found with 0.30 C and 15% Ni a T. S. of 213 400* Ibs 
 per sq. in.; when oil-tempered a T. S. of 277,290 and an E. L. of 166 300' 
 
 Riley states that steel of 25% Ni and 0.27 C gave a T S of 102 600 
 and elong. 29%, while steel of 25% Ni gave 94,300 T. S. and 40% elong. 
 Steels high m Ni are entirely different in physical properties from low- 
 nickel steels. 
 
 EFFECT OF Ni ON HARDNESS. Gun barrels with 4.5% Ni and 30 C are 
 3!&^8r lr ry C S 1 fS e iT- S ' ' 00 .' elon - 25%, red. of area 45%'. Rolls 
 with 5% Ni and 1 % C turned easier than simple steel of 1 % C. If a steel 
 contains less than 6% Ni the influence of the C present on the hardness 
 produced by water quenching is strongly marked. Above 8% Ni the effect 
 of the C seems to be masked by the Ni; steel with 18% Ni is as hard and 
 elastic with 0.30 as with 0.75 C. If steel with 18% Ni and 0.60 C be heated 
 and plunged in water it will be perceptibly softened, and if the Ni is 
 raised to 25% this softening is very noticeable. 
 ' COMPRESSION TESTS OF LOW-CARBON NICKEL STEELS. (Hadfield.) 
 
 Carbon 
 
 0.13 
 0.95 
 20 
 49 
 
 0.14 
 1.92 
 27 
 47 
 
 0.19 
 3.82 
 28 
 41 
 
 0.18 
 5.81 
 40 
 37 
 
 0.17 
 7.65 
 40 
 33 
 
 0.16 
 9.51 
 70 
 3 
 
 0.18 
 11.39 
 100 
 1 
 
 0.23 
 13.48 
 80 
 1 
 
 0.19 
 19.64 
 80 
 3 
 
 0.16 
 24.51 
 50 
 16 
 
 0.14 
 29.07 
 
 24 
 41 
 
 Nickel...- 
 E. L. t tons 
 Shortening* . . . 
 
 * Shortening by 100-ton load, %. 
 
 SPECIFIC GRAVITY. The sp. gr. of low-carbon nickel steels containing 
 up to 15% Ni is about the same as that of carbon steel, from 7.86 to 7.90; 
 from 19 to 39% Ni it is from 7.91 to 8.08; one sample of wire of 29% Ni, 
 however, being reported at 8.4. A 44% Ni steel, according to Guillaume, 
 lias a sp. gr. of 8.12. 
 
 THE RESISTANCE OF CORROSION of nickel steel increases with the per- 
 centage of Ni up to 18. "This alloy is practically non-corrodible." 
 "Tico " resistance wire, 27.5% Ni, was very slightly rusted after a year's 
 exposure in a wet cellar; iron wire under the same conditions was entirely 
 changed to oxide. With the ordinary nickel steels, 3 to 3.5% Ni, corrosion 
 is slightly less than in simple steels. 
 
 ELECTRICAL RESISTANCE. All nickel steels have a high electrical resist- 
 ance which does not seem to vary much with the percentage of Ni. The 
 resistance wires, "Tico," "Superior," and "Climax," containing from 25 
 to 30% Ni, have about 48 times, while German silver has about 18 times 
 the resistance of copper. 
 
 MAGNETIC PROPERTIES. According to Guillaume all nickel steels below 
 25.7% Ni can be, at the same temperature, either magnetic or non- 
 magnetic, according to their previous heat-treatment, and they show 
 different properties at ascending and at descending temperatures. The 
 low-nickel steels, 3 to 5% Ni, possess a magnetic permeability greater than 
 that of wrought iron. 
 
 Nickel Steel for Bridges. J. A. L. Waddell, Trans. A. S. C. E., 1908, 
 presents at length an argument in favor of the use of nickel steel in long- 
 span bridges. 
 
 Some Uses of Nickel Steel. (F. L. Sperry, A . I. M. E., xxv, 51.) The 
 propeller shaft of the U. S. cruiser Brooklyn was made of hollow-forged, 
 oil-tempered nickel steel, 17 in. outside, 11 in. inside diam., length 38 ft. 11 
 in., weight per foot, 449 Ibs. Test bars cut from the tube gave T. S., 90,350 
 to 94,245; E. L., 56,470 to 60,770; El. in 2 in., 25.5 to 28.0%; Red. of area, 
 59.8 to 61.3%. A solid shaft of the same elastic strength of simple steel, 
 having anE.L.of 3/ 5 of that of the nickel steel, would be 18.9 in. diam., and 
 would have weighed 920 Ibs. per foot. 
 
 The rotating field of the 5000 H.P. electric generators of the Niagara 
 Falls Power Co. is inclosed in a ring of forged nickel steel, outside diam. 
 1393/ 8 in.; inside, 130 in.; width, 503/4 in.; weight, 28,840 Ibs. It travels 
 at the rate of nearly two miles per minute. 
 
 Nickel steel wire with 27.7% Ni and 0.40 C used for torpedo defense 
 netting, 0.116 in. diam., gave a T. S. of 198,700; El. in 2 in., 6.25%; Red. 
 of area, 16,5%. 
 
499 
 
 Flange plate of soft nickel steel, Ni. 2.69; C, 0.08; Mn, 0.36; P, 0.045; S, 
 0.038, gave, average of 6 tests, T. S-, 65,760; E. L., 47,080; El. in 8 in., 
 24.8%: Red. of area, 52.0%. For comparison: Soft carbon steel, C, 
 0.10; Mn, 0.27; P, 0.048; S, 0.039; T. S., 54,450; E. L., 35.240; El., 27.4%; 
 Red. of area, 55.3%. 
 
 Coefficients of Expansion of Nickel Steel. (D. H. Browne, 
 A.L M. E., 1899.) Per degree C. (Prefix 0.0000 to the figures here given.) 
 % Ni. 26. 28. 28.7 30.4 31.4 34.6 35.6 37.3 39.4 44.4 
 Coeff. 1312 1131 1041 0458 0340 0137 0087 0356 0537 0856 
 
 For comparison: Brass, 1878; Hard steel, 1239; Soft steel, 1078; 
 Platinum, 0884; Glass, 0861; Nickel, 1252. Ordinary commercial nickel 
 steels, containing 3 to 4% Ni, have coefficients about the same as carbon 
 steel. See also page 567. 
 
 Invar is a nickel-iron alloy, which is characterized by an extraordinarily 
 low coefficient of expansion at ordinary temperatures. The analysis is 
 about as follows: carbon, 0.18; nickel, 35.5%; manganese, 0.42, the 
 other elements being low. Guillaume gives the mean coefficient of 
 expansion for an alloy containing 35.6% nickel as (0.877 + 0.00117 10 ~ 6 
 between temperatures C. and t C. where t does not exceed 200 C. 
 This material is used in measuring instruments and for standards of 
 length, chronometers, etc. Its expansion as compared with ordinary 
 steel is about as 1:11.5; with brass, as 1:17.2; with glass, as 1 : 8.5. Alloys 
 either richer or poorer in nickel show much greater expansion, and the 
 alloy containing 47.5% nickel, known as "Platinite," has the same 
 coefficient of expansion as platinum and glass. See also page 507. 
 
 Copper Steels. Pierre Breuil (Jour. I. and S. /., 1907) gives an account 
 of experiments on four series of copper steels containing respectively 0.15, 
 0.40, 0.65, and 1% of C with Cu in each ranging from to 34%. An ab- 
 stract of his principal conclusions is as follows: 
 
 Copper steel does not yield a metal capable of being rolled in practice, 
 if Cu exceeds 4%. 
 
 When in the ingot state copper hardens steel in proportion as there is 
 less C present. 
 
 Copper steels as rolled appear to be stronger in proportion as they con- 
 tain more Cu. This difference is the more manifest in proportion as the 
 C is lower. 
 
 Annealing leaves the steels with the same characteristics, but greatly 
 reduces the differences observed in the case of the untreated steeJs. 
 Quenching restores the differences encountered in the case of the steels 
 as cast. 
 
 Copper steels equal nickel steels in tensile strength and would be less 
 costly than the latter. They are no more brittle than nickel steels con- 
 taining equivalent percentages of Ni. The steel containing 0.16% C and 
 4% Cu is remarkable in this respect. 
 
 The presence of copper makes the cpnstituents of the steel finer, 
 approximating them to classes containing higher percentages of C. 
 While hardening the steel the presence of Cu does not render it brittle. 
 It confers upon it a very fair degree of elasticity, while leaving the elon- 
 gation good, thus conducing to the production of a most valuable metal. 
 
 Cutting tests were carried on with steels containing C about 1 % and 
 Cu 0%, 1%, and 3% respectively. The presence of Cu in no wise altered 
 the cutting properties. 
 
 The presence of Cu was found to increase the electrical resistance, 
 and a well-defined maximum was shown, coinciding with 2% Cu in 0.15 C, 
 with 1.7% in 0.35% C, and with 0.5% Cu in 0.7 to 1% carbon steels. 
 
 Nickel- Vanadium Steels. (Eng. Mag., April, 1906.) M. Leon Guillet 
 has investigated the influence of Ni and Va when used jointly. 
 
 In steels containing 0.20 C and from 2 to 12% of Ni, the tensile strength 
 and the elastic limit are both materially increased by the addition of 
 small percentages of Va. In no case should the Va exceed 1%, the best 
 results being secured by the use of 0.7 to 1 %. A steel containing 0.20 C, 
 2% of Ni, and 0.7% Va showed a tensile strength of 91,000 Ibs., an 
 elastic limit of 70,000 Ibs., and an elongation of 23.5%. With 1% Va, 
 the T. S. increased to 119,500 Ibs., and the E. L. to 91,000 Ibs., the elong. 
 falling to 22%. A nickel steel of 0.20% C and 12% Ni gave, with 
 0.7 Va, a T. S. of over 200,000 Ibs. and an E. L. of 172,000 Ibs. per sq. in., 
 the elong. being Q%, while with, 1% V$ theT. S, rose to 220,000 Ibs. 
 
500 STEEL. 
 
 and the E L. to 176,000 Ibs., the elongation remaining unchanged. 
 When the Va is increased above l%the tensile strength falls off, and the 
 material begins to show evidence of brlttleness. Similar effects are pro; 
 duced for steels of the higher carbon, but in a lesser degree. 
 
 Whpn the nickel-vanadium steels are subjected to a tempering procsss 
 th Tbeneficial Sets of theVa are still further emphasized .The temper- 
 
 
 i 
 
 and an E. L. of 150,000 Ibs., the resistance to shock and the h 
 being also increased. 
 
 Static and Dynamic Properties of Steels. (W. L. Turner, Ira 
 July 2, 1908.) The term "crystallization" is a name given to designate 
 Phenomena due to the influences of shock and alternating stresses 
 whether pure or combined. The name has been advantageously altered 
 to " intermodular disintegration," but, whatever we choose to call it, 
 there remains the evidence that some modification takes place in the 
 structure of steel when the above-named forces are to be dealt with. 
 Resistance to fatigue is not a function of static strength 
 An example of our knowledge of the. "life" properties of ordinary st 
 is the case of the staying of a locomotive fire-box. Something is 
 quired which will possess considerable strength combined with the 
 power to withstand a moderate degree of flexure in all directions. Expe- 
 rience has shown that the use of anything but the mildest steel for this 
 work is prohibitive, and that wrought iron, or even copper, is still more 
 
 The writer has completed a preliminary investigation into the relative 
 dynamic properties of iron and the various ordinary and alloy steels 
 the results being given in the accompanying table. The conditions of 
 the "dynamic" tests were as follows: 
 
 A cylindrical test-piece, 6 in. long, 3/ 8 in. diam., finished with emery to 
 remove all tool marks, is clamped at one end in a vise. A tool-steel 
 head, in which there is cut a slot, is placed over the other end, the dis- 
 tance from the striking center of this head to the vise line being 4 in. 
 A crank and connecting rod furnished the reciprocating motion for this 
 head, thereby causing the test-piece to be deflected 3/ 8 in. each side of 
 the neutral position. In addition to this alternating flexure, the test- 
 piece is also subjected, at each reversal, to an impact, due to the slot on 
 the reciprocating head. The sample undergoes 650 alternations per 
 minute. A deflection of 3/g in. on each side has the effect of imparting a 
 permanent set to the test-piece. 
 
 On each class of steel a large number of dynamic tests were made, an 
 average being taken of the results after elimination of those figures which 
 were apparently abnormal. 
 
 It is apparent that the action of nickel is twofold: 1. It statically 
 intensifies. 2. It dynamically " poisons." As an instance of this, take 
 tests Nos. 13 and 15, the former being a 3.7% nickel steel and the latter a 
 chrome-vanadium steel. In the annealed condition, the elastic limits of 
 the two are almost identical, but at the same time the alternations of 
 stress endured by the latter are 21/4 times the number sustained by the 
 nickel steel. Take again Nos. 17 and 18. The dynamic figures are more 
 than three to one in favor of the chrome-vanadium product, whereas tha 
 difference in elastic limit is only about 3%. 
 
 It is manifest that the static action of vanadium is similar to that of 
 nickel, but that its dynamic effects are the exact converse.. The differ- 
 ences are markedly brought out in the quality figures, which invite 
 attention as to comparison with those of ordinary carbon steel. Taking 
 the latter as standard, the chrome-vanadium steels are as much above it 
 as the nickel steels are below it. 
 
 Chromium, per se, does not appear to exert appreciable influence other 
 than statically, but it is possible that the effect of this metal in a ternary 
 steel might be very marked. 
 
 The dynamic attributes of plain carbon steel reach a maximum with 
 about 0.25% C. falling away on both sides of this amount. 
 
 The quality figure in the case of the chrome-vanadium steel does not 
 
ALLOY STEELS. 
 
 501 
 
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 ^^ r i a^'ir-l'i o.Vi'1 
 
502 
 
 STEEL. 
 
 appear to undergo much alteratipn in the process of oil tempering, but 
 
 there are considerable variations in other cases. The dynamic test may 
 eventually act as a reliable guide to the correct methods for the heat 
 treatment of individual steels. 
 
 Strength for strength, the chrome-vanadium steels also have the 
 advantage over all others as regards machining properties. Chrome- 
 vanadium steel may be forged with the same ease as ordinary steel of simi- 
 lar contents, no special precaution being necessary as to temperatures. 
 
 Comparative Effects of Cr and Va. Sankey and J. Kent Smith, Proc. 
 Inst. M. E., 1904. 
 
 Cr. Va. 
 
 T.S.* 
 
 E.L.* 
 
 El. in 
 2 in. 
 
 Red. A. 
 
 Cr. Va. 
 
 T.S.* 
 
 E.L.* 
 
 El. in 
 2 in. 
 
 Red. A. 
 
 0.5 . 
 
 34.0 
 
 22.9 
 
 33% 
 
 60.6% 
 
 1.0 0.15 
 
 48.6 
 
 36.2 
 
 24 
 
 56.6 
 
 1.0 . 
 
 38.2 
 
 25.0 
 
 30 
 
 57.3 
 
 1.0 0.15 
 
 f52.6 
 
 34.4 
 
 25.0 
 
 55.5 
 
 ... 0.1 
 
 34.8 
 
 28.5 
 
 31 
 
 60 
 
 1.0 0.25 
 
 60.4 
 
 49.4 
 
 18.5 
 
 46.3 
 
 ... 0.15 
 
 36.5 
 
 30.4 
 
 26 
 
 59.0 
 
 C-Mn 
 
 27.0 
 
 16.0 
 
 35. 
 
 60.0 
 
 ... 0.25 
 
 39.3 
 
 34.1 
 
 24 
 
 59.0 
 
 C-Mn 
 
 t32.2 
 
 17.7 
 
 34. 
 
 52.6 
 
 * Tons, of 2240 Ibs., per sq. in. f Open-hearth steels; all the others 
 are crucible. The last two steels in the table are ordinary carbon 
 steels. 
 
 Effect of Heat Treatment on Cr-Va Steel. (H. R. Sankey and 
 J. Kent Smith, Proc. Inst. M. E., 1904, p. 1235.) Various kinds of 
 heat treatment were given to several Cr-Va steels, the results of which 
 are recorded at length. The following is selected as a sample of the 
 results obtained. Steel with C, 0.297; Si, 0.086; Mn, 0.29; Cr, 1.02; Va, 
 0.17. gave: 
 
 
 Tens. 
 
 Str. 
 
 Yield 
 Point. 
 
 El. in 
 2 in. 
 
 Red. 
 Area. 
 
 Im- 
 pact. 
 
 Alter- 
 na- 
 tions. 
 
 
 121,200 
 
 82,650 
 
 24.0% 
 
 44.9% 
 
 3.1 
 
 1906 
 
 Annealed 1/2 hr. at 800 C 
 
 87360 
 
 47260 
 
 34 5 
 
 H 1 
 
 15 6 
 
 2237 
 
 Soaked 12 hours at 800 C 
 
 86020 
 
 68 100 
 
 33 7 
 
 51 5 
 
 11.2 
 
 
 Water quenched at 800 C. . . 
 
 167 100 
 
 135'070 
 
 7 5 
 
 16 6 
 
 1 2 
 
 174 
 
 Oil quenched at 800 C 
 
 122,080 
 
 82880 
 
 22 
 
 35 2 
 
 2.4 
 
 296 
 
 Oil quenched at 800, reheated to 
 350 
 
 132 830 
 
 111 550 
 
 23 
 
 50 8 
 
 9 
 
 1314 
 
 Water quenched at 1200 C 
 
 209 440 
 
 191 520 
 
 1 2 
 
 1 5 
 
 * 
 
 * 
 
 Oil quenched at 1200 C 
 
 140,220 
 
 118i500 
 
 8.5 
 
 21.5 
 
 3.0 
 
 
 * Too hard to machine. 
 
 The impact tests were made on a machine described in Eng'g, Sept. 25, 
 1903, p. 431. The test-piece was 8/4 in. broad, notched so that 0.137 in. in 
 depth remained to be broken through. The figures represent ft .-Ibs. of 
 energy absorbed. The piece was broken in one blow. The alternations- 
 of-stress tests were made on Prof. Arnold's machine, described in The 
 Engineer, Sept. 2, 1904, p. 227. The pieces were 3/ 8 in. square, one end 
 was gripped in the machine and the free end, 4 in. long, was bent forwards 
 and backwards about 710 times a minute, the motion of the free end being 
 3/4 in. on each side of the center line. 
 
 Tests by torsion of the same steel were made. The test-piece was 6 in. 
 long, 3/4 in. diam. The results were: 
 
 As rolled 
 
 Shearing Stress 
 
 Twist 
 Angle. 
 
 No. of 
 Twists. 
 
 ~3~92~~ 
 4.52 
 
 Elastic . 
 
 Ulti- 
 mate. 
 
 45,700 
 38,528 
 
 99,900 
 90,272 
 
 1410 
 1628 
 
 Annealed 1/2 hr. at 800 C. 
 
"ALLOY" STEELS. 503 
 
 TTont-ttoaimont of Alloy Steels. (E. F. Lake, Am. Mach., Aug. 1, 
 1907.) In working the high-grade alloy steels it is very important that 
 they be properly heat treated, as poor workmanship in this regard will 
 produce working parts that are no better than ordinary steel, although 
 the stock used be the highest grade procurable. By improperly heat- 
 treating them it is possible to make these high-grade steels more brittle 
 than ordinary carbon steels. 
 
 The theory of heat treatment rests upon the influence of the rate of 
 cooling on certain molecular changes in structure occurring at different 
 temperatures. These changes are of two classes, critical and progres- 
 sive; the former occur periodically between certain narrow temperature 
 limits, while the latter proceed gradually with the rise in temperature, 
 each change producing alterations in the physical characteristics. By 
 controlling the rate of cooling, these changes can be given a permanent 
 set, and the characteristics can thus be made different from those in the 
 metal in its normal state. 
 
 The results obtained are influenced by certain factors: 1. The original 
 chemical and physical properties of the metal; 2. The composition of 
 the gases and other substances which come in contact with the metal in 
 heating and cooling. 3. The time in which the temperature is raised 
 between certain degrees. 4. The highest temperature attained. 5. The 
 length of time the metal is maintained at the highest temperature. 
 6. The time consumed in allowing the temperature to fall to atmos- 
 pheric. 
 
 The highest temperature that it is safe to submit a steel to for heat- 
 treating is governed by the chemical composition of the steel. Thus 
 pure carbon steel should be raised to about 1300 F., while some of the 
 high-grade alloy steels may safely be raised to 1750. The alloy steels 
 must be handled very carefully in the processes of annealing, hardening, 
 and tempering; for this reason special apparatus has been installed to 
 aid in performing these operations with definite results. 
 
 The baths for quenching are composed of a large variety of materials. 
 Some of the more commonly used are as follows, being arranged accord- 
 ing to their intensity on 0.85% carbon steel: Mercury; water with sulphuric 
 acid added; nitrate of potassium; sal ammoniac; common salt; carbonate 
 of lime; carbonate of magnesia; pure water; water containing soap, 
 sugar, dextrine or alcohol; sweet milk; various oils; beef suet; tallow,- 
 wax. 
 
 With many of these alloy steels a dual quenching gives the best results, 
 that is, the metal is quenched to a certain temperature in one bath and 
 then immersed in the second one until completely cooled, or it may 
 be cooled in the air after being quenched in the first bath. For this a 
 lead bath, heated to the proper temperature, is sometimes used for the 
 first quenching. 
 
 With the exception of the oils and some of the greases, the quenching 
 effect increases as the temperature of the bath lowers. Sperm ana lin- 
 seed oils, however, at all temperatures between 32 and 250, act about 
 the same as distilled water at 160. 
 
 The more common materials used for annealing are powdered char- 
 coal, charred bone, charred leather, fire clay, magnesia or refractory 
 earth. The piece to be annealed is usually packed in a cast-iron box 
 in some of these materials or combinations of them, the whole heated 
 to the proper temperature and then set aside, with the cover left on, to 
 cool gradually to the atmospheric temperature. For certain grades of 
 steel these materials give good results; but for all kinds of steels and for 
 all grades of annealing, the slow-cooling furnace no doubt gives the 
 best satisfaction, as the temperature can be easily raised to the right 
 point, kept there as long as necessary, and then regulated to cool down 
 as slowly as is desired. The gas furnace is the easiest to handle and 
 regulate. 
 
 A high-grade alloy steel should be annealed after every process in man- 
 ufacturing which tends to throw it out of its equilibrium, such as forging, 
 rolling and rough machining, .so as to return it to its natural state of 
 repose. It should also be annealed before quenching, case-hardening 
 or carbonizing. 
 
 The wide range of strength given to some of the alloy steels by heat 
 
504 
 
 STEEL. 
 
 treatment is shown by the table below. The composition of the 
 was: Ni, 2.43; Cr, 0.42; Si, 0.26; C, 0.23; Mn, 0.43; P, 0.025; S, 0.022. 
 
 alloy 
 
 
 $* 
 
 -g* 
 
 Sfc 
 
 ^ 
 
 'S? 
 
 ^0^' 
 
 .r-r'. 
 
 So 
 
 
 -Sg 
 
 Ik 
 
 Is 
 
 
 li 
 
 |3 
 
 Ig 
 
 
 0> 
 
 
 sS 
 
 S 1 ^ 
 
 s~ 
 
 g~ 
 
 6"" 
 
 
 O 1 ^ 
 
 H * 
 
 H * 
 
 H * 
 
 H * 
 
 H^ 
 
 H^ 
 
 Tensile Strength . 
 E. L 
 
 227,000 
 208,000 
 
 219,000 
 203,500 
 
 195,500 
 150,000 
 
 172,000 
 148,500 
 
 156,500 
 125,000 
 
 141,000 
 102000 
 
 109,500 
 70,500 
 
 Elong.,% in 2 in. 
 
 4 
 
 6 
 
 8 
 
 11 
 
 13 
 
 15 
 
 22 
 
 VARIOUS SPECIFICATIONS FOR STEEL. 
 
 Structural Steel. There has been a change during the ten years from 
 1880 to 1890, in the opinions of engineers, as to the requirements in speci- 
 fications for structural steel, in the direction of a preference for metal of 
 low tensile strength and great ductility. The following specifications for 
 tension members at different dates are given by A. E. Hunt and G. H. 
 Clapp, Trans. A. I. M. E., xix, 926: 
 
 1879. 
 
 Elastic limit.. . . 50,000 40 < 
 Tensile strength 80,000 70 
 Elongation in 8 in. 12% 
 Reduction of area 20% 
 
 1881. 1882. 1885. 1887. 1888. 
 
 ^ 45,000 40,000 40,000 40,000 38,000 
 
 ^80,000 70,000 70,000 67@75,000 63 70,000 
 
 18% IS'% 18% 20% 22% 
 
 30% 45% 42% 42% 45% 
 
 F. H. Le.vis (IronAqe, Nov. 3, 1892) says: Regarding steel to be used 
 under the same conditions as wrought iron, that is, to be punched without 
 reaming, there seems to be a decided opinion (and a growing one) among 
 engineers, that it is not safe to use steel in this way, when the ultimate 
 tensile strength is above 65,000 Ibs. The reason for this is not so much 
 because there is any marked change in the material of this grade, but 
 because all steel, especially Bessemer steel, has a tendency to segregations 
 of carbon and phosphorus, producing places in the metal which are harder 
 than they normally should be. As long as the percentages of carbon and 
 phosphorus are kept low, the effect of these segregations is inconsiderable' 
 but when these percentages are increased, the existence of these hard 
 spots in the metal becomes more marked, and it is therefore less adapted 
 to the treatment to which wrought iron is subjected. 
 
 There is a wide consensus of opinion that at an ultimate of 64,000 to 
 65,000 Ibs. the percentages of carbon and phosphorus reach a point where 
 the steel has a tendency to crack when subjected to rough treatment. 
 
 A grade of steel, therefore, running in ultimate strength from 54,000 to 
 62,000 Ibs., or in some cases to 64,000 Ibs., is now generally considered a 
 proper material for this class of work. 
 
 A. E. Hunt, Trans. A. I. M. E., 1892, says: Why should the tests for steel 
 be so much more rigid than for iron destined for the same purpose? Some 
 of the reasons are as follows: Experience shows that the acceptable quali- 
 ties of one melt of steel offer no absolute guarantee that the next melt to it, 
 even though made of the same stock, will be equally satisfactory. 
 
 It is now almost universally recognized that soft steel, if properly made 
 and of good quality, is for many purposes a safe and satisfactory substitute 
 for wrought iron, being capable of standing the same shop-treatment as 
 wrought iron. But the conviction is equally general, that poor steel, or an 
 unsuitable grade of steel, is a very dangerous substitute for wrought iron 
 even under the same unit strains. 
 
 For this reason it is advisable to make more rigid requirements in select- 
 Ing material which may range between the brittleness of glass and a duc- 
 tility greater than that of wrought iron. 
 
 Specifications for Structural Steel for Bridges. (Proc. A. S. T. M. ( 
 1905.) Steel shall be made by the open-hearth process. The chemi* 
 cal and physical properties shall conform to tUe following limits; 
 
VARIOUS SPECIFICATIONS FOR STEEL-. 
 
 Elements Considered. 
 
 Structural Steel. 
 
 Rivet Steel. 
 
 Steel Castings 
 
 Phosphorus, f Basic . . . 
 Max \ Acid. . . . 
 
 0.04% 
 0.08% 
 05% 
 
 0.04% 
 0.04% 
 04% 
 
 0.05% 
 0.08% 
 05% 
 
 Tensile strength, Ibs. 
 per SQ in . . . 
 
 f Desired 
 | 60 000 
 
 Desired 
 50,000 
 
 Not less than 
 65,000 
 
 Elong.: Min. % in 8 in. 
 Elong Min % in 2 in 
 
 ( 1,500,000* 
 ( tens. str. 
 
 1,500,000 
 tens. str. 
 
 18 
 
 Fracture 
 
 Silky 
 
 Silky 
 
 Silky or fine 
 
 Cold bend without 
 fracture 
 
 180 flatf 
 
 180 flat* 
 
 granular 
 90. d=3t 
 
 
 
 
 
 * The following modifications will be allowed in. the requirements for 
 elongation for structural steel: For each Vie inch in thickness below 
 5/16 inch, a deduction of 2 1/2 will be allowed from the specified percent- 
 age. For each Vs inch in thickness above 3/4 inch, a deduction, of 1 will 
 be allowed from the specified percentage. 
 
 t Plates, shapes and bars less than 1 in. thick shall bend as called for. 
 Full-sized material for eye-bars and other steel 1 in. thick and over, tested 
 as rolled, shall bend cold 180 around a pin of a diameter twice the thick- 
 ness of the bar, without fracture on the outside of bend. When required 
 by the inspector, angles 3/ 4 in. and less in thickness shall open flat, and 
 angles 1/2 in. and less in thickness shall bend shut, cold, under blows of 
 a hammer, without sign of fracture. 
 
 J Rivet. steel, when nicked and bent around a bar of the same diam- 
 eter as the rivet rod, shall give a gradual break and a fine, silky, uniform 
 fracture. 
 
 If the ultimate strength varies more than 4000 Ibs. from that desired, 
 a retest may be made, at the discretion of the inspector, on the same 
 gauge, which, to be acceptable, shall be within 5000 ibs. of the desired 
 strength. 
 
 Chemical determinations of C, P, S, and Mn shall be made from a 
 test ingot taken at the time of the pouring of each melt of steel. Check 
 analyses shall be made from finished material, if called for by the pur- 
 chaser, in which case an excess of 25% above the required limits will be 
 allowed. 
 
 Specimens for tensile and bending tests for plates, shapes and bars 
 shall be made by cutting coupons from the finished product, which shall 
 have both faces rolled and both edges milled with edges parallel for at 
 least 9 in.; or they may be turned 3/ 4 in. diam. for a length of at least 
 9 in., with enlarged ends. Rivet rods shall be tested as rolled. Speci- 
 mens shall be cut from the finished rolled or forged bar in such manner 
 that the center of the specimen shall be 1 in. from the surface of the bar. 
 The specimen for tensile test shall be turned with a uniform section 2 in. 
 long, with enlarged ends. The specimen for bending test shall be 1 X 1/2 
 in. in section. 
 
 Specifications for Steel for the Manhattan Bridge. (Eng. News, 
 Aug. 3, 1905.) 
 
 MATERIAL FOR CABLES. SUSPENDERS AND HAND ROPES. Open- 
 hearth steel. (The wire for serving the cables shall be made of Norway 
 iron of approved quality.) The ladle tests of the steel shall contain not 
 more than : C, 0.85; Mn, 0.55; Si, 0.20; P, 0.04; S, 0.04; Cu, 0.02%. 
 The wire shall have an ultimate strength of not less than 215,000 Ibs. 
 per sq. in. before galvanizing, and an elongation of not less than 2% in 
 12 in. The bright wire shall be capable of bending cold around a rod 
 ]i/2' times its own diam. without sign of fracture. The cable wire before 
 galvanizing shall be 0.192 in. 0.003 in. in diam.; after galvanizing, the 
 wire shall have an ultimate strength of not less than 200,000 Ibs. per sq. 
 in. of gross section. 
 
506 
 
 STEEI*. 
 
 CARBON STEEL. The ladle tests as usually taken shall contain not 
 more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10%. The ladle tests of 
 the carbon rivet steel shall contain not more than: P, 0.035; S, 0.03. 
 Rivet steel shall be used for all bolts amd threaded rods. 
 
 NICKEL STEEL. The ladle test shall contain not less than 3.25 Ni, 
 and not more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10; nickel rivet steel 
 not more than: P, 0.035; S, 0.03%. 
 
 Nickel steel for plates and shapes in the finished material must show: 
 T. S., 85,000 to 95,000 Ibs. per sq. in.; E. L., 55,000 Ibs. min.; elong. in 
 8 ins., min., = 1,600,000 4- T. S.; min. red. of area, 40%. 
 
 Specimens cut from the finished material shall show the following 
 physical properties: 
 
 Material. 
 
 T. S., Ibs. persq. 
 in. 
 
 Min.E.L. 
 Ibs. per 
 sq. in. 
 
 Min. 
 Elong., 
 % in 8 in. 
 
 Min. Red. 
 of Area. 
 
 %. 
 
 Shapes and universal mill 
 plates 
 
 60,000 to 68,000 
 
 33 000 
 
 
 44 
 
 Eye-bars, pins and rollers. 
 Sheared plates 
 
 64,000 to 72,000 
 60,000 to 68 000 
 
 35,000 
 33 000 
 
 1,500,000 
 
 40 
 
 44 
 
 Rivet rods 
 
 50 000 to 58 000 
 
 30 000 
 
 ~~TT' P 
 
 50 
 
 High-carbon steel for 
 trusses 
 
 85,000 to 95,000 
 
 45,000 
 
 
 35 
 
 Nickel rivet steel: T. S., 70,000 to 80,000; E. L., min., 45,000; elong., 
 min., 1,600,000 * T. S., % in 8 ins. 
 
 STEEL CASTINGS. The ladle test of steel for castings shall contain 
 not more than: P, 0.05; S, 0.05; Mn, 0.80; Si, 0.35%. Test-pieces taken 
 from coupons on the annealed castings shall show T. S., 65,000; E. L., 
 35,000; elong. 20% in 8 ins. They shall bend without cracking around a 
 rod three times the thickness of the test-piece. 
 
 Specifications for Steel. (Proc. A. S. T. M., 1905.) 
 
 Steel Forgings. 
 
 Kind of 
 Steel. 
 
 Tensile 
 Strength. 
 
 Elast. 
 Limit. 
 
 El. in 
 2 in., 
 
 %. 
 
 Red 
 Area. 
 
 % 
 
 Solid or hollow forgings, no diam. 
 or thickness of section to exceed 
 
 IS. 
 
 Ic. 
 
 |C.A. 
 
 58,000 
 75,000 
 80,000 
 
 29,000* 
 37,500* 
 40,000 
 
 28 
 18 
 22 
 
 35 (a) 
 30 (c) 
 35 (b) 
 
 10 in. 
 
 JN.A. 
 
 80,000 
 
 50,000 
 
 25 
 
 45 (a) 
 
 Solid or hollow forgings, diam. 
 not to exceed 20 in. or thickness 
 of section 15 in. 
 
 )C.A. 
 JN.A. 
 
 75000 
 80,000 
 
 37,500 
 45,000 
 
 23 
 25 
 
 35 (b) 
 45 (a) 
 
 Solid forgings over 20 in. .... 
 
 C.A. 
 
 70,000 
 
 35,000 
 
 24 
 
 30 (c) 
 
 Solid forgings 
 
 N.A. 
 
 80,000 
 
 45,000 
 
 24 
 
 40 (a) 
 
 Solid or hollow forgings, diam. or 
 thickness not over 3 in. 
 
 )C.O. 
 
 JN.O. 
 
 90,000 
 95,000 
 
 55,000 
 65,000 
 
 20 
 21 
 
 45 (b) 
 50 (b) 
 
 Solid rectangular sections, thick- 
 ness not over 6 in., or hollow 
 with walls not over 6 in. thick. 
 
 Jc.o. 
 
 JN.O. 
 
 85,000 
 90,000 
 
 50000 
 60,000 
 
 22 
 22 
 
 45 (b) 
 50 (b) 
 
 Solid rect. sections, thickness not 
 over 10 in., or hollow with walls 
 not over 10 in. thick. 
 
 Jc.o. 
 
 JN.O. 
 
 80,000 
 85,000 
 
 45,000 
 55,000 
 
 23 
 
 24 
 
 40 (b) 
 
 45 (b) 
 
 Locomotive forgings 
 
 * 
 
 80,000 
 
 40,000 
 
 20 
 
 25 (d) 
 
 
 
 
 
 
 
 * The yield point, instead of the elastic limit, is specified for soft steel 
 and carbon steel not annealed. It is determined by the drop of the 
 beam or halt in the gauge of the testing machine. The elastic limit, 
 specified for all other steels, is determined by an extensometer, and is 
 defined as that point where the proportionality changes. The standard 
 test specimen is 1/2 in. turned diam. with a gauged length of 3 iaches. 
 
VARIOUS SPECIFICATIONS 1'OK STJEEIi. 
 
 507 
 
 Kind of steel: S., soft or low carbon. C., carbon steel, not annealed. 
 C. A., carbon steel, annealed. C. O., carbon steel, oil tempered. N. A., 
 nickel steel, annealed. N. O., nickel steel, oil tempered. Bending 
 tests: A specimen 1 X V2 in. shall bend cold 180 without fracture on 
 outside of bent portion, as follows: (a) around a diam. of 1/2 in.; (6) 
 around a diam. of 1 in.; (c) around a diam. of 1/2 in.; (d) no bending 
 test required. 
 
 Chemical composition: P and S not to exceed 0.10 in low-carbon steel, 
 0.06 in carbon steel not annealed, 0.04 in carbon or nickel steel oil tem- 
 pered or annealed, 0.05 in locomotive forgings. Mn not to exceed 0.60 
 in locomotive forgings. Ni 3 to 4% in nickel steel. 
 
 Specifications for Steel Ship Material. (Amer. Bureau of Shipping, 
 1900. Proc. A. S. T. M. t 1906, p. 175.) 
 
 For Hull Construction. 
 
 Tens. Strength. 
 
 E. L. 
 
 El. in 
 8 in.. %. 
 
 Plates, angles and shapes 
 
 58 000 to 60 000 
 
 1/2 T. S 
 
 22* 18t 
 
 Castings 
 
 60 000 to 75 000 
 
 
 15 
 
 Forgings 
 
 55 000 to 65 000 
 
 
 20 
 
 
 
 
 
 * In plates 18 Ibs. per sq. ft. and over. f In plates under 18 Ibs. 
 
 FOR MARINE BOILERS: Open-hearth steel; Shell: P and S, each not over 
 0.04%. Fire-box, not over 0.035%. Tensile Strength: Rivet steel, 
 45,000 to 55,000; Fire-box, 52,000 to 62,000; Shell, 55,000 to 73,000; 
 Braces and stays, 55,000 to 65,000; Tubes and all other steel, 52,000 to 
 62,000 Ibs. per sq. in. 
 
 Elongation in 8 in.: Rivet steel, 28%; Plates 3/ 8 in. and under, 20%; 
 3/8 to 3/4 in., 22%; 3/ 4 i n . and over, 25%. 
 
 COLD BENDING AND QUENCHING TESTS. Rivet steel and all steel of 
 52,000 to 62,000 Ibs. T. S., 1/2 in. thick and under, must bend 180 flat on 
 itself without fracture on outside of bent portion; over 1/2 in. thick, 180 
 around a mandrel 11/2 times the thickness of the test-piece. For hull 
 construction a specimen must stand bending on a radius of half its thick- 
 ness, without fracture on the convex side, either cold or after being 
 heated to cherry-red and quenched in water at 80 F. 
 
 High-strength Steel for Shipbuilding. (Eng'g, Aug. 2, 1907, p. 137.) 
 The average tensile strength of the material selected for the Lusitania 
 was 82,432 Ibs. per sq. in. for normal high-tensile steel, and 81,984 lbs> 
 for the same annealed, as compared with 66,304 Ibs. for ordinary mild 
 steel. The metal was subjected to tup tests as well as to other severe 
 punishments, including the explosion of heavy charges of dynamite 
 against the plates, and in every instance the results were satisfactory. 
 It was not deemed prudent to adopt the high-tensile steel for the rivets, 
 a point upon which there seems some difference of opinion. 
 
 Penna. R. R. Specifications for Steel. 
 
 
 B 
 
 
 
 fc 
 
 OJ 
 
 1 
 
 C. 
 
 Mn. 
 
 Si. 
 
 P. 
 
 s. 
 
 Cu. 
 
 Plates for steel cars 
 
 (1) 
 
 1899 
 
 0.12 
 
 0.35 
 
 0.05 
 
 0.04- 
 
 0.03- 
 
 
 Bar spring steel 
 
 
 1901 
 
 1.00 
 
 0.25 
 
 0.15- 
 
 0.03- 
 
 0.03- 
 
 0.03- 
 
 Steel for axles 
 
 (?) 
 
 1899 
 
 40 
 
 50 
 
 05 
 
 0.05- 
 
 0.04- 
 
 
 Steel for crank pins 
 
 O) 
 
 1904 
 
 0.45 
 
 0.60- 
 
 0.05- 
 
 0.03- 
 
 0.04- 
 
 
 Billets or blooms for forging 
 Boiler-shell sheets 
 
 (4) 
 
 (5) 
 
 1902 
 1906 
 
 0.45 
 18 
 
 0.50 
 40- 
 
 0.05 
 05- 
 
 0.03- 
 0.04- 
 
 0.02- 
 0.03- 
 
 0.03- 
 0.03- 
 
 Fire-box sheets 
 
 (6) 
 
 1906 
 
 18 
 
 40- 
 
 02- 
 
 03- 
 
 0.02- 
 
 0.03- 
 
 
 
 
 
 
 
 
 
 
508 
 
 StftEU 
 
 The minus sign after a figure means "or less." The figures without 
 the minus sign represent the composition desired. 
 
 Steel castings. Desired T. S., 70,000 Ibs. per sq. in.; elong. in 2 in.. 
 15%. Will be rejected if T. S. is below 60,000, or elong. below 12%, or if 
 the castings show blow-holes or shrinkage cracks on machining. 
 
 NOTES. (1) Tensile strength, 52,000 Ibs. per sq. in.; elong. in 8 ins. 
 = 1,500,000 -s- T. S. (2) Axles are also subjected to a drop test, similar 
 to that of the A. S. T. M. specifications. Axles will be rejected if they 
 contain C below 0.35 or above 0.50, Mn above 0.60, P above 0.07%. 
 (3) T. S. desired, 85,000 Ibs. per sq. in.; elong. in 8 ins. 18%. Pins will 
 be rejected if the T. S. is below 80,003 or above 95,000, if the elongation 
 is less than 12%, orif the P is above 0.05%. (4) The steel will be re- 
 jected if the C is below 0.35 or above 0.50, Si above 0.25, S above 0.05, 
 P above 0.05, or Mn above 0.60%. (5) T. S. desired, 60,000; elong. in 
 8 ins. 26%. Sheets will be rejected if the T. S. is less than 55,000 or 
 over 65,000, or if the elongation is less than the quotient of 1,400,000 
 divided by the T. S., or if P is over .0.05%. (6) T. S. desired, 60,000, 
 with elong. of 28% in 8 in. Sheets will be rejected if the T. S. is less 
 than 55,000 or above 65,000 (but if the elong. is 30% or over plates will 
 not be rejected for high T. S.),if the elongation is less than 1,450,000 -*- 
 T. S., if a single seam or cavity more than 1/4 in. long is shown in either 
 one of the three fractures obtained in the test for homogeneity, described 
 below, or if on analysis C is found below 0.15 or over 0.25, P over 0.035, 
 Mn over 0.45, Si over 0.03, S over 0.045, or Cu over 0.05%. 
 
 Homogeneity Test for Fire-box Steel. This test is made on one of the 
 broken tensile-test specimens, as follows: 
 
 A portion of the test-piece is nicked with a chisel, or grooved on a ma- 
 chine, transversely about a sixteenth of an inch deep, in three places 
 about 2 in. apart. The first groove should be made on one side, 2 in. from 
 the square end of the piece; the second, 2 in. from it on the opposite side; 
 and the third, 2 in. from the last, and on the opposite side from it. The 
 test-piece is then put in a vise, with the first groove about 1/4 in. above 
 the jaws, care being taken to hold it firmly. The projecting end of the 
 test-piece is then broken off by means of a hammer, a number of light 
 blows being used, and the bending being away from the groove. The 
 piece is broken at the other two grooves in the same way. The object 
 ( f this treatment is to open and render visible to the eye any seams due 
 to failure to weld up, or to foreign interposed matter, or cavities due 
 to gas bubbles in the ingot. After rupture, one side of each fracture is 
 examined, a pocket lens being used if necessary, and the length of the 
 seams and cavities is determined. The sample shall not show any single 
 seam or cavity more than 1/4 in. long in either of the three fractures. 
 
 Dr. Chas. B. Dudley, chemist of the P. R. R. (Trans. A. I. M. E., 1892), 
 referring to tests of crank-pins, says: In testing a recent shipment, the 
 piece from one side of the pm showed 88,000 Ibs. strength and 22% elon- 
 gation, and the piece from the opposite side showed 106,000 Ibs. strength 
 and 14% elongation. Each piece was above the specified strength and 
 ductility, but the lack of uniformity between the two sides of the pin was 
 so marked that it was finally determined not to put the lot of 50 pins in 
 use. To guard against trouble of this sort in future, the specifications 
 are to be amended to require that the difference in ultimate strength of 
 the two specimens shall not be more than 3000 Ibs. 
 
 Specifications for Steel Rails. (Adopted by the manufacturers of the 
 U. S. and Canada. In effect Jan. 1, 1909.) Bessemer rails: 
 Wt. per yard, Ibs. 50 to 60 61 to 70 71 to 80 81 to 90 91 to 100 
 Carbon % ....0.35-0.45 0.35-0.45 0.40-0.50 0.43-0.53 0.45-0.55 
 Manganese, %... .0.70-1 .00 0.70-1.00 0.75-1.05 0.80-1.10 0.84-1.14 
 
 Phosphorus not over 0.10%; silicon not over 0.20%. Drop Test: A 
 piece of rail 4 to 6 ft. long, selected from each blow, is placed head up- 
 wards on supports 3 it. apart. The anvil weighs at least 20,000 Ibs., 
 and the tup, or falling weight, 2000 Ibs. The rail should not break when 
 the drop is as follows: 
 
 Weight per yard, Ibs 71 to 80 81 to 90 91 to 100 
 
 Height of drop, feet 16 17 
 
 If any rail breaks when subjected to the drop test, two additional tests 
 will be made of other rails from the same blow of steel, and if either of 
 
VARIOUS SPECIFICATIONS FOE STEEL. 
 
 509 
 
 these latter tests fail, all the rails of the blow which they represent will 
 be rejected; but if both of these additional test-pieces meet the require- 
 ments, all the rails of the blow which they represent will be accepted. 
 
 Shrinkage: The number of passes and the speed of the roll train shall 
 be so regulated that for sections 75 Ibs. per yard and heavier the temper- 
 ature on leaving the rolls will not exceed that which requires a shrinkage 
 allowance at the hot saws of 611/13 inches for a 33-ft. 75-lb. rail, with an 
 increase of Vie in. for each increase of 5 Ibs. in the weight of the section. 
 
 Open-hearth rails; chemical specifications: 
 
 Weight per yard, Ibs. . . 50 to 60 61 to 70 71 to SO 81 to 90 93 to 100 
 Carbon, % 0.46-0.59 0.46-0.59 0.52-0.65 0.59-0.72 0.62-0.75 
 
 Manganese, 0.60 to 0.90; Phosphorus, not over 0.04; Silicon, not over 
 0.20. Drop Tests : 50 to 60-lb., 15 ft.; 61 to 70-lb., 16 ft.; heavier sec- 
 tions same as Bessemer. 
 
 Specifications for Steel Axles. (Proc. A. S. T. M., 1905 p. 56.) 
 
 
 P.& 
 B.| 
 
 Tens. 
 
 Str. 
 
 Yield 
 Pt. 
 
 El. in 
 2 in. 
 
 Red. 
 Area. 
 
 Car and tender truck 
 
 0.06 
 
 
 
 
 
 Driving and engine truck C. S.* .. . . 
 
 06 
 
 80000 
 
 40000 
 
 20% 
 
 25% 
 
 Driving and engine truck, N. S.'j" 
 
 0.04 
 
 80' N 000 
 
 50', 000 
 
 25% 
 
 45% 
 
 
 
 
 
 
 
 * Carbon steel. 
 
 t Nickel steel, 3 to 4% Ni. 
 
 I Each not to exceed. Mn in carbon steel not over 0.60 %. 
 
 Drop Tests. One drop test to be made from each melt. The axle 
 t.ests on supports 3 ft. apart, the tup weighs 1640 Ibs., the anvil supported 
 on springs, 17,500 Ibs.; the radius of the striking face of the tup is 5 in. 
 The axle is turned over after the first, third and fifth blows. It must 
 stand the number of blows named below without rupture and without 
 exceeding, as the result of the first blow, the deflection given. 
 
 Diam. axle at center, in.. . 
 Number of blows . . . 
 
 j% 
 
 43/8 
 
 47/16 
 
 45/ 8 
 
 43/4 
 
 53/8 
 
 r" 
 
 Height of drop ft 
 
 24 
 
 26 
 
 281/2 
 
 31 
 
 34 
 
 43 
 
 43 
 
 Deflection, in... ."*. . 
 
 81/4] 
 
 81/4 
 
 81/4 
 
 8 
 
 8 
 
 7 
 
 51/2 
 
 
 
 
 
 
 
 
 
 Specifications for Tires. (A. S. T. M., 1901.) Physical require- 
 ments of test-piece 1/2 in. diam. Tires for passenger engines: T. S., 100,000; 
 El. in 2 in., 12%. Tires for freight engines and car wheels: T. S., 110,000; 
 El., 10%. Tires for switching engines: T. S., 120,000; El., 8%. 
 
 Drop Test. If a drop test is called for, a selected tire shall be placed 
 vertically under the drop on a foundation at least 10 tons in weight and 
 subjected to successive blows from a tup weighing 2240 Ibs. falling from 
 increasing heights until the required deflection is obtained, without break- 
 ing or cracking. The minimum deflection must equal D 2 (40 T 2 + 
 27)), D being internal diameter and T thickness of tire at center of 
 tread. 
 
 Splice-bars. (A. S. T. M. t 1901.) Tensile strength of a specimen 
 cut from the head of the bar, 54,000 to 64,000 Ibs.; yield point, 32,000 
 Ibs. Elongation in 8 in., not less than 25 per cent. A test specimen 
 cut from the- head of the bar shall bend 180 flat on itself without fracture 
 on the outside of the bent portion. If preferred, the bending test may 
 be made on an unpunched splice-bar, which shall be first flattened and 
 then bent. One tensile test and one bending test to be made from each 
 blow or melt of steel. 
 
510 
 
 STEEL. 
 
 Specifications for Steel Used in Automobile Construe tiouu 
 
 (E. F. Lake, Am. Mach., March 14, 1907.) 
 
 
 C. 
 
 Mn. 
 
 Cr. 
 
 Ni. 
 
 p. 
 
 S. 
 
 t. S. 
 
 E. L. 
 
 El. in 
 2 in. 
 
 R.of 
 A. 
 
 (0 
 
 0.40-0.55 
 
 0.40- 
 
 0.80 + 
 
 1.50 + 
 
 0.04- 
 
 0.04- 
 
 f 90000 + 
 1180000 + 
 
 65000 + 
 140000 + 
 
 18+ 
 
 8 + 
 
 35+a 
 20 +b 
 
 (2) 
 
 0.20-0.35 
 
 0.40- 
 
 0.80 + 
 
 1.50 + 
 
 0.04- 
 
 0.04- 
 
 / 85000 + 
 \ 130000 + 
 
 65000 + 
 100000 + 
 
 20 + 
 12 + 
 
 50+a 
 30+b 
 
 (3) 
 
 0.25 
 
 0.40 
 
 1.50 
 
 3.50 
 
 0.015 
 
 0.025 
 
 120000 
 
 105000 
 
 20 
 
 58c 
 
 (4) 
 
 0.25-0.35 
 
 0.60 
 
 
 1.50 + 
 
 0.03 
 
 0.04 
 
 f 85000 + 
 \ 100000 + 
 
 60000 + 
 70000 + 
 
 25 + 
 20+ 
 
 50+a 
 50+b 
 
 (5) 
 
 45-0 55 
 
 1 1-1 3 
 
 
 
 065- 
 
 06- 
 
 85000 + 
 
 55000 + 
 
 15 + 
 
 45 + c 
 
 6 
 
 0.28-0.36 
 
 0.3-0.6 
 
 
 
 0.05- 
 
 0.06- 
 
 75000 + 
 
 40000 + 
 
 25 + 
 
 40 + c 
 
 (7) 
 
 0.85-1.00 
 
 0.25-0.5 
 
 
 
 0.03- 
 
 0.03- 
 
 
 
 
 
 H 
 
 0.50 
 
 1.50- 
 
 
 3o!6 
 
 04- 
 
 06- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The plus sign means "or over"; the minus sign "or less.'* 
 a, fully annealed; b, heat-treated, that is oil-quenched and partly 
 annealed; c, as rolled. 
 
 (1) 45% carbon chrome-nickel steel, for gears of high-grade cars. 
 When annealed this steel can be machined with a high-speed tool at the 
 rate of 35 ft. per min./with a Vl6-in. feed and a 3/ 16 -in. cut. It is annealed 
 at 1400 F. 4 or 5 hours, and cooled slowly. In heat-treating it is heated 
 to 1500, quenched in oil or water and drawn at 500 F. 
 
 (2) 25% carbon chrome-nickel steel, for shafts, axles, pivots, etc. 
 This steel may be machined at the same rate as (1), and it forges more 
 easily. 
 
 (3) A foreign steel used for forgings that have to withstand severe 
 alternating shocks, such as differential shafts, transmission parts, universal 
 joints, axles, etc. 
 
 (4) Nickel steel, used instead of (1) in medium and low-priced cars. 
 
 (5) "Gun-barrel " steel, used extensively for rifle barrels, also in low- 
 priced automobiles, for shafts, axles, etc. It is used as it comes from 
 the maker, without heat-treating. 
 
 (6) Machine steel. Used for parts that do not require any special 
 strength. 
 
 (7) Spring steel used in automobiles. 
 
 (8) Nickel steel for valves. Used for its heat-resisting qualities in 
 valves of internal-combustion engines. 
 
 Carbonizing or Case-hardening. Some makers carbonize the surface 
 of gears made from steel (1) above. They are packed in cast-iron boxes 
 with a mixture of bone and powdered charcoal" and heated four hours 
 at nearly the melting-point of the boxes, then cooled slowly in the boxes. 
 They are then taken out, heated to 1400 F. for four hours to break up the 
 coarse grain produced by the carbonizing temperature. After this the 
 work is heat-treated as above described. 
 
 The machine steel (6) case-hardens well by the use of this process. 
 
 Specifications for Steel Castings. (Proc. A. S. T. M ., 1905,. p. 53.) 
 Open-hearth, Bessemer, or crucible. Castings to be annealed unless 
 otherwise specified. Ordinary castings, in which no physical require- 
 ments are specified, shall contain not over 0.04 C and not over 0.08 P. 
 Castings subject to physical test shall contain not over 0.05 P and not 
 over 0.05 S. The minimum requirements are: 
 
 
 T. S. 
 
 Y. P. 
 
 El. in 2 
 in. 
 
 Red. 
 Area. 
 
 Hard castings 
 
 85.000 
 
 38,250 
 
 15 % * 
 
 20% 
 
 Medium castings 
 
 70000 
 
 31,500 
 
 18% 
 
 25% 
 
 Soft castings . 
 
 60,000 
 
 27 000 
 
 22% 
 
 30% 
 
 
 
 
 
 

 FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 511 
 
 For small or unimportant castings a test to destruction may be sub- 
 stituted. Three samples are selected from each melt or blow, annealed 
 in the same furnace charge, and shall show the material to be ductile 
 and free from injurious defects, and suitable for the purpose intended. 
 Large castings are to be suspended and hammered all over. -No cracks, 
 flaws, defects nor weakness shall appear after such treatment. A speci- 
 men 1 X V2 in. shall bend cold around a diam. of 1 in. without fracture 
 on outside of bent portion, through an angle of 120 for soft and 90 for 
 medium castings. 
 
 Specifications for steel castings issued by the U. S. Navy Department, 
 1889 (abridged): Steel for castings must be made by either the open- 
 hearth or the crucible process, and must not show more than 0.06% of 
 phosphorus. All castings must be annealed, unless otherwise directed. 
 The tensile strength of steel castings shall be at least 60,000 Ibs., with an 
 elongation of at least 15% in 8 in. for all castings for moving parts of 
 machinery, and at least 10% in 8 in. for other castings. Bars 1 in. sq. 
 shall be capable of bending cold, without fracture, through an angle of 
 90, over a radius not greater than 11/2 in. All castings must be sound, 
 free from injurious roughness, sponginess, pitting, shrinkage, or other 
 cracks, cavities, etc. 
 
 Pennsylvania Railroad specifications, 1888: Steel castings should have a 
 tensile strength of 70,000 Ibs. per sq. in. and an elongation of 15% in 
 section originally 2 in. long. Steel castings will not be accepted if tensile 
 strength falls below 60,000 Ibs., nor if the elongation is less than 12%, nor 
 if castings have blow-holes and shrinkage cracks. Castings weighing 80 
 Ibs. or more must have cast with them a strip to be used as a test-piece. 
 ""he dimensions of this strip must be 8/4 in. sq. by 12 in. long. 
 
 
 MECHANICS. 
 
 FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 
 
 MECHANICS is the science that treats of the action of force upon bodies. 
 Statics is the mechanics of bodies at rest relatively to the earth's surface. 
 Dynamics is the mechanics of bodies in motion. Hydrostatics and hydro- 
 dynamics are the mechanics of liquids, and Pneumatics the mechanics 
 of air and other gases. These are treated in other chapters. 
 
 There are four elementary quantities considered in Mechanics: Matter, 
 Force, Space, Time. 
 
 Matter. Any substance or material that can be weighed or measured. 
 It exists in three forms: solid, liquid, and gaseous. A definite portion 
 of matter is called a body. 
 
 The Quantity of Matter in a body may be determined either by 
 measuring its bulk or by weighing it, but as the bulk varies with temper- 
 ature, with porosity, with size, shape and method of piling its particles, 
 etc., weighing is generally the more accurate method of determining its 
 quantity. 
 
 Weight. Mass. The word "weight" is commonly used in two 
 senses: 1. As the measure of quantity of matter in a body, as deter- 
 mined by weighing it in an even balance scale or on a lever or platform 
 scale, and thus comparing its quantity with that of certain pieces of metal 
 called standard weights, such as the pound avoirdupois. 2. As the 
 measure of the force which the attraction of gravitation of the earth 
 exerts on the body, as determined by measuring that force with a spring 
 balance. As the force of gravity varies with the latitude and elevation 
 above sea level of different parts of the earth's surface, the weight deter- 
 mined in this second method is a variable, while that determined by 
 the first method is a constant. For this reason, and also because spring 
 balances are generally not as accurate instruments as even balances, or 
 lever or platform scales, the word "weight," in engineering, unless other- 
 wise specified, means the quantity of matter as determined by weigh- 
 ing it by the first method. The standard unit of weight is the pound. 
 
 The word "mass" is used in three senses by writers on physics and 
 engineering: 1. As a general expression of an indefinite quantity, syn- 
 onymous with lump, piece, portion, etc., as in the expression "a mass 
 whose weight is one pound," 2, As the quotient of the weight, aj 
 
512 
 
 MECHANICS. 
 
 determined by the first method of weighing given above, by 32.174, tho 
 standard value of g, the acceleration due to gravity, expressed by 
 the formula M = W/g. This value is merely the arithmetical ratio of 
 the weight in pounds to the acceleration in feet per second per second, 
 and it has no unit. 3. As a measure of the quantity of matter, ex- 
 actly synonymous with the first meaning of the word "weight," given 
 above. In this sense the word is used in many books on physics and 
 theoretical mechanics, but it is not so used by engineers. The state- 
 ment in such books that the engineers' unit of mass is 32.2 Ibs. is an 
 error. There is no such unit. Whenever the term "mass" is repre- 
 sented by M in engineering calculations it is equivalent to W/g, in 
 which Wis the quantity of matter in pounds, and g = 32.1740 (or 32.2 
 approximate) . 
 
 Local Weight. The force, measured in standard pounds of force 
 (see Unit of Force, below), with which gravity attracts a body at a 
 locality other than one where g = 32.174 is sometimes called the 
 "local weight" of the body. It is the weight that would be indicated 
 if the body was weighed on a spring balance calibrated for standard 
 pounds of force. If the balance was calibrated for the particular lo- 
 cality, it would indicate not the local weight, but the true or standard 
 weight, that is, the quantity of matter in pounds or the force that 
 gravity would exert on the body at the standard locality, these being 
 numerically identical. The difference between standard and local 
 weight is rarely large enough to be of importance in engineering 
 problems. In the United States (exclusive of Alaska), the range of 
 the value of g is only from 0.9973 (at lat. 25, 10,000 ft. above the sea) 
 to 1.0004 (lat. 49 at the sea level) of the standard value (lat. 45 at 
 the sea level) of 32.1740. 
 
 A Force is anything that tends to change the state of a body with 
 respect to rest or motion. If a body is at rest, anything that tends to 
 .put it in motion is a fores; if a body is in motion, anything that tends to 
 change either its direction or its rate of motion is a force. 
 
 A force should always mean the pull, pressure, rub, attraction (or re- 
 pulsion) of one body upon another, and always implies the existence of a 
 simultaneous equal and ppposite force exerted by that other body on tli3 
 first body, i.e., the reaction. In no case should we call anything a forc3 
 unless we can conceive of it as capable of measurement by a spring 
 balance, and are able to say from what other body it comes. (I. P. 
 Church.) 
 
 Forces may be divided into two classes, extraneous and molecular; 
 extraneous forces act on bodies from without; molecular forces are 
 exerted between the neighboring particles of bodies. 
 
 Extraneous forces are of two kinds, pressures and moving forces: pres- 
 sures simply tend to produce motion; moving forces actually produce 
 motion. Thus, if gravity act on a fixed body, it creates pressure; if on a 
 free body, it produces motion. 
 
 Molecular forces are of two kinds, attractive and repellent: attractive 
 forces tend to bind the particles of a body together; repellent forces tend 
 to thrust them asunder. Both kinds of molecular forces are continu- 
 ally exerted between the molecules of bodies, and on the predominance 
 of one or the other depends the physical state of a body, as solid, liquid, 
 or gaseous. 
 
 The Unit of Force used in engineering, by English writers, is the 
 pound avoirdupois. Strictly, it is the force which would give to a 
 pound of matter an acceleration of 32.1740 feet per sec. per sec., or tho 
 force with which gravity attracts a pound of matter at 45 latitude at 
 the sea level. In the French C. G. S. or centimeter-gram-second system, 
 the unit of force is the force which acting on a mass of one gram will 
 produce in one second a velocity of one centimeter per second. This 
 unit is called a "dyne" = 1/980-665 gram. 
 
 An attempt has been made by some writers on physics to introduce 
 the so-called "absolute system" into English weights and measures, and 
 to define the "absolute unit" of force as that force which acting on the 
 mass whose weight is one pound at London will in one second produce a 
 velocity of one foot per second, and they have given this unit the name 
 "poundal." The use of this unit only makes confusion for students, 
 and it is to be hoped that it will soon be abandoned in high-school text- 
 books. Professor Perry, in his "Calculus for Engineers," p. 26, says, 
 

 FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 513 
 
 " One might as well talk Choctaw in the shops as to speak about ... so 
 many poundals of force and so many foot-poundals of work."* 
 
 Inertia is that property of a body by virtue of which it tends to con- 
 tinue in the state of*rest or motion in which it may be placed, until acted 
 on by some force 
 
 Newton's Laws of Motion. 1st Law. If a body be at rest, it will 
 remain at rest, or if in motion it will move uniformly in a straight line till 
 acted on by some force. 
 
 2d Law. If a body be acted on by several forces, it will obey each as 
 though the others did not exist, and this whether the body be at rest or in 
 motion. (This law is expressed in different forms by various authors. 
 One of these forms is: Change of the motion of a body is proportional 
 to the force and to the time during which the force acts, and is in tho 
 same direction as the force.) 
 
 3d Law. If a force act to change the state of a body with respect to rest 
 or motion, the body will offer a resistance equal and directly opposed to the 
 force. Or, to every action there is opposed an equal and opposite reaction. 
 
 Graphic Representation of a force. Forces may be represented 
 geometrically by straight lines, proportional to the forces. A force is 
 given when we know its intensity, its point of application, and the direc- 
 tion in which it acts. When a force is represented by a ! ine, the length of 
 the line represents its intensity; one extremity represents the point of 
 application; and an arrow-head at the other extremity shows the direc- 
 tion of the force.- 
 
 Composition of Forces is the operation of finding a single force whose 
 effect is the same as that of two or more given forces. The required 
 force is called the resultant of the given forces. 
 
 Resolution of Forces is the operation of finding two or more forces 
 whose combined effect is equivalent to that of a given force. The required 
 forces are called components of the given force. 
 
 The resultant of two forces applied at a point, and acting in the same di- 
 rection, is equal to the sum of the forces. If two forces act in opposite 
 directions, their resultant is equal to their difference, and it acts in the 
 direction of the greater. 
 
 If any number of forces be applied at a point, some in one direction and 
 others in a contrary direction, their resultant is equal io the sum of those 
 that act in one direction, diminished by the sum of those that act in the 
 opposite direction; or, the resultant is equal to the algebraic sum of the 
 components. 
 
 Parallelogram of Forces. If two forces acting on a point be rep- 
 resented in direction and intensity by adjacent sides of a parallelogram, 
 their resultant will be represented by that diagonal of the parallelogram 
 which passes through the point. Thus OR, Fig. 99, is the resultant of 
 OQ and OP. 
 
 /5 
 
 FIG. 99. 
 
 FIG. 100. 
 
 Polygon of Forces. If several forces are applied at a point and act 
 in a single plane, their resultant is found as follows: 
 
 Through the point draw a line representing the first force; through the 
 
 * Professor Perry himself, however, makes a slip on the same page in 
 saying : " Force in pounds is the space-rate at which work in foot-pounds 
 is done; it is also the time-rate at which momentum is produced or de- 
 stroyed." He gets this idea, no doubt, from the equations FT = MV, 
 F = MV/T, F = Yi MV 2 -r- S. Force is not these tilings: it is merely 
 numerically equivalent, when certain units are chosen, to these last two 
 quotients. We might as- well say, since T = MV/F, that time is the 
 force-rate of momentum, 
 
514 
 
 MECHANICS. 
 
 extremity of this draw a line representing the second force; and so on, 
 throughout the system; finally, draw a line from the starting-point to the 
 extremity of the last line drawn, and this will be the resultant required. 
 
 Suppose the body A, Fig. 100, to be urged in the directions Al. A2, A3, 
 A4, and A5 by forces which are to each other as the lengths of those lines. 
 Suppose these forces to act successively and the body to first move from A 
 to 1 ; the second force A2 then acts and finding the body at 1 would take it 
 to 2'; the third force would then carry it to 3', the fourth to 4', and the fifth 
 to 5'. The line A5' represents in magnitude and direction the resultant of 
 all the forces considered. If there had been an additional force, Ax, in 
 the group, the body would be returned by that force to its original position, 
 supposing the forces to act successively, but if they had actea simul- 
 taneously the body would never have moved at all; the tendencies to 
 motion balancing each other. 
 
 It follows, therefore, that if the several forces which tend to move a 
 body can be represented in magnitude and direction by the sides of a 
 closed polygon taken in order, the body will remain at rest; but if the 
 forces are represented by the sides of an open polygon, the body will move 
 and the direction will be represented by the straight line which closes the 
 polygon. 
 
 Twisted Polygon. The rule of the polygon of forces holds true even 
 when the forces are not m one plane. In this case the lines Al, 1-2', 2 / -3', 
 etc., form a twisted polygon, that is, one whose sides are not in one plane. 
 
 Parallelopipedon of Forces. If three forces acting on a point be 
 represented by three edges of a parallelopipedon which meet in a common 
 point, their resultant will be represented by the diagonal of the parallelo- 
 pipedon that passes through their common point. 
 
 Thus O#,Fig. 101, is the resultant of OQ, OS and OP. OM is the result- 
 ant of OP and OQ, and. OR is the resultant of OM and OS. 
 
 FIG. 102. 
 
 Moment of a Force. The moment of a force (sometimes called 
 statical moment), with respect to a point, is the product of the force by 
 the perpendicular distance from the point to the direction of the force. 
 The fixed point is called the center of moments; the perpendicular distance 
 is the lever-arm of the force; and the moment itself measures the tendency 
 of the force to produce rotation about the center of moments. 
 
 If the force is expressed in pounds and the distance in feet, the moment 
 is expressed in foot-pounds. It is necessary to observe the distinction be- 
 tween foot-pounds of statical moment and foot-pounds of work or energy. 
 (See Work.) 
 
 In the bent lever, Fig. 102 (from Trautwine), if the weights n and m 
 represent forces, their moments about the point / are respectively n X af 
 and m X fc. If instead of the weight m a pulling force to balance the 
 weight n is applied in the direction bs, or by or bd, s, y, and d being the 
 amounts of these forces, their respective moments are sXft,yX fb, 
 
 It the forces acting on the lever are in equilibrium it remains at rest, and 
 the moments on each side of / are equal, that is, n X af = m Xfc, or s X 
 ft. or y Xfb, or dX hf. 
 
 The moment/ of the resultant of any number offerees acting together in 
 
. 
 
 the sarr 
 
 FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 515 
 
 e same plane is equal to the algebraic sum of the moments of the forces 
 taken separately. 
 
 Statical Moment. Stability. The statical moment of a body is 
 the product of its weight by the distance of its line of gravity from some 
 assumed line of rotation. The line of gravity is a vertical line drawn from 
 its center of gravity through the body. The stability of a body is that 
 resistance which its weight alone enables it to oppose against forces tend- 
 ing to overturn it or to slide it along its foundation. 
 
 To be safe against turning on an edge the moment of the forces tending 
 to overturn it, taken with reference to that edge, must be less than the 
 statical moment. When a body rests on an inclined plane, the line of 
 gravity, being vertical, falls toward the lower edge of the body, and the 
 condition of its not being overturned by its own weight is that the line of 
 gravity must fall within this ed^e. In the case of an inclined tower 
 resting on a plane the same condition holds the line of gravity must 
 fall within the base. The condition of stability against sliding along a 
 horizontal plane is that the horizontal component of the force exerted 
 tending to cause it to slide shall be less than the product of the weight of 
 the body into the coefficient of friction between the base of the body and 
 its supporting plane. This coefficient of friction is the tangent of the 
 angle of repose, or the maximum angle at which the supporting plane 
 might be raised from the horizontal before the body would begin to slide. 
 (See Friction.) 
 
 The Stability of a Dam against overturning about its lower edge 
 is calculated by comparing its statical moment referred to that edge with 
 the resultant pressure of the water against its upper side. The horizontal 
 pressure on a square foot at the bottom of the dam is equal to the weight of 
 a column of water of one square foot in section, and of a height equal to the 
 distance of the bottom below water-level ; or, if // is the height, the pressure 
 at the bottom per square foot = 62.4 X H Ibs. At the water-level the 
 pressure is zero, and it increases uniformly to the bottom, so that the sum 
 of the pressures on a vertical strip one foot in breadth may be represented 
 by the area of a triangle whose base is 62.4 X H and whose altitude is H t 
 or 62.4 H 2 -* 2. The center of gravity of a triangle being Va of its altitude, 
 the resultant of all the horizontal pressures may be taken as equivalent 
 to the sum of the pressures acting at 1/3 H, and the moment of the sum of 
 the pressures is therefore 62.4 X // 3 -s- 6. 
 
 Parallel Forces. If two forces are parallel and act in the same direc- 
 .tion. their resultant is parallel to both, and lies between, them, and the 
 intensity of the resultant is equal to the sum of the intensities of the two 
 forces. Thus in Fig. 102 the resultant of the forces n and m acts verti- 
 cally downward at /, and is equal to n + vn. 
 
 If two parallel forces act at the extremities of a straight line and in 
 the same direction, the resultant divides the line joining the points of 
 
 CK 
 
 FIG. 103. 
 
 / 
 
 FIG. 104. 
 
 *R 
 
 application of the components, inversely as the components. Thus in 
 Fig. 102 m: n:: af: fc* and in Fig. 103, P: Q:: SN: SM. 
 
 The resultant of two parallel forces acting in opposite directions is 
 parallel to both, lies without both, on the side and in the direction of the 
 greater, and its intensity is equal to the difference of the intensities of 
 the two forces. 
 
 Thus the resultant of the two forces Q and P, Fig. 104, is equal to 
 Q P = R. Of any two parallel forces and their resultant each is pro- 
 portional to the distance between the other two: this in both Figs. 103 
 and 104, P:Q: R:: SN: SM: MN. 
 
 Couples. If P and Q be equal and act in opposite directions, R = 0; 
 that is, they have no resultant. Two such forces constitute a couple. 
 
 The tendency of a couple is to produce rotation; the measure of this 
 tendency, called the moment of the ample- is the product of one of the 
 forces by the distance between the two. 
 
J 
 
 516 MECHANICS. 
 
 Since a couple has no single resultant, no 
 single force can balance a couple. To prevent 
 the rotation of a body acted on by a couple the 
 application of two other forces is required, 
 forming a second couple. Thus in Fig. 105, 
 P and Q, forming a couple, may be balanced 
 
 Iby a second couple formed by R and S. The 
 point of application of either R or S may be a 
 fixed pivot or axis. 
 Moment of the couple PQ = P(c + b + a) = 
 moment of RS = Rb. Also, P + R = Q + S. 
 
 The forces R and S need not be parallel to P 
 and Q, but if not, then their components par- 
 allel to PQ are to be taken instead of the forces themselves. 
 
 Equilibrium of Forces. A system of forces applied at points of a 
 solid body will be equilibrium when they have no tendency to produce 
 motion, either of translation or of rotation. 
 
 The conditions of equilibrium are: 1. The algebraic sum of the com- 
 ponents of the forces in the direction of any three rectangular axes must 
 separately equal 0. 2. The algebraic sum of the moments of the forces, 
 with respect to any three rectangular axes, must separately equal 0. 
 
 If the forces lie in a plane: 1. The algebraic sum of the components 
 of the forces, in the direction of any two rectangular axes, must be 
 separately equal to 0. 2. The algebraic sum of the moments of the 
 forces, with respect to any point in the plane, must be equal to 0. 
 
 If a body is restrained by a fixed axis, as in case of a pulley, or wheel 
 and axle, the forces will be in equilibrium when the algebraic sum of 
 the moments of the forces with respect to the axis is equal to 0. 
 
 CENTER OF GRAVITY. 
 
 The center of gravity of a body, or of a system of bodies rigidly con- 
 nected together, is that point about which, if suspended, all jthe parts will 
 be in equilibrium, that is, there will be no tendency to rotation. It is 
 the point through which passes the resultant of the efforts of gravitation 
 on each of the elementary particles of a body. In bodies of equal heavi- 
 ness throughout, the center of gravity is the center of magnitude. 
 
 (The center of magnitude of a figure is a point such that if the figure 
 be divided into equal parts the distance of the center of magnitude of 
 
 the whole figure from any given plane is the mean of the distances of 
 he centers of magnitude of the several equal parts from that plane.) 
 A body suspended at its center of gravity is in equilibrium in all 
 
 positions. If suspended at a point outside of its center of gravity, it 
 will take a position so that its center of gravity is vertically below its 
 point of suspension. 
 
 To find the center of gravity of any plane figure mechanically, sus- 
 pend the figure by any point near its edge, and mark on it the direction 
 of a plumb-line hung from that point; then suspend it from some other 
 point, and again mark the direction of the plumb-line in like manner. 
 The center of gravity will be at the intersection of the two marks. 
 
 The Center of Gravity of Regular Figures, whether plane or solid, 
 is the same as their geometrical center; for instance, a straight line, 
 parallelogram, regular polygon, circle, circular ring, prism,, cylinder, 
 sphere, spheroid, middle frustums of spheroid, etc. 
 
 Of a triangle: On a line drawn from any angle to the middle of the 
 opposite side, at a distance of one-third of the line from the side; or at 
 the intersection of such lines drawn from any two angles. 
 
 Of a trapezium or trapezoid: Draw a diagonal, dividing it into two tri- 
 angles. Draw a line joining their centers of gravity. Draw the other 
 diagonal, making two other triangles, and a line joining their centers 
 of gravity. The intersection of the two lines is the center of gravity. 
 
 Of a sector of a circle: On the radius which bisects the arc, 2 cr -r 3-1 
 from the center, c being the chord, r the radius, and I the arc. 
 
 Of a semicircle: On the middle radius, 0.4244 r from the center. 
 
 Of a Quadrant: On the middle radius, 0.600 r from the center, 
 
 Of a segment of a circle: c 3 -j- ] 2a from the center, c = chord, a =area. 
 
 Of a paraboic surface: In the axis, 3/ 5 of its length from the vertex. 
 
 Of a semi-parabola (surface): s/ 5 length of the axis from the vertex, 
 and s/s of the semi-base from the axis, 
 
MOMENT OF INERTIA. , 517 
 
 Of a cone or pyramid: In the axis, 1/4 of its length from the base. 
 
 Of a paraboloid: In the axis, 2/3 of its length from the vertex. . 
 
 Of a cylinder, or regular prism: In the middle point of the axis. 
 
 Of a frustum of a cone or pyramid' Let a = length of a line drawn from 
 the vertex of the cone when complete to the center of gravity of the base, 
 and a' that portion of it between the vertex and the top of the frustum; 
 then distance of center of gravity of the frustum from center of gravity of 
 
 its base = j - Af 2 _? a . , , 2S - 
 4 4(a 2 + aa + a 2 ) 
 
 For two bodies, fixed one at each end of a straight bar, the common 
 center of gravity is in the bar, at that point which divides the distance 
 between their respective centers of gravity in the inverse ratio of the 
 weights. In this solution the weight of the bar is neglected. But it may 
 be taken as a third body, and allowed for as in the following directions: 
 
 For more than two bodies connected in one system: Find the common 
 center of gravity of two of them; and find the common center of these two 
 jointly with a third body, and so on to the last body of the group. 
 
 Another method, by the principle of moments: To find the center of 
 gravity of a system of bodies, or a body consisting of several parts, whoso 
 several centers are known. If the bodies are in a plane, refer their several 
 centers to two rectangular coordinate axes. Multiply each weight by its 
 distance from one of the axes, add the products, and divide the sum by the 
 eum of the weights; the result is the distance of the center of gravity from 
 that axis. Do the same with regard to the other axis. If the bodies are 
 not in a plane, refer them to three planes at right angles to each other, and 
 determine the mean distance of the sum of the weights from each plane. 
 MOMENT OF INERTIA. 
 
 The moment of inertia of the weight of a body with respect to an axis 
 is the algebraic sum of the products of the weight of each elementary 
 particle by the square of its distance from the axis. If the moment of 
 inertia with respect to any axis = 7, the weight of any element of the 
 body = w, and its distance from the axis = r, we have I = 2(wr 2 ). 
 
 The moment of inertia varies, in the same body, according to the 
 position of the axis. It is the least possible when the axis passes through 
 the center of gravity. To find the moment of inertia of a body, referred 
 to a given axis, divide the body into small parts of regular figure. Multi- 
 ply the weight of each part by the square of the distance of its center of 
 gravity from the axis. The sum of the products is the moment of inertia. 
 The value of the moment of inertia thus obtained will be more nearly 
 exact, the smaller and more numerous the divisions of the body. 
 
 MOMENTS OF INERTIA OF REGULAR SOLIDS. Rod, or bar, of uniform 
 thickness, with respect to an axis perpendicular to the length of the rod, 
 
 (I 2 \ 
 
 W = weight of rod, 21 = length, d = distance of center of gravity from 
 
 axis. 
 
 Thin circular plate, axis in its ) T=w(-i-d 2 \ (2) 
 
 own plane, J \4 /' 
 
 r = radius of plate. 
 Circular plate, axis perpendicular to ) T __ w (^ , \ m 
 
 the plate, f* \2 / 
 
 Circular ring, axis perpendicular to) J^TV (r 2 + r' 2 J 
 
 its own plane, f \ 2 
 
 r and r' are the exterior and interior radii of the ring. 
 
 r = radius of base. 2 1 = length of the cylinder. 
 
 By making d = in any of the above formulae, we find the moment of 
 inertia for a parallel axis through the center of gravity. 
 
 The moment of inertia, 2iur 2 , numerically equals the weight of a body 
 which, if concentrated at the distance unity from the axis of rotation, 
 would require the same work to produce a given increase of angular 
 velocity that the actual body requires. It bears the same relation to 
 angular acceleration which weight does to linear acceleration (Rankine). 
 The term moment of inertia is also used in regard to areas, as the cross- 
 
518 MECHANICS. 
 
 sections of] beams under strain. In this case / =2ar2, a being any ele- 
 mentary area, and r its distance from the center. (See Strength of Ma- 
 terials, p. 293.) Some writers call 2wir2 = ^wr^^-g the moment of inertia. 
 
 CENTERS OF OSCILLATION AND OF PERCUSSION. 
 
 Center of Oscillation. If a body oscillate about a fixed horizontal 
 axis, not passing through its center of gravity, there is a point in the line 
 drawn from the center of gravity perpendicular to the axis whose motion 
 is the same as it would be if the whole mass were collected at that point 
 and allowed to vibrate as a pendulum about the fixed axis. This point is 
 called the center of oscillation. 
 
 The Radius of Oscillation, or distance of the center of oscillation 
 from the point of suspension = the square of the radius of gyration -s- dis- 
 tance of the center of gravity from the point of suspension or axis. The 
 centers of oscillation and suspension are convertible. 
 
 If a straight line, or uniform thin bar or cylinder, be suspended at one 
 end, oscillating about it as an axis, the center of oscillation is at 2/ 3 the 
 length of the rod from the axis. If the point of suspension is at 1/3 the 
 length from the end, the center of oscillation is also at 2/3 the length from 
 the axis, that is, it is at the other end. In both cases the oscillation will 
 be performed in the same time. If the point of suspension is at the 
 center of gravity, the length of the equivalent simple pendulum is infinite, 
 and therefore the time of vibration is infinite. 
 
 F9r a sphere suspended by a cord, r radius, h = distance of axis of 
 motion from the center of the sphere, h' = distance of center of oscillation 
 from center of sphere, I = radius of oscillation = h + h' = h + 2 /5 (r2-h h). 
 
 If the sphere vibrate about an axis tangent to its surface, h = r, and 
 l = r+2/5r. If h = 10 r, I = 10 r+ (r-r-25). 
 
 Lengths of the radius of oscillation of a few regular plane figures or 
 thin plates, suspended by the vertex or uppermost point. 
 
 1st. When the vibrations are perpendicular t9 the plane of the figure: 
 
 In an isosceles triangle the radius of oscillation is equal to 8/4 of the 
 height of the triangle. 
 
 In a circle, / 8 of the diameter. 
 
 In a parabola, 5/ 7 of the height. 
 
 2d. When the vibrations are edgewise, or in the plane of the figure: 
 
 In a circle the radius of oscillation is 3/ 4 of the diameter. 
 
 In a rectangle suspended by one angle, 2/3 of the diagonal. 
 
 In a parabola, suspended -by the vertex, 5/ 7 of the height plus 1/3 of 
 the parameter. 
 
 In a parabola, suspended by the middle of the base, 4/7 of the height plus 
 1/2 the parameter. 
 
 Center of Percussion. The center of percussion of a body oscillat- 
 ing about a fixed axis is the point at which, if a blow is struck by the body, 
 the percussive action is the same as if the whole mass of the bodv were 
 concentrated at the point. It is identical with the center of oscillation. 
 
 CENTER AND RADIUS OF GYRATION. 
 
 The center of gyration, with reference to an axis, is a point at which, if 
 the entire weight of a body be concentrated, its moment of inertia will re- 
 main unchanged; or, in a revolving body, the point in which the whole 
 weight of the body may be conceived to be concentrated, as if a pound of 
 platinum were substituted for a pound of revolving feathers,, the angular 
 velocity and the accumulated work remaining the same. The distance of 
 this point from the axis is the radius of gyration. If W = the weight of a 
 body, / = 2wr a = its moment of inertia, and k = its radius of gyration, 
 
 The moment of inertia = the weight X the square of the radius of gyration. 
 To find the radius of gyration divide the body into a considerable 
 number of equal small parts, the more numerous the more nearly exact 
 is the result, then take the mean of all the squares of the distances of the 
 parts from the axis of revolution, and find the square root of the mean 
 square. Or, if the moment o.f inertia is known, divide it by the weight 
 and extract the square root. For radius of gyration of an area, divide 
 the moment of inertia of the area by the area and extract the square 
 root. 
 
CENTEK AND RADIUS OF GYRATION. 
 
 519 
 
 The radius of gyration is the least possible when the axis passes through 
 the center of gravity. This minimum radius is called the principal radius 
 of gyration. If we denote it by k and any other radius of gyration by k', 
 we have for the five cases given under the head of moment of inertia above 
 the following values: 
 
 (1) Rod, axis perpen. 
 length, 
 
 - I ; *.- + (P. 
 
 (2) Circular plate, axis in) /. _ r , ,., _ i/C 4. ^2 
 
 its plane, t 2 : * " V 4~ ' 
 
 (3) Circular plate, axis per- ) k = 4 /I . 
 
 pen. to plane, J V 2' 
 
 (4) Circular ring, axis per- ) *. 
 
 pen. to plane, J 
 
 (5) Cylinder, axis 
 pen. to length, 
 
 per- 
 
 Principal Radii of Gyration and Squares of Radii of Gyration. 
 
 (For radii of gyration of sections of columns, see page 295.) 
 
 Surface or Solid. 
 
 Rad. of Gyration. 
 
 Square of R. 
 of Gyration. 
 
 Parallelogram: ) axis at its base 
 
 0.5773/1 
 0.2886 ft 
 
 0.5773Z 
 
 0.2886J 
 
 1/3 h 2 
 Vl2/i 2 
 
 Vs/ 2 
 
 *fo* 
 
 (b 2 + c 2 ) -s- 3 
 4^2 + 52 
 
 height h ) " mid-height .. .. 
 
 Straight rod: , ) . t d 
 
 length J. or thin S ^Sengtn 
 
 rectang. plate ) 
 Rectangular prism: 
 axes 2 a, 2b, 2c, referred to axis 2 a 
 Parallelepiped: length I, base &, axis at ) 
 
 0.577 Vb 2 + c 2 
 0.289 v / IF~Tl>2 
 
 0.289\//i2 +K2 
 .408 h 
 
 Hollow square tube: 
 out. side h, inner h' t axis mid-length .... 
 very thin, side = h, axis mid-length .... 
 Thin rectangular tube: sides 6, h, axis ) 
 
 12 
 
 (W + h'*} + n 
 
 /l2-6 
 
 h 2 h + 3b 
 12'TTft 
 l/ 4 r 3 = /i 2 - 16 
 
 (fc* + h' 2 ) -s- 16 
 
 p: > 
 
 12^ 4 
 1/2 r2 
 
 (ft 2 + r 2 ) ?- 2 
 ; 2 L ft 2 + r 
 
 0.289A J\ + \ b 
 
 Thin circ. plate: rad. r, diam. h, ax. diam. 
 Flat circ. ring: ciiams. h, ll' t axis diam.. . . 
 Solid circular cylinder: length I, axis di- ) 
 ameter at mid-length ( 
 
 h + b 
 1/4 V#z + fc'2 
 
 0.289 V/2 + 3 r 2 
 0.7071r 
 0.7071 VRZ + r 2 
 
 Circular plate: solid wheel of uniform j 
 thickness, or cylinder of any length, } 
 referred to axis of cyl ) 
 
 Hollow circ. cylinder, or flat ring:! 
 1, length; R, r, outer and inner radii. 1 
 Axis, 1, longitudinal axis; 2, diam. at J 
 mid-length . . . J 
 
 .289V/2+3 (/e2 +r2 ) 
 
 0.289V^ + 6/^2 
 r 
 
 0.707lr 
 0.6325r 
 0.6325r 
 0.5773r 
 
 12 ' 4 
 / 2 72 2 
 12 + 2 
 
 r 3 
 r 2 
 
 1/2 r 2 
 2/5 r 2 
 2/5 r 2 
 
 Vr 2 
 6* + e 2 
 
 2 ^5 - r 
 5l5TT7i 
 
 ^ 
 
 Same: very thin, axis its diameter 
 
 radius r ; axis, longitudinal axis . . 
 Circumf . of circle, axis its center 
 
 " diam 
 
 Sphere: radius r, axis its diam 
 
 Spheroid: equatorial radius r, revolving) 
 Dolar axis a . } 
 
 Paraboloid: r=rad. of base, rev. on axis. 
 Ellipsoid: semi-axes a, 6, c; revolving on ) 
 axis 2 a J 
 
 0.4472V&2 + C 2 
 
 Spherical shell: radii R t r, revolving on ) 
 
 0.25l/f 3 " rS 3 
 
 Same: very thin, radius r 
 
 V R 3 -r 3 
 8165 r 
 0.5477r 
 
 Solid cone: r==rad. of base, rev. on axis. . 
 
520 MECHANICS. 
 
 THE PENDULUM. 
 
 A body of any form suspended from a fixed axis about which it oscil- 
 lates by the force of gravity is called a compound pendulum. The ideal 
 body concentrated at the center of oscillation, suspended from the cen- 
 ter of suspension by a string without weight, is called a simple pendulum. 
 This equivalent simple pendulum has the same weight as the given body, 
 and also the same moment of inertia, referred to an axis passing through 
 the point of suspension, and it oscillates in the same time. 
 
 The ordinary pendulum of a given length vibrates in equal times when 
 the angle of the vibrations does not exceed 4 or 5 degrees, that is, 2 or 
 2 y? each side of the vertical. This property of a pendulum is called its 
 isochronism. 
 
 The time of vibration of a pendulum varies directly as the square root 
 of the length, and inversely as the square root of the acceleration due to 
 gravity at the given latitude and elevation above the earth's surface. 
 
 If T = the time of vibration, I length of the simple pendulum, g = 
 
 IT vT 
 
 the acceleration, then T = IT \ _; since TT is constant Too >r . At a 
 
 \0 Vg 
 
 giyen location g is constant and T oo \/T. If I be constant, then for any 
 
 1 n*l 
 
 location T oo -7^. If Tbe constant, g T 2 = n 2 1; I ao g; g = -=-. From this 
 
 \7g . T 2 
 
 equation the force of gravity at any place may be determined if the 
 length of the simple pendulum, vibrating seconds, at that plaee is 
 known. At New York this length is 39.1017 inches = 3.2585 ft., 
 whence g = 32.16 ft. 
 
 Time of vibration of a pendulum of a given length at New York 
 
 -H; 
 
 I VT 
 
 J 39. 1017 6.253 
 
 t being in seconds and I in inches. Length of a pendulum having a given 
 time of vibration, I = t* X 39.1017 inches. 
 
 The time of vibration of a pendulum may be varied by the addition of 
 a weight at a point above the center of suspension, which counteracts 
 the lower weight, and lengthens the period of vibration. By varying the, 
 height of the upper weight the time is varied. 
 
 To find the weight of the upper bob of a compound pendulum, vi- 
 brating seconds, when the weight of the lower bob and the distances of 
 the weights from the point of suspension are given: 
 
 _ (39- 1 * D) - D* 
 
 " (39.1 X d) +&* 
 
 W = the weight of the lower bob, w = the weight of the upper bob; 
 D = the distance of the lower bob, and d = the distance of the upper 
 bob from the point of suspension, in inches. 
 
 Thus, by means of a second bob, short pendulums may be constructed 
 to vibrate as slowly as longer pendulums. 
 
 By increasing w or d until the lower weight is entirely counterbalanced 
 the time of vibration may be made infinite. 
 
 Conical Pendulum. A weight suspended by a cord and revolving 
 at a uniform speed in the circumference of a circular horizontal plane 
 whose radius is r, the distance of the plane below the point of suspension 
 being h, is held in equilibrium by three forces the tension in the cord, 
 the centrifugal force, which tends to increase the radius r, and the force 
 of gravity acting downward. If v = the velocity in feet per second of 
 the center of gravity of the weight, as it describes the circumference, g 
 = 32.16, and r and h are taken in feet, the time in seconds of performing 
 one revolution is (at New York or other place where g = 32.16) 
 
 JL; h = --, : = 0.8146 *2. 
 g 4*2 
 
 If t = 1 second, h = 0.8146 foot =9.775 inches. 
 The principle of the conical pendulum is used in the ordinary fly-ball 
 governor for steain -engines. (See Governors,) 
 
VELOCITY, ACCELERATION, FALLING BODIES. 521 
 
 CENTRIFUGAL FORCE. 
 
 A body revolving in a curved path of radius = R in feet exerts a force, 
 called centrifugal force, F, upon the arm or cord which restrains it from 
 moving in a straight line, or " flying off at a tangent." If W = weight of 
 the body in pounds, N = number of revolutions per minute, v = linear 
 velocity of the center of gravity of the body, in feet per second, g = 32.174* 
 then 
 
 , 27T/2JV E , W& Wv* W47r*RN* WRN* 
 
 ='00034084 TF^MbS. 
 
 
 If n = number of revplutions per second, F = 1.2270 WRri*. 
 (For centrifugal force in fly-wheels, see Fly-wheels.) 
 
 VELOCITY, ACCELERATION, FALLING BODIES. 
 
 Velocity is the rate of motion, or the speed of a body at any instant. 
 If s = space in feet passed over in t seconds, and v = velocity in feet per 
 ~ J , if the velocity is uniform, 
 
 _ s ,_**_. 
 
 ~~ t ' s v ' ~~ v 
 
 If the velocity varies uniformly, the mean velocity v m = 1/2 (i + v 2 ), in which 
 Vi is the velocity at the beginning. and v 2 the velocity at the end of the time t. 
 s = i/2 (vi + Vz) t (1) 
 
 If vi = 0, then s = 1/2 v. vz = 2 s/t. 
 
 If the velocity varies, but not uniformly, v for an exceedingly short 
 interval of time = s/t, or in calculus v = ds/dt. 
 
 Acceleration is the change in velocity which takes place in a unit^of 
 time. The unit of acceleration is 1 foot per second in one second. For 
 uniformly accelerated motion the acceleration (a) is a constant quantity 
 
 Vz ~V\ i V 2 ~ Vi ^rtX 
 
 Q " ; Vo == V\ -f* dt ', V\ == V 2 &' I ' == * t V<"/ 
 
 If the body start from rest, Vi = 0; then if v m = mean velocity 
 
 t= = __ = \ 
 
 g 32.16 \ g 4.01 ~ v ' 
 u = space fallen through in the rth second = g (T y^). 
 
 If Vi =0,5= 1/2 V 2 t. 
 
 Retarded Motion. If the body start with a velocity Vi and come to 
 rest, v 2 = 0; then s = l/2Vit. 
 
 In any case, if the change in velocity is v, 
 
 s _^. s _ _!. s _ t 2 
 ~ 2*' S ~ 2a' S " 2 > 
 
 For a body starting from or ending at rest, we have the equations 
 r -at; s = |f; s = y;v2 = 2 as. 
 
 Falling Bodies. In the case of falling bodies the acceleration due 
 to gravity, at 40 latitude, is 32.16 feet per second in one second, = g. 
 Then if v = velocity acquired at the end of t seconds, or final velocity, 
 and h = height or space in feet passed over in the same time, 
 
 8.02V'Ji =* ~; 
 
 - - 
 
 20 64.32 2' 
 
 g 32.16 . 
 
 = space fallen through in the rth second = g (T - } 
 
522 
 
 MECHANICS. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 1 
 
 3 
 
 5 
 
 7 
 
 9 
 
 11 
 
 1 
 
 4 
 
 9 
 
 16 
 
 25 
 
 36 
 
 From the above formulae for falling bodies we obtain the following* 
 During the first second the body starting from a state of rest (resistance 
 of the air neglected) falls g -* 2 = 16.08 feet; the acquired velocity is g = 
 
 32.16 ft. per sec.; the distance fallen in two seconds is h = ~ = 16.08 X 4 
 
 = 64.32 ft.; and the acquired velocity is v = gt = 64.32 ft. The acceler- 
 ation, or increase of velocity in each second, is constant, and is 32.16 ft. 
 per second. Solving the equations for different times, we find for 
 
 Seconds, t 
 
 Acceleration, g 32.16 X 
 
 Velocity acquired at end of time, v . . . . 32.16 X 
 
 OO 1 C 
 
 Height of fall in each second, u - X 
 
 Total height of fall, h 32.16-4-2 x 
 
 Value of g. The value of g increases with the latitude, and decreases 
 with the elevation. At the latitude of Philadelphia, 40. its value is 
 32.16. At the sea-level, Everett gives g - 32.173 - .082 cos 2 lat. 
 .000003 height in feet. 
 
 At lat. 45 Everett's formula gives g = 32.173. The value given by the 
 International Conference on Weights and Measures, Paris, 1901, is 32. 1740. 
 
 Values of ^2g, calculated by an equation given by C. S. Pierce, are 
 given in a table in Smith's Hydraulics, from which we take the following: 
 
 Latitude 10 20 30 40 50 60 
 
 Value of ^2g.. 8.0112 8.0118 8.0137 8.0165 8.0199 8.0235 8.0269 
 Valueofp 32.090 32.094 32.105 32.132 32.160 32.189 32.216 
 
 The value of ^2g decreases about .0004 for every 1000 feet increase in 
 elevation above the sea-level. 
 
 For all ordinary^ calculations for the United States, g is generally taken 
 at 32.16, and V2g at 8.02. In England g = 32.2. \/2~g = 8.025. Practi- 
 cal limiting values of g for the United States, according to Pierce, are: 
 
 Latitude 49 at sea-level g = 32. 186 
 
 25 10,000 feet above the sea g = 32 .089 
 
 Local values of g are used in the calculation of problems that involve 
 local gravitational force, such as those of falling bodies, lifting loads, 
 and power of waterfalls. In all cases in which g appears in an equation 
 as a divisor of w (standard weight in pounds), as in the equation for 
 centrifugal force on the preceding page, the value 32.174 should be used. 
 Fig. 106 represents graphically the velocity, space, etc., of a body falling 
 for six seconds. The vertical line at the left is the time in : 
 
 horizontal lines represent the acquired 
 velocities at the end of each second = 
 32.16 1. The area of the small triangle 
 at the top represents the height fallen 
 through in the first second = 1/29= 16.08 
 feet, and each of the other triangles is an 
 equal space. The number of triangles 
 between each pair of horizontal lines rep- 
 resents the height of fall in each second, 
 and the number of triangles between any 
 horizontal line and the top is the total 
 height fallen during the time. The figures 
 under k, u and v adjoining the cut are to 
 bemultiplied by 16.08 toobtain the actual 
 velocities and heights for the given times. 
 Angular and Linear Velocity of a 
 Turning Body. Let r = radius of a 
 turning oody in feet, n = number of revo- 
 lutions per minute, v= linear velocity of 
 a point on the circumference in feet per 
 second, and 60 v = velocity in feet per 
 minute. 
 
 i seconds, the 
 
 h u, v t 
 
 .434 2" 
 
 9 5 6 3" 
 
 16 7 8 4" 
 
 9 .10 5" 
 
 \ 
 
 v\ 
 
 U 13 6- 
 
 \\\ 
 
 -~ 
 
 60 v = 2 rrn, 
 
 FIG. 106, 
 
PARALLELOGRAM OF VELOCITIES. 
 
 523 
 
 velocity is a term used to denote the angle through which any 
 radius of a body turns in a second, or the rate at which any point in it 
 having a radius equal to unity is moving, expressed in feet per second. 
 The unit of angular velocity is the angle which at a distance = radius 
 from the center is subtended by an arc equal to the radius. This unit 
 
 360, or the circumference. 
 
 angle = ~ degrees = 57.3. 2irX 57.3 
 
 If A 
 
 called a radian, 
 
 angular velocity, v = Ar, A - 
 
 T 
 
 1 80 
 The unit angle is 
 
 Height Corresponding to a Given Acquired Velocity. 
 
 Velocity. 
 
 ,d 
 bC 
 
 "S 
 
 w 
 
 Velocity. 
 
 
 
 1 
 
 Velocity. 
 
 1 
 5 
 
 S 
 
 Velocity. 
 
 ^ 
 
 M 
 
 ' 
 
 
 Velocity. 
 
 Height. 
 
 Velocity. 
 
 Height. 1 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 foot. 
 
 sec. 
 
 
 sec. 
 
 
 sec. 
 
 
 sec. 
 
 
 sec. 
 
 
 sec 
 
 
 .25 
 
 0.0010 
 
 13 
 
 2.62 
 
 34 
 
 17.9 
 
 55 
 
 47.0 
 
 76 
 
 89.8 
 
 97 
 
 146 
 
 .50 
 
 0.0039 
 
 14 
 
 3.04 
 
 35 
 
 19.0 
 
 56 
 
 48.8 
 
 77 
 
 92.2 
 
 98 
 
 149 
 
 .75 
 
 0.0087 
 
 15 
 
 3.49 
 
 36 
 
 20.1 
 
 57 
 
 50.5 
 
 78 
 
 94.6 
 
 99 
 
 152 
 
 1.00 
 
 0.016 
 
 16 
 
 3.98 
 
 37 
 
 21.3 
 
 58 
 
 52.3 
 
 79 
 
 97.0 
 
 100 
 
 155 
 
 1.25 
 
 0.024 
 
 17 
 
 4.49 
 
 38 
 
 22.4 
 
 59 
 
 54.1 
 
 80 
 
 99 5 
 
 105 
 
 171 
 
 1.50 
 
 0.035 
 
 18 
 
 5.03 
 
 39 
 
 23.6 
 
 60 
 
 56.0 
 
 81 
 
 102.0 
 
 110 
 
 188 
 
 1 75 
 
 048 
 
 1? 
 
 5.61 
 
 40 
 
 24.9 
 
 61 
 
 57.9 
 
 82 
 
 104.5 
 
 115 
 
 205 
 
 2 
 
 062 
 
 20 
 
 6.22 
 
 41 
 
 26.1 
 
 62 
 
 59.8 
 
 83 
 
 107.1 
 
 120 
 
 224 
 
 2.5 
 
 0.097 
 
 21 
 
 6.85 
 
 42 
 
 27.4 
 
 63 
 
 61.7 
 
 84 
 
 109.7 
 
 130 
 
 263 
 
 3 
 
 0.140 
 
 22 
 
 7.52 
 
 43 
 
 28.7 
 
 64 
 
 63.7 
 
 85 
 
 112.3 
 
 140 
 
 304 
 
 3 5 
 
 0.190 
 
 23 
 
 8.21 
 
 44 
 
 30.1 
 
 65 
 
 65.7 
 
 86 
 
 115.0 
 
 150 
 
 330 
 
 4 
 
 248 
 
 24 
 
 8.94 
 
 45 
 
 31.4 
 
 66 
 
 67.7 
 
 57 
 
 117.7 
 
 175 
 
 476 
 
 4.5 
 
 0.314 
 
 25 
 
 9.71 
 
 46 
 
 32.9 
 
 67 
 
 69.8 
 
 88 
 
 120.4 
 
 200 
 
 622 
 
 5 
 
 388 
 
 26 
 
 10.5 
 
 47 
 
 34.3 
 
 68 
 
 71.9 
 
 89 
 
 123.2 
 
 300 
 
 1399 
 
 6 
 
 559 
 
 27 
 
 11.3 
 
 48 
 
 35.8 
 
 69 
 
 74.0 
 
 90 
 
 125.9 
 
 400 
 
 2488 
 
 7 
 
 761 
 
 28 
 
 12.2 
 
 49 
 
 37.3 
 
 70 
 
 76.2 
 
 91 
 
 128.7 
 
 500 
 
 3887 
 
 8 
 
 0.994 
 
 29 
 
 13.1 
 
 50 
 
 38.9 
 
 71 
 
 78.4 
 
 92 
 
 131.6 
 
 600 
 
 5597 
 
 9 
 
 1.26 
 
 30 
 
 14.0 
 
 51 
 
 40.4 
 
 72 
 
 80.6 
 
 93 
 
 134.5 
 
 700 
 
 7618 
 
 10 
 
 1.55 
 
 31 
 
 14.9 
 
 52 
 
 42.0 
 
 73 
 
 82.9 
 
 94 
 
 137.4 
 
 800 
 
 9952 
 
 H 
 
 1 88 
 
 32 
 
 15.9 
 
 53 
 
 43.7 
 
 74 
 
 85.1 
 
 95 
 
 140.3 
 
 900 
 
 12,593 
 
 12 
 
 2.24 
 
 33 
 
 16.9 
 
 54 
 
 45.3 
 
 75 
 
 87.5 
 
 96 
 
 143.3 
 
 1000 
 
 15,547 
 
 3 B 
 
 Parallelogram of Velocities. The principle 9f the composition 
 and resolution of forces may also be applied to velocities or to distances 
 moved in given intervals of time. Referring 
 to Fig. 99, page 513, if a body at O has a 
 force applied to it which acting alone would 
 give it a velocity represented by OQ per 
 second, and at the same time it is acted on 
 by another force which acting alone would 
 give it a velocity OP per second, the result 
 of the two forces acting together for one sec- 
 ond will carry it to R, OR being the diagonal 
 of the parallelogram of OQ and OP, and the 
 resultant velocity. If the two component 
 velocities are uniform, the resultant will be 
 uniform and the line OR will be a straight 
 line; but if either velocity is a varying one, 
 the line will be a curve. Fig. 107 shows the 
 
 resultant velocities, also the path traversed lin ifm-m 
 
 by a body acted on by two forces, one of which would carry it at a unit 
 velocity over the intervals 1, 2, 3, B, and the other of which would carry it 
 by an accelerated motion over the intervals a.b.c.D m the same times. At 
 
 FIG. 107. 
 
524 
 
 MECHANICS. 
 
 Falling Bodies: Velocity Acquired by a Body Falling a Given 
 Height. 
 
 
 >> 
 
 
 >, 
 
 
 >> 
 
 
 >> 
 
 
 fA 
 
 
 ;>> 
 
 a 
 
 'S 
 
 w 
 
 'o 
 O 
 
 15 
 
 r* 
 
 J3 
 W! 
 
 '3 
 
 W 
 
 'S 
 _o 
 13 
 > 
 
 4 
 
 9 
 
 H 
 
 'G 
 
 jO 
 
 IS 
 > 
 
 i 
 
 as 
 
 H-l 
 
 'S 
 
 s 
 
 > 
 
 1 
 
 'o 
 
 "S . 
 
 > 
 
 4 
 
 33 
 
 w 
 
 'o 
 
 o 
 13 
 > 
 
 feet. 
 
 feet 
 p. sec. 
 
 feet. 
 
 feet 
 p.sec. 
 
 feet. 
 
 feet 
 p.sec. 
 
 feet. 
 
 feet 
 p.sec. 
 
 feet. 
 
 feet 
 p.sec. 
 
 feet. 
 
 feet 
 p.sec. 
 
 0.005 
 
 .57 
 
 0.39 
 
 5.01 
 
 .20 
 
 8.79 
 
 5. 
 
 17.9 
 
 23. 
 
 38.5 
 
 72 
 
 68.1 
 
 v.CIO 
 
 .80 
 
 0.40 
 
 5.07 
 
 .22 
 
 8.87 
 
 .2 
 
 18.3 
 
 .5 
 
 38.9 
 
 73 
 
 68.5 
 
 0.015 
 
 .98 
 
 0.41 
 
 5.14 
 
 .24 
 
 8.94 
 
 .4 
 
 18.7 
 
 24. 
 
 39.3 
 
 74 
 
 69.0 
 
 0.020 
 
 .13 
 
 0.42 
 
 5.20 
 
 .26 
 
 9.01 
 
 .6 
 
 19.0 
 
 .5 
 
 39.7 
 
 75 
 
 69.5 
 
 0.025 
 
 .27 
 
 0.43 
 
 5.26 
 
 .28 
 
 9.08 
 
 .8 
 
 19.3 
 
 25 
 
 40.1 
 
 76 
 
 69 9 
 
 0.030 
 
 .39 
 
 0.44 
 
 5.32 
 
 .30 
 
 9.15 
 
 6. 
 
 19.7 
 
 26 
 
 40.9 
 
 77 
 
 70.4 
 
 0.035 
 
 .50 
 
 0.45 
 
 5.38 
 
 .32 
 
 9.21 
 
 .2 
 
 20.0 
 
 27 
 
 41.7 
 
 78 
 
 70.9 
 
 0.040 
 
 .60 
 
 0.46 
 
 5.44 
 
 .34 
 
 9.29 
 
 .4 
 
 20.3 
 
 28 
 
 42.5 
 
 79 
 
 71.3 
 
 0.045 
 
 .70 
 
 0.47 
 
 5.50 
 
 .36 
 
 9.36 
 
 .6 
 
 20.6 
 
 29 
 
 43.2 
 
 80 
 
 71.8 
 
 0.050 
 
 .79 
 
 0.48 
 
 5.56 
 
 .38 
 
 9.43 
 
 .8 
 
 20.9 
 
 30 
 
 43.9 
 
 81 
 
 72.2 
 
 0.055 
 
 .88 
 
 0.49 
 
 5.61 
 
 .40 
 
 9.49 
 
 7. 
 
 21.2 
 
 31 
 
 44.7 
 
 82 
 
 72.6 
 
 0.060 
 
 .97 
 
 0.50 
 
 5.67 
 
 .42 
 
 9.57 
 
 .2 
 
 21.5 
 
 32 
 
 45.4 
 
 83 
 
 73.1 
 
 0.055 
 
 2.04 
 
 0.51 
 
 5.73 
 
 .44 
 
 9.62 
 
 .4 
 
 21.8 
 
 33 
 
 46.1 
 
 84 
 
 73.5 
 
 0.070 
 
 2.12 
 
 0.52 
 
 5.78 
 
 .46 
 
 9.70 
 
 .6 
 
 22.1 
 
 34 
 
 46.8 
 
 85 
 
 74.0 
 
 0.075 
 
 2.20 
 
 0.53 
 
 5.84 
 
 .48 
 
 9.77 
 
 .8 
 
 22.4 
 
 35 
 
 47.4 
 
 86 
 
 74.4 
 
 0.080 
 
 2.27 
 
 0.54 
 
 5.90 
 
 .50 
 
 9.82 
 
 8. 
 
 22.7 
 
 36 
 
 48.1 
 
 87 
 
 74.8 
 
 0.085 
 
 2.34 
 
 0.55 
 
 5.95 
 
 .52 
 
 9.90 
 
 .2 
 
 23.0 
 
 37 
 
 48.8 
 
 88 
 
 75.3 
 
 0.090 
 
 2.41 
 
 0.56 
 
 6.00 
 
 .54 
 
 9.96 
 
 .4 
 
 23.3 
 
 38 
 
 49.4 
 
 89 
 
 75.7 
 
 0.095 
 
 2.47 
 
 0.57 
 
 6.06 
 
 .56 
 
 10.0 
 
 .6 
 
 23.5 
 
 39 
 
 50.1 
 
 90 
 
 76.1 
 
 0.100 
 
 2.54 
 
 0.58 
 
 6/11 
 
 .58 
 
 10.1 
 
 .8 
 
 23.8 
 
 40 
 
 50.7 
 
 91 
 
 76.5 
 
 0.105 
 
 2.60 
 
 0.59 
 
 6.16 
 
 .60 
 
 10.2 
 
 9. 
 
 24.1 
 
 41 
 
 51.4 
 
 92 
 
 76.9 
 
 0.110 
 
 2.66 
 
 0.60 
 
 6.21 
 
 .65 
 
 10.3 
 
 .2 
 
 24.3 
 
 42 
 
 52.0 
 
 93 
 
 77.4 
 
 0.115 
 
 2.72 
 
 0.62 
 
 6.32 
 
 .70 
 
 10.5 
 
 .4 
 
 24.6 
 
 43 
 
 52.6 
 
 94 
 
 77.8 
 
 0.120 
 
 2.78 
 
 0.64 
 
 6.42 
 
 .75 
 
 10.6 
 
 .6 
 
 24.8 
 
 44 
 
 53.2 
 
 95 
 
 78.2 
 
 0.125 
 
 2.84 
 
 0.66 
 
 6.52 
 
 .80 
 
 10.8 
 
 .8 
 
 25.1 
 
 45 
 
 53.8 
 
 96 
 
 78.6 
 
 C.130 
 
 2.89 
 
 0.68 
 
 6.61 
 
 .90 
 
 11.1 
 
 10. 
 
 25.4 
 
 46 
 
 54.4 
 
 97 
 
 79.0 
 
 C.14 
 
 3.00 
 
 0.70 
 
 671 
 
 2. 
 
 11.4 
 
 .5 
 
 26.0 
 
 47 
 
 55.0 
 
 98 
 
 79.4 
 
 0.15 
 
 3.11 
 
 0.72 
 
 6.81 
 
 2.1 
 
 11.7 
 
 11. 
 
 26.6 
 
 48 
 
 55.6 
 
 99 
 
 79.8 
 
 0.16 
 
 3.21 
 
 0.74 
 
 6.90 
 
 2.2 
 
 11.9 
 
 .5 
 
 27.2 
 
 49 
 
 56.1 
 
 100 
 
 80.2 
 
 0.!7 
 
 3.31 
 
 .0.76 
 
 6.99 
 
 2.3 
 
 12.2 
 
 12. 
 
 27.8 
 
 50 
 
 56.7 
 
 125 
 
 89.7 
 
 0.18 
 
 3.40 
 
 0.78 
 
 7.09 
 
 2.4 
 
 12.4 
 
 .5 
 
 28.4 
 
 51 
 
 57.3 
 
 150 
 
 98.3 
 
 0.19 
 
 3.50 
 
 0.80 
 
 7.18 
 
 2.5 
 
 12.6 
 
 13. 
 
 28.9 
 
 52 
 
 57.8 
 
 175 
 
 106 
 
 0.20 
 
 3.59 
 
 0.82 
 
 7.26 
 
 2.6 
 
 12.0 
 
 .5 
 
 29.5 
 
 53 
 
 58.4 
 
 200 
 
 114 
 
 0.21 
 
 3.68 
 
 0.84 
 
 7.35 
 
 2.7 
 
 13.2 
 
 14. 
 
 30 
 
 54 
 
 59.0 
 
 225 
 
 120 
 
 0.22 
 
 3.76 
 
 0.86 
 
 7.44 
 
 2.8 
 
 13.4 
 
 .5 
 
 30.5 
 
 55 
 
 59.5 
 
 250 
 
 126 
 
 0.23 
 
 3.85 
 
 0.88 
 
 7.53 
 
 2.9 
 
 13.7 
 
 15. 
 
 31.1 
 
 56 
 
 60.0 
 
 275 
 
 '133 
 
 0.24 
 
 3.93 
 
 0.90 
 
 7.61 
 
 3. 
 
 13.9 
 
 .5 
 
 31.6 
 
 57 
 
 60.6 
 
 300 
 
 139 
 
 0.25 
 
 4.01 
 
 0.92 
 
 7.69 
 
 3.1 
 
 14.1 
 
 16. 
 
 32.1 
 
 58 
 
 61.1 
 
 350 
 
 150 
 
 0.26 
 
 4.09 
 
 0.94 
 
 7.78 
 
 3.2 
 
 14.3 
 
 .5 
 
 32.6 
 
 59 
 
 61.6 
 
 400 
 
 160 
 
 0.27 
 
 4.17 
 
 0.96 
 
 7.86 
 
 3.3 
 
 14.5 
 
 17. 
 
 33.1 
 
 60 
 
 62.1 
 
 450 
 
 170 
 
 0.28 
 
 4.25 
 
 0.98 
 
 7.94 
 
 3.4 
 
 14.8 
 
 .5 
 
 33.6 
 
 61 
 
 62.7 
 
 500 
 
 179 
 
 0.29 
 
 4.32 
 
 .00 
 
 8.02 
 
 3.5 
 
 15.0 
 
 18. 
 
 34.0 
 
 62 
 
 63.2 
 
 550 
 
 188 
 
 0.30 
 
 4.39 
 
 .02 
 
 8.10 
 
 3.6 
 
 15.2 
 
 .5 
 
 34.5 
 
 63 
 
 63.7 
 
 600 
 
 197 
 
 0.31 
 
 4 47 
 
 .04 
 
 8.18 
 
 3.7 
 
 15.4 
 
 19. 
 
 35.0 
 
 64 
 
 64.2 
 
 700 
 
 212 
 
 0.32 
 
 4.54 
 
 .06 
 
 8.26 
 
 3.8 
 
 15.6 
 
 .5 
 
 35.4 
 
 65 
 
 64.7 
 
 800 
 
 227 
 
 0.33 
 
 4.61 
 
 .08 
 
 8.34 
 
 3.9 
 
 15.8 
 
 20. 
 
 35.9 
 
 66 
 
 65.2 
 
 900 
 
 241 
 
 34 
 
 4.68 
 
 .10 
 
 8.41 
 
 4. 
 
 16.0 
 
 .5 
 
 36.3 
 
 67 
 
 65.7 
 
 1000 
 
 254 
 
 35 
 
 4 74 
 
 .12 
 
 8.49 
 
 .2 
 
 16.4 
 
 21. 
 
 36.8 
 
 68 
 
 66.1 
 
 2000 
 
 359 
 
 0.36 
 
 4.81 
 
 .14 
 
 8.57 
 
 .4 
 
 16.8 
 
 .5 
 
 37.2 
 
 69 
 
 66.6 
 
 3000 
 
 439 
 
 37 
 
 4.88 
 
 .16 
 
 8.64 
 
 .6 
 
 17.2 
 
 22. 
 
 37.6 
 
 70 
 
 67.1 
 
 4000 
 
 507 
 
 0.38 
 
 4.94 
 
 .18 
 
 8.72 
 
 .8 
 
 17.6 
 
 .5 
 
 38.1 
 
 71 
 
 67.6 
 
 5000 
 
 567 
 
FORCE OF ACCELERATION. 525 
 
 the end of the respective intervals the body will be found at C\, 2, Cs, C, 
 and the mean velocity during each interval is represented by the dis- 
 tances between these points. Such a curved path is traversed by a shot, 
 the impelling force from the gun giving it a uniform velocity in the 
 direction the gun is aimed, and gravity giving it an accelerated velocity 
 downward. The path of a projectile is a parabola. The distance it will 
 travel is greatest when its initial direction is at an angle 45 above the 
 horizontal. 
 
 FUNDAMENTAL EQUATIONS IN DYNAMICS. 
 
 (Uniformly Accelerated Motion) 
 
 Much difficulty to students of Mechanics has resulted from the use 
 in various text-books of such terms as "poundal" as a unit of force 
 (see page 512), "gee-pound," "slug," or "engineers' unit of mass" 
 ( = 32.2 Ibs. of matter), and by the various definitions given to the 
 words "mass" and "weight." The following elementary treatment of 
 the subject, in which all of these troublesome words are avoided, is 
 taken from an article by the author in Science, March 19, 1915. It 
 is urgently commended to the attention of text-book writers and 
 teachers, and constructive criticism of it is solicited. 
 
 The fundamental problem is: Given a constant force F Ibs. acting 
 for T seconds on a quantity of matter W Ibs., at rest at the beginning 
 of the time, but free to move, what are the results, assuming that there 
 is no frictional resistance? 
 
 The first result is motion, at a gradually increasing velocity. The 
 relati9n between the elapsed time and the velocity is determined by 
 experiment. The velocity varies directly as the time and as the force, 
 and inversely as the quantity of matter, and the equation is V oo FT/ W 
 or V = KFT/W, K being a constant whose value is approximately 32, 
 provided V is in feet per second, F and W in pounds and T in seconds. 
 
 Accurate determinations, involving precise measurements of both F 
 and W, and of S, the distance .traversed during the time T, from which 
 Vis determined, and precautions to eliminate resistance due to friction, 
 give K = 32.1740. This figure is twice the number of feet that the 
 body would fall in vacua in one second at or near latitude 45 at the sea 
 level. It is commonly represented by g, or by go, to distinguish it from 
 other values of g that may be obtained by experiments on falling 
 bodies (or on pendulums) at other latitudes and elevations. The 
 fundamental equation then is 
 
 V = FTg/W ..... ...... (1) 
 
 The quantity g is commonly called the acceleration due to gravity. 
 but it also may be considered either as an abstract figure, the constant 
 g in equation (1), or as the velocity acquired at the end of 1 second by 
 a falling body, or as the distance a body would travel in 1 second atJ 
 that same velocity if the force ceased to act and the velocity remained 
 constant. 
 
 If the velocity varies directly as the time (uniformly accelerated 
 motion), then the distance is the product of the mean velocity and the 
 time. As the body starts from rest when the velocity is 0, and the 
 velocity is V at the end of the time T, the mean velocity is 1/2 V and the 
 distance is 1/2 VT, whence V= 2S/T and T = 2S/V. 
 
 The velocity V in feet per second, at the end of the time T is numer- 
 ically equal to the number of feet the body would travel in one second 
 after the expiration of the time T if the force had then ceased to act 
 and the body continued to move at a uniform velocity. 
 
 In equation (1) substitute for V its value 2S/T and we obtain 
 
 S FT2ff (K 
 
 = ~~ 
 
 We have four elementary quantities F, T, S, W, one derived quan- 
 tity V, and one constant figure 32.1740. It is understood that F is 
 measured in standard pounds of force, one pound of force being the 
 force that gravity exerts on a pound of matter at the standard loca- 
 tion where g = 32.1740. 
 
 Each equation contains four variables, V, F, T, W, or S, F, T, W, and 
 in either equation if values be given to any three the fourth may be 
 found. By transposition, or by giving new symbols to the product or 
 
526 MECHANICS. 
 
 quotient of two of the variables, many different equations may T oe 
 derived from them, the most important of which are given below. 
 
 From (1), let F = W, the case of a body falling at latitude 45 at the 
 sea level; then V = gT. If T also = 1, then V = g, that is the velocity 
 at the end of 1 second is g. 
 
 In the equation V = gT substitute for T its value 2S/V and we have 
 V = 2gS/ V, whence V 2 = 2gS. In the case of falling bodies, the height 
 of fall H is usually substituted for S, and we obtain 
 
 V=V2gH (3) 
 
 Equation (2) with F = W gives V= 1/2 gT*. 
 From (1), by transposition we obtain 
 
 FT= WX V/g,orFT = VxW/g (4) 
 
 The product FT is sometimes called Impulse, and the expression 
 W X V/g is called momentum. It is convenient to use the letter M 
 instead of W/g, so that the equation becomes 
 
 FT = MV (5) 
 
 Impulse = Momentum 
 
 In (4) we may substitute for T its value in terms of S and V above 
 given, viz., T = 2S/V and obtain F2S/V = MV; 
 
 whence FS = 1/2 MV 2 , (6) 
 
 Work expended = Kinetic energy. 
 
 Acceleration. The quotient V/T is called the acceleration. It is 
 denned as the rate of increase of velocity. In the problem under con- 
 sideration, the action of a force on a body free to move, with no retarda- 
 tion by friction, the acceleration is a constant, V/T = A. Equation 
 (5) then may be written 
 
 F = MA (7) 
 
 Force = M times the acceleration.* 
 
 If a given body is acted on at two different times by two forces F 
 and FI, and if A and A\ are the corresponding accelerations, then 
 
 Fi =MAi whence F / Fl =^Ml (8) 
 
 By the use of these eight equations and their transformations all 
 problems relating to uniformly accelerated motion may be solved. 
 
 Force of Acceleration. Force has been denned as that which causes, 
 or tends to cause, or to destroy, motion. It may also be defined as the 
 cause of acceleration; and the unit of force, the pound, as the force re- 
 quired to produce an acceleration of 32.174 ft. per second per second of 
 one pound of matter free to move. 
 
 Force equals the product of the mass by the acceleration,* or/ = ma. 
 
 Also, if v = the velocity acquired in the time t, ft = mv; * = mv -r- 1; 
 the acceleration being uniform. 
 
 The force required to produce an acceleration of g (that is, 32.174 ft. 
 
 per sec. in one second) is / = m g = g = w, or the weight of the body. 
 Also, / = ma = m *** ~ *. in which vz is the velocity at the end, and vi 
 the velocity at the beginning of the time t, and / = mg = 2 = 
 
 ^ a; = -; or, tijie force required to give any acceleration to a body is 
 to the weight of the body as that acceleration is to the acceleration pro- 
 
 * Equation (7) is sometimes read "force equals mass times acceler- 
 ation," which is strictly true in the dyne-centimeter-gram-second, or 
 "absolute" system of measurements, in which force is measured in 
 dynes, but it is not true in the pound-foot-second system, nor in the 
 metric system where the kilogram is used as a unit of both force and 
 quantity of matter, unless it is understood that the word "mass" means 
 the quotient of W divided by g. 
 
FORCE OF ACCELERATION. 527 
 
 duced by gravity. In problems in which the local attraction of gravity 
 is a factor the local value of g must be used if great accuracy is desired. 
 EXAMPLE. Tension in a cord lifting a weight. A weight of 100 Ibs. 
 is lifted vertically by a cord a distance of 80 feet in 4 seconds, the velocity 
 uniformly increasing from to the end of the time. What tension must 
 be maintained in the cord, assuming the local value of g to be 32.108 or 
 0.998 of the standard value? Mean velocity = v m =20 ft. per sec.; 
 
 final velocity = vi = 2v m = 40; acceleration a = ~ = -^- = 10. Force 
 
 / = ma = = ^ X 10 = 31.08 Ibs. The standard value of g, 
 
 32.174 must be used here, for the force required for acceleration is 
 independent of local gravitation. This is the force required to pro- 
 duce the acceleration only ; to it must be added the force required to lift 
 the weight without acceleration, or 100 Ibs. X 0.998 = 99.8 Ibs., 
 making a total of 130.88 Ibs. (The factor 0.998 is used here because the 
 force of gravity at the given locality is 0.002 less than at the standard 
 locality) . 
 
 The Resistance to Acceleration is the same as the force required to pro- 
 duce the acceleration = - <. 
 
 Q t 
 
 Formulae for Accelerated Motion. For cases of uniformity accel- 
 erated motion other than those of falling bodies, we have the formulae 
 
 already given, / = a, = . If the body starts from rest, v\ = 
 
 0, v-2 = v and/ = - ~r\fgt = wv. We also have s = ^-. Transforming 
 
 * 
 
 id substituting for g its value 32.174, we obtain 
 
 f _ wv ~ wv _Jf?. s _. _ _ 2 _i 1 L^ - 64.35_/s. 
 
 J " 64.35 S~ 32.17 t ~ 16.09 F ' v v* 
 
 wv 2 
 
 " 
 
 64.35 / 
 t- 
 
 16.09 //a vt m Ifs 32.17ft, 
 
 W __2' \ w w 
 
 32.17 / 4.01 \ / 
 For any change in velocity,/ = w (^ ~ Vl " ) . 
 
 \ O4.OO o / 
 
 (See also Work of Acceleration, under Work.) 
 
 Motion on Inclined Planes. The velocity acquired by a body de- 
 scending an inclined plane by the force of gravity (friction neglected) is 
 equal to that acquired by a body falling freely from the height of the 
 plane. 
 
 The times of descent down different inclined planes of the same height 
 vary as the length of the planes, 
 
 The rules for uniformly accelerated motion apply to inclined planes. 
 If a is the angle of the plane with the horizontal, sin a = the ratio of the 
 
 height to the length = j- , and the constant accelerating force is g sin a. 
 
 The final velocity at the end of t seconds is v = gt sin a. The distance 
 passed over in t seconds is I = 1/2 gt 2 sin a. The time of descent is 
 
 I 
 
 | g sin a 4.01 ^/h 
 Momentum, in many books erroneously defined as the quantity of 
 motion in a body, is the product of the mass by the velocity at any 
 
 instant, = mv = v. By "mass" is "meant the quotient w/g. 
 
 Since ft = mv, the product of a constant force into the time in which 
 it acts equals numerically the momentum. 
 
 Momentum may be defined as numerically equivalent to the number 
 of pounds of force that will stop a moving body in 1 second, or the num- 
 ber of pounds of force which acting during 1 second will give it the given 
 velocity. 
 
528 MECHANICS. 
 
 Vis-viva, or living force, is a term used by early writers on Mechanics 
 to denote the energy stored in a moving body. The term is now obso- 
 lete, its place being taken by the word energy. 
 
 WORK, ENERGY, POWER. 
 
 The fundamental conceptions in Mechanics are: 
 
 Matter, Force, Time, Space, represented by W, F, T, S. 
 
 In English units W and F are measured in pounds, T in seconds, 5 
 in feet. 
 
 Velocity = space divided by time, V = S -f- T, if V be uniform. V 
 at end of time T (uniformly accelerated motion) = 2S -f- T. 
 
 Resistance is that which is opposite to an acting force. It is equal 
 and opposite to force. 
 
 Work is the overcoming of resistance through a certain distance. It 
 is measured by the product of the resistance into the space through 
 which it is overcome. It is also measured by the product of the moving 
 force into the distance through which the force acts in overcoming the 
 resistance. Thus in lifting a body from the earth against the attraction 
 of gravity, the resistance is the weight, of the body, and the product of 
 this weight into the height the body is lifted is the work done. 
 
 The Unit of Work, in British measures, is the foot-pound, or the 
 amount of work done in overcoming a pressure or weight equal to one 
 pound through one foot of space. 
 
 The work performed by a piston in driving a fluid before it, or by a 
 fluid in driving a piston before it, may be expressed in either of the fol- 
 lowing ways: 
 
 Resistance X distance traversed 
 
 = intensity of pressure X area X distance traversed ; 
 = intensity of pressure X volume traversed. 
 
 By intensity of pressure is meant pressure per unit of area, as Ibs. per 
 sq. in. 
 
 The work performed in lifting a body is the product of the weight of 
 the body into the height through which its center of gravity is lifted. 
 
 If a machine lifts the centers of gravity of several bodies at once to 
 heights either the same or different, the whole quantity of work per- 
 formed in so doing is the sum of the several products of the weights and 
 heights ; but that quantity can also be computed by multiplying the sum 
 of all the weights into the height through which their common center of 
 gravity is lifted. (Rankine.) 
 
 Power is the rate at which work is done, and is expressed by the quo- 
 tient of the work divided by the time in which it is done, or by units of 
 work per second, per minute, etc., as foot-pounds per second. The most 
 common unit of power is the horse-power, established by James Watt as 
 the power of a strong London draught-horse to do work during a short 
 interval, and used by him to measure the power of his steam-engines. 
 This unit is 33,000 foot-pounds per minute = 550 foot-pounds per sec- 
 ond = 1,980,000 foot-pounds per hour. 
 
 Power exerted for a certain time produces work; PT = FS = FVT, 
 if V be uniform. 
 
 Horse-power Hours, an expression for work measured as the product 
 of a power into the time during which it acts, = PT. Sometimes it is 
 the summation of a variable power for a given time, or the average 
 power multiplied by the time. 
 
 Energy, or stored work, is the capacity for performing work. It is 
 measured by the same unit as work, that is, in foot-pounds. It may be 
 either potential, as in the case of a body of water stored in a reservoir, 
 capable of doing work by means of a water-wheel, or actual, sometimes 
 called kinetic, which is the energy of a moving body. Potential energy 
 is measured by the product of the weight of the stored body into the dis- 
 tance through which it is capable of acting, or by the product of the 
 pressure it exerts into the distance through which that pressure is cap- 
 able of acting. Potential energy may also exist as stored heat, or as 
 stored chemical energy, as in fuel, gunpowder, etc., or as electrical en- 
 ergy, the measure of these energies being the amount of work that they 
 are capable of performing. Actual energy of a moving body is the work 
 which it is capable of performing against a retarding resistance before 
 being brought to rest, and is equal to the work which must be done 
 upon it to bring it from a state of rest to its actual velocity. 
 
WORK OF ACCELERATION, 529 
 
 The measure of actual energy is the product of the weight of the body 
 into the height from which it must fall to acquire its actual velocity. If 
 v = the velocity in feet per second, according to the principle of falling 
 
 bodies, h, the height due to the velocity, = ^\ and if w = the weight, 
 
 the energy = 1/2 nW 1 = wv% -i- 2g = wh. Since energy is the capacity for 
 performing work, the units of work and energy are equivalent, or FS = 
 1/2 mv z = wh. Energy exerted = work done. 
 
 The actual energy of a rotating body whose angular velocity is A and 
 
 A.' 2 ! 
 moment of inertia 2uT 2 = I is , that is, the product of the moment 
 
 of inertia into the height due to the velocity, A, of a point whose distance 
 from the axis of rotation is unity ; or it is equal to -jr , in which w is the 
 weight of the body and v is the velocity of the center of gyration. 
 
 Work of Acceleration. The work done in giving acceleration to a 
 body is equal to the product of the force producing the acceleration, or 
 of the resistance to acceleration, into the distance moved in a given time. 
 This force, as already stated, equals product of the mass into the acceler- 
 
 ation, or / = ma =~ . If the distance traversed in the time t = s t 
 Q t ^ 
 
 W V 1 Vi 
 
 then work =fs = -- - -- s. 
 
 EXAMPLE. What work is required to move a body weighing 100 Ibs. 
 horizontally a distance of 80 ft. in 4 seconds, the velocity uniformly 
 increasing, friction neglected? 
 
 Mean velocity v m = 20 ft. per second; final velocity = V2 = 2 v m =40; 
 
 initial velocity vi = 0; acceleration, a = - = = 10; force = 
 
 " a = lUrr x 10 = 3L1 lbs>; distance 80 ffc - work = f s = 3i.i x so 
 
 = 2488 foot-pounds. 
 
 The energy stored in the body moving at the final velocity of 40 ft. 
 per second is 
 
 1/2 ro* = \ y v 2 = Ifj^^j = 2488 foot-pounds, 
 which equals the work of acceleration, 
 
 _ w V-i _WV2V2lW 
 
 JS ~JT S ~ g~t~2 *- 2 7^ 
 
 If a body of the weight W falls from a height H, the work of accelera- 
 tion is simply WH, or the same as the work required to raise the body 
 to the same height. 
 
 Work of Accelerated Rotation. Let A angular velocity of a 
 solid body rotating about an axis, that is, the velocity of a particle 
 whose radius is unity. Then the velocity of a particle whose radius is r 
 is v = Ar. If the angular velocity is accelerated from Ai to Az, the in- 
 crease of the velocity of the particle is v* Vi = r (Ai A*), and the 
 work of accelerating it is 
 
 w^ Vi- vi 2 _ wr- A&_ Ai* 
 _ ___ = __ _ , 
 
 in which w is the weight of the particle. A is measured in radians. 
 The work of acceleration of the whole body is 
 
 The term Sir r^ is the moment of inertia of the body. 
 
 " Force of the Blow " of a Steam Hammer or Other Falling 
 Weight. The question is often asked: "With what force does a fall- 
 ing hammer strike? " The question cannot be answered directly, and it 
 is based upon a misconception or ignorance of fundamental mechanical 
 
530 MECHANICS. 
 
 laws. The energy, or capacity for doing work, of a body raised to a given 
 height and let fall cannot be expressed in pounds, simply, but only in foot- 
 pounds, which is the product of the weight into the height through which 
 it falls, or the product of its weight *- 64.32 into the square of the velocity, 
 in feet per second, which it acquires after falling through the given height. 
 If F = weight of the body, M its mass, g the acceleration due to gravity, 
 S the height of fall, and v the velocity at the end of the fall, the energy in 
 the body just before striking is FS = 1/2 Mv 2 = Wv 2 -*- 2 g = Wv 2 -s- 64.32, 
 which is the general equation of energy of a moving body. Just as the 
 energy of the body is a product of a force into a distance, so the work it 
 does when it strikes is not the manifestation of a force, which can be ex- 
 pressed simply in pounds, but it is the overcoming of a resistance through 
 a certain distance, which is expressed as the product of the average resist- 
 ance into the distance through which it is exerted. If a hammer weighing 
 100 Ibs. falls 10 ft., its energy is 1000 foot-pounds. Before being brought 
 to rest it must do 1000 foot-pounds of work against one or more resistances. 
 These are of various kinds, such as that due t9 motion imparted to the 
 body struck, penetration against friction, or against resistance to shearing 
 pr other deformation, and crushing and heating of both the falling body 
 and the body struck. The distance through which these resisting forces 
 act is generally indeterminate, and therefore the average of the resisting 
 forces, which themselves generally vary with the distance, is also indeter- 
 minate. 
 
 Impact of Bodies. If two inelastic bodies collide, they will move on 
 together as one mass, with a common velocity. The momentum of the 
 combined mass is equal to the sum of the momenta of the two bodies 
 before impact. If Wj and m 2 are the masses of the two bodies and Vi and v 2 
 their respective velocities before impact, and v their common velocity 
 after impact, (mi + w 2 )v = miVi + m 2 v 2 , 
 
 mi + m 2 
 If the bodies move in opposite directions, v= ^-. , or the velocity 
 
 mi -f- m 2 
 
 of two inelastic bodies after impact is equal to the algebraic sum of their 
 momenta before impact, divided by the sum of their masses. 
 
 If two inelastic bodies of equal momenta impinge directly upon one an- 
 other from opposite directions they will be brought to rest. 
 
 Impact of Inelastic Bodies Causes a Loss of Energy, and this loss 
 is equal to the sum of the energies due to the velocities lost and gained 
 by the bodies, respectively. 
 
 1/2 miVi 2 + 1/2 m 2 V2 2 - V2 (mi + m 2 ) v z =1/2 mi (vi - v) 2 + 1/2 mz (v* - i>) 2 ; 
 in which vi v is the velocity lost by m\ and v vi the velocity gained 
 by mi. 
 
 EXAMPLE. Let mi = 10, m* = 8, Vi = 12, v 2 = 15. 
 
 1 Q vy -jo _ O N/ 1 J 
 
 If the bodies collide they will come to rest, for v= 10 + 8 = - 
 
 The energy loss is 
 
 1/2 10 X 144+ l/ 2 8 X 225 -1/ 2 18X = 1/2 10 (12 -0)2+1/28(15- O) 2 = 
 1620 ft. -Ibs. 
 
 What becomes of the energy lost? Ans. It is used doing internal work 
 on the bodies themselves, changing their shape and heating them. 
 
 For imperfectly elastic bodies, let e = the elasticity, that is, the ratio 
 which the force of restitution, or the internal force tending to restore the 
 shape of a body after it has been compressed, bears to the force of com- 
 pression- and let mi and m 2 be the masses, Vi and v 2 their velocities before 
 impact, and Vi, vj their velocities after impact; then 
 
 , _ m^i + 7712^2 _ m 2 e (vi v 2 ) 
 
 _ 
 mi + W2 mi + mt 
 
 iVi + mzvz m\e (vi ^2 
 mi + ma mi + mz 
 
ENERGY. 531 
 
 If the bodies are perfectly efastic, their relative velocities before and 
 after impact are the same. That is, v\ f vi' = v 2 vi. 
 
 In the impact of bodies, the sum of their momenta after impact is the 
 same as the sum of their momenta before impact. 
 
 miVi + m 2 V'2 f = miVi + m 2 v 2 . 
 
 For demonstration of these and other laws of impact, see Smith's Me- 
 chanics; also, Weisbach's Mechanics. 
 
 Energy of Recoil of Guns. (Eng'g, Jan. 25, 1884, p. 72.) 
 
 Let W = the weight of the gun and carriage; 
 
 V = the maximum velocity of recoil; 
 
 w = the weight of the projectile; 
 
 v = the muzzle velocity of the projectile. 
 
 Then, since the momentum of the gun and carriage is equal to the 
 rromentum of the projectile (because both are acted on by equal force, 
 tne pressure of the gases in the gun, for equal time), we have WV wv, 
 or V = wv -f- W. 
 
 Taking the case of a 10-inch gun firing a 400-lb. projectile with a muzzle 
 velocity of 2000 feet per second, the weight of the gun and carriage being 
 22 tons = 50,000 Ibs., we find the velocity of recoil = 
 
 ^- 25 - 18feet per a^. 
 
 Now the energy of a body in motion is WV 2 -*- 2 g. 
 
 5 Q * 
 
 Therefore the energy of recoil = ' = 198,800 foot-pounds. 
 
 Z X oZ.4 
 
 The energy of the projectile is 4 * 2 o 2 = 24,844,000 foot-pounds. 
 
 i X d-Z.-Z 
 
 Conservation of Energy. No form of energy can ever be pro- 
 duced except by the expenditure of some other form, nor annihilated ex- 
 cept by being reproduced in another form. ' Consequently the sum total of 
 energy in the universe, like the sum total of matter, must always remain 
 the same. (S. Newcomb.) Energy can never be destroyed or lost; it can 
 be transformed, can be transferred from one body to another, but no 
 matter what transformations are undergone, when the total effects of the 
 exertion of a given amount of energy are summed up the result will be 
 exactly equal to the amount originally expended from the source. This 
 law is called the Conservation of Energy. (Cotterill and Slade.) 
 
 A heavy body sustained at an elevated position has potential energy. 
 When it falls, just before it reaches the earth's surface it has actual or 
 -kinetic energy, due to its velocity. When it strikes, it may penetrate the 
 earth a certain distance or may be crushed. In either case friction results 
 by which the energy is converted into heat, which is gradually radiated 
 into the earth or into the atmosphere, or both. Mechanical energy and 
 heat are mutually convertible. Electric energy is also convertible into 
 heat or mechanical energy, and either kind of energy may be converted 
 into the other. 
 
 Sources of Energy. The principal sources of energy on the earth's 
 surface are the muscular energy of men and animals, the energy of the 
 wind, of flowing water, and of fuel. These sources derive their energy 
 from the rays of the sun. Under the influence of the sun's rays vegetation 
 grows and wood is formed. The wood may be used as fuel under a steam- 
 boiler, its carbon being burned to carbon dioxide. Three-tenths of its heat 
 energy escapes in the chimney and by radiation, and seven-tenths appears 
 as potential energy in the steam. In the steam-engine, of this seven-tenths 
 six parts are dissipated in heating the condensing water and are wasted; 
 the remaining one-tenth of the original heat energy of the wood is con- 
 verted into mechanical work in the steam-engine, which may be used to 
 drive machinery. This work is finally, by friction of various kinds, or pos- 
 sibly after transformation into electric currents, transformed into neat 
 which is radiated into the atmosphere, increasing its temperature. Thus 
 
532 
 
 MECHANICS. 
 
 all the potential heat energy of the wood is, after various transformations, 
 converted into heat, which, mingling with the store of heat in the atmos- 
 
 Ehere, apparently is lost. But the carbon dioxide generated by the com- 
 ustion of the wood is, again, under the influence of the sun's rays, 
 absorbed by vegetation, and more wood may thus be formed having poten- 
 tial energy equal to the original. 
 
 Perpetual Motion. The law of the conservation of energy, than 
 which no law of mechanics is more firmly established, is an absolute barrier 
 to all schemes for obtaining by mechanical means what is called " perpetual 
 motion," or a machine which will do an amount of work greater than the 
 equivalent of the energy, whether of heat, of chemical combination, of elec- 
 tricity, or mechanical energy, that is put into it. Such a result would be 
 the creation of an additional store of energy in the universe, which is not 
 possible by any human agency. 
 
 The Efficiency of a Machine is a fraction expressing the ratio of 
 the useful work to the whole work performed, which is equal to the energy 
 expended. The limit to the efficiency of a machine is unity, denoting the 
 efficiency of a perfect machine in which no work is lost. The difference 
 between the energy expended and the useful work done, or the loss, is 
 usually expended either in overcoming friction or in doing work on bodies 
 surrounding the machine from which no useful work is received. Thus 
 in an engine propelling a vessel part of the energy exerted in the cylinder 
 does the useful work of giving motion to the vessel, and the remainder is 
 spent in overcoming the friction of the machinery and in making currents 
 and eddies in the surrounding water. 
 
 A common and useful definition of efficiency is " output divided by 
 input." 
 
 ANIMAL POWER. 
 
 Work of a Man against Known Resistances. (Rankine.) 
 
 Kind of Exertion. 
 
 R, 
 
 Ibs. 
 
 F, 
 
 ft. per 
 sec. 
 
 T" 
 3600 
 
 (hours 
 per 
 day). 
 
 R V, 
 ft.-lbs. 
 per sec. 
 
 RVT, 
 
 ft.-lbs. 
 per day. 
 
 1. Raising his own weight up 
 stair or ladder 
 
 143 
 
 0.5 
 
 8 
 
 71.5 
 
 2,059,200 
 
 2. Hauling up weights with rope, 
 
 
 
 
 
 
 and lowering the rope un- 
 
 
 
 
 
 
 loaded 
 
 40 
 
 0.75 
 
 6 
 
 30* 
 
 648,000 
 
 3. Lifting weights by hand. ..... 
 4. Carrying weights up-stairs 
 and returning unloaded 
 
 44 
 143 
 
 0.55 
 0.13 
 
 6 
 6 
 
 24.2 
 18.5 
 
 522,720 
 399,600 
 
 5. Shoveling up earth to a 
 height of 5 ft 3 in 
 
 6 
 
 1.3 
 
 10 
 
 7.8 
 
 280,800 
 
 6. Wheeling earth in barrow up 
 
 
 
 
 
 
 slope of 1 in 12, 1/2 horiz. 
 
 
 
 
 
 
 veloc. 0.9 ft. per sec., and re- 
 
 
 
 
 
 
 turning unloaded 
 
 132 
 26.5 
 
 0.075 
 2.0 
 
 10 
 
 8 
 
 9.9 
 
 53 
 
 356,400 
 1,526,400 
 
 7. Pushing or pulling horizon- 
 tally (capstan or oar) 
 
 
 !12.5 
 
 5.0 
 
 
 62.5 
 
 
 8. Turning a crank or winch 
 
 18.0 
 20.0 
 
 2.5 
 14.4 
 
 8 
 2 rain. 
 
 45 
 288 
 
 '1,296,666 
 
 9 Workin " pump 
 
 13.2 
 
 2.5 
 
 10 
 
 33 
 
 1,188.666 
 
 10. Hammering 
 
 15 
 
 
 8? 
 
 ? 
 
 480,000 
 
 
 EXPLANATION. R, resistance; F, effective velocity = distance 
 through which R is overcome -*- total time occupied, including the time 
 of moving unloaded, if any; T", time of working, in seconds per day; 
 T" -* 3600, same time, in hours per day; RV, effective power, in foot- 
 pounds per second; RVT, daily work. 
 
ANIMAL POWER. 
 
 533 
 
 Performance of a Man in Transporting Loads Horizontally. 
 (Rankine.) 
 
 
 
 
 T" 
 
 LV, 
 
 LVT, 
 
 Kind of Exertion. 
 
 L, 
 Ibs. 
 
 y, 
 
 ft.-sec. 
 
 3600 
 (hours 
 per 
 
 Ibs. 
 con- 
 veyed 
 
 Ibs. con- 
 veyed 
 1 foot. 
 
 
 
 
 day). 
 
 1 foot. 
 
 
 11. Walking unloaded, trans- 
 
 
 
 
 
 
 porting his own weight. . . 
 12. Wheeling load L in 2-whld. 
 
 140 
 
 5 
 
 10 
 
 700 
 
 25,200,000 
 
 barrow, return unloaded . 
 
 224 
 
 12/3 
 
 10 
 
 373 
 
 13,428,000 
 
 13. Ditto in 1-wh. barrow, ditto. . 
 
 132 
 
 12/3 
 
 10 
 
 220 
 
 7 920,000 
 
 14. Traveling with burden. ...... 
 
 90 
 
 21/2 
 
 7 
 
 225 
 
 5.670,000 
 
 15. Carrying burden, returning 
 unloaded 
 
 140 
 
 12/3 
 
 6 
 
 233 
 
 5,032,800 
 
 
 !252 
 
 
 
 
 
 
 
 16. Carrying burden, for 30 sec- 
 
 126 
 
 11.7 
 
 
 1474.2 
 
 
 y 
 
 
 
 23.1 
 
 
 
 
 
 EXPLANATION. L, load; V, effective velocity, computed as before; 
 T", time of working, in seconds per day; T" *- 3600, same time in hours 
 per day; LV, transport per second, in Ibs. conveyed one foot; LVT, 
 daily transport. 
 
 In the first line only of each of the two tables above is the weight of 
 the man taken into account in computing the work done. 
 
 Clark says that the average net 
 daily work of an ordinary laborer 
 at a pump, a winch, or a crane may 
 be taken at 3300 foot-pounds per 
 minute, or one-tenth of a horse- 
 power, for 8 hours a day; but for 
 shorter periods from four to five 
 times this rate may be exerted. 
 
 Mr. Glynn says that a man may 
 exert a force of 25 Ibs. at the 
 handle of a crane for short periods; 
 but that for continuous work a 
 force of 15 Ibs. is all that should 
 be assumed, moving through 220 
 feet per minute. 
 
 Man-wheel. Fig. 108 is a sketch 
 of a very efficient man-power hoist- 
 ing-machine which the author saw 
 
 FIG. 108. 
 
 in Berne, Switzerland, in ^o^. 
 
 The face of the wheel was wide 
 enough for three men to walk abreast, so that nine men could work in it 
 at one time. 
 
 Work of a Horse against a Known Resistance. (Rankine.) 
 
 Kind of Exertion. 
 
 R. 
 
 V. 
 
 T" 
 
 3600 
 
 RV. 
 
 RVT. 
 
 1. Cantering and trotting, draw- 
 ing a light railway carriage 
 (thoroughbred) 
 
 !min. 221/2 
 mean 301/2 
 max 50 
 
 j 142/3 
 
 4 
 
 4471/2 
 
 6,444,000 
 
 2. H^rse drawing cart or boat, 
 walking (draught-horse) . . . 
 
 120 
 
 3.6 
 
 8 
 
 432 
 
 12,441,600 
 
 3. Horse _ drawing a gin or mill, 
 walking 
 
 100 
 
 3.0 
 
 8 
 
 300 
 
 8,640,000 
 
 4. Ditto trotting 
 
 66 
 
 6.5 
 
 41/9 
 
 429 
 
 6,950,000 
 
 
 
 
 
 
 
534 
 
 MECHANICS. 
 
 EXPLANATION. R, resistance, in Ibs.; V, velocity, in feet per second; 
 T" -f- 3600, hours work per day; RV, work per second; RVT 9 work per 
 day. 
 
 The average power of a draught-horse, as given in line 2 of the above 
 table, being 432 foot-pounds per second, is 432/550 = 0.785 of the con- 
 ventional value assigned by Watt to the ordinary unit of the rate of 
 work of prime movers. It is the mean of several results of experiments, 
 and may be considered the average of ordinary performance under favor- 
 able circumstances. 
 
 Performance of a Horse in Transporting Loads Horizontally. 
 
 (Rankine.) 
 
 Kind of Exertion. 
 
 L. 
 
 V. 
 
 T. 
 
 LV. 
 
 LVT. 
 
 5. Walking with cart, always 
 loaded 
 
 1500 
 
 3 6 
 
 10 
 
 5400 
 
 194 400 000 
 
 6. Trotting ditto . . 
 
 750 
 
 7 2 
 
 41/2 
 
 5400 
 
 87 480 000 
 
 7. Walking with cart, going 
 loaded, returning empty; 
 V, mean velocity 
 
 1500 
 
 2 
 
 10 
 
 3000 
 
 108 000 000 
 
 8. Carrying burden, walking. . 
 9. Ditto trotting .. 
 
 270 
 180 
 
 3.6 
 
 7 2 
 
 10 
 7 
 
 972 
 1296 
 
 34,992,000 
 32 659 200 
 
 
 
 
 
 
 
 EXPLANATION. L, load in Ibs. ; F, velocity in feet per second ; T, work- 
 ing hours per day; LV, transport per second; LVT, transport per day. 
 
 This table has reference to conveyance on cpmmon roads only, and 
 those evidently in bad order as respects the resistance to traction upon 
 them. 
 
 Horse-Gin. In this machine a horse works less advantageously 
 than in drawing a carriage along a straight track. In order that the best 
 possible results may be realized with a horse-gin, the diameter of the cir- 
 cular track in which the horse walks should not be less than about forty 
 feet. 
 
 Oxen, Mules, Asses. Authorities differ considerably as to the power 
 of these animals. The following may be taken as an approximative com- 
 parison between them and draught-horses (Rankine): 
 
 Ox. Load, the same as that of average draught-horse; best velocity 
 and work, two-thirds of horse. 
 
 Mule. Load, one-half of that of average draught-horse; best velocity, 
 the same as horse; work, one-half. 
 
 Ass. Load, one-quarter that of average draught-horse; best velocity, 
 the same; work, one-quarter. 
 
 Reduction of Draught of Horses by Increase of Grade of Roads. 
 (Engineering Record, Prize Essays on Roads, 1892.) Experiments on 
 English roads by GayfRer & Parnell: 
 
 Calling load that can be drawn on a level 100: 
 
 On a rise of 1 in 100. 1 in 50. 1 in 40. 1 in 30. 1 in 26. 1 in 20. 1 in 10. 
 
 A horse can draw only 90 81 72 64 54 40 25 
 
 The Resistance of Carriages on Roads is (according to Gen. Morin) 
 given approximately by the following empirical formula: 
 
 R = I [a + b (u - 3.28)]. 
 
 In this formula R = total resistance; r = radius of wheel in inches; 
 W = gross load; u = velocity in feet per second; while a and b are 
 constants, whose values are: For good broken-stone road, a = 0.4to0.55, 
 b = 0.024 to 0.026: for paved roads, a = 0.27, b = 0.0684. 
 
 Rankine states that on gravel the resistance is about double, and on 
 sand five times, the resistance on good broken-stone roads. 
 
Ow 
 
 ELEMENTS OF MACHINES. 535 
 
 ELEMENTS OP MACHINES. 
 
 The object of a machine is usually to transform the work or mechanical 
 energy exerted at the point where the machine receives its motion into 
 work at the point where the final resistance A r n 
 
 is overcome. The specific result may be to v ;f ? 
 
 change the character or direction of mo- 
 tion, as from circular to rectilinear, or vice 
 versa, to change the velocity, or to overcome 
 a great resistance by the application of a 
 moderate force. In all cases the total energy w no 
 
 exerted equals the total work done, the latter * IG ' LUJ * 
 
 including the overcoming of all the frictional 
 resistances of the machine as well as the use- 
 ful work performed. No increase of power 
 c"an be obtained from any machine, since this 
 is impossible according to the law of conser- 
 vation of energy. In africtionless machine the "^ 
 product of the force exerted at the driving- 
 point into the velocity of the driving-point. I 
 cr the distance it moves in a given interval Ow 
 of time, equals the product of the resistance 
 into the distance' through which the resist- w 110 
 ance is overcome in the same time. ri(j * 11Ut 
 
 The most simple machines, or elementary 
 machines, are reducible to three classes, viz., 
 the Lever, the C9rd, and the Inclined Plane. 
 
 The first class includes every machine con- 
 sisting of a solid body capable of revolving 
 on an axis, as the Wheel and Axle. 
 
 The second class includes every machine in 
 which force is transmitted by means of flexi- 
 ble threads, ropes, etc., as the Pulley. 
 
 The third class includes every machine iri p IQ m 
 
 \yhich a hard surface inclined to the direc- 
 tion of ^motion is introduced, as the Wedge and the Screw. 
 
 A Lever is an inflexible rod capable of motion about a fixed point, 
 called a fulcrum. The rod may be straight or bent at any angle, or 
 curved. 
 
 It is generally regarded, at first, as without weight, but its weight may 
 be considered as another force applied in a vertical direction at its center 
 of gravity. 
 
 The arms of a lever are the portions of it intercepted between the force. 
 P, and fulcrum, C, and between the weight or load, W, and fulcrum. 
 
 Levers are divided into three kinds or orders, according to the relative 
 positions of the applied force, load, and fulcrum. 
 
 In a lever of the first order, the fulcrum lies between the points at which 
 the force and load act. "(Fig. 109.) 
 
 In a lever of the second order, the load acts at a point between the 
 fulcrum and the point of action of the force. (Fig. 110.) 
 
 In a lever of the third order, the point of action of the force is between 
 that of the load and the fulcrum. (Fig. 111.) 
 
 In all cases of levers the relation between the force exerted or- the pull, 
 P, and the load lifted, or resistance overcome, W, is expressed by the 
 equation PX AC = W X BC, in which AC is the lever-arm of P, and 
 BC is the lever-arm of W, or moment of the force = the moment of the 
 resistance. (See Moment.) 
 
 In cases in which the direction of the force (or of the~resistance) is not 
 at right angles to the arm of the lever on which it acts, the "lever-arm" 
 is the length of a perpendicular from the -fulcrum to the line of direction 
 of the force (or of the resistance). W : P : : AC : BC, or, the ratio of 
 the resistance to the applied force is the inverse ratio of their lever-arms. 
 Also, if y^is the velocity of TF, and Vp is the velocity of P, W : P : : Vp: 
 Vw, and P X Vp = WX Vw. 
 
 If 8p is the distance through which the applied force acts, and Sw is 
 the distance the load is lifted or through which the resistance is over- 
 come, W ; P ; ; Sp : Sw : W X Sw = P X Sp, or the load into the dis- 
 
536 
 
 MECHANICS. 
 
 tance it is lifted equals the force into the distance through which it is 
 exerted. 
 
 These equations are general for all classes of machines as well as for 
 levers, it being understood that friction, which in actual machines in- 
 creases the resistance, is not at present considered. 
 
 The Bent Lever. In the bent lever (see Fig. 102, p. 514), the lever- 
 arm of the weight m is cf instead of bf. The lever is in equilibrium when 
 n X af = m X cf, but it is to be observed that the action of a bent lever 
 may be very different from that of a straight lever. In the latter, so 
 long as the i'orce and the resistance act in lines parallel to each other, the 
 ratio of the lever-arms remains constant, although the lever itself changes 
 its inclination with the horizontal. In the bent lever, however, this 
 ratio changes: thus, in the cut, if the arm bf is depressed to a horizontal 
 direction, the distance cf lengthens while the horizontal projection of 
 af shortens, the latter becoming zero when the direction of af becomes 
 vertical. As the arm af approaches the vertical, the weight n which 
 may be lifted with a given force s is very great, but the distance through 
 which it may be lifted is very small. In all cases the ratio of the weight 
 m to the weight n is the inverse ratio of the horizontal projection of their 
 respective lever-arms. 
 
 The Moving Strut (Fig. 112) is similar to the bent lever, except that 
 one of the arms is missing, and that the force and the resistance to be 
 overcome act at the same end of the 
 single arm. The resistance in the 
 case shown in the cut is not the load 
 W, but its resistance to being 
 moved, R, which may be simply 
 that due to its friction on the hori- 
 zontal plane, or some other oppos- 
 ing force. When the angle between 
 the strut and the horizontal plane 
 changes, the ratio of the resistance 
 to the applied force changes. When 
 the angle becomes very small, a 
 moderate force will overcome a 
 very great resistance, which tends FIG. 112. 
 
 to become infinite as the angle ap- 
 proaches zero. If a =the angle, P X cos a = R X sin a. If a = 5 degrees, 
 cos a = 0.99619, sin a = 0.08716, R = 11.44 P. 
 
 The stone-crusher (Fig. 113) shows a practical example of the use of 
 two moving struts. 
 
 The Toggle-joint is an elbow or knee-joint consisting of two bars so 
 connected that they; may be brought into a straight line and made to 
 produce great endwise pressure when a force is applied to bring them 
 into this position. It is a case of two moving struts placed end to end, 
 
 FIG. 113. 
 
 FIG. 114. 
 
 the moving force being applied at their point of junction, in a direction 
 at right angles to the direction of the resistance, the other end of one of 
 the struts resting against a fixed abutment, and that of the other against 
 the body to be moved. If a the angle each strut makes with the straight 
 line joining the points about which their outer ends rotate, the rati9 of 
 the resistance to the applied force is R : P : : cos a : 2 sin q; 2 R sin a 
 = P cos a. The ratio varies when the angle varies, becoming infinite 
 when the angle becomes zero. 
 
ELEMENTS OF MACHINES. 
 
 537 
 
 The toggle-joint is used where great resistances are to be overcome 
 through very small distances, as in stone-crushers (Fig. 114). 
 
 The Inclined Plane, as a mechanical element, is supposed perfectly 
 hard and smooth, unless friction bs considered. It assists in sustaining 
 a heavy body by its reaction. This reaction, however, being normal to 
 the plane, cannot entirely counteract the weight of the body, which acts 
 vertically downward. Some other force must 
 therefore be made to act upon the body, in order 
 that it may be sustained. 
 
 If the sustaining force act parallel to the plane 
 (Fig. 115), the force is to the weight as the height 
 of the plane is to its length, measured on the 
 incline. 
 
 If the force act parallel to the base of the 
 plane, the force is to the weight as the height is 
 to the base. 
 
 If the force act at any other angle, let i the 
 angle of the plane with. the horizon, and e= the 
 
 FIG. 115. 
 
 le of the direction of the applied force with the angle of the plane. 
 P : W : : sin i : cos e; P X cos e = W sin i. 
 
 Problems of the inclined plane may be solved by the parallelogram of 
 forces thus: 
 
 Let the weight W be kept at rest on the incline by the force P, acting 
 in the line bP', parallel to the plane. Draw the vertical line ba to repre- 
 sent the weight; also bb' perpendicular to the plane, and complete the 
 parallelogram b'c. Then the vertical weight bais the resultant of bb', the 
 measure of support given by the plane to the weight, and be, the force of 
 gravity tending to draw the weight down the plane. The force required 
 to maintain the weight in equilibrium is represented by this force be. 
 Thus the force and the weight are in the ratio of be to ba. Since the 
 triangle of forces abc is similar to the triangle of the incline ABC, the 
 latter may be substituted for the former in determining the relative 
 magnitude of the forces, and 
 
 P : W : : be : ab : : BC : AB. 
 
 The Wedge is a pair of inclined planes united by their bases. In the 
 application of pressure to the head or butt end of the wedge, to cause it to 
 penetrate a resisting body, the applied force is to the resistance as the 
 thickness of the wedge is to its length. Let t be the thickness, I the length, 
 W the resistance, and P the applied force or pressure on the head of the 
 
 wt Pf 
 
 wedge. Then, friction neglected, P: W : : t : I; P = -^; W = =^- 
 
 I t 
 
 The Screw is an inclined plane wrapped around a cylinder in such a 
 way that the height of the plane is parallel to the axis of the cylinder. . If 
 the screw is formed upon the internal surface of a hollow cylinder, it is 
 usually called a nut. When force is applied to raise a weight or overcome 
 a resistance by means of a screw and nut, either the screw or the nut may 
 be fixed, the other being movable. The force is generally applied at the 
 end of a wrench or lever-arm, or at the circumference of a wheel. If r = 
 radius of the wheel or lever-arm, and p pitch 
 of the screw, or distance between threads, that 
 is, the height of the inclined plane for one revo- 
 lution of the screw, P = the applied force, and 
 W = the resistance overcome, then, neglecting 
 resistance due to friction, 2 irr X P = Wp; W 
 = 6.283 Pr + p. The ratio of P to W is thus 
 independent of the diameter of the screw. In 
 actual screws, much of 
 A, ----- the power transmitted is 
 
 / x lost through friction. 
 
 The Cam is a revolv- 
 ing inclined plane. It 
 may be either an in- 
 clined plane wrapped 
 around a cylinder in such 
 FIG. 116. a way that the height of 
 
 the plane is radial to the 
 
 117 
 
 cylinder, such as the ordinary lifting-cam, used in stamp-mills (Fig. 11G), 
 
538 
 
 MECHANICS. 
 
 or it may be an inclined plane curved edgewise, and rotating in a plane 
 parallel to its base (Fig. 117). The relation of the weight to the applied 
 force is calculated in the same manner as in the case of the screw. 
 
 Efficiency of a Screw. Let a = angle of the thread, that is, the 
 angle whose tangent is the pitch of the screw divided by the circum- 
 ference of a circle whose diameter is the mean of the diameters at the 
 top and bottom of the thread. Then for a square thread 
 Efficiency = (1 - /tan a) -f- (1 -f/cotan a), 
 
 in which/ is the coefficient of friction. (For demonstration, see Cotterill 
 and Slade, Applied Mechanics.) Since cotan = 1 -;- tan, we may sub- 
 stitute for cotan a the reciprocal of the tangent, or if p == pitch, and 
 c = mean circumference of the screw, 
 
 Efficiency = (1 -fp/c) -r- (1 +fc/p). 
 
 EXAMPLE. Efficiency of square-threaded screws of 1/2 inch pitch. 
 Diameter at bottom of thread, in. . . 1 2 3 4 
 
 Diameter at top of thread, in 11/2 21/2 3 1/2 41/2 
 
 Mean circumference of thread, in.. . . 3.927 7.06910.21 13.35 
 
 Cotangent a = c * p =7.85414.14 20.42 26.70 
 
 Tangenta = p-^c =0.1273 .0707 .0490 .0375 
 
 Efficiency if/ = 0.10 =55.3% 41.2% 32.7% 27.2% 
 
 Efficiency if / = 0.15 =45% 31.7% 24.4% 19.9% 
 
 The efficiency thus increases with the steepness of the pitch. 
 
 The above formulae and examples are for square-threaded screws, and 
 consider the friction of the screw-thread only, and not the friction of the 
 collar or step by which end thrust is resisted, and which further reduces 
 the efficiency. The efficiency is also further reduced by giving an inclina- 
 tion to the side of the thread, as in the V-threaded screw. For discussion 
 of this subject, see paper by Wilfred Lewis, Jour. Frank. Inst. 1880; also 
 Trans. A. S.M. E., vol. xii, 784. 
 
 Efficiency of Screw-bolts. Mr. Lewis gives the following approxi- 
 mate formula for ordinary screw-bolts (V-threads, with collars): p= pitch 
 of screw, d = outside diameter of screw, F = force applied at circum- 
 ference to lift a unit of weight, E = efficiency of screw. For an average 
 case, in which the coefficient of friction may be assumed at 0.15, 
 F = (P + d) ^ 3d, E = p -T- (p + d). 
 
 For bolts of the dimensions given above, i/2-inch pitch, and outside 
 diameters 11/2, 21/2, 3 1/2, and 41/2 inches, the efficiencies according to this 
 formula would be, respectively, 0.25, 0.167, 0.125, and 0.10. 
 
 James McBride (Trans. A. S. M. E., xii, 781) describes an experiment 
 with an ordinary 2-inch screw-bolt, with a V-thread, 41/2 threads per inch, 
 raising a weight of 7500 pounds, the force being applied by turning the 
 nut. Of the power applied 89.8 per cent was absorbed by friction of the 
 nut on its supporting washer and of the threads of the bolt in the nut. 
 The nut was not faced, and had the flat side to the washer. 
 
 Professor Ball in his "Experimental Mechanics" says: "Experiments 
 showed in two cases respectively about 2/ 3 and 3/ 4 of the power was lost. " 
 , Weisbach says: "The efficiency is from 19 per cent to 30 per cent." 
 
 JW 
 
 B. a 
 
 FiQ. U8, 
 
ELEMENTS OF MACHINES. 
 
 539 
 
 Pulleys or Blocks. P force applied, or pull; W ' = load lifted, 
 or resistance. In the simple pulley A (Fig. 118) the point P on the 
 pulling rope descends the same amount that the" load is lifted, therefore 
 P = W. In B and C the point P moves twice as far as the load is lifted, 
 therefore W = 2P. In B and C there is one movable block, and two 
 plies of the rope engage with it. In D there are three sheaves in the 
 movable block, each with two plies engaged, or six in all. Six plies of 
 the rope are therefore shortened by the same amount that the load is 
 lifted and the point P moves six times as far as the load, consequently 
 W = 6 P. In general, the ratio of W to P is equal to the number of plies 
 of the rope that are shortened, and also is equal to the number of plies that 
 engage the lower block. If the lower block has 2 sheaves and the upper 
 3, the end of the rope is fastened to a hook in the top of the lower block, 
 and then there are 5 plies shortened instead of 6, and W = 5 P. If V = 
 velocity of W, and v = velocity of P, then in all cases V W vP, whatever 
 the number of sheaves or their arrangement. If the hauling rope, at the 
 pulling end, passes first around a sheave in the upper or stationary block, 
 it makes no difference in what direction the rope is led 
 from this block to the point at which the pull on the 
 rope is applied ; but if it first passes around the movable 
 block, it is necessary that the pull be exerted in a direc- 
 tion parallel to the line of action of the resistance, or a 
 line joining the. centers of the two blocks, in order to 
 obtain the maximum effect. If the rope pulls on 'the 
 lower block at an angle, the block will be pulled out of 
 the line drawn between the load and the upper block, 
 and the effective pull will be less than the actual pull 
 on the rope in the ratio of the cosine of the angle the 
 pulling rope makes with the vertical, or line of action of 
 the resistance, to unity. 
 
 Differential Pulley. (Fig. 119. ) Two pulleys, B 
 and C, of different radii, rotate as one piece about a 
 fixed axis, A. An endless chain, BDECLKH, passes 
 over both pulleys. The rims of the pulleys are shaped 
 so as to hold the chain and prevent it from slipping. 
 One of the bights or loops in which the chain hangs, DE. 
 passes under and supports the running block F. The 
 other loop or bight, HKL, hangs freely, and is called the 
 hauling part. It is evident that the velocity of the haul- 
 ing part is equal to that of the pitch-circle of the pulley B. 
 
 In order that the velocity-ratio may be exactly 
 uniform, the radius of the sheave F should be an exact 
 mean between the radii of B and C. 
 
 Consider that the point B of the cord BD moves through an arc whose 
 length = AS, during the same time the point C or the cord CE will 
 move downward a distance = AC. The length of the bight or loop 
 BDEC will be shortened by AB - AC, which will cause the pulley F to 
 be raised half of this amount. If P = the pulling force on the cord HK, 
 and W the weight lifted at F, then P X AB = W X 1/2 (AB - AC}. 
 
 To calculate the length of chain required for a differential pulley, take 
 the following sum: Half the circumference of A + half the circumference 
 of B + half the circumference of F + twice the greatest distance of F 
 from A + the least, length of loop HKL. The last quantity is fixed 
 according to convenience. 
 
 A Wheel and Axle, or Windlass, resembles two pulleys on one axis, 
 having different diameters. If a weight be lifted by means of a rope 
 wound over the axle, the force being applied at the rim of the wheel, 
 the action is like that of a lever of which the shorter arm is equal to the 
 radius of the axle plus half the thickness of the rope, and the longer 
 arm is equal to the radius of the wheel. A wheel and axle is therefore 
 sometimes classed as a perpetual lever. If P = the applied force, D = 
 diameter of the wheel, W = the weight lifted, and d the diameter of the 
 axle + the diameter of the rope, PD = Wd. 
 
 Toothed-wheel Gearing is a combination of two or more wheels and 
 axles (Fig. 120 ). If a series of wheels and pinions gear into each other, 
 as in the cut, friction neglected, the weight lifted, or resistance over- 
 come, is to the force applied inversely as the distances through which 
 
 FIG. 119. 
 
540 
 
 MECHANICS. 
 
 they act in a given time. If R, Ri, R 2 be the radii of the successive wheels, 
 measured to the pitch-line of the teeth, and r, r t , r 2 the radii of the cor- 
 responding pinions, P the applied force, and W the weight lifted, P X 
 R X R\ X #2 == W X r X n X n, or the applied force is to the weight 
 as the product of the radii of the pinions is to the product of the radii of 
 the wheels; or, as the product of the numbers expressing the teeth in 
 each pinion is to the product of the numbers expressing the teeth in each 
 wheel. 
 
 FIG\ 120. 
 
 FIG. 121. 
 
 Endless Screw, or Worm-gear. (Fig. 121.) This gear is com- 
 monly used to convert motion at high speed into motion at very slow 
 speed. When the handle P describes a complete circumference, the pitch- 
 line of the cog-wheel moves through a distance equal to the pitch of the 
 screw, and the weight W is lifted a distance equal to the pitch of the screw 
 multiplied by the ratio of the diameter of the axle to the diameter of the 
 pitch-circle of the wheel. The ratio of the applied force to the weight 
 lifted is inversely as their velocities, friction not being considered; but the 
 friction in the worm-gear is usually very great, amounting sometimes to 
 three or four times the useful work done. 
 
 If v = the distance through which the force P acts in a given time, say 
 1 second, and V = distance the weight W is lifted in the same time, r= 
 radius of the crank or wheel through which P acts, t = pitch of the screw, 
 and also of the teeth on the cog-wheel, d = diameter of the axle, and 
 
 D = diameter of the pitch-line of the cog-wheel,] v = -^. - ^ X V; 
 V = v X td -- 6.283 rD. Pv = WV + friction. 
 
 The Differential Windlass (Fig. 122) is identical in principle with the 
 differential pulley, the difference in construction being that in the dif- 
 ferential windlass the running block hangs in the 
 bight of a rope whose two parts are wound round, 
 and have their ends respectively made fast to two 
 barrels of different radii, which rotate as one piece 
 about the axis A. The differential windlass is 
 little used in practice, because of the great length 
 of rope which it requires. 
 
 The Differential Screw (Fig. 123) is a com- 
 pound .screw of different pitches, in which the 
 threads wind the same way. Ni and N z are the 
 
 two nuts; SiSi, 
 
 the longer-pitched 
 
 thread; 8282. the 
 
 shorter-pit ched 
 
 thread: in the figure 
 
 both these threads 
 
 are left-handed. At 
 each turn of the screw the nut N 2 advances relatively to Ni through- a 
 distance equal to the difference of the pitches. The use of the differential 
 screw is to combine the slowness of advance due to a fine pitch with 
 the .strength of thread which can be obtained by means of a coarse 
 pitch only. 
 
 FIG. 123. 
 
 FIG. 122. 
 
STRESSES IN FRAMED STRUCTURES. 
 
 541 
 
 Efficiency of a Differential Screw. A correspondent of tile 
 American Machinist describes an experiment with a differential screw- 
 punch, consisting of an outer screw 2 inch diameter, 3 threads per 
 inch, and an inner screw 13/ 8 inch diameter, 3 1/2 threads per inch. The 
 pitch of the outer screw being 1/3 inch and that of the inner screw 2/ 7 inch 
 the punch would advance in one revolution 1/3 2 /7 = V2t inch. 
 Experiments were made to determine the force required to punch an 
 ii/16-inch hole in iron 1/4 inch thick, the force being applied at the end 
 of a lever-arm of 473/ 4 inch. The leverage would be 473/ 4 x 2* X 21 = 
 6300. The mean force applied at the end of the lever was 95 pounds, 
 and the force at the punch, if there was no friction, would be 6300 X 
 95 = 598,500 pounds. The force required to punch the iron, assuming 
 a shearing resistance of 50,000 pounds per square inch, would be 50,000 X 
 n/16 XT X 1/4 = 27,000 pounds, and the efficiency of the punch would 
 be 27,000 * 598,500 = only 4.5 per cent. With the larger screw only 
 used as a punch the mean force at the end of the lever was only 82 pounds. 
 The leverage in this case was 473/4 x 2ir X 3 = 900, the total force 
 referred to the punch, including friction, 900 X 82 = 73,800, and the 
 efficiency 27,000 *- 73,800 = 36.7 per cent. The screws were of tool- 
 steel, well fitted, and lubricated with lard-oil and plumbago. 
 
 STRESSES IN FRAMED STRUCTURES. 
 
 Framed structures in general consist of one or more triangles, for the 
 reason that the triangle is the one polygonal form whose shape cannot be 
 changed without distorting one of its sides. Problems in stresses of 
 simple framed structures may generally be solved either by the applica- 
 tion of the triangle, parallellogram, or polygon of forces, by the principle 
 of the lever, or by the method of moments. We shall give a few ex- 
 amples, referring the student to the works of Burr, Dubois, Johnson, and 
 others for more elaborate treatment of the subject. 
 
 1. A Simple Crane. (Figs. 124 and 125.} A is a fixed mast, B a 
 brace or boom, T a tie, and P the load. Required the strains in B and T. 
 The weight P, considered as acting at the end of the boom, is held in 
 equilibrium by three forces: first, gravity acting downwards; second, the 
 tension in T; and third, the thrust of B. Let the length of the line p 
 represent the magnitude of the downward force exerted by the load, and 
 draw a parallelogram with sides bt parallel, respectively, to B and T, 
 such that p is the diagonal of the parallelogram. Then 6 and t are the 
 components drawn to the same scale as p, p being the resultant. Then 
 if the length p represents the load, t is the tension in the tie, and b is the 
 compression in the brace. 
 
 Or, more simply, T, B, and that portion of the mast included between 
 them or A' may represent a triangle of forces, and the forces are propor- 
 tional to the length of the sides of the triangle; that is, if the height of the 
 
 
 \ 
 
 
 1 
 
 a> 
 
 t 
 
 
 
 \ 
 \ 
 
 
 B 
 
 
 
 A 
 
 & 
 
 
 FIG. 124. 
 
 FIG. 125. 
 
 FIG. 126. 
 
 triangle A' = the load, then B the compression in the brace, and T = 
 the tension in the tie; or if P the load in pounds, the tension ia T = 
 
 T R 
 
 P X -* and the compression in B = P X -p* Als t it a = the angle 
 
 the inclined member makes with the mast, the other member being 
 
542 
 
 MECHANICS. 
 
 horizontal, and the triangle being right-angled, then the length of the 
 inclined member -= height of the triangle X secant a, and the strain in the 
 inclined member = P secant a. Also, the strain in the horizontal 
 member = P tan. a. 
 
 The solution by the triangle or parallelogram of forces, and the equa- 
 tions Tension in T=P X T/A', and Compression in B = PX B/A', hold true 
 even if the triangle is not right-angled, as in Fig. 126 ; but the trigono- 
 metrical relations ab9ve given do not hold, except in the case of a right- 
 angled triangle. It is evident that as A' decreases, the strain in both T 
 and B increases, tending to become infinite as A' approaches zero. If 
 the tie T is not attached to the mast, but is extended to the ground, as 
 shown in the dotted line, the tension in it remains the same. 
 
 2. A Guyed Crane or Derrick. (Fig. 127 ) The strain in B is, as 
 before, P X B/A', A f being that portion of the vertical included between 
 B and T, wherever T may be attached to A. If, ITowever, the tie T is 
 attached to B beneath its extremity, there may be in addition a bending 
 strain in B due to a tendency to turn about the point of attachment of T 
 as a fulcrum. 
 
 The strain in T may be calculated by the principle of moments. The 
 moment of P is PC, that is, its weight X its perpendicular distance from 
 the point of rotation of B on the mast. The moment of the strain on T 
 is the product of the strain into the perpendicular distance from the line 
 
 FIG. 127. 
 
 of its direction to the same point of rotation of B, or Td. The strain in 
 T therefore = PC * d. As d decreases, the strain on T increases, tending 
 to infinity as d approaches zero. * 
 
 The strain on the guy-rope is also calculated by the method of moments. 
 The moment of the load about the bottom of the mast O is, as before, PC. 
 If the guy is horizontal, the strain in it is F and its moment is Ff, and F = 
 PC -^ /. If it is inclined, the moment is the strain G X the perpendicular 
 distance of the line of its direction from O, or Gg, and G = Pc-j-g. 
 
 The guy-rope having the least strain is the horizontal one F, and the 
 strain in G = the strain in F X the secant of the angle between F and 
 G. As G is made more nearly vertical g decreases, and the strain increases, 
 becoming infinite when g = 0. 
 
 D 3. Shear-poles with Guys. 
 
 (Fig. 128.) First assume that 
 the two masts act as one placed 
 at BD, and the two guys as 
 one at AB. Calculate the strain 
 in BD and AB as in Fig. 126. 
 Multiply half the strain in BD 
 (or AB) by the secant of half 
 
 the angle the two masts (or 
 guys) make with each other to 
 find the strain in each mast (or 
 guy). 
 
 Two Diagonal Braces and 
 a Tie-rod. (Fig. 129.) Sup- 
 pose the braces are used to 
 sustain a single load P. Compressive stress on AD = 1/2 PXAD 
 * AB\ on CA = 1/2 PX CA -T- AB. This is true only if CB and BD 
 
STRESSES IN FRAMED STRUCTURES. 
 
 543 
 
 are of equal length, in which case 1/2 of P is supported by each abutment 
 C and D. If they are unequal in length (Fig. 130), then, by the principle 
 of the lever, find the reactions of the abutments Ri and R 2 . If P is the 
 load applied at the point B on the lever CD, the fulcrum being D, 
 then Ri X CD = P X BD and R X CD = P X BC; Ri = P X BD -f- C'L>; 
 R 2 = PXBC + CD. 
 
 The strain on A(7 = Ri X AC -*- AJS, and on AD = R 2 X AD -*- AB. 
 
 The strain on the tie = RiX CB + AB = RzX BD + AB. 
 
 When CB = BD, Ri = R z , and the strain on the tie is equal to 
 l / 2 CD ~ AB. 
 
 FIG. 131. 
 
 If the braces support a uniform load, as a pair of rafters, the strains 
 caused by such a load are equivalent to that caused by one-half of the 
 load applied at the center. The horizontal thrust of the braces against 
 each other at the apex equals the tensile strain in the tie. 
 
 King-post Truss or Bridge. (Fig. 131. ) If the load is distributed 
 over the whole length of the truss, the effect is the same as if half the 
 load were placed at the center, the other 
 half being carried by the abutments. Let 
 P = one-half- the load on the truss, then 
 tension in the vertical tie AB = P. Com- 
 pression in each of the inclined braces 
 = V2 P X AD * AB. Tension in the tie 
 CD = 1/2 P X BD -T- AB. Horizontal 
 thrust of inclined brace AD at D = the 
 tension in the tie. If W = the total 
 load on one truss uniformly distributed, 
 I = its length and d = its depth, then 
 the tension on the horizontal tie = Wl -* 8 d. 
 
 Inverted King-post Truss. (Fig. 132 ) If P = a load applied at B, 
 or one-half of a uniformly distributed load, then compression on AB = P 
 (the floor-beam CD not being considered 
 to have any resistance to a slight bend- 
 ing). Tension on AC or AD = 1/2 P 
 X AD -* AB. Compression on CD = 
 V2 P X BD + AB. 
 
 Queen-post Truss. (Fig. 133.) If 
 uniformly loaded, and the queen-posts 
 divide the length into three equal bays, 
 the load may be considered to be divided 
 into three equal parts, two parts of 
 which, Pi and Pa, are concentrated at the panel joints and the remainder 
 
 is equally divided between the 
 abutments and supported by them 
 directly. The two parts Pi and Pz 
 only are considered to affect the 
 members of the truss. Strain in 
 the vertical ties BE and CF each 
 equals Pi or Pi. Strain on AB and 
 CD each = Pi X' CD + CF. Strain 
 on the tie AE or EFoT ED = Pi X 
 FD + CF. Thrust on BC = tension 
 FIG. 133. on EFf 
 
 For stability to resist heavy unequal loads the queen-post truss 
 have diagonal braces from B to F ancl from C to E, 
 
 FIG. 132. 
 
544 
 
 MECHANICS. 
 
 Inverted Queen-post Truss. (Fig. 134.) Compression on EB and 
 FC each = Pi or P 2 . Compression on AB or BC or CD = Pi X AB + EB. 
 
 Tension on AE or FD = Pi X AE-*- 
 EB. Tension on EF = compression 
 on BC. For stability to resist 
 unequal loads, ties should be run 
 from C to E and from B to F. 
 
 Burr Truss of Five Panels. 
 (Fig. 135. ) Four-fifths of the load 
 may betaken as concentrated at the 
 points E, K, L and F, the other fifth 
 being supported directly by the two 
 abutments. For the strains in BA 
 and CD the truss may be considered as a queen-post truss, with the loads 
 Pi, P 2 concentrated at E, and the loads P 3 , P 4 concentrated at F. Then 
 compressive strain on AB = (Pi + P 2 ) x AB + BE. The strain on 
 CD is the same if the loads and panel lengths are equal. The tensile 
 
 B 
 
 strain on BE or CF = Pi + P 2 . That portion of the truss between E 
 and F may be considered as a smaller queen-post truss, supporting the 
 loads P 2 , Pa at K and L. The strain on EG or HF = P 2 X EG -f- GK. 
 The diagonals GL and KH receive no strain unless the truss is unequally 
 loaded. The verticals GK and HL each receive a tensile strain equal to 
 P 2 or P 3 . 
 
 For the strain in the horizontal members: BG and CH receive a thrust 
 equal to the horizontal component of the thrust in A B or CD, = (Pi + P 2 ) 
 X tan angle ABE, or (Pi + P 2 ) X AE -r- BE. GH receives this thrust, 
 and also, in addition, a thrust equal to the horizontal component of the 
 thrust in EG or HF, or, in all, (Pi 4- P 2 + P 3 ) X AE -^ BE. 
 
 The tension in AE or FD equals the thrust in BG or HC, and the ten* 
 sion in EK, KL, and LF equals the thrust in GH. 
 
 Pratt or Whipple Truss. (Fig. 136.) In this truss the diagonals are 
 ties, and the verticals are struts or columns. . 
 
 Calculation by the method of distribution of strains: Consider first the 
 load Pi. The truss having six bays or panels, 5/ 6 of the load is trans- 
 mitted to the abutment H, and 1/6 to the abutment O, on the principle 
 of the lever. As the five-sixths must be transmitted through JA and 
 AH, write on these members the figure 5. The one-sixth is transmitted 
 successively through JC, CK, KD, DL, etc., passing alternately through 
 a tie and a strut. Write on these members, up to the strut GO inclusive, 
 the figure 1. Then consider the load P 2 , of which 4/6 goes to AH and 
 2/6 to GO. Write on KB, BJ, JA, and AH the figure 4, and on KD, 
 DL, LE, etc., the figure 2. The load P 3 transmits 3/ 6 in each direction; 
 write 3 on each of the members through which this stress passes, and so 
 on for all the loads, when the figures on the several members will appear 
 as on the cut. Adding them up, we have the following totals: 
 
 TVncinn nn rlinc ^nslc J ^ BH BK CJ CL DK DM EL EN FM FO GN 
 
 L on diagonals { 15 10 1 6 3 3 6 1 10 15 
 ** f/ C f D E 7 M ' ?? 
 
 Each of the figures in the first line is to be multiplied by Ve P X secant 
 of angle HAJ, or V0PX AJ -f- AH, to obtain the tension, and each 
 
 Compression on verticals { 
 
STRESSES IN FRAMED STRUCTURES. 
 
 545 
 
 figure in the lower line is to be multiplied by 1/8 P to obtain the com- 
 pression. The diagonals HB and FO receive no strain. 
 
 It is common to build this truss with a diagonal strut at HB instead 
 of the post HA and the diagonal AJ; in which case 5/ 6 of the load P is 
 carried through JB and the strut BH , which latter then receives a strain 
 = l/6 P X secant of HBJ. 
 
 %H ~]J |K |L \M N 0|| 
 
 66666 
 
 P! P 2 P 3 P 4 P 5 
 
 FIG. 136. 
 
 The strains in the upper and lower horizontal members or chords in- 
 crease from the ends to the center, as shown in the case of the Burr 
 truss. AB receives a thrust equal to the horizontal component of the 
 tension in AJ, or 15/e P X tan AJB. BC receives the same thrust + 
 the horizontal component of the tension in BK, and so on. ^The tension 
 in the lower chord of each panel is the same as the thrust in the upper 
 chord of the same panel. (For calculation of the chord strains by the 
 method of moments, see below.) 
 
 The maximum thrust or tension is at the- center of the chords and is 
 
 equal to . in which W is the total load supported by the truss, L is 
 
 the length, and D the depth. This is the formula for maximum stress in 
 the chords of a truss of any form whatever. 
 
 The above calculation is based on the assumption that all the loads 
 Pi, f*2, etc., are equal. If they are unequal, the value of each has to be 
 taken into account in distributing the strains. Thus the tension in AJ, 
 with unequal loads, instead of being 15 X Ve P secant 9 would be seed 
 X (5/e Pi + 4/6 P 2 + 3/6 P 3 4- 2/6 P 4 + 1/6 PS). Each panel load, Pi, etc., 
 includes its fraction of the weight of the truss. 
 
 General Formula for Strains in Diagonals and Verticals. Let 
 n = total number of panels, x = number of any vertical considered from 
 the nearest end, counting the end as 1, r = rolling load for each panel, 
 P = total load for each panel, 
 
 Strain on verticals = ' ^ + o~n ' * 
 
 For a uniformly distributed load, leave out the last term, 
 
 [r(x - 1)+ (x - 1) 2 J -5- 2n. 
 Strain on principal diagonals (AJ, GN, etc.) = strain on verticals 
 
 X secant 0, that is secant of the angle the diagonal makes with the 
 
 vertical. 
 
 Strain on the counterbraces (BH, CJ, FO, etc.): The strain on the 
 
 counterbrace in the first panel is 0, if the load is uniform. On the 2d, 
 
 1 1-4-2 i i o i o 
 
 3d, 4th, etc., it is P secant X -^ -~ n > etc., P being the total 
 
 load in one panel. 
 
 Strain in the Chords Method of Moments. Let the truss be 
 uniformly loaded, the total load acting on it = W. Weight supported at 
 each end, or reaction of the abutment = W/2. Length of the truss = L. 
 Weight on a unit of length = W/L. Horizontal distance from the nearest ' 
 abutment to the point (say M in Fig. 136) in the chord where the strain 
 is to be determined = x. Horizontal strain at that point (tension on the 
 lower chord, compression in the upper) = //. Depth of the truss = D. 
 
546 
 
 MECHANICS. 
 
 By the method of moments we take the difference of the moments, about 
 the paint M, of the reaction of the abutment and of the load between 
 M and the abutments, and equate that difference with the moment of 
 the resistance, or of the strain in the horizontal chord, considered with 
 reference to a point in the opposite chord, about which the truss would 
 turn if the first chord were severed at M . 
 
 The moment of the reaction of the abutment is W x/2. The moment of 
 the load from the abutment to M is (W/Lx) X the distance of, its center of 
 gravity from M, which is x/2, or moment = Wx* + 2 L. Moment of the 
 Wx Wx? W t T-\ 
 
 stress in the chord = HD = - whence H = (x- '\ 
 
 If x = or L, H = 0. 
 
 - 
 
 W I 
 If x = L/2, H = -:- 
 
 which is the horizontal 
 
 strain at the middle of the chords, as before given. 
 
 FIG. 137. 
 
 The Howe Truss. (Fig. 137.) In the Howe truss the diagonals are 
 struts, and the verticals are ties. The calculation of strains may be made 
 in the same method as described above for the Pratt truss. 
 
 The Warren Girder. (Fig. 138. ) In the Warren girder, or triangu- 
 lar truss, there are no vertical struts, and the diagonals may transmit either 
 tension or compression. The strains in the diagonals may be calculated by 
 the method of distribution of strains as in the case of the rectangular truss. 
 
 FIG. 138. 
 
 . On the principle of the lever, the load Pi being Vio of the length of the 
 span from the line of the nearest support a, transmits 9/io of its weight to 
 a and l/io to g. Write 9 on the right hand of the strut la, to represent the 
 compression, and 1 on the right hand of Ib, 2c, 3d, etc., to represent com- 
 pression, and on the left hand of 62, c3, etc., to represent tension. The 
 load Pz transmits 7/i of its weight to a and 3/ 10 to g. Write 7 on each 
 member from 2 to a, and 3 on each member/ rom 2 to g, placing the figures 
 representing compression on the right hand of the member, and those 
 representing tension on the left. Proceed in the same manner with all 
 the loads, then sum up the figures on each side of each diagonal, and 
 write the difference of each sum beneath, and on the side of the greater 
 Bum, to show whether the difference represents tension or compression. 
 The results are as follows: Compression, la, 25; 26, 15; 3c. 5; 3d, 5; 4e, 15; 
 &g, 25. Tension, U>, 15; 2c, 5; 4d, 5; 5e, 15. Each of these figures is to 
 
STRESSES IN FKAME0 STKUCTUKES. 
 
 547 
 
 6e multiplied by Vio of one of the loads as Pi, and by the secant of the 
 angle the diagonals make with a vertical line. 
 
 The strains in the horizontal chords may be determined by the method 
 of moments as in the case of rectangular trusses. 
 
 Roof-truss. Solution by Method of Moments. The calculation of 
 strains in structures by the method of statical moments consists in taking 
 a cross-section of the structure at a point where there are not more than 
 three members (struts, braces, or chords). 
 
 To find the strain in either one of these members take the moment about 
 the intersection of the other two as an axis of rotation. The sum of the 
 moments of these members must be if the structure is in equilibrium. 
 But the moments of the two members that pass through the point of ref- 
 erence or axis are both 0, hence one equation containing one unknown 
 quantity can be found for each cross-section. 
 
 FIG. 139. 
 
 In the truss shown in Fig. 139 take a cross-section at ts, and determine 
 the strain in the three members cut by it, viz., CE, ED, and DF. Let 
 X = force exerted in direction CE, Y = force exerted in direction DE, 
 Z = force exerted in direction FD. 
 
 For X take its moment about the intersection of Y and Z at D = Xx. 
 For Y take its moment about the intersection of X and Z at A = Yy. 
 For Z take its moment about the intersection of X and Y at E = Zz. 
 Let z = 15, x = 18.6, y = 38.4, AD = 50, CD = 20 ft. Let PI, P 2 , 
 PS, P4 be equal loads, as shown, and 3 1/2 P the reaction of the abutment A. 
 
 The sum of all the moments taken about D or A or E will be when the 
 structure is at rest. Then - Xx + 3.5 PX 50 - P 3 X 12.5 - P 2 X 25 
 
 - Pi X 37.5 = 0. 
 
 The + signs are for moments in the direction of the hands of a watch or 
 " clockwise " and signs for the reverse direction or anti-clockwise. Since 
 P = Pi = P 2 = P 3 , - 18.6 X + 175 P - 75 P = 0; - 18.6 X = - 100 P; 
 X = 100 P-5- 18.6 = 5.376 P. 
 
 - Yy + P 3 X 37.5 + P 2 X 25 -i- P x X 12.5 = 0; 38.4 Y = 75 ; Y = 
 
 75 P +- 38.4 = 1.953 P. 
 
 - Zz + 3.5 P X 37.5 - Pi X 25 - P 2 X 12.5 - P 3 X = 0; 15 3 = 
 
 93.75P;Z = 6.25 P. 
 
 In the same manner the forces exerted in the other members have been 
 found as follows: EG = 6.73 P;GJ = 8.07 P;JA = 9A2P;JH = 1.35 P; 
 GF = 1.59 P; AH = 8.75 P; IIP = 7.50 P. 
 
 The Fink Roof-truss. (Fig. 140.) An analysis by Prof. P. H. 
 Philbrick (Van N. Mag., Aug., 1880) gives the following results: 
 W= total load on roof; 
 N= No. of panels on both rafters; 
 W/N= P = load at each joint b, d, /, etc.; 
 
 V= reaction at A = l/ 2 W = 1/2 NP = 4P: 
 AD= S-, AC = L\ CD = D; 
 ti,h,ta= tension on De, eg, gA, respectively; 
 ci t ca, c, Ci= compression oa C6, bd t df, and/A. 
 
548 
 
 MECHANICS. 
 
 Strains in 
 
 1, orDe - 
 
 2, "eg - fe - 3 PS * Z); 
 
 3, M 0A = k=7/2 PS 
 
 7,or 6C==Ci=7/ 2 
 8, " 6cor/0= PS 
 9," 
 
 L; 
 
 4, " Af = c 4 =7/2 PL -s- D; 10, " cd or dg= V 2 PS -*- Z); 
 
 5, " fd = c 8 =7/ 2 PL/D-PD/L; 11," ec = PS -5- D; 
 " " 
 
 6, " db - c 2 = 
 
 12," cG 
 
 A g e D B 
 
 FIG. 140. 
 
 EXAMPLE. Given a Fink roof-truss of span 64 ft., depth 16 ft., with 
 four panels on each side, as in hecut; total load 32 tons, or 4 tons 
 each at the points /, d, b, C, etc. (and 2 tons each at A and B, which trans- 
 mit no strain to the truss members). Here W = 32tons, P = 4 tons, 
 S=32 ft., D = 16 ft., L = V^2 + >2 = 2.236 X D. L + D = 2.236, 
 D -* L = 0.4472, -f-D = 2, S -s- L = -0.8944. The strains on the 
 numbered members then are as follows: 
 
 1, 2X4X2 -16 tons; 
 
 2, 3X4X2 =24 
 
 3, 7/2X4X2 =28 " 
 
 4, 7/2X4X2.236-31.3 " 
 
 5, 31.3-4X0.447 = 29.52 " 
 
 6, 31.3-8X0.447 = 27.72 " 
 
 7,31.3-12X0.447 -25.94 tons. 
 
 8, 4X0.8944= 3.58 " 
 
 9, 8X0.8944= 7.16 " 
 
 10, 2X2 =4 
 
 11, 4X2 =8 " 
 
 12, 6X2 =12 
 
 The Economical Angle. A structure of tri- 
 angular form, Fig. 141, is supported at a and b. It 
 sustains any load L, the elements cc being in com- 
 pression and t in tension. Required the angle so 
 that the total weight of the structure shall be a 
 minimum. F. R. Honey (Sci. Am. Supp., Jan. 17, 
 1891) gives a solution of this problem, with the 
 
 result tan = 
 
 C+ T 
 
 in which C and T represent 
 
 ,-, 
 
 the crushing and the tensile strength respectively of 
 
 the, material employed. It is applicable to any 
 
 material. For C = T, = ^43/^. For C = 0.4 T (yellow pine), 
 
 493/4. For C 0.8 T (soft steel), = 53V*. For C = 6 T (cast iron), 
 
 *= 691/4. 
 
PYROMETRY. 549 
 
 HEAT. 
 
 THERMOMETERS. 
 
 The Fahrenheit thermometer is generally used in English-speaking 
 countries, and the Centigrade, or Celsius, thermometer in countries that 
 use the metric system. In many scientific treatises in English, however, 
 the Centigrade temperatures are also used, either with or without their 
 Fahrenheit equivalents. The Reaumur thermometer is used to some 
 extent on the Continent of Europe and in breweries in this country 
 
 In the Fahrenheit thermometer the freezing-point of water is taken at 
 32, and the boiling-point of water at mean atmospheric pressure at the 
 sea-level, 14.7 Ibs. per sq. in., is taken at 212, the distance between these 
 two points being divided into 180. In the Centigrade and Re"aumur 
 thermometers the freezing-point is taken at 0. The boiling-point is 
 100 in the Centigrade scale, and 80 in the Reaumur. 
 
 1 Fahrenheit degree = 5/ 9 deg. Centigrade = 4/gdeg. Reaumur. 
 
 1 Centigrade degree = 9/5 deg. Fahrenheit = 4/5 deg. Reaumur. 
 
 1 Reaumur degree = 9/ 4 deg. Fahrenheit =5/4 deg. Centigrade. 
 
 Temperature Fahrenheit = 9/ 5 x temp. C. + 32 = 9/ 4 R. + 32. 
 Temperature Centigrade = 5/ 9 (temp. F. - 32) =5/ 4 R. 
 Temperature Reaumur = 4/ 5 temp. C. =4/9 (F. 32). 
 
 HANDY RULE FOR CONVERTING CENTIGRADE TEMPERATURE TO FAH- 
 RENHEIT. Multiply by 2, subtract a tenth, add 32. 
 
 EXAMPLE. 100 C. X 2 = 200, - 20 = 180, + 32= 212 F. 
 
 Mercurial Thermometer. (Rankine, S. E., p. 234.) The rate of 
 expansion of mercury with rise of temperature increases as the temperature 
 becomes higher; from which it follows, that if a thermometer showing the 
 dilatation of mereury simply were made to agree with an air thermometer 
 at 32 and 212, the mercurial thermometer would show lower temperatures 
 than the air thermometer between those standard points, and higher tem- 
 peratures beyond them. 
 
 For example, according to Regnault, when the air thermometer marked 
 350 C. ( = 662 F.), the mercurial thermometer would mark 362.16 C. 
 (= 683.89 F.), the error of the latter being in excess 12.16 C. ( = 21.89 
 F.). 
 
 Actual mercurial thermometers indicate intervals of temperature pro- 
 portional to the difference between the expansion of mercury and that of 
 glass. 
 
 The inequalities in the rate of expansion of the glass (which are very 
 different for different kinds of glass) correct, to a greater or less extent, the 
 errors arising from the inequalities in the rate of expansion of the mercury. 
 
 For practical purposes connected with heat engines, the mercurial ther- 
 mometer made of common glass may be considered as sensibly coinciding 
 with the air-thermometer at all temperatures not exceeding 500 F. 
 
 If the mercury is not throughout its whole length at the same tempera- 
 ture as that being measured, a correction, k, must be added to the tem- 
 perature t in Fahrenheit degrees; k = 95 D (t-f) -f- 1,000,000, where D is 
 the length of the mercury column exposed, measured in Fahrenheit 
 degrees, and t is the temperature of the exposed part of the thermometer. 
 When long thermometers are used in shallow wells in high-pressure steam 
 pipes this correction is often 5 to 10 F. (Moyer on Steam Turbines.) 
 
 PYROMETRY. 
 
 Principles Used in Various Pyrometers. 
 
 Pyrometers may be classified according to the principles upon which 
 they operate, as follows: 
 
 1. Expansion of mercury in a glass tube. When the space above the 
 mercury is filled with compressed nitrogen, and a specially hard glass is 
 used for the tube, mercury thermometers may be made to indicate tem- 
 peratures as high as 1000 F. 
 
TEMPERATURES, CENTIGRADE AND FAHRENHEIT. 
 
 c. 
 
 F 
 
 C 
 
 F. 
 
 C 
 
 F. 
 
 r, 
 
 F. 
 
 C 
 
 F 
 
 
 
 F 
 
 C, 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -40 
 
 -40. 
 
 26 
 
 78.8 
 
 92 
 
 197.6 
 
 158 
 
 316.4 
 
 224 
 
 435.2 
 
 290 
 
 554 
 
 950 
 
 1742 
 
 -39 
 
 -38.2 
 
 27 
 
 80.6 
 
 93 
 
 199.4 
 
 159 
 
 318.2 
 
 225 
 
 437. 
 
 300 
 
 572 
 
 960 
 
 1760 
 
 -38 
 
 -36.4 
 
 28 
 
 82.4 
 
 94 
 
 201.2 
 
 160 
 
 320. 
 
 226 
 
 438.8 
 
 310 
 
 590 
 
 970 
 
 1778 
 
 -37 
 
 -34.6 
 
 29 
 
 84.2 
 
 95 
 
 203. 
 
 161 
 
 321.8 
 
 227 
 
 440.6 
 
 320 
 
 608 
 
 980 
 
 1796 
 
 -36 
 
 -32.8 
 
 30 
 
 86. 
 
 96 
 
 204.8 
 
 162 
 
 323.6 
 
 228 
 
 442.4 
 
 330 
 
 626 
 
 990 
 
 1814 
 
 -35 
 
 -31. 
 
 31 
 
 87.8 
 
 97 
 
 206.6 
 
 163 
 
 325.4 
 
 229 
 
 444.2 
 
 340 
 
 644 
 
 1000 
 
 1832 
 
 -34 
 
 -29.2 
 
 32 
 
 89.6 
 
 98 
 
 208.4 
 
 164 
 
 327.2 
 
 230 
 
 446. 
 
 350 
 
 662 
 
 1010 
 
 1850 
 
 -33 
 
 -27.4 
 
 33 
 
 91.4 
 
 99 
 
 210.2 
 
 165 
 
 329. 
 
 231 
 
 447.8 
 
 360 
 
 680 
 
 1020 
 
 1868 
 
 -32 
 
 -25.6 
 
 34 
 
 93.2 
 
 100 
 
 212. 
 
 166 
 
 330.8 
 
 232 
 
 449.6 
 
 370 
 
 698 
 
 1030 
 
 1886 
 
 -31 
 
 -23.8 
 
 35 
 
 95. 
 
 101 
 
 213.8 
 
 167 
 
 332.6 
 
 233 
 
 451.4 
 
 380 
 
 716 
 
 1040 
 
 1904 
 
 -30 
 
 -22. 
 
 36 
 
 96.8 
 
 102 
 
 215.6 
 
 168 
 
 334.4 
 
 234 
 
 453.2 
 
 390 
 
 734 
 
 1050 
 
 1922 
 
 -29 
 
 -20.2 
 
 37 
 
 98.6 
 
 103 
 
 217.4 
 
 169 
 
 336.2 
 
 235 
 
 455. 
 
 400 
 
 752 
 
 1060 
 
 1940 
 
 -28 
 
 -18.4 
 
 38 
 
 100.4 
 
 104 
 
 219.2 
 
 170 
 
 338. 
 
 236 
 
 456.8 
 
 410 
 
 770 
 
 1070 
 
 1958 
 
 -27 
 
 - 16.6 
 
 39 
 
 102.2 
 
 105 
 
 221. 
 
 171 
 
 339.8 
 
 237 
 
 458.6 
 
 420 
 
 788 
 
 1080 
 
 1976 
 
 -26 
 
 -14.8 
 
 40 
 
 104. 
 
 106 
 
 222.8 
 
 172 
 
 341.6 
 
 238 
 
 460.4 
 
 430 
 
 806 
 
 1090 
 
 1994 
 
 -25 
 
 -13. 
 
 41 
 
 105.8 
 
 107 
 
 224.6 
 
 173 
 
 343.4 
 
 239 
 
 462.2 
 
 440 
 
 824 
 
 1100 
 
 2012 
 
 -24 
 
 -11.2 
 
 42 
 
 107.6 
 
 108 
 
 226.4 
 
 174 
 
 345.2 
 
 240 
 
 464. 
 
 450 
 
 842 
 
 1110 
 
 2030 
 
 -23 
 
 - 9.4 
 
 43 
 
 109.4 
 
 109 
 
 228.2 
 
 175 
 
 347. 
 
 241 
 
 465.8 
 
 460 
 
 860 
 
 1120 
 
 2048 
 
 -22 
 
 - 7.6 
 
 44 
 
 111.2 
 
 110 
 
 230. 
 
 176 
 
 348.8 
 
 242 
 
 467.6 
 
 470 
 
 878 
 
 1130 
 
 2066 
 
 -21 
 
 - 5.8 
 
 45 
 
 113. 
 
 1 1 1 
 
 231.8 
 
 177 
 
 350.6 
 
 243 
 
 469.4 
 
 480 
 
 896 
 
 1140 
 
 2084 
 
 -20 
 
 - 4. 
 
 46 
 
 114.8 
 
 112 
 
 233.6 
 
 178 
 
 352.4 
 
 244 
 
 471.2 
 
 490 
 
 914 
 
 1150 
 
 2102 
 
 -19 
 
 - 2.2 
 
 47 
 
 116.6 
 
 113 
 
 235.4 
 
 179 
 
 354.2 
 
 245 
 
 473. 
 
 500 
 
 932 
 
 1160 
 
 2120 
 
 -18 
 
 - 0.4 
 
 48 
 
 118.4 
 
 114 
 
 237.2 
 
 180 
 
 356. 
 
 246 
 
 474.8 
 
 510 
 
 950 
 
 1170 
 
 2138 
 
 -17 
 
 + 1.4 
 
 49 
 
 120.2 
 
 115 
 
 239. 
 
 181 
 
 357.8 
 
 247 
 
 476.6 
 
 520 
 
 968 
 
 1180 
 
 2156 
 
 -16 
 
 3.2 
 
 50 
 
 122. 
 
 116 
 
 2408 
 
 182 
 
 359.6 
 
 243 
 
 478.4 
 
 530 
 
 986 
 
 1190 
 
 2174 
 
 -15 
 
 5. 
 
 51 
 
 123.8 
 
 117 
 
 242.6 
 
 183 
 
 361.4 
 
 249 
 
 480.2 
 
 540 
 
 1004 
 
 1200 
 
 2192 
 
 -14 
 
 6.8 
 
 52 
 
 125.6 
 
 118 
 
 244.4 
 
 184 
 
 363.2 
 
 250 
 
 482. 
 
 550 
 
 1022 
 
 1210 
 
 2210 
 
 -13 
 
 8.6 
 
 53 
 
 127.4 
 
 119 
 
 246.2 
 
 185 
 
 365. 
 
 251 
 
 483.8 
 
 560 
 
 1040 
 
 1220 
 
 2228 
 
 -12 
 
 10.4 
 
 54 
 
 129.2 
 
 120 
 
 248. 
 
 186 
 
 366.8 
 
 252 
 
 485.6 
 
 570 
 
 1058 
 
 1230 
 
 2246 
 
 -11 
 
 12.2 
 
 55 
 
 131. 
 
 121 
 
 249.8 
 
 187 
 
 368.6 
 
 253 
 
 487.4 
 
 530 
 
 1076 
 
 1240 
 
 2264 
 
 -10 
 
 14. 
 
 56 
 
 132.8 
 
 122 
 
 251.6 
 
 188 
 
 370.4 
 
 254 
 
 489.2 
 
 590 
 
 1094 
 
 1250 
 
 2282 
 
 - 9 
 
 15.8 
 
 57 
 
 134.6 
 
 123 
 
 253.4 
 
 .189 
 
 372.2 
 
 255 
 
 491. 
 
 e0o 
 
 1112 
 
 1260 
 
 2300 
 
 - 8 
 
 17.6 
 
 58 
 
 136.4 
 
 124 
 
 255.2 
 
 190 
 
 374. 
 
 256 
 
 492.8 
 
 610 
 
 1130 
 
 1270 
 
 2318 
 
 7 
 
 19.4 
 
 59 
 
 138.2 
 
 125 
 
 257. 
 
 191 
 
 375.8 
 
 257 
 
 494.6 
 
 620 
 
 1148 
 
 1280 
 
 2336 
 
 - 6 
 
 21.2 
 
 60 
 
 140. 
 
 126 
 
 258.8 
 
 192 
 
 377.6 
 
 258 
 
 496.4 
 
 630 
 
 1166 
 
 1290 
 
 2354 
 
 - 5 
 
 23. 
 
 61 
 
 141.8 
 
 127 
 
 260.6 
 
 193 
 
 379.4 
 
 259 
 
 498.2 
 
 640 
 
 1184 
 
 1300 
 
 2372 
 
 - 4 
 
 24.8 
 
 62 
 
 143.6 
 
 128 
 
 262.4 
 
 194 
 
 381.2 
 
 260 
 
 500. 
 
 650 
 
 1202 
 
 1310 
 
 2390 
 
 - 3 
 
 26.6 
 
 63 
 
 145.4 
 
 129 
 
 264.2 
 
 195 
 
 383. 
 
 261 
 
 501.8 
 
 660 
 
 1220 
 
 1320 
 
 2408 
 
 - 2 
 
 28.4 
 
 64 
 
 147.2 
 
 130 
 
 266. 
 
 196 
 
 384.8 
 
 262 
 
 503.6 
 
 670 
 
 1238 
 
 1330 
 
 2426 
 
 - 1 
 
 30.2 
 
 65 
 
 149. 
 
 131 
 
 267. 
 
 197 
 
 386.6 
 
 263 
 
 505.4 
 
 680 
 
 1256 
 
 1340 
 
 2444 
 
 
 
 32. 
 
 66 
 
 150.8 
 
 132 
 
 269.6 
 
 198 
 
 388.4 
 
 264 
 
 507.2 
 
 690 
 
 1274 
 
 1350 
 
 2462 
 
 + 1 
 
 33.8 
 
 67 
 
 152.6 
 
 133 
 
 271.4 
 
 199 
 
 390.2 
 
 265 
 
 509. 
 
 700 
 
 1292 
 
 1360 
 
 2480 
 
 2 
 
 35.6 
 
 68 
 
 154.4 
 
 134 
 
 273.2 
 
 200 
 
 392. 
 
 266 
 
 510.8 
 
 710 
 
 1310 
 
 1370 
 
 2498 
 
 3 
 
 37.4 
 
 69 
 
 156.2 
 
 135 
 
 275. 
 
 201 
 
 393.8 
 
 267 
 
 512.6 
 
 720 
 
 1328 
 
 1380 
 
 2516 
 
 4 
 
 39.2 
 
 70 
 
 153. 
 
 136 
 
 276.8 
 
 202 
 
 395.6 
 
 268 
 
 514.4 
 
 730 
 
 1346 
 
 1390 
 
 2534 
 
 5 
 
 41. 
 
 71 
 
 159.8 
 
 137 
 
 278.6 
 
 203 
 
 397.4 
 
 269 
 
 516.2 
 
 740 
 
 1364 
 
 1400 
 
 2552 
 
 6 
 
 42.8 
 
 72 
 
 161.6 
 
 138 
 
 280.4 
 
 204 
 
 399.2 
 
 270 
 
 518. 
 
 750 
 
 1382 
 
 1410 
 
 2570 
 
 7 
 
 44.6 
 
 73 
 
 163.4 
 
 139 
 
 282.2 
 
 205 
 
 401. 
 
 271 
 
 519.8 
 
 760 
 
 1400 
 
 1420 
 
 2588 
 
 8 
 
 46.4 
 
 74 
 
 165.2 
 
 140 
 
 284. 
 
 206 
 
 402.8 
 
 272 
 
 521.6 
 
 770 
 
 1418 
 
 1430 
 
 2606 
 
 9 
 
 48.2 
 
 75 
 
 167. 
 
 141 
 
 285.8 
 
 207 
 
 404.6 
 
 273 
 
 523.4 
 
 780 
 
 1436 
 
 1440 
 
 2624 
 
 10 
 
 50. 
 
 76 
 
 168.8 
 
 142 
 
 287.6 
 
 208 
 
 406.4 
 
 274 
 
 525.2 
 
 790 
 
 1454 
 
 I4M) 
 
 2642 
 
 11 
 
 51.8 
 
 77 
 
 170.6 
 
 143 
 
 289.4 
 
 209 
 
 408.2 
 
 275 
 
 527. 
 
 800 
 
 1472 
 
 1460 
 
 2660 
 
 12 
 
 53.6 
 
 78 
 
 172.4 
 
 144 
 
 291.2 
 
 210 
 
 410. 
 
 276 
 
 528.8 
 
 310 
 
 1490 
 
 1470 
 
 2678 
 
 13 
 
 55.4 
 
 79 
 
 174.2 
 
 145 
 
 293. 
 
 211 
 
 411.8 
 
 277 
 
 530.6 
 
 320 
 
 1508 
 
 1480 
 
 2696 
 
 14 
 
 57.2 
 
 80 
 
 176. 
 
 146 
 
 294.8 
 
 212 
 
 413.6 
 
 278 
 
 532.4 
 
 330 
 
 1526 
 
 1490 
 
 2714 
 
 15 
 
 59. 
 
 81 
 
 177.8 
 
 147 
 
 296.6 
 
 213 
 
 415.4 
 
 279 
 
 534.2 
 
 840 1544 
 
 1500 
 
 2732 
 
 16 
 
 60.8 
 
 82 
 
 179.6 
 
 148 
 
 298.4 
 
 214 
 
 417.2 
 
 280 
 
 536. 
 
 85011562 
 
 510 
 
 2750 
 
 17 
 
 62.6 
 
 83 
 
 181.4 
 
 149 
 
 300.2 
 
 215 
 
 419. 
 
 281 
 
 537.8 
 
 360 
 
 1580 
 
 1520 
 
 2768 
 
 18 
 
 64.4 
 
 "84 
 
 183.2 
 
 150 
 
 302. 
 
 216 
 
 420,8 
 
 282 
 
 539.6 
 
 870 
 
 1598 
 
 530 
 
 2786 
 
 19 
 
 66.2 
 
 85 
 
 185. 
 
 151 
 
 303.8 
 
 217 
 
 422.6 
 
 283 
 
 541.4 
 
 330 
 
 1616 
 
 540 
 
 2804 
 
 20 
 
 68. 
 
 86 
 
 186.8 
 
 152 
 
 305.6 
 
 218 
 
 424.4 
 
 284 
 
 543.2 
 
 390 
 
 1634 
 
 550 
 
 2822 
 
 21 
 
 69.8 
 
 87 
 
 188.6 
 
 153 
 
 307.4 
 
 219 
 
 426.2 
 
 285 
 
 545. 
 
 900 
 
 1652 
 
 600 
 
 2912 
 
 22 
 
 71.6 
 
 88 
 
 190.4 
 
 154 
 
 309.2 
 
 220 
 
 428. 
 
 286 
 
 546.8 
 
 910 
 
 1670 
 
 650 
 
 3002 
 
 23 
 
 73.4 
 
 89 
 
 192.2 
 
 155 
 
 311. 
 
 221 
 
 429.8 
 
 287 
 
 548.6 
 
 920 
 
 1688 
 
 700 3092 
 
 24 
 
 75.2 
 
 90 
 
 194. 
 
 156 
 
 312.8 
 
 222 
 
 431.6 
 
 288 
 
 550.4 
 
 930 
 
 1706 
 
 750 3182 
 
 25 
 
 77. 
 
 91 
 
 195.8 
 
 157 
 
 314.6 
 
 223 
 
 433.4 
 
 289 
 
 552.2 
 
 940 
 
 1724 
 
 800 3272 
 
 550 
 
TEMPERATURES, FAHRENHEIT AND CENTIGRADE. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 -40 
 
 -40 
 
 26 
 
 -3.3 
 
 92 
 
 33.3 
 
 158 
 
 70. 
 
 224 
 
 106. 
 
 290 
 
 143. 
 
 360 
 
 182.2 
 
 -39 
 
 -39.4 
 
 27 
 
 -2.8 
 
 93 
 
 33.9 
 
 159 
 
 70.6 
 
 225 
 
 107.2 
 
 29 
 
 143. 
 
 370 
 
 187.8 
 
 -38 
 
 -389 
 
 28 
 
 2 2 
 
 94 
 
 34.4 
 
 160 
 
 71.1 
 
 226 
 
 107.8 
 
 292 
 
 144. 
 
 380 
 
 193.3 
 
 -37 
 
 -383 
 
 29 
 
 -17 
 
 95 
 
 35. 
 
 16 
 
 71.7 
 
 227 
 
 108.3 
 
 293 
 
 145. 
 
 390 
 
 198.9 
 
 -36 
 
 -378 
 
 30 
 
 -1.1 
 
 96 
 
 35.6 
 
 162 
 
 72.2 
 
 228 
 
 108.9 
 
 294 
 
 145.6 
 
 400 
 
 204.4 
 
 -35 
 
 -372 
 
 31 
 
 -0.6 
 
 97 
 
 36.1 
 
 163 
 
 72.8 
 
 229 
 
 109.4 
 
 295 
 
 146. 
 
 410 
 
 210. 
 
 -34 
 
 -36.7 
 
 32 
 
 0. 
 
 98 
 
 36.7 
 
 164 
 
 73.3 
 
 230 
 
 110. 
 
 296 
 
 146.7 
 
 420 
 
 215.6 
 
 -33 
 
 -36.1 
 
 33 
 
 + 0.6 
 
 99 
 
 37.2 
 
 165 
 
 73.9 
 
 231 
 
 110.6 
 
 297 
 
 147.2 
 
 430 
 
 221.1 
 
 -32 
 
 -35.6 
 
 34 
 
 1.1 
 
 100 
 
 37.8 
 
 166 
 
 74.4 
 
 232 
 
 111. 
 
 298 
 
 147.8 
 
 440 
 
 226.7 
 
 -31 
 
 -35. 
 
 35 
 
 1 7 
 
 101 
 
 38.3 
 
 167 
 
 75. 
 
 233 
 
 1117 
 
 299 
 
 148.3 
 
 450 
 
 232.2 
 
 -30 
 
 -34.4 
 
 36 
 
 2^2 
 
 102 
 
 38.9 
 
 168 
 
 75.6 
 
 234 
 
 112.2 
 
 300 
 
 148.9 
 
 460 
 
 237.8 
 
 -29 
 
 -33.9 
 
 37 
 
 2.8 
 
 103 
 
 39.4 
 
 169 
 
 76.1 
 
 235 
 
 112.8 
 
 301 
 
 149.4 
 
 470 
 
 243.3 
 
 -28 
 
 -33.3 
 
 38 
 
 3.3 
 
 104 
 
 40. 
 
 170 
 
 76.7 
 
 236 
 
 113.3 
 
 302 
 
 150. 
 
 480 
 
 248.9 
 
 -27 
 
 -32.8 
 
 39 
 
 3.9 
 
 105 
 
 40.6 
 
 171 
 
 77.2 
 
 237 
 
 113.9 
 
 303 
 
 150.6 
 
 490 
 
 254.4 
 
 -26 
 
 -322 
 
 40 
 
 4.4 
 
 106 
 
 41.1 
 
 172 
 
 77.8 
 
 238 
 
 114.4 
 
 304 
 
 151.1 
 
 500 
 
 260. 
 
 -25 
 
 -31 7 
 
 41 
 
 5. 
 
 107 
 
 41.7 
 
 173 
 
 78.3 
 
 239 
 
 115. 
 
 305 
 
 151.7 
 
 510 
 
 265.6 
 
 -24 
 
 -31.1 
 
 42 
 
 5.6 
 
 108 
 
 42.2 
 
 174 
 
 78.9 
 
 240 
 
 115.6 
 
 306 
 
 152.2 
 
 520 
 
 271.1 
 
 -23 
 
 -30.6 
 
 43 
 
 6.1 
 
 109 
 
 42.8 
 
 175 
 
 79.4 
 
 241 
 
 116.1 
 
 307 
 
 152.8 
 
 530 
 
 276.7 
 
 -22 
 
 -30. 
 
 44 
 
 6.7 
 
 110 
 
 43.3 
 
 176 
 
 80. 
 
 242 
 
 116.7 
 
 308 
 
 153.3 
 
 540 
 
 282.2 
 
 -21 
 
 -29.4 
 
 45 
 
 7.2 
 
 1 1 1 
 
 43.9 
 
 177 
 
 80.6 
 
 243 
 
 117.2 
 
 309 
 
 153.9 
 
 550 
 
 287.8 
 
 -20 
 
 -28.9 
 
 46 
 
 7.8 
 
 112 
 
 44.4 
 
 178 
 
 81.1 
 
 244 
 
 117.8 
 
 310 
 
 154.4 
 
 560 
 
 293.3 
 
 -19 
 
 -28.3 
 
 47 
 
 8.3 
 
 113 
 
 45. 
 
 179 
 
 81.7 
 
 245 
 
 118.3 
 
 311 
 
 155. 
 
 570 
 
 298.9 
 
 -18 
 
 -27.8 
 
 48 
 
 8.9 
 
 114 
 
 45.6 
 
 180 
 
 82.2 
 
 246 
 
 118.9 
 
 312 
 
 155.6 
 
 580 
 
 304.4 
 
 -17 
 
 -27.2 
 
 49 
 
 9.4 
 
 115 
 
 46.1 
 
 181 
 
 82.8 
 
 247 
 
 119.4 
 
 313 
 
 156.1 
 
 590 
 
 310. 
 
 -16 
 
 -26.7 
 
 50 
 
 10. 
 
 116 
 
 46.7 
 
 182 
 
 83.3 
 
 248 
 
 120. 
 
 314 
 
 156.7 
 
 600 
 
 315.6 
 
 -15 
 
 -26.1 
 
 51 
 
 10.6 
 
 117 
 
 47.2 
 
 183 
 
 83.9 
 
 249 
 
 120.6 
 
 315 
 
 157.2 
 
 610 
 
 321.1 
 
 -14 
 
 -25.6 
 
 52 
 
 11.1 
 
 118 
 
 47.8 
 
 184 
 
 84.4 
 
 250 
 
 121.1 
 
 316 
 
 157.8 
 
 620 
 
 326.7 
 
 -13 
 
 -25. 
 
 53 
 
 11.7 
 
 119 
 
 48.3 
 
 185 
 
 85. 
 
 251 
 
 121.7 
 
 317 
 
 158.3 
 
 630 
 
 332.2 
 
 -12 
 
 -24.4 
 
 54 
 
 12.2 
 
 120 
 
 48.9 
 
 186 
 
 85.6 
 
 252 
 
 122.2 
 
 318 
 
 158.9 
 
 640 
 
 337.8 
 
 -11 
 
 -23.9 
 
 55 
 
 12.8 
 
 121 
 
 49.4 
 
 187 
 
 86.1 
 
 253 
 
 122.8 
 
 319 
 
 59.4 
 
 650 
 
 343.3 
 
 -10 
 
 -23.3 
 
 56 
 
 13.3 
 
 122 
 
 50. 
 
 188 
 
 86.7 
 
 254 
 
 123.3 
 
 320 
 
 60. 
 
 660 
 
 348.9 
 
 - 9 
 
 -22.8 
 
 57 
 
 13.9 
 
 123 
 
 50.6 
 
 189 
 
 87.2 
 
 255 
 
 123.9 
 
 321 
 
 60.6 
 
 670 
 
 354.4 
 
 - 8 
 
 -22.2 
 
 58 
 
 14.4 
 
 124 
 
 51.1 
 
 190 
 
 87.8 
 
 256 
 
 124.4 
 
 322 
 
 61.1 
 
 680 
 
 360. 
 
 - 7 
 
 -21.7 
 
 59 
 
 15. 
 
 125 
 
 51.7 
 
 191 
 
 88.3 
 
 257 
 
 125. 
 
 323 
 
 61.7 
 
 690 
 
 365.6 
 
 - 6 
 
 -21.1 
 
 60 
 
 15.6 
 
 126 
 
 52.2 
 
 192 
 
 88.9 
 
 258 
 
 125.6 
 
 324 
 
 62.2 
 
 700 
 
 371.1 
 
 - 5 
 
 -20.6 
 
 61 
 
 16.1 
 
 127 
 
 52.8 
 
 193 
 
 89.4 
 
 259 
 
 126.1 
 
 325 
 
 62.8 
 
 710 
 
 376.7 
 
 - 4 
 
 -20. 
 
 62 
 
 16.7 
 
 128 
 
 53.3 
 
 194 
 
 90. 
 
 260 
 
 126.7 
 
 326 
 
 63.3 
 
 720 
 
 382.2 
 
 - 3 
 
 -19.4 
 
 63 
 
 17.2 
 
 129 
 
 J3.9 
 
 195 
 
 90.6 
 
 261 
 
 127.2 
 
 327 
 
 63.9 
 
 730 
 
 387.5 
 
 - 2 
 
 -18.9 
 
 64 
 
 17.8 
 
 130 
 
 4.4 
 
 196 
 
 91.1 
 
 262 
 
 127.8 
 
 328 
 
 64.4 
 
 740 
 
 3933 
 
 - 1 
 
 -18.3 
 
 65 
 
 18.3 
 
 131 
 
 55. 
 
 197 
 
 91.7 
 
 263 
 
 128.3 
 
 329 
 
 65. 
 
 750 
 
 398.9 
 
 
 
 -17.8 
 
 66 
 
 18.9 
 
 132 
 
 5.6 
 
 198 
 
 92.2 
 
 264 
 
 128.9 
 
 330 
 
 65.6 
 
 760 
 
 404.4 
 
 + 1 
 
 -17.2 
 
 67 
 
 19.4 
 
 133 
 
 6.1 
 
 199 
 
 92.8 
 
 265 
 
 129.4 
 
 331 
 
 66.1 
 
 770 
 
 410. 
 
 2 
 
 -16.7 
 
 68 
 
 20. 
 
 134 
 
 6.7 
 
 200 
 
 93.3 
 
 266 
 
 130. 
 
 332 
 
 66.7 
 
 780 
 
 415.6 
 
 3 
 
 -16.1 
 
 69 
 
 20.6 
 
 135 
 
 7.2 
 
 201 
 
 93.9 
 
 267 
 
 130.6 
 
 333 
 
 67.2 
 
 790 
 
 421.1 
 
 4 
 
 -15.6 
 
 70 
 
 21.1 
 
 136 
 
 7.8 
 
 202 
 
 94.4 
 
 268 
 
 131.1 
 
 334 
 
 67.8 
 
 800 
 
 426.7 
 
 5 
 
 -15. 
 
 71 
 
 21.7 
 
 137 
 
 8.3 
 
 203 
 
 95. 
 
 269 
 
 131.7 
 
 335 
 
 68.3 
 
 810 
 
 432.2 
 
 6 
 
 -14.4 
 
 72 
 
 22.2 
 
 138 
 
 8.9 
 
 204 
 
 95.6 
 
 270 
 
 132.2 
 
 336 
 
 68.9 
 
 820 
 
 437.8 
 
 7 
 
 -13.9 
 
 73 
 
 22.8 
 
 139 
 
 9.4 
 
 205 
 
 96.1 
 
 271 
 
 132.8 
 
 337 
 
 69.4 
 
 830 
 
 443.3 
 
 8 
 
 -13.3 
 
 74 
 
 23.3 
 
 140 
 
 60. 
 
 206 
 
 96.7 
 
 272 
 
 133.3 
 
 338 
 
 70. 
 
 840 
 
 448.9 
 
 9 
 
 -12.8 
 
 75 
 
 23.9 
 
 141 
 
 60.6 
 
 207 
 
 97.2 
 
 273 
 
 133.9 
 
 339 
 
 70.6 
 
 850 
 
 45^,4 
 
 10 
 
 -12.2 
 
 76 
 
 24.4 
 
 142 
 
 61.1 
 
 208 
 
 97.8 
 
 274 
 
 134.4 
 
 340 
 
 71.1 
 
 860 
 
 460. 
 
 11 
 
 -11.7 
 
 77 
 
 25. 
 
 143 
 
 61.7 
 
 209 
 
 98.3 
 
 275 
 
 135. 
 
 341 
 
 71.7 
 
 870 
 
 465.6 
 
 12 
 
 - 11.1 
 
 78 
 
 25.6 
 
 144 
 
 62.2 
 
 210 
 
 98.9 
 
 276 
 
 135.6 
 
 342 
 
 72.2 
 
 880 
 
 471.1 
 
 13 
 
 -10.6 
 
 79 
 
 26.1 
 
 145 
 
 62.8 
 
 211 
 
 99.4 
 
 277 
 
 136.1 
 
 343 
 
 72.8 
 
 890 
 
 476.7 
 
 14 
 
 -10. 
 
 80 
 
 26.7 
 
 146 
 
 63.3 
 
 212 
 
 00. 
 
 278 
 
 136.7 
 
 344 
 
 73.3 
 
 900 
 
 482.2 
 
 15 
 
 - 9.4 
 
 81 
 
 27.2 
 
 147 
 
 63.9 
 
 213 
 
 00.6 
 
 279 
 
 137.2 
 
 345 
 
 73.9 
 
 910 
 
 487.8 
 
 16 
 
 - 8.9 
 
 82 
 
 27.8 
 
 148 
 
 644 
 
 214 
 
 01.1 
 
 280 
 
 137.8 
 
 346 
 
 74.4 
 
 920 
 
 493.3 
 
 17 
 
 - 8.3 
 
 83 
 
 28.3 
 
 149 
 
 65. 
 
 215 
 
 01.7 
 
 281 
 
 138.3 
 
 347 
 
 75. 
 
 930 
 
 498.9 
 
 18 
 
 - 7.8 
 
 84 
 
 28.9 
 
 150 
 
 65.6 
 
 216 
 
 02.2 
 
 282 
 
 138.9 
 
 348 
 
 75.6 
 
 940 
 
 504.4 
 
 19 
 
 - 7.2 
 
 85 
 
 29.4 
 
 151 
 
 66.1 
 
 217 
 
 02.8 
 
 283 
 
 139.4 
 
 349 
 
 76.1 
 
 950 
 
 510. 
 
 20 
 
 - 6.7 
 
 86 
 
 30. 
 
 152 
 
 66.7 
 
 218 
 
 03.3 
 
 284 
 
 140. 
 
 350 
 
 76.7 
 
 960 
 
 515.6 
 
 21 
 
 - 6.1 
 
 87 
 
 30.6 
 
 153 
 
 67.2 
 
 219 
 
 03.9 
 
 285 
 
 140.6 
 
 351 
 
 77.2 
 
 970 
 
 521.1 
 
 22 
 
 - 5.6 
 
 88 
 
 31.1 
 
 154 
 
 67.8 
 
 220 
 
 04.4 
 
 286 
 
 141.1 
 
 352 
 
 77.8 
 
 980 
 
 526.7 
 
 23 
 
 - 5. 
 
 89 
 
 31.7 
 
 155 
 
 68.3 
 
 221 
 
 05. 
 
 287 
 
 141.7 
 
 353 
 
 78.3 
 
 990 
 
 532.2 
 
 24 
 
 - 4.4 
 
 90 
 
 32.2 
 
 156 
 
 68.9 
 
 222 
 
 05.6 
 
 288 
 
 142.2 
 
 354 
 
 78.9 
 
 000 
 
 537.8 
 
 25 
 
 - 3.9 
 
 91 
 
 32.8 
 
 157)69.4 
 
 223 
 
 06.1 
 
 289 
 
 142.8 
 
 355 
 
 79.4 
 
 010 
 
 543.3 
 
 551 
 
552 
 
 HEAT. 
 
 Temperature Conversion Table. 
 
 (By Dr. Leonard Waldo.) 
 Reprint from Metallurgical and Chemical Engineering* 
 
 c 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 -200 
 -100 
 -0 
 
 F 
 
 -328 
 -148 
 
 +32 
 
 F 
 
 -346 
 -166 
 
 + 14 
 
 F 
 
 -364 
 -184 
 -4 
 
 F 
 
 -382 
 -202 
 -22 
 
 F 
 
 -400 
 -220 
 -40 
 
 F 
 
 -418 
 -238 
 -58 
 
 F 
 
 -436 
 -256 
 -76 
 
 F 
 
 -454 
 -274 
 -94 
 
 F 
 
 -292 
 -112 
 
 F 
 
 -310 
 -130 
 
 
 
 32 
 
 50 
 
 68 
 
 86 104 
 
 122 
 
 140 
 
 158 
 
 176 
 
 194 
 
 100 
 200 
 300 
 
 212 
 392 
 572 
 
 230 
 410 
 590 
 
 248 
 428 
 608 
 
 266 
 446 
 626 
 
 284 
 464 
 644 
 
 302 
 482 
 662 
 
 320 
 500 
 680 
 
 338 
 518 
 698 
 
 356 
 536 
 716 
 
 374 
 554 
 734 
 
 400 
 500 
 600 
 
 752 
 932 
 1112 
 
 770 
 950 
 1130 
 
 788 
 968 
 1148 
 
 806 
 986 
 1166 
 
 824 
 1004 
 1184 
 
 842 
 1022 
 1202 
 
 860 
 1040 
 1220 
 
 878 
 1058 
 1238 
 
 896 
 1076 
 1256 
 
 914 
 1094 
 1274 
 
 700 
 800 
 900 
 
 1292 
 1472 
 1652 
 
 1310 
 1490 
 1670 
 
 1328 
 1508 
 1688 
 
 1346 
 1526 
 1706 
 
 1364 
 1544 
 1724 
 
 1382 
 1562 
 1742 
 
 1400 
 1580 
 1760 
 
 1418 
 1598 
 1778 
 
 1436 
 1616 
 1796 
 
 1454 
 1634 
 1814 
 
 1000 
 
 1832 
 
 1850 
 
 1868 
 
 1886 
 
 1904 
 
 1922 
 
 1940 
 
 1958 
 
 1976 
 
 1994 
 
 1100 
 1200 
 1300 
 
 2012 
 2192 
 2372 
 
 2030 
 2210 
 2390 
 
 2048 
 2228 
 2408 
 
 2066 
 2246 
 2426 
 
 2084 
 2264 
 2444 
 
 2102 
 2282 
 2462 
 
 2120 
 2300 
 2480 
 
 2138 
 2318 
 2498 
 
 2156 
 2336 
 2516 
 
 2174 
 2354 
 2534 
 
 1400 
 1500 
 1600 
 
 2552 
 2732 
 2912 
 
 2570 
 2750 
 2930 
 
 2588 
 2768 
 2948 
 
 2606 
 2786 
 2966 
 
 2624 
 2804 
 2984 
 
 2642 
 2822 
 3002 
 
 2660 
 2840 
 3020 
 
 2678 
 2858 
 3038 
 
 2696 
 2876 
 3056 
 
 2714 
 2894 
 3074 
 
 1700 
 1800 
 1900 
 
 3092 
 3272 
 3452 
 
 3110 
 3290 
 3470 
 
 3128 
 3308 
 3488 
 
 3146 
 3326 
 3506 
 
 3164 
 3344 
 3524 
 
 3182 
 3362 
 3542 
 
 3200 
 3380 
 3560 
 
 3218 
 3398 
 3578 
 
 3236 
 3416 
 3596 
 
 3254 
 3434 
 3614 
 
 2000 
 
 3632 
 
 3650 
 
 3668 
 
 3686 
 
 3704 
 
 3722 
 
 3740 
 
 3758 
 
 3776 
 
 3794 
 
 2100 
 2200 
 2300 
 
 3812 
 3992 
 4172 
 
 3830 
 4010 
 4190 
 
 3848 
 4028 
 4208 
 
 3866 
 4046 
 4226 
 
 3884 
 4064 
 4244 
 
 3902 
 4082 
 4262 
 
 3920 
 4100 
 4280 
 
 3938 
 4118 
 4298 
 
 3956 
 4136 
 4316 
 
 3974 
 4154 
 4334 
 
 2400 
 2500 
 2600 
 
 4352 
 4532 
 4712 
 
 4370 
 4550 
 4730 
 
 4388 
 4568 
 4748 
 
 4406 
 4586 
 4766 
 
 4424 
 4604 
 4784 
 
 4442 
 4622 
 4802 
 
 4460 
 4640 
 4820 
 
 4478 
 4658 
 4838 
 
 4496 
 4676 
 4856 
 
 4514 
 4694 
 4874 
 
 2700 
 2800 
 2900 
 
 4892 
 5072 
 5252 
 
 4910 
 5090 
 5270 
 
 4928 
 5108 
 5288 
 
 4946 
 5126 
 5306 
 
 4964 
 5144 
 5324 
 
 4982 
 5162 
 5342 
 
 5000 
 5180 
 5360 
 
 5018 
 5198 
 5378 
 
 5036 
 5216 
 5396 
 
 5054 
 5234 
 5414 
 
 3000 
 
 5432 
 
 5450 
 
 5468 
 
 5486 
 
 5504 
 
 5522 
 
 5540 
 
 5558 
 
 5576 
 
 5594 
 
 3100 
 3200 
 3300 
 
 5612 
 5792 
 5972 
 
 5630 
 5810 
 5990 
 
 5648 
 5828 
 6008 
 
 5666 
 5846 
 6026 
 
 5684 
 5864 
 6044 
 
 5702 
 5882 
 6062 
 
 5720 
 5900 
 6080 
 
 5738 
 5918 
 6098 
 
 5756 
 5936 
 6116 
 
 5774 
 5954 
 6134 
 
 3400 
 3500 
 3600 
 
 6152 
 6332 
 6512 
 
 6170 
 6350 
 6530 
 
 6188 
 6368 
 6548 
 
 6206 
 6386 
 6566 
 
 6224 
 6404 
 6584 
 
 6242 6260 
 
 6422 6440 
 6602| 6620 
 
 6278 
 6458 
 6638 
 
 6296 
 6476 
 6656 
 
 6314 
 6494 
 6674 
 
 3700 
 3800 
 3900 
 
 6692 
 6872 
 7052 
 
 6710 
 6890 
 7070 
 
 6728 
 6908 
 7088 
 
 6746 
 6926 
 7106 
 
 6764 
 6944 
 7124 
 
 6782 
 6962 
 7142 
 
 50 
 
 6800 
 6980 
 7160 
 
 6818 
 6998 
 7178 
 
 6836 
 7016 
 7196 
 
 6854 
 7034 
 72.14 
 
 C 
 
 OJ 10 
 
 20 
 
 30 
 
 40 
 
 60 
 
 70 
 
 80 
 
 90 
 
 EXAMPLES: 1347. C = 2444 F+ 12.6F=2456.6F: 3367 F= 1850 
 I852.78 C. For other tables of temperatures, see pages 550 and 551- 
 
PYEOMETRY. 553 
 
 2. Contraction of clay, as in the old Wedgwood pyrometer, at one time 
 used by potters. This instrument was very inaccurate, as the contraction 
 of clay varied with its nature. 
 
 3. Expansion of air, as in the air-thermometer, Wiborgh's pyrometer. 
 Uehling and Steinbart's pyrometer, etc. 
 
 4. Pressure of vapors, as in some forms of Bristol's recording pyrometer. 
 
 5. Relative expansion of two metals or other substances, as in Brown's, 
 Bulkley's and other metallic pyrometers, consisting of a copper rod or 
 tube inside of an iron tube, or vice versa, with the difference of expansion 
 multiplied by gearing and indicated on a dial. 
 
 6. Specific heat of solids, as in the copper-ball and platinum-ball 
 pyrometers. 
 
 7. Melting-points of metals, alloys, or other substances, as in approxi- 
 mate determination of temperature by melting pieces of zinc, lead, etc., 
 or as in Seger's fire-clay pyrometer. 
 
 8. Time required to heat a weighed quantity of water inclosed in a 
 vessel, as in one form of water pyrometer. , 
 
 9. Increase in temperature of a stream of water or other liquid flow- 
 ing at a given rate through a tube inserted into the heated chamber. 
 
 10. Changes in the electric resistance of platinum or other metal, as 
 in the Siemens pyrometer. 
 
 11. Measurement of an electric current produced by heating the 
 junction of two metals, as in the Le Chatelier pyrometer. 
 
 12. Dilution by cold air of a stream of hot air or gas flowing from a 
 heated chamber and determination of the temperature of the mixture by 
 a mercury thermometer, as in Hobson's hot-blast pyrometer. 
 
 13. Polarization and refraction by prisms and plates of light radiated 
 from heated surfaces, as in Mesure" and Nouel's pyrometric telescope or 
 optical pyrometer, and Warmer's pyrometer. 
 
 14. Heating the filament of an electric lamp to the same color as that 
 of an incandescent body, so that when the latter is observed through a 
 telescope containing the lamp the filament becomes invisible, as in Hoi- 
 born and Kurlbaum's and Morse's optical pyrometers. The current 
 required to heat the filament is a measure of the temperature. 
 
 15. The radiation pyrometer. The radiation from an incandescent 
 surface is received in a telescope containing a thermo-couple, and the 
 electric current generated therein is measured, as in Fdry's radiation 
 pyrometer. 
 
 (See "Optical Pyrometry " by C. W. W. Waidner and G. K. Burgess, 
 Bulletin No. 2. Bureau of Standards, Department of Commerce and 
 Labor; also Eng'g, Mar. 1, 1907.) 
 
 The "Veritas" Pyrometer (called Buller's Rings in England) is an 
 improvement on the Wedge wood pyrometer. It is based on the con- 
 traction of a flat ring of a special clay mixture, which is made with 
 great care to secure uniformity of composition. The contraction is 
 found to be directly proportional to the increase of temperature above 
 800 C. (1472 F.) and its amount is measured by a multiplying index. 
 The rings are 21/2 in. external and 3 A in. internal diam., 5/16 in. thick. 
 They are made by Veritas Firing System Co., Trenton, N. J., and are 
 largely used by potters. 
 
 Platinum or Copper Ball Pyrometer. A weighed piece of platinum, 
 copper, or iron is allowed to remain in the furnace or heated chamber till 
 it has attained the temperature of its surroundings. It is then suddenly 
 taken out and dropped into a vessel containing water of a known weight 
 and temperature. The water is stirred rapidly and its maximum tem- 
 perature taken. Let W = weight of the water, w the weight of the ball, 
 I = the original and T the final heat of the water, and S the specific heat of 
 the metal; then the temperature of fire may be found from the formula 
 
 The mean specific heat of platinum between 32 and 446 F. is 0.03333 or 
 1/30 that of water, and it increases with the temperature about 0.000305 
 for each 100 F. For a fuller description, by J. C. Hoadley, see Trans. 
 
 A. S. M. E., vi, 702. Compare also Henry M. Howe, Trans. A. I. M. E. t 
 "\\. 728. 
 'or accuracy corrections are required for variations in the specific heat 
 
 xviii. 728. 
 F< 
 
554 
 
 HEAT. 
 
 of ttie water and of the metal at different temperatures, for loss of heat by 
 radiation from the metal during the transfer from the furnace to the water, 
 and from the apparatus during the heating of the water; also for the heat- 
 absorbing capacity of the vessel containing the water. 
 
 Fire-clay or fire-brick may be used instead of the metal ball. 
 
 L,e Chatelier's Thermo-electric Pyrometer. For a very full 
 description, see paper by Joseph Struthers, School of Mines Quarterly, 
 vol. xii, 1891; also, paper read by Prof. Roberts- Austen before the Iron 
 and Steel Institute, May 7, 1891. 
 
 The principle upon which this pyrometer is constructed is the measure- 
 ment of a current of electricity produced by heating a couple comp9sed of 
 two wires, one platinum and the other platinum with 10% rhodium 
 the current produced being measured by a galvanometer. 
 
 The composition of the gas which surrounds the couple has no influence 
 on the indications. 
 
 When temperatures above 2500 F. are to be studied, the wires must 
 have an isolating support and must be of good length, so that all parts 
 of a furnace can be reached. The wires are supported in an iron tube 1/3 
 inch interior diameter and held in place by a cylinder of refractory clay 
 having two holes bored -through, in which the wires are placed. The 
 shortness of time (five seconds) allows the temperature to be taken with- 
 out deteriorating the tube. 
 
 Tests made by this pyrometer in measuring furnace temperatures under 
 a great variety of conditions show that the readings of the scale unconnected 
 are always within 45 F. of the correct temperature, and in the majority 
 of industrial measurements this is sufficiently accurate. 
 
 Graduation of Le Chatelier's Pyrometer. W. C. Roberts- Austen 
 in his Researches on the Properties of Alloys, Froc. Inst. M. E., 189 
 says: The electromotive force produced by heating the thermo- junction 
 to any given temperature is measured by the movement of the spot 01 light 
 on tne scale graduated in millimeters. The scale is calibrated by heating 
 the thermo-junction to temperatures which have been carefully deter- 
 mined by the aid of the air-thermometer, and plotting the curve from 
 the data so obtained. Many fusion and boiling-points have been estab- 
 lished by concurrent evidence of various kinds, and are now generally 
 accepted. The following table contains certain of these: 
 
 Deg. F. 
 
 Deg. < 
 
 > 
 
 Deg. F. 
 
 Deg. C 
 
 
 212 
 618 
 
 100 
 326 
 
 ^'Water boils. 
 Lead melts. 
 
 1733 
 1859 
 
 945 
 1015 
 
 Silver melts. 
 Potassium sulphate 
 
 676 
 779 
 
 358 
 415 
 
 Mercury boils. 
 Zinc melts. 
 
 1913 
 
 1045 
 
 melts. 
 Gold melts. 
 
 838 
 1157 
 
 448 
 625 
 
 Sulphur boils. 
 Aluminum melts. 
 
 1929 
 2732 
 
 1054 
 1500 
 
 Copper melts. 
 Palladium melts. 
 
 1229 
 
 665 
 
 Selenium boils. 
 
 3227 
 
 1775 
 
 Platinum melts. 
 
 Chatelier Vtates lhat^by^eans^This"py"ometerhe j has discovered that 
 
 " .en 
 
 The Temperatures Developed in Industrial Furnaces. 
 
 hatelier states that by 
 the temperatures whicn 
 
 occur in melting steel and in other industrial 
 - " finds the melting 
 ray cast iron 1220 
 
 "Mild steel melts at 1475 (2687 F.), and hard steel at 1410 
 (257G J F ) The furnace for hard porcelain at the end of the baking has a 
 heat of 1370 (2498 F.). The heat of a normal incandescent lamp is 
 1800 (3272 F.), but it may be pushed to beyond 2100 (3812 F.). 
 
 Prof Roberts- Austen (Recent Advances in Pyrometry, Trans. A.I.M.E., 
 Chicago Meeting, 1893) gives an excellent description of modern forms of 
 pyrometers. The following are some of his temperature determinations. 
 TEN-TON OPEN-HEARTH FURNACE, WOOLWICH ARSENAL. 
 
 Degrees Degrees 
 Centigrade. Fahr. 
 Temperature of steel, 0.3% carbon, pouring into ladle. 1645 
 
 Steel, 0.3 % carbon, pouring into large mold 1 ^7b 
 
 Reheating furnace, interior v 
 
 Cupola furnace, No. 2 cast iron, pouring into ladle 
 
 The following determinations have been effected by M. Le Chatelier: 
 
PYBOMETKY. 555 
 
 i 
 
 BESSEMER PROCESS. SIX-TON CONVERTER. Deg. O. Deg F,. 
 
 A. Bath of Slag 1580 2876 
 
 B. Metal in ladle , 1640 2984 
 
 C. Metal in ingot mold 1580 2876 
 
 D. Ingot in reheating furnace 1200 2192 
 
 E. Ingot under the hammer 1080 1976 
 
 OPEN-HEARTH FURNACE (Semi-mild Steel). 
 
 A. Fuel gas near gas generator 720 1328 
 
 B. Fuel gas entering into bottom of regenerator chamber 400 752 
 
 C. Fuel gas issuing from regenerator chamber 1200 2192 
 
 Air issuing from regenerator chamber 1000 1832 
 
 Chimney gases. Furnace in perfect condition 300 590 
 
 End of the melting of pig charge 1420 2588 
 
 Completion of conversion 1500 2732 
 
 Molten steel. In the ladle Commencement of casting. 1580 2876 
 
 End of casting 1490 2714 
 
 In the molds 1520 2768 
 
 For very mild (soft) steel the temperatures are higher by 50 C. 
 BLAST-FURNACE (Gray-Bessemer Pig). 
 
 Opening in face of tuyere 1930 3506 
 
 Molten metal Commencement of fusion 1400 2552 
 
 End, or prior to tapping 1570 2858 
 
 HOFFMAN RED-BRICK KILN 
 Burning temperatures 1100 2012 
 
 R. Moldenke (The Foundry, Nov., 1898) determined with a Le 
 Chatelier pyrometer the melting-point of 42 samples of pig iron of 
 different grades. The range was from 2030 F. for pig containing 
 3.98% combined carbon to 2280 for pig containing 0.13 combined car- 
 bon and 3.43% graphite. The results of the whole series may be ex- 
 pressed within 30 F. by the formula Temp. = 2300 - 70 X % of 
 combined carbon. 
 
 Hobson's Hot-blast Pyrometer consists of a brass chamber having 
 three hollow arms and a handle. The hot blast enters one of the arms 
 and induces a current of atmospheric air to flow into the second arm. 
 The two currents mix in the chamber and flow out through the third 
 arm, in which the temperature of the mixture is taken by a mercury 
 thermometer. The openings in the arms are adjusted so that the pro- 
 portion of hot blast to the atmospheric air remains the same. 
 
 The Wiborgh Air-pyrometer. (E. Trotz, Trans. A.I.M.E., 1892.) 
 The inventor using the expansion-coefficient of air, as determined by 
 Gay-Lussac, Dulon, Rudberg, and Regnault, bases his construction on 
 the following theory: If an air- volume, V, inclosed in a porcelain globe 
 and connected through a capillary pipe with the outside air, be heated 
 to the temperature T (which is to be determined) and thereupon the 
 connection be discontinued, and there be then forced into the globe 
 containing V another volume of air V of known temperature t, which 
 was previously under atmospheric pressure H , the additional pressure 
 h, due to the addition of the air- volume V to the air- volume V, can be 
 measured by a manometer. But this pressure is of course a function 
 of the temperature T. Before the introduction of V, we have the two 
 separate air-volumes, V at the temperature T, and V at the tempera- 
 ture t, both under the atmospheric pressure H. After the forcing in 
 of V into the globe, we have, on the contrary, only the volume V of 
 the temperature T, but under the pressure H + h. 
 
 Seger Cones. (Stowe-Fuller Co., Cleveland, 1914). Seger Cones 
 were developed in 1886 in Germany, by Dr. Herman A. Seger. They 
 comprise a series of triangular cones, of pyramidal shape, of differing 
 mineral compositions, each one of which requires a different amount of 
 heat work to soften and deform it. They are used principally in the 
 clay, pottery, and allied industries to determine the proper heat con- 
 ditions of kilns, furnaces, etc. The difference in softening point 
 between any two adjoining member of the series, is kept as nearly 
 equal as possible, so that the cones form a sort of pyrometric scale. 
 The softening or fusion is not altogether a matter of temperature, the 
 element of time entering in also. A longer exposure at a slightly lower 
 temperature will accomplish the same amount of heat work in clay- 
 working as a shorter exposure at a somewhat higher temperature, pro- 
 
556 
 
 HEAT. 
 
 vided it is always above the critical temperature at which chemical 
 reactions take place in the clay. Although the time element must be 
 considered, a melting point in degrees F. has been assigned to each cone 
 number for convenience. For rapid burning, this temperature is 
 fairly accurate, but in commercial clay-burning, the cones melt at 
 lower temperatures than those given in the table. In extremely long 
 firings the difference between the actual and assigned temperatures 
 may be as much as 100 or 150 C. (212 to 297 F.) 
 
 Dr. Seger's original series consisted of twenty different mixtures, 
 and covered a relatively narrow range of temperatures. Several other 
 series have since been devised, as follows: Hecht series, used by 
 china and glass decorators, consisting of fusible lead-soda borate glass 
 and kaolin, the glass alone making the softest cone, successive addi- 
 tions of kaolin raising the fusing point. The Cremer series, used for 
 red burning clays and for soft glazes, sewer pipe, drain tiles, roof tiles, 
 etc., consisting of a lime-soda borate glass, oxide of iron, feldspar, 
 carbonate of lime, potters flint and kaolin, it begins witja a large 
 amount of glass for the softest cone, and decreasing to almost none at 
 the upper end. The Seger series, used for harder red burning wares of 
 vitrified variety, and for all buff burning and white burning clay wares 
 consisting of potters flint, feldspar, carbonate of lime and feldspar, 
 oxide of iron appearing in the three lowest temperature cones; no glass 
 is used and the proportion of kaolin and flint increases with the fusion 
 temperature. High temperature series, used for testing refractory 
 materials only, consisting except in the two lowest numbers of kaolin 
 potters flint, and oxide of alumina; the highest cone consists of pure 
 oxide of alumina. No temperatures can be assigned to this series, 
 although 1850 C. (3362 F.) has been set as the melting point of 
 No. 36. The table gives the approximate fusion points of the various 
 cones. 
 
 Fusion Points of Seger Cones. 
 
 Symbol 
 or 
 Cone 
 No. 
 
 Melting Point 
 
 Sym- 
 bol 
 or 
 Cone 
 
 No. 
 
 Melting Point 
 
 Sym- 
 bol 
 or 
 Cone 
 
 No. 
 
 Melting Point 
 
 Deg.C 
 
 Deg.F 
 
 Deg.C 
 
 Deg.F 
 
 Deg.C 
 
 Deg.F 
 
 HECHT 
 
 
 
 
 
 
 
 
 
 SERIES 
 
 
 
 04 
 
 1070 
 
 1958 
 
 13 
 
 1390 
 
 2534 
 
 022 
 
 590 
 
 1094 
 
 03 
 
 1090 
 
 1994 
 
 14 
 
 1410 
 
 2570 
 
 021 
 
 620 
 
 1148 
 
 02 
 
 1110 
 
 2030 
 
 15 
 
 1430 
 
 2606 
 
 020 
 
 650 
 
 1202 
 
 01 
 
 1130 
 
 2066 
 
 16 
 
 1450 
 
 2642 
 
 019 
 
 680 
 
 1256 
 
 SEGER 
 
 
 
 17 
 
 1470 
 
 2678 
 
 
 
 
 SERIES 
 
 
 
 
 
 
 018 
 
 710 
 
 1310 
 
 1 
 
 1150 
 
 '2102 
 
 18 
 
 1490 
 
 2714 
 
 017 
 
 740 
 
 1364 
 
 2 
 
 1170 
 
 2138 
 
 19 
 
 1510 
 
 2759 
 
 016 
 
 770 
 
 1418 
 
 3 
 
 1190 
 
 2174 
 
 20 
 
 1530 
 
 2786 
 
 
 
 
 
 
 
 HIGH 
 
 
 
 015 
 
 800 
 
 1472 
 
 4 
 
 1210 
 
 2210 
 
 TEMP. 
 
 
 
 012V 2 
 
 875 
 
 1607 
 
 5 
 
 1230 
 
 2246 
 
 SERIES 
 
 
 
 CREMER 
 
 
 
 
 
 
 
 
 SERIES 
 
 
 
 6 
 
 1250 
 
 2282 
 
 26 
 
 Lowest Grade for No. 2 Refractories. 
 
 010 
 
 950 
 
 1742 
 
 7 
 
 1270 
 
 2318 
 
 30 
 
 Lowest Grade for No. 1 Refractories. 
 
 09 
 
 970 
 
 1778 
 
 8 
 
 1290 
 
 2354 
 
 32 
 
 Good Qual. No. 1 Firebrick. 
 
 08 
 07 
 06 
 
 990 
 1010 
 1030 
 
 1814 
 1850 
 1886 
 
 9 
 10 
 11 
 
 1310 
 1330 
 1350 
 
 2390 
 2476 
 2462 
 
 34 
 36 
 
 38 
 
 Excellent Qual. No. 1 Firebrick. 
 Melting point pure Kaolin. 
 Melting point good qual. Bauxite. 
 
 05 
 
 1050 
 
 1922 
 
 12 
 
 1370 
 
 2498 
 
 42 
 
 Melting point pure Alumina. 
 
 The German cones are manufactured by the German Government 
 at the Royal Porcelain Factory, Charlottenburg, and can be obtained 
 in the United States through Eimer and Amend, New York, and other 
 chemical supply houses. In 1896, Prof. Edw. Orton, Jr., of the Ohio 
 State University, Columbus, Ohio, began their manufacture in Amer- 
 ica. The American cones agree with the German cones in all re- 
 pects, and have come into general use in America. They are not sold 
 through dealers, but must be obtained direct from the maker. 
 
 Mesure and NouePs Pyrometric Telescope. (H. M. Howe, E. and 
 M. J., June 7, 1890) Mesure and Nouel's telescope gives an immediate 
 
PYROMETRY. 657 
 
 determination of the temperature of incandescent bodies, and is there- 
 fore better adapted to cases where a great number of observations are 
 to be made, and at short intervals, than Seger's. The little telescope, 
 carried in the pocket or hung from the neck, can be used by foreman 
 or heater at any moment. 
 
 It is based on the fact that a plate of quartz, cut at right angles to the 
 axis, rotates the plane of polarization of polarized light to a degree nearly 
 inversely proportional to the square of the length of the waves; and, 
 further, on the fact that while a body at dull redness merely emits red 
 light, as the temperature rises, the orange, yellow, green, and blue waves 
 successively appear. 
 
 If, now, such. a plate of quartz is placed between two Nicol prisms at 
 right angles, "a ray of monochromatic light which passes the first, or 
 polarizer, and is watched through the second, or analyzer, is not extin- 
 guished as it was before interposing the quartz. Part of the light passes 
 the analyzer, and, to again extinguish it, we must turn one of the Nicols a 
 certain angle," depending on the length of the waves of light, and hence on 
 the temperature of the incandescent object which emits this light. Hence 
 the angle through which we must turn the analyzer to extinguish the light 
 is a measure of the temperature of the object observed. 
 
 The Uehling and Steinbart Pyrometer. (For illustrated descrip- 
 tion see Engineering, Aug. 24, 1894.) The action of the pyrometer is 
 based on a principle which involves the law of the flow of gas through 
 minute apertures in the following manner: If a closed tube or chamber be 
 supplied with a minute inlet and a minute outlet aperture, and air be 
 caused by a constant suction to flow in through one and out through the 
 other of these apertures, the tension in the chamber between the apelrtures 
 will vary with the difference of temperature between the inflowing and 
 outflowing air. If the inflowing air be made to vary with the tem- 
 perature to be measured, and the outflowing air be kept at a certain con- 
 stant temperature, then the tension in the space or chamber between the 
 two apertures will be an exact measure of the temperature of the inflow- 
 ing air, and hence of the temperature to be measured. 
 
 In operation it is necessary that the air be sucked into it through the 
 first minute aperture at the temperature to be measured, through the 
 second aperture at a lower but constant temperature, and that the suc- 
 tion be of a constant tension. The first aperture is therefore located 
 in the end of a platinum tube in the bulb of a porcelain tube over which 
 the hot blast sweeps, or inserted into the pipe or chamber containing 
 the gas whose temperature is to be ascertained. 
 
 The second aperture is located in a coupling, surrounded by boiling 
 water, and the suction is obtained by an aspirator and regulated by a 
 column of water of constant height. 
 
 The tension in the chamber between the apertures is indicated by a 
 manometer. 
 
 The Air-thermometer. (Prof. R. C. Carpenter, Eng'g News, Jan. 5, 
 1893.) Air is a perfect thermometric substance, and if a given mass of 
 air be considered, the product of its pressure and volume divided by its 
 absolute temperature is in every case constant. If the volume of air 
 remain constant, the temperature will vary with the pressure; if the 
 pressure remain constant, the temperature will vary with the volume. As 
 the former condition is more easily attained, air-thermometers are usually 
 constructed of constant volume, in which case the absolute temperature 
 will vary with the pressure. 
 
 If we denote pressures by p and p', and the corresponding absolute 
 temperatures by T and T' t we should have 
 
 p :p' :: T : rand T' = p f - 
 
 The absolute temperature T is to be considered in every case 460 higher 
 than the thermometer-reading expressed in Fahrenheit degrees. From 
 the form of the above equation, if the pressure p corresponding to a 
 known absolute temperature T be known, T' can be found. The quotient 
 T/p is a constant which may be used in all determinations with the 
 instrument. The pressure on the instrument can be expressed in inches 
 of mercury, and is evidently the atmospheric pressure b as shown by a 
 barometer, plus or minus an additional amount h shown by a manometer 
 attached to the air-thermometer. That is, in general, p = b h. 
 
558 HEAT. 
 
 casr -0+ ij* SS*** ihe *<> <* melting ice, in which 
 
 case 1 = 460 + 32 = 492 F. This temperature can~be produced bv sur 
 rounding the bulb in melting ice and leaving it several [ mfnutes^so that the 
 
 \C^n t a h tUre - f - the f C ?i? f \ n f d air sha11 acquire that of the surrounding ice 
 TV hen the air is at that temperature, note the reading of the attached 
 manometer ft and that of a barometer; the sum will be the value of p 
 corresponding to the absolute temperature of 492 F The constant 
 
 = p ' ^ btained ' can be ^M 
 
 o*? 1 ? 11 Tem P e ?*atures judged by Color. The temperature of a body 
 pSrilfe ?n P % C S imate J y J u <J,sed b y the experienced eye unaided. M. 
 Pouillet in 1836 constructed a table, which has been generally quoted in 
 the text-books, giving the colors and their corresponding temperature, 
 Whi H'I^W r P la ; ced bv the tables of H. M. Howe and ofMaunse 
 below y (7>ans - A - s - M - E - 18 "). which are given 
 
 Howe. C. F. White and Taylor. C. F. 
 Lowest red vis- Dark blood-red, black- 
 
 ible in dark . . 470 878 red 990 
 Lowest red vis- Dark red,' biood-Ved,' low 
 
 ible in day- re j 55 6 j 050 
 
 n % h t- ........ 475 887 Dark cherry-red:'.: '. 635 1175 
 
 u r d ........ 550 ,! 625 1022to1157 Medium cherry- red. .. 1250 
 
 Full cherry.... 700 1292 Cherry, full red .......... 746 1375 
 
 feJSi * r . d ...... 8 50 1A/ ^ 1562 Light cherry, light red*. 843 1550 
 
 Full yellow ..... 950 to 1000 1742 to 1832 Orange, free scalingheat 899 1650 
 
 Light yellow... 050 1922 Light orange ..... ...... 941 1725 
 
 Whl te ......... 1150 2102 Yellow..... . 996 1825 
 
 Light yellow ............. 1079 1975 
 
 White ................... 1205 2200 
 
 * Heat at which scale forms and adheres on iron and steel, i.e., does 
 not fall away from the piece when allowed to cool in air. 
 
 Skilled observers may vary 100 F. or more in their estimation of 
 relatively low temperatures by color, and beyond 2200 F. it is practically 
 impossible to make estimations with any certainty whatever. (Bulletin 
 No. 2, Bureau of Standards, 1905.) 
 
 In confirmation of the above paragraph we have the following, in a 
 booklet published by the Halcomb Steel Co., 1908. 
 C. F. Colors. C. F. Colors. 
 
 400 752 Red, visible in the dark. 1000 1832 Bright cherry-red. 
 
 474 885 Red, visible in the twilight. 1100 2012 Orange-red. 
 
 525 975 Red, visible in the day- 1200 2192 Orange-yellow. 
 light. 1300 2372 Yellow-white. 
 
 581 1077 Red, visible in the sun- 1400 2552 White welding heat. 
 light. 1500 2732 Brilliant white. 
 
 700 1292 Dark red. 1600 2912 Dazzling white (bluish 
 
 800 1472 Dull cherry-red. white). 
 
 900 1652 Cherry-red. 
 
 Different substances heated to the same temperature give out the 
 same color tints. Objects which emit the same tint and intensity of light 
 cannot be distinguished from each other, no matter how different their 
 texture, surface, or shape may be. When the temperature at all parts of 
 a furnace at a low yellow heat is the same, different objects inside the 
 furnace (firebrick, sand, platinum, iron) become absolutely invisible. 
 (H. M. Howe.) 
 
 A bright bar of iron, slowly heated in contact with air, assumes the fol- 
 lowing tints at annexed temperatures (Claudel): 
 
 Cent. Fahr. 
 
 Yellow at 225 437 
 
 Orange at 243 473 
 
 Red at 265 509 
 
 Violet at 277 531 
 
 Cent. Fahr. 
 
 Indigo at 288 5 30 
 
 Blue at 293 559 
 
 Green at 332 630 
 
 "Oxide-gray"... 400 762 
 
 The Halcomb Steel Co. (1908) gives the following heats and temper 
 colors of steel: 
 
MELTING POINTS OF METALS. 559 
 
 Cent. Fahr. Colors. Cent.Fahr. Colors. 
 
 221.1 430 Very pale yellow. 265.6 510 Spotted red-brown. 
 
 226.7 440 Light yellow. 271.1 520 Brown-purple. 
 
 232.2 450 Pale straw-yellow. 276.7 530 Light purple. 
 
 237.8 460 Straw-yellow. 282.2 540 Full purple. 
 
 243.3 470 Deep straw-yellow. 287.8 550 Dark purple. 
 
 248.9 480 Dark yellow. 293.3 560 Full blue. 
 
 254.4 490 Yellow-brown. 298.9 570 Dark blue. 
 260.0 500 Brown-yellow. 315.6 600 Very dark blue. 
 
 BOILING-POINT AT ATMOSPHERIC PRESSURE. 
 
 14.7 Ib. per square inch. 
 
 Ether, sulphuric 100 F. Saturated brine 226 F. 
 
 Carbon bisulphide 118 Nitric acid 248 
 
 Chloroform 140 Oil of turpentine 315 
 
 Bromine 145 Aniline 363 
 
 Aqua ammonia, sp.gr. 0.95. 146 Naphthaline 428 
 
 Wood spirit 150 Phosphorus 554 
 
 Alcohol 173 Sulphur 800 
 
 Benzine 176 Sulphuric acid 590 
 
 Water 212 Linseed oil 597 
 
 Average sea-water 213.2 Mercury 676 
 
 The boiling-points of liquids increase as the pressure increases. 
 
 3IELTING-POINTS OF VARIOUS SUBSTANCES. 
 
 The following figures are given by Clark (on the authority of Pouillett 
 Claudel, and Wilson), except those marked *, which are given by Prof. 
 Roberts- Austen, and those marked t, which are given by Dr. J. A. Marker. 
 These latter are probably the most reliable figures. 
 
 Sulphurous acid - 148 F. Cadmium 442 F. 
 
 Carbonic acid - 108 Bismuth 504 to 507 
 
 Mercury - 39, - 38f Lead 618*, 620f 
 
 Bromine + 9.5 Zinc 779*, 786f 
 
 Turpentine 14 Antimony 1150, 1169J 
 
 Hyponitric acid . . 16 Aluminum 1157*, 1214f 
 
 Ice 32 Magnesium 1200 
 
 Nitro-glycerine 45 NaCl, common salt 1472f 
 
 Tallow 92 - Calcium Full red heat. 
 
 Phosphorus 112 Bronze 1692 
 
 Acetic acid 113 Silver 17b3*, 1751" 
 
 Stearine 109 to 120 Potassium sulphate.. 1859*, 1958" 
 
 Spermaceti 120 Gold 1913*, 1947" 
 
 Margaric acid .... 131 to 140 Copper 1929*, 1943" 
 
 Potassium 136 to 144 Nickel 2600" 
 
 Wax 142 to 154 Cast iron, white 1922,2075" 
 
 Stearic acid 158 " gray 2012 to 2786, 2228* 
 
 Sodium 194 to 208 Steel 2372 to 2532* 
 
 Iodine.. 225 " hard . . . 2570*; mild, 2687 
 
 Sulphur 239 Wrought iron 2732 to 2912, 2737* 
 
 Alloy, 1 1/2 tin, 1 lead 334, 367f Palladium 2732* 
 
 Tin 446, 449f Platinum 3227*, 3110t 
 
 Cobalt and manganese, fusible in highest heat of a forge. Tungsten 
 and chromium, not fusible in forge, but soften and agglomerate. Plati- 
 num and iridium, fusible only before the oxyhydrogen blowpipe, or in an 
 electrical furnace. For melting-point of fusible alloys see Alloys. For 
 boiling and freezing points of air and other gases see p. 606. 
 
 Melting Points of Rare Metals. H. Von Wartenberg has deter- 
 mined the melting points of some rare metals. The temperature was 
 measured by a Wanner pyrometer. The following melting points were 
 thus obtained: 
 
 Vanadium 1710 C. = 3110 F. 
 
 Rhodium 1970 C. = 3578 F. 
 
 Iridium 2360 C. = 4280 F. 
 
 Molybdenum over 2550 C. = 4622 F. 
 
 Tungsten 2900 C. = 5252 F. 
 
 The metals were as pure as possible. It is. stated that the vanadium 
 
560 
 
 HEAT. 
 
 used was of 97% purity. The results were published in a German 
 periodical. Brass World, June, 1910. 
 
 QUANTITATIVE MEASUREMENT OF HEAT. 
 
 Unit of Heat. The British thermal unit, or heat unit (B.T.U.), is the 
 quantity of heat required to raise the temperature of 1 Ib. of pure water 
 from 62 to 63 F. (Peabody>, or i/igo of the heat required to raise the 
 temperature of 1 Ib. of water from 32 to 212 F. (Marks and Davis, 
 see Steam, p. 867). 
 
 The French thermal unit, or calorie, is the quantity of heat required 
 to raise the temperature of 1 kilogram of pure water from 15 to 16 C. 
 
 1 French calorie = 3.968 British thermal units; 1 B.T.U. = 0.252 
 calorie. The "pound calorie" is sometimes used by English writers; 
 it is the quantity of heat required to raise the temperature of 1 Ib. of 
 water 1 C. 1 Ib. calorie = 9/ 5 B.T.U. = 0.4536 calorie. The heat of 
 combustion of carbon to CO 2 is said to be 8080 calories. This figure is 
 used either for French calories or for pound calories, as it is the number 
 of pounds of water that can be raised 1 C. by the complete combustion 
 of 1 Ib. of carbon, or the number of kilograms of water that can be 
 raised 1 C. by the combustion of 1 kilo, of carbon; assuming in each 
 case that all the heat generated is transferred to the water. 
 
 The Mechanical Equivalent of Heat is the number of foot-pounds 
 of mechanical energy equivalent to one British thermal unit, heat and 
 mechanical energy being mutually convertible. Joule's experiments, 
 1843-50, gave the figure 772, which is known as Joule's equivalent. 
 More recent experiments by Prof. Rowland (1880) and others give higher 
 figures; 778 is generally accepted, but 777.6 is probably more nearly 
 correct. (Goodenough's " Properties of Steam and Ammonia," 1915.) 
 
 1 heat-unit is equivalent to 778 ft.-lbs. of energy. 1 ft.-lb. = 1/778 = 
 0.0012852 heat-unit. 1 horse-power = 33,000 ft.-lbs. per minute = 
 2545 heat-units per hour = 42.416 + per minute = 0.70694 per second. 
 1 Ib. carbon burned to CO 2 = 14,600 heat-units. 1 Ib. C per H.P. per 
 hour = 2545 -=- 14,600 = 17.43% efficiency. 
 
 Heat of Combustion of Various Substances in Oxygen. 
 
 
 Heat-units. 
 
 Authority. 
 
 Cent. 
 
 Fahr. 
 
 Hydrogen to liquid water at C. . 
 
 to steam at 100 C 
 Carbon (wood charcoal) to car- 
 bonic acid, CO2J ordinary tem- 
 peratures . . 
 
 I 34,462 
 \ 33,808 
 ( 34,342 
 28,732 
 ( 8,080 
 \ 7,900 
 ( 8,137 
 7,859 
 7,861 
 7,901 
 2,473 
 ( 2,403 
 i 2,431 
 ( 2,385 
 5,607 
 (13,120 
 \ 13, 108 
 ( 13,063 
 (11,858 
 h 1,942 
 (11,957 
 ( 10,102 
 1 9,915 
 2,250 
 
 62,032 
 60,854 
 61,816 
 51,717 
 14,544 
 14,220 
 14,647 
 14,146 
 14,150 
 14,222 
 4,451 
 4,325 
 4,376 
 4,293 
 10,093 
 23,616 
 23,594 
 23,513 
 21,344 
 21,496 
 21,523 
 18,184 
 17.847 
 4,050 
 
 Favre and Silbermann. 
 Andrews. 
 Thomsen. 
 Favre and Silbermann. 
 
 Andrews. 
 Berthelot. 
 
 Fay re and Silbermann. 
 
 Andrews. 
 Thomsen. 
 Favre and Silbermann. 
 Thomsen. 
 Andrews. 
 Favre and Silbermana. 
 
 Andrews. 
 Thomsen. 
 
 Favre and Silbermann. 
 N. W. Lord. 
 
 Carbon, diamond to CO2 
 
 black diamond to COa 
 graphite to CO2 . 
 
 Carbon to carbonic oxide, CO 
 
 Carbonic oxide to CO2 per unit of 
 CO . 
 
 CO to CO2 per unit of C=21/s x 2403 
 
 Marsh-gas,Methane, CH4,to water 
 and CO2 
 
 Olefiant gas, Ethylene, C2H 4 , to 
 water and CO2 
 
 Benzole gas,CeH6,to water and CO2 
 Sulphur to sulphur dioxide, SO2. . . 
 
HEAT OF COMBUSTION. 561 
 
 In calculations of the heating value of mixed fuels the value for carbon 
 Is commonly taken at 14,600 B.T.U., and that of hydrogen at 62,000. 
 Taking the heating value of C burned to CO2 at 14,600, and that of C to 
 CO at 4450, the difference, 10,150 B.T.U., is the heat lost by the imperfect 
 combustion of each Ib. of C burned to CO instead of to CO2. If the CO 
 formed by this imperfect combustion is afterwards burned to CO2 the lost 
 heat is regained. 
 
 In burning 1 pound of hydrogen with 8 pounds of oxygen to form 9 
 pounds of water, the units of heat evolved are 62,000; but if the resulting 
 product is not cooled to the initial temperature of the gases, part of the 
 heat is rendered latent in the steam. The total heat of 1 Ib. of steam at 
 212 F. is 1150.0 heat-units above that of water at 32, and 9 X 1150 
 10,350 heat-units, which deducted from 62,000 gives 51,650 as the heat 
 evolved by the combustion of 1 Ib. of hydrogen and 8 Ibs. of oxygen at 
 32 F. to form steam at 212 F. 
 
 Some writers subtract from the total heating value of hydrogen only 
 the latent heat of the 9 Ibs. of steam, or 9 X 970.4 = 8734 B.T.U., leaving 
 as the " low " heating value 53,266 B.T.U. 
 
 The use of heating values of hydrogen "burned to steam," in compu- 
 tations relating to combustion of fuel, is inconvenient, since it necessi- 
 tates a statement of the conditions upon which the figures are based ; and 
 It is, moreover, misleading, if not inaccurate, since hydrogen in fuel is not 
 often burned in pure oxygen, but in air; the temperature of the gases 
 before burning is not often the assumed standard temperature, and the 
 Droducts of combustion are not often discharged at 212. In steam- 
 boiler practice the chimney gases are usually discharged above 300; but 
 if economizers are used, and the water supplied to them is cold, the gases 
 may be cooled to below 212, in which case the steam in the gases is con- 
 densed and its latent heat of evaporation is utilized. If there is any need 
 at all of using figures of the "available" heating value of hydrogen, or its 
 heating value when "burned to steam," the fact that the gas is burned in 
 air and not in pure oxygen should be taken into consideration. The 
 resulting figures will then be much lower than those above given, and they 
 will vary with different conditions. (Kent, '* Steam Boiler Economy," 
 p. 23.) 
 
 Suppose that 1 Ib. of H is burned in twice the quantity of air required 
 for complete combustion, or 2 X (8 O + 26.56 N) = 69.12 Ibs. air 
 supplied at 62 F., and that the products of combustion escape at 562 F. 
 The heat lost in the products of combustion will be 
 
 Q Ibs. water heated from 62 to 212 1352 B.T.U. 
 
 Latent heat of 9 Ibs. H 2 O at 212, 9 X 969.7 8727 
 
 Superheated steam, 9 Ibs. X (562 - 212) X 0.48 (sp. ht.) 1512 
 
 Nitrogen, 26.56 X (562 - 62) X 0.2438 3238 
 
 Excess air, 34.56 X (562 - 62) X 0.2375 4104 
 
 Total 18,933 " 
 
 which subtracted from 62,000 gives 43,067 B.T.U. as the net available 
 heating value under the conditions named. 
 
 Heating Value of Compound or Mixed Fuels. The heating value 
 of a solid compound or mixed fuel is the sum of its elementary constituents, 
 and is calculated as follows by Dulong's formula: 
 
 B.T.U. = i[ 14,600 C + 62,000 (H - Q + 4500 SJ ; 
 
 in which C, H, O, and S are respectively the percentages of the several 
 elements. The term H - 1/8 O is called the "available" or "disposable" 
 hydrogen, or that which is not combined with oxygen in the fuel. For 
 all the common varieties of coal, cannel coal and some lignites excepted, 
 the formula is accurate within the limits of error of chemical analyses and 
 calorimetric determinations. 
 
 Heat Absorbed by Decomposition. By the decomposition of a 
 chemical compound as much heat is absorbed or rendered latent as was 
 evolved when the compound was formed. If 1 Ib. of carbon is burned to 
 COz, generating 14,600 B.T.U., and the CO2 thus formed is immediately 
 reduced to CO in the presence of glowing carbon, by the reaction CO2 4- 
 C = 2 CO. the result is the same as if the 2 Ibs. C had been purned directly 
 to 2 CO, generating 2X4450=8900 B.T.U. The 2 Ibs. C burned to CO 3 
 
562 
 
 HEAT. 
 
 would generate 2 X 14,600 = 29,200 B.T.U., the difference, 29 200 - 
 8900 = 20,300 B.T.U., being absorbed or rendered latent in the 2 CO 'or 
 10,150 B.T.U. for each pound of carbon. 
 
 In like manner if 9 Ibs. of water be injected into a large bed of glowing 
 coal, it will be decomposed into 1 Ib. H and 8 Ibs. O. The decomposition 
 will absorb 62,000 B.T.U., cooling the bed of coal this amount, and the 
 same quantity of heat will again be evolved if the H is subsequently 
 burned with a fresh supply of O. The 8 Ibs. of O will combine with 6 Ibs. 
 C, forming 14 Ibs. CO (since CO is composed of 12 parts C to 16 parts O) 
 generating 6 X 4450 = 26,700 B.T.U. , and 6 X 10,150 = 60,900 B.T.U. 
 will be latent in this 14 Ibs. CO, to be evolved later if it is burned to CO 2 
 with an additional supply of 8 Ibs. O. 
 
 SPECIFIC HEAT. 
 
 Thermal Capacity. The thermal capacity of a body between two 
 temperatures To and T\ is the quantity of heat required to raise the tem- 
 perature from To to Ti. The ratio of the heat required to raise the temper- 
 ature of a certain weight of a given substance one degree to that required 
 to raise the temperature of the same weight of water from 62 to 63 F. 
 is commonly called the specific heat of the substance. Some writers 
 object to the term as being an inaccurate use of the words " specific " 
 and " heat." A more correct name would be " coefficient of thermal 
 capacity." 
 
 Determination of Specific Heat. Method by Mixture. The body 
 whose specific heat is to be determined is raised to a known temperature, 
 a,nd is then immersed in a mass of liquid of which the weight, specific 
 heat, and temperature are known. When both the body and the liquid 
 have attained the same temperature, this is carefully ascertained. 
 
 Now the quantity of heat lost by the body is the same as the quantity of 
 heat absorbed by the liquid. 
 
 Let c, w, and t be the specific heat, weight, and temperature of the hot 
 body, and c', w', and t f of the liquid. Let T be the temperature the mix- 
 ture assumes. 
 
 Then, by the definition of specific heat, c X w X (t T) = heat-units 
 lost by the hot body, and cf X w/ X (T t') = heat-units gained by the 
 cold liquid. If there is no heat lost by radiation or conduction, these 
 must be equal, and 
 
 cw (t- 
 
 c'w* (T-n or c 
 
 Electrical Method. This method is believed to be more accurate in 
 many cases than the method by mixture. It consists in measuring the 
 quantity of current in watts required to heat a unit weight of a substance 
 One degree in one minute, and translating ,the result into heat-units. 
 i Watt =0.0569 B.T.U. per minute. 
 
 Specific Heats of Various Substances. 
 
 The specific heats of substances, as given by different authorities show 
 considerable lack of agreement, especially in the case of gases. 
 
 The following tables give the mean specific heats of the substances 
 named according to Regnault. (From Rontgen's Thermodynamics, p. 
 134.) These specific heats are average values, taken at temperatures 
 which usually come under observation in technical application. The 
 actual specific heats of all substances, in the solid or liquid state, increase 
 slowly as the body expands or as the temperature rises. It is probable 
 that the specific heat of a body when liquid is greater than when solid. 
 For many bodies this has been verified by experiment. 
 
 SOLIDS. 
 
 Antimony . 0508 
 
 Copper . 0951 
 
 Gold. 0.0324 
 
 Wrought iron 0. 1138 
 
 Glass 0.1937 
 
 Cast iron 0. 1298 
 
 Lead 0.0314 
 
 Platinum . 0324 
 
 Silver... 0,0570 
 
 Hn 0.0582 
 
 Steel (soft) 0.1165 
 
 Steel (hard) 0.1175 
 
 Zinc . 0956 
 
 Brass . 0939 
 
 Ice : 0.5040 
 
 Sulphur 0.2026 
 
 Charcoal . 2410 
 
 Alumina 0. 1970 
 
 Phosphorus 0. 1887 
 
SPECIFIC HEAT. 
 
 563 
 
 Water 1.0000 
 
 Lead (melted) 0.0402 
 
 Sulphur " 0.2340 
 
 Bismuth " . 0308 
 
 Tin " 0.0637 
 
 Sulphuric acid 0.3350 
 
 LIQUIDS. 
 
 Mercury . 0333 
 
 Alcohol (absolute) . 7000 
 
 Fusel oil 0.5640 
 
 Benzine . 4500 
 
 Ether 0.5034 
 
 GASES. 
 Constant Pressure. 
 
 Air 0.23751 
 
 Oxygen 0.21751 
 
 Hydrogen 3 . 40900 
 
 Nitrogen 0. 24380 
 
 Superheated steam* 0. 4805 
 
 Carbonic acid . 217 
 
 Olefiant gas C 2 H 4 (ethylene). , '. . . 0.404 
 
 Carbonic oxide. . 2479 
 
 Ammonia "..... . 508 
 
 Ether 0.4797 
 
 Alcohol * 0.4534 
 
 Acetic acid 0. 4125 
 
 Chloroform 0. 1567 
 
 In addition to the above, the following are given by other authorities. 
 (Selected from various sources.) 
 
 METALS. 
 
 Platinum, 32 to 446 F.. . . 0.0333 
 (increased .000305 for each 100 F.) 
 
 Cadmium . 0567 
 
 Brass , . 0939 
 
 Copper, 32 to 212 F 0.094 
 
 32 to 572 F 0.1013 
 
 Zinc, 32 to 21 2 F 0.0927 
 
 32 to 572 F 0.1015 
 
 Nickel 0.1086 
 
 Aluminum, F. to melting- 
 point (A. E. Hunt) 0..2185 
 
 Dr.-Ing. P. Oberhoffer, in Zeit. des Vereines Deutscher Ingenieure (Eng. 
 Digest, Sept., 1908), describes some experiments on the specific heat of 
 nearly pure iron. The following mean specific heats were obtained: 
 Temp. F. 500 600 800 1000 1200 1300 
 
 Sp. Ht. 0.1228 0.1266 0.1324 0.1388 0.1462 0.1601 
 Temp. F. 1500 1800 2100 2400 2700 
 
 Sp. Ht. 0.1698 0.1682 0.1667 0.1662 0.1666 
 
 The specific heat increases steadily between 500 and 1200 F. Then It 
 increases rapidly to 1400, after which it remains nearly constant. 
 OTHER SOLIDS. 
 
 Constant Volume. 
 0.16847 
 0.15507 
 2.41226 
 0.17273 
 0.346 
 0.171 
 0.332 
 0.1758 
 0.299 
 0.3411 
 0.399 
 
 Wrought iron (Petit & Dulong). 
 
 32 to 212.. 0.109S- 
 32 to 392.. 0.115 
 32 to 572. . 0.1218 
 32 to 662. . 0.1255 
 Iron at high temperatures. 
 (Pionchon, Comptcs Rendus, 1887.) > 
 
 1382 3 to 1832 F 0.213 
 
 1749' to 1843 F.. . . . 0.218 
 1922 to 2192 F 0.199 
 
 Brickwork and masonry, about . 20 
 
 Marble 0.210 
 
 Chalk 0. 215 
 
 Quicklime 0. 217 
 
 Magnesian limestone 0. 217 
 
 Silica. . % 0. 191 
 
 Corundum 0. 198 
 
 Stones generally 0. 2 to 0. 22 
 
 WOODS. 
 
 Oven dried, 20 varieties, sp. ht. nearly the same for all, average 
 0.327. (U. S. Forest Service, 1911.) 
 
 LIQUIDS. 
 
 Coal 0.20 to 0.241 
 
 Coke 0.203 
 
 Graphite 0. 202 
 
 Sulphate of lime 0. 197 
 
 Magnesia 0. 222 
 
 Soda 0.231 
 
 Quartz 0. 188 
 
 River sand 0. 195 
 
 Alcohol, density 0.793 0.622 
 
 Sulphuric acid, density 1.87. . 0.335 
 
 1.30. . 0.661 
 
 Hydrochloric acid 0. 600 
 
 Olive oil 0. 310 
 
 Benzine . 393 
 
 Turpentine, density 0.872 . . . 472 
 
 Bromine I. Ill 
 
 * See Superheated Steam, page 869. 
 
564 
 
 HEAT. 
 
 GASES. 
 
 At Constant At Constant 
 Pressure. Volume. 
 
 Sulphurous acid 0. 1553 0. 1246 
 
 Light carbureted hydrogen, marsh gas (CH 4 ) . . 5929 . 4683 
 Blast-furnace gases . 2277 ........ 
 
 Specific Heat of Water. 
 
 (Peabody's Steam Tables, from Barnes and 
 Regnault.) 
 
 C. 
 
 F. 
 
 Sp. Ht. 
 
 .c. 
 
 T. 
 
 Sp. Ht. 
 
 c. 
 
 F. 
 
 Sp. Ht. 
 
 c. 
 
 F. 
 
 Sp. Ht. 
 
 
 5 
 
 10 
 
 20 
 25 
 30 
 
 32 
 
 41 
 50 
 
 68 
 77 
 86 
 
 1.0094 
 1.00530 
 1.00230 
 1.00030 
 0.99895 
 0.99806 
 0.99759 
 
 35 
 40 
 45 
 50 
 55 
 60 
 65 
 
 95 
 
 104 
 113 
 
 122 
 131 
 
 140 
 149 
 
 0.99735 
 0.99735 
 0.99760 
 0.99800 
 0.99850 
 99940 
 1.00040 
 
 70 
 75 
 
 80 
 85 
 90- 
 95 
 100 
 
 158 
 167 
 176 
 
 188 
 194 
 203 
 21? 
 
 .00150 
 .00275 
 .00415 
 .00557 
 .00705 
 .00855 
 .01010 
 
 120 
 
 140 
 160 
 180 
 200 
 220 
 
 248 
 284 
 320 
 356 
 392 
 428 
 
 .01620 
 .02230 
 .02850 
 .03475 
 .04100 
 .04760 
 
 Specific Heat of Salt Solution. (Schuller.) 
 
 Per cent salt in solution .... 5 10 15 20 25 
 
 Specific heat 0.9306 0.8909 0.8606 0.8490 0.8073 
 
 Specific Heat of Air. Regnault gives for the mean value at constant 
 pressure 
 
 Between 30 C. and + 10 C 0.23771 
 
 C. ' 100 C 0.23741 
 
 0C. ' 200 C 0.23751 
 
 Hanssen uses 0.1686 for the specific heat of tir it constant volume. 
 The value of this constant has never been found to any degree 'of accuracy 
 by direct experiment. Prof. Wood gives 0.2375 -f- 1.406 = 0.1689. The 
 ratio of the specific heat of a fixed gas at constant pressure to the sp. ht. 
 at constant volume is given as follows by different writers (Eng'g, July 12, 
 1889): Regnault, 1.3953; Moll and Beck, 1.4085; Szathmari, 1.4027; J. 
 Macfarlane Gray, 1.4. The first three are obtained from the velocity of 
 sound in air. The fourth is derived from theory. Prof. Wood says: 
 The value of the ratio for air, as found in the days of La Place, was 1.41, 
 and we have 0.2377 *- 1.41 = 0.1686, the value used by Clausius, Hanssen, 
 and many others. But this ratio is not definitely known. Rankine in 
 his later writings used 1.408, and Tait in a recent work gives 1.404, while 
 some experiments give less than 1.4, and others more than 1.41. Prof. 
 Wood uses 1,406. 
 
 Specific Heat of Gases. Experiments by Mallard and Le Chatelier 
 indicate a continuous increase in the specific heat at constant volume of 
 steam, CO2, and even of the perfect gases, with rise of temperature. The 
 variation is inappreciable at 100 C., but increases rapidly at the high tem- 
 peratures of the gas-engine cylinder. (Robinson's Gas and Petroleum 
 Engines.) 
 
 Thermal Capacity and Specific Heat of Gases. (From Damour'a 
 11 Industrial Furnaces.") The specific heat of a gas at any temperature is 
 the first derivative of the function expressing the thermal capacity. It 
 is not possible to derive from the specific heat of a gas at a given temper- 
 ature, or even from the mean specific heat between and 100 C., the 
 thermal capacity at a temperature above 100 C. The specific heats of 
 gases under constant pressure between and 100 C., given by Regnault, 
 are not sufficient to calculate the quantity of heat absorbed by a gas in 
 heating or radiated in cooling, hence all calculations based on these 
 figures are subject to a more or less grave error. 
 
 The thermal capacities of a molecular volume (22.32 liters) of gases 
 from absolute ( 273 C.) to a temperature T ( = 273 + t) may be 
 expressed by the formula Q = 0.001 aT + 0.000,001 bT z , in which a is a 
 constant, 6.5, for all gases, and b has the following values for different 
 gases: O 2 , N, H 2 , CO, 0.6; H 2 O vapor, 2.9; CO 2 , 3.7; CH 4 , 6.0. The 
 tables on page 565 give the thermal capacities of different gases under 
 varying conditions of pressure, temperature and volume. 
 
EXPANSION BY HEAT. 
 
 565 
 
 SPECIFIC HEATS OF GASES PER KILOGRAM. 
 
 Gases. 
 
 Under Constant 
 Pressure. 
 
 Under Constant 
 Volume. 
 
 Oxygen 
 
 213+ 38X10 ~*t 
 
 150+ 38X10" 6 * 
 
 Nitrogen and Carbon Monoxide. . 
 Hydrogen 
 
 0.243+ 42X10 -t 
 3.400+600X10 ~ & t 
 
 0.171+ 42X10~ 6 * 
 2.400+600X10~ 6 Z 
 
 Water Vapor . ... 
 
 447+324X10 ~ 6 t 
 
 0.335+324X10 ~ 6 t 
 
 Carbon Dioxide 
 
 0.193 + 168X10 ~ 6 t 
 
 0.150 + 168X10- 6 * 
 
 Methane 
 
 0.608+748X10 ~ 6 t 
 
 0.491 +748X10 ~*t 
 
 THERMAL CAPACITIES OF GASES PER KILOGRAM IN CENTIGRADE DEGS. 
 
 Gases. 
 
 Under Constant 
 Pressure. 
 
 Under Constant 
 Volume. 
 
 Oxygen 
 
 213^+ 19X10~ 6 J 2 
 
 150*+ 19X10~ 6 < 2 
 
 Nitrogen and Carbon Monoxide. . 
 Hydrogen 
 
 0.243+ 21 X10- 6 * 2 
 3.400+300X10~ 6 Z 2 
 
 0.171 t + 21 XlO~ 6 t 2 
 2.400<+300X10~ 2 
 
 Water Vapor 
 
 447 + 162XlO~ 6 2 
 
 3352 + 162X10- 6 * 2 
 
 Carbon Dioxide 
 Methane or Marsh Gas 
 
 0.193J+ 84X10- 6 * 2 
 0.608^+374XlO~n 2 
 
 0.150J+ 84X10- 6 * 2 
 0.491 <+374XlO~ 6 * 2 
 
 THERMAL CAPACITIES OF GASES PER KILOGRAM. 
 
 Temperatures. 
 
 2 
 
 N 2 ,CO 
 
 H 2 
 
 H 2 
 
 CO 2 
 
 CH 4 
 
 Degrees Centigrade. 
 200. . 
 
 
 47 
 
 
 
 50 
 
 
 
 700 
 
 
 100 
 
 
 43 1 
 
 
 136.6 
 
 400 
 
 88 
 
 100 
 
 1400 
 
 203 
 
 91 
 
 303 
 
 600. . 
 
 134 
 
 154 
 
 2150 
 
 326 
 
 145 
 
 499.0 
 
 800 
 
 181 
 
 207 
 
 2900 
 
 461 
 
 208 
 
 726 
 
 1000. . 
 
 232 
 
 264 
 
 3700 
 
 609 
 
 277 
 
 982 
 
 1200 
 
 284 
 
 325 
 
 4550 
 
 770 
 
 354 
 
 1269 
 
 1400. . 
 
 334 
 
 383 
 
 5350 
 
 943 
 
 435 
 
 1584 
 
 1600 
 
 391 
 
 445 
 
 6250 
 
 1130 
 
 523 
 
 1931 
 
 1 800 . . 
 
 444 
 
 508 
 
 7100 
 
 1330 
 
 618 
 
 2307 
 
 2000 . . 
 
 503 
 
 575 
 
 8050 
 
 1542 
 
 728 
 
 2712 
 
 2200 . . 
 
 558 
 
 637 
 
 8950 
 
 1751 
 
 840 
 
 3148 
 
 2400 
 
 670 
 
 708 
 
 9900 
 
 1985 
 
 950 
 
 3614 
 
 2600 . . 
 
 681 
 
 777 
 
 10900 
 
 2241 
 
 1070 
 
 4109 
 
 2800 . . 
 
 735 
 
 850 
 
 11900 
 
 2520 
 
 1200 
 
 4635 
 
 3000 
 
 810.0 
 
 921 
 
 12950 
 
 2799 
 
 1355.0 
 
 5190.0 
 
 EXPANSION BY HEAT. 
 
 In the centigrade scale the coefficient of expansion of air per degree 
 is 0.003665 = 1/273; that is, the pressure being constant, the volume 
 of a perfect gas increases 1/273 of its volume at C. for every in- 
 crease in temperature of 1 C. In Fahrenheit units it increases 1/491.6 
 = 0.002034 of its volume at 32 F. for every increase of 1 F. 
 Expansion of Gases by Heat from 32 to 212 F. (Regnault.) 
 
 
 Increase in Volume, 
 Pressure Constant. 
 Volume at 32 Fahr. 
 = 1.0, for 
 
 Increase in Pressure, 
 Volume Constant. 
 Pressure at 32 
 Fahr. = 1.0, for 
 
 100 C. 
 
 1F. 
 
 100 C. 
 
 1F. 
 
 Hydrogen. . 
 
 0.3661 
 0.3670 
 0.3670 
 0.3669 
 0.3710 
 0.3903 
 
 0.002034 
 0.002039 
 0.002039 
 0.002038 
 0.002061 
 0.002168 
 
 0.3667 
 0.3665 
 0.3668 
 0.3667 
 0.3688 
 0.3845 
 
 0.002037 
 0.002036 
 0.002039 
 0.002037 
 0.002039 
 0.002136 
 
 Atmospheric air 
 
 Nitrogen . . . 
 
 Carbon monoxide . . 
 
 Carbon dioxide ". 
 
 Sulphur dioxide 
 
 If the volume is kept constant, the pressure varies directly as the 
 absolute temperature. 
 
5G6 
 
 HEAT. 
 
 Lineal Expansion of Solids at Ordinary Temperature*. 
 
 (Mostly British Board of Trade; from Clark.) 
 
 
 For 
 1Fahr. 
 Length 
 
 For 
 lCent. 
 Length 
 
 Cxpan- 
 sion 
 from 
 32 to 
 212 F. 
 
 Accord- 
 ing to 
 Other 
 Author- 
 ities. 
 
 Aluminum (drawn) . . 
 
 0.00001360 
 0.00001234 
 0.00000627 
 0.00000957 
 0.00001052 
 0.00000306 
 0.00000300 
 0.00000985 
 0.00000975 
 0.00000594 
 0.00000795 
 0.00000887 
 0.00004278 
 0.00000451 
 0.00000499 
 0.00000397 
 0.00000438 
 0.00000498 
 0.00000786 
 0.00000356 
 0.00000648 
 0.00000556 
 0.00001571 
 
 0.00002450 
 .00002221 
 .00001129 
 .00001722 
 .00001894 
 .00000550 
 .00000540 
 r!774 
 1755 
 0.00001070 
 0.00001430 
 0.00001596 
 3.00007700 
 3.00000812 
 0.00000897 
 0.00000714 
 .00000789 
 0.00000897 
 0.00001415 
 0.00000641 
 0.00001166 
 0.00001001 
 0.00002828 
 
 . 002450 
 0.002221 
 3.001129 
 3.001722 
 0.001894 
 0.000550 
 0.005400 
 0.001774 
 0.001755 
 0.001070 
 0.001430 
 0.001596 
 0.007700 
 0.000812 
 0.000897 
 0.000714 
 0.000789 
 0. 000897 
 0.001415, 
 0.00064 
 0.001166 
 0.00100 
 0.00282 
 
 
 Aluminum, (cast) . ... 
 
 1661683 
 0.001868 
 
 Antimony (cryst.) 
 
 
 Brass plat6 
 
 Brick 
 
 Brick (fire) 
 
 
 Bronze (Copper, 17; Tin, 21/ 2 ; Zinc, 1). . 
 
 
 0.001392 
 
 Cement Portland (mixed), pure. . 
 
 Concrete: cement-mortar and pebbles. . 
 
 
 0.001718 
 
 Ebonite 
 
 Glass, English flint 
 
 Glass thermometer ... . 1 . . 
 
 
 
 
 
 
 Granite red dry 
 
 
 
 
 
 
 
 0.001235 
 0.001110 
 
 
 Lead . . 
 
 
 0.002694 
 
 
 0.00000308 
 0.00000786 
 0.00000256 
 0.00000494 
 0.00009984 
 0.00000695 
 0.00001129 
 0.00000922 
 00000479 
 0.00000453 
 0.00000200 
 0.00000434 
 0.00000788 
 00001079 
 0.00000577 
 0.00000636 
 0.00000689 
 0.00000652 
 0.00000417 
 0.00001163 
 0.00000489 
 0.0000027 
 0.0000140 
 0.0000149 
 
 0.00000554 
 0.00001415 
 0.00000460 
 0.00000890 
 0.0001797 
 0.00001251 
 0.00002033 
 0.00001660 
 0.00000863 
 0.00000815 
 0.00000360 
 0.00000781 
 0.00001419 
 0.00001943 
 0.00001038 
 0.00001144 
 0.00001240 
 0.00001174 
 0.00000750 
 0.00002094 
 0.00000881 
 0.00000496 
 0.00002532 
 0.00002692 
 
 0.00055 
 0.00141 
 0.00046 
 0.00089 
 0.01797 
 0.00125 
 0.00203 
 0.00166 
 0.00086 
 0.00081 
 0.00036 
 0.00078 
 0.00141 
 0.00194 
 0.00103 
 0.00114 
 0.00124 
 0.00117 
 0.00075 
 0.00209 
 0.00088 
 0.00049 
 0.00253 
 0.00269 
 
 Marbles, various j to 
 
 
 
 
 Masonry, brick j to 
 
 
 Mercury (cubic expansion) 
 
 0.018018 
 0.001279 
 
 Nickel 
 
 Pewter 
 
 
 
 
 
 Platinum 85% Iridium, 15% 
 
 0.000884 
 
 
 Quartz, parallel to maj. axis, to 40 C 
 Quartz, perpend, to maj. axis, to 40C 
 
 
 
 0.001908 
 
 6!66io79 
 
 Slate 
 
 Steel, cast 
 
 Steel tempered . . . . ... 
 
 
 
 
 Stone (sandstone) Rauville . . 
 
 Tin 
 
 0.001938 
 
 "Wedgwood ware 
 
 Wood, pine 
 
 
 Zinc , 
 
 0.002942 
 
 Zinc. 8. Tin. 1 . . 
 
 Invar (see next page), .000.000.374 to 0.000.000.44 for 1 C. 
 
 Cubical expansion, or expansion of volume = linear expansion X 3. 
 
 Expansion of Steel at High Temperatures. (Charpy and Grenet. 
 Comptes Rendut, 1902.) Coefficients of expansion (for l b C.) of annealed 
 carbon and nickel steels at temperatures at which there is no transformer 
 
ABSOLUTE TEMPERATURE. 
 
 567 
 
 tion of the sieel. The results seem to show that iron and carbide of iron 
 have appreciably the same coefficient of expansion. [See also p. 449.] 
 
 Composition 
 of Steels. 
 
 Mean Coefficients of Expansion 
 from 
 
 Coefficients between 
 
 C 
 
 Mn 
 
 Si 
 
 P 
 
 1.5to 200 
 
 200to500 
 
 500to650 c 
 
 
 
 0.03 
 
 0.01 
 
 0.03 
 
 0.013 
 
 11.8X10-6 
 
 14.3X10-6 
 
 17.0X10~ ( 
 
 '2475X10-6 
 
 880 & 950 
 
 0.25 
 
 0.04 
 
 0.05 
 
 0.010 
 
 11.5 
 
 14.5 
 
 17.5 
 
 23.3 
 
 800 & 950 
 
 0.64 
 
 0.12 
 
 0.14 
 
 0.009 
 
 12.1 
 
 14.1 
 
 16.5 
 
 23.3 
 
 720 & 950 
 
 0.93 
 
 0.10 
 
 0.05 
 
 0.005 
 
 11.6 
 
 14.9 
 
 16.0 
 
 27.5 
 
 
 
 1.23 
 
 0.10 
 
 0.08 
 
 0.005 
 
 11.9 
 
 14.3 
 
 16.5 
 
 33.8 
 
 
 
 1.50 
 
 0.04 
 
 0.09 
 
 0.010 
 
 11.5 
 
 14.9 
 
 16.5 
 
 36.7 
 
 
 
 3.50 
 
 0.03 
 
 0.07 
 
 0.005 
 
 11.2 
 
 14.2 
 
 18.0 
 
 33.3 
 
 
 Nickel Steels. 
 
 Mean Coefficients of Expansion from 
 
 Ni 
 
 C 
 
 Mn 
 
 15 to 100 
 
 100 
 
 to 200 
 
 200 to 400 
 
 400 to 600 
 
 600 to 900 
 
 26.9 
 
 0.35 
 
 0.30 
 
 1 1.0X10~ 6 
 
 18.0X10-6 
 
 18.7X10~6 
 
 22.0X10-6 
 
 23.0X10-6 
 
 28.9 
 
 0.35 
 
 0.36 
 
 10.0 
 
 21.3 
 
 
 1< 
 
 ).0 
 
 20.0 
 
 22.7 
 
 30.1 
 
 0.35 
 
 0.34 
 
 9.5 
 
 14.0 
 
 19.5 
 
 19.0 
 
 21.3 
 
 34.7 
 
 0.36 
 
 0.36 
 
 2.0 
 
 2.f 
 
 
 1 
 
 .75 
 
 19.5 
 
 20.7 
 
 36.1 
 
 0.39 
 
 0.39 
 
 1.5 
 
 1.5 
 
 11.75 
 
 17.0 
 
 20.3. 
 
 32.8 
 
 0.29 
 
 0.66 
 
 8.0 
 
 14.C 
 
 I 
 
 If 
 
 $.0 
 
 21.5 
 
 22.3 
 
 3?. 8 
 
 0.31 
 
 0.69 
 
 2.5 
 
 2.5 
 
 12.5 
 
 18.75 
 
 19.3 
 
 37.4 
 
 0.30 
 
 0.69 
 
 2.5 
 
 1.5 
 
 8.5 
 
 19.75 
 
 18.3 
 
 25.4 
 
 1.01 
 
 0.79 
 
 12.5 
 
 18.5 
 
 
 1< 
 
 >.75 
 
 21.0 
 
 35.0 
 
 29.4 
 
 0.99 
 
 0.89 
 
 11.0 
 
 12.5 
 
 19.0 
 
 20.5 
 
 31.7 
 
 34.5 
 
 0.97 
 
 0.84 
 
 3.0 
 
 3.5 
 
 13.0 
 
 18.75 
 
 26.7 
 
 Invar, an alloy of iron with 36 per cent of nickel, has a smaller coeffi- 
 cient of expansion with the ordinary atmospheric changes of tempera- 
 ture than any other metal or alloy known. This alloy is sold under the 
 name of "Invar," and is used for scientific instruments, pendulums of 
 clocks, steel tape-measures for survey work, etc. The Bureau of Stand- 
 ards found its coefficient of expansion to range from 0.000 000 374 to 
 0.00000044 for 1 C.,qr about 1/28 of that of steel. For all surveys 
 except in the most precise geodetic work a tape of invar may be used 
 without correction for temperature. (Eng. News, Aug. 13, 1908.) 
 
 Platinite, an alloy of iron with 42 per cent of nickel, has the same 
 coefficient of expansion and contraction at atmospheric temperatures as 
 has glass. It can, therefore, be used for the manufacture of armored 
 glass, that is, a plate of glass into which a network of steel wire has toeen 
 rolled, and which is used for fire-proofing, etc. It can also be used in- 
 stead of platinum for the electric connections passing through the glass 
 plugs in the base of incandescent electric lights. (Stoughton's "Metal- 
 lurgy of Steel.") 
 
 Expansion of Liquids from 32 to 212 F. Apparent expansion 
 
 in glass (Clark). 
 
 Water 
 
 Water saturated with salt. 
 
 Mercury 
 
 Alcohol 
 
 Volume at 212 
 
 0466 
 05 
 
 0182 
 11 
 
 1.11 
 1.08 
 1.07 
 
 volume at 32 being 1: 
 
 Nitric acid 
 
 Olive and linseed oils 
 
 Turpentine and ether 
 
 Hydrochloric and sulphuric 
 
 acids . 1.06 
 
 For water at various temperatures, see Water. 
 For air at various temperatures, see Air. 
 
 ABSOLUTE TEMPERATURE ABSOLUTE ZERO. 
 
 The absolute zero of a gas is a theoretical consequence of the law of 
 expansion by heat, assuming that it is possible to continue the cooling of 
 a perfect gas until its volume is diminished to nothing. 
 
568 HEAT. 
 
 The volume of a perfect gas increases 1/273-1 of its volume at C. for 
 every increase of temperature of 1 C., and decreases 1/273-1 of its 
 volume at C . for every decrease of temperature of 1 C . At - 273 . 1 C . . 
 the volume would then be reduced to nothing. This point, - 273. 1 C. = 
 459.6 F., or 491.6 F. below the temperature of melting ice, is called 
 the absolute zero, and absolute temperatures are measured on either the 
 Centigrade or the Fahrenheit scale, from this zero. The freezing-point, 
 32 F., corresponds to 491.6 F. absolute. If p be the pressure and VQ 
 the volume of a perfect gas at 32 F. = 491.6 absolute, = To, and p the 
 pressure and v the volume of the same weight of gas at any other 
 absolute temperature T, then 
 
 pv __T_ = < + 459.6. pv poVo = _ 
 poVo To~ 491.6 ' T = To 
 
 A cubic foot of dry air at 32 F. at the sea level (barometer = 29.921 
 in. of mercury) weighs 0.080728 Ib. The volume of one pound is 
 1/0.080728 = 12.387 cu. ft. The pressure is 2116.3 Ib. per sq. ft. 
 D - P< - 2116.3 X 12.387 _ 26,214 _ KQ , 
 -~ZV~ 491.6 ~ = 
 
 LATENT HEATS OF FUSION AND EVAPORATION. 
 
 Latent Heat means a quantity of heat which has disappeared, having 
 been employed to produce some change other than elevation of tempera- 
 ture. By exactly reversing that change, the quantity of heat which 
 has disappeared is reproduced. Maxwell defines it as the quantity of 
 heat which must be communicated to a body in a given state in order to 
 convert it into another state without changing its temperature. 
 
 Latent Heat of Fusion. When a body passes from the solid to the 
 liquid state, its temperature remains stationary, or nearly stationary, at 
 a certain melting-point during the whole operation of melting; and in 
 order to make that operation go on, a quantity of heat must be trans- 
 ferred to the substance melted, being a certain amount for each unit 
 of weight of the substance. This quantity is called the latent heat of 
 fusion. 
 
 When a body passes from the liquid to the solid state, its temperature 
 remains stationary or nearly stationary during the whole operation of 
 freezing; a quantity of heat equal to the latent heat of fusion is pro- 
 duced in the body and rejected into the atmosphere or other surround- 
 ing bodies. 
 
 The following are examples in British thermal units per pound, as 
 given in Landolt and Bernstein's " Physikalische-Chemische Tabellen" 
 (Berlin, 1894). 
 
 Miih5tanr>p<3 Latent Heat QnhtanrPs Latent Heat 
 
 ^stances. o f Fusion. ubstances. O f Fusion. 
 
 Bismuth ......... 22.75 Silver ........... 37.93 
 
 Cast iron, gray ... 41.4 Beeswax ......... 76.14 
 
 Cast iron, white. . . 59.4 Parafflne ......... 63.27 
 
 Lead ............ 9.66 Spermaceti ....... 66.56 
 
 Tin .............. 25.65 Phosphorus ...... 9.06 
 
 Zinc ............. 50.63 Sulphur .......... 16.86 
 
 The latent heat of fusion of ice is generally taken at 144 B.T.U. per 
 Ib. The U. S. Bureau of Standards (1915) gives it as 79.76 20-calories 
 per gram = 143.57 B.T.U. per Ib. 
 
 Latent Heat of Evaporation. When a body passes from the 
 solid or liquid to the gaseous state, its temperature during the operation 
 remains stationary at a certain boiling-point, depending on the pressure of 
 the vapor produced; and in order to make the evaporation go on, a 
 quantity of heat must be transferred to the substance evaporated, whose 
 amount for each unit of weight of the substance evaporated depends on 
 the temperature. That heat does not raise the temperature of the sub- 
 stance, but disappears in causing it to assume the gaseous state, and it is 
 called the latent heat of evaporation. 
 
 When a body passes from the gaseous state to the liquid or solid state. 
 its temperature remains stationary, during that operation, at the boiling- 
 point corresponding to the pressure of the vapor : a quantity of heat 
 equal to the latent heat of evaporation at that temperature is produced 
 
EVAPORATION AND DRYING. 569 
 
 in the body; and in order that the operation of cond'ensation may go on, 
 that heat must be transferred from the body condensed to some other 
 body. 
 
 The following are examples of the latent heat of evaporation in British 
 thermal units, of one pound of certain substances, when the pressure of 
 the vapor is one atmosphere of 14.7 Ibs. on the square inch: 
 
 Boiling-point under Latent Heat in 
 
 one atm. Fahr. British units. 
 
 Water 212.0 965.7 (Regnault). 
 
 Alcohol..; 172.2 364.3 (Andrews). 
 
 Ether 95.0 162.8 
 
 Bisulphide of carbon 114.8 156.0 
 
 The latent heat of evaporation of water at a series of boiling-points ex- 
 tending from a few degrees below its freezing-point up to about 375 
 degrees Fahrenheit has been determined experimentally by M. Regnault. 
 The results of those experiments are represented approximately by the 
 formula, in British thermal units per pound, 
 
 I nearly = 1091.7 - 0.7 (t - 32) = 965.7 - 0.7 (t - 212). 
 
 Henning (Ann. der Physik, 1906) gives for t from to 100 C. 
 
 Forl kg., 1= 94.210 (365-T C.) 0.31249. 
 
 Forl lb., 1 = 141. 124 (689-2 F.) 0.31249. 
 
 The last formula gives for the latent heat at 212 F., 969.7 B.T.U. 
 
 The Total Heat of Evaporation is the sum of the heat which dis- 
 appears in evaporating one pound of a given substance at a given tem- 
 perature (or latent heat of evaporation) and of the heat required to raise its 
 temperature, before evaporation, from some fixed temperature up to the 
 temperature of evaporation. The latter part of the total heat is called the 
 sensible heat. 
 
 In the case of water, the experiments of M. Regnault show that the 
 total heat of steam from the temperature of melting ice increases at a 
 uniform rate as the temperature of evaporation rises. The following is 
 the formula in British thermal units per pound: 
 
 h = 1091.7 + 0.305 (t - 32). 
 
 H. N. Davis (Trans. A. S. M. E., 1908) gives, in British units, 
 h -1150 +0.3745 (t- 21 2) -0.000550 (J-212)*. 
 
 For the total heat, latent heat, etc., of steam at different pressures, see 
 table of the Properties of Saturated Steam. For tables of total heat, 
 latent heat, and other properties of steams of ether, alcohol, acetone, 
 chloroform, chloride of carbon, and bisulphide of carbon, see ROntgen's 
 Thermodynamics (Dubois's translation). For ammonia and sulphur 
 dioxide, see Wood's Thermodynamics; also, tables under Refrigerating 
 Machinery, in this book. 
 
 EVAPORATION AND DRYING. 
 
 In evaporation, the formation of vapor takes place on the surface; in 
 boiling, within the liquid: the former is a slow, the latter a quick, method 
 of evaporation. 
 
 If we bring an open vessel with water under the receiver of an air-pump 
 and exhaust the air, the water in the vessel will commence to boil, and if we 
 keep up the vacuum the water will actually boil near its freezing-point. 
 The formation of steam in this case is due to the heat which the water 
 takes out of the surroundings. 
 
 Steam formed under pressure has the same temperature as the liquid in 
 which it was formed, provided the steam is kept under the same pressure. 
 
 By properly cooling the rising steam from boiling water, as in the mul- 
 tiple-effect evaporating systems, we can regulate the pressure so that the 
 water boils at low temperatures. 
 
 Evaporation of Water in Reservoirs. Experiments at the Mount 
 Hope Keservoir, Rochester, N. Y., in 1891, gave the following results: 
 
 July. Aug. Sept. Oct. 
 
 Mean temperature of air in shade 70.5 70.3 68.7 53.3 
 
 44 water in reservoir. .. 68.2 70.2 66.1 54.4 
 
 " humidity of air, per cent 67.0 74.6 75.2 74.7 
 
 Evaporation in inches during month 5.59 4.93 4.05 3.23 
 
 Rainfall in inches during month 3 . 44 2 , 95 1 . 44 2,16 
 
570 HEAT. 
 
 Evaporation of Water from Open Channels. (Flynn's Irrigation 
 Canals and Flow of Water.) Experiments from 1881 to 1885 in Tulare 
 County, California, showed an evaporation from a pan in the river" 
 equal to an average depth of i/s in. per day throughout the year. 
 
 When the pan was in the air the average evaporation was less than 
 3/i6 in. per day. The average for the month of August was 1/3 in. per 
 day, and for March and April 1/12 in. per day. Experiments in Colorado 
 show that evaporation ranges from 0.088 to 0.16 in. per day during 
 the irrigating season. 
 
 In Northern Italy the evaporation was from 1/12 to 1/9 inch per day 
 while in the south, under the influence of hot winds, it was from 1/e 
 to l /5 inch per day. 
 
 In the hot season in Northern India, with a decidedly hot wind blow- 
 ing, the average evaporation was 1/2' inch per day. The evaporation 
 increases with the temperature of the water. 
 
 Evaporation by the Multiple System. A multiple effect is a series 
 of evaporating vessels each having a steam chamber, so connected that 
 the heat of the steam or vapor produced in the first vessel heats the 
 second, the vapor or steam produced in the second heats the third, and 
 so on. The vapor from the last vessel is condensed in a condenser. 
 Three vessels are generally used, in which case the apparatus is called 
 a Triple Effect. In evaporating in a triple effect the vacuum is gradu- 
 ated so that the liquid is boiled at a constant and low temperature. 
 
 A series distilling apparatus of high efficiency is described by W.F. 
 M. Goss in Trans. A. S. M. E., 1903. It has seven chambers in series, 
 and is designed to distill 500 gallons of water per hour with an effi- 
 ciency of approximately 60 Ibs. of water per pound of coal. 
 
 Tests of Yaryan six-effect machines have shown as high as 44 Ibs. of 
 water evaporated per pound of fuel consumed. Mach'y, April, 1905. 
 A description of a large distilling apparatus, using three 125-H.P. boilers 
 and a Lillie triple effect, with record of tests, is given in Eng. Ncu-s. 
 Mar. 29, 1900, and in Jour. Am. Soc'y of Naval Engineers, Feb., 1900. . 
 
 Tests of heating and evaporating apparatus used in sugar houses, " 
 including calandrias, multiple effects, vacuum pans, and condensers, 
 are described by E. W. Kerr in a 178-page pamphlet, Bulletin 149 <f 
 the Agricultural Experiment Station of the Louisiana State University, 
 August, 1914. 
 
 Resistance to Boiling. Brine. (Rankine.) The presence in a 
 liquid of a substance dissolved in it (as salt in water) resists ebullition, and 
 raises the temperature at which the liquid boils, under a given pressure; but 
 unless the dissolved substance enters into the composition of the vapor, 
 the relation between the temperature and pressure of saturation of the 
 vapor remains unchanged. A resistance to ebullition is also offered by a 
 vessel of a material which attracts the liquid (as when water boils in a 
 glass vessel), and the boiling take place by starts. To avoid the errors 
 which causes of this kind produce in the measurement of boiling-points, 
 it is advisable to place the thermometer, not in the liquid, but in the 
 vapor, which shows the true boiling-point, freed from the disturbing 
 effect of the attractive nature of the vessel. The boiling-point of saturated 
 brine under one atmosphere is 226 F., and that of weaker brine is higher 
 than the boiling-point of pure water by 1.2 F., for each 1/32 of salt that 
 the water contains. Average sea-water contains 1/32; and the brine in 
 marine boilers is not suffered to contain more than from 2/33 to 3/ 32 . 
 
 Methods of Evaporation Employed in the Manufacture of Salt* 
 (F. E. Engelhardt, Chemist On9ndaga Salt Springs; Report for 1889.) 
 1. Solar heat solar evaporation. 2. Direct fire, applied to the heat- 
 ing surface of the vessels containing brine kettle and pan methods. 
 3. The steam-grainer system steam-pans, steam-kettles, etc. 4. Use 
 of steam and a reduction of the atmospheric pressure over the boiling 
 brine vacuum system. 
 
 When a saturated salt solution boils, it is immaterial whether it is done 
 under ordinary atmospheric pressure at 228 F., or under four atmospheres 
 with a temperature of 320 F., or in a vacuum under Vio atmosphere, the 
 result will always be a fine-grained salt. 
 
 The fuel consumption is stated to be as follows: By the kettle method, 
 40 to 45 bu. of salt evaporated per ton of fuel, anthracite dust burned on 
 perforated grates; evaporation, 5.53 Ibs. of water per pound of coal, By 
 
EVAPORATION AND DHYING. 
 
 571 
 
 the pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single 
 effect, 86 bu. per ton of anthracite dust (2000 Ibs.). With a double 
 effect nearly double that amount can be produced. 
 
 Solubility of Common Salt in Pure Water. (Andreae.) 
 
 Temp, of brine, F 32 50 86 104 140 176 
 
 100 parts water dissolve parts. . 35.63 35.69 36.03 36.32 37.06 38.00 
 100 parts brine contain salt 26.27 26.30 26.49 26.64 27.04 27.54 
 
 According to Poggial, 100 parts of water dissolve at 229.66 F., 40.35 
 parts of salt, or in per cent of brine, 28.749. Gay-Lussac found that at 
 229.72 F., 100 parts of pure water would dissolve 40.38 parts of salt, in 
 per cent of brine, 28.764 parts. 
 
 The solubility of salt at 229 F. is only 2.5% greater than at 32. Hence 
 we cannot, as in the case 9f alum, separate the salt from the water by 
 allowing a saturated solution at the boiling-point to cool to a lower 
 temperature. 
 
 Strength of Salt Brines. The following table is condensed from 
 one given in U. S. Mineral Resources for 1888, on the authority of Dr. 
 Engelhardt. 
 
 Relations between Salinometer Strength, Specific Gravity, Solid 
 Contents, etc., of Brines of Different Strengths. 
 
 
 
 
 
 "8 
 
 fl.2 
 
 i 
 
 O 0) 
 
 11 
 
 3oi 
 
 _. a*: 
 
 o _. 
 
 1 
 
 
 
 
 C 09 
 :" 
 
 S | 
 
 c3 
 
 
 
 
 ^_ W QJ 
 
 'd *^_^ pj 
 
 Q 
 
 1;| 
 
 *rl 
 
 8 
 
 Pj 
 
 ** 
 
 
 " 
 
 c*S 
 
 "cl -2"c3 
 
 ^ 0*0 
 
 *^ 
 
 p 
 
 2 
 
 ' 
 
 i 
 
 < 
 
 "^*o 
 
 "E< 
 
 ^ M 
 
 1 ' 
 
 *c3.t2 Q 
 
 1 
 
 -1 
 
 g 
 
 N 
 
 3, 
 
 s'g 
 
 go 
 
 ,Q 4> 
 
 g|*8 
 
 l*a| 
 
 "8*1 
 
 3 
 
 *? 
 
 o 
 
 I 
 
 52 
 
 ' c 
 
 s| 
 
 -S o-l 
 
 *s S"* * 
 
 Si's 
 
 .a 
 
 | 
 
 'i 
 
 jj 
 
 .* c .2 
 
 3 o 
 
 ^0 o3 
 
 &5 
 
 'l^f'-S 
 
 "w 
 
 "3 
 
 03 
 
 & 
 
 5 
 
 K? 1 ^ 
 
 O *g C 
 
 13 o 
 
 o t* 
 
 Q ^ e3 c3 
 
 53 S 
 
 GO 
 
 PQ 
 
 2 
 
 PH 
 
 ^ "^ 
 
 PH "" 
 
 o 
 
 Pn 
 
 J 
 
 09 
 
 1 
 
 0.26 
 
 .002 
 
 0.265 
 
 8.347 
 
 0.022 
 
 2,531 
 
 21,076 
 
 3,513 
 
 0.569 
 
 2 
 
 0.52 
 
 .003 
 
 0.530 
 
 8.356 
 
 0.044 
 
 1,264 
 
 10,510 
 
 1,752 
 
 1.141 
 
 4 
 
 1.04 
 
 .007 
 
 1.060 
 
 8.385 
 
 0.088 
 
 629.7 
 
 5,227 
 
 871.2 
 
 2.295 
 
 6 
 
 1.56 
 
 .010 
 
 1.590 
 
 8.414 
 
 0.133 
 
 418.6 
 
 3,466 
 
 577. / 
 
 3.462 
 
 8... 
 
 2.08 
 
 .014 
 
 2.120 
 
 8.447 
 
 0.179 
 
 312.7 
 
 2,585 
 
 430.9 
 
 4.641 
 
 10 
 
 2.60 
 
 .017 
 
 2.650 
 
 8.472 
 
 0.224 
 
 249.4 
 
 2,057 
 
 342.9 
 
 5.833 
 
 12.... 
 
 3.12 
 
 .021 
 
 3.180 
 
 8.506 
 
 0.270 
 
 207.0 
 
 1,705 
 
 284.2 
 
 7.038 
 
 14 
 
 3.64 
 
 .025 
 
 3.710 
 
 8.539 
 
 0.316 
 
 176.8 
 
 1,453 
 
 242.2 
 
 8.256 
 
 16.... 
 
 4.16 
 
 .028 
 
 4.240 
 
 8.564 
 
 0.364 
 
 154.2 
 
 1,265 
 
 210.8 
 
 9.488 
 
 18 
 
 4.68 
 
 .032 
 
 4.770 
 
 8.597 
 
 0.410 
 
 136.5 
 
 1,118 
 
 186 3 
 
 10.73 
 
 20 
 
 5.20 
 
 .035 
 
 5.300 
 
 8.622 
 
 0.457 
 
 122.5 
 
 1,001 
 
 176.8 
 
 11.99 
 
 30 
 
 7.80 
 
 .054 
 
 7.950 
 
 8.781 
 
 0.698 
 
 80.21 
 
 648.4 
 
 108.1 
 
 18.51 
 
 40 
 
 10.40 
 
 .073 
 
 10.600 
 
 8.939 
 
 0.947 
 
 59.09 
 
 472.3 
 
 78.71 
 
 25.41 
 
 50 
 
 13.00 
 
 .093 
 
 13.250 
 
 9.105 
 
 1.206 
 
 46.41 
 
 366.6 
 
 61.10 
 
 32.73 
 
 60 
 
 15.60 
 
 .114 
 
 15.900 
 
 9.280 
 
 1.475 
 
 37.94 
 
 296.2 
 
 49.36 
 
 40.51 
 
 70 
 
 18.20 
 
 .136 
 
 18.550 
 
 9 464 
 
 1.755 
 
 31.89 
 
 245.9 
 
 40.98 
 
 48.80 
 
 80... 
 
 20.80 
 
 .158 
 
 21.200 
 
 9.647 
 
 2.045 
 
 27.38 
 
 208.1 
 
 34.69 
 
 57.65 
 
 90 
 
 23.40 
 
 1.182 
 
 23.850 
 
 9.847 
 
 2.348 
 
 23.84 
 
 178.8 
 
 29.80 
 
 67.11 
 
 100 
 
 26.00 
 
 .205 
 
 26.500 
 
 10.039 
 
 2.660 
 
 21.04 
 
 155 3 
 
 25.88 
 
 77 26 
 
 Solubility of Sulphate of Lime in Pure Water. (Marignac.) 
 Temperature F. degrees..^ 32 64.5 89.6 100.4 105.8 127.4 186.8 212 
 
 371 368 370 375 417 452 
 
 470 466 468 474 528 572 
 
 Parts water to dissolve!, , ,- 
 1 part gypsum 410 
 
 Parts water to dissolve 
 part anhydrous CaSO* 
 
 s.. 32 
 lve }415 
 
 3 U-or 
 
 34 r- 
 
 In salt brine sulphate of lime is much more soluble than in pure water. 
 In the evaporation of salt brine the accumulation of sulphate of lime tends 
 
572 HEAT. 
 
 to stop the operation, and it must be removed from the pans to avoid 
 waste of fuel. The average strength of brine in the New York salt 
 districts in 1889 was 69.38 degrees of the salinometer. 
 
 Concentration of Sugar Solutions.* ( From " Heating and Con- " 
 centrating Liquids by Steam," by John G.Hudson; The Engineer, June 13, 
 1890.) In the early stages of the process, when the liquor is of low 
 density, the evaporative duty will be high, say two to three (British) 
 gallons per square foot of heating surface with 10 Ibs. steam pressure, 
 but will gradually fall to an almost nominal amount as the final stage is 
 approached. As a generally safe basis for designing, Mr. Hudson takes 
 an evaporation of one gallon per hour for each square foot of gross heating 
 surface, with steam of the pressure of about 10 Ibs. 
 
 As examples of the evaporative duty of a vacuum pan when performing 
 the earlier stages of concentration, during which all the heating surface 
 can be employed, he gives the following: 
 
 COIL VACUUM PAN. 4 3 Ain. copper coils, 528 square feet of surface; 
 steam in coils, 15 Ibs.; temperature in pan, 141 to 148; density of feed, 
 2o Baume*, and concentrated to 31 Baume*. 
 
 First Trial. Evaporation at the rate of 2000 gallons per hour = 3.8 
 gallons per square foot ; transmission, 376 units per degree of difference of 
 temperature. 
 
 Second Trial. Evaporation at the rate of 1503 gallons per hour = 
 2.8 gallons per square foot ; transmission, 265 units per degree. 
 
 As regards the total time needed to work up a charge of massecuite from 
 liquor of a given density, the following figures, obtained by plotting the 
 results from a large number of pans, form a guide to practical working. 
 The pans were all of the coil type, some with and some without jackets, 
 the gross heating surface probably averaging, and not greatly differing 
 from, 0.25 square foot per gallon capacity, and the steam pressure 10 Ibs. 
 per square inch. Both plantation and refining pans are included, making 
 various grades of sugar: 
 
 Density of feed (degs. Baume') 10 15 20 25 30 
 
 Evaporation required per gallon masse- 
 cuite discharged 6.1233.62.261.5 .97 
 
 Average working hours required per charge . 12. 9. 6.5 5. 4. 
 
 Equivalent average evaporation per hour 
 per square foot of gross surface, assum- 
 ing 0.25 sq. ft. per gallon capacity 2.04 1.61.391.2 0.97 
 
 Fastest working hours required per charge . 8.5 5.53.8 2. 75 2.0 
 
 Equivalent average evaporation per hour 
 
 per square foot 2.88 2.62.382.181.9 
 
 The quantity of heating steam needed is practically the same in vacuum 
 as in open pans. The advantages proper to the vacuum system are pri- 
 marily the reduced temperature of boiling, and incidentally the possibility 
 of using heating steam of low pressure. 
 
 In a solution of- sugar in water, each pound of sugar adds to the volume 
 of the water to the extent of 0.061 gallon at a low density to 0.0638 gallon 
 at high densities. 
 
 A Method of Evaporating by Exhaust Steam is described by 
 Albert Stearns in Trans. A. S. M. E., vol. viii. A pan 17' 6" X 11' X I' 6. 
 fitted with cast-iron condensing pipes of about 250 sq. ft. of surface, 
 evaporated 120 gallons per hour from clear water, condensing only about 
 one-half of the steam supplied by a plain slide-valve engine of 14" X 32" 
 cylinder, making 65 revs, per min., cutting off about two-thirds stroke, 
 with steam at 75 Ibs. boiler pressure. 
 
 It was found that keeping the pan-room warm and letting only sufficient 
 air in to carry the vapor up out of a ventilator adds to its efficiency, as 
 the average temperature of the water in the pan was only about 165 F. 
 
 Experiments were made with coils of pipe in a small pan, first with no 
 agitator, then with one having straight blades, and lastly with troughed 
 blades; the evaporative results being about the proportions of one, two, 
 and three respectively. 
 
 In evaporating liquors whose boiling-point is 220 F.. or much above 
 that of water, it is found that exhaust steam can do but little more than 
 
 * For other sugar data, see Bagasse as Fuel, under Fuel. 
 
EVAPORATION AND DRYING. 573 
 
 bring them up to saturation strength, but on weak liquors, sirups, glues, 
 etc., it should be very useful. 
 
 Drying in Vacuum. An apparatus for drying grain and other sub- 
 stances in vacuum is described by Mr. Emil Passburg in Proc.Inst. Mech. 
 Engrs., 1889. The three essential lequirements for a successful and eco- 
 nomical process of drying are: 1. Cheap evaporation of the moisture; 
 2. Quick drying at a low temperature; 3. Large capacity of the apparatus, 
 
 The removal of the moisture can be effected in either of two ways: either 
 by slow evaporation, or by quick evaporation that is, by boiling. 
 
 Slow Evaporation. The principal idea carried into practice in machines 
 acting by slow evaporation is to bring the wet substance repeatedly into 
 contact with the inner surfaces of the apparatus, which are heated by 
 steam, while at the same time a current of hot air is also passing througk 
 the substances for carrying off the moisture. This method requires much 
 heat, because the hot-air current has to move at a considerable speed in 
 order to shorten the drying process as much as possible; consequently a 
 great quantity of heated air passes through and escapes unused. As a 
 carrier of moisture hot air cannot in practice be charged beyond half its full 
 saturation; and it is in fact considered a satisfactory result if even this 
 proportion be attained. A great amount of heat is here produced which is 
 not used; while, with scarcely half the cost for fuel, a much quicker 
 removal of the water is obtained by heating it to the boiling-point. 
 
 Quick Evaporation by Boiling. This does not take place until the 
 water is brought up to the boiling-point and kept there, namely, 212 F. t 
 under atmospheric pressure. The vapor generated then escapes freely. 
 Liquids are easily evaporated in this way, because by their motion conse- 
 quent on boiling the heat is continuously conveyed from the heating sur- 
 faces through the liquid, but it is different with solid substances, and 
 many more difficulties have to be overcome, because convection of the 
 heat ceases entirely in solids. The substance remains motionless, and 
 consequently a much greater quantity of heat is required than with 
 liquids for obtaining the same results. 
 
 Evaporation in Vacuum. All the foregoing disadvantages are avoided 
 If the boiling-point of water is lowered, that is, if the evaporation is carried 
 out under vacuum. 
 
 This plan has been successfully applied in Mr. Passburg's vacuum drying 
 apparatus, which is designed to evaporate large quantities of water con- 
 tained in solid substances. 
 
 The drying apparatus consists of a top horizontal cylinder, surmounted 
 by a charging vessel at one end, and a bottom horizontal cylinder with a 
 discharging vessel beneath it at the same end. Both cylinders are 
 incased in steam-jackets heated by exhaust steam. In the top cylinder 
 works a revolving cast-iron screw with hollow blades, which is also heated 
 by exhaust steam. . The bottom cylinder contains a revolving drum of 
 tubes, consisting of one large central tube surrounded by 24 smaller ones, 
 all fixed in tube-plates at both ends; this drum is heated by live steam 
 direct from the boiler. The substance to be dried is fed into the charg- 
 ing vessel through two manholes, and is carried along the top cylinder 
 by the screw creeper to the back end, where it drops through a valve 
 into the bottom cylinder, in which it is lifted by blades attached to the 
 drum and travels forward in the reverse direction; from the front end of 
 the bottom cylinder it falls into a discharging vessel through another 
 valve, having by this time become dried. The vapor arising during the 
 process is carried off by an air-pump, through a dome and air-valve on 
 the top of the upper cylinder, and also through a throttle-valve on 
 the top of the lower cylinder; both of these valves are supplied with 
 strainers. 
 
 As soon as the discharging vessel is filled with dried material the valve 
 connecting it with the bottom cylinder is shut, and the dried charge taken 
 out without impairing the vacuum in the apparatus. When the charging 
 vessel requires replenishing, the intermediate valve between the two cylin- 
 ders is shut, and the charging vessel filled with a fresh supply of wet mate- 
 rial; the vacuum still remains unimpaired in the bottom cylinder, and has 
 to be restored only in the top cylinder after the charging vessel has been 
 closed again. 
 
 . In this vacuum the boiling-point of the water contained in the wet mate- 
 rial is brought down as low as 110 F. The difference between tnis tern* 
 
574 HEAT. 
 
 perature and that of the heating surfaces is ampiy sufficient for obtaining 
 good results from the employment of exhaust steam for heating all the 
 surfaces except the revolving drum of tubes. The water contained in 
 the solid substance to be dried evaporates as soon as the latter is heated 
 to about 110 F., and as long as there is any moisture to be removed the 
 solid substance is not heated above this temperature. 
 
 Wet grains from a brewery or distillery, containing from 75% to 78% of 
 water, have by this drying process been converted from a worthless incum- 
 brance into a valuable fo9d-stuff. The water is removed by evaporation 
 only, no previous mechanical pressing being resorted to. 
 
 At Guinness's brewery in Dublin two of these machines are employed. 
 In each of these the top cylinder is 20 ft. 4 in. long and 2 ft. 8 in. diam., 
 and the screw working inside it makes 7 revs, per min.; the bottom 
 cylinder is 19 ft. 2 in. long and 5 ft. 4 in. diam., and the drum of the tubes 
 inside it makes 5 revs, per min. The drying surfaces of the two cylinders 
 amount together to a total area of about 1000 sq. ft., of which about 40% 
 is heated by exhaust steam direct from the boiler. There is only one air- 
 pump, which is made large enough for three machines; it is hori- 
 zontal, and has only one air-cylinder, which is double-acting, 173/4 in. 
 diam. and 173/4 in. stroke; and it is driven at about 45 revs, per min. 
 As the result of about eight months' experience, the two machines 
 have been drying the wet grains from about 500 cwt. of malt per day of 
 24 hours. 
 
 Roughly speaking, 3 cwt. of malt gave 4 cwt. of wet grains, and the 
 latter yield 1 cwt. of dried grains; 500 cwt. of malt will therefore yield 
 about 670 cwt. of wet grains, or 335 cwt. per machine. The quantity of 
 water to be evaporated from the wet grains is from 75% to 78% of their 
 total weight, or, say, about 512 cwt. altogether, being 256 cwt. per 
 machine. 
 
 Driers and Drying. 
 (Contributed by W. B. Ruggles, 1909.) 
 
 Materials of different physical and chemical properties require different 
 types of drying apparatus. It is therefore necessary to classify mate- 
 rials into groups, as below, and design different machines for each 
 grpup. 
 
 Group A: Materials which may be heated to a high temperature and 
 are not injured by being in contact with products of combustion. These 
 include cement rock, sand, gravel, granulated slag, clay, marl, chalk, ore, 
 graphite, asbestos, phosphate rock, slacked lime, etc. 
 
 The most simple machine for drying these materials is a single revolving 
 shell with lifting flights on the inside, the shell resting on bearing wheels 
 and having a furnace at one end and a stack or fan at the other. The 
 advantage of this style of machine is its low cost of installation and the 
 small number of parts. The disadvantages are great cost of repairs and 
 excessive fuel consumption, due to radiation and high temperature of the 
 stack gases. If the material is fed from the stack and towards the furnace 
 end, the shell near the furnace gets red-hot, causing excessive radiation and 
 frequent repairs. Should the feed be reversed the exhaust temperature 
 must be kept above 212 F. t or recondensation will take place, wetting the 
 material. 
 
 In order to economize fuel the shell is sometimes supported at the 
 ends and brickwork is erected around the shell, the hot gases passing 
 under the shell and back through it. Although this method is more 
 economical in the use of fuel, the cost of installation and the cost of 
 repairs are greater. 
 
 Group B: Materials such as will not be injured by the products of com- 
 bustion but cannot be raised to a high temperature on account of driving 
 off water of crystallizatipn, breaking up chemical combinations, or en 
 account of danger from ignition. Included in these are gypsum, fluor- 
 spar, iron pyrites, coal,. coke, lignite, sawdust, leather scraps, cork chips, 
 tobacco stems, fish scraps, tankage, peat, etc. Some of these materials 
 may be dried in a single-shell drier and some in a bricked-in machine, 
 but none of them in a satisfactory way on account of the difficulty of 
 regulating the temperature and, in some cases, the danger of explosion of 
 dust. 
 
 Group C: Materials which are not injured by a high temperature but 
 which cannot be allowed to come into contact with products of combus- 
 
EVAPORATION AND DRYING. 575 
 
 tion. These are kaolin, ocher and other pigments, fuller's earth, which is 
 to be used in filtering vegetable or animal oils, whiting and similar earthy 
 materials, a large proportion of which would be lost as dust in direct-heat 
 drying. These may be dried by passing through a single-shell drier 
 incased in brickwork and allowing heat to come into contact with the 
 shell only, but this is an uneconomical machine to operate, due to the 
 high temperature of the escaping gases. 
 
 Group D: Organic materials which are used for food either by man or 
 the lower animals, such as grain which has been wet, cotton seed, starch 
 feed, corn germs, brewers' grains, and breakfast foods, which must be 
 dried after cooking. These, of course, cannot be brought into contact 
 with furnace gases and must be kept at a low temperature. For these 
 materials a drier using either exhaust or live steam is the only practical 
 one. This is generally a revolving shell in which are arranged steam 
 pipes. Care should be exercised in selecting a steam drier which has 
 perfect and automatic drainage of the pipes. The condensed steam 
 always amounts to more than the water evaporated from the material. 
 
 Group E: Materials which are composed wholly or contain a large pro- 
 portion of soluble salts, such as nitrate of soda, nitrate of potash, car- 
 bonates of soda or potash, chlorates of soda or potash, etc. These in 
 drying form a hard scale which adheres to the shell, and a rotary drier 
 cannot be profitably used on account of frequent stops for cleaning. The 
 only practical machine for such materials is a semicircular cast-iron 
 trough having a shaft through the center carrying paddles that C9n- 
 stantl.y stir up the material and feed it through the drier. This machine 
 has brick side walls and an exterior furnace; the heat from the furnace 
 passing under the shell and back through the drying material or out 
 through a stack or fan without passing through the material, as may bo 
 desired. Should the material also require a low temperature, the same 
 type of drier can be used by substituting steam-jacketed steel sections 
 instead of cast iron. 
 
 The efficiency of a drier is the ratio of the theoretical heat required to 
 do the drying to the total heat supplied. The greatest loss is the heat 
 carried out by the exhaust or waste gases; this may be as great as 40% 
 of the total heat from the fuel, or with a properly designed drier may be 
 as small as 8%. The radiation from the shell or walls may be as high as 
 25% or as low as 4%. The heat carried away by the dried material may 
 amount under conditions of careless operation to as much as 25% or may 
 be as low as nothing. 
 
 A properly designed drier of the direct-heat type for either group " A " 
 or "B" will give an efficiency of from 75% to 85%; a bricked-in return- 
 draught single-shell drier, from 60% to 70%; and a single-shell straight- 
 draught dryer, from 45% to 55%. A properly designed indirect-heat 
 drier for group "C" will give an efficiency of 50% to 60%, and a poorly 
 designed one may not give more than 30%; The best designed steam 
 drier for group " D," in which the losses in the boiler producing the 
 steam must be considered, will not often give an efficiency of more than 
 42%; and, while a poorly designed one may have an equal efficiency, 
 its capacity may be not more than one-half of a good drier of equal size. 
 The drier described for group "E" will not give an efficiency of more 
 than 55%. 
 
 PERFORMANCE OF A STEAM DRIER. 
 
 Material; Starch feed. Moisture, initial 39.8%, final 0.22%. 
 Dried* material per hour, 831 Ibs. Water evaporated per hour, 548 Ibs. 
 Steam consumed per hour, 793 Ibs. Water evaporated per pound 
 steam, 0.691 Ib. Temperature of material, moist, 58, dry, 212. 
 Steam pressure, 98 Ibs. gauge. 
 
 Total heat to evaporate 548 Ibs. water at 58 into steam, 
 548 X (154.2 + 969.7) = 615,897 B.T.U. 
 
 Heat supplied by 793 Ibs. steam condensed to water at 212, 
 793 X (1188.2 - 180.3) = 799,265 B.T.U. 
 
 Heat used to evaporate water, 
 
 (615,897 -f- 799,265) = 77.1%. 
 
 Heat used to raise temperature of material, 
 
 (831 X 154 X 0.492) = 62,963 = 7.9%. 
 
 Loss by radiation . . 100 - (77.1 + 7.9) = 15%. 
 
 Total efficiency . 85.0%. 
 
576 
 
 HEAT. 
 
 Performance of Different Types of Driers. 
 
 (W. B. Ruggles.) 
 
 
 . 
 
 s 
 
 
 
 !l 
 
 Type of drier 
 
 l| 
 
 Is 
 
 ^.S g 
 
 Hi 
 
 t-< > 
 
 
 3| 
 
 "o 6* 
 
 V M 
 
 ^si2 
 
 |J| 
 
 '5c 
 
 J 
 
 '12"^ 
 
 
 Q^ 
 
 1? 
 
 .A| 
 
 I* 
 
 -u ^q 
 
 Material ,,,,,,,..,,., 
 
 Sand 
 
 Coal 
 
 Cement 
 
 Lime- 
 
 Nitrate 
 
 Moisture, initial, per cent ....... 
 
 4 58 
 
 10 2 
 
 slurry. 
 61 2 
 
 stone. 
 3 6 
 
 of soda. 
 7 2 
 
 Moisture, final, per cent 
 
 
 
 
 
 40 7 
 
 5 
 
 3 
 
 Calorific value of fuel, B.T.U. . . 
 
 12100 
 
 12290 
 
 13200 
 
 13180 
 
 13600 
 
 Fuel consumed per hour, Ibs. . . 
 Water evaporated per hour, Ibs 
 Water evap. per pound fuel, Ibs 
 Material dried per hour, Ibs. . . . 
 Fuel per ton dried material, Ibs. 
 Heat lost in exhaust air, per cent 
 
 398 
 2196 
 5.3 
 36460 
 21.8 
 11.3 
 
 213.6 
 924.2 
 4.3 
 8300 
 51.3 
 42.8 
 
 667 
 4057 
 6.1 
 7680 
 17.3 
 38.4 
 
 460 
 1325 
 2.3 
 41400 
 22.2 
 38.2 
 
 87 
 349 
 4.0 
 4581 
 38.0 
 40.7 
 
 Heat lost by radiation, etc., per 
 
 
 
 
 
 
 cent 
 
 7.6 
 
 7.7 
 
 12 5 
 
 15 6 
 
 13 8 
 
 Heat used to evaporate water, 
 
 
 
 
 
 
 per cent 
 
 52 5 
 
 39 4 
 
 52 
 
 24 4 
 
 33 1 
 
 Heat used to raise temperature of 
 material, per cent 
 
 28.6 
 
 10.1 
 
 7 1 
 
 21 8 
 
 12 4 
 
 Total efficiency, per cent 
 
 81 1 
 
 49 5 
 
 59 1 
 
 46 2 
 
 45 5 
 
 
 
 
 
 
 
 M 
 
 3 
 
 WATER EVAPORATED AND HEAT REQUIRED FOR DRYING. 
 percentage of moisture in material to be dried. 
 Ibs. water evaporated per ton (2000 Ibs.) of dry material. 
 = British thermal units required for drying, per ton of dry material. 
 
 M 
 
 Q 
 
 H 
 
 M 
 
 Q 
 
 H 
 
 M 
 
 Q 
 
 H 
 
 1 
 
 20.2 
 
 85,624 
 
 14 
 
 325.6 
 
 424,884 
 
 35 
 
 1,077 
 
 1,269,240 
 
 2 
 
 40.8 
 
 108,696 
 
 15 
 
 352.9 
 
 458,248 
 
 40 
 
 1,333 
 
 1,555,960 
 
 3 
 
 61.9 
 
 130,424 
 
 16 
 
 381.0 
 
 489,720 
 
 45 
 
 1,636 
 
 1,895,320 
 
 4 
 
 83.3 
 
 156,296 
 
 17 
 
 409.6 
 
 521,752 
 
 50 
 
 2,000 
 
 2.303,000 
 
 5 
 
 105.3 
 
 180,936 
 
 18 
 
 439.0 
 
 554,680 
 
 55 
 
 2,444 
 
 2,800,280 
 
 6 
 
 127.7 
 
 206,024 
 
 19 
 
 469.1 
 
 588,392 
 
 60 
 
 3,000 
 
 3,423,000 
 
 7 
 
 150.,? 
 
 231,560 
 
 20 
 
 500.0 
 
 623,000 
 
 65 
 
 3,714 
 
 4,222,680 
 
 8 
 
 173.9 
 
 257,768 
 
 21 
 
 531.6 
 
 658,392 
 
 70 
 
 4,667 
 
 5,290,040 
 
 9 
 
 197.8 
 
 284,536 
 
 22 
 
 564.1 
 
 694,792 
 
 75 
 
 6,000 
 
 6,783,000 
 
 10 
 
 222.2 
 
 311.864 
 
 23 
 
 597.4 
 
 732.088 
 
 80 
 
 8,000 
 
 9,023,000 
 
 11 
 
 247.2 
 
 339,864 
 
 24 
 
 631.6 
 
 770,392 
 
 85 
 
 11,333 
 
 12,755.960 
 
 12 
 
 272.7 
 
 368,424 
 
 25 
 
 666.7 
 
 809,704 
 
 90 
 
 18,000 
 
 20,223,000 
 
 13 
 
 298.9 
 
 397,768 
 
 30 
 
 857.0 
 
 1 .022,840 
 
 95 
 
 38,000 
 
 42,623,000 
 
 Formulae: Q = 
 
 1120 Q + 63,000. 
 
 The value of H is found on the assumption that the moisture is heated 
 from 62 to 212 and evaporated at that temperature, and that the 
 specific heat of the material is 0.21. [2000 X (212 - 62) X 0.21] = 63,000. 
 
 Calculations for Design of Drying Apparatus. A most efficient 
 system of drying of moist materials consists in a continuous circulation of a 
 volume of warm dry air over or through the moist material, then passing 
 the air charged with moisture over the cold surfaces of condenser coils to 
 remove the moisture, then heating the same air by steam-heating coils 
 or other means, and again passing it over the material. In the design of 
 apparatus to work on this system it is necessary to know the amount 
 of moisture to be removed in a given time, and to calculate the volume of 
 air that will carry that moisture at the temperature at which it leaves the 
 material, making allowanceforthefactthatthemoist, warm air on leaving 
 
EVAPORATION AND DRYING. 
 
 577 
 
 the material may not be fully saturated, and for the fact that the cooled 
 air is nearly or fully saturated at the temperature at which it leaves the 
 cooling coils. A paper by Wm. M. Grosvenor, read before the Am. Inst. 
 of Chemical Engineers (Heating and Ventilating Mag., May, 1909) con- 
 tains a "humidity table" and a "humidity chart" which greatly facilitate 
 the calculations required. The table is given in a condensed form below. 
 It is based on the following data: Density of air 4- 0.04% CO> = 
 
 0.001293052 .. __. _ 
 
 1 + 0.00367 X Temp. C. (m Kg ' P6F CU ' m ' ) ' DenSlty af Water Vapor 
 = 0.62186 X density of air. Density at partial pressure * density at 760 
 m.m. =partiai pressure * 760 m.m. Specific heat of water vapor = 0.475; 
 ep. ht. of air = 0.2373. Kg. per cu. meter X 0.062428 = Ibs. per cu. ft. 
 The results given in the table agree within 1/4% with the figures of the 
 U. S. Weather Bureau. (Compare also the tables of H. M. Prevost 
 Murphy, given under "Air," page 612.) The term "humid heat" in 
 the heading of the table is defined as the B.T.U. required to raise 
 1 F. one pound of air plus the vapor it may carry when saturated at 
 the given temperature and pressure; and "humid volume" is the 
 volume of one pound of air when saturated at the given temperature 
 and pressure. 
 
 Humidity Table. 
 
 Temp. 
 F. 
 
 Vapor 
 Tension, 
 Milli- 
 meters of 
 Mercury. 
 
 Lbs. 
 Water 
 Vapor 
 per Ib. 
 Air. 
 
 Humid 
 Heat, 
 B.T.U. 
 
 Humid 
 Volume 
 cu.ft. 
 
 Density, Ibs. 
 per cu.ft. at 760 
 
 Millimeters. 
 
 Volume in cu. 
 ft. per Ib. of 
 
 Dry 
 Air. 
 
 Sat'd 
 Mix. 
 
 Dry 
 Air. 
 
 Sat'd 
 Mix. 
 
 32 
 
 4.569 
 
 0.003761 
 
 0.2391 
 
 12.462 
 
 0.080726 
 
 0.080556 
 
 12.388 
 
 12.414 
 
 35 
 
 5.152 
 
 .0042435 
 
 .2393 
 
 12.549 
 
 .080231 
 
 .080085 
 
 12.464 
 
 12.496 
 
 40 
 
 6.264 
 
 .0050463 
 
 ,2398 
 
 12.695 
 
 .079420 
 
 .079181 
 
 12.590 
 
 12.629 
 
 45 
 
 7.582 
 
 .0062670 
 
 .2403 
 
 12.843 
 
 .078641 
 
 .078348 
 
 12.718 
 
 12.763 
 
 50 
 
 9.140 
 
 .0075697 
 
 .2409 
 
 12.999 
 
 .077867 
 
 .077511 
 
 12.842 
 
 12.901 
 
 55 
 
 10.980 
 
 .0091163 
 
 .2416 
 
 13.159 
 
 .077109 
 
 .076685 
 
 12.968 
 
 13.041 
 
 60 
 
 13.138 
 
 .010939 
 
 .2425 
 
 13.326 
 
 .076363 
 
 .075865 
 
 13.095 
 
 13.180 
 
 65 
 
 15.660 
 
 .013081 
 
 .2435 
 
 13.501 
 
 .075635 
 
 .075039 
 
 13.222 
 
 13.325 
 
 70 
 
 18.595 
 
 .Oi5597 
 
 .2447 
 
 13.683 
 
 .074921 
 
 .074219 
 
 13.348 
 
 13.471 
 
 75 
 
 22.008 
 
 .018545 
 
 .2461 
 
 13.876 
 
 .074218 
 
 .073471 
 
 13.474 
 
 13.624 
 
 80 
 
 25.965 
 
 .021998 
 
 .2478 
 
 14.081 
 
 .073531 
 
 .072644 
 
 13.600 
 
 13.777 
 
 85 
 
 30.573 
 
 .026026 
 
 .2497 
 
 14.301 
 
 .072852 
 
 .071744 
 
 13.726 
 
 13.938 
 
 90 
 
 35.774 
 
 .030718 
 
 .2519 
 
 14.539 
 
 .072189 
 
 .070894 
 
 13.852 
 
 14.106 
 
 95 
 
 41.784 
 
 .036174 
 
 .2545 
 
 14.793 
 
 .071535 
 
 .070051 
 
 13.979 
 
 14.275 
 
 100 
 
 48.679 
 
 .042116 
 
 .2575 
 
 15.071 
 
 .070894 
 
 .069179 
 
 14.106 
 
 14.455 
 
 105 
 
 56.534 
 
 .049973 
 
 .2610 
 
 15.376 
 
 .070264 
 
 .068288 
 
 14.232 
 
 14.643 
 
 110 
 
 65.459 
 
 .058613 
 
 .2651 
 
 15.711 
 
 .069647 
 
 .067383 
 
 14.358 
 
 14.840 
 
 115 
 
 75.591 
 
 .068662 
 
 .2699 
 
 16.084 
 
 .069040 
 
 .066447 
 
 14.484 
 
 15.050 
 
 120 
 
 87.010 
 
 .080402 
 
 .2755 
 
 16.499 
 
 .068443 
 
 .065477 
 
 14.611 
 
 15.272 
 
 125 
 
 99.024 
 
 .094147 
 
 .2820 
 
 16.968 
 
 .067857 
 
 .064480 
 
 14.736 
 
 15.509 
 
 130 
 
 114.437 
 
 .11022 
 
 .2896 
 
 17.499 
 
 .067380 
 
 .063449 
 
 14.863 
 
 15.761 
 
 135 
 
 130.702 
 
 .12927 
 
 .2987 
 
 18.103 
 
 .066713 
 
 .062374 
 
 14.989 
 
 16.032 
 
 140 
 
 148.885 
 
 .15150 
 
 .3093 
 
 18.800 
 
 .066156 
 
 .061255 
 
 15.116 
 
 16.325 
 
 145 
 
 169.227 
 
 .17816 
 
 .3219 
 
 19.609 
 
 .065601 
 
 .060104 
 
 15.242 
 
 16.643 
 
 150 
 
 191.860 
 
 .21005 
 
 .3371 
 
 20.559 
 
 .065154 
 
 .058865 
 
 15.368 
 
 16.993 
 
 155 
 
 216.983 
 
 .24534 
 
 .3553 
 
 21.687 
 
 .064539 
 
 .057570 
 
 15.494 
 
 17.370 
 
 160 
 
 244.803 
 
 .29553 
 
 .3776 
 
 23.045 
 
 .064016 
 
 .056218 
 
 15.621 
 
 17.788 
 
 165 
 
 275.592 
 
 .35286 
 
 .4054 
 
 24.708 
 
 .063502 
 
 .054795 
 
 15.748 
 
 18.250 
 
 170 
 
 309.593 
 
 .42756 
 
 .4405 
 
 26.790 
 
 .062997 
 
 .053305 
 
 15 874 
 
 18.761 
 
 175 
 
 347.015 
 
 .52285 
 
 .4856 
 
 29.454 
 
 .062500 
 
 .051708 
 
 16.000 
 
 19.339 
 
 180 
 
 388.121 
 
 .64942 
 
 .5458 
 
 32.967 
 
 .062015 
 
 .050035 
 
 16.126 
 
 19.987 
 
 185 
 
 433.194 
 
 .82430 
 
 .6288 
 
 37.796 
 
 .061529 
 
 .048265 
 
 16.253 
 
 20.719 
 
 190 
 
 482.668 
 
 1 .00805 
 
 .7519 
 
 44.918 
 
 .061053 
 
 .046391 
 
 16.379 
 
 21.557 
 
 195 
 
 536.744 
 
 1.4994 
 
 .9494 
 
 56.302 
 
 .060588 
 
 .044405 
 
 16.505 
 
 22.521 
 
 200 
 
 595.771 
 
 2.2680 
 
 1.3147 
 
 77.304 
 
 .060127 
 
 .042308 
 
 16.631 
 
 23.638 
 
 205 
 
 660.116 
 
 4.2272 
 
 2.1562 
 
 131.028 
 
 .059674 
 
 .040075 
 
 16.758 
 
 24.954 
 
 210 
 
 730.267 
 
 15.8174 
 
 15.9148 
 
 562.054 
 
 .059228 
 
 .037323 
 
 16.884 
 
 26.796 
 
578 
 
 HEAT. 
 
 RADIATION OF HEAT 
 
 Radiation of heat takes place between bodies at all distances apart, and 
 follows the laws for the radiation of light. 
 
 The heat rays proceed in straight lines, and the intensity of the rays 
 radiated from any one source varies inversely as the square of their 
 distance from the source. 
 
 This statement has been erroneously interpreted by some writers, who 
 have assumed .from it that a boiler placed two feet above a fire would re- 
 ceive by radiation only one-fourth as much heat as if it were only one foot 
 above. In the case of boiler furnaces the side walls reflect those rays that 
 are received at an angle, following the law of optics, that the angle oj 
 incidence is equal to the angle of reflection, with the result that the 
 intensity of heat two feet above the fire is practically the same as at one 
 foot above, instead of only one-fourth as much. 
 
 The rate at which a hotter body radiates heat, and a colder body 
 absorbs heat, depends upon the state of the surfaces of the bodies as 
 well as on their temperatures. The rate of radiation and of absorption 
 are increased by darkness and roughness of the surfaces of the bodies, 
 and diminished by smoothness and polish. For this reason the covering 
 
 absorbing power under the same circumstances. When a polished body 
 is struck by a ray of heat, it absorbs part of the heat and reflects the rest. 
 
 - - A1 - -j complement of its absorb- 
 power. 
 
 ft'erent bodies has been 
 
 determined by experiment, as shown m the table below, but as far as 
 quantities of heat are C9ncerned, says Prof. Trowbridge (Johnson's 
 Cyclopaedia, art. Heat), it is doubtful whether anything further than the 
 said relative determinations can, in the present state of our knowledge, 
 be depended upon, the actual or absolute quantities for different tem- 
 peratures being still uncertain. The authorities do not even agree on the 
 relative radiating powers. Thus, Leslie gives for tin plate, gold, silver, 
 and copper the figure 12, which differs considerably from the figures in 
 the table below, given by Clark, stated to be on the authority of Leslie, 
 De La Provostaye and Desains, and Melloni. 
 
 Relative Radiating and Reflecting Power of Different Substances. 
 
 
 Radiating or 
 Absorbing 
 Power. 
 
 Reflecting 
 Power. 
 
 
 Radiating or 
 Absorbing 
 Power. 
 
 Reflecting 
 Power. 
 
 
 100 
 100 
 100 
 98 
 93 to 98 
 90 
 85 
 72 
 27 
 
 25 
 23 
 
 23 
 
 
 
 
 2 
 7 to 2 
 10 
 15 
 28 
 73 
 
 75 
 
 77 
 
 77 
 
 Zinc, polished 
 Steel, polished 
 Platinum, polished. 
 Platinum in sheet . . 
 Tin 
 
 19 
 17 
 24 
 17 
 15 
 
 11 
 
 14 
 7 
 5 
 
 3 
 3 
 
 81 
 83 
 76 
 
 83 
 
 85 
 
 89 
 
 93 
 86 
 93 
 95 
 
 97 
 97 
 
 Water 
 
 Carbonate of lead . . . 
 ^Vri ting-paper 
 
 Ivory, jet, marble... 
 Ordinary glass 
 Ice 
 
 Brass, cast, dead 
 
 Gum lac 
 
 Brass, bright pol- 
 ished 
 
 Silver-leaf on glass . . 
 Cast iron, bright pol- 
 
 Copper, varnished. . 
 Copper, hammered . 
 Gold plated.. .. 
 
 Mercury, about 
 Wrought iron, pol- 
 ished 
 
 Gold on polished 
 steel . . 
 
 
 Silver, polished 
 bright. 
 
 
 Experiments of Dr. A.M. Mayer give the following: The relative radi- 
 ations from a cube of cast iron, having faces rough, as from the foundry, 
 
CONDUCTION AND CONVECTION OF HEAT. 579 
 
 planed, "drawfiled,"and polished, and from the same surfaces oiled, are as 
 below (Prof. Thurston, in Trans. A. S. M. E., vol. xvi): 
 
 
 Rough. 
 
 Planed. 
 
 Drawfiled. 
 
 Polished. 
 
 
 100 
 
 60 
 
 49 
 
 45 
 
 Surface dry 
 
 100 
 
 32 
 
 20 
 
 18 
 
 
 
 
 
 
 It here appears that the oiling of smoothly polished castings, as of 
 cylinder-heads of steam-engines, more than doubles the loss of heat by 
 radiation, while it doer- not seriously affect rough castings. 
 
 " Black Body " Radiation. Stefan and Boltzman's Law. (Eng'q, 
 March 1, 1907.) Kirchhoff defined a black body as one that would absorb 
 all radiations falling on it, and would neither reflect nor transmit any. 
 The radiation from such a body is a function of the temperature alone, 
 and is identical with the radiation inside an inclosure all parts ol wtncn 
 have the same temperature. By heating the walls of an inclosure as 
 uniformly as possible, and observing the radiation through a very small 
 opening, a practical realization of a black body is obtained. Stefan and 
 Boltzman's law is: The energy radiated by a black body is proportional 
 to the fourth power of the absolute temperature, or E = K (T 4 T 4 ), 
 where E = total energy radiated by the body at T to the body at TO, and 
 K is a constant. The total radiation from other than black bodies increases 
 more rapidly than the fourth power of the absolute temperature, so that 
 as the temperature is raised the radiation of all bodies approaches that of 
 the black body. A confirmation of the Stefan and Boltzman law is given 
 in the results of experiments by Lummer and Kurlbaum, as below (T Q = 
 290 degrees C. t abs. in all cases). 
 
 7*= 492. 654. 795. 
 108.4 109.9 
 6.56 8.14 
 33.1 36.6 
 
 E (Black body 109.1 
 
 =ri \ Polished platinum. . 4 .28 
 - T " 4 (Iron oxide 33.1 
 
 1108. 1481. 1761 k 
 
 109.0 110.7 
 
 12.18 16.69 19.64 
 46.9 65.3 
 
 The Stefan-Boltzman law as applied to radiation from a given body 
 may be written W = 5.7 e [(0.001T) 4 - (0.001 T e )] 4 ; W = energy in 
 watts radiated per square centimeter of surface, T = temperature of 
 the hot body, T e = temperature of the surrounding space, e = relative 
 emissivity, a characteristic of the radiating body, always less than 
 unity. For clean polished metal surfaces e ranges from 0.02 to 0.20; 
 for non-metallic surfaces, from about 0.3 to about 0.9. 
 
 CONDUCTION AND CONVECTION OF HEAT. 
 
 Conduction is the transfer of heat between two bodies or parts of a 
 body which touch each other. Internal conduction takes place between 
 the parts of one continuous body, and external conduction through the 
 surface of contact of a pair of distinct bodies. 
 
 The rate at which conduction, whether internal or external, goes on, 
 being proportional to the area of the section or surface through which it 
 takes place, may be expressed in thermal units per square foot of area per 
 hour. 
 
 Internal Conduction varies with the heat conductivity, which depends 
 upon the nature of the substance, and is directly proportional to the 
 difference between the temperatures of the two faces of a layer, and in- 
 versely as its thickness. The reciprocal of the conductivity is called the 
 internal thermal resistance of the substance. If r represents this resist- 
 ance, x the thickness of the layer in inches, T f and T the temperatures 
 on the two faces, and q the quantity in thermal units transmitted per 
 
 hour per square foot of area, q 
 Pe"clet gives the following values of r: 
 
 (Rankine.) 
 
 Gold, platinum, silver 0.0016 
 
 Copper 0.0018 
 
 Iron 0.0043 
 
 Zinc 0.0045 
 
 Lead 0.0090 
 
 Marble 0.0716 
 
 Brick 0.1500 
 
680 
 
 HEAT. 
 
 Metals. 
 
 Relative Heat-conducting Power of Metals. 
 
 *C.&J. fW.&F. 
 
 Silver 1000 ' 1000 
 
 Gold 981 532 
 
 Gold, with 1 % of silver. 840 
 
 Copper, rolled 845 736 
 
 Copper, cast 811 
 
 Mercury 677 
 
 Mercury, with 1.25% of 
 
 tin.... 412 
 
 Aluminum 665 ... 
 
 Zinc: 
 
 cast vertically 628 
 
 cast horizontally. . . 608 
 
 rolled 641 
 
 * Calvert & Johnson. 
 
 Metals. *C.&J. fW.&F. 
 
 Cadmium 577 
 
 Wrought iron 436 
 
 Tin 422 
 
 Steel 397 
 
 Platinum. 380 
 
 Sodium 365 
 
 Cast iron 359 
 
 Lead 287 
 
 Antimony: 
 
 cast horizontally. . 215 
 
 cast vertically. ... 192 
 
 Bismuth 61 
 
 119 
 145 
 116 
 
 84 
 
 85 
 
 18 
 
 t Weidemann & Franz. 
 
 INFLUENCE OF A NON-METALLIC SUBSTANCE IN COMBINATION ON THE 
 
 CONDUCTING POWER OF A METAL. 
 Influence of carbon on iron: 
 
 Wrought iron 436 
 
 Steel 397 
 
 Cast iron 359 
 
 Cast copper , 811 
 
 Copper with 1 % of arsenic 570 
 
 with 0.5% of arsenic. . 669 
 with 0.25% of arsenic, 771 
 
 The Rate of External Conduction through the bounding surface 
 between a solid body and a fluid is approximately proportional to the 
 difference of temperature, when that is small; but when that difference is 
 considerable, the rate of conduction increases faster than the simple ratio of 
 that difference. (Rankine.) 
 
 If r, as before, is the coefficient of internal thermal resistance, e and e f 
 the coefficient of external resistance of the two surfaces, x the thickness of 
 the plate, and T f and T the temperatures of the two fluids in contact 
 
 with the two surfaces, the rate of conduction is q 
 
 Accord- 
 
 ing to Pellet, e + e' = 
 
 e + e' + rx 
 in which the constants A and 
 
 A [1 -f B (T f - T}\ 
 B have the following values: 
 
 B for polished metallic surfaces . 0028 
 
 B for rough metallic surfaces and for non-metallic surfaces . . 0. 0037 
 
 A for polished metals, about 0.90 
 
 A for glassy and varnished surfaces 1 . 34 
 
 A for dull metallic surfaces 1 . 58 
 
 A for lampblack 1 . 78 
 
 When a metal plate has a liquid at each side of it, it appears from experi- 
 ments by Pe"clet that B = 0.058, A = 8.8; 
 
 The results of experiments on the evaporative power of boilers agree 
 very well with the following approximate formula for the thermal resist- 
 ance of boiler plates and tubes: 
 
 e+er -(T^T)' 
 
 which gives for the rate of conduction, per square foot of surface per hour, 
 
 (T r -T 7 ) 2 
 
 This formula is proposed by Rankine as a rough approximation, near 
 enough to the truth for its purpose. The value of a lies between 160 and 
 200. Experiments on modern boilers usually give higher values. 
 
 Convection, or carrying of heat, means the transfer and diffusion of the 
 heat in a fluid mass by means of the motion of the particles of that mass. 
 
 The conduction, properly so called, of heat through a stagnant mass of 
 fluid is very slow in liquids, and almost, if not whplly, inappreciable in 
 gases. It is only by the continual circulation and mixture of the particles 
 of the fluid that uniformity of temperature can be maintained in the fluid 
 mass, or heat transferred between the fluid mass and a solid body. 
 
 The free circulation of each of the fluids which touch the side of a solid 
 plate is a necessary condition of the correctness of Rankine's formulae for 
 tne conduction of heat through that plate; and in these formulae it is 
 
CONDUCTION AND CONVECTION OF HEAT. 581 
 
 fmplied that the circulation of each of the fluids by currents and eddies is 
 such as to prevent any considerable difference of temperature between the 
 fluid particles in contact with one side of the solid plate and those at con- 
 siderable distances from it. 
 
 When heat is to be transferred by convection from one fluid to another, 
 through an intervening layer of metal, the nations of the two fluid masses 
 should, if possible, be in opposite directions, in order that the hottest par- 
 ticles of each fluid may be m communication with the hottest particles of 
 the other, and that the minimum difference of temperature between the 
 adjacent particles of the two fluids may be the greatest possible. 
 
 Thus, in the surface condensation of steam, by passing it through metal 
 tubes immersed in a current of cold water or air, the cooling fluid should 
 be made to move in the opposite direction to the condensing steam. 
 
 Coefficients of Heat Conduction of Different Materials. (W. 
 Nusselt, Zeit des Ver. Deut. Ing., June, 1908. Eng. Digest, Aug., 1908.) 
 The materials were inclosed between two concentric metal vessels, the 
 inner of which contained an electric heating device. 
 
 It was found that the materials tested all followed Fourier's law, the 
 quantity of heat transmitted being directly proportional to the extent of 
 surface, the duration of flow and the temperature difference between the 
 inner and outer surfaces; and inversely proportional to the thickness of 
 the mass of material. It was also found that the coefficient of conduction 
 increased as the temperature increased. The table gives the British 
 equivalents of the average coefficients obtained. 
 
 COEFFICIENTS OF HEAT CONDUCTION AT DIFFERENT TEMPERATURES 
 
 FOR VARIOUS INSULATING MATERIALS. 
 
 (B.T.U. per hour = Area of surface in square feet X coefficient -f- thick- 
 ness in inches.) 
 
 Lb. per 
 cu. ft. 
 
 Materials. 
 
 32 
 F. 
 
 212 
 F. 
 
 392 
 F. 
 
 572 
 F. 
 
 752 
 F. 
 
 10 
 
 Ground cork 
 
 0.250 
 
 0.387 
 
 0.443 
 
 
 
 8.5 
 
 Sheep's wool* 
 
 0.266 
 
 0.403 
 
 
 
 
 6 3 
 
 Silk waste 
 
 0.306 
 
 0.411 
 
 
 
 
 9.18 
 5 06 
 
 Silk, tufted 
 Cotton wool 
 
 0.314 
 0.379 
 
 0.419 
 0.476 
 
 
 
 
 J1.86 
 
 Charcoal (carbonized cabbage 
 leaves) 
 
 0.403 
 
 0.508 
 
 
 
 
 13 42 
 
 Sawdust (0 443 at 1 12 F ) 
 
 
 
 
 
 
 10 
 
 Peat refusef (0 443 at 77 F ) 
 
 
 
 
 
 
 2' .85 
 
 Kieselguhr (infusorial earth), 
 loose .... ... 
 
 3.419 
 
 0.532 
 
 3.596 
 
 0.629 
 
 
 12.49 
 
 Asphalt-cork composition (0.492 
 at65F.). . 
 
 
 
 
 
 
 25.28 
 12 49 
 
 Composition, j loose 
 Kieselguhr stone ... 
 
 0.484 
 0.516 
 
 0.613 
 0.629 
 
 0.653 
 0.742 
 
 J!854' 
 
 o:%r 
 
 12 17 
 
 Peat refusef (0 564 at 68 -F ) 
 
 
 
 
 
 
 36.2 
 
 Kieselguhr, dry and compacted 
 (0 669 at 302 F 991 at 662 F.) 
 
 
 
 
 
 
 43.07 
 
 Composition, compacted (0.806 
 at 302 F 967 at 428 F.) 
 
 
 
 
 
 
 22.47 
 
 Porous blast-furnace slag (0.766 
 at I12F.) .... 
 
 
 
 
 
 
 35 96 
 
 Asbestos (1 .644 at 1112 F.) 
 
 1.048 
 
 1.346 
 
 1.451 
 
 1.499 
 
 1.548 
 
 34 33 
 
 Slag concrete! (1 532 at 112 F ) 
 
 
 
 
 
 
 18.23 
 
 Eumice stone gravel (1.612 at 
 112 F ) 
 
 
 
 
 
 
 128.5 
 
 Portland cement, neat (6.287 at 
 95 F.) 
 
 
 
 
 
 
 Tufted, oily, and containing foreign matter. Used in Linde's 
 apparatus, t Hygroscopic; measurements made in moist zones. \ Cork, 
 asbestos, kieselguhr and chopped straw, mixed with a binder and made 
 in sheets for application to steam pipes in successive layers, the whole 
 being wrapped in canvas and painted. Kieselguhr, mixed with a binder 
 and burned; very porous and hygroscopic. Ingredients of ($) mixed 
 with water and compacted. || 1 part cement, 9 parts porous blast-furnace 
 slag, by volume. 
 
582 HEAT. 
 
 Heat Resistance, the Reciprocal of Heat Conductivity. (W. 
 
 Kent, Trans. A. S. M. E., xxi-7, 278.) The resistance to the passage of 
 heat through a plate consists of three separate resistances; viz., the 
 resistances of the two surfaces and the resistance of the body of the plate 
 which latter is proportional to the thickness of the plate. It is probable 
 also that the resistance of the surface differs with the nature of the body 
 or medium with which it is in contact. 
 
 A complete set of experiments on the heat-resisting power of heat- 
 insulating substances should include an investigation into the difference 
 in surface resistance when a surface is in contact with air and when it is 
 in contact with another solid body. Suppose we find that the total resist- 
 ance of a certain non-conductor may be represented by the figure 10, and 
 that similar pieces all give the same figure. Two pieces in contact give 16. 
 One piece of half the thickness of the others gives 8. What is the resist- 
 ance of the surface exposed to the air in either piece, of the surface in 
 contact with another surface, and of the interior of the body itself? Let 
 the resistance of the material itself, of the regular thickness, be rep- 
 resented by A, that of the surface exposed to the air by a, and that of the 
 surface in contact with another surface by c. 
 
 We then have for the three cases, 
 
 Resistance of one piece .4 -t- 2 a ^ 10 
 
 of two pieces in contact .... 2A+2c+2a = 16 
 of the thin piece i/2A+2a= 8 
 
 These three equations contain three unknown quantities. Solving the 
 equations we find A = 4, a = 3, and c = 1. Suppose that another 
 experiment be made with the two pieces separated by an air space, and 
 that the total resistance is then 22. If the resistance of the air space be 
 represented by s we have the two equations: Resistance of one piece, 
 A + 2 a = 10; resistance of two pieces and air space, 2 A + 4a + a = 22, 
 from which we find s = 2. Having these results we can easily estimate 
 what will be the resistance to heat transfer of any number of layers of the 
 material, whether in contact or separated by air spaces. 
 
 The writer has computed the figures for heat resistance of several 
 insulating substances from the figures of conducting power given in a table 
 
 Published by John E. Starr, in Ice and Refrigeration, Nov., 1901. Mr. 
 tarr's figures are given in terms of the B.T.U. transmitted per sq. ft. o* 
 surface per day per degree of difference of temperatures of the air adjacent 
 to each surface. The writer's figures, th9se in the last column of the table 
 given on p. 583, are calculated by dividing Mr. Starr's figures by 24, to 
 obtain the hourly rate, and then taking their reciprocals. They may be 
 called "coefficients of heat resistance" and defined as the reciprocals of 
 the B.T.U. per sq. ft. per hour per degree of difference of temperature. 
 
 Analyzing some of the results given in the last column of the table, we 
 observe that, comparing Nos. 2 and 3, 1 in. added thickness of pitch 
 increased the coefficient 0.74; comparing Nos. 4 and 5, 1 1/2 in. of mineral 
 wool increased the coefficient 1.11. If we assume that the 1 in. of mineral 
 wool in No. 4 was equal in heat resistance to the additional 11/2 in. added 
 in No. 5, or 1.11 reciprocal units, and subtract this from 5.22, we get 4.11 
 as the resistance of two 7/ 8 -in. boards and two sheets of paper. This 
 would indicate that one 7/g-in. boaj*d and one sheet of paper give nearly 
 twice as much resistance as 1 in. of mineral wool. In like manner any 
 number of deductions may be drawn from the table, and some of them 
 will be rather questionable, such as the comparison of No. 15 and No. 16, 
 showing that 1 in. additional sheet cork increased the resistance given by 
 four sheets 6.67 reciprocal units, or one-third the total resistance of No. 15. 
 This result is extraordinary, and indicates that there must have been 
 considerable differences of conditions during the two tests. 
 
 For comparison with the coefficients of heat resistance computed from 
 Mr. Starr's results we may take the reciprocals of the figures given by 
 Mr. Alfred R. Wolff as the result of German experiments on the heat 
 transmitted through various building materials, as below: 
 
 K = B.T.U. transmitted per hour per sq. ft. of surface, per degree 
 F. difference of temperature. 
 
 C = coefficient of heat resistance = reciprocal of K. 
 
 The irregularity of the differences of C computed from the original 
 values of K for each increase of 4 inches in thickness of the brick walls 
 inoUcates a difference in the conditions of the experiments. The average 
 
CONDUCTION AND CONVECTION OF HEAT. 583 
 
 HEAT CONDUCTING AND RESISTING VALUES OF DIFFERENT MATERIALS. 
 
 Insulating Material. 
 
 Conductance, 
 B.T.U. per 
 Sq. Ft. per 
 Day per Deg., 
 Difference of 
 Temperature. 
 
 Coefficient 
 of Heat 
 Resistance. 
 C. 
 
 1. 5/ 8 -in. oak board, 1 in. lampblacK, 7/g-in. pine 
 board (ordinary family refrigerator) 
 2. 7/8-in. board, 1 in. pitch, 7/ 8 -in. board 
 3 7/8-in board 2 in pitch 7/8-in. board. . . . 
 
 5.7 
 
 4.89 
 4.25 
 
 4.6 
 3.62 
 
 3.38 
 3.90 
 
 2.10 
 4.28 
 3.71 
 3.32 
 
 1.35 
 
 1.80 
 2.10 
 
 1.20 
 0.90 
 1.70 
 3.30 
 
 2.70 
 2.52 
 2.48 
 
 4.21 
 4.91 
 5.65 
 
 5.22 
 6.63 
 
 7.10 
 6.15 
 
 11.43 
 
 5.61 
 6.47 
 
 7.23 
 
 17.78 
 13.33 
 11.43 
 
 20.00 
 26.67 
 14.12 
 7.27 
 
 8.89 
 9.52 
 9.68 
 
 4. 7/s-in. board' paper, 1 in. mineral wool, paper, 
 7/8-in. board 
 
 5. 7/8-in. board, paper, 21/2 in. mineral wool, 
 paper, 7/8-in. board 
 
 6. 7/8-in. board, paper, 21/2 in. calcined pumice, 
 7/8-in. board 
 
 7 Same as above when wet 
 
 8. 7/8-in. board, paper, 3 in. sheet cork, 7/8-in. 
 board . 
 
 9. Two 7/8-in. boards, paper, solid, no air space, 
 
 10. Two 7/8-in. boards, paper, 1 in. air space, 
 
 11. Two 7/8-in. boards, paper, 1 in. hair felt, 
 paper two 7/8-in boards 
 
 12. Two 7/8-in. boards, paper, 8 in. mill shav- 
 ings paper two 7/8-in boards 
 
 
 
 15. Two 7/8-in. boards, paper, 3 in. air, 4 in. 
 sheet cork paper two 7/8-in. boards... . . . . 
 
 
 1 7 Same with 4 in granulated cork . 
 
 18 Same with 1 in sheet cork 
 
 19. Four double 7/ 8 -in. boards (8 boards), with 
 paper between, three 8-in. air spaces 
 20. Four 7/8-in. boards, with three quilts of l/4-in 
 hair between, papers separating boards . . 
 21. 7/8-in. board, 6 in. patented silicated straw 
 board, finished inside with thin cement. . 
 
 difference of C for each 4 inches of thickness is about 0.80. Using this 
 average difference to even up the figures we find the value of C is ex- 
 pressed by the approximate formula C = 0.70 + 0.20 t, in which t is the 
 thickness in inches. The revised values of C, computed by this formula, 
 and the corresponding revised values of K, are as follows: 
 
 Thick., In. 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 C 
 
 1 50 
 
 2 30 
 
 3 10 
 
 3 90 
 
 4 70 
 
 5 50 
 
 6 30 
 
 7 10 
 
 7 90 
 
 8 70 
 
 K, revised.. 
 K, original . 
 Difference. . 
 
 0.667 
 0.68 
 0.013 
 
 0.435 
 0.46 
 0.025 
 
 0.323 
 0.32 
 0.003 
 
 0.256 
 0.26 
 0.004 
 
 0.213 
 0.23 
 0.017 
 
 0.182 
 0.20 
 0.018 
 
 0.159 
 0.174 
 0.015 
 
 0.141 
 0.15 
 0.009 
 
 0.127 
 0.129 
 0.002 
 
 0.115 
 0.115 
 0.0 
 
 The following additional values of C are computed from Mr. Wolff's 
 figures for K: 
 
 Wooden beams planked over, or ceiled : K C 
 
 As flooring 0.083 12.05 
 
 As ceiling 0.104 9.71 
 
 Fireproof construction, floored over: 
 
 As flooring 0.124 8.06 
 
 As ceiling 0.145 6.90 
 
 Single window : 1.030 0.97 
 
 Single skylight 1.118 0.89 
 
 Double window 0.518 1.93 
 
 Double skylight . 621 1 . 61 
 
 Poor,, , , .0.414 2,42 
 
584 
 
 HEAT. 
 
 It should be noted that the coefficient of resistance thus defined will be 
 approximately a constant quantity for a given substance under certain 
 fixed conditions, only when the difference of temperature of the air on its 
 two sides is small say less than 100 F. When the range of tem- 
 perature is great, experiments on heat transmission indicate that the 
 quantity of heat transmitted varies, not directly as the difference of tem- 
 perature, but as the square of that difference. In this case a coefficient 
 of resistance with a different definition may be found viz., that ob- 
 tained from the formula a = (T t) 2 * q, in which a is the coefficient, 
 T t the range of temperature, and q the quantity of heat transmitted, 
 in British thermal units per square foot per hour, 
 
 Steam-pipe Coverings. 
 
 Experiments by Prof. Ordway, Trans. A. S. M. E., vi, 168; also Circular 
 No. 27 of Boston Mfrs. Mutual Fire Ins. Co., 1890. 
 
 Substance 1 In. Thick. Heat 
 Applied, 310 F. 
 
 Pounds of 
 Water 
 Heated 
 10 F., per 
 Hour, 
 Through 
 1 Sq. Ft. 
 
 British 
 Thermal 
 Units per 
 Sq. Ft. per 
 Minute. 
 
 Solid Mat- 
 ter in 1 Sq. 
 Ft., 1 In. 
 Thick, 
 Parts in 
 1000. 
 
 Air included. 
 Parts in 100. 
 
 
 8.1 
 
 .35 
 
 56 
 
 944 
 
 
 9.6 
 
 60 
 
 50 
 
 950 
 
 3. Carded cotton wool 
 
 10.4 
 
 73 
 
 20 
 
 980 
 
 4 Hair felt 
 
 10 3 
 
 72 
 
 185 
 
 815 
 
 5 Loose lampblack. 
 
 9 8 
 
 63 
 
 56 
 
 944 
 
 6. Compressed lampblack 
 
 10.6 
 
 77 
 
 244 
 
 756 
 
 7 Cork charcoal 
 
 11 9 
 
 1 98 
 
 53 
 
 947 
 
 8. White-pine charcoal 
 
 13 9 
 
 2 32 
 
 119 
 
 881 
 
 
 35.7 
 
 5.95' 
 
 506 
 
 494 
 
 10 Loose calcined magnesia 
 
 12 4 
 
 2 07 
 
 23 
 
 977 
 
 1 1 . Compressed calcined magnesia . . 
 12. Light carbonate of magnesia. . . . 
 13. Compressed carb. of magnesia.. . 
 1 4 Loose fossil-meal 
 
 42.6 
 13 7 
 15.4 
 14 5 
 
 7.10 
 2.28 
 2.57 
 2 42 
 
 285 
 60 
 15<0 
 60 
 
 715 
 940 
 850 
 940 
 
 1 5 Crowded fossil-meal ... 
 
 15 7 
 
 2 62 
 
 112 
 
 888 
 
 16. Ground chalk (Paris white). 
 1 7 Dry plaster of Paris . 
 
 20.6 
 30 9 
 
 3.43 
 5 15 
 
 253 
 
 368 
 
 747 
 632 
 
 1 8 Fine asbestos 
 
 49 
 
 8 17 
 
 81 
 
 919 
 
 
 48.0 
 
 8 00 
 
 
 
 1000 
 
 20 Sand 
 
 62 1 
 
 10 35 
 
 529 
 
 471 
 
 2 1 . Best slag- wool 
 
 13. 
 
 2 17 
 
 
 
 22. Paper 
 
 14. 
 
 2.33 
 
 
 
 23. Blotting-paper wound tight . . . 
 
 21 
 
 3 50 
 
 
 
 
 21.7 
 
 3.62 
 
 
 
 25 Cork strips bound on . . . 
 
 14 6 
 
 2 43 
 
 
 
 
 18. 
 
 3. 
 
 
 
 27 Loose rice chaff . 
 
 18 7 
 
 3 12 
 
 
 
 28. Paste of fossil-meal with hair . . 
 
 16.7 
 
 2 78 
 
 
 
 29. Paste of fossil-meal with asbestos. 
 
 22. 
 
 3.67 
 
 
 
 30. Loose bituminous-coal ashes. . . . 
 
 21. 
 
 3.50 
 
 
 
 31. Loose anthracite-coal ashes 
 
 27. 
 
 4.50 
 
 
 
 32. Paste of clay and vegetable fiber 
 
 30.9 
 
 5. 15 
 
 
 
 
 
 
 
 
 It will be 9bserved that several of the incombustible materials are 
 nearly as efficient as wool, cotton, and feathers, with which they may be 
 compared in the preceding table. The materials which may be con- 
 sidered wholly free from the danger of being carbonized or ignited by 
 slow contact with pipes or boilers are printed in Roman type. Those 
 which are more or less liable to be carbonized are printed in italics. 
 
 The results Nos. 1 to 20 inclusive were from experiments with the 
 various non-conductors each used in a mass one inch thick, placed on a 
 flat surface of iron kept headed by steam to 310 F, The substances 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 585 
 
 Nos. 21 to 32 were tried as coverings for two-inch steam-pipe; the 
 results being reduced to the same terms as the others for convenience 
 of comparison. 
 
 Experiments on still air gave results which differ little from those of 
 Nos. 3, 4, and 6. The bulk of matter in the best non-conductors is 
 relatively too small to have any specific effect except to trap the air and 
 keep it stagnant. These substances keep the air still by virtue of the 
 roughness of their fibers or particles. The asbestos, No. 18, had smooth 
 fibers. Asbestos with exceedingly fine fiber made a somewhat better 
 showing, but asbestos is really one of the poorest non-conductors. It 
 may be used advantageously to hold together other incombustible sub- 
 stances, but the less of it the better. A "magnesia" covering, made of 
 carbonate of magnesia with a small percentage of good asbestos fiber 
 and containing 0.25 of solid matter, transmitted 2.5 B.T.U. per square 
 foot per minute, and one containing 0.396 of solid matter transmitted 
 3.33 B.T.U. 
 
 Any suitable substance which is used to prevent the escape of steam 
 heat should not be less than one inch thick. 
 
 Any covering should be kept perfectly dry, for not only is water a good 
 carrier of heat, but it has been found that still water conducts heat about 
 eight times as rapidly as still air. 
 
 Tests of Commercial Coverings were made by Mr. Geo. M. Brill 
 and reported in Trans. A. S. M. E., xvi, 827. A length of 60 feet of 8-inch 
 steam-pipe was used in the tests, and the heat loss was determined by the 
 condensation. The steam pressure was from 109 to 117 Ibs. gauge, and 
 the temperature of the air from 58 to 81 F. The difference between the 
 temperature of steam and air ranged from 263 to 286, averaging 
 272. 
 
 The following are the principal results: 
 
 
 1 
 
 Is 
 
 I 
 
 fto3 
 
 si 8 
 
 . i-i 
 
 II 
 
 1] 
 
 *! 
 
 
 3 
 
 ss 
 
 s 1 
 
 . S 
 
 l| 
 
 0) 
 
 -^2 
 
 Kind of Covering. 
 
 "8 
 
 
 IU 
 
 ""-SIS ! 
 
 0) d 
 
 W o 
 
 03 ^ 
 
 
 
 
 ft 
 
 
 s 9 
 
 
 
 
 03 
 
 -2 
 
 
 ^ ft *" 
 
 -6| 
 
 x 
 
 ~ n 
 
 
 -% 
 
 02 
 
 1 
 
 g||| 
 
 IK 
 
 | 51 
 
 ?fl 
 
 
 H ~ 
 
 
 
 W 
 
 ca 
 
 GQ"" W 
 
 p^W 
 
 W ' d 
 
 Bare pipe.. . 
 
 
 0.846 
 
 12.27 
 
 2.706 
 
 
 100. 
 
 2.819 
 
 Magnesia 
 
 .25 
 
 0.120 
 
 1.74 
 
 0.384 
 
 0.726 
 
 14 2 
 
 400 
 
 Rock wool 
 
 .60 
 
 0.080 
 
 1.16 
 
 0.256 
 
 0.766 
 
 9.5 
 
 0.267 
 
 Mineral wool 
 
 .30 
 
 0.089 
 
 1.29 
 
 0.285 
 
 0.757 
 
 10 5 
 
 297 
 
 Fire-felt 
 
 30 
 
 157 
 
 2 28 
 
 0.502 
 
 689 
 
 18 6 
 
 523 
 
 Manville sectional 
 
 .70 
 
 0.109 
 
 1.59 
 
 0.350 
 
 0.737 
 
 12.9 
 
 0.364 
 
 Manv. sect and hair-felt 
 
 2.40 
 
 0.066 
 
 0.96 
 
 0.212 
 
 0.780 
 
 7.8 
 
 0.221 
 
 Manville wopl-cement . . . 
 
 2.20 
 
 0.108 
 
 1.56 
 
 0.345 
 
 0.738 
 
 12.7 
 
 0.359 
 
 Champion mineral wool . 
 
 1.44 
 
 0.099 
 
 1.44 
 
 0.317 
 
 0.747 
 
 11.7 
 
 0.330 
 
 Hair-felt 
 
 H2 
 
 0.132 
 
 1.91 
 
 0.422 
 
 0.714 
 
 15.6 
 
 0.439 
 
 Riley cement 
 
 75 
 
 298 
 
 4.32 
 
 0.953 
 
 0.548 
 
 35 2 
 
 993 
 
 Fossil-meal 
 
 0.75 
 
 0.275 
 
 3.99 
 
 0.879 
 
 0.571 
 
 32 5 
 
 919 
 
 
 
 
 
 
 
 
 
 Tests of Pipe Coverings by an Electrical Method. (H. G. Stott, 
 Power, 1902.) A length of about 200 ft. of 2-in. pipe was heated to a 
 known temperature by an electrical current. The pipe was covered with 
 different materials, and the heat radiated by each covering was deter- 
 mined by measuring the current required to keep the pipe at a constant 
 temperature. A brief description of the various coverings is given below. 
 
 No. 2. Sclid sectional covering, 11/2 in. thick, of granulated cork 
 molded under pressure and then baked at a temperature of 500 F.; 
 1/8 in. asbestos paper next to pipe. 
 
 No. 3. Solid 1-in. molded sectional, 85% carbonate of magnesia. 
 
580 HEAT. 
 
 No. 4. Solid 1-in. sectional, granulated cork molded under pressure 
 and baked at 500 F.; 1/8 in. asbestos next to pipe. 
 
 No. 5. Solid 1-in. molded sectional, 85% carbonate of magnesia; out- 
 side of sections covered with canvas pasted on. 
 
 No. 6. Laminated 1-in. sectional, nine layers of asbestos paper with 
 granulated cork between; outside of sections covered with canvas, i/s in. 
 asbestos paper next to pipe. 
 
 No. 7. Solid 1-in. molded sectional, of 85% carbonate of magnesia; 
 outside of sections covered with light canvas. 
 
 No. 8. Laminated 1-in. sectional, seven layers of asbestos paper 
 indented with i/4-in. square indentations, which serve to keep the asbestos 
 layers from coming in close contact with one another; 1/8 in. asbestos 
 paper next to pipe. 
 
 No. 9. Laminated 1-in. sectional, 64 layers of asbestos paper, in which 
 were embedded small pieces of sponge; outside covered with canvas. 
 
 No. 10. Laminated li/2-in. sectional, 12 plain layers of asbestos paper 
 with corrugated layers between, forming longitudinal air cells; 1/8 in. 
 asbestos paper next to pipe; sections wired on. 
 
 No. 11. Laminated 1-in. sectional, 8 layers of asbestos paper with 
 corrugated layers between, forming small air ducts radially around the 
 covering. 
 
 No. 12. Laminated 11/4-in. sectional, 6 layers of asbestos paper 
 with corrugated layers; outside of sections covered with two layers of 
 canvas. 
 
 No. 15. "Remanit," composed of 2 layers wound in reverse direction 
 with ropes of carbonized silk. Inner layer 21/2 in. wide and 1/2 in. thick; 
 outer layer 2 in. wide and 3/ 4 in. thick, over which was wound a network 
 of fine wire; Vsin. asbestos next to pipe. Made in Germany. 
 
 No. 16. 2i/2-in. covering, 85% carbonate of magnesia, 1/2-in. blocks 
 about 3 in. wide and 18 in. long next to pipe and wired on; over these 
 blocks were placed solid 2-in. molded sectional covering. 
 
 No. 17. 2i/2-in. covering, 85% magnesia. Put on in a 2-in. molded 
 section wired on; next to the pipe and over this a i/2-in. layer of magnesia 
 plaster. 
 
 No. 18. 2 i/2-in. covering, 85% carbonate of magnesia. Put on in two 
 solid 1-in. molded sections with i/2-in. layer of magnesia plaster between; 
 two 1-in. coverings wired on and placed so as to break joints. 
 
 No. 19. 2-in. covering, of 85% carbonate of magnesia, put on in two 
 1-in. layers so as to break joints. 
 
 No. 20. Solid 2-in. molded sectional, 85% magnesia. 
 
 No. 21. Solid 2-in. molded sectional, 85% magnesia. 
 
 Two samples covered with the same thickness of similar material give 
 different results;- for example, Nos. 3 and 5, and also Nos. 20 and 21. 
 The cause of this difference was found to be in the care with which the 
 joints between sections were made. A comparison between Nos. 19 and 
 20, having the same total thickness, but one applied in a solid 2-in. section, 
 and the other in two 1-in. sections, proved the desirability of breaking 
 joints. 
 
 An attempt was made to determine the law governing the effect of 
 increasing the thickness of the insulating material, and for all the 85% 
 magnesia coverings the efficiency varied directly as the square root of the 
 thickness, but the other materials tested did not follow this simple law 
 closely, each one involving a different constant. 
 
 To determine which covering is the most economical the following 
 quantities must be considered: (1) Investment in covering. (2) Cost 
 of coal required to supply lost heat. (3) Five per cent interest on 
 capital invested in boilers and stokers rendered idle through having to 
 supply lost heat. (4) Guaranteed life of covering. (5) Thickness of 
 covering. 
 
 The coverings Nos. 2 to 15 were finished on the outside with resin paper 
 and 8-ounce canvas; the others had canvas pasted on outside of the sec- 
 tions, and an 8-oz. canvas finish. The following is a condensed statement 
 of the results with the temperature of the pipe corresponding to 160 Ib. 
 steam pressure. 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 587 
 
 ELECTRICAL TEST OF STEAM-PIPE COVERINGS. 
 
 No. 
 
 Covering. 
 
 Aver. 
 Thick- 
 ness. 
 
 B.T.U. 
 
 Loss 
 per 
 Min. 
 persq. 
 ft. at 
 160 Ib. 
 Pres. 
 
 B.T.U. 
 persq. 
 ft. per 
 Hr. per 
 Deg. 
 Diff. of 
 Temp. 
 
 Per 
 
 cent 
 Heat 
 Saved 
 by 
 Cover- 
 ing. 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 II 
 12 
 15 
 16 
 
 17 
 
 J8 
 (9 
 20 
 21 
 
 Solid cork 
 
 1.68 
 .13 
 .20 
 .19 
 .48 
 .12 
 .26 
 .24 
 .70 
 .22 
 .29 
 1.51 
 
 2.71 
 
 2.45 
 2.50 
 2.24 
 2.34 
 2.20 
 
 1.672 
 2.008 
 2.048 
 2.130 
 2.123 
 2.190 
 2.333 
 2.552 
 2.750 
 2.801 
 2.812 
 1.452 
 
 1.381 
 
 .387 
 .412 
 .465 
 .555 
 .568 
 13. 
 
 0.348 
 0.418 
 0.427 
 0.444 
 0.442 
 0.456 
 0.486 
 0.532 
 0.573 
 0.584 
 0.586 
 0.302 
 
 0.288 
 
 0.289 
 0.294 
 0.305 
 0.324 
 0.314 
 2.708 
 
 87.1 
 84.5 
 84.2 
 83.6 
 83.7 
 S3. 2 
 83.1 
 80.3 
 78.8 
 78.5 
 78.4 
 88.8 
 
 89.4 
 
 88.7 
 89.0 
 88.7 
 88.0 
 87.9 
 
 85 % magnesia/ 
 
 Solid cork 
 
 85% magnesia 
 
 Laminated asbestos cork . . 
 
 85% magnesia 
 
 Asbestos air cell [indent! 
 
 Asbestos sponge felted '. 
 
 Asbestos air cell [long] 
 
 " Asbestoscel " [radial] 
 
 Asbestos air cell [long] 
 
 " Remanit" [silk] wrapped 
 
 85 % magnesia, 2" sectional and 1/2" 
 block 
 
 85 % magnesia, 2!' sectional and 1/2" 
 plaster . . 
 
 85% magnesia, two 1" sectional 
 
 85% magnesia, two \" sectional . 
 
 85% magnesia 2" sectional 
 
 85% magnesia, 2" sectional . . . . 
 
 Bare pipe [from outside tests] 
 
 
 
 
 Transmission of Heat, through Solid Plates, from Water to Water. 
 
 (Clark, S. E.) M. Pe"clet found, from experiments made with plates of 
 wrought iron, cast iron, copper, lead, zinc, and tin, that when the fluid 
 in contact with the surface of the plate was not circulated by artificial 
 means, the rate of conduction was the same for different metals and for 
 plates of the same metal of different thicknesses. But when the water 
 was thoroughly circulated over the surfaces, and when these were perfectly 
 clean, the quantity of transmitted heat was inversely proportional to the 
 thickness, and directly as the difference in temperature of the two faces 
 of the plate. When the metal surface became dull, the rate of trans- 
 mission of heat through all the metals was very nearly the same. 
 
 It follows, says Clark, that the absorption of heat through metal plates 
 is more active whilst evaporation is in progress when the circulation of 
 the water is more active than while the water is being heated up to the 
 boiling-point. 
 
 Transmission from Steam to Water. M. Pellet's principle is 
 supported by the results of experiments made in 1867 by Mr. Isherwood on 
 the conductivity of different metals. Cylindrical pots, 10 inches in 
 diameter, 211/4 inches deep inside, and Vs inch, 1/4 inch, and 3/ 8 inch 
 thick, turned and bored, were formed of pure copper, brass (60 copper 
 and 40 zinc), rolled wrought iron, and remelted cast iron. They were 
 immersed in a steam bath, which was varied from 220 to 320 F. Water 
 at 212 was supplied to the pots, which were kept filled. It was ascer- 
 tained that the rate of evaporation was in the direct ratio of the difference 
 of the temperatures inside and outside of the pots; that is, that the rate 
 of evaporation per degree of difference of temperatures was the same for 
 all temperatures; and that the rate of evaporation was exactly the same 
 for different thicknesses of the metal. The respective rates of conductiv- 
 ity of the several metals were as follows, expressed in weight of water 
 evaporated from and at 212 F, per square foot of the interior surface of 
 the pots per degree of difference of temperature per hour, together witfc 
 tbe equivalent quantities of heat-units: 
 
588 
 
 HEAT. 
 
 Water at 212. Heat-units. Ratio. 
 
 Copper 0.665 Ib. 642.5 1.00 
 
 Brass 577 ' 556.8 0.87 
 
 Wrought iron .387 " 373.6 .58 
 
 Cast iron .327 - 315.7 .49 
 
 Whitham, "Steam Engine Design," p. 283, also Trans. A. S. M. E., ix f 
 425, in using these data in deriving a formula for surface condensers, calls 
 these figures those of perfect conductivity, and multiplies them by a 
 coefficient C, which he takes at 0.323, to obtain the efficiency of con- 
 denser surface in ordinary use, i.e., coated with saline and greasy deposits. 
 
 Transmission of Heat from Steam to Water through Coils of Iron 
 Pipe. H. G. C. Kopp and F. J. Meystre (Stevens Indicator, Jan., 1894) 
 give an account of some experiments on transmission of heat through 
 coils of pipe. They collate the results of earlier experiments as follows, 
 for comparison: 
 
 
 
 Steam con- 
 
 Heat trans- 
 
 
 
 ID 
 
 n 
 
 densed per 
 square foot 
 per degree 
 difference of 
 
 mitted per 
 square foot 
 per degree 
 difference of 
 
 
 i 
 
 1 
 
 "3 
 
 temperature 
 per hour. 
 
 temperature 
 per hour. 
 
 Remarks. 
 
 d 
 
 B 
 
 B 
 
 ffi 
 
 bC co 
 
 .' 
 
 bC . 
 
 
 
 ' 
 
 B 
 
 O 
 
 2 
 
 If 
 
 Rc'c 
 
 Jfcj 
 
 i c^ 
 
 
 ft 
 
 
 
 
 
 
 
 X 
 
 w 
 
 I 
 
 w a 
 
 W^ a 
 
 &M 
 
 |2 
 
 
 Laurens . 
 
 Copper coils . . 
 2 Copper coils 
 
 0.292 
 
 0.981 
 1 20 
 
 315 
 
 974 
 1120 
 
 
 Havrez . . 
 
 Copper coil . . . 
 
 0.268 
 
 1.26 
 
 280 
 
 1200 
 
 
 Perkins. . 
 
 Iron coil 
 
 
 0.24 
 
 
 215 
 
 ( Steam pressure 
 = 100. 
 
 
 
 " 
 
 
 0.22 
 
 
 208.2 
 
 ( Steam pressure 
 i =10. 
 
 Box 
 
 Iron tube 
 
 0.235 
 
 
 230 
 
 
 
 
 " " 
 
 0.196 
 
 
 207 
 
 
 
 
 
 d i 
 
 206 
 
 
 210 
 
 
 
 Havrez . . 
 
 Cast-iron boiler 
 
 0.077 
 
 0.105 
 
 82 
 
 "166" 
 
 
 From the above it would appear that the efficiency of iron surfaces Is 
 less than that of copper coils, plate surfaces being far inferior. 
 
 In all experiments made up to the present time, it appears that the 
 temperature of the condensing water was allowed to rise, a mean between 
 the initial and final temperatures being accepted as the effective tempera- 
 ture. But as water becomes warmer it circulates more rapidly, thereby 
 causing the water surrounding the coil to become agitated and replaced 
 by cooler water, which allows more heat to be transmitted. 
 
 Again, in accepting the mean temperature as that of the condensing 
 medium, the assumption is made that the rate of condensation is in direct 
 proportion to the temperature of the condensing water. 
 
 In order to correct and avoid any error arising from these assumptions 
 and approximations, experiments were undertaken,, in which all the condi- 
 tions were constant during each test. 
 
 The pressure was maintained uniform throughout the coil, and pro- 
 vision was made for the free outflow of the condensed steam, in order to 
 obtain at all times the full efficiency of the condensing surface. The con- 
 densing water was continually stirred to secure uniformity of temperature, 
 which was regulated by means of a steam-pipe and a cold-water pipe 
 entering the tank in which the coil was placed. 
 
CONDUCTION AND CONVECTION OF HEAT. 589 
 
 The following is a condensed statement of the results. 
 
 HEAT TRANSMITTED PER SQUARE FOOT OF COOLING SURFACE, PER HOUR, 
 PER DEGREE OF DIFFERENCE OF TEMPERATURE. (British Thermal Units.) 
 
 Temperature 
 of Condens- 
 ing Water. 
 
 1-in. Iron Pipe; 
 Steam inside, 
 60 Ibs. Gauge 
 Pressure. 
 
 H/2-in. Pipe; 
 Steam inside, 
 10 Ibs. 
 Pressure. 
 
 1 1/2-m. Pipe; 
 Steam outside, 
 10 Ibs. 
 Pressure. 
 
 1 1/2-in. Pipe; 
 Steam inside, 
 60 Ibs 
 Pressure. 
 
 80" 
 
 265 
 
 128 
 
 200 
 
 
 100 
 120 
 140 
 160 
 180 
 200 
 
 269 
 272 
 277 
 281 
 299 
 313 
 
 130 
 137 
 145 
 158 
 174 
 
 230 
 260 
 267 
 271 
 270 
 
 239 
 247 
 276 
 306 
 349 
 419 
 
 
 
 
 
 
 The results indicate that the heat transmitted per degree of difference of 
 temperature in general increases as the temperature of the condensing 
 water is increased. 
 
 The amount transmitted is much larger with the steam on the outside of 
 the coil than with the steam inside the coil. This may be explained in 
 part by the fact that the condensing water when inside the coil flows over 
 the surface of conduction very rapidly, and is more efficient for cooling 
 than when contained in a tank outside of the coil. 
 
 This result is in accordance with that found by Mr. Thomas Craddock, 
 which indicated that the rate of cooling by transmission of heat through 
 metallic surfaces was almost wholly dependent on the rate of circulation of 
 the cooling medium over the surface to be cooled. 
 
 Transmission of Heat in Condenser Tubes. (Eng'g, Dec. 10, 1875, 
 p. 449.) In 1874 B. C. Nichol made experiments for determining the 
 rate at which heat was transmitted through a condenser tube. The 
 results went to show that the amount of heat transmitted through the 
 walls of the tube per estimated degree of mean difference of temperature 
 increased considerably with this difference. For example: 
 
 Estimated mean difference of 
 temperature between inside and 
 outside of tube, degrees Fahr. . . . 
 
 Vertical Tube. Horizontal Tube. 
 
 128 151.9 152.9 111.6 146.2 150.4 
 
 Heat-units transmitted per hour 
 per square foot of surface per 
 degree of mean diff. of temp 422 531 
 
 561 610 737 823 
 
 These results seem to throw doubt upon Mr. Isherwood's statement that 
 the rate of evaporation per degree of difference of temperature is the same 
 for all temperatures. 
 
 Mr. Thomas Craddock found that water was enormously more efficient 
 than air for the abstraction of heat through metallic surfaces in the process 
 of cooling. He proved that the rate of cooling by transmission of heat 
 through metallic surfaces depends upon the rate of circulation of the cool- 
 in? medium over the surface to be cooled. A tube filled with hot 'water, 
 moved by rapid rotation at the rate of 59 ft. per second, through air, lost as 
 much heat in one minute as it did in still air in 12 minutes. In water, at a 
 velocity of 3 ft. per second, as much heat was abstracted in half a minute 
 as was abstracted in one minute when it was at rest in the water. Mr. 
 Craddock concluded, further, that the circulation cf the cooling fluid 
 became of greater importance as the difference of temperature on the 
 two sides of the plate became less. (Clark, R. T. D., p. 461.) 
 
 G. A. Orrok (Power, Aug. 11, 1908) gives a diagram showing the relation 
 of the B.T.U. transmitted per hour per sq. ft. of surface per degree of 
 difference of temperature to the velocity of the water in the condenser 
 tubes, in feet per second, as obtained by different experimenters. Approx* 
 Imate figures taken from the several curves are given below. 
 
590 
 
 HEAT. 
 
 Authority. 
 
 Tubes. 
 
 Velocity of Water, Feet per 
 Second. 
 
 0.5 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 B.T.U. per sq. ft. per hr. per 
 deg. difif. 
 
 1. Stanton 
 2. Stanton 
 3. Nichols 
 4. Nichols 
 5. Hepburn 
 6. Hepburn . . . 
 7. Richter 
 8. Weighton. . . 
 9. Alien 
 
 l/2-jn. vert, copper 
 l/2~i n - vert, copper . 
 
 
 325 
 420 
 340 
 500 
 365 
 560 
 
 400 
 470 
 370 
 530 
 590 
 
 465 
 525 
 405 
 560 
 
 520 
 560 
 435 
 
 585 
 
 550 
 585 
 460 
 615 
 
 470 
 650 
 
 3/4-in. vert, brass 
 3/4-in. horiz. brass 
 1 i/4-in. horiz. copper. . . . 
 1 l/4-in. horiz. corrugated 
 1 1/2-in. horiz. corrugated 
 5/g-in. plain tubes. . . . 
 
 "250" 
 360 
 <60 
 
 
 
 
 
 
 
 
 380 
 225 
 
 615 
 290 
 
 760 
 365 
 
 865 
 
 940 
 
 5/s-in. horizontal 
 
 
 No. 1, water flowing up. Nos. 2 and 3, water flowing down. 
 
 Transmission of Heat in Feed-water Heaters. (W. R. Billings, 
 The National Engineer, June, 1907.) Experiments show that the rate of 
 transmission of heat through metal surfaces from steam to water increases 
 rapidly with the increased rate of flow of the water. Mr. Billings there- 
 fore recommends the use of small tubes in heaters in which the water is 
 inside of the tubes. He says: A high velocity through the tubes causes 
 friction between the water and the walls of the tubes; this friction is not 
 the same as the friction between the particles of water themselves, and it 
 tends to break up the column of water and bring fresh and cooler particles 
 against the hot walls of the tubes. 
 
 The following results were obtained in tests: 
 
 li/4-m. smooth tubes j ^ II 1 ||' 5 \}Q 67Q 
 
 1 i/2-in. corrugated tubes j ^ II 3 ^| 4 |^ ,g| ,,! 
 
 V = velocity of the water, ft. per min. U = B.T.U. transmitted per 
 sq. ft. per hour per degree difference of temperature. (See Condensers.) 
 
 In calculations of heat transmission in heaters it is customary to take 
 as the mean difference of temperature the difference between the tem- 
 perature of the steam and the arithmetical mean of the initial and final 
 temperatures of the water; thus if S = steam temperature, / = initial 
 and F = final temperature of the water, and D = mean difference, then 
 D = S - 1/2 (/ + F). Mr. Billings shows that this is incorrect, and on 
 the assumption that the rate of transmission through any portion of the 
 surface is directly proportional to the difference he finds the true mean 
 
 to be D - hyp lQg [( /_- f) 7 + {S _ pn (This formula was derived by 
 
 Cecil P. Poole in 1899, Power, Dec., 1906.) 
 
 The following table is calculated from the formula: 
 
 DEGREES OF DIFFERENCE BETWEEN STEAM TEMPERATURE AND ACTUAII 
 AVERAGE TEMPERATURE OF WATER. 
 
 Vacuum Heaters Between Engine and Condenser. 
 
 Initial 
 Temperature 
 of Water. 
 
 26" Vac. Temp. 126 F. 
 
 24" Vac. Temp. 141 F. 
 
 Final Temp, of Water. 
 
 Final Temp, of Water. 
 
 105 
 
 110 
 
 115 
 
 120 
 
 105 
 
 110 
 
 115 
 
 120 
 
 125 
 
 130 
 
 40.6 
 37.9 
 35.0 
 32.2 
 29.2 
 
 40. ,, 
 
 46.1 
 42.8 
 39,3 
 35.6 
 31.8 
 
 41.6 
 38.4 
 35.3 
 31.9 
 28.3 
 
 36.9 
 33.6 
 30.7 
 27,6 
 24,3 
 
 30.1 
 27.6 
 25.0 
 22,4 
 19.6 
 
 62.9 
 59.2 
 55.5 
 51.6 
 47.6 
 
 60.2 
 56.6 
 52.1 
 48.2 
 44.2 
 
 55.3 
 51.8 
 48.4 
 45.0 
 41.2 
 
 50.9 
 47.7 
 44.4 
 41.0 
 37.3 
 
 46.1 
 43.2 
 40.1 
 36,9 
 33.6 
 
 30., 
 
 60... 
 
 70.,, 
 
 80 
 
 
CONDUCTION ATSTD CONVECTION OF HEAT. 591 
 
 Initial Temp, 
 of Water. 
 
 Atmospheric Heaters. 
 
 Atmos. Press. Temp. 
 212 F. 
 
 Initial Temp, of 
 Water. 
 
 Atmos. Press. Temp. 
 212 F. 
 
 Final Temp, of Water. 
 
 Final Temp, of Water. 
 
 192 
 
 196 
 
 200 
 
 204 
 
 208 
 
 210 
 
 192 
 
 196 
 
 200 
 
 204 
 
 208 
 
 210 
 
 40 
 
 70.6 
 
 67.9 
 65.1 
 62.2 
 59.4 
 
 65.7 
 63.1 
 60.4 
 57.7 
 54.9 
 
 60.1 
 57.6 
 55.2 
 52.6 
 50.0 
 
 53.5 
 
 51.2 
 48.9 
 46.6 
 44.2 
 
 44.8 
 42.8 
 40.7 
 38.7 
 36.6 
 
 38.0 
 36.4 
 34.7 
 32.9 
 31.0 
 
 105 
 110 
 115 
 120 
 125 
 
 51.9 
 50.3 
 48.8 
 47.2 
 45.6 
 
 47.9 
 46.4 
 45.0 
 43.5 
 41.9 
 
 43.4 
 42.1 
 40.6 
 39.2 
 37.8 
 
 38.2 
 36.9 
 35.7 
 34.4 
 33.1 
 
 31.4 
 30.2 
 29.2 
 28.0 
 26.9 
 
 26.4 
 25.5 
 24.5 
 23.5 
 22.5 
 
 50... 
 
 60 .. 
 
 70... 
 
 80 
 
 
 The error in using the arithmetic mean for the value of D is not impor- 
 tant if F is very much lower than S, but if it is within 10 of S then the 
 error may be a large one. With S = 212, 7 = 40, F = 110, the arith- 
 metic mean difference is 137, and the value by the logarithmic formula 
 131, an error of less than 5%; but if F is 204, the arithmetic mean is 90, 
 and the value by the formula 53.5. 
 
 It should be observed, however, that the formula is based on an assump- 
 tion that is probably greatly in error for high temperature differences, 
 i.e., that the transmission of heat is directly proportional to the tem- 
 perature difference. It may be more nearly proportional to the square 
 of the difference, as stated by Rankine. This seems to be indicated by 
 the results of heating water by steam coils, given below. 
 
 Heating Water by Steam Coils. A catalogue of the American 
 Radiator Co. (1908) gives a chart showing the pounds of steam condensed 
 per hour per sq. ft. of iron, brass and copper pipe surface, for different 
 mean or average differences of temperature between the steam and the 
 water. Taking the latent heat of the steam at 966 B.T.U. per lb., the fol- 
 lowing figures are derived from the table. 
 
 Mean 
 
 Lb. Steam Condensed 
 per Hour per Sq. Ft. 
 of Pipe. 
 
 Lb. Steam Condensed 
 per Hour per Sq. Ft. 
 per Deg. Diff. 
 
 B.T.U. per Sq. 
 Ft. per Hour 
 per Deg. Diff. 
 
 Iron. 
 
 Brass. 
 
 Copper 
 
 Iron. 
 
 Brass. 
 
 Copper 
 
 Iron. 
 
 Brass 
 
 Cop. 
 
 50 
 100 
 150 
 200 
 
 7.5 
 18.5 
 32.2 
 48 
 
 12.5 
 38 
 76.5 
 128 
 
 14.5 
 43.5 
 87.8 
 144 
 
 0.150 
 0.185 
 0.215 
 0.240 
 
 0.250 
 0.380 
 0.510 
 0.640 
 
 0.290 
 0.435 
 0.585 
 0.720 
 
 101 
 179 
 208 
 232 
 
 198 
 367 
 493 
 618 
 
 280 
 415 
 565 
 696 
 
 The chart is said to be plotted from a large number of tests with pipes 
 placed vertically in a tank of water, about 20 per cent being deducted 
 from the actual results as a margin of safety. 
 
 W. R. Billings (Eng. Rec., Feb., 1898) gives as the results of one set of 
 experiments with a closed feed-water heater: 
 
 Diff. bet. temp, of steam and final temp, of 
 
 water, deg. F 5 6 8 11 15 18 
 
 B.T.U. per sq. ft. per hr. per deg. mean diff ... 67 79 89 114 129 139 
 
 Heat Transmission through Cast-iron Plates Pickled in Nitric 
 Acid. Experiments by R. C. Carpenter (Trans. A. S. M. E., xii, 179) 
 show a marked change in the conducting power of the plates (from 
 steam to water), due to prolonged treatment with dilute nitric acid. 
 
592 
 
 HEAT. 
 
 The action of the nitric acid, by dissolving the free iron and not attack- 
 ing the carbon, forms a protecting surface to the iron, which is largely 
 composed of carbon. The following is a summary of results: 
 
 
 Increase 
 
 Proportionate 
 
 
 
 in Tem- 
 
 Thermal Units 
 
 Rela- 
 
 
 perature 
 
 Transmitted for 
 
 tive 
 
 Character of Plates, each plate 8.4 in. 
 by 5.4 in., exposed surface 27 sq. ft. 
 
 of 3.125 
 
 Ibs. of 
 
 each Degree* of 
 Difference of 
 
 Trans- 
 mission 
 
 
 Water 
 
 Temperature per 
 
 of 
 
 
 each 
 
 Square Foot per 
 
 Heat. 
 
 
 Minute. 
 
 Hour. 
 
 
 Cast iron untreated skin on, but 
 
 
 
 
 clean, free from rust 
 
 13 90 
 
 113 2 
 
 100 
 
 Cast iron nitric acid, 1 % sol., 9 days . . 
 
 11.5 
 
 97J 
 
 86J 
 
 1% sol., 18 days 
 
 9.7 
 
 80.08 
 
 70.7 
 
 1% sol., 40 days 
 
 9.6 
 
 77.8 
 
 68.7 
 
 5% sol., 9 days.. 
 
 9.93 
 
 87.0 
 
 76. 8 
 
 5% sol., 40 days 
 
 10.6 
 
 77.4 
 
 68. 5 
 
 Plate of pine wood, same dimensions as 
 
 
 
 
 the plate of cast iron 
 
 0.33 
 
 1 .9 
 
 J.6 
 
 
 
 
 
 The effect of covering cast-iron surfaces with varnish has been investi- 
 gated by P. M. Chamberlain. He subjected the plate to the action of strong 
 acid for a few hours, and then applied a non-conducting varnish. One 
 surface only was treated. Some of his results are as follows: 
 
 tfo 
 
 <#=+-! 
 
 o> b oT 
 
 W 
 
 170. As finished greasy. 
 
 152. washed with benzine and dried. 
 
 169. Oiled with lubricating oil. 
 
 162. After exposure to nitric acid sixteen hours, then oiled 
 
 (linseed oil). 
 166. After exposure to hydrochloric acid twelve hours, then 
 
 oiled (linseed oil). 
 
 113. (After exposure to sulphuric acid 1, water 2, for 48 
 < hours, then oiled, varnished, and allowed to dry for 
 117. ( 24 hours. 
 
 Transmission of Heat through Solid Plates from Air or other Dry 
 Gases to Water. (From Clark on the Steam Engine.) The law of the 
 transmission of heat from hot air or other gases to water, through metallic 
 plates, has not been exactly determined by experiment. The general 
 results of experiments on the evaporative action of different portions of 
 the heating surface of a steam-boiler point to the general law that the 
 quantity of heat transmitted per degree difference of temperature is 
 practically uniform for various differences of temperature. 
 
 The communication of heat from the gas to the plate surface is much 
 accelerated by mechanical impingement of the gaseous products upon the 
 surface. 
 
 Clark says that when the surfaces are perfectly clean, the rate of trans- 
 mission of heat through plates of metal from air or gas to water is greater 
 for copper, next for brass, and next for wrought iron. But when the 
 surfaces are dimmed or coated, the rate is the same for the different 
 metals. 
 
 With respect to the influence of the conductivity of metals and of the 
 thickness of the plate on the transmission of heat from burnt gases to 
 water, Mr. Napier made experiments with small boilers of iron and copper 
 placed over a gas-flame. The vessels were 5 inches in diameter and 2 1/2 
 inches deep. From three vessels, one of iron, one of copper, and one 
 of iron sides and copper bottom, each of them i/so inch in thickness, 
 
CONDUCTION AND CONVECTION OF HEAT. 593 
 
 equal quantities of water were evaporated to dryness, in the times as 
 follows: 
 
 Water. Iron Vessel. Copper Vessel. Iron f c d es C e ?. Pper 
 
 4 ounces 19 minutes 18.5 minutes 
 
 11 " 33 30.75 
 
 5J/2 " 50 " 44 
 
 4 " 35.7 ' 36.83 minutes 
 
 Two other vessels of iron sides 1/30 inch thick, one having a i/4-inch 
 copper bottom and the other a i/4-inch lead bottom, were tested against 
 the iron and copper vessel, Vso inch thick. Equal quantities of water were 
 evaporated in 54, 55, and 531/2 minutes respectively. Taken generally, 
 the results of these experiments show that there are practically but slight 
 differences between iron, copper, and lead in evaporative activity, and 
 that the activity is not affected by the thickness of the bottom. . 
 
 Mr. W. B. Johnson formed a like conclusion from the results of his 
 observations of two boilers of 160 horse-power each, made exactly alike, 
 except that one had iron flue-tubes and the other copper flue-tubes. No 
 difference could be detected between the performances of these boilers. 
 
 Divergencies between the results of different experimenters are attrib- 
 utable probably to the difference of conditions under which the heat was 
 transmitted, as between water or steam and water, and between gaseous 
 matter and water. On one point the divergence is extreme: the rate of 
 transmission of heat per degree of difference of temperature. Whilst from 
 400 to 600 units of heat are transmitted from water to water through iron 
 plates, per degree of difference per square foot per hour, the quantity of 
 heat transmitted between water and air, or other dry gas, is only about 
 from 2 to 5 units, according as the surrounding air is at rest or in move- 
 ment: In a locomotive boiler, where radiant heat was brought into play, 
 17 units of heat were transmitted through the plates of the fire-box per 
 degree of difference of temperature per square foot per hour. 
 
 Transmission of Heat through Plates from Flame to Water. 
 Much controversy has arisen over the assertion by some makers of live- 
 steam feed-water heaters that if the water fed to a boiler was first heated to 
 the boiling point before being fed into the boiler, by means of steam taken 
 from the boiler, an economy of fuel would result; the theory being that 
 the rate of transmission through a plate to water was very much greater 
 when the water was boiling than when it was being heated to the boiling 
 point, on account of the greatly increased rapidity of circulation of the 
 water when boiling. (See Eng'g, Nov. 16, 1906, and Bnff. Review [London], 
 Jan., 1908.) Two experiments by Sir Wm. Anderson (1872), with a steam- 
 jacketed pan, are quoted, one of which showed an increased transmission 
 when boiling of 133%, and the other of 80%; also an experiment by 
 Sir F. Bramwell, with a steam-heated copper pan, which showed a gain of 
 164% with boiling water. On the other hand, experiments by S. B. Bil- 
 brough (Transvaal Inst. Mining Engineers, Feb., 1908) showed in tests 
 with a flame-heated pan that there was no difference in the rate of trans- 
 mission whether the water was cold or boiling. W. M. Sawdon (Ptiwer, 
 Jan. 12, 1909) objects to Mr. Bilbrough's conclusions on the ground that 
 no corrections for radiation were made, and finds by a similar experiment, 
 with corrections, that the increased rate of transmission with boiling water 
 is at least 38%. All of these experiments were on a small scale, and in 
 view of their conflict no conclusions can be drawn from them as to the 
 value of live-steam feed-water heating in improving the economy of a 
 steam boiler. 
 
 A. Blechynden's Tests. A series of steel plates from 0.125 in. to 
 1.187 in. thick were tested with hot gas on one side and water on the other 
 with differences of temperature ranging from 373 to 1318 F. Trans.') 
 Inst. Naval Architects, 1894.) Mr. Blechynden found that the heat 
 transmitted is proportional to the square of the difference between the 
 temperatures at the two sides of the plate, or: Heat transmitted per sq. 
 ft. -4- (diff. of temp.) 2 = a constant. A study of the results of these 
 tests is made in Kent's " Steam Boiler Economy," p. 325, and it is shown 
 that the value of a in Rankine's formula q =(T\ T) 2 -5- a, which a is the 
 reciprocal of Mr. Blechynden's constant and is a function of the thickness 
 of the plate. One of the plates, A, originally 1.187 in. thick, was reduced 
 
594 
 
 HEAT. 
 
 in four successive operations, by machining to 0.125 in. Another, , was 
 tested in four thicknesses. The other plates were tested in one or two 
 thicknesses. Each plate was found to have a law of transmission of its 
 own. For plate A the value of a is represented closely by the formula 
 a = 40 4- 20 t, in which t is the thickness in inches. The formula a = 
 40 + 20 t 10 covers the whole range of the experiments. The whole 
 range of values is 38.6 to 71.9, which are very low when compared with 
 values of a computed from the results of boiler tests, which are usually 
 from 200 to 400, the low values obtained by Blechynden no doubt being 
 due to the exceptionally favorable conditions of his tests as compared 
 with those of boiler tests. Rankine says the value of a lies between 160 
 and 200, but values below 200 are rarely found in tests of modern types 
 of boilers. (See Steam-Boilers.) 
 
 Cooling of Air. H. F. Benson (Am. Mach., Aug. 31, 1905) derives 
 the following formula for transmission of heat from air to water through 
 copper tubes. It is assumed that the rate of transmission at any point of 
 the surface is directly proportional to the difference of temperature 
 between the air and water. 
 
 Let A = cooling surface, sq. ft.; K = Ib. of air per hour; S a = specific 
 heat of air; T ai temp, of hot inlet air; T a ^ =temp. of cooled outlet air; 
 d = actual average diff. of temp, bet ween "the air and the water; 17 = 
 B.T.U. absorbed by the water per degree of diff. of temp, per sq. ft. per 
 hour. W = Ib. of water per hour; T Wl = temp, of inlet water; T W2 = 
 temp, of outlet water. Then 
 
 AdU = KS a (T ai - 
 
 A = KS a (T ai - 
 
 - dU. 
 
 KSgW 
 
 W-KS n 
 
 T a , ~ T w 
 
 T 
 
 * in 
 
 T W2 - (S a K + W) (T ai - T a J + T wr 
 
 The more cooling water used, the lower is the temperature T wr Also 
 the less T Wz is, the larger d becomes and the less surface is needed. About 
 10 is the largest value of W/K that it is economical to use, as there is a 
 saving of less than 0.5% in increasing it from 10 to 15. When desirable 
 to save water it will be advisable to make W/K = 5. Values of U 
 obtained by experiment with a Wainwright cooler made with corrugated 
 copper tubes are given in the following table. K and W are in Ib. per 
 minute, B a = B.T.U. from air per min., B w = B.T.U. from water per 
 min., Vw = velocity of water, ft. per min. 
 
 r.i 
 
 ** 
 
 T 
 
 l Wt 
 
 T 
 
 /H>2 
 
 K 
 
 W 
 
 * 
 
 B* 
 
 v w 
 
 U 
 
 221.0 
 
 76.3 
 
 50.0 
 
 169.0 
 
 125.2 
 
 28.50 
 
 4303 
 
 3392 
 
 2.20 
 
 6.75 
 
 217.0 
 
 64.3 
 
 45.8 
 
 146.4 
 
 122.8 
 
 36.73 
 
 4452 
 
 3695 
 
 2.84 
 
 7.12 
 
 224.0 
 
 63.3 
 
 45.7 
 
 149. 2 
 
 126.3 
 
 40.30 
 
 4819 
 
 4171 
 
 3.11 
 
 7.91 
 
 209.6 
 
 54.0 
 
 43.8 
 
 125.9 
 
 122.1 
 
 50.00 
 
 4511 
 
 4105 
 
 3.86 
 
 8.81 
 
 214.5 
 
 46.3 
 
 43.0 
 
 106.2 
 
 124.6 
 
 68.95 
 
 4976 
 
 4357 
 
 5.32 
 
 10.55 
 
 234.6 
 
 63.6 
 
 52.6 
 
 120.2 
 
 124.4 
 
 73.25 
 
 5051 
 
 4852 
 
 5.65 
 
 8.41 
 
 214.2 
 
 43.5 
 
 43.0 
 
 94.7 
 
 117.3 
 
 79.84 
 
 4753 
 
 4128 
 
 6.16 
 
 14.32 
 
 242.9 
 
 61.7 
 
 55.3 
 
 114.0 
 
 133.6 
 
 92.72 
 
 5649 
 
 5443 
 
 7.15 
 
 10.01 
 
 223.0 
 
 46.0 
 
 40.1 
 
 79.1 
 
 130.5 
 
 114 80 
 
 5484 
 
 4477 
 
 8.86 
 
 7.86 
 
 239.3 
 
 57.5 
 
 51.0 
 
 95.2 
 
 130.0 
 
 125.70 
 
 5612 
 
 5556 
 
 9.70 
 
 9.38 
 
 246 
 
 58.0 
 
 52.3 
 
 95.1 
 
 133.8 
 
 145.90 
 
 5977 
 
 6244 
 
 11.26 
 
 10.57 
 
 Sixteen other tests were made besides those given above, and their 
 plotted results all come within the field covered by those in the table. 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 595 
 
 There is apparently an error in the last line of the table, for the heat 
 gained by the water could not be greater than that lost by the air. The 
 excess lost by the air may be due to radiation, but it shows a great irregu- 
 larity. It appears that for velocities of water between 2.2 and 5.3 ft. per 
 min. the value of U increases with the velocity, but for higher velocities 
 the value of U is very irregular, and the cause of the irregularity is not 
 explained. 
 
 Chas. L. Hubbard (The Engineer, Chicago, May 18, 1902) made some 
 tests by blowing air through a tight wooden box which contained a nest 
 of 30 li/2-in. tin tubes, of a total surface of about 20 sq. ft., through 
 which cold water flowed. The results were as follows: 
 
 Cu. ft. of air per minute 
 
 768 
 
 268 
 
 469 
 
 469 
 
 636 
 
 636 
 
 Velocity over cooling surface 
 Initial temperature of air 
 
 638 
 
 77 
 
 638 
 72 
 
 1116 
 
 72 
 
 1116 
 74 
 
 1514 
 
 74 
 
 1514 
 74 
 
 Drop in temperature 
 
 
 12 
 
 8 
 
 10 
 
 8 
 
 10 
 
 Average temp, of water 
 Average temp, of air 
 
 50 
 68 
 
 43 
 66 
 
 48 
 68 
 
 48 
 69 
 
 50 
 
 70 
 
 44 
 68 
 
 Difference 
 
 18 
 
 23 
 
 20 
 
 21 
 
 20 
 
 24 
 
 B.T.U. per hour per sq. ft. per degree 
 difference 
 
 6.5 
 
 7.6 
 
 10.2 
 
 12.1 
 
 13.8 
 
 14.4 
 
 
 
 
 
 
 
 
 Transmission of Heat through Plates and Tubes from Steam or 
 Hot Water to Air. The transfer of heat from steam or water through 
 a plate or tube into the surrounding air is a complex operation, in which 
 the internal and external conductivity of the metal, the radiating power 
 of the surface, and the convection of heat in the surrounding air, are all 
 concerned. Since the quantity of heat radiated from a surface varies with 
 the condition of the surface and with the surroundings, according to laws 
 not yet determined, and since the heat carried away by convection varies 
 with the rate of the flow of the air over the surface, it is evident that no 
 general law can be laid down for the total quantity of heat emitted. 
 
 The following is condensed from an article on "Loss of Heat from 
 Steampipes," in The Locomotive, Sept. and Oct., 1892. 
 
 A hot steam-pipe is radiating heat constantly off into space, but at the 
 same time it is cooling also by convection. Experimental data on which 
 to base calculations of the heat radiated and otherwise lost by steam-pipes 
 are neither numerous nor satisfactory. 
 
 In Box's " Practical Treatise on Heat" a number of results are given for 
 the amount of heat radiated by different substances when the temperature 
 of the air is 1 Fahr. lower than the temperature of the radiating body. A 
 portion of this table is given below. It is said to be based on Pellet's 
 experiments. 
 
 HEAT UNITS RADIATED PER HOUR, PER SQUARE FOOT OP SURFACE, 
 FOR 1 FAHRENHEIT EXCESS IN TEMPERATURE. 
 
 Copper, polished 0.0327 
 
 Tin, polished 0.0440 
 
 Zinc and brass, polished . . . 0.0491 
 
 Tinned iron, polished 0.0858 
 
 Sheet iron, polished 0.0920 
 
 Sheet lead 0.1329 
 
 Sheet iron, ordinary 0.5662 
 
 Glass 0.5948 
 
 Cast iron, new 0.6480 
 
 Common steam-pipe, in- 
 ferred 0.6400 
 
 Cast and sheet iron, rusted . . 0.6868 
 Wood, building stone, and 
 
 brick. . ... 0.7358 
 
 When the temperature of the air is about 50 or 60 Fahr., and the radiat- 
 ing body is not more than about 30 hotter than the air, we may calculate 
 the radiation of a given surface by assuming the amount of heat given off 
 by it in a given time to be proportional to the difference in temperature 
 between the radiating body and the air. This is " Newton's law of cooling. " 
 But when the difference in temperature is great, Newton's law does not 
 hold good; the radiation is no longer proportional to the difference in tern* 
 perature, but must be calculated by a complex formula established experi- 
 mentally by Dulong and Petit. Box has computed a table from thit 
 
596 
 
 HEAT. 
 
 formula, which greatly facilitates its application, and which is given 
 below: 
 
 FACTORS FOR REDUCTION TO DULONG'S LAW OF RADIATION. 
 
 Differences in Tem- 
 perature between 
 Radiating Body 
 and the Air. 
 
 Temperature of the Air on the Fahrenheit Scale. 
 
 32 
 
 50 
 
 59 
 
 68 
 
 86 
 
 104 
 
 122 
 
 140 
 
 158 
 
 176 
 
 194 
 
 212 C 
 
 Deg. Fahr. 
 18 
 
 .00 
 
 .07 
 
 .12 
 
 .16 
 
 .25 
 
 .36 
 
 .47 
 
 .58 
 
 1.70 
 
 1.85 
 
 1.99 
 
 2.15 
 
 36 
 
 .03 
 
 .11 
 
 .16 
 
 .21 
 
 .30 
 
 .40 
 
 .52 
 
 .68 
 
 1.76 
 
 1.91 
 
 2.06 
 
 2.23 
 
 54 
 
 .07 
 
 .16 
 
 .20 
 
 .25 
 
 .35 
 
 .45 
 
 .58 
 
 .70 
 
 1.83 
 
 1.99 
 
 2.14 
 
 2.31 
 
 72 
 
 .12 
 
 .20 
 
 .25 
 
 .30 
 
 .40 
 
 .52 
 
 .64 
 
 .76 
 
 1.90 
 
 2.07 
 
 2.23 
 
 2 40 
 
 90 
 
 .16 
 
 .25 
 
 .31 
 
 .36 
 
 .46 
 
 .58 
 
 .71 
 
 .84 
 
 1.98 
 
 2.15 
 
 2.33 
 
 2.51 
 
 108 
 
 .21 
 
 .31 
 
 .36 
 
 .42 
 
 .52 
 
 .65 
 
 .78 
 
 .92 
 
 2.07 
 
 2.28 
 
 2.42 
 
 2.62 
 
 126 
 
 .26 
 
 .36 
 
 .42 
 
 .48 
 
 .60 
 
 .72 
 
 .86 
 
 2.00 
 
 2.16 
 
 2.34 
 
 2.52 
 
 2.72 
 
 144 
 
 .32 
 
 .42 
 
 .48 
 
 .54 
 
 .65 
 
 .79 
 
 .94 
 
 2.08 
 
 2.24 
 
 2.44 
 
 2.64 
 
 2.83 
 
 162 
 
 .37 
 
 .48 
 
 .54 
 
 .60 
 
 .73 
 
 .86 
 
 2.02 
 
 2.17 
 
 2.34 
 
 2.54 
 
 2.74 
 
 2.96 
 
 180 
 
 44 
 
 .55 
 
 61 
 
 .68 
 
 .81 
 
 .95 
 
 2.11 
 
 2.27 
 
 2.46 
 
 2.66 
 
 2.87 
 
 3.10 
 
 198 
 
 .50 
 
 .62 
 
 .69! .75ll.89 l 2.04 
 
 2.21 
 
 2.38 
 
 2.56 
 
 2.78 
 
 3. CO 
 
 3.24 
 
 216 
 
 .58 
 
 .69 
 
 .76 
 
 .83 
 
 1.97 
 
 2.13 
 
 2.32 
 
 2.48 
 
 2.68 
 
 2.91 
 
 3.13 
 
 3.38 
 
 234 
 
 .64 
 
 .77 
 
 .84 
 
 .90 
 
 2.06 
 
 2.23 
 
 2.43 
 
 2.52 
 
 2.80 
 
 3.03 
 
 3.28 
 
 3.46 
 
 252 
 
 .71 
 
 .85 
 
 .92 
 
 2.00 
 
 2.15 
 
 2.33 
 
 2.52 
 
 2.71 
 
 2.92 
 
 3.18 
 
 3.43 
 
 3.70 
 
 270 
 
 .79 
 
 .93 
 
 2.01 
 
 2.09 
 
 2.26 
 
 2.44 
 
 2.64 
 
 2.84 
 
 3.06 
 
 3.32 
 
 3.58 
 
 3 87 
 
 288 
 
 .89 
 
 2.03 
 
 2.12 
 
 2.20 
 
 2.37 
 
 2.56 
 
 2.78 
 
 2.99 
 
 3.22 
 
 3.50 
 
 3.77 
 
 4.07 
 
 306 
 
 .98 
 
 2.13 
 
 2.22 
 
 2.31 
 
 2.49 
 
 2.69 
 
 2.90 
 
 3.12 
 
 3.37 
 
 3.66 
 
 3 95 
 
 4.26 
 
 324 
 
 2.07 
 
 2.23 
 
 2.33 
 
 2.42 
 
 2.62 
 
 2.81 
 
 3.04 
 
 3.28 
 
 3.53 
 
 3.84 
 
 4.14 
 
 4.46 
 
 342 
 
 2.17 
 
 2.34 
 
 2.44 
 
 2.54 
 
 2.73 
 
 2.95 
 
 3.19 
 
 3.44 
 
 3.70 
 
 4.02 
 
 4.34 
 
 4.68 
 
 360 
 
 2.27 
 
 2.45 
 
 2.56 
 
 2.66 
 
 2.86 
 
 3.09 
 
 3.35 
 
 3.60 
 
 3.88 
 
 4,22 
 
 4.55 
 
 4.91 
 
 378 
 
 2.39 
 
 2.57 
 
 2.68 
 
 2.79 
 
 3.00 
 
 3.24 
 
 3.51 
 
 3.78 
 
 4.08 
 
 4.42 
 
 4.77 
 
 5.15 
 
 396 
 
 2.50 
 
 2.70 
 
 2.81 
 
 2.93 
 
 3.15 
 
 3.40 
 
 3.68 
 
 3.97 
 
 4.28 
 
 4.64 
 
 5.01 
 
 5.40 
 
 414 
 
 2.63 
 
 2.84 
 
 2.95 
 
 3.07 
 
 3.31 
 
 3.56 
 
 3.87 
 
 4.12 
 
 4.48 
 
 4.87 
 
 5.26 
 
 5.67 
 
 432 
 
 2 76 
 
 7 98 
 
 3 10 
 
 ^ 73 
 
 3 47 
 
 3 76 
 
 4 10 
 
 4 37, 
 
 4 61 
 
 5 17 
 
 5 53 
 
 6.04 
 
 
 
 
 
 
 
 
 
 
 
 
 The loss of heat by convection appears to be independent of the nature 
 of the surface, that is, it is the same for iron, stone, wood, and other 
 materials. It is different for bodies of different shape, however, and it 
 varies with the position of the body. Thus a vertical steam-pipe will not 
 lose so much heat by convection as a horizontal one will; for the 'air 
 heated at the lower part of the vertical pipe will rise along the surface of 
 the pipe, protecting it to some extent from the chilling action of the sur- 
 rounding cooler air. For a similar reason the shape of a body has an 
 important influence on the result, those bodies losing most heat whose 
 forms are such as to allow the cool air free access to every part of their 
 surface. The following table from Box gives the number of heat units 
 that horizontal cylinders or pipes lose by convection per square foot of 
 surface per hour, for one degree difference in temperature between the 
 pipe and the air. 
 
 HEAT UNITS LOST BY CONVECTION FROM HORIZONTAL PIPES, PER SQUARE 
 FOOT OF SURFACE PER HOUR, FOR A TEMPERATURE 
 DIFFERENCE OF 1 FAHR. 
 
 External 
 Diameter 
 of Pipe 
 in Inches. 
 
 Heat 
 Units 
 Lost. 
 
 External 
 Diameter 
 of Pipe 
 in Inches. 
 
 Heat 
 Units 
 Lost. 
 
 External 
 Diameter 
 of Pipe 
 in Inches. 
 
 Heat 
 Units 
 Lost. 
 
 2 
 3 
 4 
 5 
 6 
 
 0.728 
 0.626 
 0.574 
 0.544 
 523 
 
 7 
 8 
 9 
 10 
 12 
 
 0.509 
 0.498 
 0.489 
 482 
 472 
 
 18 
 24 
 36 
 
 48 
 
 0.455 
 0.447 
 438 
 434 
 
 
 
 
 
 
 
THERMODYNAMICS. 
 
 597 
 
 The loss of heat by convection is nearly proportional to the difference 
 In temperature between the hot body and the air, but the experiments of 
 Dulong and Pficlet show that this is not exactly true, and we may here also 
 resort to a table of factors for correcting the results obtained by sample 
 proportion. 
 
 FACTORS FOR REDUCTION TO DULONG'S LAW OF CONVECTION. 
 
 Difference 
 in Temp, 
 between Hot 
 Body and 
 Air. 
 
 Factor. 
 
 Difference 
 in Temp, 
 between Hot 
 Body and 
 Air. 
 
 Factor. 
 
 Difference 
 in Temp, 
 between Hot 
 Body and 
 Air.. 
 
 Factor. 
 
 18 F. 
 36 
 
 540 
 
 72 
 90 
 108 
 126 
 144 
 162 
 
 0.94 
 .11 
 
 .22 
 .30 
 .37 
 .43 
 49 
 .53 
 .58 
 
 H80F. 
 198 
 216 
 234 
 252 
 270 
 288 
 306 
 324 
 
 1.62 
 .65 
 .68 
 .72 
 .74 
 .77 
 .80 
 .83 
 .85 
 
 342 F. 
 360 
 378 
 396 
 414 
 432 
 450 
 468 
 
 .87 
 .90 
 .92 
 .94 
 .96 
 .98 
 2.00 
 2.02 
 
 
 
 
 
 
 
 EXAMPLE IN THE USE OF THE TABLES. Required the total loss of heat 
 by both radiation and convection, per foot of length of a steam-pipe 211/33 
 in. external diameter, steam pressure 60 Ibs., temperature of the air in the 
 room 68 Fahr. 
 
 Temperature corresponding to 60 Ibs. equals 307; temperature dif- 
 ference = 307 - 68 = 239. 
 
 Area of one foot length of steam-pipe = 211/32 X 3.1416 -*- 12 = 
 0.614 sq. ft. 
 
 Heat radiated per hour per square foot per degree of difference, from 
 table, 0.64. 
 
 Radiation loss per hour by Newton's law = 239 X 0.614 ft. X 0.64 = 
 93 9 heat units. Same reduced to conform with Dulong's law of radiation: 
 factor from table for temperature difference of 239 and temperature of 
 air 68 = 1.93. 93.9 X 1.93 = 181.2 heat units, total loss by radiation. 
 
 Convection loss per square foot per hour from a 2ii/32-inch pipe: by 
 interpolation from table, 2" = 0.728, 3" = 0.626, 211/32" = 0.693. 
 
 Area, 0.614 X 0.693 X 239 = 101.7 heat units. Same reduced to 
 conform with Dulong's law of convection: 101.7 X 1.73 (from table) = 
 175.9 heat units per hour. Total 'loss by radiation and convection = 
 181.2 + 175.9 = 357.1 heat units per hour. Loss per degree of difference 
 of temperature per linear foot of pipe per hour = 357.1 -* 239 = 1.494 
 heat units = 2.433 per sq. ft. 
 
 It is not claimed, says The Locomotive, that the results obtained by this 
 method of calculation are strictly accurate. The experimental data are 
 not sufficient to allow us to compute the heat-loss from steam-pipes with 
 any great degree of refinement: yet it is believed that the results obtained 
 as indicated above will be sufficiently near the truth for most purposes. 
 An experiment by Prof. Ordway, in a pipe 211/33 in. diam. 'under the above 
 conditions (Trans. A. S. M. E. t v. 73), showed a condensation of steam of 
 181 grams per hour, which is equivalent to a loss of heat of 358.7 heat 
 units per hour, or within half of one per cent of that given by the above 
 calculation. 
 
 The quantity of heat given off by steam and hot-water radiators in 
 ordinary practice of heating buildings by direct radiation varies from 1.25 
 to about 3.25 heat units per hour per square foot per degree of difference 
 of temperature. (See Heating and Ventilation.) 
 
 THERMODYNAMICS. 
 
 Thermodynamics, the science of heat considered as a form of energy, 
 is useful in advanced studies of the theory of steam, gas, and air engines, 
 refrigerating machines, compressed air, etc. The method of treatment 
 adopted by the standard writers is severely mathematical, involving 
 constant application of the calculus. The student will find the subject 
 
598 HEAT. 
 
 thoroughly treated in the works by Rontgen (Dubois's translation), Wood. 
 Peabody, and Zeuner. 
 
 First Law of Thermodynamics. ' Heat and mechanical energy are 
 mutually convertible in the ratio of about 778 foot-pounds for the British 
 thermal unit. (Wood.) 
 
 Second Law of Thermodynamics. The second law has by different 
 writers been stated in a variety of ways, and apparently with ideas so 
 diverse as not to cover a common principle. (Wood, Therm., p. 389.) 
 
 It is impossible for a self-acting machine, unaided by any external. 
 agency, to convert heat from one body to another at a higher temperature. 
 (Clausius.) 
 
 If all the heat absorbed be at one temperature, and that rejected be at 
 one lower temperature, then will the heat which is transmuted into work 
 be to the entire heat absorbed in the same jatio as the difference between 
 the absolute temperature of the source and refrigerator is to the absolute 
 temperature of the source. In other words, the second law is an expression 
 for the efficiency of the perfect elementary engine. (Wood.) 
 
 The expression ~ = l ^ 2 may be called the symbolical or 
 
 algebraic enunciation of the second law, the law which limits the 
 efficiency of heat engines, and which does not depend on the nature of the 
 working medium employed. (Trowbridge.) Qi and T\ = quantity and 
 absolute temperature of the heat received; 2 and Tz = quantity and 
 absolute temperature of the heat rejected. 
 
 The expression 1 ~ - represents the efficiency of a perfect heat 
 
 engine which receives all its heat at the absolute temperature T\, and 
 rejects heat at the temperature Tz, converting into work the difference 
 between the quantity received and rejected. 
 
 EXAMPLE. What is the efficiency of a perfect heat engine which 
 receives heat at 388 F. (the temperature of steam of 200 Ibs. gauge 
 
 Pressure) and rejects heat at 100 F. (temperature of a condenser, pressure 
 Ib. above vacuum)? 
 
 pv o 
 let it 
 
 In the actual engine this efficiency can never be attained, for the difference 
 between the quantity of heat received into the cylinder and that rejected 
 into the condenser is not all converted into work, much of it being lost by 
 radiation, leakage, etc. In the steam engine the phenomenon of cylinder 
 condensation also tends to reduce the efficiency. 
 
 The Carnot Cycle. Let one pound of gas of a pressure p it volume v\ 
 and absolute temperature T\ be enclosed in an ideal cylinder, having non- 
 conducting walls but the bottom a perfect cpn- 
 ductor, and having a moving non-conducting 
 frictionless piston. Let the pressure and volume 
 of the gas be represented by the point A on the 
 or pressure- volume diagram, Fig. 142, and 
 it pass through four operations, as follows: 
 1. Apply heat at a temperature of T\ to the 
 bottom of the cylinder and let the gas expand, 
 doing work against the piston, at the constant 
 temperature Ti, or isothermally, to p*oz. or B. 
 .., 2. Remove the source of heat and put a non- 
 
 X IG. 14J. conducting cover on the bottom, and let the gas 
 
 expand adiabatically, or without transmission of heat, to pzvz, or C, while 
 its temperature is being reduced to 7Y 
 
 3. Apply to the bottom of the cylinder a cold body, or refrigerator, of 
 the temperature !T 2 , and let the gas be compressed by the piston isother- 
 mally to the point D, or p*V4, rejecting heat into the cold body. 
 
 4. Remove the cold body, restore the non-conducting bottom, and 
 compress the gas adiabatically to A , or the original pm, while its tempera- 
 ture is being raised to the original T\. The point D on the isothermal 
 line CD is chosen so that an adiabatic line passing through it will also pass 
 through A, and so that ft/ft'"" v*/vt. 
 
 The area aABCc represents the work done by the gas on the piston; 
 
 a 
 
THERMOD Y N AMICS. 599 
 
 the area CDAac the negative work, or the work done by the piston on the 
 gas; the difference, ABCD, is the net work. 
 
 la. The area aABb represents the work done during isothermal expan- 
 sion. It is equal in foot-pounds to Wi = pivi \og e (v<i/v\), where pi = the 
 initial absolute pressure in Ibs. per sq. ft. and vi = the initial volume in 
 cubic feet. It is also equal to the quantity of heat supplied to the gas,= 
 Ui = RTi log e (vi/v\). R is a constant for a given gas, = 53.35 for air. 
 
 2a. The area bBCc is the work done during adiabatic expansion, = Wz 
 
 = * ] 1 ( | } , y being the ratio of the specific heat at constant 
 
 V 1 I \vz/ ' 
 
 pressure to the specific heat at constant volume. For air y = 1.406. 
 The loss of intrinsic energy = K v (Ti Tz) ft.-lbs. K v = specific heat 
 at constant volume X 778. 
 
 3a. CDdc is the work of isothermal compression, = Ws = pw\ log e 
 (vsM) = heat rejected = Uz = RTz\og e (vz/vi). 
 
 4a. DAad is the work of adiabatic compression 
 
 which is the same as Wt and therefore, being negative, cancels it, and the 
 
 net work ABCD = Wi - W-&, The gain of intrinsic energy is K v (Ti T 2 ). 
 
 Comparing la and 3a, we have pivi= p^vz; pxvz = p*Vi; vi/vz = vi/v* =r. 
 
 -- pivi log e r = RTi log e r\ Wz = pm \og e r = RTz log e r. 
 
 Efficiency __! _ ^^ _ _1_J _ j _ _ 
 
 Entropy. In the pv or pressure- volume diagram, energy exerted or 
 expended is represented by an area the lines of which show the changes 
 of the values of p and v. In the Carnot cycle these changes are shown 
 by curved lines. If a given quantity of heat Q is added to a substance 
 at a constant temperature, we may represent it by a rectangular area 
 in which the temperature is represented by a vertical line, and the base 
 is the quotient of the area divided by the length of the vertical line. To 
 this quotient is given the name entropy. When the temperature at 
 which the heat is added is not constant a ..more general definition is 
 needed, viz.: Entropy is length on a diagram the area of which represents 
 a quantity of heat, and the height at any point represents absolute tempera- 
 ture. The value of the increase of entropy is given in the language of 
 
 calculus, E= | -7p-, which may be interpreted thus: increase of entropy 
 
 between the temperatures Tz and T\ equals the summation of all the 
 quotients arising by dividing each small quantity of heat added by 
 the absolute temperature at which it is added. It is evident that if 
 the several small quantities of heat added are equal, while the values of 
 T constantly increase, the quotients are not equal, but are constantly 
 decreasing. The diagram, called the temperature-entropy diagram, or 
 the 00, theta-phi, diagram, is one in which the abscissas, or horizontal 
 distances, represent ^ntropy, and vertical distances absolute temperature. 
 The horizontal distances are measured from an arbitrary vertical line 
 representing entropy at 32 F., and values of entropy are given as values 
 beyond that point, while the temperatures are measured above absolute 
 zero. Horizontal lines are isothermals, vertical lines adiabatics. The use- 
 fulness of entropy in thermodynamic studies is due to the fact that in 
 many cases it simplifies calculations and makes it possible to use alge- 
 braic or graphical methods instead of the more difficult methods of the 
 calculus. 
 
n 
 
 600 HEAT. 
 
 The Carnot Cycle in the Temperature-Entropy Diagram. Let a 
 
 pound of gas having a temperature T\ and entropy E be subjected to the 
 four operations described above. (1) T\ being 
 constant, heat (area aABc, Fig. 143) is added and 
 the entropy increases from A to B: isothermal 
 expansion. (2) No heat is transferred, as heat, 
 but the temperature is reduced from T\ to TV, 
 entropy constant ; adiabatic expansion. (3) Heat 
 is rejected at the constant temperature T 2 , the 
 area CcaD being subtracted; entropy decreases 
 from C to D; isothermal compression. (4) En- 
 tropy constant, temperature increases from D to 
 A, or from T 2 to Ti; no heat transferred as heat; 
 . adiabatic compression. The area aABc repre- 
 k sents the total heat added during the cycle, the 
 -, area cCDa the heat rejected ; the difference, or the 
 pi Tr 140 > area ABCD, is the heat utilized or converted into 
 
 work. The ratio of this area to the whole area 
 
 aABc is the efficiency; it is the same as the ratio (T\ T 2 ) '* Ti. It 
 appears from this diagram that the efficiency may be increased by in- 
 creasing T\ or by decreasing T 2 ; also that since T 2 cannot be lowered by 
 any self-acting engine below the temperature of the surrounding atmos- 
 phere, say 460+ 62 F.= 522 F., it is not possible even in a perfect 
 engine to obtain an efficiency of 50 per cent unless the temperature of 
 the source of heat is above 1000 F. It is shown also by this diagram 
 that the Carnot cycle gives the highest possible efficiency of a heat engine 
 working between any given temperatures T\ and Tz, and that the admis- 
 sion and rejection of heat each at a constant temperature gives a higher 
 efficiency than the admission or rejection at any variable temperatures 
 within the range Ti Tz. 
 
 The Reversed Carnot Cycle Refrigeration. Let a pound of cool 
 gas whose temperature and entropy are represented by the "state- 
 point" D on the diagram (1) receive heat at a constant temperature Ti 
 (the temperature of a refrigerating room) until its entropy is C; (2) then 
 let it be compressed adiabatically (no heat transmission, CB} to a high 
 temperature T\-, (3) then let it reject heat into the atmosphere at this 
 temperature Ti (isothermal compression); (4) then let it expand adia- 
 batically, doing work, as through a throttled expansion cock, or by 
 pushing a piston, it will then cool to a temperature which may be far 
 below that of the atmosphere and be used to absorb heat from the 
 atmosphere. (See Refrigeration.) 
 
 Principal Equations of a Perfect Gas. Notation: P = pressure in 
 Ib. per sq. ft. V= volume in cu. ft. PoVo, pressure and volume at 
 32 F. T, absolute temperature = t F. + 459.6. C p , specific heat at 
 constant pressure. C v , specific heat at constant volume. K p = 
 C p X 777. 6; K v = C v X 777.6; specific heats taken in foot-pounds of 
 energy. R, a constant, = K p - K v . y = C p /C v . r = ratio of iso- 
 thermal expansion or compression = P 2 /Pi or Vi/V 2 . 
 
 For air; C p = 0.2375; C v = 0.1689; K p = 184.8; K v = 131.4; 
 R = 53.32; y = 1.406. 
 
 Boyle's Law, PV = constant when T is constant. PiVi = P 2 V2. 
 For 1 Ib. air PoVo = 2116.3 X 12.387 = 26,215 ft.-lb. 
 
 Charles's Law, PiVi/Ti = P 2 V 2 /T 2 ; Pi Vi = PoVo X Ti/To; To = 32 
 + 459.6 = 491.6; Pi Vi for air = 26,215 -^ 491.6 = 53.32. v 
 
 General Equation, PV = RT. R is a constant which is different for 
 different gases. , 
 
 Internal or Intrinsic Energy K v (Ti - To) = R (Ti - To) -5- (y - 1) 
 = PiVi -T- (y - 1) = amount of heat in a body, measured above abso- 
 lute zero. For air at 32 F., K v (Ti - To) = 131.4 X 491.6 = 64,600 
 ft.-lb. When air is expanded or compressed isothermally, PV = con- 
 stant, and the internal energy remains constant, the work done in 
 expansion = the heat added, and the work done in compression = the 
 heat rejected. 
 
THERMODYNAMICS. 601 
 
 Work done by Adiabatic Expansion, no transmission of heat, from PiFi to 
 p 2 F 2 = PiFi }l - (Fi/VV) 7 "^ -*(?- 1), = (PiFi - P 2 F 2 ) -5- (y - 1) 
 
 r -I 
 
 - Pi Fiji ~(P 2 /Pl) Y } - (y - 1). 
 
 Work of Adiabatic Compression from PiFi to P 2 F 2 (P 2 here being the 
 higher pressure) = Pi Fi {(Fi/Fo) 7 " 1 -l} *- (y- 1) = (P 2 F 2 -PiFi)-^ y-1 
 
 ( *=! ) 
 
 = PiFi {(Pa/Pi) y -IJ-J-(y-l). 
 
 7^m w/ Intrinsic Energy in adiabatic expansion, or gain in compression 
 = K V (T\. T->), T\ being the higher temperature. 
 
 Work of Isothermal Expansion, temperature constant, = heat expended 
 = Pi Fi log e Fo / Fi = Pi Ft log e r = R T log e r. 
 
 Work of Isothermal Compression from Pi to P 2 = PiFi log e Pi/P 2 
 = RT\og e r= heat discharged. 
 
 Relation between Pressure, Volume and Temperature: 
 
 For air, y = 1,406; y - 1 = 0.406; 1/y- = 0.711; l/(y - 1) = 2.463; 
 y/(y-l)= 3.463; (y - l)/y = 0.289. 
 
 Differential Equations of a Perfect Gas. Q = quantity of heat. $ = 
 entropy. 
 
 T (IT f?P 
 
 dQ = C p dT+ (C v -C p ) dV. d4>= C p ~ + (C v - Cp) ~ . 
 
 T T riP f?V 
 
 dQ=C v jjdP+C p | dV. di= C v Q -f+C p y- 
 
 fr-<j>i = C v log e -^ + (C p - C v ) log e ^ 
 <h-fr = C p log, |> + (C v - C p ) log e || 
 < 2 - ^i = C v log e ^ + C p log e 
 
 / F 2 ,7 F V* 
 
 Work of Isothermal Expansion, W= PiFi I ^ =PiFi log e ~ 
 
 / FI i 
 
 Heat supplied during isothermal expansion, 
 
 ^ - (C p - C v ) ITi log, ^ 
 
 Heat added = work done= ^/eT 7 ! log e F 2 /Fi= ^PiFi log e F 2 /Fi; (A* 
 1/778). 
 
 Work of adiabatic expansion, 
 
 w- pav= Vl yp t f^^^-^h-^ 
 JV\ F Y-1 1 MV 
 
602 
 
 HEAT. 
 
 Construction of the Curve P V = C. (Am. Mach., June 21, 1900.) 
 Referring to Fig. 144, on a system of rectangular coordinates YOX lay 
 
 off OB = pi and BA v\. 
 Draw 0.7, extended, at 
 any convenient angle a, 
 say 15, with OX, and OC 
 at an angle ft with OY. ft 
 is found from the equation 
 1 + tan B =[l + tana] n . 
 Draw AJ parallel to YO. 
 From B draw BC at 45 
 with 0, and draw CE 
 parallel to OX. From J 
 draw J# at 45 with A J, 
 and draw HE and ///] 
 parallel to YO. The inter- 
 section of CE and HE is 
 the second point on the 
 curve, or pzvz. From J\ 
 draw JiHi at 45 to HJi 
 and draw the vertical 
 JtHiR. Draw D# at 45 
 to DOi and KE parallel 
 to OX. R is the third 
 point on the curve, and 
 so on. 
 
 Conversely, if we have 
 a curve for which we wish 
 
 144. 
 
 
 to derive an exponent, we can, by working backward, locate the lines 
 OC and OJ, measure the angles a and ft, and solve for n. 
 A The smaller the angle a is taken the more closely the points of the 
 curve may be located. If a = ft the curve is the isothermal curve, 
 pv = constant. If a = 15 and ft = 21 30' the curve is the adiabatic 
 for air, n = 1.41. (See Index of the Curve of an Air Diagram, p. 636.) 
 
 Temperature-Entropy Diagram of Water . and Steam. The line 
 OA, Fig. 145, is the origin from which entropy is measured on horizontal 
 tines, and the line Og is the line of zero 
 temperature, absolute. The diagram 
 represents the changes in the state 
 of one pound of water due to the 
 addition or subtraction of heat or to 
 changes in temperature. Any point on 
 the diagram is called a "state point." 
 A is the state of 1 Ib. of water at 
 32 F. or 492 abs., B the state at 
 212, and C at 392 F., correspond- 
 ing to about 226 Ibs. absolute pres- 
 sure. At 212 F. the area OABb is 
 the heat added, and Ob is the increase 
 of entropy. At 392 F., bBcC is the 
 further addition of heat, and the 
 entropy, measured from OA, is Oc. 
 The two quantities added are nearly 
 the same, but the second increase 
 of entropy is the smaller, since the 
 mean temperature at which it is 
 added is higher. If Q = the quantity 
 of heat added, and T\ and Tz are 
 respectively the lower and the 
 higher temperatures, the addition of 
 entropy, , is approximately Q -H i/ 2 (7*2 4- Ti) = 180 *- 1/2 (672 + 492) 
 = 0.3093. More accurately it is <j> = log e (Tz/Ti) = 0.3119. In both of 
 these expressions it is assumed that the specific heat of water = 1 at all 
 temperatures, which is not strictly true. Accurate values of the entropy 
 9f water, taking into account the variation in specific heat, will be found 
 in. Marks and Davis 's Steam Tables. 
 
 Let the l Ib. of water at the state have heat added to it at the eon-, 
 
 
 Abs.., 
 
 QCO 
 
 
 C 
 
 5 T 2 D 
 
 / 
 
 
 
 
 
 P 
 
 /j 
 
 X Ti ft 
 
 t 
 
 \ 
 
 
 
 OO- 
 
 492 
 
 / 
 
 
 To 
 
 
 \ 
 
 
 460 
 
 
 
 A 
 O & 
 
 
 c d e 
 
 
 f 
 
 9 
 
 
 
 K 
 
 - I 
 
 Entropy 
 
 
 > 
 
 \ 
 
 FIG. 145. 
 
PHYSICAL PKOPEKTIES OF GASES. 603 
 
 slant temperature of 212 F. until it is evaporated. The quantity of 
 heat added will be the latent heat of evaporation at 212 (see Steam 
 Table) or L = 970.4 B.T.U., and it will be represented on the diagram by 
 the rectangle bBFf. Dividing by T\ = 672, the absolute temperature, 
 gives <J> 2 -</>i = 1.444 = BF. Adding fa = 0.312 gives fa = 1.756, the 
 entropy of 1 Ib. steam at 212 F. measured from water at 32 F. 
 
 In like manner if we take L = 834.4 for steam at 852 abs., $* $\ = 
 0.980 = CE, and 4>i = entropy of water at 852 = 0.556, the sum fa^ 
 1.536. = Oe on the diagram. 
 
 E is the state point of dry saturated steam at 852 abs. and F the 
 state point at 672. The line EFG is the line of saturated steam and the 
 line ABC the water line. The line CE represents the increase of entropy 
 in the evaporation of water at 852 abs. If entropy CD only is added, 
 or cCDd of heat, then a part of the water will remain unevaporated, 
 viz.: the fraction DE/CE of 1 Ib. The state point D thus represents wet 
 steam having a dry ness fraction of CD/CE. 
 
 If steam having a state point E is expanded adiabatically to 672 
 abs. its state point is then ei, having the same entropy as at E, a total 
 heat less by the amount represented by the area BCEei, and a dryness 
 fraction Bei/BF. If it is expanded while remaining saturated, heat 
 must be added equal to eEFf, and the entropy increases by ef. 
 
 If heat is added to the steam at E, the temperature and the entropy 
 both increase, the line EH representing the superheating, and the area 
 EH, down to the line Og, is the heat added. If from the state point H 
 the steam is expended adiabatically, the state point follows the line HJ 
 until it cuts the line JEFG, when the steam is dry saturated, and if it 
 crosses this line the steam becomes wet. 
 
 If the state point follows a horizontal line to the left, it represents 
 condensation at a constant temperature, the amount of heat rejected 
 being shown by the area under the horizontal line. If heat is rejected 
 at a decreasing temperature, corresponding with the decreasing pressure 
 at release in a steam engine, or condensation in a cylinder at a decreasing 
 pressure, the state point follows a curved line to the left, as shown in 
 the dotted curved line on the diagram. 
 
 In practical calculations with the entropy-temperature diagram it is 
 necessary to have at hand tables or charts of entropy, total heat, etc., 
 Bucn as are given in Peabody's or Marks and Dayis's Steam Tables, 
 and other works. The diagram is of especial service in the study of 
 steam turbines, and an excellent chart for this purpose will be found in 
 Moyer's Steam Turbine. It gives for all pressures of steam from 0.5 
 to 300 Ibs. absolute, and for different degrees of dryness up to 300 of 
 superheating, the total heat contents in B.T.U. per pound, the entropy, 
 and the velocity of steam through nozzles. 
 
 PHYSICAL PROPERTIES OP GASES. 
 
 (Additional matter on this subject will be found under Heat, Air, Gas 
 and Steam.) 
 
 When a mass of gas is inclosed in a vessel it exerts a pressure against the 
 walls. This pressure is uniform on every square inch of the surface of the 
 vessel; also, at any point in the fluid mass the pressure is the same in every 
 direction. 
 
 In small vessels containing gases the increase of pressure due to weight 
 may be neglected, since all gases are very light; but where liquids are 
 concerned, the increase in pressure due to their weight must always be 
 taken into account. 
 
 Expansion of Gases, Mariotte's L.aw. The volume of a gas dimin- 
 ishes in the same ratio as the pressure upon it is increased, if the tem- 
 perature is unchanged. 
 
 This law is by experiment found to be very nearly true for all gases, and 
 is known as -Boyle's or Mariotte's law. 
 
 If p = pressure at a volume v, and pi = pressure at a volume Vi, pivi = 
 
 pv, Pi = ^ P; pv = a constant. 
 
 The constant, C, varies with the temperature, everything else re- 
 maining the same. 
 
604 PHYSICAL PROPERTIES OF GASES^, 
 
 Air compressed by a pressure of seventy-five atmospheres has a 
 volume about 2 % less than that computed from Boyle's law, but this is 
 the greatest divergence that is found below 160 atmospheres pressure. 
 
 Law of Charles. The volume of a perfect gas at a constant pressure 
 is proportional to its absolute temperature. If VQ be the volume of a 
 gas at 32 F., and vi the volume at any other temperature, h, then 
 
 jh + 459. 6\ / ., , ti 32 \ 
 
 Vi = r ' 
 
 or vi = [I + 0.002034 (ti - 32 )] VQ. 
 If the pressure also change from pa to pi, 
 
 The Densities of the elementary gases are simply proportional to 
 their atomic weights. The density of a compound gas, referred to 
 hydrogen as 1, is one-half its molecular weight; thus the relative den- 
 sity of CO 2 is 1/2 (12 + 32) = 22. 
 
 Avogadro's Law. Equal volumes of all gases, under the same condi- 
 tions of temperature and pressure, contain the same number of molecules. 
 
 To find the weight of a gas in pounds per cubic foot at 32 F., multiply 
 half the molecular weight of the gas by 0.00559. Thus 1 cu. ft. of marsh- 
 gas, CH 4 , = 1/2 (12 + 4) x 0.00559 = 0> o447 Ib. 
 
 When a certain volume of hydrogen combines with one-half its volume 
 of oxygen, there is produced an amount of water vapor which will 
 occupy the same volume as that which was occupied by the hydrogen 
 gas when at the same temperature and pressure. 
 
 Physical Laws of Methane Gas. (P. F. Walker, Trans. A. S. M. E., 
 1914.) The specific heat of CH* under constant pressure at tempera- 
 tures from 18 to 218 C. is 0.5929 according to Landolt and Bornsfcein's 
 Tables. The same tables, on the authority of Lussana, give values of 
 0.5915 at a pressure of 1 atmosphere and 0.6919 at 30 atmospheres. The 
 ratio of specific heats at constant pressure and constant volume is given 
 variously at from 1.235 to 1.315. The gas shows a considerable varia- 
 tion from Boyle's law. PV = constant, or P V = P\V\. The variation 
 amounts to as much as 4% in the case of CH* gas at 300 Ib. per square 
 inch reduced to the equivalent volume at atmospheric pressure. The 
 difference is of commercial importance when natural gas is sold measured 
 at high pressures and the price based on. the equivalent volume at 
 atmospheric pressure. The relation of pressure and volume is ex- 
 pressed by PV n = a constant and the value of n for C7/4 ranges from 
 0.98 to 0.995, varying with pressure and temperature, averaging 0.99. 
 Sufficient data are not yet available for the construction of tables 
 showing the variation of the pressure-volume relation from that given 
 by Boyle's law. 
 
 Saturation Point of Vapors. A vapor that is not near the satura- 
 tion point behaves like a gas under changes of temperature and pressure; 
 but if it is sufficiently compressed or cooled, it reaches a point where it 
 begins to condense: it then no longer obeys the same laws as a gas, but 
 its pressure cannot be increased by diminishing the size of the vessel con- 
 taining it, but remains constant, except when the temperature is changed. 
 The only gas that can prevent a liquid evaporating seems to be its own 
 vapor. 
 
 Dalton's Law of Gaseous Pressures. Every pprtion of a mass of 
 gas inclosed in a vessel contributes to the pressure against the sides of the 
 vessel the same amount that it would have exerted by itself had no other 
 gas been present. 
 
 Mixtures of Vapors and Gases. The pressure exerted against the 
 interior of a vessel by a given quantity of a perfect gas inclosed in it is the 
 sum of the pressures which any number of parts into which such quan- 
 tity might be divided would exert separately, if each were inclosed in a 
 vessel of the same bulk alone, at the same temperature. Although this 
 law is not exactly true for any actual gas, it is very nearly true for many. 
 Thus if 0.080728 Ib. of air at 32 F., being inclosed in a vessel of one cubic 
 foot capacity, exerts a pressure of one atmosphere, or 14.7 pounds, oji each 
 
PHYSICAL PROPERTIES OF GASES. 605 
 
 square inch of the interior of the vessel, then will each additional 0.080728 
 
 Ib. of air which is inclosed, at 32, in the same vessel, produce very nearly 
 an additional atmosphere of pressure. The same law is applicable to 
 mixtures of gases of different kinds. For example, 0.1 2344 Ib. of carbonic- 
 acid gas, at 32, being inclosed in a vessel of one cubic foot in capacity, 
 exerts a pressure of one atmosphere; consequently, if 0.080728 Ib. of air 
 and 0.12344 Ib. of carbonic acid, mixed, be inclosed at the temperature 
 of 32, in a vessel of one cubic foot of capacity, the mixture will exert a 
 pressure of two atmospheres. As a second example: Let 0.080728 Ib. 
 of air, at 212, be inclosed in a vessel of one cubic foot; it will exert a 
 pressure of 
 
 = 1.366 atmospheres. 
 
 Let 0.03797 Ib. of steam, at 212, be inclosed in a vessel of one cubic 
 foot ; it will exert a pressure of one atmosphere. Consequently, if 0.080728 
 Ib. of air and 0.03797 Ib. of steam be mixed and inclosed together, at 21 2, 
 in a vessel of one cubic foot, the mixture will exert a pressure of 2.366 
 atmospheres. It is a common but erroneous practice, in elementary 
 books on physics, to describe this law as constituting a difference between 
 mixed and homogeneous gases; whereas it is obvious that for mixed and 
 homogeneous gases the law of pressure is exactly the same, viz., that the 
 pressure of the whole of a gaseous mass is the sum of the pressures of all 
 its parts. This is one of the laws of mixture of gases and vapors. 
 
 A second law is that the presence of a foreign gaseous substance in con- 
 tact with the surface of a solid or liquid does not affect the density of the 
 vapor of that solid or liquid unless there is a tendency to chemical com- 
 bination between the two substances, in which case the density of the 
 vapor is slightly increased. (Rankine, S. E., p. 239.) 
 
 If 0.0591 Ib. of air, = 1 cu. ft. at 212 and atmospheric pressure, is con- 
 tained in a vessel of 1 cu. ft. capacity, and water at 212 is introduced, 
 heat at 212 being furnished by a steam jacket, the pressure will rise to 
 two atmospheres. 
 
 If air is present in a condenser along with water vapor, the pressure is 
 that due to the temperature of the vapor plus that due to the quantity of 
 air present. 
 
 Flow of Gases. By the principle of the conservation of energy, it 
 may be shown that the velocity with which a gas under pressure will 
 escape into a vacuum is inversely proportional to the square root of its 
 density; that is, oxygen, which is sixteen times as heavy as hydrogen, 
 would, under exactly the same circumstances, escape through an opening 
 only one fourth as fast as the latter gas. 
 
 Absorption of Gases by Liquids. Many gases are readily absorbed 
 by water. Other liquids also possess this power in a greater 9r less 
 degree. Water will, for example, absorb its own volume of carbonic-acid 
 gas, 800 times its volume of ammonia, 2 Va times its volume of chlorine, 
 and only about 1/20 of its volume of oxygen. 
 
 The weight of gas that is absorbed by a given volume of liquid is pro- 
 portional to the pressure. But as the volume of a mass of gas is less as 
 the pressure is greater, the volume which a given amount of liquid can 
 absorb at a certain temperature will be constant, whatever the pressure. 
 Water, for example, can absorb its own volume of carbonic-acid gas at 
 atmospheric pressure; it will also dissolve its own volume if the pressure 
 is twice as great, but in that case the gas will be twice as dense, and con- 
 sequently twice the weight of gas is dissolved. 
 
 Liquefaction of Gases. Liquid Air. (A. L. Rice, Trans. A.S.M. E., 
 xxi, 156.) Oxygen was first liquefied in 1877 by Cailletet and Pictet, 
 working independently. In 1884 Dewar liquefied air, and in 1898 he 
 liquefied hydrogen at a temperature of - 396.4 F., or only 65 above the 
 absolute zero. The method of obtaining the low temperatures required 
 for liquefying gases was suggested by Sir W. Siemens, in 1857. It consists 
 in expanding a compressed gas in a cylinder doing work, or through a 
 small orifice, to a lower pressure, and using the cold gas thereby produced 
 to cool, before expansion, the gas coming to the apparatus. Hampson 
 claims to have condensed about 1.2 Quarts of liquid air per hour at an 
 
606 
 
 AIR. 
 
 expenditure of 3.5 H.P. for compression, using a pressure of 120 atmos- 
 pheres expanded to 1, and getting 6.6 per cent of the air handled as 
 liquid. 
 
 The following table gives some physical constants of the principal gases 
 that have been liquefied. The critical temperature is that at which the 
 properties of a liquid and its vapor are indistinguishable, and above wnich 
 the vapor cannot be liquefied by compression. The critical pressure is 
 the pressure of the vapor at the critical temperature. 
 
 
 
 Criti- 
 cal 
 Temp. 
 Deg. F. 
 
 Criti- 
 cal 
 Pres- 
 sure in 
 Atmo- 
 spheres 
 
 Temp, 
 of 
 Satu- 
 rated 
 Vapor 
 at 
 Atmos. 
 Pres- 
 sure 
 Deg. F. 
 
 Freez- 
 ing 
 Point. 
 Deg. F. 
 
 Density of 
 Liquid at 
 Temperature 
 Given. 
 
 Water.. . 
 
 HjjO 
 
 689 
 
 200 
 
 212 
 
 32 
 
 1 at 39 F. 
 
 Ammonia. 
 
 NH 4 
 
 266 
 
 115 
 
 27 
 
 107 
 
 0.6364 at 32 F. 
 
 Acotylene 
 
 
 98 6 
 
 
 121 
 
 113 8 
 
 
 Carbon Dioxide 
 
 EthylenC 
 
 iV? 2 
 
 CO2 
 
 C 2 H 4 
 
 88 
 50 
 
 75 
 51.7 
 
 112 
 150 
 
 69 
 
 272 
 
 0. 83 at 32 F. 
 
 Methane . . . 
 
 CH 4 
 
 115.2 
 
 54.9 
 
 263.4 
 
 302.4 
 
 l 0.415 1 
 
 Oxygen 
 
 C 2 
 
 182 
 
 50.8 
 
 294.5 
 
 
 ( at 263 F. ) 
 1 1J24 
 
 
 A 
 
 -185.8 
 
 50.6 
 
 304.6 
 
 309.3 
 
 \ at 294 F. I 
 ( about 1.5 | 
 1 of ini TT ( 
 
 Carbon Monoxide 
 
 CO 
 
 219 1 
 
 35.5 
 
 310 
 
 340.6 
 
 
 Air 
 
 
 220 
 
 39 
 
 312.6 
 
 
 ( 0.933 ) 
 
 
 N 2 
 
 231 
 
 35 
 
 318 
 
 353.2 
 
 ( at 313 F. 1 
 ( 0.885 ) 
 
 I of 31R T? 
 
 Hydrogen 
 
 H 2 
 
 389 
 
 20 
 
 -405 
 
 
 
 AIR. 
 
 Properties of Air. Air is a mechanical mixture of the gases oxygen 
 and nitrogen, with about 1% by volume of argon. Atmospheric air of 
 ordinary purity contains about 0.04% of carbon dioxide. The com- 
 position of air is variously given as follows : 
 
 
 I 
 
 >y Volume 
 
 . 
 
 1 
 
 By Weight 
 
 
 
 N 
 
 
 
 Ar 
 
 N 
 
 O 
 
 Ar 
 
 1.. 
 
 79.3 
 
 20.7 
 
 
 77 
 
 23 
 
 
 2 
 
 79 09 
 
 20 91 
 
 
 76 85 
 
 23 15 
 
 
 3 
 
 78.122 
 
 20 941 
 
 0.937 
 
 75.539 
 
 23.024 
 
 1 437 
 
 4 
 
 78.06 
 
 21. 
 
 0.94 
 
 75.5 
 
 23.2 
 
 1.3 
 
 (1) Values formerly given in works on physics. (2) Average results 
 of several determinations, Hempel's Gas Analysis. (3) Sir. Wm. Ram- 
 say, Bull. U. S. Geol. Survey, No. 330. (4) A. Leduc, Comptes Rendus, 
 1896, Jour. F. I., Jan., 1898. Leduc gives for the density of oxygen 
 relatively to air 1.10523; for nitrogen 0.9671; for argon, 1.376. 
 
 The weight of pure air at 32 F. and a barometric pressure of 29.92 
 inches of mercury, or 14.6963 Ibs. per sq. in., or 2116.3 Ibs. per sq. ft., is 
 0.080728 Ib. per cubic foot. Volume of 1 Ib. = 12.387 cu. ft. At any 
 other temperature and barometric pressure its weight in Ibs. per cubic 
 
 foot is W 
 
 > wnere B = height of the barometer, T = tern- 
 
 . . 
 
 perature Fahr., and 1.3253 = weight in Ib. of 459.6 cu. ft. of air at F. 
 and one inch barometric pressure. Air expands 1/491.6 of its volume at 
 
AIR. 
 
 607 
 
 32 F. for every increase of 1 F., and its volume varies inversely as the 
 pressure. 
 
 Conversion Table for Air Pressures. 
 
 
 le 
 & 
 
 +*% 
 1 
 
 & 
 
 M 
 $$ 
 
 Ft. of 
 Water. 
 
 o 
 % 
 
 M 
 
 & 
 
 Ft. of Air 
 at 62 F. 
 
 |&! 
 
 n 
 
 >& 
 
 i* 
 
 1 Ib. per sq. ft . . 
 1 in. water at 
 62 F 
 
 5.196 
 9 
 
 62.355 
 
 70.73 
 144 
 2116.3 
 
 (2) 
 
 0.19245 
 
 1.732 
 12 
 
 13.612 
 27.712 
 407.27 
 
 (3) 
 
 V9 
 
 0.5774 
 
 1 
 
 6.928 
 
 7.859 
 16 
 
 ' (4) ' 
 
 .01604 
 
 Vl2 
 
 0.1443 
 
 1 
 
 1.1343 
 2.3094 
 33.94 
 
 (5) 
 
 0.01414 
 
 0.07347 
 0.1272 
 
 0.8816 
 
 2.036 
 29.921 
 
 (6) 
 
 Vl44 
 
 0.036085 
 
 Vl6 
 
 0.43302 
 
 0.49117 
 1 
 14.6963 
 
 (7) 
 
 13.14 
 
 68.30 
 118.3 
 
 819.6 
 
 929.6 
 1893 
 27,815 
 
 (8) 
 
 29.1 
 
 66.3 
 87.2 
 
 230 
 
 245 
 349 
 1338 
 (9) 
 
 1 oz. per sq. in . . 
 1 ft. water at 
 62 F 
 1 in. mercury at 
 32 F 
 1 Ib. per sq. in . . 
 1 atmosphere. . . 
 (1) 
 
 The figures in column (8) show the head in feet of air of uniform 
 density at atmospheric pressure and 62 F. corresponding to the pres- 
 sure in the preceding columns, and those in column (9) the theoretical 
 velocities corresponding to these heads, or the velocities of a jet flowing 
 from a frictionless conical orifice whose flow coefficient is unity. 
 
 The Air-manometer consists of a long, vertical glass tube, closed at 
 the upper end, open at the lower end, containing air, provided with a 
 scale, and immersed, along with a thermometer, in a transparent liquid, 
 such as water or oil, contained in a strong cylinder of glass, which com- 
 municates with the vessel in which the pressure is to be ascertained. 
 The scale shows the volume occupied by the air in the tube. 
 
 Let vo be that volume, at the temperature of 32 Fahrenheit, and mean 
 pressure of the atmosphere, po ; let vi be the volume of the air at the 
 temperature t, and under the absolute pressure to be measured pi ; then 
 U + 459.6) pwo 
 491.6V! 
 
 Pressure of the Atmosphere at Different Altitudes. 
 
 At the sea level the pressure of the air is 14.7 pounds per square inch; at 
 1/4 of a mile above the sea level it is 14.02 pounds; at 1/2 mile, 13.33; at 
 Simile, 12.66; at 1 mile, 12.02; at li/4mile, 11.42; at 11/2 mile, 10.88; and 
 at 2 miles, 9.80 pounds per square inch. For a rough approximation we 
 may assume that the pressure decreases 1/2 pound per square inch for 
 every 1000 feet of ascent. (See table, p. 608.) 
 
 It is calculated that at a height of about 31/2 miles above the sea level 
 the weight of a cubic foot of air is only one-half what it is at the surface of 
 the earth, at seven miles only one-fourth, at fourteen miles only one- 
 sixteenth, at twenty-one miles only one sixty-fourth, and at a height of 
 over forty-five miles it becomes so attenuated as to have no appreciable 
 weight. 
 
 The pressure of the atmosphere increases with the depth of shafts, equal 
 to about one inch rise in the barometer for each 900 feet increase in depth: 
 this may be taken as a rough-and-ready rule for ascertaining the depth of 
 shafts. 
 
 Leveling by the Barometer and by Boiling Water. (Trautwine.) 
 Many circumstances combine to render the results of this kind of 
 leveling unreliable where great accuracy is required. It is difficult to 
 read off from an aneroid (the kind of barometer usually employed for 
 engineering purposes) to within from two to five or six feet, depending on 
 its size. The moisture or dryness of the air affects the results; also winds, 
 the vicinity of mountains, and the daily atmospheric tides, which cause 
 incessant and irregular fluctuations in the barometer. A barometer 
 hanging quietly in a room will often vary Vio of an inch within a few 
 
608 
 
 Am. 
 
 hours, corresponding to a difference of elevation of nearly 100 feet. 
 No formula can be devised that shall embrace these sources of error. 
 Boiling Point of Water. Temperature in degrees F., barometer in 
 in. of mercury. 
 
 In. 
 
 
 
 1 
 
 .2 
 
 .3 
 
 .4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 28 
 29 
 30 
 
 208.7 
 210.5 
 212.1 
 
 208.9 
 210.6 
 212.3 
 
 209.1 
 210.8 
 212.4 
 
 209.2 
 210.9 
 212.6 
 
 209.4 
 211.1 
 212.8 
 
 209.5 
 211.3 
 212.9 
 
 209.7 
 211.4 
 213.1 
 
 209.9 
 211.6 
 213.3 
 
 210.1 
 211.8 
 213.5 
 
 210.3 
 212.0 
 213.6 
 
 To Find the Difference in Altitude of Two Places. Take from the 
 table the altitudes opposite to the two boiling temperatures, or to the two 
 barometer readings. Subtract the one opposite the lower reading from 
 that opposite the upper reading. The remainder will be the required 
 height, as a rough approximation. To correct this, add together the 
 two thermometer readings, and divide the sum by 2, for their mean. 
 From table of corrections for temperature, take the number under this 
 mean. Multiply the approximate height just found by this number 
 
 At 70 F. pure water will boil at 1 less of temperature tor an average of 
 about 550 feet of elevation above sea level, up to a height of 1/2 a mile. 
 At the height of 1 mile, 1 of boiling temperature will correspond to aoout 
 560 feet of elevation. In the table the mean of the temperatures at the 
 two stations is assumed to be 32 F., at which no correction- for temperature 
 is necessary in using the table. 
 
 &-$' 
 
 a 
 
 8.1 . 
 
 , . 
 
 r 
 d . 
 
 1 21- 
 
 *-#c 
 
 1 
 
 Isl* 
 
 tit* 
 
 23 
 
 1 
 
 4 o^l 
 
 3-S8* 
 
 ^ 02 
 
 f 
 
 25 
 & 
 
 tP 1 
 
 3*8* 
 
 ^ 02 
 
 |IS 
 
 8 
 
 Sgjjf 
 
 3-8 * 
 
 ^ WJ 
 
 184 
 
 16.79 
 
 15,221 
 
 196 
 
 21.71 
 
 8,481 
 
 208 
 
 27.73 
 
 2,063 
 
 185 
 
 17.16 
 
 14,649 
 
 197 
 
 22.17 
 
 7,932 
 
 208.5 
 
 28.00 
 
 1,809 
 
 186 
 
 17.54 
 
 14,075 
 
 198 
 
 22.64 
 
 7,381 
 
 209 
 
 28.29 
 
 1,539 
 
 187 
 
 17.93 
 
 13,498 
 
 199 
 
 23.11 
 
 6,843 
 
 209.5 
 
 28.56 
 
 1,290 
 
 188 
 
 18.32 
 
 12,934 
 
 200 
 
 23.59 
 
 6,304 
 
 210 
 
 28.85 
 
 1,025 
 
 189 
 
 18.72 
 
 12,367 
 
 201 
 
 24.08 
 
 5,764 
 
 210.5 
 
 29.15 
 
 754 
 
 190 
 
 19.13 
 
 11,799 
 
 202 
 
 24.58 
 
 5,225 
 
 2.11 
 
 29.42 
 
 512 
 
 191 
 
 19.54 
 
 11,243 
 
 203 
 
 25.08 
 
 4,697 
 
 211.5 
 
 29.71 
 
 255 
 
 192 
 
 19.96 
 
 10,685 
 
 204 
 
 25.59 
 
 4,169 
 
 212 
 
 30.00 
 
 S.L.= 
 
 193 
 
 20.39 
 
 10,127 
 
 205 
 
 26.11 
 
 3,642 
 
 212.5 
 
 30.30 
 
 261 
 
 194 
 
 20.82 
 
 9,579 
 
 206 
 
 26.64 
 
 3,115 
 
 213 
 
 30.59 
 
 511 
 
 195 
 
 21.26 
 
 9,031 
 
 207 
 
 27 18 
 
 2589 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CORRECTIONS FOR TEMPERATURE. 
 
 Mean temp. F. in shade 
 Multiply by .933 
 
 10l 20 
 .9541.975 
 
 30 
 .996 
 
 40 
 1.016 
 
 50 1 60 
 1.036|1.058 
 
 70 
 1.079 
 
 80 
 1.100 
 
 90 
 1.121 
 
 100 
 1.142 
 
 Pressure of the Atmosphere per Square Inch and per Square Foot 
 at Various Readings of the Barometer. 
 
 r RULE. Barometer in inches x 0.49 16 = pressure per square inch; 
 pressure per square inch X 144 = pressure per square foot. 
 
 Barometer. 
 
 Pressure 
 per Sq. In. 
 
 Pressure 
 per Sq. Ft. 
 
 Barometer. 
 
 Pressure 
 per Sq. In. 
 
 Pressure 
 per Sq. Ft. 
 
 In. 
 : 28.00 ' 
 28.25 
 28.50 
 28.75 
 29.00 
 29.25 
 29.50 
 
 Lb. 
 13.75 
 13.88 
 14.00 
 14.12 
 14.24 
 14.37 
 14.49 
 
 Lb.* 
 1980 
 1998 
 2016 
 2033 
 2051 
 2069 
 2086 
 
 In. 
 29.75 
 30.00 
 30.25 
 30.50 
 30.75 
 31.00 
 
 Lb. 
 
 14.61 
 14.73 
 14.86 
 14.98 
 15.10 
 15.23 
 
 Lb.* 
 2104 
 2122 
 2140 
 2157 
 2175 
 2193 
 
 * Decimals omitted. 
 For lower pressures see table of the Properties of Steam 
 
AIB. 
 
 609 
 
 Barometric Readings corresponding with Different 
 Altitudes, in French and English Measures. 
 
 Alti- 
 tude. 
 
 Read- 
 ing of 
 Barom- 
 
 Altitude. 
 
 Reading 
 of 
 Barom- 
 
 Alti- 
 tude. 
 
 Reading 
 of 
 Barom- 
 
 Altitude. 
 
 Reading 
 of 
 Barom- 
 
 
 eter. 
 
 
 eter. 
 
 
 eter. 
 
 
 eter. 
 
 meters 
 
 mm. 
 
 feet. 
 
 inches. 
 
 meters. 
 
 mm. 
 
 feet. 
 
 inches. 
 
 
 
 762 
 
 0. 
 
 30. 
 
 1147 
 
 660 
 
 3763.2 
 
 25.98 
 
 21 
 
 760 
 
 68.9 
 
 29.92 
 
 1269 
 
 650 
 
 4163.3 
 
 25.59 
 
 127 
 
 750 
 
 416.7 
 
 29.52 
 
 1393 
 
 640 
 
 4568.3 
 
 25.19 
 
 234 
 
 740 
 
 767.7 
 
 29.13 
 
 1519 
 
 630 
 
 4983.1 
 
 24.80 
 
 342 
 
 730 
 
 1122.1 
 
 28.74 
 
 1647 
 
 620 
 
 5403.2 
 
 24.41 
 
 453 
 
 720 
 
 1486.2 
 
 28.35 
 
 1777 
 
 610 
 
 5830.2 
 
 24.01 
 
 564 
 
 710 
 
 1850.4 
 
 27.95 
 
 1909 
 
 600 
 
 6243. 
 
 23.62 
 
 678 
 
 700 
 
 2224.5 
 
 27.55 
 
 2043 
 
 590 
 
 6702.9 
 
 23.22 
 
 793 
 
 690 
 
 2599.7 
 
 27.16 
 
 2180 
 
 580 
 
 7152.4 
 
 22.83 
 
 909 
 
 680 
 
 2962.1 
 
 26.77 
 
 2318 
 
 570 
 
 7605.1 
 
 22.44 
 
 1027 
 
 670 
 
 3369.5 
 
 26.38 
 
 2460 
 
 560 
 
 8071. 
 
 22.04 
 
 Weight of Air per Cubic Foot at Different Pressures and 
 . Temperatures. 
 
 Formula: W = 0.080728 X - 
 
 Tempera- 
 ture 
 
 Gage. 
 
 P = 
 14.6963 
 
 P= 
 15.696 
 
 2 
 
 P = 
 16.696 
 
 5 
 
 P = 
 
 19.696 
 
 10 
 P = 
 24.696 
 
 20 
 P = 
 34.696 
 
 40 
 P = 
 54.696 
 
 60 
 P = 
 74.696 
 
 80 
 P = 
 94.696 
 
 100 
 P = 
 1 14.696 
 
 120 
 P = 
 134.696 
 
 D f 
 
 Ab. 
 
 
 
 459.6 
 
 .086349 
 
 .09222 
 
 .09810 
 
 .11573 
 
 .14511 
 
 .20385 
 
 .32137 
 
 .43S8& 
 
 .55639 
 
 .67391 
 
 .79141 
 
 32 
 
 491.6 
 
 .080728 
 
 .08622 
 
 .09171 
 
 .10819 
 
 .13566 
 
 . 19059 
 
 .30045 
 
 .41031 
 
 .52017 
 
 .63004 
 
 .73990 
 
 42 
 
 501.6 
 
 .079119 
 
 .08450 
 
 .08989 
 
 .10604 
 
 13295 
 
 .18679 
 
 .29446 
 
 .40213 
 
 .50980 
 
 .61748 
 
 .72515 
 
 52 
 
 511.6 
 
 .077572 
 
 .08285 
 
 .08813 
 
 . 10396 
 
 .13035 
 
 .18314 
 
 .28871 
 
 .39427 
 
 .49984 
 
 .60541 
 
 .71097 
 
 62 
 
 521.6 
 
 076085 
 
 .08126 
 
 .08644 
 
 .10197 
 
 .12786 
 
 .17963 
 
 .28317 
 
 .38671 
 
 .49026 
 
 .59380 
 
 .69734 
 
 70 
 
 529.6 
 
 .074936 
 
 .08004 
 
 .08513 
 
 . 10043 
 
 .12592 
 
 .17691 
 
 .27887 
 
 .38087 
 
 .48285 
 
 .58483 
 
 .68681 
 
 80 
 
 539.6 
 
 073547 
 
 07855 
 
 08356 
 
 .09857 
 
 .12359 
 
 .17364 
 
 .27372 
 
 .37381 
 
 .47390 
 
 .57399 
 
 .67408 
 
 90 
 
 549.6 
 
 072209 
 
 07712 
 
 08204 
 
 .09678 
 
 .12134 
 
 . 17048 
 
 .26874 
 
 .36701 
 
 .46528 
 
 .56355 
 
 .66182 
 
 100 
 
 559.6 
 
 070918 
 
 07574 
 
 08057 
 
 .09504 
 
 .11937 
 
 .16743 
 
 .26394 
 
 .36045 
 
 .45697 
 
 .55348 
 
 .64999 
 
 120 
 
 579.6 
 
 068471 
 
 07313 
 
 07779 
 
 .09177 
 
 .11506 
 
 .16165 
 
 .25483 
 
 .34802 
 
 .44120 
 
 .53438 
 
 .62756 
 
 140 
 
 599.6 
 
 066187 
 
 07069 
 
 07519 
 
 .08871 
 
 .11122 
 
 .15626 
 
 . 24633 
 
 .33641 
 
 .42648 
 
 .51656 
 
 .60663 
 
 160 
 
 619.6 
 
 064051 
 
 06841 
 
 07277 
 
 . 08584 
 
 .10763 
 
 .15122 
 
 .23838 
 
 .32555 
 
 .41272 
 
 .49988 
 
 .58705 
 
 180 
 
 639.6 
 
 062048 
 
 06627 
 
 07049 
 
 08316 
 
 .10427 
 
 .14649 
 
 .23093 
 
 .31537 
 
 .39981 
 
 .48425 
 
 .56869 
 
 200 
 
 659.6 
 
 060167 
 
 06426 
 
 06835 
 
 08064 
 
 .10111 
 
 .14205 
 
 .22393 
 
 .30581 
 
 .38769 
 
 .46957 
 
 .55145 
 
 250 
 
 709.6 
 
 055927 
 
 05973 
 
 06354 
 
 .07496 
 
 .09398 
 
 .13204 
 
 .20815 
 
 .28426 
 
 .36037 
 
 .43649 
 
 .51259 
 
 300 
 
 759.6.052245 
 
 05580 
 
 05936 
 
 .07002 
 
 .08779 
 
 .12335 
 
 . 19445 
 
 .26555 
 
 .33665 
 
 .40775 
 
 .47885 
 
 350 
 
 809.6.049019 
 
 05236 
 
 05569 
 
 .06570 
 
 .08237 
 
 .11573 
 
 .18244 
 
 .24915 
 
 .31586 
 
 .38257 
 
 .44925 
 
 400 
 
 859.6.046163 
 
 04931 
 
 05245 
 
 .06188 
 
 . 07758 
 
 .10900 
 
 .17183 
 
 .23466 
 
 .29748 
 
 .36032 
 
 .42314 
 
 450 
 
 909.6 043630 
 
 04660 
 
 04957 
 
 .05847 
 
 .07332 
 
 . 10301 
 
 .16238 
 
 .22176 
 
 .28113 
 
 .34051 
 
 .39988 
 
 500 
 
 959.6.041357 
 
 04417 
 
 04699 
 
 .05543 
 
 .06950 
 
 .09764 
 
 .15392 
 
 .21020 
 
 .26648 
 
 .32277 
 
 .37905 
 
 550 
 
 1009.6 
 
 .039309 
 
 04198 
 
 04466 
 
 .05268 
 
 .06606 
 
 .09280 
 
 .14630 
 
 . 19979 
 
 .25329 
 
 .30678 
 
 .36028 
 
 600 
 
 1059.6 
 
 .037454 
 
 04000 
 
 04255 
 
 .05020 
 
 .06294 
 
 .08842 
 
 .13939 
 
 .19037 
 
 .24133 
 
 .29230 
 
 .34327 
 
 650 
 
 1109.6 
 
 .035766 
 
 03820 
 
 04063 
 
 .04793 
 
 .06010 
 
 .08444 
 
 .13311 
 
 .18179 
 
 .23046 
 
 .27913 
 
 .32781 
 
 700 
 
 1159.6.034224 
 
 .03655 
 
 .03888 
 
 .04587 
 
 .05751 
 
 .08080 
 
 .12737 
 
 .17395 
 
 .22052 
 
 .26710 
 
 .31367 
 
 800 
 
 1259.6.031507 
 
 . 03365 
 
 .03579 
 
 .04223 
 
 .05294 
 
 .07438 
 
 .11726 
 
 .16014 
 
 .20301 
 
 .24589 
 
 .28877 
 
 900 
 
 1359.6.029190 
 
 .03118 
 
 .03316 
 
 .03912 
 
 .04905 
 
 .06891 
 
 .10864 
 
 .14836 
 
 .18808 
 
 .22781 
 
 .26753 
 
 1000 
 
 1459. 6). 0271901.02904 
 
 .03089 
 
 .03644 
 
 .04569 
 
 .06419 
 
 .10119 
 
 .13830 
 
 .17519 
 
 .21220 
 
 .24920 
 
 Moisture in the Atmosphere. Atmospheric air always contains a 
 small quantity of carbonic acid (see Ventilation), and a varying quantity 
 of aqueous vapor or moisture. The relative humidity of the air at anytime 
 is the percentage of moisture contained in it as compared with the amount 
 it is capable of holding at the same temperature. 
 
 The degree of saturation or relative humidity of the air is determined 
 bv the use of the dry and wet bulb thermometer. The degree of satura- 
 tion for a number of different readings of the thermometer is given In 
 
610 
 
 AIR. 
 
 the following table, condensed from the Hygrometric Tables of the 
 U. S. Weather Bureau: 
 
 RELATIVE HUMIDITY, PER CENT. 
 
 if* 
 
 H g M 
 
 $! 
 
 Difference between the Dry and Wet Thermometers, Deg. F. 
 
 | 2| 3| 4| 5| 6| 7| 8| 9|10|1 1|12|13|14[15|16|17118|19|20J21|22|23|24[26|28|3Q 
 Relative Humidity, Saturation being 100. (Barometer = 30 in.) 
 
 32 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 110 
 120 
 140 
 
 89 79 69|59 49 3930|20| II 2 
 
 92 83 75 68 60 52 45 37 29 23j 15 
 
 93 87 80 74167161 554943 38 32 27 21 16 
 
 94 89 83;78 73 i 68!63!58!53!48i43 39 34 30 26 21 
 
 95 90|86j81 77 72 68 64 59 55 51 48;44I40 36 33 29J25 22 
 
 96 91 187 83 7975 72 ; 68 64J61 |57;54 50i47 44J41 
 
 96 92,89 85 81 78 74 71 68i65|61 58 55 52 49 47 44141 39 36 34 31 29 26 22 17 13 
 
 96 93 89 86183180 77i73 70]68:65i62 59!56 54 51 49|46|44|41 39 37 35 33 28 24 21 
 
 97 93^90 87 84 81 78 75 73 70'67 65;62i60 57 55 52 ! 50 48 46j44 42 40J38 34,30 26 
 97 94 91 88:85 82 80 77 74 72 69 67<65 \62\6Q 58i55 i 53 51 49147 45 43 41 ,38j34 31 
 97 95 92!89i87j84l82!79l77 75!73i7Q!68;66S64l62;60i58|56l54i53 51 49|47|44|41|38 
 
 
 17 13 
 
 38J35 32 29 ! 26|23|20 18 12 7 
 
 Mixtures of Air and Saturated Vapor. 
 
 (From Goodenough's Tables.) 
 
 
 ' Pressure of 
 
 Weight of 
 
 Volume 
 
 -Q > 
 
 "op 
 
 -fi^EJ 
 
 
 Saturated 
 
 Saturated 
 
 in Cu. Ft. 
 
 (-3 o 
 
 "csH 
 
 ^'fe "cS 
 
 fe 
 
 Vapor. 
 
 Vapor. 
 
 
 fc OJ 
 
 o> 
 
 h 
 
 
 
 ft 
 
 In., 
 Mer- 
 
 Lb. per 
 
 Per Cu. 
 
 PerLb. 
 
 nf 
 
 Of 
 
 1 Lb. 
 
 Of one 
 
 Ib.Dry 
 
 ^tfc 
 
 ft 
 
 ^I 
 
 i 
 
 cury. 
 
 Sq. In. 
 
 Ft. 
 
 OI 
 
 Dry Air. 
 
 Dry 
 
 Air. 
 
 Air + 
 Vapor. 
 
 o 
 
 rt * 
 
 Q|| 
 
 
 
 0.0375 
 
 0.0184 
 
 0.0000674 
 
 0.000781 
 
 11.58 
 
 11.59 
 
 0.0 
 
 0.964 
 
 0.964 
 
 10 
 
 .0628 
 
 .0308 
 
 .0001103. 
 
 .001309 
 
 11.83 
 
 11.86 
 
 2.411 
 
 1.608 
 
 4.019 
 
 20 
 
 .1027 
 
 .0504 
 
 .000177 
 
 .002144 
 
 12.09 
 
 12.13 
 
 4.823 
 
 2.623 
 
 7.446 
 
 32 
 
 .1806 
 
 .0887 
 
 .000303 
 
 .003782 
 
 12.39 
 
 12.47 
 
 7.716 
 
 4.058 
 
 11.783 
 
 35 
 
 .2036 
 
 .1000 
 
 .000340 
 
 .004268 
 
 12.47 
 
 12.55 
 
 8.44 
 
 4.57 
 
 13.02 
 
 40 
 
 .2478 
 
 .1217 
 
 .000410 
 
 .005202 
 
 12.59 
 
 12.70 
 
 9.65 
 
 5.56 
 
 15.21 
 
 45 
 
 .3003 
 
 .1475 
 
 .000492 
 
 .00632 
 
 12.72 
 
 12.85 
 
 10.86 
 
 6.73 
 
 17.59 
 
 50 
 
 .3624 
 
 .1780 
 
 .000588 
 
 .00764 
 
 12.84 
 
 13.00 
 
 12.07 
 
 8.12 
 
 20.19 
 
 55 
 
 .4356 
 
 .2140 
 
 .000699 
 
 .00920 
 
 12.97 
 
 13.16 
 
 13.28 
 
 9.76 
 
 23.04 
 
 60 
 
 .5214 
 
 .2561 
 
 .000829 
 
 .01105 
 
 13.10 
 
 13.33 
 
 14.48 
 
 11.69 
 
 26.18 
 
 65 
 
 .6218 
 
 .3054 
 
 .000979 
 
 .01323 
 
 13.22 
 
 13.50 
 
 15.69 
 
 13.96 
 
 29.65 
 
 70 
 
 .7386 
 
 .3628 
 
 .001153 
 
 .01578 
 
 13.35 
 
 13.69 
 
 16.90 
 
 16.61 
 
 33.51 
 
 75 
 
 .8744 
 
 .4295 
 
 .001352 
 
 .01877 
 
 13.48 
 
 13.88 
 
 18.11 
 
 19.71 
 
 37.81 
 
 80 
 
 1.0314 
 
 .5066 
 
 .001580 
 
 .02226 
 
 13.60 
 
 14.09 
 
 19.32 
 
 23.31 
 
 42.64 
 
 85 
 
 1.212 
 
 .5955 
 
 .001841 
 
 .02634 
 
 13.73 
 
 14.31 
 
 20.53 
 
 27.51 
 
 48.04 
 
 90 
 
 1.421 
 
 .6977 
 
 .002137 
 
 .03109 
 
 13.86 
 
 14.55 
 
 21.74 
 
 32.39 
 
 54.13 
 
 95 
 
 1.659 
 
 .8148 
 
 .002474 
 
 .03662 
 
 13.98 
 
 14.80 
 
 22.95 
 
 38.06 
 
 61.01 
 
 100 
 
 1.931 
 
 .9486 
 
 .002855 
 
 .04305 
 
 14.11 
 
 15.08 
 
 24.16 
 
 44.63 
 
 68.79 
 
 105 
 
 2.241 
 
 1.1010 
 
 .003285 
 
 .0505 
 
 14.24 
 
 15.39 
 
 25.37 
 
 52.26 
 
 77.63 
 
 110 
 
 2.594 
 
 1.274 
 
 .003769 
 
 .0593 
 
 14.36 
 
 15.73 
 
 26.58 
 
 61.11 
 
 87.69 
 
 115 
 
 2.994 
 
 1.470 
 
 .004312 
 
 .0694 
 
 14.49 
 
 16.10 
 
 27.79 
 
 71.40 
 
 99.10 
 
 120 
 
 3.444 
 
 1.692 
 
 .004920 
 
 .0813 
 
 14.62 
 
 16.52 
 
 29.00 
 
 83.37 
 
 112.37 
 
 130 
 
 4.523 
 
 2.221 
 
 .006356 
 
 .1114 
 
 14.88 
 
 17.53 
 
 31.42 
 
 113.64 
 
 145.06 
 
 140 
 
 5.878 
 
 2.887 
 
 .008130 
 
 .1532 
 
 15.13 
 
 18.84 
 
 33.85 
 
 155.37 
 
 189.22 
 
 150 
 
 7.566 
 
 3.716 
 
 .01030 
 
 .2122 
 
 15.39 
 
 20.60 
 
 36.27 
 
 214.03 
 
 250.3 
 
 160 
 
 9.649 
 
 4.739 
 
 .01294 
 
 .2987 
 
 15.64 
 
 23.09 
 
 38.69 
 
 299.55 
 
 338.2 
 
 170 
 
 12.20 
 
 5.990 
 
 .01611 
 
 .4324 
 
 15.90 
 
 26.84 
 
 41.12 
 
 431.2 
 
 472.3 
 
 180 
 
 15.29 
 
 7.51 
 
 .01991 
 
 .6577 
 
 16.16 
 
 33.04 
 
 43.55 
 
 651.9 
 
 695.5 
 
 190 
 
 19.01 
 
 9.34 
 
 .02441 
 
 1.0985 
 
 16.41 
 
 45.00 
 
 45.97 
 
 1082.3 
 
 1128.3 
 
 200 
 
 23.46 
 
 11.53 
 
 .02972 
 
 2.2953 
 
 16.67 
 
 77.24 
 
 48.40 
 
 2247.5 
 
 2296 
 
 Below 32 F. the pressure of saturated vapor in contact with ice is 
 given. Values in the last column do not include the heat of the liquid. 
 Below 32 F. the heat of sublimation of ice rather than tue latent heat of 
 vaporization is used. 
 
AIR. 611 
 
 Moisture in Air at Different Pressures and Temperatures. (H. M. 
 
 Prevost Murphy, Eng. News, June 18, 1908.) 1. The maximum amount 
 of moisture that pure air can contain depends only on its temperature 
 and pressure, and has an unvarying value for each condition. 
 
 2. "The higher the temperature of the air, the greater Is the amount 
 of moisture that it can contain. 
 
 3. The higher the pressure of the air, the smaller is the amount of 
 moisture that it can contain. 
 
 4. When air is compressed, the rise of temperature due to the com- 
 pression, in all cases found in practice, far more than offsets the opposite 
 effect of the rise of pressure on the moisture-carrying capacity of the air. 
 Water is deposited, therefore, by compressed air as it passes from the com- 
 pressor to the various portions of the system. 
 
 Suppose that a certain amount of atmospheric air enters a compressor 
 and that it contains all the moisture possible at the existing outside tem- 
 perature and pressure. As this air is compressed its moisture-carrying 
 capacity rapidly increases, consequently all the moisture is retained by 
 the air and passes with it into the main or storage reservoir. Now if 
 this air is permitted to pass from the reservoir into the various parts of 
 the system before being cooled to the outside temperature, it will carry 
 more moisture than it is capable of holding when the temperature 
 finally drops to the normal point, and this excess quantity will be de- 
 posited, because, the pressure being high, the air cannot hold as much 
 moisture as it did at the same temperature and only atmospheric pressure. 
 In order to reduce the moisture to a minimum, it is desirable to cool 
 the air to the outside temperature before it leaves the reservoir, thereby 
 causing it to deposit all of its excess moisture, which may be easily removed 
 by drain cocks. 
 
 Although compressed air may be properly dried before leaving the 
 main reservoirs, some moisture may be temporarily deposited when the 
 air is subsequently expanded to lower pressures, as its moisture-carry- 
 ing capacity is usually affected more by the drop in temperature, result- 
 ing from the expansion, than by the drop in pressure, but when the air 
 again attains the outside temperature, the moisture thus deposited will 
 be re-absorbed if it is freely exposed to the compressed air. 
 
 In order to determine what percentage of moisture pure air can contain 
 at various pressures and temperatures, to ascertain how low the "rela- 
 tive humidity" of the atmosphere must be in order that no water will be 
 deposited in any part of a compressed-air system and also to find to what 
 temperature air drawn from a saturated atmosphere must be cooled in 
 order to cause the deposition of moisture to commence, the following 
 formulae and tables are used, based on Dalton's law of gaseous pressures, 
 which may be stated as follows: 
 
 The total pressure exerted against the interior of a vessel by a given 
 
 quantity of a mixed gas enclosed in it is the sum ot the pressures which 
 
 each of the component gases, or vapors, would exert separately if it were 
 
 enclosed alone in a vessel of the same bulk, at the same temperature. 
 
 [The derivation of the formulae is given at length in the original paper.) 
 
 Formulae for the Weight, in Lbs., of 1 Cu. Ft. of Dry Air, of 1 Cu. 
 
 Ft. of Saturated Steam or Water Vapor and the Maximum Weight 
 
 of Water Vapor that 1 IJb. of Pure Air Can Carry at Any Pressure 
 
 and Temperature. (Copyright, 1908, by H. M. Prevost Murphy.) 
 
 The values K and H being given in the table for various temperatures, 
 
 t, in Fahrenheit degrees, the formulae are: 
 
 Weight of 1 cu. ft. saturated steam = 
 
 77 = elastic force or tension of water vapor or saturated steam, in in. of 
 mercury corresponding to the temperature t (Fahr.) = 2.036 X (gauge pres- 
 sure -t- atmospheric pressure, in pounds per square inch). 
 
 K = the ratio of the weight of a volume of saturated steam to an equal 
 volume of pure dry air at the same temperature and pressure, 
 
 Values of K and 77 corresponding to the various temperatures t are 
 given in the table on p. 612, 
 
612 
 
 AIB. 
 
 Weight of 1 cu. ft. pure dry air = 
 
 1.325271 M ~_ 2.698192 P 
 459.2 + 1 * 
 
 459.2 + t 
 
 M = absolute pressure in inches of mercury. 
 P == absolute pressure in pounds per square inch. 
 W = maximum weight, in Ibs., of water vapor, that 1 Ib. of pure air 
 can contain, when the temperature of the mixture is t, and the total, 
 or observed, absolute pressure in pounds per square incli is P. 
 
 KH 
 
 ~" 2.036 P - H' 
 
 NOTE. The results obtained by the use of any of the above formulae 
 agree exactly with the average data for air and steam weights as given 
 by the most reliable authorities and careful experiments, for all pres- 
 sures and temperatures; the value of K being correct for all tempera- 
 tures up to the critical steam temperature of 689 F. 
 
 VALUES OF "IT" AND "H" CORRESPONDING TO TEMPERATURES t 
 FROM - 30 TO 434 P. 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K H 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K H 
 
 -30 
 
 .6082 
 
 .0099 
 
 64 
 
 .61 88'. 5962 
 
 158 
 
 .63239.177 
 
 252 
 
 .6501 
 
 62.97 
 
 344 
 
 .6739 254.2 
 
 -28 
 
 .6084 
 
 .0111 
 
 66 
 
 .6190 .6393 
 
 160 
 
 .63269.628 
 
 254 
 
 .6505 
 
 65.21 
 
 346 
 
 .6745 261.0 
 
 -26 
 
 .6086 
 
 .0123 
 
 68 
 
 .6193 .6848 
 
 162 
 
 .6330 
 
 10.10 
 
 256 
 
 .6510 
 
 67.49 
 
 348 
 
 .6751268.0 
 
 -24 
 
 .6088 
 
 .0137 
 
 70 
 
 .6196 
 
 .7332 
 
 164 
 
 .6333 10.59 
 
 258 .6514 
 
 69.85 
 
 350 
 
 .6757 275.0 
 
 -22 
 
 .6090 
 
 .0152 
 
 72 
 
 .6198 
 
 .7846 
 
 166 
 
 .6336 11.10 
 
 260 .6518 
 
 72.26 
 
 352 
 
 .6763282.2 
 
 -20 
 
 .6092 
 
 .0168 
 
 74 
 
 .6201 
 
 .8391 
 
 168 
 
 .6340 11.63 
 
 262 .6523 
 
 74.75 
 
 354 
 
 .6770289.6 
 
 -18 
 
 .6094 
 
 .0186 
 
 76 
 
 .6203 
 
 .3969 
 
 170 
 
 .6343 12.18 
 
 264 
 
 .6528 
 
 77.30 
 
 356 
 
 .6776297.1 
 
 -16 
 
 .6096 
 
 .0206 
 
 78 
 
 .6206 
 
 .9585 
 
 172 
 
 .6346 
 
 12.75 
 
 266 
 
 .6532 
 
 79.93 
 
 358 
 
 .6783304.8 
 
 -14 
 
 .6098 
 
 .0227 
 
 80 
 
 .6209 
 
 .024 
 
 174 
 
 .6350 
 
 13.34 
 
 268 
 
 .6537 
 
 82.62 
 
 360 
 
 .6789312.6 
 
 -12 
 
 .6100 
 
 .0250 
 
 82 
 
 .6211 
 
 .092 
 
 176 
 
 .6353 
 
 13.96 
 
 270 
 
 .6541 
 
 85.39 
 
 362 
 
 .6795320.6 
 
 -10 
 
 .6102 
 
 .0275 
 
 84 
 
 .6214 
 
 .165 
 
 178 
 
 .6357 
 
 14.60 
 
 272 
 
 .6546 
 
 88.26 
 
 364 
 
 .6803328.7 
 
 - 8 
 
 .6104 
 
 .0303 
 
 86 
 
 .6217 
 
 .242 
 
 180 
 
 .6360 
 
 15.27 
 
 274 
 
 .6551 
 
 91.18 
 
 366 
 
 .6809337.0 
 
 - 6 
 
 .6107 
 
 .0332 
 
 88 
 
 .6219 .324 
 
 182 
 
 .6364 
 
 15.97 
 
 276 
 
 .6555 
 
 94.18 
 
 368 
 
 .6816345.4 
 
 - 4 
 
 .6109 
 
 .0365 
 
 90 
 
 .6222 .410 
 
 184 
 
 .6367 
 
 16.68 
 
 278 
 
 .6560 
 
 97.26 
 
 370 
 
 .6822 354.0 
 
 - 2 
 
 .6111 
 
 .0400 
 
 92 
 
 .6225 .501 
 
 186 
 
 .6371 
 
 17.43 
 
 280 
 
 .6565 
 
 100.4 
 
 372 
 
 .6829362.8 
 
 
 
 .6'113 
 
 .0439 
 
 94 
 
 .6227 .597 
 
 188 
 
 .6374 
 
 18.20 
 
 282 
 
 .6570 
 
 103.7 
 
 374 
 
 .6836371.8 
 
 2 
 
 .6115 
 
 .0481 
 
 96 
 
 .6230' .698 
 
 190 
 
 .6377 
 
 19.00 
 
 284 
 
 .6575 
 
 107.0 
 
 376 
 
 .6843 380.9 
 
 4 
 
 .6117 
 
 .0526 
 
 98 
 
 .6233 .805 
 
 192 
 
 .6381 
 
 19.83 
 
 286 
 
 .6580 
 
 110.4 
 
 378 
 
 .6850390.2 
 
 6 
 
 .6120 
 
 .0576 
 
 100 
 
 .6236 .918 
 
 194 
 
 .6385 
 
 20.69 
 
 288 
 
 .6584 
 
 113.9 
 
 380 
 
 .6857399.6 
 
 8 
 
 .6122 
 
 .0630 
 
 102 
 
 .62382.036 
 
 196 
 
 .6389 
 
 21.58 
 
 290 
 
 .6590 
 
 117.5 
 
 382 
 
 .6865409.3 
 
 10 
 
 .6124 
 
 .0690 
 
 104 
 
 .6241 
 
 2.161 
 
 198 
 
 .6393 
 
 22.50 
 
 292 
 
 .6594 
 
 121.2 
 
 384 
 
 .6871 419.1 
 
 12 
 
 .6126 
 
 .0754 
 
 106 
 
 .62442.294 
 
 200 
 
 .6396 
 
 23.46 
 
 294 
 
 .66CO 
 
 125.0 
 
 386 
 
 .6879429.1 
 
 14 
 
 .6128 
 
 .0824 
 
 108 
 
 .62472.432 
 
 202 
 
 .6400 
 
 24.44 
 
 296 .6604 
 
 128.8 
 
 388 
 
 .6886439.3 
 
 16 
 
 .6131 
 
 .0900 
 
 110 
 
 .6250 ! 2.578 
 
 204 
 
 .6404 
 
 25.47 
 
 298 .6610 
 
 132.8 
 
 390 .6893 449.6 
 
 181.6133 
 
 .0983 
 
 112 
 
 .625312.731 
 
 206 
 
 .6407 
 
 26.53 
 
 300 .6615 
 
 136.8 
 
 392 .6901 460.2 
 
 20'.6135 
 
 .1074 
 
 114 
 
 .62562.892 
 
 208 
 
 .6411 
 
 27.62 
 
 302 .6620 
 
 141.0 
 
 394 .6908 470.9 
 
 22-. 6137 
 
 .1172 
 
 116 
 
 .62583.061 
 
 210 
 
 .6415 
 
 28.75 
 
 304 
 
 .6625 
 
 145.3 
 
 396 .6915481.9 
 
 24J.6140 
 
 .1279 
 
 118 
 
 .6261 
 
 3.239 
 
 212 
 
 .6419 
 
 29.92 
 
 306 
 
 .6631 
 
 149.6 
 
 398 ,6923 493.0 
 
 26 ! .6142 
 
 .1396 
 
 120 
 
 .6264 
 
 3.425 
 
 214 
 
 .6423 
 
 31.14 
 
 308 
 
 .6636 
 
 154.1 
 
 400 .69311504.4 
 
 28 .6144 
 
 .1523 
 
 122 
 
 .6267 
 
 3.621 
 
 216 
 
 .6426 
 
 32.38 
 
 310 .6641 
 
 158.7 
 
 402 
 
 .6939515.9 
 
 30 .6147 
 
 .1661 
 
 124 
 
 .6270 
 
 3.826 
 
 218 
 
 .6430 
 
 33.67 
 
 312 
 
 .6647 
 
 163.3 
 
 404 
 
 .6947527.6 
 
 32 .6149 
 
 .1811 
 
 126 
 
 .6273 4.042 
 
 220 
 
 .643435.01 
 
 314 
 
 .6652 
 
 168.1 
 
 406 
 
 .6955539.5 
 
 34 
 
 .6151 
 
 .1960 
 
 128 
 
 .62764.267 
 
 222 
 
 .643836.38 
 
 316 
 
 .6658 173.0 
 
 408 .6962551.6 
 
 36 
 
 .6154 
 
 .2120 
 
 130 
 
 .62794.503 
 
 224 
 
 .644237.80 
 
 318 
 
 .6663 178.0 
 
 4101.6970564.0 
 
 38 
 
 ..6156 
 
 .2292 
 
 132 
 
 .62824.750 
 
 226 
 
 .644639.27 
 
 320 
 
 .6669i183.1 
 
 412 .6979576.5 
 
 40 
 
 .6158 
 
 .2476 
 
 134 
 
 .6285 5.008 
 
 228 
 
 .6451 
 
 40.78 
 
 322 
 
 .66741 188. 3 
 
 414 
 
 .6987 ; 589.3 
 
 42 
 
 .6161 
 
 .2673 
 
 136 
 
 .62885.280 
 
 230 
 
 .6455 
 
 42.34 
 
 324 
 
 .6680 193.7 
 
 416 
 
 .6995602.2 
 
 44 
 
 .6163 
 
 .2883 
 
 138 
 
 .6291 5.563 
 
 232 
 
 .6458 
 
 43.95 
 
 326 
 
 .6686 199.2 
 
 418 
 
 .7003*615.4 
 
 46 
 
 .6166 
 
 .3109 
 
 140 
 
 .62945.859 
 
 234 
 
 .6463 
 
 45.61 
 
 328 
 
 .6691 
 
 204.8 
 
 420 
 
 .7012628.8 
 
 48 
 
 .6168 
 
 .3350 
 
 142 
 
 .629816.167 
 
 236 
 
 .6467 
 
 47.32 
 
 330 
 
 .6697 
 
 210.5 
 
 422 
 
 .70211642.5 
 
 50 
 
 .6170 
 
 .3608 
 
 144 
 
 .6301 
 
 6.490 
 
 238 
 
 .6471 
 
 49.08 
 
 332 
 
 .6703216.4 
 
 424 
 
 .7029656.3 
 
 52 
 
 .6173 
 
 .3883 
 
 146 
 
 .6304 
 
 6.827 
 
 240 
 
 .647550.89 
 
 334 
 
 .6709222.4 
 
 426 
 
 .7037 670.4 
 
 54 
 
 .6175 
 
 .4176 
 
 148 .630717.178 
 
 242 
 
 .647952.77 
 
 336 
 
 .6715228.5 
 
 428 
 
 .7046684.7 
 
 56 
 
 .6178 
 
 .4490 
 
 150 .6310 7.545 
 
 244 .648454.69 
 
 338 
 
 .6721 234.7 
 
 430 
 
 .7055699.2 
 
 58 
 
 .6180 
 
 .4824 
 
 152 ! .6313 7.929 
 
 246 .6488 56.67 
 
 340 
 
 .6727(241.1 
 
 432 
 
 .7064713.9 
 
 60 
 
 .6183 
 
 .5180 
 
 154;. 6317 8. 328 
 
 248 .6492 58.71 
 
 342 
 
 .6733 i247.6 
 
 434 
 
 .7073728.9 
 
 62 
 
 .6185 
 
 .5559 
 
 156 .632018.744 
 
 250 
 
 .649660.811 
 
 
 
 
 
AIK. 
 
 613 
 
 Weights In Pounds, of Pure Dry Air, Water Vapor and Saturated 
 
 Mixtures of Air and Water Vapor at Various Temperatures, at 
 
 Atmospheric Pressure, 29.921 In. of Mercury or 14.6963 
 
 Lb. per Sq. In. Also the Elastic Force or Pressure 
 
 of the Air and Vapor Present in Saturated 
 
 Mixtures. 
 (Copyright, 1908, by H. M. Prevost Murphy.) 
 
 
 
 Saturated Mixtures of Air and Water Vapor. 
 
 
 , d 
 
 
 . 
 
 i*" = 
 
 
 
 S3 .^ 
 
 N 
 
 8<s.sT 
 
 ^b 
 
 8 a . 
 
 S.K t| j3 
 
 5^' 
 
 S^aJ 
 
 3*2 
 
 5 
 |ll 
 
 2^< 
 
 >> 
 
 +3&H *"* 
 
 III 
 
 l|lii 
 
 l^|^l 
 
 ii 
 
 jsi^ 
 
 gg-s 
 
 OJg.Q 
 
 &S8 1 
 
 ^ o^ 
 
 "43 *** 
 
 ' "S S kS 
 
 J3 ^u-i ^-rt 
 
 fid * 
 
 'os3 
 
 S p 
 
 SQ 
 
 'SlS 2 
 
 ^ ' 
 
 d'sJ-S J 
 
 ~ ft g" . 
 
 '55 tn -^ 
 
 2 <B 
 
 'si^2 : 
 
 
 SocS 
 
 3*0 HH 
 
 3 ^rn 
 
 ^^^5o 2 
 
 ^<'o 
 
 H'S'S 
 
 ^>'5 
 
 
 
 0.086354 
 
 0.0439 
 
 29.877 
 
 0.000077 
 
 0.086226 
 
 0.086303 
 
 0.000898 
 
 12 
 
 0.084154 
 
 0.0754 
 
 29.846 
 
 0.000130 
 
 0.083943 
 
 0.084073 
 
 0.001548 
 
 22 
 
 0.082405 
 
 0.1172 
 
 29.804 
 
 0.000198 
 
 0.082083 
 
 0.082281 
 
 0.002413 
 
 32 
 
 0.080728 
 
 0.1811 
 
 29.740 
 
 0.000300 
 
 0.080239 
 
 0.080539 
 
 0.003744 
 
 42 
 
 0.079117 
 
 0.2673 
 
 29.654 
 
 0.000435 
 
 0.078411 
 
 0.078846 
 
 0.005554 
 
 52 
 
 0.077569 
 
 0.3883 
 
 29.533 
 
 0.000621 
 
 0.076563 
 
 0.077184 
 
 0.008116 
 
 62 
 
 0.076081 
 
 0.5559 
 
 29.365 
 
 0.000874 
 
 0.074667 
 
 0.075541 
 
 0.011709 
 
 72 
 
 0.074649 
 
 0.7846 
 
 29.136 
 
 0.001213 
 
 0.072690 
 
 0.073903 
 
 0.016691 
 
 82 
 
 0.073270 
 
 1.092 
 
 28.829 
 
 0.001661 
 
 0.070595 
 
 0.072256 
 
 6.023526 
 
 92 
 
 0.071940 
 
 1.501 
 
 28.420 
 
 0.002247 
 
 0.068331 
 
 0.070578 
 
 0.032877 
 
 02 
 
 0.070658 
 
 2.036 
 
 27.885 
 
 0.002999 
 
 0.065850 
 
 0.068849 
 
 0.045546 
 
 112 
 
 0.069421 
 
 2.731 
 
 27.190 
 
 0.003962 
 
 0.063085 
 
 0.067047 
 
 0.062806 
 
 122 
 
 0.068227 
 
 3.621 
 
 26.300 
 
 0.005175 
 
 0.059970 
 
 0.065145 
 
 0.086285 
 
 132 
 
 0.067073 
 
 4.750 
 
 25.171 
 
 0.006689 
 
 0.056425 
 
 0.063114 
 
 0.118548 
 
 142 
 
 0.065957 
 
 6.167 
 
 23.754 
 
 0.008562 
 
 0.052363 
 
 0.060925 
 
 0.163508 
 
 152 
 
 0.064878 
 
 7.929 
 
 21.992 
 
 0.010854 
 
 0.047686 
 
 0.058540 
 
 0.227609 
 
 162 
 
 0.063834 
 
 10.097 
 
 19.824 
 
 0.013636 
 
 0.042293 
 
 0.055929 
 
 0.322407 
 
 172 
 
 062822 
 
 12.749 
 
 17.172 
 
 0.016987 
 
 0.036055 
 
 0.053042 
 
 0.471146 
 
 182 
 
 0.061843 
 
 15.965 
 
 13.956 
 
 0.021000 
 
 0.028845 
 
 0.049845 
 
 0.728012 
 
 192 " 
 
 0.060893 
 
 19.826 
 
 10.095 
 
 0.025746 
 
 0.020545 
 
 0.046291 
 
 1.25319 
 
 202 
 
 0.059972 
 
 24.442 
 
 5.479 
 
 0.031354 
 
 0.010982 
 
 0.042336 
 
 2.85507 
 
 212 
 
 0.059079 
 
 29.921 
 
 0.000 
 
 0.037922 
 
 0.000000 
 
 0.037922 
 
 Infinite- 
 
 Applications of the Formula 1 and Tables. 
 
 EXAMPLE 1. How low must the relative humidity be, when the at- 
 mospheric pressure is 14.7 Ib. per sq. in. and the outside temperature is 
 60, in order that no moisture may be deposited in any part of a com- 
 pressed air system carrying a constant gauge pressure of 90 Ib. per sq. in? 
 A n s. The maximum amount of moisture that 1 Ib. of pure air can 
 contain at 90 Ib. gauge, = 104.7 Ib. (absolute pressure) and 60 F., is 
 W - KH - 0.6183X0.5180 __ 
 
 2.036 P-r-H~ 2.036 X 104.7 - 0.5180 ~ a 
 
 The maximum weight of moisture that 1 Ib. of air can contain at 60 
 F. and 14.7 Ib. (absolute pressure) is 
 
 W (at 14 7) - 0-618 X 0.5180 _ 
 
 14>7} " 2.036 X 14.7 - 05180 ' 01 lb * 
 
 In order that no moisture may be deposited, the relative humidity 
 must not be above 
 
 (0.001506 -^ 0.01089) X 100 = 13.83%. 
 
 NOTE. Air is said to be saturated with water vapor when it contains 
 the maximum amount possible at the existing temperature and pressure. 
 EXAMPLE 2. When compressing air into a reservoir carrying a con- 
 stant gauge pressure of 75 lb., from a saturated atmosphere of 14.7 lb. 
 abs. press, and 70 F., to what temperature must the air be cooled after 
 compression in order to cause the deposition of moisture to commence? 
 Ans. First find the maximum weight of moisture contained in 
 1 lb. of pure air at 14.7 lb. pressure and 70 F. 
 
614 AIR. 
 
 KH 0.6196 X 0.7332 
 
 2.036P-# = 2d36~X 14.7 - 0.7332 = ' 1556 lb ' 
 
 The temperature to which the air must be cooled in order to cause 
 the deposition of moisture may be found by placing this value of 0.01556 
 together with P equal to 75 + 14.7 in the equation thus: 
 
 _ _ 
 
 2.036 X 89.7 -# ~ 182.63 - H 
 
 2 842 
 
 or H . ' ; ~ , and the temperature which satisfies this equation 
 U.Ulooo ~r zi. 
 
 is found by aid of the table [by trial and error] to be approximately 
 129 F. 
 
 EXAMPLE 3, When the outside temperature is 82 F., and the 
 pressure of the atmosphere is 14.6963 Ib. per sq. in., the relative humid- 
 ity being 100%, how many cu. ft. of free air must be compressed 
 and delivered into a reservoir at 100 Ib. gauge in order to cause 1 Ib. of 
 water to be deposited when the air is cooled to 82 F.? 
 
 Ans. Weight of moisture mixed with 1 Ib. of air at 82 F. t and 
 atmospheric pressure = 0.023526 Ib. For 100 Ib. gauge pressure, 
 
 W- KH 0.6211 X 1.092 _o 002918 Ib 
 
 2.036 P-H 2.036 X 114.6963 - 1.092 ~ 
 
 Weight of moisture deposited by each Ib. of compressed air = 0.023526 
 0.002918 = 0.020608 Ib. Each cu. ft. of the moist atmosphere con- 
 tains 0.070595 Ib. of pure air, therefore the number of cu. ft. that must 
 be delivered to cause 1 Ib. of water to be deposited is 
 
 X TTT; ^= 687.37 cu. ft. 
 
 0.070595 0.020608 
 
 EXAMPLE 4. Under the same conditions as stated in Example 3, 
 what is the loss in volumetric efficiency of the plant when the excess 
 moisture is properly trapped in the main reservoirs? 
 
 Ans. Before compression, each pound of air is mixed with 0.023526 
 Ib. of water vapor and the weight of 1 cu. ft. of the mixture is 0.072256 Ib., 
 consequently the volume of the mixture is 
 
 1.023526 ^ 0.072256 = 14.165 cu. ft. 
 
 For 100 Ib. gauge pressure and 82 F. as shown in Example 3, 1 Ib. 
 of air can hold 0.002918 Ib. of water in suspension, having deposited 
 0.020608 Ib. in the reservoir. The weight of 1 cu. ft. of water vapor at 
 82 is 0.001661 Ib., consequently by Dalton's law the volume of the. mix- 
 ture of 1 Ib. of air and 0.002918 Ib. of water vapor at 100 Ib. gauge press- 
 ure is the same as that of the vapor or saturated steam alone; that is, 
 0.002918 + 0.001661 = 1.757 cu. ft. 
 
 By Mariotte's law, the volume of the 1.757 cu. ft. of mixed gas at 
 114.6963 Ib. absolute when expanded to atmospheric pressure will be 
 
 (114.6963 -^ 14.6963) X 1.757 = 13.712 cu. ft.; 
 
 consequently the decrease of volume, that is, the loss of volumetric 
 efficiency, is 
 14.165 - 13.712 = 0.453 cu. ft., or (0.453 -f- 14.165) X 100 = 3.2%. 
 
 This example shows that, particularly in warm, moist climates, there 
 Is a very appreciable loss in the efficiency of compressors, due to the 
 condensation of water vapor. 
 
 Specific Heat of Air at Constant Volume and at Constant Pressure. 
 Volume of 1 Ib. of air at 32 F. and pressure of 14.7 Ibs. per sq. in. = 
 12.387 cu. ft. =a column 1 sq. ft. area X 12.387 ft. high. Raising tem- 
 perature 1 F. expands it 1/492, or to 12.4122 ft. high, a rise of 0.02522ft. 
 
 Work done = 2116 Ibs. per sq. ft. X .02522 = 53.37 foot-pounds, or 
 53.37 -i- 778 = 0.0686 heat units. 
 
 The specific heat of air at constant pressure, according to Regnault, is 
 0.2375; but this includes the work of expansion, or 0.0686 heat units; hence 
 the specific heat at constant volume = 0.2375 0.0686 = 0.1689. 
 
 Ratio of specific heat at constant pressure to specific heat at constant 
 volume = 0.2375 -T- 0.1689 = 1.406. (See Specific Heat, p. 562.) 
 
FLOW OF AIR THROUGH ORIFICES. 615 
 
 Flow of Air through Orifices. Tne tneoreticai velocity in feet per 
 second of_flow of any fluid, liquid, or gas through an orifice is v = ^2~gh 
 = 8.02 V/i, in which h the " head " or height of the fluid in feet required 
 to produce the pressure of the fluid at the level of the orifice. (For gases 
 the formula holds good only for small difference of pressure on the two 
 sides of the orifice.) The quantity of flow in cubic feet per second is equal 
 to the product of this velocity by the area of the orifice, in square feet, 
 multiplied by a "coefficient of flow," which takes into account the con- 
 traction of the vein or flowing stream, the friction of the orifice, etc. 
 
 For air flowing through an orifice or short tube, from a reservoir of the 
 pressure p\ into a reservoir of the pressure pz, Weisbach gives the following 
 values for the coefficient of flow, obtained from his experiments. 
 
 FLOW OP AlR THROUGH AN ORIFICE. 
 
 Coefficient c in formula v = c \/2'gh 
 
 Diam. 1 cm. = 0.394 in.: 
 
 Ratio of pressures ... 1.05 1.09 1.43 1.65 1.89 2.15 
 
 Coefficient 555 .589 .692 .724 .754 .788 
 
 Diam. 2.14 cm. '= 0.843 in.: 
 
 Ratio of pressures ... 1.05 1.09 1.36 1.67 2.01 
 
 Coefficient 558 .573 .634 .678 .723 
 
 FLOW OF AlR THROUGH A SHORT TUBE. 
 
 Diam. 1 cm., = 6.394 in., length 3 cm. = 1.181 in. 
 
 Ratio of pressures pi -&-p2... 1.05 1.10 1.30 
 
 Coefficient 730 .771 .830 
 
 Diam. 1.414 cm. = 0.557 in., length 4.242 cm. = 1.670 in.: 
 
 Ratio of pressures 1.41 1 . 69 
 
 Coefficient 813 .822 
 
 Diam. 1 cm. = 0.394 in., length 1.6 cm. = 0.630 in. Orifice rounded: 
 
 Ratio of pressures 1.24 1.38 1.59 1.85 2.14 
 
 Coefficient 979 .986 .965 .971 .978.... 
 
 Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow 
 of air through an orifice due to small differences of pressure, 
 
 V - C i^ k X 773.2 X (l 1 * ~ 32 ) >< 29 - 92 
 
 in which V = Velocity in feet per second; 2 g = 64.4; h height of the 
 column of water in inches, measuring the difference of pressure; t = the 
 temperature Fahr.; and p = barometric pressure in inches of mercury. 
 773.2 is the volume of air at 32 under a pressure of 29.92 inches of mercury 
 when that of an equal weight of water is taken as 1. 
 
 For 62 F., the formula becomes V = 363 C ^h/p, and if p = 29.92 
 inches, V = 66.35 C Vft. 
 
 The coefficient of efflux C, according to Weisbach, is: 
 For conoidal mouthpiece, of form of the contracted vein, 
 
 with pressures of from 0.23 to 1.1 atmospheres C = 0.97 to 0.99 
 
 Circular orifices in thin plates C = 0.56 to 79 
 
 Short cylindrical mouthpieces C = 0.81 to 0.84 
 
 The same rounded at the inner end C = 92 to 93 
 
 Conical converging mouthpieces C = 0.90 to 0.99 
 
 JR. J. Durley, Trans. A. S. M. E., xxvii, 193, gives the following: 
 
 The consideration of the adiabatic flow of a perfect gas through a 
 frictionless orifice leads to the equation 
 
 2 7 + 1 
 
 W = weight of gas discharged per second in pounds. 
 A = area of cross section of jet in square feet. 
 P\ pressure inside orifice in pounds per square foot. 
 Jrt pressure outside orifice. 
 
 Vi = specific volume of gas inside orifice in cu. ft. per Ib. 
 y = ratio of the specific heat at constant pressure to that at constant 
 volume. 
 
616 
 
 AIR. 
 
 For air, where y = 1.404, we have for a circular orifice of diameter d 
 inches, the initial temperature of the air being 60 Fahr. (or 521 abs.), 
 
 W = 0.000491 d*l 
 
 In practice the flow is not frictionless, nor is it perfectly adiabatic, 
 and the amount of heat entering or leaving the gas is not known. Hence 
 the weight actually discharged is to be found from the formulas by in- 
 troducing a coefficient of discharge (generally less than unity) dep'end- 
 ing on the conditions of the experiment and on the construction of 
 the particular form of orifice employed. 
 
 If we neglect the changes of density and temperature occurring as 
 the air passes through the orifice, we may obtain a simpler though 
 approximate formula for the ideal discharge: 
 
 W 
 
 0.01369 d- \l~ 
 
 (3) 
 
 in which d = diam. in inches, i = difference of pressures measured in 
 inches of water, P = mean absolute pressure in Ibs. per sq. ft., and T = 
 absolute temperature on the Fahrenheit scale = degrees F. + 461. In 
 the usual case, in which the discharge takes place into the atmosphere, 
 P is approximately 2117 pounds per square foot and 
 
 W = 0.6299 d 
 
 'V? 
 
 (4) 
 
 To obtain the actual discharge the values found by the formula are to be 
 multiplied by an experimental coefficient C, values of which are given in 
 the table below. 
 
 Up to a pressure of about 20 ins. of water (or 0.722 Ibs. per sq. in.) above 
 the atmospheric pressure, the results of formulae (2) and (4) agree very 
 closely. At higher differences of pressure divergence becomes noticeable. 
 
 They hold good only for orifices of the particular form experimented 
 with, and bored in plates of the same thickness, viz.: iron plates 0.057 in. 
 thick. 
 
 The experiments and curves plotted from them Indicate that: 
 
 (1) The coefficient for small orifices increases as the head increases, but 
 at a lesser rate the larger the orifices, till for the 2-in. orifice it is almost 
 constant. For orifices larger than 2 ins. it decreases as the head increases, 
 and at a greater rate the larger the orifice. 
 
 (2) The coefficient decreases as the diameter of the orifice increases, and 
 at a greater rate the higher the head. 
 
 (3) The coefficient does not change appreciably with temperature 
 (between 40 and 100 F.). 
 
 (4) The coefficient (at heads under 6 ins.) is not appreciably affected 
 by the size of the box in which the orifice is placed if the ratio of the areas 
 of the box and orifice is at least 20 : 1. 
 
 MEAN DISCHARGE IN POUNDS PER SQUARE FOOT OF ORIFICE PER SECOND 
 AS FOUND FROM EXPERIMENTS. 
 
 Diameter 
 Orifice, 
 Inches. 
 
 1-inch 
 Head 
 Discharge 
 per Sq. Ft. 
 
 2-inch Head 
 Discharge 
 per Sq. Ft. 
 
 3-inch Head 
 Discharge 
 per Sq. Ft. 
 
 4-inch 
 Head 
 Discharge 
 per Sq. Ft. 
 
 5-inch 
 Head 
 Discharge 
 per Sq. Ft. 
 
 0.3125 
 
 3.060 
 
 4.336 
 
 5.395 
 
 6.188 
 
 7.024 
 
 0.5005 
 
 3.012 
 
 4.297 
 
 5.242 
 
 6.129 
 
 6.821 
 
 1.002 
 
 3.058 
 
 4.341 
 
 5.348 
 
 6.214 
 
 6.838 
 
 ' 1.505 
 
 3.050 
 
 4.257 
 
 5.222 
 
 6.071 
 
 6.775 
 
 2.002 
 
 2.983 
 
 4.286 
 
 5.284 
 
 6.107 
 
 6.788 
 
 2.502 
 
 3.041 
 
 4.303 
 
 5.224 
 
 5.991 
 
 6.762 
 
 3.001 
 
 3.078 
 
 4.297 
 
 5.219 
 
 6.033 
 
 6.802 
 
 3.497 
 
 3.051 
 
 4.258 
 
 5.202 
 
 5.966 
 
 6.814 
 
 4.002 
 
 3.046 
 
 4.325 
 
 5.264 
 
 5.951 
 
 6.774 
 
 4.506 
 
 3.075 
 
 4.383 
 
 5.508 
 
 6.260 
 
 7.028 
 
FLOW OF AIR IN PIPES. 
 
 617 
 
 COEFFICIENTS OF DISCHAEGE FOI^VARIOUS HEADS AND DIAMETERS OF 
 ORIFICE. 
 
 Diameter 
 of Orifice, 
 Inches. 
 
 1-inch 
 Head. 
 
 2-inch 
 Head. 
 
 3-inch 
 Head. 
 
 4-inch 
 Head. 
 
 5-inch 
 Head. 
 
 5 /16 
 
 0.603 * 
 
 0.606 
 
 0.610 
 
 0.613 
 
 0.616 
 
 V2 
 
 0.602 
 
 0.605 
 
 0.608 
 
 0.610 
 
 0.613 
 
 
 0.601 
 
 0.603 
 
 0.605 
 
 0.606 
 
 0.607 
 
 H/2 
 
 0.601 
 
 0.601 
 
 0.602 
 
 0.603 
 
 0.603 
 
 2 
 
 0.600 
 
 0.600 
 
 0.600 
 
 0.600 
 
 0.600 
 
 21/2 
 
 0.599 
 
 0.599 
 
 0.599 
 
 0.598 
 
 0.598 
 
 3 
 
 0.599 
 
 0.598 
 
 0.597 
 
 0.596 
 
 0.596 
 
 31/2 
 
 0.599 
 
 0.597 
 
 0.596 
 
 0.595 
 
 0.594 
 
 4 
 
 0.598 
 
 0.597 
 
 0.595 
 
 0.594 
 
 0.593 
 
 41/2 
 
 0.598 
 
 0.596 
 
 0.594 
 
 0.593 
 
 0.592 
 
 CORRECTED ACTUAL DISCHARGE IN POUNDS PER SECOND AT 60 F. AND 
 
 14.7 LBS. BAROMETRIC PRESSURE FOR CIRCULAR ORIFICES IN 
 
 PLATE 0.057 IN. THICK. 
 
 Diameter of Orifice in Inches. 
 
 rt 
 
 or 
 Wo 
 
 0.3125 
 
 0.500 | i.OOO 
 
 1.500 
 
 2.000 
 
 2.500 
 
 3.000 
 
 3.500 
 
 4.000 
 
 4.500 
 
 5.000 
 
 I 172 
 
 U/ 2 
 
 21/2 
 31/2 
 41/2 
 
 5V2 
 6 
 
 0.00114 
 OC162 
 
 0.00293 
 00416 
 
 0.0117 
 0166 
 
 0.0263 
 0373 
 
 0.0468 
 0663 
 
 0.0732 
 103 
 
 0.105 
 149 
 
 0.143 
 202 
 
 0.187 
 264 
 
 0.237 
 0.334 
 
 0.292 
 413 
 
 0.00199 
 
 0.00510 
 
 0.0203 
 
 0.0457 
 
 .081 1 
 
 0.127 
 
 0.182 
 
 0.248 
 
 0.323 
 
 0.409 
 
 0.505 
 
 0.00231 
 00259 
 
 C. 00590 
 00662 
 
 0.0235 
 0.0263 
 
 0.0528 
 1591 
 
 0.0937 
 105 
 
 0.146 
 0.163 
 
 0.210 
 235 
 
 0.285 
 319 
 
 0.373 
 416 
 
 0.471 
 0.526 
 
 0.582 
 649 
 
 0.00285 
 
 0.00726 
 
 0.0289 
 
 0.0648 
 
 0.115 
 
 0.179 
 
 0.257 
 
 0.349 
 
 0.455 
 
 0.575 
 
 0.710 
 
 0.00308 
 
 0.00786 
 
 0.0312 
 
 0.0700 
 
 0.124 
 
 0.193 
 
 0.277 
 
 0.377 
 
 0.491 
 
 0.621 
 
 0.766 
 
 0.00330 
 0.00351 
 0.00371 
 0.00390 
 0.00408 
 
 0.00842 
 0.00695 
 0.00945 
 .00993 
 0.01049 
 
 0.0334 
 0.0355 
 0.0375 
 0.0393 
 0.0411 
 
 0.0749 
 0.0794 
 0.0838 
 0.0879 
 0.0918 
 
 0.133 
 0.141 
 0.148 
 0.155 
 0.162 
 
 0.206 
 0.219 
 0.231 
 0.242 
 0.252 
 
 0.296 
 0.314 
 0.331 
 0.347 
 0.362 
 
 0.402 
 0.426 
 0.449 
 0.471 
 0.492 
 
 0.525 
 0.556 
 0.586 
 0.613 
 0.640 
 
 0.663 
 0.702 
 0.739 
 0.774 
 0.808 
 
 0.817 
 0.865 
 0.912 
 0.953 
 0.995 
 
 Fliegner's Equation for Flow of Air through an Orifice. (Peabody's 
 "Thermodynamics," also Trans. A. S. M. E., vol. 27, p. 194.) 
 
 - 
 
 W = flow in pounds per second; A = area of the orifice (or sum of the 
 areas of all the orifices) in square inches; P = absolute pressure in the 
 orifice chamber Ib. per sq. in.; T = absolute temperature, deg. F., of the 
 air in the chamber. The formula applies only when the absolute 
 pressure in the reservoir is greater than twice the atmospheric pressure, 
 and for orifices properly made. The orifices are in hardened steel 
 plates 3/ 8 in. to 1/2 in. thick, accurately ground, with the inside orifice 
 rounded to a radius I/IG in. less than the thickness of the plate, leaving 
 1/16 in. of the hole straight. 
 
 FLOW OF AIR IN PIPES. 
 
 In the steady flow of any liquid or gas, without friction, the sum of 
 the velocity head, V 2 -5- 2 g, pressure head p/w, and potential head, z, 
 (that is the distance in feet above an assumed datum) at any section of 
 
 the pipe is a constant quantity. ~ + + z = a constant. This 
 
 statement is known as Bernoulli's theorem. 
 
 V = velocity in ft. per sec.; 2 g = 64.35; p = absolute pressure in 
 pounds per sqiiare feet; w = density, pounds per cubic feet; z = height 
 of the section above a given datum level. When the pipe is level we 
 may take its axis as datum, and then 2=0. 
 
 When "fluid friction" or "skin friction" is taken into account there 
 
618 AIK. 
 
 is a "loss of head" or "friction head" between any two selected points, 
 
 / D 2 
 
 such as the two ends of the pipe, H ~ fLv* * R 2 g; or H = 4/ ; 
 
 H is the loss of head, or head causing the flow, measured in feet of the 
 fluid, / is a coefficient of friction and R the mean hydraulic radius, 
 which in circular pipes = 1/4 D. L is the length of the pipe and D the 
 diameter, both in feet. By transposition the .velocity in feet per 
 
 second is V=^ f ^ = 4.0103 ^/y^- 
 
 The value of/ in this formula varies through a considerable range 
 with the roughness of the pipe, with the diameter, and probably to 
 some extent with the velocity. For a rough approximation its value 
 for air and other gases may be taken as 0.005. 
 
 For convenience in calculation, the loss of head in feet of H may be 
 replaced by the difference in pressure in Ib. per sq. in., H = 144 (p\ pz) 
 -r W, and the diameter d may be taken in inches. We thus obtain 
 
 v = 
 
 The quantity of flow in cubic feet per minute, Q = 60 A V. A being 
 the area in sq. ft. =60 X 0.7854 X d 2 -r- 144, whence we have (by multi- 
 plying 60 X 0.7854 X 13.89 4- 144), Q = 4.546 ^~ X 
 
 i P 2 ) which is the common formula for flow of any liquid or 
 
 w 
 
 gas when Q is in cubic feet per minute measured at the density w cor- 
 responding to the higher pressure pi. To reduce this to the equivalent 
 
 volume of "free air" at atmospheric pressure, Qa = Q X T* 
 
 The weight flowing per minute is Q w = W = c - Values 
 
 of c corresponding to different values of/ are as follows: 
 
 /. . . . 003 . 0035 . 004 . 0045 . 005 . 0055 . 006 . 0065 . 007 . 0075 
 C... 83.0 76.9 71.9 67.8 64.3 61.3 58.7 56.4 54.7 52.4 
 
 The experimental data from which the values of c and / for air and 
 gas may be determined are few in number and of doubtful accuracy. 
 Probably the most reliable are those obtained by Stockalper at the 
 St. Gothard tunnel. Unwin found from these data that the value of/ 
 varied with the diameter and that it might be expressed by the formula 
 /= 0.0028 (1 + 3.6/tf), d being taken in inches. 
 
 Ford= I 2 3 4 6 12 24 48 In. 
 
 / = 0.013 .0078 .0062 .0053 .0045 .0036 .0032 .0030 
 c=40.0 51.3 57.9 62.3 67.9 75.3 80.1 82.8 
 
 Unwin 's formula may be given the form Q = K \ w jf(I~+ ? 3 6d)' 
 
 in which K = 4.546 V 1 -T- .0028 = 85.9. This is practically the 
 same as Babcock's formula for steam, in which / is taken at 0.0027, 
 giving K = 87.5. 
 
 Formulae for Flow with Large Drop in Pressure. The above for- 
 mulae are based on the assumption that the drop in pressure is small, 
 and that, therefore, the density remains practically constant during 
 the flow. When the drop is large the density decreases with the pres- 
 sure and the velocity increases. Church ("Mechanics of Engineering," 
 p. 791) and Unwin (Ency. Brit., llth ed., vol. xiv., p. 67), develop 
 formulae for compressible fluids with large drop of pressure and in- 
 creasing velocity. The temperature is assumed to be constant, the 
 heat generated by friction balancing the cooling due to the work done 
 in expansion. 
 
FLOW OF AIR IN PIPES. 619 
 
 Church's formula: Q = 1/4 ir d* -V/T77 w^ ^ l * ~" p *^' 
 
 Unwind formula: v- 
 
 V = velocity, ft. per sec. ; Q = volume, cu. ft. per sec. at the pressure 
 PI; g = 32.2; R = the constant in the formula PV = RT (see Thermody- 
 
 namics) = 53.32 for air; d = diam., and L = length, in feet; pi, pz = 
 absolute!- pressures in Ib. per sq. ft.; w = density, Ib. per cu. ft.; 2'== 
 temperature F. + 459.6. The value of / is given by Church as from 
 
 0.004 to 0.005. Unwin makes it vary with the diameter as stated 
 above. 
 
 These two formulae give identical results when the value of/ is taken 
 the same in both, for RT/pi 2 =1-7- wpi. 
 
 J. E. Johnson, Jr. (Am. Mach., July 27, 1899) gives Church's formula 
 in a simpler form as follows: pi 2 pz z = KQ*L -5- d 5 , in which pi and 
 pz are the initial and final pressures in Ib. per sq. in., Q the volume of 
 free air (that is the volume reduced to atmospheric pressure) in cubic 
 feet per minute, d the diameter of the pipe in inches, L the length in feet, 
 and K a numerical coefficient which from the Mt. Cenis and St. Gothard 
 experiments has a value of about 0.0006. E. A. Rix, in a paper on the 
 Compression and Transmission of Illuminating Gas, read before the 
 Pacific Coast Gas Ass'n, 1905, says he uses Johnson's formula, with a 
 coefficient of 0.0005, which he considers more nearly correct than 0.0006. 
 For gas the velocity varies inversely as the square root of the density, 
 and for gas of a density G, relative to air as 1, Rix gives the formula 
 Pl z _ p 2 2 = 0.0005 VOX Q*L/d*. 
 
 If Church's formula is translated into the same form as Johnson's, 
 taking/ = 0.005, w = 0.07608 for air at 62 F., and atmospheric pressure, 
 14.7 Ibs. per sq. in., the value of K is 0.00054. A more convenient 
 
 form is Q a = Ci l ~ i n w hich Ci = \/^/K. With K in 
 
 Johnson's formula taken at 0.0006, Ci = 40.8. With / in Church's 
 formula taken at 0.005, Ci = 43.0. 
 
 Note that Church's formula gives Q in cubic feet per second meas- 
 ured at the pressure p\, while Johnson's Qa is in cubic feet per minute 
 reduced to atmospheric pressure. 
 
 Both Church and Johnson assume that the flow varies as \/d*, the 
 coefficients/ and K being independent of the diameter. In this respect 
 their formulae are faulty, for, as Unwin shows, the coefficient of friction 
 is a function of the diameter. 
 
 The relation between the results given by these formulae and those 
 given by the common formula is the relation between \/pi* - pz 2 and 
 \/pi pz. Taking pi (in any unit) as 100, and different drops in 
 pressure, the relative results are as follows: 
 
 Pressure drop .............. 1 10 20 40 60 80 
 
 Values of pz. . . ....... ........ 99 90 80 60 40 20 
 
 Vpi*-pz 2 + Vpi - PZ ...... 14.1 13.8 13.4 12.2 11.8 10.8 
 
 Ratio, 14.1 = 100 ........... 100 97.6 95.0 86.5 83.7 76.6 
 
 It thus appears that the calculated result by Johnson's formula is 
 not more than 5 per cent less than that calculated by the common 
 formula, when the same value of / is used, if the drop in pressure is 
 not greater than 20 per cent of p\. 
 
 Comparison of Different Formulae. We may compare the several 
 formulas given above by applying them to the data of the St. Gothard 
 experiments, as in table p. 620. 
 
 The value of Q is given as reduced to atmospheric pressure, 14.7 Ib. 
 per sq. in. and 62 F. The length of the pipe 7.87 in. diam. was 15,092 
 ft., and that of the pipe 5.91 in diam., 1712.6 ft. The mean tempera- 
 ture of the air in the large pipe was 70 F. and in the small pipe 80 F, 
 
620 
 
 AIR. 
 
 In the table, Formula (1) Is the commonTormula, Qi 
 
 CAT 
 
 (Pi - P2) ( 
 
 w L 
 
 Formula (2) is Unwin's, 
 
 Formula (3) is Johnson's, Q 
 
 } d 
 
 Qi = cubic ft. per min. at pressure pi. 
 
 Q a = cubic ft. per min. reduced to atmospheric pressure =Q pi -7-14.7. 
 
 Di- 
 am- 
 eter, 
 In. 
 
 Mean 
 Vel. 
 Ft. 
 Per 
 Sec. 
 
 Cu. 
 
 Ft. 
 Per 
 
 Min. 
 
 Q 
 
 Lb. 
 Per 
 Sec. 
 
 Absolute 
 Pressures. 
 Ib. per sq. in. 
 
 Coefficient in 
 Formula. 
 
 Ratio of 
 Coefficient to 
 Average Value. 
 
 (0 
 c 
 
 ( l> 
 
 & 
 
 Pi 
 
 P2 
 
 (D 
 
 (2) 
 
 (3) 
 
 7.87 
 7.87 
 7.87 
 5.91 
 5.91 
 
 Av< 
 
 19.3 
 16.3 
 15.6 
 37.1 
 29.3 
 
 jrage. 
 
 2105 
 1401 
 1169 
 2105 
 1169 
 
 2.669 
 1.776 
 
 1.483 
 2.669 
 1.483 
 
 82.32 
 63.95 
 56.45 
 77.03 
 53.66 
 
 77.03 
 60.71 
 53.66 
 73.50 
 52.04 
 
 76.0 
 73.5 
 
 70.2 
 74.8 
 65.5 
 
 89.6 
 86.5 
 82.8 
 94.9 
 83.1 
 
 51.3 
 
 49.3 
 46.0 
 44.5 
 43.6 
 
 1.06 
 1.02 
 0.98 
 1.04 
 0.91 
 
 1.03 
 0.99 
 0.95 
 1.09 
 0.95 
 
 1.09 
 1.05 
 0.98 
 0.95 
 0.93 
 
 72.0 
 
 87.4 
 
 46.9 
 
 The above comparison shows that no one of three formulae fits the 
 St. Gotnard experiments better than any other; each one when applied 
 with the average value of its coefficient may give a result that differs 
 as much as 9 per cent from the observed result. 
 
 Arson's Experiments. Unwin quotes some experiments by A. Arson 
 on the flow of air through cast-iron pipes which showed that the co- 
 efficient of friction varied with the velocity. For a velocity of 100 ft. 
 per sec., and without much error for higher velocities, Unwin finds 
 that the values of / agree fairly with the formula /= 0.005 (1 +3.6/d). 
 Translating the figures given by him for the varying values 9f / into 
 values of c for use in the common formula, we have the following: 
 
 Diameter of pipe, inches.. . .1.97 3.19 4.06 10 12.8 19.7 
 volume ( V = 10 ft. per sec. 35 . 7 39.4 39.8 49.2 52.8 64.7 
 Values J 5Q ,. ,. 38 6 42 5 45 51 5 55 7 65 2 
 
 ofc - ( 100 " " ' 41.3 45.5 46.0 53.6 56.4 65.4 
 The values of c for the same diameter with / = 0.0028 (1 +3.6/d), as 
 deduced by Unwin from Stockalper's experiments are: 51.4, 57.9, 
 62.3, 73.7, 75.9, 79.1. 
 
 Unwin says that Stockalper's pipes were probably less rough than 
 Arson's. The values of c according to Stockalper's experiments range 
 from 21 to 37 per cent higher than those calculated from the formula 
 derived from Arson's experiments. 
 
 Use of the Formulae. It is evident from the above comparisons 
 that any formula for the flow of air or gas must be considered as only 
 a rough approximation to the actual flow, and that an observed result 
 may differ as much as 40 per cent from that calculated by a formula. 
 Part of this error is due to variations in the roughness of pipes, part 
 due to error in measurements of the actual flow, and part due to the 
 fact that the coefficients of the several formulae are based on too few 
 experiments. In the light of our present knowledge, Unwin's formula 
 
 for moderate drop, Q = 87 
 
 (pi 
 
 is probably the best one 
 
 1 w L (I + 3.6/rf) 
 
 to use for all cases in which the drop in pressure does not exceed 20 
 per cent of the absolute initial pressure, and Johnson's formula, 
 
 Qa= 47-J (pl2 ~^ 22) rf5 for cases in which the drop is larger and the pipes 
 
FLOW OF AIR AT LOW PRESSURES. 
 
 621 
 
 are not less than 12 inches diameter. For smaller pipes the term 
 (1 + 3.6/d) had better be used after L in the denominator. These 
 formulae with the coefficients given apply only to straight pipes with a 
 fairly smooth interior surface. For crooked or rough pipes it may be 
 well to use the common formula with the coefficients derived from 
 Arson's experiments, given above. 
 
 Another comparison of the three formulas may be made by applying 
 them to some extreme cases, as follows: The initial pressure is taken 
 at 100 Ib. absolute per sq. in., the corresponding, density is 0.5176 Ib. 
 per cu. ft.; diameters are assumed at 1 in. and 48 in., the drop in pres- 
 sure 1 Ib. and 40 Ib. and the length 100 ft. and 40,000 ft., making 
 eight cases in all. A ninth case is taken with intermediate values: 
 diameter, 10 in.; length, 1,000 ft.; and drop, 1 Ib. The results are 
 given in the following table. The results obtained by Johnson's for- 
 mula have been reduced by dividing them by the ratio (100 -%- 14.7) 
 to obtain Q. The value of c in the common formula is taken at 72, the 
 average figure from the St. Gothard experiments. 
 
 Diarri., In. 
 
 1 
 
 48 
 
 10 
 1 
 1,000 
 
 Pi- P2, Ib. 
 
 1 
 
 40 
 
 1 
 
 40 
 
 L, f t 
 
 100 
 
 40,000 
 
 100 
 
 40,000 
 
 100 1 40,000 
 
 100 
 
 40,000 
 
 
 Formula 
 
 Cubic feet of air per minute at the pressure p. 
 
 Common .... 
 
 10.08 
 5.64 
 9.75 
 
 0.50 
 0.28 
 0.49 
 
 63.3 
 35.7 
 55.3 
 
 3.16 
 1.78 
 2.76 
 
 1 59,800 
 186,200 
 155,600 
 
 7,990 
 9,310 
 7,778 
 
 1,010,000 
 1,178,000 
 882,300 
 
 50,500 
 58,900 
 44,110 
 
 1,008 
 1,037 
 974 
 
 Unwin 
 
 Johnson 
 
 Ratio of results to Unwin's = 1. 
 
 Common 
 Johnson 
 
 1.79 
 1.73 
 
 1.79 
 1.75 
 
 1.78 
 1.55 
 
 1.78 
 1.55 
 
 0.86 
 0.84 
 
 0.86 
 0.84 
 
 0.86 
 0.75 
 
 0.86 
 0.75 
 
 0.96 
 0.94 
 
 These figures show that while the three formulae agree fairly well for 
 the 10-in. pipe with 1-lb. drop in 1,000 ft., they show wide disagreements 
 when a great range of diameters, lengths, and drops in pressure are 
 taken. For the 1-in. pipe Unwin's figures are from 35 to 45 per cent 
 lower than those given by the common formula or by Johnson's, but 
 they are not therefore certainly too low. We have a check on them 
 in Culley and Sabine's experiments on 2 V4-in. lead pipes, 2000 to 
 nearly 6000 ft. long, quoted by Unwin, which gave a value of = 0.07. 
 Unwin's formula, / = 0.0028 (1 + 3.6/rf) gives / = 0.0073. The cor- 
 responding values of c in the common formula are 54.7 and 53.2. 
 
 Formula for Flow of Air at Low Pressures. For ventilating and 
 similar purposes, air is usually carried at pressures, but slightly above 
 that of the atmosphere. Pressures are measured in inches of w T ater 
 column or in ounces per square inch above atmospheric pressure. 
 For smooth and straight circular pipes, probably the best formula to 
 
 use is Unwin's, Q 
 rived from the St. 
 
 = 87 \l 
 
 if 
 
 P ~ 
 
 the coefficient 87 being de- 
 
 j 
 
 f W Li \L 
 
 . Gothard experiments on compressed air. In 
 order to put the formula into a more convenient form for low pres- 
 sures, let h = head or difference in pressures measured in inches of 
 water column, = 27.712 (pi - p 2 ), and take w = 0.07493 = density 
 of air, Ib. per cu. ft. at 70 and atmospheric pressure, then Q = 
 
 87 X 
 
 27.71 .07493 L (1 + 3.6/d) 
 
 60.37 
 
 L (I +3.6/d)' 
 
 or Q =3 
 
 L~' in which C is a coefficient varying with the diameter, values 
 
 for different diameters being given in the table below. For other 
 temperatures and pressures, the flow varying inversely as the square 
 root of the density, the figure 0.07493 in the above equation should be 
 
 replaced by 0.07493 X ~ X in which p = absolute pressure, 
 
622 
 
 AIR. 
 
 Ib. per sq. in.; and T = degrees F. Q is the quantity in cubic feet per 
 minute measured at the given pressure and temperature. 
 Flow of Air at Low Pressures. 
 
 Q - cubic feet per minute = C 
 
 , h = drop in pressure, inches of 
 
 water column, d = diameter in inches, L = length of pipe in feet. C, a 
 coefficient varying with the diameter. The values of C in the table 
 are based on air at atmospheric pressure and 70 F., and the values of 
 Q are calculated for the same pressure and temperature and for a drop 
 of 1-inch water column in 100 ft. 
 
 d. 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 C. 
 
 Q. 
 
 d. 
 
 C. 
 
 Q. 
 
 d. 
 
 ~22~ 
 24 
 26 
 28 
 30 
 36 
 
 C. 
 
 Q. 
 
 d. 
 
 C. 
 
 Q. 
 
 43.9 
 46.1 
 47.7 
 49.1 
 50.1 
 51.0 
 
 140 
 257 
 421 
 636 
 908 
 1,240 
 
 10 
 12 
 14 
 16 
 18 
 20 
 
 51.8 
 53.0 
 53.9 
 54.6 
 55.1 
 55.6 
 
 1,637 
 2,642 
 3,950 
 5,585 
 7,579 
 9,946 
 
 56.0 
 56.3 
 56.6 
 56.8 
 57.1 
 57.6 
 
 12,700 
 15,880 
 19,500 
 23,580 
 28,130 
 44,760 
 
 42 
 48 
 54 
 60 
 66 
 72 
 
 57.9 
 58.2 
 58.4 
 58.6 
 58.8 
 58.9 
 
 66,240 
 92,930 
 125,200 
 163,500 
 208,000 
 259,200 
 
 For any other pressure drop than 1-inch water column per 100 ft., 
 multiply Q by the square root of the drop, or by the factor given below: 
 Drop, h.... 0.5 2 3468 10 12 14 16 18 20 
 Factor 0.71 1.41 1.73 2 2.45 2.83 3.16 3.46 3.74 4 4.24 4.47 
 
 For drop in ounces per square inch (1 oz. = 1.732 in. of water) the 
 factors are: 
 
 Drop, oz. . 0.5 1 2 3 4 5 6 7 8 9 10 12 
 Factor 0.93 1.32 1.86 2.28 2.63 2.94 3.22 3.48 3.72 3.95 4.16 4.56 
 
 Loss of Pressure in Ounces per Square Inch. B. F. Sturtevant Co. 
 
 gives the following formula: 
 
 ^25,000 dpi. d = 0.0000025 L& 
 
 PI = loss of pressure, ounces per sq. in. ; v = velocity, ft. per sec. ; 
 d = diameter, inches; L = length, ft. From the value of v we obtain 
 the flow in cubic feet per minute. Q = 60 a v = 60 X 0.7854rf 2 -f- 144 x 
 25,000 dpi _ K1 f?A ^ IPI d* Jf the drop . g taken , n inches Qf water 
 
 V 
 
 51.74 
 
 column, h, then Q = 39.24 \l~~f~* This formula gives a value of Q 9 per 
 
 cent less than that given in the above table for a 4-inch pipe, and 33 per 
 cent less for a 72-inch pipe. 
 
 Flow in Rectangular Pipes. It is common practice to make air 
 pipes for ventilating purposes rectangular instead of circular section 
 in order to economize space. No records of experiments on the flow 
 of air in such pipes are available, but a fair estimate of their capacity 
 as compared with that of circular pipes of the same area may be made 
 on the assumption that they follow the law of Chezy's formula for flow 
 of water, viz.: that the flow is proportional to the square root of the 
 mean hydraulic radius r, which is defined as the quotient of the area 
 divided by the perimeter of the wetted surface. For a circular pipe 
 r = 1/4 diameter in feet, and for a square pipe of the same area, r = 
 0.222d. For rectangles of the same area r will decrease as the ratio 
 of the longer to the shorter side increases. For different proportions 
 of sides, the values of r and the ratio of \/Fto the value of \XrT. the 
 hydraulic radius of a circular pipe having the same area, are as below: 
 
 Ratio of sides .. (circle) l(sq.) 1.5 2 3 4 5 6 
 
 r = ^0.25 0.222 0.217 0.209 0.192 0.177 0.165 0.155 
 
 Ratio vT* \/n . 1 -0.942 0.932 0.914 0.875 0.842 0.813 0.787 
 
 That is, a square pipe will have 94 percent of the carrying capacity of 
 a circular pipe of the same area, and a rectangular pipe whose sides are 
 in the ratio of 6 to 1 will have only 79 per cent of thf capacity of a 
 circular pipe of the same area. 
 
fLOW OF AIR. 
 
 623 
 
 sa fl - 
 
 o5.2^ 
 
 !Q 
 
 NO 
 
 Ooo 
 
 GQQQQ 
 
 coooom'f 
 
 
 3TJ-COOO 
 ^cviaNt- 
 - 
 
 ^eNr^oo 
 
 
 00 ( 
 
 
 
 poo - 
 
 60 
 
 CO 
 
 ;aB* 
 
 o 
 
 I 
 
 
 
 55 o 
 
624 
 
 Volume of Air Transmitted in Cubic Feet per Minute in 
 Pipes of Various Diameters, 
 
 Formula Q = 
 
 0.7854 
 144 
 
 Is 
 
 Actual Diameter of Pipe in Inches. 
 
 ll 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 16 
 
 20 
 
 24 
 
 1 
 
 0.327 
 
 1.31 
 
 2.95 
 
 5.24 
 
 8.18 
 
 11.78 
 
 20,94 
 
 32.73 
 
 47.12 
 
 83.77 
 
 130^ 
 
 188 5 
 
 2 
 
 0.655 
 
 2.62 
 
 5.89 
 
 10.47 
 
 16.36 
 
 23.56 
 
 41'. 89 
 
 65.45 
 
 94.25 
 
 167.5 
 
 261 8 
 
 377 
 
 3 
 
 0.982 
 
 3.93 
 
 8.84 
 
 15.7 
 
 24.5 
 
 35.3 
 
 62.8 
 
 98.2 
 
 141.4 
 
 251.3 
 
 392.7 
 
 565 .'5 
 
 4 
 
 1.31 
 
 5.24 
 
 11.78 
 
 20.9 
 
 32.7 
 
 47.1 
 
 83.8 
 
 131 
 
 188 
 
 335 
 
 523 
 
 754 
 
 5 
 
 1.64 
 
 6.54 
 
 14.7 
 
 26.2 
 
 41.0 
 
 59.0 
 
 104 
 
 163 
 
 235 
 
 419 
 
 654 
 
 942 
 
 6 
 
 1.96 
 
 7.85 
 
 17.7 
 
 31.4 
 
 49.1 
 
 70.7 
 
 125 
 
 196 
 
 283 
 
 502 
 
 785 
 
 1131 
 
 7 
 
 2.29 
 
 9.16 
 
 20.6 
 
 36.6 
 
 57.2 
 
 82.4 
 
 146 
 
 229 
 
 330 
 
 586 
 
 916 
 
 1319 
 
 8 
 
 2.62 
 
 0.5 
 
 23,5 
 
 41.9 
 
 65.4 
 
 94 
 
 167 
 
 262 
 
 377 
 
 670 
 
 1047 
 
 1508 
 
 9 
 
 2.95 
 
 1.78 
 
 26.5 
 
 47 
 
 73 
 
 106 
 
 188 
 
 294 
 
 424 
 
 754 
 
 1178 
 
 1696 
 
 10 
 
 3.27 
 
 3.1 
 
 29.4 
 
 52 
 
 82 
 
 118 
 
 209 
 
 327 
 
 471 
 
 838 
 
 1307 
 
 1885 
 
 12 
 
 3.93 
 
 5.7 
 
 353 
 
 63 
 
 98 
 
 141 
 
 251 
 
 393 
 
 565 
 
 1005 
 
 1571 
 
 2262 
 
 15 
 
 4.91 
 
 9.6 
 
 44.2 
 
 78 
 
 122 
 
 177 
 
 314 
 
 491 
 
 707 
 
 1256 
 
 1963 
 
 2827 
 
 18 
 
 5.89 
 
 23.5 
 
 53 
 
 94 
 
 147 
 
 212 
 
 377 
 
 589 
 
 848 
 
 1508 
 
 2356 
 
 3393 
 
 20 
 
 6.54 
 
 26.2 
 
 59 
 
 105 
 
 164 
 
 235 
 
 419 
 
 654 
 
 942 
 
 1675 
 
 2618 
 
 3770 
 
 24 
 
 7.85 
 
 31.4 
 
 71 
 
 125 
 
 196 
 
 283 
 
 502 
 
 785 
 
 1131 
 
 2010 
 
 3141 
 
 4524 
 
 25 
 
 8.18 
 
 32.7 
 
 73 
 
 131 
 
 204 
 
 294 
 
 523 
 
 818 
 
 1178 
 
 2094 
 
 3272 
 
 4712 
 
 28 
 
 9.16 
 
 36.6 
 
 82 
 
 146 
 
 229 
 
 330 
 
 586 
 
 916 
 
 1319 
 
 2346 
 
 3665 
 
 5278 
 
 30 
 
 9.8 
 
 39.3 
 
 88 
 
 157- 
 
 245 
 
 353 
 
 628 
 
 982 
 
 1414 
 
 2513 
 
 3927 
 
 5655 
 
 Effect of Bends in Pipes. (Norwalk Iron Works Co.) 
 Radius of elbow, in diameter 
 
 of pipe = 5321i/2li/4l 3/ 4 l/ 3 
 
 Equivalent lengths of straight 
 
 pipe, diams. 7.85 8.24 9.03 10.36 12.72 J 7.51 35.09 121 .2 
 
 E. A. Rix and A. E. Chodzko, in their treatise on Compressed Air 
 (189G), give the following as the loss in pressure through 90 bends. 
 Had. of bend 4- internal 
 
 diam. of pipe , . . 1 2 3 4 5 
 
 Loss in lb. per sq. in O.OOSr 2 .0022r 2 .0016i> 2 .0013r 2 .0012r 2 
 
 v is the velocity of air at entrance, in feet per second. 
 
 Friction of Air in Passing through Valves and Elbows. W. L. 
 Saunders, Compressed Air, Dec., 1902. The following figures give the 
 length in feet of straight pipe which will cause a reduction in pressure equal 
 to that caused by globe valves, elbows, and tees in different diameters of 
 pipe. 
 Diam. of pipe, in.. 1 H/ 2 2 2l/ 2 3 31/2 4 5 6 7 8 10 
 
 Globe Valves 24 7 10 13 16 20 28 36 44 63 70 
 
 Elbows and Tees .23 5 7 911 13 19 24 30 35 47 
 
 Measurement of the Velocity of Air in Pipes by an Anemometer. 
 Tests were made by B. Donkin, Jr. (hist. Civil Engrs., 1892). to com- 
 pare the velocity of air in pipes from 8 in. to 24 in. diam., as shown by an 
 anemometer 2 3/4 in. diam. with the true velocity as measured by the time 
 of descent of a gas-holder holding 1622 cubic feet. A table of the results 
 with discussion is given in Eng'g News, Dec. 22, 1892. In pipes from 8 in. 
 to 20 in. diam. with air velocities of from 140 to 690 feet per minute the 
 anemometer showed errors varying from 14.5% fast to 10% slow. With 
 a 24-inch pipe and a velocity of 73 ft. per minute, the anemometer gave 
 from 44 to 63 feet, or from 13.6 to 39.6% slow. The practical conclusion 
 drawn from these experiments is that anemometers for the measurement 
 of velocities of air in pipes of these diameters should be used with great 
 caution. The percentage of error is not constant, and varies considerably 
 with the diameter of the pipes and the speeds of air. The use of a baffle 
 consisting of a perforated plate, which tended to equalize the velocity in 
 the/center and at the sides in some cases diminished the error. 
 
PLOW OF AIR. 
 
 625 
 
 The impossibility of measuring the true quantity of air by an anemometer 
 held stationary in one position is shown by the following figures, given by 
 Win. Daniel (Proc. Inst. M. E.. 1875), of the velocities of air found at 
 different points in the cross-sections of two different airways in a mine. 
 
 DIFFERENCES OF ANEMOMETER READINGS IN AIRWAYS. 
 
 8ft. square. 
 
 5 x8ft. 
 
 1712 
 1622 
 
 1795 
 
 1859 
 
 1329 
 
 1685 
 1344 
 
 1782 
 
 1091 
 
 1477 
 1262 
 
 1524 
 
 1049 
 
 1356 
 
 1293 
 
 1333 
 
 Average 1132. 
 
 Average 1469. 
 
 Equalization of Pipes. It is frequently desired to know what number 
 of pipes of a given size are equal in carrying capacity to one pipe of a 
 larger size. At the same velocity of flow the volume delivered by two 
 pipes of different sizes is proportional to the squares of their diameters; 
 thus, one 4-inch pipe will deliver the same volume as four 2-inch pipes, 
 With the same head, however, the velocity is less in the smaller pipe, and 
 the volume delivered varies about as the square root of the fifth power 
 (i.e., as the 2.5 power). The following table has been calculated on this 
 basis. The figures opposite the intersection of any two sizes is the num- 
 ber of the smaller-sized pipes required to equal one of the larger. Thus 
 one 4-inch pipe is equal to 5.7 two-inch pipes. 
 
 | d 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 2 
 
 5.7 
 15.6 
 
 2.8 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 32,0 
 
 57 
 
 2,1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 55.9 
 
 9.9 
 
 3.6 
 
 1.7 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 88.2 
 
 15.6 
 
 5.7 
 
 2.8 
 
 1,6 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 130 
 
 22.9 
 
 8.3 
 
 4.1 
 
 2.3 
 
 1.5 
 
 1 
 
 
 
 
 
 
 
 
 
 
 8 
 
 181 
 
 32.0 
 
 11.7 
 
 5.7 
 
 3.2 
 
 2.1 
 
 1.4 
 
 1 
 
 
 
 
 
 
 
 
 
 9 
 
 243 
 
 43 
 
 15 6 
 
 7,6 
 
 4.3 
 
 2 8 
 
 1 9 
 
 1 3 
 
 1 
 
 
 
 
 
 
 
 
 10 
 
 316 
 
 55.9 
 
 20.3 
 
 9.9 
 
 5.7 
 
 3.6 
 
 2.4 
 
 1.7 
 
 1.3 
 
 1 
 
 
 
 
 
 
 
 11 
 
 401 
 
 70 9 
 
 25.7 
 
 12 5 
 
 7,2 
 
 4.6 
 
 31 
 
 2 2 
 
 1 7 
 
 1 3 
 
 
 
 
 
 
 
 12 
 
 499 
 
 88.2 
 
 32.0 
 
 15.6 
 
 8.9 
 
 5.7 
 
 3.8 
 
 2.8 
 
 2.1 
 
 1.6 
 
 1 
 
 
 
 
 
 
 13 
 
 609 
 
 108 
 
 39,1 
 
 19 
 
 10.9 
 
 7.1 
 
 4.7 
 
 3.4 
 
 2.5 
 
 1.9 
 
 12 
 
 
 
 
 
 
 14 
 
 733 
 
 130 
 
 47.0 
 
 22.9 
 
 13.1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3.0 
 
 2.3 
 
 1.5 
 
 
 
 
 
 
 15 
 
 871 
 
 154 
 
 55.9 
 
 27.2 
 
 i5.6 
 
 9.9 
 
 6,7 
 
 4.8 
 
 3.6 
 
 2.8 
 
 1.7 
 
 .2 
 
 
 
 
 
 16 
 
 
 181 
 
 65.7 
 
 32.0 
 
 18.3 
 
 11.7 
 
 7.9 
 
 5.7 
 
 4.2 
 
 3.2 
 
 2.1 
 
 .4 
 
 1 
 
 
 
 
 17 
 
 
 711 
 
 76 4 
 
 37 221 3 
 
 13 5 
 
 9 7 
 
 6 6 
 
 4 9 
 
 3 fl 
 
 ? 4 
 
 6 
 
 1 ? 
 
 
 
 
 18 
 
 
 7.43 
 
 88 ?, 
 
 43.024.6 
 
 15 6 
 
 10 6 
 
 76 
 
 5 7 
 
 4 3 
 
 2.8 
 
 ,9 
 
 1 3 
 
 1 
 
 
 
 19 
 
 
 778 
 
 101 
 
 49 1j28 1 
 
 17 8 
 
 17 1 
 
 8 7 
 
 6 5 
 
 5 
 
 3 ? 
 
 ? 1 
 
 1 5 
 
 1 1 
 
 
 
 70 
 
 
 316 
 
 115 
 
 55 Q 
 
 37 
 
 70 3 
 
 1* 8 
 
 9 9 
 
 7 4 
 
 5 7 
 
 3 6 
 
 2 4 
 
 1 7 
 
 1 3 
 
 1 
 
 
 
 
 401 
 
 146 
 
 70 9 
 
 40 6 
 
 75 7 
 
 17 5 
 
 1? 5 
 
 Q 3 
 
 7 ? 
 
 4 6 
 
 3 1 
 
 
 1 7 
 
 1 3 
 
 
 24 
 
 
 499 
 
 181 
 
 88 ? 
 
 50 5 
 
 37 
 
 71 8 
 
 15 6 
 
 11 6 
 
 8 9 
 
 5 7 
 
 3 8 
 
 ?, 8 
 
 7 1 
 
 1 6 
 
 1 
 
 ?n 
 
 
 609 
 
 
 108 
 
 61 7 
 
 39 1 
 
 26 6 
 
 19 
 
 14 7 
 
 10 9 
 
 
 4 7 
 
 3 4 
 
 ? 5 
 
 1 9 
 
 1 ? 
 
 28 
 
 
 733 
 
 266 
 
 130 
 
 74 2 
 
 47 
 
 37. 
 
 22 9 
 
 17 1 
 
 13 1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3,0 
 
 23 
 
 1 5 
 
 30 
 
 
 871 
 
 316 
 
 154 
 
 88 7 
 
 55 Q 
 
 38 
 
 ?7 7 
 
 70 3 
 
 15 6 
 
 9 9 
 
 6 7 
 
 4 8 
 
 3 6 
 
 ? 8 
 
 1 7 
 
 36 
 
 
 
 499 
 
 
 J30 
 
 88 2 
 
 60 
 
 43 
 
 32 
 
 74 6 
 
 15 6 
 
 10 6 
 
 7 6 
 
 5 7 
 
 4 3 
 
 ? 8 
 
 42 
 
 
 
 733 
 
 357 
 
 ?05 
 
 130 
 
 88 7 
 
 63 ? 
 
 47 
 
 36 ? 
 
 19 
 
 15 6 
 
 11 ? 
 
 8 3 
 
 6 4 
 
 4 1 
 
 48 
 
 
 
 
 499 
 
 286 
 
 181 
 
 123 
 
 88 7 
 
 6? 7 
 
 50 5 
 
 3? 
 
 71 8 
 
 15 6 
 
 11 6 
 
 8 9 
 
 5 7 
 
 14 
 
 
 
 
 670 
 
 383 
 
 ?43 
 
 165 
 
 118 
 
 88 ? 
 
 67 8 
 
 43 
 
 79 2 
 
 ?rt 9 
 
 15 6 
 
 1? 
 
 7 6 
 
 60 
 
 
 
 
 871 
 
 499 
 
 316 
 
 215 
 
 154 
 
 115 
 
 88.2 
 
 55.9 
 
 38.0 
 
 27.2 
 
 20.3 
 
 15.6 
 
 9.9 
 
626 
 
 AIR. 
 
 WIND. 
 
 Force of the Wind. Smeaton in 1759 published a table of the 
 velocity and pressure of wind, as follows: 
 
 VELOCITY AND FORCE OP WIND, IN POUNDS PER SQUARE INCH 
 
 | Miles per 
 1 Hour. 
 
 li 
 If 
 
 Force per 
 
 Sq. Ft., 
 Pounds. 
 
 Common Appella- 
 tion of the 
 Force of Wind. 
 
 I Miles per 
 j Hour. 
 
 Feet per 
 Second. 
 
 M-3 
 
 q>" c 
 
 P ~3 
 && 
 
 Common Appella- 
 tion of the 
 Force of Wind. 
 
 1 
 
 1.47 
 
 0.005 
 
 Hardly perceptible. 
 
 18 
 
 26.4 
 
 1.55 
 
 ) 
 
 2 
 3 
 
 2.93 
 4.4 
 
 0.020 
 0.044 
 
 Just perceptible. 
 
 20 
 
 25 
 
 29.34 
 36.67 
 
 1.968 
 3.075 
 
 > Very brisk. 
 
 A 
 5 
 
 5.87 
 7.33 
 
 0.079 
 0.123 
 
 Gentle, pleasant 
 
 30 
 35 
 
 44.00 
 51.34 
 
 4.429 
 6.027 
 
 High wind. 
 
 6 
 
 8.8 
 
 0.177 
 
 wind. 
 
 40 
 
 58.68 
 
 7.873 
 
 
 7 
 
 8 
 
 10.25 
 11.75 
 
 0.241 
 0.315 
 
 
 45 
 50 
 
 66.01 
 73.35 
 
 9.963 
 12.30 
 
 Very high storm. 
 
 9 
 
 13.2 
 
 0.400 
 
 
 55 
 
 80.7 
 
 14.9 
 
 
 1G 
 
 14.67 
 
 0.492 
 
 
 60 
 
 88.00 
 
 17.71 
 
 
 12 
 
 17.6 
 
 0.708 
 
 Pleasant, brisk gale 
 
 65 
 
 95.3 
 
 20.85 
 
 Great storm. 
 
 14 
 
 20.5 
 
 0.964 
 
 
 70 
 
 102.5 
 
 24.1 
 
 
 15 
 16 
 
 22.00 
 23.45 
 
 1.107 
 1.25 
 
 
 75 
 
 80 
 
 110.00 
 117.36 
 
 27.7 
 31.49 
 
 Hurricane. 
 
 
 
 
 
 100 
 
 146.67 
 
 49.2 
 
 Immense hurri- 
 
 
 
 
 
 
 cane. 
 
 The pressures per square foot in the above table correspond to the 
 formula P = 0.005 F 2 , in which V is the velocity in miles per hour. 
 Eng'g News, Feb. 9, 1893, says that the formula was never well established, 
 and has floated chiefly on Smeaton's name and for lack of a better. It 
 was put forward only for surfaces for use in windmill practice. The 
 trend of modern evidence is that it is approximately correct only for such 
 surfaces, and that for large, solid bodies it often gives greatly too large 
 results. Observations by others are thus compared with Smeaton's 
 formula: 
 
 Old Smeaton formula ........................ P = 0.005 F 2 
 
 As determined by Prof. Martin ................ P = 0.004 F 2 
 
 ' Whipple and Dines .......... P = 0.0029 F a 
 
 At 60 miles per hour these formulas give for the pressure per square foot, 
 18, 14.4, and 10.44 Ibs., respectively, the pressure varying by all of them as 
 the square of the velocity. Lieut. Crosby's experiments (Eng'g, June 13, 
 1890), claiming to prove that P = fV instead of P = /F 2 , are discredited. 
 
 Experiments by M. Eiffel on plates let fall from the Eiffel tower in Paris 
 gave coefficients of F 2 ranging from 0.0027 for small plates to 0.0032 for 
 plates 10 sq. ft. area. For plates larger than 10 sq. ft. the coefficient 
 remained constant at 0.0032. Eng'g, May 8, 1908. 
 
 A. R. Wolff (" The Windmill as a Prime Mover," p. 9) gives as the theo- 
 retical pressure per sq. ft. of surface, P=dQv/g, in which d = density of 
 
 air in pounds per cu. ft. = 
 
 . p being the barometric pres- 
 
 sure per square foot at any level, and temperature of 32? F., t any 
 absolute temperature, Q = volume of air carried along per square foot in 
 one second, v=* velocity of the wind in feet per second, # = 32. 16. Since 
 Q = v cu. ft. per sec., P=dv 2 /g. Multiplying this by a coefficient 0.93 
 nt, and substituting the above value of d, he obtains 
 
 found by experime ... 
 p _ 0.017431 X P 
 
 t X 32.16 
 
 , and when p = 2116.5 Ib. per sq. ft.,or average 
 
 
 atmospheric pressure at the sea-level, P =* . oo- 1ft 
 
 ^ 
 
 36 89^9 
 
 -0.018743 
 
 pression in which the pressure is shown, to vary with the temperature; 
 and he gives a table showing the relation between velocity and pressure 
 
WINDMILLS. 627 
 
 for temperatures from to 100 F., and velocities from 1 to 80 miles per 
 hour. For a temperature of 45 F. the pressures agree with those in 
 Smeaton's table, for F. they are about 10 per cent greater, and for 100, 
 x 10 per cent less. 
 
 ^rof. H. Allen Hazen, Eng'g News, July 5, 1890, says that experiments 
 with whirling arms, by exposing plates to direct wind, and on locomotives 
 with velocities running up to 40 miles per hour, have invariably shown the 
 resistance to vary with V 2 . The coefficient of V 2 has been found in some 
 experiments with very short whirling arms and low velocities to vary with 
 the perimeter of .the plate, but this entirely disappears with longer arms 
 or straight line motion, and the only question now to be determined is 
 the value of the coefficient. Perhaps some of the best experiments for 
 determining this value were tried in France in 1886 by carrying flat 
 boards on trains. The resulting formula in this case was, for 44.5 miles 
 per nour, p = 0.00535 SV 2 . 
 
 Prof. Kernot. of Melbourne (Eng. Rec., Feb. 20, 1894), states that 
 experiments at the Forth Bridge showed that the average pressure on sur- 
 faces as /arge as railway carriages, houses, or bridges never exceeded two- 
 thirds of that upon rmall surfaces of one or two square feet, and also that 
 an inertia effect, which is frequently overlooked, may cause some forms 
 of anemometer to give false results enormously exceeding the correct 
 indication. Experiments made by Prof. Kernot at speeds varying from 
 2 to 15 miles per hour agreed with the earlier authorities. The pressure 
 upon one side of a cube, or of a block proportioned like an ordinary 
 carriage, was found to be 0.9 of that upon a thin plate of the same area. 
 The same result was obtained for a square tower. A square pyramid, 
 whose height was three times its base, experienced 0.8 of the pressure 
 upon a thin plate equal to one of its sides, but if an angle was turned to 
 the wind the pressure was increased by fully 20%. A bridge consisting 
 of two plate-girders connected by a deck at the top was found to expe- 
 rience 0.9 or the pressure on a thin plate equal in size to one girder, when 
 the distance between the girders was equal to their depth, and this was 
 increased by one-fifth when the distance between the girders was double 
 the depth. A lattice- work in which the area of the openings was 55% of 
 the whole area experienced a pressure of 80% of that upon a plate of the 
 same area. The pressure upon cylinders and cones was proved to be equal 
 to half that upon the diametral planes, and that upon an octagonal prism 
 to be 20% greater than upon the circumscribing cylinder. A sphere was 
 subject to a pressure of 0.36 of that upon a thin circular plate of equal 
 diameter. A hemispherical cup gave the same result as the sphere; when 
 its concavity was turned to the wind the pressure was 1.15 of that on a 
 flat plate of equal diameter. When a plane surface parallel to the direc- 
 tion of the wind was brought nearly into contact with a cylinder or sphere, 
 the pressure on the latter bodies was augmented by about 20%, owing to 
 the lateral escape of the air being checked. Thus it is possible for the 
 security of a tower or chimney to be impaired by the erection of a building 
 nearly touching it on one side. 
 
 Pressures of Wind Registered in Storms. Mr. Frizell has examined 
 the published records of Greenwich Observatory from 1849 to 1869, and 
 reports that the highest pressure of wind he finds recorded is 41 Ib. per 
 sq. ft., and there are numerous instances in which it was between 30 and 
 40 Ib. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a 
 velocity of 150 miles per hour has been observed, and at New York City 
 60 miles an hour, and that the highest winds observed in 1870 were of 72 
 and 63 miles per hour, respectively. Lieut. Dunwoody, U. S. A., says, 
 in substance, that the New England coast is exposed to storms which 
 produce a pressure of 50 Ib. per sq. ft. Eng. News, Aug. 20, 1880. 
 
 WINDMILLS. 
 
 Power and Efficiency of Windmills. Rankine, S. E., p. 215, gives 
 the following: Let Q volume of air which acts on the sail, or part of a 
 sail, in cubic feet per second, v = velocity of the wind in feet per second, 
 8 =* sectional area of the cylinder, or annular cylinder of wind, through 
 which the sail, or part of the sail, sweeps in one revolution, & a coeffi- 
 cient to be found by experience; then =* cvs. Rankine, from experi- 
 mental data given by Smeaton, and taking c to include an allowance for 
 
628 AIR. 
 
 friction, gives for a wheel with four sails, proportioned in the best manner, 
 c = 0.75. Let A = weather angle of the sail at any distance from the 
 axis, i.e., the angle the portion of the sail considered makes with its plane 
 of revolution. This angle gradually diminishes from the inner end of the 
 sail to the tip; u = the velocity of the same portion of the sail, and E = 
 the efficiency. The efficiency is the ratio of the useful work performed to 
 the whole energy of the stream of wind acting on the surface s of the wheel, 
 which energy is D s v 3 * 2 g, D being the weight of a cubic foot of air* 
 Rankine's formula for efficiency is 
 
 in which c = 0.75 and / is a coefficient of friction found from Smeaton's 
 data = 0.016. Rankine gives the following from Smeaton's data: 
 
 A = weather-angle =7 13 19 
 
 V # v *= ratio of speed of greatest 
 efficiency, for a given 
 weather-angle, to that 
 
 ofthewind =2.63 1.86 1.41 
 
 #-* efficiency = 0.24 0.29 0.31 
 
 Rankine gives the following as the best values for the angle of weather 
 at different distances from the axis: 
 
 Distance in sixths of total radius 12345 6 
 Weather angle 18 19 18 16 121/2 7 
 
 But Wolff (p. 125) shows that Smeaton did not term these the best 
 angles but simply says they "answer as well as any," possibly any that 
 were in existence in "his time. Wolff says that they ** cannot in the nature 
 of things be the most desirable angles." Mathematical considerations, 
 he says, conclusively show that the angle of impulse depends on the 
 relative velocity of each point of the sail and the wind, the angle growing 
 larger as the ratio becomes greater. Smeaton's angles do not fulfil this 
 condition. Wolff develops a theoretical formula for the best angle of 
 weather, and from it calculates a table of the best angles for different 
 relative velocities of the blades and the wind, which differ widely from 
 those given by Rankine. 
 
 A. R. Wolff, in an article in the American Engineer, gives the following 
 (see also his treatise on Windmills) : 
 
 Let c = velocity of wind in feet per sec9nd; 
 
 n = number of revolutions of the windmill per minute; 
 
 6ot hi fo, b x be the breadth of the sail or blade at distances Zo, h, It, 
 1 3 , and I, respectively, from the axis of the shaft; 
 
 Z = distance from axis of shaft to beginning of sail or blade proper. 
 
 I = distance from axis of shaft to extremity of sail proper; 
 
 V , vi, vz, v 3 , v x = the velocity of the sail in feet per second at dis- 
 tances IQ, li, Iz, h, I, respectively, from the axis of the shaft; 
 
 do, 01, 02, a 3 , a x = the angles of impulse for maximum effect at dis- 
 tances TO, li t k, 3, I, respectively, from the axis of the shaft; 
 
 a = the angle of impulse when the sails or blocks are plane surfaces 
 so that there is but one angle to be considered; 
 
 N = number of sails or blades of windmill; 
 
 K = 0.93; 
 
 d = density of wind (weight of a cubic foot of air at average tem- 
 perature and barometric pressure where mill is erected); 
 W = weight of wind-wheel in pounds; 
 
 / = coefficient of friction of shaft and bearings; 
 
 D = diameter of bearing of windmill in feet. 
 
 The effective horse-power of a windmill with plane sails will equal 
 L of < v Q fsin a cos ajb cos a 
 
WINDMILLS. 
 
 629 
 
 The effective horse-power of a windmill of shape of sail for maximum 
 effect equals 
 
 N (I- Ip) Kdc 3 
 2200 g 
 
 X mean 
 
 ./2sin 2 
 
 H Mi 
 
 o 1 ; 
 
 sin 2 a 
 
 2 sin 2 ai - 1 . 
 sin 2 ai 
 
 2 sin 2 a x - 1 
 ' 5E?aI Z 
 
 /TFX 0.05236 nD g 
 550 
 
 The mean value of quantities in brackets is to be found according to 
 Simpson's rule. Dividing I into 7 parts, finding the angles and breadths 
 corresponding to these divisions by substituting them in quantities within 
 brackets will be found satisfactory. Comparison of these formulae with 
 the only fairly reliable experiments in windmills (Coulomb's) showed a 
 close agreement of results. 
 
 Approximate formulae of simpler form for windmills of present con- 
 struction can be based upon the above, substituting actual average values 
 for o, c, d, and e, but since improvement in the present angles is possible, 
 it is better to give the formulas in their general and accurate form. 
 
 Wolff gives the following table, based on the practice of an American 
 manufacturer. Since its preparation, he says, over 1500 windmills have 
 been sold on its guaranty (1885), and in all cases the results obtained did 
 not vary sufficiently from those presented to cause any complaint. The 
 actual results obtained are in close agreement with those obtained by 
 theoretical analysis/ of the impulse of wind upon windmill blades. 
 
 Capacity of the Windmill. 
 
 
 
 
 
 A 
 
 
 d 
 
 d 
 
 ~v 
 
 * 
 
 
 CO 
 
 p 
 
 gflf 
 
 s 
 
 w 
 
 DO fl 
 
 Gallons of Water raised per Minute 
 to an Elevation of 
 
 3 0) 
 
 * J 
 
 .2 
 
 ^1 
 
 .P 
 
 
 -^i'g 
 
 jISs"! 
 
 cj 
 .1 
 
 $ 
 
 ^2 I 
 
 
 .loo 
 
 & Q 
 
 "w 
 
 Jl 
 
 i 
 
 
 
 
 
 
 
 > W 
 
 2 
 
 a* 
 
 13 
 
 I 
 
 25 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 
 
 5"5 
 
 o> 5>I5n3 
 
 Q 
 
 ^ 
 
 * 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 O < +H'^ 
 
 ^P,^? 
 
 wheel 
 
 81/9 ft 
 
 16 
 
 70 to 75 
 
 6 162 
 
 3.016 
 
 
 
 
 
 04 
 
 8 
 
 10 
 
 16 
 
 60 to 65 
 
 19.179 
 
 9.563 
 
 6.638 
 
 4.750 
 
 
 
 12 
 
 8 
 
 12 
 
 16 
 
 55 to 60 
 
 33.941 
 
 17.952 
 
 11.851 
 
 8.485 
 
 5.680 
 
 
 0.21 
 
 8 
 
 14 
 
 16 
 
 50 to 55 
 
 45.139 
 
 22.569 
 
 15.304 
 
 11.246 
 
 7.807 
 
 4 998 
 
 0.28 
 
 8 
 
 16 
 
 16 
 
 45 to 50 
 
 64.600 
 
 31.654 
 
 19.542 
 
 16.150 
 
 9.771 
 
 8 '.075 
 
 0.41 
 
 8 
 
 18 
 
 16 
 
 40 to 45 
 
 97.682 
 
 52.165 
 
 32.513 
 
 24.421 
 
 17.485 
 
 12.211 
 
 0.61 
 
 8 
 
 20 
 
 16 
 
 35 to 40 
 
 124.950 
 
 63.750 
 
 40.800 
 
 31.248 
 
 19.284 
 
 15.938 
 
 0.78 
 
 8 
 
 25 
 
 16 
 
 30 to 35 
 
 212.381 
 
 106.964 
 
 71.604 
 
 49.725 
 
 37.349 
 
 26.741 
 
 1.34 
 
 8 
 
 These windmills are made in regular sizes, as high as sixty feet diameter 
 of wheel; but the experience with the larger class of mills is too limited to 
 enable the presentation of precise data as to their performance. 
 
 If the wind can be relied upon in exceptional localities to average a 
 higher velocity for eight hours a day than that stated in the above table, 
 the performance or horse-power of the mill will be increased, and can be 
 obtained by multiplying the figures in the table by the ratio of the cube 
 of the higher average velocity of wind to the cube of the velocity above 
 recorded. 
 
 He also gives the following table showing the economy of the windmill. 
 All the items of expense, including both interest and repairs, are reduced 
 to the hour by dividing tha costs per annum by 365 X 8 = 2920; the 
 Interest, etc., for the twenty-four hours being charged to the eight hours of 
 actual work. By multiplying the figures in the 5th column by 584, the 
 first cost of the windmill, in dollars, is obtained. 
 
630 
 
 AIR. 
 Economy of the Windmill. 
 
 
 1 
 
 J> 4 
 
 *!! 
 
 Expense of Actual Useful Power 
 Developed, in Cents, per Hour. 
 
 "" 
 
 o o 
 
 2 a 
 
 
 '1 . 
 
 
 
 t, 3 fl 
 
 
 
 
 
 
 . 
 
 Designa- 
 tion of 
 Mill. 
 
 of Water r 
 , per Hour 
 
 jnt Actual 
 rse-power 
 
 JJ-0J 
 
 2 .2 cj 
 
 31I| 
 
 03 fl 
 - r^ 
 c3'-5^ 
 ftg^^ 
 
 tendance. 
 
 O 
 m 
 
 *e8 
 
 W.J2 
 
 
 1$ 
 
 !*! 
 
 |jj| 
 
 ^4J3^S 
 
 
 g 
 
 o 
 
 ^ 
 
 co ^ . 
 
 IS| 
 
 
 3 
 
 |si 
 
 ^J 
 
 IES&S? 
 
 !^ 
 
 (2 
 
 
 
 |&3 
 
 wheel 
 
 
 
 
 
 
 
 
 
 
 81/2 ft. 
 
 370 
 
 0.04 
 
 8 
 
 0.25 
 
 0.25 
 
 0.06 
 
 0.04 
 
 0.60 
 
 15.0 
 
 10 
 
 1151 
 
 0.12 
 
 8 
 
 0.30 
 
 0.30 
 
 0.06 
 
 0.04 
 
 0.70 
 
 5.8 
 
 12 
 
 2036 
 
 0.21 
 
 8 
 
 0.36 
 
 0.36 
 
 0.06 
 
 0.04 
 
 0.82 
 
 5.9 
 
 14 
 
 2708 
 
 0.28 
 
 8 
 
 0.75 
 
 0.75 
 
 0.06 
 
 0.07 
 
 1.63 
 
 5.8 
 
 16 
 
 3876 
 
 0.41 
 
 8 
 
 1.15 
 
 1.15 
 
 0.06 
 
 0.07 
 
 2.43 
 
 5.9 
 
 18 
 
 5861 
 
 0.61 
 
 8 
 
 1.35 
 
 1.35 
 
 0.06 
 
 0.07 
 
 2.83 
 
 4.6 
 
 20 
 
 7497 
 
 0.79 
 
 8 
 
 1.70 
 
 1.70 
 
 0.06 
 
 0.10 
 
 3.56 
 
 4.5 
 
 25 
 
 12743 
 
 1.34 
 
 8 
 
 2.05 
 
 2.05 
 
 0.06 
 
 0.10 
 
 4.26 
 
 3.2 
 
 Prof. De Volson Wood (Am. Mach., Oct. 29, 1896) quotes some results 
 by Thos. O. Perry on three wheels, each 5 ft. diam.: A, a good "stock" 
 wheel, B and C, improved wheels. Each wheel was tested with a dyna- 
 mometer placed 1 ft. from the axis of the wheel, and it registered a 
 constant load at that point of 1.9 Ibs. The velocity of the wind in each 
 ;est was 8.45 miles per hour = 12.4 ft. per second. The number of turns 
 per minute was: A, 30.67; B, 38.13; C, 56.50. The efficiency was: A t 
 0.142; B, 0.176; C, 0.261. The work of wheel C was 674.5 ft. Ib. per 
 min. = 0.020 H.P. Assuming that the power increases as the square 
 of the diameter and as the cube of the velocity, a wheel of the quality of 
 C, 121/2 ft. diam., with a wind velocity of 17 miles per hour, would be re- 
 quired for 1 H.P.; but wheel C had an exceptionally high efficiency, and 
 such a high delivery would not likely be obtained in practice. 
 
 Prof. O. P. Hood (Am. Mach., April 22, 1897) quotes the following 
 results of experiments by E. C. Murphy; the mills were tested by pumping 
 water: 
 
 Wind, miles per hour 8 12. 16. 20. 25. 30 
 
 Strokes per min., Mill No. 1, 8-ft. wheel . . 10.2 19.3 25.3 28.1 25 
 Strokes per min., Mill No. 2, 8-ft. wheel 8 20.2 26.1 28. 27.5 . . 
 Strokes per min., Mill No. 3, 12-ft. wheel . . 4.8 12.7 18.8 23.3 25 
 Strokes per min., Mill No. 4, 12-ft. wheel . . 6.2 11.9 14.7 16. 
 
 Mill No. 3 was loaded nearly 90% heavier than mill No. 4. 
 
 In a 25-mile wind, seven 12-ft. mills developed, respectively, 0.379, 
 0.291, 0.309, 0.6, 0.247, 0.219, and 0.184 H.P.; and five 8-ft. mills, 0.043, 
 0.099, 0.059, 0.099, and 0.005 H.P. These effects include the effects of 
 
 Sumps of unknown and variable efficiency. The variations are largely 
 ue to the variable relation of the fixed load on the mill to the most 
 favorable load which that mill might carry at each wind velocity. With 
 each mill the efficiency is a maximum only for a certain load and a certain 
 velocity, and for different loads and velocities the efficiency varies greatly. 
 The useful work of mill No. 3 was equal to 0.6 H.P. in a 25-mile wind, 
 and its efficiency was 5.8%. In a 16-mile wind the efficiency rose to 12.1 %, 
 and in a 12-mile wind it fell to 10.9%. The rule of the power developed, 
 varying as the cube of the velocity, is far from true for a single wheel 
 fitted with a single non-adjustable pump, and can only be true when the 
 work of the pump per stroke is adjusted by varying the stroke of the 
 pump, or by other means, for each change of velocity. 
 
 R. M. Dyer (The Iowa Engineer, July, 1906; also Mach'y, Aug., 1907) 
 gives a brief review of the history of windmills, and quotes experiments 
 by T. O. Perry, E. C. Murphy, Prof. F. H. King, and the Aermotor Co. 
 Mr. Perry's experiments are reported in pamphlet No. 20 of the Water 
 
WINDMILLS. 631 
 
 Supply and Irrigation Papers of the U. a. Geological Survey, Mr. Murphy's 
 In pamphlets Nos. 41 and 42 of the same Papers, and Prof. lung's, in 
 Bulletin No. 82 of the Agricultural Experiment Station of the University 
 of Wisconsin. The Aermotor Co .'s experiments are described in catalogues 
 of that company. Some of Mr. Dyer's conclusions are as follows: 
 
 Experiments showed that 7/ 8 of the zone of interruption could be covered 
 with sails ; that the gain in power in from 3/4 to 1/3 of the surface was so small 
 that the use of the additional material was not justifiable; that the sail 
 surface should extend only two-thirds the distance from the outer diam- 
 eter to the center; that a wheel running behind the carrying mast is not 
 nearly as efficient as one running in front of the mast; that there should 
 be the least possible obstruction behind the wheel; that to be efficient 
 the velocity of the travel of the vertical circumference of the wheel 
 should be from 1 to U/4 times the velocity of the wind, hence the 
 necessity of back gearing to reduce the pump speed to 40 strokes per 
 minute as a maximum, which is the limit of safety at which ordinary 
 pumps can be operated. 
 
 I hold that no manufacturer will be able to produce a marketable 
 motor which will absorb and deliver, when acted upon by an elastic fluid, 
 like air, in which it is entirely surrounded and submerged, more than 
 35% of the kinetic energy of the impinging current. 
 
 Theoretical demonstrations show that the kinetic energy of the air, 
 impinging on the intercepted area of a wheel, varies as the cube of the 
 wind velocity; consequently, the power of windmills of the same type 
 varies theoretically as the square of the diameter, and as the cube of the 
 wind velocity; but as a wheel is designed to give its best efficiency in low 
 winds, say 10 to 15 miles per hour, we cannot expect that the same 
 angle of sail would obtain the same percentage of efficiency in winds of 
 Considerably higher velocity. 
 
 The ordinary wheel works most efficiently under wind velocities of from 
 10 to 12 miles per hour; such wheels will give reasonable efficiency in from 
 5- to 6-mile winds, while, if the wind blows more than 12 miles per hour, 
 there will be power to spare. Our wheel must work in light winds, such 
 being nearly always present, while the higher velocities only occur at 
 intervals. Mills built for grinding purposes, or geared mills, will develop 
 power almost approaching to the cube of the wind velocity, within reason- 
 able limits, as their speed need not be kept down to a certain number of 
 revolutions per minute, as in the case of the pumping mill. 
 
 Should this theoretic condition hold, the following table, showing the 
 amount of power for different sizes of mills at different wind velocities, 
 would apply: Figures show Horse Power,, 
 
 5 10 15 20 25 30 35 40 
 
 Size mile. mile. mile. mile. mile. mile. mile. mile. 
 
 8ft 0.011 0.088 0.297 0.704 1.375 2.176 
 
 12ft 0.025 0.20 0.675 1.6 3.125 5.4 8.57 12.8 
 
 16ft 0.045 0.36 1.215 2.88 5.52 9.75 15.3 21.04 
 
 These figures have been proven by laboratory tests at velocities 
 ranging from 10 to 25 miles per hour and more practically by the 
 Murphy tests on mills actually in use, which show very close relation 
 at the wind velocities at which the mills are best adapted. 
 
 The Murphy figures are as follows: 
 
 Size of mill. 10 mile. 15 mile. 20 mile. 
 12 ft. 0.21 H.P. 0.58 H.P. 1.05 H.P. 
 16 ft. 0.29 0.82 1.55 
 
 For higher wind velocities the Murphy values fall much under the 
 theoretical values, but the range of velocities over which his experi- 
 ments extend does not justify any change in the general law except 
 inasmuch as common sense teaches us that theoretic conditions can 
 rarely be attained in actual practice. 
 
 In view of the fact that a windmill does not work as efficiently in 
 high winds as in winds under 20 miles per hour my experience would 
 lead me to believe that the following figures (H.P.) would be the 
 probable extension of the Murphy tests: 
 
 Size of mill. 25 mile. 30 mile. 35 mile. 40 mile. 
 12 ft. 2.5 4 5 6 
 
 16 ft. 4. 6 8 10 
 
 A 20-ft. mill would deliver approximately 50% greater than a 16-ft 
 
632 AIR. 
 
 The foregoing table must be translated with reasonable allowances for 
 conditions under which wind wheels must work and which cannot well 
 be avoided, e.g: Pumping mills must be made to regulate off at a certain 
 maximum speed to prevent damage to the attached pumping devices. 
 The regulating point is usually between 20- and 25-mile wind velocities, 
 so that no matter how much higher the wind velocity may be the power 
 absorbed and delivered by the wheel will be no greater than that indicated 
 at the regulating point. 
 
 Electric storage and lighting from the power of a windmill has been 
 tested on a large scale for several years by Charles F. Brush, at Cleveland, 
 Ohio. In 1887 he erected on the grounds of his dwelling a windmill 56 ft. 
 in diameter, that operates with ordinary wind a dynamo at 500 revolutions 
 per minute, with an output of 12,000 watts 16 electric horse-power 
 charging a storage system that gives a constant lighting capacity of 100 
 16 to 20 candle-power lamps. The current from the dynamo is auto- 
 matically regulated to commence charging at 330 revolutions and 70 volts, 
 and cutting the circuit at 75 volts. Thus, by its 24 hours' work, the 
 storage system of 408 cells in 12 parallel series, each cell having a capacity 
 of 100 ampere-hours, is kept in constant readiness for all the requirements 
 of the establishment, it being fitted up with 350 incandescent lamps, 
 about 100 being in use each evening. The plant runs at a mere nominal 
 expense for oil, repairs, and attention. (For a fuller description of this 
 plant, and of a more recent one at Marblehead Neck, Mass., see Lieut. 
 Lewis's paper in Engineering Magazine, Dec., 1894, p. 475.) 
 
 COMPRESSED AIR. 
 
 Heating of Air by Compression. Kimball, in his treatise on Physi- 
 cal Properties of Gases, says: When air is compressed, all the work which 
 is done in the compression is converted into heat, and shows itself in the 
 rise in temperature of the compressed gas. In practice many devices are 
 employed to carry off the heat as fast as it is developed, and keep the tem- 
 perature down. But it is not possible in any way to totally remove this 
 difficulty. But, it may be objected, if all the work done in compression is 
 converted into heat, and if this heat is got rid of as soon as possible, then 
 the work may be virtually thrown away, and the compressed air can have 
 no more energy than it had before compression. It is true that the com- 
 pressed gas has no more energy than the gas had before compression, if 
 its temperature is no higher, but the advantage of the compression lies in 
 bringing its energy into more available form. 
 
 The total energy of the compressed and uncompressed gas is the same 
 at the same temperature, but the available energy is much greater in the 
 former. 
 
 When the compressed air is used in driving a rock-drill, or any other 
 piece of machinery, it gives up energy equal in amount to the work it does, 
 and its temperature is accordingly greatly reduced. 
 
 Causes of Loss of Energy in Use of Compressed Air. (Zahner, on 
 Transmission of Power by Compressed Air.) 1. The compression of 
 air always develops heat, and as the compressed air always cools down to 
 the temperature of the surrounding atmosphere before it is used, the 
 mechanical equivalent of this dissipated heat is work lost. 
 
 2. The heat of compression increases the volume 9f the air-, and hence 
 it is necessary to carry the air to a higher pressure in the compressor in 
 order that we may finally have a given volume of air at a given pressure, 
 and at the temperature of the surrounding atmosphere. The work spent 
 in effecting this excess of pressure is work lost. 
 
 3. Friction of the air in the pipes, leakage, dead spaces, the resistance 
 offered by the valves, insufficiency of valve-area, inferior workmanship, 
 and slovenly attendance, are all more or less serious causes of loss of 
 power. 
 
 The first cause of loss of work, namely, the heat developed by compres- 
 sion, is entirely unavoidable. The whole of the mechanical energy which 
 the compressor-piston spends upon the air is converted into heat. This 
 heat is dissipated by conduction and radiation, and its mechanical equiva- 
 lent is work lost. The compressed air, having again reached thermal 
 
COMPRESSED-AIR. 633 
 
 equilibrium with the surrounding atmosphere, expands and does work in 
 an air motor, losing temperature and intrinsic energy in proportion to 
 the work dt>ne. 
 
 A large fall in temperature will cause any moisture in the air to 
 freeze, and, unless the air is pre-heated before use in the motor, per- 
 mitting it to expand to more than two volumes will cause difficulties. 
 It is for this reason, and also because of the heat-losses in the compressor, 
 that the lower the pressure at which compressed air is used for power 
 transmission the more efficient is the system. Against the increased 
 efficiencies of the lower pressures must be balanced the higher cost of 
 the mechanisms, on account of size, to utilize the lower pressures. 
 
 The intrinsic energy of any gas is the energy which it is capable of 
 exerting against a piston in changing from a given state as to temper- 
 ature and volume to a total privation of heat and indefinite expansion. 
 The intrinsic energy of 1 Ib. of gas at any pressure and volume is the 
 product of its absolute temperature and its specific heat .at constant 
 volume. (See Thermodynamics.) 
 
 Loss due to Excess of Pressure caused by Heating In the Com- 
 pression-cylinder. If the air during compression were kept at a con- 
 stant temperature, the compression-curve of an indicator-diagram taken 
 from the cylinder would be an isothermal curve, and would follow the law 
 
 of Boyle and Mariotte, pv = a constant, or pwi = Pov 0t or pi = p ,povo 
 
 being the pressure and volume at the beginning of compression, and 
 PIVI the pressure and volume at the end, or at any intermediate point. 
 But as the air is heated during compression the pressure increases faster 
 than the volume decreases, causing the work required for any given pres- 
 sure to be increased. If none of the heat were abstracted by radiation or 
 by injection of water, the curve of the diagram would be an adiabatic 
 
 / v \ 1.405 
 
 curve, with the equation pi = p Mj . Cooling the air during com- 
 pression, or compressing it in two cylinders, called compounding, and 
 cooling the air as it passes from one cylinder to the other, reduces the 
 exponent of this equation, and reduces the quantity of work necessary to 
 effect a given compression. F. T. Cause (Am. Mach., Oct. 20, 1892), 
 describing the operations of the Popp air-compressors in Paris, says: 
 The greatest saving realized in compressing in a single cylinder was 33 per 
 cent of that theoretically possible. In cards taken from the 2000 H.P. 
 compound compressor at Quai De La Gare, Paris, 'the saving realized is 
 85 per cent of the theoretical amount. Of this amount only 8 per cent is 
 due to cooling during C9rnpression, so that the increase of economy in the 
 compound compressor is mainly due to cooling the air between the two 
 stages of compression. A compression-curve with exponent 1.25 is the 
 best result that was obtained for compression in a single cylinder and 
 cooling with a very fine spray. The curve with exponent 1.15 is that 
 which must be realized in a single cylinder to equal the present economy 
 of the compound compressor at Quai De La Gare. 
 
 Adiabatic and Isothermal Compression. Theoretically, air may 
 be compressed adiabatically, in which case all the heat of compression 
 is retained in the air, or isothermally, in which case the heat of com- 
 pression is removed as rapidly as it is generated, by some refrigerating 
 process. Adiabatic compression is impossible as some of the heat will 
 be radiated into the compressor walls, and isothermal compression is 
 practically impossible, as the heat must be generated before it can be 
 absorbed. The best practical results that have been obtained by 
 compressing air in a single stage compressor make it possible to save 
 approximately one-third of the loss due to the heat generated in the 
 compressor. 
 
 Formulae for Adiabatic Compression or Expansion of Air (or 
 Other Sensibly Perfect Gas). 
 
 Let air at an absolute temperature Ti, absolute pressure pi, and volume 
 vi be compressed to an absolute pressure #2 and corresponding volume v* 
 and absolute temperature Tz', or let compressed air of an initial pressure, 
 volume, and temperature #2, vz, and Ti be expanded to pi, vi, and T\, there 
 being no transmission of heat from or into the air during the operation/. 
 
634 AIR. 
 
 Then the following equations express the relations -between pressure, 
 volume, and temperature (see works on Thermodynamics): 
 
 B = (&\' n . & = (vi\ lmU . vi = /TYv 2 ' 46 . 
 
 vt \pj pi \vj m \Tj 
 
 T2_M\- T? /PA ' 29 P? /?l2\ 3 - 46 
 
 Ti~W ' Ti~\pJ ; pi^VTi/ 
 
 The exponents are derived from the ratio c p -* c v = k of the specific 
 heats of air at constant pressure and constant volume. Taking k = 
 1.406, 1 -s- k = 0.711; k - 1 = 0.406; 1 -*- (k - 1) = 2.463; k + 
 (k - 1) = 3.463; (k - 1) *- k = 0.289. 
 
 Work of Adiabatic Compression of Air. If air is compressed in a 
 cylinder without clearance from a volume vi and pressure pi to a smaller 
 volume vz and higher pressure pz, work equal to p\vi is done by the external 
 air on the piston while the air is drawn into the cylinder. Work is then 
 done by the piston on the air, first, in compressing it to the pressure pa 
 and volume vz, and then in expelling the volume vz from the cylinder 
 
 against the pressure p 2 . If the compression is adiabatic, piVj. = Pzv a => 
 constant, k = 1.406. . 
 
 The work of compression of a given quantity of air is, in foot-pounds, 
 
 - 1 
 
 k-l(\p 
 
 f /?)A"'*1 % f /7)o\0-29 \ 
 
 or 2.463 P m {(I) -1} -2.463 ft* {(I) -l}. 
 
 The work of expulsion is pzvi Pivi ( } ~ 
 
 \Pi/ 
 
 The total work is the sum of the work of compression and expulsion less 
 the work done on the piston during admission, and it equals 
 
 PlVl 
 
 The mean effective 'pressure during the stroke is 
 
 Pi and p 2 are absolute pressures above a vacuum, in pounds per square 
 foot. 
 
 EXAMPLE. Required the work done in compressing 1 cubic foot of 
 air per second from 1 to 6 atmospheres, including the work of expulsion 
 from the cylinder. 
 
 pi -* pi = 6; 6 - 29 - 1 = 0.681; 3.463 X 0.681 = 2.358 atmospheres 
 X 14.7 = 34.66 Ib. per sq. in. mean effective pressure, X 144 = 4991 Ib. 
 persq. ft., XI ft. stroke = 4991 ft.-lb.,-*- 550 ft.-lb. per second = 9.08 H.P. 
 
 If R ratio of pressures = pz * pi, and if Vi = 1 cubic foot, the work 
 done in compressing 1 cubic foot from pi to pz is, in foot-pounds, 
 
 3.463 pi CRo-29_ i), 
 
 Pi being taken in Ib. per sq. ft. For compression at the sea level PI may 
 be taken at 14 Ibs. per sq. in. = 2016 Ib. per sq. ft., as there is some loss 
 of pressure due to friction of valves and passages. 
 
 Horse-power required to compress and deliver 100 cubic feet of free air 
 per minute = 1.511 Pj (fl' 29 - 1); Pj being the pressure of the free air in 
 pounds per sq. in., absolute. 
 
 EXAMPLE. To compress 100 cu. ft. from 1 to 6 atmospheres. Pj= 14.7: 
 R 6: 1.511 X 14.7 X 0.681 = 15.13 H.P. 
 
 Indicator-cards from compressors in good condition and under working- 
 speeds usually follow the adiabatic line closely. A low curve indicates 
 piston leakage. Such cooling as there may be from the cylinder- jacket 
 an<1 the re-expansion of the air in clearance-spaces tends to reduce the 
 
COMPRESSED AIR. 
 
 635 
 
 mean effective pressure, while the "camel-backs" in the expulsion-line, 
 due to resistance to opening of the discharge-valve, tend to increase it. 
 
 Work of one stroke of a compressor, with adiabatic compression, in 
 foot-pounds, 
 
 W= 3.463 Pi Vi (R ' 29 - 1). 
 
 in which Pi = initial absolute pressure in Ib. per sq. ft. and Vi = volume 
 traversed by piston in cubic feet. 
 
 The work done during adiabatic compression (or expansion) of 1 pound 
 of air from a volume vi and pressure p\ to another volume vz and pressure 
 Pz is equal to the mechanical equivalent of the heating (or cooling). 
 ti is the higher and h the lower temperature, Fahr., the work done is 
 c v J (ti fe) foot-pounds, c v being the specific heat of air at constant 
 volume = 0.1689, and J = 778, c v J = 131.4. 
 
 The work during compression also equals 
 
 R a being the value of pv + absolute temperature for 1 Ib. of air = 53.32. 
 The work during expansion is 
 
 t/ Vl> \ 0.29-1 r / v .\ 0.29 "I 
 
 l -&) J = 2 - 463p2 n(s) - J J' 
 
 in which pivi are the initial and pzVz the final pressures and volumes. 
 
 Compound Compression, with Air Cooled between the Two Cyl- 
 inders. (Am. Mach., March 10 and 31, 1898.) Work in low-pressure 
 cylinder = W^ in high-pressure cylinder TF 2 . Total work 
 
 Wi + W 2 = 3.46 PxFi [r^-29 + #0.29 x Ti -0-29 _ 2 ]. 
 
 TI = ratio of pressures in 1. p. cyl., r 2 = ratio in h.p. cyl., R = nr 2 . When 
 ri = r' 2 = ^ R, the sum Wi + W 2 is a minimum. Hence for a given total 
 ratio of pressures, R, the work of compression, will be least when the ratios 
 of the pressures in each of the two cylinders are equal. 
 
 The equation may be simplified, when ri = **/R, to the following: 
 
 Wj. + W 2 = 6.92 P^ffl -^ - 1]. 
 
 Dividing by TI gives the mean effective pressure reduced to the low- 
 pressure cylinder M.E.P. = 6.92 PI [R Q -^ - 1]. 
 
 In the above equati9n the compression in each cylinder is supposed to 
 be adiabatic, but the intercooler is supposed to reduce the temperature 
 of the air to that at which compression began. 
 
 Horse-power required to compress adiabatically 100 cu. ft. of free air 
 per minute in two stages with interceding, and with equal ratio of com- 
 ression in each cylinder, = 3.022 Pj (R 145 -1); PI being the pressure in 
 DS. per sq. in., absolute, of the free air, and Rthe total ratio of compression. 
 
 EXAMPLE. To compress 100 cu. ft. per min. from 1 to 6 atmospheres 
 P = 14.7; R = 6; 3.022 X 14.7 X 0.2964 = 13.17 H.P. 
 
 Mean Effective Pressures of Air Compressed in Two Stages, assum- 
 ing the Intercooler to Reduce the Temperature to that at which 
 Compression Began. (F. A. Halsey, Am. Mach., Mar. 31, 1898.) 
 
 p 
 I 
 
 R. 
 
 0.145. 
 
 M.E.P. 
 
 from 
 14 Ibs. 
 Initial. 
 
 Ultimate 
 Saving 
 by Com- 
 pound- 
 ing^. 
 
 R. 
 
 0.145. 
 
 M.E.P. 
 from 
 14 Ibs. 
 Initial. 
 
 Ultimate 
 Saving 
 by Com 
 pound- 
 ing,%. 
 
 5.0 
 5.5 
 6.0 
 6.5 
 7.0 
 7.5 
 8.0 
 8.5 
 
 .263 
 .280 
 .296 
 .312 
 .326 
 .336 
 .352 
 .364 
 
 25.4 
 27.0 
 28.6 
 30.1 
 31.5 
 32.8 
 34.0 
 35.2 
 
 11.5 
 12.3 
 
 12.8 
 13.2 
 13.7 
 14.3 
 14.8 
 15.3 
 
 9.0 
 9.5 
 10 
 11 
 12 
 13 
 14 
 15 
 
 .375 
 .386 
 .396 
 .416 
 .434 
 .451 
 .466 
 .481 
 
 36.3 
 37.3 
 38.3 
 40.2 
 41.9 
 43.5 
 45.0 
 46.4 
 
 15.8 
 16.2 
 16.6 
 17.2 
 17.8 
 18.4 
 19.0 
 19.4 
 
 R = final -T- initial absolute pressure. 
 M.E.P. = mean effective pressure, Ib. per sq. in., based on 14 Ib. 
 absolute initial pressure reduced to the low-pressure cylinder. 
 
636 
 
 AIK. 
 
 To find the Index of the Curve of an Air-diagram. If P, V l be 
 
 pressure and volume at one point on the curve, and P V the pressure and 
 
 P /Vi\ x 
 volume at another point, then -p- = fyj , in which x is the index to be 
 
 found. Let P -$-_Pi = R, and Vi + V r; then R = r x ; log R =x log r. 
 whence x = log R -r- log r. (See also graphic method on page 602.) 
 
 Pressures, Volumes, Mean Effective Pressures, and Final Temper- 
 atures, in Single-stage Compression from 1 Atmosphere and 60 Fahr. 
 
 (Contributed by M. C. Wilkinson, San Pedro, CaL, 1914.) 
 
 Pressure. 
 
 Volume. 
 
 M.E.P.of 
 Stroke 
 
 Final Tem- 
 perature. 
 
 
 
 * 
 
 1 
 
 i. 
 
 ,,-i 
 
 
 
 m 
 
 
 1 
 
 | 
 
 1 
 
 Jr 
 
 pi 
 
 & 
 
 o II 
 
 
 |2 
 
 |ll 
 f 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 
 
 14.7 
 
 1.0 
 
 1 .0000 
 
 1.000 
 
 1 .000 
 
 0.000 
 
 o.ooo 
 
 60.0 
 
 60.0 
 
 
 15.7 
 
 1 .068 
 
 0.9363 
 
 0.948 
 
 0.954 
 
 0.974 
 
 0.982 
 
 66.3 
 
 70.0 
 
 2 
 
 16.7 
 
 .136 
 
 .8803 
 
 .903 
 
 .910 
 
 1 .896 
 
 1 .913 
 
 73.4 
 
 79.6 
 
 3 
 
 17.7 
 
 .204 
 
 .8305 
 
 .862 
 
 .876 
 
 2.778 
 
 2.810 
 
 79.7 
 
 88.8 
 
 4 
 
 18.7 
 
 .272 
 
 .7862 
 
 .825 
 
 .841 
 
 3.624 
 
 3.681 
 
 85.6 
 
 97.6 
 
 5 
 
 19.7 
 
 .340 
 
 .7463 
 
 .791 
 
 .812 
 
 4.432 
 
 4:510 
 
 91.7 
 
 106.1 
 
 10 
 
 24.7 
 
 .680 
 
 .5952 
 
 .660 
 
 .692 
 
 8.041 
 
 8.267 
 
 116.9 
 
 144 5 
 
 15 
 
 29.7 
 
 2.020 
 
 .4950 
 
 .570 
 
 .607 
 
 11.099 
 
 11.515 
 
 .138.5 
 
 177.7 
 
 20 
 
 34.7 
 
 2.360 
 
 .4237 
 
 .503 
 
 .544 
 
 13.774 
 
 14.396 
 
 157.5 
 
 207.1 
 
 25 
 
 39.7 
 
 2.701 
 
 .3702 
 
 .452 
 
 .494 
 
 16.155 
 
 16.998 
 
 174.3 
 
 233.6 
 
 30 
 
 44.7 
 
 3.041 
 
 .3288 
 
 .411 
 
 .454 
 
 18.309 
 
 19.375 
 
 189.5 
 
 257.9 
 
 35 
 
 49.7 
 
 3.381 
 
 .2955 
 
 .377 
 
 .421 
 
 20 259 
 
 21.569 
 
 203.5 
 
 280.3 
 
 40 
 
 54.7 
 
 3.721 
 
 .2687 
 
 .349 
 
 .393 
 
 22.101 
 
 23.610 
 
 216.3 
 
 301.2 
 
 45 
 
 59.7 
 
 4.061 
 
 .2462 
 
 .326 
 
 .370 
 
 23.777 
 
 25.529 
 
 228.2 
 
 320 8 
 
 50 
 
 64.7 
 
 4.401 
 
 .2272 
 
 .303 
 
 .349 
 
 25.358 
 
 27.331 
 
 239.4 
 
 339.2 
 
 55 
 
 69.7 
 
 4.742 
 
 .2109 
 
 .288 
 
 .329 
 
 26 842 
 
 29.037 
 
 249.9 
 
 356.7 
 
 60 
 
 74.7 
 
 5.082 
 
 .1968 
 
 .272 
 
 .315 
 
 28.239 
 
 30.661 
 
 259.8 
 
 373.2 
 
 65 
 
 79.7 
 
 5.422 
 
 .1844 
 
 .258 
 
 .301 
 
 29.562 
 
 32.808 
 
 269.2 
 
 388.9 
 
 70 
 
 84.7 
 
 5.762 
 
 .1736 
 
 .247 
 
 .288 
 
 30.826 
 
 33.680 
 
 278.1 
 
 404.0 
 
 75 
 
 89.7 
 
 6.102 
 
 .1639 
 
 .235 
 
 .277 
 
 32.031 
 
 35.105 
 
 286.6 
 
 418.6 
 
 80 
 
 94.7 
 
 6.442 
 
 .1552 
 
 .225 
 
 .266 
 
 33.185 
 
 36.469 
 
 294.8 
 
 432.5 
 
 85 
 
 99.7 
 
 6.782 
 
 .1474 
 
 .216 
 
 .257 
 
 34.288 
 
 37.782 
 
 302.6 
 
 446.0 
 
 90 
 
 104.7 
 
 7.122 
 
 .1404 
 
 .208 
 
 .248 
 
 35.346 
 
 39.050 
 
 310.1 
 
 458.9 
 
 95 
 
 109.7 
 
 7.463 
 
 .1340 
 
 .200 
 
 .240 
 
 36.368 
 
 40.277 
 
 317.3 
 
 471.4 
 
 100 
 
 114.7 
 
 7.803 
 
 .1282 
 
 .192 
 
 .233 
 
 37.354 
 
 41 .463 
 
 324.3 
 
 483.5 
 
 105 
 
 119.7 
 
 8.143 
 
 .1228 
 
 .186 
 
 .226 
 
 38.401 
 
 42.613 
 
 331.0 
 
 495.3 
 
 110 
 
 124.7 
 
 8.483 
 
 .1179 
 
 .181 
 
 .219 
 
 39.220 
 
 43.728 
 
 337.5 
 
 506.7 
 
 115 
 
 129.7 
 
 8.823 
 
 .1133 
 
 .175 
 
 .213 
 
 40.109 
 
 44.813 
 
 343.8 
 
 517.8 
 
 120 
 
 134.7 
 
 9.163 
 
 .1091 
 
 .170 
 
 .207 
 
 40.969 
 
 45.866 
 
 349.9 
 
 528.6 
 
 125 
 
 139.7 
 
 9.503 
 
 .1052 
 
 .165 
 
 .202 
 
 41 .807 
 
 46.900 
 
 355.8 
 
 539.1 
 
 130 
 
 144.7 
 
 9.844 
 
 .1015 
 
 .160 
 
 .197 
 
 42.623 
 
 47.898 
 
 361.6 
 
 549.3 
 
 135 
 
 149.7 
 
 10.184 
 
 .0982 
 
 .156 
 
 .192 
 
 43.416 
 
 48.880 
 
 367.2 
 
 559.3 
 
 140 
 
 154.7 
 
 10.524 
 
 .0950 
 
 .152 
 
 .188 
 
 44.189 
 
 49.832 
 
 372.6 
 
 569.0 
 
 145 
 
 159.7 
 
 10.864 
 
 .0921 
 
 .148 
 
 .184 
 
 44.938 
 
 50.769 
 
 377.9 
 
 578.6 
 
 150 
 
 164.7 
 
 11 .204 
 
 .0893 
 
 .145 
 
 .180 
 
 45.766 
 
 51.681 
 
 383.1 
 
 587.9 
 
 160 
 
 174.7 
 
 11 .884 
 
 .0841 
 
 .138 
 
 .172 
 
 47.084 
 
 53.451 
 
 393.1 
 
 606.0 
 
 170 
 
 184.7 
 
 12.565 
 
 .0796 
 
 .132 
 
 .166 
 
 48.429 
 
 55.147 
 
 402.7 
 
 623.3 
 
 180 
 
 194.7 
 
 13.245 
 
 .0755 
 
 .126 
 
 .160 
 
 49.723 
 
 56.781 
 
 411.8 
 
 641 .0 
 
 190 
 
 204.7 
 
 13.295 
 
 .0718 
 
 .121 
 
 .154 
 
 50.968 
 
 58.359 
 
 420.6 
 
 656.1 
 
 200 
 
 214.7 
 
 14.605 
 
 .0685 
 
 .117 
 
 .147 
 
 52.156 
 
 59.881 
 
 429.0 
 
 671.7 
 
 Columns 1, 2 and 3 give the relative pressure readings in gage, 
 absolute and atmospheric pressures. 
 
COMPRESSED AIR. 
 
 637 
 
 Column 4 gives the relative volumes of the air after compression and 
 with the temperature reduced to 60 F. These are the volumes that 
 are available for use in the operation of the driven mechanisms. 
 
 Column 5 gives the relative volumes of the air as the compressor 
 has to deal with it. 
 
 Column 7 gives the mean effective pressures of a single stroke of the 
 compressor, including the compression and expulsion of air from the 
 cylinder. In computing the power required to operate the com- 
 pressor a certain percentage (usually from 5 to 20) must be added 
 for mechanical friction and valve resistance and other compressor 
 characteristics. 
 
 Column 9 gives the temperature of the air as it leaves the com- 
 pressor. 
 
 Columns 6, 8 and 10 give the theoretical, final volumes, mean effec- 
 tive pressures and final temperatures of air compressed adiabatically. 
 
 Mean Effective Pressures of Air Compressed Adiabatically. 
 
 (F. A. Halsey, Am. Mack., Mar. 10, 1898.) 
 
 1_ 
 
 R-. 
 
 M.E.P. from 
 Hlbs. 
 Initial. 
 
 R. 
 
 #0.29. 
 
 M.E.P. from 
 I41bs. 
 Initial. 
 
 ..25 
 
 .067 
 
 3.24 
 
 4.75 
 
 .570 
 
 27.5 
 
 1.59 
 
 .125 
 
 6.04 
 
 5 
 
 .594 
 
 28.7 
 
 1.75 
 
 .176 
 
 8.51 
 
 5.25 
 
 .617 
 
 29.8 
 
 2 
 
 .223 
 
 10.8 
 
 5.5 
 
 .639 
 
 30.8 
 
 2.25 
 
 .265 
 
 12.8 
 
 5.75 
 
 .660 
 
 31.8 
 
 2.5 
 
 .304 
 
 14.7 
 
 6 
 
 .681 
 
 32.8 
 
 2.75 
 
 .341 
 
 16.4 
 
 6.25 
 
 .701 
 
 33.8 
 
 3 
 
 .375 
 
 18.1 
 
 6.5 
 
 .720 
 
 34.7 
 
 3.25 
 
 .407 
 
 19.6 
 
 6.75 
 
 .739 
 
 35 6 
 
 3.5 
 
 .438 
 
 21.1 
 
 7 
 
 .757 
 
 36.5 
 
 3.75 
 
 .467 
 
 22.5 
 
 7.25 
 
 .775 
 
 37.4 
 
 4 
 
 .495 
 
 23.9 
 
 7.5 
 
 .793 
 
 ,.38.3 
 
 4.25 
 
 .521 
 
 25.2 
 
 8 
 
 .827 
 
 39.9 
 
 4.5 
 
 .546 
 
 26.4 
 
 
 
 
 R final -4- initial absolute pressure. 
 
 M.E.P. =mean effective pressure, Ib. per sq. in., based on 14 Ib. initial. 
 
 Horse-power required to com- 
 press and deliver One Cubic Foot 
 of Free Air per minute to a given 
 pressure with no cooling of the air 
 during the compression; also the 
 horse power required, supposing the 
 air to be maintained at constant 
 temperature during the compression. 
 
 H.P. required to compress and 
 deliver One Cubic Foot of Com- 
 pressed Air per minute at a given 
 pressure (the air being measured at 
 the atmospheric temperature) with 
 no cooling of the air during the 
 compression; also supposing the air 
 to be maintained at constant tem- 
 perature during the compression. 
 
 Gauge- 
 
 Air hot 
 
 Air constant 
 
 Gauge- 
 
 Air not 
 
 Air constant 
 
 pressure. 
 
 cooled. 
 
 temperature. 
 
 pressure. 
 
 cooled. 
 
 temperature. 
 
 5 
 
 0.0196 
 
 0.0188 
 
 5 
 
 0.0263 
 
 0.0251 
 
 10 
 
 0.0361 
 
 0.0333 
 
 10 
 
 0.0606 
 
 0.0559 
 
 20 
 
 0.0628 
 
 0.0551 
 
 20 
 
 0.1483 
 
 0.1300 
 
 30 
 
 0.0846 
 
 0.0713 
 
 30 
 
 0.2573 
 
 2168 
 
 40 
 
 0.1032 
 
 0.0843 
 
 40 
 
 0.3842 
 
 0.3138 
 
 50 
 
 0.1195 
 
 0.0946 
 
 50 
 
 0.5261 
 
 0.4166 
 
 60 
 
 0. 1342 
 
 0.1036 
 
 60 
 
 0.6818 
 
 0.5266 
 
 70 
 
 0.1476 
 
 0.1120 
 
 70 
 
 0.8508 
 
 0.6456 
 
 80 
 
 0.1599 
 
 0.1195 
 
 80 
 
 1.0302 
 
 0.7700 
 
 90 
 
 0.1710 
 
 0.1261 
 
 90 
 
 1.2177 
 
 0.8979 
 
 100 
 
 0.1815 
 
 0.1318 
 
 100 
 
 1.4171 
 
 1.0291 
 
 The. horse-power given above is the theoretical power, no allowance 
 being made for friction of the compressor or other losses, which may 
 amount to 10 per cent or more. 
 
638 
 
 AIR. 
 
 Compressed-air Engines, Adiabatic Expansion. Let the initial 
 pressure and volume taken into the cylinder be pi Ib. per sq. ft. and Vi 
 cubic feet ; let expansion take place to PZ and vi according to the adiabatic 
 law pivi 1 - 41 = P202 1 - 41 ; f/hen at the end of the stroke let the pressure drop 
 to the back-pressure p 3 , at which the air is exhausted. Assuming no 
 clearance, the work done by one pound of air during admission, measured 
 
 above vacuum, is PIVI, the work during expansion is 2.463 PiVi I 
 
 / P2 v 0.29-1 
 
 ( J , and the negative or back pressure work is p^vz. The total 
 
 t/7)A 0-29~| 
 1 _ f ? ) _ p 3V2> an d the mean effective pres- 
 va/ J 
 sure is the t9tal work divided by vt. 
 
 If the air is expanded down to the back-pressure PS the total work is 
 
 3.463 PiVi 1 1 - ( \ J , 
 or, in terms of the final pressure and volume, 
 
 I /T)i\Q'2& ) 
 
 I \P3/ 9 
 
 and the mean effective pressure is 
 
 The actual work is reduced by clearance. When this is considered, the 
 product of the initial pressure PI by the clearance volume is to be sub- 
 tracted from the total work calculated from the initial volume vi, including 
 clearance. (See p t 961 under " Steam-engine. ") 
 
 Mean and Terminal Pressures of Compressed Air used Expansively 
 for Gauge Pressures from 60 to 100 Ib. 
 
 (Frank Richards, Am. Mack., April 13, 1893.) 
 
 to 
 
 Initial Pressure. 
 
 1 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 1 
 
 . 
 
 p 
 
 1 , ^ 
 
 41 
 
 U 
 
 || 
 
 lt| 
 
 sUi 
 
 |,s 
 
 flj 
 
 "3 
 
 .s 
 
 'o 
 
 C w 
 
 Pi 
 
 1 
 
 <u ^ 
 
 2 <? en 
 ** <u 
 o t-< 
 
 il 
 
 
 
 *'^ M 
 1 
 
 |3f 
 
 1^1 
 
 P* 
 
 ji D. 
 
 H < 
 
 g ft 
 
 
 ^ & 
 
 H ft 
 
 a 
 
 H ft 
 
 ft 
 
 H ft 
 
 .25 
 
 23.6 
 
 1O.65 
 
 28.74 
 
 12.01 
 
 33.89 
 
 13.49 
 
 39.04 
 
 14.91 
 
 44.19 
 
 1.33 
 
 .30 
 
 28.9 
 
 13.77 
 
 34.75 
 
 0.6 
 
 40.61 
 
 2.44 
 
 46.46 
 
 4.27 
 
 53.32 
 
 6.!! 
 
 I 
 
 32.13 
 
 0.96 
 
 38.41 
 
 3.09 
 
 44.69 
 
 5.22 
 
 50.98 
 
 7.35 
 
 57.26 
 
 9.48 
 
 .35 
 
 33.66 
 
 2.33 
 
 40.15 
 
 4.38 
 
 46.64 
 
 6.66 
 
 53.13 
 
 8.95 
 
 59.62 
 
 11.23 
 
 
 35.85 
 
 3.85 
 
 42.63 
 
 6.36 
 
 49.41 
 
 7.88 
 
 56.2 
 
 11.39 
 
 62.98 
 
 13.89 
 
 .40 
 
 37.93 
 
 5.64 
 
 44.99 
 
 8.39 
 
 52.05 
 
 11.14 
 
 59.11 
 
 13.88 
 
 66.16 
 
 16.64 
 
 .45 
 
 41.75 
 
 10.71 
 
 49.31 
 
 12.61 
 
 56.9 
 
 15.86 
 
 64.45 
 
 19.11 
 
 72.02 
 
 22.36 
 
 .50 
 
 45.14 
 
 13.26 
 
 53.16 
 
 17. 
 
 61.18 
 
 20.81 
 
 69.19 
 
 24.56 
 
 77.21 
 
 28.33 
 
 .60 
 
 50.75 
 
 21.53 
 
 59.51 
 
 26.4 
 
 68.28 
 
 31.27 
 
 77.05 
 
 36.14 
 
 85.82 
 
 41.01 
 
 I 
 
 51.92 
 53.67 
 54.93 
 
 23.69 
 27.94 
 30.39 
 
 60.84 
 62.83 
 64.25 
 
 28.85 
 33.03 
 36.44 
 
 69.76 
 71.99 
 73.57 
 
 34.01 
 38.68 
 42.49 
 
 78.69 
 81.14 
 82.9 
 
 39.16 
 44.33 
 48.54 
 
 87.61 
 90.32 
 
 92.22 
 
 44.32 
 49.97 
 54.59 
 
 .75 
 
 56.52 
 
 35.01 
 
 66.05 
 
 41.68 
 
 75.59 
 
 48.35 
 
 85.12 
 
 55.02 
 
 94.66 
 
 61.69 
 
 .80 
 
 57.79 
 
 39.78 
 
 67.5 
 
 47.08 
 
 77.2 
 
 54.38 
 
 86.91 
 
 61.69 
 
 96.61 
 
 68.99 
 
 .to 
 
 59.15 
 59.46 
 
 47.14 
 49.65 
 
 69.03 
 69.38 
 
 55.43 
 58.27 
 
 78.92 
 79.31 
 
 63.81 
 66.89 
 
 88.81 
 89.24 
 
 72. 
 75.52 
 
 98.7 
 99.17 
 
 80.28 
 87.82 
 
 Pressures in italics are absolute; all others are gage pressures 
 
AIR COMPRESSION AT ALTITUDES. 
 
 639 
 
 AIR COMPRESSION AT ALTITUDES. 
 
 (Ingersoll-Rand Co. Copyright, 1906, by F. M. Hitchcock.) 
 Multipliers to Determine the Volume of Free Air which, when 
 Compressed, is Equivalent in Effect to a Given Volume of Free 
 Air at Sea Level. 
 
 Alti- 
 tucle 
 
 Barometric 
 Pressure. 
 
 Gauge Pressure (Pounds). 
 
 Feet*. 
 
 In. of 
 Mercury. 
 
 Lb. per 
 Sq. In. 
 
 60 
 
 80 
 
 100 
 
 125 
 
 150 
 
 1,000 
 
 28.88 
 
 14.20 
 
 .032 
 
 .033 
 
 .034 
 
 .035 
 
 .036 
 
 2,000 
 
 27.80 
 
 13.67 
 
 .064 
 
 .066 
 
 .068 
 
 .071 
 
 .072 
 
 3,000 
 
 26.76 
 
 13.16 
 
 .097 
 
 .102 
 
 .105 
 
 .107 
 
 .109 
 
 4,000 
 
 25.76 
 
 12.67 
 
 .132 
 
 .139 
 
 .142 
 
 .147 
 
 .149 
 
 5,000 
 
 24.79 
 
 12.20 
 
 .168 
 
 .178 
 
 .182 
 
 .187 
 
 .190 
 
 6,000 
 
 23.86 
 
 11.73 
 
 .206 
 
 .218 
 
 .224 
 
 .231 
 
 .234 
 
 7,000 
 
 22.97 
 
 11.30 
 
 .245 
 
 .258 
 
 .267 
 
 .274 
 
 .278 
 
 8,000 
 
 22.11 
 
 10.87 
 
 .287 
 
 .300 
 
 .310 
 
 .319 
 
 .326 
 
 9,000 
 
 21.29 
 
 10.46 
 
 .329 
 
 .346 
 
 .356 
 
 .366 
 
 .374 
 
 10,000 
 
 20 49 
 
 10.07 
 
 .373 
 
 .394 
 
 .404 
 
 416 
 
 .424 
 
 Horse-power Developed in Compressing One Cubic Foot of Free Air 
 at Various Altitudes from Atmospheric to Various Pressures. 
 
 Initial Temperature of the Air in Each Cylinder Taken as 60 F.; Jacket 
 Cooling not Considered ; Allowance made for usual losses. 
 
 Simple Compression. 
 
 Two Stage Compression. 
 
 Altitude, 
 Feet. 
 
 Gauge Pressure 
 (Pounds). 
 
 Gauge Pressure (Pounds). 
 
 60 
 
 80 
 
 100 
 
 60 
 
 80 
 
 100 
 
 125 
 
 150 
 
 
 1,000 
 2,000 
 3,000 
 4,000 
 5,000 
 6,000 
 7,000 
 8,000 
 9,000 
 10,000 
 
 0.1533 
 0.1511 
 0.1489 
 0.1469 
 0.1448 
 0.1425 
 0.1402 
 0.1379 
 0.1358 
 0.1337 
 0.1316 
 
 0.1824 
 0.1795 
 0.1766 
 0.1739 
 0.1712 
 0.1685 
 0.1656 
 0.1628 
 0.1600 
 0.1572 
 0.1547 
 
 0.2075 
 0.2040 
 0.2006 
 0.1971 
 0.1939 
 0.1906 
 0.1872 
 0.1839 
 0.1807 
 0.1774 
 0.1743 
 
 0.1354 
 0.1332 
 0.1310 
 0.1286 
 0.1263 
 0.1241 
 0.1218 
 0.1197 
 0.1173 
 0.1151 
 0.1132 
 
 0.1580 
 0.1553 
 0.1524 
 0.1493 
 0. 1464 
 0.1438 
 0.1409 
 0.1383 
 0.1358 
 0.1329 
 0.1303 
 
 0.1765 
 0.1734 
 0.1700 
 0.1666 
 0.1635 
 0.1600 
 0.1566 
 0.1536 
 0.1504 
 0.1473 
 0.1442 
 
 0.1964 
 0.1926 
 0.1887 
 0.1848 
 0.1810 
 0.1772 
 0.1737 
 0.1700 
 0.1662 
 0.1627 
 0.1592 
 
 0.2138 
 0.2093 
 0.2048 
 0.2003 
 0.1963 
 0.1921 
 0.1879 
 0.1838 
 0.1797 
 0.1758 
 0.1717 
 
 EXAMPLE. Required the volume of free air which when compressed 
 to 100 Ib. gauge at 9,000 ft. altitude will be equivalent to 1,000 cu. ft. 
 of free air at sea level; also the power developed in compressing this 
 volume to 100 Ib. gauge in two stage compression at this altitude. 
 
 From first table the multiplier is 1.356. Equivalent free air = 1,000 X 
 1.356 = 1,356 cu. ft. 
 
 From second table, power developed in compressing 1 cu. ft. of free air 
 is 0.1473 H.P.; 1,356 X 0.1473 = 199.73 H.P. 
 
 The Popp Compressed-air System in Paris. A most extensive 
 system of distribution of power by means of compressed air is that of 
 M. Popp, in Paris. One of the central stations is laid out for 24,000 
 horse-power. For a very complete description of the system, see Engineer- 
 ing, Feb. 15, June 7, 21, and 28, 1889, and March 13 and 20, April 10, and 
 May 1, 1891. Als9 Proc. Inst. M. E., July, 1889. A condensed descrip- 
 tion will be found in Modern Mechanism, p. 12. 
 
 Utilization of Compressed Air in Small Motors. In the earliest 
 stages of the Popp system in Paris it was recognized that no good results 
 
640 AIR, 
 
 could be obtained if the air were allowed to expand direct into the motor; 
 not only did the formation of ice due to the expansion of the air rapidly 
 accumulate and choke the exhaust, but the percentage of useful work 
 obtained, compared with that put into the air at the central station, was 
 so small as to render commercial results hopeless. 
 
 After a number of experiments M. Popp adopted a simple form of 
 cast-iron stove lined with fire-clay, heated either by a gas jet or by a 
 small coke fire. This apparatus answered the desired purpose until a 
 better arrangement was perfected, and the type was accordingly adopted 
 throughout the whole system. The economy resulting from the use of 
 the improved form was very marked. 
 
 It was found that more than 70% of the total heating value of the fuel 
 employed was absorbed by the air and transformed into useful work. 
 The efficiency of fuel consumed in this way is at least six times greater 
 than when utilized in a boiler and steam-engine. According to Prof. 
 Riedler, from 15% to 20% above the power at the central station can be 
 obtained by means at the disposal of the power users. By heating the 
 air to 480 F. an increased efficiency of 30% can be obtained. 
 
 A large number of motors in use among the subscribers to the Com- 
 pressed Air Company of Paris are rotary engines developing 1 H.P. and 
 less, and these in the early times of the industry were very extravagant 
 in their consumption. Small rotary engines, working cold air without 
 expansion, used as high as 2330 cu. ft. of air per brake H.P. per hour, 
 and with heated air 1624 cu. ft. Working expansively, a 1-H.P. rotary 
 engine used 1469 cu. ft. of cold air, or 960 cu. ft. of heated air. and a 
 2-H.P. rotary engine 1059 cu. ft. of cold air, or 847 cu. ft. of air, heated 
 to about 122 F. 
 
 The efficiency of this type of rotary motors, with air heated to 122 F., 
 may now be assumed at 43%. 
 
 Tests of a small Riedinger rotary engine, used for driving sewing- 
 machines and indicating about 0.1 H.P., showed an air-consumption of 
 1377 cu. ft. per H.P. per hour when the initial pressure of the air was 
 86 Ib. per sq. in. and its temperature 54 F., and 988 cu. ft. when the air 
 was heated to 338 F., its pressure being 72 Ib. With a 1/2-H.P. variable- 
 expansion rotary engine the air-consumption was from 800 to 900 cu. ft. 
 per H.P. per hour for initial pressures of 54 to 85 Ib. per sq. in. with the 
 air heated from 336 to 388 F., and 1148 cu. ft. with cold air, 46 F., and 
 an initial pressure of 72 Ib. The volumes of air were all taken at atmos- 
 pheric pressure. 
 
 Trials made with an old single-cylinder 80-horse-power Farcot steam- 
 engine, indicating 72 H.P., gave a consumption of air per brake H.P. as 
 low as 465 cu. ft. per hour. The temperature of admission was 320 F., 
 and of exhaust 95 F. 
 
 Prof. Elliott gives the following as typical results of efficiency for 
 various systems of compressors and air-motors: 
 
 Simple compressor and simple motor, efficiency 39.1% 
 
 Compound compressor and simple motor, 44.9 
 
 " compound motor, efficiency. . 50.7 
 Triple compressor and triple motor, efficiency 55.3 
 
 The efficiency is the ratio of the I. H.P. in the motor cylinders to the 
 I.H.P. in the steam-cylinders of the compressor. The pressure as- 
 sumed is 6 atmospheres absolute, and the losses are equal to those 
 found in Paris over a distance of 4 miles. 
 Summary of Efficiencies of Compressed-air Transmission at Paris, 
 
 between the Central Station at St. Fargeau and a 10-horse-power 
 
 Mo tor Working with Pressure Reduced to 4 1/2 Atmospheres. 
 
 (The figures below correspond to mean results of two experiments cold and 
 
 two heated.) 
 
 One indicated horse-power at central station gives 0.845 I.H.P. in com- 
 pressors, and corresponds to the compression of 348 cu. ft. of air per hour 
 from atmospheric pressure to 6 atmospheres absolute. 
 
 0.845 I.H.P. in compressors delivers as much air as will do 0.52 I.H.P. 
 in adiabatic expansion after it has fallen to the normal temperature of the 
 
 The fall of pressure in mains between central station and Paris (say 5 
 kilometres) reduces the possibility of work from 0,53 to 0,51 J.H.P, 
 
AIR COMPRESSORS. 
 
 641 
 
 The further fall of pressure through the reducing valve to 41/2 atmos- 
 pheres (absolute) reduces the possibility of work from 0.51 to 0.50. 
 
 Incomplete expansion, wire-drawing, and other such causes reduce the 
 actual I.H.P. of the motor from 0.50 to 0.39. 
 
 By heating the air before it enters the motor to about 320 F., the 
 actual I.H.P. at the motor is, however, increased to 0.54. The ratio of 
 gain by heating the air is, therefore, 0.54 -5- 0.39 = 1.38. 
 
 In this process additional heat is supplied by the combustion of about 
 0.39 Ib. of coke per I.H.P. per hour, and if this be taken into account, the 
 real indicated efficiency of the whole process becomes 0.47 instead of 0.54. 
 
 Working with cold air the work spent in driving the' motor itself reduces 
 the available horse-power from 0.39 to 0.26. 
 
 Working with heated air the work spent in driving the motor itself 
 reduces the available horse-p9wer from 0.54 to 0.44. 
 
 A summary of the efficiencies is as follows: 
 
 Efficiency of main engines 0.845. 
 
 Efficiency of compressors 0.52 -?- 0.845 = 0.61. 
 
 Efficiency of transmission through mains 0.51 -5- 0.52 = 0.98. 
 
 Efficiency of reducing valve 0.50 -~ 0.51 = 0.98. 
 
 The combined efficiency of the mains and reducing valve between 5 and 
 41/2 atmospheres is thus 0.98 X 0.98 = 0.96. If the reduction had been 
 to 4, 31/2, or 3 atmospheres, the corresponding efficiencies would have 
 been 0.93, 0.89, and 0.85 respectively. 
 
 Indicated efficiency of motor 0.39 * 0.50 = 0.78. 
 
 Indicated efficiency of whole process with cold air 0.39. Apparent 
 indicated efficiency of whole process with heated air 0.54. 
 
 Real indicated efficiency of whole process with heated air 0.47. 
 
 Mechanical efficiency of motor, cold, 0.67. 
 
 Mechanical efficiency of motor, hot, 0.81. 
 
 Ingersoll-Rand Co.'s Air Compressors.* 
 
 STRAIGHT LINE POWER-DRIVEN COMPRESSORS, CLASS "ER-1." 
 Air Pressure 10 to 125 Pounds per sq. in. 
 
 Cylinders, 
 Inches. 
 
 Piston 
 Dis- 
 place- 
 ment 
 Cu.ft. 
 per 
 Min. 
 
 Air 
 Pres. 
 De- 
 signed 
 for 
 Lb. 
 Gage. 
 
 Braize 
 H.P. at 
 Motor, 
 includ- 
 ing 
 Belt 
 Loss. 
 
 Cylinders, 
 Inches. 
 
 Piston 
 Dis- 
 place- 
 ment 
 Cu.ft. 
 
 Min. 
 
 Air 
 Pres. 
 De- 
 signed 
 for 
 Lb. 
 Gage. 
 
 Brake 
 H.P. at 
 Motor, 
 includ- 
 ing 
 Belt 
 Loss. 
 
 3 
 
 1 
 
 VI 
 
 1 
 
 s 
 
 1 
 
 w 
 
 6 
 7 
 8 
 9 
 12 
 
 8 
 9 
 10 
 12 
 14 
 
 6 
 6 
 6 
 6 
 6 
 
 52 
 
 72 
 94 
 121 
 215 
 
 80-125 
 50-100 
 25-50 
 10- 25 
 10- 
 
 8 -10 
 
 9V2-12 
 9V2-12 
 10 -121/4 
 15 - 
 
 10 
 12 
 
 14 
 17 
 
 10 
 10 
 10 
 10 
 
 210 
 304 
 415 
 615 
 
 80-125 
 50-100 
 20-50 
 10- 20 
 
 33-38 
 38-50 
 32-50 
 27-48 
 
 8 
 8 
 8 
 8 
 8 
 
 113 
 145 
 179 
 258 
 354 
 
 80-125 
 60-100 
 25-60 
 15- 25 
 10- 15 
 
 17 -22 
 19V2-24 
 18 -25 
 201/2-25 
 21 -25 
 
 12 
 14 
 17 
 20 
 
 12 
 
 12 
 12 
 12 
 
 340 
 464 
 688 
 955 
 
 80-125 
 45-100 
 30- 45 
 15- 30 
 
 54-61 
 53-73 
 55-73 
 35-70 
 
 Stroke, inches 6 
 
 Revolutions per minute. . 275 
 Belt wheel 36 X 5 1/2 
 
 8 10 12 
 
 250 235 220 
 
 45 X 81/2 58 X 101/2 72 X 141/2 
 
 These machines are also built for steam-drive. 
 
 * These tables are considerably abridged from the originals, and show 
 only the small and medium-sized machines. Large machines up to 
 8,f>00 cu, ft. capacity are made, usually of special designs, 
 
642 
 
 AIR. 
 
 'IMPERIAL XB-1" DUPLEX POWER-DRIVEN COMPRESSORS. 
 Air Pressure, 15 to 100 Pounds per sq. in. 
 
 d 
 
 X"" 
 
 i 
 
 , 8 
 
 |KS 
 
 
 
 * 
 
 Ig 
 
 WTJ 
 
 1 
 
 tt 
 
 ilc 
 
 IS 
 t 
 
 <*J 
 
 || 
 
 | 
 
 I**? 
 
 11 
 
 W|| 
 
 
 1 
 
 |fe? 
 
 
 EI! 
 
 .^ 
 
 oT 
 
 Q o ^ 
 
 ^'5? 
 
 lovS 
 
 s 
 
 I 
 
 Q O a 
 
 
 IS '|,4a 
 
 
 
 O +*< 
 
 
 S w'aJ 
 
 
 g 
 
 
 
 
 .2 .fa 
 
 ! 
 
 P J3<jj 
 
 <!Q 
 
 PQtfW 
 
 Q^ 
 
 GO 
 
 w-g^ 
 
 <!Q 
 
 w tfpq 
 
 Q<< 
 
 CO 
 
 S a 
 
 
 
 
 
 S S 
 
 
 
 7 
 
 10 
 
 198 
 
 60-100 
 
 27-37 
 
 14 
 
 14 
 
 916 
 
 35-40 
 
 93-102 
 
 8 
 
 10 
 
 258 
 
 40-55 
 
 29-35 
 
 16 
 
 14 
 
 1198 
 
 25-30 
 
 99-112 
 
 9 
 
 10 
 
 327 
 
 27-35 
 
 27-34 
 
 18 
 
 14 
 
 1518 
 
 15-20 
 
 87-108 
 
 10 
 
 10 
 
 405 
 
 22-25 
 
 29-33 
 
 
 
 
 
 
 11 
 
 10 
 
 491 
 
 15-20 
 
 28-35 
 
 13 
 
 16 
 
 826 
 
 80-100 
 
 135-154 
 
 8 
 
 12 
 
 289 
 
 75-100 
 
 47-55 
 
 14 
 15 
 
 16 
 16 
 
 959 
 1103 
 
 65-75 
 45-60 
 
 142-155 
 125-155 
 
 9 
 
 12 
 
 367 
 
 55-70 
 
 50-58 
 
 17 
 
 16 
 
 1419 
 
 30-40 
 
 129-158 
 
 10 
 
 12 
 
 454 
 
 40-50 
 
 51-58 
 
 19 
 
 16 
 
 1775 
 
 20-25 
 
 123-145 
 
 11 
 
 12 
 
 549 
 
 27-35 
 
 46-57 
 
 21 
 
 16 
 
 2171 
 
 15-20 
 
 126-157 
 
 12 
 
 12 
 
 655 
 
 22-25 
 
 47-54 
 
 
 
 
 
 
 13 
 
 12 
 
 770 
 
 15-20 
 
 44-55 
 
 15 
 
 16o 
 
 1100 
 
 80-100 
 
 181-206 
 
 
 
 
 
 
 16 
 
 16a 
 
 1253 
 
 55-75 
 
 188-202 
 
 9 
 
 12a 
 
 365 
 
 85-100 
 
 62-69 
 
 18 
 
 16fl 
 
 1592 
 
 35-50 
 
 161-205 
 
 10 
 
 12a 
 
 453 
 
 60-80 
 
 64-75 
 
 21 
 
 
 2168 
 
 25-30 
 
 177-202 
 
 11 
 
 12ft 
 
 549 
 
 47-55 
 
 66-74 
 
 24 
 
 16a 
 
 2836 
 
 15-20 
 
 162-202 
 
 12 
 
 12a 
 
 654 
 
 37-45 
 
 67-78 
 
 
 
 
 
 
 13 
 
 12a 
 
 769 
 
 25-35 
 
 63-80 
 
 15 
 
 20 
 
 1254 
 
 75-100 
 
 197-232 
 
 15 
 
 12a 
 
 1025 
 
 15-20 
 
 58-72 
 
 17 
 
 20 
 
 1615 
 
 50-70 
 
 204-251 
 
 
 
 
 
 
 19 
 
 20 
 
 2020 
 
 35-45 
 
 214-242 
 
 11 
 
 14 
 
 563 
 
 80-100 
 
 94-106 
 
 22 
 
 20 
 
 2714 
 
 25-30 
 
 223-255 
 
 12 
 
 14 
 
 671 
 
 60-75 
 
 95-108 
 
 25 
 
 20 
 
 3508 
 
 15-20 
 
 203-253 
 
 13 
 
 14 
 
 789 
 
 45-55 
 
 94-106 
 
 
 
 
 
 
 Stroke of cylinder, in. . 10 12 I2a 14 16 16ff 20 
 Revolutions per niin. . 225 210 210 185 170 170 155 
 Belt wheel, diameter in. 54 60 72 84 96 96 108 
 Belt wheel, face in 8l/ 2 101/2 12 1/2 161/2 20.1/2 281/2 31 1/2 
 
 "IMPERIAL XB-2" TWO-STAGE POW*ER~DRIVEN AIR COMPRESSORS. 
 For air pressure of 80 to 100 pounds per sq. in. For sea level. 
 
 Diameter of Air 
 Cylinders, Inches 
 
 Rev. 
 per 
 Min. 
 
 Piston 
 Dis- 
 place- 
 ment, 
 Cu. Ft. 
 Free Air 
 per Min. 
 
 Brake H.P. 
 Required at 
 Belt Wheel. 
 
 Belt 
 Wheel. 
 
 Low 
 Press. 
 
 High 
 Press. 
 
 Stroke. 
 
 Air Pressure. 
 
 Diam., 
 Inches. 
 
 Face, 
 Inches. 
 
 80 
 
 100 
 
 10 
 12 
 14 
 16 
 19 
 22 
 23 
 
 6V 2 
 7 V2 
 
 10 
 12 
 13 
 14 
 
 10 
 12 
 12 
 14 
 16 
 16 
 20 
 
 225 
 210 
 210 
 185 
 170 
 170 
 155 
 
 203 
 327 
 446 
 599 
 888 
 1190 
 1482 
 
 32 
 50 
 68 
 92 
 135 
 183 
 226 
 
 36 
 
 57 
 76 
 104 
 152 
 206 
 254 
 
 54 
 60 
 72 
 84 
 96 
 96 
 108 
 
 8V2 
 
 10i/ 2 
 
 121/2 
 
 16V 2 
 201/2 
 281/2 
 
 31V 2 
 
 For 5,000 feet altitude the low-pressure cylinders are made 1 inch 
 larger diameter, and for 10,000 feet altitude 2 inches larger. 
 
 "IMPERIAL X-2" DUPLEX STEAM-DRIVEN TWO-STAGE AIR COMPRESSORS. 
 
 Air cylinders of the same dimensions as the XB-2 compressors. 
 The duplex steam cylinders have diameters 7, 8, 9, 10, 12, and 14 
 inches. The 14 X 20-inch cylinder is designed for 150 r. p. m, 
 
TESTS OF AIK COMPRESSORS. 
 
 643 
 
 DUPLEX STEAM-DRIVEN "IMPERIAL X-l" COMPRESSORS. 
 For air pressures of 15 to 100 Ib. per sq. in. Steam, 80 to 120 Ib. 
 
 Cylinder 
 Diam., In. 
 
 jj 
 
 if* 
 
 || 
 
 Jti 
 
 Cylinder 
 Diam., In. 
 
 ri 
 
 |i 
 
 || 
 
 it 
 
 VI fc 
 
 Is 
 Ij 
 
 fa 
 
 0) 
 
 A* 
 
 ill 
 
 ,|> 
 
 aj 
 
 
 
 a as 
 
 3 
 
 h 
 
 1 
 
 AH' 
 tf 
 
 111 
 
 .!> 
 
 ^ 
 
 *I 
 
 
 Q 
 
 m 
 
 
 
 
 w 
 
 
 Q^ 
 
 *-> 
 
 
 
 
 -5 
 
 7 
 
 7 
 
 10 
 
 225 
 
 198 
 
 60-100 
 
 28-38 
 
 10 
 
 14 
 
 14 
 
 185 
 
 916 
 
 35-40 
 
 96-105 
 
 7 
 
 8 
 
 10 
 
 225 
 
 258 
 
 40-55 
 
 30-36 
 
 10 
 
 16 
 
 14 
 
 185 
 
 1198 
 
 25-30 
 
 103-116 
 
 7 
 
 9 
 
 10 
 
 225 
 
 327 
 
 27-35 
 
 27-34 
 
 10 
 
 18 
 
 1.4 
 
 185 
 
 1518 
 
 15-20 
 
 90-112 
 
 7 
 
 10 
 
 10 
 
 225 
 
 405 
 
 22-25 
 
 29-34 
 
 
 
 
 
 
 
 
 7 
 
 11 
 
 10 
 
 225 
 
 491 
 
 15-20 
 
 29-36 
 
 12 
 
 13 
 
 16 
 
 170 
 
 826 
 
 80-100 
 
 141-161 
 
 
 
 
 
 
 
 
 12 
 
 14 
 
 16 
 
 170 
 
 959 
 
 65-75 
 
 149-162 
 
 8 
 
 8 
 
 12 
 
 210 
 
 289 
 
 75-100 
 
 48-57 
 
 12 
 
 15 
 
 16 
 
 170 
 
 1103 
 
 45-60 
 
 135-163 
 
 8 
 
 9 
 
 12 
 
 210 
 
 367 
 
 55-70 
 
 51-60 
 
 12 
 
 17 
 
 16 
 
 170 
 
 1419 
 
 30-40 
 
 135-165 
 
 8 
 
 10 
 
 12 
 
 210 
 
 454 
 
 40-50 
 
 53-61 
 
 12 
 
 19 
 
 16 
 
 170 
 
 1775 
 
 20-25 
 
 128-151 
 
 8 
 
 11 
 
 12 
 
 210 
 
 549 
 
 27-35 
 
 46-59 
 
 12 
 
 21 
 
 16 
 
 170 
 
 2171 
 
 15-20 
 
 131-164 
 
 8 
 
 12 
 
 12 
 
 210 
 
 655 
 
 22-25 
 
 47-56 
 
 
 
 
 
 
 
 
 8 
 
 13 
 
 12 
 
 210 
 
 770 
 
 15-20 
 
 46-57 
 
 14 
 
 15 
 
 16 
 
 170 
 
 1100 
 
 80-100 
 
 186-212 
 
 
 
 
 
 
 
 
 14 
 
 16 
 
 16 
 
 170 
 
 1253 
 
 55-75 
 
 173-209 
 
 9 
 
 9 
 
 12 
 
 210 
 
 365 
 
 85-100 
 
 65-72 
 
 14 
 
 18 
 
 16 
 
 170 
 
 1592 
 
 35-50 
 
 166-212 
 
 9 
 
 10 
 
 12 
 
 210 
 
 453 
 
 60-80 
 
 67-79 
 
 14 
 
 21 
 
 16 
 
 170 
 
 2168 
 
 25-30 
 
 183-208 
 
 9 
 
 11 
 
 12 
 
 210 
 
 549 
 
 47-55 
 
 69-78 
 
 14 
 
 24 
 
 16 
 
 170 
 
 2836 
 
 15-20 
 
 168-209 
 
 9 
 
 12 
 
 12 
 
 210 
 
 654 
 
 37-45 
 
 69-81 
 
 
 
 
 
 
 
 
 9 
 
 13 
 
 12 
 
 210 
 
 769 
 
 25-35 
 
 66-84 
 
 14 
 
 15 
 
 20 
 
 150 
 
 1213 
 
 75-100 
 
 196-232 
 
 9 
 
 15 
 
 12 
 
 210 
 
 1025 
 
 15-20 
 
 61-76 
 
 14 
 
 17 
 
 20 
 
 150 
 
 1562 
 
 50-70 
 
 204-251 
 
 
 
 
 
 
 
 
 14 
 
 19 
 
 20 
 
 150 
 
 1955 
 
 35-45 
 
 204-242 
 
 10 
 
 11 
 
 14 
 
 185 
 
 563 
 
 80-100 
 
 98-110 
 
 14 
 
 22 
 
 20 
 
 150 
 
 2626 
 
 25-30 
 
 224-255 
 
 10 
 
 12 
 
 14 
 
 185 
 
 671 
 
 60-75 
 
 98-112 
 
 14 
 
 25 
 
 20 
 
 150 
 
 3395 
 
 15-20 
 
 203-253 
 
 10 
 
 13 
 
 14 
 
 185 
 
 789 
 
 45-55 
 
 97-110 
 
 
 
 
 
 
 
 
 COMPOUND STEAM CYLINDERS FOR "IMPERIAL X" COMPRESSORS. 
 
 For substituting in place of Duplex Steam Cylinders in the "Imperial 
 
 X-l and X-2" Tables for Steam-Pressures of 100 to 120 Lbs. 
 
 Condensing of Non-Condensing. 
 
 Compound Engines with Plain "D" 
 Steam Valves. 
 
 Compound Engines with Meyer 
 Cut-off Valves. 
 
 Standard 
 
 Standard 
 
 
 Standard 
 
 Standard 
 
 
 Duplex 
 Steam 
 
 Compound 
 Steam 
 
 Stroke. 
 
 Duplex 
 Steam 
 
 Compound 
 Steam 
 
 Stroke. 
 
 Cylinders. 
 
 Cylinders. 
 
 
 Cylinders. 
 
 Cylinders. 
 
 
 7& 7 
 
 7& 11 
 
 10 
 
 10& 10 
 
 12& 19 
 
 14 
 
 8&8 
 
 8& 13 
 
 12 
 
 12& 12 
 
 14&22 
 
 16 
 
 9&9 
 
 10& 16 
 
 12 
 
 14& 14 
 
 16& 25 
 
 16 
 
 
 
 
 14& 14 
 
 16&25 
 
 20 
 
 Tests of Power-driven Air Compressors. R. L. Webb, Portland, Ore., 
 has furnished the author with a copy of a complete report of a test 
 made by him in 1912, of three air compressors, two of them 18 in. diam. 
 X 12 in. stroke, rated at 1000 cu. ft. per min. displacement, and the 
 third 22 X 12 in., rated at 1500 cu. ft. Nos. 1 and 3 were designed for 
 35 to 45 Ib. gage-pressure and No. 2 for 15 to 20 Ib. The compres- 
 sors were driven by 500 volt d.c. shunt, commutating pole' motors, with 
 a speed range of 2 to 1 , through Link-Belt silent chain drives, 2 in. pitch, 
 9 in. wide, chain speed, 1600 ft. per min., pinions 17 and 64 teeth, chain 
 gear efficiency about 98%; gear submerged in oil. The speed control 
 was regulated by the air pressure. The air delivered was measured 
 
644 
 
 AIR. 
 
 by the orifice method, using Fliegner's equation. The results of the 
 tests are summarized in the table below: 
 
 TESTS OF AIR COMPRESSORS. 
 
 I 
 
 t.3 
 
 s l 
 
 Volumetric 
 Efficiency 
 Per cent. 
 
 Electric 
 Horse- 
 pttwer. 
 
 $ 
 
 Compressor No. 1, 18 X 12 in. 
 
 71.6 
 
 502.1 
 
 412.3 
 
 82.11 
 
 45.6 
 
 61.2 
 
 51.75 
 
 84.5 
 
 44.6 
 
 102.0 
 
 715.3 
 
 597.4 
 
 83.2 
 
 67.7 
 
 90.7 
 
 75.28 
 
 83.0 
 
 44.5 
 
 143.0 
 
 1002.8 
 
 873.3 
 
 87.1 
 
 87.1 
 
 133.4 
 
 106.73 
 
 80.0 
 
 44.2 
 
 Compressor No. 2, 22 X 12 in. 
 
 70.7 
 
 749.8 
 
 657.1 
 
 85.6 
 
 42.1 
 
 56.4 
 
 48.3 
 
 85.7 
 
 19.6 
 
 103.8 
 
 1100.8 
 
 986.0 
 
 89.5 
 
 65.0 
 
 87.1 
 
 73.1 
 
 83.0 
 
 19.2 
 
 141.0 
 
 1495.3 
 
 1333.9 
 
 89.2 
 
 97.6 
 
 130.8 
 
 106.5 
 
 80.0 
 
 19.5 
 
 Compressor No. 3, 18 X 12 in. 
 
 70.2 
 101.0 
 145.0 
 
 492.3 
 708.3 
 1016.9 
 
 371.1 
 567.2 
 837.1 
 
 75.4 
 80.1 
 82.3 
 
 43.9 
 65.8 
 100.7 
 
 58.8 
 88.3 
 135.0 
 
 50.0 
 73.4 
 109.1 
 
 85.0 
 84.0 
 80.7 
 
 44.8 
 44.7 
 44.4 
 
 Steam Required to Compress 100 Cu. Ft. of Free Air. (O. S. 
 
 Shantz, Power, Feb. 4, 1908.) The following tables show the number of 
 pounds of steam required to compress 100 cu. ft. of free air to different 
 gauge pressures, by means of steam engines using from 12 to 40 Ibs. of 
 steam per I.H.P. per hour. The figures assume adiabatic compression 
 in the air cylinders, with intercooling to atmospheric temperature in the 
 case of two-stage compression, and 90% mechanical efficiency of the 
 compressor. 
 
 STEAM CONSUMPTION OF AIR COMPRESSORS SINGLE-STAGE COMPRESSION. 
 
 Air 
 Gage 
 Pres- 
 sure. 
 
 Steam per I.H.P. Hour. Lb. 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 36 
 
 40 
 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 110 
 120 
 
 1.36 
 1 84 
 
 1.58 
 ? 14 
 
 1.82 
 ? 45 
 
 2.04 
 ? 76 
 
 2.26 
 3.06 
 
 [ 2.49 
 3 37 
 
 2.72 
 3 68 
 
 2.94 
 3.98 
 
 3.17 
 4 29 
 
 3.40 
 4.60 
 
 3.61 
 4.90 
 
 4.08 
 5 51 
 
 4.54 
 6 17. 
 
 2.26 
 2.62 
 2 92 
 
 2.64 
 3.06 
 3 41 
 
 3.02 
 3.50 
 3 % 
 
 3.39 
 3.93 
 4 38 
 
 3.77 
 4.36 
 4 80 
 
 4.15 
 4.80 
 5 36 
 
 4.52 
 5.25 
 5 85 
 
 4.90 
 5.68 
 6 32 
 
 5.26 
 6.10 
 
 6 80 
 
 5.65 
 6.55 
 7 30 
 
 6.03 
 7.00 
 7 80 
 
 6.78 
 8.86 
 8 76 
 
 7.50 
 8.71 
 9 71 
 
 3.22 
 3.50 
 3.72 
 3.96 
 4.18 
 4.38 
 
 3.76 
 4.08 
 4.34 
 4.61 
 4.87 
 5.11 
 
 4.30 
 4.67 
 4.96 
 5.29 
 5.58 
 5.85 
 
 4.83 
 5.25 
 5.58 
 5.95 
 6.26 
 6.57 
 
 5.36 
 5.84 
 6.20 
 6.60 
 6.96 
 7.30 
 
 5.90 
 6.42 
 6.82 
 7.25 
 7.66 
 8.04 
 
 6.45 
 7.00 
 7.45 
 7.92 
 8.36 
 8.76 
 
 6.97 
 7.59 
 8.05 
 8.58 
 9.05 
 9.50 
 
 7.50 
 8.15 
 8.66 
 9.22 
 9.75 
 10.20 
 
 8.05 
 8.75 
 9.30 
 9.90 
 10.45 
 10.95 
 
 8.60 
 9.34 
 9.94 
 10.56 
 11.15 
 11.66 
 
 9.66 
 10.50 
 11.15 
 11.88 
 12.52 
 13.13 
 
 10.70 
 11.61 
 12.35 
 13.15 
 13.90 
 14.55 
 
 TWO-STAGE COMPRESSION. 
 
 70 
 80 
 90 
 100 
 110 
 120 
 130 
 140 
 150 
 
 2.82 
 3.01 
 3.19 
 3.37 
 3.54 
 3.69 
 3.83 
 3.96 
 4.10 
 
 3.25 
 3.51 
 3.72 
 3.93 
 4.14 
 4.30 
 4.46 
 4.62 
 4.76 
 
 3.76 
 4.03 
 4.26 
 4.50 
 4.74 
 4.93 
 5.11 
 5.29 
 5.46 
 
 4.23 
 4.52 
 4.79 
 5.05 
 5.32 
 5.54 
 5.75 
 5.94 
 6.14 
 
 4.69 
 5.02 
 5.32 
 5.61 
 5.91 
 6.15 
 6.38 
 6.60 
 6.81 
 
 5.16 
 5.53 
 5.85 
 6.19 
 6.51 
 6.78 
 7.03 
 7.26 
 7.50 
 
 5.63 
 6.03 
 6.38 
 6.74 
 7.10 
 7.38 
 7.66 
 7.92 
 6.74 
 
 6.10 
 6.53 
 6.91 
 7.30 
 7.70 
 8.00 
 8.30 
 8.60 
 8.86 
 
 6.56 
 7.03 
 7.44 
 7.85 
 8.27 
 8.61 
 8.92 
 9.23 
 9.55 
 
 7.04 
 7.53 
 7.98 
 8.42 
 8.86 
 9.24 
 9.57 
 9.90 
 10.20 
 
 7.50 
 8.03 
 8.50 
 8.99 
 9.46 
 9.85 
 10.20 
 10.56 
 10.90 
 
 8.45 
 9.05 
 9.57 
 10.10 
 10.64 
 11.05 
 11.48 
 11.88 
 12.26 
 
 9.35 
 10.01 
 10.60 
 11.20 
 11.80 
 12.27 
 12.72 
 13.15 
 13.60 
 
COMPRESSED AIR FOR PUMPING. 
 
 645 
 
 Cubic Feet of Air Required to Run Rock Drills at Various Pressures 
 and Altitudes. 
 
 (Ingersoll-Rand Co., 1908.) 
 TABLE I. CUBIC FEET OF FREE AIR REQUIRED TO RUN ONE DRILL. 
 
 Gauge Pressure, 
 Lb. per Sq. In. 
 
 Size and Cylinder Diameter of Drill. 
 
 A 35 
 
 A 32 
 A 86 
 
 B 
 
 C 
 
 D 
 
 D 
 
 D 
 
 E 
 
 F 
 
 F 
 
 G 
 
 H 
 
 H9 
 
 2" 
 
 21/4* 
 
 21/2" 
 
 23/4* 
 
 3" 
 
 31/8* 
 
 33/16* 
 
 31/ 4 " 
 
 31/2* 
 
 35/ 8 " 
 
 41/4* 
 
 5" 
 
 5V2" 
 
 60 
 70 
 80 
 90 
 100 
 
 50 
 56 
 63 
 70 
 
 77 
 
 60 
 68 
 76 
 84 
 92 
 
 68 
 77 
 86 
 95 
 104 
 
 82 
 93 
 104 
 115 
 126 
 
 90 
 102 
 114 
 126 
 138 
 
 95 
 108 
 120 
 133 
 146 
 
 97 
 110 
 123 
 136 
 149 
 
 100 
 113 
 127 
 141 
 154 
 
 108 
 124 
 131 
 152 
 166 
 
 113 
 129 
 143 
 159 
 174 
 
 130 
 147 
 164 
 182 
 199 
 
 150 
 170 
 190 
 210 
 240 
 
 164 
 181 
 207 
 230 
 252 
 
 TABLE II. MULTIPLIERS TO GIVE CAPACITY OF COMPRESSOR TO OPERATE 
 
 FROM 1 TO 70 ROCK DRILLS AT VARIOUS ALTITUDES. 
 
 Number of Drills. 
 
 ^g 
 
 +2GQ 
 < 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 40 
 
 50 
 
 
 1030 
 2330 
 3300 
 5300 
 8030 
 13330 
 13030 
 
 1. 
 1.03 
 1.07 
 1.10 
 1.17 
 1.26 
 1.32 
 1.43 
 
 1.8 
 1.85 
 9? 
 
 2.7 
 
 2.78 
 789 
 
 3.4 
 3.5 
 3 64 
 
 4.1 
 
 4.22 
 439 
 
 4.8 
 4.94 
 5 14 
 
 5.4 
 5.56 
 
 5 78 
 
 6.0 
 6.18 
 64? 
 
 6.5 
 6.69 
 695 
 
 7.1 
 7.3 
 
 760 
 
 9.5 
 9.78 
 10.17 
 
 11.7 
 12.05 
 1252 
 
 13.7 
 14.1 
 1466 
 
 15.8 
 16.3 
 169 
 
 21.4 
 22.0 
 22.9 
 23.54 
 25.04 
 26.% 
 28.25 
 30.6 
 
 25.5 
 26.26 
 27.28 
 28.05 
 29.84 
 32.13 
 33.66 
 36.49 
 
 .98 
 2.10 
 2.27 
 2.38 
 2.57 
 
 2.97 
 3.16 
 3.40 
 3.56 
 3.86 
 
 3.74 
 3 98 
 
 4.28 
 4.49 
 4.86 
 
 4.51 
 4.8 
 5.17 
 5.41 
 5.86 
 
 5.28 
 5.62 
 6.05 
 6.34 
 6.86 
 
 5.94 
 6.32 
 6.8 
 7.13 
 7.72 
 
 6.6 
 7.02 
 7.56 
 7.92 
 8.58 
 
 7.15 
 7.61 
 8.19 
 8.58 
 9.3 
 
 7.81 
 8.31 
 8.95 
 9.37 
 10.15 
 
 10.45 
 11.12 
 11.97 
 12.54 
 13.58 
 
 12.87 
 13.69 
 14.74 
 15.44 
 16.73 
 
 15.07 
 16.03 
 17.26 
 18.08 
 19.59 
 
 17.38 
 18.49 
 19.9 
 20.86 
 22.59 
 
 EXAMPLE. Required the amount of free air to operate thirty 5-inch 
 "H" drills at 8,000 ft. altitude, using air at a gauge pressure of 80 Ib per 
 sq. in. From Table I, we find that one 5-inch " H " drill operating at 80 Ib. 
 
 fauge pressure requires 190 cu. ft. of free air per minute. From Table 
 I, the factor for 30 drills at 8,000 feet altitude is 19.9; 190 X 19.9 = 
 3781 = the displacement of a compressor under average conditions, to 
 which must be added pipe line losses. 
 
 The tables above are for fair conditions in ordinary hard rock. In 
 soft material, where the drilling time is short more drills can be run with 
 a given compressor than when working in hard material. In tunnel 
 work, more rapid progress can be made if the drills are run at high air 
 pressure, and it is advisable to have an excess of compressor capacity 
 of about 25%. No allowance has been made in the tables for friction 
 of pipe line losses. 
 
 Compressed-air Table for Pumping Plants* 
 (Ingersoll-Rand Co., 1908.) 
 
 The following table shows the pressure and volume of air required for 
 any size pump for pumping by compressed air. Reasonable allowances 
 have been made for loss due to clearances in pump and friction in pipe. 
 
 To find the amount of air and pressure required to pump a given quan- 
 tity of water a given height, find the ratio of diameters between water 
 and air cylinders, and multiply the number of gallons of water by the 
 
646 
 
 AIR. 
 
 figure found in the column for the required lift. The result is the number 
 of cubic feet of free air. The pressure required on the pump will be found 
 directly above in the same column. For examole: The ratio between 
 cylinders being 2 to 1, required to pump 100 gallons, height of lift 250 
 feet. We find under 250 feet at ratio 2 to 1 the figures 2.11 ; 2.11 X 100 = 
 211 cubic feet of free air. The pressure required is 34.38 pounds deliv- 
 ered at the pump piston. 
 
 Ratio of 
 Diameters. 
 
 
 Perpendicular Height, in Feet, to which the Water 
 is to be Pumped. 
 
 25 
 
 50 
 
 75 
 
 100 
 
 125 
 
 150 
 
 175 
 
 200 
 
 250 
 
 300 
 
 400 
 
 1 to 1 
 1 1/2 to 1 
 1 3/4 to 1 
 2 to 1 
 2 1/4 to 1 
 2l/ 2 to 1 { 
 
 A 
 B 
 A 
 B 
 A 
 B 
 A 
 B 
 A 
 B 
 A 
 B 
 
 13.75 
 0.21 
 
 27.5 
 0.45 
 12.22 
 0.65 
 
 41.25 
 0.60 
 18.33 
 0.80 
 13.75 
 0.94 
 
 55.0 
 0.75 
 24.44 
 0.95 
 19.8 
 1.14 
 13.75 
 1.23 
 
 68.25 
 0.89 
 30.33 
 1.09 
 22.8 
 1.24 
 17.19 
 1.37 
 13.75 
 1.53 
 
 82.5 
 1.04 
 36.66 
 1.24 
 27.5 
 1.30 
 20.63 
 1.52 
 16.5 
 1.68 
 13.2 
 1.79 
 
 96.25 
 1.20 
 42.76 
 1.39 
 32.1 
 1.54 
 24.06 
 1.66 
 19.25 
 1.83 
 15.4 
 1.98 
 
 110.0 
 1.34 
 48.88 
 1.53 
 36.66 
 1.69 
 27.5 
 1.81 
 22.0 
 1.97 
 17.6 
 2.06 
 
 
 
 
 
 
 
 61.11 
 1.83 
 45.83 
 1.99 
 34.38 
 2.11 
 27.5 
 2.26 
 22.0 
 2.34 
 
 73.32 
 2.12 
 55.0 
 2.39 
 41.25 
 2.40 
 33.0 
 2.56 
 26.4 
 2.62 
 
 97.66 
 2.70 
 73.33 
 2.88 
 55.0 
 2.98 
 44.0 
 3.15 
 35.2 
 3.18 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A = air-pressure at pump. B = cubic feet of free air per gallon of water. 
 
 Compressed-air Table for Hoisting-engines. 
 
 (Ingersoll-Rand Co., 1908.) 
 
 The following table gives an approximate idea of the volume of free air 
 required for operating hoisting-engines, the air being delivered to the 
 engine at 60 Ibs. gauge. There are so many variable conditions to the 
 operation of hoisting-engines in common use that accurate computations 
 can only be offered when fixed data are given. In the table the engine is 
 assumed to actually run but one-half of the time for hoisting, while the 
 compressor runs continuously. If the engine runs less than one-half the 
 time, the volume of air required will be proportionately less, and vice 
 versa. The table is computed for maximum loads, which also in practice 
 may vary widely. From the intermittent character of the work of a 
 hoisting-engine the parts are able to resume their normal temperature 
 between the hoists, and there is little probability of freezing up the 
 exhaust-passages. 
 
 Volume of Free Air Required for Operating Hoisting-engines, the 
 Air Compressed to 6O Pounds Gauge Pressure. 
 
 SINGLE-CYLINDER HOISTING-ENGINE. 
 
 Diam. of 
 Cylinder, 
 Inches. 
 
 Stroke, 
 Inches. 
 
 Revolu- 
 tions per 
 Minute. 
 
 Normal 
 Horse- 
 power. 
 
 Actual 
 Horse- 
 power. 
 
 Weight 
 Lifted, 
 Single 
 Rope. 
 
 Cubic Ft. 
 of Free Air 
 Required. 
 
 5 
 
 61/4 
 81/4 
 
 , 8 o V2 
 
 6 
 
 8 
 8. 
 10 
 10 
 12 
 12 
 
 200 
 160 
 160 
 125 
 125 
 110 
 110 
 
 3 
 
 4 
 6 
 10 
 . 15 
 20 
 25 
 
 5.9 
 6.3 
 9.9 
 12.1 
 16.8 
 18.9 
 26.2 
 
 600 
 1,000 
 1,500 
 2,000 
 3,000 
 5,000 
 6000 
 
 75 
 
 80 
 125 
 151 
 170 
 
 238 
 330 
 
COMPRESSED AIR. 
 
 DOUBLE-CYLINDER HOISTING-ENGINE. 
 
 647 
 
 Diam. of 
 Cylinder, 
 Inches. 
 
 Stroke, 
 Inches. 
 
 Revolu- 
 tions per 
 Minute. 
 
 Normal 
 Horse- 
 power. 
 
 Actual 
 Horse- 
 power. 
 
 Weight 
 Lifted, 
 Single 
 Rope. 
 
 Cubic Ft. 
 of Free Air 
 Required. 
 
 5 
 
 6 
 
 200 
 
 6 
 
 11.8 
 
 1 ,000 
 
 150 
 
 5 
 
 8 
 
 160 
 
 8 
 
 12.6 
 
 1,650 
 
 160 
 
 61/4 
 
 8 
 
 160 
 
 12 
 
 19.8 
 
 2,500 
 
 250 
 
 7 
 
 10 
 
 125 
 
 20 
 
 24.2 
 
 3,500 
 
 302 
 
 81/4 
 
 10 
 
 125 
 
 30 
 
 33.6 
 
 6000 
 
 340 
 
 81/2 
 
 12 
 
 110 
 
 40 
 
 37.8 
 
 8000 
 
 476 
 
 10 
 
 12 
 
 110 
 
 50 
 
 52.4 
 
 lO'.OOO 
 
 660 
 
 121/4 
 
 15 
 
 100 
 
 75 
 
 89.2 
 
 
 1,125 
 
 14 
 
 18 
 
 90 
 
 100 
 
 125. 
 
 
 1,587 
 
 
 
 
 
 
 
 
 Practical Results with Compressed Air. Compressed-air System 
 at the Chapin Mines, Iron Mountain, Mich. These mines are three miles 
 from the falls which supply the power. There are four turbines at the 
 falls, one of 1000 horse-power and three of 900 horse-power each. The 
 pressure is 60 pounds at 60 Fahr. Each turbine runs a pair of compress- 
 ors. The pipe to the mines is 24 ins. diameter. The power is applied at 
 the mines to Corliss engines, running pumps, hoists, etc., and direct to 
 rock-drills. 
 
 A test made in 1888 gave 1430.27 H.P. at the compressors, and 390.17 
 H.P. as the sum of the horse-power of the engines at the mines. There- 
 fore, only 27% of the power generated was recovered at the mines. This 
 includes the loss due to leakage and the loss of energy in heat, but not the 
 friction in the engines or compressors. (F. A. Pocock, Trans. A. I. M. E., 
 1890.) 
 
 W. L. Saunders (Jour. F.I., 1892) says: "There is not a properly designed 
 compressed-air installation in operation to-day that loses over 5% by 
 transmission alone. The question is altogether one of the size of pipe; 
 and if the pipe is large enough, the friction loss is a small item. 
 
 " The loss of power in common practice, where compressed air is used 
 to drive machinery in mines and tunnels, is about 70% . In the best prac- 
 tice, with the best air-compressors, and without reheating, the loss is about 
 60%. These losses may be reduced to a point as low as 20% by combin- 
 ing the best systems of 'reheating with the best air-compressors." 
 
 Gain due to Reheating:. Prof. Kennedy says compressed-air trans- 
 mission system is now being carried on, on a large commercial scale, 
 in such a fashion that a small motor four miles away from the central 
 station can indicate in round numbers 10 horse-power, for 20 horse- 
 power at the station itaelf, allowing for the value of the coke used in heat- 
 ing the air. 
 
 The limit to successful reheating lies in the fact that air-engines can- 
 not work to advantage at temperatures over 350. 
 
 The efficiency pf the common system of reheating is shown by the re- 
 sults obtained with the Popp system in Paris. Air is admitted to the 
 reheater at about 83, and passes to the engine at about 3i5, thus being 
 increased in volume about 42%. The air used in Paris is about 11 cubic 
 feet of free air per minute per horse-power. The ordinary practice in 
 America with cold air is from 15 to 25 cubic feet per minute per horse- 
 power. When the Paris engines were worked without reheating the air 
 consumption was increased to about 15 cubic feet per horse-power per 
 minute. The amount of fuel consumed during reheating is trifling. 
 
 Effect of Temperature of Intake upon the Discharge of a Com- 
 pressor. Air should be drawn from outside the engine-room, and 
 from as cool a place as possible. The gain in efficiency amounts to one 
 per cent for every five degrees that the air is taken in lower than the 
 temperature of the engine-room. The inlet conduit should have an area 
 at least 50% of the area of the air-piston, and should be made of wood, 
 brick, or other non-conductor of heat. 
 
 Discharge of a compressor having an intake capacity of 1000 cubic feet 
 per minute, and volumes of the discharge reduced to cubic feet at atmos- 
 pheric pressure and at temperature of 62 degrees Fahrenheit: 
 Temperature of Intake, F. ... 32 62 75 80 90 100 110 
 V"Jume discharged, cubic ft. U35 1060 1000 975 966 949 932 910 
 
648 
 
 AIR. 
 
 Compressed-Air Motors with a Return Air Circuit. In the ordinary 
 use of motors, such as rock-drills, the air, after doing its work in the 
 motor, is allowed to escape into the atmosphere. In some systems, 
 however, notably in the electric air-drill, the air exhausted from the 
 cylinder of the motor is returned to the air compressor. A marked 
 increase in economy is claimed to have been effected in this way (Cass. 
 Mag., 1907). 
 
 Intercoolers for Air Compressors. H. V. Haight (Am. Mach., 
 Aug. 30, 1906). In multi-stage air compressors, the efficiency is greater 
 the more nearly the temperature of the air leaving the intercooler ap- 
 proaches that of the water entering it. The difference of these tem- 
 peratures for given temperatures of the entering water and air is 
 diminished by increasing the surface of the intercooler and thereby 
 decreasing the ratio of the quantity of air cooled to the area of cooling 
 surface. Numerous tests of intercoolers with different ratios of quan- 
 tity of air to area of surface, on being plotted, approximate to a straight- 
 line diagram, from which the following figures are taken. 
 Cu. ft. of free air per min. per sq. ft. of air cooling surface 5 10 15 
 Diff.of temp. F. between water entering and air leaving 12.5 25 37.5 
 
 Centrifugal Air Compressors. The General Electric Company has 
 placed on the; market a line of single stage centrifugal air compressors 
 with pressure ratings from 0.75 to 4 Ib. per sq. in., and capacity from 
 500 to 10,000 cu. ft. of free air per min. The compresspr consists 
 essentially of a rotating impeller surrounded by a rigid cast-iron casing 
 and suitable conversion nozzles to convert velocity of the air into 
 pressure. It is similar to the centrifugal pump, efficiency depending 
 entirely upon the design of the passages throughout the machine. 
 
 The compressors are driven by Curtis steam-turbines or by electric 
 motors specially designed for thein. The induction nwtors used are of 
 the squirrel-cage type which do not permit any variation in the speed 
 and care must be taken to specify a pressure sufficiently high to coyer 
 the operating requirements, because the pressure cannot be varied 
 at constant speed without altering the design of the impeller. The 
 pressure of the D. C. motor-driven unit can be changed by changing 
 the speed of the motor by means of the field rheostat. 
 
 
 Standard 
 
 Off-Standard 
 
 Off-Standard 
 
 
 
 Designs, 
 
 Designs, 
 
 Designs, 
 
 
 Motor 
 
 3450 r.p.m. 
 
 3450 r.p.m. 
 
 3850 r.p.m. 
 
 Pipe 
 
 Rating 
 H.P. 
 
 Lb. 
 
 Cu. Ft. 
 
 Lb. 
 
 Cu. Ft. 
 
 Lb. 
 
 Cu. Ft. 
 
 Diam., 
 Inches. 
 
 
 per 
 
 per 
 
 per 
 
 per 
 
 per 
 
 per 
 
 
 
 Sq. In. 
 
 Min. 
 
 Sq. In. 
 
 Min. 
 
 Sq. In. 
 
 Min. 
 
 
 5 
 
 
 800 
 
 0.75 
 
 1,100 
 
 .25 
 
 600 
 
 10 
 
 10 
 
 
 1,600 
 
 0.75 
 
 2,100 
 
 .25 
 
 1,300 
 
 12 
 
 20 
 
 
 3,200 
 
 0.75 
 
 4,100 
 
 .25 
 
 2,600 
 
 16 
 
 30 
 
 
 4,500 
 
 0.75 
 
 5,900 
 
 .25 
 
 3,800 
 
 20 
 
 50 
 
 
 7,200 
 
 0.75 
 
 8,800 
 
 .25 
 
 6,000 
 
 20 
 
 75 
 
 
 10,200 
 
 0.75 
 
 12,000 
 
 .25 
 
 8,700 
 
 26 
 
 10 
 
 2 
 
 750 
 
 1.5 
 
 1,000 
 
 2.50 
 
 500 
 
 8 
 
 20 
 
 2 
 
 1,600 
 
 1.5 
 
 2,103 
 
 2.50 
 
 1,200 
 
 10 
 
 30 
 
 2 
 
 2,500 
 
 1.5 
 
 3,300 
 
 2.50 
 
 1,900 
 
 12 
 
 50 
 
 2 
 
 4,200 
 
 1.5 
 
 5,400 
 
 2.50 
 
 3,300 
 
 16 
 
 75 
 
 2 
 
 6,200 
 
 1.5 
 
 8,000 
 
 2.50 
 
 5,000 
 
 20 
 
 30 
 
 3.25 
 
 1,250 
 
 2.5 
 
 1,800 
 
 4.00 
 
 900 
 
 8 
 
 50 
 
 3.25 
 
 2,400 
 
 2.5 
 
 3,200 
 
 4.00 
 
 1,900 
 
 12 
 
 75 
 
 3.25 
 
 3,800 
 
 2.5 
 
 5,000 
 
 4.00 
 
 3,000 
 
 14 
 
 Multi-stage compressors have been built in the following sizes: 
 
 Cubic feet free air 
 
 per 'minute 4,500 9,000 16,000 25,000 40,000 50,000. 
 
 Pressure, pounds 
 
 per square inch. . 6 to 35 6 to 25 8 to 25 12 to 30 12 to 30 12 to 30 
 AS in the case of centrifugal pumps, the pressure depends upon the 
 
HIGH PRESSURE CENTRIFUGAL FANS. 649 
 
 peripheral velocity of the impeller. The volume of free air delivered 
 is limited, however, by the capacity of the driver. It must never be 
 operated without being piped to a load sufficient to restrict the flow of 
 air to the rated value, otherwise the driver will become seriously 
 overloaded. 
 
 The power required to drive the centrifugal compressor varies ap- 
 proximately with the volume of air delivered when operating at a 
 constant speed, between the limits of 50 per cent and 125 per cent of 
 the rated load. This gives flexibility and economy to the centrifugal 
 type where variable volumetric loads are required. 
 
 When the compressor is operating as an exhauster discharging against 
 atmospheric pressure, the rated pressure P, in Ib. per sq. in., must 
 be multiplied by 14.7 and then divided by 14.7 plus P to obtain the 
 vacuum in Ibs. per sq. in. below atmosphere. The rated pressures are 
 ?iven for an atmospheric pressure of 14.7 Ib. per sq. in. and a tempera- 
 ture of 60 F. When the compressors are operated at an altitude, the 
 pressure will be reduced directly in proportion to the barometric 
 pressure. For other temperatui es, the pressures will be inversely 
 proportioned to the absolute temperature, or P X 520 -r- (460 + T). 
 When operated on gas the rated pressure is to be corrected by multiply- 
 ing it by the relative density of the gas, taking air = 1. A large 
 number of machines have been installed to operate on illuminating 
 ?as, by-product coke oven gas, or producer gas. Constant suction 
 governors controlling the speed of the turbine drivers are employed 
 where close control of the suction head is desired, as in the case of gas 
 exhausters. 
 
 Ten large machines (2000 to 5000 H.P.) for blowing blast furnaces 
 have also been installed. These have steam turbines for drivers and 
 are controlled by constant volume governors, giving a constant speed, 
 so that a definite volume of air per minute is delivered, regardless of 
 the resistance of the furnace. 
 
 High-Pressure Centrifugal Fans. (A. Rateau, Engg., Aug. 16, 1907.) 
 In 1900, a single wheel fan driven by a steam turbine at 20,200 revs, per 
 min. gave an air pressure of 81/4 IDS. per sq. in.; an output of 26.7 cu. ft. 
 free air per second; useful work in H.P. adiabatic compression, 45.5; 
 theoretical work in H.P. of steam-flow, 162; efficiency of the set, fan and 
 turbine, 28%. An efficiency of 30.7% was obtained with an output of 
 23 cu. ft. per sec. and 132 theoretical H.P. of steam. The pressure 
 obtained with a fan is all things being equal proportional to the 
 specific weight of the gas which flows through it ; therefore, if, instead of 
 air at atmospheric pressure, air, the pressure of which has already been 
 raised, or a gas of higher density, such as carbonic acid, be used, com- 
 paratively higher pressures still will be obtained, or the engine can. run at 
 lower speeds for the same increase of pressure. 
 
 Multiple Wheel Fans. The apparatus having a single impeller gives 
 satisfaction only when the duty and speed are sufficiently high. The 
 speed is limited by the resistance of the metal of which the impeller is 
 made, and also by the speed of the motor driving the fan. But by con- 
 necting several fans in series, as is done with high-lift centrifugal pumps, 
 it is possible to obtain as high a pressure as may be desired. 
 
 Turbo-Compressor, Bethune Mines, 1906. This machine compresses air 
 to 6 and 7 atmospheres by utilizing the exhaust steam from the winding- 
 engines. It consists of four sets of multi-cellular fans through which the 
 air flows in succession. They are fitted on two parallel shafts, and each 
 shaft is driven by a low-pressure turbine. A high-pressure turbine is 
 also mounted on one of the shafts, but supplies no work in ordinary times. 
 An automatic device divides the load equally between the two shafts. 
 Between the two compressors are fitted refrigerators, in which cold water 
 is made to circulate by the action of a small centrifugal pump keyed at 
 the end of the shaft. In tests at a speed of 5000 r.p.m., the volume of 
 air drawn per second was 31.7 cu. ft. and the discharge pressure 119.5 Ib. 
 per sq. in. absolute. These conditions of working correspond to an effect- 
 ive work in isothermal compression of 252 H.P. The efficiency of the 
 compressor has been as high as 70%. The results of two tests of the 
 compressor are given below. In the first test the air discharged, reduced 
 to atmospheric pressure, was 26 cu. Ct. per sec.; in the second test it was 
 46 cu, *W 
 
650 
 
 FIRST TEST. 
 
 Stages. 1st. 2d. 3d. 4th. 
 
 Abs. pressure at inlet, Ibs. per sq. in. ... 15.18 23.37 38.69 66.44 
 
 Abs. pressure at discharge 24 . 10 39 . 98 66 . 44 102 . 60 
 
 Speed, revs, per min 4660 4660 4660 4660 
 
 Temperature of air at inlet, deg. F. ... 57.2 67.8 63. 66. 
 
 Temperature of air at discharge, deg. F. 171. 205. 216. 215.6 
 
 Adiabatic rise in temp., deg. F 106. 122. 114.8 105.8 
 
 Actual rise in temperature; deg. F. ... 113.8 137.2 153. 149.6 
 
 Efficiency, per cent 60.5 60.5 54. 46.2 
 
 SECOND TEST. 
 
 Stages. 1st. 2d. 3d. 4th. 
 
 Abs. pressure at inlet, Ibs. per sq. in 15.18 21.31 37.33 65.12 
 
 Abs. pressure at discharge 23.52 38 . 22 65 . 1 2 99 . 66 
 
 Speed, revs, per min 5000 5000 4840 4840 
 
 Temp, of air at inlet, deg. F 55 . 69 . 8 64 . 4 68 . 5 
 
 Temp, of air at discharge, deg. F 160.7 208.4 208.4 199.6 
 
 Adiabatic rise in temp., deg. F 102.2 131. 123.8 100.4 
 
 Efficiency, per cent 62.3 66.6 58.7 48.6 
 
 The Gutehoffnungshiitte Co. in Germany have m course of construc- 
 tion several centrifugal blowing-machines to be driven by an electric 
 motor, and up to 2000 H.P. Several machines are now being designed 
 for Bessemer converters, some of which will develop urj to 4000 H.P. 
 The multicellular centrifugal compressors are identical in every point 
 with centrifugal pumps. In the new machines cooling water is intro- 
 duced inside the diaphragms, which are built hollow for this purpose, 
 and also inside the diffuser vanes. By this means it is hoped to reduce 
 proportionally the heating of the air: thus approaching isothermal com- 
 pression much more nearly than is done in the case of reciprocating 
 compressors. 
 
 Test of a Hydraulic Air Compressor. (W. O. Webber, Trans. 
 A. S. M. E., xxii, 599.) The compressor embodies the principles of 
 the old trompe used in connection with the Catalan forges some centuries 
 ago, modified according to principles first described by J. P. Frizell, in 
 Jour. F. /., Sept., 1880, and improved by Charles H. Taylor, of Montreal. 
 (Patent July 23, 1895.) It consists principally of a down-flow passage 
 having an enlarged chamber at the bottom and an enlarged tank at 
 the top. A series of small air pipes project into the mouth of the water 
 inlet and the large chamber at the upper end of the vertically descending 
 passage, so as to cause a number of small jets of air to be entrained by the 
 water. At the lower end of the apparatus, deflector plates in connection 
 with a gradually enlarging section of the lower end of the down-flow pipe 
 are used to decrease the velocity of the air and water, and cause a partial 
 separation to take place. The deflector plates change the direction of 
 the flow of the water and are intended to facilitate the escape of the air, 
 the water then passing out at the bottom of the enlarged chamber into an 
 ascending shaft, maintaining upon the air a pressure due to the height of 
 the water in the uptake, the compressed air being led on from the top 
 of the enlarged chamber by means of a pipe. The general dimensions of 
 the compressor plant are: 
 
 Supply penstock, 60 ins. diam.; supply tank at top, 8 ft. diam. X 10 ft. 
 high; air inlets (feeding numerous small tubes), 34 2-in. pipes; down tube, 
 44 ins. diam.: down tube, at lower end, 60 ins. diam.; length of taper in 
 down tube, 20 ft.; air chamber in lower end of shaft, 16 ft. diam.; total 
 depth of shaft below normal level of head water, about 150ft.; normal 
 head and fall, about 22 ft.; air discharge pipe, 7 ins. diam. 
 
 It is used to supply power to engines for operating the printing depart- 
 ment of the Dominion Cotton Mills, Magog, P. Q., Canada. 
 
 There were three series of tests, viz.: (1) Three tests at different rates 
 of flow of water, the compressor being as originally constructed. (2) Four 
 tests at different rates of flow of water, the compressor inlet tubes for air 
 being increased by 30 3/ 4 -in. pipes. (3) Four tests at different rates of 
 flow of water, the compressor inlet tubes for air being increased by 153/4-m. 
 pipes. 
 
HYDRAULIC AIR COMPRESSION. 
 
 651 
 
 The water used was measured by a weir, and the compressed air by air 
 meters. The table on p. 623 shows the principal results: 
 
 Test 1, when the flow was about 3800 cu. ft. per min., showed a decided 
 advantage by the use of 30 3/ 4 _in. extra air inlet pipes. Test 5 shows, 
 when the flow of water is about 4200 cu. ft. per mm., that the economy 
 is highest when only 15 extra air tubes are employed. Tests 8 and 9 show, 
 when the flow is about 4600 cu. ft. per min., that there is no advantage in 
 increasing the air-inlet area. Tests 10 and 11 show that a flow of 5000 
 or more cu. ft. of water is in excess of the capacity of the plant. These 
 four tests may be summarized as follows: 
 
 The tests show: (1) That the most economic rate of flow of water with 
 this particular installation is about 4300 cu. ft. per min. (2) That this 
 plant has shown an efficiency of 70.7 % under such a flow, which is ex- 
 cellent for a first installation. (3) That the compressed air contains only 
 from 30 to 20% as much moisture as does the atmosphere. (4) That the 
 air is compressed at the temperature of the water. 
 
 Using an old Corliss engine without any changes in the valve gear 
 as a motor there was recovered 81 H.P. This would represent a total 
 efficiency of work recovered from the falling water, of 51.2%. When 
 the compressed air was preheated to 267 F. before being used in the 
 engine, 111 H.P. was recovered, using 115 Ibs. coke per hour, which would 
 equal about 23 H.P. The efficiency of work recovered from the falling 
 water and the fuel burned would be, therefore, about 61 1/2% . On the basis 
 
 of Prof. Riedler's experiments, which require only about 425 cu. ft. of air 
 per B.H.P. per hour, when preheated to 300 F. and used in a hot-air 
 jacketed cylinder, the total efficiency secured would have been about 
 
 871/2%. 
 
 Test No 
 
 1 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 
 
 10 
 
 
 Flow of water, cu. ft. per min.. . 
 Available head in ft. . . . 
 
 3772 
 20.54 
 146.3 
 
 864 
 51.9 
 
 83.3 
 56.8 
 68.3 
 
 66 
 4.37 
 
 61 
 51.5 
 
 3628 
 20.00 
 136.9 
 
 901 
 53.7 
 
 88.2 
 64.4 
 57.7 
 
 65.5 
 4.03 
 
 77.5 
 44 
 
 4066 
 20.35 
 156.2 
 
 967 
 53.2 
 
 94.3 
 60,3 
 66.4 
 
 66.4 
 4.20 
 
 7! 
 
 38.5 
 
 4292 
 19.51 
 158.1 
 
 1148 
 53.3 
 
 111.74 
 70.7 
 65.2 
 
 66.5 
 3.74 
 
 68 
 35 
 
 4408 
 19.93 
 165.8 
 
 1091 
 53.7 
 
 107 
 64.5 
 59.7 
 
 67 
 
 4.04 
 
 90 
 
 29 
 
 4700 
 19.31 
 171.4 
 
 1103 
 52.9 
 
 r06.8 
 62.2 
 65 
 
 66.5 
 4.26 
 
 60.5 
 31.2 
 
 5058 
 18.75 
 179.1 
 
 1165 
 53.3 
 
 113.4 
 63.3 
 64.2 
 
 66 
 4.34 
 
 63 
 30 
 
 Gross water, H.P 
 
 Cu. ft. air, at atmos. press., per 
 minute 
 
 Pressure of air at comp., Ibs 
 Effective work in compressing, 
 H.P 
 
 Efficiency of compressor, % 
 Temp, of external air, deg. F.. . . 
 Temp, of water and comp. air, 
 deg. F 
 
 Ratio of water to air, volumes... 
 Moisture in external air, p. c. of 
 saturation , 
 
 Moisture in comp. air, p. c. of 
 saturation 
 
 
 Tests 1, 4, and 7 were made with the original air inlets; 2, 5, 8 and 10 
 with the inlets increased by 153/4-in. pipes, and 3, 6, 9 and 11 with the 
 inlets increased by 303/4-in. pipes. Tests 2, 6,9 and 11 are omitted here. 
 They gave, respectively, 55.5, 61.3, 62, and 55.4% efficiency. 
 
 Three other hydraulic air-compressor plants are mentioned in Mr. 
 Webber's paper, some of the principal data of which are given below: 
 
 Peterboro, Norwich, 
 
 Ont. Conn. 
 
 Head of water 14ft. 18^ ft. 
 
 Gauge pressure 25 Ibs. 85 Ibs. 
 
 Diam. of shaft 42 in. 24 ft. 
 
 Diam. of compressor pipe 18 ft. 13 ft. 
 
 Depth below tailrace 64 ft. 215 ft. 
 
 Horse-power 1365 
 
 Cascade 
 Range, 
 Wash. 
 
 45 ft. 
 
 85 Ibs. 
 
 3 ft. 
 200 
 
 In the Cascade Range plant there is no shaft, as the apparatus is con- 
 structed against the vertical walls of a canyon. The diameter of tne up- 
 flow pipe is 4 ft. 9 in. 
 
652 AIR. 
 
 A description of the Norwich plant is given by J. Herbert Shedd In a 
 paper read before the New England Water Works Assn., 1905 (Compressed 
 Air, April, 1906). The shaft, 24 ft. diam., is enlarged at the bottom into 
 a chamber 52 ft. diam., from which leads an air reservoir 100 ft. long, 18 ft. 
 wide and 15 to 20 ft. high. Suspended in the shaft is a downflow pipe 
 14 ft. diam. connected at the top with a head tank, and at the bottom with 
 the air-chamber, from which a 16-in. main conveys the air four miles to 
 Norwich, where it is used in engines in several establishments. 
 
 The Mekarski Compressed-air Tramway at Berne, Switzerland. 
 (Eng'q News, April 20, 1893.) The Mekarski system has been intro- 
 duced in Berne, Switzerland, on a line about two miles long, with grades 
 of 0.25% to 3.7% and 5.2%. The air is heated by passing it through 
 superheated water at 330 F. It thus becomes saturated with steam, 
 which subsequently partly condenses, its latent heat being absorbed by 
 the expanding air. The pressure in the car reservoirs is 440 Ib. per sq. in. 
 
 The engine is constructed like an ordinary steam tramway locomotive, 
 and drives two coupled axles, the wheel-base being 5.2 ft. It has a 
 pair of outside horizontal cylinders, 5.1 X 8.6 in.; four coupled wheels, 
 27.5 in. diameter. The total weight of the car, including compressed 
 air, is 7.25 tons, and with 30 passengers, including the driver and 
 conductor, about 9:5 tons. The authorized speed is about 7 miles 
 per hour. 
 
 The aisad vantages of this system consist in the extremely delicate adjust- 
 ment of the different parts of the system, in the comparatively small 
 supply of air carried by oie motor car, which necessitates the ear return- 
 ing to the depot for refilling after a run of only four miles or 40 minutes, 
 although on the Nogent and Paris lines the cars, which are, moreover, 
 larger, and carry outside passengers on the top, run seven miles, and the 
 loading pressure is 547 Ib. per sq. in. as against only 440 Ib. at Berne. 
 
 For description of the Mekarski system as used at Nantes, Franco, see 
 paper by Prof. D. S. Jacobus, Trans. A. S. M. E., xix. 553. 
 
 American Experiments on Compressed Air for Street Railways. 
 Experiments have been made in Washington, D. C., and in New York 
 City on the use of compressed air for street-railway traction. The air 
 was compressed to 2000 Ib. per sq. in. and passed through a reducing- 
 valve and a heater before being admitted to the engine. The system has 
 since been abandoned. For an extended discussion of the relative merits 
 of compressed air and electric traction, with an account of a test of a 
 four-stage compressor giving a pressure of 2500 Ib. per sq. in., see Eng'g 
 News, Oct. 7 and Nov. 4, 1897. A summarized statement of the probable 
 efficiency of compressed-air traction is given as follows: Efficiency of com- 
 pression to 2000 Ib. per sq. in. 65%. By wire-drawing to 100 Ibs. 57.5% 
 of theavailable energy of the air will be lost, leaving 65 X 0.425 = 27.625% 
 as the net efficiency of the air. This may be doubled by heating, making 
 55.25%, and if the motor has an efficiency of 80% the net efficiency of 
 traction by compressed air will be 55.25 X 0.80 = 44.2%. For a descrip- 
 tion of the Hardie compressed-air locomotive, designed for street-railway 
 work, see Eng'g News, June 24, 1897. For use of compressed air in mine 
 haulage, see Eng'g News, Feb. 10, 1898. 
 
 Operation of Mine Pumps by Compressed Air. The advantages 
 of compressed air over steam for the operation of mine pumps are: Absence 
 of condensation and radiation losses in pipe lines; high efficiency of com- 
 pressed-air transmission; ease of disposal of exhaust; absence of danger 
 from broken pipes. The disadvantage is that, at a given initial pressure 
 without reheating, a cylinder full of air develops less power than steam. 
 The power end of the pump should be designed for the use of air, with 
 low clearances and with proper proportions of air and water ends, with 
 regard to the head under which the pump is to operate. Wm. Cox (Comp. 
 Air Mag., Feb., 1899) states the relations of simple or single-cylinder 
 pumps to be A/W = Vzh/p, where A = area of air cylinder, sq. in., W 
 = area of water cylinder, sq. in., h = head, ft., and p = air pressure, Ib. 
 per sq. in. Mr. Cox gives the volume V of free air in cu. ft. per minute 
 to operate a direct-acting, single-cylinder pump, working without cut off, 
 to be 
 
 V = 0.093 W 2 hG/P. 
 
 Where W 2 = volume of 1 cu. ft. of free air corresponding: to 1 cu. ft. of 
 free air at pressure P, G => gallons of water to be raised per minute, P => 
 
FANS AND BLOWERS. 653 
 
 receiver-gauge pressure of air to be used, and h = head in feet under 
 which pump works. This formula is based on a piston speed of 100 ft. 
 per minute arid 15% has been added to the volume ot air to cover losses. 
 The useful work done in a pump using air at full pressure is greater at 
 low pressures than at high, and the efficiency is increased. High pressures 
 are not so economical for simple pumps as low pressures. As high-pressure 
 air is required for drills, etc., and as the air for pumps is drawn from the 
 same main, the air must either be wire-drawn into the pumps, or a reducing 
 valve be inserted between the pump and main. Wire-drawing causes a 
 low efficiency in the pump. If a reducing valve is used, the increase of 
 volume will be accompanied with a drop in temperature, so that the full 
 value of the increase is not realized. Part of the lost heat may be regained 
 by friction, and from external sources. The efficiency of the system may 
 be increased by the use of underground receivers for the expanded air 
 before it passes to the pump. If the receiver be of ample size, the air 
 will regain nearly its normal temperature, the entrained moisture will be 
 deposited and freezing troubles avoided. By compounding the pumps, 
 the efficiency may be increased to about 25 per cent. In simple purnps it 
 ranges from 7 to 16 per cent: For much further information on this sub- 
 ject see Peele's " Compressed- Air Plant for Mines," 1908. 
 
 FANS AND BLOWEES. 
 
 Centrifugal Fans. The ordinary centrifugal fan consists of a number 
 of blades fixed to arms revolving at high speed. The width of the blade 
 is parallel to the shaft. The experiments of W. Buckle (Proc. Inst. M. E., 
 1847) are often quoted as still standard. Mr. Buckle's conclusions, how- 
 ever, do not agree with those of modern experimenters, nor do the propor- 
 tions of fans as determined by him have any similarity to those of modern 
 fans. The experiments were made on fans of the " paddle-wheel" 
 type, and have no bearing on the more modern multiblade fans of the 
 " Sirocco " type. 
 
 The rules laid down by Buckle do not give a fan the highest volu- 
 metric efficiency without loss of mechanical efficiency. By volumetric 
 efficiency is meant the ratio of the volume of air delivered per revo- 
 lution to the cubical contents of the wheel, if the wheel be considered 
 a solid whose dimensions are those of the wheel. Inasmuch as the 
 loss due to friction of the air entering the fan will be less with a large 
 inlet than with a small one, in a wheel of given diameter, more power 
 will be consumed in delivering a given volume of air with a small 
 inlet than with a larger one. 
 
 In the ordinary fan the number of blades varies from 4 to 8, while 
 with multiblade fans it is from 48 to 64. The number of blades has 
 a direct relation to the size of the inlet. This is made as large as 
 possible for the reason given above. Any increase in the diameter 
 of the inlet necessarily decreases the depth of the blade, thus di- 
 minishing the capacity and pressure. To overcome this decrease, 
 the number of blades is increased to the limit placed by construc- 
 tional considerati9ns. A properly proportioned fan is one in which 
 a balance is obtained between these two features of maximum inlet 
 and maximum number of blades. 
 
 In some cases two fans mounted on one shaft may be more useful than 
 a single wide one, as in such an arrangement -twice the area of inlet opening 
 is obtained, as compared with a single wide fan. Such an arrangement 
 may be adopted where occasionally half the full quantity of air is required, 
 as one of the fans may be put out of gear and thus save power. 
 
 Rules for Fan Design. It is impossible to give any general rules 
 or formulse covering the proportions of parts of fans and blowers. There 
 are no less than 14 variables involved in the construction and operation of 
 fans, a slight change in any one producing wide variations in the perform- 
 ance. The design of a new fan by manufacturers is largely a matter of 
 trial and error, based on experiments, until a compromise with all the 
 variables is obtained which most nearly conforms to the given conditions. 
 
 Pressure Due to Velocity of the Fan Blades. The pressure of the 
 air due to the velocity of the fan blades .may be determined by the formula 
 
 <y2 
 
 H = ' deduced from the law of falling bodies, in which H is the " head " 
 or height of a homogeneous column of air one inch square whose weight is 
 
654 
 
 AIR. 
 
 equai to the pressure per square inch of the air leaving the fan, v is the 
 velocity of the air leaving the fan in feet per second, and g the acceleration 
 
 , . , 
 
 -* 2 g, the formula according to him being H = v 2 -*- g See also Trow- 
 bridge (Trans. A. S. M. E., vii., 536). This law is analogous to that of 
 the pressure of a fluid jet striking a plane surface perpendicularly and 
 escaping at right angles to its original path, this pressure beins: twice that 
 due the height calculated from the formula h = v 2 -s- 2 g. (See HawksTey, 
 Proc. Inst. M. E., 1882.) Buckle says: " From the experiments 
 it appears that the velocity of the tips of the fan is equal to nine- 
 tenths of the velocity a body would acquire in falling the height of a 
 homogeneous column of air equivalent to the density." 
 
 To convert the head H expressed in feet to pressure in Ib. per sq. in. 
 multiply it by the weight of a cubic foot of air at the pressure and tem- 
 perature of the air expelled from the fan (about 0.08 Ib. usually) 
 and divide by 144. Multiply this by 16 to obtain pressure in ounces 
 per sq. in. or by 2.035 to obtain inches of mercury, or by 27.71 to 
 obtain pressure in inches of water_column. Taking 0.08 as the weight 
 of 1 cu. ft. of air, and v =0.9 ^YgH, 
 
 =0.00001066 v 2 ; v =310 ^p_ nearly; 
 =0.0001706 v*; v = 80 ^p\ " 
 =0.00002169 v-; v =220 Vp 2 
 =0.0002954 v 2 ; v = 60 ^ps " 
 in which v = velocity of tips of blades in feet per second. 
 
 Testing the above formula by one of Buckle's experiments with a 
 vane 14 inches long, we have p =0.00001066 v 2 =9.56 oz. The experi- 
 ment gave 9.4 oz. 
 
 Taking the formula v =80 v^, we have for different pressures in 
 ounces per square inch the following velocities of the tips of the blades 
 in feet per second: 
 
 Pi = ounces per square inch 2 3 4 5 6 7 8 10 12 14 
 v =feet per second ______ 113 139 160 179 196 212 226 253 277 299 
 
 Commenting on the statements and formulae given above, the 
 B. F. Sturtevant Co., in a letter to the author, says: " Let us assume 
 that the fan considered is of the centrifugal type, which is a wheel 
 in a spiral casing. In any case of centrifugal fan the pressure at the 
 
 p Ib. per sq. in. 
 pi ounces per sq. in. 
 P2 inches of mercury 
 ps inches of water 
 
 Straight- /Forward Backward 
 
 FIG. 146. TYPES OF FAN BLOWERS. 
 
 fan outlet is wholly dependent upon the load on the fan, and, there- 
 fore, the pressure cannot well be expressed by a formula, unless it 
 includes some term which is an expression in some way of the load 
 upon the fan. The actual pressure depends upon the design of both 
 wheel and housing, upon the blade area and also upon the form of the 
 blades. With a curved blade running with the concave side forward 
 it is possible to obtain a much higher pressure than if the blade is run- 
 ning with the convex side forward. This can only be shown by tests, 
 and can be figured out by blade-velocity diagrams." 
 
 It should be noted, however, that while the fan with a blade con- 
 caved in the direction of rotation has the highest efficiency, all other 
 
PRESSURE CHARACTERISTICS OF FANS. 655* 
 
 things being equal, the noise of operation is increased. A blade con- 
 vex in the direction of retain runs more quietly, and in most situa- 
 tions it is necessary to sacrifice efficiency in order to obtain quiet 
 operation. 
 
 Fig. 146 shows the relation of the velocity of air leaving a fan to 
 the velocity of the tips of the blades for radial, bent forward, and 
 bent backward blades. V represents the direction and amount of 
 the velocity relative to the blade as the air leaves the blade, U the 
 tangential velocity of the tip of the blade, and R the component of 
 U and V, the velocity of the air relative to the fan casing. 
 
 The kinetic energy of the air due to its velocity as it leaves the 
 blades is partially converted into pressure energy as the velocity 
 is reduced in the expanding scroll casing of the fan, and in the 
 diverging outlet of the fan if such an outlet is used. The total or 
 dynamic pressure is the sum of the static pressure and the velocity 
 pressure. 
 
 QUANTITY OF Am OF A GIVEN DENSITY DELIVERED BY A FAN. 
 
 Total area of nozzles in square feet X velocity in feet per minute corre- 
 sponding to density (see table) = air delivered in cubic feet per minute, 
 discharging freely into the atmosphere (approximate). See p. 670. 
 
 Density, 
 
 Velocity, 
 
 Density, 
 
 Velocity, 
 
 Density, 
 
 Velocity, 
 
 ounces 
 
 feet. per 
 
 ounces 
 
 feet per 
 
 ounces 
 
 feet per 
 
 per sq. in. 
 
 minute. 
 
 per sq. in. 
 
 minute. 
 
 per sq. in. 
 
 minute. 
 
 1 
 
 5,000 
 
 5 
 
 11,000 
 
 9 
 
 15,000 
 
 2 
 
 7,000 
 
 6 
 
 12,250 
 
 10 
 
 15,800 
 
 3 
 
 8,600 
 
 7 
 
 13,200 
 
 11 
 
 16,500 
 
 4 
 
 10,000 
 
 8 
 
 14,150 
 
 12 
 
 17,300 
 
 M Blast Area," or " Capacity Area." When the fan outlet is small 
 the velocity of the outflow is equal to the peripheral velocity of the fan. 
 
 Start with the outlet closed; then if the opening be slowly increased 
 while the speed of the fan remains constant the air will continue to flow 
 with the same velocity as the fan tips until a certain size of outlet is 
 reached. If the outlet is still further increased the pressure within the 
 casing will drop, and the velocity of outflow will become less than the 
 tip velocity. The size of the outlet at which this change takes place is 
 called the blast area, or capacity area, of the fan. This varies somewhat 
 with different types and makes of fans, but for the common form of 
 blower it is approximately, DW -s- 3, in which D is the diameter of the 
 fan wheel and W its width at the circumference. (C. L. Hubbard.) 
 
 .This established capacity area has no relation to the area of the outlet 
 in the casing, which may be of any size, but is usually about twice the 
 capacity area. The velocity of the air discharged through this latter 
 area is practically that of the circumference of the wheel, and the pressure 
 created is that corresponding thereto. W.'B. Sno_w. 
 
 Pressure Characteristics of Fans. Figs. 147 and 148 show 
 the relation of the static and total pressures, the efficiency and the 
 horse-power, to the capacity of two fans, one a radial blade fan, and 
 the other a multi-blade (conoidal) as determined by tests by the 
 Buffalo Forge Co. In the test the fan was run at a uniform speed 
 and the capacity was varied by varying the area of outlet. The 
 characteristics of the two fans differ greatly. In the case of the 
 radial fan the highest pressure corresponds to zero capacity, while 
 with the multi-blade fan the static pressure increases as the capacity 
 increases up to 100 per cent, or rated capacity, which is the point of 
 maximum efficiency. 
 
 If a forward-curved blade fan is intended to operate at a certain 
 pressure and capacity, and if for any reason, such as resistance greater 
 than expected, the quantity of air handled is less than the fan's 
 rating for the speed maintained, the total pressure will also be less 
 than that specified. With the straight-blade fan the opposite holds 
 true, for as the capacity is reduced the pressure will increase, at con- 
 stant speed. 
 
 Care should be taken in the selection of a fan with forward-curved 
 blades in case it is to be driven by a motor. If for any reason there 
 
056 
 
 AIR. 
 
 should be a tendency to operate above rated capacity, both the air 
 quantity and the pressure will increase, which may overload the 
 motor in case sufficient margin of motor capacity has not been pro- 
 vided. (Buffalo Forge Co.) 
 
 For a given fan area of outlet, piping system, and air density, the 
 
 20 40 60 80 100 
 
 Per Cent of Rated Capacity 
 FIG. 147. CHARACTERISTICS OF A RADIAL BLADE FAN. 
 
 relations of volume delivered, pressure at the fan outlet, speed and 
 horse-power theoretically vary as follows: 
 
 Volume delivered varies directly as speed of the fan. 
 
 Pressure varies as the square of the speed. 
 
 Horse-power varies as the cube of the speed. 
 
 For a given volume the horse-power varies as the square of the 
 speed, showing the great advantage of large fans at slow speeds over 
 
 w 
 180 
 '160 
 140 
 -gl20 
 
 03 
 
 ^100 
 
 
 
 to 80 
 60 
 .40 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 <t& 
 Rat< 
 
 d A^ 
 
 S 
 
 ^~^~ 
 
 / 
 
 
 ' . 
 
 - -^ 
 
 
 
 
 
 
 ^5^ 
 
 ^ - 
 
 g^ 
 
 n_ _ o 
 
 l^> 
 
 itic ^ 
 
 
 
 
 
 
 
 
 ^ 
 
 ^$ 
 
 i,aU 
 
 7C55 
 
 ^^- 
 
 t o3^f^ 
 
 
 
 iSS-j 
 
 ^ 
 
 
 
 . 
 
 ^^ 
 
 ^ 
 
 ^^ 
 
 
 
 
 Total E 
 
 fficiei 
 
 icy 
 
 
 
 s 
 
 x 
 
 
 
 
 
 
 -J 
 
 
 
 
 
 ^ 
 
 ^ 
 
 - 
 
 
 
 
 
 
 ^ 
 
 igns. 
 
 
 
 ^" 
 
 
 
 
 s* 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 < ^- 
 
 -^ 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 20 40 60 80 100 120 140 16 
 Per Cent of Rated Capacity 
 FIG. 148. CHARACTERISTICS OF A MULTI-BLADE FAN. 
 
 small fans at high speeds delivering the same volume, the type of fan 
 being the same. The theoretical values are greatly modified by vari- 
 ations in practical conditions. For every fan running at constant speed 
 there is a pressure and corresponding volume at which a fan will 
 operate at its maximum efficiency (see characteristic curves), and a 
 
FANS AND BLOWERS. 
 
 C57 
 
 wide variation in these conditions will give a great drop in efficiency. 
 In selecting a fan for any purpose the catalogues and bulletins issued 
 by manufacturers should be examined, and a tabular comparison 
 made of the sizes, speed, etc., of different fans which may be used for 
 the given purpose and conditions. The following is an example of 
 such a comparison of three multi-blade fans (Sturtevant) which may be 
 used to deliver approximately 15,000 cu. ft. of air against a resistance, 
 of 5 in. of water column. . 
 
 
 Wheel 
 
 Resistance, 5 in. 
 
 
 
 
 
 
 
 Size 
 
 R P M 
 
 H P 
 
 
 Inches. 
 
 Vol. 
 
 R.P.M. 
 
 H.P. 
 
 
 
 
 Turbovane.. 
 
 221/2 
 
 15,500 
 
 2210 
 
 25 
 
 Smallest 
 
 Highest 
 
 Medium 
 
 Supervane. . 
 Multivane. . 
 
 25 
 26 
 
 15,400 
 15,900 
 
 1033 
 1103 
 
 23.5 
 26 
 
 Medium 
 Largest 
 
 Lowest 
 Medium 
 
 Lowest 
 Highest 
 
 Experiments on a Fan with Constant Discharge-opening and 
 Varying Speed. The first four columns are given by Mr. Snell, the 
 others are calculated by the author. 
 
 
 , 
 
 . 
 
 
 ._ ^ 
 
 vi i 
 
 i +* 
 
 X 
 
 I 
 
 ^ 
 
 
 9 
 
 
 
 
 J 
 
 4) Ol i 
 
 S'\ 
 
 ? P 
 
 ft 3 . 
 
 o 
 
 
 
 a 
 1 
 
 
 O 
 
 || 
 
 i 
 
 ?! 
 
 || 
 
 o B l 
 
 5? 
 
 w 
 
 0) 
 
 ft 
 
 fe 
 
 *2 
 
 <<-S 
 
 a 
 
 >> ^ 
 
 S* * 
 
 ^H 
 
 ^-S^ 
 
 ^ ^ 
 
 
 
 ft 
 
 $ 
 
 QJ 
 
 3 
 
 *1 
 
 *o ft 
 
 i 
 
 
 
 13 
 
 -is 
 
 III 
 
 a g 2 
 
 2 " 
 
 o--- ft 
 13 S5 
 
 11 
 
 1 
 
 
 
 
 
 w 
 
 
 > 
 
 o *". 
 
 t> .. 
 
 H 
 
 8 
 
 600 
 
 0.50 
 
 1336 
 
 0.25 
 
 60.2 
 
 56.6 
 
 85.1 
 
 3,630 
 
 0.182 
 
 73 
 
 800 
 
 0.88 
 
 1787 
 
 0.70 
 
 80.3 
 
 75.0 
 
 85.6 
 
 4,856 
 
 0.429 
 
 61 
 
 1000 
 
 1.38 
 
 2245 
 
 1.35 
 
 100.4 
 
 94 
 
 85.4 
 
 6,100 
 
 0.845 
 
 63 
 
 1200 
 
 2.00 
 
 2712 
 
 2.20 
 
 120.4 
 
 113 
 
 85.1 
 
 7,370 
 
 1.479 
 
 67 
 
 1400 
 
 2.75 
 
 3177 
 
 3.45 
 
 140.5 
 
 133 
 
 84.8 
 
 8,633 
 
 2.283 
 
 66 
 
 1600 
 
 3.80 
 
 3670 
 
 5.10 
 
 160.6 
 
 156 
 
 82.4 
 
 9,973 
 
 3.803 
 
 74 
 
 1800 
 
 4.80 
 
 4172 
 
 8.00 
 
 180.6 
 
 175 
 
 82.4 
 
 11,337 
 
 5.462 
 
 68 
 
 2000 
 
 5.95 
 
 4674 
 
 11.40 
 
 200.7 
 
 195 
 
 85.6 
 
 12,701 
 
 7.586 
 
 67 
 
 Mr. Snell has not found any practical difference between the mechanical 
 efficiencies of blowers with curved blades and those with straight radial 
 ones. From these experiments, says Mr. Snell, it appears that we may 
 expect to receive back 65% to 75% of the power expended, and no more. 
 The great amount of power often used to run a fan is not due to the fan 
 itself, but to the method of selecting, erecting, and piping it. (For opin- 
 ions on the relative merits of fans and positive rotary blowers, see discus- 
 sion of Mr. Snell's paper, Trans. A. S. M. E., ix. 66, etc.) 
 
 Comparative Efficiency of Fans and Positive Blowers. (H. M. 
 Howe, Trans. A. I. M. E., x. 482.) Experiments with fans and positive 
 (Baker) blowers working at moderately low pressures, under 20 ounces, 
 .show that they work more efficiently at a given pressure when delivering 
 large volumes (i.e., when working nearly up to their maximum capacity) 
 than when delivering comparatively small volumes. Therefore, when 
 great variations in the quantity and"^ pressure of blast required are liable 
 to arise, the highest efficiency would be obtained by having a number of 
 blowers, always driving them up to their full capacity, ana regulating the 
 amount of blast by altering the number of blowers at work, instead of 
 having one or two very large blowers and regulating the amount of blast 
 by the speed of the blowers. 
 
 There appears to be little difference between the efficiency of fans and 
 of Baker blowers when each works under favorable conditions as regards 
 quantity of work, and when each is in good order. 
 
 For a given speed of fan, any diminution in the size of the blast-orifice 
 decreases the consumption of power and at the same time raises the pros- 
 
658 
 
 AIR. 
 
 sure of tlie blast; but it increases the consumption of power per unit of 
 prince for a given pressure of blast. When the orifice has been reduced to 
 the normal size for any given fan, further diminishing it causes but slight 
 elevation of the blast pressure; and, when the orifice becomes compara- 
 tively small, further diminishing it causes no sensible elevation of the 
 blast pressure, which remains practically constant, even when the orifice is 
 entirely closed. 
 
 Many of the failures of fans have been due to too low speed, to too small 
 pulleys, to improper fastening of belts, or to the belts being too nearly ver- 
 tical; m brief, to bad mechanical arrangement, rather than to inherent 
 defects in the principles of the machine. 
 
 If several fans are used, it is probably essential to high efficiency to pro- 
 vide a separate blast pipe for each (at least if the fans are of different size 
 or speed), while any number of positive blowers may deliver into the same 
 pipe without lowering their efficiency. 
 
 The Sturtevant Multi-blade Fans. The B. F. Sturteyant Co. 
 has developed three styles of fans with numerous blades which have 
 been given the trade names Multivane, Supervane, and Turbovane. 
 The Multivane and Supervane fans are used for the same kind of 
 service, that is, mostly for heating, ventilating, and mechanical 
 draught. For a given diameter, the Supervane operates at lower speed 
 and requires less power than the Multivane. The Turbovane fan 
 is designed for high-speed direct-connected drives, such as steam 
 turbines. It is a very wide fan, made double inlet, and for a given 
 volume and pressure will be smaller in diameter and operate at about 
 twice the speed of the Multivane and require about the same power. 
 The Turbovane and Supervane fans have blades considerably deeper 
 than the Multivane. The curvature is also radically different in 
 all three types. The spiral or housing is considerably different in the 
 three types. 
 
 Sturtevant Multivane Fan. 
 
 
 
 Resistance 1/2 in. 
 
 Resistance 2 in. 
 
 Resistance 5 in. 
 
 
 
 |ll 
 
 s|. 
 
 g 
 
 
 L 
 
 % 
 
 
 gs rf 
 
 g 
 
 
 ! 
 
 N 
 
 'SnJ 
 
 34* g 
 
 PH' 
 
 04 
 
 o^d'S 
 
 W 
 
 PH 
 
 ^s's 
 
 PH' 
 
 PH' 
 
 -^55 
 
 S3 
 
 W 
 
 t> 
 
 gj 
 
 g 
 
 ^ 
 
 gj 
 
 w 
 
 > 
 
 ti 
 
 g 
 
 fe 
 
 2 
 
 21 
 
 1,300 
 
 705 
 
 0.220 
 
 2,850 
 
 1471 
 
 2.15 
 
 3,980 
 
 2205 
 
 6.6 
 
 13 
 
 3 
 
 26l'2 
 
 2,030 
 
 565 
 
 0.345 
 
 4,440 
 
 1178 
 
 3.3 
 
 6,210 
 
 1764 
 
 10.0 
 
 161/2 
 
 4 
 
 31 1/2 
 
 2,920 
 
 470 
 
 0.495 
 
 6,400 
 
 980 
 
 4.8 
 
 8,940 
 
 1471 
 
 14.5 
 
 191/2 
 
 5 
 
 37 
 
 3,980 
 
 404 
 
 0.67 
 
 8,720 
 
 840 
 
 6.5 
 
 12,200 
 
 1260 
 
 20 
 
 23 
 
 6 
 
 42 
 
 5,200 
 
 353 
 
 0.88 
 
 11,400 
 
 735 
 
 8.5 
 
 15,900 
 
 1103 
 
 26 
 
 26 
 
 61/2 
 
 47 
 
 6,570 314 
 
 1.10 
 
 14,400 
 
 654 
 
 11.0 
 
 20,100 
 
 980 
 
 33 
 
 291/2 
 
 7 
 
 521/2 
 
 8,110 
 
 282 
 
 1.40 
 
 17/800 
 
 588 
 
 13.5 
 
 24,800 
 
 882 
 
 41 
 
 32 1/2 
 
 8 
 
 63 
 
 11,700 
 
 235 
 
 2.00 
 
 25,600 
 
 490 
 
 19 
 
 35,800 
 
 735 
 
 60 
 
 39 
 
 9 
 
 73V2 
 
 15,900 
 
 202 
 
 2.70 
 
 34,800 
 
 420 
 
 26 
 
 48,700 
 
 631 
 
 80 
 
 451/2 
 
 10 
 
 831/2 
 
 20,800 
 
 176 
 
 3.50 
 
 45,500 
 
 368 
 
 34 
 
 63,600 
 
 552 
 
 105 
 
 52 
 
 11 
 
 94 
 
 26,300 
 
 157 
 
 4.45 
 
 57,600 
 
 327 
 
 43 
 
 80,500 
 
 490 
 
 135 
 
 581/2 
 
 12 
 
 1041/2 
 
 32,500 
 
 141 
 
 5.5 
 
 71,000 
 
 294 
 
 54 
 
 99,400 
 
 441 
 
 165 
 
 65 
 
 13 
 
 115 
 
 39,400 
 
 128 
 
 6.7 
 
 86,100 
 
 268 j 64 
 
 121,000 
 
 401 
 
 200 
 
 71 1/2 
 
 14 
 
 1251/2 
 
 46,800 
 
 118 
 
 7.9 
 
 102,000 
 
 245 76 
 
 143,000 
 
 368 
 
 235 
 
 78 
 
 15 . 
 
 136 
 
 54,800 
 
 109 
 
 9.3 
 
 120,000 
 
 226 90 
 
 168,000 
 
 340 
 
 275 
 
 841/2 
 
 16 
 
 1461/2 
 
 63,500 
 
 101 
 
 11.0 
 
 139,000 
 
 210 105 
 
 195.000 
 
 315 
 
 320 
 
 91 
 
 17 
 
 157 
 
 73,000 
 
 94 
 
 12.5 
 
 160,000 
 
 196 120 
 
 224,000 
 
 294 
 
 370 
 
 971/2 
 
 18 
 
 167 
 
 83,100 
 
 88 
 
 14 
 
 182,000 
 
 184 135 
 
 255,000 
 
 276 
 
 420 
 
 104 
 
 20 
 
 188 
 
 105,000 
 
 78 
 
 18 
 
 230,000 
 
 163 170 
 
 322,000 
 
 245 
 
 530 
 
 117 
 
 22 
 
 209 
 
 130,000 
 
 71 
 
 22 
 
 285,000 
 
 147 : 215 
 
 398.000 
 
 221 
 
 655 
 
 130 
 
 24 
 
 230 
 
 157,000 
 
 64 
 
 27 
 
 344,000 
 
 134 260 
 
 481,000 
 
 200 
 
 795 
 
 143 
 
 26 
 
 2501/2 
 
 187,000 
 
 55 
 
 32 
 
 410,000 
 
 115305 
 
 573.000 
 
 173 
 
 945 
 
 156 
 
FANS AND BLOWERS. 
 
 659' 
 
 Sturtevant Supervane Fan. 
 
 
 
 Resistance 1/2 in. 
 
 Resistance 2 in. 
 
 Resistance 5 in. 
 
 
 
 b<- 
 
 
 
 
 
 
 
 
 
 
 7 oj 
 
 
 
 & 
 
 g 
 
 
 g a 
 
 ^ 
 
 
 S ft . 
 
 ^' 
 
 
 l-2 
 
 N 
 
 'Soli 
 
 -oVe 
 
 PH 
 
 P^ 
 
 oV 
 
 P^ 
 
 PH 
 
 'oVl 
 
 P^ 
 
 PH' 
 
 33 
 
 OQ 
 
 
 
 
 PJ 
 
 W 
 
 > 
 
 tf 
 
 W 
 
 > 
 
 PJ 
 
 W 
 
 ^ 
 
 A 
 
 26 
 
 1,470 
 
 645 
 
 0.235 
 
 2,940 
 
 1290 
 
 1.90 
 
 4,160 
 
 1980 
 
 6.4 
 
 13 
 
 B 
 
 32 
 
 2,230 
 
 525 
 
 0.355 
 
 4,460 
 
 1051 
 
 2.90 
 
 6,320 
 
 1610 
 
 9.7 
 
 16 
 
 C 
 
 38 
 
 3,150 
 
 442 
 
 0.50 
 
 6,300 
 
 885 
 
 4.05 
 
 8,910 
 
 1358 
 
 13.5 
 
 19 
 
 D 
 
 44 
 
 4,200 
 
 382 
 
 0.67 
 
 8,420 
 
 764 
 
 5.4 
 
 11,900 
 
 1171 
 
 18.0 
 
 22 
 
 E 
 
 491/2 
 
 5,450 
 
 337 
 
 0.87 
 
 10,900 
 
 673 
 
 7.0 
 
 15,400 
 
 1033 
 
 23.5 
 
 25 
 
 F 
 
 55V2 
 
 6,820 
 
 300 
 
 1.10 
 
 13,600 
 
 600 
 
 8.8 
 
 19,300 
 
 921 
 
 30 
 
 28 
 
 G 
 
 631/2 
 
 8,900 
 
 262 
 
 1.40 
 
 17,800 
 
 525 
 
 11.5 
 
 25,200 
 
 805 
 
 38 
 
 32 
 
 H 
 
 73V2 
 
 11,300 
 
 233 
 
 1.80 
 
 22,600 
 
 467 
 
 14.5 
 
 32,000 
 
 716 
 
 49 
 
 36 
 
 J 
 
 791/2 
 
 13,900 
 
 210 
 
 2.20 
 
 27,800 
 
 420 
 
 18 
 
 39,400 
 
 645 
 
 60 
 
 40 
 
 K 
 
 9H/2 
 
 18,500 
 
 183 
 
 2.90 
 
 36,900 
 
 365 
 
 24 
 
 52,300 
 
 560 
 
 80 
 
 46 
 
 L 
 
 103 
 
 23,500 
 
 162 
 
 3.75 
 
 47,000 
 
 323 
 
 30 
 
 66,600 
 
 496 
 
 100 
 
 52 
 
 M 
 
 115 
 
 29,300 
 
 145 
 
 4.65 
 
 58,500 
 
 290 
 
 38 
 
 83,000 
 
 444 
 
 125 
 
 58 
 
 N 
 
 127 
 
 35,600 
 
 131 
 
 5.7 
 
 71,200 
 
 263 
 
 46 
 
 101,000 
 
 403 
 
 155 
 
 64 
 
 P 
 
 139 
 
 42,700 
 
 120 
 
 6.8 
 
 85,400 
 
 240 
 
 56 
 
 121,000 
 
 368 
 
 185 
 
 70 
 
 
 1501/2 
 
 50,300 
 
 111 
 
 8.0 
 
 101,000 
 
 221 
 
 66 
 
 143,000 
 
 339 
 
 220 
 
 76 
 
 R 
 
 166V2 
 
 61,400 
 
 100 
 
 9.8 
 
 123,000 
 
 200 
 
 80 
 
 174,000 
 
 307 
 
 265 
 
 84 
 
 S 
 
 1821/2 
 
 73,500 
 
 91 
 
 11.5 
 
 147,000 
 
 183 
 
 96 
 
 208,000 
 
 280 
 
 320 
 
 92 
 
 T 
 
 I98V2 
 
 86,900 
 
 84 
 
 14.0 
 
 174,000 
 
 168 
 
 110 
 
 246,000 
 
 258 
 
 375 
 
 100 
 
 U 
 
 2141/2 
 
 102,000 
 
 78 
 
 16.0 
 
 204,000 
 
 156 130" 
 
 288,000 
 
 239 440 
 
 108 
 
 V 
 
 230 
 
 117,000 
 
 72 
 
 18.5 
 
 234,000 
 
 145 
 
 150 
 
 332,000 
 
 222 505 
 
 116 
 
 W 
 
 254 
 
 143,000 
 
 66 
 
 23 
 
 285,000 
 
 131 
 
 185 
 
 404,000 
 
 202 
 
 615 
 
 128 
 
 X 
 
 2771/2 
 
 171,000 
 
 6027 
 
 341,000 
 
 120 
 
 220 
 
 483,000 
 
 184 
 
 740 
 
 140 
 
 Y 
 
 301 1/2 
 
 201,000 
 
 5532 
 
 401,000 
 
 111 260 
 
 569,000 
 
 170 
 
 870 
 
 152 
 
 Sturtevant Turbovane Fan. 
 
 
 
 Resistance 1 in. 
 
 Resistance 3 in. 
 
 Resistance 6 in. 
 
 
 
 o -^ 
 
 
 
 
 
 
 
 
 
 
 Too 
 
 
 all 
 
 3 d 
 
 g 
 
 
 gY. 
 
 ,a 
 
 
 8 . 
 
 g 
 
 
 3 11 
 
 N 
 
 rl 
 
 J+rg 
 
 PH' 
 
 PH 
 
 ^c's 
 
 pj 
 
 PH 
 
 'o'd's 
 
 PH' 
 
 PH 
 
 j55S 
 
 33 
 
 W 
 
 >. 
 
 tf 
 
 W 
 
 !*_ 
 
 PH' 
 
 W 
 
 >*" 
 
 P4 
 
 W 
 
 ^ 
 
 40 
 
 28 
 
 1,670 
 
 1958 
 
 0.53 
 
 2,930 
 
 3400 
 
 2.85 
 
 4,010 
 
 47oO 
 
 7.8 
 
 IH/2 
 
 45 
 
 35 
 
 2,610 
 
 1563 
 
 0.83 
 
 4,560 
 
 2720 
 
 4.4 
 
 6,250 
 
 3800 
 
 12.0 
 
 141/2 
 
 50 
 
 42 
 
 3,770 
 
 1300 
 
 1.20 
 
 6,600 
 
 2260 
 
 6.5 
 
 9,050 
 
 3161 
 
 17.5 
 
 17 
 
 55 
 
 49 
 
 5,100 
 
 1118 
 
 1.65 
 
 8,950 
 
 1940 
 
 8.8 
 
 12,300 
 
 2719 
 
 23.5 
 
 20' 
 
 60 
 
 56 
 
 6,700 
 
 978 
 
 2.15 
 
 11,700 
 
 1700 
 
 11.0 
 
 16,100 
 
 2380 
 
 31 
 
 221/2 
 
 65 
 
 63 
 
 8,500 
 
 868 
 
 2.75 
 
 14,900 
 
 1510 
 
 14.5 
 
 20,400 
 
 2115 
 
 39 
 
 251/2 
 
 70 
 
 70 
 
 10,500 
 
 781 
 
 3.35 
 
 18,300 
 
 1358 
 
 17.5 
 
 25,100 
 
 1900 
 
 48 
 
 281/2 
 
 80 
 
 84 
 
 15,100 
 
 651 
 
 4.85 
 
 26,300 
 
 1131 
 
 26 
 
 36,100 
 
 1582 
 
 70 
 
 34 
 
 90 
 
 97 
 
 20,500 
 
 558 
 
 6.5 
 
 35,800 
 
 971 
 
 35 
 
 49,100 
 
 1360 
 
 92 
 
 39 1/2 
 
 100 
 
 112 
 
 26,800 
 
 490 
 
 8.5 
 
 46,800 
 
 851 
 
 45 
 
 64,000 
 
 1192 
 
 120 
 
 45 
 
 110 
 
 126 
 
 34,000 
 
 435 
 
 11.0 
 
 59,500 
 
 755 
 
 58 
 
 81,500 
 
 1058 
 
 155 
 
 51 
 
 120 
 
 140 
 
 41,800 
 
 391 
 
 13.5 
 
 73,000 
 
 679 
 
 70 
 
 101,000 
 
 950 
 
 190 
 
 561/2 
 
 130 
 
 154 
 
 50,500 
 
 353 
 
 16.5 
 
 88,500 
 
 617 
 
 86 
 
 122,000 
 
 865 
 
 230 
 
 62 
 
 140 
 
 168 
 
 60,500 
 
 326 
 
 19.5 
 
 106,000 
 
 566 
 
 100 
 
 145,000 
 
 792 
 
 280 
 
 67 1/2 
 
 150 
 
 182 
 
 71,000 
 
 300 
 
 22.5 
 
 124,000 
 
 521 
 
 120 
 
 170,000 
 
 729 
 
 325 
 
 73 1/2 
 
 160 
 
 196 
 
 82,000 
 
 279 
 
 26 
 
 144,000 
 
 485 
 
 140 
 
 197,000 
 
 680 380 
 
 79 
 
660 
 
 AIR. 
 
 Capacity of Fans and Blowers. The folio wing .tables supplied (1909) 
 by the American Blower Co., Detroit, show the capacities of exhaust fans 
 and volume and pressure blowers. The tables are all based on curves 
 established by experiment. The pressures, volumes and horse-powers 
 were all actually measured with the apparatus working against maintained 
 resistances formed by restrictions equivalent to those found in actual prac- 
 tice, and which experience shows will produce the best results. 
 
 Speed, Capacity and Horse-power of Steel Plate Exhaust Fans. 
 
 (American Blower Co., Type E, 1908.) 
 
 Diameter of 
 wheel, in. 
 
 i 
 
 '5 
 
 ft s 
 
 9 
 
 15 .g 
 
 1/2 oz. pres- 
 sure. 
 
 3/4 oz. pres- 
 sure. 
 
 1 oz. pres- 
 sure. 
 
 2 oz. pres- 
 sure. 
 
 
 fc 
 ft . 
 
 | 
 
 
 b 
 
 0) 
 ft . 
 
 ft 
 
 
 1. 
 
 1 
 
 
 ft. 
 
 1 
 
 ^ 
 
 II 
 w 
 
 si 
 
 cTC- 
 
 5 
 
 aj 
 
 t 3 
 
 o fl 
 
 11 
 
 O 
 
 11 
 
 P^ 
 tf 
 
 o 
 O 
 
 % 1 
 
 
 PH 
 
 P3 
 
 " C 
 
 11 
 
 O 
 
 -o % 
 
 si 
 
 |a 
 
 PS 
 
 <+" 3. 
 1 S 
 
 16 
 19 
 22 
 25 
 28 
 31 
 34 
 38 
 44 
 50 
 
 61/8 
 71/8 
 81/8 
 93/8 
 107/s 
 123/g 
 131/2 
 
 151/8 
 161/2 
 
 10 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 27 
 29 
 
 985 
 830 
 
 715 
 630 
 563 
 
 508 
 464 
 415 
 375 
 
 328 
 
 1,09 
 1 580 
 2,155 
 2,820 
 3 560 
 4,400 
 5,330 
 6,350 
 7,440 
 10,050 
 
 0.30 
 0.43 
 0.59 
 0.77 
 0.97 
 1.20 
 1.45 
 1.73 
 2.02 
 2.75 
 
 1200 
 1012 
 876 
 772 
 689 
 622 
 567 
 509 
 459 
 402 
 
 1,345 
 1,940 
 2,635 
 3,450 
 4,360 
 5,390 
 6,525 
 7,775 
 9,120 
 12,100 
 
 0.56 
 0.80 
 1.08 
 1.41 
 1.78 
 2.20 
 2.66 
 3.18 
 3.72 
 4.94 
 
 1390 
 1170 
 1010 
 890 
 795 
 719 
 655 
 587 
 530 
 464 
 
 1 555 
 2,240 
 3,040 
 3.980 
 5030 
 6,220 
 7,530 
 8,960 
 10.500 
 13,980 
 
 0.85 
 1.22 
 1.66 
 2.17 
 2.74 
 3.39 
 4.10 
 4.89 
 5.72 
 7.62 
 
 1966 
 1655 
 1430 
 1260 
 1125 
 1015 
 927 
 830 
 750 
 656 
 
 2.200 
 3,175 
 4,310 
 5.646 
 7,140 
 8,820 
 10,650 
 12700 
 14,875 
 19,800 
 
 2.40 
 3.46 
 4.70 
 0.15 
 7.79 
 9.63 
 11.60 
 13.85 
 16.20 
 21.60 
 
 Speed, Capacity and Horse-power of Volume Blowers. 
 
 (American Blower Co., Type V, 1909.) 
 
 
 
 
 1/2 oz. pres- 
 
 3/4 oz. pres- 
 
 1 oz. pres- 
 
 1 1/2 oz. pres- 
 
 
 
 
 sure. 
 
 sure. 
 
 sure. 
 
 sure. 
 
 
 ft 
 
 ~.s 
 
 
 (_ 
 
 
 
 JLi 
 
 
 
 -, 
 
 i> 
 
 
 t_ 
 
 
 "o.d 
 
 o> 
 
 ~ .. 
 
 
 ft. 
 
 cc 
 
 
 ft. 
 
 g 
 
 
 ft. 
 
 
 
 ft. 
 
 
 
 _r 
 
 ^c 
 
 *- 
 
 
 
 O j/ 
 
 
 
 o ^ 
 
 
 ^^ 
 
 o ^ 
 
 
 
 
 Ji ^ 
 
 1 * 
 
 fi < 
 
 <D'S 
 
 2 e 
 
 ^ 
 
 t> c 
 
 s 1 
 
 a 
 
 * 
 
 <u | 
 
 g 
 
 Cf g 
 
 ? 
 
 JEJ 
 
 C3 
 
 2 S 
 
 i*i 
 
 72 
 
 
 PH 
 
 " S 
 
 B3 ^ 
 
 PH 
 
 & g 
 
 2 ft 
 
 PH 
 
 " S 
 
 ^ 
 
 PH 
 
 ^a 
 
 2 ft 
 
 Q 
 
 
 
 Q 
 
 P^ 
 
 o 
 
 PQ 
 
 tf 
 
 O 
 
 
 PJ 
 
 
 
 
 P^ 
 
 -6 
 
 P3 
 
 81/2 
 
 ? 
 
 41/o 
 
 1850 
 
 223 
 
 06 
 
 7.270 
 
 273 
 
 11 
 
 2620 
 
 315 
 
 0.17 
 
 3210 
 
 386 
 
 0.32 
 
 101/4 
 
 73/8 
 
 5 1/2 
 
 1535 
 
 332 
 
 09 
 
 1880 
 
 407 
 
 0,17 
 
 2170 
 
 469 
 
 0.26 
 
 2660 
 
 576 
 
 0.48 
 
 17, 
 
 
 61/2 
 
 1310 
 
 464 
 
 13 
 
 1600 
 
 569 
 
 0.23 
 
 1850 
 
 656 
 
 0.36 
 
 2275 
 
 805 
 
 0.66 
 
 !^ 1/2 
 
 43/2 
 51/8 
 
 81/2 
 
 1015 
 830 
 
 795 
 1185 
 
 0.22 
 32 
 
 1240 
 1013 
 
 975 
 1450 
 
 0.40 
 0.59 
 
 1435 
 1170 
 
 1122 
 1675 
 
 0.61 
 0.92 
 
 1760 
 1435 
 
 1377 
 2055 
 
 1.13 
 1.68 
 
 i V2 
 
 6V2 
 7l/o 
 
 123/ 8 
 
 700 
 606 
 
 1686 
 
 7735 
 
 0.46 
 61 
 
 858 
 742 
 
 2065 
 2740 
 
 0.84 
 1.12 
 
 990 
 858 
 
 2385 
 3160 
 
 1.30 
 1.72 
 
 1215 
 1050 
 
 2930 
 3880 
 
 2.40 
 3.18 
 
 291/ 2 
 
 8i/2 
 91/2 
 
 161/4 
 181/4 
 
 534 
 477 
 
 2910 
 3660 
 
 0.79 
 1.00 
 
 654 
 585 
 
 3560 
 4490 
 
 1 45 
 1.83 
 
 755 
 675 
 
 4110 
 5175 
 
 2.24 
 2.82 
 
 928 
 825 
 
 5040 
 6350 
 
 4.13 
 5.20 
 
 NOTE: This table also applies to Type V, cast-iron exhaust fans. 
 
FANS AND BLOWERS. 
 
 661 
 
 Steel Pressure Blowers for Cupolas (Average Application). 
 
 (American Blower Co., 1909.) 
 
 _ 1 JSo. of blower. | 
 
 Dia. of wheel, 
 in. 
 
 Width periph'y. 
 in. 
 
 ^ 
 
 P 
 
 il 
 
 o 
 
 |.s 
 
 3 cp 
 
 
 
 OS'S, 
 
 Q 
 
 53/4 
 
 Area of outlet, 
 sq.ft. 
 
 Oz. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 In. 
 
 3.46 
 
 5.19 
 
 6.92 
 
 8.65 
 
 10.38 
 
 12.12 
 
 13.83 
 
 15.56 
 
 H.P. 
 
 const, 
 at 1000 
 cu. ft. 
 
 1.242 
 
 1960 
 361 
 0.45 
 
 1.86 
 
 2400 
 434 
 0.81 
 
 2.48 
 
 3.10 
 
 3095 
 560 
 1.74 
 
 3.73 
 
 4.35 
 
 3666 
 665 
 2.89 
 
 4.95 
 
 3915 
 708 
 3.51 
 
 5.58 
 
 4150 
 
 752 
 4.20 
 
 41,2 
 
 3/8 
 
 3.80 
 
 0.18 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 2770 
 500 
 1.24 
 
 3390 
 610 
 
 2.28 
 
 2895 
 843 
 3.15 
 
 2 
 
 7 
 
 15/8 
 
 4.45 
 
 63/4 
 73/4 
 
 0.2485 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1675 
 
 498 
 0.62 
 
 2050 
 600 
 1.12 
 
 2362 
 691 
 1.72 
 
 2645 
 774 
 2.40 
 
 3130 
 916 
 3.99 
 
 3340 
 978 
 4.84 
 
 3540 
 1038 
 5.79 
 
 3 
 
 4 
 
 9V2 
 
 17/8 
 
 5.11 
 
 0.327 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1460 
 655 
 0.82 
 
 1785 
 789 
 1.47 
 
 2060 
 910 
 2.26 
 
 2300 
 1018 
 3.16 
 
 2520 
 1110 
 4.15 
 
 2730 
 1207 
 5.25 
 
 2910 
 1286 
 6.36 
 
 3085 
 1365 
 7.62 
 
 22 
 
 21/8 
 
 5.76 
 
 83/4 
 
 0.4176 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1292 
 838 
 1.04 
 
 1582 
 1006 
 1.87 
 
 1825 
 1162 
 
 2.88 
 
 2040 
 1300 
 4.03 
 
 2235 
 1415 
 5.28 
 
 2420 
 1540 
 6.70 
 
 2585 
 1643 
 8.14 
 
 2740 
 1746 
 9.74 
 
 5 
 
 241/2 
 
 23/8 
 
 6.41 
 
 93/4 
 
 0.519 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1162 
 1040 
 1.30 
 
 1422 
 1250 
 2.33 
 
 1640 
 1442 
 3.58 
 
 1835 
 1612 
 5.00 
 
 2010 
 1760 
 6.57 
 
 2175 
 1915 
 8.34 
 
 2320 
 2040 
 10.10 
 
 2460 
 2166 
 12.10 
 
 6 
 
 27 
 
 27/8 
 
 7.06 
 
 103/4 
 
 0.63 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1055 
 1262 
 1.57 
 
 1290 
 1520 
 2.83 
 
 1490 
 1750 
 4.34 
 
 1665 
 1960 
 6.08 
 
 1825 
 2135 
 7.96 
 
 1975 
 2375 
 10.10 
 
 2105 
 2475 
 12.25 
 
 2233 
 2630 
 14,12 
 
 7 
 
 32 
 
 33/8 
 
 8.39 
 
 121/2 
 
 0.852 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 889 
 1705 
 2.12 
 
 1087 
 2055 
 3.83 
 
 1255 
 2366 
 5.86 
 
 1405 
 2650 
 8.23 
 
 1535 
 2890 
 10.78 
 
 1660 
 3140 
 13.66 
 
 1775 
 3350 
 16.60 
 
 1880 
 3555 
 19.83 
 
 8 
 
 37 
 
 37/8 
 
 9.70 
 
 14 
 
 1.069 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 769 
 2140 
 2.66 
 
 940 
 2575 
 4.79 
 
 1085 
 2970 
 7.36 
 
 1212 
 3325 
 10.3 
 
 1328 
 3620 
 13.5 
 
 1446 
 3940 
 17.15 
 
 1533 
 4200 
 20.80 
 
 1625 
 4460 
 24.90 
 
 9 
 
 10 
 
 42 
 
 43/8 
 
 10.98 
 
 16 
 
 1.396 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 679 
 2800 
 3.48 
 
 830 
 3370 
 6.27 
 
 958 
 3880 
 9.63 
 
 1072 
 4340 
 13.46 
 
 1172 
 4730 
 17.65 
 
 1270 
 5150 
 22.40 
 
 1355 
 5500 
 27.25 
 
 1435 
 5825 
 32.50 
 
 47 
 
 47/8 
 
 12.30 
 
 171/2 
 
 1.67 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 606 
 3350 
 4.17 
 
 742 
 4025 
 7.5 
 
 855 
 4640 
 11.5 
 
 956 
 5200 
 16.12 
 
 1048 
 5660 
 21.12 
 
 1133 
 6160 
 26.80 
 
 1210 
 6570 
 32.55 
 
 1280 
 6970 
 38.90 
 
 11 
 12 
 
 52 
 
 33/8 
 
 13.6 
 
 191/4 
 21 
 
 2.02 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 548 
 4050 
 5.03 
 
 670 
 4870 
 9.06 
 
 774 
 5610 
 13.9 
 
 865 
 6290 
 '19.5 
 
 947 
 6850 
 25.55 
 
 1025 
 7450 
 32.40 
 
 1093 
 7950 
 39.33 
 
 1160 
 8440 
 47.10 
 
 57 
 
 57/8 
 
 14.92 
 
 2.405 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 500 
 4820 
 6.00 
 
 611 
 5800 
 10.78 
 
 705 
 6700 
 16.62 
 
 789 
 7490 
 23.25 
 
 863 
 8160 
 30.45 
 
 934 
 8870 
 38.60 
 
 996 
 9460 
 46.85 
 
 1056 
 10040 
 56.10 
 
662 
 
 AIR. 
 
 Steel Pressure Blowers for Cupolas (Average Application). 
 
 Continued. 
 
 to | No. of blower. 
 
 "o3 
 1 
 
 s-3 
 
 cS 
 
 Q 
 
 >. 
 
 Xs 
 
 *'~ 
 
 T3 
 
 
 
 1 5 /8 
 
 o '*"' 
 
 .s 
 
 is 
 
 .S'ft 
 Q 
 
 63/ 4 
 
 Area of outlet, 
 sq.ft. 
 
 Oz. 
 
 10 
 
 17.28 
 
 11 
 19.02 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 In. 
 
 20.75 
 
 22.5 
 
 24.22 
 
 25.95 
 
 27.66 
 
 Circum 
 whee 
 
 H.P. 
 
 const, 
 at 1000 
 cu.ft. 
 
 6.20 
 
 6.82 
 
 7.44 
 
 8.07 
 
 8.69 
 
 9.30 
 
 9.9.. 
 
 17 
 
 4.45 
 
 0.2485 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 3740 
 1093 
 6.78 
 
 3920 
 1148 
 7.83 
 
 4090 
 1196 
 8.9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 191/2 
 
 17/8 
 
 5.11 
 
 73/ 4 
 
 0.327 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 3255 
 1440 
 8.93 
 
 3415 
 1510 
 10.3 
 
 3570 
 1575 
 11.72 
 
 3710 
 1642 
 13.26 
 
 3955 
 1700 
 14.75 
 
 3985 
 1762 
 16.4 
 
 4120 
 1820 
 18.05 
 
 4 
 5 
 
 6 
 
 22 
 241/2 
 
 2V8 
 
 5.76 
 
 83/4 
 93/4 
 
 0.4176 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 2890 
 1840 
 11.40 
 
 3030 
 1930 
 13.16 
 
 3163 
 2012 
 14.96 
 
 3290 
 2095 
 16.9 
 
 3420 
 2175 
 18.9 
 
 3535 
 
 2250 
 20.9 
 
 3650 
 2325 
 23.1 
 
 23/8 
 
 6.41 
 
 0.519 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 2595 
 2280 
 14.13 
 
 2720 
 2395 
 16.33 
 
 2845 
 2500 
 18.6 
 
 2960 
 2605 
 21.05 
 
 3075 
 2700 
 23.45 
 
 3180 
 2800 
 26.05 
 
 3280 
 2885 
 28.66 
 
 27 
 
 27/8 
 
 7.06 
 
 103/4 
 
 0.63 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 2355 
 2770 
 17.18 
 
 2470 
 2910 
 19.85 
 
 2580 
 3033 
 22.6 
 
 2685 
 3165 
 25.55 
 
 2790 
 3280 
 28.50 
 
 2885 
 3395 
 31.55 
 
 2980 
 3500 
 34.7 
 
 7 
 8 
 
 32 
 
 33/8 
 
 8.39 
 
 121/2 
 
 0.852 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1983 
 3750 
 23.25 
 
 2080 
 3930 
 26.80 
 
 2170 
 4110 
 30.6 
 
 2260 
 4276 
 34.5 
 
 2345 
 4430 
 33. 5 
 
 2430 
 4590 
 42.7 
 
 251C 
 4730 
 47. 
 
 37 
 
 37/8 
 
 9.70 
 
 14 
 
 1.069 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1715 
 4700 
 29.15 
 
 1800 
 4930 
 33.66 
 
 1880 
 5150 
 38.33 
 
 1955 
 5360 
 43.25 
 
 2030 
 5560 
 48.30 
 
 2100 
 5760 
 53.55 
 
 2170 
 5940 
 59. 
 
 9 
 
 42 
 
 43/8 
 
 10.98 
 
 16 
 
 1.396 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1515 
 6150 
 38.15 
 
 1590 
 6450 
 44.00 
 
 1660 
 6730 
 50.15 
 
 1728 
 7010 
 56.60 
 
 1792 
 7270 
 63.2 
 
 1855 
 7525 
 70. 
 
 1916 
 7760 
 77. 
 
 10 
 11 
 
 47 
 
 47/8 
 
 12.30 
 
 171/2 
 
 1.67 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1352 
 7350 
 45.60 
 
 1418 
 7715 
 52.66 
 
 1480 
 8055 
 60, 
 
 1540 
 8390 
 67.66 
 
 1600 
 8700 
 75.6 
 
 1655 
 9010 
 83.9 
 
 1710 
 9300 
 92.25 
 
 52 
 
 53/8 
 57/8 
 
 3.6 
 
 91/4 
 
 2.02 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1222 
 8900 
 55.20 
 
 1282 
 9330 
 63.6 
 
 1340 
 9750 
 72.5 
 
 1393 
 10140 
 82. 
 
 1447 
 10520 
 91.5 
 
 1498 
 10890 
 101.2 
 
 1546 
 H220 
 111.33 
 
 12 
 
 57 
 
 4.92 
 
 2, 
 
 2.405 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1113 
 10580 
 65.5 
 
 1168 
 11100 
 75.70 
 
 1220 
 11600 
 86.33 
 
 1270 
 12080 
 97.5 
 
 1318 
 12520 
 10? 
 
 1363 
 12960 
 120.5 
 
 1410 
 13380 
 132.75 
 
 Caution in Regard to Use of Fan and Blower Tables. Many en- 
 gineers report that some manufacturers' tables overrate the capacity of 
 their fans and underestimate the horse-power required to drive them. In 
 some cases the complaints may be due to restricted air outlets, long and 
 crooked pipes, slipping of belts, too small engines, etc. It may also be 
 due to the fact that the volumes are stated without being accompanied 
 by information as to the maintained resistance, and the volumes givea 
 
FANS AND BLOWERS. 
 
 663 
 
 may be those delivered with an unrestricted inlet and outlet. As this 
 condition is not a practical one, the volume delivered in an installation 
 is much smaller than that given in the tables. The underestimating of 
 horse-power required may be due to the fact that the volumes given in 
 tables are for operation against a practical resistance, and in an installa- 
 tion it might be that the resistance was low, consequently the volume 
 and also the horse-powei required would be greater. 
 
 Capacity of Sturtevant High-Pressure Blowers (1908). 
 
 Number of 
 blower. 
 
 Capacity in cubic feet 
 per minute, 1/2 lb. pres- 
 sure. 
 
 Revolutions per 
 minute. 
 
 Inside dia. 
 of inlet 
 and outbt, 
 inches. 
 
 Approx. 
 weight, 
 pounds.* 
 
 000 
 
 1 to 5 
 
 200 to 1000 
 
 13 ' 8 
 
 40 
 
 00 
 
 5 to 25 
 
 375 to 800 
 
 11/3 
 
 80 
 
 
 
 25 to 45 
 
 370 to 800 
 
 21/2 
 
 140 
 
 ] 
 
 45 to 130 
 
 240 to 600 
 
 3 
 
 330 
 
 2 
 
 130 to 225 
 
 300 to 500 
 
 4 
 
 550 
 
 3 
 
 225 to 325 
 
 380 to 525 
 
 4 
 
 760 
 
 4 
 
 325 to 560 
 
 350 to 565 
 
 6 
 
 1,080 
 
 5 
 
 560 to 1 ,030 
 
 300 to 475 
 
 8 
 
 1,670 
 
 6 
 
 1,030 to 1,540 
 
 290 to 415 
 
 10 
 
 2,500 
 
 7 
 
 1,540 to 2,300 
 
 280 to 410 
 
 10 
 
 3,200 
 
 8 
 
 2,300 to 3,300 
 
 265 to 375 
 
 12 
 
 4,700 
 
 9 
 
 3,300 to 4,700 
 
 250 to 350 
 
 16 
 
 6,100 
 
 10 
 
 4,700 to 6,000 
 
 260 to 330 
 
 16 
 
 8,000 
 
 11 
 
 6,000 to 8,500 
 
 220 to 310 
 
 20 
 
 12,100 
 
 12 
 
 8500 to 11,300 
 
 190 to 250 
 
 24 
 
 18,700 
 
 13 
 
 11, 300 to 15,500 
 
 190 to 260 
 
 30 
 
 22,700 
 
 * Of blower for 1/2 lb. pressure. 
 
 Performance of a No. 7 Steel Pressure Blower under Varying 
 
 Conditions of Outlet. 
 
 Per cent of 
 Rated Ca- 
 pacity 20 40 60 80 100 120 140 160 180 200 220 240 
 
 Per cent of 
 
 Rated H.P. 28 42 57 72 86 100 116 130 144 159 173 187 202 
 
 Total pres- 
 sure, oz 10.211.411.912.011.911.410.910.39.7 9.1 8.5 7.9 7.2 
 
 Static pres- 
 sure, oz ..10.211.211.611.411.0 10.29.2 8.0 6.6 5.0 3.5 1.9 0.3 
 
 Efficiency, per 
 
 cent 26 40 50 56 60 62 61 59 56 52 48 45 
 
 The above figures are taken from a plotted curve of the results of 
 a test by the Buffalo Forge Co. in 1905. A letter describing the test 
 eavs : 
 
 The object was to determine the variation of pressure, power and 
 efficiency obtained at a constant speed with capacities varying from zero 
 discharge to free delivery. A series of capacity conditions were secured 
 by restricting the outlet of the blower by a series of converging cones, 
 so arranged as to make the convergence in each case very slight, and of 
 sufficient length to avoid any noticeable inequality in velocities at the 
 discharge orifice. The fan was operated as nearly at constant speed as 
 possible. The velocity of the air at the point of discharge was measured 
 by a Pitot tube and draft gauge of usual construction. Readings were 
 taken over several points of the outlet and the average taken, although 
 
664 
 
 AlE. 
 
 the variation under nearly all conditions was scarcely perceptible. A 
 coefficient of 93% was assumed for the discharge orifice. The pressure 
 was taken as the reading given by the Pitot tube and draft gauge at 
 outlet. The agreement of this reading with the static pressure in a 
 chamber from which a nozzle was conducted had been checked by a 
 previous test in which the two readings, i.e., velocity and static pressure, 
 were found to agree exactly within the limit of accuracy of the draft 
 gauge, which was about 0.01 in., or, in this case, within 1% The horse- 
 power was determined by means of a motor which had been previously 
 calibrated by a series of brake tests. Variations in speed were assumed 
 to produce variation in capacity in proportion to the speed, variation in 
 pressure to the square of the speed, and variation in H.P. in proportion to 
 the cube of the speed. These relations had been previously shown to 
 hold true for fans in other tests. They were also checked up by oper- 
 ating the fan at various speeds and plotting the capacities directly with 
 the speed as abscissa, the pressure with the square of the speed as abscissa, 
 and the horse power with the cube of the speed as abscissa. These were 
 found, as in previous cases, to have a practically straight-line relation, in 
 which the line passed through the origin. 
 
 Effect of Resistance upon the Capacity of a Fan. A study of the 
 figures in the above table shows the importance of having ample capacity 
 in the air mains and delivery pipes, an.i of the absence of sharp bends 
 or other obstructions to the flow which may increase the resistance or 
 pressure against which the fan operates. The fan delivering its rated 
 capacity against a static pressure of 10.2 ounces delivers only 40 % 
 of that capacity, with the same number of revolutions, if the pressure is 
 increased to 11.6 ounces; the power is reduced only to 57%, instead of 
 40%, and the efficiency drops from 60% to 40%. 
 
 Dimensions of Sirocco Fans. 
 
 (American Blower Co., 1909.) 
 
 s 
 
 i 
 
 i 
 
 .2 
 
 
 
 
 ^d 
 
 <3 
 
 
 
 Ov<n <* 
 
 0) 
 
 d 
 
 -."*. 
 
 7R 
 
 -tj 
 
 C3 >> 
 
 1 
 
 1% 
 
 "S.si 
 
 .S 
 
 *.S 
 
 ^ 
 
 t, to 
 
 W 93 
 
 ^ 
 
 U m 
 ^ > *? 
 
 ^S 
 
 tsj 
 
 " E? 
 
 3.8 
 
 "o 
 
 5g 
 
 lit 
 
 3j 
 
 | 
 
 JH 
 
 ^j? 
 
 o5 
 
 -oW| 
 
 5 n 
 
 c3 
 
 -S 
 
 Q 
 
 -g<jj 
 
 swi 
 
 2 35 
 
 ^ w 
 
 c3i5 
 
 BM 
 
 0>,jO 
 
 S_^Q *i 
 
 ^ W 
 
 s 
 
 s "" 
 
 
 H 
 
 H 
 
 & 
 
 ^ 
 
 ^ 
 
 s 
 
 < 
 
 ^ ** 
 
 ^ 
 
 6 
 
 3 
 
 48 
 
 56 
 
 ii" 
 
 4 
 
 10" 
 
 .23 
 
 .123 
 
 .11 
 
 .12 
 
 3" 
 
 9 
 
 41/2 
 
 48 
 
 127 
 
 r 4" 
 
 6 
 
 r 3" 
 
 .49* 
 
 .349 
 
 .25 
 
 .35 
 
 41/4" 
 
 12 
 
 6 
 
 64 
 
 226 
 
 r 9" 
 
 8 
 
 ,/ 7 // 
 
 .85 
 
 .616 
 
 .44 
 
 .60 
 
 53/ 4 " 
 
 15 
 
 71/2 
 
 64 
 
 353 
 
 2' 4" 
 
 10 
 
 2' 0" 
 
 1.46 
 
 .957 
 
 .69 
 
 .92 
 
 71/ 4 ;; 
 
 18 
 
 9 
 
 64 
 
 509 
 
 2' 10" 
 
 12 
 
 2' 5" 
 
 1.87 
 
 1.37 
 
 1.00 
 
 1.40 
 
 
 21 
 
 101/2 
 
 64 
 
 693 
 
 3 / 4 // 
 
 14 
 
 2' 10" 
 
 2.40 
 
 1.87 
 
 1.34 
 
 1.87 
 
 10" 2 
 
 24 
 
 12 
 
 64 
 
 904 
 
 y 8" 
 
 16 
 
 y 3" 
 
 3.14 
 
 2.46 
 
 1.78 
 
 2.40 
 
 1 1 1/2" 
 
 27 
 
 131/2 
 
 64 
 
 1144 
 
 4 / 3" 
 
 18 
 
 3' 7" 
 
 4.59 
 
 3.11 
 
 2.25 
 
 3.14 
 
 13" 
 
 30 
 
 15 
 
 64 
 
 1413 
 
 4' 7" 
 
 20 
 
 4' 0" 
 
 5.58 
 
 3.83 
 
 2.78 
 
 3.83 
 
 1 4 1/2" 
 
 36 
 
 18 
 
 64 
 
 2036 
 
 5' 6" 
 
 24 
 
 4' 10" 
 
 7.87 
 
 5.50 
 
 4.00 
 
 5.58 
 
 17" 
 
 42 
 
 21 
 
 64 
 
 2770 
 
 6' 5" 
 
 23 
 
 5' 7" 
 
 10.56 
 
 7.47 
 
 5.44 
 
 7.47 
 
 20" 
 
 48 
 
 24 
 
 64 
 
 3617 
 
 7' 3" 
 
 32 
 
 6' 5" 
 
 13.6 
 
 9.79 
 
 7.11 
 
 9.85 
 
 23" 
 
 54 
 
 27 
 
 64 
 
 4578 
 
 8' 2" 
 
 36 
 
 7' 3" 
 
 17.0 
 
 12.3 
 
 9.00 
 
 12.3 
 
 26" 
 
 60 
 
 30 
 
 64 
 
 5652 
 
 y ,// 
 
 40 
 
 S' 0" 
 
 20.9 
 
 15.2 
 
 11.11 
 
 15.3 
 
 281/ 2 " 
 
 66 
 
 33 
 
 64 
 
 6839 
 
 y ||// 
 
 44 
 
 8' 10'J 
 
 25.2 
 
 18.4 
 
 13.41 
 
 18.3 
 
 311/ 2 " 
 
 72 
 
 36 
 
 64 
 
 8144 
 
 lO' 10" 
 
 43 
 
 9, r 
 
 29.8 
 
 22.2 
 
 16.00 
 
 22.3 
 
 341/ 2 " 
 
 Sirocco or Multtvane Fans. There has recently (1909) come into use 
 a fan of radically different proportions and characteristics from the ordi- 
 nary centrifugal fan. This fan is composed of a great number of shallow 
 vanes, ranging from 48 to 64, set close together around the periphery of 
 the fan wheel. Over a large range of sizes, 64 vanes appear to give the 
 
Speed, Capacities and Horse-power of Sirocco Fans. (American 
 
 Blower Co., 1909.) 
 
 The figures given represent dynamic pressures in oz. per sq. in. For 
 static pressure, deduct 28.8%; for velocity pressure, deduct 71.2%. 
 
 4, 
 
 . 
 
 
 N 
 
 P 
 
 N 
 
 
 
 
 eo~ 
 
 o 
 
 1 1/4 OZ. 
 
 N 
 
 O 
 
 o 
 
 
 
 o 
 
 N 
 
 O 
 
 6 
 9 
 \2 
 15 
 18 
 21 
 24 
 27 
 30 
 36 
 42 
 48 
 
 Cu.ft. 
 R.P.M. 
 B.H.P. 
 
 155 
 1,145 
 .0185 
 
 220 
 1,615 
 .052 
 
 270 
 1,980 
 .095 
 
 310 
 2,290 
 .147 
 
 350 
 2,560 
 .205 
 
 380 
 2,800 
 .270 
 
 410 
 3,025 
 .34 
 
 440 
 
 3,230 
 .42 
 
 490 
 3,616 
 .58 
 
 540 
 3,960 
 .76 
 
 Cu.ft, 
 R.P.M. 
 B.H.P. 
 
 350 
 762 
 .042 
 
 500 
 1,076 
 .118 
 
 610 
 1,320 
 .216 
 
 700 
 1,524 
 .333 
 
 790 
 1,700 
 .463 
 
 860 
 1,866 
 .610 
 
 930 
 2,020 
 .77 
 
 1,000 
 2,152 
 .95 
 
 1,110 
 2,408 
 1.32 
 
 1,220 
 2,640 
 1.73 
 
 Cu.ft, 
 R.P.M. 
 B.H.P. 
 
 625 
 572 
 .074 
 
 880 
 808 
 .208 
 
 1,080 
 990 
 .381 
 
 1,250 
 1,145 
 .588 
 
 1,400 
 
 1,280 
 .82 
 
 1,530 
 1,400 
 1.08 
 
 1,650 
 1,512 
 1.36 
 
 1,770 
 1,615 
 1.66 
 
 1,970 
 1,808 
 2.32 
 
 2,170 
 1,980 
 3.05 
 
 Cu.ft. 
 R.P.M. 
 B.H.P. 
 
 975 
 456 
 .115 
 
 1,380 
 645 
 .326 
 
 1,690 
 790 
 .600 
 
 1,950 
 912 
 .923 
 
 2,180 
 1,020 
 1.29 
 
 2,400 
 1,120 
 1.69 
 
 2,590 
 1,210 
 2.14 
 
 2,760 
 1,290 
 2.61 
 
 3,090 
 1,444 
 3.65 
 
 3,390 
 1,580 
 4.8 
 "4^880 
 1,320 
 6.9 
 
 Cu. ft, 
 R.P.M. 
 B.H.P. 
 
 1,410 
 381 
 .167 
 
 1,990 
 538 
 .470 
 
 2,440 
 660 
 .862 
 
 2,820 
 762 
 1.33 
 
 3,160 
 850 
 
 1.85 
 
 3,450 
 933 
 2.43 
 
 3,720 
 1,010 
 3.07 
 
 3,980 
 1,076 
 3.75 
 
 4,450 
 1,204 
 5.25 
 
 Cu. ft, 
 R.P.M. 
 B.H.P. 
 
 1,925 
 326 
 
 .227 
 
 2,710 
 462 
 .640 
 
 3,310 
 565 
 1.17 
 
 3,850 
 652 
 1.81 
 
 4,290 
 730 
 2.53 
 
 4,700 
 800 
 3.33 
 
 5,070 
 864 
 4.18 
 
 5,420 
 924 
 5.11 
 
 6,060 
 1,032 
 7.15 
 
 6,620 
 1,130 
 9.4 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 2,500 
 286 
 .296 
 
 3,540 
 404 
 .832 
 
 4,340 
 495 
 1.53 
 
 5,000 
 572 
 2.35 
 
 5,600 
 640 
 3.28 
 
 6,120 
 700 
 
 4.32 
 
 6,620 
 756 
 
 5.44 
 
 7,080 
 807 
 6.64 
 
 7.900 
 904 
 9.3 
 
 8,680 
 990 
 12.2 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 3,175 
 254 
 .373 
 
 4,490 
 359 
 1.05 
 
 5,500 
 440 
 1.94 
 
 6,350 
 508 
 2.98 
 
 7,100 
 568 
 4.16 
 
 7,780 
 622 
 5.48 
 
 8,400 
 672 
 6.90 
 
 8,980 
 718 
 8.44 
 
 10,050 
 804 
 11.8 
 
 11,000 
 880 
 15.5 
 
 Cu. ft, 
 R.P.M. 
 B.H.P. 
 
 3,910 
 228 
 .460 
 
 5,520 
 322 
 1.30 
 
 6,770 
 395 
 2.40 
 
 7,820 
 456 
 3.68 
 
 8,750 
 510 
 5.15 
 
 9,600 
 560 
 6.75 
 
 10,350 
 604 
 8.53 
 
 11,050 
 645 
 10.4 
 
 12,350 
 722 
 14.5 
 
 13,550 
 790 
 19.1 
 
 Cu.ft. 
 R.P.M. 
 B.H.P. 
 
 5,650 
 190 
 .665 
 
 7,950 
 269 
 1.87 
 
 9,750 
 330 
 3.44 
 
 11,300 
 381 
 5.30 
 
 12,640 
 425 
 7.40 
 
 13,800 
 466 
 9.72 
 
 14,900 
 504 
 12.25 
 
 15,900 
 538 
 15.0 
 
 17,800 
 602 
 20.9 
 
 19,500 
 660 
 27.5 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 7,700 
 163 
 .903 
 
 10,850 
 231 
 2.55 
 
 13,300 
 283 
 4.69 
 
 15,400 
 326 
 7.24 
 "207)00 
 286 
 9.40 
 
 17,170 
 365 
 10.1 
 
 18,800 
 400 
 13.3 
 
 20,300 
 432 
 16.7 
 
 21,700 
 462 
 20.4 
 
 24,250 
 516 
 28.5 
 
 26,600 
 566 
 37.5 
 
 Cu.ft. 
 R.P.M. 
 B.H.P. 
 
 10,000 
 143 
 1.18 
 
 14,150 
 202 
 3.32 
 
 17,350 
 248 
 6.10 
 
 22,400 
 320 
 13.1 
 
 24,500 
 350 
 17.2 
 
 26,500 
 378 
 21.75 
 
 28,300 
 403 
 26.6 
 
 31,600 
 452 
 37.1 
 
 34,700 
 495 
 48.8 
 
 54 
 60 
 66 
 72 
 78 
 84 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 12,700 
 127 
 1.49 
 
 17,950 
 179 
 4.20 
 
 22,000 
 220 
 7.75 
 
 25,400 
 254 
 11.9 
 
 28,400 
 284 
 16.6 
 
 31,100 
 311 
 21.9 
 
 33,600 
 336 
 27.6 
 
 35,900 
 359 
 33.7 
 
 40,200 
 402 
 47.1 
 
 44,000 
 440 
 62. 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 15,650 
 114 
 1.84 
 
 22,100 
 161 
 5.20 
 2MOO 
 147 
 6.30 
 
 27,100 
 198 
 9.58 
 
 31,300 
 
 228 
 14.7 
 
 35,000 
 255 
 20.6 
 
 38,400 
 280 
 27.0 
 
 41,400 
 302 
 34.1 
 
 44,200 
 322 
 41.6 
 
 49,400 
 361 
 58.2 
 
 54,200 
 396 
 76.5 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 18,950 
 104 
 2.23 
 
 32,850 
 180 
 11.6 
 
 37,900 
 208 
 17.8 
 
 42,300 
 232 
 24.9 
 
 46,400 
 254 
 32.7 
 
 50,100 
 275 
 41.2 
 
 53,600 
 294 
 50.4 
 
 60,000 
 328 
 70.4 
 
 65,700 
 360 
 92.6 
 78,000 
 330 
 110. 
 
 Cu. ft. 
 R.P.M. 
 B.II.P. 
 
 22,600 
 95 
 2.66 
 
 31,800 
 134 
 7.48 
 
 39,000 
 165 
 13.7 
 
 45,200 
 190 
 21.2 
 
 50,600 
 212 
 29.6 
 
 55,200 
 233 
 38.9 
 
 59,600 
 252 
 49.0 
 
 63,600 
 269 
 59.8 
 
 71,200 
 301 
 83.6 
 
 Cu. ft. 
 R.P.M 
 B.H.P. 
 
 26,400 
 88 
 3.10 
 
 37,350 
 124 
 8.77 
 
 45,800 
 153 
 16.1 
 
 52,800 
 176 
 24.8 
 
 59,100 
 197 
 34.7 
 
 64,700 
 215 
 45.6 
 
 70,000 
 233 
 57.5 
 
 74,700 
 248 
 70.2 
 
 83,500 
 278 
 98. 
 
 91,600 
 305 
 129. 
 
 Cu. ft. 
 R.P.M. 
 B.H.P 
 
 30,800 
 81 
 3.61 
 
 43,400 
 115 
 10.2 
 
 53,200 
 142 
 18.7 
 
 61,600 
 163 
 28.9 
 
 68,700 
 182 
 40.4 
 
 75,200 
 200 
 53.0 
 
 81,200 
 216 
 66.8 
 
 86,800 
 231 
 81.7 
 
 97,100 
 258 
 114. 
 
 106,400 
 283 
 150. 
 
 90 
 
 Cu. ft 
 R.P.M 
 B.H.P 
 
 35,250 
 76 
 4 14 
 
 49,800 
 107 
 1 11.7 
 
 61.000 
 132 
 21.5 
 
 70,500 
 152 
 33.1 
 
 78,800 
 170 
 46.2 
 
 86,400 
 186 
 60.7 
 
 93,300 
 201 
 76.7 
 
 99,600 
 214 
 93 6 
 
 111,200 
 241 
 131. 
 
 122.000 
 264 
 172. 
 
 665 
 
666 
 
 AIR. 
 
 best results. The vanes, measured radially, have a depth l/ie the fan 
 diameter. Axialiy, they are much longer than those of the ordinary fan, 
 being 3/ 5 the fan diameter. The fan occupies about 1/2 the space, and is 
 about 2/3 the weight of the ordinary fan. The vanes are concaved in the 
 direction of rotation and the outer edge is set forward of the inner edge. 
 The inlet area is of the same diameter as the inner edge of the blades. 
 Usually the inlet is on one side of the fan only, and is unobstructed, the 
 wheel being overhung from a bearing at the opposite end. A peculiarity 
 of this type of fan is that the air leaves it at a velocity about 80 per 
 cent in excess of the peripheral speed of the blades. The velocity of 
 the air through the inlet is practically uniform over the entire inlet 
 area. The power consumption is relatively low. This type of fan was 
 invented by S. C. Davidson of Belfast, Ireland, and is known at the 
 "Sirocco" fan. It is made under that name in this country by the 
 American Blower Co., to which the author in indebted for the preceding 
 tables. 
 
 A Test of a " Sirocco " Mine Fan at Llwnypia, Wales, is reported in 
 Eng'g., April 16, 1909. The fan is 11 ft. Sin. diam., double inlet, direct- 
 coupled to a 3-phase motor. Average of three tests: Revs, per min., 184; 
 Seripheral speed, 6,705 ft. per min.; water-gauge in fan drift and in main 
 rift, each 6 in.; area of drift, 184.6 sq. ft.; av. velocity of air, 1842 
 ft. per min; volume of air, 340,033 cu. ft. per min.; H.P. input at motor, 
 420; Brake H.P. on fan shaft, 390; Indicated H.P. in air, 321.5; efficiency 
 of motor, 93%; mechanical efficiency of fan, 82.43%; combined mechan- 
 ical efficiency of fan and motor, 76.6%. 
 
 High-Pressure Centrifugal Fans. (See page 648.) 
 The Conoidal Fan. A multiblade fan in which the blades are 
 not parallel to the shaft, but inclined to it, so that their tips form 
 the shape of a cone, the inlet being the large diameter, is made by the 
 Buffalo Forge Co. It is known as the Buffalo Niagara Conoidal 
 Fan. A table of the regular sizes of these fans is given below. 
 
 Capacities of Buffalo Niagara Conoidal Fans. 
 
 Under Average Working Conditions at 70 F. and 30 in. Barometer. 
 Static Pressure is 77.5% of Total Pressure. Volumes in cu. ft. per min. 
 
 
 J 
 
 <x> 
 P 
 
 1-in. Total 
 Pressure, or 
 0.577 oz. 
 
 2-in. Total 
 Pressure, or 
 1.154 oz. 
 
 4-in. Total 
 Pressure, or 
 2.307 oz. 
 
 6 
 
 ll 
 
 O 
 
 a 
 
 
 
 Uj 
 
 
 
 a 
 
 
 
 d 
 
 cuS 
 
 <l>J/2 
 
 PH 
 
 ,_; 
 
 p* 
 
 PH 
 
 ,_; 
 
 PH* 
 
 PH 
 
 
 
 PH 
 
 c3 
 
 E 
 
 ii 
 
 tf 
 
 O 
 
 w 
 
 A 
 
 {> 
 
 w 
 
 P4 
 
 > 
 
 H 
 
 ~3~ 
 
 155/8 
 
 1.31 
 
 675 
 
 2,440 
 
 0.54 
 
 955 
 
 3,450 
 
 1.54 
 
 1350 
 
 4,480 
 
 4.35 
 
 31/2 
 
 181/8 
 
 1.79 
 
 579 
 
 3,320 
 
 0.74 
 
 818 
 
 4,690 
 
 2.09 
 
 1157 
 
 6,640 
 
 5.92 
 
 
 201/2 
 
 2.33 
 
 506 
 
 4,340 
 
 0.97 
 
 716 
 
 6,130 
 
 2.73 
 
 1013 
 
 8,670 
 
 7.73 
 
 41/2 
 
 231/2 
 
 2.95 
 
 450 
 
 5,490 
 
 1.22 
 
 636 
 
 7,760 
 
 3.46 
 
 900 
 
 10,970 
 
 9.78 
 
 5 
 
 261,8 
 
 3.64 
 
 405 
 
 6,770 
 
 1.51 
 
 573 
 
 9,580 
 
 4.27 
 
 810 
 
 13,550 
 
 12.1 
 
 51/2 
 
 283/4 
 
 4.41 
 
 368 
 
 8,200 
 
 1.83 
 
 521 
 
 11,590 
 
 5.17 
 
 736 
 
 16,390 
 
 14.6 
 
 6 
 
 313/8 
 
 5.25 
 
 338 
 
 9,750 
 
 2.17 
 
 477 
 
 13,790 
 
 6.15 
 
 675 
 
 19,510 
 
 17.4 
 
 7 
 
 361/2 
 
 7.14 
 
 289 
 
 13,280 
 
 2.96 
 
 409 
 
 18,770 
 
 8.37 
 
 579 
 
 26,550 
 
 23.7 
 
 8 
 
 42 
 
 9.33 
 
 253 
 
 17,340 
 
 3.87 
 
 358 
 
 24,520 
 
 10.9 
 
 506 
 
 34,680 
 
 30.9 
 
 9 
 
 47 
 
 11.81 
 
 225 
 
 21,950 
 
 4.89 
 
 318 
 
 31,020 
 
 13.8 
 
 450 
 
 43.890 
 
 39.1 
 
 10 
 
 52 
 
 14.58 
 
 203 
 
 27,090 
 
 6.04 
 
 286 
 
 38,310 
 
 17.1 
 
 405 
 
 54,180 
 
 48.3 
 
 11 
 
 58 
 
 17.64 
 
 184 
 
 32,780 
 
 7.31 
 
 260 
 
 46,360 
 
 20.7 
 
 368 
 
 65,560 
 
 58.5 
 
 12 
 
 63 
 
 21.00 
 
 169 
 
 39,010 
 
 8.70 
 
 239 
 
 55,170 
 
 24.6 
 
 338 
 
 78,020 
 
 69.6 
 
 13 
 
 68 
 
 24.65 
 
 156 
 
 45,780 
 
 10.2 
 
 220 
 
 64,730 
 
 28.9 
 
 312 
 
 91,560 
 
 81.6 
 
 14 
 
 73 
 
 28.68 
 
 145 
 
 53,100 
 
 11.8 
 
 205 
 
 75,090 
 
 33.5 
 
 289 
 
 106,200 
 
 94.7 
 
 15 
 
 78 
 
 32.80 
 
 135 
 
 60,960 
 
 13.6 
 
 191 
 
 86,200 
 
 38.4 
 
 270 
 
 121,920 
 
 108.7 
 
 16 
 
 84 
 
 37.32 
 
 127 
 
 69,360 
 
 15.5 
 
 179 
 
 98,060 
 
 43.7 
 
 253 
 
 138,700 
 
 123.7 . 
 
 17 
 
 89 
 
 42.14 
 
 119 
 
 78,300 
 
 17.5 
 
 169 
 
 110,720 
 
 49.4 
 
 238 
 
 156,600 
 
 139.6 
 
 18 
 
 94 
 
 47.24 
 
 113 
 
 87,780 
 
 19.6 
 
 159 
 
 124,110 
 
 55.3 
 
 225 
 
 175,550 
 
 156.5 
 
 19 
 
 99 
 
 52.63 
 
 107 
 
 97,800 
 
 21.8 
 
 151 
 
 138,280 
 
 61.7 
 
 213 
 
 195,600 
 
 174.4 
 
 20 1105 
 
 58.32 
 
 101 
 
 108,370 
 
 24.2 
 
 143 
 
 153,250 
 
 68.3 
 
 202 
 
 216,720 
 
 193.2 
 
FANS AND BLOWERS. ' 667 
 
 METHODS OF TESTING FANS. 
 
 Anemometer Method. Measurements by anemometers are liable to 
 be very inaccurate (see page 625) and results obtained by them should 
 be considered only as rough approximations. 
 
 Water Gauge Readings at End of Tapered Cone. This method is 
 also far from accurate on account of variable eddies in the air column. 
 
 Pitot Tube Readings in Center of Discharge Pipe. This method 
 gives fairly accurate results when the discharge pipe is the same size 
 as the fan outlet, when the Pitot tube is placed at a distance equal to 
 at least 15 diameters of the pipe from the fan outlet, when the tube is 
 so made that it will give correct readings of the static pressure, and 
 when the velocities computed from the readings are corrected by a 
 coefficient (0.87 to 0.92 in different experiments) for the ratio between 
 the average velocity and the velocity at the center of the tube. 
 
 Pitot Tube Readings in Zones of Equal Area. More accurate results 
 may be obtained if the tube is traversed across two diameters of the 
 tube at right angles to each other, placing the nozzle successively at 
 points which will divide the cross-sectional area into equal annular 
 areas (with one central circular area). If ten such points are taken 
 on each diameter, the radial distances of the points from the center . of 
 the pipe will be 31, 55, 71, 84, and 95% of the radius of the pipe from 
 the center. Since the velocity at any point is proportional to the 
 square root of the velocity head, it is necessary for accurate results 
 to take the average of the square root of the readings, and square this 
 average to obtain the mean velocity head of the whole area of the pipe. 
 For low pressures an inclined manometer should be used with the Pitot 
 tube, and it should contain gasoline instead of water, as it keeps the 
 tubes clean, has a definite meniscus and almost no capillary attraction 
 for the glass. The readings of the tube are to be corrected for the 
 inclination and for the specific gravity of the gasoline to reduce them 
 to equivalent inches of water column. 
 
 The best form of Pitot tube is one made of two thin brass tubes, the 
 outer one i/4-in. and the inner one i/s-in. external diameter, each about 
 4 or 5 in. long, the two being soldered together at one end and the end 
 then tapered down to a sharp edged nozzle. Each tube is connected 
 near the rear end to tubes at right angles to the double tube, leading 
 to two manometers, one for reading the total, or dynamic or impact 
 pressure, the other the static pressure. The difference between these 
 two readings is the velocity head. It may be obtained in one reading 
 by connecting both parts of the tube to a single manometer. The 
 outer, or static, tube has two or more smooth holes drilled in it, diamet- 
 rically opposite, at right angles to the axis, to receive the static pressure. 
 The exact form of the nozzle of the impact tube is not of importance, 
 as different forms give identical readings, but care must be taken with 
 the holes of the static tube or errors will be made in the readings due 
 to action of the dynamic pressure on these holes if they are not properly 
 made. A thin slot instead of the holes has been found to give in- 
 accurate readings. (See papers by Chas. S. Treat, Trans. A. S. M. E., 
 vol. 34, and W. C. Rowse, Jour. A. S. M. E., Sept., 1913.) 
 
 For accurate scientific work it is well to check the static tube read- 
 ings by manometer readings from a piezometer ring, which is a narrow 
 annular channel encircling the pipe and soldered to it to make it air- 
 tight. Six or more smooth holes are bored into the pipe at right angles 
 to its axis, to connect the interior of the pipe with the ring. The Pitot 
 tube may also be calibrated by means of a Thomas electric gas meter. 
 
 The Thomas Electric Meter for air and gas consists of an enlargement 
 of section of the flow pipe into a chamber of a diameter equal to about 
 two diameters of the pipe, with conical ends connecting it with the 
 pipe. In the interior is placed an electric heater made of bare resistance 
 wire mounted on a fiber frame and equally distributed over the section 
 of the chamber, and also two electric resistance thermometers, one in 
 front of and the other behind the heater. An electric current, meas- 
 ured by a wattmeter, is passed through the heater and the temperatures 
 before and after the heating are measured by the thermometers. If 
 Ti and T* are the temperatures before and after the heating, H the 
 heat units corresponding to the watts delivered to the heater (1 watt 
 
668 
 
 AIK. 
 
 3.415 B.T.TJ. per hour), .and S the Specific heat of the air, then the 
 weight of air heated in Ib. per min. is W = f . nfsf r r -r- 
 
 OUO \2 2 JL I). 
 
 When the Pitot tube is correctly made and used its formula is 
 v = \/2gh, in which h is the mean velocity head, measured as the height 
 in feet of a column of air which would produce the observed velocity 
 and v the velocity in ft. per sec. 
 
 To convert the velocity head as measured in the Pitot tube in inches 
 of water column into velocity of the air in feet per min. we have the 
 following formulae: 
 
 p = velocity pressure in inches of water gage. 
 
 h = corresponding heat in feet of a column of air. 
 
 v = velocity of air in ft. per sec. V = velocity in ft. per min. 
 
 w = weight of 1 cu. ft. of air under existing conditions. 
 
 , = 62 - 3 *>. = . / 64.32X62.3 p. = 1R 97 ^ fi> 
 
 I to" 
 
 12 w 
 
 V = 18.27 
 
 V, ft. per min. = 1096.2 *I!L 
 \tc 
 
 The average weight of 1 cu. ft. of air was found by the American 
 Blower Co. in a large number of tests to be 0.0715 Ib. per cu. ft., whence 
 V 
 
 The velocity of flow of air at a given density produced by a pres- 
 sure of 1 in. of water is called the "velocity constant" of air at that 
 density. A table of such constants is given by the American Blower 
 Co., from which the following table is condensed: 
 
 AIR CONSTANTS FOR DRY AIR AT SEA LEVEL, BAR. 29.92 IN. 
 
 o. . 
 Sfe 
 
 H 
 
 K. 
 
 6 
 33 
 
 & 
 
 d . 
 
 Sfe 
 
 EH 
 
 K. 
 
 .2 
 
 3 
 
 d . 
 Sfc 
 
 
 K. 
 
 
 
 a 
 
 i 
 
 tf 
 
 d 
 6fe 
 H 
 
 K. 
 
 _o 
 
 3 
 
 -40 
 -20 
 
 10 
 20 
 30 
 40 
 50 
 
 3567 
 3651 
 3733 
 3773 
 3813 
 3852 
 3891 
 3930 
 
 0.890 
 .911 
 .932 
 .942 
 .952 
 .961 
 .971 
 .981 
 
 60 
 70 
 80 
 90 
 100 
 HO 
 120 
 140 
 
 3968 
 4006 
 4044 
 4081 
 4118 
 4155 
 4191 
 4263 
 
 0.990 
 .000 
 .009 
 .018 
 .028 
 .037 
 .046 
 .064 
 
 160 
 180 
 200 
 250 
 300 
 350 
 400 
 450 
 
 4333 
 4402 
 4470 
 4636 
 4796 
 4890 
 5101 
 5246 
 
 .082 
 .098 
 .114 
 .157 
 .197 
 .236 
 .273 
 .310 
 
 500 
 600 
 700 
 800 
 900 
 1000 
 1100 
 1200 
 
 5389 
 5663 
 5925 
 6177 
 6418 
 6650 
 6873 
 7090 
 
 .345 
 .413 
 .478 
 .542 
 .602 
 .660 
 .715 
 .770 
 
 Constant K 
 
 weight of 1 cu " ft ' water at 62 F ' 
 
 12 X weight of 1 cu. ft. air at temp, stated. 
 
 The values under Ratio give ratios of fan speeds necessary at the 
 various temperatures to produce the same water gage indication. 
 
 Horse-power of a Fan. If C = cu. ft. of air delivered per minute, 
 W = weight of 1 cu. ft. of air under existing conditions, H the height 
 in feet of an air column equivalent to the total pressure, D the dynamic 
 pressure in inches of water column = WH -h 5.2, the horse-power 
 developed by the delivery of the air is A = CWH -r- 33,000 = CD -f- 6356. 
 One inch water gage = 5.2 Ib. per sq. ft. The total pressure D with 
 which the fan should be credited is the difference between the total 
 pressure in the discharge pipe and that in the inlet pipe. 
 
 The air horse-power divided by the power required to drive the fan, 
 as measured by a dynamometer, gives the mechanical efficiency of the 
 fan. 
 
 From the above formulae the air horse-power is a function of two 
 variables, volume and pressure. To obtain what is called the " static 
 efficiency," the fan should be credited with the difference between 
 the static pressure in the medium from which the fan is drawing 
 air and the static pressure in the discharge pipe. To obtain the 
 
FANS AND BLOWERS. 669 
 
 Impact or total efficiency the fan should be credited with the kinetic 
 energy in the air in the discharge pipe or with the difference between 
 the static pressure in the medium from which the fan is drawing 
 air and the total or impact pressure in the discharge pipe. 
 
 The work of compression is negligible, as these methods have to do 
 with air under low pressure. When readings are taken on the suction 
 side of the fan, for the purpose of determining static efficiency, the 
 fan should be credited only with the difference between the static 
 pressure in the discharging medium and the impact pressure in the 
 inlet pipe. If the object is to determine the impact efficiency where 
 readings are taken at the suction side of the fan, the pressure with 
 which the fan should be credited is the difference between the impact 
 reading at the fan discharge and the impact reading obtained in the 
 inlet pipe. This total pressure with which the fan is credited may 
 also be expressed as the difference between the static pressure in the 
 discharge pipe and the static suction in the inlet pipe, plus the increase 
 of the velocity pressure in the outlet pipe over the velocity pressure 
 in the inlet pipe. 
 
 Accuracy of Pitot Tube Measurements. To obtain even approx- 
 imately accurate results v/ith Pitot tubes it is necessary both to have 
 the tube properly made and to take great precautions in using it. 
 W. C. Rowse, Trans. A. S. M. E., vol. 35 (1913), p. 633, tested several 
 forms of tube, comparing their readings with those of a Thomas 
 electric gas meter. He found the best tube to be one made of a 
 i/4-in. outer and a Vs-in. inner thin brass tube, 4 or 5 in. long, soldered 
 together at one end, which was tapered for 3/4 in. down to the internal 
 diameter of the inner tube, which was thus given a sharp edge. The 
 outer tube was perforated with a small smooth hole 0.02 in. diameter 
 on each side at the middle of its length. The rear end of the small 
 tube and the annular space between the two tubes were each con- 
 nected to 1/4 in. upright tubes, from which rubber tubes led to two 
 manometers. The inner tube received the impact pressure and the 
 annular space the static pressure. The difference between the two 
 is the velocity pressure, a direct reading of which could be made by 
 connecting the two rubber tubes, or branches from them, to the two 
 legs of a single manometer. The manometers were U tubes, of glass 
 about 1/2 in. internal diameter, containing gasoline, and were inclined 
 at an angle of 1 vertical to 10 horizontal in order to magnify the 
 readings. The scale was graduated so as to read in hundredths of 
 ari inch of water column. To obtain mean velocities and pressures 
 the tube was traversed across two diameters of the pipe, vertical and 
 horizontal, ten readings being taken on each diameter, at points 
 located at the center of five annular areas into which the total area 
 of the pipe was divided. The radial distances of these points from the 
 center of the pipe were 32, 55, 71, 84 and 95 per cent, respectively, 
 of the radius of the pipe. (See Appendix No. 6 of the report of the 
 Power Test Committee of the A. S. M. E., 1915.) The results of these 
 tests showed that accuracy within 1 % could be obtained when all 
 readings were obtained with a sufficient degree of refinement and 
 when the Pitot tube was preceded by a length of pipe 20 to 38 times 
 the pipe diameter in order to make the flow as nearly uniform across 
 the section of the pipe as possible. 
 
 When readings were taken at the center of a 12-in. galvanized iron 
 pipe the mean pressure was 0.80 of the pressure at the center, corre- 
 sponding to a mean velocity of "^0.80 or 0.894 of the velocity at the 
 center, within a limit of error of 2%. The mean velocity head was 
 obtained by taking the square of the average of the square roots of 
 each of the 20 readings. Tests of Pitot tubes with long narrow slots 
 in the outer tube, instead of the small holes, gave results which were 
 in error from 3.5 to 10%. 
 
 The Thomas Electric Gas Meter, referred to above, is. described 
 in Trans. A. S. M. E., vol. 31, p. 655. It consists in an enlarged 
 section of the gas or air pipe containing an electric heating device 
 with electric instruments for determining both the increase of tem- 
 perature and the energy absorbed in heating. Given the specific 
 neat, the rise in temperature, and the watts of energy absorbed, the 
 weight of gas flowing in a given time may be computed. 
 
670 
 
 AIR. 
 
 Flow of Air through an Orifice. 
 
 VELOCITY, VOLUME, AND H.P. REQUIRED WHEN AIR UNDER GIVEN PRESSURE 
 IN OUNCES PER SQ. IN. IS ALLOWED TO ESCAPE INTO THE ATMOSPHERE. 
 
 (B. F. Sturtevant Co.) 
 
 sr 
 t-, 
 
 1 
 
 ft 
 
 1| 
 
 : i 
 
 S, & 
 
 t_, 
 
 1 
 
 ||g. 
 
 o ^ 
 
 "** S 
 
 - j3 
 
 (-> . 
 
 
 .2 
 
 -t-s 
 
 *-" * c3'3 
 
 Q 0J2 
 
 >< 
 
 .3 & 
 
 4J 
 
 2 * cf-~ 
 
 
 
 O> W 
 
 *J}<3 
 
 "I 
 
 "5 d 2 
 
 Isg 
 
 O 3 
 
 d GO 
 
 "t 
 
 5 d ^ 
 
 0-5 ^ 
 
 1*3 
 
 -, 0) 
 
 S l 
 
 'o d 
 
 '~ ^ 
 S 6* 3) ft 
 
 |>S~ 
 
 Jo d 
 
 IH 0) 
 
 3 o 
 
 w fl 
 
 'o d 
 
 1*^*8, 
 
 i>S-^ 
 
 ^|d 
 
 o,S 
 
 !* 
 
 I 1 
 
 "Q '+-<+_, 
 
 o S'Sb'o 
 
 ol'g 
 
 Bia 
 
 i'a 
 
 !-' 
 
 o S'Ei'o 
 
 1- 
 
 PL. 
 
 ^ 
 
 
 
 w 
 
 w 
 
 PH 
 
 > 
 
 > 
 
 w 
 
 
 
 1/8 
 
 0.216 
 
 1.828 
 
 12.69 
 
 0.00043 
 
 0.0340 
 
 2 
 
 7.284 
 
 50.59 
 
 0.02759 
 
 0.5454 
 
 1/4 
 
 0.432 
 
 2,585 
 
 17.95 
 
 0.00122 
 
 0.0680 
 
 21/8 
 
 7.507 
 
 52.13 
 
 0.03021 
 
 0.5795 
 
 3/8 
 
 0.648 
 
 3,165 
 
 21.98 
 
 0.00225 
 
 0.1022 
 
 21/4 
 
 7.722 
 
 53.63 
 
 0.03291 
 
 0.6136 
 
 1/2 
 
 0.864 
 
 3.654 
 
 25.37 
 
 0.00346 
 
 0.1363 
 
 23/8 
 
 7.932 
 
 55.08 
 
 0.03568 
 
 0.6476 
 
 5/8 
 
 .080 
 
 4.084 
 
 28.36 
 
 0.00483 
 
 0.1703 
 
 21 2 
 
 8.136 
 
 56.50 
 
 0.03852 
 
 0.6818 
 
 3/4 
 
 .296 
 
 4.473 
 
 31.06 
 
 0.00635 
 
 0.2044 
 
 25/ 8 
 
 8,334 
 
 57.88 
 
 0.04144 
 
 0.7160 
 
 7/8 
 
 .512 
 
 4.830 
 
 33.54 
 
 0.00800 
 
 0.2385 
 
 23/4 
 
 8.528 
 
 59.22 
 
 0.04442 
 
 0.7500 
 
 
 .728 
 
 5.162 
 
 35.85 
 
 0.00978 
 
 0.2728 
 
 27/8 
 
 8,718 
 
 60.54 
 
 0.04747 
 
 0.7841 
 
 H/8 
 
 .944 
 
 5.473 
 
 38.01 
 
 0.01166 
 
 0.3068 
 
 3 
 
 8.903 
 
 61.83 
 
 0.05058 
 
 0.8180 
 
 
 2.160 
 
 5.768 
 
 40.06 
 
 0.01366 
 
 0.3410 
 
 31/8 
 
 9.084 
 
 63.08 
 
 0.05376 
 
 0.8522 
 
 13/8 
 
 2.376 
 
 6.048 
 
 42.00 
 
 0.01575 
 
 0.3750 
 
 31/4 
 
 9.262 
 
 64.32 
 
 0.05701 
 
 0.8863 
 
 U/2 
 
 2.59? 
 
 6.315 
 
 43.86 
 
 0.01794 
 
 0.4090 
 
 33/8 
 
 9.435 
 
 65.52 
 
 0.06031 
 
 0.9205 
 
 15/8 
 
 2.808 
 
 6.571 
 
 45.63 
 
 0.02022 
 
 0.4431 
 
 31/2 
 
 9.606 
 
 66.71 
 
 0.06368 
 
 0.9546 
 
 13/4 
 
 3.024 
 
 6.818 
 
 47.34 
 
 0.02260 
 
 0.4772 
 
 35/8 
 
 9,773 
 
 67.87 
 
 0.06740 
 
 0.9887 
 
 17/8 
 
 3.240 
 
 7,055 
 
 49.00 
 
 0.02505 
 
 0.5112 
 
 33/4 
 
 9.938 
 
 69.01 
 
 0.07058 
 
 1.0227 
 
 
 
 
 
 
 
 37/8 
 
 10.100 
 
 70.14 
 
 0.07412 
 
 1 .0567 
 
 (0 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 d) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 The headings of the 3d and 4th columns in the above table have been 
 abridged from the original, which read as follows: Velocity of dry air, 
 50 F., escaping into the atmosphere through any shaped orifice in any 
 pipe or reservoir in which the given pressure is maintained. Volume of 
 air in cubic feet which may be discharged in one minute through an orifice 
 having an effective area of discharge of one square inch. The 6th column, 
 not in the original, has been calculated by the author. The figures repre- 
 sent the horse-power theoretically required to move 1000 cu. ft. of air of 
 the given pressures through an orifice, without allowance for the work of 
 compression or for friction or other losses of the fan. These losses may 
 amount to 60% or more of the given horse-power. 
 
 The change in density which results from a change in pressure has been 
 . taken into account in the calculations of the table. The volume of air at 
 a given velocity discharged through an orifice depends upon its shape, and 
 is always less than that measured by its full area. For a given effective 
 area the volume is proportional to the velocity. The power required to 
 move air through an orifice is measured by the product of the velocity and 
 the total resisting pressure. This power for a given orifice varies as the 
 cube of the velocity. For a given volume it varies as the square of the 
 velocity. In the movement of air by means of a fan there are unavoidable 
 resistances which, in proportion to their amount, increase the actual power 
 considerably above the amount here given. 
 
 Pipe Lines for Fans and Blowers. In installing fane and blowers 
 careful consideration should be given to the pipe line conducting the air 
 from the fan or blower. Bends and turns in the pipe, even of long radii, 
 will cause considerable drop in pressure, and in straight pipe the friction of 
 the moving air is a source of considerable loss. The friction increases with 
 the length of the pipe and is inversely as the diameter. It also varies as the 
 square of the velocity. In long runs of pipe, the increased cost of a larger 
 pipe can often be compensated by the decreased cost of the motor and 
 power for operating the blower. 
 
 The advisability of using a large pipe for conveying the air is shown by 
 
FANS AND BLOWERS. 
 
 671 
 
 the following table which gives the size of pipe which should be used for 
 pressure losses not exceeding one-fourth and one-half ounce per square 
 inch, for various lengths of pipe. 
 
 Diameters of Blast Pipes. 
 
 (B. F. Sturtevant Co., 1908.) 
 
 (H 
 
 
 H 
 
 Length of Pipe in Feet. 
 
 ft 
 
 o 
 
 '3 
 
 
 
 .A 
 
 "1 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 *L 
 
 41 
 
 1 
 
 Diameter of Pipe with Drop of 
 
 |l 
 
 fa 
 
 1* 
 
 1/4 
 Oz. 
 
 1/2 
 Oz. 
 
 1/4 
 Oz. 
 
 1/2 
 Oz. 
 
 1/4 
 Oz. 
 
 1/2 
 Oz. 
 
 1/4 
 Oz. 
 
 1/2 
 Oz. 
 
 1/4 
 Oz. 
 
 1/2 
 Oz. 
 
 
 
 ol 
 
 1/4 
 Oz 
 
 1/2 
 Oz. 
 
 1 
 
 23 
 
 500 
 
 6 
 
 5 
 
 7 
 
 6 
 
 7 
 
 6 
 
 8 
 
 7 
 
 9 
 
 8 
 
 9 
 
 8 
 
 9 
 
 8 
 
 2 
 
 27 
 
 1,000 
 
 8 
 
 7 
 
 9 
 
 8 
 
 10 
 
 9 
 
 11 
 
 9 
 
 11 
 
 10 
 
 12 
 
 11 
 
 12 
 
 11 
 
 3 
 
 30 
 
 1,500 
 
 10 
 
 8 
 
 11 
 
 10 
 
 11 
 
 10 
 
 12 
 
 11 
 
 13 
 
 11 
 
 13 
 
 12 
 
 14 
 
 12 
 
 4 
 
 32 
 
 2,000 
 
 11 
 
 9 
 
 12 
 
 11 
 
 13 
 
 12 
 
 14 
 
 12 
 
 15 
 
 .13 
 
 15 
 
 14 
 
 16 
 
 14 
 
 5 
 
 36 
 
 2,500 
 
 12 
 
 10 
 
 14 
 
 12 
 
 15 
 
 13 
 
 15 
 
 14 
 
 16 
 
 14 
 
 17 
 
 15 
 
 17 
 
 15 
 
 6 
 
 39 
 
 3,000 
 
 13 
 
 11 
 
 15 
 
 13 
 
 16 
 
 14 
 
 17 
 
 15 
 
 18 
 
 15 
 
 18 
 
 16 
 
 18 
 
 16 
 
 7 
 
 42 
 
 3,500 
 
 13 
 
 12 
 
 15 
 
 13 
 
 17 
 
 15 
 
 17 
 
 15 
 
 18 
 
 16 
 
 19 
 
 17 
 
 20 
 
 18 
 
 8 
 
 45 
 
 4,000 
 
 15 
 
 12 
 
 16 
 
 15 
 
 18 
 
 15 
 
 18 
 
 16 
 
 19 
 
 17 
 
 20 
 
 18 
 
 21 
 
 18 
 
 9 
 
 48 
 
 4,500 
 
 15 
 
 13 
 
 17 
 
 15 
 
 18 
 
 16 
 
 19 
 
 17 
 
 20 
 
 18 
 
 21 
 
 19 
 
 22 
 
 19 
 
 10 
 
 54 
 
 5,000 
 
 15 
 
 13 
 
 18 
 
 15 
 
 19 
 
 17 
 
 20 
 
 18 
 
 21 
 
 18 
 
 22 
 
 19 
 
 23 
 
 20 
 
 11 
 
 54 
 
 5,500 
 
 16 
 
 14 
 
 18 
 
 16 
 
 20 
 
 17 
 
 21 
 
 18 
 
 22 
 
 19 
 
 23 
 
 20 
 
 23 
 
 20 
 
 12 
 
 60 
 
 6,000 
 
 17 
 
 14 
 
 19 
 
 17 
 
 20 
 
 17 
 
 21 
 
 19 
 
 22 
 
 20 
 
 23 
 
 21 
 
 24 
 
 21 
 
 13 
 
 60 
 
 6,500 
 
 17 
 
 14 
 
 19 
 
 17 
 
 21 
 
 18 
 
 23 
 
 19 
 
 23 
 
 20 
 
 24 
 
 21 
 
 25 
 
 22 
 
 14 
 
 60 
 
 7,000 
 
 18 
 
 15 
 
 20 
 
 18 
 
 22 
 
 19 
 
 23 
 
 20 
 
 24 
 
 21 
 
 25 
 
 22 
 
 26 
 
 23 
 
 15 
 
 66 
 
 7,500 
 
 18 
 
 16 
 
 21 
 
 18 
 
 22 
 
 19 
 
 24 
 
 21 
 
 25 
 
 22 
 
 26 
 
 22 
 
 27 
 
 23 
 
 16 
 
 66 
 
 8,000 
 
 18 
 
 16 
 
 22 
 
 18 
 
 23 
 
 20 
 
 24 
 
 22 
 
 26 
 
 22 
 
 26 
 
 23 
 
 27 
 
 24 
 
 17 
 
 66 
 
 8.500 
 
 18 
 
 16 
 
 22 
 
 18 
 
 23 
 
 20 
 
 24 
 
 22 
 
 26 
 
 22 
 
 27 
 
 24 
 
 28 
 
 24 
 
 18 
 
 72 
 
 9,000 
 
 18 
 
 17 
 
 22 
 
 18 
 
 24 
 
 21 
 
 25 
 
 22 
 
 27 
 
 23 
 
 27 
 
 24 
 
 28 
 
 25 
 
 19 
 
 72 
 
 9,500 
 
 20 
 
 17 
 
 -23 
 
 20 
 
 24 
 
 22 
 
 26 
 
 23 
 
 28 
 
 23 
 
 28 
 
 25 
 
 29 
 
 26 
 
 20 
 
 72 
 
 10,000 
 
 20 
 
 18 
 
 23 
 
 20 
 
 25 
 
 22 
 
 27 
 
 23 
 
 28 
 
 24 
 
 29 
 
 25 
 
 30 
 
 26 
 
 21 
 
 78 
 
 10,500 
 
 21 
 
 18 
 
 24 
 
 21 
 
 26 
 
 23 
 
 27 
 
 23 
 
 29 
 
 25 
 
 30 
 
 26 
 
 30 
 
 26 
 
 22 
 
 78 
 
 11,000 
 
 21 
 
 18 
 
 24 
 
 21 
 
 27 
 
 23 
 
 28 
 
 24 
 
 29 
 
 26 
 
 30 
 
 27 
 
 31 
 
 27 
 
 23 
 
 78 
 
 11,500 
 
 21 
 
 19 
 
 25 
 
 21 
 
 27 
 
 24 
 
 28 
 
 25 
 
 30 
 
 26 
 
 30 
 
 27 
 
 31 
 
 27 
 
 24 
 
 84 
 
 12,000 
 
 22 
 
 19 
 
 25 
 
 22 
 
 28 
 
 24 
 
 28 
 
 25 
 
 31 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 25 
 
 84 
 
 12,500 
 
 22 
 
 19 
 
 26 
 
 22 
 
 28 
 
 24 
 
 29 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 33 
 
 28 
 
 26 
 
 84 
 
 13,000 
 
 22 
 
 19 
 
 26 
 
 22 
 
 28 
 
 24 
 
 29 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 33 
 
 28 
 
 27 
 
 90 
 
 13.500 
 
 23 
 
 20 
 
 26 
 
 23 
 
 28 
 
 24 
 
 30 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 34 
 
 28 
 
 28 
 
 90 
 
 14,000 
 
 23 
 
 20 
 
 27 
 
 23 
 
 29 
 
 25 
 
 30 
 
 27 
 
 32 
 
 28 
 
 33 
 
 29 
 
 34 
 
 29 
 
 29 
 
 90 
 
 14,500 
 
 23 
 
 20 
 
 27 
 
 23 
 
 29 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 33 
 
 29 
 
 34 
 
 30 
 
 30 
 
 90 
 
 15.000 
 
 24 
 
 21 
 
 27 
 
 24 
 
 29 
 
 26 
 
 31 
 
 27 
 
 32 
 
 28 
 
 34 
 
 30 
 
 35 
 
 30 
 
 The minimum radius of each turn should be equal to the diameter of the 
 pipe. For each turn thus made add three feet in length, when using this 
 table. If the turns are of less radius, the length added should be increased 
 proportionately. 
 
 The above table has been constructed on the following basis: A loss of, 
 say, 1/2 oz. pressure was allowed as a standard for the transmission of a 
 given quantity of air through a given length of pipe of any diameter. The 
 increased loss due to increasing the length of pipe was compensated for by 
 increasing the diameter sufficiently to keep the loss still at 1/2 oz. Thus, 
 if 2500 cu. ft. of air is to be delivered per minute through 100 ft of pipe 
 with a loss of not more than i/ 2 oz., a H-in. pipe will be required, If it is 
 
672 AIR. 
 
 necessary to increase the length of pipe to 140 ft., a pipe 15 in. diameter 
 will be required if the loss in pressure is not to exceed 1/2 oz. In deciding 
 the size of pipe the loss in pressure in the pipe must be added to the pres- 
 sure to be maintained at the fan or blower, if the tabulated efficiency of 
 the latter is to be secured at the delivery end of the pipe. 
 
 Centrifugal Ventilators for Mines. Of different appliances for ven- 
 tilating mines various forms of centrifugal machines having proved their 
 efficiency have now almost completely replaced all others. Most if not all 
 of the machines in use in this country are of this class, being either open- 
 periphery fans, or closed, with chimney and spiral casing, of a more or less 
 modified Guibal type. The theory of such machines has been demonstrated 
 by Mr. Daniel Murgue in " Theories and Practices of Centrifugal Ventilating 
 Machines," translated by A. L. Stevenson, and is discussed in a paper by R. 
 Van A. Norris, Trans. A. I. M. E., xx. 637. From this paper the following 
 formula are taken: 
 
 Let a = area in sq. ft. of an orifice in a thin plate, of such area that its 
 resistance to the passage of a given quantity of air equals the 
 resistance of the mine; 
 o = orifice in a thin plate of such area that its resistance to the pas- 
 
 sage of a given quantity of air equals that of the machine; 
 Q^= quantity of air passing in cubic feet per minute; 
 V = velocity of air passing through a in feet per second; 
 V = velocity of air passing through o in feet per second ; 
 h, = head in feet air-column to produce velocity V; 
 ho = head in feet air-column to produce velocity VQ. 
 
 , 
 
 feet per minute 
 
 0.403 Q 
 = 
 
 Q = 0.65 aV; V = ^Tgh; Q = Q.65a^2gh' t 
 
 a = , = equivalent orifice of mine; 
 
 0.65 v 2 gh 
 
 or, reducing to water-gauge in inches and quantity in thousands of cubic 
 fpftt, npr minute. 
 
 = 0.65 oF ; Fo = ^2 ^ ; (? = 0.65 o ^ / 2gh - l 
 
 v/ 
 
 O 2 
 
 equivalent orifice of machine. 
 
 0.65%2 g 
 
 The theoretical depression which can be produced by any centrifugal 
 ventilator is double that due to its tangential speed. The formula 
 
 T y 2 
 H -2~g- 2~g' 
 
 in which Tis the tangential speed, V the velocity of exit of the air from the 
 space between the blades, and H the depression measured in feet of air- 
 column, is an expression for the theoretical depression which can be pro- 
 duced by an uncovered ventilator: this reaches a maximum when the air 
 leaves the blades without speed, that is, V = 0, and H = T z * 2 g. 
 
 Hence the theoretical depression which can be produced by any uncov- 
 ered ventilator is equal to the height due to its tangential speed, and one- 
 half tnat which can be produced by a covered ventilator with expanding 
 chimney. Practical considerations in the design of the fan wheel and 
 casing will probably cause the actual results obtained with fans to vary 
 considerably from these formulae. 
 
 So long as the condition of the mine remains constant: 
 
 (1) The volume produced by any ventilator varies directly as the speed 
 of rotation. 
 
 (2) The depression produced by any ventilator varies as the square of 
 the speed of rotation. 
 
 (3) For the same tangential speed with decreased resistance the quantity 
 of air increases and the depression diminishes, 
 
MINE VENTILATING FANS. 
 
 673 
 
 The following table shows a few results, selected from Mr. Norris's 
 paper, giving the range of efficiency which may be expected under dif- 
 ferent circumstances. Details of these and other fans, with diagrams 
 of the results, are given in the paper. 
 
 Experiments on Mine-Ventilating Fans. 
 
 
 
 tf 
 
 t-i 
 "2 
 
 * 
 
 vi 
 
 ."1* 
 
 
 49 
 
 <L o 
 
 , 
 
 g 
 
 
 IN 
 
 S 
 
 <& 
 
 & g 
 
 
 ^'E 
 
 
 
 .2 
 
 v 
 
 td d 
 
 
 g 
 
 fa 
 
 &| 
 
 f 
 
 Jo5 
 gj 
 
 Oftg 
 
 
 
 B 
 
 -| 
 
 "I 
 
 o| 
 
 
 1*2" 
 
 
 |l 
 
 "3 
 
 
 8| 
 
 o "o 
 
 i 
 
 
 
 || 
 
 &! 
 
 1 
 
 
 "i 
 
 It 
 
 .of 
 
 o ^ 
 
 1^ 
 
 -2 7 ^ 
 
 .S'o 
 
 6 
 
 
 "v ti 
 
 > S -t5 
 
 1 
 
 l 
 
 CJS 
 
 !* 
 
 O 
 
 'P 
 
 O 
 
 p 
 
 o'S 
 ffl 
 
 I a 
 
 
 |^| 
 
 
 84 
 
 5517 
 
 236,684 
 
 2818 
 
 3040 
 
 4290 
 
 1 80 
 
 67.13 
 
 88.40 
 
 75.9 
 
 ^ S 
 
 
 100 
 
 6282 
 
 336,862 
 
 3369 
 
 3040 
 
 5393 
 
 2.50 
 
 132.70 
 
 155.43 
 
 85.4 
 
 11 
 
 
 1 1 1 
 
 6973 
 
 347,396 
 
 3130 
 
 3040 
 
 5002 
 
 3.20 
 
 175.17 
 
 209.64 
 
 83.6 
 
 rS 
 
 
 123 
 
 7727 
 
 394,100 
 
 3204 
 
 3040 
 
 5100 
 
 3.60 
 
 223.56 
 
 295.21 
 
 75.7 
 
 )> 
 
 
 100 
 
 6282 
 
 188,888 
 
 1889 
 
 1520 
 
 3007 
 
 1.40 
 
 41.67 
 
 97.99 
 
 42.5 
 
 
 
 130 
 
 8167 
 
 274,876 
 
 2114 
 
 1520 
 
 3366 
 
 2.00 
 
 86.63 
 
 194.95 
 
 44.6 
 
 22 
 
 CJ 
 
 59 
 
 3702 
 
 59,587 
 
 1010 
 
 1520 
 
 1610 
 
 1.20 
 
 11.27 
 
 16.76 
 
 67.83 
 
 
 < 
 
 83 
 
 5208 
 
 82,969 
 
 1000 
 
 1520 
 
 1593 
 
 2.15 
 
 27.86 
 
 48.54 
 
 57.38 
 
 
 n J 
 
 40 
 
 3140 
 
 49,611 
 
 1240 
 
 3096 
 
 1580 
 
 0.87 
 
 6.80 
 
 13.82 
 
 49.2 
 
 32 
 
 D l 
 
 70 
 
 5495 
 
 137,760 
 
 1825 
 
 3096 
 
 2507 
 
 2.55 
 
 55.35 
 
 67.44 
 
 82.07 
 
 
 
 50 
 
 2749 
 
 147,232 
 
 2944 
 
 1522 
 
 5356 
 
 0.50 
 
 11.60 
 
 28.55 
 
 40.63 
 
 
 E s 
 
 69 
 
 3793 
 
 205,761 
 
 2982 
 
 1522 
 
 5451 
 
 1.00 
 
 32.42 
 
 45.98 
 
 70.50 
 
 83 
 
 ( 
 
 96 
 
 5278 
 
 299,600 
 
 3121 
 
 1522 
 
 5676 
 
 2.15 
 
 101.50 
 
 120.64 
 
 84.10 
 
 
 
 200 
 
 7540 
 
 133,198 
 
 666 
 
 746 
 
 1767 
 
 3.35 
 
 70.30 
 
 102.79 
 
 68.40 
 
 26.9 
 
 
 200 
 
 7540 
 
 180,809 
 
 904 
 
 746 
 
 2398 
 
 3.05 
 
 86.89 
 
 129.07 
 
 67.30 
 
 38.3 
 
 
 200 
 
 7540 
 
 209,150 
 
 1046 
 
 746 
 
 2774 
 
 2.80 
 
 92.50 
 
 150.08 
 
 61.70 
 
 46.3 
 
 
 10 
 
 785 
 
 28,896 
 
 2890 
 
 3022 
 
 3680 
 
 0.10 
 
 0.45 
 
 1.30 
 
 35. 
 
 
 
 20 
 
 1570 
 
 57,120 
 
 2856 
 
 3022 
 
 3637 
 
 0.20 
 
 1.80 
 
 3.70 
 
 49. 
 
 
 
 25 
 
 1962 
 
 66,640 
 
 2665 
 
 3022 
 
 3399 
 
 0.29 
 
 2.90 
 
 6.10 
 
 48. 
 
 
 
 30 
 
 2355 
 
 73,080 
 
 2436 
 
 3022 
 
 3103 
 
 0.40 
 
 4.60 
 
 9.70 
 
 47. 
 
 52 
 
 G,^ 
 
 35 
 
 2747 
 
 94,080 
 
 2688 
 
 3022 
 
 3425 
 
 0.50 
 
 7.40 
 
 15.00 
 
 48. 
 
 
 ^ 
 
 40 
 
 3140 
 
 112,000 
 
 2800 
 
 3022 
 
 3567 
 
 0.70 
 
 12.30 
 
 24.90 
 
 49. 
 
 
 
 50 
 
 3925 
 
 132,700 
 
 2654 
 
 3022 
 
 3381 
 
 0.90 
 
 18.80 
 
 38.80 
 
 48. 
 
 
 
 60 
 
 4710 
 
 173,600 
 
 2893 
 
 3022 
 
 3686 
 
 1.35 
 
 36.90 
 
 66.40 
 
 55. 
 
 
 
 70 
 
 5495 
 
 203,280 
 
 2904 
 
 3022 
 
 3718 
 
 1.80 
 
 57.70 
 
 107.10 
 
 54. 
 
 
 
 m 
 
 6280 
 
 222,320 
 
 2779 
 
 3022 
 
 3540 
 
 2.25 
 
 78.80 
 
 152.60 
 
 52. 
 
 
 Type of fan. 
 
 Diam. 
 
 Width. 
 
 No. inlets. 
 
 Diam. 
 inlets. 
 
 A. Guibal, double . ... 
 
 20ft. 
 
 6ft. 
 
 4 
 
 8ft. 10 in. 
 
 B. Same, only left hand running 
 C Guibal 
 
 20 
 20 
 
 6 
 6 
 
 4 
 2 
 
 8 10 
 8 10 
 
 D. Guibal 
 
 25 
 
 8 
 
 1 
 
 11 6 
 
 E. Guibal double 
 
 171/o 
 
 4 
 
 4 
 
 8 
 
 F. Capell...... 
 
 12 
 
 10 
 
 2 
 
 7 
 
 G. Guibal 
 
 25 
 
 8 
 
 
 12 
 
 
 
 
 
 
 An examination of the detailed results of each test in Mr. Norris's table 
 shows a mass of contradictions from which it is exceedingly diffiault to 
 draw any satisfactory conclusions. The following, he states, appear to be 
 more or less warranted by some of the figures: 
 
 1. Influence of the Condition of the Airways on the Fan. Mines with 
 varying equivalent orifices give air per 100 ft. speed of tip of fan, within 
 limits as follows, the quantity depending on the resistance of the mine; 
 
674 
 
 AIR. 
 
 E quivalent 
 orifice, 
 sq. ft. 
 
 Cu.ft.air 
 per 100 ft. 
 speed of fan. 
 
 Average. 
 
 Equivalent 
 orifice, 
 sq. ft. 
 
 Cu.ft. air 
 per 100 ft. 
 speed of fan. 
 
 Average. 
 
 Under 20 
 20 to 30 
 30 to 40 
 40 to 50 
 
 1100 to 1700 
 1300 to 1800 
 1500 to 2500 
 2300 to 3500 
 
 13QO 
 1600 
 2100 
 2700 
 
 60 to 70 
 70 to 80 
 80 to 90 
 90 to 100 
 
 3300 to 5100 
 4000 to 4700 
 3000 to 5600 
 
 4000 
 4400 
 4800 
 
 50 to 60 
 
 2700 to 4800 
 
 3500 
 
 100 to 114 
 
 5200 to 6200 
 
 5700 
 
 The influence of the mine on the efficiency of the fan does not seem to be 
 very clear. Eight fans, with equivalent orifices over 50 square feet, give 
 efficiencies over 70%; four, with smaller equivalent mine-orifices, give 
 about the same figures; while, on the contrary, six fans, with equivalent 
 orifices of over 50 square feet, give lower efficiencies, as do ten fans, all 
 drawing from mines with small equivalent orifices. It would seem that, 
 on the whole, large airways tend to assist somewhat in attaining high 
 efficiency. 
 
 2. Influence of the Diameter of the Fan. This seems to be practically nil, 
 the only advantage of large fans being in their greater width and the lower 
 speed required of the engines. 
 
 3. Influence of the Width of a Fan. This appears to be small as regards 
 the efficiency of the machine; but the wider fans are, as a rule, exhausting 
 more air. However, increasing the width of the fan of a given diameter 
 causes an increase in the velocity of the air through the wheel inlet, and 
 this increased velocity will become at a certain point a serious loss and 
 will decrease the mechanical efficiency. 
 
 4. Influence of Shape of Blades. This appears, within reasonable limits, 
 to be practically nil. Thus, six fans with tips of blades curved forward, 
 three fans with flat blades, and one with blades curved back to a tangent 
 with the circumference, all give very high efficiencies over 70 per cent. 
 A prominent manufacturer claims, however, that his tests show a higher 
 efficiency with vanes curved forward as compared with straight or back- 
 wardiy curved vanes. 
 
 5. Influence of the Shape of the Spiral Casing. This appears to be 
 considerable. The shapes of spiral casing in use fall into two classes, 
 the first presenting a large spiral, beginning at or near the point of cut-off, 
 and the second a circular casing reaching around three-quarters of the 
 circumference of the fan, with a short spiral reaching to the evasee 
 chimney. Fans having the first form of casing appear to give in 
 almost every case high efficiencies. 
 
 Fans that have a spiral belonging to the first class, but very much con- 
 tracted, give only medium efficiencies. It seems probable that the proper 
 shape of spiral casing would be one of such form that the air between each 
 pair of blades could constantly and freely discharge into the space between 
 the fan and casing, the whole being swept along to the evasee chimney. 
 This would require a spiral beginning near the point of cut-off, enlarging by 
 gradually increasing increments, to allow for the slowing of the air caused 
 by its friction against the casing, and reaching the chimney with an area 
 such that the air could make its exit with its then existing speed some- 
 what less than the periphery-speed of the fan. 
 
 6. Influence of the Shutter. The shutter certainly appears. to be an ad- 
 vantage, as by it the exit area can be regulated to suit the varying quantity 
 of air given by the fan, and in this way re-entries can be prevented J 
 not uncommon to find shutterless fans, into the chimneys of which bits of 
 paper may be dropped, which are drawn into the fan, make the circuit, and 
 are again thrown out. This peculiarity has not been noticed with fans 
 provided with shutters. 
 
 7. Influence of the Speed at which a Fan is Run. It is noticeable that 
 most of the fans giving high efficiency were running at a rather high 
 periphery velocity. The best speed seems to be between 5000 and 6000 
 feet per minute. The fans appear to reach a maximum efficiency at some- 
 where about the speed given, and to decrease rapidly in efficiency when 
 this maximum point is passed. The same manufacturer mentioned in 
 note 4 states that the efficiency is not affected by the tip speed, providing 
 that the comparison is always made at the same point in the efficiency 
 curve. ' 
 
DISK FANS. 
 
 675 
 
 In discussion, of Mr. JN orris's paper, Mr. A. H. Starrs says: From the " cu- 
 bic feet per revolution" and "cubical contents of fan-blades," as given in 
 the table, we find that the enclosed fans empty themselves from one-half to 
 twice per *re volution, while the open fans are emptied from one and three- 
 quarters to nearly three times ; this for fans of both types, on mines covering 
 the same range of equivalent orifices. One open fan, on a very large 
 orifice, was emptied nearly four times, while a closed fan, on a still 
 larger orifice, only shows one and one-half times. For the open fans the 
 "cubic feet per 100 ft. motion" is greater, in proportion to the fan 
 width and equivalent orifice, than for the enclosed type. Notwithstand- 
 ing this apparently free discharge of the open fans, they show very low 
 efficiencies. 
 
 As illustrating the very large capacity of centrifugal fans to pass air, if 
 the conditions of the mine are made favorable, a 16-ft. diam. fan, 4 ft. 6 in. 
 wide, at 130 revolutions, passed 360,000 cu. ft. per min., and another, of 
 same diameter, but slightly wider and with larger intake circles, passed 
 500,000 cu. ft., the water-gauge in both instances being about 1/2 in. 
 
 T. D. Jones says: The efficiency reported in some cases by Mr. Norris is 
 larger than I have ever been able to determine by experiment. My own 
 experiments, recorded in the Pennsylvania Mine Inspectors' Reports from 
 1875 to 1881, did not show more than 60% to 65%. 
 
 DISK FANS. 
 
 Efficiency of Disk Fans. Prof. A. B. W. Kennedy (Industries, Jan. 
 17, 1890) made a series of tests on two disk fans, 2 and 3 ft. diameter, 
 known as the Verity Silent Air-propeller. The principal results and 
 conclusions are condense'd as below. 
 
 
 Propeller, 
 2ft. diam. 
 i 
 
 Propeller, 
 3 ft. diam. 
 
 Speed of fan, revolutions per minute. . 
 Net H P to drive fan and belt 
 
 750 
 42 
 
 676 
 0.32 
 
 577 
 0.227 
 
 576 
 1.02 
 
 459 
 0.575 
 
 373 
 
 0.324 
 
 Cubic feet of air per minute 
 
 4,183 
 
 3,830 
 
 3,410 
 
 7,400 
 
 5,800 
 
 4,470 
 
 Mean velocity of air in 3-ft. flue, feet 
 
 
 
 
 
 
 
 
 593 
 
 5'43 
 
 482 
 
 1,046 
 
 820 
 
 632 
 
 Mean velocity of air in flue, same 
 
 
 
 
 
 
 
 diameter as fan/ 
 
 1,330 
 
 1,220 
 
 1,085 
 
 
 
 
 Cu. ft. of air per min. per effective H.P 
 Motion given to air per rev. of fan, ft.. 
 Cubic feet of air per rev. of fan 
 
 9,980 
 1.77 
 5.58 
 
 11,970 
 1.81 
 5.66 
 
 15,000 
 1.88 
 5.90 
 
 7,250 
 1.82 
 12.8 
 
 10,070 
 1.79 
 12.6 
 
 13,800 
 1.70 
 12.0 
 
 In each case the efficiency of the fan, that is, the quantity of air delivered 
 per effective horse-power, increases very rapidly as the speed diminishes, 
 so that lower speeds are much m9re economical than higher pnes. On the 
 other hand, as the quantity of air delivered per revolution is very nearly 
 constant, the actual useful work done by the fan increases almost directly 
 with its speed. Comparing the large and small fans with about the 
 same air delivery, the former (running at a much lower speed, of course) 
 is much the more economical. Comparing the two fans running at the 
 same speed, however, the smaller fan is very much the more economical. 
 The delivery of air per revolution of fan is very nearly directly propor- 
 tional to the area of the fan's diameter. 
 
 The air delivered per minute by the 3-ft. fan is nearly 12.5 R cubic feet 
 (R being the number of revolutions made by the fan per minute). For 
 the 2-ft. fan the quantity is 5.7R cubic feet. For either of these or any 
 other similar fans of which the area is A square feet, the delivery will be 
 about 1.8 A R cubic feet. Of course any change in the pitch of the blades 
 might entirely change these figures. 
 
 The net H.P. taken up is not far from proportional to the square of the 
 number of revolutions above 100 per minute. Thus for the 3-ft. fan the 
 
 net 
 
 ' while for the 2 - ft - fan the net H - p is 
 
 . 
 
 The denominators of these two fractions are very nearly proportional 
 inversely to ,the square of the fan areas or the fourth power of the fan 
 
676 
 
 AIR. 
 
 diameters. The net H.P. required to drive a fan of diameter D feet or 
 area A square feet, at a speed of R revolutions per minute, will therefore 
 
 The 3-ft. fan was also noiseless 
 
 The 2-ft. fan was noiseless at all speeds. 
 up to over 450 revolutions per minute. 
 
 Experiments made with a Blackmail Disk Fan, 4 ft. diam. by Geo. 
 A. Suter, to determine the volumes of air delivered under various con- 
 ditions, and the power required; with calculations of efficiency and ratio 
 of increase of power to increase of velocity, by G. H. Babcock. (Trans. 
 A.S.M.E.,vii.54,7): 
 
 gj 
 
 a 
 1 
 
 > 
 
 i 
 
 Cu. ft. of Air 
 delivered 
 per min., 
 
 j_T 
 o 
 
 jgj 
 
 O 
 
 i.S 
 
 . 
 
 ,Sr* 
 ^ s 
 r~ d 
 p 
 
 id 
 
 Wt s 
 
 *o vj& 
 
 |fc& 
 | 
 
 Ratio of In- 
 crease of 
 Delivery 
 
 Ratio of In- 
 crease of 
 Power. 
 
 Exponent x, 
 HP* V x . 
 
 Exponent y, 
 
 fcoo yy. 
 
 Efficiency 
 of Fan. 
 
 350 
 
 25 797 
 
 65 
 
 
 
 
 
 
 
 1 682 
 
 440 
 
 32575 
 
 2 29 
 
 
 257 
 
 262 
 
 3 523 
 
 5 4 
 
 
 9553 
 
 534 
 
 41,929 
 
 4 42 
 
 
 .186 
 
 .287 
 
 1.843 
 
 2.4 
 
 
 1.062 
 
 612 
 
 47 756 
 
 7 41 
 
 
 146 
 
 139 
 
 1 677 
 
 3 97 
 
 
 9358 
 
 
 For 
 
 series 
 
 
 .749 
 
 .851 
 
 11.140 
 
 4. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 340 
 
 20372 
 
 76 
 
 
 
 
 
 
 
 7110 
 
 453 
 
 26660 
 
 1 99 
 
 
 .332 
 
 .308 
 
 2.6J8 
 
 3.55 
 
 
 .6063 
 
 536 
 
 31 649 
 
 3 86 
 
 
 183 
 
 187 
 
 1 940 
 
 3 86 
 
 
 5205 
 
 627 
 
 36543 
 
 '6 47 
 
 
 .167 
 
 .155 
 
 1.676 
 
 3 59 
 
 
 .4802 
 
 
 For 
 
 series 
 
 
 .761 
 
 .794 
 
 8.513 
 
 3.63 
 
 
 
 
 
 
 
 
 
 
 
 
 
 340 
 
 9 983 
 
 1 12 
 
 28 
 
 
 
 
 
 
 3939 
 
 430 
 534 
 570 
 
 n;oi7 
 
 17,018 
 18,649 
 For 
 
 3.17 
 6.07 
 8.46 
 series 
 
 0.47 
 0.75 
 0.87 
 
 .265 
 .242 
 .068 
 .676 
 
 .304 
 .307 
 .096 
 .704 
 
 2.837 
 1.915 
 1.394 
 7.554 
 
 3.93 
 2.25 
 3.63 
 3.24 
 
 1.95 
 1.74 
 1.60 
 1.81 
 
 .3046 
 .3319 
 .3027 
 
 330 
 
 8399 
 
 1 31 
 
 26 
 
 
 
 
 
 
 2631 
 
 437 
 516 
 
 10,071 
 11,157 
 For 
 
 3.27 
 6.00 
 series 
 
 0.45 
 0.75 
 
 .324 
 .181 
 563 
 
 .199 
 .103 
 329 
 
 3.J42 
 1.457 
 4 580 
 
 6.31 
 
 3.66 
 5 35 
 
 3.06 
 4.96 
 3 72 
 
 .2188 
 .2202 
 
 
 
 
 
 
 
 
 
 
 
 Nature of the Experiments. First Series: Drawing air through 30 ft. 
 of 48-in. diam. pipe on inlet side of the fan. 
 
 Second Series: Forcing air through 30 ft. of 48-in. diam. pipe on outlet 
 side of the fan. 
 
 Third Series: Drawing air through 30 ft. of 48-in. pipe on inlet side of 
 the fan the pipe being obstructed by a diaphragm of cheese-cloth. 
 
 Fourth Series: Forcing air through 30 ft. of 48-in. pipe on outlet side 
 of fan the pipe being obstructed by a diaphragm of cheese-cloth. 
 
 Mr. Babcock says concerning these experiments: The first four experi- 
 ments are evidently the subject of some error, because the efficiency is 
 such as to prove on an average that the fan was a source of power sufficient 
 to overcome all losses and help drive the engine besides. The second 
 series is less questionable, but still the efficiency in the first two experi- 
 ments is larger than might be expected. In the third and fourth series 
 the resistance of the cheese-cloth in the pipe reduces the efficiency largely, 
 as would be expected. In this case the value has been calculated from 
 the height equivalent to the water-pressure, rather than the actual veloc- 
 ity of the air. 
 
 This record of experiments made with the disk fan shows that this kind 
 of fan is not adapted for use where there is any material resistance to the 
 flow of the air. In the centrifugal fan the power used is nearly propor- 
 tioned to the amount of air moved under a given head, while in this fan 
 the power required for the same number of revolutions of the fan increases 
 very materially with the resistance, notwithstanding the quantity of air 
 moved is at the same time considerably reduced. In fact from the inspec- 
 
POSITIVE ROTARY BLOWERS. 677 
 
 tion of the third and lourth series of tests, it would appear that the power 
 required is very nearly the same for a given pressure, whether more or 
 less air be in motion. It would seem that the main advantage, if any, 
 of the disk fan over the centrifugal fan for slight resistances consists in the 
 fact that the delivery is the full area of the disk, while with centrifugal 
 fans intended to move the same quantity of air the opening is much 
 smaller. 
 
 It will be seen by columns 8 and 9 of the table that the power used in- 
 creased much more rapidly than the cube of the velocity, as in centrifugal 
 fans. The different experiments do not agree with each other, but a 
 general average may be assumed as about the cube root of the eleventh 
 power. 
 
 Capacity of Disk Fans. (C. L. Hubbard, The Metal Worker, Sept. 5, 
 1908.) The rated capacities given in catalogues are for fans revolving 
 in free air that is, mounted in an opening without being connected with 
 ducts or subject to other frictional resistance. 
 
 The following data, based upon tests, apply to fans working against a 
 resistance equivalent to that of a shallow heater of open pattern, and 
 connecting with ducts of medium length through which the air flows at a 
 velocity not greater than 600 or 800 ft. per minute. Under these con- 
 ditions a good type of fan will propel the air in a direction parallel to the 
 shaft, a distance equal to about 0.7 of its diameter at each revolution. 
 From this we have the equation Q = 0.7 D X R X A, in which Q = cu. 
 ft. of air discharged per minute; D = diam. of fan, in ft.; R = revs, per 
 min.; A = area of fan, in sq. ft. The following table is calculated on this 
 basis. 
 Diam. of fan, in. 
 
 18 24 30 36 42 48 54 60 72 84 96 
 Cu. ft per rev. 
 
 1.85 4.40 8.59 14.8 23.6 35.2 50.1 68.7 118.7188.6 281.5 
 
 Revolutions per min. for velocity of air through fan = 1000 ft. per min. 
 952 714 571 476 408 357 317 286 238 204 179 
 
 The velocity of the air through the fan is proportional to the number 
 of revolutions. For the conditions stated the H.P. required per 1000 cu. 
 ft of air moved will be about 0.16 when the velocity through the fan is 
 1000 ft. per min., 0.14 for a velocity of 800 ft., and 0.18 for 1200 ft. For 
 a fan moving in free air the required speed for moving a given volume of 
 air will be about 0.6 of the number of revolutions given above and the 
 H.P. about 0.3 of that required when moving against the resistance stated. 
 
 POSITIVE ROTARY BLOWERS. 
 
 Rotary Blowers, Centrifugal Fans, and Piston Blowers. (Cata- 
 logue of the Connersville Blower Co.) In ordinary work the advantage 
 of a positive blower 9ver a fan begins at about 8 oz. pressure, and the 
 efficiency of the positive blower increases from 8 oz. as the pressure goes 
 up to a point where the ordinary centrifugal fan fails entirely. The 
 highest efficiency of rotary blowers is when they are working against 
 pressures ranging between 1 and 8 Ibs. 
 
 Fans, when run at constant speed, cannot be made to handle a constant 
 volume of fluid when the pressure is variable; and they cannot give a high 
 efficiency except for low and uniform pressures. 
 
 When a fan blower is used to furnish blast for a cup9la it is driven at a 
 constant speed, and the amount of air discharged by it varies according 
 to the resistance met with in the cupola. With a positive blower running 
 at a constant speed, however, there is a constant volume of air forced 
 into the cupola, regardless of changing resistance. 
 
 A rotary blower of the two-impeller type is not an economical com- 
 pressor, because the impellers are working against the full pressure c.t all 
 times, while in an ideal blowing engine the theoretical mean -effective 
 pressure on the piston, when discharging air at 15 Ibs. pressure, is 111/2 Ibs. 
 For high pressures, on account of the increase of leakage and the increase 
 of power required because it does not compress gradually, the rotary 
 blower must give way to the piston type of machine. Commercially, the 
 line is crossed at about 8 Ibs. pressure. 
 
 1. A fan is the cheapest in first cost, and if properly applied may be 
 used economically for pressures up to 8 oz. 
 
678 
 
 AIR. 
 
 2. A rotary blower costs more than a fan, but much less than a blowing 
 engine; is more economical than either between 8 oz..and 8 Ibs. pressure, 
 and can be arranged to give a constant pressure or a constant volume. 
 
 3. Piston machines cost much more than rotary blowers, but should 
 be used for continuous duty for pressures above 8 Ibs., and may be econom- 
 ical if they are properly constructed and not run at too high a piston speed. 
 
 The horse-power required to operate rotary blowers is prop9rtional to 
 the volume and pressure of air discharged. In making estimates for 
 power it is safe to assume that for each 1000 cu. ft. of free air discharged, 
 at one pound pressure, 5 H.P. should be provided. 
 
 Test of a Rotary Blower. (Connersville Blower Co.) The test was 
 made in 1904 on two 39 X 84 in. blowers coupled direct to two 12 and 24 X 
 36 in. compound Corliss engines. The results given below are for the 
 combined units. 
 
 Air pressure, Ibs 
 Engine, I.H.P 
 
 
 19.30 
 
 0.05 
 23.76 
 
 0.5 
 
 52.83 
 
 1.0 
 
 100.91 
 
 1.5 
 
 132.67 
 
 2. 
 176.11 
 
 2.5 
 223.20 
 
 3. 
 
 256.87 
 
 3.5 
 
 287.56 
 
 Displacement, cu.ft. 
 
 
 19,212 
 
 18,727 
 
 18,508 
 
 18,344 
 
 18,200 
 
 18,028 
 
 17,966 
 
 17,863 
 
 Efficiency 
 
 
 
 68.5 
 
 79 
 
 84 
 
 85.6 
 
 86 
 
 86 
 
 85.9 
 
 In calculating the efficiency the theoretical horse-power was taken as 
 the power required to compress adiabatically and to discharge the net 
 amount of air at the different pressures and at the same altitude. The 
 test was made up to 3.5 Ibs. only. Estimated efficiencies for higher 
 pressures from an extension of the plotted curve are: 6 Ibs. 84%, 8 Ibs. 
 82%, 10 Ibs. 79.5%. The theoretical discharge of the blower was 19,250 
 cu. ft. 
 
 CAPACITY OF ROTAIIY BLOWERS FOR CUPOLAS. 
 
 Cu.ft 
 per 
 rev. 
 
 Revs, 
 per 
 min. 
 
 Tons 
 per 
 hour. 
 
 Suitable 
 for cupola 
 in. diam.* 
 
 Cu. ft. 
 per 
 rev. 
 
 Revs, 
 per 
 min. 
 
 Tons 
 per 
 hour. 
 
 Suitable 
 for cupola 
 in. diam. 
 
 1.5 
 
 ( 200 
 i 400 
 
 2 
 
 | 18 to 20 
 
 45 
 
 ( 135 
 \ 165 
 
 12 
 15 
 
 i 54 to 66 
 
 3.3 
 
 i 175 
 { 335 
 
 2 
 
 | 24 to 27 
 
 
 ( 200 
 ( 130 
 
 18 
 15 
 
 1 
 
 6 
 
 j 185 
 i 275 
 
 2 
 3 
 
 } 28 to 32 
 
 57 
 
 1 155 
 ( 185 
 
 18 
 21 
 
 60 to 72 
 
 10 
 
 \ 200 
 \ 250 
 
 4 
 
 5 
 
 j 32 to 38 
 
 65 
 
 ( 140 
 < 160 
 
 18 
 21 
 
 [ 66 to 84 
 
 
 ( 150 
 
 4 
 
 ! 
 
 
 I 185 
 
 24 
 
 ) 
 
 13 
 
 t 190 
 ( 175 
 
 5 
 61/2 
 
 32 to 40 
 
 84 
 
 ( 125 
 ] 145 
 
 21 
 24 
 
 [ 72 to 90 
 
 
 ( 150 
 
 5 
 
 ) 
 
 
 I 160 
 
 27 
 
 ) 
 
 17 
 
 < 205 
 ( 250 
 
 61/2 
 81/ 2 
 
 j- 36 to 45 
 
 100 
 
 ( 120 
 1 135 
 
 24 
 27 
 
 \ 84 to 96 
 
 
 ( 166 
 
 8 
 
 ) 
 
 
 ( 160 
 
 30 
 
 ) 
 
 24 
 
 < 200 
 ( 240 
 ( 150 
 
 10 
 12 
 10 
 
 > 42 to 54 
 ) 
 
 118 
 
 ( 115 
 < 130 
 ( 140 
 
 27 
 30 
 33 
 
 ) Two 
 ( cupolas 
 ) 60 to 66 
 
 33 
 
 < 180 
 
 12 
 
 > 48 to 60 
 
 
 
 
 
 
 ( 210 
 
 14 
 
 ) 
 
 
 
 
 
 * Inside diam. The capacity in tons per hour is based on 30,000 cu. ft. 
 of air Der ton of iron melted. 
 
 For smith fires: an ordinary fire requires about 60 cu. ft. per min. 
 
 For oil furnaces : an ordinary furnace burns about 2 gallons of oil per 
 hour and 1800 cu. ft. of air should be provided for each gallon of oil. For 
 each 100 cu. ft. of air discharged per minute at 16 oz. pressure, 1/2 H.P. 
 should be provided. 
 Sizes of small blowers. 173 288 576 cu. in. per rev. 
 
 Revs, per min 800 to 1500 500 to 900 300 to 600 
 
 Diam. of outlet, in 21/2 21/2 3 
 
STEAM JET BLOWER AND EXHAUSTER. 
 
 G79 
 
 ROTARY GAS EXHAUSTERS. 
 
 Cu. ft. per rev 
 
 2ft 
 
 H/2 
 
 3.3 
 
 6 
 
 10 
 
 13 
 
 17 
 
 24 
 
 33 
 
 Rev. per min. . 
 
 200 
 
 180 
 
 170 
 
 160 
 
 150 
 
 150 
 
 140 
 
 130 
 
 120 
 
 Diam. of pipe open- 
 
 
 
 
 
 
 
 
 
 
 ing . . . 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 12 
 
 16 
 
 16 
 
 20 
 
 Cu. ft. per rev 
 
 45 
 
 57 
 
 65 
 
 84 
 
 100 
 
 118 
 
 155 
 
 200 
 
 300 
 
 Rev. per min 
 
 110 
 
 100 
 
 95 
 
 90 
 
 85 
 
 82 
 
 80 
 
 80 
 
 75 
 
 Diam. pipe opening 
 
 20 
 
 24 
 
 24 
 
 30 
 
 30 
 
 30 
 
 36 
 
 36 
 
 42 
 
 There is no gradual compressing of air in a rotary machine, and the 
 unbalanced areas of the impellers are working against the full difference 
 of pressure at all times. The possible efficiency of such a machine under 
 ordinary temperature and conditions of atmosphere, assuming no me- 
 chanical friction, leakage, nor radiation of heat of compression, would be 
 as follows: 
 
 Gauge pres. Ib 1 2 3 4 5 10 - 15 
 
 Efficiency % 97.5 95.5 93.3 91.7 90 82.7 76.7 
 
 The proper application of rotary positive machines when operating in 
 air or gas under differences of pressures from 8 oz. to 5 Ibs. is where con- 
 stant quantities of -fluid are required to be delivered against a variable 
 resistance, or where a constant pressure is required and the volume is 
 variable. These are the requirements of gas works, pneumatic-tube 
 transmission (both the vacuum and pressure systems), foundry cupolas, 
 smelting furnaces, knobbling fires, sand blast, burning of fuel oil, con- 
 veying granular substances, the operation of many kinds of metallurgical 
 furnaces, etc. J. T. Wilkin, Trans. A. S. M. E., Vol. xxiv. 
 
 STEAM-JET BLOWER AND EXHAUSTER 
 
 The Steam-jet as a Means for Ventilation. Between 1810 and 
 1850 the steam-jet was employed to a considerable extent for ventilating 
 English collieries, and in 1852 a committee of the House of Commons 
 reported that it was the most powerful and at the same time the cheapest 
 method for the ventilation of mines; but experiments made shortly after- 
 wards proved that this opinion was erroneous, and that furnace ventila- 
 tion was less than half as expensive, and in consequence the jet was soon 
 abandoned as a permanent method of ventilation. 
 
 For an account of these experiments see Colliery Engineer, Feb., 1890. 
 The jet, however, is sometimes advantageously used as a substitute, for 
 instance, in the case of a fan standing for repairs, or after an explosion, 
 when the furnace may not be kept going, or in the case of the fan having 
 been rendered useless. 
 
 A Blower and Exhauster is made by Schutte & Koerting Co., Phil- 
 adelphia, on the principle of the steam-jet ejector. The following is a 
 table of capacities. 
 
 Diameter of 
 Pipes, Inches. 
 
 Capacity 
 per 
 
 Diameter of 
 Pipes, Inches. 
 
 Capacity 
 Per 
 
 Diameter of 
 Pipes, Inches. 
 
 Capacity 
 
 TT/vni 
 
 _ A :- 
 
 Steam. 
 
 Cu. ft. 
 
 Air. 
 
 Steam. 
 
 H-.,,- 
 Cu. ft. 
 
 Air. 
 
 Steam. 
 
 Cu. ft. 
 
 V. 
 
 l /4 
 
 300 
 
 2 
 
 3 /4 
 
 4,000 
 
 5 
 
 2 
 
 27,000 
 
 a /4 
 
 3 /8 
 
 600 
 
 2V'2 
 
 
 6,000 
 
 6 
 
 2 
 
 35,000 
 
 1 
 
 3 /8 
 
 1,000 
 
 3 
 
 M/4 
 
 12,000 
 
 7 
 
 2V2 
 
 48,000 
 
 IVa 
 
 Va 
 
 2,000 
 
 4 
 
 n/ 2 
 
 18,000 
 
 8 
 
 3 
 
 60,000 
 
 When used as exhausters with a steam pressure of 45 Ib., these 
 machines will produce a vacuum of 20 in. mercury (23.3 ft. water 
 column), but they can be specially constructed to produce a vacuum 
 of 25 in. mercury (29.3 ft. water column). 
 
G80 
 
 AIR. 
 
 When used as compressors, they will operate against a counter-pres- 
 sure equal to 1/7 of the steam pressure. 
 
 Another steam-jet blower is used for boiler-firing, ventilation, and 
 similar purposes where a low counter-pressure or rarefaction meets the 
 requirements. 
 
 The y9lumes as given in the following table of capacities are under the 
 supposition of a steam-pressure of 60 Ibs. and a counter-pressure of, 
 say, from 0.5 to 2 inches of water: 
 
 Diameter 
 in Inches. 
 
 Capacity 
 per 
 Hour, 
 Cubic 
 Feet. 
 
 Diameter 
 in Inches. 
 
 Capacity 
 per 
 Hour, 
 Cubic 
 Feet. 
 
 Diameter 
 in Inches. 
 
 Capacity 
 per 
 Hour, 
 Cubic 
 Feet. 
 
 4 
 
 4 
 
 if 
 
 M 
 
 4 
 
 || 
 
 4 
 
 ^5 
 
 6 cJ 
 
 4 
 
 8 
 9 
 
 3 
 
 4 
 
 6 
 
 J/8 
 
 V2 
 V2 
 3 /4 
 
 10,000 
 20,000 
 30,000 
 45,000 
 
 11 
 
 12 
 14 
 16 
 
 7 
 8 
 10 
 12 
 
 V4 
 
 1 
 1 
 
 60,000 
 90,000 
 120,000 
 180,000 
 
 18 
 24 
 32 
 42 
 
 14 
 18 
 24 
 32 
 
 2 
 
 2V2 
 
 240,000 
 500,000 
 1,000,000 
 2,000,000 
 
 Maximum coal burning capacity per hour = cu. ft. air per hr. -:- 200. 
 
 BLOWING-ENGINES. 
 
 Blowing- engines. The following table showing dimensions, 
 capacity, etc., of Corliss horizontal cross-compound condensing 
 blowing engines is condensed from a table published about 1901 by 
 the Philadelphia Engineering Works. Similar engines are built by 
 William Tod & Co., Youngstown, Ohio, and other builders. 
 
 Corliss Horizontal Cross-compound Condensing Blowing- 
 engines. 
 
 Indicated 
 Horse-power. 
 
 d 
 
 a 
 I 
 
 CO 
 
 k 
 
 o> 
 tf 
 
 * 
 
 
 53.J3 
 
 o< 
 
 1 - 
 
 1-3 
 ad 4 
 
 J 02 
 
 CG M 
 
 -ft- ' 
 s ^ 
 
 g 
 
 |J9 
 
 l 
 
 Q 
 a 
 
 o> 
 
 -OC 
 
 i 
 
 4S 
 
 Blast Cylinders, 
 Diam., in. 
 
 StrokeofAllCyl- 
 inders, in. 
 
 s 
 
 ,C bO 
 
 tc' 
 
 | 
 
 P,G . 
 
 ^5S 
 
 i 
 
 ft . 
 
 &$% 
 
 /* 
 &%$ 
 $*> 
 
 15 Exp. 
 125 Ib. 
 Steam. 
 
 1,596 
 
 13 Exp. 
 100 Ib. 
 
 Steam. 
 
 2,280 
 2,060 
 
 "i.980" 
 1,702 
 1,386 
 1,175 
 822 
 
 60 
 60 
 60 
 60 
 60 
 60 
 60 
 60 
 
 45,600 
 45,600 
 45,600 
 39,600 
 39,600 
 39,600 
 23,500 
 23,500 
 
 15 
 
 12 
 10 
 15 
 12 
 10 
 15 
 10 
 
 44 
 42 
 32 
 40 
 38 
 36 
 34 
 28 
 
 78 
 72 
 60 
 72 
 70 
 66 
 60 
 50 
 
 (2) 84 
 (2) 84 
 (2) 84 
 (2) 78 
 (2) 78 
 (2) 78 
 (2) 72 
 (2) 72 
 
 60 
 60 
 60 
 60 
 60 
 60 
 60 
 60 
 
 505,000 
 475,000 
 355,000 
 445,000 
 425,000 
 415,000 
 340,000 
 270,000 
 
 605,000 
 550,000 
 436,000 
 545,000 
 491,000 
 450,000 
 430,000 
 300,000 
 
 Vertical engines are built of the same dimensions as above, except 
 that the stroke is 48 in. instead of 60, and they are run at a higher 
 number of revolutions to give the same piston-speed and the same 
 I.H.P. 
 
 The calculations of power, capacity, etc., of blowing-engines are the 
 same as those for air-compressors. They are built without any provision 
 for cooling the air during compression. About 400 feet per minute is the 
 usual piston-speed for recent forms of engines, but with positive air-valves, 
 which have been introduced to some extent, this speed may be increased. 
 The efficiency of the engine, that is, the ratio of the I.H.P. of the air- 
 cylinder to that of the steam-cylinder, is usually taken at 90 per cent, the 
 losses by friction, leakage, etc., being taken at 10 per cent. 
 
 Horse-power of Steam Cylinders of Blowing-engines. (Wm. 
 Tod & Co., 1914.) To find the indicated horse-power to be developed 
 in the steam cylinders of a blowing-engine, multiply the number of 
 
HEATING AND VENTILATION. 681 
 
 cubic feet of free air to be compressed per minute by the figures given 
 below for the respective pressures named. 
 
 Gage press. Ib. 
 
 persq. in. ... 5 10 15 20 25 30 35 40 
 
 Factor... 0.0226 .0415 .0577 .0722 .0853 .0973 .1084 .1187 
 
 These factors are based on the theoretical horse-power required 
 to compress and deliver 1 cu. ft. of air to the pressure stated, plus 
 an allowance of 15%, which is stated to be about right for mechanically- 
 operated air valves. With poppet air valves the loss may be about 
 10%. 
 
 HEATING AND VENTILATION. 
 
 Ventilation. (A. R. Wolff, Stevens Indicator, April, 1890.) The 
 popular impression that the impure air falls to the bottom of a crowded 
 room is erroneous. There is a constant mingling of the fresh air admitted 
 with the impure air due to the law of diffusion of gases, to difference of 
 temperature, etc. The process of ventilation is one of dilution of the 
 impure air by the fresh, and a room is properly ventilated in the opinion 
 of the hygienists when the dilution is such that the carbonic acid in the 
 air does not exceed from 6 to 8 parts by volume in 10,000. Pure country 
 air contains about 4 parts CO2 in 10,000, and badly-ventilated quarters 
 as high as 80 parts. 
 
 An ordinary man exhales 0.6 of a cubic foot of CO2 per hour. New 
 York gas gives 9ut 0.75 of a cubic feet of CO 2 for each cubic foot of gas 
 burnt. An ordinary lamp gives out 1 cu. ft. of CO 2 per hour. An 
 ordinary candle gives out 0.3 cu. ft. per hour. [The use of gaslight for 
 interior lighting does not affect the atmosphere deleteriously. See 
 pamphlet issued by National Commercial Gas Assn., 1914. 1 
 
 To determine the quantity of air to be supplied to the inmates of an 
 unlighted room, to dilute the air to a desired standard of purity, we 
 can establish equations as follows: 
 
 Let v = cubic feet of fresh air to be supplied per hour. 
 
 r = cubic feet of CO 2 in each 10,000 cu. ft. of the entering air; 
 R = cubic feet of CO 2 which each 10,000 cu. ft. 9f the air in the 
 
 room may contain for proper health conditions ; 
 n = number of persons in the room ; 
 0.6 = cubic feet of COz exhaled by one man per hour. 
 
 Tnen in nrm +- 6 n equals cubic feet of CO2 communicated to the room 
 
 1U,UUU 
 
 during one hour. 
 
 This value divided by v and multiplied by 10,000 gives the proportion 
 of COa in 10,000 parts of the air in the room, and this should equal R, the 
 standard of purity desired. Therefore 
 
 c 
 ' TV 
 
 R-r 
 
 If we place r at 4 and R at 6, v = 6000 n -f- (6 - 4) = 3000 n, or the 
 quantity of air to be supplied per person is 3000 cubic feet per hour. 
 
 If the original air in the room is of the purity of external air, and the 
 cubic contents of the room is equal to 100 cu. ft. per inmate, only 3000 
 100 = 2900 cu. ft. of fresh air from without will have to be supplied the 
 first hour to keep the air within the standard purity of 6 parts of CCh in 
 10,000. If the cubic contents of the room equals 200 cu. ft. per inmate, 
 only 3000 200 = 2800 cu. ft. will have to be supplied the first hour to 
 keep the air within the standard purity, and so on. 
 
 Again, if we only desire to maintain a standard of purity of 8 parts 
 Of carbonic acid in 10,000, the equation gives as the required air-supply 
 per hour 
 
 v=- 8 _ 4 - n 1500 n, or 1500 cu. ft. of fresh air per inmate per hour. 
 
682 
 
 HEATING AND VENTILATION. 
 
 Cubic feet of air containing 4 parts of carbonic acid in 10,000 necessary 
 per person per hour to keep the air in room at the composition of 
 
 6 7 8 9 10 15 20 parts of CO 2 in 10,000. 
 
 3000 2000 1500 1200 1000 545 375 cubic feet. 
 
 If the original air in the room is of purity of external atmosphere (4 parts 
 of carbonic acid in 10,000), the amount of air to be supplied the first hour, 
 for given cubic spaces per inmate, to have given standards of purity not 
 exceeded at the end of the hour, is obtained from the following table: 
 
 Cubic 
 Feet of 
 f Space 
 in Room 
 per 
 Individ- 
 ual. 
 
 Proportion of Carbonic Acid in 10,000 Parts of the Air, not to 
 be Exceeded at End of Hour. 
 
 a | 7 
 
 8 
 
 9 
 
 10 
 
 15 
 
 20 
 
 Cubic Feet of Air, of Composition 4 Parts of Carbonic Acid in 
 10,000, to be Supplied the First Hour. 
 
 100 
 200 
 300 
 400 
 500 
 600 
 700 
 800 
 900 
 1000 
 1500 
 2000 
 2500 
 
 2900 
 2800 
 2700 
 2600 
 2500 
 2400 
 2300 
 2200 
 2100 
 2000 
 1500 
 1000 
 500 
 
 1900 
 1800 
 1700 
 1600 
 1500 
 1400 
 1300 
 1200 
 1100 
 1000 
 500 
 None 
 
 1400 
 1300 
 1200 
 1100 
 1000 
 900 
 800 
 700 
 600 
 500 
 None 
 
 1100 
 1000 
 900 
 800 
 700 
 600 
 500 
 400 
 300 
 200 
 None 
 
 900 
 800 
 700 
 600 
 500 
 400 
 300 
 200 
 100 
 None 
 
 445 
 345 
 245 
 145 
 45 
 None 
 
 275 
 175 
 75 
 None 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 It is exceptional that systematic ventilation supplies the 3000 cubic 
 feet per inmate per lumr, which adequate health considerations demand. 
 For large auditoriums in which the cubic space perindividual is great, and in 
 which the atmosphere is thoroughly fresh before the rooms are occupied, 
 and the occupancy is of two or three hours' duration, the systematic air- 
 supply may be reduced, and 2000 to 2500 cubic feet per inmate per hour 
 is a satisfactory allowance. 
 
 In hospitals where, on account of unhealthy excretions of various kinds, 
 the air-dilution must be largest, an air-supply of from 4000 to 6000 cubic 
 feet per inmate per hour should be provided, and this is actually secured 
 in some hospitals. A report dated March 15, 1882, by a commission ap- 
 pointed to examine the public schools of the District of Columbia, says: 
 
 " In each class-room not less than 15 square feet of floor-space should be 
 allotted to each pupil. In each class-room the window-space should not 
 be less than one-fourth the floor-space, and the distance of desk most 
 remote from the window should not be more than one and a half times the 
 height of the top of the window from the floor. The height of the class- 
 room should never exceed 14 feet. The provisions for ventilation should 
 be such as to provide for each person in a class-room not less than 30 cubic 
 feet of fresh air per minute (1800 per hour), which amount must be intro- 
 duced and thoroughly distributed without creating unpleasant draughts, 
 or causing any two parts of the room to differ in temperature more than 
 2 Fahr., or the maximum temperature to exceed 70 Fahr." [The provi- 
 sion of 30 cu. ft. p_T minute for each person in a class-room is now (1909) 
 required by law in several states.] 
 
 When the air enters at or near the floor, it is desirable that the velocity 
 of inlet should not exceed 2 feet per second, which means larger sizes of 
 register openings and flues than are usually obtainable, and much higher 
 velocities of inlet than two feet per second are the rule in practice. 
 The velocity of current into vent-flues can safely be as high as 6 or even 
 10 feet per second, without being disagreeably perceptible. 
 
 The entrance of fresh air into a room is coincident with, or dependent 
 on, the removal of an equal amount of air from the room. The ordinary 
 means of removal is the vertical vent-duct, rising to the top of the build- 
 
HEATING AND VENTILATION. 
 
 683 
 
 Ing. Sometimes reliance for the production of the current in this vent- 
 duct is placed solely on the difference of temperature of the air in the 
 room and that of the external atmosphere; sometimes a steam coil is 
 placed within the flue near its bottom to heat the air within the duct 
 sometimes steam pipes (risers and returns) run up the duct performing 
 the same functions: or steam jets within the flue, or exhaust fans, driven 
 by steam or electric power, act directly as exhausters; sometimes the 
 heating of the air in the flue is accomplished by gas-jets. 
 
 The draft of such a duct is caused by the difference of weight of the 
 heated air in the duct, and of a column of equal height and cross-sectional 
 area of the external air. 
 
 Let d density, or weight in pounds, of a cubic foot of the external air. 
 
 Let d\ = density, or weight in pounds, of a cubic foot of the heated air 
 within the duct. 
 
 Let h = vertical height, in feet, of the vent-duct. 
 
 h (d di) = the pressure, in pounds per square foot, with which the 
 air is forced into and out of the vent-duct. 
 
 This pressure expressed in height of a column of air of density within 
 the vent-duct is h (d di) -r- d\. 
 
 Or, if t = absolute temperature of external air, and ti = absolute tem- 
 perature of the air in the vent-duct, then the pressure = h (t\ - t) *- t. 
 
 The theoretical velocity, in feet per second, with which the air would 
 travel through the vent-duct under this pressure is 
 
 2gh(t l -t) 
 t 
 
 = 8.02 
 
 The actual velocity will be considerably less than this, on account of loss 
 due to friction. This friction will vary with the form and cross-sectional 
 area of the vent-duct and its connections, and with the degree of smooth- 
 ness of its interior surface. On this account, as well as to prevent leakage 
 of air through crevices in the wall, tin lining of vent-flues is desirable. 
 
 The loss by friction may be estimated at approximately 50%, and the 
 actual velocity of the air as it flows through the vent-duct is 
 
 ii, 
 
 it/ 2gh y - 
 
 -, or, approximately, v=4 
 
 y h 
 
 V = velocity of air in vent-duct, in feet per minute, and the external 
 _-r be at 32 Fahr., since the absolute temperature on Fahrenheit scale 
 equals thermometric temperature plus 459.4, 
 
 fro 
 
 = 240^ 
 
 491.4 
 >m which has been computed the following table: 
 
 Quantity of Air, in Cubic Feet, Discharged per 3Iinute through a 
 Ventilating Duct, of which the Cross-sectional 'Area is One 
 Square Foot (the External Temperature of Air being 32 Fahr.). 
 
 Height of 
 
 Excess of Temperature of Air in Vent-duct above 
 that of External Air. 
 
 feet. 
 
 5 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 50 
 
 100 
 
 150 
 
 10 
 
 77 
 
 108 
 
 133 
 
 153 
 
 171 
 
 188 
 
 242 
 
 342 
 
 419 
 
 15 
 
 94 
 
 133 
 
 162 
 
 188 
 
 210 
 
 230 
 
 297 
 
 419 
 
 514 
 
 20 
 
 108 
 
 153 
 
 188 
 
 217 
 
 242 
 
 265 
 
 342 
 
 484 
 
 593 
 
 25 . 
 
 121 
 
 171 
 
 210 
 
 242 
 
 271 
 
 297 
 
 383 
 
 541 
 
 663 
 
 30 
 
 133 
 
 188 
 
 230 
 
 265 
 
 297 
 
 325 
 
 419 
 
 593 
 
 726 
 
 35 . 
 
 143 
 
 203 
 
 248 
 
 286 
 
 320 
 
 351 
 
 453 
 
 640 
 
 784 
 
 40 
 
 153 
 
 217 
 
 265 
 
 306 
 
 342 
 
 375 
 
 484 
 
 683 
 
 838 
 
 43 
 
 162 
 
 230 
 
 282 
 
 325 
 
 363 
 
 398 
 
 514 
 
 723 
 
 889 
 
 50... 
 
 171 
 
 242 
 
 297 
 
 342 
 
 383 
 
 419 
 
 541 
 
 760 
 
 937 
 
684 HEATING AND VENTILATION. 
 
 Multiplying the figures in preceding table by 60 gives the cubic feet 
 of air discharged per hour per square foot of cross-section of vent-duct. 
 Knowing the cross-sectional area of vent-ducts we can find the total dis- 
 charge; or for a desired air-removal, we can proportion the cross-sectional 
 area of vent-ducts required. 
 
 Heating and Ventilating of L.arge Buildings. (A. R. Wolff, Jour. 
 Frank. Inst., 1893.) The transmission of heat from the interior to the 
 exterior of a room or building, through the walls, ceilings, windows, etc., 
 is calculated as follows: 
 
 S = amount of transmitting surface in square feet ; 
 t = temperature F. inside, = temperature outside; 
 
 K = a coefficient representing, for various materials composing build- 
 ings, the loss by transmission per square foot of surface in British 
 thermal units per hour, for each degree of difference of tempera- 
 ture on the two sides of the material; 
 
 Q total heat transmission = SK (t o). 
 
 This quantity of heat is also the amount that must be conveyed to the 
 room in order to make good the loss by transmission, but it does not 
 cover the additional heat to be conveyed on -account of the change of 
 air for purposes of ventilation. (See Wolff's coefficients below, page 
 688.) 
 
 These coefficients are to be increased respectively as follows: 10% when 
 the exposure is a northerly one, and winds are to be counted on as impor- 
 tant factors; 10% when the building is heated during the daytime only, 
 and the location of the building is not an exposed one: 30% when the 
 building is heated during the daytime only, and the location of the build- 
 ing is exposed; 50% when the building is heated during the winter months 
 intermittently, with long intervals (say days or weeks) of non-heating. 
 
 The value of the radiating-surface is about as follows: Ordinary bronzed 
 cast-iron radiating-surfaces, in American radiators (of Bundy or similar 
 type), located in rooms, give out about 250 heat-units per hour for each 
 square foot of surface, with ordinary steam-pressure, say 3 to 5 Ibs, per 
 sq. in., and about 0.6 this amount with ordinary hot-water heating. 
 
 Non-painted radiating-surfaces, of the ordinary "indirect" type 
 (Climax or pin surfaces), give out about 400 heat-units per hour for each 
 square foot of heating-surface, with ordinary steam-pressure, say 3 to 
 5 Ibs. per sq. in.; and about 0.6 this amount with ordinary hot-water 
 heating. 
 
 A person gives out about 400 heat-units per hour; an ordinary gas- 
 burner, about 4800 heat-units per hour; an incandescent electric (16 
 candle-power) light, about 200 heat-units per hour. 
 
 The following example is given by Mr. Wolff to show the application of 
 the formula and coefficients : 
 
 Lecture-room 40 X 60 ft., 20 ft. high, 48,000 cubic feet, to be heated 
 to 69 F.; exposures as follows: North wall, 60 X 20 ft., with four windows, 
 each 14 X 8 feet, outside temperature F. Room beyond west wall and 
 room overhead heated to 69, except a double skylight in ceiling, 14 X 24 
 ft., exposed to the outside temperature of 0. Store-room beyond east 
 wall at 36. Door 6X12 ft. in wall. Corridor beyond south wall heated 
 to 59. Two doors, 6 X 12, in wall. Cellar below, temperature 36. 
 
 If we assume that the lecture-room must be heated to 69 F. in the 
 daytime when unoccupied, so as to be at this temperature when first 
 persons arrive, there will be required, ventilation not being considered, 
 and bronzed direct low-pressure steam-radiators being the heating media, 
 about 113,550 -s- 250 = 455 sq. ft. of radiating-surface. 
 
 If we assume that there are 160 persons in the lecture-room, and we 
 provide 2500 cubic feet of fresh air per person per hour, we will supply 
 160 X 2500 = 400,000 cubic feet of air per hour (i.e., over eight changes 
 of contents of room per hour). 
 
 To heat this air from F. to 69 F. will require 400,000 X 0.01785 X 
 69 = 492.660 thermal units per hour (0.01785 being the product of the 
 weight of a cubic foot, 0.075, by the specific heat of air, 0.238). Accord- 
 ingly there must be provided 492,660 * 400 = 1232 sq. ft. of indirect 
 
HEATING AND VENTILATION. 
 
 685 
 
 surface, to heat the air required for ventilation, in zero weather. If the 
 room were to be warmed entirely indirectly, that is, by the air supplied 
 to room (including the heat to be conveyed to cover loss by transmission 
 through walls, etc.), there would have to be conveyed to the fresh-air 
 supply 492,660 + 118,443 = 611,103 heat-units. This would imply the 
 provision of an amount of indirect heating-surface of the "Climax" type 
 of 611,103 + 400 = 1527 sq. ft., and the fresh air entering the room 
 would have to b? at a temperature of about 86 F., viz., 
 
 The above calculations do not, however, take into account that 160 
 persons in the lecture-room give out 160 X 400 = 64,000 thermal units 
 per hour; and that, say, 50 electric lights give out 50 X 200 = 10,000 
 thermal units per hour; or, say, 50 gaslights, 50 X 4800 = 240,000 
 thermal units per hour. The presence of 160 people and the gaslighting 
 would diminish considerably the amount of heat required. If the 50 
 gaslights give out 240,000 thermal units per hour, the air supplied for 
 ventilation must enter considerably below 69 Fahr., or the room will be 
 heated to an unbearably high temperature. If 400,000 cubic feet of fresh 
 air per hour are supplied, and 240,000 thermal units per hour generated 
 by the gas must be abstracted, it means that the air must, under these 
 
 240 000 
 conditions, enter .^^ ^ OM785 - about 34 less than 86. or at 
 
 about 52 Fahr. Recent researches show that the increase of CO 2 in 
 air due to gas lighting is not detrimental to health. 
 
 The following table shows the calculation of heat transmission (some 
 figures changed from the original) : 
 
 * . 
 
 .g~ 
 
 fe * 
 
 n!^ 
 
 Kind of Transmitting 
 Surface. 
 
 Thickness 
 of Wall in 
 inches. 
 
 Calculation 
 of Area of 
 Transmit- 
 ting Sur- 
 face. 
 
 Square feet 
 of Surface. 
 
 3 
 t 
 
 uj 
 
 Thermal 
 
 Units. 
 
 69 
 69 
 33 
 33 
 10 
 10 
 10 
 10 
 69 
 69 
 33 
 
 Outside wall 
 
 36" 
 36* 
 24" 
 36" 
 
 63x22-448 
 4x 8X 14 
 42x22- 72 
 6x12 
 45x22- 72 
 6x12 
 17x22- 72 
 6x12 
 32x42-336 
 14x24 
 62x42 
 
 wall, 10%.. 
 
 938 
 448 
 852 
 72 
 918 
 72 
 302 
 72 
 1,008 
 336 
 2,604 
 
 10 
 83 
 4 
 19 
 2 
 5 
 
 5 
 10 
 35 
 4 
 
 9,380 
 37,186 
 3,408 
 1,368 
 1,836 
 360 
 302 
 360 
 10,080 
 11,760 
 10,416 
 
 Four windows (single) . . . . 
 
 Inside wall (store-room) 
 Door 
 
 Inside wall (corridor) 
 
 
 Inside wall (corridor) 
 
 Door 
 
 Roof 
 
 Double skylight 
 
 Floor I 
 
 Supplementary allowance, north outside 
 Supplementary allowance, north outside 
 
 Exposed location and intermittent day c 
 Total thermal units 
 
 86,456 
 ^938 
 3,718 
 
 windows, 1C 
 r night use, '. 
 
 % 
 
 M)%.r..... 
 
 91,112 
 27,333 
 
 
 118,445 
 
 Comfortable Temperatures and Humidities. A. G. Woodman and 
 J. F. Norton, in a work on Air, Water, and Food (1914), give, on the 
 authority of Hill's Recent Advances in Physiology and Biochemistry, 
 a "curve of comfort," practically a straight line, which runs from 20% 
 relative humidity at 87 F. to 75% at 55 F. It approximates 40, 50 
 and 60% respectively at 75, 70 and 65 F, showing that to secure 
 comfort as temperature rises, the humidity must be decreased. The 
 most comfortable conditions for indoor workers are given at 40% 
 humidity at 68 and 60 % at 64 F. 
 
 Carbon Dioxide Allowable in Factories. Haldane and Osborne 
 (London, 1902) recommend that the COa in the air at the breathing 
 
686 HEATING AND VENTILATION. 
 
 line in factories, and away from the immediate influence of special 
 sources of contamination, such as persons or gas lights, should not 
 rise during daylight, or after dark when electric lights only are used, 
 beyond 12 volumes in 10,000 of air, and when gas or oil is used for 
 lighting not over 20 volumes after dark. 
 
 A pamphlet issued by the National Commercial Gas Association 
 (1914) states that the use of gas for interior lighting does not affect the 
 atmosphere of interiors deleteriously. 
 
 Heat Produced by Human Beings. According to Landry and 
 Roseman, the average man produces every 24 hours per kilogram of 
 body 32 to 38 calories when at rest, 35 to 45 when in easy action, and 
 50 to 70 when at hard work. Translating this into British thermal 
 units per hour, and taking the weight of an average man at 140 lb., 
 these figures are equivalent, approximately, to a man giving off 336 to 
 400 B. T. U. per hour when at rest, 368 to 473 when in easy action, 
 and 525 to 735 when at hard work. 
 
 Atwater and Rosa, average of 13 experiments, found that a man gave 
 off 2200 cal. per 24 hours at rest and 3400 at work, equivalent to 364 
 and 562 B. T. U. per hour, respectively. 
 
 Standards of Ventilation. (C-E.A. Winslow, N. Y. State Com- 
 mission on Ventilation, 'Science, April 30, 1915.) Pettenkoffer in 1863 
 showed that CO2 in itself is without effect in the highest concentrations 
 which it ever attains in occupied rooms. During the last fifteen years 
 the researches of Fliigge, Haldane, Hill, Benedict and others indicate 
 that the effects experienced in a badly ventilated room are due to the 
 heat and moisture produced by the bodies of the occupants rather than 
 to CO2 or other substances from the breath. Subjects immured in 
 close chambers are not at all relieved by breathing pure outdoor air 
 through a tube, but are relieved completely by keeping the chamber 
 artificially cool, and to a considerable extent by the mere circulating of 
 the air by an electric fan. 
 
 The experiments of the N. Y. State Commission show that the work- 
 ing of the circulatory and heat regulating machinery of the body was 
 markedly influenced by a slight increase in room temperature, as from 
 68 to 75 with 50% relative humidity in both cases. Psychological 
 tests failed to show that 86 and 80 % relative humidity had any effect 
 on the power to dp mental work, but with physical work (lifting 
 dumb bells and riding a stationary bicycle), when the subjects had 
 a choice they accomplished 15 % less work at 75, and 37 % less at 
 86, than they did at 68. As to the effect of stagnant breathed air 
 contaminated so as to show from 20 to 60 parts CO 2 per 10,000, the re- 
 sults are entirely negative so far as mental and physical tests are con- 
 cerned. 
 
 In practice, an unventilated room is an overheated room. Ventila- 
 tion is just as essential to remove the heat produced by human bodies as 
 it was once thought to be to remove the CO2 produced by the lungs. 
 The quantitative standards of air change established on the old chemical 
 basis serve very well in the new, or heat change, basis. An average 
 adult producing 400 B.T.U. per hour will require 2000 cubic feet of 
 air per hour at 60 to prevent the temperature rising above 70. An 
 ordinary gas burner produces 300 B.T.U. per candle-power hour, and 
 requires 1500 cubic feet of air per hour per candle power. In crowded 
 auditoria every bit of the 2000 cubic feet of air per hour per person is 
 needed, and in many industrial processes, where the heat from human 
 beings is reinforced by friction and other sources, even more will be 
 required. 
 
 Recent research has on the whole strengthened the arguments for 
 ventilation. The thermometer is the first essential; a rise above 70 
 must be recognized as a sign of discomfort, of decreased efficiency and 
 lowered vitality. The standard of 30 cubic feet of air per minute per 
 capita remains as the amount necessary to supply if an occupied room 
 is to be kept cool and fresh. 
 
 The question of humidity remains to be solved. A lack of humidity 
 makes hot air feel cooler and cold air feel warmer. Extreme dryness, 
 at high or moderate temperatures, is believed by many to be in itself 
 harmful, but there is no solid experimental evidence on this point. 
 
 Air Washing. (D D. Kimball, N. Y. State Commission on Ventila- 
 tion, Science, April 30, 1915.) An air washer consists of a sheet-metal 
 
HEATING AND VENTILATING PROBLEMS. 
 
 687 
 
 chamber in which the air is passed through a heavy mist and then 
 through baffles or eliminator plates by which the entrained moisture is 
 remoTed. The base of the washer is a tank into which the spray falls 
 and from which it is drawn by a centrifugal pump. The pump forces 
 the water through spray nozzles in the spray chamber of the washer. 
 Manufacturers customarily guarantee the removal of 98% of the dust 
 in the air. Practically all the larger particles are removed, but there is 
 always a residue of fine dust which no washer will remove. When there 
 is very little dust in the air, as after a heavy rain, the percentage of the 
 remaining dust that can be removed is quite small. M. C. Whipple's 
 tests showed that the dust removed varied from 64 % down to 7%. 
 
 The best results in artificial humidification have been obtained by 
 means of the air washer. The degree of humidification is controlled by 
 thermostatic devices. The air washer may also be used for air cooling. 
 The evaporation in the spray chamber will lower the temperature to 
 the extent of 75% or more of the difference between the wet and dry 
 bulb temperatures, equivalent to a temperature reduction often 
 amounting to 10 to 15 degrees. Unfortunately cooling by means of an 
 air washer is expensive. Roughly, the cost of cooling 10 degrees equals 
 the cost of heating 70 degrees. 
 
 Contamination of Air. The following data are found in "The Air 
 and Ventilation of Subways," by G. A. Soper (1908). 
 
 Carbon dioxide in air in streets of European cities, 3.01 to 5.02 parts 
 in 10,000. Center of Paris annual average varied from 3.06 to 3.44 
 parts. Average 'of 309 analyses in New York, 3.67 parts. 
 
 An average adult inhales about 396 cubic inches per minute. Analysis 
 of inspired air: O, 20.81; N, 79.15; CO 2 , 0.04. Expired air: O, 16.00; 
 N, 79.59; CO-2, 4.38. Air highly charged with CO2 is not dangerous to 
 breathe for a considerable time. CCh must be present to 40 times the 
 amount present when the room begins to smell "stuffy" before it in- 
 creases the rate of breathing. Neither does a decrease of 2 or 3 per cent 
 in the oxygen produce any immediate effect. Long before the air be- 
 comes so vitiated as this other impurities from the lungs make the air 
 extremely unpleasant. 
 
 The CO2 in badly vitiated places seldom rises above 50 parts in 
 10,000. 
 
 The air becomes uncomfortably close and musty when CCh exceeds 
 8 parts in 10,000. 
 
 Amount of CO2 exhaled by a man, average per hour: at rest, 16.11 
 grams, or 8198 cu. cm.; at work, 30.71 grams, or 15,628 cu. cm. 
 
 STANDARD VALUES FOR USE IN CALCULATION OF HEATING 
 AND VENTILATING PROBLEMS. 
 
 Heating Value of Coal. 
 
 
 Volatile 
 Matter in 
 the Com- 
 bustible, 
 Per Cent. 
 
 Heating Value 
 per Ib. 
 Combustible, 
 B.T.U. 
 
 Aver- 
 age. 
 
 Moisture, 
 in 
 Air-dried 
 Coal, 
 Per Cent. 
 
 Ash in 
 Air-dried 
 Coal, 
 Per Cent. 
 
 Anthracite 
 Semi-anthracite . . 
 Semi-bituminous . 
 Bit. eastern 
 Bit western 
 Lignite 
 
 3 to 7.5 
 7.5 to 12.5 
 12.5 to 25 
 25 to 40 
 35 to 50 
 Over 50 
 
 14,700 to 14,900 
 14,900 to 15,500 
 15,500 to 16,000 
 14,800 to 15,000 
 13,500 to 14,800 
 11, 000 to 13,500 
 
 14,800 
 15,200 
 15,750 
 15,150 
 14,150 
 12,250 
 
 0.5 to 1.0 
 0.5 to 1.0 
 0.5 to 1.0 
 1. to 4. 
 4. to 14. 
 10. to 18. 
 
 10. to 18. 
 10. to 18. 
 5. to 10. 
 5. to 15. 
 10. to 25. 
 5. to 25. 
 
 Average Heating Value of Air-Dried Coal. Anthracite, 12,600; semi- 
 anthracite, 12,950; semi-bituminous, 14,450; bituminous eastern, 13,250; 
 bituminous western, 10,400; lignite, 9,700. 
 
 Eastern bituminous coal is that of the Appalachian coal field extending 
 from Pennsylvania and Ohio to Alabama. Western bituminous coal 
 is that of the great coal fields west of Ohio. 
 
 Steam Boiler Efficiency. The maximum efficiency obtainable with 
 anthracite in low-pressure steam b9ilers, water heaters or hot-air furnaces 
 is about 80 per cent, when the thickness of. the coal bed and the draft 
 are such as to cause enough air to be supplied to effect complete combus- 
 tion of the carbon to CO2. With coals high in volatile matter the max- 
 
688 
 
 HEATING AND VENTILATION. 
 
 imum efficiency is probably not over 70 per cent. Very much lower 
 efficiencies than these figures are obtained when* the air supply is either 
 deficient or greatly in excess, or when the furnace is not adapted to burn 
 the volatile matter in the coal. D. T. Randall, in tests made in 1908 
 for the U. S. Geological Survey, with house-heating boilers, obtained 
 efficiencies ranging from 0.62 with coke, 0.61 with anthracite, and 0.58 
 with semi-bituminous, down to 0.39 with Illinois coal. 
 
 Available Heating Value of the Coal. Using the figures given above as 
 the average heating value of coal stored in a dry cellar, the following are 
 the probable maximum values in B. T.U., of the heat available for fur- 
 nishing steam or heating water or air, for the several efficiencies stated : 
 
 Anthracite. 
 
 Semi-An. 
 
 Semi-Bit. 
 
 Bit. East. 
 
 Bit. West. 
 
 Lignite. 
 
 Eff'y 0.80 
 
 0.77 
 
 0.75 
 
 0.70 
 
 0.65 
 
 0.60 
 
 B.T.U... 10,080 
 
 9,933 
 
 10,837 
 
 9,275 
 
 6,760 
 
 5.820 
 
 For average values in practice, about 10 per cent may be deducted from 
 these figures. (It is possible that an efficiency higher than 80% may be 
 obtained with anthracite in some forms of air-heating furnaces in which 
 the escaping chimney gases are cooled, by contact with the cold air inlet 
 pipes, to comparatively low temperatures.) 
 
 The value 10,000 B.T.U. is usually taken as the figure to be used in 
 calculation for design of heating and ventilating apparatus. For coals 
 with lower available heating values proper reductions must be made. 
 
 Heat Transmission through Walls, Windows, etc., in B.T.U. per 
 Sq. Ft. per Hour per Degree of Difference of Temperature. 
 
 
 Wolff. 
 B.T.U. 
 
 Hauss. 
 B.T.U. 
 
 
 Wolff. 
 B.T.U. 
 
 Hauss . 
 B.T.U. 
 
 GLASS SURFACES. 
 Vault light 
 
 1.42 
 
 
 FLOORS. 
 Toists with double 
 
 0.10 
 0.31 
 
 0.07 
 
 Single window 
 Double window 
 Single skylight 
 
 1.20 
 0.56 
 1.03 
 0.50 
 
 40 
 
 1.00 
 0.46 
 1.06 
 0.48 
 
 0.40 
 
 Concrete floor 
 
 Fireproof construc- 
 tion, planked over. 
 Wooden beam con- 
 struction, planked 
 over 
 
 0.124 
 083 
 
 
 
 Double skylight 
 
 DOORS. 
 Door 
 l-in. pine...- 
 
 Concrete floor on 
 brick arch 
 
 
 0.22 
 0.20 
 0.16 
 
 0.20 
 0.09 
 0.08 
 
 0.10 
 0.14 
 
 2-in. pine 
 
 PARTITIONS. 
 
 Solid plaster, 
 1 3/4 to 2 1/4 in 
 
 0.28 
 
 0.60 
 0.48 
 
 Stone floor on arches 
 Planks laid on earth. 
 Planks laid on as- 
 phalt 
 
 
 Arch with air space 
 
 
 Stones laid on earth. 
 
 CEILINGS. 
 Joists with single 
 floor 
 
 
 
 2 1/2 to 3 1/4 in.... 
 
 
 Fireproof 
 
 0.30 
 0.28 
 
 2-in. pine board 
 
 
 
 
 A.rches with air space 
 
 
 BRICK WALLS. 
 
 Thickness , 
 In. 
 
 Wolff. 
 
 Hauss. 
 
 Average . 
 B.T.U.* 
 
 Thickness, 
 In. 
 
 Wolff. 
 
 Hauss. 
 
 Average, 
 B.T.U.* 
 
 4 
 
 0.66 
 
 
 0.537 
 
 25 
 
 
 18 
 
 188 
 
 43/ 4 
 
 
 0.48 
 
 508 
 
 28 
 
 18 
 
 
 017? 
 
 8 
 
 0.45 
 
 
 397 
 
 30 
 
 
 16 
 
 163 
 
 10 
 
 
 0.34 
 
 0.351 
 
 32 
 
 0.16 
 
 
 154 
 
 12 
 
 6.33 
 
 
 313 
 
 35 
 
 
 Oil 
 
 01 A\ 
 
 15 
 
 
 0.26 
 
 0.272 
 
 36 
 
 145 
 
 
 140 
 
 16 
 
 0.27 
 
 
 260 
 
 40 
 
 13 
 
 01? 
 
 01 ?fl 
 
 20 
 
 0.23 
 
 0.22 
 
 0.222 
 
 45 
 
 
 0.11 
 
 116 
 
 24 
 
 0.20 
 
 
 194 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fure for brick walls was obtained by plotting the 
 's and Hauss 's figures and drawing a straight line 
 
 * The average _ 
 reciprocals of Wo] 
 
RESIDENCE HEATING. 
 
 689 
 
 SOLID SANDSTONE WALLS. (Hauss.) 
 
 Thickness, in. . . 12 16 20 24 28 32 36 40 44 48 
 
 B.T.U 0.45 0.39 0.35 0.32 0.29 0.26 0.24 0.22 0.20 0.19 
 
 For limestone walls, add 10 per cent. 
 
 Allowances for Exposures. Wolff adds 25% for north and west ex- 
 posures, 15% for east, and 5% for south exposures, also 10% additional 
 for reheating, and 10% to the transmission through floor and ceilings. 
 The allowance for reheating Mr. Wolff explains as follows in a letter to 
 the author, Mar. 10, 1905. The allowance is made on the basis that the 
 apparatus will not be run continuously; in other words, that it will not be 
 run at all, or only lightly, overnight. The rooms will cool off below the 
 required temperature of 70, and to be able to heat up quickly in the 
 morning an allowance of 10% is made to the transmission figures to meet 
 this condition. Hauss makes allowances as follows: 5% for rooms with 
 unusual exposure; 10% where exposures are north, east, northeast, 
 northwest and west; 81/3% where the height of ceiling is more than 13 ft.; 
 62/3% where it is more than 15 ft.; 10% where it is more than 18 ft. For 
 rooms heated daily, but where heating is interrupted at night, add 
 
 A = 0.0025 [(N - 1) Wi] - Z. 
 
 For rooms not heated daily, add B = [0.1 W (8 Z)] * Z. 
 In these formulas W\ = B.T.U. transmitted per hour by exposed sur- 
 faces; W = total B.T.U. necessary, including that for ventilation or 
 changes of air; AT = time from cessation of heating to time of starting 
 fire again, hours; Z time necessary after fire is started until required 
 room temperature is reached, hours. 
 
 Allowance for Exposure and for Leakage. In calculations of the 
 quantity of neat required by ordinary residences, the formula total heat 
 
 (Ti- To) (~+ G + } is commonly used. Ti = temp, of room, 
 
 To = outside temp., W = exposed wall surface less window surface, 
 O = glass surface, C = cubic C9ntents of room, n = number of changes 
 of air per hour. The factor n is usually assumed arbitrarily or guessed 
 at; some writers take its value at 1, others 1 for the rooms, 2 for the halls, 
 etc.; others object to the use of C as a factor, saying that the allowance for 
 exposure and leakage should be made proportional to the exposed wall 
 and glass surface since it is on these surfaces that the leakage occurs, 
 and omitting the term nC/56 they multiply the remainder of the ex- 
 pression by a factor for exposure, c = 1.1 to 1.3, depending on toe direc- 
 ion of the exposure. To show what different results may be obtained 
 by the use of the two methods, the following table is calculated, apply- 
 ing both to six rooms of widely differing sizes. Two sides of each room, 
 north and east, are exposed. Ti = 70; T Q = 0; G = 1/5 (W + G). 
 
 
 
 
 
 
 O 
 
 s 
 
 
 
 
 
 
 *-. 
 
 Total Wall, 
 
 <5 
 
 + 
 
 + 
 
 CD* 
 
 
 
 g 
 
 Size, ft. 
 
 
 o 
 
 (W + G) 
 
 
 U 
 
 1 
 
 
 
 
 
 . 
 
 
 
 II 
 
 sq. ft. 
 
 1 
 
 + 
 
 
 5 
 
 ] 
 
 &J 
 
 & 
 
 
 O 
 
 
 
 
 
 
 is* 
 
 ^t^. 
 
 o 
 
 l>. 
 
 <N 
 
 
 
 CO 
 
 6 
 
 A 
 
 10x10x10 
 
 1,000 
 
 20x10= 200 
 
 40 
 
 5 
 
 5,600 
 
 1,250 
 
 1,120 
 
 1,680 
 
 B 
 
 10x20x10 
 
 2,000 
 
 30x10= 300 
 
 60 
 
 62/3 
 
 8,400 
 
 2,500 
 
 1,680 
 
 2,520 
 
 C 
 D 
 
 20x20x12 
 20x40x14 
 
 4,800 
 11,200 
 
 40x12= 480 
 60x14= 840 
 
 96 
 
 168 
 
 10 
 171/3 
 
 13,440 
 23,520 
 
 6,000 
 14.000 
 
 2,688 
 4,704 
 
 4,032 
 7,056 
 
 E 
 
 40x40x13 
 
 24.000 
 
 80x15=1200 
 
 240 
 
 20 
 
 33.600 
 
 30.000 
 
 6,720 
 
 10.0^0 
 
 F 
 
 40x80x16 
 
 51.200 
 
 120x16=1920 
 
 384 
 
 262/ 3 
 
 54.460 
 
 64.000 
 
 10.892 
 
 16.33d 
 
 The figures in the column headed H = 70 (TF/4 + G) represent the 
 heat transmitted through the walls, those in the column 70 C756 are the 
 
 between them, representing the average heat resistances, and then taking 
 the reciprocals of the resistances for different thicknesses. The resist- 
 ance corresponds to the straight line formula R = 0.12 + 0.165 t, where 
 t = thickness in inches. (Hauss's figures are from a paper by Chas. 
 F. Hauss, of Antwerp, Belgium, in Trans. A. S. H. V. E., 1904.) 
 
690 HEATING AND VENTILATION. 
 
 heat required for one change of air per hour ; 0.2 H is the heat correspond- 
 ing to an allowance ol 20% lor exposure and leakage, and 0.3 H corre- 
 sponds to an allowance of 30%. For the small rooms A and B the 
 difference between 70 C/56 and 0.2 H or 0.3 H is not of great importance, 
 but it becomes very important in the largest rooms; in room F the differ- 
 ence between 70 C/56 and 0.2 H is nearly equal to the total heat trans- 
 mitted through the walls, indicating that the use of the cubic contents 
 as a factor in calculations of large rooms is likely to lead to great errors. 
 This is due to the fact that the ratio C * (W + G) varies greatly with 
 different sizes of rooms. 
 
 With forced ventilation, the quantity of heat needed depends chiefly 
 upon the number of persons to be provided for. Assuming 2000 cu. ft. 
 per hour per person, heated from to 70, and 1, 2 and 4 persons per 
 100 sq. ft. of floor surface, the heat required for the air is as follows: 
 Room A B C D E F 
 
 1 person per 100 sq. ft. 2,500 5,000 10,000 20,000 40,000 80.000 
 
 2 persons per 100 sq.ft. 5,000 10,000 20,000 40,000 80,000 160,000 
 4 persons per 100 sq. ft. 10,000 20,000 40,000 80,000 160,000 320,000 
 Ratio of last line to H.. 1.8 2.4 3.0 3.4 4.8 5.9 
 
 Heating by Hot-air Furnaces. A simple formula for calculating the 
 total heat in British Thermal Units required for heating and ventilating 
 
 by any system is H = Fc ( G + ) + ^~\ ( Ti - T ) . (See notation above.) 
 
 The formula is derived as follows: The heat transmitted through 1 sq. ft. 
 of single glass window is approximately 1 B.T.U. per hour per degree of 
 difference of temperature, and that through 1 sq. ft. of 16-in. brick wall 
 about 0.25 B.T.U. (For more accurate calculations figures taken from 
 the tables (p. 688) should be used.) The specific heat of air is taken at 
 0.238, and the weight of 1 cu. ft. air at 70 F. at 0.075 Ib. per cu. ft. 
 The product of these figures is 0.01785, and its reciprocal is 56. 
 
 For a difference T\ - T = 70, 0.01785 X 70 = 1.2495, we may. 
 therefore, write the formula 
 
 Total heat = 70 [C(G + 2^1 + 1.25 A 
 . L V i4 / J 
 
 - - . - 
 
 = heat conducted through walls + heat exhausted in 
 ventilation. 
 
 A is the cubic feet of air (measured at 70) supplied to and exhausted 
 from the building. This formula neglects the heat conducted through 
 the roof, for which a proper addition should be made. 
 
 There are two methods of heating by hot-air furnaces; one in which 
 all the air for both heating and ventilation is taken from outdoors and 
 exhausted from the building, and the other in which only the air for 
 ventilation is taken from outdoors, and additional air is recirculated 
 through the furnace from the building itself. The first method is an 
 exceedingly wasteful one in cold weather. By the second it is possible 
 to heat a building with no greater expenditure of fuel than is required 
 for steam or hot-water heating. 
 
 EXAMPLE. Required the amount of heat and the quantity of air to be 
 circulated by the two methods named for a building which has G = 400, 
 W = 2000, C = 16,000, n = 2, Ti = 70, To = 0, T 2 , the temperature 
 at which the air leaves the furnace, being taken for three cases as 100, 
 120, and 140. Assume c, the coefficient for exposure, including heat 
 lost through roof, = 1.2. When only enough air for ventilation is taken 
 into and exhausted from the building, the formula gives 
 70 X 1.2 (500 + 400) +1.25 X 32,000 = 115,600 B.T.U. = 75,600 for 
 heat + 40,000 for ventilation. 
 
 Suppose all the air required for heating is taken from outdoors at F., 
 and all exhausted at 70, the quantity, A, then, instead of being 32,000 
 cu. ft., has to be calculated as follows: 
 
 Total heat = c (G + ^\ (Ti- TO) + A X 0.01785 X (Ti - T ) 
 
 = 0.01785 A (T 2 - To). 
 Heat supplied by furnace = heat for conduction + heat for ventilation 
 
CARRYING CAPACITY OF AIR PIPES. 
 
 691 
 
 from which we find A = c <3+ (Ti - To) * 0.01785 (T 2 - Ti) 
 
 = 75,600 ^ 0.01785 (T 2 - 70). 
 
 For the value of Ti T 2 = 100 T 2 = 120 !T2 = 140 
 
 A = cu. ft 141,117 84,706 60,504 
 
 Heat lost by exhausting this air at 70 ... 176,396 105,882 75,630 
 
 Adding 75,600 loss by walls gives total . . . 251,996 181,482 152,230 
 Excess above 115,600 actually required 
 
 for heating and ventilating, % .-. 118.0 57.0 31.7 
 
 British Thermal Units Absorbed in Heating 1 Cu. Ft. of Air, or given 
 
 up in cooling it. (The air is measured at 70 F.) 
 
 Ti - Ti = 
 
 10 20 30 40 50 56 60 70 80 90 100 110 120 126 130 140 
 0.18 0.36 0.54 0.71 0.89 1. 1.07 1.25 1.43 1.61 1.78 1.96 2.14 2.25 2.32 2.5 
 
 Area in Square Inches of Pipe required to Deliver 10O Cu. Ft. of 
 Air per Minute, at Different Velocities. The air is measured at the 
 temperature of the air in the pipe. 
 
 Velocity per second 2 3 
 
 Area, sq. in 120 80 
 
 4 
 60 
 
 5 
 
 48 
 
 6 
 40 
 
 7 
 34.3 
 
 8 9 10 
 30 26.7 24 
 
 The quantity of air required for ventilation or heating should be 
 figured at a standard temperature, say 70 F., but when warmer air is 
 to be delivered into the room through pipes, the area of the pipes should 
 be calculated on the basis of the temperature of the warm air, and not on 
 that of the room. 
 
 EXAMPLE. A room requires to be supplied with 1000 cu. ft. per min. 
 at 70 F. for ventilation, but the air is also used for heating and is delivered 
 into the room at 120 F. Required, the area of the delivery pipe, if the 
 velocity of the heated ai; In the pipe is 6 ft. per second. 
 
 From the table of volumes, given on the next page, 1000 cu. ft. at 70 
 
 ' 1094 cu. ft. at 120. From the above table of areas, at 6 ft. velocity 
 40 sq. in. area is required for 100 cu. ft., therefore 1094 cu. ft. will require 
 10.94 X 40 = 437.6 sq. in. or about 3 sq. ft. 
 
 Carrying Capacity of Air Pipes. 
 
 Diam. 
 
 Area in 
 Sq. In. 
 
 Area, 
 Sq. Ft. 
 
 Velocity, Feet per Second. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 Cu. Ft. per Min. 
 
 5 
 
 19.63 
 
 .1364 
 
 24.6 
 
 32.7 
 
 40.9 
 
 49.1 
 
 57.3 
 
 65.5 
 
 6 
 
 28.27 
 
 .1963 
 
 35.3 
 
 47.1 
 
 58.9 
 
 70.7 
 
 82.4 
 
 94.2 
 
 7 
 
 38.48 
 
 .2673 
 
 48.1 
 
 64.2 
 
 80.2 
 
 96.2 
 
 112. 
 
 128. 
 
 8 
 
 50.27 
 
 .3491 
 
 62.8 
 
 83.8 
 
 105. 
 
 126. 
 
 147. 
 
 168. 
 
 9 
 
 63.62 
 
 .4418 
 
 80.0 
 
 106. 
 
 133. 
 
 159. 
 
 186. 
 
 212. 
 
 10 
 
 78.54 
 
 .5454 
 
 98.2 
 
 131. 
 
 164. 
 
 196. 
 
 229. 
 
 262. 
 
 11 
 
 95.03 
 
 .6600 
 
 119. 
 
 158. 
 
 198. 
 
 238. 
 
 277. 
 
 317. 
 
 12 
 
 113.1 
 
 .7854 
 
 141. 
 
 188. 
 
 236. 
 
 283. 
 
 330. 
 
 377. 
 
 13 
 
 132.7 
 
 .9218 
 
 166. 
 
 221. 
 
 277. 
 
 332. 
 
 - 387. 
 
 442. 
 
 14 
 
 153.9 
 
 1.069 
 
 192. 
 
 257. 
 
 321. 
 
 385. 
 
 449. 
 
 513. 
 
 15 
 
 176.7 
 
 1.227 
 
 221. 
 
 294. 
 
 368. 
 
 442. 
 
 515. 
 
 589. 
 
 11.3 
 
 100. 
 
 0.694 
 
 125. 
 
 167. 
 
 208. 
 
 250. 
 
 292. 
 
 333. 
 
 13.6 
 
 144. 
 
 1. 
 
 180. 
 
 240. 
 
 300. 
 
 360. 
 
 420. 
 
 480. 
 
 The figures in the table give the carrying capacity of pipes in cu. ft. 
 of air at the temperature of the air flowing in the pipes. To reduce the 
 figures to cu. ft. at a standard temperature (such as 70 F.) divide by 
 the ratio of the volume per cu. ft. of the air in the pipe to that of the ftfr 
 of the standard temperature, as in the following table; 
 
692 
 
 HEATING AND VENTILATION. 
 
 Volume of Air at Different Temperatures. 
 
 (Atmospheric pressure.) 
 
 Fahr. 
 Deg. 
 
 Cu. Ft. 
 in 1 Ib. 
 
 Compar- 
 ative 
 Volume. 
 
 Fahr. 
 Deg. 
 
 Cu. Ft. 
 in 1 Ib. 
 
 Compar- 
 ative 
 Volume. 
 
 Fahr. 
 Deg. 
 
 Cu.Ft. 
 in 1 Ib. 
 
 Compar- 
 ative 
 Volume 
 
 
 
 11.583 
 
 0.867 
 
 90 
 
 13.845 
 
 .038 
 
 160 
 
 15.603 
 
 .169 
 
 32 
 
 12.387 
 
 0.928 
 
 100 
 
 14.096 
 
 .056 
 
 170 
 
 15.854 
 
 .188 
 
 40 
 
 12.586 
 
 0.943 
 
 110 
 
 14.346 
 
 .075 
 
 180 
 
 16.106 
 
 .207 
 
 50 
 
 12.840 
 
 0.962 
 
 120 
 
 14.596 
 
 .094 
 
 190 
 
 16.357 
 
 .226 
 
 62 
 
 13.141 
 
 0.985 
 
 130 
 
 14.848 
 
 .113 
 
 200 
 
 16.608 
 
 .245 
 
 70 
 
 13.342 
 
 1.000 
 
 140 
 
 15.100 
 
 .132 
 
 210 
 
 16.860 
 
 .264 
 
 80 
 
 13.593 
 
 1.019 
 
 150 
 
 15.351 
 
 .151 
 
 212 
 
 16.910 
 
 .267 
 
 Sizes of Air Pipes Used in Furnace Heating. (W. G. Snow, Eng. 
 News, April 12, 1900.) 
 
 W'th. 
 of 
 Room 
 Ft. 
 
 8... 
 10.... 
 12 
 
 Length of Room, Ft. 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 Diameter of Pipe, Ins. 
 
 8,7 
 8,7 
 
 8,7 
 9, 8 
 9,8 
 
 9, 8 
 9, 8 
 10, 8 
 
 9, 8 
 10, 8 
 10, 8 
 
 
 
 
 
 
 
 
 10, 8 
 10, 9 
 
 10, 9 
 11, 9 
 
 
 
 
 
 
 11, 9 
 
 12, 10 
 
 
 
 
 14 . 
 
 
 
 10, 8 
 
 10,9 
 11,9 
 
 11, 9 
 11, 9 
 
 12, 10 
 
 11, 9 
 12, 10 
 12, 10 
 13, 11 
 
 12, 10 
 12, 10 
 13, 11 
 13, 11 
 
 12, 10 
 13, 10 
 13, 11 
 13, 11 
 
 13, 10 
 13, 10 
 13, 11 
 14, 12 
 
 13, 10 
 13, 11 
 14, 12 
 14, 12 
 
 13, 11 
 14, 12 
 14, 12 
 
 16 
 
 
 
 18 
 
 
 
 
 20.. 
 
 
 
 
 
 
 
 
 
 
 
 The first figure in each column shows the size of pipe for the first floor 
 and the second figure the size for the second floor. Temperature at regis- 
 ter, 140; room, 70; outside, 0. Rooms 8 to 16 ft. in width assumed to 
 .be 9 ft. high; 18 to 20 ft. width, 10 ft. high. When first-floor pipes are 
 longer than 15 ft. use one size larger than that stated. For third floor, 
 use one size smaller than for second floor. For rooms with three expo- 
 sures, increase the area of pipe in proportion to the exposure. 
 
 The table was calculated on the following basis: 
 
 The loss of heat is calculated by first reducing the total exposure to 
 equivalent glass surface. This is done by adding to the actual glass 
 surface one-quarter the area of exposed wood and plaster or brick walls 
 and 1/20 the area of floor or ceiling. Ten per cent is added where the 
 exposure is severe. The window area assumed is 20% of the entire ex- 
 posure of the room. 
 
 Multiply the equivalent of glass surface by 85. The product will be 
 the total loss of heat by transmission per hour. 
 
 Assuming the temperature of the entering air to be 140 and that of 
 the room to be 70, the air escaping at approximately the latter tempera- 
 ture will carry away one-half the heat brought in. The 9ther half, corre- 
 sponding to the drop in temperature from 140 to 70, is lost by trans- 
 mission. With outside temperature zero, each cubic foot of air at 140 
 brings into the room 2.2 heat units. Since one-half of this, or 1.1 heat 
 units, can be utilized to offset the loss by transmission, to ascertain the 
 volume of air per hour at 140 required to heat a given room, divide the 
 loss of heat by transmission by 1.1. This result divided by 60 gives the 
 number of cubic feet per minute. In calculating the table, maximum 
 velocities of 280 and 400 ft. were used for pipes leading t6 the first and 
 second floors respectively. The size of the smaller pipes was based on 
 lower velocities, according to their size, to allow for their greater resist* 
 ance and loss of temperature. 
 
BOILERS FOR HOUSE HEATING. 
 
 693 
 
 Furnace-Heating with Forced Air Supply. (The Metal Worker, 
 April 8, 1905.) Tests were made of a Kelsey furnace with the air supply 
 furnished by a 48-in. Sturtevant disk fan driven by a 5 H.P. electric 
 motor. A connection was made from the air intake, between the fan and 
 the furnace, to the ash pit so that the rate of combustion could be regu- 
 lated independently of the chimney-draft condition. The furnace had 
 4.91 sq. ft. of grate surface and 238 sq. ft. of heating surface. The volume 
 of air was determined by anemometer readings at 24 points in a cross- 
 section of a rectangular intake of 11.88 sq. ft. area. The principal 
 results obtained in two tests of 8 hours each are as follows: 
 
 Av. temp, of the cold air 
 
 Per cent humidity of the cold air. 
 Ay. temp, of the warm air. 
 
 39 
 
 71 
 
 135 
 
 Air delivered to heater, cu. ft. per hour. . . . 250,896 
 B.T.U. absorbed by the dry air per hour. . . 451,872 
 B.T.U. absorbed by the vapor per hour .... 2,016 
 Avge. no. of pounds of coal burned per hour 36 
 
 B.T.U. given by the coal per hour 529,200 
 
 Per cent efficiency of the furnace. 
 
 85.7 
 
 58 
 
 56 
 
 152 
 
 249,195 
 
 421,496 
 
 3,102 
 
 33.5 
 
 492,450 
 
 86.2 
 
 Grate Surface and Bate of Burning Coal. 
 
 In steam boilers for power plants, which are constantly attended by 
 firemen, coal is generally burned at between 10 and 30 Ibs. per sq. ft. 
 of grate per hour. In small boilers, house heaters and furnaces, which 
 . even in the C9ldest weather are supplied with fresh coal only once in 
 several hours, it is necessary to. burn the coal at very much slower rates. 
 Taking a cubic foot of coal as weighing 60 Ibs., in a bed 12 inches deep, 
 and 1 sq. ft. of grate area, it would be one-half burned away in 71/2 hours 
 at a rate of burning of 4 Ibs. per sq. ft. of grate per hour. This figure, 
 4 Ibs., is commonly taken in designing grate surface for house-heating 
 boilers and furnaces. Using this figure we have the following as the 
 rated capacity of different areas of grate surface. 
 
 Rated Capacity of Furnaces and Boilers for House Heating. 
 
 
 
 fYml 
 
 
 Equiv. 
 
 Equiv. 
 
 Equiv. 
 
 Diam. 
 of 
 Round 
 Grate. 
 
 Area in 
 
 ^oai- 
 burning 
 Capacity 
 per 
 
 TT_, 1T , 
 
 Capacity, 
 B.T.U. 
 per 
 Hour. 
 
 Ibs. 
 Steam 
 Evap. 
 2 12 per 
 
 Ibs. 
 Air per 
 Hour 
 Heated 
 
 cu. ft. 
 Air at 
 70 
 Heated 
 
 
 
 .clour. 
 
 
 Hour. 
 
 100. 
 
 100. 
 
 ins. 
 12 
 
 sq.in. 
 113.1 
 
 sq.ft. 
 .785 
 
 Ibs. 
 3.142 
 
 (a) 
 31,420 
 
 (b) 
 32.5 
 
 (c) 
 1,320 
 
 (d) 
 17,610 
 
 14 
 
 153.9 
 
 1.069 
 
 4.276 
 
 42,760 
 
 44.3 
 
 1,797 
 
 23,970 
 
 16 
 
 201.1 
 
 1.396 
 
 5.585 
 
 55,850 
 
 57.8 
 
 2,347 
 
 31,300 
 
 18 
 
 254.5 
 
 1.767 
 
 7.069 
 
 70,690 
 
 73.2 
 
 2,970 
 
 39,620 
 
 20 
 
 314.2 
 
 2.182 
 
 8.728 
 
 87,280 
 
 90.4 
 
 3,667 
 
 48,920 
 
 22 
 
 380.1 
 
 2.640 
 
 10.560 
 
 105,600 
 
 109.4 
 
 4,437 
 
 59,190 
 
 24 
 
 452.4 
 
 3.142 
 
 12.566 
 
 125,660 
 
 130.1 
 
 5,280 
 
 70,430 
 
 26 
 
 530.9 
 
 3.687 
 
 14.748 
 
 147,480 
 
 152.7 
 
 6,197 
 
 82,670 
 
 28 
 
 615.8 
 
 4.276 
 
 17.104 
 
 171,040 
 
 177.1 
 
 7,187 
 
 95,870 
 
 30 
 
 706.9 
 
 4.909 
 
 19.636 
 
 196,360 
 
 203.3 
 
 8,260 
 
 110,190 
 
 32 
 
 804.2 
 
 5.585 
 
 22.340 
 
 223,400 
 
 231.3 
 
 9,387 
 
 125,220 
 
 34 
 
 907.9 
 
 6.305 
 
 25.220 
 
 252,200 
 
 261.2 
 
 10,597 
 
 141 360 
 
 36 
 
 1017.9 
 
 7.069 
 
 28.276 
 
 282,760 
 
 292.8 
 
 11,881 
 
 158,490 
 
 Figures in column (b) = (a) -* 965.7. 
 
 Figures in column (c) = (a) -4- (100 X 0.238). 
 
 Figures in-column (d) = (c) X 13.34. 
 
 Latent heat of steam at 212 = 965.7 B.T.U. [new steam tables give 
 970.4]. 
 
 Specific heat of air = 0.238. 
 
 Note that the figures in the last three columns are all based on the rate 
 of combustion of 4 Ibs. of coal per sq. ft. of grate per hour, which is taken 
 as the standard for house heating. For heating schoolhouses and other 
 large buildings where th3 furnace is fed with coal more frequently a 
 
694 HEATING AND VENTILATION. 
 
 much higher actual capacity may be obtained from the grate surface 
 named. A committee of the Am. Soc. H. and V. Engrs. in 1909 says: 
 
 The grate surface to be provided depends on the rate of combustion, 
 and this in turn depends on the attendance and draft, and on the size or 
 the boiler. Small boilers are usually adapted for intermittent attention 
 and a slow rate of combustion. The larger the boiler, the more attention 
 Is given to it, and the more heating surface is provided per square foot 
 of grate. The following rates of combustion are common for internally 
 fired heating boilers: 
 
 Sq. ft. of grate 4 to 8 10 to 18 20 to 30 
 
 Lbs. coal per sq. ft. grate per hr. not over 4 -6 10 
 
 Capacity of 1 sq. ft. and of 10O sq. in. of Grate Surface, for Steam, 
 Hot-water, or Furnace Heating. 
 
 (Based on burning 4 Ibs. of coal per sq. ft. of grate per hour and 10,000 
 
 B.T.U. available heating value of 1 Ib. of coal.) 
 1 sq. ft. 100 sq. ins. 
 grate equals grate equals 
 
 4 2.775 Ibs. of coal per hour. 
 
 40,000 27,750 B.T.U. per hour. 
 
 41.25 28.61 Ibs. of steam evap. from and at 212 per hr. 
 
 156.5 108.7 sq. ft. of steam radiating surface =- B.T.U. 
 
 -i- 255.6*. 
 261.4 181.5 sq. ft. of hot-water radiating surface = 
 
 B.T.U. -153 f. 
 22,420. 15,570. cu. ft. of air (measured at 70 F.) per hour 
 
 heated 100. 
 
 * Steam temperature 212, room temperature 70, radiator coefficient, 
 that is the B.T.U, transmitted per sq. ft. of surface per hour per degree of 
 difference of temperature, 1.8. 
 
 t Water temperature 160, room temperature 70, radiator co- 
 efficient 1.7. 
 
 For any other rate of combustion than 4 Ibs., multiply the figures In the 
 table by that rate and divide by 4. 
 
 STEAM-HEATING. 
 
 The Rating of House-heating Boilers. 
 
 (W. Kent, Trans. A. S. H. V. E., 1909.) 
 
 The rating of a steam-boiler for house-heating may be based upon one 
 or more of several data: 1, square feet of grate-surface; 2, square feet of 
 heating-surface; 3, coal-burning capacity; 4, steam-making capacity; 
 5, square feet of steam-radiating-surface, including mains, that it will 
 supply. In establishing such a rating the following considerations should 
 be taken into account: 
 
 1. One sq. ft. of cast-iron radiator surface will give off about 250 B.T.U. 
 per hour under ordinary conditions of temperature of steam 212, and 
 temperature of room 70. 
 
 2. One pound of good anthracite or semi-bituminous coal under the 
 best conditions of air-supply, in a boiler properly proportioned, will 
 transmit about 10,000 B.T.U. to the boiler. 
 
 3. In order to obtain this economical result from trie coal the boilers 
 should be driven at a rate not greatly exceeding 2 Ibs. of water evaporated 
 from and at 212 per sq. ft. of heating-surface per hour, corresponding 
 to a heat transmission of 2 X 970 = 1940, or, say, approximately 2000 
 B.T.U. per hour per sq. ft. of heating-surface. 
 
 4. A satisfactory boiler or furnace for house-heating should not 
 require coal to be fed oftener than once in 8 hours: this requires a rate 
 of burning of only 3 to 5 pounds of coal per sq. ft. of grate per hour. 
 
 5. For commercial and constructive reasons, it Is not convenient to 
 establish a fixed ratio of heating- to grate-surface for all sizes of boilers. 
 The grate-surface is limited by the available area in which it may be 
 placed, but on a given grate more heating-surface may be piled in one 
 form of boiler than in another, and in boilers of one general form one 
 boiler may be built higher than another, Urns obtaining a greater amount 
 of heating-surface. 
 
STEAM- HEATING. 
 
 695 
 
 6. The rate of burning coal and the ratio of heating- to grate-surface 
 both being variable, the coal-burning rate and the ratio may be so related 
 to each other as to establish condition 3, viz., a rate of evaporation of 
 2 Ibs. of water from and at 212 per sq. ft. of heating-surface per hour. 
 These general considerations lead to the following calculations: 
 1 Ib. of coal, 10,000 B.T.U. utilized in the boiler, will supply 10,000 + 
 250 = 40 sq. ft. radiating-surface, and will require 10,000 *- 2000 = 
 5 sq. ft. boiler heating-surface. 1 sq. ft. of boiler-surface will supply 
 2000 * 250 or 40 * 5 = 8 sq. ft. radiating-surface. 
 
 
 Low 
 Boiler. 
 
 Medi- 
 um. 
 
 High Boiler. 
 
 1 sq. ft. of grate should burn 
 
 3 
 
 4 
 
 5 Ib. coal per hour. 
 
 1 sq. ft. of grate should develop. 
 
 30,000 
 
 40,000 
 
 50,000 B.T.U. per hour. 
 
 1 sq. ft. of grate will require 
 1 sq. ft. of grate will supply 
 
 15 
 120 
 
 20 
 160 
 
 25 sq. ft. heating-surf. 
 200 sq.ft. radiating-sur 
 
 Type of boiler, depending on 
 
 
 
 
 ratio heating- -r- grate-surface. 
 
 A. 
 
 B. 
 
 C. 
 
 TABLE OF RATINGS. 
 
 Type and No. 
 
 6 
 O 
 
 
 
 " 
 ' ! tJj 
 
 Coal Burned 
 per Hour, Ibs. 
 
 J-, O 
 
 i^ 
 
 Type and No. 
 
 O 
 
 
 
 IS 
 
 -^ m 
 ^W 
 
 Coal Burned 
 per Hour, Ibs. 
 
 ^ o 
 
 i, . 
 
 tf 00 
 
 A 1... 
 A 2... 
 A 3... 
 A 4... 
 A 5... 
 B 4... 
 F 5... 
 B 6 
 B 7... 
 
 1 
 2 
 3 
 4 
 5 
 4 
 5 
 6 
 
 15 
 30 
 45 
 60 
 75 
 80 
 100 
 120 
 140 
 
 3 
 6 
 9 
 12 
 15 
 16 
 20 
 24 
 28 
 
 30 
 60 
 90 
 120 
 150 
 160 
 200 
 240 
 280 
 
 120 
 240 
 360 
 480 
 600 
 640 
 800 
 960 
 1,120 
 
 B 8... 
 C 6... 
 C 7... 
 C 8... 
 C 10... 
 C 12... 
 C 14... 
 C 16... 
 
 8 
 6 
 7 
 8 
 10 
 12 
 14 
 16 
 
 160 
 150 
 175 
 200 
 250 
 300 
 350 
 400 
 
 32 
 30 
 35 
 40 
 50 
 60 
 70 
 80 
 
 320 
 300 
 350 
 400 
 500 
 600 
 700 
 800 
 
 1,280 
 1,200 
 1,400 
 1,600 
 2,000 
 2,400 
 2,800 
 3,200 
 
 The table is based on the utilization- in the boiler of 10,000 B.T.U. per 
 pound of good coal. For poorer coal the same figures will hold good 
 except the pounds coal burned per hour, which should be increased in 
 the ratio of the B.T.U. of the good to that of the poor coal. Thus for 
 coal from which 8000 B.T.U. can be utilized the coal burned per hour 
 will be 25 per cent greater. 
 
 For comparison with the above table the following figures are taken 
 and calculated from the catalogue of a prominent maker of cast-iron 
 boilers: 
 
 
 
 
 
 
 
 
 
 
 Coal 
 
 
 
 H 
 Heat- 
 
 R 
 Radiat- 
 
 // 
 
 5 
 
 R 
 
 B.T.U. 
 
 P 'N, 
 
 per 
 Hour 
 
 Height. 
 
 Q 
 
 mg- 
 
 ing-sur- 
 
 
 
 
 per Hour 
 
 H I* 
 
 per 
 
 
 Grate. 
 
 sur- 
 
 face. 
 
 
 
 G 
 
 H 
 
 = flx250 
 
 
 
 sq.ft. 
 
 
 
 face. 
 
 
 
 
 
 
 
 Grate 
 
 * 
 
 Low 
 
 i 2.1 
 4.7 
 
 45 
 90 
 
 210 
 600 
 
 21.5 
 19.1 
 
 100 
 128 
 
 4.7 
 6.7 
 
 52,500 
 150,000 
 
 ,167 
 ,667 
 
 2.5 
 3.2 
 
 Medium.. 
 
 ] 4.2 
 \ 8.2 
 
 103 
 195 
 
 600 
 1,500 
 
 24.5 
 23.8 
 
 143 
 183 
 
 5.8 
 7.7 
 
 150,000 
 375,000 
 
 ,456 
 ,923 
 
 3.6 
 4.6 
 
 High 
 
 ( 6.7 
 1147 
 
 210 
 420 
 
 1,200 
 3,300 
 
 31.3 
 28.6 
 
 179 
 225 
 
 5.7 
 7.9 
 
 300,000 
 825,000 
 
 ,476 
 ,964 
 
 4.5 
 5.6 
 
 * Equals B.T.U. per hour 4- 10,000 O. 
 
696 HEATING AND VENTILATION. 
 
 TESTING CAST-IRON HOUSE-HEATING BOILERS. 
 
 The testing of the evaporating power and the economy of small-sized 
 boilers is more difficult than the testing of large steam-boilers for the 
 reason that the small quantity of coal burned in a day makes it impossible 
 to procure a uniform condition of the coal on the grate throughout the 
 test, and large errors are apt to be made in the calculation on account of 
 the difference of condition at the beginning and end of a test. The 
 following is suggested as a method of test which will avoid these errors. 
 
 (a) Measure the grate-surface and weigh out an amount of coal equal 
 to 30, 40, or 50 Ibs. per sq. ft. of grate, according to the type A, B, or C, 
 or the ratio of heating- to grate-surface. 
 
 (&) Disconnect the steam-pipe, so that the steam may be wasted at 
 atmospheric pressure. Fill the boiler with cold water to a marked level, 
 and take the weight of this water and its temperature. 
 
 (c) Start a brisk fire with plenty of wood, so as to cause the coal to 
 ignite rapidly; feed the coal as needed, and gradually increase the thick- 
 ness of the bed of coal as it burns brightly on top, getting the fire-pot full 
 as the last of the coal is fired. Then burn away all the coal until it ceases 
 to make steam, when the test may be considered as at an end. 
 
 (d) Record the temperature of the gases of combustion in the flue every 
 half-hour. 
 
 (e) Periodically, as needed, feed cold water, which has been weighed, 
 to bring the water level to the original mark. Record the time and the 
 weight. 
 
 CALCULATIONS. 
 
 Total water fed to the boiler, including original cold 
 water, pounds X (212 original cold-water tem- 
 perature) = B.T.U. 
 
 Water apparently evaporated, pounds X 970 = B.T.U. 
 
 Add correction for increased bulk of hot water: 
 Original water, pounds x (62 ' 3 L~ 59 ' 8) X 970 = B.T.U. 
 
 O^J.o 
 
 Total B.T.U. 
 
 Divide by 970 to obtain equivalent water evaporation from and at 
 212 F. 
 
 Divide by the number of pounds of coal to obtain equivalent water per 
 pound of coal. 
 
 The last result may be considerably less than 10 pounds on account of 
 imperfect combustion at the beginning of the test, excessive air-supply 
 when the coal bed is thin in the latter half of the test, and loss by radiation, 
 but the results will be fairly comparable with results from other boilers 
 of the same size and run under the same conditions. The records of water 
 fed and of temperature of gases should be plotted, with time as the base, 
 for comparison with other tests. 
 
 Proportions of House-heating Boilers. A committee of the Am. 
 Soc. Heating and Ventilating Engineers, reporting in 1909 on the method 
 of rating small house-heating boilers, shows the following ratings, in square 
 feet of radiating surface supplied by certain boilers of nearly the same 
 nominal capacity, as given in makers' catalogues. 
 
 Boiler.... . A. B. C. D. E. F. 
 
 Rated capacity 800 800 775 750 750 750 
 
 Square inches of grate 616 740 648 528 630 648 
 
 Ratio of grate to 100 sq. ft. of capacity 77 92.5 83.6 70.4 84 86.2 
 
 Estimated rate of combustion 5.1 4.2 4.65 5.63 4.4 % 4.5 
 
 The figures in the last line are Ibs. of coal per sq. ft. of grate surface per 
 hour, and are based on the assumptions of 10,000 B.T.U. utilized per 
 Ib. of coal and 270 B.T.U. transmitted by each sq. ft. of radiating sur- 
 face per hour. 
 
STEAM- HEATING. 
 
 697 
 
 " The question of heating surface in a boiler seems to be an unknown 
 quantity, and inquiry among the manufacturers does not produce much 
 information on the subject." 
 
 Folio wing is the list of sizes and ratings of the "Manhattan" sectional 
 steam boiler. The figures for sq. ft. of grate surface and for the ratio of 
 heating to grate surface (approx.) have been computed from the sizes 
 given in the catalogue (1909). 
 
 
 "S.A 
 
 
 *> 
 0>i 
 
 bib- 
 
 
 "S.S 
 
 
 ^.s 
 
 tii 
 
 ^ c 
 
 0} O 
 
 i||j 
 
 Size of 
 
 0> <u 
 
 ^Jj 
 
 ?5g 
 
 OB 
 JH C 
 QJ O 
 
 |l| 
 
 Size of 
 
 a flj 
 
 S . 
 
 <3g8 
 
 e tj 
 
 c ~ 
 
 Grate. 
 
 08 cc^ 
 
 oO<g 
 
 JS'S 
 
 S w 
 
 lid 
 
 Grate. 
 
 5^ 
 
 .20-g 
 
 1* 
 
 s.i 0^2 
 
 
 t 
 
 S** 
 
 S o> 
 1^ 
 
 ls-il 
 
 
 J** 
 
 |s<2 
 
 
 
 ins. 
 
 sq.ft. 
 
 
 
 
 
 ins. 
 
 sq.ft. 
 
 
 
 4 
 
 450 
 
 18x19 
 
 2.37 
 
 68 
 
 29 
 
 10 
 
 2250 
 
 24x63 
 
 10.5 
 
 212 
 
 20 
 
 5 
 
 600 
 
 18x25 
 
 3.75 
 
 84 
 
 23 
 
 6 
 
 2200 
 
 36x36 
 
 9 
 
 256 
 
 28 
 
 6 
 
 750 
 
 18x31 
 
 3.87 
 
 100 
 
 26 
 
 7 
 
 2700 
 
 36x43 
 
 11.74 
 
 298 
 
 26 
 
 7 
 
 900 
 
 18x37 
 
 4.65 
 
 116 
 
 25 
 
 8 
 
 3200 
 
 36x50 
 
 13.33 
 
 340 
 
 26 
 
 8 
 
 1050 
 
 18x43 
 
 5.37 
 
 132 
 
 25 
 
 9 
 
 3700 
 
 36x57 
 
 14.25 
 
 382 
 
 26 
 
 5 
 
 1000 
 
 24x30 
 
 5 
 
 111 
 
 22 
 
 10 
 
 4200 
 
 36x64 
 
 16 
 
 424 
 
 26 
 
 6 
 
 1250 
 
 24x36 
 
 6 
 
 128 
 
 21 
 
 11 
 
 4700 
 
 36x71 
 
 17.5 
 
 466 
 
 27 
 
 7 
 
 1500 
 
 24x43 
 
 7.16 
 
 149 
 
 21 
 
 12 
 
 5200 
 
 36x78 
 
 19.5 
 
 508 
 
 26 
 
 8 
 
 1750 
 
 24x50 
 
 8.33 
 
 170 
 
 20 
 
 13 
 
 5700 
 
 36x84 
 
 21 
 
 550 
 
 26 
 
 9 
 
 2000 
 
 24x57 
 
 9.5 
 
 191 
 
 20 
 
 14 
 
 6200 
 
 36x90 
 
 22.5 
 
 592 
 
 26 
 
 It appears from this list that there are three sets of proportions, corre- 
 sponding to the three widths of grate surface. The average ratio of 
 heating to grate surface in the three sets is respectively 25.0, 20.7, and 
 25.8; the rated sq. ft. of radiating surface per sq. ft. of grate is 185, 208, 
 and 259, and the sq. ft. of radiating surface per sq. ft. of boiler heating 
 surface is 7.4, 10.1, and 9.8. Taking 10,000 B.T.U. utilized per Ib. of 
 coal, and 250 B.T.U. emitted per sq. ft. of radiating surface per hour, 
 the rate of combustion required to supply the radiating surface is respec- 
 tively 4.62, 5.22, and 6.40 Ibs. per sq. ft. of grate per hour. 
 
 Coefficient of Heat Transmission in Direct Radiation. The value 
 of K, or the B.T.U. transmitted per sq. ft. of radiating surface per hour 
 per degree of difference of temperature between the steam (or hot water) 
 and the air in the room, is commonly taken at 1.8 in steam heating, 
 with a temperature difference of about 142, and 1.6 in hot-water heat- 
 ing, with a temperature difference averaging 80. Its value as found by 
 test varies with the conditions; thus the total heat transmitted is not 
 directly proportional to the temperature difference, but increases at a 
 faster rate; single pipes exposed on all sides transmit more heat than 
 pipes in a group; low radiators more than high ones; radiators exposed 
 to currents of cool air more than those in relatively quiet air; radiators 
 with a free circulation of steam throughout more than those that are 
 partly filled with water or air, etc. The total range of the value of K, 
 for ordinary conditions of practice, is probably between 1.5 and 2.0 for 
 steam-heating with a temperature difference of 140, averaging 1.8, and 
 between 1.2 and 1.7, averaging 1.6, for hot-water heating, with a tem- 
 perature difference of 80. 
 
 C. F. Hauss, Trans. A. S. H. V. E., 1904, gives as a basis for calcula- 
 tion, for a room heated to 70 with steam at 11/2 Ibs. gauge pressure 
 (temperature difference 146 F.) 1 sq. ft. of single column radiator gives 
 off 300 B.T.U. per hour; 2-column, 275; 3-column, 250; 4-column, 225. 
 
 Value of K in Cast-iron Direct Radiators. (J. R. Allen, Trans. 
 A. S. H. V. E., 1908.) Ts = temp, of steam; Tj_= temp, of room. 
 
 Ts - T! = 
 
 110 
 
 
 120 
 
 130 
 
 140 
 
 150 
 
 
 160 
 
 2-col. 
 
 rad .... 
 
 .1.71 
 
 1 
 
 .745 
 
 1.76 
 
 1. 
 
 82 
 
 1, 
 
 ,855 
 
 1 
 
 .895 
 
 3-col. 
 
 rad 
 
 .1.65 
 
 1 
 
 .695 
 
 1.745 
 
 1. 
 
 79 
 
 1. 
 
 835 
 
 1. 
 
 ,885 
 
 Ts 
 
 -5Ti = 
 
 170 
 
 
 180 
 
 200 
 
 
 220 
 
 
 240 
 
 
 260 
 
 2-col. 
 
 rad 
 
 .1.93 
 
 1 
 
 .965 
 
 2.04 
 
 2. 
 
 11 
 
 2. 
 
 ,185 
 
 2 
 
 ,265 
 
 3-col. 
 
 rad.... 
 
 .1.93 
 
 1 
 
 .98 
 
 2.075 
 
 2 
 
 .165 
 
 2. 
 
 260 
 
 2. 
 
 36 
 
698 HEATING AND VENTILATION. 
 
 B.T.U. Transmitted per Hour per Sq. Ft. of Heating Surface in 
 Indirect Radiators. (W. S. Munroe, Eng. Rec., Nov. 18, 1899.) 
 
 Cu. ft. of air per hour per sq. ft. of surface. 
 100 200 300 400 500 600 700 800 900 
 
 B.T.U. per hour per sq. ft. of heating surface. 
 "Gold Pin ")(a). .. 200 325 450 560 370 780 870 950 1030 
 
 radiator ((&). 300 550 760 950 1130 1300 
 "Whittier" (6)... 250 400 520 620 710 
 
 B.T.U. per hr. per sq. ft. per deg. diff. of temp.* 
 
 Gold Pin (a) 1.3 2.2 3.0 3.7 4.5 5.2 5.8 6.3 6.9 
 
 Gold Pin (6) 2.0 3.7 5.1 6.3 7.7 8.7 
 
 Whittier (6) 1.7 2.7 3.5 4.1 4.7 
 
 Temperature difference between steam and entering air, (a) 150; 
 (6) 215. 
 
 * Between steam and entering air. 
 
 Short Rules for Computing Radiating-Surfaces. In the early days 
 of steam-heating, when little was known about " British Thermal Units," 
 it was customary to estimate the amount of radiating-surface by dividing 
 the cubic contents of the room to be heated by a certain factor supposed 
 to be derived from "experience." Two of these rules are as follows: 
 
 One square foot of surface will heat from 40 to 100 cu. ft. of space to 
 75 in 10 latitudes. This range is intended to meet conditions of 
 exposed or corner rooms of buildings, and those less so, as intermediate 
 ones of a block. As a general rule, 1 sq. ft. of surface will heat 70 cu. ft. 
 of air in outer or front rooms and 100 cu. ft. in inner rooms. In large 
 stores in cities, with buildings on each side, 1 to 100 is ample. The 
 following are approximate proportions: 
 
 One square foot radiating-surface will heat: 
 
 In Dwellings, In Hall, Stores, In Churches, 
 Schoolrooms, Lofts, Factories, Large Audito- 
 Offices, etc. etc. riums, etc. 
 
 By direct radiation.. . . 60 to 80 ft. 75 to 100 ft. 150 to 200 ft. 
 
 By indirect radiation.. 40 to 50 ft. 50 to 70 ft. 100 to 140 ft. 
 
 Isolated buildings exposed to prevailing north or west winds should 
 have a generous addition made to the heating-surface on their exposed 
 sides. 
 
 1 sq. ft. of boiler-surface will supply from 7 to 10 sq. ft. of radiating- 
 surface, depending upon the size of boiler and the efficiency of its surface, 
 as well as that of the radiating-surface. Small boilers for house use 
 should be much larger proportionately than large plants. Each horse- 
 power of boiler will supply from 240 to 360 ft. of 1-in. steam-pipe, or 
 80 to 120 sq. ft. of radiating-surface. Under ordinary conditions 1 
 horse-power will heat, approximately, in 
 
 Brick dwellings, in blocks, as in cities 15,000 to 20,000 cu. ft. 
 
 Brick stores, in blocks 10,000 15,000 
 
 Brick dwellings, exposed all round 10,000 15,000 
 
 Brick mills, shops, factories, etc 7,000 10,000 
 
 Wooden dwellings, exposed 7,000 10,000 
 
 Foundries and wooden shops 6,000 10,000 
 
 Exhibition buildings, largely glass, etc 4,000 15,000 
 
 Such "rules of thumb," as they are called, are generally supplanted by 
 the modern "heat-unit" methods. 
 
 Carrying Capacity of Pipes in Low -Pressure Steam Heating. (W. 
 
 Kent, Trans. A. S. II. V. E., 1907.) The following table is based on an 
 assumed drop of 1 pound pressure per 1000 feet, not because that is 
 the drop which should always be used in fact the writer believes that 
 in large installations a far greater drop is permissible but because it 
 gives a basis upon which the flow for any other drop may be calculated, 
 
FLOW OF STEAM IN PIPES. 
 
 699 
 
 merely by multiplying the figures in the tables by the square root 9f the 
 assigned drop. The formula from which the tables are calculated is the 
 
 in which W= weight of steam 
 
 well known one, W 
 in Ibs. per hour; 
 
 weight of steam in pounds per cubic foot, at 
 
 eng n ee. e coecens c are erve rom acocs o 
 
 (see page 618) which is believed to be as accurate as any that has been 
 
 derived from the very few recorded experiments on steam. 
 
 Nominal diam. of 
 pipe 
 
 1/2 
 
 3/4 
 
 1 
 
 U/4 
 
 11/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 Value of c 
 
 334 
 
 37.5 
 
 41 .3 
 
 45.8 
 
 48.4 
 
 52.5 
 
 55.5 
 
 59.0 
 
 61 3 
 
 Nominal diam. of 
 pipe 
 
 4 
 
 41/2 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 1?. 
 
 Value of c 
 
 63.2 
 
 64.8 
 
 66.5 
 
 68.7 
 
 70.7 
 
 72.2 
 
 73.4 
 
 74.5 
 
 76.3 
 
 Flow of Steam in Pipes for a Drop of 1 Ifo. per 1000 Ft. Length. 
 
 (Pounds per Hour.) 
 
 i 
 
 .2 
 
 
 
 
 
 
 
 
 
 
 fi 
 
 IH 
 
 Pi =0.3 
 
 pi=1.3 
 
 Pi=2.3 
 
 Pi=3.3 
 
 pi=4.3 
 
 pi=5.3 
 
 Pi = 6.3 
 
 pi = 8.3 
 
 pi=10.3 
 
 3.0. 
 
 
 
 
 
 
 
 
 
 
 
 
 3 s 
 
 W 
 
 w 
 
 W 
 
 w~ 
 
 w= 
 
 W 
 
 w = 
 
 w= 
 
 W 
 
 'SvH 
 
 11 
 
 .03732 
 
 .04042 
 
 .04277 
 
 .04512 
 
 .04746 
 
 .04980 
 
 .05213 
 
 .05676 
 
 .0614 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T~~ 
 
 H/4 
 
 1.049 
 1.380 
 
 17.1 
 37.6 
 
 17.8 
 39.4 
 
 18.3 
 40.2 
 
 18.8 
 41.3 
 
 19.2 
 
 42.4 
 
 19.7 
 43.4 
 
 20.2 
 44.4 
 
 21.0 
 46.3 
 
 21.9 
 
 48.2 
 
 H/2 
 
 1.610 
 
 58.4 
 
 60.7 
 
 62.5 
 
 64.1 
 
 65.8 
 
 67.4 
 
 68.9 
 
 71.9 
 
 74.8 
 
 2 
 
 2.067 
 
 118.2 
 
 123.0 
 
 126.6 
 
 130.0 
 
 133.3 
 
 136.6 
 
 139.7 
 
 145.8 
 
 151.6 
 
 21/2 
 
 2.469 
 
 194.9 
 
 202.8 
 
 208.7 
 
 214.3 
 
 219.7 
 
 225.1 
 
 230.3 
 
 240.3 
 
 250.0 
 
 3 
 
 3.068 
 
 356.6 
 
 371.0 
 
 381.8 
 
 392.0 
 
 402.1 
 
 411.9 
 
 421.4 
 
 439.7 
 
 457.3 
 
 31/2 
 
 3.548 
 
 532.7 
 
 554.5 
 
 570.5 
 
 585.8 
 
 600.8 
 
 615.4 
 
 629.8 
 
 481.5 
 
 683.8 
 
 4 
 
 4.026 
 
 753.6 
 
 784.2 
 
 807.0 
 
 828.6 
 
 849.6 
 
 870.6 
 
 890.4 
 
 929.4 
 
 966.6 
 
 41/2 
 
 4.506 
 
 1025. 
 
 1066. 
 
 1096. 
 
 1126. 
 
 1154. 
 
 1184. 
 
 1210. 
 
 1262. 
 
 1315. 
 
 5 
 
 5.047 
 
 1395. 
 
 1451. 
 
 1494. 
 
 1534. 
 
 1573. 
 
 1611. 
 
 1649. 
 
 1720. 
 
 1789. 
 
 6 
 
 6.065 
 
 2281. 
 
 2374. 
 
 2443. 
 
 2509. 
 
 2573. 
 
 2635. 
 
 2696. 
 
 2813. 
 
 2926. 
 
 7 
 
 7.023 
 
 3387. 
 
 3525. 
 
 3628. 
 
 3725. 
 
 3820. 
 
 3913. 
 
 4003. 
 
 4177. 
 
 4345. 
 
 8 
 
 7.981 
 
 4776. 
 
 4970. 
 
 5114. 
 
 5250. 
 
 5385. 
 
 5518. 
 
 5644. 
 
 5889. 
 
 6123. 
 
 9 
 
 8.941 
 
 6429. 
 
 6693. 
 
 6885. 
 
 7070. 
 
 7250. 
 
 7430. 
 
 7604. 
 
 7934. 
 
 8251. 
 
 10 
 
 10.020 
 
 8676 
 
 9030. 
 
 9294. 
 
 9545. 
 
 9785. 
 
 10025. 
 
 10259. 
 
 10702. 
 
 11123. 
 
 It 
 
 11.000 
 
 11106. 
 
 11556. 
 
 11892. 
 
 12210. 
 
 12522. 
 
 12828. 
 
 13128. 
 
 13698. 
 
 14244. 
 
 12 112.000 
 
 13950. 
 
 14520. 
 
 14940. 
 
 15342. 
 
 15732. 
 
 16116. 
 
 16488. 
 
 17202. 
 
 17892. 
 
 Pi = initial pressure, by gauge, Ib. per sq. in. w = density, Ib. 
 per cu. ft. 
 
 For any other drop of pressure per 1000 feet length, multiply the fig- 
 ures in the table by the square root of that drop, or by the factor below. 
 
 Drop Ib. per 
 
 1000 ft.... 14 1/2 2 3 4 
 
 Factor 0.5 0.71 1.41 1.73 2.0 
 
 6 8 10 15 20 
 2.45 2.83 3.16 3.87 4.47 
 
 In all cases the judgment of the engineer must be used in the assump- 
 tion of the drop to be allowed. For small distributing pipes it will gen- 
 erally be desirable to assume a drop of not more than one pound per 
 1000 feet to insure that each single radiator shall always have an ample 
 supply for the worst conditions, and in that case the size of piping given 
 in the table up to two inches may be used; but for main pipes supplying 
 totals of more than 500 square feet, greater drops may be allowed. 
 
'700 
 
 HEATING AND VENTILATION. 
 
 Proportioning Pipes to Radiating Surface. 
 
 FIGURES USED IN CALCULATION OF RADIATING SURFA.CE. 
 
 P = Pressure by gauge, Ibs. per sq. in. 
 0. 0.3 1.3 2.3 3.3 4.3 5.3 6.3 8.3 
 
 L = latent heat of evaporation, B.T.U. per lb.* 
 965.7 965.0 962.6 960.4 958.3 956.3 954.4 952.6 949.1 945.8 
 
 10.3 
 
 212. 
 
 Temperature Fahrenheit, T\. 
 213. 216.3 219.4 222.4 225.2 227.9 
 
 142. 143. 
 Hi = T t X 1.8 
 
 230.5 2.35.4 240.0 
 !T 2 = TI 70, difference of temperature. 
 146.3 149.4 152.4 155.2 157.9 160.5 165.4 170.0 
 
 heat transmission per sq. ft. radiating surface, B.T.U. 
 
 per hour. 
 255.6 257.4 263.3 268.9 274.3 279.2 284.2 288.9 297.7 306.0 
 
 H t + L = steam condensed per sq. ft. radiating surface, Ibs. per hour. 
 0.2647 0.267 0.274 0.280 0.286 0.292 0.298 0.303 0.314 0.324 
 
 Heciprocal of above = radiating surface per lb. of steam condensed per 
 
 hour. 
 
 3.42 3.36 
 
 3.78 3.75 3.65 3.57 3.50 
 
 3.30 3.18 3.09 
 
 The last three lines of figures are based on the empirical constant 1.8 
 for the average British thermal units transmitted per square foot of radi- 
 ating surface per hour per degree of difference of temperature. This 
 figure is approximately correct for several forms of both cast-iron radia- 
 tors and pipe coils, not over 30 inches high and not over two pipes in 
 width. 
 
 RADIATING SURFACE SUPPIJED BY DIFFERENT SIZES OF PIPE. 
 
 On basis of steam in pipe at 0.3 and 10.3 Ibs. gauge pressure, tempera- 
 ture of room 70, heat transmitted per square foot radiating surface 257.4 
 and 306 British thermal units per hour, and drop of pressure in pipe at 
 the rate of 1 lb. per 1000 feet length; = pounds of steam per hour in the 
 table on the preceding page, 1st column, X 3.75, and last column, X 3.09. 
 
 Size of 
 Pipe. 
 
 Radiating 
 Surface, 
 Sq. Ft. 
 
 Size of 
 Pipe, 
 
 Radiating 
 Surface, 
 Sq.Ft. 
 
 Size of 
 Pipe. 
 
 Radiating 
 Surface, 
 Sq. Ft. 
 
 In. 
 
 0.3 lb. 
 
 10.3 lb. 
 
 In, 
 
 0.3 lb. 
 
 10.3 lb. 
 
 In. 
 
 0.3 lb. 
 
 10.31b. 
 
 1/2 
 
 16 
 
 16 
 
 21/2 
 
 734 
 
 769 
 
 6 
 
 7,541 
 
 7,90! 
 
 3/4 
 
 36 
 
 38 
 
 3 
 
 1,296 
 
 1,357 
 
 7 
 
 11,010 
 
 11,535 
 
 1 
 
 71 
 
 75 
 
 31/2 
 
 1,895 
 
 1,986 
 
 8 
 
 15,307 
 
 16,040 
 
 11/4 
 
 150 
 
 157 
 
 
 2,630 
 
 2,755 
 
 9 
 
 20,482 
 
 21,451 
 
 H/2 
 
 230 
 
 241 
 
 41/2 
 
 3,520 
 
 3,686 
 
 10 
 
 27,427 
 
 28,718 
 
 2 
 
 453 
 
 475 
 
 5 
 
 4,695 
 
 4,919 
 
 12 
 
 43,312 
 
 45,423 
 
 For greater drops than 1 lb. per 1000 ft. length of pipe, multiply the 
 figures by the square root of the drop. 
 
 * The latest steam tables (1909) give somewhat higher figures, but the 
 difference is unimportant here. 
 
SIZES OF STEAM PIPES FOB HEATING, 
 
 701 
 
 Sizes of Steam Pipes in Heating Plants. G. W. Stanton, in HeatinQ 
 and Ventilating Mag., April, 1908, gives tables for proportioning pipes to 
 radiating surface, from which the following tablets condensed: 
 
 Sup- 
 ply 
 
 Pipe. 
 Ins. 
 
 Radiating Surface Sq. Ft. 
 
 Returns. 
 
 Drips. 
 
 Connections. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 B 
 
 CxD 
 
 A 
 
 BAD 
 
 At 
 
 A2BA 
 
 1 
 
 H/4 
 H/2 
 
 BjA 
 
 U'4 
 
 H/2 
 
 2l/ 2 
 31/2 
 
 h 
 
 6 
 7 
 8 
 9 
 10 
 12 
 14 
 16 
 
 24 
 60 
 125 
 250 
 600 
 800 
 1,000 
 1,600 
 1,900 
 2,300 
 4,100 
 6,500 
 9,600 
 13,600 
 
 60 
 100 
 200 
 400 
 700 
 1,000 
 1,600 
 2,300 
 3,200 
 4 100 
 6,500 
 9,600 
 13,600 
 
 36 
 72 
 120 
 280 
 528 
 900 
 1,320 
 1,920 
 2,760 
 3,720 
 6,000 
 9,000 
 12,800 
 17,800 
 23,200 
 37,000 
 54,000 
 76,000 
 
 60 
 120 
 240 
 480 
 880 
 1,500 
 2,200 
 3,200 
 4,600 
 6,200 
 10,000 
 15,000 
 21,600 
 30,000 
 39,000 
 62,000 
 92,000 
 130,000 
 
 1 
 1 
 
 11/4 
 
 I V2 
 
 2 
 21/2 
 21/ 2 
 21/2 
 
 3 
 
 31/2 
 4 
 
 1 
 1 
 U/4 
 U/2 
 
 21/2 
 21/2 
 
 3 
 
 31/2 
 3 V , 
 
 4 
 41/2 
 
 6 
 
 7 
 8 
 
 3/4 
 
 1 3/4 
 
 H/4 
 U/4 
 11/2 
 
 U/2 
 U/2 
 
 3/4 
 3/4 
 
 1 
 
 U/4 
 U/4 
 U/4 
 11/4 
 
 U/4 
 
 u/ 2 
 
 2V, 
 31/2 
 41/2 
 
 U/4 
 U/2 
 
 
 
 
 
 Supply mains and risers 
 are of the same size. 
 Riser connections on 
 the two-pipe system to 
 be the same size as the 
 riser. 
 
 
 
 
 
 
 
 
 
 
 A. For single-pipe steam-heating system to 
 riser connections. A 2, radiator connections. 
 
 Ib. pressure. A\, 
 
 B. Two-pipe system to 5 Ib. pressure; Bi, Ci, radiator connections, 
 supply; B%, Ci, radiator connections, return. 
 
 C, D. Two-pipe system 2 and 5 Ibs. respectively, mains and risers not 
 over 100 ft. length. For other lengths, multiply the given radiating 
 surface by factors, as below: 
 
 Length, ft... . 200 
 Factor ...... 0.71 
 
 300 
 0.58 
 
 400 
 0.5 
 
 500 
 0.45 
 
 600 
 0.41 
 
 700 
 0.38 
 
 800 
 0.35 
 
 900 
 0.33 
 
 1000 
 0.32 
 
 Mr. Stanton says: Theoretically both supply and return mains could 
 be much smaller, but in practice it has been found that while -smaller 
 pipes can be used if a job is properly and carefully figured and propor- 
 tioned and installed, for work as ordinarily installed it is far safer to use 
 the sizes that have been tried and proven. By using the sizes given a 
 job will circulate throughout with 1 Ib. steam pressure at the boiler. 
 
 Resistance of Fittings. Where the pipe supplying the radiation con- 
 tains a large number of fittings, or other conditions make such a refine- 
 ment necessary, it is advisable to add to the actual distance of the radia- 
 tion from the source of supply a distance equivalent to the resistance 
 offered by the fittings, and by the entrance to the radiator, the value of 
 which, expressed in feet of pipe of the same diameter as the fitting, will 
 be found in the accompanying table. Power, Dec., 1907. 
 
 FEET OF PIPE TO BE ADDED FOR EACH FITTING. 
 
 Size Pipe. 
 
 ' 
 
 U/4 
 
 11/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Elbows... 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 
 
 10 
 
 12 
 
 13 
 
 15 
 
 17 
 
 20 
 
 23 
 
 27 
 
 30 
 
 33 
 
 Globe V.. 
 
 7 
 
 8 
 
 10 
 
 13 
 
 17 
 
 20 
 
 23 
 
 27 
 
 30 
 
 33 
 
 40 
 
 47 
 
 53 
 
 60 
 
 67 
 
 Entrance 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 15 
 
 18 
 
 20 
 
 23 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
702 HEATING AND VENTILATION. 
 
 Overhead Steam-pipes. (A. R. Wolff, Stevens Indicator, 1887.) 
 When the overhead system of steam-heating is employed, in which sys- 
 tem direct radiating-pipes, usually 1 1/4 in. in diam., are placed in rows 
 overhead, suspended upon horizontal racks, the pipes running horizon- 
 tally, and side by side, around the whole interior of the building from 2 
 to 3 ft. from the walls, and from 2 to 4 ft. from the ceiling, the amount 
 of li/4-in. pipe required, according to Mr. C. J. H. Woodbury, for heating 
 mills (for which use this system is deservedly much in vogue), is about 
 1 ft. in length for every 90 cu. ft. of space. Of course a great range of 
 difference exists, due to the special character of the operating machinery 
 in the mill, both in respect to the amount of air circulated by the ma- 
 chinery, and also the aid to warming the room by the friction of the 
 journals. 
 
 Removal of Air from Radiators. Vacuum Systems. In order 
 that a steam radiator may work at its highest capacity it is necessary 
 that it be neither water-bound nor air-bound. Proper drainage must 
 therefore be provided, and also means for continuously, or frequently, 
 removing air from the system, such as automatic air-valves on each 
 radiator, an air-pump or an air-ejector on a chamber or receiver into 
 which the returns are carried, or separate air-pipes connecting each 
 radiator with a vacuum chamber. When a vacuum system is used, 
 especially with a high vacuum, much lower temperatures than usual may 
 be used in the radiators, which is an advantage in moderate weather. 
 
 Steam-consumption in Car-heating. 
 
 C., M. & ST. PAUL RAILWAY TESTS. (Engineering, June 27, 1890, p. 764.) 
 
 Outside Temperature. Inside Temperature. ^^rte^THw^ 
 
 40 70 70 Ibs. 
 
 30 70 85 
 
 10 70 100 
 
 Heating a Greenhouse by Steam. Wm. J. Baldwin answers . a 
 question in the American Machinist as below: With five pounds steam- 
 pressure, how many square feet or inches of heating-surface is necessary 
 to heat 100 square feet of glass on the roof, ends, and sides of a green- 
 house in order to maintain a night heat of 55 to 65, while the thermom- 
 eter outside ranges at from 15 to 20 below zero: also, what boiler- 
 surface is necessary? Which is the best for the purpose to use 2" pipe 
 or 1 1/4" pipe? 
 
 Ans. Reliable authorities agree that 1.25 to 1.50 cubic feet of air in 
 an enclosed space will be cooled per minute per sq. ft. of glass as many 
 degrees as the internal temperature of the house exceeds that of the air 
 outside. Between + 65 and 20 there will be a difference of 85, or, 
 say, one cubic foot 9f air cooled 127.5 F. for each sq. ft. of glass for the 
 most extreme condition mentioned. Multiply this by the number of 
 square feet of glass and by 60, and we have the number of cubic feet of 
 air cooled 1 per hour within the building or house. Divide the number 
 thus found by 48, and it gives the units of heat required, approximately. 
 Divide again by 953, and it will give the number of pounds of steam that 
 must be condensed from a pressure and temperature of five pounds 
 above atmosphere to water at the same temperature in an hour to main- 
 tain the heat. Each square foot of surface of pipe will condense from 
 1/4 to nearly 1/2 lb. of steam per hour, according as the coils are exposed 
 or well or poorly arranged, for which an average of 1/3 lb. may .be taken. 
 According to this, it will require 3 sq. ft. of pipe surface per lb. of steam 
 to be condensed. Proportion the heating-surface of the boiler to have 
 about one fifth the actual radiating-surface, if you wish to keep steam 
 over night, and proportion the grate to burn not more than six pounds 
 of coal per sq. ft. of grate per hour. With very slow combustion, such 
 as takes place in base-burning boilers, the grate might be proportioned 
 for four to five pounds of coal per hour. It is cheaper to make coils of 
 H/4" pipe than of 2", and there is nothing to be gained by using 2" pipe 
 unless the coils are very long. The pipes in a greenhouse should be 
 under or in front of the benches, with every chance for a good circulation 
 
HOT-WATER HEATING. 703 
 
 of air. "Header" coils are better than "return-bend" coils for this 
 purpose. 
 
 Mr. Baldwin's rule may be given the following form: Let H = heat- 
 units transferred per hour, T = temperature inside the greenhouse, t = 
 temperature outside, S = sq. ft. of glass surface; then H = 1.5 S (T t) 
 X 60 -*- 48 = 1.875 S (T t). Mr. Wolff's coefficient K for single sky- 
 lights gives H = 1.03 S (T - 0, and for single windows, 1.20 S (T - t). 
 
 Heating a Greenhouse by Hot Water. W. M. Mackay, of the 
 Richardson & Boynton Co., in a lecture before the Master Plumbers' 
 Association, N. Y., 1889, says: I find that while greenhouses were for- 
 merly heated by 4-inch and 3-inch cast-iron pipe, ,on account of the large 
 body of water which they contained, and the supposition that they gave 
 better satisfaction and a more even temperature, florists of long experi- 
 ence who have tried 4 -inch and 3-inch cast-iron pipe, and also 2-inch 
 wrought-iron pipe for a number of years in heating their greenhouses 
 by hot water, and who have also tried steam-heat, tell me that they get 
 better satisfaction, greater economy, and are able to maintain a more 
 even temperature with 2-inch wrought-iron pipe and hot water than by 
 any other system they have used. They attribute this result principally 
 to 'the fact that this size pipe contains less water and on this account the 
 heat can be raised and lowered quicker than, by any other arrangement 
 of pipes, and a more uniform temperature maintained than by steam or 
 any other system. 
 
 HOT- WATER HEATING. 
 
 The following notes are from the catalogue of the Nason Mfg. Co.: 
 
 There are two distinct forms or modifications of hot-water apparatus, 
 depending upon the temperature of the water. 
 
 In the first or open-tank system the water is never above 212 tempera- 
 ture, arfd rarely above 200. This method always gives satisfaction 
 where the surface is sufficiently liberal, but in making it so its cost is 
 considerably greater than that for a steam-heating apparatus. 
 
 In the second method, sometimes called (erroneously) high-pressure 
 hot-water heating, or the closed -system apparatus, the tank is closed. 
 If it is provided with a safety-valve set at 10 Ibs. it is practically as safe 
 as the open-tank system. 
 
 Law of Velocity of Flow. The motive power of the circulation in a 
 hot-water apparatus is the difference between the specific gravities of 
 the water in the ascending and the descending pipes. This effective 
 pressure is very small, and is equal to about one grain for each foot in 
 height for each degree difference between the pipes; thus, with a height 
 of 1 ft. " up " pipe, and a difference between the temperatures of the 
 up and down pipes of 8, the difference in their specific gravities is equal 
 to 8.16 grains (0.001166 Ib.) on each square inch of the section of return- 
 pipe, and the velocity of the circulation is proportioned to these differ- 
 ences in temperature and height. 
 
 Main flow-pipes from the heater, from which branches may be taken, 
 are to be preferred to the practice of taking off nearly as many pipes from 
 the heater as there are radiators to supply. 
 
 It is not necessary that the main flow and return pipes should equal in 
 capacity that of all their branches. The hottest water will seek the 
 highest level, while gravity will cause an even distribution of the heated 
 water if the surface is properly proportioned. 
 
 It is good practice to reduce the size of the vertical mains as they ascend, 
 say at the rate of one size for each floor. 
 
 As with steam, so with hot water, the pipes must be unconfined to allow 
 for expansion of the pipes consequent on having their temperatures in- 
 creased. 
 
 An expansion tank is required to keep the apparatus filled with water, 
 which latter expands 1/24 of its bulk on being heated from 40 to 212, 
 and the cistern must have capacity to hold certainly this increased bulk. 
 It is recommended that the supply cistern be placed on level with or 
 above the highest pipes of the apparatus, in order to receive the air which 
 collects in the mains and radiators, and capable of holding at least 1/30 of 
 the water in the entire apparatus. 
 
 Arrangement of Mains for Hot-water Heating. (W. M. Mackay, 
 Lecture before Master Plumbers' Assoc., N. Y., 1889). There are two 
 different systems of mains in general use, either of which, if properly 
 
704 HEATING AND VENTILATION. 
 
 placed, will give good satisfaction. One is the taking of a single large- 
 flow main from the heater to supply all the radiators on the several floors, 
 with a corresponding return mam of the same size. The other is the tak- 
 ing of a number of 2-inch wrought-iron mains from the heater, with the 
 same number of return mains of the same size, branching off to the several 
 radiators or coils with li/4-inch or 1-inch pipe, according to the size of 
 the radiator or coil. A 2-inch main will supply three U/4-inch or four 
 1-inch branches, and these branches should be taken from the top of the 
 horizontal main with a nipple and elbow, except in special cases where it 
 it is found necessary to retard the flow of water to the near radiator, for 
 the purpose of assisting the circulation in the far radiator; in this case 
 the branch is taken from the side of the horizontal main. The flow and 
 return mains are usually run side by side, suspended from the basement 
 ceiling, and should have a gradual ascent from the heater to the radiators 
 of at least 1 inch in 10 feet. It is customary, and an advantage where 
 2-inch mains are used, to reduce the size of the main at every point where 
 a branch is taken off. 
 
 The single or large main system is best adapted for large buildings ; but 
 there is a limit as to size of main which it is not wise to go beyond 
 generally 6-inch, except in special cases. 
 
 The proper area of cold-air pipe necessary for 100 square feet of indi- 
 rect radiation in hot-water heating is 75 square inches, while the hot-air 
 pipe should have at least 100 square inches of area. There should be a 
 damper in the cold-air pipe for the purpose of controlling the amount of 
 air admitted to the radiator, depending on the severity of the weather. 
 
 Sizes of Pipe for Hot-water Heating. A theoretical calculation of 
 the required size of pipe in hot-water heating may be made in the follow- 
 ing manner. Having given the amount of heat, in B.T.U. to be emitted 
 by a radiator per minute, assume the temperatures of the water entering 
 and leaving, say 160 and 140. Dividing the B.T.U. by the difference 
 in temperatures gives the number of pounds of water to be circulated, 
 and this divided by the weight of water per cubic foot gives the number 
 of cubic feet per minute. The motive force to move this water, per 
 square inch of the area of the riser, is the difference in weight per cu. ft. 
 of water at the two temperatures, divided by 144, and multiplied by H, 
 the height of the riser, or for Ti = 160 and T 2 = 140, (61.37 - 60.98) 
 + 144 = q.00271 Ib. per sq. in. for each foot of the riser. Dividing 144 
 by 61.37 gives 2.34, the ft. head of water corresponding to 1 Ib. per sq. 
 in., and 0.00271 X 2.34 = 0.0066 ft. head, or if the riser is 20 ft. high, 
 20 X 0.0066 = 0.132 ft. head, which is the motive force to move the water 
 over the whole length of the circuit, overcoming the friction of the riser, 
 the return pipe, the radiator and its connections. If the circuit has a 
 resistance equal to that of a 50-ft. pipe, then 50 -*- 0.132 = 380 is the 
 ratio of length of pipe to the head, which ratio is to be taken with the 
 number of cubic feet to be circulated, and by means of formulae for flow 
 of water, such as Darcy's, or hydraulic tables, the diameter of pipe re- 
 quired to convey the given quantity of water with this ratio of length of 
 pipe to head is found. This tedious calculation is made more complicated 
 by the fact that estimates have to be made of the frictional resistance of 
 the radiator and its connections, elbows, valves, etc., so that in practice 
 it is almost never used, and "rules of thumb" and tables derived from 
 experience are used instead. 
 
 On this subject a committee of the Am. Soc. Heating and Ventilating 
 Engineers reported in 1909 as follows: 
 
 The amount of water of a certain temperature required per hour by 
 radiation may be determined by the following formula: 
 
 g)-x*eo/xeo - cu - ft - ot water per minute - 
 
 R = square feet of radiation; X = B.T.U. given off per hour by 1 sq. 
 ft. of radiation (150 for direct and 230 for indirect) with water at 170*. 
 Twenty is the drop in temperature in degrees between the water entering- 
 the radiation and that leaving it; 60.8 is the weight of a cubic foot of 
 water at 170 degrees; 60 is to reduce the result from hours to minutes. 
 
 The average sizes of mains, as used by seven prominent engineers in 
 regular practice for 1800 square feet of radiation, are given below: 
 
HOT- WATER HEATING. 
 
 705 
 
 2-pipe open-tank system, 100 ft. mains, 5-in. pipe = 26.6 ft. per min. 
 
 1-pipe open-tank system, 100 ft. mains, 6-in. pipe = 18.4 ft. per min. 
 
 Overhead open-tank system, 100 ft. mains, 4-in. pipe = 41.8 ft. per min. 
 
 Overhead open-tank system, 100 ft. mains, 3-in. pipe = 72.1 ft. per 
 min. 
 
 For 1200 sq; ft. indirect radiation with separate main, 100 ft. long, 
 direct from boiler, open system, the bottom of the radiator being 1 ft. 
 above the top of the boiler 5-in. pipe = 22.4 ft. per min. 
 
 CAPACITY OF MAINS 100 FT. LONG. 
 
 Expressed in the number of square feet of hot-water radiating sur- 
 face they will supply, the radiators being placed in rooms at 70 F., and 
 20 drop assumed. 
 
 Diameter of 
 Pipes, Ins. 
 
 Two-Pipe 
 up Feed 
 Open Tank. 
 
 One-Pipe 
 up Feed 
 Open Tank. 
 
 Overhead 
 Open 
 Tank. 
 
 Overhead 
 Closed 
 Tank. 
 
 Two-Pipe 
 Open 
 Tank. 
 
 H/4 
 
 75 
 
 45 
 
 127 
 
 250 
 
 48 
 
 I 1/2 
 
 107 
 
 65 
 
 181 
 
 335 
 
 69 
 
 2 
 
 200 
 
 121 
 
 339 
 
 667 
 
 129 
 
 21/2... 
 
 314 
 
 190 
 
 533 
 
 1,060 
 
 202 
 
 3 
 
 540 
 
 328 
 
 916 
 
 1,800 
 
 348 
 
 31/2 
 
 780 
 
 474 
 
 1,334 
 
 2,600 
 
 502 
 
 4. 
 
 1 060 
 
 645 
 
 1,800 
 
 3,350 
 
 684 
 
 5 
 
 1 860 
 
 1 130 
 
 3 150 
 
 6200 
 
 1 200 
 
 6 
 
 2960 
 
 1,800 
 
 5,000 
 
 9] 800 
 
 1,910 
 
 7 ... 
 
 4,280 
 
 2,700 
 
 7,200 
 
 13,900 
 
 2,760 
 
 8 
 
 5,850 
 
 3,500 
 
 9,900 
 
 19500 
 
 3,778 
 
 
 
 
 
 
 
 The figures are for direct radiation except the last column which is for 
 indirect, 12 in. above boiler. 
 
 CAPACITY OF RISERS. 
 
 Expressed in the number of sq. ft. of direct lK)t-water radiating sur- 
 face they will supply, the radiators being placed in rooms at 70 F., and 
 20 drop-assumed. The figures in the last column are for the closed-tank 
 overhead system the others are for the open-tank system. 
 
 Diameter 
 of Riser. 
 Inches. 
 
 1st Floor. 
 
 2d Floor. 
 
 3d Floor. 
 
 4th Floor. 
 
 Drop 
 Risers, not 
 exceeding 
 4 floors. 
 
 1 
 
 33 
 
 46 
 
 57 
 
 64 
 
 48 
 
 1 1/4. . . 
 
 71 
 
 104 
 
 124 
 
 142 
 
 112 
 
 11/2 . 
 
 100 
 
 140 - 
 
 175 
 
 200 
 
 160 
 
 2. ........ 
 
 187 
 
 262 
 
 325 
 
 375 
 
 300 
 
 21/7 . 
 
 292 
 
 410 
 
 492 
 
 580 
 
 471 
 
 3/ 2 :. :.:::::::.. 
 
 500 
 
 755 
 
 875 
 
 1,000 
 
 810 
 
 All horizontal branches from mains to risers or from risers to radiators, 
 more than 10 ft. long (unless within 15 ft. of the boiler), should be in- 
 creased one size over that indicated for risers in the above table. 
 
 For indirect radiation, the amount of surface may be computed as 
 follows : 
 
 Temperature of the air entering the room, 110 = T. 
 
 Average temperature of the air passing through the radiator, 55. 
 
 Temperature of the air leaving the room, 70 = t. 
 
 Velocity of the air passing through the radiator, 240 ft. per min. 
 
 Cubic feet of air to be conveyed per hour, = C = (H X 55) + (T - f). 
 
 H = exposure loss in B.T.U. per hour. 
 
 Heat necessary to raise this air to the entering temperature from 
 F., T X C + 55 =- JJ . 
 
706 
 
 HEATING AND VENTILATION. 
 
 The amount of radiation is found by dividing the total heat by the 
 emission of heat by indirect radiators per square foot per hour per degree 
 difference in temperature. This varies with the velocity, as shown below: 
 Velocity, ft. per min... . 174 246 300 342 378 400 428 450 474 492 
 B.T.U 1.70 2.00 2.22 2.38 2.52 2.60 2.67 2.72 2.76 2.80 
 
 The difference between 170 degrees (average temperature of the water 
 in the radiator) and 55 degrees (average temperature of the air in the 
 radiator) being 115, the emission at 240 ft. per min. is 2. per degree differ- 
 ence or 230 B.T.U. 
 
 Ordinarily the amount of indirect radiation required is computed by 
 adding a percentage to the amount of direct radiation [computed by the 
 usual rules], and an addition of 50% has been found sufficient in many 
 cases; but in buildings where a standard of ventilation is to be maintained, 
 the formula mentioned seems more likely to give satisfactory results. 
 Free area between the sections of radiation to allow passage of the re- 
 quired volume of air at the assumed velocity must be maintained. The 
 cold-air supply duct, on account of less frictional resistance, may ordi- 
 narily have 80% of the area between the radiator sections. The hot-air 
 flues may safely be proportioned for the following air velocities per min- 
 ute: First floor, 200 feet; second floor, 300 feet; third floor, 400 feet. 
 
 PIPE SIZES FOR HOT- WATER HEATING. 
 
 Based on 20 difference in temperature between flow and return water. 
 (C. L. Hubbard, The Engineer July 1, 1902.) 
 
 Diam. of ) i 
 -Pipe, f ' 
 
 U/4 
 
 H/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 5 ' 
 
 6 
 
 7 
 
 Length of 
 Run. 
 
 Square Feet of Direct Radiating Surface. 
 
 Feet. 
 100 
 200 
 300 
 400 
 500 
 600 
 700 
 800 
 1000 
 
 100 
 200 
 
 1st story 
 2d 
 
 3d 
 4th 
 5th 
 6th 
 
 30 
 
 60 
 50 
 
 100 
 75 
 50 
 
 200 
 150 
 125 
 100 
 75 
 
 350 
 250 
 200 
 175 
 150 
 125 
 
 550 
 400 
 300 
 275 
 250 
 225 
 200 
 175 
 150 
 
 850 
 600 
 450 
 400 
 350 
 325 
 300 
 250 
 225 
 
 1,200 
 850 
 700 
 600 
 525 
 475 
 450 
 400 
 350 
 
 
 
 
 1,400 
 1,150 
 1.000 
 900 
 850 
 775 
 725 
 650 
 
 
 
 
 
 
 
 ,600 
 ,400 
 ,300 
 ,200 
 ,150 
 ,000 
 
 
 
 
 
 
 
 
 
 1,700 
 1,600 
 1,500 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Square Feet of Indirect Radiation. 
 
 15 
 
 30 
 20 
 
 50 
 30 
 
 100 
 70 
 
 200 
 120 
 
 300 
 200 
 
 400 
 300 
 
 600 
 400 
 
 1,000 
 700 
 
 
 
 
 
 
 
 Square Feet of Direct Radiating Surface. 
 
 30 
 55 
 65 
 75 
 85 
 95 
 
 60 
 90 
 110 
 125 
 140 
 160 
 
 100 
 140 
 165 
 185 
 210 
 240 
 
 200 
 275 
 375 
 425 
 500 
 
 350 
 275 
 
 550 
 
 850 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The size of pipe required to supply any given amount of hot-water 
 radiating surface depends upon (1) The square feet of radiation; (2) its 
 elevation above the boiler; (3) the difference in temperature of the water 
 in the supply and return pipes; (4) the length of the pipe connecting the 
 radiator with the boiler. 
 
 In estimating the length of a pipe the number of bends and valves must 
 be taken into account. It is customary to consider an elbow as equivalent 
 to a pipe 60 diameters in length, and a return bend to 120 diameters. A 
 globe valve may be taken about the same as an elbow. 
 
 A series of articles on The Determination of the Sizes of Pipe for Hot 
 Water Heating, by F. E. Geisecke, is printed in Domestic Engineering, 
 beginning in May, 1909. 
 
HOT -WATER HEATING. 
 
 707 
 
 Sizes of Flow and Return Pipes Approximately Proportioned to 
 Surface of Direct Radiators for Gravity Hot-Water Heating. 
 
 (G. W. Stanton, Heat. & Ventg. Mag., April, 1908.) 
 
 
 Mains. 
 
 Branches of Mains. 
 
 Size 
 of 
 Mains. 
 
 In Cellar 
 or 
 Basement. 
 
 On One 
 or More 
 Floors. 
 Average. 
 
 First 
 Floor 
 10'-15'. 
 
 Second 
 Floor 
 15'-25'. 
 
 Third 
 Floor 
 25'-35'. 
 
 Fourth 
 or Fifth 
 Floor 
 35'-45'. 
 
 Square Feet of Radiating Surface. 
 
 ,, 
 
 H/4 
 
 u/ 2 
 
 21/2 
 
 3 V2 
 41/2 
 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 
 
 
 
 40 
 75 
 120 
 195 
 320 
 490 
 650 
 870 
 1,120 
 1,400 
 
 45 
 80 
 135 
 210 
 350 
 525 
 690 
 920 
 1,185 
 1,485 
 
 50 
 85 
 150 
 230 
 370 
 550 
 730 
 970 
 1,250 
 1,560 
 
 
 
 50 
 110 
 180 
 290 
 400 
 620 
 820 
 1,050 
 1,325 
 
 100 
 135 
 225 
 320 
 500 
 650 
 850 
 1,050 
 1,350 
 2,900 
 3,900 
 5,000 
 6,300 
 7,900 
 9,500 
 11,400 
 
 135 
 
 220 
 350 
 460 
 675 
 850 
 1,100 
 1,350 
 1,700 
 3,600 
 4,800 
 6,200 
 7,700 
 9,800 
 11,800 
 14.000 
 
 Note. The heights of the several 
 floors are taken as: 
 1st. 10 to 15ft.; 2d. 15 to 25 ft. 
 3d. 25 to 35 ft.; 4th. 35 to 45 ft. 
 
 Sizes of Pipe for Gravity Hot-Water Heating. (John Jaeger, Heating 
 and Ventilating Mag., Feb., 1912.) The assumed temperature of the 
 water supplied to the radiators is 185, and the drop 36, giving a mean 
 temperature of 170. The temperature difference creates a water 
 pressure of 0.148 in. of water per foot of height. With the assumed 
 heights, H, between the center of the boiler and the center of the 
 radiator on the several floors, and the assumed lengths, L, of the 
 circuit, making allowance for resistance of connections, as given in the 
 table, and using the ordinary tables for flow of water in pipes, the 
 figures for number of square feet of radiating surface that will be 
 supplied by different sizes of pipe are obtained, assuming that each 
 square foot emits 170 B. T. U. per hour. 
 
 L. Size of Pipe, In. 
 
 Ft. 1/2 3/ 4 1 11/4 11/2 
 
 Sq. Ft. of Radiating Surface. 
 
 Floor 
 
 H. 
 
 Ft. 
 
 Basement. . . . 
 First floor . . . 
 Second floor . . 
 Third floor. . . 
 Fourth floor . , 
 
 3.5 
 
 6 
 19 
 31 
 
 42 
 
 80 
 100 
 125 
 150 
 175 
 
 11 
 
 13 
 
 22 
 
 26.5 
 
 29 
 
 32 
 39 
 
 62 
 74 
 81 
 
 57 
 70 
 130 
 160 
 175 
 
 127 180 
 
 156 221 
 
 238 377 
 
 290 450 
 
 314 490 
 
 Heating by Hot Water, with Forced Circulation. The principal 
 defect of gravity hot-water systems, that the motive force is only the 
 difference in weight of two columns of water of different temperatures, is 
 overcome by giving the water a forced circulation, either by means of a 
 pump or by a steam ejector. For large installations a pump gives facili- 
 ties for forcing the hot water to any distance required. The design of 
 such a system is chiefly a problem in hydraulics. After determining the 
 quantity of heat to be given out by each radiator, a certain drop in 
 temperature is assumed, andjrom that the volume of water required by 
 each radiator is calculated. The piping system then has to be designed 
 so that it will carry the proper supply of water to each radiator without 
 short-circuiting, and with a minimum total cost for power to force the 
 water, for loss by radiation, and for interest, etc., on cost of plant. No 
 short rules or formulae have been established for designing a forced hot- 
 water system, and each case has to be studied as an original problem to 
 
708 pEATTNG AND VENTILATION. 
 
 be solved by application or tne laws of heat transmission and hydraulics. 
 Forced systems using steam ejectors have come into use to some dtent 
 in Europe in small installations, and some of them are described in the 
 Transactions of the Amer. Soc'y of Heating and Ventilating Engineers. 
 
 A system of distributing heat and power to customers by means of hot 
 water pumped from a central station was adopted by the Boston Heating 
 Co. in 1888. It was not commercially successful. A description of the 
 plant is given by A. V. Abbott in Trans. A. I. M. E., 1888. 
 
 Corrosion of Pipe in Hot-Water Heating .Systems. The chief agent 
 of internal corrosion in hot- water pipes appears to be oxygen dissolved 
 in the water. If this is removed corrosion is prevented. Buildings 
 equipped with closed heating systems have suffered serious damage in 
 six or eight years, while no such damage has been found in open or 
 vented systems, in which the air dissolved in the water is allowed to 
 escape in an open tank placed at the top of the system. (F. N. Speller, 
 Eng. News, Feb. 13, 1913.) 
 
 THE BLOWER SYSTEM OF HEATING. 
 
 The system provides for the use of a fan or blower which takes its sup- 
 ply of fresh air from the outside of the building to be heated, forces it 
 over steam coils, located either centrally or divided up into a number oi 
 independent groups, and then into the several ducts or flues leading to the 
 various rooms. The movement of the warmed air is positive, and the 
 delivery of the air to the various points of supply is certain and entirely 
 independent of atmospheric conditions. 
 
 Advantages and Disadvantages of the Plenum System. (Prof. 
 W. F. Barrett, Brit. Inst. H. & V. Engrs., 1905.) Advantages: (1) The 
 evenness of temperature produced; (2) the ventilation of the building 
 is concurrent with its warming; (3) the air can be drawn from sources 
 free from contamination and can be filtered from suspended impurities, 
 warmed and brought to the proper hygrometric state before its intro- 
 duction to the different rooms or wards; (4) the degree of temperature 
 and of ventilation can be easily controlled in any part of the building, 
 and (5) the removal of ugly pipes running through the rooms has a great 
 architectural and esthetic advantage. 
 
 Disadvantages: (1) The most obvious is that no windows can be 
 opened nor doors left open; double doors with an air lock between must 
 also be provided if the doors are frequently opened and closed; (2) the 
 mechanical arrangements are elaborate and the system requires to be 
 used with intelligent care; (3) the whole elaborate system needs to be 
 set going even if only one or two rooms in a large building require to 
 be warmed, as often happens in the winter vacation of a college; (4) the 
 temporary failure of the system, through the breakdown of the engines 
 or other cause, throws the whole system into confusion, and if, as in the 
 Royal Victoria Hospital, the windows are not made to open, imminent 
 danger results; (5) then, also, in the case of hospital wards and asylums 
 it is possible that the outlet ducts may become coated with disease germs, 
 and unless periodically cleansed, a back current, through a high wind or 
 temporary failure of the system may bring a cloud of these disease germs 
 back into the wards. 
 
 Heat Radiated from Coils in the Blower System. The committee 
 on Fan-blast Heating, of the A. S. H. V. E., in 1909, gives the following 
 formula for amount of heat radiated from hot-blast coils with different 
 velocities of air passing through the heater: # = B.T.U. per sq. ft. of sur- 
 face per hour per degree of difference between the average temperature of 
 the air and the steam temperature, = V4 v, in which V= velocity of the 
 air through the free area of the coil in feet per second. A plotted curve 
 of 20 tests of different heaters shows that the formula represents the aver- 
 age results, but individual tests show a wide variation from the average, 
 thus: For velocity 1000 ft. per min., average 9 B.T.U., range 7.5 to 11; 
 1600 ft. per min., average 10.4, range 9.5 to 12. 
 
 The committee also gives the following formula for the rise in tem- 
 perature of each two-row section of a coil: 
 
 ' A X V m X W X 60 X 0.2377 
 In which R = degrees F. rise for each two-row section ; T s = tern- 
 
THE BLOWER SYSTEM OF HEATING. 
 
 709' 
 
 perature of steam; T a = temperature of air; H ** square feet of sur- 
 face in two-row section-, B = B.T.U. per degree difference between air 
 and steam; E >/4 F s , in which V s air velocity in ft. per sec.; 
 A = area through heater in sq. ft.; V m = velocity of air in ft. per min.; 
 TF = weight of 1 cu. ft. of air, Ibs. 
 
 The value of R is computed for each two-row section in a coil, and the 
 results added. From a set of curves plotted from the formula the follow- 
 ing figures are taken. 
 
 
 Number of Rows. 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 Temperature Rise, Degrees. 
 
 Steam, 80 Ibs: V m = 1,200. . . 
 
 43 
 36 
 31 
 25 
 
 83 
 68 
 53 
 48 
 
 115 
 96 
 80 
 68 
 
 144 
 122 
 100 
 85 
 
 167 
 145 
 118 
 101 
 
 189 
 165 
 133 
 115 
 
 209 
 182 
 146 
 128 
 
 Steam, 80 Ibs. Vm = 1,800 
 Steam, 5 Ibs. Vm = 1,200. . . 
 
 Steam, 5 Ibs. V m = 1,800 
 
 A formula for the rise in temperature of air in passing through the 
 coils of a hot-blast heater is given by Perry West, Trans. A. S. H. V. E., 
 
 1909, page 57, as follows: R= KDZ m N -r- %/V, in which #=rise in 
 temperature of the air; K = a constant depending on the kind of heat- 
 ing surface; D = an average of the summation of temperature differ- 
 ences between the air and the steam = -(Ti-T D ) * log e [(T s - To) -* 
 (T s - Ti)]; Z = number of sq. ft. of heating surface per sq. ft. of clear 
 area per unit depth of heater, m a power applicable to Z and depend- 
 ing on the type of heating surface; N = number of units in depth of 
 heater- V = velocity of the air at 70 F. in ft. per min. through the clear 
 area- n = a root applicable to F and depending on experiment. 
 
 For practical purposes and within the range of present knowledge on 
 the subject the formula may be written #= 0.085 DZN -*- %Jv, and from 
 this formula with T s = 227 and T = 0, with different values of Ti, the 
 temperature of the air leaving the coils, a set of curves is plotted, from 
 which the figures in the following table are taken. 
 
 Sq. ft. of heating surface * sq. ft. free area through heater. 
 
 Velocity, 
 Ft. per Min. 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 CO 
 
 90 
 
 100 | 120 
 
 Rise in Temperature, Degrees F. 
 
 500 
 
 43 
 38 
 36 
 34 
 29 
 
 63 
 55 
 52 
 49 
 42 
 
 79 
 70 
 66 
 63 
 55 
 
 95 
 84 
 79 
 75 
 66 
 
 108 
 97 
 92 
 87 
 76 
 
 120 
 108 
 102 
 98 
 86 
 
 131 
 118 
 112 
 108 
 95 
 
 141 
 128 
 121 
 117 
 104 
 
 151 
 138 
 130 
 125 
 112 
 
 170 
 157 
 147 
 140 
 127 
 
 800 
 
 1000 .. 
 
 1200 
 
 2000 
 
 
 Burt-S. Harrison (Htg, and Ventg. Mag., Oct. and Nov., 1907) gives the 
 
 folio wing for 
 
 2 4' 
 
 ' in which 2^ = temp, of steam 
 
 in coils, i = temp. of air entering coils, V = velocity of air through coils in 
 ft. per sec., N= no. of rows of 1-in. pipe in depth of heater. Charts are 
 given by means of which heaters may be designed for any set of con- 
 ditions. 
 
 Tests of Cast-iron Heaters for Hot-blast Work. An extensive 
 series of tests of the Amer. Radiator Go's, "Vento" cast-iron heater is 
 described by Theo. Weinshank in Trans. A. S. H. V. E., 1908. The tests 
 were made under the supervision of Prof, J. H. Kinealy. The principal 
 results are given in the table on page 710. 
 
710 
 
 HEATING AND VENTILATION. 
 
 TESTS OF A "VENTO" CAST-IRON HEATER. 
 
 Velocity, 
 Ft. per 
 Min. 
 
 Number of sections heater is 
 deep. 
 
 Number of sections heater is 
 deep. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 1 6 
 
 1 
 
 2 
 
 3 1 4 
 
 5 | 6 
 
 Rise of temperature, K, per de- 
 gree difference between tem- 
 perature of steam and mean 
 temperature of air for differ- 
 ent velocities of air. 
 
 Heat units transmitted per 
 square foot of heating surface 
 per hour per degree difference 
 between the temperature of 
 the steam and the mean tem- 
 perature of the air. 
 
 1600... 
 1500 
 
 0.124 
 0.132 
 0.139 
 0.147 
 0.154 
 0.162 
 0.170 
 0.177 
 0.185 
 
 0.253 
 0.261 
 0.268 
 0.276 
 283 
 
 0.395 
 0.403 
 0.410 
 0.418 
 425 
 
 0.527 
 0.535 
 0.542 
 0.550 
 557 
 
 0.649 
 0.657 
 0.664 
 0.672 
 679 
 
 0.761 
 0.769 
 0.776 
 0.784 
 791 
 
 11.94 
 11.91 
 11.70 
 11.50 
 11 11 
 
 12.17 
 11.76 
 11.28 
 10.79 
 10 21 
 
 12.67 
 12.11 
 11.50 
 10.89 
 10.22 
 
 12.67 
 12.06 
 11.41 
 10.75 
 10 05 
 
 12.50 
 11.86 
 11.18 
 10.51 
 9 81 
 
 12.20 
 11.56 
 10.89 
 10.22 
 9.52 
 
 1400 
 
 1300 
 
 1200 
 1100 
 
 0.291 
 0.299 
 0.306 
 0.314 
 
 0.433 
 0.441 
 0.448 
 0.456 
 
 0.565 
 0.573 
 0.580 
 0.588 
 
 0.687 
 0.695 
 0.702 
 0.710 
 
 0.799 
 0.807 
 0.814 
 0.822 
 
 10.72 
 10.23 
 9.59 
 8.90 
 
 9.63 
 8.99 
 8.28 
 7.56 
 
 9.55 
 8.84 
 8.08 
 7.31 
 
 9.34 
 8.61 
 7.85 
 7.08 
 
 9.09 
 8.36 
 7.60 
 6.48 
 
 8.82 
 8.10 
 7.35 
 6.60 
 
 1000 
 900 
 
 800 
 
 Velocity, 
 Ft. per 
 Min. 
 
 Final temperature, T, of air 
 when entering heater at F. 
 Temperature of steam in 
 heater, 227. 
 
 Friction loss in inches of water 
 due to the sections. 
 
 1600... 
 
 ?6 5 
 
 51 
 
 74 9 
 
 94 7 
 
 111 3 
 
 17<> 7 
 
 236 
 
 288 
 
 416 
 
 543 
 
 0.672 
 0.590 
 0.514 
 0.443 
 0.378 
 0.318 
 0.262 
 212 
 
 0.800 
 0.703 
 0.613 
 0.528 
 0.450 
 0.378 
 0.312 
 253 
 
 1500 
 1400 
 1300... 
 
 28.1 
 29.5 
 31.1 
 32.4 
 34.0 
 35.6 
 36 9 
 
 52.4 
 53.8 
 55.0 
 56.4 
 57.7 
 59.1 
 60.1 
 
 76.3 
 77.2 
 77.6 
 79.6 
 80.5 
 82.0 
 83 
 
 95.8 
 96.7 
 97.9 
 99.0 
 100.0 
 100.1 
 102.1 
 
 112.4 
 113.3 
 114.3 
 115.3 
 116.2 
 117.2 
 118 
 
 126.0 
 126.8 
 127.7 
 128.7 
 1 29/6 
 130.5 
 131.3 
 
 0.207 
 0.180 
 0.156 
 0.133 
 0.111 
 0.092 
 074 
 
 0.253 
 0.220 
 0.190 
 0.162 
 0.136 
 0.112 
 091 
 
 0.366 
 0.318 
 0.274 
 0.234 
 0.197 
 0.162 
 132 
 
 0.477 
 0.415 
 0.358 
 0.306 
 0.257 
 0.212 
 172 
 
 1200 
 
 1100 .. 
 
 1000 
 
 900 
 
 800 
 
 38.5 
 
 61.6 
 
 84.3 
 
 103.1 
 
 119.0 
 
 132.3 
 
 0.059 
 
 0.072 
 
 0.104 
 
 0.136 
 
 0.167 
 
 0.200 
 
 Formulae. s = no. of sections; V= velocity, ft. per min., air meas- 
 ured afc70; k = rise of temp, per degree difference; t = final tempera- 
 ture. / = friction loss in in. of water, t = 454 k -t- (2 + k) . k = 
 
 s (0.167 - 0.005 s) - 0.061 (^ g Q) /= (-8s + 0.2) (V/4000)2. 
 Values of k and/ when s = 2 or more. 
 
 Factory Heating by the Fan System. 
 
 In factories where the space provided per operative is large, warm air 
 is recirculated, sufficient air for ventilation being provided by leakage 
 through the walls and windows. The air is commonly heated by steam 
 coils furnished with exhaust steam from the factory engine. When the 
 engine is not running, or when it does not supply enough exhaust steam 
 for the purpose, steam from the boilers is admitted to the coils through 
 a reducing valve. The following proportions are commonly used in de- 
 signing. Coils, pipes 1-in., set 2i/s in. centers; free area through coils, 
 40% of cross area. Velocity of air through free area, 1200 to 1800 ft. 
 per min. ; number of coils in series 8 to 20 ; circumferential speed of fan, 
 4000 to 6000 ft. per min.; temperature of air leaving coils, 120 to 160 
 F.; velocity of air at outlet of coil stack, 3000 to 4000 ft. per min.; veloc- 
 ity in branch pipes, 2000 to 2800 ft., the lower velocities in the longest 
 pipes. 
 
 In factories in which mechanical ventilation as well as heating is re- 
 quired, outlet flues at proper points must be provided, to avoid the neces- 
 sity of opening windows, and the outflow of air in them may be assisted 
 either by exhaust fans or by steam coils in the flues. 
 
 Cooling Air for Ventilation. 
 
 The chief difficulty in the artificial cooling of air is due to the moisture 
 it contains, and the great quantity of heat that has to be absorbed or 
 abstracted from the air in order to condense this moisture. The cooled 
 
THE BLOWER SYSTEM OF HEATING. 
 
 711 
 
 and moisture-laden air also needs to be partially reheated in order to 
 bring it to a degree of relative humidity that will make it suitable for ven- 
 tilation. To cool 1 Ib. of dry air from 82 to 72 requires the abstracting 
 
 of 10 X 0.2375 B.T.U. (0.2375 being the specific heat at constant pres- 
 sure). If thejdr at 82 is saturated, or 100% ^relative humidity, it 
 
 __ . -_, 100% relative humidity 
 
 contains 0.0235 Ib. of water vapor, while 1 Ib. at 72 contains 0.0167 
 BO that 0.0068 Ib. will be condensed in cooling from vapor at 82 to 
 water at 72. The total heat (above 32) in 1 Ib. vapor at 82 is 1095.6 
 B.T.U. and that in 1 Ib. of water at 72 is 40 B.T.U. The difference, 
 1055.6 X 0.0068 = 7.178 B.T.U., is the amount of heat abstracted in 
 condensing the moisture. The B.T.U. in 1 Ib. vapor at 72 is 1091.2. 
 and the B.T.U. abstracted in cooling the remaining vapor from 82 to 
 72 is 0.0167 X (1095.6 - 1091.2) = 0.073 B.T.U. The sum, 7.251 
 B.T.U., is more than three times that required to cool the dry air from 
 82 to 72. Expressing these principles in formulae we have: 
 
 Let Ti = original and Tz the final temperature of the air, 
 a = vapor in 1 Ib. saturated air at Ti; b = do. at Tz, 
 H = relative humidity of the air at Ti\h desired do. at Tz, 
 U = total heat, in B.T.U., in 1 Ib. vapor at Ti; u = do. at Tz, 
 w = total heat in water at Ti. 
 
 Then total heat abstracted in cooling air from T\ to Tz = (aH bh) X 
 (U _ W ) -|- bh (u - u) + 0.2375 (Ti - Tz), or aHU - bhu - (aH - bh) w 
 + 0.2375 (Ti - Tz), or aH (U- w) - bh (u - w) + 0.2375 (Ti - Tz). 
 
 EXAMPLE. Required the amount of heat to be abstracted per hour 
 in cooling the air for an audience chamber containing 1000 persons, 
 1500 cu. ft. (measured at 70 P.), being supplied per person per hour, 
 the temperature of the air before cooling being 82, with relative 
 humidity 80%, and after cooling 72, with humidity 70%. 
 1000 X 1500 = 1,500,000 cu. ft., at 0.075 Ib. per cu. ft. 
 
 = 112,500 Ibs. 
 For 1 Ib. aH (U - w) - bh (u - w) + 0.2375 (Ti - Tz). 
 
 0.0235 X 0.8 X (1095.6 - 40) - 0.0167 X 0.7 X (1091.2 - 40) 
 + 2.375 = 9.932 B.T.U. 
 
 112,500 X 9.932 = 1,061,100 B.T.U. 
 
 Taking 142 B.T.U. as the latent heat of melting ice, this amount is 
 equivalent to the heat that would melt 7472 Ibs. of ice per hour. 
 
 See also paper by W. W. Macon, Trans. A. S. H. V. E., 1909, and 
 Air-cooling of the New York Stock Exchange, Eng. Rec., April, 1905, 
 and The Metal Worker, Aug. 5, 1905. 
 
 Capacities of Fans or Blowers for Hot-Blast or Plenum Heating. 
 
 (Computed by F. R. Still, American Blower Co., Detroit, Mich.) 
 
 
 ^ 
 
 i 
 
 o 
 
 > 
 
 0) 
 
 ^0,0; 
 
 
 
 d 
 
 ?! 
 
 i 
 
 
 
 
 s 
 
 
 TJ o 
 
 ft 
 
 '33 
 
 .s 
 
 1 
 
 fi *t! 
 
 d 
 
 to 
 
 1 
 
 ! 
 
 03 
 
 ft 
 
 1. 
 
 d d 
 
 III 
 
 ! 
 
 ^ 
 
 eg 
 
 ll 
 
 ri_ 
 
 || 
 
 .2 M 
 
 (a, 
 
 g 
 
 SjjS 
 
 tM IH 2 
 
 o 
 
 .s 3 a 
 
 'Srd ^ 
 
 8d 
 
 ^ 3 
 
 w ^ 
 
 tt.S 
 
 *-. 2 
 
 "8 
 
 a 
 
 ^<o 
 
 ^ft| 
 
 * 4 
 
 !?! 
 
 ^sg 
 
 Ca 
 
 '5 D<O 
 
 .fS 
 
 <> 
 
 g 
 
 1/8 
 
 Pn'C 
 
 f^'S 
 
 plH g 
 
 
 'S 8 frH 
 
 .l 
 
 -P tn Ul 
 
 Ss 
 
 w 
 
 e3 
 
 
 . 
 
 2 St^M 
 
 a W 
 
 o ft<3 
 
 o^c ^ 
 
 S^ 
 
 U ftft 
 
 . 0} 
 
 w 
 
 Q 
 
 PH 
 
 W 
 
 Q 
 
 o 
 
 W 
 
 > 
 
 
 W 
 
 a 
 
 70 
 80 
 
 42 
 
 48 
 
 360 
 320 
 
 1* 
 
 6,900 
 8,500 
 
 415,200 
 510,000 
 
 1,021,000 
 1,255,000 
 
 900 
 
 7.7 
 9.45 
 
 1760 
 
 580 
 
 714 
 
 90 
 
 54 
 
 280 
 
 4 
 
 10,500 
 
 630,000 
 
 1,550,000 
 
 " 
 
 11.66 
 
 
 880 
 
 100 
 
 60 
 
 250 
 
 5 
 
 12,500 
 
 750,000 
 
 1,845,000 
 
 " 
 
 13.9 
 
 
 1050 
 
 110 
 
 66 
 
 230 
 
 6 
 
 15,800 
 
 948,000 
 
 2,335,000 
 
 " 
 
 17.55 
 
 
 1325 
 
 120 
 
 72 
 
 210 
 
 8 
 
 19,800 
 
 1,118,000 
 
 2,900,000 
 
 " 
 
 22. 
 
 
 1650 
 
 140 
 
 84 
 
 180 
 
 10 
 
 26,200 
 
 1,572,000 
 
 3,870,000 
 
 " 
 
 29.1 
 
 
 2200 
 
 160 
 
 96 
 
 160 
 
 12 
 
 33,000 
 
 1,980,000 
 
 4,870,000 
 
 " 
 
 36.7 
 
 
 2770 
 
 180 
 
 108 
 
 140 
 
 15 
 
 41,600 
 
 2,496,000 
 
 6,130,000 
 
 " 
 
 46.3 
 
 
 3490 
 
 200 
 
 120 
 
 125 
 
 18 
 
 50,000 
 
 3,000,000 
 
 7.375,000 
 
 " 
 
 55.5 
 
 
 4140 
 
712 
 
 HEATING AND VENTILATION. 
 
 Capacities of Fans or Blowers for Hot-blast or Plenum Heating 
 
 Continued. 
 
 
 M 
 
 *g 
 
 
 
 T^ OJ 
 
 # 
 
 10 
 
 o 
 
 ^ , 
 
 > i a 
 
 
 9 
 
 a 
 
 V 
 
 i 
 
 1 
 
 |& 
 
 o 1 ^ 
 
 ?' 
 
 ^ 
 
 ^1 
 
 ||| 
 
 M 
 
 a 
 
 A 
 a 
 
 73 
 
 r! 
 
 '3 
 
 3 
 
 n< 
 
 |l 
 
 ^ 
 
 
 
 |3 gj 
 
 ^S. 
 
 ^"0^ 
 
 of Blower-Housi 
 
 
 
 1& 
 
 ids of Steam Coi 
 r Hour to 2 12. 
 
 Steam-Main Req 
 
 Return-Main Rei 
 
 co 
 
 IT 
 
 T t-i 
 
 a 6 1 
 
 '.CO 
 c3 A 
 o> 
 
 . (4 
 
 ""^-2 
 
 Ft. Grate-Surf ac 
 . Ft. Heating Su 
 . Ft. Grate. 
 
 me Air Will Ex] 
 Heating from O c 
 pacity per Minul 
 
 i of Conduit in 
 900Ft. Velocity] 
 
 9. 
 
 Volume Deli verec 
 ce Being Made f 
 n Equal to 100 Ft 
 it. 
 
 S 
 
 |s 
 
 
 
 S 
 
 0) 
 
 itiw 
 
 tf 
 
 . Jf 
 
 f^o 
 
 oj^o "5 
 
 $s*- 
 
 CO 
 
 r 
 
 ^ 
 
 CO 
 
 CO 
 
 PQ 
 
 CO 
 
 CO 
 
 > 
 
 ^ 
 
 5 
 
 70 
 
 1,740 
 
 1055 
 
 31/2 
 
 2 
 
 35 
 
 525 
 
 15 
 
 8,700 
 
 9.67 
 
 8,200 
 
 80 
 
 2,142 
 
 1295 
 
 4 
 
 2 
 
 43 
 
 645 
 
 18 
 
 10,700 
 
 13.05 
 
 10,000 
 
 90 
 
 2,640 
 
 1600 
 
 41/2 
 
 21/2 
 
 53 
 
 795 
 
 23 
 
 13,200 
 
 14.72 
 
 12,500 
 
 100 
 
 3,150 
 
 1900 
 
 5 
 
 2V2 
 
 63 
 
 945 
 
 27 
 
 15,800 
 
 17.55 
 
 15,000 
 
 110 
 
 3,975 
 
 2410 
 
 51/2 
 
 3 
 
 80 
 
 1200 
 
 34 
 
 19,900 
 
 22.20 
 
 18,900 
 
 120 
 
 4,950 
 
 2990 
 
 6 
 
 3 
 
 100 
 
 1500 
 
 43 
 
 25,000 
 
 27.80 
 
 23,800 
 
 140 
 
 6,600 
 
 3990 
 
 7 
 
 31/ 2 
 
 133 
 
 1995 
 
 57 
 
 33,100 
 
 36.80 
 
 31,400 
 
 160 
 
 8,310 
 
 5025 
 
 8 
 
 4 
 
 167 
 
 2505 
 
 72 
 
 41,700 
 
 46 30 
 
 39,600 
 
 180 
 
 10,470 
 
 6325 
 
 9 
 
 41/9 
 
 211 
 
 3165 
 
 90 
 
 52,500 
 
 58.40 
 
 50,000 
 
 200 
 
 12,420 
 
 7560 
 
 10 
 
 5 
 
 252 
 
 3780 
 
 108 
 
 63,200 
 
 70.25 
 
 60,000 
 
 Temperature of fresh air, 0; of air from coils, 120; of steam, 227; 
 Pressure of steam, 5 Ibs. 
 
 Pe ipheral velocity of fan-tips, 4000 ft.; number of pipes deep in coil, 
 24; depth of coil, 60 inches; area of coils approximately twice free area. 
 
 Relative Efficiency of Fans and Heated Chimneys for Ventila- 
 tion. W. P. Trowbridge, Trans. A.S. M. E. vii. 531, gives a theoretical 
 solution of the relative amounts of heat expended to remove a given 
 volume of impure air by a fan and by a chimney. Assuming the total 
 efficiency of a fan to be only 1/25, which is made up of an efficiency of l/io 
 for the engine, 5/ 10 for the fan itself, and 8/ 10 for efficiency as regards 
 friction, the fan requires an expenditure of heat to drive it of only Vss of 
 the amount that would be required to produce the same ventilation by 
 a chimney 100 ft. high. For a chimney 500 ft. high the fan will be 7.6 
 times more efficient. 
 
 The following figures are given by Atkinson (Coll. Engr., 1889), show- 
 ing the minimum depth at which a furnace would be equal to a ventilating. 
 machine, assuming that the sources of loss are the same in each case, i.e., 
 that the loss of fuel in a furnace from the cooling in the upcast is equiva- 
 lent to the power expended in overcoming the friction in the machine, 
 and also assuming that the ventilating-rnachine utilizes 60 per cent of the 
 engine-power. The coal consumption of the engine per I.H.P. is taken 
 at 8 Ibs. per hour. 
 
 Average temperature in upcast 100 F. 150 F. ' 200 F. 
 
 Minimum depth for equal economy.. 960 yards. 1040 yards. 1130 yards. 
 
 PERFORMANCE OF HEATING GUARANTEE. 
 
 Heating a Building to 70 F. Inside when the Outside Tempera- 
 ture is Zero. It is customary in some contracts for heating to guaran- 
 tee that the apparatus will heat the interior of the building to 70 in zero 
 weather. As it may not be practicable to obtain zero weather for the 
 purpose of a test, it may be difficult to prove the performance of the 
 guarantee unless an equivalent test may be made when the outside tem- 
 perature is above zero, heating the building to a higher temperature 
 than 70, The following method was proposed by the author (Eng. Rec tt 
 
ELECTRICAL HEATING. 713 
 
 Aug. 11, 1894) for determining to what temperature the rooms should 
 be heated for various temperatures of the outside atmosphere and of the 
 steam or hot water in the radiators. 
 
 Let S = sq. ft. of surface of the steam or hot-water radiator; 
 W = sq. ft. of surface of exposed walls, windows, etc.; 
 T s = temp, of the steam or hot water, 7\= temp, of inside of 
 building or room, TO = temp, of outside of building or room ; 
 a = heat-units transmitted per sq. ft. of surface of radiator per 
 
 hour per degree of difference of temperature; 
 6 = average heat-units transmitted per sq. ft. of wails per hour 
 per degree of difference of temperature, including allow- 
 ance for ventilation. 
 
 Tt is assumed that within the range of temperatures considered New- 
 ton's law of cooling holds good, viz., that it is proportional to the differ- 
 ence of temperature between the two sides of the radiating-surface, 
 
 hW 
 
 Then aS (T s - 7\) = bW (^ - T ~). Let -^ = C; then 
 
 T\- r - TS + CT r - T * ~ Tl 
 
 -L Q) i * 1 i f i t W 
 - 
 
 - 
 
 i f i t W Tfi Tfi * 
 
 1-rU ./I 1 o 
 
 T s - 70 
 If T 7 ! = 70, and T Q = 0, C = -^ 
 
 Let T s = 140 160 180 200 212 220 250 300 
 
 Then C = 1 1.286 1.571 1.857 2.029 2.143 2.571. 3.286 
 
 and from the formula TI= (T s + CTo) --s- (1 + C) we find the inside 
 
 temperatures corresponding to the given values of T s and T which 
 
 should be produced by an apparatus capable of heating the building to 
 70 in zero weather. 
 
 For T Q = -20 - 10 10 20 30 40 F. 
 
 Inside Temperatures TV 
 
 For Ts = 140 F. 60 65 70 75 .80 85 90 
 
 160 58.7 64.3 70 75.6 81.3 86.9 92.5 
 
 180 57.8 63.9 70 76.1 82.2 88.4 94.5 
 
 200 57.0 63.5 70 76.5 83.0 89.5 96.0 
 
 212 56.6 63.3 70 76.7 83.4 90.1 96.8 
 
 220 56.4 63.2 70 76.8 83.6 90.5 97.3 
 
 250 55.6 62.8 70 77.2 84.4 91.6 98.8 
 
 300 54.7 62.4 70 77.7 85.3 93.0 100.7 
 
 J. R. Allen (Trans. A. S. H. V. E., 1908) develops a complex formula 
 for the inside temperature which takes into consideration the fact that 
 the coefficient of transmission of the radiator is not constant but in- 
 creases with the temperature. With T s = 227 and a two-column cast-iron 
 radiator he finds for T = -20 -10 10 20 30 40 
 Tj. = 58 64 70 77.5 83 90 97 
 
 For all values of T n between 10 and 40 these figures are within one 
 ree of those computed by the author's method. 
 
 ELECTRICAL HEATING. 
 
 Heating by Electricity. If the electric currents are generated by a 
 dynamo driven by a steam-engine, electric heating will prove very ex- 
 pensive, since the steam-engine wastes in the exhaust-steam and by 
 radiation about 90% of the heat-units supplied to it. In direct steam- 
 heating, with a good boiler and properly covered supply-pipes, we can 
 utilize about 60% of the total heat value of the fuel. One pound of coal, 
 with a heating value of 13,000 heat-units, would supply to the radiators 
 about 13,000 X 0.60 = 7800 heat-units. In electric heating, suppose we 
 have a first-class condensing-engine developing 1 H.P. for every 2 Ibs. of 
 coal burned per hour. This would be equivalent to 1,980,000 ft.-lbs. -t- 
 
714 HEATING AND VENTILATION. 
 
 778 = 2545 heat-units, or 1272 heat-units for 1 Ib. of coal. The friction 
 of the engine and of the dynamo and the loss by electric leakage and 
 by heat radiation from the conducting wires might reduce the heat- 
 units delivered as electric current to the electric radiator, and there con- 
 verted into heat, to 50% of this, or only 636 heat-units, or less than one 
 twelfth of that delivered to the steam-radiators in direct steam-heating. 
 Electric heating, therefore, will prove uneconomical unless the electric 
 current is derived from water or wind power which would otherwise be 
 wasted. (See Electrical Engineering.) 
 
 MINE-VENTILATION. 
 
 Friction of Air in Underground Passages. In ventilating a mine or 
 other underground passage the resistance to be overcome is, according 
 to most writers on the subject, proportional to the extent of the fric- 
 tional surface exposed; that is, to the product lo of the length of the ganr- 
 way by its perimeter, to the density of the air in circulation, to the 
 square of its average speed, v, and lastly to a coefficient k, whose numer- 
 ical value varies according to the nature of the sides of the gangway and 
 the irregularities of its course. 
 
 The formula for the loss of head, neglecting the variation in density as 
 
 ks v 2 
 unimportant, is p = , in which p = loss of pressure in pounds per 
 
 square foot, s = square feet of rubbing-surface exposed to the air, v the 
 velocity of the air in feet per minute, a the area of the passage in square 
 feet, and k the coefficient of friction. W. Fairley, in Colliery Engineer, 
 Oct. and Nov., 1893, gives the following formulae for all the quantities 
 involved, using the same notation as the above, with these additions: 
 h = horse-power of ventilation; I = length of air-channel; o = perimeter 
 of air-channel; q = quantity of air circulating in cubic feet per minute 
 u = units of work, in foot-pounds, applied to circulate the air ; w = water^ 
 gauge in inches. Then, 
 
 _ ksv 2 _ ksv 2 q _ ksv 3 _ _w _ g 
 " p " u ~ pv ~ pv ~ v ' 
 u gj> _ 5.2 qw 
 
 ~ 33,000 ~" 33,000 ~~ 33,000 * 
 
 3 fc = pa = u = - P = 5>2 w 
 sv 2 sv 3 sv 2 * a sv 2 *- a' 
 
 '' kv*o' 
 
 5 o = - = pa - 
 I kvH ' 
 
 ks j a q av' 
 
 I AY ' C 
 
 7. pa = ksv 2 = i / r- ) ks = - ; pa 3 = ksq 2 . 
 
 W r/ v _ __ 
 
 i /% = 4 /*L O 
 
 y ks y ks ' 
 
 u ksv 3 
 8. - . - - - 
 
 pa_ u_ _ qp_ vpa , 
 kv* kv* kv* kv* 
 
 10. u = qp = vpa = ^2- = ksv 3 = 5.2 qw = 33,000 h. 
 
 U v _ M. _ ff _ //^ _ t 3 /^ = 4 /P* m 
 
 ~ pa ~ a ~ ks ks ks 
 
MINE -VENTILATION. 
 
 715 
 
 * fi 
 
 5.2 a 
 
 To find the quantity of air with a given horse-power and efficiency (e) 
 of engine: 
 
 h X 33,000 X e 
 "- 
 
 The value of fc, the coefficient of friction, as stated, varies according to 
 the nature of the sides of the gangway. Widely divergent values have 
 been given by different authorities (see Colliery Engineer, Nov., 1893), the 
 most generally accepted one until recently being probably that of J. J. 
 Atkinson, .0000000217, which is the pressure per square foot in decimals 
 of a pound for each square foot of rubbing-surface and a velocity of one 
 foot per minute. Mr. Fairley, in his "Theory and Practice of Ventilating 
 Coal-mines," gives a value less than half of Atkinson's or .00000001; and 
 recent experiments by D. Murgue show that even this value is high under 
 most conditions. Murgue's results are given in his paper on Experi- 
 mental Investigations in the Loss of Head of Air-currents in Under- 
 ground Workings, Trans. A. I. M. E., 1893, vol. xxiii. 63. His coefficients 
 are given in the following table, as determined in twelve experiments: 
 
 Coefficient of Loss of 
 
 Head by Friction. 
 French. British. 
 
 (Straight, normal section ......... 00092 .000,000,00486 
 Straight, normal section ......... 00094 
 Straight, large section ........... 00104 
 
 Brick-lined 
 
 arched 
 gangways. 
 
 Timbered 
 gangways. 
 
 I Straight, normal section 00122 
 
 Straight, normal section 00030 
 
 Straight, normal section 00036 
 
 Continuous curve, normal section . 00062 
 
 Sinuous, intermediate section 00051 
 
 Sinuous, small section 00055 
 
 ! Straight, normal section 00168 
 Straight, normal section 00144 
 Slightly sinuous, small section. . . . 00238 
 
 .000,000,00497. 
 
 .000,000,00549 
 
 .000,000,00645 
 
 .000,000,00158 
 
 .000,000,00190 
 
 .000,000,00328 
 
 .000,000,00269 
 
 .000,000,00291 
 
 .000,000,00888 
 
 .000,000,00761 
 
 .000,000,01257 
 
 The French coefficients which are given by Murgue represent the height 
 of water-gauge in millimeters for each square meter of rubbing-surface 
 and a velocity of one meter per second. To convert them to the British 
 measure of pounds per square foot for each square foot of rubbing-surface 
 and a velocity of one foot per minute they have been multiplied by the 
 factor of conversion, .000005283. For a velocity of 1000 feet per minute, 
 since the loss of head varies as -y 2 , move the decimal point in the coefficients 
 six places to the right. 
 
 Equivalent Orifice. The head absorbed by the working-chambers 
 of a mine cannot be computed a priori, because the openings, cross- 
 passages, irregular-shaped gob-piles, and daily changes in the size and 
 shape of the chambers present much too complicated a network for accu- 
 rate analysis. In order to overcome this difficulty Murgue proposed in 
 1872 the method of equivalent orifice. This method consists in substitut- 
 ing for the mine to be considered the equivalent thin-lipped orifice, 
 requiring the same height of head for the discharge of an equal volume 
 of air. The area of this orifice is obtained when the head and the dis- 
 charge are known, by means of the following formulae, as given by Fairley: 
 Let Q = quantity of air in thousands of cubic feet per minute; 
 w = inches of water-gauge; 
 A = area in square feet of equivalent orifice. 
 
 Then 
 
 0.37 
 
 * Murgue gives A 
 
 and Norris A 
 
 ^ 0.403^ 
 
 V'U 
 
 See page 072, ante. 
 
716 
 
 WATER. 
 
 Motive Column or the Head of Air Due to Differences of Tem- 
 perature, etc. (Fairley.) 
 
 Let M = motive column in feet; 
 
 T = temperature of upcast; 
 
 / = weight of one cubic foot of the flowing air; 
 
 t temperature of downcast; 
 
 D = depth of downcast. 
 Then 
 
 T-t _5.2Xt _, y M . w _ /XM_ P . 
 -JXM,W - 52 - 
 
 M = D- 
 
 T+459" 1 / 
 
 To find diameter of a round airway to pass the same amount of air as a 
 square airway, the length and power remaining the same: 
 
 Let D ~ diameter of round airway, A = area of square airway; O = 
 
 perimeter of square airway. Then D 3 = t / A * X 3.1416 
 
 y 0.7854 3 X O 
 
 If two fans are employed to ventilate a mine, each of which when 
 worked separately produces a certain quantity, which may be indicated 
 by A and B, then the quantity of air that will pass when the two fans are 
 worked together will be <\/A*+B*. (For mine-ventilating fans, see 
 page 672.) 
 
 WATER. 
 
 Expansion of Water. The following table gives the relative vol- 
 umes of water at different temperatures, compared with its volume at 
 4 C. according to Kopp, as corrected by Porter. 
 
 Cent. 
 
 Fahr. 
 
 Volume. 
 
 Cent. 
 
 Fahr. 
 
 Volume. 
 
 Cent. 
 
 Fahr. 
 
 Volume. 
 
 4 
 5 
 10 
 15 
 20 
 25 
 30 
 
 39.1 
 41 
 50 
 59 
 68 
 77 
 86 
 
 .09000 
 .00001 
 .00025 
 .00083 
 .00171 
 .00286 
 .00425 
 
 35 
 40 
 45 
 50 
 55 
 60 
 65 
 
 95 
 104 
 113 
 122 
 131 
 140 
 149 
 
 .00586 
 .00767 
 .00967 
 .01186 
 .01423 
 .01678 
 .01951 
 
 70 
 75 
 80 
 85 
 90 
 95 
 100 
 
 158 
 167 
 176 
 185 
 194 
 203 
 212 
 
 .02241 
 .02548 
 .02872 
 .03213 
 .03570 
 .03943 
 .04332 
 
 Weight of 1 cu. ft. at 39.1 F. = 62.4245 Ib. -4- 1.04332 = 59.833. 
 weight of 1 cu. ft. at 212 F. 
 
 Weight of Water at Different Temperatures. The weight of 
 water at maximum density, 39.1, is generally taken at the figure given 
 by Rankine, 62.425 Ibs. per cubic foot. Some authorities give as low as 
 62.379. The figure 62.5 commonly given is approximate. The highest 
 authoritative figure is 62.428. At 62 F. the figures range from 62.291 to 
 62.360. The figure 62.355 is generally accepted as the most accurate. 
 
 At 32 F. figures given by different writers range from 62.379 to 62.418. 
 Hamilton Smith, Jr. (from Rosetti) gives 62.416. 
 
 Weight of Water at Temperatures above 200 F. 
 
 BOrnstein's Tables, 1905.) 
 
 (Landolt and 
 
 
 Lbs. 
 
 
 Lbs. 
 
 
 Lbs. 
 
 
 Lbs. 
 
 
 Lbs. 
 
 
 Lbs. 
 
 Deg. 
 
 Per 
 
 Deg. 
 
 Per 
 
 Deg. 
 
 Per 
 
 Deg. 
 
 Per 
 
 Deg. 
 
 Per 
 
 Deg. 
 
 Per 
 
 . F. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 F 
 
 Cu. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 200 
 
 60.12 
 
 270 
 
 58.26 
 
 340 
 
 55.94 
 
 410 
 
 53.0 
 
 480 
 
 49.7 
 
 550 
 
 45.6 
 
 210 
 
 59.88 
 
 280 
 
 57.96 
 
 350 
 
 55.57 
 
 420 
 
 52.6 
 
 490 
 
 49.2 
 
 560 
 
 44.9 
 
 220 
 
 59.63 
 
 290 
 
 57.65 
 
 360 
 
 55.18 
 
 430 
 
 52.2 
 
 500 
 
 48.7 
 
 570 
 
 44.1 
 
 239 
 
 59.37 
 
 300 
 
 57.33 
 
 370 
 
 54.78 
 
 440 
 
 51.7 
 
 510 
 
 48.1 
 
 580 
 
 43.3 
 
 240 
 
 59.11 
 
 310 
 
 57.00 
 
 380 
 
 54.36 
 
 450 
 
 51.2 
 
 520 
 
 47.6 
 
 590 
 
 42.6 
 
 250 
 
 58.83 
 
 320 
 
 56 66 
 
 390 
 
 53.94 
 
 460 
 
 50.7 
 
 530 
 
 47.0 
 
 600 
 
 41.8 
 
 260 
 
 58.55 
 
 330 
 
 56.30 
 
 400 
 
 53.5 
 
 470 
 
 50.2 
 
 540 
 
 46.3 
 
 
 
WATER. 
 
 717 
 
 Weight of Water per Cubic Foot, from 32 to 212 F., and heat* 
 units per pound, reckoned above 32 F.: The figures for weight of water 
 in following table, made by interpolating the table given by Clark as cal- 
 culated from Rankine's formula, with corrections for apparent errors, was 
 published by the author in 1884, Trans. A. S. M. E., vi. 90. The figures 
 tor heat units are from Marks and Da vis's Steam Tables, 1909. 
 
 & 
 
 &M 
 
 g 0> 
 
 &H3 
 
 H 
 
 As 
 
 ',0 
 
 It 
 
 .2? o> 2 
 
 > ft 
 
 Heat-units. 
 
 L* 
 
 l^fcc 
 
 j5- 
 
 Jo 
 
 ~~3 
 
 A +: 
 .^2 
 2&2 
 
 Heat-units. 
 
 h fa- 
 is* 
 
 fl 3 0> 
 
 +-~ 
 
 -S.2 
 
 ""-Q 
 
 ill 
 
 ^ a 
 & 
 
 Heat-units. 
 
 Tempera- 
 ture, 
 deg. F. 
 
 J 
 "~1' Q 
 
 A *. 1 
 
 |fc! 
 
 Heat-units. 
 
 32 
 
 62.42 
 
 0. 
 
 78 
 
 62.25 
 
 46.04 
 
 123 
 
 61.68 
 
 90.90 
 
 168 
 
 60.81 
 
 135.86 
 
 33 
 
 62.42 
 
 1.01 
 
 79 
 
 62.24 
 
 47.04 
 
 124 
 
 61.67 
 
 91.90 
 
 169 
 
 60.79 
 
 136.86 
 
 34 
 
 62.42 
 
 2.02 
 
 80 
 
 62.23 
 
 48.03 
 
 125 
 
 61.65 
 
 92.90 
 
 170 
 
 60.77 
 
 137.87 
 
 35 
 
 62.42 
 
 3.02 
 
 81 
 
 62.22 
 
 49.03 
 
 126 
 
 61.63 
 
 93.90 
 
 171 
 
 60.75 
 
 138.87 
 
 36 
 
 62.42 
 
 4.03 
 
 82 
 
 62.21 
 
 50.03 
 
 127 
 
 61.61 
 
 94.89 
 
 172 
 
 60.73 
 
 139.87 
 
 37 
 
 62.42 
 
 5.04 
 
 83 
 
 62.20 
 
 51.02 
 
 128 
 
 61.60 
 
 95.89 
 
 173 
 
 60.70 
 
 140.87 
 
 38 
 
 62.42 
 
 6.04 
 
 84 
 
 62.19 
 
 52.02 
 
 129 
 
 61.58 
 
 96.89 
 
 174 
 
 60.68 
 
 141.87 
 
 39 
 
 62.42 
 
 7.05 
 
 85 
 
 62.18 
 
 53.02 
 
 130 
 
 61.56 
 
 97.89 
 
 175 
 
 60.66 
 
 142.87 
 
 40 
 
 62.42 
 
 8.05 
 
 86 
 
 62.17 
 
 54.01 
 
 131 
 
 61.54 
 
 98.89 
 
 176 
 
 60.64 
 
 143.87 
 
 41 
 
 62.42 
 
 9.05 
 
 87 
 
 62.16 
 
 55.01 
 
 132 
 
 61.52 
 
 99.88 
 
 177 
 
 60.62 
 
 144.88 
 
 42 
 
 62.42 
 
 10.06 
 
 88 
 
 62.15 
 
 56.01 
 
 133 
 
 61.51 
 
 100.88 
 
 178 
 
 60.59 
 
 145.88 
 
 43 
 
 62.42 
 
 11.06 
 
 89 
 
 62.14 
 
 57.00 
 
 134 
 
 61.49 
 
 101.88 
 
 179 
 
 60.57 
 
 146.88 
 
 44 
 
 62.42 
 
 12.06 
 
 90 
 
 62.13 
 
 58.00 
 
 135 
 
 61.47 
 
 102.88 
 
 180 
 
 60.55 
 
 147.88 
 
 45 
 
 62.42 
 
 13.07 
 
 91 
 
 62.12 
 
 59.00 
 
 136 
 
 61.45 
 
 103.88 
 
 181 
 
 60.53 
 
 148.88 
 
 46 
 
 62.42 
 
 14.07 
 
 92 
 
 62.11 
 
 60.00 
 
 137 
 
 61.43 
 
 104.87 
 
 182 
 
 60.50 
 
 149.89 
 
 47 
 
 62.42 
 
 15.07 
 
 93 
 
 62.10 
 
 60.99 
 
 138 
 
 61.41 
 
 105.87 
 
 183 
 
 60.48 
 
 150.89 
 
 48 
 
 62.41 
 
 16.07 
 
 94 
 
 62.09 
 
 61.99 
 
 139 
 
 61.39 
 
 106.87 
 
 184 
 
 60.46 
 
 151 89 
 
 49 
 
 62.41 
 
 17.08 
 
 95 
 
 62.08 
 
 62.99 
 
 140 
 
 61.37 
 
 107.87 
 
 185 
 
 60.44 
 
 152.89 
 
 50 
 
 62.41 
 
 18.08 
 
 96 
 
 62.07 
 
 63 98 
 
 141 
 
 61.36 
 
 108 87 
 
 186 
 
 60.41 
 
 153.89 
 
 51 
 
 62.41 
 
 19.08 
 
 97 
 
 62.06 
 
 64.98 
 
 142 
 
 61.34 
 
 109.87 
 
 187 
 
 60.39 
 
 154.90 
 
 52 
 
 62.40 
 
 20.08 
 
 98 
 
 62.05 
 
 65.98 
 
 143 
 
 61.32 
 
 110.87 
 
 188 
 
 60.37 
 
 155.90 
 
 53 
 
 62.40 
 
 21.08 
 
 99 
 
 62.03 
 
 66.97 
 
 144 
 
 61.30 
 
 111.87 
 
 189 
 
 60.34 
 
 156.90 
 
 54 
 
 62.40 
 
 22.08 
 
 100 
 
 62.02 
 
 67.97 
 
 145 
 
 61.28 
 
 112.86 
 
 190 
 
 60.32 
 
 157.91 
 
 55 
 
 62.39 
 
 23.08 
 
 101 
 
 62.01 
 
 68.97 
 
 146 
 
 61.26 
 
 113.86 
 
 191 
 
 60.29 
 
 158.91 
 
 56 
 
 62.39 
 
 24.08 
 
 102 
 
 62.00 
 
 69.96 
 
 147 
 
 61.24 
 
 114.86 
 
 192 
 
 60.27 
 
 159.91 
 
 57 
 
 62.39 
 
 25.08 
 
 103 
 
 61.99 
 
 70.96 
 
 148 
 
 61.22 
 
 115.86 
 
 193 
 
 60.25 
 
 160.91 
 
 58 
 
 62.38 
 
 26.08 
 
 104 
 
 61.97 
 
 71.96 
 
 149 
 
 61.20 
 
 116.86 
 
 194 
 
 60.22 
 
 161.92 
 
 59 
 
 62.38 
 
 27.08 
 
 105 
 
 61.96 
 
 72.95 
 
 150 
 
 61.18 
 
 117.86 
 
 195 
 
 60.20 
 
 162.92 
 
 60 
 
 62.37 
 
 28.08 
 
 106 
 
 61.95 
 
 73.95 
 
 151 
 
 61.16 
 
 118.86 
 
 196 
 
 60.17 
 
 163.92 
 
 61 
 
 62.37 
 
 29.08 
 
 107 
 
 61.93 
 
 74.95 
 
 152 
 
 61.14 
 
 119.86 
 
 197 
 
 60.15 
 
 164.93 
 
 62 
 
 62.36 
 
 30.08 
 
 108 
 
 61.92 
 
 75.95 
 
 153 
 
 61.12 
 
 120.86 
 
 198 
 
 60.12 
 
 165.93 
 
 63 
 
 62.36 
 
 31.07 
 
 109 
 
 61.91 
 
 76.94 
 
 154 
 
 61.10 
 
 121.86 
 
 199 
 
 60.10 
 
 166.94 
 
 64 
 
 62.35 
 
 32.07 
 
 110 
 
 61.89 
 
 77.94 
 
 155 
 
 61.08 
 
 122.86 
 
 200 
 
 60.07 
 
 167.94 
 
 65 
 
 62.34 
 
 33.07 
 
 1 1 1 
 
 61.88 
 
 78.94 
 
 156 
 
 61.06 
 
 123.86 
 
 201 
 
 60.05 
 
 168.94 
 
 66 
 
 62.34 
 
 34.07 
 
 112 
 
 61.86 
 
 79.93 
 
 157 
 
 61.04 
 
 124.86 
 
 202 
 
 60.02 
 
 169.95 
 
 67 
 
 62.33 
 
 35.07 
 
 113 
 
 61.85 
 
 80.93 
 
 158 
 
 61.02 
 
 125.86 
 
 203 
 
 60.00 
 
 170.95 
 
 68 
 
 62.33 
 
 36.07 
 
 114 
 
 61.83 
 
 81.93 
 
 159 
 
 61.00 
 
 126.86 
 
 204 
 
 59.97 
 
 171.96 
 
 69 
 
 62.32 
 
 37.06 
 
 115 
 
 61.82 
 
 82.92 
 
 160 
 
 60.98 
 
 127.86 
 
 205 
 
 59.95 
 
 172.96 
 
 70 
 
 62.31 
 
 38.06 
 
 116 
 
 61.80 
 
 83.92 
 
 161 
 
 60.96 
 
 128.86 
 
 206 
 
 59.92 
 
 173.97 
 
 71 
 
 62.31 
 
 39.06 
 
 117 
 
 61.78 
 
 84.92 
 
 162 
 
 60.94 
 
 129.86 
 
 207 
 
 59.89 
 
 174.97 
 
 72 
 
 62.30 
 
 40.05 
 
 118 
 
 61.77 
 
 85.92 
 
 163 
 
 60.92 
 
 130.86 
 
 208 
 
 59.87 
 
 175.98 
 
 73 
 
 62.29 
 
 41.05 
 
 119 
 
 61.75 
 
 86.91 
 
 164 
 
 60.90 
 
 131.86 
 
 209 
 
 59.84 
 
 176.98 
 
 74 
 
 62.28 
 
 42.05 
 
 120 
 
 61.74 
 
 87.91 
 
 165 
 
 60.87 
 
 132.86 
 
 210 
 
 59.82 
 
 177.99 
 
 75 
 
 62.28 
 
 43.05 
 
 121 
 
 61.72 
 
 88.91 
 
 166 
 
 60.85 
 
 133.86 
 
 211 
 
 59.79 
 
 178.99 
 
 76 
 
 62.27 
 
 43.04 
 
 122 
 
 61.70 
 
 89.91 
 
 167 
 
 60.83 
 
 134.86 
 
 212 
 
 59.76 
 
 180.00 
 
 77 
 
 62.261 45.04 
 
 
 
 
 
 
 
 
 
 
 Later authorities give figures for the weight of water which differ in the 
 second decimal place only from those given above, as follows: 
 
 Temp. F 40 50 60 70 80 90 
 
 Lbs. per cu. ft 62.43 62.42 62.37 62.30 62.22 62.11 
 
 110 
 
 Temp. F 100 
 
 Lbs. per cu. ft... 62.00 
 
 Temp. F 160 170 
 
 Lbs. per qu. ft. . . 61 . 00 60 . 80 
 
 120 
 
 61.86 61.71 
 180 
 60.50 
 
 130 140 150 
 61.55 61.38 61.18 
 
 190 200 210 
 60.36 60.12 59.88 
 
718 
 
 WATER. 
 
 Comparison of Heads of Water in Feet with Pressures in Various 
 
 Units. 
 
 One foot of water at 39.1 Fahr. = 62.425 Ibs. on the square foot; 
 
 = 0.4335 Ibs. on the square inch; 
 
 = 0.0295 atmosphere; 
 
 = 0.8826 inch of mercury at 32; 
 
 = 77 o o ( feet of air at 32 and 
 
 \ atmospheric pressure; 
 
 One Ib. on the square foot, at 39.1 Fahr.. = 0.01602 foot of water- 
 One Ib. on the square inch, at 39.1 Fahr . 
 One atmosphere of 29 . 922 in. of mercury . 
 
 One inch of mercury at 32 
 
 One foot of air at 32, and 1 atmosphere. 
 
 One foot of average sea-water 
 
 One foot of water at 62 F . . 
 
 One foot of water at 62 F 
 
 One inch of water at 62 F. = .5774 ounce 
 One Ib. of water on the square inch at 62 F 
 One ounce of water on the square inch at 
 
 62 F = 1 . 732 inches of water. 
 
 2.307 feet of water; 
 
 = 33.9 feet of water; 
 
 = 1.133 feet of water; 
 
 = 0.001293 feet of water; 
 
 = 1 . 026 foot of pure water; 
 
 = 62.355 Ibs. per sq. foot; 
 
 = 0.43302 Ib. per sq. inch; 
 0.036085 Ib. per sq. inch 
 2.3094 feet of water. 
 
 Pressure in Pounds per Square Inch for Different Heads of Water. 
 
 At 62 F. 1 foot head = 0.433 Ib. per square inch, 0.433 X 144 = 62.352 
 Ibs. per cubic foot. 
 
 Head, feet. 
 
 
 
 ' 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 0.433 
 
 0.866 
 
 1.299 
 
 1.732 
 
 2.165 
 
 2.598 
 
 3.031 
 
 3.464 
 
 3.897 
 
 10 
 
 4.330 
 
 4.763 
 
 5.196 
 
 5.629 
 
 6.062 
 
 6.495 
 
 6.928 
 
 7.361 
 
 7.794 
 
 8.227 
 
 20 
 
 8.660 
 
 9.093 
 
 9.526 
 
 9.959 
 
 10.392 
 
 10.825 
 
 11.258 
 
 11.691 
 
 12.124 
 
 12.557 
 
 30 
 
 12.990 
 
 13.423 
 
 13.856 
 
 14.289 
 
 14.722 
 
 15.155 
 
 15.588 
 
 16.021 
 
 16.454 
 
 16.887 
 
 40 
 
 17.320 
 
 17.753 
 
 18.186 
 
 18.619 
 
 19.052 
 
 19.485 
 
 19.918 
 
 20.351 
 
 20.784 
 
 21.217 
 
 50 
 
 21.650 
 
 22.083 
 
 22.516 
 
 22.949 
 
 23. 382123.815 
 
 24.248 
 
 24.681 
 
 25.114 
 
 25.547 
 
 60 
 
 25.980 
 
 26.413 
 
 26.846 
 
 27.279 
 
 27.712 
 
 28.145 
 
 28.578 
 
 29.011 
 
 29.444 
 
 29.877 
 
 70 
 
 30.310 
 
 30.743 
 
 31.176 
 
 31.609 
 
 32.042 
 
 32.475 
 
 32.908 
 
 33.341 
 
 33.774 
 
 34.207 
 
 80 
 
 34.640 
 
 35.073 
 
 35.506 
 
 35.939 
 
 36.372 
 
 36.805 
 
 37.238 
 
 37.671 
 
 38.104 
 
 38.537 
 
 90 
 
 38.970 
 
 39.403 
 
 39.836 
 
 40.269 
 
 40.702 
 
 41.135 
 
 41.568 
 
 42.001 
 
 42.436 
 
 42.867 
 
 Head in Feet of Water, Corresponding to Pressures in Pounds per 
 Square Inch. 
 
 1 Ib. per square inch = 2.30947 feet head, 1 atmosphere = 14.7 Ibs. 
 per sq. inch = 33.94 ft. head. 
 
 Pressure. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 2.309 
 
 4.619 
 
 6.928 
 
 9.238 
 
 11.547 
 
 13.857 
 
 16.166 
 
 18.476 
 
 20.785 
 
 10 
 
 23.0947 
 
 25.404 
 
 27.714 
 
 30.023 
 
 32.333 
 
 34.642 
 
 36.952 
 
 39.261 
 
 41.570 
 
 43.880 
 
 20 
 
 46.1894 
 
 48.499 
 
 50.808 
 
 53.118 
 
 55.427 
 
 57.737 
 
 60.046 
 
 62.356 
 
 64.665 
 
 66.975 
 
 30 
 
 69.2841 
 
 71.594 
 
 73.903 
 
 76.213 
 
 78.522 
 
 80.831 
 
 83.141 
 
 85.450 
 
 87.760 
 
 90.069 
 
 40 
 
 92.3788 
 
 94.688 
 
 96.998 
 
 99.307 
 
 101.62 
 
 103.93 
 
 106.24 
 
 108.55 
 
 110.85 
 
 113.16 
 
 50 
 
 115.4735 
 
 117.78 
 
 120.09 
 
 122.40 
 
 124.71 
 
 127.02 129.33 
 
 131.64 
 
 133.95 
 
 136.26 
 
 60 
 
 138.5682 
 
 140.88 
 
 143.19 
 
 145.50 
 
 147.81 
 
 150.12 152.42 
 
 154.73 
 
 157.04 
 
 159.35 
 
 70 
 
 161.6629 
 
 163.97 
 
 166.28 
 
 168.59 
 
 170.90 
 
 173. 211175. 52 
 
 177.83 
 
 180.14 
 
 182.45 
 
 80 
 
 184.7576 
 
 187.07 
 
 189.38 
 
 191.69 
 
 194.00 
 
 196.31 
 
 198.61 
 
 200.92 
 
 203.23 
 
 205.54 
 
 96 
 
 207,8523 
 
 210.16 
 
 212.47 
 
 214.78 
 
 217,09 
 
 219.40221.71 
 
 224.02 
 
 226.33 
 
 228.64 
 
WATER. 719 
 
 Pressure of Water due to its Weight. The pressure of still water 
 in pounds per square inch against the sides of any pipe, channel, or vessel 
 of any shape whatever is due solely to the " head," or height of the 
 level surface of the water above the point at which the pressure is con- 
 sidered, and is equal to 0.43302 Ib. per square inch for every foot of head, 
 or 62.355 Ibs. per square foot for every foot of head (at 62 F.). ' 
 
 The pressure per square inch is equal in all directions, downwards, 
 upwards, or sideways, and is independent of the shape or size of the 
 containing vessel. 
 
 The pressure against a vertical surface, as a retaining-wall, at any 
 point is in direct ratio to the head above that point, increasing from at 
 the level surface to a maximum at the bottom. The total pressure 
 against a vertical strip of a unit's breadth increases as the area of a 
 right-angled triangle whose perpendicular represents the height of the 
 strip and whose base represents the pressure on a unit of surface at the 
 bottom; that is, it increases as the square of the depth. The sum of all 
 the horizontal pressures is represented by the area of the triangle, and 
 the resultant of this sum is equal to this sum exerted at a point one third 
 of the height from the bottom. (The center of gravity of the area of a 
 triangle is one third of its height.) 
 
 The horizontal pressure is the same if the surface is inclined instead 
 of vertical. 
 
 (For an elaboration of these principles see Trautwine's Pocket-Book, 
 or the chapter on Hydrostatics in any work on Physics. For dams, 
 retaining-walls, etc., see Trautwine.) 
 
 The amount of pressure on the interior walls of a pipe has no appreci- 
 able effect upon the amount of flow. 
 
 Buoyancy. When a body is immersed in a liquid, whether it float or 
 sink, it is buoyed up by a force equal to the weight of the bulk of the 
 liquid displaced by the body. The weight of a floating body -is equal to 
 the weight of the bulk of the liquid that it displaces. The upward 
 pressure or buoyancy of the liquid may be regarded as exerted at the 
 center of gravity of the displaced water, which is called the center of 
 pressure or of buoyancy. A vertical line drawn through it is called the 
 axis of buoyancy or of flotation. In a floating body at rest a line joining 
 the center of gravity and the center of buoyancy is vertical, and is called 
 the axis of equilibrium. When an external force causes the axis of 
 equilibrium to lean, if a vertical line be drawn upward from the center 
 of buoyancy to this axis, the point where it cuts the axis is called the 
 metacenter. If the metacenter is above the center of gravity the distance 
 between them is called the metacentric height, and the body is then said 
 to be in stable equilibrium, tending to return to its original position 
 when the external force is removed. 
 
 Boiling-point. Water boils at 212 F. (100 C.) at mean atmos- 
 pheric pressure at the sea-level, 14.696 Ibs. per square inch. The tem- 
 perature at which water boils at any given pressure is the same as the 
 temperature of saturated steam at the same pressure. For boiling-point 
 of water at other pressure than 14.696 Ibs. per square inch, see table of 
 the Properties of Saturated Steam. 
 
 The Boiling-point of Water may be Raised. When water is 
 entirely freed of air, which may be accomplished by freezing or boiling, 
 the cohe ion of its atoms is greatly increased, so that its temperature 
 may be raised over 50 above the. ordinary bailing-point before ebullition 
 takes place. It was found by Faraday that when such air-freed water 
 did boil the rupture of the liquid was like an explosion. When water 
 is surrounded by a film of oil, its boiling temperature may be raised 
 considerably above its normal standard. This has been applied as a 
 theoretical explanation in the instance of boiler explosions. 
 
 The freezing-point also may be lowered, if the water is perfectly quiet, 
 to 10 C., or 18 Fahrenheit below the normal freezing-point. (Hamilton 
 Smith, Jr., on Hydraulics, p. 13.) 
 
 Kreezing-point. Water freezes at 32 F. at the ordinary atmos- 
 pheric pressure, and ice melts at the same temperature. In the melting 
 of 1 pound of ice into water at 32 F. about '142 heat-units are absorbed, 
 or become latent; and in freezing 1 Ib. of water into ice a like quantity 
 of heat is given out to the surrounding medium. 
 
 Sea-water freezes at 27 F. The ice is fresh, (Trautwine.) 
 
720 
 
 WATER. 
 
 ^Sf in nd 
 
 67.50 Ibs.; 
 
 ( rom Cla ? 1 cubic foot of ice at 32 F. weighs 
 pound of ice at 32 F. has a volume of 0.0174 cu. ft. = 30.067 
 
 Relative volume of ice to water at 32 F., 1.0855, the expansion in 
 passing into the solid state being 8.55%. Specific gravity of ice = 0.922, 
 water at 02 .r . being 1 . 
 
 , m elting-point of ice is lower than 32 F., being at 
 F. for each additional atmosphere of pressure. 
 The specific heat of ice "s 0.504, that of water being 1. 
 1 cubic foot of fresh snow, according to humidity of atmosphere: 
 
 iV 12 * lbs r rt Ju cubl ,, foot of snow moistened and compacted by 
 rain: 15 Ibs. to 50 Ibs. (Trautwine.) 
 
 The latent heat of fusion of ice is 143.6 B.T.U. per Ib. 
 
 Specific Heat of Water. (From Davis and Marks's Steam Tables.) 
 
 Deg. Sp. 
 F. Ht. 
 
 Deg. Sp. 
 F. Ht. 
 
 Deg. Sp. 
 F. Ht. 
 
 Deg. Sp. 
 F. Ht. 
 
 Deg. Sp. 
 F. Ht. 
 
 Deg. Sp. 
 F. Ht. 
 
 20 1.0168 
 
 120 0.9974 
 
 220 .007 
 
 320 .035 
 
 420 .072 
 
 520 .123 
 
 30 1.0098 
 
 130 0.9974 
 
 230 .009 
 
 330 .038 
 
 430 .077 
 
 530 .128 
 
 40 1.0045 
 
 140 0.9986 
 
 240 .012 
 
 340 .041 
 
 440 .082 
 
 540 .134 
 
 50 1.0012 
 
 150 0.9994 
 
 250 .015 
 
 350 .045 
 
 450 .086 
 
 550 .140 
 
 60 0.9990 
 
 160 .0002 
 
 260 .018 
 
 360 .048 
 
 460 .091 
 
 560 .146 
 
 70 0.9977 
 
 170 .0010 
 
 270 .021 
 
 370 .052 
 
 470 .096 
 
 570 .152 
 
 80 0.9970 
 
 180 .0019 
 
 280 .023 
 
 380 .056 
 
 480 .101 
 
 580 .158 
 
 90 0.9967 
 
 190 .0029 
 
 290 .026 
 
 390 .060 
 
 490 .106 
 
 590 .165 
 
 100 0.9967 
 
 200 .0039 
 
 300 .029 
 
 400 .064 
 
 500 .112 
 
 600 .172 
 
 110 0.9970 
 
 210 .0050 
 
 310 .032 
 
 410 .068 
 
 510 .117 
 
 
 These figures are based on the mean value of the heat unit, that is, 
 Viso of the heat needed to raise 1 Ib. of water from 32 to 212. 
 
 Compressibility of Water. Water is very slightly compressible. 
 Its compressibility is from 0.000040 to 0.000051 for one atmosphere, 
 decreasing with increase of temperature. For each foot of pressure dis- 
 tilled water will be diminished in volume 0.0000015 to 0.0000013. Water 
 is so incompressible that even at a depth of a mile a cubic foot of water 
 will weigh only about half a pound more than at the surface. 
 
 THE IMPURITIES OF WATER. 
 
 (A. E. Hunt and G. H. Clapp, Trans. A. I. M. E., xvii. 338.) 
 
 Commercial analyses are made to determine concerning a given water*. 
 (1) its applicability for making steam; (2) its hardness, or the facility 
 with which it will "form a lather" necessary for washing; or (3) its 
 adaptation to other manufacturing purposes. 
 
 At the Buffalo meeting of the Chemical Section of the A. A. A. S. it 
 was decided to report all water analyses in parts per thousand, hundred- 
 thousand, and million. 
 
 To convert grains per imperial (British) gallon into parts per 100,000, 
 divide by 0.7. To convert parts per 100,000 into grains per IT. S. gallon, 
 multiply by 0.5835.- To convert grains per U. S. gallon into parts per 
 million multiply by 17.14. 
 
 The most common commercial analysis of water is made to determine 
 its fitness for making steam. Water containing more than 5 parts per 
 100,000 of free sulphuric or nitric acid is liable to cause serious corrosion, 
 not only of the metal of the boiler itself, but of the pipes, cylinders, pistons, 
 and valves with which the steam comes in contact. 
 
 The total residue in water used for making steam causes the interior 
 linings of boilers to become coated, and often produces a dangerous hard 
 
THE IMPURITIES OF WATEB. 721 
 
 scale, which prevents the cooling action of the water from protecting 
 the metal against burning. 
 
 Lime and magnesia bicarbonates in water lose their excess of carbonic acid 
 on boiling, and often, especially when the water contains sulphuric acid, 
 produce, with the other solid residues constantly being formed by the 
 evaporation, a very hard and insoluble scale. A larger amount than 100 
 parts per 100,000 of total solid residue will ordinarily cause troublesome 
 scale, and should condemn the water for use in steam-boilers, unless a 
 better supply cannot be obtained. 
 
 The following is a tabulated form of the causes of trouble with water 
 for steam purposes, and the proposed remedies, given by Prof. L. M. 
 Norton. 
 
 CAUSES OF INCRUSTATION. 
 
 1. Deposition of suspended matter. 
 
 2. Deposition of deposed salts from concentration. 
 
 3. Deposition of carbonates of lime and magnesia by boiling off 
 carbonic acid, which holds them in solution. 
 
 4. Deposition of sulphates of lime, because sulphate of lime is but 
 slightly soluble in cold water, less soluble in hot water, insoluble above 
 270 F. 
 
 5. Deposition of magnesia, because magnesium salts decompose at high 
 temperature. 
 
 6. Deposition of lime soap, iron soap, etc., formed by saponification of 
 grease. 
 
 MEANS FOR PREVENTING INCRUSTATION. 
 
 1. Filtration. 
 
 2. Blowing off. 
 
 3. Use of internal collecting apparatus or devices for directing the 
 circulation. 
 
 4. Heating feed-water. 
 
 5. Chemical or other treatment of water in boiler. 
 
 6. Introduction of zinc into boiler. 
 
 7. Chemical treatment of -water outside of boiler. 
 
 TABULAR VIEW. 
 
 Troublesome Substance. Trouble. Remedy or Palliation. 
 
 Sediment, mud, clay, etc. Incrustation. Filtration; blowing off. 
 
 Readily soluble salts. Blowing off. 
 
 Bicarbonates of lime, magnesia, ) .< 
 
 ( magnesia, etc". 
 Quir^oto r,f li " f Addition of carb. soda, 
 
 1 barium hydrate, etc. 
 Chloride and sulphate of mag-) p rtrrrt0 : nn j Addi ion of caibonate of 
 
 nesium. f u< on - ( soda, etc. 
 
 Carbonate of soda in large) T>_: .. (Addition of barium chlo- 
 
 amounts. J J ng - { ride, etc. 
 
 Acid (in mine waters). Corrosion. Alkali. 
 
 Di nlv!jpn carbonic acid and } Corrosion, j toiler! to formTthhi in- 
 ternal coating. 
 
 G rease (from condensed water). l[? rr s ^R ^Different cases require dif- 
 
 Primine ! ferent remedies. Consult 
 
 Organic matter (sewage). ) corrosion or I a specialist on the sub- 
 
 (incrustation/ Jeci< 
 
 The mineral matters causing the most troublesome boiler-scales are 
 bicarbonates and sulphates of lime and magnesia, oxides of iron and 
 alumina, and silica. The analyses of some of the most common and 
 troublesome boiler-scales are given in the following table: 
 
722 
 
 WATER. 
 
 Analyses of Boiler-scale. (Chandler.) 
 
 
 Sul- 
 
 
 
 Per- 
 
 
 Car- 
 
 X-" 
 
 phate 
 of 
 
 Mag- 
 nesia. 
 
 Silica. 
 
 oxide 
 of 
 
 Water. 
 
 bonate 
 of 
 
 
 Lime. 
 
 
 
 Iron. 
 
 
 Lime. 
 
 N.Y.C.&H.R.Ry.,No. 1 
 
 74.07 
 
 9.19 
 
 0.65 
 
 0.08 
 
 1.14 
 
 14.78 
 
 No. 2 
 
 71.37 
 
 
 1.76 
 
 
 
 
 No. 3 
 
 62.86 
 
 J8. 95 
 
 2.60 
 
 0.92 
 
 1.28 
 
 12.62 
 
 No. 4 
 
 53.05 
 
 
 4.79 
 
 
 
 
 No. 5 
 
 46.83 
 
 
 5.32 
 
 
 
 
 No. 6 
 
 30.80 
 
 31.17 
 
 7.75 
 
 1.08 
 
 2.44 
 
 26.93 
 
 No. 7 
 
 4.95 
 
 2.61 
 
 2.07 
 
 1.03 
 
 0.63 
 
 86.25 
 
 No. 8 
 
 0.88 
 
 2.84 
 
 0.65 
 
 0.36 
 
 0.15 
 
 93.19 
 
 No. 9 
 
 4.81 
 
 
 2.92 
 
 
 
 
 No. 10 
 
 30.07 
 
 
 8.24 
 
 
 
 
 
 
 
 
 
 
 
 Analyses in parts per 100,000 of Water giving Bad Results in 
 Steam-boilers. (A. E. Hunt.) 
 
 
 . 
 
 .5 
 
 '<8 bio 
 
 
 
 
 
 
 
 
 
 
 '.TO 
 
 U 
 
 c3 O 
 
 
 
 
 
 
 
 
 g 
 
 
 ^PQ 
 
 1 
 
 
 .si 
 
 "GO 
 | 
 
 32 
 '3 
 
 
 
 C 
 
 o> 
 
 
 | 
 
 
 "Si! 
 
 |l 
 
 $ 
 
 1 
 
 o 
 
 
 
 S 
 
 
 t 
 
 
 O'co 
 
 Oce 
 
 ^ 
 
 a 
 
 i 
 
 0) 
 
 
 o 
 
 '5 
 
 4 
 
 ^g 
 
 1 
 
 
 c3 0) 
 
 jj QJ 
 
 3 
 
 d 
 
 a 
 
 o 
 
 ,- 
 
 i 
 
 S 
 
 o 
 
 
 .Si^ 
 
 o^ 
 
 o 
 
 "Q 
 
 "^ 
 
 
 o 
 
 B 
 
 3 
 
 
 
 PQ 
 
 PQ 
 
 H 
 
 ^ 
 
 02 
 
 O 
 
 (-H 
 
 o 
 
 ' 
 
 
 Coal-mine water 
 
 110 
 
 25 
 
 119 
 
 39 
 
 890 
 
 5QO 
 
 780 
 
 30 
 
 640 
 
 
 Salt-well 
 
 151 
 
 38 
 
 190 
 
 48 
 
 360 
 
 Q90 
 
 38 
 
 21 
 
 30 
 
 1310 
 
 Spring 
 
 75 
 
 89 
 
 95 
 
 PO 
 
 310 
 
 
 75 
 
 10 
 
 80 
 
 36 
 
 Moriongahela River 
 
 no 
 
 
 161 
 
 
 710 
 
 38 
 
 70 
 
 
 
 
 
 80 
 
 70 
 
 94 
 
 81 
 
 719 
 
 710 
 
 90 
 
 
 
 
 it 
 
 37 
 
 87 
 
 61 
 
 104 
 
 78 
 
 190 
 
 38 
 
 
 
 
 Allegheny R., near Oil-works. . 
 
 30 
 
 50 
 
 41 
 
 68 
 
 890 
 
 47 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Many substances have been added with the idea of causing chemical 
 action which will prevent boiler-scale. As a general rule, these do more 
 harm than good, for a boiler is one of the worst possible places in which 
 to carry on chemical reaction, where it nearly always causes more or less 
 corrosion of the metal, and is liable to cause dangerous explosions. 
 
 In cases where water containing large amounts of total solid residue is 
 necessarily used, a heavy petroleum oil, free from tar or wax, which is not 
 acted upon by acids or alkalies, not having sufficient wax in it to cause 
 saponification, and which has a vaporizing-point at nearly 600 F., will 
 give the best results in preventing boiler-scale. Its action is to form a 
 thin greasy film over the boiler linings, protecting them largely from the 
 action of acids in the water and greasing the sediment which is formed, 
 thus preventing the formation of scale and keeping the solid residue 
 from the evaporation of the water in such a plastic suspended condition 
 that it can be easily ejected from the boiler by the process of "blowing 
 off." If the water is not blown off sufficiently often, this sediment 
 forms into a "putty" that will necessitate cleaning the boilers. Any 
 boiler using bad water should be blown off every twelve hours. 
 
PURIFYING WATER. 
 
 723 
 
 Hardness of Water. The hardness of water, or its opposite quality, 
 Indicated by the ease with which it will form a lather with soap, depends 
 almost altogether upon the presence of compounds of lime and magnesia. 
 Almost all soaps consist, chemically, of oleate, stearate, and palmitate of 
 an alkaline base, usually soda and potash. The more lime and magnesia 
 in a sample of water, the more soap a given volume of the water will 
 decompose, so as to give insoluble oleate, palmitate, and stearate of 
 lime and magnesia, and consequently the more soap must be added in 
 order that the necessary quantity of soap may remain in solution to 
 form the lather. The relative hardness of samples of water is generally 
 expressed in terms of the number of standard soap-measures consumed 
 by a gallon of water in yielding a permanent lather. 
 
 In Great Britain the standard soap-measure is the quantity required to 
 precipitate one grain of carbonate of lime: in the U. S. it is the quantity 
 required to precipitate one milligramme. 
 
 If a water charged with a bicarbonate of lime, magnesia, or iron 
 is boiled, it will, on the excess of the carbonic acid being expelled, 
 deposit a considerable quantity of the lime, magnesia, or iron, and con- 
 sequently the water will be softer. The hardness of the water after 
 this deposit of lime, after long boiling, is called the permanent hardness 
 and the difference between it and the total hardness is called temporary 
 hardness. 
 
 Lime salts in water react immediately on soap-solutions, precipitating 
 the oleate, palmitate, or stearate of lime at once. Magnesia salts, on the 
 contrary, require some considerable time for reaction. They are, how- 
 ever, more powerful hardeners; one equivalent of magnesia salts con- 
 suming as much soap as one and one-half equivalents of lime. 
 
 The presence of soda and potash salts softens rather than hardens 
 water. Each grain of carbonate of lime per gallon of water causes an 
 increased expenditure for soap of about 2 ounces per 100 gallons of water. 
 (Eng'g News, Jan. 31, 1885.) 
 
 Low degrees of hardness (down to 200 parts of calcium carbonate 
 (CaCOs) per million) are usually determined by means of a standard 
 solution of soap. To 50 c.c. of the water is added alcoholic soap solu- 
 tion from a burette, shaking well after each addition, until a lather is 
 obtained which covers the entire surface of the liquid when the bottle is 
 laid on its side and which lasts five minutes. From the number of c.c. 
 of soap solution used, the hardness of the water may be calculated by 
 the use of Clark's table, given below, in parts of CaCOs per million. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOs. 
 
 c.e. Soap 
 .Sol. 
 
 Pts. 
 CaCO 3 . 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 
 CaCOs. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOa. 
 
 7 
 
 
 
 4 
 
 46 
 
 8 . 
 
 103 
 
 12 
 
 164 
 
 1 . 
 
 .. 5 
 
 50.. 
 
 ...60 
 
 9.0... 
 
 ...118 
 
 13.0. . 
 
 .180 
 
 2 
 
 19 
 
 6 
 
 74 
 
 10 
 
 133 
 
 14 
 
 196 
 
 3.0. 
 
 32 
 
 7.0 
 
 89 
 
 11.0 
 
 ....148 
 
 15.0 
 
 . ...212 
 
 
 
 
 
 
 
 
 
 For waters which are harder than 200 parts per million, a solution of 
 soap ten times as strong may be used, the end or determining point being 
 reached when sufficient soap has been added to deaden the harsh sound 
 produced on shaking the bottle containing the water. A. H. Gill, En- 
 gine-Room Chemistry. 
 
 Purifying Feed-water for Steam-boilers. (See also Incrustation 
 and Corrosion, p. 927.) When the water used for steam-boilers con- 
 tains a large amount of scale-forming material it is usually advisable to 
 purify it before allowing it to enter the boiler rather than to attempt the 
 prevention of scale by the introduction of chemicals into the boiler. 
 Carbonates of lime and magnesia may be removed to a considerable 
 extent by simple heating of the water in an exhaust-steam feed-water 
 heater or, still better, by a live-steam heater. (See circular of the Hoppes 
 Mfg. Co., Springfield, O.) When the water is very bad it is best treated 
 
724 
 
 WATER. 
 
 with chemicals lime, soda-ash, caustic soda, etc. --in tanks, the pre- 
 cipitates being separated by settling or filtering. For a description of 
 several systems of water purification see a series of articles on the sub- 
 ject by Albert A. Gary in Eng'g Mag., 1897. 
 
 Mr. H. E. Smith, chemist of the Chicago, Milwaukee & St. Paul Ry. 
 Co., in a letter to the author, June, 1902, writes as follows concerning 
 the chemical action of soda-ash on the scale-forming substances in boiler 
 waters: 
 
 Soda-ash acts on carbonates of lime and magnesia in boiler water in the 
 following manner: The carbonates are held in solution by means of 
 the carbonic acid gas also present which probably forms bicarbonates of 
 lime and magnesia. Any means which will expel or absorb this carbonic 
 acid will cause the precipitation of the carbonates. One of these means 
 is soda ash (carbonate of soda), which absorbs the gas with the forma- 
 tion of bicarbonate of soda. This method would not be practicable for 
 softening cold water, but it serves in a boiler. The carbonates precipi- 
 tated in this manner are in flocculent condition instead of semi-crystalline 
 as when thrown down by heat. In practice it is desirable and sufficient 
 to precipitate only a portion of the lime and magnesia in flocculent 
 condition. As to equations, the following represent what occurs: 
 
 Ca (HCOa)j 4- Na 2 CO 3 = CaCO 3 + 2 NaHCOs. 
 Mg (HCO)i 4- Na 2 CO 3 = MgCO 3 + 2 NaHCOs. 
 (free) CO 2 + Na 2 CO 3 + H 2 O = 2 NaHCO 3 . 
 
 Chemical equivalents: 106 pounds of pure carbonate of soda 
 equal to about 109 pounds of commercial 58 degree soda-ash are 
 chemically equivalent to i.e., react exactly with the following 
 weights of the substances named: Calcium sulphate, 136 Ibs.; magnesium 
 sulphate, 120 Ibs.; calcium carbonate, 100 Ibs.; magnesium carbonate, 
 84 Ibs.; calcium chloride, 111 Ibs.; magnesium chloride, 95 Ibs. 
 
 Such numbers are simply the molecular weights of the substances 
 reduced to a common basis with regard to the valence of the component 
 atoms. 
 
 Important work in this line should not be undertaken by an amateur. 
 " Recipes" have a certain field of usefulness, but will not coyer the whole 
 subject. In water purification, as in a problem of mechanical engineer- 
 ing, methods and apparatus must be adapted to the conditions presented. 
 Not only must the character of the raw water be considered but also the 
 conditions of purification and use. 
 
 Water-softening Apparatus. (From the Report of the Committee 
 on Water Service, of the Am. Railway Eng'g and Maintenance of Way 
 Assn., Eng. Rec., April 20, 1907). Between three and four hours is nec- 
 essary for reaction and precipitation. Water taken from running streams 
 in winter should have at least four hours' time. At least three feet of 
 the bottom of each settling tank should be reserved for the accumulation 
 of the precipitates. 
 
 The proper capacities for settling tanks, measured above the space 
 reserved for sludge, can be determined as follows: a = capacity of soft- 
 ener in gallons per hour; b = hours required for reaction and precipitation; 
 c = number of settling tanks (never less than two); x = number of 
 hours required to fill the portion of settling tank above the sludge portion; 
 y = number of hours required to transfer treated water from one settling 
 tank to the storage tank (y should never be greater than x). 
 
 Where one pump alternates between filling and emptying settling 
 tanks, x y. Settling capacity in each tank= 2 ax = ab -s- (c 1). 
 
 For plants where the quantity of water supplied to the softener and the 
 capacity of the plant are equal, the settling capacity of each tank is equal 
 to ax. The number of hours required to fill all the settling tanks should 
 equal the number of hours required to fill, precipitate and empty one 
 tank, as expressed by the following equation: ex = x + b 4- y. 
 
 If y =* x t ax = ab -* (c 2). 
 
 If y - 1/2 *, oz - 06 -* (c - 1.5). 
 
PURIFYING WATER. 
 
 725 
 
 An article on "The Present Status of Water Softening," by G. C. 
 Whipple, in Cass. Mag., Mar., 1907, illustrates several different forms of 
 water-purifying apparatus. A classification of degrees of hardness cor- 
 responding to parts of carbonates and sulphates of lime and magnesia 
 per million parts of water is given as follows: Very soft, to 10 parts; 
 soft, 10 to 20; slightly hard, 25 to 50; hard, 50 to 100; very hard, 100 to 
 200; excessively hard, 200 to 500; mineral water, 500 or more. The 
 same article gives the following figures showing the quantity of chemicals 
 required for the various constituents of hard water. For each part per 
 million of the substances mentioned it is necessary to add the stated 
 number of pounds per million gallons of lime and soda. 
 
 For Each Part per Million of 
 
 Pounds per Million 
 Gallons. 
 
 Lime. 
 
 Soda. 
 
 Free CC>2 
 
 10.62 
 4.77 
 4.67 
 0.00 
 19.48 
 
 
 9.03 
 
 
 8.85 
 
 
 Free acid (calculated as 112804) 
 
 Alkalinity 
 
 Incrustants 
 
 Magnesium 
 
 
 The above figures do not take into account any impurities in the 
 chemicals. These have to be considered in actual operation. 
 
 An illustrated description of a water-purifying plant on the Chicago 
 & Northwestern Ry. by G. M. Davidson is found in Eng. News, April 2, 
 1903. Two precipitation tanks are used, each 30 ft. diarn., 16 ft. high, 
 or 70,000 gallons each. As some water is left with the sludge in the 
 bottom after each emptying, their net capacity is about 60,000 gallons 
 each. The time required for filling, precipitating, settling and trans- 
 ferring the clear water to supply tanks is 12 hours. Once a month the 
 sludge is removed, and it is found to make a good whitewash. Lime and 
 soda-ash, in predetermined quantity, as found by analysis of the water, 
 are used as precipitants. The following table shows the effect of treat- 
 ment of well water at Council Bluffs, Iowa. 
 
 
 Before 
 Treatment. 
 
 After 
 Treatment. 
 
 Total solid matter, grains per gallon 
 
 53.67 
 
 31.35 
 
 Carbonates of lime and magnesia 
 
 25 57 
 
 3 14 
 
 Sulphates of lime and magnesia 
 
 19 55 
 
 
 Silica and oxides of iron and aluminum 
 
 1.76 
 
 40 
 
 Total incrusting solids 
 
 46 88 
 
 3 54 
 
 Alkali chlorides. 
 
 1.21 
 
 1 27 
 
 Alkali sulphates ... . 
 
 5 58 
 
 26 32 
 
 Total non-incrusting solids 
 
 6.79 
 
 27.81 
 
 Pounds scale-forming matter in 1000 gals 
 
 6.69 
 
 0.51 
 
 
 
 
 The minimum amount of scaling matter which will justify treatment 
 cannot be stated in terms of analysis alone, but should be stated in terms 
 of pounds incrusting matter held in solution in a day's supply. Besides 
 the scale-forming solids, nearly all water contains more or less free car- 
 bonic acid. Sulphuric acid is also foifnd, particularly in streams adjacent 
 to coal mines. Serious trouble from corrosion will result from a small 
 amount of this acid. In treating waters, the acids can be neutralized, 
 and the incrusting matter can be reduced to at least 5 grains per gallon in 
 most cases. 
 
726 
 
 HYDRAULICS. 
 
 QUANTITY OF PURE REAGENTS REQUIRED TO REMOVE ONE POUND OF 
 INCRUSTING OR CORROSIVE MATTER FROM THE WATER. 
 
 Incrusting or Corrosive 
 Substance Held in 
 Solution. 
 
 Amount of Reagent. (Pure.) 
 
 Foaming Mat- 
 ter Increased. 
 
 Sulphuric acid 
 
 . 57 Ib . lime plus 1 . 08 Ibs . soda ash 
 
 1 45 Ibs 
 
 Free carbonic acid .... 
 
 1.27 Ibs. lime 
 
 None 
 
 Calcium, carbonate 
 
 56 Ib. lime 
 
 
 Calcium sulphate 
 
 78 Ib. soda ash 
 
 04 Ibs 
 
 Calcium chloride. 
 
 96 Ib. soda ash 
 
 05 Ibs 
 
 Calcium nitrate 
 
 65 Ib soda ash 
 
 04 Ibs 
 
 Magnesium carbonate 
 
 1 33 Ibs. lirne 
 
 
 Magnesium sulphate. . . . 
 Magnesium chloride 
 Magnesium nitrate 
 
 Calcium carbonate 
 
 0.47lb.lime plus 0.88 Ib. soda ash. 
 0.59 Ib. lime plus 1.11 Ibs. soda ash 
 0.38 Ib. lime plus 0.72 Ib. soda ash. 
 
 1 71 Ibs barium hydrate 
 
 .18 Ibs. 
 .22 Ibs. 
 .15 Ibs. 
 
 Magnesium carbonate 
 
 4 05 Ibs barium hydrate. . 
 
 None 
 
 Magnesium sulphate 
 
 1 42 Ibs. barium hydrate. . . . 
 
 None 
 
 *Calcium sulphate 
 
 1 .26 Ibs. barium hydrate 
 
 None 
 
 * In precipitating the calcium sulphate, there would also be precipi- 
 tated 0.74 Ib. of calcium carbonate or 0.31 Ib. of magnesium carbonate, 
 the 1.26 Ibs. of barium hydrate performing the work of 0.41 Ib. of lime 
 and 0.78 Ib. of soda-ash, or for reacting on either magnesium or calcium 
 sulphate, 1 Ib. of barium hydrate performs the work of 0.33 Ib. of lime 
 plus 0.62 Ib. of soda-ash, and the lime treatment can be correspondingly 
 reduced. 
 
 Barium hydrate has no advantage over lime as a reagent to precipitate 
 the carbonates of lime and magnesia and should not be considered except 
 in connection with the treating of water containing calcium sulphate. 
 
 HYDRAULICS -FLOW OF WATER. 
 
 Formulae for Discharge of Water through Orifices and Weirs. 
 
 For rectangular or circular orifices, with the head measured from center 
 of the orifice to the surface of the still water in the feeding reservoir: 
 
 Q = c ^2gHX a (1) 
 
 For weirs with no allowance for increased head due to velocity of 
 approach: 
 
 Q = C2/ s V2gHXLH (2) 
 
 For rectangular and circular or other shaped vertical or inclined orifices: 
 formula based on the proposition that each successive horizontal layer of 
 water passing through the orifice has a velocity due to its respective 
 head: 
 
 Q 
 For rectangular vertical weirsj 
 
 Q = C 2/ 3 V20#XZ,/? (4) 
 
 Q = quantity of water discharged in cubic feet per second; C = ap- 
 proximate coefficient for formulas (1) and (2): c = correct coefficient 
 for (3) and (4). 
 
 Values of the coefficients c and C are given below. 
 
 g = 32.16; *^2g = 8.02; H = head in feet measured from center of 
 orifice to level of still water; #5 = head measured from bottom of 
 orifice; HI = head measured from top of orifice; h = H, corrected for 
 velocity of approach, V a H + 1.33 V a z /2 g for weirs with no end con- 
 traction, and H + 1.4 V 2 /2 g for weirs with end contraction; a* area in 
 square feet; L -length in feet, 
 
HYDRAULICS. 
 
 727 
 
 Flow of Water from Orifices. The theoretical velocity of water 
 flowing from an orifice is the same as the velocity of a falling body which 
 has fallen from a height equal to the head of water, = */2 gll. The 
 actual velocity at the smaller section of the vena contracta is substan- 
 tially the same as the theoretical, but the velocity at the plane of the 
 orifice is C ^2 gH, in which the coefficient C has the nearly constant 
 value of 0.62. The smallest diameter of the vena contracta is therefore 
 about 0.79 of that of the orifice. If C be the approximate coefficient 
 = 0.62, and c the correct coefficient, the ratio C/c varies with different 
 ratios of the head to the diameter of the vertical orifice, or toH/D. Ham- 
 ilton Smith, Jr., gives the following: 
 
 H/D = 0.5 0.875 1. 1.5 2. 2.5 5. 10. 
 
 C/c =0.9604 0.9849 0.9918 0.9965 0.9980 0.9987 0.9997 1. 
 
 For vertical rectangular orifices of ratio of head to width W; 
 ForH/W= 0.5 0.6 0.8 1 1.5 2. 3. 4. 5. 8. 
 C/c = .9428 .9657 .9823 .9890 .9953 .9974 .9988 .9993 .9996 .9998 
 
 For H * D or H -f- W over 8, C = c, practically. 
 
 For great heads, 312 ft. to 336 ft., with converging mouthpieces, c 
 has a value of about one, and for small circular orifices in thin plates, 
 with full contraction, c = about 0.60. 
 
 Mr. Smith as the result of the collation of many experimental data of 
 others as well as hi's own, gives tables of the value of c for vertical orifices, 
 with full contraction, with a free discharge into the air, with the inner 
 face of the plate, in which the orifice is pierced, plane, and with sharp 
 inner corners, so that the escaping vein only touches these inner edges. 
 These tables are abridged below. The coefficient c is to be used in the 
 formulae (3) and (4) above. For formulae (1) and (2) use the coefficient 
 C found from the values of the ratios C/c above. 
 
 Values of Coefficient c for Vertical Orifices with Sharp Edges, 
 Full Contraction, and Free Discharge into Air. (Hamilton 
 Smith, Jr.) 
 
 Head from 
 Center of 
 Orifice H. 
 
 Square Orifices. Length of the Side of the Square, in feet. 
 
 07 
 
 03 
 
 04 
 
 05 
 
 07 
 
 .10 
 
 .12 
 
 .15 
 
 .20 
 
 .40 
 
 .60 
 
 .80 
 
 1.0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0.4 
 0.6 
 1.0 
 3.0 
 6.0 
 10 
 
 
 
 643 
 
 637 
 
 628 
 
 621 
 
 616 
 
 .611 
 
 
 
 
 
 
 .660 
 .648 
 .632 
 .623 
 616 
 
 .645 
 .636 
 .622 
 .616 
 611 
 
 .636 
 .628 
 .616 
 
 .630 
 .622 
 .612 
 
 .623 
 .618 
 .609 
 
 .617 
 .613 
 607 
 
 .613 
 .610 
 606 
 
 .610 
 .608 
 .606 
 
 .605 
 .605 
 .605 
 
 .601 
 .603 
 605 
 
 .598 
 .601 
 604 
 
 .596 
 .600 
 .603 
 
 '!599 
 60^ 
 
 .612 
 608 
 
 .609 
 .606 
 
 .607 
 605 
 
 .605 
 604 
 
 .605 
 .604 
 
 .605 
 .603 
 
 .604 
 .603 
 
 .604 
 .603 
 
 .603 
 .602 
 
 .602 
 .602 
 
 .602 
 601 
 
 20. 
 100. (?) 
 
 .606 
 .599 
 
 .605 
 .598 
 
 .604 
 .598 
 
 .603 
 .598 
 
 .602 
 .598 
 
 .602 
 .598 
 
 .602 
 .598 
 
 .602 
 .598 
 
 .602 
 .598 
 
 .601 
 .598 
 
 .601 
 .598 
 
 .601 
 .598 
 
 .600 
 .598 
 
 Circular Orifices. Diameters, in feet. 
 
 H. 
 
 0? 
 
 03 
 
 04 
 
 05 
 
 07 
 
 10 
 
 1? 
 
 15 
 
 70 
 
 40 
 
 60 
 
 .80 
 
 1.0 
 
 0.4 
 
 
 
 
 637 
 
 67.8 
 
 618 
 
 ,612 
 
 .606 
 
 
 
 
 
 
 0.6 
 
 .655 
 
 .640 
 
 .630 
 
 .624 
 
 .618 
 
 .613 
 
 .609 
 
 .605 
 
 .601 
 
 .596 
 
 .593 
 
 .590 
 
 
 1.0 
 
 644 
 
 ,631 
 
 67.3 
 
 617 
 
 617. 
 
 ,608 
 
 ,605 
 
 603 
 
 600 
 
 .598 
 
 .595 
 
 .593 
 
 .591 
 
 2. 
 
 .632 
 
 .621 
 
 .614 
 
 .610 
 
 .607 
 
 .604 
 
 .601 
 
 .600 
 
 .599 
 
 .599 
 
 .597 
 
 .596 
 
 .595 
 
 4. 
 
 67.3 
 
 614 
 
 609 
 
 605 
 
 603 
 
 607, 
 
 600 
 
 ,599 
 
 .599 
 
 .598 
 
 .597 
 
 .597 
 
 .596 
 
 6. 
 
 .618 
 
 .611 
 
 .607 
 
 .604 
 
 607. 
 
 .600 
 
 .599 
 
 .599 
 
 .598 
 
 .598 
 
 .597 
 
 .596 
 
 .596 
 
 10. 
 
 611 
 
 606 
 
 603 
 
 601 
 
 .599 
 
 598 
 
 .598 
 
 .597 
 
 .597 
 
 .597 
 
 .596 
 
 ,596 
 
 .595 
 
 20. 
 
 601 
 
 600 
 
 599 
 
 598 
 
 597 
 
 596 
 
 596 
 
 596 
 
 596 
 
 596 
 
 ,596 
 
 .595 
 
 .594 
 
 50.(?) 
 
 ,596 
 
 596 
 
 595 
 
 ,595 
 
 594 
 
 .594 
 
 .594 
 
 .594 
 
 .594 
 
 .594 
 
 .594 
 
 .593 
 
 .593 
 
 100. (?) 
 
 .593 
 
 .593 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
 .592 
 
728 HYDRAULICS, 
 
 HYDRAULIC FORMULA. FLOW OF WATER IN OPEN AND 
 CLOSED CHANNELS. 
 
 Flow of Water in Pipes. The quantity of water discharged 
 through a pipe depends on the "head"; that is, the vertical distance 
 between the level surface of still water in the chamber at the entrance 
 end of the pipe and the level of the center of the discharge end of the 
 pipe; also upon the length of the pipe, upon the character of its interior 
 surface as to smoothness, and upon the number and sharpness of the 
 bends; but it is independent of the position of the pipe, as horizontal, 
 or inclined upwards or downwards. 
 
 The head, instead of being an actual distance between levels, may be 
 caused by pressure, as by a pump, in which case the head is calculated 
 as a vertical distance corresponding to the pressure, 1 Ib. per sq. in. 
 = 2.309 ft. head, or 1 ft. head = 0.433 Ib. per sq. in. 
 
 The total head operating to cause flow is divided into three parts: 
 
 1. The velocity-head, which is the height through which a body must 
 fall in vacuo to acquire the velocity with which the water flows into the 
 pipe = v z -f- 2 g, in which v is the velocity in ft. per sec. and 2 g = 64.32; 
 
 2. the entry-head, that required to overcome the resistance to entrance 
 to the pipe. With sharp-edged entrance the entry-head = about 1/2 the 
 velocity-head; with smooth rounded entrance the entry-head is inap- 
 preciable; 3. the friction-head, due to the frictional resistance to flow 
 within the pipe. 
 
 In ordinary cases of pipes of considerable length the sum of the entry 
 and velocity heads required scarcely exceeds 1 foot. In the case of 
 long pipes with low heads the sum of the velocity and entry heads is 
 generally so small that it may be neglected. 
 
 General Formula for Flow of Water in Pipes or Conduits. 
 
 Mean velocity in ft. per sec. = c v'mean hydraulic radius X slope 
 
 Do. for pipes running full - c y dlameter x slope, 
 
 in which c is a coefficient determined by experiment. (See pages following.) 
 
 area of wet cross-section 
 
 The mean hydraulic- radius 
 
 wet perimeter 
 
 In pipes running full, or exactly half full, and in semicircular open 
 channels, running full it is equal to 1/4 diameter. 
 
 The slope = the head (or pressure expressed as a head, in feet) 
 
 * length of pipe measured in a straight line from end to end. 
 
 In open channels the slope is the actual slope of the surface, or its 
 fall per unit of length, or the sine of the angle of the slope with the horizon. 
 
 Chezy's Formula: v = c *^r V = c ^rs; r = mean hydraulic 
 idius, s = slope = ' * * 
 dimensions in feet. 
 
 radius, s = slope = head -s- length, v = velocity in feet per second, all 
 -'--i fee" 
 
 Quantity of Water Discharged. If Q discharge in cubic feet 
 per second and a = area of channel, Q = av = ac v'rs. 
 
 mu 
 and 
 one completely filled. 
 
 Values of the Coefficient c. (Chiefly condensed from P. J. Flynn 
 in Flow of Water.) Almost all the old hydraulic formulae for finding the 
 
HYDRAULIC FORMULAE. 
 
 729 
 
 mean velocity in open and closed channels have constant coefficients, 
 and are therefore correct for only a small range of channels. They 
 have often been found to give incorrect results with disastrous effects. 
 Ganguillet and Kutter thoroughly investigated the American, French, 
 and other experiments, and they gave as the result of their labors the 
 formula now generally known as Kutter's formula. There are so many 
 varying conditions affecting the flow of water, that all hydraulic for- 
 mulae are only approximations to the correct result. 
 
 When the surface-slope measurement is good, Kutter's formula will 
 give results seldom exceeding 71/2% error, provided the rugosity co- 
 efficient of the formula is known for the site. For small open channels 
 Darcy's and Bazin's formulae, and for cast-iron pipes Darcy's formulas, 
 are generally accepted as being approximately correct. 
 
 Table giving Fall in Feet per Mile, the Distance on Slope corresponding 
 to 1 Ft. Fall, the Fall in 1000 Ft., the Equivalent Loss in Pressure 
 in Pipes per 1000_Ft. Length; also Values of VTfor Use in the 
 Formula v = c \/rs~. ' 
 
 s = H -5- L = sine of angle of slope = fall of water surface (Jf) 
 in any distance (L) divided by that distance. 
 
 
 
 
 Loss of 
 
 
 
 
 
 Loss of 
 
 
 Fall 
 
 
 Slope, 
 
 Pres- 
 
 
 Fall 
 
 
 Slope, 
 
 Pres- 
 
 
 in 
 Feet 
 per 
 
 S,0 F pe, 
 In 
 
 Feet 
 per 
 1000. 
 
 sure per 
 1000 
 Feet. 
 
 VT 
 
 in 
 Feet 
 per 
 
 Slope, 
 IFt. 
 In 
 
 Feet 
 1000. 
 
 sure per 
 1000 
 Feet. 
 
 vT 
 
 Mile. 
 
 
 
 Lb. per 
 
 
 Mile. 
 
 
 
 Lb. per 
 
 
 
 
 
 sq. in. 
 
 
 
 
 
 sq. in. 
 
 
 0.25 
 
 21120ft. 
 
 0.0473 
 
 0.02048 
 
 0.00688 
 
 20 
 
 264 ft. 
 
 3.7879 
 
 1.640 
 
 0.06155 
 
 .30 
 
 17600 
 
 .0568 
 
 .02459 
 
 .00754 
 
 21.12 
 
 250 
 
 4.0000 
 
 1.732 
 
 .06325 
 
 .40 
 
 13200 
 
 .0758 
 
 .03282 
 
 .00870 
 
 22 
 
 1240 
 
 4.1667 
 
 1.804 
 
 .06455 
 
 .50 
 
 10560 
 
 .0947 
 
 .04101 
 
 .00973 
 
 24 
 
 220 
 
 4.5455 
 
 1.968 
 
 .06742 
 
 .60 
 
 8800 
 
 .1136 
 
 .04919 
 
 .01066 
 
 26.4 
 
 200 
 
 5.0000 
 
 2.165 
 
 .07071 
 
 .80 
 
 6600 
 
 .1515 
 
 .06560 
 
 .01231 
 
 28 
 
 188.6 
 
 5.3030 
 
 2.296 
 
 .07282 
 
 1 
 
 5280 
 
 .1894 
 
 .08201 
 
 .01376 
 
 31.68 
 
 166.7 
 
 6.0000 
 
 2.598 
 
 .07746 
 
 1.056 
 
 5000 
 
 .2000 
 
 .08660 
 
 .01414 
 
 35.20 
 
 150 
 
 6.6667 
 
 2.887 
 
 .08165 
 
 1.25 
 
 4224 
 
 .2367 
 
 .1025 
 
 .01539 
 
 42.24 
 
 125 
 
 8.0000 
 
 3.464 
 
 .08944 
 
 1.5 
 
 3520 
 
 .2841 
 
 .1230 
 
 .01685 
 
 44 
 
 120 
 
 8.3333 
 
 3.608 
 
 .09129 
 
 1.75 
 
 3017 
 
 .3314 
 
 .1435 
 
 .01821 
 
 48 
 
 110 
 
 9.0909 
 
 3.936 
 
 .09535 
 
 2 
 
 2640 
 
 .3788 
 
 .1640 
 
 .01946 
 
 52.8 
 
 100 . 
 
 10.000 
 
 4.330 
 
 .10000 
 
 2.5 
 
 2112 
 
 .4735 
 
 .2050 
 
 .02176 
 
 60 
 
 88 
 
 11.364 
 
 4.913 
 
 .10660 
 
 2.64 
 
 2000 
 
 .5000 
 
 .2165 
 
 .02236 
 
 63.36 
 
 83.3 
 
 12.000 
 
 5.196 
 
 .10954 
 
 3 
 
 1760 
 
 .5632 
 
 .2460 
 
 .02384 
 
 66 
 
 83 
 
 12.500 
 
 5.413 
 
 .11180 
 
 3.5 
 
 1508 
 
 .6631 
 
 .2871 
 
 .02575 
 
 70.4 
 
 75 
 
 13.333 
 
 5.773 
 
 .11547 
 
 4 
 
 1320 
 
 .7576 
 
 .3280 
 
 .02752 
 
 79.20 
 
 66.7 
 
 15.000 
 
 6.495 
 
 .12247 
 
 5 
 
 1056 
 
 .9470 
 
 .4101 
 
 .03077 
 
 88 
 
 60 
 
 16.667 
 
 7.217 
 
 .12910 
 
 5.28 
 
 1000 
 
 .0000 
 
 .4330 
 
 .03162 
 
 105.6 
 
 50 
 
 20.000 
 
 8.660 
 
 .14142 
 
 6 
 
 880 
 
 .1364 
 
 .4921 
 
 .03371 
 
 120 
 
 44 
 
 22.727 
 
 9.841 
 
 .15076 
 
 7 
 
 754.3 
 
 .3257 
 
 .5740 
 
 .03642 
 
 132 
 
 40 
 
 25.000 
 
 10.83 
 
 .15811 
 
 8 
 
 660 
 
 .5152 
 
 .6561 
 
 .03893 
 
 160 
 
 33 
 
 30.303 
 
 13.12 
 
 .17408 
 
 9 
 
 586.6 
 
 .7044 
 
 .7380 
 
 .04129 
 
 220 
 
 24 
 
 41.667 
 
 18.04 
 
 .20412 
 
 10 
 
 528 
 
 .8939 
 
 .8201 
 
 .04352 
 
 264 
 
 20 
 
 50.000 
 
 21.65 
 
 .22361 
 
 10.56 
 
 500 
 
 2.0000 
 
 .8660 
 
 .04472 
 
 330 
 
 16 
 
 62.500 
 
 27.06 
 
 .25000 
 
 12 
 
 440 
 
 2.2727 
 
 .9841 
 
 .04767 
 
 440 
 
 12 
 
 83.333 
 
 36.08 
 
 .28868 
 
 13 
 
 406.1 
 
 2.4621 
 
 1.066 
 
 .04962 
 
 528 
 
 10 
 
 100.00 
 
 43.30 
 
 .31623 
 
 14 
 
 377.1 
 
 2.6515 
 
 1.148 
 
 .05149 
 
 660 
 
 8 
 
 125.00 
 
 54.13 
 
 .35355 
 
 15 
 
 352 
 
 2.8409 
 
 1.230 
 
 .05330 
 
 880 
 
 6 
 
 166.67 
 
 72.17 
 
 .40825 
 
 16 
 
 330 
 
 3.0303 
 
 1.312 
 
 .05505 
 
 1056 
 
 5 
 
 200 
 
 86.60 
 
 .44721 
 
 18 
 
 293.3 
 
 3.4091 
 
 1.476 
 
 .05839 
 
 1320 
 
 4 
 
 250 
 
 108.25 
 
 .50000 
 
730 
 
 HYDRAULICS. 
 
 Values of Vr" for Circular Pipes, Sewers, and Conduits of Different 
 Diameters. 
 
 r = mean hydraulic depth = 
 funning full or exactly half full. 
 
 p^Hmeter 
 
 = 1/4 diam * for circular 
 
 Diam., 
 ft. in. 
 
 V7 
 
 In Feet. 
 
 Diam., 
 ft. in. 
 
 Vr 
 in Feet. 
 
 Diam., 
 ft. in. 
 
 V7 
 
 in Feet. 
 
 Diam., 
 ft. in. 
 
 v; 
 
 in Feet. 
 
 3/8 
 
 0.088 
 
 2 
 
 0.707 
 
 4 6 
 
 .061 
 
 9 
 
 .500 
 
 1/2 
 
 .102 
 
 2 1 
 
 .722 
 
 4 7 
 
 .070 
 
 9 3 
 
 .521 
 
 3/4 
 
 .125 
 
 2 2 
 
 .736 
 
 4 8 
 
 .080 
 
 9 6 
 
 .541 
 
 1 
 
 .144 
 
 2 3 
 
 .750 
 
 4 9 
 
 .089 
 
 9 9 
 
 .561 
 
 H/4 
 
 .161 
 
 2 4 
 
 .764 
 
 4 10 
 
 .099 
 
 10 
 
 .581 
 
 U/2 
 
 .177 
 
 2 5 
 
 .777 
 
 4 11 
 
 .109 
 
 10 3 
 
 .601 
 
 13/4 
 
 .191 
 
 2 6 
 
 .790 
 
 5 
 
 .118 
 
 10 6 
 
 .620 
 
 2 
 
 .204 
 
 2 7 
 
 .804 
 
 5 1 
 
 .127 
 
 10 9 
 
 .639 
 
 21/2 
 
 .228 
 
 2 8 
 
 .817 
 
 5 2 
 
 .137 
 
 11 
 
 .658 
 
 3 
 
 .251 
 
 2 9 
 
 .829 
 
 5 3 
 
 .146 
 
 11 3 
 
 .677 
 
 4 
 
 .290 
 
 2 10 
 
 .842 
 
 5 4 
 
 .155 
 
 11 6 
 
 .696 
 
 5 
 
 .323 
 
 2 11 
 
 .854 
 
 5 5 
 
 .164 
 
 11 9 
 
 .714 
 
 6 
 
 .354 
 
 3 
 
 .866 
 
 5 6 
 
 .173 
 
 12 
 
 .732 
 
 7 
 
 .382 
 
 3 1 
 
 .878 
 
 5 7 
 
 .181 
 
 12 3 
 
 .750 
 
 8 
 
 .408 
 
 3 2 
 
 .890 
 
 5 8 
 
 .190 
 
 12 6 
 
 .768 
 
 9 
 
 .433 
 
 3 3 
 
 .901 
 
 5 9 
 
 .199 
 
 12 9 
 
 .785 
 
 10 
 
 .456 
 
 3 4 
 
 .913 
 
 5 10 
 
 .208 
 
 13 
 
 ,803 
 
 11 
 
 .479 
 
 3 5 
 
 .924 
 
 5 11 
 
 .216 
 
 13 3 
 
 .820 
 
 
 .500 
 
 3 6 
 
 .935 
 
 6 
 
 .225 
 
 13 6 
 
 .837 
 
 | 
 
 .520 
 
 3 7 
 
 .946 
 
 6 3 
 
 .250 
 
 14 
 
 .871 
 
 2 
 
 .540 
 
 3 8 
 
 .957 
 
 6 6 
 
 .275 
 
 14 6 
 
 .904 
 
 3 
 
 .559 
 
 3 9 
 
 .968 
 
 6 9 
 
 .299 
 
 15 
 
 .936 
 
 4 
 
 .577 
 
 3 10 
 
 .979 
 
 7 
 
 .323 
 
 15 6 
 
 .968 
 
 5 
 
 .595 
 
 3 11 
 
 .990 
 
 7 3 
 
 .346 
 
 16 
 
 2. 
 
 6 
 
 .612 
 
 4 
 
 
 7 6 
 
 .369 
 
 16 6 
 
 2 031 
 
 7 
 
 .629 
 
 4 1 
 
 !oio 
 
 7 9 
 
 .392 
 
 17 
 
 2.061 
 
 8 
 
 .646 
 
 4 2 
 
 .021 
 
 8 
 
 .414 
 
 17 6 
 
 2.091 
 
 9 
 
 .661 
 
 4 3 
 
 .031 
 
 8 3 
 
 .436 
 
 18 
 
 2.121 
 
 1 10 
 
 .677 
 
 4 4 
 
 .041 
 
 8 6 
 
 .458 
 
 19 
 
 2.180 
 
 1 11 
 
 .692 
 
 4 5 
 
 .051 
 
 8 9 
 
 .479 
 
 20 
 
 2.236 
 
 Kutter's Formula for measures in feet is 
 
 1.811 
 
 + 41.6 + 
 
 0.00281 
 
 1+ ( 41 . 6+ M0281) X 
 \ S / Vi 
 
 a 
 
 in which v = mean velocity in feet per second ; r = - = hydraulic mean 
 
 depth in feet = area of cross-section in square feet divided by wetted 
 perimeter in lineal feet ; s = fall of water-surface (/i) in any distance (I) 
 
 divided by that distance, = r = sine of slope; n = the coefficient of 
 
 rugosity, depending on the nature of the lining or surface of the channel. 
 If we let the first term of the right-hand side of the equation equal c, we 
 have Chezy's formula, v c vVs = c X ^/rX Vs. 
 
 Values of n in Kutter's Formula. The accuracy of Kutter's for- 
 mula depends, in a great measure, on the proper selection of the coefficient 
 
HYDRAULIC FORMULAE. 731 
 
 of roughness n. Experience is required in order to give the right value to 
 this coefficient, and to this end great assistance can be obtained, in making 
 this selection, by consulting and comparing the results obtained from 
 experiments on the flow of water already made in different channels. 
 
 In some cases it would be well to provide for the contingency of future 
 deterioration of channel, by selecting a high value of rc, as, for instance, 
 where a dense growth of weeds is likely to occur in small channels, and 
 also where channels are likely not to be kept in a state of good repair. 
 
 The following table, giving the value of n for different materials, is 
 compiled from Kutter, Jackson, and Hering, and this value of n applies 
 also in each instance to the surfaces of other materials equally rough. 
 
 VALUE OP n IN KUTTER'S FORMULA FOR DIFFERENT CHANNELS. 
 
 n .009, well-planed timber, in perfect order and alignment; otherwise, 
 perhaps .01 would be suitable. 
 
 n = .010, plaster in pure cement; planed timber; glazed, coated, or 
 enameled stoneware and iron pipes; glazed surfaces of every sort in 
 perfect order. 
 
 n = .011, plaster in cement with one-third sand, in good condition; 
 also for iron, cement, and terra-cotta pipes, well joined, and in best order. 
 
 n = .012, unplaned timber, when perfectly continuous on the inside; 
 flumes. 
 
 n = .013, ashlar and well-laid brickwork; ordinary metal; earthen and 
 stoneware pipe in good condition, but not new; cement and terra-cotta 
 pipe not well jointed nor in perfect order, plaster and planed wood in 
 imperfect or inferior condition; and, generally, the materials mentioned 
 with n = .010, when in imperfect or inferior condition. 
 
 n = .015, second class or rough-faced brickwork; well-dressed stone- 
 work; foul and slightly tuberculated iron; cement and terra-cotta pipes, 
 with imperfect joints and in bad order; and canvas lining on wooden 
 frames. 
 
 n .017, brickwork, ashlar, and stoneware in an inferior condition; 
 tuberculated iron pipes; rubble in cement or plaster in good order; tine 
 gravel, well rammed, Vs to 2/3 inch diameter; and, generally, the materials 
 mentioned with n = .013 when in bad order and condition. 
 
 n = .020, rubble in cement in an inferior condition; coarse rubble, 
 rough set in a normal condition; coarse rubble set dry: ruined brickwork 
 and masonry; coarse gravel well rammed, from 1 to 11/3 inch diameter; 
 canals with beds and banks of very firm, regular gravel, carefully trimmed 
 and rammed in defective places; rough rubble with bed*partially covered 
 with silt and mud; rectangular wooden troughs with battens on the 
 inside two inches apart; trimmed earth in perfect order. 
 
 n = .0225, canals in earth above the average in order and regimen. 
 
 n = .025, canals and rivers in earth of tolerably uniform cross-section; 
 slope and direction, in moderately good order and regimen, and free from 
 stones and weeds. 
 
 n = .0275, canals and rivers in earth below the average in order and 
 regimen. 
 
 n = .030, canals and rivers in earth in rather bad order and regimen, 
 having stones and weeds occasionally, and obstructed by detritus. 
 
 n = .035, suitable for rivers and canals with earthen beds in bad order 
 and regimen, and having stones and weeds in great quantities. 
 
 n = .05, torrents encumbered with detritus. 
 
 Kutter's formula has the advantage of being easily adapted to a change 
 in the surface of the pipe exposed to the flow of water, by a change in 
 the value of n. For cast-iron pipes it is usual to use n = .013 to provide 
 for the future deterioration of the surface. _ __ 
 
 Reducing Kutter's formula to the form v = c X **r X ^s, and taking 
 n, the coefficient of roughness in the formula, = .011, .012, and .013, and 
 a = .001, we have the following values of the coefficient c of different 
 diameters of conduit. 
 
732 
 
 HYDRAULICS. 
 
 Values of c in Formula * = e X vVx ^s~toT Metal Pipes and 
 Moderately Smooth Conduits Generally. 
 
 By KUTTER'S FORMULA, (s =0.001 or greater.) 
 
 Diameter. 
 
 n = .OI1 
 
 n=.0l2 
 
 n = .013 
 
 Diameter. 
 
 n = .011 
 
 n = .0)2 
 
 n =.013 
 
 ft. in. 
 
 c = 
 
 c = 
 
 c = 
 
 ft. 
 
 c = 
 
 c = 
 
 c = 
 
 6 
 
 87.4 
 
 77.5 
 
 69.5 
 
 8 
 
 155.4 
 
 141.9 
 
 130.4 
 
 1 
 
 105.7 
 
 94.6 
 
 85.3 
 
 9 
 
 157.7 
 
 144.1 
 
 132.7 
 
 1 6 
 
 116.1 
 
 104.3 
 
 94.4 
 
 10 
 
 159.7 
 
 146 
 
 134.5 
 
 2 
 
 123.6 
 
 111.3 
 
 101.1 
 
 11 
 
 161.5 
 
 147.8 
 
 136.2 
 
 3 
 
 133.6 
 
 120.8 
 
 110.1 
 
 12 
 
 163 
 
 149.3 
 
 137.7 
 
 4 
 
 140.4 
 
 127.4 
 
 116.5 
 
 14 
 
 165.8 
 
 152 
 
 140.4 
 
 5 
 
 145.4 
 
 132.3 
 
 121.1 
 
 16 
 
 168 
 
 154.2 
 
 142.1 
 
 6 
 
 149.4 
 
 136.1 
 
 124.8 
 
 18 
 
 169.9 
 
 156.1 
 
 144.4 
 
 7 
 
 152.7 
 
 139.2 
 
 127.9 
 
 20 
 
 171.6 
 
 157.7 
 
 146 
 
 For circular pipes the hydraulic mean depth r equals 1/4 of the 
 diameter. 
 
 According to Kutter's formula the value of c, the coefficient of 
 discharge, is the same for all slopes greater than 1 in 1000. At a 
 slope of 1 in 5000 the value of c is slightly lower, and it further 
 decreases as the slope becomes flatter. 
 
 The reliability of the values of the coefficient of Kutter's formula for 
 pipes of less than 6 in. diameter is considered doubtful. 
 
 Values of c ror Earthen Channels, by Kutter's Formula, for Use 
 in Formula v = c vV*. 
 
 
 Coefficient of Roughness, 
 
 Coefficient of Roughness, 
 
 
 n=.0225. 
 
 n=.035. 
 
 
 >/r in feet. 
 
 V^ in feet. 
 
 
 0.4 
 
 1.0 
 
 1.8 
 
 2.5 
 
 4.0 
 
 0.4 
 
 1 .0 
 
 1.8 
 
 2.5 I 4.0 
 
 Slope, 1 in 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 c 
 
 1,000 
 
 35.7 
 
 62.5 
 
 80.3 
 
 89.2 
 
 99.9 
 
 19.7 
 
 37.6 
 
 51.6 
 
 59.3 
 
 69 2 
 
 1,250 
 
 35.5 
 
 62.3 
 
 80.3 
 
 89.3 
 
 100.2 
 
 19.6 
 
 37.6 
 
 51.6 
 
 59.4 
 
 69 4 
 
 1,667 
 
 35.2 
 
 62.1 
 
 80.3 
 
 89.5 
 
 100.6 
 
 19.4 
 
 37.4 
 
 51.6 
 
 59.5 
 
 69 8 
 
 2,500 
 
 34.6 
 
 61.7 
 
 80.3 
 
 89.8 
 
 101.4 
 
 19.1 
 
 37.1 
 
 51.6 
 
 59.7 
 
 70 4 
 
 3333 
 
 34. 
 
 61.2 
 
 80.3 
 
 90.1 
 
 102.2 
 
 18.8 
 
 36.9 
 
 51.6 
 
 59.9 
 
 71.0 
 
 5,000 
 
 33. 
 
 60.5 
 
 80.3 
 
 90.7 
 
 103.7 
 
 18.3 
 
 36.4 
 
 51.6 
 
 60.4 
 
 7? ? 
 
 7,500 
 
 31.6 
 
 59.4 
 
 80.3 
 
 91.5 
 
 106.0 
 
 17.6 
 
 35.8 
 
 51.6 
 
 60.9 
 
 73 9 
 
 10,000 
 
 30.5 
 
 58.5 
 
 80.3 
 
 92.3 
 
 107.9 
 
 17.1 
 
 35.3 
 
 51.6 
 
 60.5 
 
 75 4 
 
 15,840 
 
 28.5 
 
 56.7 
 
 80.2 
 
 93.9 
 
 112.2 
 
 16.2 
 
 34.3 
 
 51.6 
 
 62.5 
 
 78 6 
 
 20,000 
 
 27.4 
 
 55.7 
 
 80.2 
 
 94.8 
 
 115.0 
 
 15.6 
 
 33.8 
 
 51.5 
 
 63.1 
 
 80.6 
 
 Darcy's Formula for clean iron pipes under pressure is 
 
 rs ) 1/2 
 
 v= ) ' , , 0.00000162 
 
 0.00007726 + 
 
 According to Unwin and other authors Darcy's experiments are 
 represented approximately by the formula 
 
 in which/, called the "coefficient of friction," =0.006 I 1 +~[2d ) ' ^ 
 
 being the loss of head, I the length of the pipe, h/l the slope s, and 
 d/4 the mean hydraulic radius r, of the Chezy formula. All the dimen- 
 sions are in feet. 
 
 Darcy's formula, as given by J. B. Francis, for old cast-iron pipe, 
 lined with deposit and under pressure is 
 
 / 144d 2 s \l/2 
 
 =1 . . . . I . 
 
 in which d 
 
 V0,00082(12f+l)/ 
 
 = diameter in feet. 
 
HYDRAULIC FORMULA. 
 
 733 
 
 .s 
 
 d 
 
 i 
 
 E . 
 
 P^ 
 
 ffi 
 
 t fno* CO c 
 
 or^sO^ o 
 
 ~ 
 
 O O o o O o O O ' ' ' ~ ' < 
 
 ~ 
 
 500 r 
 
 
 ~ * 
 
 8OOOO (NC^ro, 
 OOOOOOOOO 
 
 -o^rris 
 OON^O'OO^<^rOOvO<N<NQ^I s N '^J-O'^-^ 
 
 
 
 
 i fS 
 
 50000 r 
 
 qqq 
 2606 
 
734 
 
 HYDRAULICS. 
 
 The relation of the value of c in Chezy's formula V 
 value of the coefficient of friction /is c 
 
 to the 
 
 
 / = 
 
 .0035 
 
 .0040 
 
 
 .0045 
 
 .0050 
 
 .0055 
 
 .0060 
 
 
 .0065 
 
 
 
 135.5 
 
 127.8 
 
 
 119.6 
 
 113.4 
 
 108.1 
 
 , 103.5 
 
 
 99.4 
 
 
 / = 
 
 .0070 
 
 .0075 
 
 
 .0080 
 
 .0090 
 
 .010 
 
 .011 
 
 
 .012 
 
 
 C = 
 
 95.8 
 
 92.6 
 
 
 89.7 
 
 84.5 
 
 80.2 
 
 76.5 
 
 
 73.2 
 
 c = 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 / 7r 
 
 .018 
 
 ,^, T ;^ 
 
 .013 
 
 rl K*~l-r-r^r 
 
 .010 . 
 
 * -4-V,^ -P^l 
 
 008 .0064 
 
 .0053 
 
 .0045 
 
 ^^ 4.V, 1 
 
 .0038 . 
 
 0033 .002 
 
 . . _____ ._ ._ ., 
 
 Unwin derives the following equations from the Darcy formula: 
 
 Velocity, ft. per sec ...... v = 4.012 ^dh/(fl) = 1.273 _/d2= c 
 
 Diameter, ft ............. d= Q.QG22fvl/h = 1.128 ^Q/v. 
 
 Quantity, cu. ft. per sec. Q= 3.149 ^/htf/fl. 
 Head, ft ................. h = O.WQ8fQH/d&. 
 
 Rough preliminary calculations may be made by the following approx- 
 imate formulae. They are least accurate for small pipes, s = slope, = h/l. 
 New and clean pipes. Old and incrusted pipes. 
 
 v = 56 
 Q = 44 rfss. Q = 31.4 
 
 d = 0. 
 
 d = 0. 
 
 Weisbach gives/ =0.00644, which Unwin says is possibly too small 
 for tubes of small bore, and he gives/ =0.006 to 0.01 for 4-in. tubes 
 and/ =0.0084 to 0.012 for 2-in. tubes. Another formula by Weisbach is 
 
 , 0.01716W j?2 
 }d 2g 
 
 William Cox (Amer. Mach., Dec. 28, 1893) gives a simpler formula 
 which gives almost identical results: 
 
 h= (0.0144 +- 
 
 H = friction-head in feet = -v- - 
 d 
 
 4V 2 _j_ 5V_ 2 
 
 (!) 
 
 V in 
 
 (2) 
 feet 
 
 Hd : 
 L 1200 
 
 In this formula H and L are in feet, d in inches, and 
 per second. 
 
 Values of the Coefficient of Friction. Un win's "Hydraulics" gives 
 values of/, based on Darcy 's experiments, as follows: Clean and smooth 
 pipes, /= 0.005 [1 + l/(12d)]. Incrusted pipes, /= O.Oiqi + l/(12d)]. 
 In 1886 Unwin examined all the more carefully made experiments on 
 flow in pipes, including those of Darcy, classifying them according to 
 the quality and condition of their surfaces, and showing the relation 
 of the value of / to both diameter and velocity. The results agree 
 fairly closely with the following values, /= a (1 + P/d). (d is in feet.) 
 
 Kind of Pipe. 
 
 Values of a for Velocities in ft. per Second. 
 
 Values 
 of /3 
 
 Drawn wought iron 
 Asphalted cast iron 
 Clean cast iron 
 Incrusted cast iron at all ^ 
 
 1-2 
 .00375 
 .00492 
 .00405 
 velocities a 
 
 2-3 
 
 .00322 
 .00455 
 .00395 
 = 0.0085* 
 
 3-4 
 .00297 
 .00432 
 .00387 
 
 4-5 
 .00275 
 .00415 
 .00382 
 
 0.37 
 0.20 
 0.28 
 0.26 
 
 From the experiments of Clemens Herschel, 1892-6, on clean steel 
 
 riveted pipes, Unwin derives the following values of / for different 
 velocities. 
 
 2 34 5 6 
 
 OOGO .0057 .0055 .0055 .0055 
 
 0058 .0054 .0054 .0054 .0054 
 
 .0071 .0060 .0053 .0047 .0042 
 
 Ft. per sec 1 
 
 48-in. pipe, av. of 2 0066 
 
 42-in. pipe, av. of 2 0067 
 
 36-in. pipe 0087 
 
 Unwin attributes the anomalies in this table to errors of observation. 
 In comparing the results with those on cast-iron pipes, the roughness of 
 the rivet heads and joints must be considered, and the resistance can 
 only be determined by direct experiment on riveted pipes. 
 
HYDRAULIC FORMULA. 
 
 735 
 
 Two portions of the 48-in. main were tested after being four years in 
 i use, and the coefficients derived from them differ remarkably. 
 
 Ft. per sec 1 2 3 4 5 6 
 
 Upper part 0106 .0080 .0075 .0073 .0072 .0072 
 
 Lower part 0068 .0060 .0058 .0060 .0060 .0060 
 
 Marx, Wing, and Hopkins in 1897 and 1899 made gaugings on a 6-ft. 
 main, part of which was of riveted steel and part of wood staves. (Trans. 
 A. S. C. E., xl, 471, and xliv, 34.) From these tests Unwin derives the 
 following values of/. 
 
 Ft. per sec. 1 1.5 2 2.5 3 4 5 5.5 
 
 Steel pipe: 
 
 1897... / = .0053 .0052 .0053 .0055 .0055 .0052 
 
 1899... /== .0097 .0076 .0067 .0063 .0061 .0060 .0058 .0058 
 
 Wood staves: 
 
 1897. ../= .0064 .0053 .0048 ...... .0043 .0041 ... 
 
 1899.. ./= .0048 .0046 .0045 0044 .0043 .0043 .0043 
 
 Freeman's experiments on fire hose pipes (Trans. A. S. C. Ef, xxi, 303) 
 give the following values of/. 
 
 Velocity, ft. per sec 4 6 10 15 20 
 
 Unlined canvas 0095 .0095 .0093 .0088 .0085 
 
 Rough rubber-lined cotton 0078 .0078 .0078 .0075 .0073 
 
 Smooth rubber-lined cotton 0060 .0058 .0055 .0048 .0045 
 
 The Resistance at the Inlet of a Pipe is equal to the frictional resist- 
 ance of a straight pipe whose length is 1 = (1 +/o) d * 4 /. Values of / are: 
 (A) for end of pipe flush with reservoir wall, 0.5; (B) pipe entering wall, 
 straight edges, 0.56; (C) pipe entering wall, sharp edges, 1.30; (D) bell- 
 mouthed inlet, 0.02 to 0.05. Values of l Q /d are for 
 
 /= 0.005 4,53 ,75 C, 78 D, 115 
 
 0.010 26 38 39 58 
 
 Multiplying these figures by d gives the length of straight pipe to be 
 added to the actual length to allow for the inlet resistance. In long 
 lengths of pipe the relative value of this length is so small that it may be 
 neglected in practical calculations. (Unwin.) 
 
 Loss of Head in Pipe by Friction. Loss of head by friction in 
 each 100 feet in length of riveted pipe when discharging the following 
 quantities of water per minute (Pelton Water-wheel Co.). 
 
 V = velocity in feet per second; h = loss of head in feet; Q = dis- 
 charge in cubic feet per minute. 
 
 Inside Diameter of Pipe in Inches. 
 
 V 
 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 h \ Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 0.338 
 0.698 
 1.175 
 1.76 
 
 2.46 
 3.26 
 
 32.0 
 48.1 
 64.1 
 80.2 
 96.2 
 112.0 
 
 0.296 
 0.611 
 1.027 
 1.54 
 2.15 
 2.85 
 
 41.9 
 
 62.8 
 83.7 
 105 
 125 
 146 
 
 0.264 
 0.544 
 0.913 
 1.37 
 1.92 
 2.52 
 
 53 
 79.5 
 
 106 
 132 
 159 
 185 
 
 0.237 
 
 0.488 
 0.822 
 1.23 
 1.71 
 2.28 
 
 65.4 
 98.2 
 131 
 163 
 196 
 229 
 
 0.216 
 0.444 
 0.747 
 1.122 
 1.56 
 2.07 
 
 79.2 
 119 
 158 
 198 
 237 
 277 
 
 0.198 
 0.407 
 0.685 
 1.028 
 1.43 
 1.91 
 
 94.2 
 141 
 188 
 235 
 283 
 330 
 
 V 
 
 13 in. 
 
 14 in. 
 
 15 in. 
 
 16 in. 
 
 18 in. 
 
 20 in. 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 167 
 251 
 335 
 419 
 502 
 586 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 
 0.183 
 .375 
 .632 
 .949 
 1.325 
 1.75 
 
 110 
 166 
 221 
 276 
 332 
 387 
 
 0.169 
 .349 
 .587 
 .881 
 1.229 
 1.63 
 
 128 
 192 
 256 
 321 
 385 
 449 
 
 0.158 
 .325 
 .548 
 .822 
 1.H8 
 1.52 
 
 147 
 221 
 294 
 368 
 442 
 515 
 
 0.147 
 .306 
 .513 
 .770 
 1.076 
 1.43 
 
 0.132 
 .271 
 .456 
 .685 
 .957 
 1.27 
 
 212 
 318 
 424 
 530 
 636 
 742 
 
 0.119 
 .245 
 .410 
 .617 
 .861 
 1.143 
 
 262 
 393 
 523 
 654 
 785 
 916 
 
736 
 
 HYDRAULICS. 
 
 Loss of Head (Continued). 
 
 
 Diameter of Pipe in Inches. 
 
 22 in. 
 
 24 in. 
 
 26 in. 
 
 28 in. 
 
 30 in. 
 
 36 in. 
 
 V 
 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 848 
 1273 
 1697 
 2121 
 
 2545 
 2868 
 
 0.108 
 .222 
 .373 
 .561 
 .782 
 1.040 
 
 316 
 475 
 633 
 792 
 950 
 1109 
 
 0.098 
 .204 
 .342 
 .513 
 .717 
 .953 
 
 377 
 565 
 754 
 942 
 1131 
 1319 
 
 0.091 
 .188 
 .315 
 .474 
 .662 
 .879 
 
 442 
 663 
 885 
 1106 
 1327 
 1548 
 
 0.084 
 .174 
 .293 
 .440 
 .615 
 .817 
 
 513 
 770 
 1026 
 1283 
 1539 
 1796 
 
 0.079 
 .163 
 .273 
 .411 
 .574 
 .762 
 
 589 
 883 
 1178 
 1472 
 1767 
 2061 
 
 0.066 
 .135 
 .228 
 .342 
 .479 
 .636 
 
 This table is based on Cox's reconstruction of Weisbach's formula, 
 using the denominator 1000 instead of 1200, to be on the safe side, allow- 
 ing 20% for the loss of head due to the laps and rivet-heads in the pipe. 
 
 EXAMPLE. Given 200 ft. head and 600 ft. of 11-inch pipe, carrying 
 119 cubic feet of water per minute. To find effective head: In right- 
 hand column, under 11-inch pipe, find 119 cubic ft.; opposite this will 
 be found the loss by friction in 100 ft. of length for this amount of water, 
 which is 0.444. Multiply this by the number of hundred feet of pipe, 
 which is 6, and we have 2.66 ft., which is the loss of head. Therefore 
 the effective head is 200 - 2.66 = 197.34. 
 
 EXPLANATION. The loss of head by friction in a pipe depends not 
 only upon diameter and length, but upon the quantity of water passed 
 through it. The head or pressure is what would be indicated by a 
 pressure-gauge attached to the pipe near the wheel. Readings of gauge 
 should be taken while the water is flowing from the nozzle. 
 
 To reduce heads in feet to pressure in pounds multiply by 0.433. Ta 
 reduce pounds pressure to feet multiply by 2.309. 
 
 Exponential Formulae. Williams and Hazen's Tables. From 
 Chezy's formula, v = c vVs, it would appear that the velocity varies as 
 the square root of the head, or that the head varies as the square of the 
 velocity; this is not true, however, for c is not a constant, but a variable, 
 depending on both r and s. Hazen and Williams, as a result of a study 
 of the best records of experiments and plotting them on logarithmic ruled 
 paper, found an exponential formula v = cr'W s' 54 , in which the coefficient 
 c is practically independent of the diameter and the slope, and varies only 
 with the condition of the surface. In order to equalize the numerical 
 value of c to that of the c in the Chezy formula, at a slope of 0.001, they 
 added the factor q.OOl-o-04 to the formula, so that the working formula 
 of Hazen and Williams is 
 
 v = cr - 63 s - 54 O.OOl-o- 04 = 1.318 crO- 63 s*&. 
 
 APPROXIMATE VALUES OF C IN THE HAZEN & WILLIAMS FORMULA. 
 (a) 140 for the very best cast-iron pipe, laid straight and when new; 
 for very smooth and clean masonry conduits; 
 for straight lead, copper, brass, tin, and glass pipes. 
 (6) 130 for good new cast-iron pipe, and other pipes under (a) when 
 not quite smooth.* 
 
 (c) 120 for cast-iron pipe 5 years old, for smooth new iron pipes, 
 
 smooth wooden stave pipes and ordinary masonry conduits. 
 
 (d) 110 for new riveted steel pipe, for vitrified pipe, and for cast-iron 
 
 pipe 10 years old. 
 
 (e) 100 for ordinary iron pipes, 14 to 20 years old, for riveted steel 
 
 pipe 10 years old, and for brick sewers. 
 (/) 80 for old iron pipes, and for very rough cast-iron pipes over 
 
 60 inches diameter. 
 (g) 60 down to 40, for very rough pipes, the lower figure for the 
 
 smaller diameters. 
 
 * 130 may also be used for straight lead, tin, and drawn copper pipes. 
 Computations of the exponential formula are made by logarithms, or by 
 the Hazen- Williams hydraulic slide rule. On logarithmic ruled paper 
 values of v for different values of c, r and s may be plotted in straight 
 lines. (See "Hydraulic Tables," by Williams and Hazen, John Wiley & 
 Sons.) 
 
FLOW OF WATER. 
 
 737 
 
 Values of Coefficient K for Reducing the Hazen and_Williams 
 Formula to the Style of Chezy's Formula v = c \/r \/s~ 
 
 Diam., 
 Ft.In. 
 
 Slope = Head -v- Length of Pipe. 
 
 0005 
 
 001 
 
 002 
 
 0.003 
 
 0.005 
 
 0.01 
 
 0.02 
 
 0.04 
 
 0.06 
 
 0.10 
 
 0.20 
 
 
 
 
 
 
 
 
 
 
 
 
 ri 2 
 
 2 
 4 
 8 
 12 
 2 
 
 8 
 12 
 16 
 20 
 
 5374 
 
 5525 
 
 5680 
 
 5773 
 
 0.5892 
 
 6058 
 
 6228 
 
 6403 
 
 6508 
 
 6642 
 
 6829 
 
 .5880 
 .6435 
 7042 
 
 .6046 
 .6616 
 7240 
 
 .6216 
 .6802 
 7443 
 
 .6317 
 .6913 
 .7565 
 
 .6448 
 .7056 
 .7721 
 
 .6629 
 .7254 
 .7938 
 
 .6815 
 .7458 
 8161 
 
 .7007 
 .7667 
 8390 
 
 .7122 
 .7793 
 8528 
 
 .7269 
 .7954 
 8704 
 
 .7473 
 .8177 
 8949 
 
 .7706 
 .8123 
 .8889 
 .9727 
 1.064 
 1.122 
 1.165 
 1.199 
 
 .7922 
 .8351 
 .9138 
 .000 
 .094 
 .154 
 .197 
 .233 
 
 .8145 
 .8586 
 .9395 
 .028 
 .125 
 .186 
 .231 
 .267 
 
 .8278 
 .8726 
 .9549 
 1.045 
 1.143 
 1.205 
 1.251 
 1.288 
 
 .8449 
 .8906 
 .9746 
 .067 
 .167 
 .230 
 .277 
 .315 
 
 .8686 
 .9157 
 .002 
 .096 
 .200 
 .265 
 .313 
 .352 
 
 .8931 
 .9414 
 .030 
 .127 
 .234 
 .300 
 .350 
 .390 
 
 .9182 
 .9679 
 .059 
 .159 
 .268 
 .337 
 .388 
 .429 
 
 .9332 
 .9837 
 .076 
 .178 
 .289 
 .359 
 .411 
 .452 
 
 .9525 
 .004 
 .099 
 .202 
 .316 
 .387 
 .440 
 1.482 
 
 .9792 
 .032 
 .130 
 .236 
 .353 
 .426 
 .480 
 .524 
 
 H. & W. Formula: V= 1.318 cr- 63 s- 54 = 
 
 Short Formulae. E. Sherman 
 
 0.50 
 
 Gould, 
 
 (T) ' a - 04 
 
 Eng. News, Sept. 6, 1900, 
 
 8 in. to 48 in. diam. 
 
 ( Rough, 
 ( Smooth, 
 
 v = 1> 
 ; v = 1.80 
 
 3 to 6 in, diam. 
 
 ( Rough, Q 2 =0.785 M*; v 
 
 1.1 
 
 t Smooth, Q z = 1 .57 M 5 ; v = 1 .6 
 FLOW OF WATER EXPERIMENTS AND TABLES. 
 
 The Flow of Water through New Cast-iron Pipe was measured by 
 S. Bent Russell, of the St. Louis, Mo., Water-works. The pipe was 12 
 inches in diameter, 1631 feet long, and laid on a uniform grade from 
 end to end. Under an average total head of 3.36 feet the flow was 
 43,200 cubic feet in seven hours; under an average head of 3.37 feet the 
 flow was the same; under an average total head of 3.41 feet the flow 
 was 46,700 cubic feet in 8 hours and 35 minutes. Making allowance for 
 loss of head due to entrance__and to curves, it was found that the value 
 of c in the formula v = c Vrs was from 88 to 93. (Eng'g Record, April 
 
 Flow of Water in a 20-inch Pipe 75,000 Feet Long. A com- 
 parison of experimental data with calculations by different formulae is 
 given by Chas. B. Brush, Trans. A. S. C. E., 1888. The pipe experi- 
 mented with was that supplying the city of Hoboken, N. J. 
 
 RESULTS OBTAINED BY THE HACKENSACK WATER Co., FROM 1882-1887, 
 IN PUMPING THROUGH A 20-iN. CAST-IRON MAIN 75,000 FEET LONG. 
 
 Pressure in Ibs. per sq. in. at pumping-station: 
 
 95 100 105 110 115 120 125 130 
 
 Total effective head in feet: 
 
 55 66 77 89 100 112 123 135 
 
 Discharge in U. S. gallons in 24 hours, 1 = 1000: 
 
 2,848 3,165 3,354 3,566 3,804 3,904 4,116 4,255 
 Theoretical discharge by Darcy's formula: 
 
 2,743 3,004 3,244 3,488 3,699 3,915 4,102 4,297 
 Actual velocity in main in feet per second: 
 
 2,00 2,24 2,36 2.52 2,63 2,70 2,92 3,00 
 
738 
 
 HYDRAULICS. 
 
 Flow of Water In Circular Pipes, Sewers, etc., Flowing Full. 
 Based on Kutter's Formula, with n - 0.013. 
 
 Discharge in cubic feet per second. 
 
 Diam- 
 eter. 
 
 Slope, or Head Divided by Length of Pipe. 
 
 1 in 40 
 
 1 in 70 1 in 100| 1 in 200| 1 in 300| 1 in 400| 1 in 500[ 1 in 600 
 
 5 in. 
 6 " 
 7 " 
 8 " 
 9 " 
 
 0.456 
 0.762 
 1.17 
 
 1.70 
 2.37 
 
 0.344 
 0.576 
 
 0.889 
 1.29 
 1.79 
 
 0.288 
 0.482 
 0.744 
 1.08 
 1.50 
 
 0.204 
 0.341 
 0.526 
 0.765 
 1.06 
 
 0.166 
 0.278 
 0.430 
 0.624 
 0.868 
 
 0.144 
 0.241 
 0.372 
 0.54 
 0.75 
 
 0.137 
 0.230 
 0.355 
 0.516 
 0.717 
 
 0.118 
 0.197 
 0.304 
 0.441 
 0.613 
 
 10 in. S 
 
 It " 
 12 " 
 13 " 
 14 " 
 
 1 in 60 
 2.59 
 3.39 
 4.32 
 5.38 
 6.60 
 
 1 in 80 
 2.24 
 2.94 
 3.74 
 4.66 
 5.72 
 
 1 in 100 
 2.01 
 2.63 
 3.35 
 4.16 
 5.15 
 
 1 in 200 
 1.42 
 1.86 
 2.37 
 2.95 
 3.62 
 
 1 in 300 
 1.16 
 1.52 
 1.93 
 2.40 
 2.95 
 
 1 in 400 
 1.00 
 1.31 
 1.67 
 2.08 
 2.57 
 
 1 in 500 
 0.90 
 1.17 
 1.5 
 1.86 
 2.29 
 
 1 in 600 
 0.82 
 1.07 
 1.37 
 1.70 
 2.09 
 
 s = 
 15 in. 
 16 " 
 
 18 " 
 20 " 
 22 " 
 
 1 in 100 
 6.18 
 7.38 
 10.2! 
 13.65 
 17.71 
 
 1 in 200 
 4.37 
 5.22 
 7.22 
 9.65 
 12.52 
 
 1 in 300 
 3.57 
 4.26 
 5.89 
 7.88 
 10.22 
 
 1 in 400 
 3.09 
 3.69 
 5.10 
 6.82 
 8.85 
 
 1 in 500 
 2.77 
 3.30 
 4.56 
 6.10 
 7.92 
 
 1 in 600 
 2.52 
 3.01 
 4.17 
 5.57 
 7.23 
 
 1 in 700 
 2.34 
 2.79 
 3.86 
 5.16 
 6.69 
 
 1 in 800 
 2.19 
 2.61 
 3.61 
 4.83 
 6.26 
 
 , s = 
 
 2ft. 
 2ft.2in. 
 2 " 4" 
 2 " 6 " 
 2 " 8 " 
 
 1 in 200 
 15.88 
 19.73 
 24.15 
 29.08 
 34.71 
 
 1 in 400 
 11.23 
 13.96 
 17.07 
 20.56 
 24.54 
 
 1 in 600 
 9.13 
 
 11.39 
 13.94 
 16.79 
 20.04 
 
 1 in 800 
 7.94 
 9.87 
 12.07 
 14.54 
 17.35 
 
 1 in 1000 
 7.10 
 8.82 
 10.80 
 13.00 
 15.52 
 
 1 in 1250 
 6.35 
 7.89 
 9.66 
 11.63 
 13.88 
 
 1 in 1500 
 5.80 
 7.20 
 8.82 
 10.62 
 12.67 
 
 1 in 1800 
 5.29 
 6.58 
 8.05 
 9 69 
 11.57 
 
 2ft.lofnT 
 
 3 " 
 3 " 2in. 
 3 " 4 " 
 3 " 6 " 
 
 1 in 500 
 25.84 
 30.14 
 34.90 
 40.08 
 45.66 
 
 1 in 750 
 21.10 
 24.61 
 28.50 
 32.72 
 37.28 
 
 1 in 1000 
 18.27 
 21.31 
 24.68 
 28.34 
 32.28 
 
 1 in 1250 
 16.34 
 19.06 
 22.07 
 25.35 
 28.87 
 
 1 in 1500 
 14.92 
 17.40 
 20.15 
 23.14 
 26.36 
 
 1 in 1750 
 13.81 
 16.11 
 18.66 
 21.42 
 24.40 
 
 1 in 2000 
 12.92 
 15.07 
 17.45 
 20.04 
 22.83 
 
 1 in 2000 
 25.87 
 29.18 
 32.74 
 44.88 
 59.46 
 
 1 in 2500 
 11.55 
 13.48 
 15.61 
 17.93 
 20.41 
 
 1 in 2500 
 23.14 
 26.10 
 29.28 
 40.14 
 53.18 
 
 3ft. 8in. 
 3 " 10 " 
 4 " 
 4 " 6in. 
 
 5 " 
 
 1 in 500 
 51.74 
 58.36 
 65.47 
 89.75 
 118.9 
 
 1 in 750 
 42.52 
 47.65 
 53.46 
 73.28 
 97.09 
 
 1 in 1000 
 36.59 
 41.27 
 46.30 
 63.47 
 84.08 
 
 1 in 1250 
 32.72 
 36.91 
 41.41 
 56.76 
 75.21 
 
 1 in 1500 
 29.87 
 33.69 
 37.80 
 51.82 
 68.65 
 
 lin 1750 
 27.66 
 31.20 
 34.50 
 47.97 
 63.56 
 
 5ft.6in7 
 6 " 
 6 " 6 " 
 7 " 
 7 " 6 " 
 
 1 in 750 
 125.2 
 
 157.8 
 195.0 
 237.7 
 285.3 
 
 1 in 1000 
 108.4 
 136.7 
 168.8 
 205.9 
 247.1 
 
 1 in 1 500 
 88.54 
 111.6 
 137.9 
 168.1 
 201.7 
 
 1 in 2000 
 76.67 
 96.66 
 119.4 
 145.6 
 174.7 
 
 1 in 2500 
 68.58 
 86.45 
 106.8 
 130.2 
 156.3 
 
 1 in 3000 
 62.60 
 78.92 
 97.49 
 118.8 
 142.6 
 
 1 in 3500 
 57.96 
 73.07 
 90.26 
 110.00 
 132.1 
 
 1 in 4000 
 54.21 
 68.35 
 84.43 
 102.9 
 123.5 
 
 s = 
 
 8ft. 
 8 " 6in. 
 
 9 " 
 9 " 6 " 
 10 " 
 
 1 in 1500 
 239.4 
 281.1 
 327.0 
 376.9 
 431.4 
 
 1 in 2000 
 207.3 
 243.5 
 283.1 
 326.4 
 373.6 
 
 1 in 2500 
 195.4 
 217.8 
 253.3 
 291.9 
 334. 1 
 
 1 in 3000 
 169.3 
 198.8 
 231.2 
 266.5 
 305.0 
 
 1 in 3500 
 156.7 
 184.0 
 214.0 
 246.7 
 282.4 
 
 1 in 4000 
 146.6 
 172.2 
 200.2 
 230.8 
 264.2 
 
 1 in 4500 
 138.2 
 162.3 
 188.7 
 217.6 
 249.1 
 
 1 in 5000 
 131.1 
 154.0 
 179.1 
 206.4 
 236.3 
 
 For U. S. gallons multiply the figures in the table by 7.4805. 
 
 For a given diameter the quantity of flow varies as the square root of 
 the sine of the slope. From this principle the flow for other slopes than 
 those given in the table may be found. Thus, what is the flow for a 
 
FLOW OF WATER IN PIPES. 
 
 739 
 
 pipe 8 feet diameter, slope 1 in 125? From the table take Q = 207.3 
 for slope 1 in 2000. The given slope 1 in 125 is to 1 in 2000 as 16 to 
 1, and the square root of this ratio is 4 to 1. Therefore the flow required 
 is 207.3 X 4 = 829.2 cu. ft. 
 
 Circular Pipes, Conduits, etc., Flowing FulL 
 
 Values of the factor ac \/r in the formula Q = ac \/r X \/s corre- 
 sponding to different values of the coefficient of roughness, n. (Based 
 on Kutter's formula.) 
 
 Diam., 
 Ft. In. 
 
 Value of ac \A. 
 
 w=.010. 
 
 n=.011. 
 
 n=.012. 
 
 n=.013. 
 
 n=.015. 
 
 n=.017. 
 
 2 
 
 307.6 
 
 274.50 
 
 247.33 
 
 224.63 
 
 188.77 
 
 164 
 
 2 3 
 
 421.9 
 
 377.07 
 
 340.10 
 
 309.23 
 
 260.47 
 
 223.9 
 
 2 6 
 
 559.6 
 
 500.78 
 
 452.07 
 
 411.27 
 
 347.28 
 
 299.3 
 
 2 9 
 
 722.4 
 
 647.18 
 
 584.90 
 
 532.76 
 
 451.23 
 
 388.8 
 
 3 
 
 911.8 
 
 817.50 
 
 739.59 
 
 674.09 
 
 570.90 
 
 493.3 
 
 3 3 
 
 1128.9 
 
 1013.1 
 
 917.41 
 
 836.69 
 
 709.56 
 
 613.9 
 
 3 6 
 
 1374.7 
 
 1234.4 
 
 1118.6 
 
 1021.1 
 
 866.91 
 
 750.8 
 
 3 9 
 
 1652.1 
 
 1484.2 
 
 1345.9 
 
 1229.7 
 
 1045 
 
 906 
 
 4 
 
 1962.8 
 
 1764.3 
 
 1600.9 
 
 1463.9 
 
 1245.3 
 
 1080.7 
 
 4 6 
 
 2682.1 
 
 2413.3 
 
 2193 
 
 2007 
 
 1711.4 
 
 1487.3 
 
 5 
 
 3543 
 
 3191.8 
 
 2903.6 
 
 2659 
 
 2272.7 
 
 1977 
 
 5 6 
 
 4557.8 
 
 4111.9 
 
 3742.7 
 
 3429 
 
 2934. 8 
 
 2557.2 
 
 6 
 
 5731.5 
 
 5176.3 
 
 4713.9 
 
 4322 
 
 3702.3 
 
 3232.5 
 
 6 6 
 
 7075.2 
 
 6394.9 
 
 5825.9 
 
 5339 
 
 4588.3 
 
 4010 
 
 7 
 
 8595.1 
 
 7774.3 
 
 7087 
 
 6510 
 
 5591.6 
 
 4893.2 
 
 7 6 
 
 10296 
 
 9318.3 
 
 8501.8 
 
 7814 
 
 6717 
 
 5884.3 
 
 6 
 
 12196 
 
 11044 
 
 10083 
 
 9272 
 
 7978.3 
 
 "6995.3 
 
 8 6 
 
 14298 
 
 12954 
 
 11832 
 
 10889 
 
 9377.9 
 
 8226.7 
 
 9 
 
 16604 
 
 15049 
 
 13751 
 
 12663 
 
 10917 
 
 9580 
 
 9 6 
 
 19118 
 
 17338 
 
 15847 
 
 14597 
 
 12594 
 
 11061 
 
 10 
 
 21858 
 
 19834 
 
 18134 
 
 16709 
 
 14426 
 
 12678 
 
 10 6 
 
 24823 
 
 22534 
 
 20612 
 
 18996 
 
 16412 
 
 14434 
 
 11 
 
 28020 
 
 25444 
 
 23285 
 
 21464 
 
 18555 
 
 16333 
 
 11 6 
 
 31482 
 
 28593 
 
 26179 
 
 24139 
 
 20879 
 
 18395 
 
 12 
 
 35156 
 
 31937 
 
 29254 
 
 26981 
 
 23352 
 
 20584 
 
 12 6 
 
 39104 
 
 35529 
 
 32558 
 
 30041 
 
 26012 
 
 22938 
 
 13 
 
 43307 
 
 39358 
 
 36077 
 
 33301 
 
 28850 
 
 25451 
 
 13 6 
 
 47751 
 
 43412 
 
 39802 
 
 36752 
 
 31860 
 
 28117 
 
 14 
 
 52491 
 
 47739 
 
 43773 
 
 40432 
 
 35073 
 
 30965 
 
 14 6 
 
 57496 
 
 52308 
 
 47969 
 
 44322 
 
 38454 
 
 33973 
 
 15 
 
 62748 
 
 57103 
 
 52382 
 
 48413 
 
 42040 
 
 37147 
 
 16 
 
 74191 
 
 67557 
 
 62008 
 
 57343 
 
 49823 
 
 44073 
 
 17 
 
 86769 
 
 79050 . 
 
 72594 . 
 
 67140 
 
 58387 
 
 51669 
 
 18 
 
 00617 
 
 91711 
 
 84247 
 
 77932 
 
 67839 
 
 60067 
 
 19 
 
 115769 
 
 105570 
 
 96991 
 
 89759 
 
 78201 
 
 69301 
 
 20 
 
 32133 
 
 120570 
 
 110905 
 
 102559 
 
 89423 
 
 79259 
 
 Flow of Water in Pipes from 3/g Inch to 13 Inches Diameter for a 
 Uniform Velocity of 100 Ft. per Min. 
 
 Diam. 
 ID In. 
 
 Area 
 Sq. Ft. 
 
 Cu. Ft. 
 per. Min. 
 
 U. S. 
 Gallons 
 per Min. 
 
 Diam. 
 in In. 
 
 Area 
 Sq. Ft. 
 
 Cu. Ft. 
 per Min. 
 
 U.S. 
 Gallons 
 per Min. 
 
 3/8 
 
 .00077 
 
 0.077 
 
 .57 
 
 4 
 
 .0873 
 
 8.73 
 
 65.28 
 
 !/2 
 
 .00136 
 
 0.136 
 
 1.02 
 
 5 
 
 .136 
 
 13.6 
 
 102.00 
 
 3/4 
 
 .00307 
 
 0.307 
 
 2.30 
 
 6 
 
 .196 
 
 19.6 
 
 146.88 
 
 
 .00545 
 
 0.545 
 
 4.08 
 
 7 
 
 .267 
 
 26.7 
 
 199.92 
 
 n/4 
 
 .00852 
 
 0.852 
 
 6.38 
 
 8 
 
 .349 
 
 34.9 
 
 261.12 
 
 11/2 
 
 .01227 
 
 1.227 
 
 9.18 
 
 9 
 
 .442 
 
 44.2 
 
 330.48 
 
 13/4 
 
 .01670 
 
 1.670 
 
 12.50 
 
 10 
 
 .545 
 
 54.5 
 
 408.00 
 
 
 .02182 
 
 2.182 
 
 16.32 
 
 11 
 
 .660 
 
 66.0 
 
 493.68 
 
 21/2 
 
 .0341 
 
 3.41 
 
 25.50 
 
 12 
 
 .785 
 
 78.5 
 
 587.52 
 
 3 
 
 .0491 
 
 4.91 
 
 36.72 
 
 
 
 
 
740 
 
 HYDRAULICS. 
 
 Flow of Water in Circular Pipes, Conduits, etc., Flowing; under 
 Pressure. 
 
 Based on Darcy's formulae for the flow of water through cast-iron 
 pipes. With comparison of results obtained by Kutter's formula, with 
 ft = 0.013. (Condensed from Flynn on Water Power.) _ 
 
 Values of a, and also the values of the factors c Vr and ac vV for use 
 
 In the formulae Q = av; v = c \/ r X Vs, and Q = ac V7x ^s. 
 
 Q = discharge in cubic feet per second, a = area in square feet, v = 
 velocity in feet per second, r = mean hydraulic depth, 1/4 diam. for 
 pipes running full, s, = sine of slope. 
 
 (For values of V? see page 729.) 
 
 Size of Pipe. 
 
 Clean Cast-iron 
 Pipes. 
 
 Value of 
 ac Vrby 
 Kutter's 
 Formula, 
 when 
 n=.OI3. 
 
 Old Cast-iron Pipes 
 Lined with Deposit. 
 
 ddiam. 
 in 
 ft. in. 
 
 a = area in 
 square 
 feet. 
 
 For 
 Velocity, 
 
 For Dis- 
 charge, 
 
 For 
 Velocity, 
 
 For 
 Discharge, 
 
 2 
 
 3.142 
 
 78.80 
 
 247.57 
 
 224.63 
 
 52.961 
 
 166.41 
 
 2 2 
 
 3.687 
 
 28.15 
 
 302.90 
 
 
 55.258 
 
 203.74 
 
 2 4 
 
 4.276 
 
 85.39 
 
 365.14 
 
 
 57.436 
 
 245.60 
 
 2 6 
 
 4.909 
 
 88.39 
 
 433.92 
 
 411.37 
 
 59.455 
 
 291.87 
 
 2 8 
 
 5.585 
 
 91.51 
 
 511.10 
 
 
 61.55 
 
 343.8 
 
 2 10 
 
 6.305 
 
 94.40 
 
 595.17 
 
 
 63.49 
 
 400.3 
 
 3 
 
 7 068 
 
 97.17 
 
 686.76 
 
 674.09 
 
 65.35 
 
 461.9 
 
 3 2 
 
 7.875 
 
 99.93 
 
 786.94 
 
 
 67.21 
 
 529.3 
 
 3 4 
 
 8.726 
 
 102.6 
 
 895.7 
 
 
 69 
 
 602 
 
 3 6 
 
 9.621 
 
 105.1 
 
 1011.2 
 
 1021.1 
 
 70.70 
 
 680.2 
 
 3 8 
 
 10.559 
 
 107.6 
 
 1136.5 
 
 
 72.40 
 
 764.5 
 
 3 10 
 
 11.541 
 
 110.2 
 
 1271.4 
 
 
 74.10 
 
 855.2 
 
 4 
 
 12.566 
 
 112.6 
 
 1414.7 
 
 1463.9 
 
 75.73 
 
 951.6 
 
 4 3 
 
 14.186 
 
 116.1 
 
 1647.6 
 
 
 78.12 
 
 1108.2 
 
 4 6 
 
 15.904 
 
 119.6 
 
 1901.9 
 
 2007 
 
 80.43 
 
 1279.2 
 
 4 9 
 
 17.721 
 
 122.8 
 
 2176.1 
 
 
 82.20 
 
 1456.8 
 
 5 
 
 19.635 
 
 126.1 
 
 2476.4 
 
 2659 
 
 84.83 
 
 1665.7 
 
 5 3 
 
 21.648 
 
 129.3 
 
 2799.7 
 
 
 86.99 
 
 1883.2 
 
 5 6 
 
 23.758 
 
 132.4 
 
 3146.3 
 
 3429 
 
 89.07 
 
 2116.2 
 
 5 9 
 
 25 967 
 
 135.4 
 
 3516 
 
 
 91.08 
 
 2365 
 
 5 
 
 28.274 
 
 138.4 
 
 3912.8 
 
 4322 
 
 93.08 
 
 2631.7 
 
 6 6 
 
 33 183 
 
 144.1 
 
 4728.1 
 
 5339 
 
 96.93 
 
 3216.4 
 
 7 
 
 38 485 
 
 149.6 
 
 5757.5 
 
 6510 
 
 100.61 
 
 3872.5 
 
 7 6 
 
 44 179 
 
 154.9 
 
 6841.6 
 
 7814 
 
 104.11 
 
 4601.9 
 
 g 
 
 50 266 
 
 160 
 
 8043 
 
 9272 
 
 107.61 
 
 5409.9 
 
 8 6 
 
 56.745 
 
 165 
 
 9463.7 
 
 10889 
 
 111 
 
 6299.1 
 
 9 
 
 63.617 
 
 169.8 
 
 10804 
 
 12663 
 
 114.2 
 
 7267.3 
 
 9 6 
 
 70 882 
 
 174.5 
 
 12370 
 
 14597 
 
 117.4 
 
 8329.6 
 
 10 
 
 78.540 
 
 179.1 
 
 14066 
 
 16709 
 
 120.4 
 
 9460.9 
 
 10 6 
 
 68.590 
 
 183.6 
 
 15893 
 
 18996 
 
 123.4 
 
 10690 
 
 11 
 
 95 033 
 
 187.9 
 
 17855 
 
 21464 
 
 126.3 
 
 12010 
 
 11 6 
 
 103 869 
 
 192.2 
 
 19966 
 
 24139 
 
 129.3 
 
 13429 
 
 12 
 
 113.098 
 
 196.3 
 
 22204 
 
 26981 
 
 132 
 
 14935 
 
 12 6 
 
 122 719 
 
 200.4 
 
 24598 
 
 30041 
 
 134.8 
 
 16545 
 
 13 
 
 132.733 
 
 204.4 
 
 27134 
 
 33301 
 
 137.5 
 
 18252 
 
 13 6 
 
 143 139 
 
 208.3 
 
 29818 
 
 36752 
 
 140.1 
 
 20056 
 
 14 
 
 153 938 
 
 212.2 
 
 32664 
 
 40432 
 
 142.7 
 
 21971 
 
 14 6 
 15 
 
 165.130 
 176 715 
 
 216.0 
 219.6 
 
 35660 
 38807 
 
 44322 
 48413 
 
 145.2 
 147.7 
 
 23986 
 26103 
 
 15 6 
 16 
 
 188.692 
 201 062 
 
 223.3 
 226.9 
 
 42125 
 45621 
 
 52753 
 57343 
 
 150.1 
 152.6 
 
 28335 
 30686 
 
 16 6 
 
 213 825 
 
 230.4 
 
 49273 
 
 62132 
 
 155 
 
 33144 
 
 17 
 
 226 981 
 
 233.9 
 
 53082 
 
 67140 
 
 157.3 
 
 35704 
 
 17 i 
 
 240 529 
 
 237.3 
 
 57074 
 
 72409 
 
 159.6 
 
 38389 
 
 18 
 
 254 170 
 
 240.7 
 
 61249 
 
 77932 
 
 161.9 
 
 41199 
 
 19 
 
 283 529 
 
 247.3 
 
 70154 
 
 89759 
 
 166.4 
 
 47186 
 
 20 
 
 314.159 
 
 253.8 
 
 79736 
 
 102559 
 
 170.7 
 
 53633 
 
FLOW OP WATEB IN PIPES. 
 
 741 
 
 Flow of Water in Circular Pipes from 3/s Inch to 12 Inches 
 Diameter. 
 
 Based on Darcy's formula for clean cast-iron pipes. Q = ac v'r VJ. 
 
 Value 
 
 Dia. 
 
 Slope, or Jlead Divided by Length of Pipe. 
 
 ofocVr. 
 
 in. 
 
 1 in 10 
 
 1in20 
 
 1 in 40 
 
 1 in 60 
 
 1 in 80 
 
 1 in 100 
 
 1 in 150 
 
 1 in 200 
 
 
 
 
 Quan 
 
 tityin 
 
 cubic 
 
 feet per 
 
 second. 
 
 
 
 .00403 
 
 s /8 
 
 .00127 
 
 .00090 
 
 .00064 
 
 .00052 
 
 .00045 
 
 .00040 
 
 .00033 
 
 .00028 
 
 .00914 
 
 1/2 
 
 .00289 
 
 .00204 
 
 .00145 
 
 .00118 
 
 .00102 
 
 .00091 
 
 .00075 
 
 .00065 
 
 .02855 
 
 3/4 
 
 .00903 
 
 .00638 
 
 .00451 
 
 .00369 
 
 .00319 
 
 .00286 
 
 .00233 
 
 .00202 
 
 .06334 
 
 
 .02003 
 
 .01416 
 
 .01001 
 
 .00818 
 
 .00708 
 
 .00633 
 
 .00517 
 
 .00448 
 
 .11659 
 
 11/4 
 
 .03687 
 
 .02607 
 
 .01843 
 
 .01505 
 
 .01303 
 
 .01166 
 
 .00952 
 
 .00824 
 
 .19115 
 
 U/9 
 
 .06044 
 
 .04274 
 
 .03022 
 
 .02468 
 
 .02137 
 
 .01912 
 
 .01561 
 
 .01352 
 
 .28936 
 
 13/4 
 
 .09140 
 
 .06470 
 
 .04575 
 
 .03736 
 
 .03235 
 
 .02894 
 
 .02363 
 
 .02046 
 
 .41357 
 
 
 .13077 
 
 .09247 
 
 .06539 
 
 .05339 
 
 .04624 
 
 .04136 
 
 .03377 
 
 .02927 
 
 .74786 
 
 21/2 
 
 .23647 
 
 .16722 
 
 .11824 
 
 .09655 
 
 .08361 
 
 .07479 
 
 .06106 
 
 .05288 
 
 1.2089 
 
 3 
 
 .38225 
 
 .27031 
 
 .19113 
 
 .15607 
 
 .13515 
 
 .12089 
 
 .09871 
 
 .08548 
 
 2.5630 
 
 4 
 
 .81042 
 
 .57309 
 
 .40521 
 
 .33088 
 
 .28654 
 
 .25630 
 
 .20927 
 
 .18123 
 
 4.5610 
 
 5 
 
 1.4422 
 
 1.0198 
 
 .72109 
 
 .58882 
 
 .50992 
 
 .45610 
 
 .37241 
 
 .32251 
 
 '7.3068 
 
 6 
 
 2.3104 
 
 1 .6338 
 
 1.1552 
 
 .94331 
 
 .81690 
 
 .73068 
 
 .59660 
 
 .51666 
 
 10.852 
 
 7 
 
 3.4314 
 
 2.4265 
 
 1.7157 
 
 1.4110 
 
 1.2132 
 
 1.0852 
 
 .88607 
 
 .76734 
 
 15.270 
 
 8 
 
 4.8284 
 
 3.4143 
 
 2.4141 
 
 1.9713 
 
 1.7072 
 
 1.5270 
 
 1.2468 
 
 1 .0797 
 
 20.652 
 
 9 
 
 6.5302 
 
 4.6178 
 
 3.2651 
 
 2.6662 
 
 2.3089 
 
 2.0652 
 
 1.6862 
 
 1.4603 
 
 26.952 
 
 10 
 
 8.5222 
 
 6.0265 
 
 4.2611 
 
 3.4795 
 
 3.0132 
 
 2.6952 
 
 2.2006 
 
 1.9058 
 
 34.428 
 
 11 
 
 10.886 
 
 7.6981 
 
 5.4431 
 
 4.4447 
 
 3.8491 
 
 3.4428. 
 
 2.8110 
 
 2.4344 
 
 42.918 
 
 12 
 
 13.571 
 
 9.5965 
 
 6.7853 
 
 5.5407 
 
 4.7982 
 
 4.2918 
 
 3.5043 
 
 3.0347 
 
 Value of Vs^ 
 
 0.3162 
 
 0.2236 
 
 0.1581 
 
 0.1291 
 
 0.1118 
 
 0.1 
 
 0.08165 
 
 0.07071 
 
 Value 
 
 f A / 
 
 Dia 
 
 1 in 250 
 
 1 in 300 
 
 1 in 350 
 
 1 in 400 
 
 1 in 450 
 
 1 in 500 
 
 1 in 550 
 
 1 in 600 
 
 of ocv r. 
 
 in. 
 
 
 
 
 
 
 
 
 
 .00403 
 
 3/8 
 
 .00025 
 
 .00023 
 
 .00022 
 
 .00020 
 
 .00019 
 
 .00018 
 
 .00017 
 
 .00016 
 
 .00914 
 
 1/2 
 
 .00058 
 
 .00033 
 
 .00049 
 
 .00046 
 
 .00043 
 
 .00041 
 
 .00039 
 
 .00037 
 
 .02855 
 
 3 /4 
 
 .00181 
 
 .00165 
 
 .00153 
 
 .00143 
 
 .00134 
 
 .00128 
 
 .00122 
 
 .00117 
 
 .06334 
 
 1 
 
 .00400 
 
 .00366 
 
 .00339 
 
 .00317 
 
 .00298 
 
 .00283 
 
 .00270 
 
 .00259 
 
 .11659 
 
 H/4 
 
 .00737 
 
 .00673 
 
 .00623 
 
 .00583 
 
 .00549 
 
 .00521 
 
 .00497 
 
 .00476 
 
 .19115 
 
 H/2 
 
 .01209 
 
 .01104 
 
 .01022 
 
 .00956 
 
 .00901 
 
 .00855 
 
 .00815 
 
 .00780 
 
 .28936 
 
 13/4 
 
 .01830 
 
 .01671 
 
 .01547 
 
 .01447 
 
 .01363 
 
 .01294 
 
 .01234 
 
 .01181 
 
 .41357 
 
 2 
 
 .02615 
 
 .02388 
 
 .02211 
 
 .02068 
 
 .01948 
 
 .01849 
 
 .01763 
 
 .01688 
 
 .74786 
 
 21/2 
 
 .04730 
 
 .04318 
 
 .03997 
 
 .03739 
 
 .03523 
 
 .03344 
 
 .03189 
 
 .03053 
 
 1.2089 
 
 3 
 
 .07645 
 
 .06980 
 
 .06462 
 
 .06045 
 
 .05695 
 
 .05406 
 
 .05155 
 
 .04935 
 
 2.5630 
 
 4 
 
 .16208 
 
 .14799 
 
 . 13699 
 
 .12815 
 
 .12074 
 
 .11461 
 
 .10929 
 
 . 10463 
 
 4.5610 
 
 5 
 
 .28843 
 
 .26335 
 
 .24379 
 
 .22805 
 
 .21487 
 
 .20397 
 
 .19448 
 
 .19620 
 
 7.3068 
 
 6 
 
 .46208 
 
 .42189 
 
 .39055 
 
 .36534 
 
 .34422 
 
 .32676 
 
 .31156 
 
 .29830 
 
 10.852 
 
 7 
 
 .68628 
 
 .62660 
 
 .58005 
 
 .54260 
 
 .51124 
 
 .48530 
 
 .46273 
 
 .44303 
 
 15.270 
 
 8 
 
 .96567 
 
 .88158 
 
 .81617 
 
 .76350 
 
 .71936 
 
 .68286 
 
 .65111 
 
 .62340 
 
 20.652 
 
 9 
 
 1 3060 
 
 1.1924 
 
 1.1038 
 
 1.0326 
 
 .97292 
 
 .92356 
 
 .88060 
 
 .84310 
 
 26.952 
 
 10 
 
 1.7044 
 
 1.5562 
 
 1.4405 
 
 1 .3476 
 
 1.2697 
 
 1.2053 
 
 1.1492 
 
 1.1003 
 
 34.428 
 
 11 
 
 2.1772 
 
 1.9878 
 
 1.8402 
 
 1.7214 
 
 1.6219 
 
 1.5396 
 
 1.4680 
 
 1.4055 
 
 42.918 
 
 12 
 
 2.7141 
 
 2.4781 
 
 2.2940 
 
 2.1459 
 
 2.0219 
 
 1.9193 
 
 1.8300 
 
 1.7521 
 
 Value of VJ= 
 
 .06324 
 
 .05774 
 
 .05345 
 
 .05 
 
 .04711 
 
 .04472 
 
 .04264 
 
 .04082 
 
 For U. S. gals, per sec., multiply the figures in the table by 7.4805 
 
 " min., " " ... 448.83 
 
 " " hour, " " 26929.8 
 
 " " 24hrs. t " " ...646315. 
 
 'or any other slope the flow is proportional to the square root of the 
 thus, flow in slope of 1 in 100 is double that in slope of 1 in 400. 
 
742 
 
 HYDRAULICS. 
 
 I 
 
 o 
 
 sO 
 
 s 
 
 42 
 
 
 
 So S 
 
 =s : 
 
 fi- 
 ll 
 
 If- 
 
 s 
 
 -1 {> 
 
 a 
 
 *$ 
 
 l! 
 b 
 
 s 
 
 o* 
 
 8 
 
 o 
 
 O fS (S -^ >O ON fS sO O vi 
 
 O ^-<fvOGO ^oOfOOOTt-'ovOrM 
 
 
 '>i>.i^-^i. I 
 OO (Nr}-QOf^c^TfoO\OrOfNC^r^iArorsJt>.f<M> p^ TJ- vO 
 
 (N Psl m iTi \O OO f^ <O 00 <N O 1 - 
 
 SO <Ncoi\oOoor>.oo<Nm<NT}-ooa^N 
 OOOOO tNc^irisO vOm c 
 
 i 
 
 OO N -^- r^ <N CO vO vO m tN c^ oo r*> C 
 OOOOOO <NcnTt>i m o 
 
 tN 00 ^T O^ O C^ -* rj- 
 
 cor^rsjt>i <NOOfNr<>ro Or> 
 
 "~OO f>Tj-cO<NQO T J- tNt^O^txoomoOr^OOOc^O^i 
 ooooooo (NcoiAtN.o-^-aMA oo^o o 
 
 - <N co * m i^ r^ oo O 
 
 .-.ptN. i 
 
 OOO 
 OOOO 
 
 OOOO ( 
 
 5 Tj-Tj-(NvniAGOOOiAN 
 xOr^t^' oO^"^oO^Om 
 
 
 OOOO (N-^-vOQO "3- 
 OOOOOOOOO f 
 
 SOO- <N-<3-ir\aOOr^i.' 
 OOOOOOOO r 
 
 Dooa^vOc^ 
 
 ^^OOvOvO 
 
 1 
 
 III 
 
 Dt-.t^oOO <NcO|Tj-mvOr^O^ 
 
 
 s|s 
 
FLOW OF WATER. 
 
 743 
 
 Flow or Water in Cubic Feet per Second. 
 Pipes 1 Ft. to 20 Ft. Diameter. 
 
 Calculated from the Hazen and Williams formula with C = 
 
 100. 
 
 
 Fall, Feet per 1 000 
 
 Actual 
 Internal 
 
 1 1 2 1 3 
 
 4 
 
 6 
 
 8 | 10 | 15 
 
 20 
 
 40 
 
 Diam., 
 In. 
 
 Drop in Pressure, Lb. per Sq. In. per 1000 Ft. Length. 
 
 
 0.433 
 
 0.866 
 
 1.299 
 
 1.732 
 
 2.598 
 
 5.464 
 
 4.330 
 
 6.495 
 
 8.660 
 
 17.32 
 
 12 
 
 1.037 
 
 1.508 
 
 1.877 
 
 2.192 
 
 2.729 
 
 3.188 
 
 3.596 
 
 4.475 
 
 5.228 
 
 8.335 
 
 13 
 
 1.280 
 
 1.861 
 
 2.317 
 
 2.706 
 
 3.368 
 
 3.934 
 
 4.438 
 
 5.524 
 
 .6.453 
 
 10.29 
 
 14 
 
 1.555 
 
 2.262 
 
 2.815 
 
 3.288 
 
 4.093 
 
 4.781 
 
 5.393 
 
 6.713 
 
 7.842 
 
 12.50 
 
 15 
 
 1.865 
 
 2.712 
 
 3.375 
 
 3.943 
 
 4.908 
 
 5.732 
 
 6.466 
 
 8.048 
 
 9.402 
 
 14.99 
 
 16 
 
 2.210 
 
 3.213 
 
 4.000 
 
 4.672 
 
 5.815 
 
 6.793 
 
 7.663 
 
 9.537 
 
 11.14 
 
 17.76 
 
 18 
 
 3.012 
 
 4.380 
 
 5.452 
 
 6.368 
 
 7.927 
 
 9.259 
 
 10.45 
 
 13.00 
 
 15.19 
 
 24.21 
 
 20 
 
 3.974 
 
 5.778 
 
 7.193 
 
 8.402 
 
 10.46 
 
 12.22 
 
 13.78 
 
 17.15 
 
 20.04 
 
 31.94 
 
 22 
 
 5.100 
 
 7.415 
 
 9.231 
 
 10.78 
 
 13.42 
 
 15.68 
 
 17.68 
 
 22.01 
 
 25.71 
 
 40.99 
 
 Diam., Ft. 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 6.420 
 
 9.334 
 
 11.62 
 
 13.57 
 
 16.89 
 
 19.73 
 
 22.26 
 
 27.70 
 
 32.36 
 
 51.60 
 
 21/2 
 
 11.54 
 
 16.79 
 
 20.89 
 
 24.41 
 
 30.38 
 
 35.48 
 
 40.03 
 
 49.80 
 
 58.20 
 
 92.79 
 
 3 
 
 18.65 
 
 27.11 
 
 33.75 
 
 39.42 
 
 49.07 
 
 57.32 
 
 64.66 
 
 80.48 
 
 94.01 
 
 149.9 
 
 31/2 
 
 27.97 
 
 40.67 
 
 50.62 
 
 59.13 
 
 73.60 
 
 85.97 
 
 96.98 
 
 120.7 
 
 141.0 
 
 224.8 
 
 
 39.74 
 
 57.78 
 
 71.92 
 
 84.01 
 
 104.6 
 
 122.1 
 
 137.8 
 
 171.5 
 
 200.3 
 
 319.4 
 
 41/2 
 
 54.17 
 
 78.76 
 
 98.04 
 
 114.5 
 
 142.5 
 
 166.5 
 
 187.8 
 
 233.8 
 
 273.1 
 
 435.4 
 
 
 71.46 
 
 103.9 
 
 129.3 
 
 151.1 
 
 188.1 
 
 219.7 
 
 247.8 
 
 308.4 
 
 360.3 
 
 574.4 
 
 51/2 
 
 91.82 
 
 133.5 
 
 166.2 
 
 194.1 
 
 241.7 
 
 282.2 
 
 318.4 
 
 396.3 
 
 462.9 
 
 738.0 
 
 6 
 
 115.4 
 
 167.8 
 
 208.9 
 
 244.0 
 
 303.8 
 
 354.8 
 
 400.2 
 
 498.2 
 
 581.9 
 
 927.8 
 
 61/2 
 
 142.5 
 
 207.2 
 
 257.9 
 
 301.2 
 
 374.9 
 
 437.9 
 
 494.0 
 
 614.9 
 
 718.3 
 
 1145' 
 
 7 
 
 173.1 
 
 251.7 
 
 313.4 
 
 366.0 
 
 455.6 
 
 532.2 
 
 600.3 
 
 747.2 
 
 872.9 
 
 1392 
 
 71/2 
 
 207.6 
 
 301.8 
 
 375.7 
 
 438.8 
 
 546.3 
 
 638.1 
 
 719.8 
 
 859.9 
 
 1047 
 
 1668 
 
 8 
 
 246.0 
 
 357.7 
 
 445.2 
 
 520.0 
 
 647.3 
 
 756.1 
 
 852.9 
 
 1062 
 
 1240 
 
 1977 
 
 81/2 
 
 288.5 
 
 419.5 
 
 522.2 
 
 609.9 
 
 759.2 
 
 886.8 
 
 1000 
 
 1245 
 
 1455 
 
 2319 
 
 9 
 
 335.3 
 
 487.5 
 
 606.9 
 
 708.9 
 
 882.4 
 
 1031 
 
 1163 
 
 1447 
 
 1690 
 
 2695 
 
 10 
 
 442.4 
 
 643.2 
 
 800.6 
 
 935.2 
 
 1164 
 
 1360 
 
 1534 
 
 1909 
 
 2230 
 
 3556 
 
 11 
 
 568.4 
 
 826.4 
 
 1029 
 
 1202 
 
 1496 
 
 1747 
 
 1971 
 
 2453 
 
 2866 
 
 4568 
 
 12 
 
 714.6 
 
 1015 
 
 1293 
 
 1511 
 
 1880 
 
 2196 
 
 2478 
 
 3084 
 
 3602 
 
 5743 
 
 13 
 
 882.0 
 
 1282 
 
 1596 
 
 1865 
 
 2321 
 
 2711 
 
 3058 
 
 3807 
 
 4447 
 
 7089 
 
 14 
 
 1072 
 
 1558 
 
 1940 
 
 2266 
 
 2820 
 
 3294 
 
 3716 
 
 4625 
 
 5403 
 
 8614 
 
 15 
 
 1285 
 
 1868 
 
 2326 
 
 2717 
 
 3381 
 
 3950 
 
 4456 
 
 5546 
 
 6478 
 
 10328 
 
 16 
 
 1223 
 
 2214 
 
 2756 
 
 3219 
 
 4007 
 
 4681 
 
 5280 
 
 6572 
 
 7677 
 
 12239 
 
 17 
 
 1786 
 
 2597 
 
 3232 
 
 3776 
 
 4700 
 
 5490 
 
 6193 
 
 7708 
 
 9004 
 
 14354 
 
 18 
 
 2076 
 
 3018 
 
 3757 
 
 4388 
 
 5462 
 
 6380 
 
 7197 
 
 8958 
 
 10464 
 
 16683 
 
 19 
 
 2393 
 
 3479 
 
 4331 
 
 5059 
 
 6297 
 
 7355 
 
 8297 
 
 10327 
 
 12063 
 
 19232 
 
 20 
 
 2738 
 
 3982 
 
 4956 
 
 5789 
 
 7206 
 
 8417 
 
 9495 
 
 11818 
 
 13806 
 
 22010 
 
 4.5 ft. per mile, discharged 15 million gallons per day; velocity, 2.892 ft. 
 per sec., / = 0.00574. 
 
 (2) East Jersey riveted steel pipe line, Newark, N. J., 21 miles long, 48 
 in. diam., 50 million U. S. gals, per day; velocity about 6 ft. per sec. 
 
 (3) Perth to Coolgarlie, Western Australia, 351 miles, 30 in. steel pipe 
 with lock-bar joints. Eight pumping stations in the line. Two tests 
 showed delivery of 5 and 5.6 million gals, per day; hydraulic gradient 
 2.25 and 2.8 ft. per mile; velocity, 1.889 and 2.115 ft. per sec.;/= 0.00480 
 and 0.00486. 
 
 Flow of Water in Riveted Steel Pipes. The laps and rivets tend 
 to decrease the carrying capacity of the pipe. See paper on "New 
 Formulas for Calculating the Flow of Water in Pipes and Channels," by 
 W. E. Foss, Jour. Assoc. Eng. Soc., xiii, 295. Also Clemens Herschel's 
 book on "115 Experiments on the Carrying Capacity of Large Riveted 
 Metal Conduits," John Wiley & Sons, 1897. 
 
744 
 
 HYDRAULICS. 
 
 Flow of Water in House-service Pipes. 
 
 Mr. E. Kuichling, C. E., furnished the following table to the Thomson 
 Meter Co.: 
 
 Condition of 
 Discharge. 
 
 Pressure in Main, 
 pounds per 
 square inch. 
 
 Discharge, or Quantity capable of being delivered, in 
 Cubic Feet per Minute, from the Pipe, under the 
 conditions specified in the first column. 
 
 Nominal Diameters of Iron or Lead Service-pipe in 
 Inches. 
 
 1/2 
 
 5/8 
 
 3/4 
 
 1 
 
 H/2 
 
 2 
 
 3 
 
 4 
 
 6 
 
 Through 35 
 feet of ser- 
 vice-pipe, 
 no back 
 pressure. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 .10 
 .27 
 .42 
 .56 
 .74 
 2.01 
 2.29 
 
 1.92 
 2.22 
 2.48 
 2.71 
 3.03 
 3.50 
 3.99 
 
 3.01 
 3.48 
 3.89 
 4.26 
 4.77 
 5.50 
 6.28 
 
 6.13 
 7.08 
 7.92 
 8.67 
 9.70 
 11.20 
 12.77 
 
 16.58 
 19.14 
 21.40 
 23.44 
 26.21 
 30.27 
 34.51 
 
 33.34 
 
 33.50 
 43.04 
 47.15 
 52.71 
 60 87 
 69.40 
 
 88.16 
 101.80 
 113.82 
 124.68 
 139.39 
 160.96 
 183.52 
 
 173.85 
 200.75 
 224.44 
 245.87 
 274.89 
 317.41 
 361.91 
 
 444.63 
 513.42 
 574.02 
 628.81 
 703.03 
 811.79 
 925.58 
 
 Through 100 
 feet of ser- 
 vice-pipe, 
 no back 
 pressure. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.66 
 0.77 
 0.86 
 0.94 
 1.05 
 1.22 
 1.39 
 
 .16 
 .34 
 .50 
 .65 
 .84 
 2.13 
 2.42 
 
 1.84 
 2.12 
 2.37 
 2.60 
 2.91 
 3.36 
 3.83 
 
 3.78 
 4.36 
 4.88 
 5.34 
 5.97 
 6.90 
 7.86 
 
 10.40 
 12.01 
 13.43 
 14.71 
 16.45 
 18.99 
 21.66 
 
 21.30 
 24.59 
 27.50 
 30.12 
 33.68 
 38.89 
 44.34 
 
 58.19 
 67.19 
 75.13 
 82.30 
 92.01 
 106.24 
 121.14 
 
 118.13 
 136.41 
 152.51 
 167.06 
 186.78 
 215.68 
 245.91 
 
 317.23 
 366.30 
 409.54 
 448.63 
 501.58 
 579.18 
 660.36 
 
 Through 100 
 feet of ser- 
 vice-pipe, 
 and 15 feet 
 vertical 
 rise. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.55 
 0.66 
 0.75 
 0.83 
 0.94 
 .10 
 1.26 
 
 0.96 
 .15 
 .31 
 .45 
 .64 
 .92 
 2.20 
 
 1.52 
 1.81 
 2.06 
 2.29 
 2.59 
 3.02 
 3.48 
 
 3.11 
 3.72 
 4.24 
 4.70 
 5.32 
 6.21 
 7.14 
 
 8.57 
 10.24 
 11.67 
 12.94 
 14.64 
 17.10 
 19.66 
 
 17.55 
 20.95 
 23.87 
 26.48 
 29.96 
 35.00 
 40.23 
 
 47.90 
 57.20 
 65.18 
 72.28 
 81.79 
 95.55 
 109.82 
 
 97.17 
 116.01 
 132.20 
 146.61 
 165.90 
 193.82 
 222.75 
 
 260.56 
 311.09 
 354.49 
 393.13 
 444.85 
 519.72 
 597.31 
 
 Through 100 
 feet of ser- 
 vice-pipe, 
 and 30 feet 
 vertical 
 rise. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.44 
 0.55 
 65 
 0.73 
 JO. 84 
 1.00 
 1.15 
 
 0.77 
 0.97 
 1.14 
 1.28 
 1.47 
 1.74 
 2.02 
 
 1.22 
 1.53 
 1.79 
 2.02 
 2.32 
 2.75 
 3.19 
 
 2.50 
 3.15 
 3.69 
 4.15 
 4.77 
 5.65 
 6.55 
 
 6.80 
 8 68 
 10.16 
 11.45 
 13.15 
 15.58 
 18.07 
 
 14.11 
 17.79 
 20.82 
 23.47 
 26.95 
 31.93 
 37.02 
 
 38.63 
 48.68 
 56.98 
 64.22 
 73.76 
 87.38 
 101.33 
 
 78.54 
 98 98 
 115.87 
 130.59 
 149.99 
 177.67 
 206.04 
 
 211.54 
 266.59 
 312.08 
 351.73 
 403.98 
 478.55 
 554.96 
 
 In this table it is assumed that the pipe is straight and smooth inside; 
 that the friction of the main and meter are disregarded; that the inlet 
 from the main is of ordinary character, sharp, not flaring or rounded, and 
 that the outlet is the full diameter of pipe. The deliveries given will be 
 increased if, first, the pipe between the meter and the main is of larger 
 diameter than the outlet; second, if the main is tapped, say for 1-inch 
 pipe, but is enlarged from the tap to 1 1/4 or 1 1/2 inch; or, third, if pipe on 
 the outlet is larger than that on the inlet side of the meter. The exact 
 details of the conditions given are rarely met in practice; consequently 
 the quantities of the table may be expected to be decreased, because the 
 pipe is liable to be throttled at the joints, additional bends may inter- 
 pose, or stop-cocks may be used, or the back-pressure may be increased. 
 
LOSS OF HEAD. 
 
 745 
 
 Friction Loss iu Clean Cast-iron Pipe. 
 
 Compiled from Weston's "Friction of Water in Pipes" as computed from 
 
 formulas of Henry Darcy. 
 
 Pounds loss per 1000 feet in pipe of given diameter. (Small lower 
 figures give Velocity in Feet per Second.) 
 
 U. S.Gals per 
 Mill, and (Cu. 
 Ft. per Sec.) 
 
 Diameter of Pipe in Inches. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 20 
 
 24 
 
 30 
 
 0.66 
 
 0.23 
 
 0~01 
 0.45 
 
 Q.03 
 
 fi8 
 
 250 
 
 (0.56) 
 500 
 (1.11) 
 750 
 (1.67) 
 1,000 
 (2.23) 
 
 60 
 11 
 220 
 23 
 477 
 34 
 
 20 
 6.4 
 82 
 13.0 
 184 
 19.0 
 328 
 26.0 
 
 6.4 
 4.0 
 25.8 
 8.2 
 58.0 
 12.2 
 103.0 
 16.3 
 
 2.5 
 
 2.8 
 10.0 
 6.0 
 23.0 
 8.0 
 40.0 
 11.0 
 
 0.6 
 1.6 
 2.3 
 3.2 
 5.0 
 4.8 
 9.0 
 6.4 
 
 0.2 
 1.2 
 0.7 
 2.4 
 1.6 
 3.1 
 2.9 
 4.1 
 
 0.07 
 0.7 
 0.29 
 1.4 
 0.66 
 2.1 
 1.20 
 2.8 
 
 0.03 
 0.52 
 0.13 
 1.04 
 0.30 
 1.56 
 0.53 
 2.08 
 
 0.83 
 2.60 
 1.10 
 ? 1? 
 
 0.02 
 0.4 
 0.07 
 0.8 
 0.15 
 1.2 
 0.27 
 1.6 
 
 0.01 
 
 0.26 
 0.02 
 0.51 
 0.05 
 0.77 
 0.09 
 1.0 
 
 0.00 
 0.18 
 0.01 
 0.35 
 0.02 
 0.53 
 0.03 
 0.71 
 
 1,250 
 
 (2.79) 
 1,500 
 (3.34) 
 1,750 
 (3.90) 
 2,000 
 (4.46) 
 
 ..*.. 
 
 
 161.0 
 20.4 
 231.9 
 24.5 
 
 63.0 
 14.0 
 91.0 
 17.0 
 123.0 
 20.0 
 160.0 
 23.0 
 
 14.0 
 8.0 
 21.0 
 10.0 
 28.0 
 11.0 
 37.0 
 13.0 
 
 4.6 
 5.1 
 6.6 
 6.1 
 
 1.80 
 3.6 
 2.60 
 4 3 
 
 0.42 
 2.0 
 0.61 
 2 4 
 
 0.14 
 1.3 
 0.20 
 1 5 
 
 0.06 
 0.89 
 0.08 
 1 06 
 
 
 
 
 
 9.0 
 
 7.1 
 12.0 
 
 8.2 
 
 3.60 
 5.0 
 4.70 
 5.7 
 
 1.64 
 3.65 
 2.14 
 4.17 
 
 0.83 
 2.8 
 1.10 
 3.2 
 
 0.27 
 1.8 
 0.35 
 2.0 
 
 0.11 
 1.24 
 0.14 
 1.42 
 
 6:65 
 0.91 
 
 
 
 
 
 
 
 
 
 
 
 
 2,500 
 
 (5.57) 
 3,000 
 (6.68) 
 4,000 
 (8.91) 
 5,000 
 (11.14) 
 
 Diam. of 
 Pipeinln. 
 
 
 
 58.0 
 16.0 
 
 18.0 
 10.2 
 26.0 
 12.0 
 
 7.30 
 7.1 
 10.00 
 
 8.5 
 
 3.34 
 5.21 
 4.81 
 6.25 
 8.55 
 8.34 
 
 1.70 
 4.0 
 2.40 
 4.8 
 4.30 
 6.4 
 6.80 
 8.0 
 
 0.55 
 2.6 
 0.79 
 3.1 
 .40 
 4.1 
 2.20 
 5.1 
 
 0.22 
 1.80 
 0.32 
 2.10 
 0.56 
 2.80 
 1.00 
 3 .-60 
 
 0.07 
 1.13 
 0.10 
 1.40 
 0.18 
 l.SO 
 0.29 
 2.30 
 
 0.41 
 2.70 
 0.56 
 3.20 
 0.73 
 3 fiO 
 
 
 
 
 
 36 
 
 48 
 
 
 
 
 
 
 
 
 
 
 
 
 0.11 
 1.6 
 
 0.03 
 
 0.89 
 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 6,000 
 
 (13.37) 
 7,000 
 (15.60) 
 8,000 
 (17.82) 
 9,000 
 (20.05) 
 10,000 
 (22.28) 
 
 0.16 
 1.9 
 0.23 
 2.2 
 0.29 
 2.5 
 0.37 
 2.8 
 0.45 
 3.1 
 
 0.04 
 1.06 
 0.05 
 1.2 
 0.07 
 1.4 
 0.09 
 1.6 
 0.11 
 1.8 
 
 
 
 
 
 
 3.20 
 6.1 
 4.30 
 7.1 
 
 1.30 
 4.30 
 1.70 
 5.00 
 2.20 
 "> 70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2.80 
 6.40 
 
 0.92 
 4.10 
 1.13 
 4.50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Vel.ft.persec.. 
 Hd.duevel.ft . 
 
 0.016 
 
 2 
 0.062 
 
 3 
 0.14 
 
 4 
 0.25 
 
 5 
 
 0.39 
 
 6 
 0.56 
 
 7 
 0.76 
 
 8 
 1.0 
 
 9 
 1.3 
 
 10 
 1.6 
 
 It 
 1.9 
 
 12 
 2.2 
 
 Vel.ft.persec.. 
 Hd.duevel.ft.. 
 
 13 
 2.6 
 
 14 
 3.1 
 
 15 
 3.5 
 
 16 
 4.0 
 
 17 
 
 4.5 
 
 18 
 5.0 
 
 19 
 5.6 
 
 20 
 6.2 
 
 25 
 9.3 
 
 30 
 14.0 
 
 40 
 24.8 
 
 50 
 
 38.8 
 
 These losses are for new, clean, straight, tar-coated, cast-iron pipes. For 
 pipes that have been in service a number of years the losses 
 will be larger on account of corrosion and incrustation, and 10 years 1.3 
 the losses in the tables should be multiplied under average 20 1.6 
 
 conditions by the factors opposite; but they must be used 30 2.0 
 
 with much discretion, for some waters corrode pipes much 50 2.6 
 
 more rapiclly than others. 75 3.4 
 
 The same figures may be used for wrought-iron pipes which are not 
 subject to a frequent change of water. 
 
746 HYDRAULIC FORMULAE 
 
 Hydraulic Formulae. (The Lombard Governor Co., 
 
 Head (#) in feet. Pressure (P). in Ibs. per sq. in. Diameter (>) in 
 feet Area (A) m sq. ft. Quantity (Q) in cubic ft. per second. Time 
 (T) in seconds. 
 
 Spouting velocity = 8.02 \/~H. 
 
 Time (TJ to acquire spouting velocity in a vertical pipe, or (Ti) in a 
 pipe on an angle (0) from horizontal: 
 
 T!= 8.02 *SH + 32.17, T 2 = 8.02 V# + 32.17 sin Q. 
 
 Head (H) or pressure (P) which will vent any quantity (Q) through a 
 round orifice of any diameter (Z>) or area (A): 
 H = Q2 .=- 14.1 >4 = QZ + 23.75 A2; P = Q* -*- 34.1 M = 2 -j- 55.3 A\ 
 
 Quantity (Q) discharged through a round orifice of any diameter (D) or 
 area (A) under any pressure (P) or under any head (H} : 
 
 Q = VP X 55.3 X A 2 =Vpx 34.1 X Z> 4 ; 
 = V# x 23.75 X A 2 =V#X 14.71 X Z> 4 . 
 
 Diameter (D) or area (A) of a round orifice to vent any quantity (Q) 
 under any head (H) or under any pressure (P): 
 
 Time (T) of emptying a vessel of any area (A) through an orifice of any 
 area (a) anywhere in its side: T = 0.416 A VH * a. 
 ; Time (T) of lowering a water level from (H) to (ft) in a tank of area A 
 through an orifice of any area (a) in its side. 2 7 =0.416A(V / ^ \/&) -=- a . 
 
 Kinetic energy (K) or foot-pounds in water in a round pipe of any 
 diameter (Z>) when moving at velocity (F): K = 0.76 X D 2 X L X V 2 . 
 
 Area (a) of an orifice to empty a tank of any area (A) in any time (T) 
 from any head (H): a = T * 0.409 A V#. 
 
 Area (a) of an orifice to lower water in a tank of area (A) from head (//) 
 to (ft) in time (T 7 ): a = T * 0.409 X AX (^H - Vft). 
 
 Compound Pipes and Pipes with Branches. (Unwin.) Loss of 
 head in a main consisting of different diameters. (1) Constant discharge. 
 Total loss of head H = hi + ft 2 + ft 3 = 0.1008/Q 2 (li/dj + h/dv> + h/d^}. 
 
 (2) Constant velocity in the main, the discharge Diminishing from sec- 
 tion to section. H = 0.0551 /y 5 /2(Z 1 /x / Q 1 + 1 2 /VQ 2 + 1 3 /VQ S ), Equiv- 
 alent main of uniform diameter. Length of equivalent main 
 
 Loss of head in a main of uniform diameter in which the discharge de- 
 creases uniformly along its length, such as a main with numerous branch 
 pipes uniformly spaced and delivering equal quantities: ft = 0.0336 
 fQH/d*, Q being the quantity entering the pipe. The loss of head is just 
 one-third of the loss in a pipe carrying the uniform quantity Q through- 
 out its length. 
 
 Loss of head in a pipe that receives Q cu. ft. per sec. at the inlet, and 
 delivers Q x cu. ft. at x ft. from the inlet, having distributed qx cu. ft. 
 uniformly in that distance, h x 0.1008/z (Q x + 0.55 qx)/d 5 . 
 
 Delivery by two or more mains, in parallel. Total discharge = Q t + Q 
 4-Qa = 3.149 ^h/f (V^s/k+Vd^H- VdsVfc) . Diameter ofan equivalent 
 main to discharge the same total quantity, d=(v^+v / (/ 2 5+\/^5) 2 /5. 
 
 Rifled Pipes for Conveying Heavy Oils. (Eng. Rec., May 23, 1908.) 
 The oil from the California fields is a heavy, viscous fluid. Attempts 
 to handle it in long pipe lines of the ordinary type have not been practi- 
 cally successful. High pumping pressures are required, resulting in large 
 expense for pipe and for pumping equipment. 
 
LOSS OF HEAD. 
 
 747 
 
 The method of pumping in the rifled-pipe line is to inject about 10 per 
 cent of water with the oil and to give the cil and water a centrifugal 
 motion, by means of the rifled pipe, sufficient to throw the water to the 
 outside, where it forms a thin film of 'lubrication between the oil and the 
 sides of the pipe that greatly reduces the friction. The rifled pipe de- 
 livers at ordinary temperatures eight t9 ten times as much oil, through a 
 long line, as does a line of ordinary pipe under similar conditions. An 
 8-in. rifled pipe line 282 miles in length has been built from the Kern oil 
 fields to Porta Costa, on tidewater near San Francisco. The pipe is 
 rifled with six helical grooves to the circumference, these grooves making 
 a complete turn through 360 deg. in 10 ft. of length. 
 
 Loss of Pressure Caused by Valves and Fittings The data given 
 below are condensed from the results of experiments by John R. Freeman 
 for the Inspection Department of the Assoc. Facty. Mut. Ins. Cos. The 
 friction losses in ells and tees are approximate. Fittings of the same nom- 
 inal size with the different curvatures and different smoothness as made 
 by different manufacturers will cause materially different friction losses. 
 The figures are the number of feet of clean, straight pipe of same size 
 which would cause the same loss as the fitting. Grinnell dry-pipe valve. 
 6-in., 80 ft.; 4-in., 47 ft. Grinnell alarm check, 6-in., 100 ft.; 4-in., 47 ft. 
 Pratt & Cady check valve, 6-in., 50 ft.; 4-in., 25 ft. 4-in. Walworth globe 
 check valve, 6-in., 200 ft.; 4-in., 130' ft. 21/2 in. to 8-in. ells, long-turn, 
 4 ft.; short-turn 9 ft. 3-in. to 8-in, tees, long-turn, 9 ft.; short-turn, 17 ft. 
 One-eighth bend, 5 ft. 
 
 Effect of Bends and Curves in Pipes. Weisbach's rule for bends: 
 Loss of head in feet = [0.131 + 1.847 (^) 7/2 J X ~ X ^~, in which r 
 
 * internal radius of pipe in feet, R- = radius of curvature of axis of pipe, 
 v = velocity in feet per second, and a = the central angle, or angle sub- 
 tended by the bend. 
 
 Hamilton Smith, Jr., in his work on Hydraulics, says: The experimental 
 data at hand are entirely insufficient to permit a satisfactory analysis of 
 this quite complicated subject; in fact, about the only experiments of 
 value are those made by Bossut and Dubuat with small pipes. 
 
 Curves. If the pipe has easy curves, say with radius not less than 5 
 diameters of the pipe, the flow will not be materially diminished, provided 
 the tops of all curves are kept below the hydraulic grade-line and provision 
 be made for escape of air from the tops of all curves. (Trautwine.) 
 
 Williams, Hubbell and Fenkel (Trans. A. S. C. E., 1901) C9nclude from 
 an extensive series of experiments that curves of short radius, down to 
 about 21/2 diameters, offer less resistance to the flow of water than do 
 those of longer radius, and that earlier theories and practices regarding 
 curve resistance are incorrect. For a 90 curve in 30 in. cast-iron pipe, 
 6 ft. radius, they found the loss of head 15.7% greater than that of a 
 straight pipe of equal length; with 10 ft. radius. 17.3% greater: with 25 ft. 
 radius, 52.7% greater; and with 60 ft. radius, 90.2% greater. 
 
 Friction Heads for Elbows. Heads Required to Overcome the 
 Resistance of Circular 90 Bends. 
 
 (U. S. Cast Iron Pipe & Foundry Co.) 
 
 Velocity 
 
 Radius of Bend in Diameters of Pipe. 
 
 in Feet 
 Per 
 
 0.5 
 
 0.75 
 
 1.00 
 
 1.25 
 
 1.5 | 2.0 
 
 3.0 
 
 5.0 
 
 Second. 
 
 Head, in Feet. 
 
 1 
 
 0.016 
 
 0.005 
 
 0.002 
 
 0.002 
 
 0.001 
 
 0.001 
 
 0.001 
 
 0.001 
 
 2 
 
 .062 
 
 .018 
 
 .009 
 
 .007 
 
 .005 
 
 .005 
 
 .004 
 
 .004 
 
 3 
 
 .140 
 
 .041 
 
 .020 
 
 .015 
 
 .012 
 
 .011 
 
 .010 
 
 .009 
 
 4 
 
 .245 
 
 .072 
 
 .036 
 
 .026 
 
 .021 
 
 .019 
 
 .017 
 
 .016 
 
 5 
 
 .388 
 
 .113 
 
 .056 
 
 .041 
 
 .033 
 
 .029 
 
 .027 
 
 .025 
 
 6 
 
 .559 
 
 .162 
 
 .081 
 
 .059 
 
 .048 
 
 .042 
 
 .038 
 
 .036 
 
 7 
 
 .761 
 
 .221 
 
 .110 
 
 .080' 
 
 .066 
 
 .057 
 
 .052 
 
 .050 
 
 8 
 
 .994 
 
 .288 
 
 .144 
 
 .104 
 
 .086 
 
 .074 
 
 .069 
 
 .065 
 
 9 
 
 1.260 
 
 .365 
 
 .182 
 
 .132 
 
 .108 
 
 .094 
 
 .086 
 
 .082 
 
 10 
 
 1.550 
 
 .450 
 
 .225 
 
 .163 
 
 .134 
 
 .116 
 
 .106 
 
 .101 
 
 12 
 
 2.340 
 
 .649 
 
 .324 
 
 .236 
 
 .192 
 
 .167 
 
 .153 
 
 .145 
 
748 
 
 HYDRAULICS. 
 
 Loss of Head In Pipes, Tees and Elbows. Results of tests made 
 on locomotive water columns by Arthur N. Talbot and Melvin L. 
 Enger (Bulletin No. 48, Univ. of 111. Engineering Experiment Station) 
 may be expressed by the following formula: Loss of head in 100 ft. of 
 new cast-iron pipe for sizes above 6 in. diam. = 0.044 v 1 * * d 1 - 25 , in 
 which v = velocity of flow in feet per sec., and d = internal diameter of 
 pipe, in ft. The results for pipes from 8 to 24 in. in diameter agree 
 closely with those obtained by Williams and Hazen for pipes after 
 about three years of service, with the diagram given in Turneaure and 
 Russell's "Public Water Supplies," and with the formula of Unwin; 
 they are, however, generally smaller than those given by the Ellis and 
 Howland tables and by Darcy's formula. 
 
 The following tables are taken from diagrams included in the Bulle- 
 tin; they give the values selected by the Committee on Water Service, 
 Am. Ry. Eng'g and Maintenance of Way Association, as representing 
 the maximum results of numerous tests. 
 
 LOSS OF HEAD IN TEES, IN FEET. 
 
 Discharge, 
 Gal per 
 
 Cu. Ft. 
 
 
 
 Sizes o 
 
 f Tees. 
 
 
 
 Min. 
 
 Sec. 
 
 8 In. 
 
 10 In. 
 
 12 In. 
 
 14 In. 
 
 16 In. 
 
 18 In. 
 
 1000. ., 
 
 20.5 
 
 1.1 
 
 0.4 
 
 0.25 
 
 
 
 
 2000. ., 
 
 41 
 
 4 
 
 1 7 
 
 95 
 
 40 
 
 25 
 
 13 
 
 3000 
 
 61 5 
 
 8 7 
 
 3 9 
 
 1 95 
 
 1 00 
 
 60 
 
 35 
 
 4000 
 
 82 
 
 
 6 7 
 
 3 35 
 
 1 75 
 
 1.10 
 
 65 
 
 5000. . 
 
 102 5 
 
 
 10 3 
 
 5 20 
 
 2 70 
 
 1 60 
 
 1 00 
 
 6000. ., 
 
 123 
 
 
 
 7 30 
 
 3 90 
 
 2 30 
 
 1 45 
 
 7000 
 
 143.5 
 
 
 
 
 5 30 
 
 3 10 
 
 2 00 
 
 8000 
 
 164 
 
 
 
 
 6.80 
 
 3.90 
 
 2.60 
 
 LOSS OF HEAD IN ELBOWS, IN FEET. 
 
 (Radius of curvature of elbow axis = 1.5 X diameter of elbow.) 
 
 Discharge, 
 Gal per 
 
 Cu. Ft. 
 Der 
 
 
 
 Sizes of 
 
 Elbows. 
 
 
 
 Min. 
 
 Sec. 
 
 8 In. 
 
 10 In. 
 
 12 In. 
 
 14 In. 
 
 16 In. 
 
 18 In. 
 
 1000. . 
 
 20.5 
 
 0.2 
 
 
 
 
 
 
 2000 
 
 41 
 
 1.2 
 
 0.5 
 
 0.20 
 
 0.10 
 
 
 
 3000. ., 
 
 61.5 
 
 2.8 
 
 ] 1 
 
 50 
 
 25 
 
 15 
 
 
 4000 
 
 82 
 
 
 1 9 
 
 95 
 
 50 
 
 25 
 
 10 
 
 5000 
 6000. . 
 
 102.5 
 123 
 
 
 3.2 
 
 1.50 
 2 20 
 
 0.75 
 1 15 
 
 0.40 
 60 
 
 0.15 
 25 
 
 7000 ' ! 
 8000.., 
 
 143.5 
 164 
 
 
 
 3.00 
 
 1.65 
 2.10 
 
 0.87 
 1.15 
 
 0.50 
 0.70 
 
 (Radius of curvature = 3 X diameter.) 
 
 1000 
 2000. .. 
 
 20.5 
 41 
 
 0.25 
 0.75 
 
 0.35 
 
 10 
 
 
 
 
 
 
 3000 
 
 61.5 
 
 2.00 
 
 0.80 
 
 0.40 
 
 0.15 
 
 
 
 4000. ., 
 
 82 
 
 4 00 
 
 1 45 
 
 70 
 
 33 
 
 12 
 
 
 5000 
 6000. 
 
 102.5 
 123 
 
 
 2.25 
 
 1.10 
 1 60 
 
 0.50 
 70 
 
 0.20 
 40 
 
 0.07 
 10 
 
 7000. . 
 
 143 5 
 
 
 
 2 20 
 
 1 00 
 
 58 
 
 25 
 
 8000 
 
 164 
 
 
 
 3.00 
 
 1.45 
 
 0.85 
 
 0.45 
 
 Hydraulic Grade-line. In a straight tube of uniform diameter 
 throughout, running full and discharging freely into the air, the hydraulic 
 grade-line is a straight line drawn from the discharge end to a point imme- 
 diately over the entry end of the pipe and at a depth below the surface 
 equal to the entry and velocity heads. (Trautwine.) 
 
 In a pipe leading from a reservoir, no part of its length should be above 
 the hydraulic grade-line. 
 
 Air-bound Pipes. A pipe is said to be air-bound when, In conse- 
 quence of air being entrapped at the high points of vertical curves in the 
 line, water will not flow out of the pipe, although the supply is higher than 
 the outlet. The remedy is to provide cocks or valves at the high points, 
 
FIRE-STREAMS. . 749 
 
 through which the air may be discharged. The valve may be made 
 automatic by means of a float. 
 
 Water-Hammer. When selecting valves and fittings, the possibility 
 of shock or strain due to water-hammer, in excess of the average work- 
 ing pressure of the line or system, should be considered. Many valves 
 and fittings, installed where the working pressure under nomal con- 
 ditions would be low, have failed because of pressure due to water- 
 hammer. This danger can be avoided by proper cushioning of the 
 line by air chambers, or by relief valves. 
 
 When a valve in a pipe is closed while the water is flowing, the velocity 
 of the water behind the valve is retarded and a dynamic pressure is 
 produced. When the valve is closed quickly this dynamic pressure 
 may be very great. It is then called "water-hammer" or "water- 
 ram," and it causes in many cases fracture of the pipe. It is provided 
 against by arrangements which prevent the rapid closing of the valve. 
 Formulae for the pressure produced by this shock are (see Merriman's 
 Hydraulics) 
 
 p = 0.027 H_po + pi. . . (1) P=63v-Po+Pi (2) 
 
 where po = the static pressure, Ib. per sq. in., when there is no flow, 
 Pi = the static pressure when the flow is in progress, p = the maximum 
 dynamic pressure due to the water-hammer in excess over the pressure 
 p* v = the velocity in feet per second, L = length of pipe back from 
 the valve in feet, and t = time of closing the valve in seconds. Formula 
 (1) is to be used when t is greater than 0.000428L and (2) when t is 
 equal to or less than this. 
 
 From the first of these formulae the value of t when p is found 
 to be t = 0.027 Lv - (PO-PI), which is the time required for the 
 valve closing in order that there may be no water-hammer. 
 
 Vertical Jets. (Molesworth.) H = head of water, h = height of 
 jet, d = diameter of jet, K = coefficient, varying with ratio of diameter 
 of jet to head;' then h = KH. 
 
 If H = d X 300 600 1000 1500 1800 2800 3500 4500 
 K = 0.96 0.9 O.S5 0.8 0.7 0.6 0.5 0.25 
 
 Water Delivered through Meters. (Thomson Meter Co.) The 
 best modern practice limits the velocity in water-pipes to 10 lineal feet 
 per second. Assume this as a basis of delivery, and we find, for the sev- 
 eral sizes of pipes usually metered, the following approximate results: 
 Nominal diameter of pipe in inches: 
 
 3/8 5 /8 3/4 1 11/2 2 3 4 6 
 
 Quantity delivered, in cubic feet per minute, due to said velocity: 
 0.46 1.28 1.85 3.28 7.36 13.1 29.5 52.4 117.9 
 
 Prices Charged for Water in Different Cities. (National Meter Co.) 
 
 Average minimum price for 1000 gallons in 163 places .9.4 cents. 
 
 Average maximum price for 1000 gallons in 163 places 28 
 
 Extremes, 21/2 cents to 100 
 
 FIRE-STREAMS. 
 
 Fire-Stream Tables. The tables on pages 750 and 751 are con- 
 densed from one contained in the pamphlet of "Fire-Stream Tables" 
 of the Associated Factory Mutual Fire Ins. Cos., based on the experi- 
 ments of John K. Freeman, Trans. A. S. C. E., vol. xxi, 1889. 
 
 The pressure in the first column is that indicated by a gauge attached 
 at the base of the play pipe and set level with the end of the nozzle. The 
 vertical and horizontal distances, in 2d and 3d cols., are those of effective 
 fire-streams with moderate wind. The maximum limit of a " fair stream " 
 is about 10% greater for a vertical stream; 12% for a horizontal stream. 
 In still air much greater distances are reached by the extreme drops. 
 The pressures given are for the best quality of rubber-lined hose, smooth 
 inside. The hose friction varies greatly in different kinds of hose, accord- 
 ing to smoothness of inside surface, and pressures as much as 50% 
 greater are required for the same delivery in long lengths of inferior 
 rubber-lined or linen hose. The pressures at the hydrant are those while 
 the stream is flowing, and are those required with smooth nozzles. Ring 
 
750 
 
 HYDRAULICS. 
 
 nozzles require greater pressures. With the same pressures at the base 
 01 tne play pipe, the discharge of a3/ 4 -in. smooth nozzle is the same as that 
 or a 7/8-m. ring nozzle; of a 7/g-in. smooth nozzle, the same as that of a ' 
 1-in. ring nozzle. 
 
 The figures for hydrant pressure in the body of the table are derived 
 py adding to the nozzle or play-pipe pressure the friction loss in the 
 nose, and also the friction loss of a Chapman 4-way independent gate 
 hydrant ranging from 0.86 Ib. for 200 gals, per min. flowing to 2.31 Ibs. 
 for 600 gals. 
 
 The following notes are taken from the pamphlet referred to. The 
 discharge as stated in Ellis's tables and in their numerous copies in trade 
 catalogues is from 15 to 20% in error. 
 
 In the best rubber-lined hose, 2i/2-in. diam., the loss of head due to 
 friction, for a discharge of 240 gallons per minute, is 14.1 Ibs. per 100 ft. 
 length; in inferior rubber-lined mill hose, 25.5 Ibs., and in unlined linen 
 hose, 33.2 Ibs. 
 
 Less than a ll/s-in. smooth-nozzle stream with 40 Ibs. pressure at the 
 base of the play pipe, discharging about 240 gals, per min., cannot be 
 called a first-class stream for a factory fire. 80 Ibs. per sq. in. is con- 
 sidered the best hydrant pressure for general use; 100 Ibs. should not be 
 exceeded, except for very high buildings, or lengths of hose over 300 ft. 
 
 Hydrant Pressures Required with Different Sizes and Lengths of 
 Hose. (J. R. Freeman, Trans. A. S. C. E., 1889.) 
 
 3/4-inch smooth nozzle. * 
 
 J 
 
 r 
 
 1 
 
 Fire- 
 steam 
 Distance. 
 
 Gal. per Min. 
 
 Hydrant Pressure with Different Lengths of 
 Hose to Maintain Pressure at Base of Play Pipe. 
 
 Vert. 
 
 Hor. 
 
 50ft. 
 
 100ft. 
 
 200ft. 
 
 300ft. 
 
 400ft. 
 
 500ft. 
 
 600ft. 
 
 800ft. 
 
 1000 
 ft. 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 
 17 
 33 
 
 48 
 60 
 67 
 72 
 76 
 79 
 81 
 83 
 
 19 
 29 
 37 
 44 
 50 
 54 
 58 
 62 
 65 
 68 
 
 52 
 73 
 90 
 104 
 116 
 127 
 137 
 147 
 156 
 164 
 
 10 
 21 
 31 
 42 
 52 
 63 
 73 
 84 
 94 
 105 
 
 11 
 
 22 
 32 
 43 
 54 
 65 
 75 
 86 
 97 
 108 
 
 11 
 23 
 34 
 46 
 57 
 68 
 80 
 91 
 102 
 114 
 
 12 
 24 
 36 
 48 
 60 
 72 
 84 
 96 
 108 
 120 
 
 13 
 25 
 38 
 50 
 63 
 76 
 88 
 101 
 113 
 126 
 
 13 
 26 
 40 
 53 
 66 
 79 
 92 
 106 
 119 
 132 
 
 14 
 28 
 41 
 55 
 69 
 83 
 97 
 111 
 124 
 138 
 
 15 
 30 
 45 
 60 
 75 
 90 
 105 
 120 
 135 
 150 
 
 16 
 32 
 49 
 65 
 81 
 97 
 114 
 130 
 146 
 163 
 
 7/8-inch smooth nozzle. 
 
 10 
 
 18 
 
 21 
 
 71 
 
 11 
 
 11 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 19 
 
 22 
 
 20 
 
 34 
 
 33 
 
 100 
 
 22 
 
 23 
 
 25 
 
 27 
 
 30 
 
 32 
 
 34 
 
 39 
 
 43 
 
 30 
 
 49 
 
 42 
 
 123 
 
 33 
 
 34 
 
 38 
 
 41 
 
 45 
 
 48 
 
 51 
 
 58 
 
 65 
 
 40 
 
 62 
 
 49 
 
 142 
 
 43 
 
 46 
 
 50 
 
 55 
 
 59 
 
 64 
 
 68 
 
 78 
 
 87 
 
 50 
 
 71 
 
 55 
 
 159 
 
 54 
 
 57 
 
 63 
 
 69 
 
 74 
 
 80 
 
 86 
 
 97 
 
 108 
 
 60 
 
 77 
 
 61 
 
 174 
 
 65 
 
 69 
 
 75 
 
 82 
 
 89 
 
 96 
 
 103 
 
 116 
 
 130 
 
 70 
 
 81 
 
 66 
 
 188 
 
 76 
 
 80 
 
 88 
 
 96 
 
 104 
 
 112 
 
 120 
 
 136 
 
 152 
 
 80 
 
 85 
 
 70 
 
 201 
 
 87 
 
 91 
 
 101 
 
 110 
 
 119 
 
 128 
 
 137 
 
 155 
 
 173 
 
 90 
 
 88 
 
 74 
 
 213 
 
 98 
 
 103 
 
 113 
 
 123 
 
 134 
 
 144 
 
 154 
 
 174 
 
 195 
 
 100 
 
 90 
 
 76 
 
 224 
 
 109 
 
 114 
 
 126 
 
 137 
 
 148 
 
 160 
 
 171 
 
 194 
 
 216 
 
 1-inch smooth nozzle. 
 
 10 
 
 18 
 
 21 
 
 93 
 
 12 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 26 
 
 30 
 
 20 
 
 35 
 
 37 
 
 132 
 
 23 
 
 25 
 
 29 
 
 33 
 
 37 
 
 41 
 
 45 
 
 52 
 
 60 
 
 30 
 
 51 
 
 47 
 
 161 
 
 34 
 
 37 
 
 43 
 
 49 
 
 55 
 
 61 
 
 67 
 
 79 
 
 90 
 
 40 
 
 64 
 
 55 
 
 186 
 
 46 
 
 50 
 
 58 
 
 66 
 
 73 
 
 81 
 
 89 
 
 105 
 
 120 
 
 50 
 
 73 
 
 61 
 
 208 
 
 57 
 
 62 
 
 72 
 
 82 
 
 92 
 
 102 
 
 111 
 
 131 
 
 151 
 
 60 
 
 79 
 
 67 
 
 228 
 
 69 
 
 75 
 
 87 
 
 98 
 
 110 
 
 122 
 
 134 
 
 157 
 
 181 
 
 70 
 
 85 
 
 72 
 
 246 
 
 80 
 
 87 
 
 101 
 
 115 
 
 128 
 
 142 
 
 156 
 
 183 
 
 211 
 
 80 
 
 89 
 
 76 
 
 263 
 
 92 
 
 100 
 
 115 
 
 131 
 
 147 
 
 162 
 
 178 
 
 209 
 
 241 
 
 90 
 
 92 
 
 80 
 
 279 
 
 103 
 
 112 
 
 130 
 
 147 
 
 165 
 
 183 
 
 200 
 
 236 
 
 .... 
 
 100 
 
 96 
 
 83 
 
 295 
 
 115 
 
 125 
 
 144 
 
 164 
 
 183 
 
 203 
 
 223 
 
 
 
FIBE-STREAMS. 
 
 751 
 
 Hydrant Pressures Required with Different Sizes and Lengths of 
 
 Hose. Continued. 
 1 i/8-inch smooth nozzle. 
 
 A 
 
 Fire- 
 Steam 
 Distance. 
 
 a 
 
 1. 
 
 h 
 
 
 
 a 
 
 "08 
 
 o 
 
 Hydrant Pressure with Different Lengths of 
 Hose to Maintain Pressure at Base of Play Pipe. 
 
 Vert. 
 
 Hor. 
 
 50ft. 
 
 100ft. 
 
 200ft. 
 
 300ft. 
 
 400ft. 
 
 500ft. 
 
 600ft. 
 
 800ft. 
 
 1000 
 ft. 
 
 10 
 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 
 18 
 36 
 52 
 65 
 75 
 83 
 88 
 92 
 96 
 99 
 
 22 
 38 
 50 
 59 
 66 
 72 
 77 
 81 
 85 
 89 
 
 119 
 168 
 206 
 238 
 266 
 291 
 314 
 336 
 356 
 376 
 
 12 
 25 
 37 
 50 
 62 
 74 
 87 
 99 
 112 
 124 
 
 14 
 
 28 
 42 
 56 
 70 
 84 
 98 
 112 
 126 
 140 
 
 17 
 34 
 52 
 69 
 86 
 103 
 120 
 138 
 155 
 172 
 
 20 
 41 
 61 
 81 
 102 
 122 
 143 
 163 
 183 
 204 
 
 24 
 47 
 71 
 94 
 118 
 141 
 165 
 188 
 212 
 236 
 
 27 
 54 
 80 
 107 
 134 
 160 
 187 
 214 
 241 
 
 30 
 60 
 90^ 
 120 
 150 
 180 
 209 
 239 
 
 36 
 73 
 109 
 145 
 181 
 218 
 254 
 
 43 
 85 
 128 
 171 
 213 
 256 
 
 
 
 
 
 
 1 i/4-inch smooth nozzle. 
 
 10 
 20 
 30 
 40 
 50 
 60 
 
 19 
 37 
 53 
 67 
 77 
 85 
 
 22 
 40 
 54 
 63 
 70 
 76 
 
 1-48 
 209 
 256 
 296 
 331 
 363 
 
 14 
 27 
 41 
 55 
 68 
 82 
 
 16 
 32 
 49 
 65 
 81 
 97 
 
 21 
 42 
 63 
 84 
 106 
 127 
 
 26 
 52 
 78 
 104 
 130 
 156 
 
 31 
 62 
 93 
 124 
 155 
 186 
 
 36 
 72 
 108 
 144 
 180 
 216 
 
 41 
 
 82 
 123 
 164 
 204 
 245 
 
 51 
 
 101 
 
 152 
 203 
 
 254 
 
 61 
 
 121 
 
 182 
 243 
 
 70 
 
 91 
 
 81 
 
 39? 
 
 96 
 
 113 
 
 148 
 
 182 
 
 217 
 
 252 
 
 
 
 
 80 
 
 95 
 
 85 
 
 410 
 
 110 
 
 129 
 
 169 
 
 208 
 
 248 
 
 
 
 
 
 90 
 
 99 
 
 90 
 
 444 
 
 123 
 
 145 
 
 190 
 
 234 
 
 
 
 
 
 
 100 
 
 101 
 
 93 
 
 468 
 
 137 
 
 162 
 
 211 
 
 261 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 3/8-inch smooth nozzle. 
 
 10 
 
 20 
 30 
 40 
 
 20 
 38 
 55 
 69 
 
 23 
 42 
 56 
 66 
 
 182 
 257 
 315 
 363 
 
 16 
 31 
 47 
 62 
 
 19 
 39 
 
 58 
 77 
 
 27 
 53 
 80 
 107 
 
 34 
 68 
 103 
 137 
 
 42 
 83 
 125 
 166 
 
 49 
 98 
 147 
 196 
 
 56 
 113 
 169 
 226 
 
 71 
 143 
 214 
 
 86 
 173 
 259 
 
 50 
 
 79 
 
 73 
 
 405 
 
 78 
 
 96 
 
 134 
 
 171 
 
 208 
 
 245 
 
 
 
 
 60 
 
 87 
 
 79 
 
 445 
 
 93 
 
 116 
 
 160 
 
 205 
 
 250 
 
 
 
 
 
 70 
 
 92 
 
 84 
 
 480 
 
 109 
 
 135 
 
 187 
 
 239 
 
 
 
 
 
 
 
 80 
 
 97 
 
 88 
 
 514 
 
 \?A 
 
 154 
 
 214 
 
 
 
 
 
 
 
 90 
 
 100 
 
 92 
 
 M 1 ) 
 
 140 
 
 173 
 
 240 
 
 
 
 
 
 
 
 too 
 
 103 
 
 96 
 
 574 
 
 156 
 
 193 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Pump Inspection Table. 
 
 Discharge of nozzles attached to 50 ft. of 2 1 ,/2-in. best quality rubber- 
 lined hose, inside smooth. (J. R. Freeman.) 
 
 d 3 
 
 Size of Smooth Nozzle. 
 
 Ring Nozzle. 
 
 Wftj 
 
 1 3/4 
 
 1 1/2 
 
 1 3/8 
 
 1 V4 
 
 1 VS. 
 
 1 
 
 7/8 
 
 3/4 
 
 1 3 /8 
 
 1 V4 
 
 1 1/8 
 
 10 
 
 193 
 
 163 
 
 146 
 
 127 
 
 107 
 
 87 
 
 68 
 
 5? 
 
 118 
 
 101 
 
 84 
 
 20 
 
 274 
 
 232 
 
 206 
 
 179 
 
 151 
 
 123 
 
 96 
 
 72 
 
 167 
 
 143 
 
 119 
 
 30 
 
 335 
 
 283 
 
 251 
 
 219 
 
 184 
 
 150 
 
 118 
 
 88 
 
 205 
 
 175 
 
 145 
 
 40 
 
 387 
 
 327 
 
 291 
 
 253 
 
 213 
 
 173 
 
 136 
 
 101 
 
 237 
 
 202 
 
 168 
 
 50 
 
 432 
 
 366 
 
 323 
 
 283 
 
 238 
 
 194 
 
 152 
 
 113 
 
 264 
 
 226 
 
 188 
 
 60 
 
 473 
 
 400 
 
 357 
 
 309 
 
 261 
 
 213 
 
 167 
 
 124 
 
 289 
 
 247 
 
 205 
 
 70 
 
 510 
 
 432 
 
 385 
 
 334 
 
 281 
 
 230 
 
 180 
 
 134 
 
 313 
 
 267 
 
 222 
 
 80 
 
 546 
 
 461 
 
 412 
 
 357 
 
 301 
 
 246 
 
 192 
 
 144 
 
 334 
 
 285 
 
 237 
 
 90 
 
 579 
 
 490 
 
 437 
 
 379 
 
 319 
 
 261 
 
 204 
 
 152 
 
 355 
 
 303 
 
 252 
 
 100 
 
 610 
 
 515 
 
 461 
 
 400 
 
 337 
 
 275 
 
 215 
 
 161 
 
 374 
 
 319 
 
 266 
 
752 
 
 HYDRAULICS. 
 
 Pipe Sizes for Ordinary Fire-Streams. 
 
 (U. S. Cast Iron Pipe & Foundry Co., 1914.) 
 
 No. 
 
 40 Lb. 
 
 50 Lb. 
 
 60 Lb. 
 
 70 Lb. 
 
 80 Lb. 
 
 90 Lb. 
 
 of 
 
 1 l/o 
 
 Pressure. 
 
 Pressure. 
 
 Pressure. 
 
 Pressure. 
 
 Pressure. 
 
 Pressure. 
 
 / 8 
 
 In. 
 
 a 
 
 
 
 
 
 a 
 
 
 d 
 
 
 ^a 
 
 
 3 
 
 
 Hose 
 Noz- 
 
 || 
 
 1 
 
 II 
 
 o 
 
 .11 
 
 o 
 
 it 
 
 o 
 
 li 
 
 o 
 
 |i 
 
 ! 
 
 zles. 
 
 *'& 
 
 E 
 
 c/] 
 
 | 
 
 Pn03 
 
 E 
 
 fig 
 
 g 
 
 f^'m 
 
 g 
 
 ftai 
 
 E 
 
 1 
 
 4 
 
 20 
 
 6 
 
 23 
 
 6 
 
 25 
 
 6 
 
 27 
 
 6 
 
 29 
 
 6 
 
 30 
 
 2 
 
 6 
 
 40 
 
 8 
 
 45 
 
 8 
 
 50 
 
 8 
 
 53 
 
 8 
 
 57 
 
 8 
 
 61 
 
 3 
 
 8 
 
 61 
 
 8 
 
 68 
 
 10 
 
 74 
 
 10 
 
 80 
 
 10 
 
 86 
 
 10 
 
 91 
 
 4 
 
 10 
 
 81 
 
 10 
 
 90 
 
 10 
 
 99 
 
 10 
 
 107 
 
 12 
 
 114 
 
 12 
 
 121 
 
 5 
 
 10 
 
 101 
 
 12 
 
 113 
 
 12 
 
 124 
 
 12 
 
 134 
 
 12 
 
 143 
 
 12 
 
 152 
 
 6 
 
 12 
 
 121 
 
 12 
 
 135 
 
 12 
 
 149 
 
 14 
 
 160 
 
 14 
 
 172 
 
 14 
 
 182 
 
 7 
 
 12 
 
 141 
 
 14 
 
 158 
 
 14 
 
 174 
 
 14 
 
 187 
 
 14 
 
 200 
 
 16 
 
 212 
 
 8 
 
 12 
 
 162 
 
 14 
 
 181 
 
 14 
 
 199 
 
 16 
 
 214 
 
 16 
 
 229 
 
 16 
 
 242 
 
 9 
 
 14 
 
 182 
 
 14 
 
 203 
 
 16 
 
 223 
 
 16 
 
 241 
 
 16 
 
 257 
 
 18 
 
 273 
 
 10 
 
 14 
 
 202 
 
 16 
 
 226 
 
 16 
 
 248 
 
 16 
 
 267 
 
 18 
 
 286 
 
 18 
 
 303 
 
 11 
 
 16 
 
 222 
 
 16 
 
 248 
 
 18 
 
 273 
 
 18 
 
 294 
 
 18 
 
 314 
 
 18 
 
 333 
 
 12 
 
 16 
 
 243 
 
 18 
 
 271 
 
 18 
 
 298 
 
 18 
 
 321 
 
 20 
 
 343 
 
 20 
 
 364 
 
 13 
 
 16 
 
 263 
 
 18 
 
 293 
 
 18 
 
 323 
 
 20 
 
 348 
 
 20 
 
 372 
 
 20 
 
 394 
 
 14 
 
 18 
 
 283 
 
 18 
 
 316 
 
 20 
 
 348 
 
 20 
 
 374 
 
 20 
 
 400 
 
 20 
 
 424 
 
 15 
 
 18 
 
 303 
 
 20 
 
 339 
 
 20 
 
 372 
 
 20 
 
 401 
 
 20 
 
 429 
 
 24 
 
 455 
 
 Flow given in cubic feet per minute. Figures are based on 1 %-in. 
 smooth-bore nozzles, playing simultaneously and attached to 200 ft. 
 of best quality rubber-lined hose; pressures measured at hose connec- 
 tions. Velocity of water in pipe, approximately 3 ft. per second. 
 
 Friction Loss in Rubber-Lined Cotton Hose with Smoothest Lining. 
 
 03 
 
 1 
 "o 
 
 a 
 
 c3 
 
 3 
 
 2 
 21/8 
 21/4 
 23/8 
 
 21/2 
 
 18 
 
 fa 
 
 * 
 
 Gallons per Minute Flowing. 
 
 dj 
 
 |l 
 
 > & 
 
 Velocity 
 Head 
 72 - 20. 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 1000 
 
 Friction Loss, Pounds per 100ft. Length. 
 
 Ft. 
 
 Lbs. 
 
 0.17 
 0.69 
 1.5 
 2.7 
 4.2 
 6.1 
 8.2 
 10.7 
 13.6 
 16.7 
 
 6.836 
 5.170 
 3.790 
 2.895 
 2.240 
 1.748 
 1.391 
 1.097 
 0.900 
 0:416 
 0.214 
 
 27.3 
 20.7 
 15.2 
 11.6 
 9.0 
 7.0 
 5.6 
 4.4 
 3.6 
 1.7 
 0.9 
 
 61.5 
 46.5 
 34.1 
 26.1 
 20.2 
 15.7 
 12.5 
 9.9 
 8.1 
 3.7 
 1.9 
 
 109 
 82.7 
 60.6 
 46.3 
 35.8 
 23.0 
 22.3 
 17.6 
 14.4 
 6.7 
 3.4 
 
 171 
 129 
 94.7 
 72.4 
 56.0 
 43.7 
 34.8 
 27.4 
 22.5 
 10.4 
 5.4 
 
 
 
 
 
 5 
 
 10 
 15 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 
 0.39 
 1.6 
 3.5 
 6.2 
 9.7 
 14.0 
 19.0 
 24.8 
 31.4 
 38.8 
 
 189 
 136 
 104 
 80.6 
 62.9 
 50.1 
 39.5 
 32.4 
 15.0 
 7.7 
 
 
 
 
 186 
 138 
 110 
 85.7 
 68.2 
 53.8 
 44.1 
 20.4 
 10.5 
 
 
 
 185 
 143 
 112 
 89.0 
 70.2 
 57.6 
 26.6 
 13.7 
 
 224 
 175 
 139 
 110 
 90 
 41.6 
 21.4 
 
 The above table is computed on the basis of 14 Ibs. per 100 ft. length 
 of 2i/2-in. hose with 250 gals, per min. flowing, as found in Freeman's 
 tests, assuming that the loss varies as the square of the quantity, and 
 for different diameters and the same quantity inversely as the 5th power 
 of the diameter. 
 
 Rated Capacities of Steam Fire-engines, which is perhaps one third 
 greater than their ordinary rate of work at fires, are substantially as 
 follows : 
 
 3d size, 550 gals, per min., or 792,000 gals, per 24 hours. 
 
 2d " 700 " 1,008,000 
 
 1st " 900 " " 1,296,000 
 
 1 ext.. 1,100 " !' 1.584,000 !! 
 
FLOW OF WATER THROUGH NOZZLES. 
 
 753 
 
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 B 
 
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 N ft 
 
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 ^ o o cs cs CN i cs i cs cs w> c^> f^i \**\ T ^t in \tr\ m \o i >c i t>i I r> i oo i oo i o o o cs 
 
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754 HYDRAULICS. 
 
 THE SIPHON. 
 
 The Siphon is a bent tube of unequal branches, open at both ends, and 
 is used to convey a liquid from a higher to a lower level, over an interme- 
 diate point higher than either. Its parallel branches being in a vertical 
 plane and plunged into two bodies of liquid whose upper surfaces are at 
 different levels, the fluid will stand at the same level both within and 
 without each branch of the tube when a vent or small opening is made 
 at the bend. If the air be withdrawn from the siphon through this vent, 
 the water will rise in the branches by the atmospheric pressure without, 
 and when the two columns unite and the vent is closed, the liquid will 
 flow from the upper reservoir as long as the end of the shorter branch 
 of the siphon is below the surface of the liquid in the reservoir. 
 
 If the water was free from air the height of the bend above the supply 
 level might be as great as 33 feet. 
 
 If A = area of cross-section of the tube in square feet, H = the differ- 
 ence in level between the two reservoirs in feet, D the density of the 
 liquid in pounds per cubic foot, then ADH measures the intensity of the 
 force which causes the movement of the fluid, and V = ^2gH= 8.02 
 "*/H is the theoretical velocity, in feet per second, which is reduced by 
 the loss of head for entry and friction, as in other cases of flow of liquids 
 through pipes. In the case of the difference of level being greater than 
 33 feet, however, the velocity of the water in the shorter leg is limited 
 to that due to a height of 33 feet, or that due to the difference between 
 the atmospheric pressure at the entrance and the vacuum at the bend. 
 
 Long Siphons. Prof. Joseph Torrey, in the Amer. Machinist, de- 
 scribes a long siphon which was a partial failure. 
 
 The length of the pipe was 1792 feet. The pipe was 3 inches diameter, 
 and rose at one point 9 feet above the initial level. The final level was 
 20 feet below the initial level. No automatic air valve was provided. 
 The highest point in the siphon was about one third the total distance 
 from the pond and nearest the pond. At this point a pump was placed, 
 whose mission was to fill the pipe when necessary. This siphon would 
 flow for about two hours and then cease, owing to accumulation of air in 
 the pipe. When in full operation it discharged 431/2 gallons per minute. 
 The theoretical discharge from such a sized pipe with the specified head 
 is 551/2 gallons per minute. 
 
 Siphon on the Water-supply of Mount Vernon, X, T. (Eng'g 
 News, May 4, 1893.) A 12-inch siphon, 925 feet long, with a maximum 
 lift of 22.12 feet and a 45 change in alignment, was put in use in 1892 
 by the New York City Suburban Water Co. At its summit the siphon 
 crosses a supply main, which is tapped to charge the siphon. The air- 
 chamber at the siphon is 12 inches by 16 feet long. A i/2-inch tap and 
 cock at the top of the chamber provide an outlet for the collected air. 
 
 It was found that the siphon with air-chamber as described would run 
 until 125 cubic feet of air had gathered, and that this took place only 
 half as soon with a 14-foot lift as with the full lift of 22.12 feet. The 
 siphon will operate about 12 hours without being recharged, but more 
 water can be gotten over by charging every six hours. It can be kept 
 running 23 hours out of 24 with only one man in attendance. With the 
 siphon as described above it is necessary to close the valves at each end 
 of the siphon to recharge it. It has been found by weir measurements 
 that the discharge of the siphon before air accumulates at the summit is 
 practically the same as through a straight pipe. 
 
 A successful siphon is described by R. S. Hale in Jour. Assoc. Eng. 
 Soc., 1900. A 2-in. galvanized pipe had been used, and it had been nec- 
 essary to open a waste-pipe and thus secure a continuous flow in order 
 to keep the siphon in operation. The trouble seemed to be due to very 
 small air leaks in the joints. When the 2-in. iron pipe was replaced by a 
 1-in lead pipe, the siphon was entirely successful. The maximum rise 
 of the pipe above the level of the pond was 12 ft., the discharge about 
 850 ft. below the level, and the length 500 ft. 
 
VELOCITY OF ^ATER IN OPEN CHANNELS. 755 
 
 VELOCITY OF WATER IN OPEN CHANNELS. 
 
 Irrigation Canals. The minimum mean velocity required to pre- 
 vent the deposit of silt or the growth of aquatic plants is in Northern 
 India taken at 1 1/2 feet per second. It is stated that in America a higher 
 velocity is required for this purpose, and it varies from 2 to 3 1/2 feet per 
 second. The maximum allowable velocity will vary with the nature of 
 the soil of the bed. A sandy bed will be disturbed if the velocity exceeds 
 3 feet per second. Good loam with not too much sand will bear a velocity 
 of 4 feet per second. The Cavour Canal in Italy, over a gravel bed, has a 
 velocity of about 5 per second. (Flynn's "Irrigation Canals.") 
 
 Mean Surface and Bottom Velocities. According to the formula 
 
 of Bazin. 
 
 v= 1W^- 25-4 Vrs; v = Vb + 10.87 \/rs. 
 
 .*. vj) =* v 10.87 Vrs, in which v = mean velocity in feet per second, 
 v max = maximum surface velocity in feet per second, v&= bottom velocity 
 in feet per second, r = hydraulic mean depth in feet = area of cross-section 
 in square feet divided by wetted perimeter in feet, s = sine of slope. 
 
 The least velocity, or that of the particles in contact with the bed, is 
 almost as much less than the mean velocity as the greatest velocity is 
 greater than the mean. 
 
 Rankine states that in ordinary cases the velocities may be taken as 
 bearing to each other nearly the proportions of 3, 4, and 5. In very slow 
 currents they are nearly as 2, 3, and 4. 
 
 Safe Bottom and Mean Velocities. Ganguillet & Kutter give the 
 following table of. safe bottom and mean velocities in channels, calculated 
 from the formula v = Vb + 
 
 Material of Channel. 
 
 Safe Bottom Velocity 
 Vfr, in Feet per Second. 
 
 Mean Velocity v, in 
 Feet per Second. 
 
 Soft brown earth 
 
 249 
 
 328 
 
 
 499 
 
 656 
 
 Sar d 
 
 1 000 
 
 1 312 
 
 Gravel 
 
 1.998 
 
 2.625 
 
 Pebbles 
 
 2 999 
 
 3 938 
 
 Broken stone, flint . 
 
 4 003 
 
 5 579 
 
 Conglomerate, soft slate. . . . 
 Stratified rock 
 
 4.988 
 6 006 
 
 6.564 
 8 204 
 
 Hard rock 
 
 10.009 
 
 13.127 
 
 
 
 
 Ganguillet & Kutter state that they are unable for want of observations 
 to judge how far these figures are trustworthy. They consider them to be 
 rather disproportionately small than too large, and therefore recommend 
 them more confidently. 
 
 Water flowing at a high velocity and carrying large quantities of silt is 
 
 very destructive to channels, even when constructed of the best masonry. 
 
 Resistance of Soils to Erosion by Water. W. A. Burr, En&g 
 
 News, Feb. 8, 1894, gives a diagram showing the resistance of various soils 
 
 to erosion by flowing water. 
 
 Experiments show that a velocity greater than 1.1 feet per second will 
 erode sand, while pure clay will stand a velocity of 7.35 feet per second. 
 The greater the proportion of clay carried by any soil, the higher the per- 
 missible velocity. Mr. Burr states that experiments have shown that the 
 line describing the power of soils to resist erosion is parabolic. From his 
 diagram the following figures are selected as representing different classes 
 of soils: 
 
 Pure sand resists erosion by flow of 1.1 feet per second. 
 
 Sandy soil, 15% clay 1.2 ' " 
 
 Sandy loam, 40% clay 1.8 
 
 Loamy soil, 65% clay 3.0 
 
 Clay loam, 85% clay 4.8 
 
 Agricultural clay, 95% clay 6.2 
 
 Clay. ! 7.35 
 
 Abrading and Transporting Power of Water. Prof. J. LeConte, 
 in his "Elements of Geology," states: 
 
 The erosive power of water, or its power of overcoming cohesion, 
 5. varies as the square of the velocity of the current, 
 
756 
 
 HYDFAULTCS. 
 
 The transporting power* of a current varies as "the sixth power of the 
 velocity. * * * If the velocity therefore be increased ten times, the 
 transporting power is increased 1,000,000 times. A current running 
 three feet per second, or about two miles per hour, will bear fragments 
 of stone of the size of a hen's egg, or about three ounces weight. A 
 current of ten miles an hour will bear fragments of one and a half tons, 
 and a torrent of twenty miles an hour will carry fragments of 100 tons. 
 
 The transporting power of water must not be confounded with its 
 erosive power. The resistance to be overcome in the one case is weight, 
 in the other, cohesion; the latter varies as the square: the former as the 
 sixth power of the velocity. 
 
 In many cases of removal of slightly cohering material, the resistance 
 is a mixture of these two resistances, and the power of removing mate- 
 rial will vary at some rate between v 2 and v 6 . 
 
 Baldwin Latham has found that in order to prevent deposits of sewage 
 silt in small sewers or drains, such as those from 6 inches to 9 inches 
 diameter, a mean velocity of not less than 3 feet per second should be 
 produced. Sewers from 12 to 24 inches diameter should have a velocity 
 of not less than 21/2 feet per second, and in sewers of larger dimensions 
 in no case should the velocity be less than 2 feet per second. 
 
 The specific gravity of the materials has a marked effect upon the 
 mean velocities necessary to move them. T. E. Blackwell found that 
 coal of a sp. gr. of 1.26 was moved by a current of from 1.25 to 1.50 ft. 
 per second, while stones of a sp. gr. of 2.32 to 3.00 required a velocity of 
 2.5 to 2.75 ft. per second. 
 
 Chailly gives the following formula for finding the velocity required to 
 move rounded stones or shingle: 
 
 v = 5.67 ^ag, 
 
 in which v = velocity of water in feet per second, a = average diameter 
 in feet of the body to be moved, g = its specific gravity. 
 
 Geo. Y. Wisner, Eng'g News, Jan. 10, 1895, doubts the general accuracy 
 of statements made by many authorities concerning the rate of flow of 
 a current and the size of particles which different velocities will move. 
 He says: 
 
 The scouring action of any river, for any given rate of current, must 
 be an inverse function of the depth. The fact that some engineer has 
 found that a given velocity of current on some stream of unknown depth 
 will move sand or gravel has no bearing whatever on what may be ex- 
 pected of currents of the same velocity in streams of greater depths. In 
 channels 3 to 5 ft. deep a mean velocity of 3 to 5 ft. per second may 
 produce rapid scouring, while in depths of 18 ft. and upwards current 
 velocities of 6 to 8 ft. per second often have no effect whatever on the 
 Channel bed. 
 
 Frictional Resistance of Surfaces Moved in Water. (Ency. Brit., 
 llth ed. Vol. xiv, p. 58.) Froude's experiments were made by pulling 
 boards 19 in. wide, 3/ 8 in. thick, finely sharpened at both ends, set edge- 
 wise in water. The following table gives: A, the power of the speed 
 to which the resistance is proportional; B, the mean resistance in 
 pounds per sq. ft. of the whole surface of a board of the lengths stated 
 In the table, at the standard speed of 10 ft. per second. 
 
 Surface. 
 
 Length of Surface, in Feet. 
 
 2ft. 
 
 8ft. 
 
 20ft. 
 
 50ft. 
 
 Varnish ..... 
 
 A 
 2.00 
 
 B 
 0.41 
 0.38 
 0.30 
 0.87 
 0.81 
 0.90 
 1.10 
 
 A 
 1.85 
 1 .94 
 1.99 
 1.92 
 2.00 
 2.00 
 2.00 
 
 B 
 0.325 
 0.314 
 0.278 
 0.626 
 0.583 
 0.625 
 0.714 
 
 A 
 1.85 
 1.93 
 1.90 
 1.89 
 2.00 
 2.00 
 2.00 
 
 B 
 0.278 
 0.271 
 0.262 
 0.531 
 0.480 
 0.534 
 0.588 
 
 A 
 1.83 
 
 B 
 0.226 
 
 Paraffin 
 
 Tinfoil 
 
 2.J6 
 1.93 
 2.00 
 2.00 
 2.00 
 
 1.83 
 1 .87 
 2.06 
 2.00 
 
 0.232 
 0.423 
 0.337 
 0.456 
 
 Calico .... 
 
 Fine Sand 
 Medium Sand. . 
 Coarse Sand . . . 
 
 Unwin's experiments (Proc. Inst. Civ. Engrs., Ixxx) were made with 
 disks 10, 15, and 20 in. diam. rotated in water by a vertical shaft, in 
 Chambers 22 in. diam., and 3, 6, and 12 in. deep r In all cases the fric- 
 
MEASUREMENT OF FLOWING WATER, 757 
 
 tional resistances increased a little as the chamber was made larger. 
 The friction depends not only on the surface of the disk, but to some 
 extent on the surface of the chamber in which it rotates. For the 
 smoother surface the friction varied as the 1.85 power of the velocity. 
 For rougher surfaces it varied as the 1.9 to the 2.1 power. The friction 
 decreased 18 per cent with increase of temperature from 41 to 130 P. 
 The resistances in pounds per sq. ft. at 10 ft. per second were as 
 follows for different surfaces: Bright brass, 0.202 to 0.229; Varnish, 
 0.220 to 0.233; Fine sand, 0.339; Very cparse sand, 0.587 to 0.715. 
 The results agree fairly well with those obtained by Froude with planks 
 50 ft. long. 
 
 Grade of Sewers. The following empirical formula is given in Bau- 
 meister's "Cleaning and Sewerage of Cities," for the minimum grade 
 for a sewer of clear diameter equal to d inches, and either circular or 
 oval in section: 
 
 ' Minimum grade, in per cent 
 
 As the lowest limit of grades which can be flushed, 0.1 to 0.2 per cent 
 may be assumed for sewers which are sometimes dry, while 0.3 per cent 
 is allowable for the trunk sewers in large cities. The sewers should run 
 dry as rarely as possible. 
 
 MEASUREMENT OF FLOWING WATER. 
 
 Piezometer. If a vertical or oblique tube be inserted into a pipe 
 containing water under pressure, the water will rise in the former, and the 
 vertical height to which it rises will be the head producing the pressure 
 at the point where the tube is attached. Such a tube is called a piezom- 
 eter or pressure measure. If the water in the piezometer falls below 
 its proper level it shows that the pressure in the main pipe has been 
 reduced by an obstruction between the piezometer and the reservoir. If 
 the water rises above its proper level, it indicates that the pressure there 
 has been increased by an obstruction beyond the piezometer. 
 
 If we imagine a pipe full of water to be provided with a number of pie- 
 zometers, then a line joining the tops of the columns of water in them la 
 the hydraulic grade-line. 
 
 Pitot Tub 6 Gauge. The Pitot tube is used for measuring the veloc- 
 ity of fluids in motion. It has been used with great success in measuring 
 the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.) 
 (See also Van Nostrand's Mag., vol. xxxv.) It is simply a tube so bent 
 that a short leg extends into the current of fluid flowing from a tube, with 
 the plane of the entering orifice opposed at right angles to the direction of 
 the current. The pressure caused by the impact of the current is trans- 
 mitted through the tube to a pressure-gauge of any kind, such as a column 
 of water or of mercury, or a Bourdon spring-gauge. From the pressure 
 thus indicated and the known density and temperature of the flowing gas 
 is obtained the head corresponding to the pressure, and from this the 
 velocity. In a modification of the Pitot tube described by Prof Robinson, 
 there are two tubes inserted into the pipe conveying the gas, one of which 
 has the plane of the orifice at right angles to the current, to receive the 
 static pressure plus the pressure due to impact; the other has the plane of 
 its orifice parallel to the current, so as to receive the static pressure only. 
 These tubes are connected to the legs of a t/tube partly filled with mercury, 
 which then registers the difference in pressure in the two tubes, from which, 
 the velocity may be calculated. Comparative tests of Pitot tubes with 
 gas-meters, for measurement of the flow of natural gas, have shown an 
 agreement within 3%. 
 
 It appears from experiments made by W. M. White, described in a 
 paper before the Louisiana Eng'g Socy., 1901, by Williams, Hubbell and 
 Fenkel (Trans. A. S. C. E., 1901), and by W. B. Gregory (Trans. A. 8. 
 M. E., 1903), that in the formula, for the Pitot tube, V=cV2gH t ln 
 which V is the velocity of the current in feet per second, // the head in 
 feet cf the fluid corresponding to the pressure measured by the tube, 
 and c an experimental coefficient, c = 1 when the plane at the point of 
 
758 HYDRAULICS. 
 
 the tube is /exactly at right angles with the direction of the current 
 and when the static pressure is correctly measured. The total pressure 
 produced by a jet striking an extended plane surface at right angles to 
 it, and escaping parallel to the plate, equals twice the product of the 
 area of the jet into the pressure calculated from the " head due the veloc- 
 
 Ufc'I a > nd for ^ 1S case H = 2 * V2/2 9 inste ad of V*/2 g; but as found in 
 Whites experiments the maximum pressure at a point on the plate 
 exactly opposite the jet corresponds to h= V*/2 g. Experiments made 
 with four different shapes of nozzles placed under the center of a falling 
 stream of water showed that the pressure produced was capable of sus- 
 
 l t0 the height * the 
 
 Tests by J. A. Knesche (Indust. Eng'g, Nov., 1909), in which a Pitot 
 tube was inserted ma 4-m. water pipe, gave C = about 0.77 for velocities 
 f 2.5 to 8 ft. per sec., and smaller values for lower velocities. He holds 
 that the coefficient of a tube should be determined by experiment before 
 its readings can be considered accurate. 
 
 For a brief discussion of various theories of the Pitot tube see Eng'g 
 News, April 17, June 5, and July 31, 1913. 
 
 Maximum and Mean Velocities in Pipes. Williams, Hubbell and 
 Fenkel (Trans. A. S. C. E., 1901) found a ratio of 0.84 between the mean 
 and the maximum velocities of water flowing in closed circular conduits, 
 under normal conditions, at ordinary velocities; whereby observations of 
 velocity taken at the center under such conditions, with a properly rated 
 Pitot tube, may be relied on to give results within 3 % of correctness. 
 The Venturi Meter, invented by Clemens Herschel, and described in 
 a pamphlet issued by the Builders' Iron Foundry of Providence, R.I. , la 
 named from Venturi, who first called attention, in 1796, to the relation be- 
 tween the velocities and pressures of fluids when flowing through converg- 
 ing and diverging tubes. It consists of two parts the tube, through 
 which the water flows, and the recorder, which registers the quantity of 
 water that passes through the tube. The tube takes the shape of two trun- 
 cated cones joined in their smallest diameters by a short throat-piece. At 
 the up-stream end and at the throat there are pressure-chambers, at 
 which points the pressures are taken. 
 
 The action of the tube is based on that property which causes the small 
 section of a gently expanding frustum of a cone to receive, without material 
 resultant loss of head, as much water at the smallest diameter as is dis- 
 charged at the large end, and on that further property which causes the 
 pressure of the water flowing through the throat to be less, by virtue of its 
 greater velocity, than the pressure at the up-stream end of the tube, each 
 pressure being at the same time a function of the velocity at that point and 
 of the hydrostatic pressure which would obtain were the water motionless 
 within the pipe. 
 
 Tne recorder is connected with the tube by pressure-pipes which lead to 
 it from the chambers surrounding the up-stream end and the throat of the 
 tube. It may be placed in any convenient position within 1000 feet of the 
 meter. It is operated by a weight and clockwork. The difference of pres- 
 sure or head at the entrance and at the throat of the meter is balanced in 
 the recorder by the difference of level in two columns of mercury in 
 cylindrical receivers, one within the other. The inner carries a float, the 
 position of which is indicative of the quantity of water flowing through 
 the tube. By its rise and fall the float varies the time of contact between 
 an integrating drum and the counters by which the successive readings 
 are registered. 
 
 There is no limit to the sizes of the meters nor the quantity of water 
 that may be measured. Meters with 24-inch, 36-inch, 48-inch, and even 
 20-foot tubes can be readily made. 
 
 Measurement by Venturi Tubes. (Trans. A. S. C. E., Npv., 1887, 
 and Jan., 1888.) Mr. Herschel recommends the use of a Venturi tube, in- 
 serted in the force-main of the pumping engine, for determining the 
 quantity of water discharged. Such a tube applied to a 24-inch main has 
 a total length of about 20 feet. At a distance of 4 feet from the end 
 nearest the engine the inside diameter of the tube is contracted to a throat 
 having a diameter of about 8 inches. A pressure-gauge is attached to each 
 of two chambers, the onesurroundingand communicating with.the entrance 
 or main pipe, the other with the throat. According to experiments made 
 
tirrn f.wn f. 
 
 MEASUREMENT OF FLOWING WATER, 759 
 
 upon two tubes of this kind, one 4 in. in diameter at the throat and 12 in. 
 at the entrance, and the other about 36 in. in diameter at the throat and 
 9 feet at its entrance, the quantity of water which passes through the tube 
 is very nearly the theoretical discharge through an opening having an area 
 equal to that of the throat, and a velocity which is that due to the difference 
 in head shown by the two gauges. Mr. Herschel states that the coefficient 
 for these two widely-varying sizes of tubes and for a wide range of velocity 
 through the pipe, was found to be within two per cent, either way, of 98%. 
 In other words, the quantity of water flowing through the tube per second 
 is expressed within two per cent by the formula W= 0.98 X A X ^2 gh, 
 in which A is the area of the throat of the tube, h the head, in feet, corre- 
 sponding to the difference in the pressure of the water entering the tube and 
 that found at the throat, and g = 32.16. 
 
 Coefficient of Flow in Venturi Meters. (Allen Hazen, Eng. News, 
 July 31, 1913.) The formula for flow in a Venturi meter is 
 
 d and D respectively are diameters of the throat and entrance, in inches, 
 h is the head on the meter, C a coefficient which depends on the fractional 
 resistance and has an average value of very close to 0.99 for ordinary 
 waterworks conditions. K = 28",276 if Q is the quantity in U. S. gal- 
 lons per 24 hours and h is measured in feet of water. If C = 0.99 then 
 KC = 27,993 for h in feet of water, 8081 if h is in inches of water and 
 28,684 if h is in inches of mercury. For Q in cubic feet per second, di- 
 vide these figures by 646,315 giving respectively KC = 0.04331, 0.01250 
 and 0.04438. 
 
 Measurement of Discharge of Pumping-engines by means of 
 Nozzles. (Trans. A. S. M. E., xii, 575.) The measurement of water 
 by computation from its discharge through orifices, or through the nozzles 
 of fire-hose, furnishes a means of determining the quantity of water de- 
 livered by a pumping-engine which can be applied without much difficulty. 
 John R. Freeman, Trans. A. S. C. E., Nov., 1889, describes a series of ex- 
 periments covering a wide range of pressures and sizes, and the results 
 showed that the coefficient of discharge for a smooth nozzle of ordinary 
 good form was within one-half of one per cent, either way, of 0.977; the 
 diameter of the nozzle being accurately calipered, and the pressures being 
 determined by means of an accurate gauge attached to a suitable piezom- 
 eter at the base of the play-pipe. 
 
 In order to use this method for determining the quantity of water dis- 
 charged by a pumping-engine, it would be necessary to provide a pressure- 
 box, to which the water would be conducted, and attach to the box as 
 many nozzles as would be required to carry off the water. According to 
 Mr. Freeman's estimate, four 1 1/4-inch nozzles, thus connected, with a 
 pressure of 80 Ibs. per square inch, would discharge the full capacity of a 
 two-and-a-half-million engine. He also suggests the use of a portable 
 apparatus with a single opening for discharge, consisting essentially of a 
 Siamese nozzle, so-called, the water being carried to it by three or more 
 lines of fire-hose. 
 
 To insure reliability for these measurements, it is necessary that the 
 ehut-off valve in the force-main, or the several shut-off valves, should be 
 tight, so that all the water discharged by the engine may pass through the 
 nozzles. 
 
 The Lea V-Notch Recording Water Meter is described by D. Robert 
 YarnaU in Trans. A. S. M. E., 1912. It is extensively used in large 
 power plants for recording the flow of boiler feed water. It consists 
 of a metering tank or flume from which the water passes over a 90 
 V-notch into a catch basin below, the height of the water above the 
 notch being recorded on a clock-driven paper chart which revolves 
 once in 24 jiours. The formula for the 90 V-notch is cu. ft. per min. = 
 Q.3Q5H 2 \/H, in which H is the height in inches of the still water behind 
 the notch measured above the level of the bottom of the notch. Tests 
 by Mr. YarnaU of a recording meter made on this principle showed an 
 
760 
 
 HYDEAULICS. 
 
 average error of 0.5%. The Yarnall- Waring Co., Philadelphia, makers 
 of the meter give the following figures for the flow of water in pounds 
 per hour corresponding to different heights of water in inches above 
 the notch: 
 
 Height, in.: 
 1234 
 Flow, Ib. per hour: 
 1,140 6,480 17,830 36,610 
 
 Height, in.: 
 9 10 11 
 Flow, Ib. per hour: 
 277,960 361,740 459,030 
 
 5 
 63,940 
 
 12 
 568,720 
 
 6 
 
 100,860 
 
 13 
 694,710 
 
 7 
 148,290 
 
 14 
 836,110 
 
 8 
 207,060 
 
 15 
 993,510 
 
 Flow through Rectangular Orifices. (Approximate. See p. 727.) 
 
 CUBIC FEET OF WATER DISCHARGED PER MINUTE THROUGH AN ORIFICE 
 ONE INCH SQUARE, UNDER ANY HEAD OF WATER FROM 3 TO 72 INCHES. 
 
 For any other orifice multiply by its area in square inches. 
 Formula, Q' = 0.624 *Sh" X a. Q'*= cu. ft. per min.; a = area in sq. in. 
 
 
 1 
 
 g W) . 
 
 
 $. 
 
 
 ? 
 
 w> 
 
 
 1 
 
 "S M ' 
 
 
 i 
 t> 
 
 
 "S 
 
 g & 
 
 
 V 
 
 *" Si . 
 
 d j 
 
 s.s 
 
 d m 
 
 8S.S 
 
 d 
 
 u Js.S 
 
 Cl n? 
 
 s.e 
 
 fl oJ 
 
 o> fe.S 
 
 d 
 
 s.s 
 
 d : 
 
 SS-9 
 
 i-i 
 If 
 
 Cubic F 
 Dischj 
 per m 
 
 i-s 
 
 $.s 
 
 H 
 
 Cubic F 
 Dischj 
 per m 
 
 
 
 "2J-S 
 
 ; 
 $ 
 
 w 
 
 Cubic F 
 Dischj 
 per m 
 
 S g 
 
 i! 
 
 a 
 
 Cubic F 
 Dischs 
 
 H 
 
 H 
 
 Cubic F 
 Disch: 
 
 Heads i: 
 inches 
 
 Cubic F 
 Disch! 
 
 a 
 
 -S-g 
 8.S 
 
 n 
 
 ^-ga 
 
 |ln 
 
 3 
 
 .12 
 
 13 
 
 2.20 
 
 23 
 
 2.90 
 
 33 
 
 3.47 
 
 43 
 
 3.95 
 
 53 
 
 4.39 
 
 63 
 
 4.78 
 
 4 
 
 .27 
 
 14 
 
 2.28 
 
 24 
 
 2.97 
 
 34 
 
 3.52 
 
 44 
 
 4.00 
 
 54 
 
 4.42 
 
 64 
 
 4.81 
 
 5 
 
 .40 
 
 15 
 
 2.36 
 
 25 
 
 3.03 
 
 35 
 
 3.57 
 
 45 
 
 4.05 
 
 55 
 
 4.46 
 
 65 
 
 4.85 
 
 6 
 
 .52 
 
 16 
 
 2.43 
 
 26 
 
 3.08 
 
 36 
 
 3.62 
 
 46 
 
 4.09 
 
 56 
 
 4.52 
 
 66 
 
 4.89 
 
 7 
 
 .64 
 
 17 
 
 2.51 
 
 27 
 
 3.14 
 
 37 
 
 3.67 
 
 47 
 
 4.12 
 
 57 
 
 4.55 
 
 67 
 
 4.92 
 
 8 
 
 .75 
 
 18 
 
 2.58 
 
 28 
 
 3.20 
 
 38 
 
 3.72 
 
 48 
 
 4.18 
 
 58 
 
 4.58 
 
 68 
 
 4.97 
 
 9 
 
 .84 
 
 19 
 
 2.64 
 
 29 
 
 3.25 
 
 39 
 
 3.77 
 
 49 
 
 4.21 
 
 59 
 
 4.63 
 
 69 
 
 5.00 
 
 10 
 
 .94 
 
 20 
 
 2.71 
 
 30 
 
 3.31 
 
 40 
 
 3.81 
 
 50 
 
 4.27 
 
 60 
 
 4.65 
 
 70 
 
 5.03 
 
 11 
 
 2.03 
 
 21 
 
 2.78 
 
 31 
 
 3.36 
 
 41 
 
 3.86 
 
 51 
 
 4.30 
 
 61 
 
 4.72 
 
 71 
 
 5.07 
 
 12 
 
 2.12 
 
 22 
 
 2.84 
 
 32 
 
 3.41 
 
 42 
 
 3.91 
 
 52 
 
 4.34 
 
 62 
 
 4.74 
 
 72 
 
 5.09 
 
 Measurement of an Open Stream by Velocity and Cross-section. 
 
 Measure the depth of the water at from 6 to 12 points across the stream at 
 equal distances between. Add all the depths in feet together and divide 
 by the number of measurements made; this will be the average depth of 
 the stream, which multiplied by its width will give its area or cross-section. 
 Multiply this by the velocity of the stream in feet per minute, and the 
 result will be the discharge in cubic feet per minute of the stream. 
 
 The velocity of the stream can be found by laying off 100 feet of the bank 
 and throwing a float into the middle, noting the time taken in passing over 
 the 100 ft. Do this a number of times and take the average; then, divid- 
 ing this distance by the time gives the velocity at the surface. As the top 
 of the stream flows faster than the bottom or sides the average velocity 
 being about 83% of the surface velocity at the middle it is convenient to 
 measure a distance of 120 feet for the float and reckon it as 100 
 
MEASUREMENT OF FLOWING WATER. 
 
 761 
 
 Miner's Inch Measurements. (Pelton Water Wheel Co.) 
 
 The cut, Fig. 149, shows the form of measuring-box ordinarily used, and 
 the following table gives the discharge in cubic feet per minute of a miner's 
 inch of water, as measured under the various heads and different lengths 
 and heights of apertures used in California. 
 
 
 FIG. 149. 
 
 Length 
 
 Openings 2 Inches High. 
 
 Openings 4 Inches High. 
 
 of 
 
 
 
 Opening 
 in 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 inches. 
 
 Center, 
 5 inches. 
 
 Center, 
 6 inches. 
 
 Center, 
 7 inches. 
 
 Center, 
 5 inches. 
 
 Center, 
 6 inches. 
 
 Center, 
 7 inches. 
 
 
 Cu. ft. 
 
 Cu. ft. 
 
 Cu.ft. 
 
 c 
 
 j.ft. 
 
 Cu. ft. 
 
 Cu. ft. 
 
 4 
 
 
 .348 
 
 
 .473 
 
 
 .589 
 
 
 .320 
 
 
 .450 
 
 1.570 
 
 6 
 
 
 .355 
 
 
 .480 
 
 
 .596 
 
 
 .336 
 
 
 .470 
 
 1.595 
 
 8 
 
 
 .359 
 
 
 .484 
 
 
 .600 
 
 
 .344 
 
 
 .481 
 
 
 .608 
 
 10 
 
 
 .361 
 
 
 .485 
 
 
 .602 
 
 
 .349 
 
 
 .487 
 
 
 .615 
 
 12 
 
 
 .363 
 
 
 .487 
 
 
 .604 
 
 
 .352 
 
 
 .491 
 
 
 .620 
 
 14 
 
 
 .364 
 
 
 .488 
 
 
 .604 
 
 
 .354 
 
 
 .494 
 
 
 .623 
 
 16 
 
 
 .365 
 
 
 .489 
 
 
 .605 
 
 
 .356 
 
 
 .496 
 
 
 .626 
 
 18 
 
 
 .365 
 
 
 .489 
 
 
 .606 
 
 
 .357 
 
 
 .498 
 
 
 .628 
 
 20 
 
 
 .365 
 
 
 .490 
 
 
 .606 
 
 
 .359 
 
 
 .499 
 
 
 .630 
 
 22 
 
 
 .366 
 
 
 .490 
 
 
 .607 
 
 
 .359 
 
 
 .500 
 
 
 .631 
 
 24 
 
 
 .366 
 
 
 .490 
 
 
 .607 
 
 
 .360 
 
 
 .501 
 
 
 .632 
 
 26 
 
 
 .366 
 
 
 .490 
 
 
 .607 
 
 
 .361 
 
 
 .502 
 
 
 .633 
 
 28 
 
 
 .367 
 
 
 .491 
 
 
 .607 
 
 
 .361 
 
 
 .503 
 
 
 .634 
 
 30 
 
 
 .367 
 
 
 .491 
 
 
 .608 
 
 
 .362 
 
 
 .505 
 
 
 .635 
 
 40 
 
 
 .367 
 
 
 .492 
 
 
 .608 
 
 
 .363 
 
 
 .505 
 
 
 .637 
 
 50 
 
 
 .368 
 
 
 .493 
 
 
 .609 
 
 
 .364 
 
 
 .507 
 
 
 .639 
 
 60 
 
 
 .368 
 
 
 .493 
 
 
 .609 
 
 
 .365 
 
 
 .508 
 
 
 .640 
 
 70 
 
 
 .368 
 
 
 .493 
 
 
 .609 
 
 
 .365 
 
 
 .508 
 
 
 .641 
 
 80 
 
 
 .368 
 
 
 .493 
 
 
 .609 
 
 
 .366 
 
 
 .509 
 
 
 .641 
 
 90 
 
 
 .369 
 
 
 .493 
 
 1.610 
 
 
 .366 
 
 
 .509 
 
 
 .641 
 
 100 
 
 
 .369 
 
 
 .494 
 
 1.610 
 
 
 .366 
 
 
 .509 
 
 
 .642 
 
 NOTE. The apertures from which the above measurements were ob- 
 tained were through material 1 1/4 inches thick, and the lower edge 2 inches 
 above the bottom of the measuring-box, thus giving full contraction,. 
 
762 
 
 HYDRAULICS. 
 
 Flow of Water Over Weirs. Weir Dam Measurement. " (Pelton 
 Water Wheel Co.) Place a board or plank in the stream, as shown in 
 the sketch, at some point where a pond will form above. The length of 
 the notch in the dam should be from two to four times its depth for small 
 quantities and longer for large quantities. The edges of the notch should 
 be beveled -to ward the intake side, as shown. The overfall below the notch 
 should not be less than twice its depth. Francis says a fall below the 
 crest equal to one-half the head is sufficient, but there must be a free access 
 of air under the sheet. 
 
 FIG. 150. 
 
 In the pond, about 6 ft. above the dam, drive a stake, and then obstruct 
 the water until it rises precisely to the bottom of the notch and mark the 
 stake at this level. Then complete the dam so as to cause all the water to 
 flow through the notch, and, after time for the water to settle, mark the 
 stake again for this new level. If preferred the stake can be driven with 
 its top precisely level with the bottom of the notch and the depth of the 
 water be measured with a rule after the water is flowing free, but the marks 
 are preferable in most cases. The stake can then be withdrawn; and the 
 distance between the marks is the theoretical depth of flow corresponding 
 to the quantities in the weir table on the following page. 
 
 Francis's Formulae for Weirs. 
 
 Q = discharge in cubic feet per second, L = length of the weir, 
 H = depth of water on the weir, h = head due the velocity of ap- 
 proach = V2 ~- 64.3; dimensions in feet, velocity in feet per second. 
 
 Francis's formula, Q = 3.33 (L - 0.2H) X H *h. 
 
 This formula applies to weirs having perfect contraction at each end 
 and the velocity of approach negligible. When the velocity of approach 
 is considered the formula is Q = 3.33 (L - 0.2 H} X [(H + h) 3 / 2 - h 3 / 2 ]. 
 The Francis formula is not applicable when the depth on the weir 
 exceeds one- third of the length nor to very small depths. The distance 
 from the side of the canal to the end of the weir should not be less than 
 three times the .depth on the weir, 
 
MEASUREMENT OP FLOWING WATER. 
 
 763 
 
 With both end contractions suppressed the term 0.2 H is omitted from 
 the formula, and with one end contraction suppressed it becomes 
 0.1 tf. 
 
 If Q' - discharge in cubic feet per minute, and I' and h' are taken in 
 inches, the first of the above formulae reduces to Q' = 0.4 I' h' 3 /2- From this 
 formula the following table is calculated. The values are sufficiently 
 accurate for ordinary computations of water-power for weirs without end 
 contraction, that is, for a weir the full width of the channel of approach. 
 For weirs with full end contraction multiply the values taken from the 
 table by the length of the weir crest in inches less 0.2 times the head in 
 inches, to obtain the discharge. 
 
 Weir Table. 
 
 GIVING CUBIC FEET OF WATER PER MINUTE THAT WILL FLOW OVER" A. WEIR 
 ONE INCH WIDE AND FROM 1/3 TO 207/8 INCHES DEEP. 
 
 For other widths multiply by the width in inches. 
 
 Depth. 
 
 
 1/8 in. 
 
 1/4 in. 
 
 3/8 in. 
 
 1/2 in. 
 
 5/8 in. 
 
 3/4 in. 
 
 7/8 in. 
 
 In. 
 
 cu. ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 cu.ft. 
 
 
 
 .00 
 
 .01 
 
 .05 
 
 .09 
 
 .14 
 
 .19 
 
 .26 
 
 .32 
 
 1 
 
 .40 
 
 .47 
 
 .55 
 
 .64 
 
 .73 
 
 .82 
 
 .92 
 
 1.02 
 
 2 
 
 1.13 
 
 1.23 
 
 1.35 
 
 1.46 
 
 1.58 
 
 1.70 
 
 1.82 
 
 1.95 
 
 3 
 
 2.07 
 
 2.21 
 
 2.34 
 
 2.48 
 
 2.61 
 
 2.76 
 
 2.90 
 
 3.05 
 
 4 
 
 3.20 
 
 ,3.35 
 
 3.50 
 
 3.66 
 
 3.81 
 
 3.97 
 
 4.14 
 
 4.30 
 
 5 
 
 4.47 
 
 4.64 
 
 4.81 
 
 4.98 
 
 5.15 
 
 5.33 
 
 3.51 
 
 5.69 
 
 6 
 
 5.87 
 
 6.06 
 
 6.25 
 
 6.44 
 
 6.62 
 
 6.82 
 
 7.01 
 
 7.21 
 
 7 
 
 7.40 
 
 7.60 
 
 7.80 
 
 8.01 
 
 8.21 
 
 8.42 
 
 8.63 
 
 8.83 
 
 8 
 
 9.05 
 
 9.26 
 
 9.47 
 
 9.69 
 
 9.91 
 
 10.13 
 
 10.35 
 
 10.57 
 
 9 
 
 10.80 
 
 11.02 
 
 11.25 
 
 11.48 
 
 11.71 
 
 11.94 
 
 12.17 
 
 12.41 
 
 10 
 
 12.64 
 
 12.88 
 
 13.12 
 
 13.36 
 
 13.60 
 
 13.85 
 
 14.09 
 
 14.34 
 
 11 
 
 14.59 
 
 14.84 
 
 15.09 
 
 15.34 
 
 . 15.59 
 
 15.85 
 
 16.11 
 
 16.36 
 
 12 
 
 16.62 
 
 16.88 
 
 17.15 
 
 17.41 
 
 17.67 
 
 17.94 
 
 18.21 
 
 18.47 
 
 13 
 
 18.74 
 
 19.01 
 
 19.29 
 
 19.56 
 
 19.84 
 
 20.11 
 
 20.39 
 
 20.67 
 
 14 
 
 20.95 
 
 21.23 
 
 21.51 
 
 21.80 
 
 22.08 
 
 22.37 
 
 22.65 
 
 22.94 
 
 15 
 
 23.23 
 
 23.52 
 
 23.82 
 
 24.11 
 
 24.40 
 
 24.70 
 
 25.00 
 
 25.30 
 
 16 
 
 25.60 
 
 25.90 
 
 26.20 
 
 26.50 
 
 26.80 
 
 27.11 
 
 27.42 
 
 27.72 
 
 17 
 
 28.03 
 
 28.34 
 
 28.65 
 
 28.97 
 
 29.28 
 
 29.59 
 
 29.91 
 
 30.22 
 
 18 
 
 30.54 
 
 30.86 
 
 31.18 
 
 31 .50 
 
 31.82 
 
 32.15 
 
 32.47 
 
 32.80 
 
 19 
 
 33.12 
 
 33.45 
 
 33.78 
 
 34.11 
 
 34.44 
 
 34.77 
 
 35.10 
 
 35.44 
 
 20 
 
 35.77 
 
 36.11 
 
 36.45 
 
 36.78 
 
 37.12 
 
 37.46 
 
 37.80 
 
 38.15 
 
 When the velocity of the approaching water is less than 1/2 foot per 
 second, the result obtained by the table is fairly accurate. When the vel- 
 ocity of approach is greater than 1/2 foot per second, a correction should be 
 applied, see page 727. 
 
 For more accurate computations, the coefficients of flow of Hamilton 
 Smith, Jr., or of Bazin should be used. In Smith's Hydraulics will be found 
 a collection of results of experiments on orifices and weirs of various shapes 
 made by many different authorities, together with a discussion of their 
 several formula. (See also Trautwine's Pocket Book, Unwin's Hydrau- 
 lics, Church's Mechanics of Engineering, Merriman's Hydraulics, 
 Williams and Hazen's Hydraulic Tables, Hughes and Safford's Hydrau- 
 lics, and Weir Experiments, Coefficients and Formulas, by R. E. 
 Horton, Water Supply and Irrigation paper No. 200 of the U. S. 
 Geological Survey.) 
 
 Bazin's Experiments. M. Bazin (Annales des Fonts et Chaussees, 
 Oct., 1888, translated by Marichal and Trautwine, Proc. Engrs. Club of 
 Phila., Jan., 1890) made an extensive series of experiments with a sharp- 
 crested weir without lateral contraction, the air being admitted freely be- 
 hind the falling sheet, and found values of m varying from 0.42 to 0.50, 
 with variations of the length of the weir from 19 3/ 4 to 78 3/ 4 in., of the 
 height of the crest above the bottom of the channel from 0.79 to 2.46 ft., 
 
764 
 
 HYDRAULICS. 
 
 and of the head from 1.97 to 23.62 In. 
 the following formula: 
 
 From these experiments he deduces 
 
 0.425+ 0.21 (-5-^-77) 
 
 In which P is the height in feet of the crest of the weir above the bottom of 
 the chanriel of approach, L the length of the weir, H the head, both in feet, 
 and Q the discharge in cu. ft. per sec. This formula, says M. Bazin, is 
 entirely practical where errors of 2% to 3% are admissible. The following 
 table is condensed from M. Bazin's paper: 
 
 VALUES .OF THE COEFFICIENT m IN THE FORMULA Q- = mLH V2 gH, FOR A 
 SHARP-CRESTED WEIR WITHOUT LATERAL CONTRACTION; THE Am 
 BEING ADMITTED FREELY BEHIND THE FALLING SHEET. 
 
 Head, H. 
 
 Height of Crest of Weir Above Bed of Channel. 
 
 Feet... 0.66 
 Inches 7.87 
 
 0.98 
 11.81 
 
 1.31 
 15.75 
 
 1.64| 1.97 
 19.69|23.62 
 
 2.62 
 31.50 
 
 3.28 
 39.38 
 
 4.92 
 59.07 
 
 6.56 
 78.76 
 
 00 
 00 
 
 Ft. 
 0.164 
 0.230 
 0.295 
 0.394 
 0.525 
 0.656 
 0.787 
 919 
 .050 
 .181 
 .312 
 .444 
 .575 
 .706 
 .837 
 .969 
 
 In. 
 1.97 
 2.76 
 3.54 
 4.72 
 6.30 
 7.87 
 9.45 
 11.02 
 12.60 
 14.17 
 15.75 
 17.32 
 18.90 
 20.47 
 22.05 
 23.62 
 
 m 
 0.458 
 0.455 
 0.457 
 0.462 
 0.471 
 0.480 
 0.488 
 0.496 
 
 m 
 0.453 
 0.448 
 0.447 
 0.448 
 0.453 
 0.459 
 0.465 
 0.472 
 0.478 
 0.483 
 0.489 
 0.494 
 
 m 
 0.451 
 0.445 
 0.442 
 0.442 
 0.444 
 0.447 
 0.452 
 0.457 
 0.462 
 0.467 
 0.472 
 0.476 
 0.480 
 0.483 
 0.487 
 0.490 
 
 m 
 0.450 
 0.443 
 0.440 
 0.438 
 0.438 
 0.440 
 0.444 
 0.448 
 0.452 
 0.456 
 0.459 
 0.463 
 0.467 
 0.470 
 0.473 
 0.476 
 
 m 
 0.449 
 0.442 
 0.438 
 0.436 
 0.435 
 0.436 
 0.438 
 0.441 
 0.444 
 0.448 
 0.451 
 0.454 
 0.457 
 0.460 
 0.463 
 0.466 
 
 m 
 0.449 
 0.441 
 0.436 
 0.433 
 0.431 
 0.431 
 0.432 
 0.433 
 0.436 
 0.438 
 0.440 
 0.442 
 0.444 
 0.446 
 0.448 
 0.451 
 
 m 
 0.449 
 0.440 
 0.436 
 0.432 
 0.429 
 0.428 
 0.428 
 0.429 
 '0.430 
 0.432 
 0.433 
 0.435 
 0.436 
 0.438 
 0.439 
 0.441 
 
 m 
 0.448 
 0.440 
 0.435 
 0.430 
 0.427 
 0.425 
 0.424 
 0.424 
 0.424 
 0.424 
 0.424 
 0.425 
 0.425 
 0.426 
 0.427 
 0.427 
 
 m 
 0.448 
 0.439 
 0.434 
 0.430 
 0.426 
 0.423 
 0.422 
 0.422 
 0.421 
 0.421 
 0.421 
 0.421 
 0.421 
 0.421 
 0.421 
 0.421 
 
 m 
 0.4481 
 0.4391 
 0.4340 
 0.4291 
 0.4246 
 0.4215 
 0.4194 
 0.4181 
 0.4J68 
 0.4156 
 0.4144 
 0.4134 
 0.4122 
 0.4112 
 0.4101 
 0.4092 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A comparison of the results of this formula with those of experiments, 
 says M. Bazin, justifies us in believing that, except in the unusual case of a 
 very low weir (which should always be avoided), the preceding table will 
 give the coefficient m in all cases within 1% ; provided, however, that the 
 arrangements of the standard weir are exactly reproduced. It is especially 
 important that the admission of the air behind the falling sheet be perfectly 
 assured. If this condition is not complied with, m may vary within much 
 wider limits. The type adopted gives the least possible variation in the 
 coefficient. 
 
 Triangular Weir. For the formula of the triangular or V-notch 
 weir, see the Lea Recorder, page 759. 
 
 The Cippoleti, or Trapezoidal Weir. Cippoleti found that by using 
 a trapezoidal weir with the sides inclined 1 horizontal to 4 vertical, with 
 end contraction, the discharge is equal to that of a rectangular weir 
 without end contraction (that is with the width of the weir equal to the 
 width of the channel) and is represented by the simple formula Q = 3.367 
 L# 3 /2. A. D. Flinn and C. W. D. Dyer (Trans. A. S. C. E. t 1894), in 
 experiments with a trapezoidal weir, with values of L from 3 to 9 ft. 
 and .of H from 0.24 to 1.40 ft., found the value of the coefficient to aver- 
 age 3.334, the water being measured by a rectangular weir and the results 
 being computed by Francis's formula, and 3.354 when Smith's formula 
 was used. They conclude that Cippoleti's formula when applied to a 
 properly constructed trapezoidal weir will give the discharge with an 
 error due to combined inaccuracies, not greater than 1%. 
 
WATEK-POWEfU 765 
 
 WATER-POWER, 
 
 Power of a Fall of Water Efficiency. The gross power of a fall 
 
 Kf water is the produc* of the weight of water discharged in a unit of time 
 ito the total head, i.e., the difference of vertical elevation of the upper 
 surface of the water at the points where the fall in question begins and 
 ends. The term "head" used in connection with water-wheels is the 
 difference in height from the surface of the water in the wheel-pit to the 
 surface in the pen-stock when the wheel is running. 
 
 If Q = cubic feet of water discharged per second, D = weight of a cubic 
 foot of water = 62.36 Ibs. at 60 F., H = total head in feet; then 
 
 DQH = gross power in foot-pounds per second, 
 and DQH -* 550 = 0.1134 QH = gross horse-power. 
 
 If Q f is taken in cubic feet per minute, H.P.= Q ' X ' 36 = .00189Q'g. 
 
 A water-wheel or motor of any kind cannot utilize the whole of the head 
 H, since there are losses of head at both the entrance to and the exit from 
 the wheel. There are also losses of energy due to friction of the water in 
 its passage through the wheel. The ratio of the power developed by the 
 wheel to the gross' power of the fall is the efficiency of the wheel. For 75 % 
 
 efficiency, net horse-power = 0.00142 Q'H = -g 
 
 A head of water can be made use of in one or other of the following ways, 
 viz.: 
 
 1st. By its weight, as in the water-balance and in the overshot-wheel. 
 
 2d. By its pressure, as in turbines and in the hydraulic engine, hydraulic 
 press, crane, etc. 
 
 3d. By its impulse, as in the undershot-wheel, and in the Pelton wheel. 
 
 4th. By a combination of the above. 
 
 Horse-power of a Running Stream. The gross horse-power is 
 H.P. = QH X 62.36 *- 550 = 0.1134 QH, in which Q is the discharge in 
 cubic feet per second actually impinging on the float or bucket, and H = 
 
 1)2 <y2 
 
 theoretical head due to the velocity of the stream = ^- = ^. . in which 
 
 2 g o4.4 
 
 v is the velocity in feet per second. If Q' be taken in cubic feet per minute, 
 H.P. = 0.00189 Q'H. 
 
 Thus, if the floats of an undershot-wheel driven by a current alone be 5 
 feet X 1 foot, and the velocity of stream = 210 ft. per minute, or 31/2 ft. 
 per sec., of which the theoretical head is 0.19 ft., Q = 5 sq. ft. X 210 = 1050 
 cu. ft. per minute; H.P. = 1050 X 0.19 X 0.00189 =. 0.377 H.P. 
 
 The wheels would realize only about 0.4 of this power, on account of 
 friction and slip, or 0.151 H.P., or about 0.03 H.P. per square foot of 
 float, which is equivalent to 33 sq. ft, of float per H.P. 
 
 Current Motors. A current motor could only utilize the whole 
 power of a running stream if it could take all the velocity out of the water, 
 so that it would leave the floats or buckets with no velocity at all; or in 
 other words, it would require the backing up of the whole volume of the 
 stream until the actual head was equivalent to the theoretical head due to 
 the velocity of the stream. As but a small fraction of the velocity of the 
 stream can be taken up by a current motor, its efficiency is very small. 
 Current motors may be used to obtain small amounts of power from large 
 streams, but for large powers they are not practicable. 
 
 Bernoulli's Theorem. Energy of Water Flowing in a Tube. 
 
 tfi f 
 
 The head due to the velocity is ; the head due to the pressure is ; the 
 
 head due to actual height above the datum plane is h feet. The total head 
 
 v^ f 
 
 is the sum of these = - -- \-h+ , in feet, in which v = velocity in feet per 
 
 second, f pressure in Ibs. per sq. ft., w = weight of 1 cu. ft. of water ** 
 
766 WATER- POWER. 
 
 62.36 Ibs. If p = pressure in Ibs. per sq. in., ^ = 2.309 p. If a constant 
 
 quantity of water is flowing through a tube in a given time, the velocity 
 varying at different points on account of changes in the diameter, the 
 energy remains constant (loss by friction excepted) and the sum of the 
 three heads is constant, the pressure head increasing as the velocity de- 
 creases, and vice-versa. This principle is known as " Bernoulli's Theo- 
 rem." 
 
 In hydraulic transmission the velocity and the height above datum are 
 usually small compared with the pressure-head. The work or energy of a 
 given quantity of water under pressure = its volume in cubic feet X its 
 pressure in Ibs. per sq. ft.; or if Q = quantity in cubic feet per second, 
 and p = pressure in Ibs. per square inch, W = 144 pQ, and the H.P. 
 
 Maximum Efficiency of a Long Conduit. A. L. Adams and R. C. 
 Gemmell (Eng'g News, May 4, 1893) show by mathematical analysis that 
 the conditions for securing the maximum amount of power through a long 
 conduit of fixed diameter, without regard to the economy of water, is that 
 the draught from the pipe should be such that the frictional loss in the pipe 
 will be equal to one-third of the entire static head. 
 
 Mill-Power. A "mill-power" is a unit used to rate a water-power 
 for the purpose of renting it. The value of the unit is different in different 
 localities. The following are examples (from Emerson): 
 
 Holyoke, Mass. Each mill-power at the respective falls is declared to 
 be the right during 16 hours in a day to draw 38 cu. ft. of water per second 
 at the upper fall when the head there is 20 feet, or a quantity proportionate 
 to the height at the falls. This is equal to 86.2 horse-power as a maximum. 
 
 Lowell, Mass. The right to draw during 15 hours in the day so much 
 water as shall give a power equal to 25 cu. ft. a second at the great fall, 
 when the fall there is 30 feet. Equal to 85 H.P. maximum. 
 
 Lawrence, Mass. The right to draw during 16 hours in a day so much 
 water as shall give a power equal to 30 cu. ft. per second when the head is 
 25 feet. Equal to 85 H.P. maximum. 
 
 Minneapolis, Minn. 30 cu. ft. of water per second with head of 22 feet. 
 Equal to 74.8 H.P. 
 
 Manchester, N.H. Divide 725 by the number of feet of fall minus 1, 
 and the quotient will be the number of cubic feet per second in that fall. 
 For 20 feet fall this equals 38.1 cu. ft., equal to 86.4 H.P. maximum. 
 
 Cohoes, N.Y. " Mill-power" equivalent to the power given by 6 cu. ft. 
 per second, when the fall is 20 feet. Equal to 13.6 H.P., maximum. 
 
 Passaic, N.J. Mill-power: The right to draw 81/2 cu. ft. of water per 
 sec., fall of 22 feet, equal to 21.2 horse-power. Maximum rental $700 per 
 year for each mill-power = $33.00 per H.P. 
 
 The horse-power maximum above given is that due theoretically to the 
 weight of water and the height of the fall, assuming the water-wheel to 
 have perfect efficiency. It should be multiplied by the efficiency of the 
 wheel, say 75% for good turbines, to obtain the H.P. delivered by the 
 wheel. 
 
 Value of a Water-power. In estimating the value of a water- 
 power, especially where such value is used as testimony for a plaintiff 
 whose water-power has been diminished or confiscated, it is a common 
 custom for the person making such estimate to say that the value is repre- 
 sented by a sum of money which, when put at interest, would maintain a 
 steam-plant of the same power in the same place. 
 
 Mr. Charles T. Main (Trans. A. S. M. E., xiii. 140) points out that this 
 system of estimating is erroneous; that the value of a power depends upon 
 a great number of conditions, such as location, quantity of water, fall or 
 head, uniformity of flow, conditions which fix the expense of dams, canals, 
 foundations of buildings, freight charges for fuel, raw materials and finished 
 product, etc. He gives an estimate of relative cost of steam and water- 
 power for a 500 H.P. plant from which the following is condensed: 
 
 The amount of heat required per H.P. varies with different kinds of 
 business, but in an average plain cotton-mill, the steam required for heat- 
 ing and slashing is equivalent to about 25% of steam exhausted from the 
 high-pressure cylinder of a compound engine of the power required to run 
 that mill, the steam to be taken from the receiver. 
 
WATER-POWER. 767 
 
 The coal consumption per H.P. per hour for a compound engine is taken 
 at 1 3/4 ibs. per hour, when no steam is taken from the receiver for heating 
 purposes. The gross consumption when 25% is taken from the receiver is 
 about 2.06 Ibs. 
 
 75% of the steam is used as in a compound engine at 1.75 Ibs. = 1.31 Ibs. 
 25% of the steam is used as in a high-pressure engine at 3.00 Ibs. = .75 Ib. 
 
 2.06 Ibs. 
 
 The running expenses per H. P. per year are as follows: 
 2.06 Ibs. coal per hour = 21.115 Ibs. for 101/4 hours or one day = 
 
 6503.42 Ibs. for 308 days, which, at $3.00 per long ton = $8.71 
 
 Atendance of boilers, one man @ $2.00, and one man @ $1.25 = 2.00 
 Attendance of engine, one man @ $3.50. 2.16 
 
 Oil, waste, and supplies. .80 
 
 The cost of such a steam-plant in New England and vicinity of 500 
 H. P. is about $65 per H. P. Taking the fixed expenses as 4% 
 on engine, 5% on boilers, and 2% on other portions, repairs at 
 2%, interest at 5%, taxes at U/2% on 8/4 cost, and insurance at 
 1/2% on exposed portion, the total average per cent is about 
 121/2%, or $65 X 0.121/2 = 8.13 
 
 Gross cost of power and low-pressure steam per H. P. $21.80 
 
 Comparing this with water-power, Mr. Main says: "At Lawrence the 
 cost of dam and canals was about $650,000, or $65 per H. P The cost 
 per H. P. of wheel-plant from canal to river is about $45 per H. P. of 
 plant, or about $65 per H. P. used, the additional $20 being caused by 
 making the plant large enough to compensate for fluctuation of power 
 due to rise and fall of river. The total cost per H. P. of developed plant 
 is then about $130 per H. P. Placing the depreciation on the whole 
 plant at 2%, repairs at 1%, interest at 5%, taxes and insurance at 1%, 
 or a total of 9%, gives: 
 
 Fixed expenses per H. P. $130 x .09 = $11.70 
 Running expenses per H. P. (Estimated) 2.00 
 
 $13.70 
 
 "To this has to be added the amount of steam required for heating 
 purposes, said to be about 25% of the total amount used, but in winter 
 months the consumption is at least 371/2%. It is therefore necessary to 
 have a boiler plant of about 37 1/2% of the size of the one considered with 
 the steam-plant, costing about $20 X 0.375 = $7.50 per H.P of total 
 power used. The expense of running this boiler-plant is, per H. P of 
 the total plant per year: 
 
 Fixed expenses 121/2% on $7.50 . $0.94 
 
 Coal 3 20 
 
 Labor ? . . i . 23 
 
 Total $<T43 
 
 Making a total cost per year for water-power with the auxiliary boiler 
 plant $13.70 + $5.43 = $19.13 which deducted from $21.80 makes a 
 difference in favor of water-power of $2.67, or for 10,000 H P a savinsr 
 of $26,700 per year. 
 
 "It is fair to say," says Mr. Main, "that the value of this constant 
 power is a sum of money which when put at interest will produce the 
 saying; or if 6% is a fair interest to receive on money thus invested the 
 value would be $26,700 -4- 0.06 = $445,000." 
 
 Mr. Main makes the following general statements as to the value of a 
 water-power: "The value of an undeveloped variable power is usually 
 nothing if its variation is great, unless it is to be supplemented by a 
 steam-plant. It is of value then only when the cost per horse-power for 
 
 le double-plant is less than the cost of steam-power under the same 
 conditions as mentioned for a permanent power, and its value can be 
 represented m the same manner as the value of a permanent power lias 
 
7G8 
 
 WATER-POWER. 
 
 "The value of a developed power is as follows: If the power can be 
 run cheaper than steam, the value is that of the power, plus the cost of 
 plant, less depreciation. If it cannot be run as cheaply as steam, con- 
 sidering its cost, etc., the value of the power itself is nothing, but the 
 value of the plant is such as could be paid for it new, which would bring 
 the total cost of running down to the cost of steam-power, less de- 
 preciation." 
 
 Mr. Samuel Webber, Iron Age, Feb. and March, 1893, writes a series 
 of articles showing the development of American turbine wheels, and 
 incidentally criticises the statements of Mr. Main and others who have 
 made comparisons of costs of steam and of water-power unfavorable to 
 the latter. He says : ' ' They have based their calculations on the cost 
 of steam, on large compound engines of 1000 or more H. P. and 120 
 pounds pressure of steam in their boilers, and by careful 10-hour trials 
 succeeded in figuring down steam to a cost of about $20 per H. P., ignor- 
 ing the well-known fact that its average cost in practical use, except 
 near the coal mines, is from $40 to $50. In many instances, dams, 
 canals, and modern turbines can be all completed for a cost of $100 per 
 H. P. ; and the interest on that, and the cost of attendance and oil, will 
 bring water-power up to about $10 or $12 per annum; and with a man 
 competent to attend the dynamo in attendance, it can probably be 
 safely estimated at not over $15 per H. P." 
 
 WATER-WHEELS. 
 
 Water-wheels are classified as vertical wheels (including current 
 motors, undershot, breast, and overshot wheels), turbine wheels, and 
 impulse wheels. Undershot and breast wheels give very low efficiency, 
 and are now no longer built. The overshot wheels when made of large 
 diameter (wheels as high as 72 ft. diameter have been made) and prop- 
 erly designed have given efficiencies of over 80%, but they have been 
 almost entirely supplanted by turbines, on account of their cumbersome- 
 ness, high cost, leakage, and inability to work in back water. 
 
 Turbines are generally classified according to the direction in which 
 the water flows through them, as follows: 
 
 Tangential flow : Barker's mill. Parallel flow: Jonval. Radial out- 
 ward flow: Fourneyron. Radial inward flow: Thompson vortex; 
 Francis. Inward and downward flow: Central discharge scroll wheels 
 and earlier American type of wheels; Swain turbine. 
 
 HYDRAULIC TURBINES 
 
 Theory and Proportions. For the theory of water turbines consult 
 Prof. De Volson Wood's paper on Hydraulic Reaction Motors, Trans. 
 A. S. M. E., xiv, 266; also Prof. Unwin's paper on Hydraulics, Ency. 
 Brit., llth ed., vol. 14; Merriman's and Bovey's books on Hydraulics, 
 Church's Hydraulic Motors, and Daugherty's Hydraulic Turbines. 
 The following formulae and example are condensed from Church's 
 theoretical discussion of the subject. 
 
 Fig. 151 represents a simple Fourneyron or radial outward flow 
 turbine placed at the bottom of an open wheel-pit. PP is a short 
 penstock through which the water descends into a cylindrical gate CC, 
 which is movable vertically. The water passes through the guides 
 G into the wheel or runner W. R f represents the resistance overcome 
 by the turbine acting through the pulley M at a velocity of v l ft. per 
 second. The turbine itself is shown in black shading. EE and DD 
 are the two crowns or rings between which are inserted the curved 
 vertical buckets W. 
 
 Notation. Referring to Figs. 152 and 152a. 
 
 w n = absolute velocity of the water leaving the wheel at N, 
 being represented by the diagonal of the parallelogram 
 
 Gn % 
 
 c n = relative velocity of the water at N. 
 % = velocity of the outer rim of the wheel, 
 
HYDRAULIC TURBINES 
 
 768A 
 
 L = absolute velocity of the water entering the wheel channel at 
 the point 1 on inner rim of the runner, represented by the 
 diagonal of the parallelogram ci vi. 
 = relative velocity of the water at the point 1. 
 
 = velocity of the inner 
 rim of the wheel, tan- 
 gent to the vane curve 
 at 1." 
 
 : angle between the tan- 
 gent to the inner rim 
 Vi and a tangent to 
 the direction of the 
 water at 1. 
 
 = angle between tangent 
 i>i and the tangent to 
 
 Pthe vane at 1. 
 fj. = angle between v n and 
 w n . 
 
 5 = angle between c n and 
 the tangent to the 
 outer rim. 
 
 h = height, in feet, from the 
 surface of head- water 
 to that of tail-water. 
 h hn = h e i g h t respectively 
 from a point halfway 
 between the crowns 
 (top and bottom of 
 the vanes) and the 
 head-water and tail- 
 water. 
 
 e = height or vertical dis- 
 tance between crowns. 
 h 7*2 radii of inner and outer 
 
 edges of the wheel. 
 Q = cubic feet of water used 
 per second, in steady 
 flow. 
 7 = weight of 1 cubic foot 
 
 Wheel or 
 Runner 
 
 Horizontal Section N A X. 
 FIG. 151. Fourneyron Turbine* 
 
 of water, Ib. 
 
 Pi Pn ~ internal pressure of 
 the water at entrance 
 and exit of the wheel. 
 p a = pressure of atmosphere, Ib per sq. ft. 
 
 b = height of the water barometer in feet. 
 
 If the wheel is run at the proper speed and the angle ft has been 
 given a value such that the tangent to the vane curve at 1 coincides 
 in direction with the relative velocity CL there will be no "elbow" 
 or sharp turn in the absolute path of the water as it enters the wheel, 
 but the path will be a smooth curve, GIN, Fig. 1520. In this way 
 impact or shock and the corresponding loss of energy are avoided. 
 
 The quantities, Q, hi h n , 7, r\, TZ, a, and 5 being given, it is required 
 to determine the best value for the velocity v n of the outer wheel-rim 
 and the proper height e between crowns so that the whole available 
 flow Q may be utilized. Nine unknown quantities are involved, viz.: 
 Vi, v n , Wi, w n , e, GI, c n , PI, and p n , and nine independent and simul- 
 taneous equations are needed. 
 
 Disregarding friction for the present, the following are the equations: 
 
 (1) d2 = Wi* + Vi 2 2 Wi vi cos a. 
 
 (2) Wrf = C n 2 + V n 2 -2C n V n COS g. 
 
768s 
 
 WATER-POWER 
 
 2g 
 
 (5) Vn *= c n , when tne angle 5 is small. 
 
 (6) [27r ri e sin a] w l = [2wr n e sin 5] c n . 
 
 (7) Q = [27rr n e sin 5] c n . 
 
 (9) p n = 7^ + P a - 
 
 From these equations the following are derived: 
 
 (10) Velocity of outer rim for max. efficiency, v n = . 
 
 gh (tan a) 
 sin 5 
 
 (11) Power, ft.-lbs. per sec. exerted by the water on the turbine, 
 L = Q7h ~. This power L equals the whole theoretic power 
 
 of the mill-site less the kinetic energy carried away per second by the 
 water leaving the wheel at N. 
 
 - ~ (Wi vi cos a - [w n cos M] %). 
 
 (12) L 
 
 Efficiency, i\ = 1 - (2 tan 
 
 a sin2 --T- sin 6). 
 
 FIG. 152. Path of Water. 
 ft. 
 
 FIG. 152a. Velocity Diagrams. 
 
 From (17) 
 v n = 0.92 
 
 From this expression we see 
 that the smaller the angles a 
 and 5 can be made the greater 
 the efficiency. In practice a is 
 taken from 20 to 30 and 5 from 
 15 to 20. 
 
 With a = 25 and 5 = 15 we 
 obtain t] = 0.92, but in actual 
 practice this figure is reduced to 
 80 per cent or less (unless in ex- 
 ceptional cases) on account of 
 fluid friction and imperfect 
 guidance of the water; 75 per 
 cent is a fairly good perform- 
 ance. When a turbine (fric- 
 tionless) is running with the 
 speed of maximum efficiency, 
 the following formula holds 
 good for an kinds of turbines: 
 
 (13) Wi Vi cos a = gh. 
 
 EXAMPLE. Given 7i = 60 ft., 
 Q = 150 cu. ft. per sec., n = 2 
 ft., r n = 2.5 ft., angle a = 20, 
 5 = 15, it is required to de- 
 sign an outward radial dis- 
 charge turbine having parallel 
 crowns, to find the outer rim 
 velocity v n for the best effect, 
 the vane tangent angle p at 
 entrance and the proper dis- 
 tance e between crowns, that all 
 the water available may be used 
 at full gate. 
 
 = 48 ft. per sec, 
 
HYDRAULIC TURBINES. 769 
 
 48 X 60 
 With r n = 2.5 ft. this is equivalent to 2 ^ ^ 2 5 = 183 revs, permin. 
 
 From (6) taking c n = v n , 
 
 v n r n sin 5 43 x 2.5 X 0.259 
 
 5.4 ft. per sec. 
 
 2.0X0.342 
 From (8) Vi = n % *- r n = (2-5- 2.5) 48 = 38.4 ft. per sec. 
 
 From (14 ) tan USO* - ft - - 
 
 Whence 180 - ft = 105 19'; /3 = 74 41'. 
 
 From (15) e = Q -f- 2irr n sin 5 v n = 150 -f- (2?r x 2.5 X 0.259 X 48) = 
 0.768 ft., or, adding 10 per cent for thickness of vanes, 0.845 ft. 
 
 Assuming 75 per cent efficiency, the power of this wheel is 
 0.75 X Qjh = 0.75 X 150X 62.4 X 60 = 421,200 ft.-lbs. per sec. = 766 H.P. 
 
 The formulae above given apply to inward flow as well as to outward 
 ial 
 
 flow turbines. For axial flow turbines r\ = r^ = r, which is measured 
 
 ining the wheel vanes. 
 v n for the best effect, assuming 
 
 to the middle point of the ring containing the wheel vanes. 
 Another formula for the value of v n for the best 
 
 8 per cent friction losses, is 
 
 % = 0.92 o r n 
 
 F n being the aggregate sectional area of the exit passages of the 
 turbine, that of each passage being taken at right angles to the relative 
 velocity c n , and F o the aggregate sectional areas of the guide passages 
 at the entrance point, 1. 
 
 To find j8, the vane tangent angle at the point 1, 
 
 (14) tan (180 - 
 
 . 
 i - Wi cos a 
 
 To find e, the distance between crowns (the common height of all 
 the wheel passages at full gate), 
 (15) e = Q -r 2wr n (sin 6) %. 
 
 This value should be increased somewhat (perhaps 10 per cent in 
 some cases) to allow for the thickness of the vanes. 
 
 When friction is taken into account, the value of v n (the velocity of 
 the outer rim) for best effect is 
 
 } l 
 
 f and f n are coefficients of resistance due to friction, respectively, of 
 the passages between the head water surface and the guide outlets 
 and the passages through the vanes. According to Weisbach, each of 
 these coefficients may be taken at from 0.05 to 0.10. Taking the 
 larger value the equation reduces to 
 
 (17) v n = 0.92 
 
 Besides the loss due to friction of the passages there are other losses, 
 such as those due to the friction of the wheel in the tail-water, to axle 
 friction, and to leakage between the edges of the wheel-crowns and 
 the guides. Refined analysis of these losses is impracticable, and the 
 efficiency of any given wheel can be determined only by actual test. 
 
 The formulae given above may be used for approximate computations 
 in the preliminary design of a turbine, but in practical design many 
 
769A 
 
 WATER-POWER 
 
 considerations enter which the formulas do not cover, such as the 
 number of vanes and guides, their shape and proportions. 
 Determination of the Dimensions of Water Turbine Runners. S. J. 
 
 Zowski (Eng. News, Jan. 6, 1910) developed a series of empirical 
 formulae for the design of water turbine runners. The starting point 
 of the theory upon which the formulae are built is the formula for the 
 peripheral velocity of the mean circumference of the runner; 
 
 Transformations of this equation and the application of certain 
 constants result in the empirical formulae given in the accompanying 
 table: 
 
 Comparison of Formulae for Dimensions of Hydraulic Turbines 
 
 (Zowski). 
 
 
 Bucket 
 Angle ft 
 deg. 
 
 Vane 
 Angle a 
 deg. 
 
 Speed 
 Constant 
 
 Entrance 
 Diameter 
 D 
 
 No. of 
 
 Buckets 
 n 
 
 No. of 
 Guide 
 Vanes 
 n' 
 
 Low speed 
 
 60-90 
 
 20 or less 
 
 5 4.588 to 
 
 87 to 99 / 
 
 3.7 V^~ 
 
 2.5 VoT 
 
 N NH 
 
 Medium speed. 
 
 901 
 
 25-32 
 
 5.198 
 
 99 _ 
 
 3.0Vd~ 
 
 3.0 Vd" 
 
 High speed. . . . 
 
 90-135 
 
 30-40 
 
 5 5. 198 to 
 \ 7.006 
 
 99 to 134 
 
 2.2Vd~ 
 
 3.5 V<T 
 
 N VH 
 
 NOTES: Efficiency. In the calculations leading to the figures in 
 the above table, a hydraulic efficiency of 84 per cent has been assumed 
 for medium-speed runners, and of 83 per cent for other types. These 
 efficiencies are not unusual for runners of fair design and construction, 
 and with them the values of K v above are obtained. 
 
 Values of (3 and a For high heads, requiring low-speed runners, it 
 Will be advisable to keep # in the neighborhood of 90, since the smaller 
 the ratio /3/a the smaller is the pressure head under which the water 
 passes from the guide case into the runner buckets. 
 
 Number of Buckets and Guide Vanes n and n'. Some turbine builders 
 use in every case as many buckets as possible, but the majority use 
 less in a high-speed than in a low-speed runner. A few more guide 
 vanes than buckets should be used. It is advisable to use an even 
 number of guide vanes, and often, for manufacturing reasons, to make 
 this number divisible by 4. The number of buckets should be un- 
 even to avoid haying more than one bucket edge coincide with a vane 
 tip at the same time. 
 
 Prof. Zowski classifies turbines with respect to speed as low speed, 
 medium speed, and high speed. High-speed runners are those in 
 which the angle is greater than 90, medium speed, those in which 
 is 90, and low speed, those in which P is less than 90. High-speed 
 runners are frequently known as the "American" type. He also 
 classifies them with respect to capacity, as low capacity, medium 
 capacity, and high capacity, based on the proportions of the runner 
 profile or the ratios of (a) diameter, D, at entrance point of buckets; 
 (&) diameter at exit point of buckets, D'\ (c) diameter at neck of draft 
 tube, D". See Fig. 153. 
 
 The capacity depends on the relation of B/D and varies between 
 the limits of Vso D and 1/2 -D. The minimum value depends on the 
 purity of the water. Low capacity runners are stated to be those 
 in which the diameter of the draft tube is equal to or less than the 
 bucket exit diameter, and B/D will lie between 1/30 and Vs. In 
 medium capacity runners, the draft tube diameter is larger than the 
 
HYDRAULIC TURBINES. 
 
 769s 
 
 bucket exit diameter, but less than the mean diameter of the runner; 
 B/D lies between i/g and 1/4. In high capacity runners, the draft 
 tube diameter is greater than the mean exit diameter of the runner, 
 and B/D lies between 1/4 and 1/2. 
 
 D" > D" 
 
 FIG. 153. Limiting Profiles of Three Types of Radial Inward 
 Flow Turbine. 
 
 The capacity of runners may be characterized by the capacity 
 constant 
 
 If a series of values, as in the table below, be assigned to Kq and 
 these values substituted in the above equation, we may obtain the 
 diameter of the runner in terms of the discharge per foot of head. 
 The constants and resulting formulae for diameter are as follows: 
 
 Type of 
 Turbine. 
 
 Range of 
 
 K v. 
 
 Diam. in 
 Terms of Qi. 
 
 Discharge Loss 
 in Terms of 
 Total Head. 
 
 Low speed, low capa- 
 city 
 
 21 to 89 
 
 (2.20 to 1.06) V(?i 
 
 (0.04 to 0.06) H 
 
 Medium speed, medi- 
 um capacity 
 
 0.89 to 2. 19 
 
 (1.06 to 0.67) V5i 
 
 (00.5 to 0.08)H 
 
 High speed, high capa- 
 city 
 
 2. 19 to 4.66 
 
 (0.67 to 0.46) V<?I 
 
 (0.08 to O.I5)H 
 
 The discharge loss represents the flow velocity at the neck of the 
 draft tube. With properly designed runners it is about the same as 
 the ftow velocity in the discharge area of the runner. This velocity 
 is a direct loss, which, however, is partly recovered by the conical lower 
 part of the draft tube. In low capacity runners it is not difficult to 
 reduce the discharge loss to a minimum in the runner itself, while 
 in high capacity runners large discharge losses must be allowed. The 
 values given for discharge losses in the above table represent good 
 practice. 
 
 The speed and capacity constants have been combined by Prof. 
 Zowski to form a type -characteristic Kj, described below. The range 
 of KI is as follows: 
 
 Low Speed, Low 
 Capacity. 
 12 to 28 
 
 Medium Speed, Medium 
 Capacity 
 28 to 44 
 
 High Speed, High 
 Capacity 
 44 to 87 
 
 Compare the above ranges with those given by Baashuus on page. 771. 
 
770 
 
 WATER-POWEB. 
 
 ft: 
 
 Comparison of American High-Speed Runners Type Characteristic. 
 
 S. J. Zowski (Eng. News, Jan. 28, 1909) compares the runners of 
 standard American high-speed turbines by means of speed and capa- 
 city criteria. Referring to Fig. 154, he uses the notation: 
 H.P. = effective power of the runner. 
 N = speed of runner, r. p. m. 
 Q = discharge of runner, cu. ft. per sec. 
 i = specific discharge of runner = Q -4- V H . 
 [ = net head acting on turbine = gross head minus all losses in 
 
 head race conduit and tail race, in feet. 
 e^ = hydraulic efficiency of the turbine ; (1 e^) H = head lost 
 
 inside of turbine due to friction, eddies and shocks. 
 D = mean entrance diameter of runner, feet. 
 d = mean entrance diameter of runner, inches. 
 B = height of guide case, feet. 
 a = angle between entrance speed and peripheral speed at D 
 
 (see Fig. 154). 
 P = bucket angle at D 
 c = real entrance speed at D. 
 w = relative entrance speed at D. 
 v = peripheral speed at D. 
 n = number of buckets. 
 n f number of guide vanes. 
 c r = radial entrance speed at D = 
 radial component of c (see Fig. 
 154). 
 
 Kv = s P eed constant. 
 Kq = capacity constant. 
 KI = type constant. 
 
 - V 
 
 For a value of e^ = 0.83, 
 
 = 5.167 
 
 \ 
 
 
 sin (3 cos a 
 
 For the conditions, /3 = 135, a = 40, and 
 e^ = 0.83; the value of K v is about 7.0. 
 
 The constant K v can also be used to de- 
 termine whether a further increase of speed 
 is possible. If K^ be considerably larger 
 than 7, either the guaranteed speed is higher 
 than the speed at which the runner gives 
 maximum efficiency, or the nominal diam- 
 eter of the runner is larger than the mean 
 diameter D. 
 
 K = Q = -2- 1 
 q Z>2 V H D* 
 
 Kq is the specific discharge of a runner 
 with its diameter reduced to 1 ft. Kq will 
 have nearly the same value for all runners 
 of the same type and is a criterion for ca- 
 pacities of different runner types. 
 
 FIG. 154. Horizontal 
 and Vertical Sections of 
 High-speed Turbine. 
 
 The speed and capacity criteria, however, 
 fail to give the information as to what ex- 
 tent each type of runner meets the require- 
 ment of highest possible speed with highest capacity in cubic feet per 
 second. Two runners with different values of K v and Kq may be equiv- 
 alent when the speed and capacity are considered together. A third 
 criterion K>. known as the type characteristic or specific speed, which 
 
HYDRAULIC TURBINES. 
 
 770A 
 
 combines K v and K q must be introduced to give this information. 
 A convenient method of combination has been indicated by Professor 
 
 Camerer, of Munich, and gives a value of K^ - 
 Values of H I >M for different heads are given below. 
 VALUES OP 
 
 H 
 
 #1.25 
 
 H 
 
 Hl-25 
 
 H 
 
 Hi.25 
 
 H 
 
 Hi.25 
 
 H 
 
 Hi.25 
 
 2 
 
 2.38 
 
 35 
 
 85.13 
 
 140 
 
 841.6 
 
 400 
 
 1789 
 
 900 
 
 4930 
 
 4 
 
 5.66 
 
 40 
 
 100.6 
 
 160 
 
 569.0 
 
 450 
 
 2073 
 
 950 
 
 5274 
 
 6 
 
 9.39 
 
 45 
 
 116.6 
 
 180 
 
 659.3 
 
 500 
 
 2364 
 
 1000 
 
 5623 
 
 8 
 
 13.45 
 
 50 
 
 133.0 
 
 200 
 
 752.2 
 
 550 
 
 2663 
 
 1200 
 
 7079 
 
 10 
 
 17.78 
 
 60 
 
 167.0 
 
 220 
 
 847.3 
 
 600 
 
 2970 
 
 1400 
 
 8564 
 
 12 
 
 22.33 
 
 70 
 
 202.5 
 
 240 
 
 944.6 
 
 650 
 
 3282 
 
 1600 
 
 10120 
 
 15 
 
 29.52 
 
 80 
 
 239.3 
 
 260 
 
 1044 
 
 700 
 
 3601 
 
 1800 
 
 11724 
 
 20 
 
 42.29 
 
 90 
 
 277.2 
 
 280 
 
 1145 
 
 750 
 
 3925 
 
 2000 
 
 13375 
 
 25 
 
 55.90 
 
 100 
 
 316.2 
 
 300 
 
 1249 
 
 800 
 
 4255 
 
 2500 
 
 17678 
 
 30 
 
 70.21 
 
 120 
 
 397.2 
 
 350 
 
 1514 
 
 850 
 
 4590 
 
 3000 
 
 22202 
 
 The value of K^ is an absolute criterion for turbines in reference to 
 the combination of highest speed, highest capacity and good efficiency. 
 Its meaning can be found by assuming H.P. = 1 and H = 1, when 
 KI = N in r. p. m. The following table compares the capacity and 
 speed constants and type characteristics of the standard American 
 turbines by means of this criterion: 
 
 Mean Values of Capacity Constants, Speed Constants and Type Char- 
 acteristics of American High-Speed Runners. 
 
 Values in Foot and Pound System. 
 
 
 
 Capa- 
 
 Speed 
 
 Type 
 
 Velocity 
 Coefficient, 
 
 K> V 
 
 Name of Runner Type. 
 
 Maker 
 
 city 
 Con- 
 stant, 
 JC fl 
 
 Con- 
 stant, 
 K v 
 
 Charac- 
 teristic, 
 
 *t 
 
 V V17H 
 Kv 
 
 
 
 ( 2 
 
 
 
 VT5 
 
 Smith 
 
 , 
 
 3.68 
 
 7.26 
 
 80.6 
 
 0.905 
 
 Improved New American . . 
 Leviathan 
 
 2 
 3 
 
 3.43 
 2.96 
 
 7!47 
 
 79 
 74.1 
 
 0.885 
 0.931 
 
 Improved Samson 
 
 4 
 
 3.18 
 
 7.07 
 
 73.1 
 
 881 
 
 Victor Increased Capacity.. 
 Victor Standard Capacity. . 
 Trump 
 
 5 
 5 
 
 6 
 
 3.59 
 3.26 
 3.52 
 
 6.1 
 6.1 
 5.87 
 
 66.6 
 63.5 
 63.4 
 
 0.761 
 0.761 
 0.729 
 
 New Success 
 
 1 
 
 2 75 
 
 5.88 
 
 55 
 
 733 
 
 New American 
 
 2 
 
 2.8 
 
 5.6 
 
 54.1 
 
 0.69 
 
 McCormick* 
 
 1 ) 
 
 
 
 
 
 Jolly McCormick* 
 
 7 } 
 
 2.8 
 
 5.35 
 
 51.4 
 
 0.667 
 
 Alcott High Duty Special. . 
 Risdon Double Capacity. . . 
 
 3 X 
 3 
 
 2.25 
 1.7 
 
 5.46 
 5.9 
 
 46.7 
 43.8 
 
 0.681 
 0.735 
 
 *These two runners are identical and have the same characteristics. 
 The makers of the above turbines are as follows: 1. S. Morgan Smith Co. 
 2. Dayton Globe Iron Works Co. 3. Risdon-Alcott Turbine Co. 4. The James 
 Leffel & Co. 5. Platt Iron Works Co. 6. Trump Mfg. Co. 7. Wellman- 
 Seaver-Morgan Co. 
 
 The data were gathered from catalogs of the different concerns and 
 the values of power and speed tabulated in the catalogs were based 
 on tests made in the Holyoke flume. The values of the discharge are 
 based on tfoe assumption of 80 per cent efficiency, 
 
770s 
 
 WATER-POWER . 
 
 Specific Discharge. Prof. Merriman (Hydraulics, 10th ed., p. 476) 
 uses a coefficient or efficiency which he calls the specific discharge. 
 It is the discharge of a 1-H.P. turbine under a head of 1 foot. If Q is 
 the discharge of a turbine, in cubic feet per second, // the head in feet 
 and H.P. the horsepower, then the specific discharge Q s =QH/H.P. 
 The specific discharge is characteristic of the efficiency of a given type, 
 and is the greater the lower the efficiency. For high, medium and 
 low efficiency, respectively, the specific discharge is less than 10, from 
 10.5 to 11.5 and greater than 12. 
 
 The specific diameter of a given type is the diameter D correspond- 
 ing to a head of 1 foot and the specific speed N 8 (or type characteristic 
 KI). By means of a test on one size of a given type the quantities 
 N s , Q s and a constant, k\, can be computed. For any other size of 
 that type under any head H 
 
 N = N S ft 1 ' 25 + V HJF Q =Qo H.P. - H D = ki V1F-*- N 
 
 N VHJP? 
 
 Qs- 
 
 ND 
 
 H.P. 
 
 The following values of these constants have been obtained in tests 
 of the turbines named : 
 
 Manufacturer. 
 Allis-Chalmers Co 
 
 Type. 
 
 ( A 
 j B 
 
 Specific 
 Speed 
 
 ^s 
 13.4 
 20.4 
 29.4 
 40.6 
 47 
 47.5 
 74.1 
 53 
 57 
 81 
 
 etermine 
 
 March 2, 
 
 Specific Specific 
 Dis- Con- 
 charge, stant 
 
 Qs *i 
 11.6 1078 
 11.6 1149 
 11.6 1224 
 11.1 1280 
 11.1 1250 
 10.4 1350 
 11.0 1714 
 11.0 1260 
 11.0 1350 
 10.9 1660 
 
 the Size and Type 
 
 1911) discusses the 
 
 Risdon-Alcott Co. . . 
 
 ) c 
 
 ( D 
 
 ( Alcott 
 I Risdon 
 
 ( Leviathan 
 1 McCormick 
 S. Morgan Smith Co. . . . < New Success 
 ( Smith 
 
 The Use of Type Characteristics to DI 
 of Turbines. N. Baashuus (Eng. News, 
 
 use of type characteristics as developed by Zowski for determining 
 the size and type of turbine to be used in power plants. If H.P. be 
 the horsepower capacity of a single turbine unit, N the speed of 
 the turbine in r. p m., H effective head at the turbine casing in 
 
 N /H P 
 feet, KV = T?A/ The value of KV for radial inward flow tur- 
 
 H \ Vtf 
 
 bines will lie between 10 and 100, while for impulse wheels it will lie 
 between 5 and 1, or even a lower figure. The practical type char- 
 acteristics will always be within these limits irrespective of the capacity, 
 speed, head, size or design of the turbine. Where an inward flow 
 turbine has more than one runner, or the impulse wheel more than 
 one nozzle, the H.P. to be applied in the above formula is the power 
 developed by one runner or one nozzle only. 
 
 EXAMPLE. Assuming an available effective head of 324 feet and an 
 available flow of about 310 cu. ft. per sec. at the power-plant site, 
 
 = 9,100. Of this, 103 H.P. will be 
 
 the total capacity is H.P.i = 
 
 required for exciters and lighting purposes, calling for two 100-H.P. 
 exciter units running at 550 r. p. m., one being in reserve. The remain- 
 ing 9,000 H.P. would be generated by three 3,000-H.P. units run- 
 ning at 500 r. p. m. with a fourth unit as a reserve. From these 
 
 data we find the type characteristic of the main unit K t = ^ - 
 
 5= 2J calling for a radial inward flow turbine, Likewise for an exciter 
 
HYDRAULIC TURBINES. 
 
 771 
 
 unit, KI = 4.25, calling for an impulse wheel. This characteristic is 
 not only intended to give information as to the class of wheel to be 
 used, but it will also indicate the particular variety in each class. 
 The accompanying table shows the values of K^ and the efficiency 
 
 
 Classes of Radial Inward Flow Turbines 
 
 Type of Turbine. 
 
 *t* 
 
 Efficiency! 
 
 Maximum. 
 
 Power. 
 
 Efficiency 
 at Half 
 Power. 
 
 Low speed. . . . 
 
 10 to 20 
 30 to 50 
 60 to 80 
 90 to 100 
 
 82 
 82 
 80 
 73 
 
 3/ 4 
 3/4 
 8/10 
 9/10 
 
 76 
 75 
 70 
 53 
 
 Medium speed 
 
 High speed 
 
 Very high speed 
 
 of various classes of radial inward flow types. The figures are only 
 approximate and there are turbine tests on record showing better 
 results. The table, however, is a guide as to the particular type of 
 machine to be installed. Similarly the relation of type characteristic 
 to efficiency in impulse wheels is as follows: 
 
 K t l 
 
 Efficiency at about 
 
 = 12345 
 
 powert =80 79 78 77 76 
 
 In selecting a type for a proposed turbine plant, the speed in revolu- 
 tions can be chosen so that turbines of high efficiency are secured. 
 In cases of low head, the turbines would run too slowly for most pur- 
 poses, which disadvantage can be overcome by keying several runners 
 to one shaft. For instance: A 750-H.P. dynamo is to be driven at 
 257 r. p. m. under 36 ft. head. We may use one, two or four turbines 
 to develop the power, the values of K^ being 80, 56.5 and 40 respec- 
 tively. The first corresponds to the high-speed turbine which would 
 be unsuitable if water were scarce in dry seasons. The second would 
 utilize water in a more economical way, while the third combination 
 represents the most favorable type as to efficiency. Similarly, the 
 number of runners or nozzles on impulse wheel installations may be 
 determined. 
 
 With a 400-ft. head, and 1300 H.P. to be developed at an efficiency 
 of not less than 78 per cent, a turbine whose value of K^ is about 3 
 
 Lould be used. The revolutions with a single turbine wheel will be 
 
 N = K t XHX T/H7N = 150. 
 
 If this is too slow, two nozzles can be arranged to supply water to 
 the runner, each supplying one-half of the 1300 H.P., and the cor- 
 responding r. p. m. would be 212. Likewise, with four nozzles N = 
 300, and with six N = 357, giving the same efficiency in each case. 
 
 The characteristic K^ also can be used to determine the principal 
 dimensions of turbines for any given installation. The various di- 
 mensions of a given type of standard turbine can usually be expressed 
 as functions of the diameter of the runner, which functions are prac- 
 tically the same for all sizes of the same type. If a turbine plant of 
 a certain type characteristic K^ is proposed, it may be compared with 
 
 *KI refers to the maximum power of one runner only. In some 
 cases where K^ exceeds 100, multiplex turbines must be used. 
 
 fAt maximum power the efficiencies are a few per cent lower than 
 at maximum efficiency. 
 
 %K refers to maximum power of one nozzle only. In cases where the 
 type characteristic is between 5 and 10, turbines with more than one 
 nozzle must be used. 
 
 IfAt maximum and half power, the efficiencies are a few per cent lower. 
 
77U 
 
 WATER-POWER. 
 
 any existing plant of the same type characteristic built in the same way 
 as the natural conditions dictate that the new one should be built. 
 Standardized turbines of the same type will have runner diameters in 
 the ratio of ^N/H, and this ratio may be applied to the dimensions of 
 the existing plant, to determine those of the new one. 
 
 EXAMPLE. A proposed power house is to have three turbines on 
 horizontal shafts, two runners per turbine, developing 625 H.P. per 
 runner at 257 r. p. m. under an effective head of 39 ft. The type 
 characteristic for a twin turbine is __ 
 257 1250 
 
 Assume that the dimensions of an existing plant of similar type 
 to the proposed are available, and that this plant operates under an 
 effective head of 53 ft., and develops 650 H.P. per runner in twin tur- 
 bines, at 360 r. p. m. Its type characteristic would be 64, which would 
 be close enough to that of the proposed plant for our purpose. The 
 ratio between the sizes of the turbines would be 
 
 a. 
 
 IV 
 
 
 257 = 
 
 1.2 
 
 and all dimensions of turbines in the new plant would be 1.2 times 
 those of the old. This method is, of course, approximate, and it may 
 be sometimes advisable to increase somewhat the obtained results. 
 
 Estimating the Weight of a Turbine. A preliminary approximate 
 estimate of the weight of a turbine may be determined in the same 
 manner from the known weights of existing plants. If designed for 
 the same head, turbines of different sizes of a standardized series will 
 have weights approximately proportional to a function of the ratio of 
 diameters: 
 
 The first value should be used with D^/Di less than 1, and the second 
 with DZ/DI greater than 1. For different heads the weights of turbines 
 of the same size are approximately in the proportion: 
 
 The first value should be used with H 2 /Hi less than 1, and the 
 second with HZ /Hi greater than 1. 
 
 Wi t DI and if i always refer to the installation whose weight is known. 
 
 Selecting a Turbine. In selecting a turbine for a given location 
 manufacturers' catalogs should be consulted, and the characteristics 
 of the several designs that seem to fit the conditions should be com- 
 pared before making a decision. Considerations of first cost, space 
 occupied, number of revolutions, regulation, etc., tend to complicate 
 the problem. The type of wheel that is best suited for different heads 
 is roughly indicated in the following table: 
 
 Head. 
 
 Type. 
 
 Remarks. 
 
 Under 30 ft. 
 
 Open flume. 
 
 Except single units of less than 100 H.P. 
 
 
 
 when the encased type may be preferable. 
 
 30 to 50ft. 
 
 Open flume or 
 
 The latter most economical for units of less 
 
 
 steel encased. 
 
 than 500 H.P. 
 
 50 to 100 ft. 
 
 Steel-plate en- 
 
 Except small units, when cast-iron casings 
 
 
 cased. 
 
 may be lower in cost. 
 
 100 to 600 ft. 
 
 Cast-iron cas- 
 
 Cast steel for large units under high heads. 
 
 
 ings. 
 
 
 300 to 600 ft. 
 
 Impulse wheels. 
 
 For wheels under about 500 H.P. 
 
 600 to 3000 ft. 
 
 Impulse wheels. 
 
 Reaction wheels for special conditions, where 
 little or no regulation is required. 
 
 Limits to type characteristics K^ may be imposed by runner strength, 
 tendency to erosion or pitting, or limits in the generator construction. 
 
HYDRAULIC TURBINES 
 
 771s 
 
 The approximate relation of the characteristic ,to the head, in general 
 use, is as follows: 
 
 Head in feet 20 50 100 200 300 400 500 600 
 
 Type characteristic 90 70 50 37 31 28 26.5 25 
 
 The relation of type characteristic K^ to other ^variables is about as 
 below : 
 K t 10 20 30 40 50 60 70 80 90 100 
 
 0.64 0.68 0.71 0.74 0.76 0.78 0.80 0.82 0.83 
 
 5.1 5.4 5.7 
 
 11 18 
 
 25 
 
 89 100 
 
 6 
 
 33 
 
 110 
 
 6.2 6.4 6.5 6.6 6.7 
 
 42 
 120 
 
 48 53 57 60 
 130 140 149 157 
 
 Speed coeff.* ____ 4.8 
 Width of runner, 
 
 per cent of I>i.. 7 
 Runner discharge 
 
 diam.%ofZ>i.. 48 72 
 
 *Runner inlet peripheral velocity, ft. per sec., for 1 ft. head. 
 
 Di t inlet diameter. 
 
 Efficiency of Turbine Wheels. Up to about 1910, the opinion was 
 commonly held that high efficiencies were unobtainable with wheels of 
 high type characteristics (K t ). Tests of turbines at the Holyoke 
 flume of wheels designed since that time, show that this opinion is 
 erroneous. S. J. Zowski (Eng. Rec., Nov. 28, 1914, Dec. 26, 1914) 
 presents curves of several tests wherein remarkably high efficiencies 
 have been obtained with high type characteristic wheels. The follow- 
 ing table gives the principal data and best efficiency of the several 
 wheels. 
 
 Efficiency of Turbine Wheels. 
 
 Holyoke 
 Test 
 No. 
 
 Diam., 
 In. 
 
 Best 
 Efficiency, 
 Per Cent. 
 
 Normal 
 Speed, 
 R.P.M.* 
 
 Normal 
 Power, 
 H.P.i* 
 
 Type 
 Charac- 
 teristic, 
 
 *f 
 
 B'lder. 
 See 
 note. 
 
 1900 
 2060 
 2068 
 2121 
 2122 
 2208 
 2359 
 2363 
 
 35 
 30 
 30 
 30 
 30 
 30 
 35 
 30 
 
 90 
 87.2 
 83.2 
 89.2 
 89.3 
 90.1 
 93.07 
 90.7 
 
 45.3 
 49.0 
 51.8 
 48.0 
 49.9 
 47.8 
 47.2 
 50 
 
 2.48 
 3.19 
 3.20 
 2.65 
 3.25 
 3.60 
 2.7 
 4.17 
 
 71.3 
 87.4 
 92.8 
 78.0 
 90.0 
 91.0 
 77.6 
 102 
 
 A 
 B 
 B 
 B 
 B 
 C 
 A 
 A 
 
 *The normal power and normal speed are the speed jmd power of 
 thejurbine reduced to 1 ft. head. H.P.], = H.P. -^ H V-ff. N! = N + 
 V H where H.P. is the actual horsepower developed, N the actual 
 r.p.m. and H the head in feet. 
 
 NOTE. The builders of the above turbines are: A The James Leffel 
 & Co. ; B Allis-Chalmers Co. ; C I. P. Morris Co. 
 
 Further details of the tests of the last two turbines are reported 
 by the maker as follows. 
 
 Holyoke Test No. 3359, Vertical 35, Type F Turbines 
 
 Rev. 
 per 
 
 Min. 
 
 Propor- 
 tional 
 Gateage. 
 
 1 1 Ft. Head. 
 
 14 Ft. Head. 
 
 17 Ft. Head. 
 
 20 Ft. Head. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 175 
 175 
 175 
 175 
 175 
 175 
 
 1.000 
 .889 
 .833 
 ,778 
 .667 
 .556 
 
 88.00 
 89.30 
 86.45 
 84.85 
 81.25 
 76.00 
 
 108.5 
 99.6 
 87.0 
 80.1 
 66.9 
 49.5 
 
 87.47 
 91.08 
 93.00 
 90.80 
 87.45 
 83.45 
 
 154.5 
 147.6 
 141.4 
 127.5 
 103.2 
 80.1 
 
 86.00 
 88.60 
 90.15 
 90.10 
 88.00 
 84.83 
 
 202.4 
 190.6 
 182.2 
 172.4 
 141.6 
 112.2 
 
 84.25 
 86.30 
 86.65 
 86.70 
 86.60 
 84.35 
 
 251.5 
 234.5 
 222.5 
 210.0 
 180.2 
 142.3 
 
772 
 
 WATER-POWER , 
 
 Holyoke Test No. 2362, Vertical 30, Type Z Turbines 
 
 Rev. 
 per 
 Min. 
 
 Propor- 
 tional 
 Gateage . 
 
 1 1 Ft. Head. 
 
 14 Ft. Head. 
 
 17 Ft. Head. 
 
 20 Ft. Head. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 Effi- 
 ciency. 
 
 Horse- 
 Power. 
 
 175 
 175 
 175 
 175 
 175 
 175 
 175 
 
 1.000 
 .891 
 .796 
 .749 
 .700 
 .600 
 .500 
 
 83.50 
 87.30 
 88.35 
 86.65 
 84.20 
 77.20 
 70.90 
 
 162.3 
 160.0 
 148.7 
 137.8 
 127.0 
 100.4 
 77.8 
 
 83.35 
 87.30 
 90.00 
 90.50 
 89.55 
 83.90 
 77.20 
 
 227.5 
 223.5 
 215.5 
 206.5 
 192.5 
 155.2 
 121.0 
 
 81.40 
 85.35 
 87.90 
 89.07 
 89.28 
 87.23 
 80.65 
 
 288.0 
 285.0 
 
 273 ;o 
 
 265.0 
 252.0 
 215.5 
 168.0 
 
 79.30 
 83.30 
 85.85 
 86.75 
 87.00 
 85.90 
 81.60 
 
 348.0 
 344.0 
 330.5 
 320.8 
 305.0 
 269.5 
 217.5 
 
 Relation of Gate Opening to Efficiency. The per cent of gate opening 
 corresponding to different efficiencies and different type characteristics 
 are approximately as follows in modern types of turbines: 
 
 Effi- 
 ciency. 
 85 
 90 
 85 
 80 
 75 
 70 
 
 20 30 
 
 40 
 
 -Type Characteristics. 
 50 60 70 
 
 80 90 100 
 
 Gate Openings Corresponding to the Stated Efficiencies. 
 
 95 
 
 57 
 45' 
 36 
 27 
 
 96 
 75 
 56 
 44 
 35 
 26 
 
 97 
 
 65-82 
 55 
 44 
 35 
 25 
 
 98 
 
 65-82 
 55 
 45 
 36 
 26 
 
 68-80 
 57 
 47 
 37 
 
 28 
 
 98 
 
 72-78 
 60 
 50 
 39 
 32 
 
 97 
 77 
 64 
 55 
 46 
 38 
 
 96 94 
 
 70 
 60 
 55 
 
 48 
 
 82 
 70 
 64 
 60 
 
 Relation of Efficiency and of Water Consumption to Speed. Fig. 155 
 
 (from Church) shows graphically the results of tests of a 160-H.P. 
 
 0.2, 
 
 0.4, 
 
 0.6 0.8 1.0 1.2 
 . Keys, per Second 
 
 1.6 
 
 FIG. 155. Test Results of a 160-H.P. Fourneyron Turbine. 
 
 Fourneyron turbine. It will be seen that there is a certain speed at 
 which the turbine gives its maximum efficiency, and that the efficiency 
 decreases rapidly as the speed is either decreased or increased. 
 
 Tests at the Philadelphia Exhibition, 1876 (R. H. Thurston, Trans. 
 A. S. M. E., viii, 359). Twenty wheels were tested, of which thirteen 
 
 fave efficiencies ranging from 75.15 to 87.68 at full gate, averaging 
 8.66 per cent. The other seven gave results between 65 and 75 per 
 
_ . HYDRAULIC TURBINES. 773 
 
 cent. At less than full gate the following average results were ob- 
 tained from the thirteen wheels : 
 
 Per cent of full discharge, 
 
 about 9/10 7/8 3/4 5/8 l/ 2 1 
 
 Number of wheels tested 4 6 8 6 4 1 
 
 Efficiencies, average 73.5 74.6 70.8 65.1 70.7 55.0 
 
 Rating and Efficiency of Turbines. The following notes and tables 
 are condensed from a pamphlet entitled "Turbine Water-wheel Tests 
 and Power Tables," by it. E. Horton. Water-supply and Irrigation 
 Paper No. ISO, U. S. Geol. Survey, 1906. 
 
 Theory does not indicate the numbers of guides of buckets most de- 
 sirable. If, however, they are too few, the stream will not properly 
 follow the flow lines indicated by theory. If the buckets are too small 
 and too numerous, the surface-friction factor will be large. 
 
 It is customary to make the number of guide chutes greater than the 
 number of buckets, so that any object passing through the chutes will 
 be likely to pass through the buckets also. 
 
 With most forms of gates the size of the jet is decreased as the gate is 
 closed, the bucket area remaining unchanged, so that the wheel operates 
 mostly by reaction at full gate and by impulse to an increasing extent as 
 the gate is closed. Hence, the speed of maximum efficiency varies as 
 the gate is closed. The ratio peripheral velocity -5- velocity due head 
 for maximum efficiency for a 36-inch Hercules turbine is given below: 
 
 Proportional gate opening. Full 0.806 0.647 0.489 0.379 
 
 Maximum efficiency 85 . 6 87 . 1 86 . 3 80 73 . 1 
 
 Periph. vel. + vel.due head 0.677 0.648 0.641 0.603 0.585 
 
 The double Fourneyron turbine used in the first installation of the 
 Niagara Falls Power Co. is operated under a head of about 135 ft. Two 
 wheels are used, one being placed at the top and the other at the bottom 
 of the globe penstock. The runner and buckets are attached to the ver- 
 tical shaft. Holes are provided in the upper penstock drum to allow 
 water under full pressure of the head to pass through and act vertically 
 against the upper runner. In this way the vertical pressure of the great 
 column of water is neutralized and a means is provided to counter- 
 balance the weight of the long vertical shaft and the armature of the 
 dynamo at its upper end. These turbines discharge 430 cu. ft. per 
 second, make 250 rev. per min., and are rated at 5000 H.P. 
 
 A Fourneyron turbine at Trenton Falls, N. Y., operates under 265 ft. 
 gross head and has 37 buckets, each 5y 2 in. deep and is/ieinch wide at the 
 least section. The total area of outflow at the minimum section is 165 
 sq. in. The wheel develops 950 H.P. 
 
 The theoretical horse-power of a given quantity of water Q, in cu. ft. 
 per min., falling through a height H, in ft., is H.P. = 0.00189 QH. 
 
 In practice the theoretical power is multiplied by an efficiency factor 
 E to obtain the net power available on the turbine shaft as determin- 
 able by dynamometer test. 
 
 Manufacturers' rating tables are usually based on.efficiencies of about 
 80%. In selecting turbines from a maker's list the rated efficiency 
 may be obtained by the following formula: 
 
 E = tabled efficiency. H.P. = tabled horse-power. Q = tabled dis- 
 charge (cu.ft.per min.) for any head H. E = - 3 f; *!* J*- = 528.8 5i 
 
 b^ . 4 X Q fi Q a. 
 
 Relations of Power, Speed and Discharge. Nearly all American tur- 
 bine builders publish rating tables showing the discharge in cu. ft. per 
 min., rev. per min., and H.P. for each size pattern under heads varying 
 from 3 or 4 ft. to 40 ft. or more. 
 
 Examples of each size of a number of the leading types of turbines 
 have been tested in the Holyoke flume. For such turbines the rating 
 tables have usually been prepared directly from the tests. 
 
 Let M, R, and Q denote, respectively, the H.P., r.p.m., and discharge 
 in cu. ft. per min. of a turbine, as expressed in the tables, for any head 
 H in feet. The subscripts 1 and 16 added signify the power, speed, and 
 discharge for the particular heads 1 and 16 ft., respectively. 
 
 Let P, N, and F denote coefficients of power, speed, and discharge^ 
 
774 WATER-POWER. 
 
 which represent, respectively, the H.P., r.p.m., and discharge in cu. ft. 
 per sec. under a head of 1 ft. 
 
 The speed of a turbine or the number of rev. per min. and the dis- 
 charge are proportional to the square root of the head. The H.P. 
 varies with the product of the head and discharge, and is consequently 
 proportional to the three-halves power of the head. 
 
 Given the values of M, R, and Q from the tables for any head H, these 
 quantities for any other head h are: 
 
 M H :M h :: H 3 /2 : 7i 3 /2; R H : E h : : H^ : fti/2; Q H : Q h : : H 1 '*' : tf/2. 
 
 If H and h are taken at 16 ft. and 1 ft., respectively, the values of 
 the coefficients P, N, and F are: 
 
 P = Mi6/H 3/2 = Mi6/64 = 0.01562 M w 
 N = #i 6 /H 1/2 = #16/4 = 0.25 #16 
 F = #16/60 H J/ 2 = Che/240 = 0.00417 Qie. 
 
 P, N, and F, when derived for a given wheel, enable the power, speed, 
 and discharge to be calculated without the aid of the tables, and for 
 any head H, by means of the following formula : 
 M 
 
 R = 
 Q = 
 
 Since at a head of 1 ft^andMi, Ri, and Q\ equal P, N, and 60 F, re- 
 spectively, JJi 3 /2 and \/H\ each equals 1. Calculations involving .72^2 
 may be facilitated by the use of the appended table of three-halves 
 powers. Rating tables for sizes other than those tested are computed 
 usually on the following basis: 
 
 1. The efficiency and coefficients of gate and bucket discharge for the 
 sizes tested are assumed to apply to the other sizes also. 
 
 2. The discharge for additional sizes is computed in proportion to 
 the measured area of the vent or discharge orifices. 
 
 Having these data, together with the efficiency, the tables of dis- 
 charge and horse-power can be prepared. The peripheral speed cor- 
 responding to maximum efficiency determined from tests of one size 
 of turbine may be assumed to apply to the other sizes also. From this 
 datum the revolutions per minute can be computed, the number of 
 revolutions required to give a constant peripheral speed being inversely 
 proportional to the diameter of the turbine. 
 
 In point of discharge, the writer's observation has been that the rat- 
 ing tables are usually fairly accurate. In the matter of efficiency there 
 are undoubtedly much larger discrepancies. 
 
 The discharge of turbines is nearly always expressed in cubic feet per 
 minute. The "vent" in square inches is also used by millwrights and 
 manufacturers, although to a decreasing extent. The vent of a turbine 
 is^the area of van orifice which would, under any given head, theoretically 
 discharge the same quantity of water that is vented or passed through a 
 turbine under that same head when the wheel is so loaded as to be 
 
 running at maximum efficiency. 
 
 If V = vent in sq. in., Q = disc 
 H , F = discharge in cu. ft. per sec. under a head of 1 foot, then Q = 
 
 If y = vent in sq. in., Q = discharge in cu. ft. per min. under a head 
 
 60 V/144\/2 gH = 3.344 V\/H, and V= 0.3 Q/VH; also V= 17.94 F 
 and F = 0.0557 V. 
 
 The vent of a turbine should not be confused with the area of the 
 outlet orifice of the buckets. The actual discharge through a turbine 
 is commonly from 40 to 60% of the theoretical discharge of an orifice 
 whose area equals the combined cross-sectional areas of the outlet 
 ports measured in the narrowest section. 
 
 Tests of Turbine Discharge by Salt Solution. Abraham Streiflf 
 (Eng. Rec., Jan. 31, 1914) describes a method of determining the dis- 
 charge of a turbine by means of a concentrated salt solution injected 
 in the head or tail race. The degree of dilution of the salt in the 
 tail race after a certain period of time is an index of the discharge of 
 the turbine. The ratio of the discharge of the initial solution to the 
 discharge of tiie turbine varies inversely as their concentrations. 
 
 (Continued on page 778) 
 
HYDBAULIC TURBINES.' 775' 
 
 TABLE OP H 3/2 FOB CALCULATING HORSE-POWER OF TURBINES. 
 
 o 
 
 * 
 w fe 
 
 0.0 
 
 0.2 
 
 0.4 
 
 0.6 
 
 0.8 
 
 T3 
 
 |e 
 
 0.0 
 
 0.2 
 
 0.4 
 
 0.6 
 
 0.8 
 
 
 
 0.00 
 
 0.09 
 
 0.25 
 
 0.46 
 
 0.72 
 
 
 
 
 
 
 
 1 
 
 1.00 
 
 1.32 
 
 1.66 
 
 2.02 
 
 2.42 
 
 51 
 
 364.21 
 
 366.36 
 
 368.50 
 
 370.66 
 
 372.82 
 
 2 
 
 2.83 
 
 3.26 
 
 3.72 
 
 4.19 
 
 4.69 
 
 52 
 
 374.98 
 
 377.14 
 
 379.31 
 
 381.48 
 
 383.66 
 
 3 
 
 5.20 
 
 5.72 
 
 6.27 
 
 6.83 
 
 7.41 
 
 53 
 
 385.85 
 
 388.03 
 
 390.22 
 
 392.42 
 
 394.61 
 
 4 
 
 8.00 
 
 8.61 
 
 9.23 
 
 9.87 
 
 10.52 
 
 54 
 
 396.81 
 
 399.02 
 
 401.23 
 
 403.45 
 
 405.67 
 
 
 11.18 
 
 11.86 
 
 12.55 
 
 13.25 
 
 13.97 
 
 55 
 
 407.89 
 
 410.11 
 
 412.35 
 
 414.58 
 
 416.82 
 
 6 
 
 14.70 
 
 15.44 
 
 16.19 
 
 16.96 
 
 17.73 
 
 56 
 
 419.07 
 
 421.31 
 
 423.56 
 
 425.81 
 
 428.07 
 
 
 18.52 
 
 19.32 
 
 20.13 
 
 20.95 
 
 21.78 
 
 57 
 
 430.34 
 
 432.60 
 
 434.87 
 
 437.15 
 
 439.43 
 
 8 
 
 22.63 
 
 23.48 
 
 24.35 
 
 25.22 
 
 26.11 
 
 58 
 
 441.71 
 
 444.00 
 
 446.29 
 
 448.58 
 
 450.88 
 
 9 
 
 27.00 
 
 27.91 
 
 28.82 
 
 29.75 
 
 30.68 
 
 59 
 
 453.09 
 
 455.49 
 
 457.80 
 
 460.12 
 
 462.43 
 
 10 
 
 31.62 
 
 32.58 
 
 33.54 
 
 34.51 
 
 35.49 
 
 60 
 
 464.75 
 
 467.08 
 
 469.41 
 
 471.75 
 
 474.08 
 
 11 
 
 36.48 
 
 37.48 
 
 38.49 
 
 39.51 
 
 40.53 
 
 61 
 
 476.42 
 
 478.77 
 
 481.12 
 
 483.47 
 
 485.82 
 
 12 
 
 41.57 
 
 42.61 
 
 43.66 
 
 44.73 
 
 45.79 
 
 62 
 
 488.19 
 
 490.55 
 
 492.92 
 
 495.29 
 
 497.67 
 
 13 
 
 46.87 
 
 47.96 
 
 49.05 
 
 50.15 
 
 51.26 
 
 63 
 
 500.04 
 
 502.43 
 
 504.82 
 
 507.20 
 
 509.60 
 
 14 
 
 52.38 
 
 53.51 
 
 54.64 
 
 55.79 
 
 56.94 
 
 64 
 
 512.00 
 
 514.40 
 
 516.80 
 
 519.22 
 
 521.63 
 
 15 
 
 58.09 
 
 59.26 
 
 60.43 
 
 61.61 
 
 62.80 
 
 65 
 
 524.04 
 
 526.46 
 
 528.89 
 
 531.31 
 
 533.75 
 
 16 
 
 64.00 
 
 65.20 
 
 66.41 
 
 67.63 
 
 68.85 
 
 66 
 
 536.18 
 
 538.62 
 
 541.07 
 
 543.51 
 
 545.96 
 
 17 
 
 70.09 
 
 71.33 
 
 75.58 
 
 73.84 
 
 75.10 
 
 67 
 
 548.42 
 
 550.87 
 
 553.33 
 
 555.80 
 
 558.27 
 
 18 
 
 76.37 
 
 77.64 
 
 78.93 
 
 80.22 
 
 81.52 
 
 68 
 
 560.74 
 
 563.22 
 
 565.70 
 
 568.18 
 
 570.66 
 
 19 
 
 82.82 
 
 84.13 
 
 85.45 
 
 86.77 
 
 88.10 
 
 69 
 
 573.16 
 
 575.65 
 
 578.14 
 
 580.65 
 
 583.15 
 
 20 
 
 89.44 
 
 90.79 
 
 92.14 
 
 93.50 
 
 94.86 
 
 70 
 
 585.66 
 
 588.17 
 
 590.68 
 
 593.20 
 
 595.73 
 
 21 
 
 96.23 
 
 97.61 
 
 99.00 
 
 100.39 
 
 101.79 
 
 71 
 
 598.25 
 
 600.79 
 
 603.32 
 
 605.85 
 
 608.39 
 
 22 
 
 103.19 
 
 104.60 
 
 106.02 
 
 107.44 
 
 108.87 
 
 72 
 
 610.93 
 
 613.48 
 
 616.04 
 
 618.59 
 
 621.15 
 
 23 
 
 110.30 
 
 111.74 
 
 113.19 
 
 114.65 
 
 116.11 
 
 73 
 
 623.71 
 
 626.27 
 
 628.84 
 
 631.41 
 
 633.99 
 
 24 
 
 117.58 
 
 119.05 
 
 120.53 
 
 122.01 
 
 123.50 
 
 74 
 
 636.57 
 
 639.15 
 
 641.74 
 
 644.33 
 
 646.92 
 
 25 
 
 125.00 
 
 126.50 
 
 128.01 
 
 129.53 
 
 131.05 
 
 75 
 
 649.52 
 
 652.11 
 
 654.72 
 
 657.33 
 
 659.94 
 
 26 
 
 132.57 
 
 134.11 
 
 135.65 
 
 137.19 
 
 138.74 
 
 76 
 
 662.55 
 
 665,17 
 
 667.79 
 
 670.41 
 
 673.04 
 
 27 
 
 140.30 
 
 141.86 
 
 143.43 
 
 145.00 
 
 146.58 
 
 77 
 
 675.67 
 
 678.20 
 
 680.94 
 
 683.58 
 
 686.23 
 
 28 
 
 148.16 
 
 149.75 
 
 151.35 
 
 152.95 
 
 154.56 
 
 78 
 
 688.87 
 
 691.52 
 
 694.18 
 
 696.84 
 
 699.50 
 
 29 
 
 156.17 
 
 157.79 
 
 159.41 
 
 161.04 
 
 162.68 
 
 79 
 
 702.16 
 
 704.83 
 
 707.50 
 
 710.18 
 
 712.85 
 
 30 
 
 164.32 
 
 165.96 
 
 167.61 
 
 169.27 
 
 170.93 
 
 80 
 
 715.54 
 
 718.22 
 
 720.92 
 
 723.60 
 
 726.30 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 31 
 
 172.60 
 
 174.27 
 
 175.95 
 
 177.64 
 
 179.33 
 
 81 
 
 729.00 
 
 731.70 
 
 734.40 
 
 737.11 
 
 739.82 
 
 32 
 
 181.02 
 
 182.72 
 
 184.42 
 
 186.13 
 
 187.85 
 
 82 
 
 742.54 
 
 745.26 
 
 747.98 
 
 750.70 
 
 753.43 
 
 33 
 
 189.57 
 
 191.30 
 
 193.03 
 
 194.76 
 
 196.51 
 
 83 
 
 756.16 
 
 758.90 
 
 761.63 
 
 764.38 
 
 767.12 
 
 34 
 
 198.25 
 
 200.00 
 
 201.76 
 
 203.52 
 
 205.29 
 
 84 
 
 769.87 
 
 772.62 
 
 775.37 
 
 778.13 
 
 780.89 
 
 35 
 
 207.06 
 
 208.84 
 
 210.62 
 
 212.41 
 
 214.20 
 
 85 
 
 783.66 
 
 786.42 
 
 789.20 
 
 791.97 
 
 794.75 
 
 36 
 
 216.00 
 
 217.80 
 
 219.61 
 
 221.42 
 
 223.24 
 
 86 
 
 797.53 
 
 800.31 
 
 803.10 
 
 805.89 
 
 808.68 
 
 37 
 
 225.06 
 
 226.89228.72 
 
 230.56 
 
 232.40 
 
 87 
 
 811.48 
 
 814.27 
 
 817.08 
 
 819.88 
 
 822.70 
 
 38 
 
 234.25 
 
 236.10237.96 
 
 239.82 
 
 241.68 
 
 88 
 
 825.51 
 
 828.32 
 
 831.15 
 
 833.97 
 
 836.79 
 
 39 
 
 243.56 
 
 245.43247.31 
 
 249.20 
 
 251.09 
 
 89 
 
 839.62 
 
 842.45 
 
 845.29 
 
 848.13 
 
 850.96 
 
 40 
 
 252.98 
 
 254.88'256.79 
 
 258.70 
 
 260.61 
 
 90 
 
 853.81 
 
 856.66 
 
 859.51 
 
 848.37 
 
 865.22 
 
 41 
 
 262.53 
 
 264.45266.38 
 
 268.31 
 
 270.25 
 
 91 
 
 868.08 
 
 870.94 
 
 873.81 
 
 876.68 
 
 879.55 
 
 42 
 
 272.19 
 
 274.14 
 
 276.09 
 
 278.05 
 
 280.01 
 
 92 
 
 882.43 
 
 885.30 
 
 888.19 
 
 891.07 
 
 893.96 
 
 43 
 
 281.97 
 
 283.94 
 
 285.91 
 
 287.89 
 
 289.88 
 
 93 
 
 896.86 
 
 899. 75 1902.65 
 
 905.55 
 
 908.45 
 
 44 
 
 291.86 
 
 293.86 
 
 295.85 
 
 297.85 
 
 299.86 
 
 94 
 
 911.36 
 
 914.27 
 
 917.18 
 
 920.10 
 
 923.02 
 
 45 
 
 301.87 
 
 303.88 
 
 305.90 
 
 307.93 
 
 309.95 
 
 95 
 
 925.94 
 
 928.87 
 
 931.79 
 
 934.73 
 
 937.66 
 
 46 
 
 311.99 
 
 314.02 
 
 316.07 
 
 318.11 
 
 330.16 
 
 96 
 
 940.60 
 
 943.54 
 
 946.48 
 
 949.43 
 
 952 38 
 
 47 
 
 322.22 
 
 324.27 
 
 326.34 
 
 328.41 
 
 330.48 
 
 97 
 
 955.33 
 
 958.29 
 
 961.25 
 
 964.21 
 
 967.17 
 
 48 
 
 332.55 
 
 334.63 
 
 336.72 
 
 338.81 
 
 340.90 
 
 98 
 
 970.14 
 
 973.11 
 
 976.09 
 
 979.07 
 
 982.05 
 
 49 
 
 343.00 
 
 345.10 
 
 347.21 
 
 349.32 
 
 351.43 
 
 99 
 
 985.03 
 
 988.02 
 
 991.01 
 
 994.00 
 
 996.99 
 
 50 
 
 353.55 
 
 355.67 
 
 357.80359.93 
 
 362.07 
 
 100 
 
 1000.00 
 
 
 
 
 
 
 
 
 
776 
 
 WATER-POWER. 
 
 Power Table for Turbines LEFPEL VERTICAL STANDARD SAMSON TYPE (1916) 
 P = horsepower; W = quantity of water, cu. ft. per sec.; S = speed, r.p.m. 
 
 Size. 
 
 
 Head, Feet. 
 
 3 
 
 5 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 50 
 
 
 p 
 
 1.1 
 
 2.5 
 
 7.0 
 
 12.9 
 
 19.9 
 
 27.8 
 
 36.5 
 
 46.2 
 
 56. 3- 
 
 78.0 
 
 
 W 
 
 252 
 
 325 
 
 460 
 
 553 
 
 650 
 
 727 
 
 796 
 
 860 
 
 919 
 
 1026 
 
 
 S 
 
 161 
 
 208 
 
 294 
 
 360 
 
 416 
 
 464 
 
 510 
 
 550 
 
 588 
 
 657 
 
 
 p 
 
 1.5 
 
 3.2 
 
 9.2 
 
 16.9 
 
 25.9 
 
 36.2 
 
 47.6 
 
 60.3 
 
 73.5 
 
 102.0 
 
 
 W 
 
 328 
 
 423 
 
 601 
 
 734 
 
 848 
 
 948 
 
 1039 
 
 1121 
 
 1199 
 
 1338 
 
 
 S 
 
 161 
 
 208 
 
 294 
 
 360 
 
 416 
 
 464 
 
 510 
 
 550 
 
 588 
 
 657 
 
 ( 
 
 p 
 
 2.0 
 
 4.3 
 
 12.1 
 
 22.2 
 
 34.1 
 
 47.7 
 
 62.6 
 
 79.4 
 
 96.7 
 
 135.0 
 
 17C-< 
 
 W 
 
 433 
 
 558 
 
 791 
 
 967 
 
 1116 
 
 1248 
 
 1367 
 
 1476 
 
 1579 
 
 1763 
 
 1 
 
 S 
 
 161 
 
 208 
 
 294 
 
 360 
 
 416 
 
 464 
 
 510 
 
 550 
 
 588 
 
 657 
 
 I 
 
 p 
 
 2.4 
 
 5.3 
 
 14.9 
 
 27.4 
 
 42.1 
 
 58.9 
 
 77.3 
 
 97.9 
 
 119.0 
 
 167.0 
 
 17B^ 
 
 W 
 
 533 
 
 689 
 
 975 
 
 1193 
 
 1377 
 
 1540 
 
 1687 
 
 1821 
 
 1948 
 
 2179 
 
 1 
 
 S 
 
 161 
 
 208 
 
 294 
 
 360 
 
 416 
 
 464 
 
 510 
 
 550 
 
 588 
 
 657 
 
 ( 
 
 p 
 
 3.2 
 
 6.9 
 
 19.5 
 
 35.6 
 
 55.0 
 
 77.0 
 
 101.0 
 
 128.0 
 
 156.0 
 
 218.0 
 
 17A-J 
 
 W 
 
 697 
 
 900 
 
 1275 
 
 1559 
 
 1800 
 
 2013 
 
 2205 
 
 2381 
 
 2546 
 
 2846 
 
 
 S 
 
 161 
 
 208 
 
 294 
 
 360 
 
 416 
 
 464 
 
 510 
 
 550 
 
 588 
 
 657 
 
 ( 
 
 p 
 
 4.2 
 
 9.0 
 
 25.5 
 
 46.9 
 
 72.2 
 
 101. 
 
 133.0 
 
 167.0 
 
 204.0 
 
 285.0 
 
 20 4 
 
 W 
 
 914 
 
 1180 
 
 1669 
 
 2044 
 
 2360 
 
 2639 
 
 2891 
 
 3127 
 
 3338 
 
 3731 
 
 ( 
 
 S 
 
 140 
 
 182 
 
 257 
 
 315 
 
 364 
 
 407 
 
 445 
 
 481 
 
 514 
 
 575 
 
 ( 
 
 p 
 
 5.5 
 
 11.9 
 
 33.8 
 
 62.0 
 
 95.5 
 
 133.0 
 
 175.0 
 
 221.0 
 
 270.0 
 
 377.0 
 
 23 \ 
 
 W 
 
 1209 
 
 1561 
 
 2207 
 
 2703 
 
 3122 
 
 3489 
 
 3823 
 
 4130 
 
 4415 
 
 4935 
 
 1 
 
 S 
 
 127 
 
 158 
 
 224 
 
 274 
 
 316 
 
 354 
 
 387 
 
 418 
 
 447 
 
 500 
 
 
 p 
 
 7.10 
 
 15.2 
 
 43.2 
 
 79.3 
 
 121.0 
 
 171.0 
 
 224.0 
 
 283.0 
 
 345.0 
 
 482.0 
 
 
 W 
 
 1545 
 
 1995 
 
 2821 
 
 3455 
 
 3919 
 
 4460 
 
 4886 
 
 5278 
 
 5642 
 
 6306 
 
 
 S 
 
 108 
 
 140 
 
 198 
 
 242 
 
 280 
 
 313 
 
 343 
 
 370 
 
 396 
 
 442 
 
 
 p 
 
 9.44 
 
 20.3 
 
 57.5 
 
 106.0 
 
 162.0 
 
 227.0 
 
 299.0 
 
 376.0 
 
 460.0 
 
 642.0 
 
 
 W 
 
 2057 
 
 2656 
 
 3756 
 
 4600 
 
 5312 
 
 5938 
 
 6505 
 
 7026 
 
 7512 
 
 8400 
 
 
 S 
 
 94 
 
 121 
 
 171 
 
 210 
 
 242 
 
 271 
 
 297 
 
 321 
 
 343 
 
 381 
 
 I 
 
 p 
 
 12.8 
 
 27.5 
 
 77.9 
 
 143.0 
 
 220.0 
 
 308.0 
 
 405.0 
 
 510.0 
 
 623.0 
 
 871.0 
 
 35 \ 
 
 W 
 
 2789 
 
 3600 
 
 5091 
 
 6236 
 
 7200 
 
 8050 
 
 8818 
 
 9525 
 
 10183 
 
 11385 
 
 I 
 
 S 
 
 81 
 
 104 
 
 147 
 
 180 
 
 208 
 
 232 
 
 255 
 
 275 
 
 294 
 
 329 
 
 ( 
 
 p 
 
 16.8 
 
 36.1 
 
 102.0 
 
 188.0 
 
 289.0 
 
 404.0 
 
 531.0 
 
 668.0 
 
 817.0 
 
 1143.0 
 
 40 
 
 W 
 
 3657 
 
 4722 
 
 6677 
 
 8178 
 
 9443 
 
 10558 11565 
 
 12472 
 
 13354 
 
 14930 
 
 1 
 
 S 
 
 70 
 
 91 
 
 129 
 
 157 
 
 182 
 
 203 
 
 223 
 
 240 
 
 257 
 
 288 
 
 ( 
 
 p 
 
 21.2 
 
 45.7 
 
 129.0 
 
 238.0 
 
 366.0 
 
 511.0 
 
 672.0 
 
 847.0 
 
 1034.0 
 
 1448.0 
 
 45 
 
 W 
 
 4629 
 
 5975 
 
 8450 
 
 10350 
 
 11951 
 
 13361 
 
 14636 
 
 15809 
 
 16901 
 
 18900 
 
 / 
 
 S 
 
 63 
 
 81 
 
 114 
 
 140 
 
 162 
 
 181 
 
 198 
 
 214 
 
 229 
 
 256 
 
 ( 
 
 p 
 
 26.2 
 
 56.4 
 
 160.0 
 
 293.0 
 
 451.0 
 
 631.0 
 
 829.0 
 
 1045.0 
 
 1280.0 
 
 1789.0 
 
 50 - 
 
 W 
 
 5714 
 
 7377 
 
 10433 
 
 12777 
 
 14754 
 
 16496 
 
 18070 
 
 19518 
 
 20870 
 
 23330 
 
 1 
 
 S 
 
 56 
 
 73 
 
 103 
 
 126 
 
 145 
 
 162 
 
 178 
 
 192 
 
 205 
 
 230 
 
 \ 
 
 p 
 
 32.9 
 
 70.8 
 
 200.0 
 
 368.0 
 
 566.0 
 
 791.0 
 
 1040.0 
 
 1314.0 
 
 1602.0 
 
 2239.0 
 
 56 
 
 W 
 
 7168 
 
 9254 
 
 13087 
 
 16028 
 
 18508 
 
 20692 
 
 22667 
 
 24506 
 
 26200 
 
 29260 
 
 ) 
 
 S 
 
 50 
 
 65 
 
 92 
 
 112 
 
 130 
 
 145 
 
 159 
 
 172 
 
 183 
 
 205 
 
 I 
 
 p 
 
 40.3 
 
 86.8 
 
 245.0 
 
 451.0 
 
 694.0 
 
 970.0 
 
 1275.0 
 
 1608.0 
 
 1963.0 
 
 2743.0 
 
 63 \ 
 
 W 
 
 8787 
 
 11344 
 
 16042 
 
 19648 
 
 22688 
 
 25365 
 
 27786 
 
 30092 
 
 32100 
 
 35900 
 
 I 
 
 S 
 
 ' 45 
 
 59 
 
 83 
 
 102 
 
 117 
 
 131 
 
 144 
 
 155 
 
 166 
 
 186 
 
 ( 
 
 p 
 
 48.5 
 
 104.0 
 
 295.0 
 
 542.0 
 
 835.0 
 
 1167.0 
 
 1534.0 
 
 1932.0 
 
 2361.0 
 
 3300.0 
 
 68 \ 
 
 W 
 
 10570 
 
 13645 
 
 19297 
 
 23634 
 
 27290 
 
 30511 
 
 33450 
 
 36120 
 
 38620 
 
 43200 
 
 i 
 
 S 
 
 41 
 
 53 
 
 76 
 
 93 
 
 107 
 
 120 
 
 131 
 
 142 
 
 152 
 
 170 
 
 ( 
 
 p 
 
 57.5 
 
 124.0 
 
 350.0 
 
 642.0 
 
 992.0 
 
 1382.0 
 
 1818.0 
 
 2292.0 
 
 2800.0 
 
 3912.0 
 
 74 1 
 
 W 
 
 12517 
 
 16159 
 
 22852 
 
 27988 
 
 32318 
 
 36132 
 
 39560 
 
 42750 
 
 45700 
 
 51100 
 
 1 
 
 S 
 
 38 
 
 49 
 
 70 
 
 85 
 
 99 
 
 110 
 
 120 
 
 130 
 
 139 
 
 156 
 
HYDRAULIC TURBINES. 
 
 777 
 
 Power Table for Turbines. LEFPEL VERTICAL Z-TYPE (1916). 
 = horsepower; W = quantity of water, cu. ft. per sec.; S = speed, r.p.m. 
 
 Size. 
 
 
 Head, Feet 
 
 6 
 
 7 
 
 8 
 
 10 
 
 15 
 
 W 
 
 25 
 
 30 
 
 35 
 
 40 
 
 I 
 
 p 
 
 9.05 
 
 11.53 
 
 14.30 
 
 20.40 
 
 38.15 
 
 58.90 
 
 82.30 
 
 108.2 
 
 136.2 
 
 166.5 
 
 13 J 
 
 W 
 
 1035 
 
 1120 
 
 1202 
 
 1352 
 
 1670 
 
 1933 
 
 2160 
 
 2368 
 
 2557 
 
 2730 
 
 1 
 
 s 
 
 306.0 
 
 331.0 
 
 354.0 
 
 395.0 
 
 484.0 
 
 559.0 
 
 625.0 
 
 685.0 
 
 740.0 
 
 790.0 
 
 ( 
 
 p 
 
 14.47 
 
 18.24 
 
 22.50 
 
 31.85 
 
 60.20 
 
 93.00 
 
 130.0 
 
 171.0 
 
 215.5 
 
 263.0 
 
 15 J 
 
 W 
 
 1625 
 
 1755 
 
 1885 
 
 2115 
 
 2620 
 
 3030 
 
 3390 
 
 3710 
 
 4015 
 
 4280 
 
 1 
 
 s 
 
 245.0 
 
 265.0 
 
 283.0 
 
 316.0 
 
 387.0 
 
 447.0 
 
 500.0 
 
 548.0 
 
 592.0 
 
 632.0 
 
 
 p 
 
 21.08 
 
 26.70 
 
 32.80 
 
 46.40 
 
 87.50 
 
 135.0 
 
 189.5 
 
 249.0 
 
 314.0 
 
 383.0 
 
 
 W 
 
 2350 
 
 2550 
 
 2725 
 
 3060 
 
 3785 
 
 4385 
 
 4910 
 
 5375 
 
 5805 
 
 6200 
 
 
 s 
 
 204.0 
 
 221.0 
 
 236.0 
 
 263.0 
 
 323.0 
 
 372.0 
 
 417.0 
 
 456.0 
 
 493.0 
 
 526.0 
 
 ( 
 
 p 
 
 29.05 
 
 36.72 
 
 45.30 
 
 63.90 
 
 121.0 
 
 187.0 
 
 261.5 
 
 343.0 
 
 433.0 
 
 528.0 
 
 31 J 
 
 W 
 
 3225 
 
 3485 
 
 3740 
 
 4190 
 
 5200 
 
 6015 
 
 6730 
 
 7370 
 
 7965 
 
 8505 
 
 1 
 
 s 
 
 175.0 
 
 189.1 
 
 202.0 
 
 225.5 
 
 277.0 
 
 319.0 
 
 357.0 
 
 391.0 
 
 423.0 
 
 452.0 
 
 
 p 
 
 38.35 
 
 48.50 
 
 60.00 
 
 84.50 
 
 160.0 
 
 247.0 
 
 345.0 
 
 454.0 
 
 571.5 
 
 698.0 
 
 
 W 
 
 4230 
 
 4580 
 
 4920 
 
 5510 
 
 6835 
 
 7900 
 
 8840 
 
 9680 
 
 10460 
 
 11170 
 
 
 s 
 
 153.0 
 
 165.5 
 
 177.0 
 
 197.5 
 
 242.0 
 
 279.0 
 
 312.5 
 
 342.0 
 
 370.0 
 
 395.0 
 
 
 p 
 
 49.25 
 
 62.00 
 
 76.60 
 
 108.1 
 
 204.5 
 
 316.0 
 
 442.2 
 
 580.0 
 
 732.0 
 
 893.0 
 
 
 W 
 
 5375 
 
 5825 
 
 6250 
 
 7000 
 
 8700 
 
 10040 
 
 11225 
 
 12300 
 
 13300 
 
 14200 
 
 
 s 
 
 136.0 
 
 147.0 
 
 157.0 
 
 175.6 
 
 215.0 
 
 248.5 
 
 278.0 
 
 304.5 
 
 329.0 
 
 351.0 
 
 ( 
 
 p 
 
 61.40 
 
 77.50 
 
 95.70 
 
 135.0 
 
 255.5 
 
 395.4 
 
 551.5 
 
 725.0 
 
 912.5 
 
 1116.0 
 
 30 -1 
 
 W 
 
 6680 
 
 7230 
 
 7760 
 
 8700 
 
 10790 
 
 12500 
 
 13960 
 
 15295 
 
 16500 
 
 17640 
 
 1 
 
 s 
 
 122.5 
 
 132.2 
 
 141.4 
 
 158.1 
 
 193.6 
 
 223.5 
 
 250.0 
 
 274.0 
 
 296.0 
 
 316.0 
 
 ( 
 
 p 
 
 74.25 
 
 93.55 
 
 115.2 
 
 163.2 
 
 308.0 
 
 479.0 
 
 670.0 
 
 879.0 
 
 1108.0 
 
 1355.0 
 
 33 - 
 
 W 
 
 8050 
 
 8720 
 
 9350 
 
 10500 
 
 13000 
 
 15110 
 
 16900 
 
 18500 
 
 19950 
 
 21340 
 
 1 
 
 s 
 
 111.3 
 
 120.5 
 
 128.5 
 
 143.5 
 
 176.0 
 
 203.0 
 
 227.0 
 
 249.0 
 
 269.0 
 
 287.0 
 
 ( 
 
 p 
 
 88.15 
 
 111.9 
 
 138.0 
 
 195.0 
 
 367.5 
 
 570.0 
 
 796.0 
 
 1045.0 
 
 1318.0 
 
 1613.0 
 
 36 I 
 
 W 
 
 9610 
 
 10420 
 
 11180 
 
 12560 
 
 15510 
 
 18000 
 
 20100 
 
 22000 
 
 23750 
 
 25400 
 
 1 
 
 s 
 
 102.0 
 
 110.5 
 
 118.0 
 
 131.5 
 
 161.0 
 
 186.0 
 
 208.0 
 
 228.0 
 
 247.0 
 
 263.0 
 
 { 
 
 p 
 
 103.7 
 
 131.0 
 
 162.0 
 
 228.3 
 
 431.5 
 
 669.0 
 
 935.0 
 
 1229.0 
 
 1548.0 
 
 1892.0 
 
 
 W 
 
 11290 
 
 12210 
 
 13110 
 
 14700 
 
 18200 
 
 21110 
 
 23600 
 
 25820 
 
 27900 
 
 29800 
 
 
 s 
 
 94.0 
 
 102.0 
 
 109.0 
 
 121.5 
 
 148.9 
 
 172.0 
 
 192.2 
 
 211.0 
 
 227.5 
 
 243.0 
 
 t 
 
 p 
 
 120.1 
 
 152.0 
 
 187.7 
 
 265.0 
 
 500.0 
 
 776.0 
 
 1085.0 
 
 1423.0 
 
 1703.0 
 
 2188.0 
 
 & \ 
 
 W 
 
 13100 
 
 14170 
 
 15210 
 
 17050 
 
 21130 
 
 24500 
 
 27350 
 
 29990 
 
 32340 
 
 34590 
 
 I 
 
 s 
 
 87.5 
 
 94.5 
 
 101.0 
 
 113.0 
 
 138.5 
 
 159.5 
 
 178.5 
 
 195.5 
 
 211.0 
 
 226.0 
 
 
 p 
 
 138.0 
 
 174.5 
 
 215.3 
 
 304.0 
 
 575.0 
 
 890.0 
 
 1245.0 
 
 1634.0 
 
 2060.0 
 
 2512.0 
 
 
 W 
 
 15030 
 
 16270 
 
 17450 
 
 19570 
 
 24270 
 
 28100 
 
 31400 
 
 34400 
 
 37100 
 
 39700 
 
 
 s 
 
 81.5 
 
 88.3 
 
 94.2 
 
 105.4 
 
 129.0 
 
 149.0 
 
 166.5 
 
 182.5 
 
 197.2 
 
 211.0 
 
 \ 
 
 p 
 
 157.0 
 
 199.2 
 
 245.0 
 
 346.0 
 
 654.0 
 
 1013.0 
 
 1417.0 
 
 1858.0 
 
 2342.0 
 
 2855.0 
 
 48 \ 
 
 W 
 
 17100 
 
 18515 
 
 19860 
 
 22300 
 
 27600 
 
 32000 
 
 35720 
 
 39150 
 
 42250 
 
 45120 
 
 1 
 
 s 
 
 76.5 
 
 82.7 
 
 88.4 
 
 98.7 
 
 121.0 
 
 139.5 
 
 156.0 
 
 171.0 
 
 185.0 
 
 197.5 
 
 ( 
 
 p 
 
 176.5 
 
 224.0 
 
 276.5 
 
 391.0 
 
 738.0 
 
 1144.0 
 
 1600.0 
 
 2100.0 
 
 2645.0 
 
 3225.0 
 
 51 1 
 
 W 
 
 19300 
 
 20900 
 
 22410 
 
 25150 
 
 31160 
 
 36100 
 
 40290 
 
 44120 
 
 47600 
 
 51000 
 
 I 
 
 s 
 
 72.0 
 
 78.0 
 
 83.2 
 
 93.0 
 
 114.0 
 
 131.5 
 
 147.0 
 
 161.0 
 
 174.0 
 
 186.0 
 
 
 p 
 
 198.0 
 
 251.3 
 
 310.0 
 
 438.0 
 
 827.5 
 
 1283.0 
 
 1792.0 
 
 2353.0 
 
 2950.0 
 
 3610.0* 
 
 
 W 
 
 21640 
 
 23430 
 
 25120 
 
 28200 
 
 34930 
 
 40450 
 
 45250 
 
 49550 
 
 53400 
 
 57100" 
 
 
 s 
 
 68.0 
 
 73.6 
 
 78.5 
 
 87.8 
 
 107.5 
 
 124.0 
 
 139.0 
 
 152.0 
 
 164.5 
 
 176.5 
 
 ( 
 
 p 
 
 220.6 
 
 280.0 
 
 345.2 
 
 488.0 
 
 921.0 
 
 1430.0 
 
 1998.0 
 
 2623.0 
 
 3290.0 
 
 4027.0 
 
 57 \ 
 
 W 
 
 24120 
 
 26120 
 
 28000 
 
 31400 
 
 38900 
 
 45150 
 
 50360 
 
 55150 
 
 59500 
 
 63650 
 
 ( 
 
 s 
 
 64.5 
 
 69.6 
 
 74.5 
 
 83.0 
 
 101.7 
 
 117.6 
 
 131.5 
 
 144.0 
 
 156.0 
 
 166.5 
 
 ( 
 
 p 
 
 244.5 
 
 310.0 
 
 383.0 
 
 541.0 
 
 1020.0 
 
 1584.0 
 
 2212.0 
 
 2904.0 
 
 3640.0 
 
 4465.0 
 
 60 i 
 
 W 
 
 26730 
 
 28920 
 
 31040 
 
 34800 
 
 43125 
 
 50000 
 
 55840 
 
 61180 
 
 65950 
 
 70550 
 
 } 
 
 s 
 
 61.2 
 
 66.2 
 
 70.7 
 
 79.0 
 
 96.7 
 
 111.7 
 
 125.0 
 
 137.0 
 
 148.0 
 
 158.0 
 
778 
 
 WATER-POWER. 
 
 Three conditions must be fulfilled to obtain accuracy! (1) Constant 
 initial discharge of solution; (2) perfect mix; (3) precise titration of 
 the salt solutions. The solution should be clear and free from im- 
 purities. The amount of initial solution injected should be about 
 0.0001 of the approximate discharge of the turbine, and a volumetric 
 analysis of the salt solution can measure the discharge with an ac- 
 curacy of 0.1 per cent. To make the analysis, three solutions are 
 needed: Silver nitrate, salt and potassium chromate. 
 
 If D is the discharge of the turbine in liters per second, NI the cubic 
 centimeters of silver nitrate solution required to titrate one liter of 
 initial salt solution, n the cubic centimeters of silver nitrate required to 
 titrate one liter of turbine discharge before the test, N 2 the cubic 
 centimeters of silver nitrate solution to titrate one liter of turbine dis- 
 charge after the test, and d the cubic centimeters discharge of initial 
 solution 
 
 The value of D may be expressed in cu. ft. by multiplying the result 
 by 0.03531. 
 
 Results of a comparison of this method of measuring the discharge 
 of a 5500 H.P. turbine at 500 r. p. m. under a head of 2300 ft., with 
 a weir, a current meter and a moving screen, are as follows: 
 
 Salt Current Moving Weir. 
 Solution. Meter. Screen. 
 Discharge, cu. ft. per sec ....... = 46 . 086 45 . 585 45 . 867 46 . 326 
 
 Mr. Streifl describes (Eng. Rec., Sept. 5, 1914) the application of 
 this method to the testing of the low-head turbines of the Grand 
 Rapids-Muskegon Power Co. The plant comprised two 7200-H.P. 
 horizontal, 8-runner units operating at 225 r. p. m. under 39^ ft. 
 head. The water consumption was found to be 2140 cu. ft. per sec. 
 The results were within 1.3 per cent of the results as obtained by 
 Ott current meters. 
 
 Draft Tubes. Conical draft tubes are commonly used with inward 
 flow turbines for the purpose of enabling the turbine to be set high above 
 the tail- water and also of reducing the loss of power due to the velocity 
 of the discharge. The maximum height of these tubes should not be 
 over 20 ft., and the angle of flare should not be greater than 7 with 
 the vertical. For the best results a parabolic cone should be used, 
 so as to decrease the velocity in direct proportion to the height above 
 the tail water, and in that case the angle of flare at the bottom may 
 be increased, so that the velocity of the water at the exit does not 
 exceed 6 ft. per second or 0.1 V2 gH. 
 
 Recent Turbine Practice (H. Birchard Taylor, Gen. Elec. Rev., 
 June, 1914). The single runner vertical unit has (1914) almost dis- 
 placed the multi-runner, horizontal type of turbine in large first-class, 
 low-head installations. It has had increasing application in moderate 
 and high-head plants. Present practice favors molding of the volute 
 casing directly in the substructure of the power house for all low-head 
 turbines. For heads exceeding 100 ft., the amount of concrete rein- 
 forcement required is usually sufficiently great to warrant the use of 
 cast-iron casings, which must be increased in thickness with increase 
 of head, until at 250 ft. head, cast steel becomes the standard material. 
 
 The thrust bearing of vertical wheels is almost universally located 
 above the generator on a cast-iron supporting truss which forms at 
 the same time a generator head cover. This truss must be rigid and 
 the upper face on which the bearing is mounted must be level. Up 
 to about 1909, the thrust bearing comprised an annular chamber be- 
 tween a revolving and stationary disk, into which oil under pressure 
 was pumped. The disadvantage of the oil pressure bearing is that 
 an excessive drop in pressure; or a momentary failure of the oil supply 
 to the bearing will result in its immediate destruction. This bearing 
 has now (1914) been generally superseded by roller bearings or a com- 
 bination of roller and pressure bearing. 
 
 Lignum vitse guide bearings have recently come into general use 
 with vertical turbines for both high- and low-head installations. These 
 
[HYDRAULIC TURBINES. 
 
 779 
 
 bearings are now so designed as to present a somewhat greater projected 
 
 area to the shaft than is called for by a babbitted bearing. The lignum 
 
 vitae is dovetailed into the bearing boxes in the form of strips running 
 
 parallel to the axis of the shaft, and 
 
 with the end grain of the wood pre- 
 
 sented normally to the surface of the 
 
 shaft. Twenty or more of these 
 
 strips are used, evenly spaced in a 
 
 liberal length and separated by spaces 
 
 for cooling water circulation. The 
 
 resultant bearing pressure may be 
 
 made so light as to eliminate the 
 
 necessity of making adjustment to 
 
 take up wear. Clear water is piped 
 
 to these bearings in the same manner 
 
 as oil. A bronze sleeve is used on 
 
 the shaft where it passes through the 
 
 bearing and stuffing box. 
 
 A 10,000 H.P. Turbine at Sno- 
 qualmie, Wash. (Arthur Giesler, 
 Enq. News, Mar. 20, 1906). The fall 
 is about 270 ft. high. The wheel was 
 designed by the Platt Iron Works Co., 
 Dayton, O., for an effective head of 
 260 ft. and 300 r.p.m., the latter 
 being fixed by the limitations of 
 dynamo design. The turbine is a 
 horizontal shaft machine, of the 
 
 Francis Turbine Runner. 
 
 Francis type, radial inward flow with 
 central axial discharge. The turbine proper has only one bearing, 8% 
 X 26 in., the generator having three bearings. The wheel is 66 in. out- 
 side diam. by 9 in. wide through the vanes. It has 34 vanes which ex- 
 tend a short distance beyond the end plate of the wheel on the dis- 
 charge side. There are 32 guide vanes, of the swivel type, connected 
 to a rotatable ring which is actuated by a Lombard governor. The tur- 
 bine wheel or runner is an annular steel casting. It is bolted to a 
 disk 46 in. diam., which is an enlargement of the 13 Ms in. hollow 
 nickel-steel shaft. A test for efficiency was made, in which the output 
 was measured on the electrical side, and the input by the drop of head 
 across the head gate. At 10,000 H.P. the efficiency shown was 84%, 
 the figure being subject to the inaccuracy of the water measurement. 
 The maximum capacity registered was 8250 K.W. or 11,000 H.P. 
 With the generator and the governor disconnected, with full gates 
 and no load, the wheel ran at 505 r.p.m. 
 
 Turbines of 13,500 H.P. Four Francis turbines, with vertical shafts, 
 rated at 13,500 H.P. each, have been built by Allis-Chalmers Co., for the 
 Great Northern Power Co., Duluth, Minn. The available head is 
 365 ft., and the wheels run at 375 r.p.m.; discharging, at full load, 
 about 400 cu. ft. per second, each. The runners are 62 in. diameter. 
 The penstock for each wheel is 84 in. diameter, reduced gradually to 
 66 in. at the wheel. 
 
 Some Large Turbines. Much larger turbines than those above 
 noted have been built in the years 1910^-1915. From a long list of 
 turbines constructed by I. P. Morris Co. in these years, the following 
 are selected: 
 
 Capacity 
 
 No. Each Head Rev. 
 
 Location. Date of Unit, in per 
 
 Units. H.P. Ft. Min. 
 
 McCall Ferry, Penna .. 1910 5 13,500 53 94 
 
 Holtwood, Pa., Susquehanna R. 1913 2 17,000 62 116 
 
 Grandmere, P. Q., Canada ..... 1915 6 20,000 76 120 
 
 Shawinigan Falls, P. Q ........ 1913 2 18,500 145 225 
 
 Long Lake, Washington ....... 1912 2 22,500 168 200 
 
 Grace Station, Idaho .......... 1913 2 16,500 482 514 
 
 Feather River, Cal ............ 19H 2 18,500 465 400 
 
780 WATER-POWER. 
 
 The " Fall-increaser" for Turbines. A circular issued Nov.; 1908, 
 by Clemens Herschel, the inventor of the Venturi meter, illustrates a 
 device, based on the principle of the meter, for diminishing the back- 
 water head which acts against the turbine. The surplus water, which 
 would otherwise run to waste, is caused to flow into a tube of the 
 Venturi shape, and the pressure in the narrow section, or throat of this 
 tube, is less than that due to the head of the back-water into which the 
 tube discharges. The throat is perforated with a great number of 
 6-in. holes, through which the discharge-water of the turbine is caused 
 to flow, the velocity through the holes being never over 4 ft. per second. 
 The circular says, that fall-increasers add about 10% to the annual 
 output of power with no appreciable increase in operating expenses. 
 
 For half the days of the year the fall-increasers are shut down be- 
 cause there is not enough, or only enough, water to supply the plain 
 turbines ; but for the other half of the year the f all-increasers keep the 
 output of power practically constant, and at the full output, where this 
 power output would fall to half the full output or less if the fall-increases 
 had not been built. An illustrated description of the fall-increaser, 
 with results of tests, is given in the Harvard Eng'g Journal, June, 1908. 
 See also U. S. Pat. No. 873,435 and Eng. News, June 11, 1908. 
 
 TANGENTIAL OE IMPULSE WATER-WHEELS. 
 
 The Pelton Water-wheel. Mr. Ross E. Browne (Eng'g News, Feb. 
 20, 1892) thus outlines the principles upon which this water-wheel is 
 constructed : 
 
 The function of a water-wheel, operated by a jet of water escaping 
 from a nozzle, is to convert the energy of the jet, due to its velocity, 
 into useful work. In order to utilize this energy fully the wheel-bucket, 
 after catching the jet, must bring it to rest before discharging it, with- 
 out inducing turbulence or agitation of the particles. 
 
 This cannot be fully effected, and unavoidable difficulties necessitate 
 the loss of a portion of the energy. The principal losses occur as 
 follows: First, in sharp or angular diversion of the jet in entering, or 
 in its course through the bucket, causing impact, or the conversion of a 
 portion of the energy into heat instead of useful work. Second, in the 
 
 FIG. 155a. FIG. 156&. FIG. i5bc. 
 
 so-called frictional resistance offered to the motion of the water by the 
 wetted surfaces of the buckets. Third, in the velocity of the water, as 
 it leaves the bucket, representing energy which has not been con- 
 verted into work. 
 
 Hence, in seeking a high efficiency: 1. The bucket-surface at the en- 
 trance will be approximately parallel to the relative course of the jet, 
 and the bucket should be curved in such a manner as to avoid sharp 
 angular deflection of the stream. 
 
 2. The path of the jet in the bucket should be short; in other words, 
 the total wetted surface of the bucket should be small. 
 
 3. The discharge end of the bucket should be as nearly tangential to 
 the wheel periphery as compatible with the clearance of the bucket 
 which follows; and great differences of velocity in the parts of the 
 escaping water should be avoided. In order to bring the water to rest 
 at the discharge end of the bucket, it is shown, mathematically, that 
 the velocity of the bucket should be one-half the velocity of the jet. 
 
 A bucket, such as shown in Fig. 156a, will cause the heaping of more 
 or less dead or turbulent water at the point indicated by dark shading. 
 This dead water is subsequently thrown from the wheel with con- 
 siderable velocity, and represents a large loss of energy. The intro- 
 duction of the wedge in the Pelton bucket (see Fig. 156&) avoids this 
 loss. 
 
TANGENTIAL OR IMPULSE WATER-WHEELS. 781 
 
 A wheel of the form of the Pelton (Fig. 156c) conforms closely in con- 
 struction to each of these requirements. [In wheels as now made 
 (1916) the sharp corners shown in this bucket are eliminated. 1 
 
 Considerations in the Choice of a Tangential Wheel (Joshua 
 Hendy Iron Works). The horse-power that can be developed by a tan- 
 gential wheel does not depend upon the size of the wheel but solely upon 
 the head and volume of water available. The number of revolutions per 
 minute that a wheel makes (running under normal conditions) depends 
 solely upon two factors, viz., its diameter and the head of water. 
 
 The choice of the diameter of a wheel is not therefore controlled by tho 
 power required but by the speed required when working under a given 
 head. If a wheel has no load, and is not governed, it will speed up until 
 the periphery is revolving at approximately the same velocity as tho 
 spouting velocity of the jet, but as soon as the wheel commences to 
 
 The diameter of pulley wheels on wheel shaft and countershafts of 
 machinery should be so proportioned that the water-wheel shall run at 
 the speed given in the table. The width, area and curvature of buckets 
 are designed to meet conditions of volume of flow under given heads. 
 The higher the peripheral velocity of the wheel, the greater the volume 
 of water that the buckets can handle, and consequently the same 
 standard wheel can handle more water, the higher the head. 
 
 Wheels designed for a given horse-power can be used for smaller 
 powers (within reasonable limits) with very little loss of efficiency, but 
 an increase in the volume to be used requires a larger bucket. If, for 
 the purpose of maintaining the same speed conditions, the same diam- 
 eter of wheel is to be adhered to, then a special wheel must be built 
 with either very large buckets or with two or more nozzles, or else a 
 double or multiple unit must be adopted. 
 
 It is advised to subdivide large streams between two, three or more 
 runners, as this insures a greater freedom from breakdown and is often 
 cheapest in the end. Single-nozzle, multiple runner units are easier to 
 govern than multiple-nozzle, single runner units. When two or more 
 nozzles are used in combination on one runner, the increased volume 
 to be dealt with is divided between the different nozzles, which ar.3 
 so arranged that their respective jets impinge on different buckets at 
 different parts of the periphery. 
 
 Combined Heads. When two or moue water powers are available at 
 the same site, but under different heads, it is possible to utilize them by 
 mounting wheels of different diameters in parallel, or, when the differ- 
 ence of head and volume is very great, it would even be possible to 
 arrange for a turbine for the low head and a tangential wheel for the 
 high head, although, in the latter case, it would probably be best to 
 mount them independently and connect to the machinery through the 
 medium of belts and countershafts. In either case, separate pipe lines 
 must be employed. 
 
 Reversible Wheels. In the case of reversible wheels desired for use 
 with hoists, cableways, etc., two wheels of proper dimensions and the 
 same type may be mounted parallel on the same shaft, one of the wheels 
 having the buckets and nozzles arranged to run in the opposite direction 
 to the other. Suitable valves, levers and pipe connections, can be ar- 
 ranged to cut the water off one wheel and turn it on to the other. 
 
 Control of Tangential Water-wheels. The methods of regulating 
 tangential water-wheels may be classified under ftve heads: 
 
 1. Permanently or semi-permanently altering the area of efflux of the 
 nozzles, with water economy and without loss of efficiency. 
 
 2. Reducing the volume of flow without altering the area of efflux, 
 with water economy but with loss of efficiency. 
 
 3. Variable alteration of the area of efflux without loss of efficiency 
 and with water economy. 
 
 4. Deflection of the jet, so that only a portion of its energy is trans- 
 mitted to the wheel, without water economy. 
 
 5. Combined regulation of 3 and 4, producing an effect whereby the 
 energy of the jet is reduced rapidly without water ram and the area of 
 efflux reduced slowly to effect water economy, or by a combination of 
 3 with some form of by-pass. 
 
782 WATER-POWER. 
 
 Governors.* Of the five methods of control enumerated above, the 
 first cannot be done automatically ; the other four, however, are suscep- 
 tible to either hand regulation or automatic regulation by means of gov- 
 ernors, the function of the governor being merely to automatically bring 
 into action the particular controlling device with which the wheel has 
 been equipped. There are two leading types of governors, the hydraulic 
 and the mechanical. In the first, the mechanism of the water-wheel 
 regulator is actuated by a hydraulically operated piston, the motive 
 power being taken from a small branch pipe from the main water supply, 
 or from an independent high-pressure oil-pumping system, the position 
 of the piston in the cylinder and consequent relative position ef the 
 controlling mechanism being dependent upon the amount of fluid under 
 pressure admitted to the cylinder at either end. This is controlled by a 
 main valve, operated by a very sensitive relay valve which, in turn, is 
 directly controlled by the centrifugal balls of the governor. 
 
 The second type, or mechanically operated governor, consists of a 
 device for automatically controlling and directing the transmission of 
 the requisite amount of energy taken from the wheel shaft, to operate 
 the water-regulating mechanism. The Lombard governor represents 
 the first type, and the Lombard-Replogle governor the second. 
 
 The close regulation that can be obtained with the latter is remark- 
 able. Any size will go into operation and make correction at so slight 
 a deviation as one-tenth of one per cent from normal, and in installa- 
 tions which have been made they will not permit of a departure of more 
 than five to eight per cent temporarily where there is an instantaneous 
 drop from full load to practically no load. When there is sufficient 
 fly-wheel effect, the deviation will not be over two per cent. The 
 adoption of fly wheels greatly facilitates many problems of governing. 
 
 Efficiency of the Doble Nozzle. The nozzle tip is of brass, highly 
 polished in the interior, with concave curves near the end. It contains 
 a conical regulating needle, which is set at any desired distance from the 
 opening to regulate the size of the opening and the diameter of the jet. 
 A jet flowing from the nozzle has a clear, glassy appearance. Tests 
 by H. C. Crowell and G. C. D. Lenth, at Mass. Inst. of Tech., 1903, gave 
 efficiencies under constant head from 96.4 to 99.3 % for different settings 
 of the needle, the coefficient of velocity being from 0.982 to 0.997. The 
 efficiency of a jet is equal to the ratio of the velocity head in the jet to 
 the total head at the entrance to the nozzle, and equal to the square of 
 the coefficient of velocity. Bulletin of the Abner Doble Co., No. 6, 1904. 
 
 Tests of a 12-in. Doble Laboratory Motor (Bulletin No. 12, 1908. 
 Abner Doble Co.). The tests were made by students at the University 
 of Missouri. The available head was 46 ft. The needle valve was 
 opened two, four, six and eight turns in the four series of tests, and with 
 each opening different loads were applied by a Prony brake. The 
 results were recorded and plotted in curves showing the relation of 
 speed, load and efficiency, and from these curves the following approxi- 
 mate figures are taken: 
 
 Speed, Revolutions per Minute. 
 
 Valve open 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 Two turns 
 
 B.H.P.. 
 
 Effy. % 
 
 0.20 
 62 
 
 0.26 
 75 
 
 0.27 
 80 
 
 0.26 
 
 77 
 
 0.22 
 64 
 
 0.14 
 41 
 
 0.03 
 13 
 
 Four turns 
 
 B.H.P.. 
 
 Effy. % 
 
 0.36 
 57 
 
 0.45 
 75 
 
 0.51 
 
 85 
 
 0.50 
 
 85 
 
 0.42 
 71 
 
 0.30 
 50 
 
 0.12 
 19 
 
 
 B.H.P.! 
 
 0.41 
 
 0.55 
 
 0.63 
 
 0.66 
 
 0.60 
 
 0.41 
 
 0.20 
 
 oix turns 
 Eight turns 
 
 Effy. % 
 B.H.P.? 
 
 Effy. % 
 
 48 
 0.48 
 53 
 
 64 
 0.62 
 70 
 
 73 
 0.70 
 79 
 
 76 
 0.71 
 81 
 
 74 
 0.64 
 
 72 
 
 66 
 0.43 
 50 
 
 51 
 0. 19 
 23 
 
 Water-power Plants Operating under High Pressures. The 
 
 fol- 
 
 lowing notes are contributed by the Pel ton Water Wheel Co.: 
 
 The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 
 3-ft. steel-disk Pelton wheel operating under 2100 ft. fall, equal to 
 911 Ib. per sq. in. It runs at a peripheral velocity of 10,804 ft. per 
 minute and has a capacity of over 100 H. P; The rigidity with which 
 water under such a high pressure as this leaves the nozzle is shown in 
 the fact that it is impossible to cut the stream with an axe, however 
 heavy the blow, as it will rebound just as it would from a steel rod 
 traveling at a high rate of speed. 
 
TANGENTIAL OK IMPULSE WATER-WHEELS. 
 
 783 
 
 In the hydraulic power-hoist of the Milwaukee Mining Co., Idaho, one 
 cage travels up as the other descends ; the maximum load of 5500 Ibs. at 
 a speed of 400 ft. per min. is carried by one of a pair of Pelton wheels (one 
 for each cage). Wheels are started and stopped by opening and closing 
 a small hydraulic valve at the engineer's stand which operates the larger 
 valves by hydraulic pressure. An air-chamber takes up the shock 
 that would otherwise occur on the pipe line under the pressure due to 
 the 850 ft. fall. 
 
 The Mannesmann Cycle Tube Works, North Adams, Mass., are using 
 four Pelton wheels, having a fly-wheel rim, under a pump pressure of 
 600 Ibs. per sq. in. These wheels are direct-connected to the rolls 
 through which the ingots are passed for drawing out seamless tubing. 
 
 The Alaska Gold Mining Co., Douglass Island, Alaska, has a |22-ft 
 Pelton wheel on the shaft of a Riedler duplex compressor. It is used as 
 a fly-wheel as well, weighing 25,000 lb., and develops 500 H.P. at 75 
 revolutions. A valve connected to the pressure-chamber starts and 
 stops the wheel automatically, thus maintaining the pressure in the 
 air-receiver. 
 At Pachuca in Mexico five Pelton wheels having a capacity of 600 
 
 Amount of Water Required to Develop a Given Horse-Power, with a 
 Given Available Effective Head. 
 
 Effective 
 Head in 
 Feet. 
 
 Horse-Power Based on 85% Efficiency of the Water "Wheel. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 Flow in Cubic Feet of Water per Minute Required to 
 Develop Power. 
 
 50 
 
 125 
 104 
 88 
 77 
 70 
 63 
 59 
 52 
 48 
 45 
 42 
 39 
 37 
 35 
 33 
 31 
 30 
 28 
 27 
 26 
 25 
 24 
 23 
 22 
 21 
 20 
 19 
 19 
 19 
 18 
 18 
 18 
 17 
 17 
 16 
 16 
 
 250 
 208 
 177 
 155 
 140 
 125 
 118 
 104 
 96 
 89 
 83 
 78 
 73 
 69 
 65 
 62 
 59 
 57 
 54 
 52 
 50 
 48 
 46 
 45 
 43 
 42 
 41 
 40 
 38 
 37 
 36 
 35 
 34 
 33 
 32 
 31 
 
 375 
 312 
 266 
 232 
 210 
 186 
 176 
 156 
 143 
 133 
 125 
 117 
 110 
 104 
 98 
 93 
 89 
 85 
 81 
 78 
 75 
 72 
 69 
 67 
 65 
 62 
 60 
 59 
 57 
 55 
 53 
 52 
 50 
 49 
 48 
 47 
 
 500 
 416 
 355 
 311 
 280 
 248 
 234 
 208 
 192 
 178 
 166 
 155 
 146 
 138 
 132 
 124 
 118 
 113 
 108 
 104 
 100 
 96 
 92 
 89 
 86 
 83 
 80 
 78 
 76 
 74 
 71 
 69 
 67 
 66 
 64 
 63 
 
 625 
 520 
 444 
 388 
 350 
 312 
 293 
 260 
 240 
 222 
 208 
 195 
 183 
 172 
 164 
 155 
 148 
 141 
 135 
 130 
 125 
 120 
 115 
 111 
 107 
 104 
 100 
 97 
 94 
 92 
 89 
 86 
 84 
 82 
 80 
 77 
 
 750 
 624 
 532 
 466 
 420 
 372 
 350 
 312 
 287 
 266 
 250 
 233 
 220 
 207 
 198 
 186 
 177 
 169 
 162 
 155 
 149 
 144 
 138 
 133 
 129 
 124 
 120 
 117 
 113 
 110 
 106 
 102 
 100 
 98 
 96 
 94 
 
 875 
 726 
 621 
 544 
 490 
 435 
 410 
 364 
 335 
 310 
 292, 
 272 
 256 
 242 
 230 
 218 
 206 
 198 
 190 
 181 
 174 
 167 
 161 
 156 
 150 
 145 
 140 
 136 
 132 
 128 
 124 
 121 
 117 
 114 
 111 
 105 
 
 1000 
 830 
 709 
 622 
 560 
 498 
 467 
 415 
 385 
 355 
 332 
 312 
 293 
 276 
 262 
 248 
 236 
 225 
 216 
 207 
 199 
 191 
 184 
 178 
 172 
 166 
 160 
 156 
 151 
 146 
 142 
 138 
 134 
 130 
 127 
 124 
 
 1125 
 934 
 798 
 699 
 630 
 558 
 525 
 467 
 430 
 400 
 375 
 350 
 330 
 310 
 295 
 280 . 
 266 
 255 
 243 
 233 
 224 
 215 
 207 
 200 
 193 
 187 
 180 
 175 
 170 
 165 
 160 
 155 
 151 
 147 
 144 
 140 
 
 1250 
 1038 
 886 
 876 
 700 
 622 
 585 
 520 
 478 
 443 
 416 
 388 
 365 
 345 
 326 
 310 
 295 
 283 
 270 
 258 
 248 
 238 
 230 
 222 
 215 
 208 
 200 
 194 
 . 188 
 183 
 178 
 172 
 168 
 164 
 160 
 156 
 
 60.. . 
 
 70 
 80. . . 
 
 90 
 
 100. 
 
 110.. . 
 
 120 
 130 
 
 140 
 
 150.. . 
 
 160 . 
 
 170.. . 
 
 180 
 
 190.. . 
 
 200 
 210. . . 
 
 22*0 
 230. . . 
 
 240 
 250.. . 
 
 260 
 
 270.. . 
 
 280 
 
 29"0.. . 
 
 300. . 
 
 310 
 
 320.. . 
 
 330 
 340. .. 
 
 350 
 
 360. . . 
 
 370. . . 
 
 380... 
 
 390.. . 
 
 400 
 
784 POWER OF OCEAN WAVES. 
 
 H.P. each under 800 ft. head are driving an electric transmission plant. 
 These wheels weigh less than 500 Ib. each, showing over a horse-power 
 per pound of metal. 
 
 Formulae for Calculating the Power of Jet Water-wheels, such as 
 the Pelton (F. K. Blue). H.P. = horse-power delivered; d = 62.36 Ib. 
 per cu. ft.; E = efficiency of turbine; q = quantity of water, cubic feet 
 per minute; h = feet effective head: d = inches diameter of jet; p = 
 pounds per square inch effective head ; c = coefficient of discharge from 
 nozzle which may be ordinarily taken at 0.9. 
 
 H.P.= 
 
 d2= 201.6 
 
 .Ec Vft 3 J^C VpS c Y//i c >y^ 
 
 Tangential Water-wheel Tables. The tables on pages 785 and 786 are 
 compiled on the following basis : 
 
 The head (h) is the net effective head at the nozzle. Proper allow- 
 ance must be made for all losses in the pipe line. 
 
 The velocity of efflux ( V) is the approximate spouting velocity of the , 
 jet in ft. per min. as it issues from the nozzle = \/2 gh X 60 = 481.2 \/hl 
 
 The discharge in cubic feet per minute = Q = V X a, where a equals 
 the cross-section area of nozzle opening in sq. ft., no allowance being 
 made for friction in the nozzle. 
 
 The weight of a cubic foot of water is taken at 39.2 Fahr. = 62.425 Ib. 
 
 The theoretical horse-power = Q X 62.425 X h ~ 33,000 = 0.00189ft. 
 
 The horse-power in the tables is based on 85 % mechanical efficiency 
 for the wheels. 
 
 The diameter is the effective diameter at the line of the nozzle center, 
 where the jet impinges on the center of the bucket. 
 
 The number of revolutions is based on a peripheral speed for the 
 effective diameter, of half the velocity of efflux of the jet, and equals 
 V -T- 2 C, where C = the circumference (in feet) of the effective diameter. 
 
 Small wheels, up to 24-in. diam., are commonly called motors. 
 
 THE POWER OF OCEAN WAVES. 
 
 Albert W. Stahl, U. S. N. (Trans. A. S. M. E., xiii, 438), gives the 
 following formulae and table, based upon a theoretical discussion of 
 wave motion : 
 
 The total energy of one whole wave-length of a wave H feet high, 
 L feet long, and one foot in breadth, the length being the distance 
 between successive crests, and the height the vertical distance between 
 
 the\ crest and the trough, is E = 8 LH% t I 4.935 j foot-pounds. 
 
 The time required for each wave to travel through a distance equal to 
 its own length is P <= -%/ seconds, and the number of waves passing 
 
 60 /5 1^3 
 
 any given point in 0110 minute is N = -p = 60^ ' *" Hence the total 
 
 energy of an indefinite series of such waves, expressed in horse-power per 
 foot*of breadth, is 
 
 By substituting various values for H -*- L, within the limits of such 
 values actually occurring in nature, we obtain the table on page 787. 
 The figures are correct for trochoidal deep-sea waves only, but they 
 
 (Continued on pag* 786) 
 
TANGENTIAL OR IMPULSE WATER WHEELS. 785 
 
 Tangential Water- Wheel Table. (Joshua Hendy Iron Works.) 
 
 P = horse-power, Q = cubic feet per minute, R = revs, per min. The 
 smaller figures in the first column give the spouting velocity of the jet 
 in feet per minute. (The table is greatly condensed from the original; 
 6-in., 15-in., and 30-in. wheels are also listed. P and Q are the same, 
 with any given head, for a 30 as for a 36-in. wheel, but R is 20% greater.) - 
 
 f 
 
 K.S 
 
 
 12 
 
 Inch. 
 
 18 
 
 Inch. 
 
 24 
 
 Inch. 
 
 36 
 
 Inch. 
 
 48 
 
 Inch. 
 
 60 
 
 Inch. 
 
 72 
 
 Inch. 
 
 8 
 
 Feet. 
 
 10 
 
 Feet. 
 
 12 
 
 Feet. 
 
 20 ' 
 
 P 
 
 .12 
 
 .37 
 
 .66 
 
 1.50 
 
 2.64 
 
 4.18 
 
 6.00 
 
 10.64 
 
 16.48 
 
 23.80 
 
 91')'? J 
 
 
 3.91 
 
 11.72 
 
 20.83 
 
 46.93 
 
 83.32 
 
 130.36 
 
 187.72 
 
 332.70 
 
 515.04 
 
 748.95 
 
 L\ JL 1 
 
 R 
 
 342 
 
 228 
 
 171 
 
 114 
 
 85 
 
 70 
 
 57 
 
 43 
 
 34 
 
 29 
 
 *A( 
 
 P 
 
 .23 
 
 .69 
 
 1.22 
 
 2.76 
 
 4.88 
 
 7.69 
 
 11.04 
 
 19.53 
 
 30.00 
 
 43.80 
 
 30 ) 
 
 ?f\if\ i 
 
 
 4.79 
 
 14.36 
 
 25.51 
 
 57.44 
 
 102.04 
 
 159.66 
 
 229.76 
 
 407.03 
 
 630.00 
 
 916.4? 
 
 iOJO 1 
 
 R 
 
 418 
 
 279 
 
 209 
 
 139 
 
 104 
 
 83 
 
 69 
 
 52 
 
 41 
 
 35 
 
 **( 
 
 P 
 
 .35 
 
 U)6 
 
 1.89 
 
 4.24 
 
 7.58 
 
 11.85 
 
 16.96 
 
 30.08 
 
 46.60 
 
 67.60 
 
 40) 
 
 
 5.53 
 
 16.59 
 
 29.46 
 
 66.36 
 
 107.84 
 
 184.36 
 
 265.44 
 
 470.27 
 
 728.16 
 
 1058.86 
 
 3043 ( 
 
 R 
 
 484 
 
 323 
 
 242 
 
 161 
 
 121 
 
 96 
 
 80 
 
 62 
 
 49 
 
 40 
 
 ... ( 
 
 P 
 
 .49 
 
 1.49 
 
 2.65 
 
 5.98 
 
 10.60 
 
 16.63 
 
 23.93 
 
 42.05 
 
 65.00 
 
 94.50 
 
 50 ) 
 
 
 6.18 
 
 18.54 
 
 32.93 
 
 74.17 
 
 131.72 
 
 206.13 
 
 296.70 
 
 525.90 
 
 814.32 
 
 1184.15 
 
 3403 ( 
 
 R 
 
 541 
 
 361 
 
 270 
 
 180 
 
 135 
 
 108 
 
 90 
 
 69 
 
 55 
 
 46 
 
 CA ( 
 
 P 
 
 .65 
 
 1.96 
 
 3.48 
 
 7.84 
 
 13.94 
 
 21.77 
 
 31.36 
 
 55.20 
 
 85.62 
 
 124.50 
 
 60 V 
 
 
 6.77 
 
 20.31 
 
 36.08 
 
 81.25 
 
 144.32 
 
 225.80 
 
 325.00 
 
 576.00 
 
 892.00 
 
 1297.00 
 
 3727 ) 
 
 R 
 
 592 
 
 395 
 
 296 
 
 197 
 
 148 
 
 118 
 
 98 
 
 75 
 
 60 
 
 50 
 
 ( 
 
 P 
 
 .82 
 
 2.47 
 
 4.39 
 
 9.88 
 
 17.58 
 
 27.51 
 
 39.52 
 
 70.00 
 
 107.80 
 
 157.50 
 
 70 
 
 Q 
 
 7.31 
 
 21.94 
 
 38.97 
 
 87.76 
 
 155.88 
 
 243.89 
 
 351.04 
 
 624.00 
 
 966.24 
 
 1405.17 
 
 4026 ( 
 
 R 
 
 640 
 
 427 
 
 320 
 
 2.13 
 
 160 
 
 130 
 
 106 
 
 81 
 
 64 
 
 54 
 
 / 
 
 P 
 
 1.00 
 
 3.01 
 
 5.36 
 
 12.04 
 
 21.44 
 
 33.54 
 
 48.16 
 
 85.76 
 
 134.16 
 
 192.64 
 
 80 
 
 Q 
 
 7.82 
 
 23.46 
 
 41.66 
 
 93.84 
 
 166.64 
 
 260.73 
 
 375.36 
 
 666.56 
 
 1042.92 
 
 1501.44 
 
 4304 ( 
 
 R 
 
 684 
 
 456 
 
 342 
 
 228 
 
 171 
 
 137 
 
 114 
 
 87 
 
 69 
 
 58 
 
 ( 
 
 P 
 
 1.20 
 
 3.60 
 
 6.39 
 
 14.40 
 
 25.59 
 
 40.04 
 
 57.60 
 
 102.36 
 
 160.16 
 
 230.40 
 
 90 
 
 Q 
 
 8.29 
 
 24.88 
 
 44.19 
 
 99.52 
 
 176.75 
 
 276.55 
 
 398.08 
 
 707.00 
 
 1106.20 
 
 1592.32 
 
 4565 ( 
 
 R 
 
 726 
 
 484 
 
 363 
 
 242 
 
 181 
 
 145 
 
 121 
 
 93 
 
 73 
 
 62 
 
 ( 
 
 P 
 
 1.40 
 
 4.21 
 
 7.49 
 
 16.84 
 
 29.93 
 
 46 85 
 
 67.36 
 
 119.72 
 
 187.40 
 
 269.44 
 
 100 ) 
 
 Q 
 
 8.74 
 
 26.22 
 
 46.58 
 
 104.88 
 
 186.32 
 
 291.51 
 
 419.52 
 
 745.28 
 
 1166.04 
 
 1678.08 
 
 4812 ( 
 
 R 
 
 765 
 
 510 
 
 382 
 
 255 
 
 191 
 
 152 
 
 127 
 
 96 
 
 77 
 
 64 
 
 ( 
 
 P 
 
 1.84 
 
 5.54 
 
 9.85 
 
 22.18 
 
 39.41 
 
 61.66 
 
 88.75 
 
 157.64 
 
 246.64 
 
 355.00 
 
 120) 
 
 Q 
 
 9.57 
 
 28.72 
 
 51.02 
 
 114.91 
 
 204.10 
 
 319.33 
 
 459.64 
 
 816.40 
 
 1277.32 
 
 1838 56 
 
 5271 ( 
 
 R 
 
 838 
 
 559 
 
 419 
 
 279 
 
 209 
 
 167 
 
 139 
 
 105 
 
 83 
 
 70 
 
 1>IA ( 
 
 P 
 
 2.33 
 
 6.99 
 
 12.41 
 
 27.96 
 
 49.64 
 
 77.71 
 
 111.85 
 
 198.56 
 
 310.84 
 
 447.40 
 
 140 ) 
 
 
 10.34 
 
 31.03 
 
 55.11 
 
 124.12 
 
 220.44 
 
 344.92 
 
 496.48 
 
 881.76 
 
 1379.68 
 
 1985.92 
 
 5694 ) 
 
 R 
 
 906 
 
 604 
 
 453 
 
 302 
 
 226 
 
 181 
 
 151 
 
 114 
 
 90 
 
 75 
 
 ( 
 
 P 
 
 2.84 
 
 8.54 
 
 15.17 
 
 34.16 
 
 60.68 
 
 94.94 
 
 136.65 
 
 242.72 
 
 377.76 
 
 546.60 
 
 160 
 
 
 11.05 
 
 33.17 
 
 58.92 
 
 132.68 
 
 235.68 
 
 368.73 
 
 530.75 
 
 942.72 
 
 1474.92 
 
 2123.00 
 
 6087 ( 
 
 R 
 
 969 
 
 646 
 
 484 
 
 323 
 
 242 
 
 193 
 
 161 
 
 121 
 
 97 
 
 81 
 
 t 
 
 P 
 
 3.39 
 
 10.19 
 
 18.10 
 
 40.77 
 
 72.41 
 
 113.30 
 
 163.08 
 
 289.64 
 
 453.20 
 
 652.32 
 
 183 ) 
 
 
 11.72 
 
 35.18 
 
 62 49 
 
 140.74 
 
 249.97 
 
 391.10 
 
 562.96 
 
 999.83 
 
 1564.40 
 
 2251.84 
 
 6455 ) 
 
 
 1024 
 
 683 
 
 513 
 
 342 
 
 256 
 
 206 
 
 171 
 
 128 
 
 103 
 
 86 
 
 ( 
 
 P 
 
 3.97 
 
 11.93 
 
 21.20 
 
 47.75 
 
 84.81 
 
 132.70 
 
 191.00 
 
 339.24 
 
 530.80 
 
 764.00 
 
 200 ) 
 
 Q 
 
 12.36 
 
 37.08 
 
 65.87 
 
 148.35 
 
 263.49 
 
 412.25 
 
 593.40 
 
 1053.96 
 
 1649.00 
 
 2373.60 
 
 6805 ) 
 
 R 
 
 1080 
 
 720 
 
 540 
 
 360 
 
 270 
 
 216 
 
 180 
 
 135 
 
 108 
 
 90 
 
 QC ( 
 
 P 
 
 
 
 
 56 99 
 
 101.20 
 
 158 38 
 
 227 96 
 
 404 80 
 
 633 52 
 
 911 84 
 
 4/0 \ 
 
 7215 \ 
 
 Q 
 
 
 
 
 157 J3 
 
 279^44 
 
 437.23 
 
 629 '.32 
 
 1117^76 
 
 1748 92 
 
 2517.28 
 
 
 R 
 
 
 
 
 382 
 
 287 
 
 229 
 
 191 
 
 144 
 
 115 
 
 96 
 
 250 ( 
 
 P 
 
 5.56 
 
 16.68 
 
 29.63 
 
 66.74 
 
 118.54 
 
 185.47 
 
 266.96 
 
 474.16 
 
 741.88 
 
 1067.84 
 
 7608 j 
 
 3 
 
 13.82 
 
 41.46 
 
 73.64 
 
 165.86 
 
 294.59 
 
 460.91 
 
 663.45 
 
 1178.36 
 
 1843.64 
 
 2653.80 
 
 
 H 
 
 1209 
 
 806 
 
 605 
 
 403 
 
 302 
 
 241 
 
 202 
 
 151 
 
 n\ 
 
 101 
 
786 
 
 WATER-POWER. 
 
 Tangential Water- Wheel Table. Continued. 
 
 d^ 
 g* 
 
 W.2 
 
 
 12 
 
 Inch. 
 
 18 
 Inch. 
 
 24 
 
 Inch. 
 
 36 
 
 Inch. 
 
 48 
 
 Inch. 
 
 60 
 
 Inch. 
 
 72 
 
 Inch. 
 
 8 
 
 Feet. 
 
 10 
 
 Feet. 
 
 12 
 
 Feet. 
 
 O7 C { 
 
 P 
 
 
 
 
 77 00 
 
 136.76 
 
 214 00 
 
 308 00 
 
 547.04 
 
 856 00 
 
 173? nn 
 
 f 9 1 
 
 7O7R < 
 
 
 
 
 
 173 94 
 
 308.92 
 
 483 39 
 
 695 ! 76 
 
 1235 68 
 
 1 933 56 
 
 1 /,->. UU 
 
 7783 (\A 
 
 S7/J 1 
 
 -o 
 
 
 
 
 423 
 
 317 
 
 253 
 
 211 
 
 J59 
 
 127 
 
 /OJ . lH 
 IflA 
 
 300 ( 
 
 P 
 
 7.31 
 
 21.93 
 
 38.95 
 
 87.73 
 
 155.83 
 
 243.82 
 
 350.94 
 
 623.32 
 
 975.28 
 
 IUO 
 
 1403 76 
 
 8335 ) 
 
 Q 
 
 15.13 
 
 45.42 
 
 80.67 
 
 181.59 
 
 322.71 
 
 504.91 
 
 726.76 
 
 1290.84 
 
 2019.64 
 
 2907 . 04 
 
 ( 
 
 R 
 
 1326 
 
 884 
 
 663 
 
 442 
 
 331 
 
 265 
 
 221 
 
 166 
 
 133 
 
 
 QOK ( 
 
 P 
 
 
 
 
 98 93 
 
 175 68 
 
 274 94 
 
 395 72 
 
 702 72 
 
 1099 76 
 
 1582 88 
 
 325 ) 
 
 8A77 i 
 
 
 
 
 
 189' 10 
 
 335 '84 
 
 525 '50 
 
 756 '. 40 
 
 1343 36 
 
 2102 00 
 
 3025 60 
 
 OO/Z i 
 
 R 
 
 
 
 
 460 
 
 344 
 
 276 
 
 230 
 
 J72 
 
 J38 
 
 J15 
 
 350 ( 
 
 P 
 
 9.21 
 
 27.64 
 
 49.09 
 
 110.56 
 
 196.38 
 
 307.25 
 
 442.27 
 
 785.52 
 
 1229 00 
 
 1769 08 
 
 9002 i 
 
 Q 
 
 16.35 
 
 49.06 
 
 87.14 
 
 196.25 
 
 348.57 
 
 545.36 
 
 785.00 
 
 1394.28 
 
 2181.44 
 
 3140.00 
 
 
 R 
 
 1432 
 
 955 
 
 716 
 
 477 
 
 358 
 
 275 
 
 238 
 
 179 
 
 143 
 
 119 
 
 400 ( 
 
 P 
 
 11.25 
 
 33.77 
 
 59.98 
 
 135.08 
 
 239.94 
 
 375.40 
 
 540.35 
 
 959.76 
 
 1501.60 
 
 2161.40 
 
 9624 / 
 
 Q 
 
 17.48 
 
 52.45 
 
 93.16 
 
 209.80 
 
 372.64 
 
 583.02 
 
 839.20 
 
 1490.56 
 
 2332.08 
 
 3356.80 
 
 
 R 
 
 1531 
 
 1021 
 
 765 
 
 510 
 
 382 
 
 306 
 
 255 
 
 101 
 
 153 
 
 128 
 
 450 ( 
 
 P 
 
 13.43 
 
 40.79 
 
 71.57 
 
 161.19 
 
 286.31 
 
 447.95 
 
 644.78 
 
 1145.24 
 
 1791.80 
 
 2579.12 
 
 10208 j 
 
 Q 
 
 18.54 
 
 55.63 
 
 98.81 
 
 222.52 
 
 395.24 
 
 618.38 
 
 890.11 
 
 1580.96 
 
 2473.52 
 
 35,60.44 
 
 
 R 
 
 1624 
 
 1083 
 
 812 
 
 541 
 
 406 
 
 324 
 
 270 
 
 203 
 
 162 
 
 135 
 
 500 ( 
 
 P 
 
 15.73 
 
 47.20 
 
 83.83 
 
 188.80 
 
 335.34 
 
 524.66 
 
 755.20 
 
 1341.36 
 
 2098.64 
 
 3020.80 
 
 10760 / 
 
 Q 
 
 19.54 
 
 58.64 
 
 104.15 
 
 234.56 
 
 416.62 
 
 651.83 
 
 938.25 
 
 1666.48 
 
 2607.02 
 
 3753.00 
 
 
 R 
 
 1713 
 
 1142 
 
 856 
 
 571 
 
 428 
 
 342 
 
 285 
 
 214 
 
 171 
 
 143 
 
 - f 
 
 p 
 
 
 
 
 217 82 
 
 386 84 
 
 605 31 
 
 871 28 
 
 1547 36 
 
 2421.24 
 
 3485 12 
 
 550 ) 
 1 1*770 \ 
 
 Q 
 
 
 
 
 246.00 
 
 436.92 
 
 683 62 
 
 984.00 
 
 1747 '68 
 
 2734 48 
 
 3936 00 
 
 1 IZ/y || 
 
 R 
 
 
 
 
 599 
 
 449 
 
 359 
 
 299 
 
 225 
 
 J79 
 
 150 
 
 600 ( 
 
 P 
 
 24.26 
 
 62.04 
 
 110.19 
 
 248.16 
 
 440.77 
 
 689.63 
 
 992.65 
 
 1763.08 
 
 2758.52 
 
 3970.60 
 
 1 1 787 ) 
 
 Q 
 
 25.12 
 
 64.24 
 
 114.09 
 
 256.95 
 
 456.38 
 
 714.05 
 
 1027.80 
 
 1825.52 
 
 2856.20 
 
 4111.20 
 
 
 R 
 
 1876 
 
 1251 
 
 938 
 
 625 
 
 469 
 
 375 
 
 312 
 
 235 
 
 188 
 
 156 
 
 f 
 
 p 
 
 
 
 
 270 97 
 
 484.16 
 
 748 80 
 
 1083 88 
 
 1936.64 
 
 2995 20 
 
 4335 52 
 
 640 } 
 
 Q 
 
 
 
 
 264 '63 
 
 466 12 
 
 73l'59 
 
 1058 '52 
 
 1864 48 
 
 292636 
 
 4234^08 
 
 12169 ) 
 
 R 
 
 
 
 
 644 
 
 483 
 
 387 
 
 322 
 
 242 
 
 194 
 
 161 
 
 7Afl ( 
 
 p 
 
 30.57 
 
 78.18 
 
 138.86 
 
 312.73 
 
 555.46 
 
 869.06 
 
 1250.92 
 
 2221.84 
 
 3476.24 
 
 5003 68 
 
 1 UU 
 17731 ) 
 
 Q 
 
 27.13 
 
 69.38 
 
 123.23 
 
 277.54 
 
 492.95 
 
 771.26 
 
 1110.16 
 
 1971.80 
 
 3085.04 
 
 4440.64 
 
 l/j>l 1 
 
 R 
 
 2026 
 
 1351 
 
 1013 
 
 675 
 
 506 
 
 405 
 
 337 
 
 253 
 
 203 
 
 169 
 
 7CA ( 
 
 P 
 
 33.91 
 
 86.70 
 
 154.00 
 
 346.83 
 
 616.03 
 
 963.82 
 
 1387.34 
 
 2464.12 
 
 3855.28 
 
 5549.36 
 
 f OIF I 
 
 13178 i 
 
 Q 
 
 28.08 
 
 71.82 
 
 127.56 
 
 287.28 
 
 510.25 
 
 798.33 
 
 1149.13 
 
 2041.00 
 
 3193.32 
 
 4596.52 
 
 
 R 
 
 2098 
 
 1309 
 
 1049 
 
 699 
 
 524 
 
 419 
 
 349 
 
 262 
 
 210 
 
 175 
 
 Qf\f\ \ 
 
 P 
 
 37.35 
 
 95.52 
 
 169.66 
 
 382.09 
 
 678.66 
 
 1061.81 
 
 1528.36 
 
 2714.64 
 
 4247.24 
 
 6113.44 
 
 oUU ) 
 
 13610 ) 
 
 Q 
 
 29.00 
 
 74.17 
 
 131.74 
 
 296.70 
 
 526.99 
 
 824.51 
 
 1186.81 
 
 2107.96 
 
 3298.04 
 
 4747.24 
 
 
 R 
 
 2166 
 
 1444 
 
 1083 
 
 722 
 
 542 
 
 433 
 
 361 
 
 271 
 
 217 
 
 181 
 
 QAA ( 
 
 p 
 
 44.57 
 
 113.98 
 
 202.45 
 
 455.94 
 
 809.82 
 
 1267.02 
 
 1823.76 
 
 3239.28 
 
 5068.08 
 
 7295.04 
 
 i/UU I 
 
 IXXIA S 
 
 Q 
 
 30.76 
 
 78.67 139.74 
 
 314.70 
 
 558.96 
 
 874.53 
 
 1258.81 
 
 2235.84 
 
 3498.12 
 
 5035.24 
 
 1 *HjO i 
 
 R 
 
 .2298 
 
 15321 1149 
 
 766 
 
 574 
 
 459 
 
 383 
 
 287 
 
 229 
 
 192 
 
 i ftftft ( 
 
 P 
 
 52.20 
 
 133.50 
 
 237.12 
 
 534.01 
 
 948.48 
 
 1483.97 
 
 2136.04 
 
 3793 92 
 
 5935.88 
 
 8544.16 
 
 1UUU 1 
 
 Q 
 
 32.42 
 
 82.93 
 
 147.30 
 
 331.72 
 
 589.19 
 
 921.83 
 
 1326.91 
 
 2356.76 
 
 3687.32 
 
 5287.64 
 
 15217 ) 
 
 11 
 
 2420 
 
 1615 
 
 1210 
 
 807 
 
 605 
 
 484 
 
 403 | 303 
 
 242 
 
 202 
 
 give a close approximation for any nearly regular series of waves in deep 
 water and a fair approximation for waves in shallow water. 
 The utilization of the energy in ocean waves divides itself into: 
 
 1. The various motions of the water which may be utilized for power. 
 
 2. The wave-motor proper. That is, the portion of the apparatus 
 in direct contact with the water, and receiving and transmitting the 
 energy thereof; together with the mechanism for transmitting this 
 energy to the machinery for utilizing the same. 
 
 3. Regulating devices, for obtaining a uniform motion, from the 
 
TIDAL POWER. 
 
 787 
 
 irregular and more or less spasmodic action of the waves, as well as for 
 adjusting the apparatus to the state of the tide and condition of the sea. 
 
 4. Storage arrangements for insuring a continuous and uniform out- 
 put of power during a calm, or when the waves are comparatively small. 
 
 The motions that may be utilized for power purposes are the following : 
 1. Vertical rise and fall of particles at and near the surface. 2. Hori- 
 zontal to-and-fro motion of particles at and near the surface. 3. Vary- 
 ing slope of surface of wave. 4. Impetus of waves rolling up the beach 
 in the form of breakers. 5. Motion of distorted verticals. All of 
 these motions, except the last one mentioned, have at various times 
 been proposed to be utilized for power purposes ; and the last is proposed 
 to be used in apparatus described by Mr. Stahl. 
 
 The motion of distorted verticals is thus denned: A set of particles, 
 originally in the same vertical straight line when the water is at rest, 
 does not remain in a vertical line during the passage 9f the wave; so 
 that the line connecting a set of such particles, while vertical and 
 straight in still water, becomes distorted, as well as displaced, during 
 the passage of the wave, its upper portion moving farther and more 
 rapidly than its lower portion. 
 
 Mr. Stahl's paper contains illustrations of several wave-motors de- 
 signed upon various principles. His conclusion as to their practicability 
 is as follows : ' ' Possibly none of the methods described in this paper may 
 ever prove commerically successful; indeed the problem may not be 
 susceptible of a financially successful solution. My own investigations, 
 however, so far as I have yet been able to carry them, incline me to the 
 belief that wave-power can and will be utilized on a paying basis." 
 
 TOTAL ENERGY OF DEEP-SEA WAVES IN TERMS OP HORSE-POWER PER 
 FOOT OP BREADTH 
 
 Ratio of 
 Length to 
 Height of 
 Waves. 
 
 Length of Waves in Feet. 
 
 25 
 
 50 
 
 75 
 
 100 
 
 150 | 200 
 
 300 | 400 
 
 50 
 40 
 30 
 20 
 15 
 10 
 5 
 
 0.04 
 0.06 
 0.12 
 0.25 
 0.42 
 0.98 
 3.30 
 
 0.23 
 0.36 
 0.64 
 1.44 
 2.83 
 5.53 
 18.68 
 
 0.64 
 1.00 
 1.77 
 3.96 
 6.97 
 15.24 
 51.48 
 
 1.31 
 2.05 
 3.64 
 8.13 
 14.31 
 31.29 
 105.68 
 
 3.62 
 5.65 
 10.02 
 21.79 
 39.43 
 86.22 
 291.20 
 
 7.43 
 11.59 
 20.57 
 45.98 
 80.94 
 177.00 
 597.78 
 
 20.46 
 31.95 
 56.70 
 120.70 
 223.06 
 487.75 
 1647.31 
 
 42.01 
 65.58 
 116.38 
 260.08 
 457.89 
 1001.25 
 3381.60 
 
 Continuous Utilization of Tidal Power (P. Decceur, Proc. Inst. 
 C, E. 1890). In cpnnection with the training- walls to be constructed in 
 the estuary of the Seine, it is proposed to construct large basins, by 
 means of which the power available from the rise and fall of the tide 
 could be utilized. The method proposed is to have two basins separ- 
 ated by a bank rising above high water, within which turbines would 
 be placed. The upper basin would be in communication with the sea 
 during the higher one-third of the tidal range, rising, and the lower 
 basin during the lower one- third of the tidal range, falling. The tur- 
 bine proposed is of an improved model designed to utilize a large flow 
 with a moderate diameter. One has been designed to produce 300 
 horse-power, with a minimum head of 5 ft. 3 in. at a speed of 15 revo- 
 lutions per minute, the vanes having 13 ft. internal diameter. The 
 speed would be maintained constant by regulating sluices. 
 
788 
 
 PUMPS AND PUMPING ENGINES. 
 
 PUMPS AND PUMPING ENGINES. 
 
 Theoretical Capacity of a Pump. Let Q'*= cu. ft. per min., 
 C' U. S. gals, per min. = 7.4805 Q* \ d = diam. of pump in inches; 
 */ = stroke in inches ; N == number of single strokes per rain. 
 
 Capacity in cu. ft. per min. 
 
 I'iarn = - 004545 ^: 
 
 4 231 
 
 Capacity in U. S. gals, per min. i 
 Capacity in gals, per hour 
 
 Diameter required for a ) d = 46 Q 
 given capacity per min. ) 
 
 If v = piston speed in feet per min., d 
 If the piston speed is 100 feet per min.: 
 
 ' 0.0034 AW; 
 = 0.204 Nd*l. 
 
 ^ = 17.15 -v/-t7% 
 
 V7T, /7S7 
 
 ^ =4.95\y. 
 
 Nl = 1200, and d = 1.354 
 
 , 0.495 
 
 G' = 4.08 d z per min. 
 The actual capacity will be from 60% to 95% of the theoretical, accord- 
 ing to the tightness of the piston, valves, suction-pipe, etc. 
 
 Theoretical Horse-power .Required to Raise Water to a Given 
 Height. Horse-power = 
 Volume in cu. ft. per min. X pressure per sq. ft. _ Weight X height of lift 
 
 33,000 33,000 
 
 Q' = cu. ft. per min.; G' = gals, per min.; W = wt. in Ibs.; P =* 
 pressure in Ibs. per sq. ft.; p = pressure in Ibs. per sq. in.; // = height of 
 lift in ft.; W = 62.355 Q', P - 144 p, p = 0.433 H, H = 2.3094 p, G' = 
 7.4805 Q'. 
 
 = Q'P ^ Q' H X 144 X 0.433 = Q'H _ G'H = 1.0104 G'H 
 33,000 33,000 529,23 3958.9 4000 
 
 HP. = 
 
 WH 
 
 Q' X 62.355 X 2.3094 p = Q'p G'p 
 
 33,000 229.17 " 1714.3' 
 
 33,000 
 
 For the actual horse-power required an allowance must be made for 
 the friction, slips, etc., of engine, pump, valves, and passages. 
 
 Depth of Suction. Theoretically a perfect pump will draw water 
 to a height of nearly 34 feet, or the height corresponding to a perfect 
 vacuum (14.7 Ibs. X 2.309 = 33.95 feet); but since a perfect vacuum 
 cannot be obtained on account of valve-leakage, air contained in the 
 water, and the vapor of the water itself, the actual height is generally 
 (ess than 30 feet. When the water is warm the height to which it can be 
 lifted by suction decreases, on account of the increased pressure of the 
 vapor. In pumping hot water, therefore, the water must flow into the 
 pump by gravity. The following table shows the theoretical maximum 
 depth of suction for different temperatures, leakage not considered: 
 
 Temp. 
 Fahr. 
 
 Absolute 
 Pressure 
 of Vapor, 
 Ibs. per 
 sq. in. 
 
 Vacuum 
 in 
 Inches of 
 Mercury. 
 
 Max. 
 
 Depth 
 ( of 
 Suc- 
 tion, 
 feet. 
 
 Temp. 
 Fahr. 
 
 Absolute 
 Pressure 
 of Vapor, 
 Ibs. per 
 sq. in. 
 
 Vacuum 
 in 
 Inches of 
 Mercury. 
 
 Max. 
 Depth 
 of 
 
 Suc- 
 tion, 
 feet. 
 
 102 1 
 
 1 
 
 27.88 
 
 31.6 
 
 182.9 
 
 8 
 
 13.63 
 
 15.4 
 
 126.3 
 
 2 
 
 25.85 
 
 29.3 
 
 188.3 
 
 9 
 
 11.60 
 
 13.1 
 
 141.6 
 
 3 
 
 23.83 
 
 27.0 
 
 193.2 
 
 10 
 
 9.56 
 
 10.8 
 
 153.1 
 
 4 
 
 21.78 
 
 24.7 
 
 197.8 
 
 11 
 
 7.52 
 
 8.5 
 
 162.3 
 
 5 
 
 19.74 
 
 22.3 
 
 202.0 
 
 12 
 
 5.49 
 
 6.2 
 
 170.1 
 
 6 
 
 17.70 
 
 20.0 
 
 205.9 
 
 13 
 
 3.45 
 
 3.9 
 
 176.9 
 
 7 
 
 15.67 
 
 17.7 
 
 209.6 
 
 14 
 
 1.41 
 
 1.6 
 
PUMPS AND PUMPING ENGINES. 
 
 789 
 
 The Deane Single Boiler-feed or Pressure Pump. 
 
 pumping clear liquids at a pressure not exceeding 150 Ibs. 
 
 Suitable for 
 
 
 Sizes. 
 
 
 Capacity 
 
 
 
 Sizes of Pipes. 
 
 
 
 
 per min. 
 
 
 
 
 
 
 
 at Given 
 
 0> 
 
 
 
 
 
 
 
 
 Speed. 
 
 8 
 
 .s 
 
 1 
 
 
 
 
 
 . 
 
 j. 
 
 -7- 
 
 *H 
 
 o> 
 
 
 
 .s 
 
 & 
 
 
 
 
 
 
 1 
 
 1 t-4 
 
 || 
 
 "2 o 
 
 2 
 
 3 
 
 1 
 
 to 
 
 | 
 
 i 
 
 3 
 
 fl 
 
 1 
 
 3 
 
 |1 
 02 
 
 || 
 
 SOQ 
 
 1" 
 
 | 
 
 3 
 
 1 
 
 1 
 
 1 
 
 A 
 
 o 
 
 1 
 
 
 
 3 
 
 2 
 
 5 
 
 .07 
 
 150 
 
 10 
 
 291/ 2 
 
 7 
 
 1/2 
 
 3/4 
 
 U/4 
 
 
 1 
 
 31/2 
 
 21/4 
 
 5 
 
 .09 
 
 150 
 
 13 
 
 331/2 
 
 71/2 
 
 1/2 
 
 3/4 
 
 U/4 
 
 
 U/2 
 
 4 
 
 23/8 
 
 5' 
 
 .10 
 
 150 
 
 15 
 
 331/2 
 
 71/2 
 
 1/2 
 
 3/4 
 
 U/4 
 
 
 2 
 
 4 
 
 21/2 
 
 5 
 
 .11 
 
 150 
 
 16 
 
 331/2 
 
 71/2 
 
 1/2 
 
 3/4 
 
 U/4 
 
 
 21/2 
 
 43/4 
 
 3 
 
 5 
 
 .15 
 
 150 
 
 22 
 
 34 
 
 81/2 
 
 1/2 
 
 3/4 
 
 H/2 
 
 1/4 
 
 3 
 
 5 
 
 31/4 
 
 7 
 
 .25 
 
 125 
 
 31 
 
 431/ 2 
 
 91/4 
 
 3/4 
 
 1 
 
 2 
 
 1/2 
 
 4 
 
 51/2 
 
 33/4 
 
 7 
 
 .33 
 
 125 
 
 42 
 
 43l/ 2 
 
 91/4 
 
 3/4 
 
 1 
 
 2 
 
 U/2 
 
 41/ 2 
 
 7 
 
 41/4 
 
 8 
 
 .49 
 
 120 
 
 58 
 
 511/o 
 
 12 
 
 1 
 
 U/2 
 
 3 
 
 2 
 
 5 
 
 7 
 
 41/2 
 
 10 
 
 .69 
 
 100 
 
 69 
 
 55 
 
 12 
 
 1 
 
 U/2 
 
 3 
 
 2 
 
 6 
 
 71/2 
 
 5 
 
 10 
 
 .85 
 
 100 
 
 85 
 
 55 
 
 12 
 
 1 
 
 U/2 
 
 3 
 
 2 
 
 61/2 
 
 8 
 
 5 
 
 12 
 
 1.02 
 
 100 
 
 102 
 
 63 
 
 14 
 
 1 
 
 U/2 
 
 3 
 
 2V2 
 
 7 
 
 10 
 
 6 
 
 12 
 
 1.47 
 
 100 
 
 147 
 
 69 
 
 19 
 
 1 1/2 
 
 2 
 
 4 
 
 4 
 
 8 
 
 12 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 69 
 
 19 
 
 2 
 
 21/2 
 
 5 
 
 4 
 
 9 
 
 14 
 
 8 
 
 12 
 
 2.61 
 
 100 
 
 261 
 
 69 
 
 21 
 
 2 
 
 21/2 
 
 5 
 
 5 
 
 The Deane Single Tank or Light-service Pump. These pumps 
 will all stand a constant .working pressure of 75 Ibs. on the water-cylinders. 
 
 Sizes. 
 
 
 Capacity 
 per min. 
 
 
 
 Sizes of Pipes. 
 
 
 
 
 
 03 
 
 
 \ 
 
 
 
 
 "Speed 
 
 o 
 
 
 
 
 
 
 
 * 
 
 
 J, 
 
 
 
 
 
 
 
 
 
 
 
 
 o . 
 
 . 
 
 *o 4; 
 
 a^ 
 
 M 
 
 
 d 
 
 .S 
 
 
 -^ 
 
 g 
 
 g 
 
 fijj 
 
 QJ 
 
 o 
 
 11 
 
 B 
 
 fl 
 
 JO 
 
 tc 
 
 5 
 
 a 
 
 S 
 
 .2 
 
 1 
 
 o 
 
 "08. S 
 
 02 
 
 ^^ 
 
 2 
 
 
 9 
 
 72 
 
 i 
 
 jd 
 
 w 
 
 
 m 
 
 ^ 
 
 ^ 
 
 O 
 
 OQ 
 
 O 
 
 
 ^ 
 
 m 
 
 S 
 
 03 
 
 Q 
 
 4 
 
 4 
 
 5 
 
 .27 
 
 130 
 
 35 
 
 33 
 
 91/2 
 
 1/2 
 
 3/4 
 
 2 
 
 H/2 
 
 3 
 
 4 
 
 7 
 
 .38 
 
 125 
 
 48 
 
 451/2 
 
 15 
 
 3/4 
 
 1 
 
 3 
 
 2V2 
 
 5V2 
 
 51/2 
 
 7 
 
 .72 
 
 125 
 
 90 
 
 451/2 
 
 15 
 
 3/4 
 
 ] 
 
 3 
 
 21/2 
 
 7V2 
 
 71/2 
 
 10 
 
 1.91 
 
 110 
 
 210 
 
 58 
 
 17 
 
 1 
 
 1V2 
 
 5 
 
 4 
 
 8 
 
 6 
 
 12 
 
 1.46 
 
 100 
 
 146 
 
 67 
 
 201/2 
 
 1 
 
 11/2 
 
 4 
 
 4 
 
 6 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 66 
 
 17 
 
 3/4 
 
 
 4 
 
 4 
 
 8 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 67 
 
 201/2 
 
 1 
 
 U/2 
 
 5 
 
 4 
 
 8 
 
 8 
 
 12 
 
 2.61 
 
 100 
 
 261 
 
 68 
 
 30 
 
 1 
 
 1 V2 
 
 5 
 
 5 
 
 10 
 
 8 
 
 12 
 
 2.61 
 
 100 
 
 261 
 
 681/ 2 
 
 30 
 
 11.2 
 
 
 5 
 
 5 
 
 8 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 68 
 
 20i/ 2 
 
 
 U/2 
 
 8 
 
 8 
 
 10 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 681/2 
 
 30 
 
 U/2 
 
 2 
 
 8 
 
 8 
 
 '12 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 64 
 
 24 
 
 2 
 
 2V2 
 
 8 
 
 8 
 
 10 
 
 12 
 
 12 
 
 5.87 
 
 100 
 
 587 
 
 681/ 2 
 
 30 
 
 U/2 
 
 2 
 
 8 
 
 8 
 
 12 
 
 12 
 
 12 
 
 5.87 
 
 100 
 
 587 
 
 64 
 
 281/ 2 
 
 2 
 
 21/2 
 
 8 
 
 8 
 
 10 
 
 12 
 
 18 
 
 8.79 
 
 70 
 
 616 
 
 95 
 
 25 
 
 H/2 
 
 2 
 
 8 
 
 8 
 
 12 
 
 12 
 
 18 
 
 8.79 
 
 70 
 
 616 
 
 95 
 
 281/2 
 
 2 
 
 21/2 
 
 8 
 
 8 
 
 12 
 
 14 
 
 18 
 
 12.00 
 
 70 
 
 840 
 
 95 
 
 281/ 2 
 
 2 
 
 21/2 
 
 8 
 
 8 
 
 14 
 
 16 
 
 18 
 
 15.66 
 
 70 
 
 1096 
 
 95 
 
 34 
 
 2 
 
 21/2 
 
 12 
 
 10 
 
 16 
 
 16 
 
 18 
 
 15.66 
 
 70 
 
 1096 
 
 95 
 
 34 
 
 2 
 
 21/2 
 
 12 
 
 10 
 
 18 
 
 16 
 
 18 
 
 15 66 
 
 70 
 
 1096 
 
 97 
 
 34 
 
 3 
 
 3V2 
 
 12 
 
 10 
 
 16 
 
 18 
 
 24 
 
 26.42 
 
 50 
 
 1321 
 
 115 
 
 40 
 
 2 
 
 21/2 
 
 14 
 
 12 
 
 18 
 
 18 
 
 24 
 
 26.42 
 
 50 
 
 1321 
 
 135 
 
 40 
 
 3 
 
 3V2 
 
 14 
 
 12 
 
790 PUMPS AND PUMPING ENGINES. 
 
 Amount of Water raised by a Single-acting Lift-pump. It Is 
 
 common to estimate that the quantity of water raised by a single-acting 
 bucket-valve pump per minute is equal to the number of strokes in one 
 direction per minute, multiplied by the volume traversed by the piston 
 in a single stroke, on the theory that the water rises in the pump only 
 when the piston or bucket ascends; but the fact is that the column of 
 water does not cease flowing when the bucket descends, but flows on 
 continuously through the valve in the bucket, so that the discharge of 
 the pump, if it is operated at a high speed, may amount to considerably 
 more than that calculated from the displacement multiplied by the num- 
 ber of single strokes in one direction. 
 
 Proportioning the Steam-cylinder of a Direct-acting Pump, 
 
 Let 
 
 A = area of steam-cylinder; a = area of pump-cylinder; 
 
 D = diameter of steam-cylinder; d = diameter of pump-cylinder; 
 
 P = steam-pressure, Ibs. per sq. in.; p = resistance per sq. in. on pumps; 
 
 H = head = 2.309 p; p = 0.433 H\ 
 
 work done in pump-cylinder 
 E - efficiency of the pump = work done by ' 
 
 .- - 
 
 EP' p * \EP' 
 
 - = ^ = OA ** H ', # = 2.309 #P . If #=75%, H = 1.732P-- 
 d JbJr MiP d O> 
 
 E is commonly taken at 0.7 to 0.8 for ordinary direct-acting pumps. 
 For the highest class of pumping-engines it may amount to 0.9. The 
 steam-pressure P is the mean effective pressure, according to the indi- 
 cator-diagram; the water-pressure p is the mean total pressure acting 
 on the pump plunger or piston, including the suction, as could be shown 
 by an indicator-diagram of the water-cylinder. The pressure on the 
 pump-piston is frequently much greater than that due to the height of 
 the lift * on account of the friction of the valves and passages, which 
 increases rapidly with velocity of flow. 
 
 Speed of Water through Pipes and Pump-passages. The speed 
 of the water is commonly from 100 to 200 feet per minute. If 200 feel 
 per minute is exceeded, the loss from friction may be considerable. 
 
 gallons per minute 
 
 The diameter of pipe required is *.95^ vd ^ ty in f ^ t per 
 
 For a velocity of 200 feet per minute, diam. = 0.35 X ^gallons per min. 
 
 Sizes of Direct-acting Pumps. The tables on pages 789 and 791 
 are selected from catalogues of manufacturers, as representing the two 
 common types of direct-acting pump, viz., the single-cylinder and the 
 duplex. Both types are made by most of the leading manufacturers. 
 
 Efficiency of Small Direct-acting Pumps. Chas. E. Emery, in 
 Reports of Judges of Philadelphia Exhibition, 1876, Group xx., says: 
 " Experiments made with steam-pumps at the American Institute Exhibi- 
 tion of 1867 showed that average-sized steam-pumps do not, on the aver- 
 age utilize more than 50 per cent of the indicated power in the steam- 
 cylinders, the remainder being absorbed in the friction of the engine, but 
 more particularly in the passage of the water through the pump It 
 may be safely stated that ordinary steam-pumps rarely require less than 
 120 pounds of steam per hour for each horse-power utilized m raising 
 water, equivalent to a duty of only 15,000,000 foot-pounds per 100 
 pounds of coal. With larger steam-pumps, particularly when they are 
 proportioned for the work to be done, the duty will be materially in- 
 creased," 
 
PUMPS AND PUMPING ENGINES. 
 
 The Worthington Duplex Pump. 
 
 STANDARD SIZES FOR ORDINARY SERVICE. 
 
 791 
 
 
 
 
 03 
 & 
 
 "S-3 
 
 >> i 
 
 & 
 
 . ' 
 US 
 
 Sizes of Pipes for 
 Short Lengths. 
 
 (j 
 
 e 
 
 
 03 
 
 3 2 
 
 'i' 2 ' 
 
 
 To be increased as 
 
 1 
 
 03 
 
 
 fl 
 
 o tl 
 
 flw 
 
 c ^ 
 
 "^ s 
 
 length increases. 
 
 .s 
 
 I 
 
 
 S 03 
 
 jij'rjw 
 
 rt 
 
 8* s s 
 
 
 1 
 
 IS, 
 
 
 <ri bO 
 
 s" 
 
 Pi 49 
 
 t-t-.cc 
 03 03 +j 
 
 
 
 
 
 s 
 1 
 
 1 
 ( o5 
 
 03 
 
 "* 03 
 
 SR tn" ri 
 
 |lj 
 
 U| 
 
 
 
 
 
 5 
 02 
 
 
 | 
 
 
 Ss-s 
 
 8r* 
 
 o o 
 
 
 03 
 
 
 OJ 
 
 a 
 
 s 
 
 i_, 
 
 g 
 
 02 
 
 IS 
 
 s 
 
 Jj.g 
 
 ||2 
 
 ?^1 
 
 | 
 
 .2- 
 
 03 
 .2* 
 'ft 
 
 'S 
 
 i 
 
 
 03 
 
 O 
 
 03 03 
 
 *o 
 
 Pn 
 
 ^.S S 
 
 'a 
 
 +3 
 
 
 & 
 
 "g 
 
 "^ 
 
 xj 
 
 "0 
 
 LI 
 
 C^d o 
 
 g w w 
 
 d 
 
 ! 
 
 .2 
 
 c3 
 
 1 
 
 | 
 
 1 
 * 
 
 "& 
 
 .O2 
 
 ||| 
 
 o ^ f* 
 
 .S O 03 
 
 Is! 
 
 1 
 
 M 
 
 o 
 
 C3 
 
 5 
 
 3 
 
 
 Q 
 
 
 
 o 
 
 Q - 
 
 w 
 
 H 
 
 02 
 
 3 
 
 3 
 
 2 
 
 3 
 
 .04 
 
 100 to 250 
 
 8 to 20 
 
 27/8 
 
 3/8 
 
 1/2 
 
 H/4 
 
 i 
 
 41/2 
 
 23/4 
 
 4 
 
 .10 
 
 100 to 200 
 
 20 to 40 
 
 4 
 
 1/2 
 
 3/4 
 
 2 
 
 n/2 
 
 51/4 
 
 31/2 
 
 5 
 
 .20 
 
 100 to 200 
 
 40 to 80 
 
 5 
 
 3,4 
 
 U/4 
 
 21/2 
 
 n/2 
 
 6 
 
 4 
 
 6 
 
 .33 
 
 100 to 150 
 
 70 to 100 
 
 55/8 
 
 1 
 
 U/2 
 
 3 
 
 2 
 
 71/2 
 
 41/2 
 
 6 
 
 .42 
 
 100 to 150 
 
 85 to 125 
 
 63 8 
 
 U/2 
 
 2 
 
 4 
 
 3 
 
 71/2 
 
 5 
 
 6 
 
 .51 
 
 100 to 150 
 
 100 to 150 
 
 7 
 
 U/2 
 
 2 
 
 4 
 
 3 
 
 7l/ 2 
 
 41/2 
 
 10 
 
 .69 
 
 75 to 125 
 
 100 to 170 
 
 63/8 
 
 U/2 
 
 2 
 
 4 
 
 3 
 
 9 
 
 51/4 
 
 10 
 
 .93 
 
 75 to 125 
 
 135 to 230 
 
 71/2 
 
 2 
 
 21/2 
 
 4 
 
 3 
 
 10 
 
 6 
 
 10 
 
 1.22 
 
 75 to 125 
 
 180 to 300 
 
 81/2 
 
 2 
 
 21/2 
 
 5 
 
 4 
 
 10 
 
 7 
 
 10 
 
 1.66 
 
 75 to 125 
 
 245 to 410 
 
 97/8 
 
 2 
 
 21/2 
 
 6 
 
 5 
 
 12 
 
 7 
 
 10 
 
 1.66 
 
 75 to 125 
 
 245 to 410 
 
 97/8 
 
 21/ 2 
 
 3 
 
 6 
 
 5 
 
 14 
 
 7 
 
 10 
 
 1.66 
 
 75 to 125 
 
 245 to 410 
 
 97/8 
 
 21/2 
 
 3 
 
 6 
 
 5 
 
 12 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 to 610 
 
 12 
 
 21/2 
 
 3 
 
 6 
 
 5 
 
 14 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 co 610 
 
 12 
 
 21,2 
 
 3 
 
 6 
 
 5 
 
 16 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 to 610 
 
 12 
 
 21/2 
 
 3 
 
 6 
 
 5 
 
 181/2 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 to 610 
 
 12 
 
 3 
 
 31/2 
 
 6 
 
 5 
 
 20 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 to 610 
 
 12 
 
 4 
 
 5 
 
 6 
 
 5 
 
 12 
 
 101/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 21/2 
 
 3 
 
 8 
 
 7 
 
 14 
 
 101/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 21/2 
 
 3 
 
 8 
 
 7 
 
 16 
 
 101/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 21/2 
 
 3 
 
 8 
 
 7 
 
 181/2 
 
 101/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 3 
 
 31/2 
 
 8 
 
 7 
 
 20 
 
 101/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 4 
 
 5 
 
 8 
 
 7 
 
 14 
 
 12 
 
 10 
 
 4.89 
 
 75 to 125 
 
 730 to 1220 
 
 17 
 
 21/2 
 
 3 
 
 10 
 
 8 
 
 16 
 
 12 
 
 10 
 
 4.89 
 
 75 to 125 
 
 730 to 1220 
 
 17 
 
 21/2 
 
 3 
 
 10 
 
 8 
 
 181/ 2 
 
 12 
 
 10 
 
 4.89 
 
 75 to 125 
 
 730 to 1220 
 
 17 
 
 3 
 
 31/2 
 
 10 
 
 8 
 
 20 
 
 12 
 
 10 
 
 4.89 
 
 75 to 125 
 
 730 to 1220 
 
 17 
 
 4 
 
 5 
 
 10 
 
 8 
 
 181/ 2 
 
 14 
 
 10 
 
 6.66 
 
 75 to 125 
 
 990 to 1660 
 
 193/ 4 
 
 3 
 
 31/2 
 
 12 
 
 10 
 
 20 
 
 14 
 
 10 
 
 6.66 
 
 75 to 125 
 
 990 to 1660 
 
 193/4 
 
 4 
 
 5 
 
 12 
 
 10 
 
 17 
 
 10 
 
 15 
 
 5.10 
 
 50 to 100 
 
 510 to 1020 
 
 14 
 
 3 
 
 31/2 
 
 8 
 
 7 
 
 20 
 
 12 
 
 15 
 
 7.34 
 
 50 to 100 
 
 730 to 1460 
 
 17 
 
 4 
 
 5 
 
 12 
 
 10 
 
 20 
 
 15 
 
 15 
 
 11 47 
 
 50 to 100 
 
 1145 to 2290 
 
 21 
 
 
 
 
 
 25 
 
 15 
 
 15 
 
 11.47 
 
 50 to 100 
 
 1145 to 2290 
 
 21 
 
 
 
 
 
 
 
 
 Speed of Piston. A piston speed of 100 feet per minute is commonly 
 assumed as correct in practice, but for short-stroke pumps this gives too 
 high a speed of rotation, requiring too frequent a reversal of the valves. 
 For long-stroke pumps, 2 feet and upward, this speed may be consider- 
 ably exceeded, if valves and passages are of ample area. 
 
792 
 
 PUMPS AND PUMPING ENGINES. 
 
 Number of Strokes Required to Attain a Piston Speed from 50 to 
 
 125 Feet per Minute for Pumps Having Strokes 
 
 from 3 to 18 Inches in Length. 
 
 Speed of 
 Piston, in 
 Feet per 
 Min. 
 
 Length of Stroke in Inches. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 10 | 12 
 
 15 
 
 18 
 
 Number of Strokes per Minute. 
 
 50 
 
 200 
 
 150 
 
 120 
 
 100 
 
 86 
 
 75 
 
 60 
 
 50 
 
 40 
 
 33 
 
 55 
 
 220 
 
 165 
 
 132 
 
 110 
 
 94 
 
 82.5 
 
 66 
 
 55 
 
 44 
 
 37 
 
 60 
 
 240 
 
 180 
 
 144 
 
 120 
 
 103 
 
 90 
 
 72 
 
 60 
 
 48 
 
 40 
 
 65 
 
 260 
 
 195 
 
 156 
 
 130 
 
 111 
 
 97.5 
 
 78 
 
 65 
 
 52 
 
 43 
 
 70 
 
 280 
 
 210 
 
 168 
 
 140 
 
 120 
 
 105 
 
 84 
 
 70 
 
 56 
 
 47 
 
 75 
 
 300 
 
 225 
 
 180 
 
 150 
 
 128 
 
 112.5 
 
 90 
 
 75 
 
 60 
 
 50 
 
 80 
 
 320 
 
 1 240 
 
 192 
 
 160 
 
 137 
 
 120 
 
 96 
 
 80 
 
 64 
 
 53 
 
 85 
 
 340 
 
 255 
 
 204 
 
 170 
 
 146 
 
 127.5 
 
 102 
 
 85 
 
 68 
 
 57 
 
 90 
 
 360 
 
 270 
 
 216 
 
 180 
 
 154 
 
 135 
 
 108 
 
 90 
 
 72 
 
 60 
 
 95 
 
 380 
 
 285 
 
 228 
 
 190 
 
 163 
 
 142.5 
 
 114 
 
 95 
 
 76 
 
 63 
 
 100 
 
 400 
 
 300 
 
 240 
 
 200 
 
 171 
 
 150 
 
 120 
 
 100 
 
 80 
 
 67 
 
 105 
 
 420 
 
 315 
 
 252 
 
 210 
 
 180 
 
 157.5 
 
 126 
 
 105 
 
 84 
 
 70 
 
 110 
 
 440 
 
 330 
 
 264 
 
 220 
 
 188 
 
 165 
 
 132 
 
 110 
 
 88 
 
 73 
 
 115 
 
 460 
 
 345 
 
 276 
 
 230 
 
 197 
 
 172.5 
 
 138 
 
 115 
 
 92 
 
 77 
 
 120 
 
 480 
 
 360 
 
 288 
 
 240 
 
 206 
 
 180 
 
 144 
 
 120 
 
 96 
 
 80 
 
 125 
 
 500 
 
 375 
 
 300 
 
 250 
 
 214 
 
 187.5 
 
 150 
 
 125 
 
 100 
 
 83 
 
 Underwriters' Pumps Standard Sizes. 
 
 (National Board of Fire Underwriters, 1908.) 
 
 Pump Sizes, In. 
 
 Capacity at 100 Lb. 
 at Pump. 
 
 Boiler Power 
 Required. 
 
 Full Speed. 
 
 
 
 
 
 
 Steam 
 
 
 
 
 No. of 
 
 Nomi- 
 nal 
 
 Actual 
 
 Pfllc 
 
 Horse- 
 
 Pres- 
 sure 
 
 Revs. 
 
 Piston 
 Speed, 
 
 s & J* 
 
 1 V2-In. 
 
 Gals. 
 
 
 Power. 
 
 at 
 
 per 
 
 Ft. 
 
 J g 2 
 
 Streams . 
 
 per 
 
 Min 
 
 
 Pump, 
 
 Min. 
 
 per 
 
 CO ^ CO 
 
 
 Min. 
 
 
 
 Lb. 
 
 
 Min. 
 
 14 X 7 XI2 
 14 X 71/4X12 
 
 [TWO] 
 
 500 
 
 j 483! 
 1 520 \ 
 
 100 
 
 40 
 
 70 
 
 140 
 
 16 X 9 X12 
 
 Three 
 
 750 
 
 806 
 
 115 
 
 45 
 
 70 
 
 140 
 
 18 X20 X12 
 18V2X101/4X12 
 20 X12 X16 
 
 | Four | 
 Six 
 
 1000 
 1500 
 
 j 999) 
 1 1050 f 
 1655 
 
 150 
 200 
 
 45 
 
 50 
 
 70 
 60 
 
 140 
 160 
 
 The standard allowance for a good 1 1/8-in. (smooth nozzle) fire- 
 stream is 250 gal. per minute. 
 
 FIston Speed of Pumping-engines. (John Birkinbine, Trans. A. 7. 
 M. E., v. 459.) In dealing with such a ponderous and unyielding sub- 
 stance as water there are many difficulties to overcome in making a pump 
 work with a high piston speed. The attainment of moderately high speed 
 is, however, easily accomplished. Well-proportioned pumping-engines of 
 large capacity, provided with ample water-ways and properly constructed 
 valves, are operated successfully against heavy pressures at a speed of 
 250 ft. per minute, without "thug," concussion, or injury to the appara- 
 tus, and there is no doubt that the speed can be still further increased. 
 
 Speed of Water through Valves. If areas through valves and 
 water passages are sufficient to give a velocity of 250 ft. per min. or less, 
 they are ample. The water should be carefully guided and not too 
 abruptly deflected. (F. W. Dean, Eng. News, Aug. 10, 1893 ) 
 
 Boiler-feed Pumps. Practice has shown that 100 ft. of piston speed 
 per minute is the limit, if excessive wear and tear is to be avoided. 
 
 The velocity of water through the suction-pipe must not exceed 200 ft. 
 per minute, else the resistance of the Suction is too great, 
 
PUMPS AND PUMPING ENGINES. 793 
 
 "" Trie approximate size of suction-pipe, where the length does not exceed 
 25 ft. and there are not more than two elbows, may be found as follows: 
 
 7/io of the diameter of the cylinder multiplied by 1/100 of the piston 
 speed in feet. For duplex pumps of small size, a pipe one size larger is 
 usually employed. The velocity of flow in the discharge-pipe should not 
 exceed 500 ft. per minute. The volume of discharge and length of pipe 
 vary so greatly in different installations that where the water is to be 
 forced more than 50 ft. the size of discharge-pipe should be calculated 
 for the particular conditions, allowing no greater velocity than 500 ft. 
 per minute. The size of discharge-pipe is calculated in single-cylinder 
 pumps from 250 to 400 ft. per minute. Greater velocity is permitted in 
 the larger pipes. 
 
 In determining the proper size of pump for a steam-boiler, allowance 
 must be made for a supply of water sufficient for the maximum capacity 
 of the boiler when over driven, with an additional allowance for feeding 
 water beyond this maximum capacity when the water level in the boiler 
 becomes low. The average run of horizontal tubular boilers will evapor- 
 ate from 2 to 3 Ibs. of water per sq. ft. of heating-surface per hour, but 
 may be driven up to 6 Ibs. if the grate-surface is too large or the draught 
 too great for economical working. 
 
 Pump- Valves. A. F. Nagle (Trans. A. S. M. E., x. 521) gives a 
 number of designs with dimensions of double-beat or Cornish valves 
 used in large pumping-engines, with a discussion of the theory of their 
 proportions. Mr. Nagle says: There is one feature in which the Cornish 
 valves are necessarily defective, namely, the lift must always be quite 
 large, unless great power is sacrificed to reduce it. A small valve pre- 
 sents proportionately a larger surface of discharge with the same lift than 
 a larger valve, so that whatever the total area of valve-seat opening, its 
 full contents can be discharged with less lift through numerous small valves 
 than with one large one. See also Mr..Nagle's paper on Punip Valves and 
 Valve Areas, Trans. A. S. M. E., 1909. 
 
 Henry R. Worthington was the first to use numerous small rubber 
 valves in preference to the larger metal valves. These valves work well 
 under all the conditions of a city pumping-engine. A volute spring is 
 generally used to limit the rise of the valve. 
 
 In the Leavitt high-duty sewerage-engine at Boston (Am. Machinist, 
 May 31, 1884), the valves are of rubber, 3/ 4 inch thick, the opening in 
 valve-seat being 13 1/2X4 1/2 inches. The valves have iron face and 
 back-plates, and form their own hinges. 
 
 The large pumping engines at the St. Louis water works have rub* 
 ber valves 3V2 in. outside diam. There are seven valve cages in each 
 of the suction and discharge diaphragms, each cage having 28 valves. 
 The aggregate free area of 196 valves is 7.26 sq. ft., the area of one 
 plunger being 6.26 sq. ft. The suction and discharge pipes are each 
 36 in. diam., = 7.07 sq. ft. area. (Bull. No. 1609, Allis-Chalmers Co. 
 Such liberal proportions of valves are found usually only in the highest 
 grade of large high-duty engines. In small and medium sized pumps 
 a valve area equal to one-third the plunger area is commonly used.) 
 
 The Worthington "High-Duty" Pumping Engine dispenses with a 
 fly-wheel, and substitutes for it a pair of oscillating hydraulic cylinders, 
 which receive part of the energy exerted by the steam during the first 
 half of the stroke, and give it out in the latter half. For description see 
 catalogue of H. R. Worthington, New York. A test of a triple expan- 
 sion condensing engine of this type is reported in Eng. News, Nov. 29, 
 
 1904. Steam cylinders 13, 21, 34 ins.; plungers 30 in., stroke 25 in. 
 Steam pressure, 124 Ibs. Total head, 79 ft.; capacity, 14,267,000 gal. 
 in 24 hrs. Duty per million B.T.U., 102,224,000 ft.-lbs. 
 
 The d'Auria Pumping Engine substitutes for a fly-wheel a compen- 
 sating cylinder in line with the plunger, with a piston which pushes water 
 to and fro through a pipe connecting the ends of the cylinder. It is built 
 by the Builders' Iron Foundry, Providence, R. I. 
 
 A 72,000,000-gallon Pumping Engine at the Calf Pasture Station of 
 the Boston Main Drainage Works is described in Eng. News, July 6. 
 
 1905. It has three cylinders, 18V2, 33 and 523/ 4 ins., and two plungers, 
 60-in. diam.; stroke of all, 10 ft. The piston-rods of the two smaller 
 cylinders connect to one end of a walking beam and the rod of the third 
 cylinder to the other. Steam pressure 185 Ibs. gauge; revolutions per 
 niin. 17: static head 37 to 43 ft. Suction valves 128; ports, 4 X 161/4 in.; 
 
794 
 
 PUMPS AND PUMPING ENGINES. 
 
 total port area 8576 sq. in. Delivery valves, 96; ports, 4 X 1G3/4 to 203/4 
 in.; total port area 7215 sq. in. The valves are rectangular, rubber flaps, 
 backed and faced with bronze and weighted with lead. They are set with 
 their longest dimension horizontal, on ports which incline about 45 to the 
 horizontal. At 17 r.p.m. the displacement is 72,000,000 gallons in 24 hours. 
 The Screw Pumping Engine of the Kinnickinick Flushing Tunnel, 
 Milwaukee, has a capacity of 30,000 cubic feet per minute (= 323,000,000 
 gal. in 24 hrs.) at 55 r.p.m. The head is 31/2 ft. The wheel 12.5 ft. 
 diam., made of six blades, revolves in a casing set in the tunnel lining. 
 A cone, 6 ft. diam. at the base, placed concentric with the wheel on 
 the approach side diverts the water to the blades. A casing beyond 
 the wheel contains stationary deflector blades which reduce the swirling 
 motion of the water (Allis-Chalmers Co., Bulletin No. 1610). The two 
 screw pumping engines of the Chicago sewerage system have wheels 
 143/4 ft. diam., consisting of a hexagonal hub surmounted by six blades, 
 and revolving in cylindrical casings 16 ft. long, allowing 1/4 in. clearance 
 at the sides. The pumps are driven by vertical triple-expansion engines 
 with cylinders 22, 38 and 62 in. diam., and 42 in. stroke. 
 
 Finance of Pumping Engine Economy. A critical discussion of 
 the results obtained by the Nordberg and other high-duty engines is 
 printed in Eng. News, Sept. 27, 1900. It is shown that the practical 
 question in most cases is not how great fuel economy can be reached, 
 but how economical an engine it will pay to install, taking into consid- 
 eration interest, depreciation, repairs, cost of labor and of fuel, etc. 
 The following table is given, showing that with low cost of fuel and 
 labor it does not pay to put in a very high duty engine. Accuracy is 
 not claimed for the figures; they are given only to show the method 
 of computation that should be used, and to show the influence of different 
 factors on the final result. 
 
 TABULAR STATEMENT OP TOTAL ANNUAL COST OF PUMPING WITH AN 
 
 800-H. P. ENGINE, AS INFLUENCED BY VARYING DUTY OF ENGINE, 
 
 VARYING PRICE OF FUEL, AND VARYING TIME OF OPERATION. 
 
 
 Duty per million B.T.U. 
 
 First cost: 
 Engine . 
 
 50. 
 $24,000 
 30.00 
 27,000 
 51,000 
 
 1,440 
 2,160 
 3,600 
 6,022 
 
 17,280 
 23,040 
 28,800 
 
 25,920 
 34,560 
 43,200 
 
 26,902 
 32,662 
 38,422 
 
 35,522 
 
 44.IH2 
 
 J2$l 
 
 100. 
 $48,000 
 60.00 
 13,500 
 61,500 
 
 2,880 
 1,080 
 3,960 
 6,022 
 
 8,640 
 11,520 
 14,400 
 
 12,960 
 17,280 
 21,600 
 
 18,622 
 21,502 
 24,382 
 
 22,942 
 27,262 
 31,382 
 
 120. 
 $68,000 
 85.00 
 11,250 
 79,250 
 
 4,080 
 900 
 4,980 
 7,655 
 
 7,200 
 9,600 
 12,400 
 
 10,800 
 14,400 
 18,600 
 
 19,835 
 22,235 
 25,035 
 
 23,435 
 27,033 
 31,235 
 
 150. 
 $118,000 
 147.50 
 9,000 
 127,000 
 
 7,080 
 720 
 7,800 
 9,307 
 
 5,760 
 7,680 
 9,600 
 
 8,640 
 11,520 
 14,400 
 
 22,867 
 24,787 
 26,707 
 
 25,747 
 28,627 
 31,507 
 
 180. 
 $148,000 
 185.00 
 7,500 
 155,500 
 
 8,880 
 600 
 9,480 
 10,220 
 
 4,800 
 6,400 
 8,000 
 
 7,200 
 9,600 
 12,000 
 
 24,500 
 25,100 
 27,700 
 
 26,900 
 29,300 
 31,700 
 
 Engine per H P 
 
 Boilers economizers .... 
 
 Engine and boilers . % . . . 
 Int. and depreciation: 
 On engine at 6% 
 
 Boilers 8% 
 
 Total .. 
 
 Labor per annum 
 
 Fuel cost: 
 4,000 hrs. per yr.: 
 $3 00 per ton 
 
 4 00 per ton . . . ....... 
 
 5 00 per ton 
 
 6,000 hrs. per yr.: 
 $3 00 per ton 
 
 4 00 per ton 
 
 5 00 per ton 
 
 Total annual cost: 
 4,000 hrs. per yr.: 
 Coal $3 per ton, 
 
 4 per ton 
 
 5 per ton , 
 
 6.000 hrs, per yr. 
 CoaJi $3 per ton. ,.,,.,,,,.,,. 
 
 4 per ton,,, ,,,,,,,.,. 
 
 5 per ton 
 
PUMPS AND PUMPING ENGINES. 
 
 795 
 
 Cost of Electric Current for Pumping 1000 Gallons per Minute 
 
 100 ft. High. (Theoretical H.P. with 100% efficiency = 
 
 100,000 -3- 3958.9 = 25.259 H.P.) 
 
 Assume cost of current = 1 cent per K.W. hour delivered to the motor- 
 efficiency of motor = 90%; mechanical efficiency of triplex pumps =' 
 SJ%; of centrifugal pumps = 72%; combined efficiency, triplex pumps, 
 72%; centrifugal, 64.8%. 1 K.W. = 1.34 electrical H.P. on wire 
 
 Triplex, 1.34 X 0.72 = 0.9648 pump H.P.; X 33,000= 31 ,'838 ft -Ibs 
 per mm. 
 
 Centrifugal, 1.34 X 0.648 = 0.86382 pump H.P.; X 33,000 = 28654 
 ft .-Ibs. per min. 
 
 1000 gallons 100 ft. high = 833,400 ft .-Ibs. per min 
 
 31 ' 838 = 26 -!763 K.W. X 8760 hours per year 
 
 x, 
 
 X 
 
 , 
 
 $2293.04. 
 
 " 28 ' 655 = 29 - 0840 
 
 x 876 hours 
 
 For 100% efficiency, $2293.04 X 0.72 = $1650.00. For any other effi- 
 ciency, divide $1650.00 by the efficiency. For any other cost per K W 
 hour, in cents, multiply by that cost. 
 
 Cost of Fuel per Year 
 100 Ft. 
 
 for Pumping 1,000 Gallons per Minute 
 High by Steam Pumps. 
 
 0, 
 
 100% Effy. 90% 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 10. 
 
 198. 
 
 178.2 
 
 142.56 
 
 0.5846 
 
 0.42090 
 
 153.63 
 
 460.89 
 
 11.88 
 
 166.667 
 
 150. 
 
 120. 
 
 0.6945 
 
 0.50004 
 
 182.51 
 
 547.53 
 
 14. 
 
 141.433 
 
 127.87 
 
 101.83 
 
 0.8184 
 
 0.58926 
 
 215.08 
 
 645.24 
 
 14.256 
 
 138.889 
 
 125. 
 
 100. 
 
 0.8334 
 
 0.60005 
 
 219.02 
 
 657.06 
 
 15. 
 
 132. 
 
 118.8 
 
 95.04 
 
 0.8769 
 
 0.63125 
 
 230.44 
 
 691.32 
 
 16. 
 
 123.75 
 
 111.375 
 
 89.10 
 
 0.9354 
 
 0.67344 
 
 245.80 
 
 737.40 
 
 17.82 
 
 111.111 
 
 100. 
 
 80. 
 
 1.0417 
 
 0.75006 
 
 273.77 
 
 821.31 
 
 20. 
 
 99. 
 
 89.1 
 
 71.28 
 
 1.1692 
 
 0.84180 
 
 307.26 
 
 921.78 
 
 23.76 
 
 83.333 
 
 75. 
 
 60. 
 
 1.3890 
 
 1 .00008 
 
 365.03 
 
 1095.09 
 
 30. 
 
 66. 
 
 59.4 
 
 47.52 
 
 1.7538 
 
 1.26270 
 
 460.89 
 
 1382.67 
 
 35.64 
 
 55.556 
 
 50. 
 
 40. 
 
 2.0835 
 
 1.50012 
 
 547.54 
 
 1642.62 
 
 40. 
 
 49.5 
 
 44.5 
 
 35.64 
 
 2.3384 
 
 1.68360 
 
 614.52 
 
 1843.56 
 
 47.52 
 
 41.667 
 
 37.5 
 
 30. 
 
 2.7780 
 
 2.00016 
 
 . 730.06 
 
 2190.18 
 
 50. 
 
 39.6 
 
 35.64 
 
 28.51 
 
 2.9230 
 
 2.10450 
 
 768.15 
 
 2304.45 
 
 a 
 
 b 
 
 c 
 
 d 
 
 e 
 
 f 
 
 g 
 
 h 
 
 (1) Lbs. steam per I. H.P. per hour. 
 
 (2) Duty million ft.-lbs. per 1000 Ibs. steam, &,. 100% effy., c, 90%. 
 
 (3) Duty per 100 Ibs. coal, 90% effy., 8 Ibs. steam per Ib. coai. 
 
 (4) Lbs. coal per min. for 1000 gals., 100 ft. high. 
 
 (5) Tons, 2000 Ibs. in 24 hours. 
 
 (6) Tons per year, 365 days. 
 
 (7) Cost of fuel per year at $3.00 per ton. 
 
 Factors for calculation: fr = 1980 * a; c = b X 0.9; d = c X 0.8, 
 e = 8334 -^ 100 d; / = e X 0.72; g = f X 365; h = g X 3. 
 
 For any other cost of coal per ton, multiply the figures in the last 
 column by the ratio of that cost to $3.00. 
 
 Cost of Pumping 1000 Gallons per Minute 100 ft. High by 
 Gas Engines. 
 
 Assume a gas engine supplied by an anthracite gas producer using 1.5 
 Ibs. of coal per brake H.P. hour, coal costing $3.00 per ton of 2000 Ibs. 
 
 Efficiency of triplex pump 80%, of centrifugal pump, 72%. 
 
 1*000 gals, per min. 100 ft. high = 833,400 ft.-lbs. per min. -f. 33,000 
 = 25.2545 H.P. 
 
 Fuel cost per brake H.P. hour 1 .5 Ibs. X 300 cents -f- 2000 = 0.225 
 centX 8760 hours per year- $19.71 per H.P. X 25.2545= $497.766 for 
 100% efficiency. 
 
 For 80% effy., $622.21 ; for 72% effy., $691.34; or the same as the cost 
 with a steam pumping engine of 95,000,000 foot-pounds duty per 100 
 Ibs. of coal. 
 
796 
 
 PUMPS AND PUMPING 
 
 Cost of Fuel for Electric Current. 
 
 Based on 10 Ibs. steam per T.H.P. hour, 8 Ibs. steam per Ib. coal or 
 1.25 Ibs. coal per I.H.P. per hour. (Electric line loss not included.) 
 
 Efficiency o^ engine 0.90, of generator 0.90, combined effv. 0.81 
 
 I.H.P. = 0.746 K.W., 0.746 X 0.81 = 0.6426 K.W. on wire for'lO Ibs 
 steam. Reciprocal = 16.5492 Ibs. steam per K.W. hour. 8 Ibs. steam 
 per Ib. coal = 2.06865 Ibs. coal, at $3.00 per ton of 2,000 Ibs. = 0.3103 
 cents per K.W. hour. 
 
 Lbs. steam per I.H.P. hr. 
 
 12 14 16 18 20 30 40 
 
 Fuel cost, cents per K.W. hr. 
 
 0.3724 0.4344 0.4965 0.5585 0.6206 0.9309 1.2412 
 
 CENTRIFUGAL, PUMPS. 
 
 Theory of Centrifugal Pumps. Bulletin No. 173 of the TJniv. of 
 Wisconsin, 1907, contains an investigation by C. B. Stewart of a 6-in. 
 centrifugal pump which gave a maximum efficiency, under the best 
 conditions of load, of only 32%, together with a discussion of the general 
 theory of M. Combe, 1840, which has been followed by Weisbach, Ran- 
 kine, and Unwin. Mr. Stewart says that the theory of the centrifugal 
 pump, at the times of these writers, seemed practically settled, but it 
 was found later that the pump did not follow the theoretical laws de-^ 
 rived, and the subject is still open for investigation. The theoretical 
 head developed by the impeller can be stated for the condition of impend- 
 ing delivery, but as soon as flow begins the ordinary theory does not 
 seem to apply/ Experiment shows that the main difficulty to be over- 
 come in order to secure high efficiency with the centrifugal pump is in 
 providing some means of transforming the portion of the energy which 
 exists in the kinetic form, at the outlet of the impeller, to the pressure 
 form, or of reducing the loss of head in the pump casing to a minimum. 
 The theoretical head for impending delivery is V 2 +g, while experiment 
 shows that the maximum actual head approaches V 2 -*- 2g as a limit. 
 As the flow commences each pound of water discharged will possess the 
 kinetic energy V z +2g in addition to its pressure energy. To secure 
 high efficiency some means must be found of utilizing this kinetic energy. 
 The use of a free vortex or whirlpool, surrounding the impeller, and this 
 surrounded by a suitable spiral discharge chamber, is practically accepted 
 as one means of utilizing the energy of the velocity head. Guide vanes 
 surrounding the impeller also provide a means of changing velocity head 
 to pressure head, but the comparative advantage of these two means 
 cannot be stated until more experimental data are obtained. 
 
 The catalogue of the Alberger Pump Co., 1908, contains the following: 
 
 It was not until the year 1901 that the centrifugal pump was shown to 
 be nothing more or less than a water turbine reversed, and when designed 
 on similar lines was capable of dealing with heads as great, and with 
 efficiencies as good, as could be obtained with the turbines themselves. 
 Since this date great progress has been made in both the theory and 
 design, until now it is quite possible to build a pump for any reasonable 
 conditions and to accurately estimate the efficiency and other charac- 
 teristics to be expected during actual operation. 
 
 The mechanical power delivered to the shaft of a centrifugal pump by 
 the prime mover is transmitted to the water by means of a series of 
 radial vanes mounted together to form a single member called the im- 
 peller, and revolved by the shaft. The water is led to the inner ends of 
 the impeller vanes, which gently pick it up and with a rapidly accelerat- 
 ing motion cause it to flow radially between them so that upon reaching 
 the outer circumference of the impeller the water, owing to the velocity 
 and pressure acquired, has absorbed all the power transmitted to the 
 pump shaft. The problem to be solved in impeller design is to obtain 
 the required velocity and pressure with the minimum loss in shock and 
 friction. Since the energy of the water on leaving the pump is required to 
 be mostly in the form of pressure, the next problem is to transform into 
 pressure the kinetic energy of the water due to its velocity on leaving the 
 impeller and furthermore to accomplish this with the least possible loss. 
 
 The next consideration in impeller design is the proportions of the 
 vanes and the water passages, and to properly solve this problem an 
 
CENTRIFUGAL PUMPS. 797 
 
 extensive use of intricate mathematical formulse is necessary in addition 
 to a wide knowledge of the practical side of the question. It is possible 
 to obtain the same results as to capacity and head with practically an 
 infinite number of different shapes, each of which gives a different effi- 
 ciency as well as other varied characteristics. The change from velocity 
 to pressure is accomplished by slowing down the speed of the water in an 
 annular diffusion space extending from the impeller to the volute casing 
 itself and so designed that there is the least loss from eddies or shock. 
 It is necessary that this change shall take place gradually and uniformly, 
 as otherwise most of the velocity would be consumed in producing eddies. 
 With a proper design of the diffusion space and volute it is possible to 
 transform practically the whole of the velocity into pressure so that the 
 loss from this source may be very small. 
 
 It is necessary also to furnish a uniform supply of water to all parts of 
 the inlet or suction opening of the impeller, for unless all the impeller 
 vanes receive the same quantity of water at their inner edges, they 
 cannot deliver an equal quantity at their outer edges, and this would 
 seriously interfere with the continuity of the flow of water and the sue- . 
 cessful operation of the pump. 
 
 Relation of the Peripheral Speed to the Head. For constant speed 
 the discharge of a centrifugal pump for any lift varies with the square 
 root of the difference between the actual lift and the hydrostatic head 
 created by the pump without discharge. If any centrifugal pump con- 
 nected to a source of supply and to a discharge pipe of considerable 
 height is put in revolution, it will be found that it is necessary to main- 
 tain a certain peripheral runner speed to hold the water 1 ft. high without 
 discharge, and that for any other height the requisite speed will be very 
 nearly proportional to the square root of the height. 
 
 Experiments prove that the peripheral speed in ft. per min. neces- 
 sary to lift water to a given height with_yanes of different forms is approx; 
 Imately as follows: a, 481 \/h\ b, 554 \/h; c, 610 ^h\ d, 780 Vh ; e, 394 Vft. 
 a is a straight radial vane, b is a straight vane bent backward, c is a curved 
 vane, its extremity making an angle of 27 with a tangent to the impeller, 
 d is a curved vane with an angle of 18, e is a vane curved in the reverse 
 direction so that outer end is radial. ^ 
 
 Applying the above formula, speed ft. per min. ^coeff. X */h, to the 
 design of Mr. Clifford, gives 60 X 75.05 = C X ^85, whence C = 488. 
 The vane angle was 12. It is evident that the value of C depends on 
 other things than the shape or angle of the vanes, such as smoothness of 
 the vanes and other surfaces, shape and area of the diffusion vanes, and 
 resistance due to eddies in the pump passages. 
 
 The coefficient varies with the shape of the vanes; this means that 
 different speeds are necessary to hold water to the same heights witli 
 these different forms of vanes, and for any constant speed or lift there 
 must be a form of vane more suitable than any other. It would seem at 
 first glance that the runner which creates a given hydrostatic head with 
 the least peripheral velocity must be the most efficient, but practically 
 it is apparent from tests that the curvature of the vanes can be designed 
 to suit the speed and lift without materially lowering the efficiency. 
 (L. A. Hicks, Eng. News, Aug. 9, 1900.) 
 
 The quotient of the radial velocity of flow in a centrifugal pump 
 divided by the peripheral velocity is a constant C. By plotting effi- 
 ciency curves for various speeds in the discharge-efficiency diagram, 
 it is found that the points of maximum efficiency of the various curves 
 lie nearly in a straight line, hence the constant C varies but little with 
 the speed. Examination of the data from a large number of pumps 
 of various designs shows that high speeds are consistent with good 
 efficiency, and that the best values for C lie between the limits of 0.12 
 and 0.15. There is no advantage in the use of excessively wide im- 
 pellers. (N. W. Akimoff, Jour. Franklin Institute, May, 1911.) 
 
 Design of a Four-stage Turbine Pump. C. W. Clifford, in Am. 
 Mach., Oct. 17, 1907, describes the design of a four-stage pump of a 
 capacity of 2300 gallons per minute = 5.124 cu. ft. per sec. Following 
 is an abstract of the method adopted. The total head was 1000 ft. 
 Three sets of four-stage pumps were used at elevations of 16, 332, and 
 666 ft., the discharge of the first being the suction of the second, and so on. 
 
798 PUMPS AND PUMPING ENGINES. 
 
 The speed of the motor shaft is 850 r.p.m. This gives, for the diameter 
 of the impeller, d = 12 X 60 X 75.05 -f- 850 TT = 20.24 in. Circumfer- 
 ence C = 63.6 in; h = head for each impeller, in ft. 
 
 V = peripheral speed = 1.015 ^2 gh = 75.05 ft. per sec., 1.015 being 
 an assumed coefficient. The velocity V is divided into two parts by the 
 formula V\=V Vz; Vz = 2 gh * 2 V; whence Vi = 38.65 ft. per sec. 
 This is the tangential component of the actual velocity of the water as it 
 leaves the vane of the impeller. The radial component, or the radial 
 velocity, was taken approximately at 8 ft. per sec.; 8 * 38.65 = tang, of 
 11 42', the calculated angle between the vane and a tangent at the 
 periphery. Taking this at 12 gives tang. 12 X 38.65 = 8/215 ft. per sec. 
 = radial velocity V. The outflow area at the impeller then is 5.124 X 
 144 + (8.215 X 0.85) = 105 sq. in.; the 0.85 is an allowance for contrac- 
 tion of area in the impeller. The thickness of the vane measured on the 
 periphery is approximately 13/ 4 in.; taking this into account the width 
 of the impeller was made 17/ 8 in. [105 * (63.6 - 6 X 13/4) = 1.98 in.]. 
 The Vanes were then plotted as shown in Fig. 156, keeping the distance 
 between them nearly constant and of uniform section. Care was taken 
 to increase the velocity as gradually as possible. 
 
 The suction velocity was 9.37 ft. per sec., the diam. of the opening being 
 10 in. This was increased to 11 ft. per sec. at the opening of the im- 
 peller, from which, after deducting the area of the shaft, the diameter, d, 
 of the impeller inlet was found. Three long and three short vanes were 
 used to reduce the shock. 
 
 The diffusive vanes, Fig. 157, were then designed, the object being to 
 change the direction of the water to a radial one, and to reduce the 
 velocity gradually to 2 ft. per sec. at the discharge through the ports. 
 
 Fig. 158 shows a cross-section of the pump. The pumps were thor- 
 oughly tested, and the following figures are derived from a mean curve 
 of the results: 
 
 Gals, per min.. 500 1000 1500 2000 2200 2400 2500 3000 3500 
 
 Efficiency, % 30 51 68 78 79 78 76 61 31 
 
 A Combination Single-stage and Two-stage Pump, for low and 
 
 high heads, designed by Rateau, is described by J. B. Sperry in Power, 
 July 13, 1909. It has two runners, one carried on the main driving- 
 shaft, and the other on a hollow shaft, driven from the main shaft by a 
 clutch. It has two discharge pipes, either one of which may be closed. 
 When the hollow shaft is uncoupled, one runner only is used, and the 
 pump is then a single-stage pump for low heads. When the shafts are 
 coupled, the water passes through both runners, and may then be deliv- 
 ered against a high head. 
 
 Tests of De Laval Centrifugal Pumps. The tables on pp. 800, 801 con- 
 tain a condensed record of tests of three De Laval pumps made by Prof. 
 J. E. Denton and the author in April, 1904. Two of the pumps were 
 driven by De Laval steam turbines, and the other one by an electric 
 motor. In the two-stage pump the small wheel was coupled direct to 
 the high-speed shaft of the turbine, running at about 20,500 r.p.m., and 
 the large wheel was coupled to the low-speed shaft, which is driven by the 
 first through gears of a ratio of 1 to 10. The water delivery and the 
 duty were computed from weir measurements, Francis's formula being 
 used, and this was checked by calibration of the weir at different heads 
 by a tank, the error of the formula for the weir used being less than 1%. 
 Pitot tube measurements of the water delivered through a nozzle were 
 also made. 
 
 One inch below the center of the nozzle was located one end of a thin 
 half-inch brass tube, tapered so as to make an orifice of 3/3 2 inch diameter. 
 The other end of this tube was connected to a vertical glass tube, fastened 
 to the wall of the testing room, graduated in inches over a height of about 
 30 ft. The stream of water issuing from the nozzle impinged upon the 
 orifice of the brass tube, and thereby maintained a height of water In 
 the glass tube. This height afforded a "Pitot Tube Basis" of measure- 
 ment of the quantity of water flowing, the reliability of which was tested 
 by the flow as determined from the weir. The Pitot tube gave the 
 same result as the weir from the formula Qi C X Area of Nozzle X 
 ^2gh with a value of C varying only between 0.953 and 0.977 for the 
 large nozzle, and between 0.942 and 0.960 for the small nozzle. 
 
CENTRIFUGAL PUMPS. 
 
 799 
 
800 
 
 PUMPS AND PUMPING ENGINES. 
 
 TEST OP STEAM TURBINE CENTRIFUGAL PUMP, RATED AT 1700 GALS. 
 PER MIN., 100 FT. HEAD. 
 
 
 Steam 
 
 
 
 S 
 
 
 "So 
 
 u 
 
 bC 
 
 a 
 
 J2 
 
 0. 
 
 No. of 
 Test. 
 
 Press, at 
 the Gover- 
 nor Valve. 
 Lbs. per 
 Sq. In. 
 
 s 
 
 M 
 
 olutions 
 Minute. 
 
 Eforse-Pow 
 eulated. 
 
 i per Brake 
 se-power. 
 
 S 
 
 III 
 
 ^/3 
 
 1 
 
 t 
 
 J! 
 
 1- 
 IS 
 .S^ 
 
 73 fl 
 C3.2 
 
 o 
 
 Sd 
 
 Is 
 
 .S-' 
 
 cy of Pum] 
 
 
 
 
 
 > t* 
 
 
 e 
 
 ' J p 
 
 K 
 
 O> ^ 
 
 Ps 3 
 
 
 
 G 
 
 cs 
 
 8 
 
 a 
 
 V <O 
 
 tf ft 
 
 8? _^ 
 ><< O 
 d 
 
 03 
 
 W 
 
 >>^ 
 
 S 
 
 w 
 
 TJ 02 
 
 u, a 
 
 i 
 
 * 
 
 
 | 
 
 ^0 
 
 'o5 
 
 
 
 S 
 
 
 
 m 
 # 
 
 B" 
 Q 
 
 1 
 
 JOi 
 
 E2 
 
 i 
 
 
 
 6 
 
 190 
 
 126 
 
 251/4 
 
 ,547 
 
 47.7 
 
 25.45 
 
 37.43 
 
 22.95 
 
 45.97 
 
 1,978 
 
 0.481 
 
 10 
 
 190 
 
 148 
 
 251/2 
 
 ,536 
 
 56.65 
 
 24.42 
 
 50.44 
 
 34.95 
 
 70.75 
 
 1,958 
 
 0617 
 
 | 
 
 188 
 
 155.2 
 
 25 
 
 ,553 
 
 59.6 
 
 24.06 
 
 61.50 
 
 44.54 
 
 94.9 
 
 ,860 
 
 0.747 
 
 2 
 
 188 
 
 153.5 
 
 251/4 
 
 ,547 
 
 58.9 
 
 24.21 
 
 61.86 
 
 44.55 
 
 100.37 
 
 ,759 
 
 0.756 
 
 3 
 
 188 
 
 150.7 
 
 251/4 
 
 ,540 
 
 57.7 
 
 24.33 
 
 61.47 
 
 43.59 
 
 106.94 
 
 ,615 
 
 0.755 
 
 4 
 
 188 
 
 143.5 
 
 251/2 
 
 ,549 
 
 54.8 
 
 24.53 
 
 60.00 
 
 40.72 
 
 115.46 
 
 ,398 
 
 0.743 
 
 
 188 
 
 161 
 
 253/s 
 
 ,540 
 
 47.5 
 
 24.5 
 
 54.47 
 
 31.80 
 
 125.85 
 
 ,001 
 
 0.676 
 
 6A 
 
 189 5 
 
 170 
 
 251/2 
 
 565 
 
 24 9 
 
 
 Shut- 
 
 offT 
 
 142 15 
 
 
 
 t? 
 
 189' 
 
 169.5 
 
 
 1 537 
 
 
 
 
 45.15 
 
 43.85 
 
 95.14 
 
 ,87.6 
 
 
 1 
 
 189 
 189 
 
 169 
 169.7 
 
 
 535 
 
 
 
 45 12 
 
 43.82 
 
 99.05 
 
 753 
 
 
 
 ,538 
 
 
 
 44.62 
 
 42.93 
 
 104.42 
 
 ,629 
 
 
 * The brake H.P. and the steam per B.H.P. hour were calculated by a 
 formula derived from Prony brake tests of the turbine, 
 t Non-condensing. 
 
 TEST OF ELECTRIC MOTOR CENTRIFUGAL PUMP. DIAM. OF PUMP WHEE& 
 89/32 IN. RATED AT 1200 GALS. PER MIN. 45 FT. HEAD. 
 2000 REVS. PER MIN. 
 
 
 
 
 
 
 
 
 V 
 
 0) 
 
 T? 
 
 d 
 
 1 
 
 
 % 
 
 
 J 
 
 P 
 
 3 
 
 *^ A 
 
 & 
 
 
 
 !i 
 
 1 
 
 H 
 
 ^ 
 
 e 
 
 1 
 
 txj 
 
 ^- 
 ^ 
 
 Is 
 fS 
 
 
 ll| 
 
 i 
 
 o 
 
 1 
 
 li 
 
 ? 
 
 >, 
 
 0* 
 
 > 
 
 s 
 
 W 
 
 CQ $ 
 
 * 
 
 
 H-Q 
 
 H 
 
 -3 
 
 (H . 
 
 qjj 
 
 u 
 
 
 
 
 
 
 
 M 
 
 
 3 S3 
 
 
 2 
 
 "d"8 
 
 
 
 
 
 
 S 
 
 
 0^ 
 
 5 
 
 H 
 
 |o 
 
 '3 
 
 
 
 1.. 
 
 242.5 
 
 55.2 
 
 17.94 
 
 15.07 
 
 2,006 
 
 3.158 
 
 10.25 
 
 28.52 
 
 ,417 
 
 0.680 
 
 2.. 
 
 242.3 
 
 54.8 
 
 17.80 
 
 14.94 
 
 1,996 
 
 3.126 
 
 10.67 
 
 30.12 
 
 ,403 
 
 0.714 
 
 3.. 
 
 242 
 
 59 
 
 19.14 
 
 16.22 
 
 1,996 
 
 2.885 
 
 11.80 
 
 36.1 
 
 ,295 
 
 0.728 
 
 4.. 
 
 242 
 
 62.4 
 
 20.24 
 
 17.27 
 
 2,005 
 
 2.826 
 
 12.18 
 
 38.05 
 
 ,268 
 
 706f 
 
 5.. 
 
 241.8 
 
 62.9 
 
 20.39 
 
 17.41 
 
 2,000 
 
 2.525 
 
 13.06 
 
 45.66 
 
 ,133 
 
 0.750 
 
 6.. 
 
 240.8 
 
 66 
 
 21.30 
 
 18.28 
 
 2,005 
 
 2.504 
 
 13.40 
 
 47.25 
 
 ,124 
 
 0.733f 
 
 7.. 
 
 241.4 
 
 64 
 
 20.71 
 
 17.71 
 
 2,003 
 
 2.197 
 
 13.12 
 
 52.7 
 
 986 
 
 0.742 
 
 8.. 
 
 239.7 
 
 66.3 
 
 21.30 
 
 18.28 
 
 1,997 
 
 2.179 
 
 13.15 
 
 53.28 
 
 978 
 
 0.720t 
 
 9.. 
 
 240.9 
 
 63.2 
 
 20.41 
 
 17.43 
 
 2,007 
 
 1.735 
 
 11.42 
 
 58.10 
 
 779 
 
 0.665f 
 
 10.. 
 
 242 
 
 62 
 
 20.11 
 
 17.14 
 
 2,003 
 
 1.760 
 
 11.71 
 
 58.76 
 
 790 
 
 0.683 
 
 11.. 
 
 248 
 
 34 
 
 11.30 8.74 
 
 2,040 
 
 Shut-off 
 
 
 68.39 
 
 
 
 * Brake H.P. calculated from a formula derived from a brake test of 
 the motor. 
 
 f Tests marked t were made with the pump suction throttled so as to 
 make the suction equal to about 22 ft. of water column. In the other 
 tests the suction was from 5,6 to 10.9 ft. 
 
CENTRIFUGAL PUMPS. 
 
 801 
 
 TEST OF STEAM TURBINE TWO-STAGE CENTRIFUGAL PUMP. RATED AT 
 
 250 GALS. PER MIN. 700 FT. HEAD. LARGE PUMP WHEEL, 
 
 2050 R.P.M.; SMALL WHEEL, 20,500 R.P.M. 
 
 Steam 
 
 
 
 G" 
 
 
 
 
 tj 
 
 00 
 
 "* . 
 
 
 
 
 Press, at 
 
 1 
 
 
 & 
 
 0) 
 
 
 
 
 
 ^ 
 
 O.*3 
 
 "8 d 
 
 II 
 
 the Gover- 
 
 1 . 
 
 
 
 g 
 
 ft 
 
 "^ >4 
 
 'rf 
 
 (S 
 
 ^!^ 
 
 8l 
 
 gW 
 
 nor Valve. 
 
 "S M 
 
 
 
 CO 
 
 s 
 
 0) 
 
 
 '-5 tx 
 
 2| 
 
 o3 t< 
 
 Lbs. per 
 Sq. In. 
 
 - e o* 
 
 *| M 
 g^J 
 
 $ W 
 
 Vacuum, 
 
 y 
 
 
 
 1.1 
 
 1 a 
 
 <D 
 
 ?f 
 
 ni 
 3l 
 
 a 
 
 o 
 
 n 
 
 1 
 
 I| 
 
 C) f-i 
 
 ^S 
 
 -ft 
 0) a 
 
 'S^ 
 J 
 
 <D 
 
 > 
 
 > 
 
 ,2 
 
 u 
 
 
 -*j 
 
 W 
 
 o 
 
 
 o3 
 
 "el a 
 
 >> 1-5 
 
 
 & 
 
 "8 
 
 P* 
 
 
 02 
 
 
 
 
 ^ 
 
 * 
 
 1 
 
 
 186 
 
 120.7 
 
 28.1 
 
 25.25 
 
 341 
 
 2,104 
 
 0.830 
 
 135.76 
 
 12.83 
 
 373 
 
 18.63 
 
 106.2 
 
 175 
 
 138.3 
 
 27.5 
 
 24.4 
 
 
 2,092 
 
 0.799 
 
 193.85 
 
 17 54 
 
 359 
 
 
 
 181 
 
 162.3 
 
 27.05 
 
 25.5 
 
 '385 
 
 2,074 
 
 0.790 
 
 288 
 
 25.78 
 
 354 
 
 28.73 
 
 68.9 
 
 178 
 
 173.7 
 
 26.2 
 
 25.5 
 
 316 
 
 2,056 
 
 0.775 
 
 358.78 
 
 31.50 
 
 347 
 
 32.9 
 
 60.2 
 
 180 
 
 180.3 
 
 26 
 
 25.3 
 
 326 
 
 2,027 
 
 0.750 
 
 420.5 
 
 35.60 
 
 336 
 
 36.00 
 
 54.9 
 
 181 
 
 182 
 
 25.3 
 
 25.25 
 
 325 
 
 2,001 
 
 0.731 
 
 494.35 
 
 40.92 
 
 328 
 
 41.55 
 
 47.7 
 
 180 
 
 182 
 
 24.9 
 
 25.35 
 
 
 1,962 
 
 0.697 
 
 585.06 
 
 46.19 
 
 312 
 
 
 
 186 
 
 188.3 
 
 25.5 
 
 26.3 
 
 'iii 
 
 2,014 
 
 0.664 
 
 632.6 
 
 47.58 
 
 299 
 
 47.43 
 
 41.77 
 
 185 
 
 185 
 
 30 
 
 25.3 
 
 331 
 
 2,012 
 
 0.558 
 
 756.38 
 
 47.81 
 
 251 
 
 47.67 
 
 41.5 
 
 185 
 
 184 
 
 29 ' 
 
 26.5 
 
 325 
 
 2,029 
 
 0.544 
 
 781.4 
 
 48.15 
 
 244 
 
 48.88 
 
 40.50 
 
 . A Test of a Lea-Deagan Two-Stage Pump, by Prof. J. E. Denton, 
 
 is reported in Eng. Rec., Sept. 29, 1906. The pump had a 10-in. suction 
 
 and discharge line, and impellers 24 in. diam., each with 8 blades. The 
 
 following table shows the principal results, as taken from plotted curves 
 
 of the tests. The pump w"as designed to give equal efficiency at different 
 
 speeds. 
 
 Gal. per min. 
 
 400 800 1200 1600 2000 2400 2800 3000 3200 3400 3600 3800 
 Efficiency. 
 400 r.p.m. 42 61 69 75 77 77 70 
 
 39 56 65 71 75 77 77.6 77 74* *70' ' 
 35 50 62 68 71 74 76 77 78 78 
 
 500 
 
 600 
 
 Head. 
 
 400 r.p.m. 55 
 500 " 63 
 
 76 54 
 
 55 
 
 600 
 
 53 
 
 84 
 
 126 127 125 
 
 87 55 
 
 51 47 42 34 ... 
 
 82 78 73 67 63 58 51 
 
 122 118 115 107 104 101 97 
 
 The following results were obtained under conditions of maximum 
 efficiency: 
 
 400 r.p.m. 77.7% effy. 2296 gals, per min. 
 
 500 " 77.6 " 2794 " " 
 
 600 " 77.97 " 3235 " 
 
 43.6 ft. lift 
 67.4 
 100.7 
 
 np 
 
 A High-Duty Centrifugal Pump. A 45,000,000 gal. centrifugal punr 
 at the Deer Island sewage pumping station, Boston, Mass., was testea 
 in 1896 and showed a duty of 95,867,476 ft.-lbs., based on coal fired to 
 the boilers*. (Allis-Chalmers Co., Bulletin No. 1062.) 
 
 Rotary Pumps. Pumps with two parallel geared shafts carrying 
 vanes or impellers which mesh with each other, and other forms of posi- 
 tive driven apparatus, in which the water is pushed at a nwderate veloc- 
 ity, instead of being rotated at a high velocity as in centrifugal pumps, 
 are known as rotary pumps. They have an advantage over recipro- 
 cating pumps in being valveless, and over centrifugal pumps in working 
 under variable heads. They are usually not economical, but when care- 
 fully designed with the impellers of the correct cycloidal shape, like 
 those used in positive rotary blowers, they give a high efficiency. 
 They are especially useful in handling large volumes of water at 
 beads from JO to 50 feet arid also as vacuum pumps for condenser^. 
 
802 
 
 PUMPS AND PUMPING ENGINES. 
 
 They are not well adapted for lifting small quantities of water at 
 high pressure. 
 
 By calibrating the discharge per revolution and attaching a revolu- 
 tion counter a rotary pump may be used as a water meter. 
 
 An improvement in rotary pumps is to drive the two impellers 
 by a cross-compound engine, the two cylinders of which are so set that 
 the high-pressure pistpn drives one impeller and the low-pressure pis- 
 ton the other. In this arrangement the transmission of power from 
 one impeller shaft to the other through gearing is avoided. (Conners- 
 ville Blower Co., 1915.) 
 
 Tests of Centrifugal and Rotary Pumps. (W. B. Gregory, Bull. 
 183 U. S. Dept. of Agriculture, 1907.) These pumps are used for irri- 
 gation and drainage in Louisiana. A few records of small pumps, giving 
 very low efficiencies, are omitted. Oil was used as fuel in the boilers, 
 except in the pump of the New Orleans drainage station No. 7 (figures in 
 the last column), which was driven by a gas-engine. 
 
 Actual lift 
 
 15.5 
 
 72.6 
 127.5 
 155.6 
 
 81.7 
 72 1 
 
 16.2 
 157.0 
 287.4 
 671.2 
 
 42.9 
 34 3 
 
 11.2 
 116.0 
 147.1 
 229.8 
 
 64.2 
 40 7 
 
 30.2 
 93.2 
 318.0 
 648.0 
 
 49.0 
 33 8 
 
 9.5 
 
 71.4 
 76.5 
 137.7 
 
 55.6 
 
 23.7 
 68.7 
 222.8 
 503.9 
 
 44.3 
 33 9 
 
 31.7 
 85.6 
 306.8 
 452.3 
 
 67.9 
 78 ? 
 
 6.8 
 1-30.5 
 98.8 
 193.6 
 
 51.0 
 31 4 
 
 31.6 
 152.9 
 547.9 
 657.7 
 
 83.3 
 75 4 
 
 13.4 
 30.5 
 46.2 
 90.6 
 
 51.0 
 
 Disch. cu. ft. per sec.. . 
 Water horse-power 
 I.H.P 
 
 Effy., engine, gearing 
 and pumps. 
 
 Duty, per 1000 Ibs. stea. 
 
 Duty, per million 
 B.T.U. in fuel 
 
 37.8 
 8.16 
 
 a,f 
 
 18.3 
 4.23 
 
 b,g 
 
 20.7 
 4.68 
 
 b,g 
 
 24.2 
 4.16 
 
 b,g 
 
 22.1 
 c, g 
 
 17.3 
 4.09 
 
 b,g 
 
 51.1 
 9.70 
 
 a, g 
 
 16.7 
 3.93 
 
 d,g 
 
 50.1 
 9.61 
 
 a, g 
 
 82.4 
 e.g 
 
 Therm, effy. f ronxstea. 
 Kind of engine, and 
 pump 
 
 
 .a, Tandem compound condensing Corliss; 6, Simple condensing Cor- 
 liss; c, Simple non-condensing Corliss; d, Triple-expansion condensing, 
 vertical; e, Three-cylinder vertical gas-engine, with gas-producer, 0.85 Ib. 
 coal per I.H.P. per hour; /, Rotary pump; g, Cycloidal rotary. 
 
 The relatively low duty per million B.T.U. is due to the low efficiency 
 of the boilers. The test whose figures are given in the next to the last 
 column is reported by Prof. Gregory in Trans. A. S. M. E., to vol. xxviii. 
 
 DUTY TRIALS OF PUMPING-ENGINES. 
 
 A committee of the A. S. M. E. (Trans., xii. 530) reported in 1891 on a 
 standard method of conducting duty trials. Instead of the old unit of 
 duty of foot-pounds of work per 1 00 Ibs. of coal used, the committee recom- 
 mend a new unit, foot-pounds of work per million heat-units furnished by 
 the boiler. The variations in quantity of coal make the old standard unfit 
 as a basis of duty ratings. The new unit is the precise equivalent of 100 
 Ibs. of coal in cases where each pound of coal imparts 10,000 heat-units to 
 the water in the boiler, or where the evaporation is 10,000 + 970.4 = 10.305 
 Ibs. of water from and at 2 1 2 per pound of fuel. This evaporative result 
 is readily obtained from all grades of Cumberland or other semi-bitumi- 
 nous coal used in horizontal return tubular boilers, and, in many cases, 
 from the best grades of anthracite coal. 
 
 The committee on Power Tests (1915) reaffirmed the new unit, de- 
 fining it as follows: 
 
 The duty per million heat-units is found by dividing the number of 
 foot-pounds of work done during the trial by the total number of heat- 
 units consumed, and multiplying the quotient by 1,000,000. The 
 amount of work is found in the case of reciprocating pumps by mul- 
 tiplying the net area of the plunger in sq. in., the total head expressed 
 in pounds per square inch * by the length of the stroke in feet, and 
 the total number of single strokes during the trial ; finally correcting 
 
 * The total head is determined by adding together the pressure 
 shown by the gage on the force main, the vacuum shown by the gage 
 on -the suction main, and the vertical distance between the center of 
 the force-main gage and the point where |the suction-gage pipe con- 
 nects to the suction main, all expressed in the same units (pounds per 
 nch or foot). A pet-cock should l?e attacfiec} to the gage pipe 
 
DUTY TRIALS OF PUMPING ENGINES. 803 
 
 for the percentage of leakage of the pump. In cases where the water 
 delivered is determined by weir or other measurement, the work done is 
 found by multiplying the weight of water discharged during the trial by 
 the total head in feet. 
 
 The water noise-power of a pump is found by dividing the num- 
 ber of foot-pounds of work done per minute by 33,000. 
 
 Capacity. The capacity in gallons per 24 hours for reciprocating 
 pumps in cases where the water delivered is not measured, is found 
 by multiplying the net area of the plunger in square inches by the 
 length of the stroke in feet (in direct-connected engines the average 
 length of stroke); then by the number of single strokes per minute; 
 and the product of these three by the constant 74.8; finally correcting 
 for the percentage of leakage of the pump. 
 
 Leakage of Pump. The percentage of leakage is the percentage 
 borne by the quantity of leakage, found on the leakage trial, to the 
 quantity of water discharged on the duty run determined from plunger 
 displacement. 
 
 Leakage Test of Pump. The leakage of an inside plunger (the only 
 type which requires testing) is most satisfactorily determined by making 
 the test with the cylinder-head removed. A wide board or plank may be 
 temporarily bolted to the lower part of the end of the cylinder, so as to 
 hold back the water in the manner of a dam, and an opening made in the 
 temporary head thus provided for the reception of an overflow-pipe. 
 The plunger is blocked at some intermediate point in the stroke (or, if 
 this position is not practicable, at the end of the stroke), and the water 
 from the force main is admitted at full pressure behind it. The leakage 
 escapes through the overflow-pipe, and it is collected in barrels and 
 measured. The test should be made, if possible, with the plunger in 
 various positions. 
 
 In the case of a pump so planned that it is difficult to remove the 
 cylinder-head, it may be desirable to take the leakage from one of the 
 openings which are provided for the inspection of the suction- valves, 
 the head being allowed to remain in place. 
 
 It is assumed that there is a practical absence of valve leakage. Exami- 
 nation for such leakage should be made, and if it occurs, and it is found to 
 be due to disordered valves, it should be remedied before making the 
 plunger test. Leakage of the discharge valves will be shown by water 
 passing down into the empty cylinder at either end when they are under 
 pressure. Leakage of the suction-valves will be shown by the disappear- 
 ance of water which covers them. 
 
 If valve leakage is found which cannot be remedied the quantity of 
 water thus lost should also be tested. One method is to measure the 
 amount of water required to maintain a certain pressure in the pump 
 cylinder when this is introduced through a pipe temporarily erected, no 
 water being allowed to enter through the discharge valves of the pump. 
 > Friction. The percentage of total friction in a reciprocating 
 
 Eurnp is the percentage of the friction horse-power to the indicated 
 orse-power of the steam cylinders. 
 
 Data and Results. The data and results should be reported In 
 accordance with the form given herewith, adding lines for data not 
 
 below each gage cock, and opened occasionally so as to free the pipe 
 of air in the case of the force-main gage and of water in the case of 
 the suction gage. If the suction main is under a pressure instead of 
 a vacuum the suction gage should be attached at such a level that the 
 connecting pipe may be filled with water when the pet-cock is opened, 
 in which case the correction for difference in elevation of gages is 
 the vertical distance between the centers of the gages, and the reading 
 of the suction gage is to be subtracted from that of the force-main 
 gage. 
 
 If the water is drawn from an open well beneath the pump, the 
 total head is that shown by the force-main gage corrected for the 
 elevation of the center of the gage above the level of water in the 
 pump well. 
 
 If there is a material difference in velocity of the water at *,he 
 points where the two gages are attached, a correction should be made 
 for tne corresponding difference in "velocity-head." 1 
 
804 PUMPS AND PUMPING ENGINES. 
 
 provided for, or omitting those not required, as may conform to the 
 object in view. 
 
 In the case of a pumping engine of the reciprocating class for which 
 a record of the complete performance is desired, the additional engine 
 data and results given in the Steam Engine Code may supplement 
 those here given. 
 
 DATA AND RESULTS OF STEAM PUMPING MACHINERY 
 
 TEST. 
 
 Code of 1915. 
 
 1. Test of pump located at 
 
 To determine 
 
 Test conducted by 
 
 DIMENSIONS, ETC. 
 
 2. Type of machinery 
 
 3. Rated capacity in gallons per 24 hrs gals. 
 
 4. Size of engine or turbine 
 
 5. Size of pump 
 
 6. Auxiliaries (steam or electric driven) 
 
 7. Date 
 
 8. Duration hrs. 
 
 AVERAGE PRESSURES AND TEMPERATURES. 
 
 9. Pressure in steam pipe near throttle by gage Ibs. 
 
 10. Vacuum in condenser ins. 
 
 11. Temperature of steam, if superheated, at throttle degs. 
 
 12. Temperature corresponding to pressure in exhaust pipe 
 
 near engine or turbine degs. 
 
 13. Pressure in force main by gage Ibs. 
 
 14. Vacuum or pressure in suction main by gage ins. or Ibs. 
 
 (a) Correction for difference in elevation of the two 
 
 gages Ibs. 
 
 15. Total head expressed in Ibs. perssure per sq. in Ibs. 
 
 (a) Total head expressed in feet ft. 
 
 QUALITY OF STEAM- 
 
 1 6. Percentage of moisture in steam, degrees superheating, % or degs. 
 
 TOTAL QUANTITIES, 
 
 17. Total water fed to boilers Ibs. 
 
 18. Total condensed steam from surface condenser (corrected 
 
 i for condenser leakage) Ibs. 
 
 19. Total dry steam consumed (Item 19 or 20 less moisture 
 
 in steam) Ibs. 
 
 20. Total gals, of water discharged, by measurement gals. 
 
 (a) Total gals, of water discharged, by plunger dis- 
 placement, uncorrected gals. 
 
 (6) Percentage of slip ("^f^" "" 2 ) X 100. percent. 
 
 (c) Leakage of pump gals. 
 
 (d) Total gals, of water discharged, by calculation 
 
 from plunger displacement, corrected for 
 
 leakage gals. 
 
 (e) Total weight of water discharged, as measured . . Ibs. 
 (/) Total weight of water discharged, by calculation 
 
 from plunger displacement, corrected for 
 leakage Ibs, 
 
 HOURLY QUANTITIES. 
 
 21. Total water fed to boilers or drawn from surface con- 
 
 denser per hr Ibs. 
 
 22. Total dry steam consumed for all purposes per hour, 
 
 (Item 19 -5- Item 8) Ibs. 
 
- 
 
 DUTY TRIALS OF PUMPING ENGINES. 805 
 
 23. Steam consumed per hour for all purposes foreign to 
 
 main engine Ibs. 
 
 24. Dry steam consumed by engine or turbine per hour 
 
 (Item 23 - Item 24) Ibs. 
 
 25. Weight of water discharged per hour, by measurement. . Ibs. 
 
 (a) Weight of water discharged per hour, calculated 
 from plunger displacement, corrected Ibs. 
 
 HOURLY HEAT DATA. 
 
 26. Heat-units consumed by engine or turbine per hour 
 
 (Item 24 X total heat of one Ib. of steam above exhaust 
 temperature of Item 12) B.T.U. 
 
 INDICATOR DIAGRAMS. 
 
 Mean effective pressure, each steam cylinder Ibs. per sq. in. 
 
 (a) Mean effective pressure, each water cylinder. Ibs. per sq. in 
 
 SPEED AND STROKE. 
 
 28. Revolutions per minute R.P.M . 
 
 (a) Number of single strokes per minute strokes 
 
 (b) Average length of stroke feet. . 
 
 POWER. 
 
 29. Indicated horse-power developed I.H.P. 
 
 30. Water horse-power H.P. 
 
 31. Friction horse-power (Item 29 - Item 30) H.P. 
 
 32. Percentage of I.H.P. lost in friction per cent* 
 
 CAPACITY. 
 
 Gallons of water pumped in 24 hrs., as measured gals. 
 
 (a) Gals, of water pumped in 24 hrs., calculated from 
 plunger displacement, corrected gals. 
 
 (b) Gals, of water pumped per minute, as measured . . gals. 
 
 (c) Gals, of water pumped per minute, calculated from 
 plunger displacement, corrected gals. 
 
 ECONOMY RESULTS. 
 
 34. Heat-units consumed per I.H.P.-hr , B.T.U. 
 
 EFFICIENCY RESULTS. 
 
 35. Thermal efficiency referred to I.H.P. (2546.5 + Item 34) 
 
 X 100 per cent. 
 
 DUTY. 
 
 36. Duty per 1,000,000 heat-units ft.-lbs. 
 
 WORK DONE PER HEAT-UNIT. 
 
 37. Ft.-lbs. of work per B.T.U. (1,980,000 -T- Item 34) ft.-lbs. 
 
 The Nordberg Pumping Engine at Wildwood, Pa. Eng. News 
 May 4, 1899, Aug. 23, 1900, Trans. A. S. M. E., 1899. The peculiar 
 feature of this engine is the method used in heating the feed-water. The 
 engine is quadruple expansion, with four cylinders and three receivers. 
 There are five feed-water heaters in series, a, b, c, d, e. The water is 
 taken, from the hot-well and passed in succession through a which is 
 heated by the exhaust steam on its passage to the condenser; b receives 
 its heat from the fourth cylinder, and c, d and e respectively from the 
 third, second and first receivers. An approach is made to the requirement 
 of the Carnot thermodynamic cycle, i.e., that heat entering the system 
 should be entered at the highest temperature; in this case the water 
 receives the heat from the receivers at gradually increasing temperatures. 
 The temperatures of the water leaving the several heaters were, on the 
 test, 105, 136, 193, 260, and 311 F. The economy obtained with this 
 engine was the highest on record at the date (1900) viz., 162,948,824 ft. 
 Ibs. per million B,T.U M and it has not yet been exceeded (1909), 
 
806 
 
 PUMPS AND PUMPING ENGINES. 
 
 Notable High-duty Pumping Engine Records. 
 
 Date of test 
 
 ,& 
 Wildwood, 
 Pa. 
 
 (2) 
 1900 
 St. 
 Louis 
 (10). 
 
 (3) 
 1900 
 Boston, 
 Chest- 
 nut Hill 
 
 & 
 
 Boston, 
 Spot 
 Pond. 
 
 (5) 
 1906 
 St. 
 Louis 
 (3) 
 Bissell's 
 Point. 
 
 Locality* 
 
 
 Capacity, mil. gal., 24 hrs. . . 
 Diam. of steam cylinders, in. 
 Stroke in 
 
 6 
 .19.5,29,49.5 
 57.5x42 
 (2,14^ 
 
 504 
 200 
 712 
 6.95 
 93.05 
 12.26, 11.4 
 186* 
 162.9*147.5f 
 150.2* 
 22.81 
 
 15 
 34, 62,92 
 X42 
 
 ,$ 
 
 292 
 126 
 801 
 3.16 
 96.84 
 10.68 
 202 
 158.07 
 179.45 
 21.00 
 
 30 
 30, 56,87 
 x66 
 
 m & 
 
 140 
 185 
 801 
 6.71 
 93.29 
 10.34 
 196 
 156.8 
 178.49 
 21.63 
 
 30 
 22,41.5,62 
 x60 
 (3) 30.5 
 244 
 125 
 151 
 464 
 3.47 
 96.53 
 11.09 
 203 
 156.59 
 172.40 
 20.84 
 
 20 
 34, 62,94 
 
 (3) %! 
 
 238 
 146 
 859 
 2.27 
 97.73 
 
 No. and diam. of plungers. . . 
 Piston speed, ft. per min 
 Total head, ft 
 
 Steam pressure .... 
 
 Indicated Horse-power 
 Friction % 
 
 Mechanical efficiency, % 
 Dry steam per I.H.P. hr 
 B.T.U. per J.H.P. per min.. . 
 Duty, B.T.U. basis.. 
 Duty per 1000 Ibs. steam 
 Thermal efficiency. %..., 
 
 202.8 
 158.85 
 181.30 
 20.92 
 
 * With reheaters. 
 
 t Without reheaters. 
 
 (1), (2). From Eng. Alews, Sept. 27, 1900. (3) Do. Aug. 23, 1900. 
 (4) Do. Nov. 4, 1901. (5) Allis-Chalmers Co., Bulletin No. 1609. The 
 Wildwood engine has double-acting plungers. 
 
 The coal consumption of the Chestnut Hill engine was 1.062 Ibs. per 
 I.H.P. per hour, the lowest figure on record at that date, 1901. 
 
 VACUUM PUMPS. 
 
 . The Pulsometer. In the pulsometer the water is raised bv suction 
 into the pump-chamber by the condensation of steam within it, and is 
 then forced into the delivery-pipe by the pressure of a new quantity of 
 steam on the surface of the water. Two chambers are used which work 
 alternately, one raising while the other is discharging. 
 
 Test of a Pulsometer. A test of a pulsometer is described by De Volson 
 Wood in Trans. A. S. M. E., xiii. It had a SVz-inch suction-pipe, stood 
 40 in. high, and weighed 695 Ibs. 
 
 The steam-pipe was 1 inch in diameter. A throttle was placed about 
 2 feet from the pump, and pressure gauges placed on both sides of the 
 throttle, and a mercury well and thermometer placed beyond the throttle 
 The wire drawing due to throttling caused superheating. 
 
 The pounds of steam used were computed from the increase of the 
 temperature of the water in passing through the pump. 
 
 Pounds of steam X loss of heat = Ibs. of water sucked in X increase of 
 temp. 
 
 The loss of heat in a pound of steam is the total heat in a pound of 
 saturated steam as found from "steam tables" for the given pressure 
 plus the heat of superheating, minus the temperature of the discharged 
 water; or 
 
 Pounds of steam = 
 
 . water X increase of temp. . 
 
 The results for the four tests are given in the table on p. 807. 
 
 Of the two tests having the highest lift (54.05 ft.), that was more 
 efficient which had the smaller suction (12.26 ft.), and this was also the 
 most efficient of the four tests. But, on the other hand, the other two 
 tests having the same lift (29.9 ft.), that was the more efficient which had 
 the greater suction (19.67), so that no law in this regard was established. 
 The pressures used, 19, 30, 43.8, 26.1, follow the order of magnitude of 
 the total heads, but are not proportional thereto. No attempt was made 
 to determine what pressure would give the best efficiency for any par- 
 
THE JET PUMP. 
 Test of a Pulso meter. 
 
 807 
 
 Data and Results. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 Strokes per minute 
 
 71 
 
 60 
 
 57 
 
 64 
 
 Steam pressure in pipe before 
 
 114 
 
 110 
 
 127 
 
 104.3 
 
 Steam pressure after throttling.. 
 Steam temp, after throttling, F. . 
 Steam superheating F 
 
 19 
 270.4 
 3.1 
 
 30 
 277 
 3.4 
 
 43.8 
 309.0 
 17.4 
 
 26.1 
 270.1 
 1.4 
 
 
 1617 
 
 931 
 
 1518 
 
 1019.9 
 
 \Vater pumped Ibs . 
 
 404,786 
 
 186,362 
 
 228,425 
 
 248,053 
 
 Water temp, before entering pump 
 "Water temperature ris of 
 
 75.15 
 4.47 
 
 80.6 
 5.5 
 
 76.3 
 
 7.49 
 
 70.25 
 4.55 
 
 Water head by gauge on lift, ft.. . . 
 Water head by gauge on suction. . 
 Water head by gauge, total (//) 
 Water head by measure, total (/i) 
 Coeffi. of friction of plant, h/H .... 
 Efficiency of pulsometer 
 
 29.90 
 12.26 
 42.16 
 32.8 
 0.777 
 012 
 
 54.05 
 12.26 
 66.31 
 57.80 
 0.877 
 0.0155 
 
 54.05 
 19.67 
 73.72 
 66.6 
 0.911 
 0.0126 
 
 29.90 
 19.67 
 49.57 
 41.60 
 0.839 
 0.0138 
 
 Eff'y of plant exclusive of boiler 
 Eff'y of plant if that of boiler be 0.7 
 Duty, if 1 Ib. evaporates 10 Ibs. 
 water 
 
 0.0093 
 0.0065 
 
 10,511,400 
 
 0.0136 
 0.0095 
 
 13,391,000 
 
 0.0115 
 0.0080 
 
 11,059,000 
 
 O'.OI 16 
 0.0081 
 
 12,036,300 
 
 ticular head. The 'pressure used was intrusted to a practical runner, 
 and he judged that when the pump was running regularly and well, the 
 pressure then existing was the proper one. It is peculiar that, in the first 
 test, a pressure of 19 Ibs. of steam should produce a greater number of 
 strokes and pump over 50% more water than 26.1 Ibs., the lift being the 
 same as in the fourth experiment. 
 
 Chas. E. Emery in discussion of Prof. Wood's paper says, referring to 
 tests made by himself and others at the Centennial Exhibition in 1876 
 (see Report of the Judges, Group xx.), that a vacuum-pump tested by 
 him in 1871 gave a duty of 4.7 millions; one tested by J. F. Flagg, at the 
 Cincinnati Exposition in 1875, gave a maximum duty of 3.25 millions. 
 Several vacuum and small steam-pumps, compared later on the same 
 basis, were reported to have given duties of 10 to 11 millions, the steam- 
 pumps doing no better than the vacuum-pumps. Injectors, when used 
 for lifting water not required to be heated, have an efficiency of 2 to 5 
 millions; vacuum-pumps vary generally between 3 and 10; small steam- 
 pumps between 8 and 15; larger steam-pumps, between 15 and 30, and 
 pumping-engines between 30 and 140 millions. 
 
 1893 
 
 A very high record of test of a pulsometer is given in Eng'g, Nov. 24, 
 , p. 639, viz.: Height of suction 11.27 ft.; total height of lift, 102.6 
 
 ft.; horizontal length of delivery-pipe, 118 ft.; quantity delivered per 
 hour, 26,188 British gallons. Weight of steam used per H. P. per hour, 
 92.76 Ibs.; work done per pound of steam 21,345 foot-pounds, equal to a 
 duty of 21,345,000 foot-pounds per 100 Ibs. of coal, if 10 Ibs. of steam 
 were generated per pound of coal. 
 
 The Jet-pump. This machine works by means of the tendency of a 
 stream or jet of fluid to drive or carry contiguous particles of fluid along 
 with it. The water-jet pump, in its present form, was invented by Prof. 
 James Thomson, and first described in 1852. In some experiments on a 
 small scale as to the efficiency of the jet-pump, the greatest efficiency was 
 found to take place when the depth from which the water was drawn by 
 the suction-pipe was about nine tenths of the height from which the 
 water fell to form the jet; the flow up the suction-pipe being in that case 
 about one fifth of that of the jet, and the efficiency, consequently, 9/io X 
 1/5 = 0.18. This is but a low efficiency; but it is probable that it may be 
 increased by improvements in proportions of the machine. (Rankine, 
 S. E.) 
 
 The Injector when used as a pump has a very low efficiency. (See 
 Injectors, under Steam-boilers.) 
 
808 PUMPS AND PUMPING ENGINES. 
 
 GAS-ENGINE PUMPS. 
 
 The Humphrey Gas Pump is a single-acting reciprocating pumping 
 engine, the motive power of which is furnished by the explosion of a 
 mixture of gas and air, as in a gas engine, the force of the explosion 
 acting directly on the surface of a column of water in the vertical 
 cylindrical part of a J or V-shaped pipe instead of on a reciprocating 
 piston. The upper part of the cylinder contains the combustion 
 chamber and valves similar to those of an Otto cycle gas engine. The 
 lower part contains a suction valve box through which water enters 
 into the "play pipe" and through which it passes to a surge tank and 
 thence to the delivery pipe or reservoir. The charge of gas and air 
 for starting is forced into the combustion chamber by a 2-cylinder 
 air-compressor. When the explosion takes place the water is forced 
 into the surge tank while the products of combustion expand to a 
 low pressure, the inertia of the moving column of water in the play 
 pipe causing it to continue in motion after the pressure upon it has 
 decreased to atmospheric pressure. The scavenging valves of the gas 
 cylinder and the suction valves of the water pump then open, admitting 
 air and water. Most of the water follows the moving column in the 
 play pipe while the rest rises in the explosion cylinder. After the 
 kinetic energy in the moving column is expended in forcing water into 
 the surge tank the column comes to rest and starts to flow back into 
 the cylinder, the suction valves closing. When the surface reaches 
 the level of the exhaust valves of the gas cylinder these are closed 
 and the kinetic energy of the backward moving column is expended in 
 compressing the imprisoned mixture of gases and scavenging air to a 
 pressure higher than that of the surge tank, which starts the water 
 moving downward again until the pressure is again reduced below 
 that of the atmosphere. A fresh charge of gas and air is then drawn 
 into the explosion chamber, compressed by the next return of the 
 to-and-fro moving water column and then ignited. The motion of 
 the water is similar to the swing of the pendulum of a clock, the time 
 of vibration being nearly proportional to the square root of the length 
 of the moving column. The pump was invented in 1906 by Mr. H. A. 
 Humphrey. For illustrated descriptions see Eng'g, Nov. 26 and Dec. 
 3, 1909, and circulars of the Humphrey Gas Pump Co., Syracuse, 
 N. Y... makers under the Humphrey and Smyth patents. 
 
 Tests of five pumps at Chingford, England, gave the following 
 figures: Four pumps, capacity each 47,000 to 48,000 U. S. gal. per 
 min.; lift 30 to 32 ft.; water H.P. developed, 301 to 323; gas used per 
 min., 390 to 400 cu. ft. (at 60 F. and 30 in. bar.); heating value of 
 gas (lower value) B.T.U. per cu. ft., 142 to 146; thermal efficiency, 
 22.19 to 24.07%; anthracite per water H.P.-hour, 0.881 to 0.957 Ib. 
 A smaller pump, capacity 26,000 U. S. gal. per min., gave a thermal 
 efficiency of 26.63% and a coal consumption of 0.796 Ib. per water 
 H.P.-hour. The cylinders of the larger engine are 7 ft. diam., the play 
 pipe, 6 ft. (Eng'g, Feb. 14, 1913). 
 
 A Humphrey gas pump of 26,000 gal. capacity per min. at 37 ft. head 
 has been installed for irrigation purposes at Del Rio, Texas. It is guar- 
 anteed to deliver not less than 26,000 gal. per min. with a thermal 
 efficiency of 20% when using producer gas of a heating value of not 
 less than 100 B.T.U. per cu. ft. The principal dimensions are: Ex- 
 plosion cylinder, 66 in. diam. X 41 in.; water cylinder, 66 in. X 89 in. 
 long; valve boxes, 66 in. X 73 in. long; number of 5-in. valves, 400; 
 lift, 1 in.; total discharge area of valves, 4160 sq. in.; play pipe diam., 
 66 in., length, including 135 bend, 106 ft. Number of explosions, 12 
 to 20 per min. 
 
 Humphrey pumps without discharge valves are limited to heads of 
 about 15 to 40 ft., but a pump with an intensifier and discharge valves 
 is made for heads up to 150 ft. 
 
 PUMPING BY COMPRESSED AIR THE AIR-LIFT PUMP. 
 
 Air-lift Pump. The air-lift pump consists of a vertical water-pipe 
 with its lower end submerged in a well, and a smaller pipe delivering air 
 into it at the bottom. The rising column in the pipe consists of air 
 mingled with water, the air being in bubbles of various sizes, and is there- 
 fore lighter than a column of water of the same height; consequently the 
 
PtJMPING BY COMPRESSED AIE. 809 
 
 water in the pipe is raised above the level of the surrounding water. 
 This method of raising water was proposed as early as 1797, by Loescher, 
 of Freiberg, and was mentioned by Collon in lectures in Paris in 1876, 
 but its first practical application probably was by Werner Siemens in 
 Berlin in 1885. Dr. J. G. Pohle experimented on the principle in Cali- 
 fornia in 1886, and U. S. patents on apparatus involving it were granted 
 to Pohle and Hill in the same year. A paper describing tests of the air- 
 lift pump made by Randall, Browne and Behr was read before the Tech- 
 nical Society of the Pacific Coast in Feb., 1890. 
 
 The diameter of the pump-column was 3 in., of the air-pipe 0.9 in., and 
 of the air-discharge nozzle 5/s in. The air-pipe had four sharp bends and a 
 length of 35 ft. plus the depth of submersion. 
 
 The water was pumped from a closed pipe-well (55 ft. deep and 10 in. 
 in diameter). The efficiency of the pump was based on the least work 
 theoretically required to compress the air and deliver it to the receiver. 
 If the efficiency of the compressor be taken at 70%, the efficiency of the 
 pump and compressor together would be 70% of the efficiency found for 
 the pump alone. 
 
 For a given submersion (ft) and lift (#), the ratio of the two being kept 
 within reasonable limits, (#) being not much greater than (ft), the effi- 
 ciency was greatest when the pressure in the receiver did not greatly 
 exceed the head 'due to the submersion. The smaller the ratio H * ft, 
 the higher was the efficiency. 
 
 The pump, as erected, showed the following efficiencies: 
 
 For H *- ft = 0.5 1.0 1.5 2.0 
 
 Efficiency =50% 40% 30% 25% 
 
 The fact that there are absolutely no moving parts makes the pump 
 especially fitted for handling dirty or gritty water, sewage, mine water, 
 and acid or alkali solutions in chemical or metallurgical works. 
 
 In Newark, N. J., pumps of this type are at work having a total capacity 
 of 1,000,000 gallons daily, lifting water from three 8-in. artesian wells. 
 The Newark Chemical Works use an air-lift pump to raise sulphuric acid 
 of 1.72 gravity. The Colorado Central Consolidated Mining Co., in one 
 of its mines at Georgetown, Colo., lifts water in one case 250 ft., using a 
 series of lifts. 
 
 For a full account of the theory of the pump, and details of the tests 
 above referred to, see Eng'g News, June 8, 1893. 
 
 Numerous tests of air-lift pumps are described in Greene's "Pumping 
 Machinery." Greene says that the air pipe should be introduced near 
 the bottom of the discharge pipe and should be immersed so that the 
 ratio hi fh is 3 to 1 at the start and 2.2 to 1 in operation, hi is the 
 depth of immersion below the water level and h the height of the dis- 
 charge at the top of the well measured above the water level. Different 
 tests give the following efficiencies for various ratios hi/h. 
 h/hi = 
 
 3.1 to 2.2 0.6 1 1.4 2.4 3.91.5 1 0.660.50.43 
 
 Efficiency, % : 
 
 36 16 to 43 19 to 42 34 to 41 15 to 24 2 50 40 30 25 20 
 
 The efficiency is the ratio of the work done in raising the water to 
 the work of compressing the air. 
 
 The amount of free air required varies according to different manu- 
 facturers. One gives cu. ft. air per min. = LW + 19; another L W H-15; 
 L = lift of water above the water level, in ft., W = cu. ft. of water per 
 min. 
 
 Air-Lifts for Deep Oil- Wells are described by E. M. Ivens, in Trans. 
 A. S. M . E. 1909, p. 341. The following are some results obtained in wells 
 in Evangeline, La.: 
 
 Cu. ft. free air per minute, displacement of 
 
 compressor 650 442 702 536 
 
 Cu. ft. oil pumped per minute 4.35 4.87 13.7 5.54 
 
 Air pressure at well, Ibs. per sq. in 155 200 202 252 
 
 Pumping head, from oil level while pumping, ft. 1155 1081 1076 917 
 
 Submergence, from oil level to air entrance, ft. 358 412 419 583 
 
 Submergence -s- total ft. of vertical pipe, %. . . 23.6 27.6 28 39 
 
 Pumping efficiency, % 9.3 13.4 19.5 10.3 
 
810 PUMPS AND PUMPING ENGINES. 
 
 Artesian Well Pumping by Compressed Air. H. Tipper, Eng. News, 
 Jan. 16, 1908, mentions cases where 1-in. air lines supplied air for 6-in. 
 Wells, with the inside air-pipe system; the length of the pipe was 300 ft. 
 from the well top, and another 350 ft. to the compressor. The wells 
 pumped 75 gals, per min., using 200 cu. ft. of air, the efficiency being 61/2%. 
 Changing the pipes to 21/2 in. above the well, and 2 in. in the well, and 
 putting an air receiver near the compressor, raised the delivery to 180 
 gals, per min., with a little less air, and the efficiency to 23%. A large 
 receiver capacity, a large pipe above ground, a submergence of 55%, 
 well piping proportioned for a friction loss of not over 5%, with lifts not 
 over 200 ft., gave the best results, 1 gal. of water being raised per cu. ft. 
 of air. The utmost net efficiency of the air-lift is not over 25 to 30%. 
 
 Eng. News, June 18, 1908, contains an account of tests of eleven wells 
 at Atlantic City. The Atlantic City wells were 10 in. diam., water pipes, 
 4 to 51/4 in., air pipes, 3/ 4 to 11/4 in. The maximum lift of the several 
 wells ranged from 26 to 40 ft., the submergence, 37 to 49 ft., ratio of sub- 
 mergence to lift, 0.9 to 1.8, submergence % of length of pipe, 53 to 64. 
 Capacity test, 3,544,900 gals, in 24 hrs., mean lift, 26.88 ft., air pressure, 
 31 Ibs., duty of whole plant, 19,900,000 ft. Ibs. per 1000 Ibs. of steam used 
 by the compressors. Two-thirds capacity test, delivery, 2,642,900 gals., 
 mean lift, 25.43 ft., air pressure, 26 Ibs., duty, 24,207,000. 
 
 An article in The Engineer (Chicago), Aug. 15, 1904, gives the following 
 formulae and rules for the design of air-lifts of maximum efficiency. The 
 authority is not given. 
 
 Ratio of area of air pipe to area of water pipe, 0.16. 
 
 Submerged portion = 65% of total length of pipe. 
 
 Economical range of submersion ratio, 55 to 80%. 
 
 Velocity of air in air pipe, not over 4000 ft. per min. 
 
 Volume of air to raise 1 cu. ft. of water, 3.9 to 4.5 cu. ft. 
 
 C cu. ft. of water raised per min., A = cu. ft. of air used, L =* lift 
 above water level, D = submergence, in feet. 
 
 A = LC * 16.824; C = 8.24 AD -r- L*. 
 
 Where L exceeds 180 ft. it will be more economical to use two or more 
 air-lifts in series. 
 
 THE HYDRAULIC RAM. 
 
 Efficiency. The hydraulic ram is used where a considerable flow of 
 water with a moderate fall is available, to raise a small portion of that flow 
 to a height exceeding that of the fall. The following are rules given by 
 Eytelwem Us the results of his experiments (from Rankine) 
 . et Q be the whole supply of water in cubic feet per second, of which q 
 is lifted to the height h above the pond, and Q q runs to waste at the 
 depth // below the pond; L, the length of the supply-pipe, from the pond 
 to the waste-clack; D, its diameter in feet; then 
 
 Efficiency, ^J^ - = 1.12-0.2 T^JJ , when ^does not exceed 20; 
 or 
 
 1-4- (1 4- ft/10 H) nearly, when h/H does not exceed 12. 
 
 D'Aubuisson gives Q^ =1.42-0.28 -%/ - 
 
 . Clark, using five sixths of the values given by D'Aubuisson's formula, 
 gives: 
 
 Ratio of lift to fall. 4 6 8 10 12 14 16 18 20 22 24 
 Efficiency per cent. 72 61 52 44 37 31 25 19 14 9 4 
 
 The efficiency as calculated by the two formulas given above is nearly 
 the same for high ratios of lift, but for low ratios there is considerable 
 difference. For example: 
 
 Let Q = 100, H = 10, II + li = ' 20 40 100 200 
 Efficiency, D'Aubuisson's formula, % 80 72 44 14 
 q = effy. X QH -J- (H + h)= 40 18 4.4 0.7 
 
 Efficiency by Rankine's formula, % 662/3 65.9 41.4 13.4 
 D'Aubuisson's formula is that of the machine itself, on the basis that 
 
 
THE HYDBAXJLIC RAM. 
 
 811 
 
 the energy put into the machine is that of the whole" column of water, 
 Q, falling through the height h and that the energy delivered is that of q 
 raised through the whole height above the ram, H + h; while Rankine's 
 efficiency is that of the whole plant, assuming that the energy put in is 
 
 and that the work done is 
 j ram but only from that of 
 
 rr-s *- the one in harmony with 
 
 the usual definition of efficiency. It also is applicable (as Rankine's is 
 not) to the case of a ram which uses the quantity Q from one source of 
 supply to pump water of different quality from a source at the level of 
 the ram. 
 
 An extensive mathematical investigation of the hydraulic ram, by 
 L. F. Harza, is contained in Bulletin No. 205 of the University of Wiscon- 
 sin, 1908, together with results of tests of a Rife "hydraulic engine," 
 which appear to verify the theory. It was found both by theory and by 
 experiment that the efficiency bears a relation to the velocity in the 
 drive pipe. From plotted diagrams of the results the following figures 
 (roughly approximate) are taken: Length of 2-in. drive pipe, 85.4 ft.; 
 supply head, 8.2 ft. 
 
 Max. vel. in drive pipe, ft. per sec 1.5 2 3 4 56 
 
 Efficiency of machine, %. 
 
 Pumping head, ft 2.6 
 
 12.3 
 23.2 
 43.5 
 63.1 
 
 60 
 60 
 55 
 
 30 
 60 
 65 
 60 
 60 
 
 20 
 45 
 53 
 53 
 55 
 
 15 
 33 
 40 
 42 
 50 
 
 18 
 20 
 30 
 
 28 
 
 
 
 
 
 
 
 The author of the paper concludes that the comparison of experiment 
 and theory has demonstrated the practicability of the logical design of 
 a hydraulic ram for any given working conditions. 
 
 An interesting historical account, with illustrations, of the develop- 
 ment of the hydraulic ram, with a description of PearsaH's hydraulic 
 engine, is given by J. Richards in Jour. Assn. Eng'g Societies, Jan., 1898. 
 For a description of the Rife hydraulic engine see Eng. News, Dec. 31. 
 1896. 
 
 The Columbia Steel Co., Portland, Ore., furnished the author in July, 
 1908, records of tests of four hydraulic rams, from which the following 
 is condensed, the efficiency, by D'Aubuisson's formula, being calculated 
 from the data given. L = length in ft. and D = diam. in ins. of the 
 drive pipe, I and d, length and diameter of the discharge pipe. 
 
 Size of Ram. 
 
 H 
 
 h + 
 H 
 
 Q* 
 
 <Z* 
 
 L 
 
 D 
 
 I 
 
 d 
 
 Effy. 
 % 
 
 Ins. 
 3 
 
 Ft. 
 4 
 
 F.t. 
 28 
 
 35 
 
 3.5 
 
 Ft. 
 28 
 
 Ins. 
 3 
 
 Ft. 
 1008 
 
 Ins. 
 U/2 
 
 58.9 
 
 41/9 
 
 5 
 
 45 
 
 100 
 
 8 
 
 40 
 
 41/2 
 
 325 
 
 
 72.0 
 
 6 
 
 12 
 
 36.4 
 
 200 
 
 50.5 
 
 60 
 
 41/2 
 
 945 
 
 21/2 
 
 76.6 
 
 6 
 
 37.6 
 
 144.1 
 
 6.26 
 
 1.15 
 
 192.5 
 
 6 
 
 1785, 
 
 lot 
 
 70.4 
 
 
 
 
 
 
 
 
 
 
 
 * Q and q are in gallons per min., except the last line, which is In cu. 
 ft. per sec. 
 
 f Eleven rams discharge into one 10-in. jointed wood pipe. The loss 
 of head in the drive pipe was 0.7 ft., and in the discharge pipe, 2.7 ft. On 
 another test 1 cu. ft. per sec. was deliyered with less than 5 cu. ft. enter- 
 ing the drive pipe. Taking 5 cu. ft. gives 76.6% efficiency. 
 
 A description and record of test of the Foster "impact engine" is given 
 in Eng'g News, Aug. 3, 1905. Two engines are connected into one 8-in. 
 delivery pipe. Using the same notation as before, the data of the tests 
 of the two engines are as follows: Q, gal. per min., 582, 578; q, 232, 228; 
 H, 36.75, 37.25; H + h, 84, 84; strokes per min., 130, 130; Effy. (D'Aubu- 
 isson), 91.23, 89.06%. 
 
 Prof. R. C. Carpenter (Eng'g Mechanics, 1894) reports the results of 
 four tests of a ram constructed by Rumsey & Co., Seneca Falls. The 
 supply-pipe used was 11/2 inches in diameter, about 50 feet long, with 3 
 elbows. Each run was made with a different stroke for the waste-valve, 
 the supply and .delivery head being constant;. the obje.ct of the expert- 
 
812 
 
 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 ment was to find that stroke of clack-valve which would give the highest 
 efficiency. 
 
 Length of stroke, per cent 
 
 100 
 52 
 5.67 
 19.75 
 297 
 1615 
 64.1 
 
 80 
 56 
 5.77 
 19.75 
 296 
 1567 
 64.7 
 
 60 
 61 
 5.58 
 19.75 
 301 
 1518 
 70.2 
 
 46 
 66 
 5.65 
 19.75 
 297.5 
 1455.5 
 71.4 
 
 Number of strokes per minute 
 
 Delivery liead. feet of water . . 
 
 Total water pumped poimds 
 
 Total water supplied, pounds 
 Efficiency per cent . 
 
 
 The highest efficiency realized was obtained when the clack-valve trav- 
 eled 60% of its full stroke, the full travel being 15/ 16 in. 
 
 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 Water under high pressure (700 to 2000 Ibs. per sq. in. and upwards^ 
 affords a satisfactory method of transmitting power to a distance, espe- 
 cially for the movement of heavy loads at small velocities, as by cranes 
 and elevators. The system consists usually of one or more pumps ca- 
 pable of developing the required pressure; accumulators, which are vertical 
 cylinders with heavily-weighted plungers passing through stuffing-boxes 
 in the upper end, by which a quantity of water may be accumulated at the 
 pressure to which the plunger is weighted; the distributing-pipes; and the 
 presses, cranes, or other machinery to be operated. 
 
 The earliest important use of hydraulic pressure probably was in the 
 Bramah hydraulic press, patented in 1796. Sir. W. G. Armstrong in 
 1846 was one of the pioneers in the adaptation of the hydraulic system 
 to cranes. The use of the accumulator by Armstrong led to the extended 
 use of hydraulic machinery. Recent developments and applications of 
 the system are largely due to Ralph Tweddell, of London, and Sir Joseph 
 Whitworth. Sir Henry Bessemer, in his patent of May 13, 1856, No. 
 1292, first suggested the use of hydraulic pressure for compressing steel 
 ingots while in the fluid state. 
 
 The Gross Amount of Energy of the water under pressure stored in 
 the accumulator, measured in foot-pounds, is its volume in cubic feet X 
 its pressure in pounds per square foot. The horse-power of a given 
 quantity steadily flowing is H.P. = 144 pQ/550 =0.2618 pQ, in which Q is 
 the quantity flowing in cubic feet per second and p the pressure in pounds 
 per square inch. 
 
 The loss of energy due to velocity of flow in the pipe is calculated as 
 follows (R. G. Blaine, Eng'g, May 22 and June 5, 1891): 
 
 According to Darcy, every pound of water loses A4L/D times its kinetic 
 energy, or energy due to its velocity, in passing along a straight pipe L 
 feet in length and D feet diameter, where A is a variable coefficient. For 
 
 clean cast-iron pipes it may be taken as A =0.005 ( 1 +7^7)) or f r ^i- 
 
 ameter in inches = d. 
 
 d = 1/2 1 2 3 4 5 6 7 8 9 10 12 
 
 A = .015 .01 .0075 .00667 .00625 .006 .00583 .00571 .00563 .00556 .0055 .00542 
 
 The loss of energy per minute is 60 X 62.36 Q X -jj ~ , and the 
 
 horse-power wasted in the pipe is W = - ^j~ - , in which A 
 
 varies with the diameter as above, p = pressure at entrance in pounds 
 per square inch. Values of 0.6363 A for different diameters of pipe in 
 inches are: 
 d = 1/2 12 3 4 5 6 7 8 
 
 .00954 .00636 .00477 .00424 .00398 .00382 .00371 .00363 .00358 
 9 10 12 
 
 .00353 .00350 .00345 
 
 Efficiency of Hydraulic Apparatus. The useful effect of a direct 
 hydraulic plunger or ram is usually taken at 93%. The following is 
 given as the efficiency of a ram with chain-and-pulley multiplying gear 
 properly proportioned and well lubricated: 
 
 Gear 2 to 1 4 to 1 6 to 1 8 to 1 10 to 1 12 to 1 14 to 1 16 to 1 
 Eff'y 0.80 0.76 0.72 0.67 0.63 0.59 0.54 0,50 
 
HYDRAULIC-PRESSURE TRANSMISSION. 813 
 
 With large sheaves, small steel pins, and wire rope for multiplying 
 pear the efficiency has been found as high as 66% for a multiplication of 
 20 to 1. 
 
 Henry Adams gives the following formula for effective pressure in 
 cranes and hoists: P accumulator pressure in pounds per square inch; 
 m = ratio of multiplying power; E = effective pressure in pounds per 
 square inch, including all allowances for friction; 
 E= P (0.84 -0.02m). 
 
 J. E. Tuit (Eng'g, June 15, 1888) describes some experiments on the 
 friction of hydraulic jacks from 31/4 to 135/g-mch 'diameter, fitted with 
 cupped leather packings. The friction 'loss varied from 5.6% to 18.8% 
 according to the condition of the leather, the distribution of the load on 
 the ram, etc. The friction increased considerably with eccentric loads. 
 With hemp packing a plunger, 14-inch diameter, showed a friction loss 
 of from 11.4% to 3.4%, the load being central, and from 15.0% to 7.6% 
 with eccentric load, the percentage of loss decreasing in both cases with 
 increase of load. 
 
 Thickness of Hydraulic Cylinders. Sir W. G. Armstrong gives the 
 following, for cast-iron cylinders, for a pressure of 1000 Ibs. per sq. in.: 
 Diam. of cylinder, inches 
 
 2 4 6 8 10 12 16 20 24 
 
 Thickness, inches 
 
 0.832 1.146 1.552 1.875 2.222 2.578 3.19 3.69 4.11 
 
 For any other pressure multiply by the ratio of that pressure to 1000. 
 These figures correspond nearly to the formula t = 0.175 d + 0.48, in 
 which t = thickness and d = diameter in inches, up to 16 inches diam- 
 eter, but for 20 inches diameter the addition 0.48 is reduced to 0.19 and 
 at 24 inches it disappears. For formulae for thick cylinders see page 339. 
 
 Cast iron should not be used for pressures exceeding 2000 Ibs. per 
 square inch. For higher pressures steel castings or forged steel should 
 be used. For working pressures of 750 Ibs. per square inch the test 
 pressure should be 2500 Ibs. per square inch, and for 1500 Ibs. the test 
 pressure should not be less than 3500 Ibs. 
 
 Speed of Hoisting by Hydraulic Pressure. The maximum allow- 
 able speed for warehouse cranes is 6 feet per second ; for platform cranes 
 4 feet per second; for passenger and wagon hoists, heavy loads, 2 feet per 
 second. The maximum speed under any circumstances should never 
 exceed 10 feet per second. 
 
 The Speed of Water Through Valves should never be greater than 
 100 feet per second. 
 
 Speed of Water Through Pipes. Experiments on water at 1600 
 Ibs. pressure per square inch flowing into a flanging-machine ram, 20- 
 inch diameter, through a i/2-inch pipe contracted at one point to i/4-inch, 
 gave a velocity of 114 feet per second in the pipe, and 456 feet at the 
 reduced section. Through a i/2-mch pipe reduced to 3/ 8 _i n ch at one 
 point the velocity was 213 feet per second in the pips and 381 feet at the 
 reduced section. In a i/2-inch pipe without contraction the velocity 
 was 355 feet per second. 
 
 For many of the above notes the author is indebted to Mr. John Platt, 
 consulting engineer, of New York. 
 
 High-pressure Hydraulic Presses in Iron-works are described by 
 R. M. Daelen, of Germany, in Trans. A. I M. E., 1892. The following 
 distinct arrangements used in different systems of high-pressure hydrau- 
 lic work are discussed and illustrated: 
 
 1. Steam-pump, with fly-wheel and accumulator. 
 
 2. Steam-pump, without fly-wheel and with accumulator. 
 
 3. Steam-pump, without fly-wheel and without accumulator. 
 
 In these three systems the valve-motion of the working press is oper- 
 ated in the high-pressure column. This is avoided in the following: 
 
 4. Single-acting steam-intensifier without accumulator. 
 
 5. Steam-pump with fly-wheel, without accumulator and with DiDe- 
 circuit. 
 
 6. Steam-pump with fly-wheel, without accumulator and without 
 pipe-circuit. 
 
 The disadvantages of accumulators are thus stated: The weighted 
 
814 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 plungers which formerly served in most cases as accumulators, cause 
 violent shocks in the pipe-line when changes take place in the move- 
 ment of the water, so that in many places, in order to avoid bursting 
 from this cause, the pipes are made exclusively of forged and bored steel. 
 The seats and cones of the metallic valves are cut by the water (at high 
 speed), and in such cases only the most careful maintenance can prevent 
 great losses of power. 
 
 Hydraulic Power in Ixmdon. The general principle involved is 
 pumping water into mains laid in the streets, from which service-pipes 
 are carried into the houses to work lifts or three-cylinder motors when 
 rotary power is required. In some cases a small Pelton wheel has been 
 tried, working under a pressure of over '700 Ibs. on the square inch. 
 Over 55 miles of hydraulic mains are at present laid (1892). 
 
 The reservoir of power consists of capacious accumulators, loaded to 
 800 Ibs. per sq. in. 
 
 The engine-house contains six sets of triple-expansion pumping en- 
 gines. Each pump will deliver 300 gallons of water per minute. 
 
 The water delivered from the main pumps passes into the accumu- 
 lators. The rams are 20 inches in diameter, and have a stroke of 23 
 feet. They are each loaded with 110 tons of slag, contained in a wrought- 
 iron cylindrical box suspended from a cross-head on the top of the ram. 
 One of the accumulators is loaded a little more heavily than the other, 
 so that they rise and fall successively; the more heavily loaded actuates a 
 stop-valve on the main steam-pipe. 
 
 The mains in the public streets are so constructed and laid as to be per- 
 fectly trustworthy and free from leakage. Every pipe and valve used 
 throughout the system is tested to 2500 Ibs. per sq. in. before being placed 
 on the ground and again tested to a reduced pressure in the trenches to 
 insure the perfect tightness of the joints. The jointing material used is 
 gutta-percha. 
 
 The average rate obtained by the company is about 3 shillings per 
 thousand gallons. The principal use of the power is for intermittent 
 work in cases where direct pressure can be employed, as, for instance, 
 passenger elevators, cranes, presses, warehouse hoists, etc. 
 
 An important use of the hydraulic power is its application to the 
 extinguishing of fire by means of Greathead's injector hydrant. By the 
 use of these hydrants a continuous fire-engine is available. 
 
 Hydraulic Riveting-machines. Hydraulic riveting was introduced 
 in England by Mr. R. H. Tweddell. Fixed riveters were first used about 
 1868. Portable riveting-machines were introduced in 1872. 
 
 The riveting of the large steel plates in the Forth Bridge was done by 
 small portable machines working with a pressure of 1000 Ibs. per square 
 inch. In exceptional cases 3 tons per inch were used. (Proc. Inst. M. E.. 
 May, 1889.) 
 
 An application of hydraulic pressure invented by Andrew Higginson, 
 of Liverpool, dispenses with the necessity of accumulators. It consists 
 of a three-throw pump driven by shafting or worked by steam and 
 depends partially upon the work accumulated in a heavy fly-wheel. 
 The water in its passage from the pumps and back to them is in con- 
 stant circulation at a very feeble pressure, requiring a minimum of 
 power to preserve the tube of water ready for action at the desired 
 moment, when by the use of a tap the current is stopped from going 
 back to the pumps, and is thrown upon the piston 9f the tool to be set 
 in motion. The water is now confined, and the driving-belt or steam- 
 engine, supplemented by the momentum of the heavy fly-wheel, is 
 employed in closing up the rivet, or bending or forging the object sub- 
 jected to its operation. 
 
 Hydraulic Forging-press. 
 
 For a very complete illustrated account of the development of the 
 hydraulic forging-press, see a paper by R. H. Tweddell in Proc. Inst. 
 C. E., vol. cxvii. 1893-4. 
 
 In the Allen forging-press the force-pump and the large or main cylinder 
 of the press are in direct and constant communication. There are no 
 intermediate valves of any kind, nor has the pump any clack-valves, 
 but it simply forces its cylinder full of water direct into the cylinder of 
 the press, and receives the same water, as it were, back again on the return 
 
HYDRAULIC-PRESSURE TRANSMISSION. 815 
 
 stroke. Thus, when both cylinders and the pipe connecting them are 
 full, the large ram of the press rises and falls simultaneously with each 
 stroke of the pump, keeping up a continuous oscillating motion, the ram, 
 of course, traveling the shorter distance, owing to the larger capacity of 
 the press cylinder. (Journal Iron and Steel Institute, 1891. See also 
 illustrated article in "Modern Mechanism," page 668.) 
 
 A 2000-ton forging-press erected at the Couillet forges in Belgium is 
 described in Eng. and M. Jour., Nov. 25, 1893. The press is composed 
 essentially of two parts the press itself and the compressor. The com- 
 pressor is formed of a vertical steam-cylinder and a hydraulic cylinder. 
 The piston-rod of the former forms the piston of the latter. The hy- 
 draulic piston discharges the water into the press proper. The distribu- 
 tion is made by a cylindrical balanced valve; as soon as the pressure is 
 released the steam-piston falls automatically under the action of gravity. 
 During its descent the steam passes to the other face of the piston to 
 reheat the cylinder, and finally escapes from the upper end. 
 
 When steam enters under the piston of the compressor-cylinder the 
 piston rises, and its rod forces the water into the press proper. The 
 pressure thus exerted on the piston of the latter is transmitted through a 
 cross-head to the forging which is upon the anvil. To raise the cross- 
 head two small single-acting steam-cylinders are used, their piston-rods 
 being connected to the cross-head: steam acts only on the pistons of these 
 cylinders from below. The admission of steam to the cylinders, which 
 stand on top of the press frame, is regulated by the same lever which 
 directs the motions of the compressor. The movement given to the dies 
 is sufficient for all the ordinary purposes of forging. 
 
 A speed of 30 blows per minute has been attained. A double press on 
 the same system, having two compressors and giving a maximum pressure 
 of 6000 tons, has been erected in .the Krupp works, at Essen. 
 
 Hydraulic Engine driving an Air-compressor and a Forging- 
 hammer. ( Iron Age, May 12, 1892.) The great hammer in Terni, 
 near Rome, is one of the largest in existence. Its falling weight amounts 
 to 100 tons, and the foundation belonging to it consists of a block of cast 
 iron of 1000 tons. The stroke is 16 feet 43/4 inches; the diameter of the 
 cylinder 6 feet 31/2 inches; diameter of piston-rod 133/4 inches; total 
 height of the hammer, 62 feet 4 inches. The power to work the hammer, 
 as well as the two cranes of 100 and 150 tons respectively, and other 
 auxiliary appliances belonging to it, is furnished by four air-compressors 
 coupled together and driven directly by water-pressure engines, by 
 means of which the air is compressed to 73.5 pounds per square inch. 
 The cylinders of the water-pressure engines, which are provided with a 
 bronze lining, have a 133/4-inch bore. The stroke is 473/4 inches, with a 
 pressure of water on the piston amounting to 264.6 pounds per square 
 inch. f The compressors are bored out to 31 1/2 inches diameter, and have 
 473/4-inch stroke. Each of the four cylinders requires a power equal to 
 280 horse-power. The compressed air is delivered into huge reservoirs, 
 where a uniform pressure is kept up by means of a suitable water-column. 
 
 The Hydraulic Forging Plant at Bethlehem, Pa., is described in a 
 paper by R. W. Davenport, read before the Society of Naval Engineers 
 and Marine Architects, 1893. It includes two hydraulic forging-presses 
 complete, with engines and pumps, one of 1500 and one of 4500 tons 
 capacity, together with two Whitworth hydraulic traveling forging- 
 cranes and other necessary appliances for each press; and a complete 
 fluid-compression plant, including a press of 7000 tons capacity and a 
 125-ton, hydraulic traveling crane for. serving it _(the. upper and lower 
 heads of this press weighing respectively about 135 and 120 tons). 
 
 A later forging-press designed by John Fritz, for the Bethlehem 
 Works, of 14,000 tons capacity, is run by engines and pumps of 15,000 
 horse-power. The plant is served by four open-hearth steel furnaces of 
 a united capacity of 120 tons of steel per heat. 
 
 The Davy High-speed Steam-hydraulic Forging Press is described 
 in the Iron Age, April 15, 1909. It is built in sizes ranging from 150 to 
 12,000 tons capacity. In the four-column type, in which all but the 
 smaller sizes are built, there is a central press operated by hydraulic 
 pressure from a steam intensifier, and two steam balance cylinders 
 carried on top of the entablature. A single lever controls the press. 
 The operator admits steam to the balance cylinders, lifting the cross- 
 
816 FUEL. 
 
 head and the main plunger, and forcing the water from the press cylinder 
 into the water cylinder of the intensifier. Exhausting the steam from 
 the balance cylinders, allows the plunger to descend and rest on the 
 forging. To and fro motions of the lever, slow or fast as the operator 
 desires, up to 120 a minute, then are made to reduce the forging. The 
 smaller, or single frame, type has only one balance cylinder, immediately 
 above the press cylinder. The Davy press is made in the United States 
 by the United Engineering & Foundry Co., Pittsburgh. 
 
 Some References on Hydraulic Transmission. Reuleaux's " Con- 
 structor;" "Hydraulic Motors, Turbines, and Pressure-engines," G. 
 Bodmer, London, 1889; Robinson's "Hydraulic Power and Hydraulic 
 Machinery," London, 1888; Colyer's "Hydraulic Steam, and Hand-power 
 Lifting and Pressing Machinery " London, 1881, See also Engineering 
 (London), Aug. 1, 1884, p. 99; March 13, 1885, p. 262; May 22 and June 
 5, 1891, pp. 612, 665; Feb. 19, 1892, p. 25; Feb. 10, 1893, p. 170. 
 
 FUEL. 
 
 Theory of Combustion of Solid Fuel. (From Rankine, somewhat 
 altered.) The ingredients of every kind of fuel commonly used may be 
 thus classed: (1) Fixed or free carbon, which is left in the form of char- 
 coal or coke after the volatile ingredients of the fuel have been distilled 
 away. These ingredients burn either wholly in the solid state (C to COs), 
 or part in the solid state and part in the gaseous state (CO + O = CO2), 
 the latter part being first dissolved by previously formed carbon dioxide 
 by the reaction CO2 + C = 2 CO. Carbon monoxide, CO, is produced 
 when the supply of air to the fire is insufficient. 
 
 (2) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, etc., all of 
 which must pass into the gaseous state before being burned. 
 
 If mixed on their first issuing from amongst the burning carbon with a 
 large quantity of hot air, these inflammable gases are completely burned 
 with a transparent blue flame, producing carbon dioxide and steam. 
 When mixed with cold air they are apt to be chilled and pass off unburned. 
 When raised to a red heat, or thereabouts, before being mixed with a 
 sufficient quantity of air for perfect combustion, they disengage carbon 
 in fine powder, arid pass to the condition partly of marsh gas, CH 4 and 
 partly of free hydrogen; and the higher the temperature, the greater is 
 the proportion of carbon thus disengaged. 
 
 If the disengaged carbon is cooled below the temperature of ignition 
 before coming in contact with oxygen, it constitutes, while floating in the 
 gas, smoke, and when deposited on solid bodies, soot. 
 
 But if the disengaged carbon is maintained at the temperature of igni- 
 tion and supplied with oxygen sufficient for its combustion, it burns 
 while floating in the inflammable gas, and forms red, yellow, or white 
 flame. The flame from fuel is the larger the more slowly its combustion 
 is effected. The flame itself is apt to be chilled by radiation, as into the 
 heating surface of a steam-boiler, so that the combustion is not completed, 
 and part of the gas and smoke pass off unburned. 
 
 (3) Oxygen or hydrogen either actually forming water, or existing in 
 combination with the other constituents in the proportions which form 
 water. Such quantities of oxygen and hydrogen are to be left out of 
 account in determining the heat generated by the combustion. If the 
 quantity of water actually or virtually present in each pound of fuel is so 
 great as to make its latent heat of evaporation worth considering, that 
 heat is deducted from, the total available heat of combustion of the fuel. 
 
 (4) Nitrogen, either free or in combination with other constituents. 
 This substance is simply inert. 
 
 (5) Sulphide of iron, which exists in coal and is detrimental, as 
 tending to cause spontaneous combustion. 
 
 (6) Other inert mineral compounds of various kinds form the ash 
 left after complete combustion of the fuel, and also the clinker or glassy 
 material produced by fusion of the ash, which tends to choke the grate. 
 
 The imperfect combustion of carbon, making carbon monoxide, 
 produces less than one-third of the heat which is yielded by the com- 
 plete combustion, making carbon dioxide, 
 
FUEL. 
 
 817 
 
 The total heat of combustion of any compound of hydrogen and carbon 
 is nearly the sum of the quantities of heat which the constituents would 
 produce separately by their combustion. (Marsh-gas is an exception.) 
 
 In computing the total heat of combustion of compounds containing 
 oxygen as well as hydrogen and carbon, the following principle is to be 
 observed : When hydrogen and oxygen exist in a compound in the proper 
 proportion to form water (that is, by weight one part of hydrogen to 
 eight of oxygen), these constituents have no effect on the total heat of 
 combustion. If hydrogen exists in a greater proportion, only the surplus 
 of hydrogen above that which is required by the oxygen is to be taken 
 into account. 
 
 The following is a general formula (Dulong's) for the total heat of com- 
 bustion of any compound of carbon, hydrogen, and oxygen: 
 
 Let <7, //, and O be the fractions of one pound of'the compound, which 
 consists respectively of carbon, hydrogen, and oxygen, the remaindei 
 being nitrogen, ash, and other impurities. Let h be the total heat of 
 combustion of one pound of the compound in British thermal units. 
 
 Then h = 14,600 C -H 62,000 (H - Vs 0). 
 
 Oxygen and Air Required for the Combustion of Carbon, Hydro* 
 gen, etc. 
 
 Chemical Reaction. 
 
 Lbs. 
 perlb. 
 Fuel. 
 
 Lbs.N, 
 =3.32 O 
 
 Air per 
 lb.= 
 4.32 O. 
 
 Gase- 
 ous 
 Prod- 
 ucts 
 per Ib. 
 
 Heat of 
 Combus- 
 tion. 
 B.T.U. 
 per Ib. 
 
 CtoCCfe C+2O=CO2 
 C to CO C + O = CO 
 CO to CO 2 CO + = CO 2 
 H to H 2 O 2 H + O = H 2 O 
 CH 4 toCO 2 ) CH 4 + 4O 
 andH 2 | =CO 2 + 2H 2 O 
 StoSO 2 S + 2O = SO 2 
 CO to COa, per Ib. of C or pe 
 
 i% 
 
 8 4/? 
 
 4 
 
 1 
 r 2 1/3 11 
 
 8.85 
 4.43 
 1.90 
 26.56 
 
 13.28 
 3.32 
 
 5. Of CO 
 
 11.52 
 5.76 
 2.47 
 34.56 
 
 17.28 
 4.32 
 
 , 14,600 
 
 12.52 
 6.76 
 3.47 
 35.56 
 
 18.28 
 5.32 
 
 -4450 
 
 14,600 
 4,450 
 4,350 
 62,000 
 
 23,600 
 4,050 
 = 10,150. 
 
 For heat of combustion of various fuels see Heat, page 560. 
 
 Analyses of Gases of Combustion. The following are selected 
 from a large number of analyses of gases from locomotive boilers, to 
 show the range of composition under different circumstances (P. H. 
 Dudley, Trans. A. I. M. E., iv, 250): 
 
 Test. 
 
 CO 2 
 
 CO 
 
 O 
 
 N 
 
 
 1 
 
 13.8 
 
 2.5 
 
 2.5 
 
 81.6 
 
 No smoke visible. 
 
 2 
 
 11.5 
 
 
 
 6 
 
 82.5 
 
 Old fire, escaping gas white, engine working 
 hard. 
 
 3 
 
 8.5 
 
 
 8 
 
 83 
 
 Fresh fire, much black gas, engine working 
 hard. 
 
 4 
 5 
 
 2.3 
 5.7 
 
 
 17.2 
 14.7 
 
 80.5 
 79.6 
 
 Old fire,damper closed, engine standing still. 
 '* smoke white, engine working hard. 
 
 6 
 
 8 
 
 8.4 
 12 
 3.4 
 
 1.2 
 
 1 
 
 8.4 
 4.4 
 16.8 
 
 82 
 82.6 
 76.8 
 
 New fire, engine not workingjhard. 
 Smoke black, engine not working hard, 
 dark, blower on, engine standing still. 
 
 9 
 
 6 
 
 
 13.5 
 
 81.5 
 
 " white, engine working hard. 
 
 In analyses on the Cleveland and Pittsburgh road, in every instance 
 when the smoke was the blackest, there was found the greatest percent- 
 age of unconsumed oxygen in the product, showing that something 
 besides the mere presence of oxygen is required to effect the combustion 
 of the volatile carbon of fuels. (What is needed is thorough mixture of 
 the oxygen with the volatile gases in a hot combustion chamber.) 
 
 Temperature of the Fire. (Rankine, S. E., p. 283.) By temper- 
 ature of the fire is meant the temperature of the products of combustion 
 at the instant that the combustion is complete. The elevation of that 
 temperature above the temperature at which the air and the fuel are 
 supplied to the furnace may be computed by dividing the total heat of 
 
818 
 
 FUEL. 
 
 combustion of one Ib. of fuel by the weight and by the nicaii specific 
 heat of the whole products of combustion, and of the air employed for 
 their dilution under constant pressure. 
 
 Temperature of the Fire, the Fuel Containing Hydrogen and 
 Water. The following formula is developed in the author's " Steam- 
 boiler Economy" on the assumptions that all the hydrogen and the 
 water exist in the combustion chamber as superheated steam at the tem- 
 perature of the fire, and that the specific heat of the gases is a constant, 
 = 0,237. The last assumption is probably largely in error, since it is 
 now known that the specific heat of gases increases with the tempera- 
 ture. (See page 564. ) The formula will give approximate results, how- 
 ever, and is sufficiently accurate when relative figures only are desired. 
 
 Let C, H, O, and JV represent respectively the percentages of carbon, 
 hydrogen, oxygen, and water in a fuel, and / the pounds of dry gas per 
 pound of fuel, = COz+ N + excess air, then the theoretical elevation ol 
 the temperature of the fire above the temperature of the atmosphere, 
 = 616 (7 + 2220 H - 327 O - 44 W 
 /+0.02 W + O.IS H 
 
 EXAMPLE. Required the maximum temperature obtainable by burn- 
 ing moist wood of the composition C, 38; //, 5; O, 32; ash, 1; moisture 24; 
 the dry gas being 15 Ibs. per pound of wood, and the temperature of the 
 atmosphere 62. 
 
 T _616 X38 +2220 X5 -327 X 32 - 44 X 24 _ _ 
 
 15+0.02X24+0.18X5 
 
 Rise of Temperature in Combustion of Gases. (Eng'g, March 
 12 and April 2, 1886.) It is found that the temperatures obtained by 
 experiment fall short of those obtained by calculation. Three theories 
 have been given to account for this: 1. The cooling effect of the sides of 
 the containing vessel; 2. The retardation of the evolution of heat caused 
 by dissociation; 3. The increase of the .specific heat of the gases at very 
 high temperatures. The calculated temperatures are obtainable 9nly on 
 the condition that the gases shall combine instantaneously and simulta- 
 neously throughout their whole mass. This condition is practically im- 
 possible in experiments. The gases formed at the beginning of an explo- 
 sion dilute the remaining combustible gases and tend to retard or check 
 the combustion of the remainder. 
 
 CLASSIFICATION OF SOLID FUELS. 
 
 Gruner classifies solid fuels as follows (Eng'g and M'g Jour., July, 1874). 
 
 Name of Fuel. 
 
 Ratio TPJ. 
 O+N* 
 
 Proportion of Coke of 
 Charcoal yielded by 
 the Dry Pure Fuel. 
 
 
 H 
 
 
 Pure cellulose 
 
 8 
 
 0.28@ 0.30 
 
 Wood (cellulose and encasing matter) . . 
 Peat and fossil fuel 
 
 7 
 6@ 5 
 
 .30 .35 
 .35 @ 40 
 
 
 5 
 
 .40@ .50 
 
 Bituminous coals 
 
 4 @ 1 
 
 50 @ 90 
 
 Anthracite 
 
 1 @0.75 
 
 .90 @ .92 
 
 * The nitrogen rarely exceeds 1 per cent of the weight of the fuel. 
 
 Progressive Change from Wood to Graphite. 
 
 (J. S. Newberry in Johnson's Cyclopedia,.) 
 
 
 1 
 
 . 
 
 J 
 
 - 
 
 IN 
 
 t 
 
 || 
 
 . 
 
 o. . 
 
 
 
 
 
 
 
 .tJ SQ 
 
 
 '3 
 
 
 
 
 fr 
 
 H! 
 
 A 
 
 M 
 
 C> 
 
 ^ 
 
 V 
 
 w 
 
 O ~ 
 
 Carbon 
 
 49.1 
 
 18.65 
 
 30.45 
 
 12.35 
 
 18.10 
 
 3.57 
 
 14.53 
 
 1.42 
 
 13.11 
 
 Hydrogen. . . 
 
 6 3 
 
 3 25 
 
 3.05 
 
 1.85 
 
 1.20 
 
 0.93 
 
 71 
 
 0.14 
 
 0.13 
 
 Oxygen 
 
 44.6 
 
 24.40 
 
 20.20 
 
 18.13 
 
 2.07 
 
 1.32 
 
 0.65 
 
 0.65 
 
 0.00 
 
 
 100.0 
 
 46.30 
 
 53.70 
 
 32.33 
 
 21.37 
 
 5.82 
 
 15.45 
 
 2.21 
 
 13.24 
 
CLASSIFICATION OF SOLID FUELS. 
 
 819 
 
 
 Classification of Coals. 
 
 It is convenient to classify the several varieties of coal according to 
 the relative percentages of carbon and volatile matter contained in their 
 combustible portion as determined by proximate analysis. The follow- 
 ing is the classification given in the author's " Steam-boiler Economy": 
 
 
 
 
 Heating 
 
 Relative 
 
 
 Fixed 
 Carbon. 
 
 Volatile 
 Matter. 
 
 Value 
 per Ib. of 
 Combustible 
 
 Value of 
 Combus- 
 tible. Semi- 
 
 
 
 
 B.T.U. 
 
 bit. = 100 
 
 Anthracite 
 
 97 to 90 
 
 3 to 10 
 
 14800 to 15400 
 
 93 
 
 Semi-anthracite 
 
 90 to 85 
 
 10 to 15 
 
 15400 to 15500 
 
 97 
 
 Semi-bituminous 
 
 85 to 70 
 
 15 to 30 
 
 15400 to 16000 
 
 100 
 
 Bituminous, Eastern. . 
 
 70 to 55 
 
 30 to 45 
 
 14800 to 15600 
 
 96 
 
 Bituminous, Western . 
 
 65 to 50 
 
 35 to 50 
 
 12500 to 14800 
 
 90 
 
 Lignite 
 
 under 50 
 
 over 50 
 
 11000 to 13500 
 
 77 
 
 The anthracites, with some unimportant exceptions, are confined to 
 three small fields in eastern Pennsylvania. The semi-anthracites are 
 found in a few small areas in the western part of the anthracite field. 
 The semi-bituminous coals are found on the eastern border of the great 
 Appalachian coal field, extending from north central Pennsylvania across 
 the southern boundary of Virginia into Tennessee, a distance of over 300 
 miles. They include the coals of Clearfield, Cambria, and Somerset 
 counties, Pennsylvania, and the Cumberland, Md., the Pocahontas, Va 
 and the New River, W. Va., coals. 
 
 It is a peculiarity of the semi-bituminous coals that their combustible 
 portion is of remarkably uniform composition, the volatile matter usually 
 ranging between 18 and 22% of the combustible, and approaching in its 
 analysis marsh gas, CH 4 , with very little oxygen. They are usually low 
 also in moisture, ash, and sulphur, and rank among the best steaming 
 coals in the world. 
 
 The eastern bituminous coals occupy the remainder of the Appala- 
 chian coal field, from Pennsylvania and eastern Ohio to Alabama They 
 are higher in volatile matter, ranging from 30 to over 40%, the higher 
 figures in the western portion of the field. The volatile matter is of 
 lower heating value, being .higher in oxygen. The western bituminous 
 coals are found in most of the states west of Ohio. They are higher in 
 volatile matter and in oxygen and moisture than the bituminous coals 
 of the Appalachian field, and usually give off a denser smoke when 
 burned in ordinary furnaces. 
 
 A later classification by the author (Trans. A. S. M. E., 1914; 
 " Steam-boiler Economy," 2d edition, 1915) is given in the table below. 
 It divides the bituminous coals into three grades, high, medium and 
 low, the chief distinction between them being the percentage of 
 moisture found in the coal after it is air-dried. The coals highest 
 in inherent moisture are also highest in oxygen. 
 
 Classes: I. Anthracite. II. Semi-anthracite. III. Semi-bitumi- 
 nous. IV. Cannel. V. Bituminous, high grade. VI. Bituminous, me- 
 dium grade. VII. Bituminous, low grade. VIII. Sub-bituminous and 
 lignite. 
 
 Class. 
 
 Volatile 
 Matter, % 
 of Com- 
 bustible. 
 
 Oxygen 
 in Com- 
 bustible 
 Per Cent. 
 
 Moisture 
 in Air-dry, 
 Ash-free 
 Coal, % 
 
 B.T.U. 
 
 per Ib. 
 Combustible. 
 
 B.T.U. per 
 Ib. Air-dry, 
 Ash-free 
 Coal 
 
 J 
 
 IV* 
 V 
 VI 
 VII 
 VIII 
 
 less than 10 
 10 to 15 
 15 to 30 
 45 to 60 
 30 to 45 
 32 to 50 
 32 to 50 
 27 to 60 
 
 1 to 4 
 Ito 5 
 1 to 6 
 5 to 8 
 5 to 14 
 6 to 14 
 7 to 14 
 10 to 33 
 
 less than 1.8 
 less than 1.8 
 less than 1.8 
 less than 1.8 
 1 to 4 
 2.5 to 6.5 
 5 to 12 
 7 to 26 
 
 14,800 to 15,400 
 15,400 to 15,500 
 15,400 to 16,050 
 15,700 to 16,200 
 14,800 to 15,600 
 13,800 to 15,100 
 12,400 to 14,600 
 9,600 to 13,250 
 
 14,600 to 15,400 
 15,200 to 15,500 
 15,300 to 16,000 
 15,500 to 16,050 
 14,350 to 14,400 
 11, 300 to 14,400 
 11, 300 to 13,400 
 7,400 to 11,650 
 
 * Eastern cannel. The Utah caonel is much lower in heating value. - 
 
820 
 
 FUEL. 
 
 The U. S. Geological Survey classifies coals into six groups, as follows: 
 (1) anthracite; (2) semi-anthracite; (3) semi-bituminous; (4) bitu- 
 minous; (5) sub-bituminous, or black lignite; and (6) lignite. 
 
 Classes 5 and 6 are described as follows: 
 
 Sub-bituminous coal is commonly known as "lignite," "lignitic coal," 
 "black lignite," "brown coal," etc. It is generally black and shining, 
 closely resembling bituminous coal, but it weathers more rapidly on 
 exposure and lacks the prismatic structure of bituminous coal. Its 
 calorific value is generally less than that of bituminous coal. The local- 
 ities in which this sub-bituminous coal is found include Montana, Idaho, 
 Washington, Oregon, California, Wyoming, Utah, Colorado, New Mexico, 
 and Texas. 
 
 Lignite is commonly known as "lignite," "brown lignite," or "brown 
 coal." It usually has a woody structure and is distinctly brown in color, 
 even on a fresh fracture. It carries a higher percentage of moisture than 
 any other class of coals, its mine samples showing from 30 to 40% of 
 moisture. The localities in which lignite is found are chiefly North 
 Dakota, South Dakota, Texas, Arkansas, Louisiana, Mississippi, and 
 Alabama. 
 
 The following analyses of representative coals of the six classes are 
 given by Prof. N. W. "Lord: 
 
 Class 1 Anthracite Culm. Penna. 
 
 Class 2 Semi-anthracite. Arkansas. 
 
 Class 3 Semi-bituminous. W. Va. 
 
 Class 4(a) Bituminous coking. Connellsville, Pa. 
 
 Class 4(ft) Bituminous non-coking. Hocking Valley, Ohio. 
 
 Class 5 Sub-bituminous. Wyoming, black lignite. 
 
 Class 6 Lignite. Texas. 
 
 COMPOSITION OF ILLUSTRATIVE COALS CAR-LOAD SAMPLES. 
 Proximate Analysis of "Air-dried" Sample. 
 
 Class , 1 2 3 4a 4b 5 6 
 
 Moisture 2.08 1.28 0.65 0.97 7.55 8.68 9.88 
 
 Vol. comb 7.27 12.82 18.80 29.09 34.03 41.31 36.17 
 
 Fixed carbon 74.32 73.69 75.92 60.85 52.57 46.49 43.65 
 
 Ash 16.33 12.21 4.63 9.09 5.85 3.52 10.30 
 
 Loss on air-drying . 3.40 1.10 1.10 4.20 Undet. 11.30 23.50 
 
 Ultimate Analysis of Coal Dried at 105 C. 
 
 Hydrogen 2.63 3.63 4.54 4.57 5.06 5.31 4.47 
 
 Carbon 76.86 78.32 86.47 77.10 75.82 73.31 64.84 
 
 Oxygen 2.27 2.25 2.68 6.67 10.47 15.72 16.52 
 
 Nitrogen 0.82 1.41 1.08 1.58 1.50 1.21 1.30 
 
 Sulphur 0.78 2.03 0.57 0.90 0.82 0.60 1.44 
 
 Ash 16.64 12.36 4.66 9.18 6.33 3.85 11.43 
 
 Results Calculated to an Ash and Moisture-Free Basis. 
 
 Volatile comb 8.91 14.82 19.85 32.34 39.30 47.05 45.31 
 
 Fixed carbon 91.09 85.18 80.15 67.66 60.70 52.95 54.69 
 
 Ultimate Analysis. 
 
 Hydrogen 3.16 4.14 4.76 5.03 5.41 5.50 5.05 
 
 Carbon 92.20 89.36 90.70 84.89 80.93 76.35 73.21 
 
 Oxygen 2.72 2.57 2.81 7.34 11.18 16.28 18.65 
 
 Nitrogen 0.98 1.61 1.13 1.74 1.61 1.25 1.47 
 
 Sulphur 0.94 2.32 0.60 1.00 0.87 0.62 1.62 
 
 Calorific Value in B.T.U. per lb., by Dulong's formula. 
 Air-dried coal. 12,472 13,406 15,190 13,951 12,510 11,620 10,288 
 Combustible .. 15,286 15,496 16,037 15,511 14,446 13,235 12,889 
 
 Caking and Non-caking Coals. Bituminous coals are sometimes 
 classified as caking and non-caking coals, according to their behavior 
 when subjected to the process of coking. The former undergo an incipi- 
 ent fusion or softening when heated, so that the fragments coalesce and 
 yield a compact coke, while the latter (also called free-burning) preserve 
 their form, producing a coke which is only serviceable when made from 
 
CLASSIFICATION OF SOLID FUELS. 
 
 821 
 
 large pieces of coal, the smaller pieces being incoherent. The reason of 
 this difference is not clearly understood, as non-caking coals are often of 
 similar ultimate chemical composition to caking coals. Some coals 
 which cannot be made into coke in a bee-hive oven are easily coked in 
 gas-heated ovens. 
 
 Cannel Coals are coals that are higher in hydrogen than ordinary 
 coals. They are valuable as enrichers in gas-making. The following are 
 gome ultimate analyses: 
 
 
 C. 
 
 H. 
 
 O+N. 
 
 S. 
 
 Ash. 
 
 Combustible. 
 
 C. 
 
 H. 
 
 O+N. 
 
 Boghead, Scotland 
 Albertite, Nova Scotia . . 
 Tasmanite, Tasmania . . . 
 
 63.10 
 82.67 
 79.34 
 
 8.91 
 9.14 
 10.41 
 
 7.25 
 8.19 
 4.93 
 
 0.96 
 
 19.78 
 
 79.61 
 82.67 
 83.80 
 
 11.24 
 9.14 
 10.99 
 
 9.15 
 8.19 
 5.21 
 
 5.32 
 
 
 Rhode Island Graphitic Anthracite. A peculiar variety of coal is 
 found in the central part of Rhode Island and in Eastern Massachusetts. 
 It resembles both graphite and anthracite coal, and has about the follow- 
 ing composition (A. E. Hunt, Trans. A. I. M. E., xvii. 678: Graphitic 
 carbon, 78%; volatile matter, 2.60%; silica, 15.06%; phosphorus, .045%. 
 It burns with extreme difficulty. 
 
 ANALYSIS AND HEATING VALUE OF COALS. 
 
 Coal is composed of four different things, which may be separated by 
 proximate analysis, viz.: fixed carbon, volatile hydrocarbon, ash and 
 moisture. In making a proximate analysis of a weighed quantity, such 
 as a gram of coal, the moisture is first driven off by heating it to about 
 250 F. then the volatile matter is driven off by heating it in a closed 
 crucible to a red heat, then the carbon is burned out of the remaining 
 coke at a white heat, with sufficient air supplied, until nothing is left 
 but the ash. 
 
 The fixed carbon has a constant heating value of about 14,600 B.T.U. 
 per Ib. The value of the volatile hydrocarbon depends on its composi- 
 tion, and that depends chiefly on the district in which the coal is mined. 
 It may be as high as 21,000 B.T.U. per Ib., or about the heating value of 
 marsh gas, in the best semi-bituminous coals, which contain very small 
 percentages of oxygen, or as low as 12,000 B.T.U. per Ib., as in those 
 from some of the western states, which are high in oxygen. The ash has 
 no heating value, and the moisture has in effect less than none, for its 
 evaporation and the superheating of the steam made from it to the tem- 
 perature of the chimney gases, absorb some of the heat generated by the 
 combustion of the fixed carbon and volatile matter. 
 
 The analysis of a coal may be reported in three different forms, as per- 
 centages of the moist coal, of the dry coal or of the combustible, as in the 
 following table. By "combustible" is always meant the sum of the 
 fixed carbon and volatile matter, the moisture and ash being excluded, 
 By some writers it is called "coal dry and free from ash" and by others 
 "pure coal." 
 
 
 Moist Coal. 
 
 Dry Coal. 
 
 Combus- 
 tible. 
 
 Moisture 
 Volatile matter 
 
 10 
 30 
 
 33.33 
 
 37.50 
 
 
 50 
 
 55.56 
 
 62.50 
 
 Ash.... 
 
 10 
 
 11.11 
 
 
 
 100 
 
 100.00 
 
 100.00 
 
 The sulphur, commonly reported with a proximate analysis, is deter- 
 mined separately. In the proximate analysis part of it escapes with the 
 volatile matter and the rest of it is found in the ash as sulphide of iron. 
 The sulphur should be given separately, in the report of the analysis. 
 
 The relation of the volatile matter and of the fixed carbon in the com- 
 bustible portion of the coal enables us to judge the class to which the 
 coal belongs, as anthracite, semi-anthracite, semi-bituminous, bituminous 
 
822 
 
 FUEL. 
 
 or lignite. Coals containing less than 10 per cent volatile matter in the 
 combustible would be classed as anthracite, between 10 and 15 per 
 cent as semi-anthracite, between 15 and 30 per cent as semi- bituminous, 
 between 30 and 50 per cent as bituminous, and over 50 per cent as lig- 
 nitic coals or lignites. In the classification of the U.S. Geological Sur- 
 vey the sub-bituminous coals and lignites are distinguished by their 
 structure and color rather than by analysis. 
 
 The figures in the second column, representing the percentages in the 
 dry coal, are useful in comparing different lots of coal of one class, and 
 they are better for this purpose than the figures in the first column, for 
 the moisture is a variable constituent, depending to a large extent on the 
 weather to which the coal has been subjected since it was mined, on the 
 amount of moisture in the atmosphere at the time when it is analyzed , 
 and on the extent to which it may have accidentally been dried during 
 the process of sampling. 
 
 The heating value of a coal depends on its percentage of total combus- 
 tible matter, and on the heating value per pound of that combustible. 
 The latter differs in different districts and bears a relation to the per- 
 centage of volatile matter. It is highest in the semi-bituminous coals, 
 being nearly constant at about 15,750 B.T.U. per pound. It is between 
 14,800 and 15,500 B.T.U. in anthracite, and ranges from 15,500 down to 
 13,000 in the bituminous coals, decreasing usually as we go westward, 
 and as the volatile matter contains an increasing percentage of oxygen. 
 In some lignites it is as low as 10,000. 
 
 In reporting the heating value of a coal, the B.T.U. per pound of com- 
 bustible should always be stated, for convenient comparison with other 
 reports. 
 
 In 1892 the author deduced from Mahler's tests on European coals 
 the following table of the approximate heating value of coals of differ- 
 ent composition. 
 
 APPROXIMATE HEATING VALUES OF COALS. 
 
 
 
 Equivalent 
 
 
 
 Equivalent 
 
 Per Cent 
 Volatile 
 Matter in 
 
 Heating 
 Value, B.T.U. 
 
 Water 
 Evapora- 
 tion from 
 
 Per Cent 
 Volatile 
 Matter in 
 
 Heating 
 Value, B.T.U. 
 
 Water 
 Evapora- 
 tion from 
 
 Coal Dry 
 and Free 
 from Ash. 
 
 per Ib. 
 Combus- 
 tible. 
 
 and at 212 
 per Ib. 
 Combus- 
 
 Coal Dry 
 and Free 
 from Ash. 
 
 per Ib. 
 Combus- 
 tible. 
 
 andat212 c 
 per Ib. 
 Combus- 
 
 
 
 tible. 
 
 
 
 tible. 
 
 
 
 14,580 
 
 15.09 
 
 32 
 
 15.480 
 
 16.03 
 
 3 
 
 14,940 
 
 15.47 
 
 37 
 
 15,120 
 
 15.65 
 
 6 
 
 15,210 
 
 15.75 
 
 40 
 
 14,760 
 
 15.28 
 
 10 
 
 15,480 
 
 16.03 
 
 43 
 
 14,220 
 
 14.72 
 
 13 
 
 15,660 
 
 16.21 
 
 45 
 
 13.860 
 
 14.35 
 
 20 
 
 15.840 
 
 16.40 
 
 47 
 
 13.320 
 
 13.79 
 
 28 
 
 15.660 
 
 16.21 
 
 49 
 
 12.420 
 
 12.86 
 
 The experiments of Lord and Haas on American coals (Trans. 
 A.I.M.E., 1897) practically confirm these figures for all coals in which 
 the percentage of fixed carbon is 60% and over of the combustible, but 
 for coals containing less than 60 % fixed carbon or more than 40 % volatile 
 matter in the combustible, they are liable to an error in either direction 
 of about 4%. It appears from these experiments that the coal of one 
 seam in a given district has the same heating value per pound of com- 
 bustible within one or two per cent [true only of some districts], but coals 
 of the same proximate analysis, and containing over 40 % volatile matter, 
 but mined in different districts, may vary 6 or 8 % in heating value. 
 
 The coals containing from 72 to 87 per cent of fixed carbon in the com- 
 bustible have practically the same heating value. This is confirmed by 
 Lord and Haas's tests of Pocahontas coal. A study of these tests and of 
 Mahler's indicates that the heating value of all the semi-bituminous coals, 
 75 to 87.5% fixed carbon, is within 1 H% of 15,750 B.T.U. per pound. 
 
 The heating value of any coal may also be calculated from its ultimate 
 analysis, with a probable error not exceeding 2%, by Dulong's formula: 
 
ANALYSES AND HEATING VALUE OF COALS. 823 
 
 Heating value per Ib. = 146 C -f 620/H - ^-l + 40 S 
 
 in which C, H, S, and O are respectively the percentages of carbon, 
 hydrogen, sulphur and oxygen. Its approximate accuracy is proved by 
 both Mahler's and Lord and Haas's experiments, and any deviation of 
 the calorimetric determination of any coals (cannel coals and lignites 
 excepted) more than 2 % from that calculated by the formula, is more 
 likely to proceed from an error in either the calorimetric test or the 
 analysis, than from an error in the formula. 
 
 Average Results of Lord and Haas's Tests. (" Steam Boiler 
 Economy," p. 156.) 
 
 Name of Coal. 
 
 C. 
 
 H. 
 
 O. 
 
 N. 
 
 S. 
 
 ,d 
 
 $ 
 
 'o 
 
 ri 
 
 O 
 
 1 
 
 l,f 
 
 tf 
 
 H 
 
 
 
 
 
 
 
 03 
 
 % 
 
 > 
 
 ft 
 fi 
 
 >^ 
 
 ft 
 
 Pocahontas, Va. 
 
 84.87 
 
 4.20 
 
 2.84 
 
 0.85 
 
 0.59 
 
 5.89 
 
 0.76 
 
 18.51 
 
 74.84 
 
 19.82 
 
 15766 
 
 Thacker, W. Va. 
 
 78.65 
 
 5.00 
 
 6.01 
 
 1.41 
 
 1.28 
 
 6.27 
 
 1.38135.68 
 
 56.67 
 
 38.62 
 
 15237 
 
 Pittsburg, Pa.. . 
 
 75.24 
 
 5.01 
 
 7.04 
 
 1.51 
 
 1.79 
 
 8.02 
 
 1.3736.80 
 
 53.81 
 
 40.61 
 
 14963 
 
 Middle Kittan- 
 
 
 
 
 
 
 
 
 
 
 
 
 ing, Pa 
 
 75,. 19 
 
 4.91 
 
 7.47 
 
 1.46 
 
 1.98 
 
 7.18 
 
 1.81 
 
 36.32 
 
 54.69 
 
 39.91 
 
 14800 
 
 Upper Freeport, 
 
 
 
 
 
 
 
 
 
 
 
 
 Pa. and O . 
 
 72.65 
 
 4.82 
 
 7.26 
 
 1.34 
 
 2.89 
 
 9.10 
 
 1.93 
 
 37.35 
 
 51.63 
 
 41.98 
 
 14755 
 
 Mahoning, O . . . 
 
 71.13 
 
 4.56 
 
 7.17 
 
 1.23 
 
 1.86 
 
 10.90 
 
 3.15 
 
 35.00 
 
 50.95 
 
 40.72 
 
 14728 
 
 Jackson Co., O. . 
 
 70.72 
 
 4.45 
 
 10.82 
 
 1.47 
 
 1.13 
 
 3.25 
 
 8.17 
 
 35.79 
 
 52.78 
 
 40.41 
 
 14141 
 
 Hocking Val- 
 
 
 
 
 
 
 
 
 
 
 
 
 ley, O 
 
 68.03 
 
 4.97 
 
 9.87 
 
 1.44 
 
 1.59 
 
 8.00 
 
 6.59 
 
 35.77 
 
 49.64 
 
 41.84 
 
 14040 
 
 * Per Ib. of combustible, by the Mahler calorimeter. The average 
 figures calculated from the ultimate analyses agreed within 0.5 %, except 
 in the case of the Jackson Co. coal, in which the calorimetric result was 
 1.6% higher than that computed from the analysis. 
 
 Sizes of Anthracite Coal. When anthracite is mined it is crushed 
 in a " breaker," and passed over screens separating it into different sizes, 
 which are named as follows: 
 
 Lump, passes over bars set 3 1/2 to 5 in. apart; steamboat, over 3 1/2 
 in. and out of screen; broken, through 4 1/2 in., over 3 1/4 in.; egg, 3 1/4 
 to 2 s/ 16 in. ; stove, 2 5/i 6 to 1 5/g in. ; chestnut, 1 5/ 8 to 7/ 8 in. ; pea, 7/8 to 
 9/16 in.; buckwheat, No. 1, 9/ 16 to5/i 6 in.; No. 2, 5/i 6 to3/ 16 ; No. 3, 3/ 16 
 to 3/32 in.; culm, through 3/ 32 in. 
 
 The terms "buckwheat," "rice" and "barley" are used in some 
 localities instead of No. 1, No. 2 and No. 3 buckwheat. 
 
 When coal is screened into sizes for shipment the purity of the dif- 
 ferent sizes as regards ash varies greatly. Samples from one mine gave 
 results as follows: 
 
 LName of Coal. 
 
 Screened. 
 
 Analyses. 
 
 Through 
 Inches. 
 
 Over 
 Inches. 
 
 Fixed 
 Carbon. 
 
 Ash. 
 
 
 2.5 
 1.75 
 1.25 
 0.75 
 0.50 
 
 1.75 
 1.25 
 0.75 
 0.50 
 0.25 
 
 88.49 
 83.67 
 80.72 
 79.05 
 76.92 
 
 5.66 
 10.17 
 12.67 
 14.66 
 16.62 
 
 
 omve . . 
 
 Chestnut. . 
 
 Pea 
 
 Buckwheat .... 
 
 
 Space Occupied by Anthracite Coal. (J. C. I. W., vol. iii.) The 
 cubic contents of 2240 Ib. of hard Lehigh coal is a little over 36 feet; an 
 average Schuylkill white-ash, 37 to 38 feet; Shamokin, 38 to 39 feet; 
 Lorberry, nearly 41. 
 
 According to measurements made with Wilkes-Barre anthracite coal 
 from the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. 
 
824 
 
 FUEL. 
 
 broken, 34. 5 cu. ft. egg, 34.8 cu. ft. of stove, 35.7 cu. ft. of chestnut, and 
 
 36.7 cu. ft. of pea, to make one ton Of coal of 2240 Ib. ; while it requires 
 
 28.8 cu. ft. of lump, 30.3 cu. ft. of broken, 30.8 cu. ft. of egg, 31.1 cu. ft. 
 of stove, 31.9 cu. ft. of chestnut, or 32.8 cu. ft. of pea, for one ton (2000 Ib.) 
 
 Bernice Basin, Pa., Coals. 
 
 Water Vol. H.C. Fixed C. Ash. Sulphur. 
 Bernice Basin, Sullivan^ 0.96 3.56 82.52 3.27 0.24 
 
 and Lycoming Cos!; > to to to to to 
 
 range of 8 J 1.97 8.56 89.39 9.34 1:04 
 
 This coal is on the dividing-line between the anthracites and semi- 
 anthracites, and is similar to the coal of the Lykens Valley district. 
 
 More recent analyses (Trans. A. I. M. E., xiv. 721) give: 
 
 Water VoL H.C. Fixed C. Ash. Sulphur 
 
 Working seam 0.65 9.40 83.69 5.34 0.91 
 
 60 ft. below seam 3.67 15.42 71.34 8.97 0.59 
 
 The first is a semi-anthracite, the second a semi-bituminous. 
 
 Connellsville Coal and Coke. (Trans. A. I. M. E., xiii. 332.) The 
 Connellsville coal-field, in the southwestern part of Pennsylvania, is a 
 strip about 3 miles wide and 60 miles in length. The mine workings are 
 confined to the Pittsburgh seam, which here has its best development as 
 to size, and its quality best adapted to coke-making. It generally af- 
 fords from 7 to 8 feet of coal. 
 
 The following analyses by T. T. Morrell show about its range of com- 
 position: 
 
 Moisture. Vol. Mat. Fixed C. Ash. Sulphur. Phosph's. 
 HeroldMine 1.26 28.83 60.79 8.44 0.67 0.013 
 KintzMine. 0.79 31.91 56.46 9.52 1.32 0.02 
 
 In comparing the composition of coals across the Appalachian field, 
 in the western section of Pennsylvania, it will be noted that 'the Con- 
 nellsville variety occupies a peculiar position between the rather dry 
 semi-bituminous coals eastward of it and the fat bituminous coals flank- 
 ing it on the west. 
 
 Indiana Coals. (J. S. Alexander, Trans. A. I. M. E., iv. 100.) The 
 typical block coal of the Brazil (Indiana) district differs in chemical 
 composition but little from the coking coals of Western Pennyslvania. 
 The physical difference, however, is quite marked; the latter has a 
 cuboid structure made up of bituminous particles lying against each 
 other, so that under the action of heat fusion throughout the mass 
 readily takes place, while block coal is formed of alternate layers of rich 
 bituminous matter and a charcoal-like substance, which is not only very 
 slow of combustion, but so retards the transmission of heat that agglu- 
 tination is prevented, and the coal burns away layer by layer, retaining 
 its form until consumed. 
 
 Illinois Coals. The Illinois coals are generally high in moisture, 
 volatile matter, ash and sulphur, and the volatile matter is high in 
 oxygen; consequently the coals are low in heating value. The range of 
 quality is a wide one. The Big Muddy coal of Jackson Co., which has a 
 high reputation as a steam coal in the St. Louis market, has about 36% 
 of volatile matter in the combustible, while a. coal from Staunton, 
 Macoupin Co., tested by the author in 1883 (Trans. A. S. M. E., v. 266) 
 had 68%. A boiler, test with this coal gave only 6.19 Ibs. of water 
 evaporated from and at 212 per Ib. of combustible, in the same boiler 
 that had given 9.88 Ibs. with Jackson, O., nut. 
 
 Prof. S. W. Parr, in Bulletin No. 3 of the 111. State Geol. Survey, 1906, 
 reports the analyses and calorimetric tests of 150 Illinois coals. The 
 two having the lowest and the highest value per pound of combustible 
 have the following analysis: 
 
 
 Air-dried Coal. 
 
 Pure Coal. 
 
 Moist. 
 
 Ash. 
 
 Vol. 
 
 Fixed 
 C. 
 
 S. 
 
 Vol. 
 
 Fixed 
 C. 
 
 B.T.U. 
 per Ib. 
 
 Lowest. . 
 Highest . 
 
 9.90 
 5.68 
 
 5.02 
 8.90 
 
 40.75 
 33.32 
 
 44.33 
 52.10 
 
 2.00 
 1.18 
 
 47.90 
 39.02 
 
 52.10 
 60.98 
 
 12,162 
 14,830 
 
 The poorest coal of the series had a heating value of only 8645 B.T.U. 
 
ANALYSES AND HEATING VALUE OF COALS. 825 
 
 per lb., air dry; it contained 9.70 moisture and 31.18 ash, -and the B.T.U. 
 per lb. combustible was 14,623. The best coal had a heating value of 
 13,303 per lb.; moistures 4.20, ash 5.50, B.T.U. per lb. combustible, 
 14,734. 
 
 Of the 150 coals, 28 gave between 14,500 and 14,830 B.T.U. per lb. 
 combustible; 82 between 14,000 and 14,500; 32 between 13,500 and 
 14,000; 6 between 13,000 and 13,500; one 12,535 and one 12,162. The 
 average is about 14,200. The volatile matter ranged from 36.24% to 
 53.80% of the combustible; the sulphur from 0-.62 to 4.96%; the ash 
 from 2.32 to 31.18%, and the moisture from 3.28 to 12.74%, all calcu- 
 lated from the air-dried samples. The moisture in the coal as mined is 
 not stated, but was no doubt considerably higher. The author has 
 found over 14% moisture in a lump of Illinois coal that was apparently 
 dry, having been exposed to air, under cover, for more than a month. 
 
 Colorado Coals. The Colorado coals are of extremely variable com- 
 position, ranging all the way from lignite to anthracite. G. C. Hewitt 
 (Trans. A. I. M. E., xvii. 377) says: The coal seams, where unchanged 
 by heat and flexure, carry a lignite containing from 5 % to 20 % of water. 
 In the southeastern corner of the field the seams have been metamor- 
 phosed so that in four miles the same seams are an anthracite, coking, 
 and dry coal. The dry seams also present wide chemical and physical 
 changes in short distances. A soft and loosely bedded coal has in a 
 hundred feet become compact and hard without the interventi9n of a 
 faul( . A couple of hundred feet has reduced the water of combination 
 from 12% to 5%. 
 
 Western Arkansas and Oklahoma (formerly Indian Territory). 
 (H. M. Chance, Trans. A. I. M. E., 1890.) The western Arkansas coals 
 are dry semi-bituminous or semi-ant hracitic coals, mostly non-coking, 
 or with quite feeble coking properties, ranging from 14% to 16% in 
 volatile matter, the highest percentage yet found, according to Mr. 
 Winslow's Arkansas report, being 17.65. 
 
 In the Mitchell basin, about 10 miles west from the Arkansas line, the 
 coal shows 19 % volatile matter; the Mayberry coal, about 8 miles farther 
 west, contains 23 % ; and the Bryan Mine coal, about the same distance 
 west, shows 26%. About 30 miles farther west, the coal shows from 
 38% to 41.5 % volatile matter, which is also about the percentage in 
 coals of the McAlester and Lehigh districts. 
 
 Analyses of Foreign Coals. (Selected from D. L. Barnes's paper on 
 American Locomotive Practice, Trans. A. S. C. E., 1893.) 
 
 
 Volatile 
 Matter. 
 
 Fixed 
 Carbon. 
 
 1 
 
 
 Volatile 
 Matter. 
 
 Fixed 
 Carbon. 
 
 1 
 
 Great Britain: 
 South- Wales 
 South- Wales 
 Lancashire, Eng. 
 Derbyshire, " 
 Durham, 
 Staffordshire, " 
 Scotlandf 
 Scotlandj 
 
 8.5 
 6.2 
 17.2 
 17.7 
 15.05 
 20.4 
 17.1 
 17.5 
 
 21.93 
 
 88.3 
 92.3 
 80.1 
 79.9 
 86.8 
 78.6 
 63.1 
 80.1 
 
 70.55 
 
 3.2 
 1.5 
 2.7 
 2.4 
 1 .1 
 1.0 
 19.8 
 2.4 
 
 7.52 
 
 South America: 
 Chili, Chiroqui. . 
 Patagonia 
 
 24.11 
 24.35 
 40.5 
 
 26.8 
 26.9 
 
 15.8 
 14.98 
 26.5 
 6.16 
 
 38.98 
 62.25 
 57.9 
 
 60.7 
 67.6 
 
 64.3 
 82.39 
 70.3 
 63.4 
 
 36.91 
 13.4 
 1.6 
 
 12.5 
 5.5 
 
 10.0 
 2.04 
 14.2 
 30.45 
 
 Brazil 
 
 Canada: 
 Nova Scotia .... 
 Cape Breton. . .. 
 Australia: 
 Lignite. 
 
 South America: 
 Chili 
 
 Sydney, N.S.W.. 
 Borneo 
 Tasmania 
 
 * Semi-bit, coking coal. t Boghead cannel gas coal. 
 
 J Semi-bit, steam-coal. 
 
 An analysis of Pictou, N. S., coal, in Trans. A. I. M. E., xiv. 560, is: 
 vol., 29.63; carbon, 56.98; ash, 13.39; and one of Sydney, Cape Breton, 
 coal is: vol., 34.07; carbon, 61.43; ash, 4.50. 
 
 Sampling 'Coal for Analysis. J. P. Kimball, Trans. A. I. M. E., 
 xii. 317, says: The unsuitable sampling of a coal-seam, or the improper 
 preparation of the sample in the laboratory, often gives rise to errors in 
 
826 FUEL. 
 
 determinations of the ash so wide in range as to vitiate the analysis for 
 all practical purposes; every other single determination, excepting mois- 
 ture, showing its relative part of the error. The determinations of sul- 
 phur and ash are especially liable to error, as they are intimately asso- 
 ciated in the slates. 
 
 Wm. JForsyth, in his paper on The Heating Value of Western Coals 
 (Eng'g News, Jan. 17, 1895) , says: This trouble in getting a fairly average 
 sample of anthracite coal has compelled the Reading R. R. Co., in get- 
 ting its samples, to take as much as 300 Ib. for one sample, drawn direct 
 from the chutes, as it stands ready for shipment. 
 
 The directions for collecting samples of coal for analysis at the C., B. 
 & Q. laboratory are as follows: 
 
 Two samples should be taken, one marked "average," the other 
 "select." Each sample should contain about 10 Ib., made up of lumps 
 about the size of an orange taken from different parts of the dump or 
 car, and so selected that they shall represent as nearly as possible, first, 
 the average lot; second, the best coal. 
 
 An example ol the difference between an "average" and a "select" 
 sample, taken from Mr. Forsyth's paper, is the following of an Illinois 
 coal: 
 
 Moisture. Vol. Mat. Fixed Carbon. Ash. 
 
 Average 1.36 27.69 35.41 35.54 
 
 Select 1.90 34.70 48.23 15.17 
 
 The theoretical evaporative power of the former was 9.13 Ibs. of water 
 from and at 212 per Ib. of coal, and that of the latter 11.44 Ibs. 
 
 For methods of sampling see Kent's "Steam Boiler Economy," 2d 
 edition (1915), also Report of the Power Test Committee, A. S. M. E., 
 1915, and Technical Paper No. 8 of the U. S. Bureau of Mines, 1913. 
 
 RELATIVE VALUE OF STEAM COALS. 
 
 The heating value of a coal may be determined, with more or less 
 approximation to accuracy, by three different methods. 
 
 1st, by chemical analysis; 2d, by combustion in a coal calorimeter; 
 3d, by actual trial in a steam-boiler. 
 
 The accuracy of the first two methods depends on the precision of the 
 method of analysis or calorimetry adopted, and upon the care and skill 
 of the operator. The results of the third method are subject to numer- 
 ous sources of variation and error, and may be taken as approximately 
 true only for the particular conditions under which the test is made. 
 Analysis and calorimetry give with considerable accuracy the heating 
 value which may be obtained under the conditions of perfect combus- 
 tion and complete absorption of the heat produced. A boiler test gives 
 the actual result under conditions of more or less imperfect combustion., 
 and of numerous and variable wastes. It may give the highest practical 
 heating value, if the conditions of grate-bars, draft, extent of heating 
 surface, method of firing, etc., are the best possible for the particular 
 C9al tested, and it may give results far beneath the highest if these con- 
 ditions are adverse or unsuitable to the coal. 
 
 In a paper entitled Proposed Apparatus for Determining the Heating 
 Power of Different Coals (Trans. A. I. M. E., xiv. 727) the author de- 
 scribed and illustrated an apparatus designed to test fuel on a large 
 scale, avoiding the errors of a steam-boiler test. It consists of a fire- 
 brick furnace enclosed in a water casing, and two cylindrical shells con- 
 taining a great number of tubes, which are surrounded by cooling water 
 and through which the gases of combustion pass while being cooled. 
 No steam is generated in the apparatus, but water is passed through it 
 and allowed to escape at a temperature below 200 F. The product of 
 the weight of the water passed through the apparatus by its increase in 
 temperature is the measure of the heating value of the fuel. 
 
 A study of M. Mahler's calorimetric tests shows that the maximum 
 difference between the results of these tests and the calculated heating 
 power by Dulong's law in any single case is only a little over 3%, 
 and the results of 31 tests show that Dulong's formula gives an aver- 
 age of only 47 thermal units less than the calorimetric tests, the 
 
RELATIVE VALUE OF oTEAM COALS. 827 
 
 average total heating value being over 14.000 B.T.U., a difference of 
 less than 0.4%.* 
 
 The close agreement of the results of calorimetric tests when properly 
 conducted, and of the heating power calculated from the ultimate chemi- 
 cal analysis indicates that either the chemical or the calorimetric method 
 may be accepted as correct enough for all practical purposes for deter- 
 mining the total heating power of coal. The results obtained by either 
 method may be taken as a standard by which the results of a boiler test 
 are to be compared, and the difference between the total heating power 
 and the result of the boiler test is a measure of the inefficiency of the 
 boiler under the conditions of any particular test. 
 
 The heating value that can be obtained in boiler practice from any 
 given coal depends upon the efficiency of the boiler, and this largely 
 upon the difficulty of thoroughly burning the volatile combustible 
 matter in the boiler furnace. 
 
 With the best anthracite coal, in which the combustible portion is, 
 say, 97% fixed carbon and 3% volatile matter, the highest result that 
 can be expected in a boiler-test with all conditions favorable is 12.2 Ib. 
 of water evaporated from and at 212 per Ib. of combustible, which is 
 79% of 15.47 Ib., the theoretical heating-power. With the best semi- 
 bituminous coals, such as Cumberland and Pocahontas, in which the 
 fixed carbon is 80% of the total combustible, 12.5 Ib., or 76% of the 
 theoretical 16.4 Ib., may be obtained. For Pittsburgh coal, with a 
 fixed carbon ratio of 68%, 11 Ib., or 69% of the theoretical 16.03 Ib., is 
 about the best practically obtainable with the best boilers when hand- 
 fired, with ordinary furnaces. (The author has obtained 78% with an 
 automatic stoker set in a "Dutch oven" furnace.) With some good 
 Ohio coals, witli a fixed carbon ratio of 60%, 10 Ib., or 66% of the the- 
 oretical 15.28 Ib., has been obtained, under favorable conditions, with a 
 fire-brick arch over the furnace. With coals mined west of Ohio, with 
 lower carbon ratios, the boiler efficiency is not apt to be as high as 60% 
 unless a special furnace, adapted to the coal, is used. 
 
 From these figures a table of probable maximum boiler-test results 
 with ordinary furnaces from coals of different fixed carbon ratios may 
 be constructed as follows: 
 
 Fixed carbon ratio 97 80 68 60 54 50 
 
 Evap. from and at 212 per Ib. combustible, maximum in boiler-tests: 
 
 12.2 12.5 11 10 8.3 7.0 
 
 Boiler efficiency, per cent 80 76 69 66 60 55 
 
 Loss, chimney, radiation, imperfect combustion, etc.: 
 
 20 24 31 34 40 45 
 
 The difference between the loss of 20% with anthracite and the great- 
 er losses with the other coals is chiefly due to imperfect combustion of 
 the bituminous coals, the more highly volatile coals sending up the 
 chimney the greater quantity of smoke and unburned hydrocarbon 
 gases. It is a measure of the inefficiency of the boiler furnace and of the 
 inefficiency of heating-surface caused by the deposition of soot, the 
 latter being primarily caused by the imperfection of the ordinary 
 furnace and its unsuitability to the proper burning of bituminous coal. 
 If in a boiler-test with an ordinary furnace lower results are obtained 
 than those in the above table, it is an indication of unfavorable condi- 
 tions, such as bad firing, wrong proportions of boiler, defective draft, a 
 rate of driving beyond the capacity of the furnace, or beyond the 
 capacity of the boiler to absorb the heat produced in the furnace. It is 
 quite possible, however, with automatic stokers and fire-brick com- 
 bustion chambers to obtain an efficiency of 70% with the highly 
 volatile western coals. 
 
 Under exceptionally good conditions, with mechanical stokers, very 
 large combustion chambers, and the air supply controlled according to 
 the indications of gas analyses, as high as 81 % efficiency has been 
 obtained. See under Steam- Boilers, page 898. 
 
 * The formula commonly used in the United States is 14,600 C + 
 62,000 (H - l/gO) + 4050 S. F9r a description of the Mahler catori- 
 meter and its method of operation see the author's "Steam Boiler 
 Economy." Prof. S. W. Parr, of the University of Illinois, has put a 
 calorimeter on the market which gives results practically equal to those 
 obtained with Mahler's instrument. 
 
Classified List of Coals. 
 
 
 As Received. 
 
 Combustible. ' 
 
 Air-dry, Ash-free 
 
 Moist. Ash. 
 
 B.T.U. 
 
 Vol. 
 
 S. 
 
 0. 
 
 B.T.U. 
 
 Moist. 
 
 B.T.U. 
 
 I. ANTHRACITE. 
 
 Alaska. 
 
 7.43 
 
 14.36 
 
 11,891 
 
 8.8 
 
 0.73 
 
 4.04 
 
 15,203 
 
 1.55 
 
 14,968 
 
 Colo... 
 
 2.70 
 
 5.83 
 
 14,099 
 
 3.6 
 
 0.87 
 
 1.32 
 
 15,413 
 
 1.08 
 
 15,247 
 
 Pa 
 
 2.80 
 
 7.83 
 
 13,298 
 
 1.3 
 
 1.00 
 
 2.13 
 
 14,882 
 
 1.43 
 
 14,666 
 
 Pa 
 
 330 
 
 9.12 
 
 13,351 
 
 3.7 
 
 0.68 
 
 2.41 
 
 15,248 
 
 0.83 
 
 15,123 
 
 Wash 
 
 
 
 
 8.5 
 
 0.72 
 
 2.67 
 
 15.410 
 
 0.80 
 
 15.367 
 
 
 II. SEMI-ANTHRACITE. 
 
 Ark....| 2.36 
 
 12.08 
 
 13,259 
 
 14.8 
 
 2.33 
 
 2.57 
 
 15,496 
 
 1.45 
 
 15,272 
 
 Pa 3.38 
 
 11.50 
 
 13,156 
 
 10.0 
 
 D.74 
 
 2.17 
 
 15,457 
 
 0.91 
 
 15,398 
 
 Va | 4.80 
 
 18.03 
 
 11,961 
 
 13.1 
 
 0.82 
 
 4.18 
 
 15,500 
 
 0.90 
 
 15.439 
 
 III. SEMI-BITUMINOUS. 
 
 Ala.... 
 
 3.08 
 
 3.75 
 
 14,681 
 
 28.8 
 
 0.59 
 
 4.45 
 
 15,757 
 
 1.15 
 
 15,577 
 
 Ala.... 
 
 2.38 
 
 4.88 
 
 14,487 
 
 27.9 
 
 1.58 
 
 3.42 
 
 15,620 
 
 0.94 
 
 15,475 
 
 Alaska . 
 
 5.14 
 
 5.00 
 
 14,065 
 
 15.5 
 
 1.29 
 
 3.02 
 
 15.651 
 
 0.60 
 
 15,559 
 
 Ark. . . . 
 
 2.77 
 
 9.07 
 
 13,774 
 
 16.7 
 
 3.16 
 
 1.69 
 
 15,624 
 
 0.86 
 
 15.525 
 
 Ark.... 
 
 3.21 
 
 9.29 
 
 13,588 
 
 17.0 
 
 3.57 
 
 1.25 
 
 15,530 
 
 0.92 
 
 15,387 
 
 Colo. . . 
 
 0.96 
 
 8.62 
 
 14,330 
 
 23.8 
 
 0.58 
 
 4.34 
 
 15,849 
 
 0.83 
 
 15.716 
 
 Colo... 
 
 3.07 
 
 9.16 
 
 13,990 
 
 25.8 
 
 0.72 
 
 2.29 
 
 15,939 
 
 1.43 
 
 15.712 
 
 Ga 
 
 3.80 
 
 14.49 
 
 12,791 
 
 19.4 
 
 1.55 
 
 5.96 
 
 15,653 
 
 0.74 
 
 15,540 
 
 Md... 
 
 3.20 
 
 6.70 
 
 14,100 
 
 16.0 
 
 1.02 
 
 2.54 
 
 15,640 
 
 1.10 
 
 15,478 
 
 Md.... 
 
 2.60 
 
 6.80 
 
 14,360 
 
 17.5 
 
 0.98 
 
 2.47 
 
 15,856 
 
 0.66 
 
 15,746 
 
 Mont. . 
 
 2.05 
 
 8.31 
 
 14,092 
 
 18.3 
 
 0.96 
 
 2.93 
 
 15,721 
 
 0.61 
 
 15,625 
 
 Okla... 
 
 2.37 
 
 8.83 
 
 13,840 
 
 21.7 
 
 1.15 
 
 2.87 
 
 15.586 
 
 0.53 
 
 15,504 
 
 Okla... 
 
 5.11 
 
 8.03 
 
 13,662 
 
 15.7 
 
 1.36 
 
 1.87 
 
 15,728 
 
 0.70 
 
 15,619 
 
 Pa 
 
 425 
 
 7.87 
 
 13,513 
 
 24.8 
 
 1.81 
 
 5.50 
 
 15,376 
 
 0.40 
 
 15,316 
 
 Pa 
 
 1.10 
 
 7.41 
 
 14,499 
 
 17.3 
 
 1.63 
 
 2.82 
 
 15,847 
 
 0.65 
 
 15,744 
 
 Va 
 
 4.00 
 
 4.31 
 
 14,520 
 
 19.0 
 
 0.68 
 
 3.42 
 
 15,840 
 
 0.54 
 
 15,750 
 
 Va 
 
 4.10 
 
 3.18 
 
 14,740 
 
 17.5 
 
 0.68 
 
 2.23 
 
 15,910 
 
 0.64 
 
 15,795 
 
 Wash.. 
 
 5.81 
 
 17.04 
 
 11,776 
 
 16.3 
 
 0.48 
 
 3.97 
 
 15,264 
 
 1.67 
 
 15,013 
 
 W.Va.. 
 
 3.71 
 
 3.39 
 
 14,306 
 
 25.3 
 
 0.86 
 
 4.13 
 
 15,399 
 
 1.18 
 
 15,218 
 
 W.Va.. 
 
 1.75 
 
 4.58 
 
 15,023 
 
 19.9 
 
 0.60 
 
 2.80 
 
 16,038 
 
 0.69 
 
 15.998 
 
 IV. CANNEL.* 
 
 Ky.... 
 
 2.36 
 
 10.49 
 
 13,770 
 
 55.5 
 
 1.38 
 
 7.57 
 
 15,800 
 
 0.92 
 
 15,646 
 
 Ky.... 
 
 1.70 
 
 9.31 
 
 14,251 
 
 57.0 
 
 1.15 
 
 7.61 
 
 16,013 
 
 1.44 
 
 15784 
 
 W.Va.. 
 
 1.80 
 
 3.44 
 
 15,330 
 
 47.4 
 
 0.92 
 
 5.34 
 
 16,176 
 
 0.84 
 
 16,042 
 
 Utah... 
 
 7.35 
 
 23.24 
 
 10,355 
 
 67.6 
 
 2.32 
 
 13.68 
 
 14,918 
 
 8.26 
 
 13,686 
 
 V. BITUMINOUS, HIGH-GRADE. 
 
 Ala.... 
 
 2.18 
 
 2.79 
 
 14,816 
 
 33.4 
 
 1.13 
 
 6.99 
 
 15,590 
 
 1.23 
 
 15,400 
 
 Ala 
 
 3.83 
 
 5.48 
 
 13,799 
 
 35.3 
 
 1.07 
 
 7.00 
 
 15,214 
 
 1.77 
 
 14,947 
 
 Colo... 
 
 2.64 
 
 5.21 
 
 13,529 
 
 31.3 
 
 0.72 
 
 9.38 
 
 14,681 
 
 1.01 
 
 14,533 
 
 Colo. . . 
 
 2.28 
 
 9.16 
 
 13,781 
 
 33.7 
 
 0.56 
 
 8.77 
 
 15,559 
 
 0.87 
 
 15,423 
 
 Ill 
 
 7.81 
 
 8.38 
 
 12,418 
 
 40.0 
 
 2.82 
 
 9.74 
 
 14,818 
 
 2.34 
 
 14,470 
 
 Kan... 
 
 2.50 
 
 12.45 
 
 12,900 
 
 39.8 
 
 6.68 
 
 5.26 
 
 15,167 
 
 2.86 
 
 14,734 
 
 Kan... 
 
 9.04 
 
 15.72 
 
 11,142 
 
 39.5 
 
 4.93 
 
 7.27 
 
 14,809 
 
 2.49 
 
 14,436 
 
 Ky 
 
 3.41 
 
 5.73 
 
 13,928 
 
 35.3 
 
 0.58 
 
 8.05 
 
 15,328 
 
 1.64 
 
 15,095 
 
 N.Mex. 
 
 2.78 
 
 14.57 
 
 12,294 
 
 41.5 
 
 0.74 
 
 8.79 
 
 14,875 
 
 1.64 
 
 14,630 
 
 N.Mex. 
 
 2.45 
 
 17.40 
 
 12,200 
 
 34.4 
 
 0.96 
 
 6.93 
 
 15,221 
 
 0.80 
 
 15,099 
 
 Ohio... 
 
 3.53 
 
 9.12 
 
 13,072 
 
 42.9 
 
 3.97 
 
 7.04 
 
 14,965 
 
 2.38 
 
 14,642 
 
 Ohio... 
 
 5.59 
 
 8.29 
 
 12,773 
 
 42.8 
 
 3.66 
 
 9.01 
 
 14,832 
 
 3.83 
 
 14,431 
 
 Okla... 
 
 2.09 
 
 20.07 
 
 11,695 
 
 35.5 
 
 7.36 
 
 3.71 
 
 15,025 
 
 1.38 
 
 14,814 
 
 Okla... 
 
 2.81 
 
 8.75 
 
 13,320 
 
 40.8 
 
 2.06 
 
 7.35 
 
 15,061 
 
 1.57 
 
 14,825 
 
 Pa. .... 
 
 2.61 
 
 6.17 
 
 13,997 
 
 38.3 
 
 1.38 
 
 6.94 
 
 15,345 
 
 1.42 
 
 15,127 
 
 Pa 
 
 5.13 
 
 8.71 
 
 13,365 
 
 32.4 
 
 1.00 
 
 7.35 
 
 15,511 
 
 1.07 
 
 15,346 
 
 Tenn. . . 
 
 6.39 
 
 9.53 
 
 12,578 
 
 38.4 
 
 1.17 
 
 7.94 
 
 1 4,960 
 
 1.97 
 
 14,665 
 
 Tenn... 
 
 3.89 
 
 14 .43 
 
 12,514 
 
 33.8 
 
 0.95 
 
 6.70 
 
 15,320 
 
 1.08 
 
 15,137 
 
 Va 
 
 4.44 
 
 5.98 
 
 13,363 
 
 40.2 
 
 0.85 
 
 12.18 
 
 14.918 
 
 2.52 
 
 14,381 
 
 Va 
 
 3.31 
 
 3.76 
 
 14,209 
 
 35.3 
 
 0.97 
 
 5.65 
 
 15,291 
 
 1.49 
 
 15,069 
 
 Wash.. 
 
 2.32 
 
 13.58 
 
 12,443 
 
 44.0 
 
 5.23 
 
 13.93 
 
 14,796 
 
 1.55 
 
 14,569 
 
 W.Va.. 
 
 4.21 
 
 7.22 
 
 13,379 
 
 40.0 
 
 0.72 
 
 10.10 
 
 15,107 
 
 2.11 
 
 14,787 
 
 W.Va. . 
 
 2.86 
 
 5.83 
 
 14,105 
 
 36.4 
 
 0.73 
 
 5.14 
 
 15,448 
 
 1.36 
 
 15,237 
 
 Wyo... 
 
 5.49 
 
 3.12 
 
 13,570 
 
 39.3 
 
 0.99 
 
 11.40 
 
 14,848 
 
 2.13 
 
 14,552 
 
 * H in combustible: Ky., 7.13, and 7.40; W. Va., 7.13; Utah, 7.73 
 The highest II in the other coals is 5.78, a Missouri bituminous. 
 
ANALYSIS AND HEATING VALUE OF COALS. 829 
 
 Classified List of Coals. Continued. 
 
 
 As Received. 
 
 Combustible. 
 
 Air-dry,Ash-free 
 
 Moist. 
 
 Ash. 
 
 B.T.U. 
 
 Vol. 
 
 S. 
 
 o. 
 
 B.T.U. 
 
 Moist. 
 
 B.T.U. 
 
 VI. BITUMINOUS MEDIUM GRADE 
 
 Ala.... 
 
 3.95 
 
 14.59 
 
 11,785 
 
 37.7 
 
 1.37 
 
 10.45 
 
 14,467 
 
 2.69 
 
 14,078 
 
 Alaska . 
 
 7.06 
 
 21.78 
 
 9,846 
 
 44.2 
 
 1.83 
 
 14.11 
 
 13,838 
 
 2.55 
 
 13,484 
 
 Cal.... 
 
 6.95 
 
 6.23 
 
 12,447 
 
 53.8 
 
 4.80 
 
 11.47 
 
 14,336 
 
 5.19 
 
 13,593 
 
 Ill 
 
 8.12 
 
 8.63 
 
 1 2,064 
 
 41.4 
 
 1.36 
 
 12.02 
 
 14,492 
 
 5.15 
 
 13,745 
 
 111 
 
 8.86 
 
 11.66 
 
 1 1 ,702 
 
 39.3 
 
 3.10 
 
 9.03 
 
 14,724 
 
 3.71 
 
 14,177 
 
 Ind.... 
 
 16.91 
 
 17.37 
 
 9,524 
 
 40.9 
 
 2.88 
 
 9.50 
 
 14,492 
 
 5.48 
 
 13,698 
 
 Ind.... 
 
 7.88 
 
 14.20 
 
 11,146 
 
 47.3 
 
 6.60 
 
 9.96 
 
 14,305 
 
 5.01 
 
 13,576 
 
 Iowa. . . 
 
 13.88 
 
 14.01 
 
 10,244 
 
 51.2 
 
 8.53 
 
 8.96 
 
 14,206 
 
 5.35 
 
 13,445 
 
 Iowa. . . 
 
 8.24 
 
 16.00 
 
 11,027 
 
 40.6 
 
 6.64 
 
 8.03 
 
 14,555 
 
 6.24 
 
 13,647 
 
 Kan . . . 
 
 6.95 
 
 12.19 
 
 1 1 ,905 
 
 44.2 
 
 9.94 
 
 5.64 
 
 14,724 
 
 4.09 
 
 14,121 
 
 Kan... 
 
 2.50 
 
 12.45 
 
 1 2,900 
 
 39.8 
 
 5.22 
 
 5.98 
 
 14,922 
 
 4.30 
 
 14,269 
 
 Ky.... 
 
 7.92 
 
 10.06 
 
 12.022 
 
 44.0 
 
 4.29 
 
 8.90 
 
 14,657 
 
 6.52 
 
 13.702 
 
 Ky.... 
 
 5.27 
 
 14.18 
 
 11,950 
 
 43.5 
 
 5.64 
 
 7.46 
 
 14,836 
 
 2.98 
 
 14,394 
 
 Mich... 
 
 11.91 
 
 6.84 
 
 11,781 
 
 38.8 
 
 1.53 
 
 9.54 
 
 14,499 
 
 4.70 
 
 13,818 
 
 Mich... 
 
 11.55 
 
 3.25 
 
 12,442 
 
 37.1 
 
 1.11 
 
 10.51 
 
 14,603 
 
 5.59 
 
 13,786 
 
 Mo.... 
 
 17.30 
 
 23.38 
 
 8,240 
 
 44.6 
 
 4.96 
 
 11.83 
 
 13,892 
 
 3.42 
 
 13,416 
 
 Mo.... 
 
 12.67 
 
 4.83 
 
 12,487 
 
 50.2 
 
 6.21 
 
 6.12 
 
 15,134 
 
 5.68 
 
 14.276 
 
 Mont. . 
 
 3.51 
 
 19.50 
 
 10,881 
 
 34.3 
 
 4.86 
 
 9.50 
 
 14,134 
 
 2.42 
 
 13.791 
 
 Mont . . 
 
 5.77 
 
 10.57 
 
 12,281 
 
 39.6 
 
 0.60 
 
 9.77 
 
 14,681 
 
 2.30 
 
 14,342 
 
 N.Mex. 
 
 5.02 
 
 12.00 
 
 12,064 
 
 44.3 
 
 0.68 
 
 12.70 
 
 14,539 
 
 3.06 
 
 14,093 
 
 Ohio... 
 
 4.14 
 
 9.38 
 
 12,874 
 
 37.8 
 
 0.63 
 
 11.58 
 
 14,269 
 
 4.69 
 
 14,152 
 
 Ohio... 
 
 7.71 
 
 11.95 
 
 11,515 
 
 47.7 
 
 5.74 
 
 9.44 
 
 1 4,332 
 
 3.30 
 
 13,523 
 
 Okla... 
 
 7.04 
 
 10.01 
 
 12,202 
 
 41.7 
 
 2.31 
 
 9.26 
 
 14,711 
 
 4.31 
 
 14,075 
 
 Utah... 
 
 5.58 
 
 8.99 
 
 12,170 
 
 45.6 
 
 0.60 
 
 13.30 
 
 14,245 
 
 4.98 
 
 13,536 
 
 Utah... 
 
 6.05 
 
 4.87 
 
 13,151 
 
 47.2 
 
 0.62 
 
 10.93 
 
 14,764 
 
 2.47 
 
 14,399 
 
 Wash.. 
 
 6.02 
 
 19.35 
 
 10,708 
 
 41.8 
 
 0.57 
 
 12.38 
 
 14,348 
 
 3.26 
 
 13,879 
 
 Wyo... 
 
 3.96 
 
 4.77 
 
 13,502 
 
 39.6 
 
 0.84 
 
 9.25 
 
 14,793 
 
 2.73 
 
 14,391 
 
 VTI. BITUMINOUS Low GRADE. 
 
 Alaska. 
 
 10.77 
 
 14.87 
 
 9,641 
 
 40.8 
 
 0.94 
 
 18.83 
 
 12,964 
 
 5.42 
 
 12,261 
 
 Ill 
 
 11.35 
 
 13.40 
 
 10,733 
 
 46.0 
 
 6.33 
 
 10.53 
 
 14,263 
 
 6.75 
 
 13.300 
 
 111 
 
 14.43 
 
 13.28 
 
 1 0,064 
 
 40.8 
 
 5.55 
 
 12.02 
 
 13,921 
 
 6.02 
 
 13,084 
 
 Ind.... 
 
 12.11 
 
 6.83 
 
 11,952 
 
 42.2 
 
 1.78 
 
 10.55 
 
 14,746 
 
 9.60 
 
 13,329 
 
 Ind.... 
 
 13.18 
 
 15.63 
 
 10,030 
 
 44.8 
 
 6.73 
 
 9.69 
 
 14,089 
 
 6.17 
 
 13,220 
 
 Iowa. . . 
 
 14.08 
 
 10.96 
 
 10,723 
 
 47.5 
 
 5.69 
 
 9.73 
 
 14,305 
 
 11.33 
 
 12.684 
 
 Mo 
 
 15.36 
 
 10.99 
 
 10,460 
 
 47.3 
 
 4.85 
 
 10.68 
 
 14,202 
 
 7.37 
 
 13,156 
 
 Mont . . 
 
 9.76 
 
 16.42 
 
 10,235 
 
 37.5 
 
 0.86 
 
 16.21 
 
 13,865 
 
 7.58 
 
 12,813 
 
 Mont. . 
 
 10.88 
 
 26.88 
 
 7.742 
 
 32.6 
 
 2.88 
 
 16.14 
 
 12,438 
 
 8.09 
 
 11,432 
 
 N.Mex. 
 
 12.29 
 
 6.99 
 
 11,252 
 
 42.8 
 
 0.78 
 
 14.00 
 
 13,939 
 
 11.70 
 
 12,309* 
 
 N.Mex. 
 
 15.79 
 
 9.37 
 
 9,970 
 
 46.8 
 
 2.38 
 
 15.69 
 
 13,322 
 
 7.87 
 
 12,008* 
 
 Okla... 
 
 8.29 
 
 25.05 
 
 9,110 
 
 45.9 
 
 5.93 
 
 10.62 
 
 13,667 
 
 7.74 
 
 12,609 
 
 Ore 
 
 
 
 
 48 1 
 
 1 65 
 
 
 14618 
 
 11.88 
 
 1 2,882 
 
 Utah... 
 
 10.35 
 
 9.62 
 
 10,874 
 
 45.4 
 
 7.27 
 
 16.05 
 
 13,586 
 
 9.65 
 
 12,276 
 
 Utah... 
 
 14.19 
 
 9.92 
 
 9.927 
 
 44.0 
 
 7.10 
 
 14.18 
 
 13,081 
 
 11.47 
 
 11,374 
 
 Wash.. 
 
 12.05 
 
 10.41 
 
 10,414 
 
 47.5 
 
 0.44 
 
 17.11 
 
 13.423 
 
 6.56 
 
 12,548 
 
 VIII. SUB-BITUMINOUS AND LIGNITE. 
 
 Ark.... 
 
 39.43 
 
 9.71 
 
 6,356 
 
 52.1 
 
 0.96 
 
 21.17 
 
 12,497 
 
 22.00 
 
 9,750 
 
 Cal.... 
 
 18.51 
 
 15.49 
 
 8,507 
 
 53.5 
 
 4.62 
 
 16.79 
 
 12,890 
 
 10.95 
 
 11.478 
 
 Colo... 
 
 19.65 
 
 6.00 
 
 8,638 
 
 41.4 
 
 0.44 
 
 16.97 
 
 11,619 
 
 8.21 
 
 10,664 
 
 Colo. . . 
 
 19.28 
 
 4.70 
 
 9,064 
 
 45.5 
 
 0.51 
 
 16.52 
 
 13,239 
 
 15.35 
 
 10,094 
 
 Mont. . 
 
 30.00 
 
 11.90 
 
 6,914 
 
 69.0 
 
 1.86 
 
 23.47 
 
 11,900 
 
 15.55 
 
 10.143 
 
 Mont. . 
 
 24.59 
 
 14.01 
 
 6,208 
 
 54.1 
 
 0.67 
 
 26.64 
 
 10,211 
 
 25.02 
 
 7.656 
 
 N.Dak. 
 
 35.96 
 
 7.75 
 
 7,069 
 
 56.7 
 
 2.04 
 
 17.69 
 
 12,557 
 
 26.20 
 
 8,886 
 
 N.Dak. 
 
 38.92 
 
 5.39 
 
 6,739 
 
 45.9 
 
 0.86 
 
 22.67 
 
 12,101 
 
 11.66 
 
 10,885 
 
 Ore 
 
 16.10 
 
 13.17 
 
 9.031 
 
 44.0 
 
 1.15 
 
 19.68 
 
 12,769 
 
 10.16 
 
 11,471 
 
 Ore.... 
 
 13.77 
 
 7.46 
 
 9,054 
 
 47.0 
 
 5.52 
 
 
 11,493 
 
 7.05 
 
 10,684 
 
 S. Dak. 
 
 30.45 
 
 12.15 
 
 6,944 
 
 40.0 
 
 0.68 
 
 
 12,098 
 
 15.77 
 
 10,189 
 
 Tex.... 
 
 34.70 
 
 11.20 
 
 7,056 
 
 59.6 
 
 1.46 
 
 J8.99 
 
 13,043 
 
 15.73 
 
 11,077 
 
 Tex 
 
 33.71 
 
 7.28 
 
 7,348 
 
 49.6 
 
 0.90 
 
 20.54 
 
 12.452 
 
 11.82 
 
 11.036 
 
 (Table continued on p. 830.) 
 
830 
 
 FUEL. 
 
 Classified List of Coals. Continued. 
 
 
 As Received. 
 
 Combustible. 
 
 Air-dry, Ash-free 
 
 Moist. 
 
 Ash. 
 
 B.T.U. 
 
 Vol. 
 
 S. 
 
 o. 
 
 B.T.U. 
 
 Moist. | B.T.U. 
 
 VIII. SUB-BITUMINOUS AND LIGNITE. Continued. 
 
 Utah... 
 
 16.59 
 
 13.44 
 
 7,882 
 
 46.6 
 
 4.88 
 
 22.14 
 
 1 1 ,264 
 
 15.35 
 
 9*535 
 
 Wash.. 
 
 27 .17 
 
 10.92 
 
 7,569 
 
 54.6 
 
 0.53 
 
 22.06 
 
 12,226 
 
 17.21 
 
 10,122 
 
 Wyo... 
 
 10.26 
 
 9.83 
 
 10,354 
 
 27.8 
 
 1.09 
 
 10.94 
 
 12,956 
 
 9.56 
 
 11,573 
 
 Wyo... 
 
 31.37 
 
 10.12 
 
 5,634 
 
 50.6 
 
 2.17 
 
 29.86 
 
 9.630 
 
 22.69 
 
 7,458t 
 
 NOT CLASSIFIED^ 
 
 R. I... 
 
 23.68 
 
 30.77 
 
 5,976 
 
 6.6 
 
 0.05 
 
 5.59 
 
 13,120 
 
 1.26 
 
 12,955 
 
 R. I . . . 
 
 2.41 
 
 19.06 
 
 10,996 
 
 6.3 
 
 0.09 
 
 3.27 
 
 14,002 
 
 0.52 
 
 13,930 
 
 Alaska . 
 
 5.71 
 
 34.15 
 
 8,386 
 
 21.7 
 
 10.76 
 
 5.28 
 
 13,945 
 
 4.77 
 
 13,279 
 
 Ark. . . . 
 
 5.26 
 
 24.81 
 
 10,451 
 
 21.0 
 
 1.43 
 
 6.44 
 
 14,945 
 
 1.77 
 
 14,722 
 
 Idaho.. 
 
 34.28 
 
 13.38 
 
 8,613 
 
 50.9 
 
 4.77 
 
 
 16,457 
 
 16.42 
 
 13,757 
 
 * These two samples are classed as sub-bituminous by the Bureau of 
 Mines. 
 
 t Sample from surface exposure; coal badly weathered. 
 
 t The Rhode Island coals are graphitic and are not used as fuel. The 
 two samples from Alaska and Arkansas may be classed as semi-bitumi- 
 nous by their percentage of volatile matter, but they are higher in 
 oxygen and in moisture, and lower in heating value than other semi- 
 bituminous coals. The Idaho coal is apparently a cannel coal very 
 high in moisture, but the ultimate analysis is lacking. 
 
 Purchase of Coal under Specifications. It is customary for large 
 users of coal to purchase it under specifications of its analysis or heating 
 value with a penalty attached for failure to meet the specifications. The 
 following standards for a specification were given by the author in his 
 "Steam Boiler Economy," 1901. (Revised in 2d edition, 1915): 
 
 Anthracite and Semi-anthracite. The standard is a coal containing 
 5 % volatile matter, not over 2 % moisture, and not over 10 % ash. A 
 premium of 0.5% on the price will be given for each per cent of volatile 
 matter above 5% up to and including 15%, and a reduction of 2% on 
 the price will be made for each 1% of moisture and ash above the 
 standard. 
 
 Semi-bituminous and Bituminous. The standard is a semi-bitumi- 
 nous coal containing not over 20% volatile matter, 2 % moisture, 6 % ash. 
 A reduction of 1 % in the price will be made for each 1 % of volatile mat- 
 ter in excess of 25 % , and of 2 % for each 1 % of ash and moisture in excess 
 of the standard. 
 
 For western coals in which the volatile matter differs greatly in its 
 percentage of oxygen, the above specification based on proximate analy- 
 sis may not be sufficiently accurate, and it is well to introduce either the 
 heating value asdetermined by a calorimeter or the percentage of oxygen. 
 The author has proposed the following for Illinois coal: 
 
 The standard is a coal containing not over 6% moisture and 10% ash 
 in an air-dried sample, and whose heating value is 14,500 B.T.U. per 
 pound of combustible. For lower heating value per Ib. of the com- 
 bustible, the "price shall be reduced proportionately, and for each 1% 
 increase in ash or moisture above the specified figures, 2% of the price 
 shall be deducted. 
 
 Several departments of the U. S. government now purchase coal under 
 specifications. See paper on the subject by D. T. Randall, Bulletin No. 
 339, U. S. Geological Survey, 1908, also "Steam Boiler Economy,' 
 2d edition. 
 
 Weathering of Coal. (I. P. Kimball, Trans. A. I. M. E., viii, 204.) 
 The effect of the weathering of coal, while sometimes increasing it 
 weight, is to diminish the carbon ana disposable hydrogen and to increase 
 the oxygen and indisposable hydrogen. Hence a reduction in the cal- 
 orific value. An excess of pyrites in coal tends to produce rapid oxida- 
 tion and mechanical disintegration of the mass, with development of 
 heat, loss of coking power, and spontaneous ignition. 
 
 The only appreciable results of the weathering of anthracite are con- 
 
PRESSED FUEL. 831 
 
 fined to the oxidation of its accessory pyrites. In coking coals, however, 
 weathering reduces and finally destroys the coking power. 
 
 Richters found that at a temperature of 158 to 180 Fahr., three coals 
 lost in fourteen days an average of 3.6% of calorific power. It appears 
 from the experiments of Richters and Reder that when there is no rise 
 of temperature of coal piled in heaps and exposed to the air for nine to 
 twelve months, it undergoes no sensible change, but when the coal 
 becomes heated it suffers loss of C and H by oxidation and increases in 
 weight by the fixation of oxygen. (See also paper by R. P. Rothwell, 
 Trans. A. I. M. E., iv. 55.) 
 
 Experiments by S. W. Parr and N. D. Hamilton (Bull. No. 17 of 
 Univ'y of 111. Eng'g Experiment Station, 1907) on samples of about 
 100 Ib. each, show that no appreciable change takes place in coal sub- 
 merged in water. Their conclusions are: 
 
 (a) Submerged coal does not lose appreciably in heat value. 
 
 (ft) Outdoor exposure results in a loss of heat value varying from 2 
 to 10 per cent. 
 
 (c) Dry storage has no advantage over storage in the open except 
 with high sulphur coals, where the disintegrating effect of sulphur in the 
 process of oxidation facilitates the escape or oxidation of the hydrocar- 
 bons. 
 
 |* (d) In most cases the losses in storage appear to be practically com- 
 plete at the end of five months. From the seventh to the ninth month 
 the loss is inappreciable. 
 
 This paper contains also a historical review of the literature on weath- 
 ering and on spontaneous combustion, with a summary of the opinions 
 of various authorities. 
 
 Later experiments on storing carload lots of Illinois coals (W. F. 
 Wheeler, Trans. A. I. M. E., 1908) confirms the above conclusions, ex- 
 cept that 4 per cent seems to be amply sufficient to coyer the losses sus- 
 tained by Illinois coals under regular storage-conditions, the larger 
 losses indicated in the former series being probably due to the small size 
 of the samples exposed. 
 
 Investigations by the U. S. Bureau of Mines in 1910 (Technical 
 Paper No. 2) showed that New River (Va.) coal lost less than 1% in 
 heating value in one year by weathering in the open, and Pocahontas 
 coal less than 0.4%. 
 
 Pressed Fuel. - (E. F. Loiseau, Trans. A. I. M. E., viii. 314.) 
 Pressed fuel has been made from anthracite dust by mixing the dust with 
 ten per cent of its bulk of dry pitch, which is prepared by separating 
 from tar at a temperature of 572 F. the volatile matter it contains. The 
 mixture is kept heated by steam to 212, at which temperature the pitch 
 acquires its cementing properties, and is passed between two rollers, on 
 the periphery of which are milled out a series of semi-oval cavities. The 
 lumps of the mixture, about the size of an egg, drop out under the 
 rollers on an endless belt, which carries them to a screen in eight minutes, 
 which time is sufficient to cool the lumps, and they are then ready for 
 delivery. 
 
 The enterprise of making the pressed fuel above described was not 
 commercially successful, on account of the low price of other coal. In 
 France, however, "briquettes" are regularly made of coal-dust (bitu- 
 minous and semi-bituminous). 
 
 Experiments with briquets for use in locomotives have been made 
 by the Penna. R. R. Co., with favorable results, which were reported at 
 the convention on the Am. Ry. Mast. Mechs. Assn. (Eng. News, July 2, 
 1908). A rate of evaporation as high as 19 Ib. per sq. ft. of heating 
 surface per hour was reached. The comparative economy of raw coal 
 and of briquets was as follows: 
 
 Evap.persq. ft. heat. surf. per hr.,lbs. 8 10 12 14 16 
 Evap. from and at / Lloy dell coal.. . 9.5 8.8 8.0 7.3 6.6 
 2 1 2 per Ib. of fuel \Briquettedcoal. 10.7 10.2 9.7 9.2 8.7 
 
 The fuel consumed per draw-bar horse-power with the locomotive 
 running at 37.8 miles per hour and a cut-off of 25% was: with raw coal, 
 4.48 Ibs.; with round briquets, 3.65 Ibs. 
 
 Experiments on different binders for briquets are discussed by J. E. 
 Mills in Bulletin No. 343 of the U. S. Geological Survey, 1908. 
 
 Briquetting tests made at the St, Louis exhibition, 1904, with 
 
832 
 
 FUEL. 
 
 descriptions of the machines used are reported in Bulletin No. 201 of 
 the U. S. Geological Survey, 1905. See also paper on Coal Briquet ting 
 in the U. S., by E. W. Parker, Trans. A. I. M. E., 1907. 
 
 Spontaneous Combustion of Coal. (Technical Paper 16, U. S. 
 Bureau of Mines, 1912.) Spontaneous combustion is brought about 
 by slow oxidation in an air supply sufficient to support the oxidation, 
 but insufficient to carry away all the heat formed. Mixed lump and 
 fine, i. e., run-of-mine, with a large percentage of dust, and piled so as 
 to admit to the interior a limited supply of air, make ideal conditions 
 for spontaneous heating. High volatile matter does not of itself in- 
 crease the liability to spontaneous heating. 
 
 Pocahontas coal gives a great deal of trouble with spontaneous 
 fires in the large storage piles at Panama. The high- volatile coals of the 
 west are usually very liable to spontaneous heating. 
 
 The influence of moisture and that of sulphur upon spontaneous 
 heating of coal are questions not yet settled. Observation by the 
 Bureau of Mines in many actual cases has not developed any instances 
 where moisture could be proven to promote heating. Sulphur has been 
 shown to have, in most cases, only a minor influence. On the other 
 hand, a Boston company, using Nova Scotia coal of 3 to 4 per cent 
 sulphur, has much trouble with spontaneous fires in storage. 
 
 Freshly mined coal and even fresh surfaces exposed by crushing 
 lump coal exhibit a remarkable avidity for oxygen, but after a time be- 
 come coated with oxidized material, "seasoned," as it were, so that the 
 action of the air becomes much less vigorous. It is found that if coal 
 which has been stored for six weeks or two months and has even be- 
 come already somewhat heated, be rehandled and thoroughly cooled 
 by the air, spontaneous heating rarely begins again. 
 
 While the following recommendations may under certain conditions 
 be found impracticable, they are offered as being advisable precautions 
 for safety in storing coal whenever their use does not involve an un- 
 reasonable expense. 
 
 1. Do not pile over 12 feet deep nor so that any point in the interior 
 will be over 10 feet from an air-cooled surface. 
 
 2. If possible, store only in lump. 
 
 3. Keep dust out as much as possible; therefore reduce handling 
 to a minimum. 
 
 4. Pile so that lump and fine are distributed as evenly as possible; 
 not, as is often done, allowing lumps to roll down from a peak and form 
 air passages at the bottom. 
 
 5. Rehandle and screen after two months. 
 
 6. Keep away external sources of heat even though moderate in 
 degree. 
 
 7. Allow six weeks' "seasoning" after mining before storing. 
 
 8. Avoid alternate wetting and drying. 
 
 9. Avoid admission of air to interior of pile through interstices 
 around foreign objects such as timbers or irregular brick work; also 
 through porous bottoms such as coarse cinders. 
 
 10. Do not try to ventilate by pipes, as more harm is often done 
 than good. 
 
 COKE. 
 
 Coke is the solid material left after evaporating the volatile ingredi- 
 ents of coal, either by means of partial combustion in furnaces called 
 coke ovens, or by distillation in the retorts of gas-works. 
 
 Coke made in ovens is preferred to gas coke as fuel. It is of a dark 
 gray color, with slightly metallic luster, porous, brittle, and hard. 
 
 The proportion of coke yielded by a given weight of coal is very differ- 
 ent for different kinds of coal, ranging from 0.9 to 0.35. 
 
 Being of a porous texture, it readily attracts and retains water from 
 the atmosphere, and sometimes, if it is kept without proper shelter, 
 from 0.15 to 0,20 of its gross weight consists of moisture. 
 
COKE. 833 
 
 Analyses of Coke. 
 
 (From report of John R. Proctor, Kentucky Geological Survey.) 
 
 Where Made. 
 
 Fixed 
 Carb'n. 
 
 Ash. 
 
 Sul- 
 phur. 
 
 Connellsville, Pa. (Average of 3 samples) 
 
 88.96 
 80.51 
 87.29 
 92.53 
 92.38 
 93.23 
 
 9.74 
 16.34 
 10.54 
 5.74 
 7.21 
 5.69 
 
 0.810 
 1.595 
 1.195 
 0.597 
 0.562 
 0.749 
 
 Chattanooga, Tenn. " 4 ' 
 
 Birmingham, Ala " 4 ' 
 
 Pocahontas, Va. " 3 ' 
 
 New River, W. Va. " 8 ' 
 
 Big Stone Gap, Ky. " 7 ' 
 
 
 Experiments In Coking. CONNELLSVILLE REGION. 
 (John Fulton.'Amer. Mfr., Feb. 10, 1893.) 
 
 
 
 
 __ 
 
 
 V 
 
 X 
 
 
 Per cent of Yield. 
 
 
 In 
 
 
 
 
 
 
 S 
 
 
 
 1 
 
 3 
 
 .S a 
 
 aj s. 
 
 1 
 
 1 
 
 1 
 U<d 
 
 O 
 
 p o; 
 
 2% 
 
 g 
 
 
 1 
 
 ?! 
 
 ^j 
 
 y 
 
 O 
 
 o 
 
 So 
 
 "d^ 
 
 g 
 
 SS 
 
 ^ 
 
 ^ s 
 
 & 
 
 So 
 
 ?3 
 
 ^6 
 
 ^-1 
 
 1 
 
 H 
 
 O 
 
 ^ 
 
 s 
 
 a 
 
 h 
 
 2 
 
 S 
 
 s 
 
 H 
 
 1 
 
 
 h. m. 
 
 Ib. . 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 
 
 
 
 
 1 
 
 67 00 
 
 12.420 
 
 99 
 
 385 
 
 7,518 
 
 7.903 
 
 0.80 
 
 3 10 
 
 60.53 
 
 63.63 
 
 35.57 
 
 2 
 
 68 00 
 
 11,090 
 
 90 
 
 359 
 
 6.580 
 
 6,939 
 
 0.81 
 
 3.24 
 
 59 33 
 
 62.57 
 
 36.62 
 
 3 
 
 45 00 
 
 9.120 
 
 77 
 
 272 
 
 5.418 
 
 5,690 
 
 0.84 
 
 2.98 
 
 59.41 
 
 62.39 
 
 36.77 
 
 4 
 
 45 00 
 
 9.020 
 
 74 
 
 349 
 
 5.334 
 
 5,683 
 
 0.82 
 
 3.87 
 
 59.13 
 
 63.00 
 
 36.18 
 
 These results show, in a general average, that Connellsville coal care- 
 fully coked in a modern beehive oven will yield 66.17% of marketable 
 coke, 2.30% of small coke or breeze, and 0.82% of ash. 
 
 The total average loss in volatile matter expelled from the coal in 
 coking amounts to 30.71 %. 
 
 The beehive coke 9ven is 12 feet in diameter and 7 feet high at crown 
 of dome. It is used in making 48 and 72 hour coke. [The Belgian type 
 of beehive oven is rectangular in shape.] 
 
 In making these tests the coal was weighed as it was charged into the 
 oven; the resultant marketable coke, small coke or breeze and ashes 
 weighed dry as they were drawn from the oven. 
 
 Coal Washing. In making coke from coals that are high in ash and 
 sulphur, it is advisable to crush and wash the coal before coking it. A 
 coal- washing plant at Brookwood, Ala., has a capacity of 50 tons per 
 hour. The average percentage of ash in the coal during ten days' run 
 varied from 14 % to 21 %, in the washed coal from 4.8 % to 8.1 %, and in 
 the coke from 6.1% to 10.5%. During three months the average re- 
 duction of ash was 60.9%. (Eng. and Mining Jour., March 25, 1893.) 
 
 An experiment on washing Missouri No. 3 slack coal is described in 
 Bulletin No. 3 of the Engineering Experiment Station of Iowa State Col- 
 lege, 1905. The raw coal analyzed: moisture, 14.37; ash, 28.39; sul- 
 phur, 4.30; and the washed coal, moisture, 23.90; ash, 7.59; sulphur, 
 2.89. Nearly 25% of the coal was lost in the operation. 
 
 Recovery of By-products in Coke Manufacture. In Germany 
 considerable progress has been made in the recovery of by-products. 
 The Hoffman-Otto oven has been most largely used, its principal feature 
 being that it is connected with regenerators. In 1884 40 ovens on this 
 system were running, and in 1892 the number had increased to 1209. 
 
 A Hoffman-Otto oven in Westphalia takes a charge of 6 1/4 tons of dry 
 coal and converts it into coke in 48 hours. The product of an oven 
 annually is 1025 tons in the Ruhr district, 1170 tons in Silesia, and 960 
 tons in the Saar district. The yield from dry coal is 75% to 77% of 
 coke, 2.5% to 3% of tar, and 1.1% to 1.2% of sulphate of ammonia in 
 the Ruhr district; 65% to 70% of coke. 4% to 4.5% of tar, and 1% to 
 1 .25% of sulphate of ammonia in the Upper Silesia region, and 68% to 
 72% of coke, 4% to 4,3% of tar and 1.8% to 1.9% of sulphate of 
 
834 FUEL. 
 
 ammonia in the Saar district. A group of 60 Hoffman ovens, therefore, 
 yields annually the following: 
 
 District. 
 
 Coke, 
 tons. 
 
 Tar, 
 tons. 
 
 Sulphate 
 Ammo- 
 nia, tons. 
 
 Ruhr . 
 
 51 300 
 
 1 860 
 
 780 
 
 Upper Silesia 
 
 48.000 
 
 3,000 
 
 840 
 
 Saar 
 
 40.500 
 
 2,400 
 
 492 
 
 An oven which has been introduced lately into Germany in connection 
 with the recovery of by-products is the Semet-Solyay, which works hot- 
 ter than the Hoffman-Otto, and for this reason 73 % to 77 % of gas coal 
 can be mixed with 23% to 27% of coal low in volatile matter, and yet 
 yield a good coke. Mixtures of this kind yield a larger percentage of 
 coke, but, on the other hand, the amount of gas is lessened, and there- 
 fore the yield of tar and ammonia is not so great. 
 
 The yield of coke by the beehive and the retort ovens respectively is 
 given as follows in a pamphlet of the Solvay Process Co. : Connellsville 
 coal : beehive, 66 % , retort, 73 % ; Pocahontas : beehive, 62 % , retort, 83 % ; 
 Alabama: beehive, 60%, retort, 74%. (See article in Mineral Industry, 
 vol. viii. 1900.) 
 
 References: F. W. Luerman, Verein Deutscher Eisenhuettenleute 
 1891, Iron Age, March 31, 1892; Amer. Mfr., April 28, 1893. An ex- 
 cehent series of articles on the manufacture of coke, by John Fulton, of 
 Johnstown, Pa., is published in the Colliery Engineer, beginning in 
 January, 1893. 
 
 Since the above was written, great progress in the introduction of coke 
 ovens with by-product attachments has been made in the United States, 
 especially by the Semet-Solvay Co., Syracuse, N. Y. See paper on The 
 Development of the Modern By-product Coke-oven, by C. G. Atwater, 
 Trans. A. I. M. E., 1902. 
 
 Generation of Steam from Waste Heat and Gases of Coke-ovens. 
 (Erskine Ramsey, Amer. Mfr., Feb. 16, 1894.) The gases from a num- 
 ber of adjoining ovens of the beehive type are led into a long horizontal 
 flue, and thence to a combustion-chamber under a battery of boilers. 
 Two plants are in satisfactory operation at Tracy City, Tenn., and two 
 at Pratt Mines, Ala. 
 
 A Bushel of Coal. The weight of a bushel of coal in Indiana is 70 
 Ibs.; in Penna., 76 Ibs.; in Ala., Colo., Ga., 111., Ohio, Tenn., and W. 
 Va., it is 80 Ibs. 
 
 A Bushel of Coke is almost uniformly 40 Ibs., but in exceptional 
 cases, when the coal is very light, 38, 36, and 33 Ibs. are regarded as a 
 bushel, in others from 42 to 50 Ibs. are given as the weight of a bushel; 
 in this case the coke would be quite heavy. 
 
 Products of the Distillation of Coal. S. P. Sadler's Handbook of 
 Industrial Organic Chemistry gives a diagram showing over 50 chemical 
 products that are derived from distillation of coal. The first derivatives 
 are coal-gas, gas-liquor, coal- tar, and coke. From the gas-liquor are 
 derived ammonia and sulphate, chloride and carbonate of ammonia. 
 The coal-tar is split up into oils lighter than water or crude naphtha, 
 oils heavier than water otherwise dead oil or tar, commonly called 
 creosote, and pitch. From the two former are derived a variety of 
 chemical products. 
 
 From the coal-tar there comes an almost endless chain of known com- 
 binations. The greatest industry based upon their use is the manufac- 
 ture of dyes, and the enormous extent to which this has grown can be 
 judged from the fact that there are over 600 different coal-tar colors in 
 use, and many more which as yet are too expensive for this purpose. 
 Many medicinal preparations come from the series, pitch for paving 
 purposes, and chemicals for the photographer, the rubber manufacturers 
 and tanners, as well as for preserving timber and cloths. 
 
 The composition of the hydrocarbons in a soft coal is im certain and 
 quite complex; but the ultimate analysis of the average coal shows that 
 it approaches quite nearly to the composition of CH4 (marsh-gas). (W. 
 H. Blauvelt, Trans. A, I, M, E,, xx. 625.) 
 
WOOD AS FUEL. 
 
 835 
 
 WOOD AS FUEL. 
 
 Wood, when newly felled, contains a proportion of moisture which 
 varies very much in different kinds and in different specimens, ranging 
 between 30% and 50%, and being on an average about 40%. After 8 
 or 12 months ordinary drying in the air the proportion of moisture is 
 from 20 to 25%. This degree of dryness, or almost perfect dryness if 
 required, can be produced by a few days' drying in an oven supplied with 
 air at about 240 F. When coal or coke is used as the fuel for that oven, 
 1 Ib. of fuel suffices to expel about 3 Ib. of moisture from the wood. 
 This is the result of experiments on a large scale by Mr. J. R. Napier. 
 If air-dried wood were used as fuel for the oven, from 2 to 2 H Ib- of 
 wood would probably be required to produce the same effect. 
 
 The specific gravity of different kinds of wood ranges from 0.3 to 1.2. 
 
 Perfectly dry wood contains about 50% of carbon, the remainder con- 
 sisting almost entirely of oxygen and hydrogen in the proportions which 
 form water. The coniferous family contains a small quantity of turpen- 
 tine, which is a hydrocarbon. The proportion of ash in wood is from 
 1 % to 5 % . The total heat of combustion of all kinds of wood, when dry, 
 is almost exactly the same, and is that due to the 50% of carbon. 
 
 The above is from Rankine: but according to the table by S. P. Sharp- 
 less in Jour. C. I. W., iv. 36, the ash varies from 0.03% to 1.20% in 
 American woods, and the fuel value, instead of being the same for all 
 woods, ranges from 3667 (for white oak) to 5546 calories (for long-leaf 
 pine) = 6600 to 9883 British thermal units for dry wood, the fuel value 
 of 0.50 Ib. carbon being 7300 B.T.U. 
 
 Heating Value of Wood. The following table is given in several 
 books of reference, authority and quality of coal referred to not stated. 
 
 The weight of one cord of different woods (thoroughly air-dried) in 
 pounds is about as follows: 
 Hickory or hard maple . . 4500 equal to 1800 coal. (Others give 2000. 
 
 White oak 3850 " 1540 " ( " 1715. 
 
 Beech, red and black oak 3250 " 1300 " ( " 1450. 
 
 Poplar, chestnut, & elm. . 2350 " 940 " ( 1050. 
 
 The average pine 2000 " 800 " ( " 925. 
 
 Referring to the figures in the last column, it is said: 
 
 From the above it is safe to assume that 2 1/4 Ib. of dry wood are equal 
 to 1 Ib. average quality of soft coal and that the full value of the same 
 weight of different woods is very nearly the same^ that is, a pound of 
 hickory is worth no more for fuel than a pound of pine, assuming both to 
 be dry. It is important that the wood be dry, as each 10% of water or 
 moisture in wood will detract about 12 % from its value as fuel. 
 
 Taking an average wood of the analysis C 51 %, H 6.5%, O 42.0%, ash 
 0.5%, perfectly dry, its fuel value per pound, according to Dulong's 
 
 formula, V = Fl4,600 C + 62,000/H -)!> is 8221 British thermal 
 
 units. If the wood, as ordinarily dried in air, contains 25 % of moisture, 
 then the heating value of a pound of such wood is three quarters of 
 8221 = 6165 heat-units, less the heat required to heat and evaporate the 
 1/4 Ib. of water from the atmospheric temperature, and to heat the steam 
 made from this water to the temperature of the chimney gases, say 
 150 heat-units per pound to heat the water to 212, 970 units to evap- 
 orate it at that temperature, and 100 heat-units to raise the temperature 
 of the steam to 420 F., or 1220 in all = 305 for 1/4 Ib., which, subtracted 
 from the 6165, leaves 5860 heat-units as the net fuel value of the wood 
 per pound, or about 0.4 that of a pound of carbon. 
 
 Composition of Wood. 
 (Analysis of Woods, by M. Eugene Chevandier.) 
 
 Woods. 
 
 Carbon. 
 
 Hydro- 
 gen. 
 
 Oxygen. 
 
 Nitrogen. 
 
 Ash. 
 
 Beech . . 
 
 49.36% 
 
 6.01% 
 
 42.69% 
 
 0.91% 
 
 1 06% 
 
 Oak. . 
 
 49 64 
 
 5.92 
 
 41.16 
 
 1 29 
 
 1 97 
 
 Birch 
 
 50.20 
 
 6.20 
 
 41.62 
 
 1 15 
 
 81 
 
 Poplar. . 
 
 49.37 
 
 6 21 
 
 41 60 
 
 96 
 
 1 86 
 
 Willow 
 
 49.96 
 
 5.96 
 
 39.56 
 
 0.96 
 
 3.37 
 
 Average 
 
 49.70% 
 
 6.06% 
 
 41.30% 
 
 1.05% 
 
 1,80% 
 
836 
 
 The following table, prepared by M. Violette, shows the proportion of 
 water expelled from wood at gradually increasing temperatures: 
 
 Temperature. 
 
 Water Expelled from 100 Parts of Wood. 
 
 Oak. 
 
 Ash. 
 
 Elm. 
 
 Walnut. 
 
 257 Fahr 
 
 15.26 
 17.93 
 32.13 
 35.80 
 44.31 
 
 14.78 
 16.19 
 21.22 
 27.51 
 33.38 
 
 15.32 
 17.02 
 36.94? 
 33.38 
 40.56 
 
 15.55 
 17.43 
 21.00 
 41.77? 
 36.56 
 
 302 Fahr 
 
 347 Fahr. . 
 
 392 Fahr 
 
 437 Fahr 
 
 The wood operated upon had been kept in store during two years. 
 When wood which has been strongly dried by means of artificial heat is 
 left exposed to the atmosphere, it reabsorbs about as much water as it 
 contains in its air-dried state. 
 
 A cord of wood =4X4X8= 128 cu. ft. About 56% solid wood and 
 44% interstitial spaces. (Marcus Bull, Phila., 1829. J. C. I. W., vol. 
 i. p. 293.) 
 
 B. E. Fernow gives the percentage of solid wood in a cord as deter- 
 mined officially in Prussia (J". C. I. W., vol. iii. p. 20): 
 Timber cords, 74.07% = 80 cu. ft. per cord; 
 Firewood cords (over 6" diam.), 69.44% = 75 cu. ft. per cord; 
 "Billet" cords (over 3" diam.), 55.55% = 60 cu. ft. per cord; 
 "Brush" woods less than 3" diam., 18.52%; Roots, 37.00%. 
 
 CHARCOAL. 
 
 Charcoal is made by evaporating the volatile constituents of wood and 
 peat, either by a partial combustion of a conical heap of the material to 
 be charred, covered with a layer of earth, or by the combustion of a 
 separate portion of fuel in a furnace, in which are placed retorts con- 
 taining the material to be charged. 
 
 According to Peclet, 100 parts by weight of wood when charred in a 
 heap yield from 17 to 22 parts by weight of charcoal, and when charred 
 in a retort from 28 to 30 parts. 
 
 This has reference to the ordinary condition of the wood used in char- 
 coal-making, in which 25 parts in 100 consist of moisture. Of the re- 
 maining 75 parts the carbon amounts to one half, or 37 ^ % of the gross 
 weight of the wood. Hence it appears that on an average nearly half of 
 the carbon in the wood is lost during the partial combustion in a heap, 
 and about one quarter during the distillation in a retort. 
 
 To char 100 parts by weight of wood in a retort, 12 ^ parts of wood 
 must be burned in the furnace. Hence in this process the whole expen- 
 diture of wood to produce from 28 to 30 parts of charcoal is 112% parts; 
 so that if the weight of charcoal obtained is compared with the whole 
 weight of wood expended, its amount is from 25% to 27% and the pro- 
 portion lost is on an average 11 Yz + 37 % = 0.3, nearly. 
 
 According to Peclet, good wood charcoal contains about 0.07 of its 
 weight of ash. The proportion of ash in peat charcoal is very variable 
 and is estimated on an average at about 0.18. (Rankine.) 
 
 Much information concerning charcoal may be found in the Journal of 
 the Charcoal-iron Workers' Assn., vols. i. to vi. From this source the 
 following notes have been taken: 
 
 Yield of Charcoal from a Cord of Wood. From 45 to 50 bushels 
 to the cord in the kiln, and from 30 to 35 in the meiler. Prof. Egleston 
 in Trans. A. I. M. E., viii, 395, says the yield from kilns in the Lake 
 Champlain region is often from 50 to 60 bushels for hard wood and 50 
 for soft wood; the average is about 50 bushels. 
 
 The apparent yield per cord depends largely upon whether the cord is 
 a full cord of 128 cu. ft. or not. 
 
 In a four months' test of a kiln at Goodrich, Term., Dr. H. M. Pierce 
 found results as follows: Dimensions of kiln inside diameter of base, 
 28 ft. 8 in. ; diam. at spring of arch, 26 ft. 8 in. ; height of walls, 8 ft. ; rise 
 of arch, 5 ft. ; capacity, 30 cords. Highest yield of charcoal per cord of 
 wood (measured) 59.27 bushels, lowest 50.14 bushels, average 53.65 
 bushels. No. of charges 12, length of each turn or period from one 
 charging to another 11 days. 7. C. I. W., vol. vi. p. 26.) 
 
MISCELLANEOUS SOLID FUELS. 837 
 
 Results from Different Methods of Charcoal-making* 
 
 
 
 Yield. 
 
 11 
 
 a! 
 
 Coaling Methods. 
 
 Character of Wood Used. 
 
 Bg 
 
 II 
 
 to O< o 
 
 s |1 
 
 
 
 jj* 
 O t, 
 
 
 
 0) 
 
 V 
 
 Hts 
 
 ^0,0 
 
 Odelstjerna's experiments 
 
 Birch dried at 230 F 
 
 
 ^ 9 
 
 
 
 Mathieu's retorts, fuel ex- 
 cluded 
 
 !Air dry, av. good yel- 
 low pine weighing 
 abt.281bs.percu.ft. 
 
 77.0 
 65.8 
 
 28.3 
 24.2 
 
 63.4 
 54.2 
 
 15.7 
 15.7 
 
 Mathieu's retorts, fuel in- 
 
 Swedish ovens, av. results 
 
 f Good dry fir and pine, 
 \ mixed. 
 
 81.0 
 
 27.7 
 
 66.7 
 
 13.3 
 
 Swedish ovens, av. results 
 
 ( Poor wood, mixed fir 
 \ and pine. 
 
 70.0 
 
 25.8 
 
 62.0 
 
 13.3 
 
 Swedish meilers excep- 
 
 !Fir and white-pine 
 
 72.2 
 
 24.7 
 
 59.5 
 
 13.3 
 
 tional . . 
 
 wood mixed. Av. 25 
 
 
 
 
 
 Swedish meilers, av. results 
 
 Ibs. per cu. ft. 
 
 52,5 
 
 18.3 
 
 43.9 
 
 13.3 
 
 American kilns, av. results 
 
 !Av. good yellow pine 
 
 54.7 
 
 22.0 
 
 45.0 
 
 17.5 
 
 American meilers, av. re- 
 
 weighing abt. 25 Ibs. 
 
 
 
 
 17.5 
 
 eults... 
 
 t>er cu. ft. 
 
 42 9 
 
 17 1 
 
 35.0 
 
 
 Consumption of Charcoal in Blast-furnaces per Ton of Pig Iron: 
 
 average consumption according to census of 1880, 1.14 tons charcoal per 
 ton of pig. The consumption at the best furnaces is much below this 
 average. As low as 0.853 ton is recorded of the Morgan furnace; Bay 
 furnace, 0.858; Elk Rapids, 0.884. (1892.) 
 
 Absorption of Water and of Gases by Charcoal. Svedlius, in his 
 hand-book for charcoal-burners, prepared for the Swedish Government, 
 says: Fresh charcoal, also reheated charcoal, contains scarcely any water, 
 but when cool it absorbs it very rapidly, so that, after twenty-four hours, 
 it may contain 4 % to 8 % of water. After the lapse of a few weeks the 
 moisture of charcoal may not increase perceptibly, and may be esti- 
 mated at 10% to 15%, or an average of 12%. A thoroughly charred 
 piece of charcoal ought, then, to contain about 84 parts carbon, 12 parts 
 water, 3 parts ash, and 1 part hydrogen. 
 
 M. Saussure, operating with blocks of fine boxwood charcoal, freshly 
 
 burnt, found that by simply placing such blocks in contact with certain 
 
 gases they absorbed them in the following proportion: t 
 
 Volumes. Volumes. 
 
 Ammonia 90 . 00 Carbonic oxide 9 . 42 
 
 Oxygen 9 . 25 
 
 Nitrogen " 6 . 50 
 
 Carburetted hydrogen 5 . 00 
 
 Hydrogen 1 . 75 
 
 Hydrochloric-acid gas 85 . 00 
 
 Sulphurous acid 65 . 00 
 
 Sulphuretted hydrogen .... 55 . 00 
 Nitrous oxide (laughing-gas) 40 . 00 
 Carbonic acid 35 . 00 
 
 It is this enormous absorptive power that renders of so much value a 
 comparatively slight sprinkling of charcoal over dead animal matter, as a 
 preventive of the escape of odors arising from decomposition. 
 
 In a box or case containing one cubic foot of charcoal may be stored 
 without mechanical compression a little over nine cubic feet of oxygen, 
 representing a mechanical pressure of one hundred and twenty-six pounds 
 to the square inch. From the store thus preserved the oxgyen can be 
 drawn by a small hand-pump, 
 
 MISCELLANEOUS SOLID FUELS. 
 
 Dust Fuel Dust Explosions. Dust when mixed in air burns with 
 such extreme rapidity as in some cases to cause explosions. Explosions 
 of flour-mills have been attributed to ignition of the dust in confined 
 passages. Experiments in England in 1876 on the effect of coal-dust in 
 carrying flame in mines showed that in a dusty passage the flame from a 
 
838 FUEL. 
 
 blown-out shot may travel 50 yards. Prof. F. A. Abel (Trans. A. I. M. E., 
 xiii. 260) says that coal-dust in mines much promotes and extends 
 explosions, and that it may readily be brought into operation as a 
 fiercely burning agent which will carry flame -rapidly as far as its mixture 
 with air extends, and will operate as an explosive agent through the me- 
 dium of a very small proportion of fire-damp in the air of the mine. 
 The explosive violence of the combustion of dust is largely due to the 
 instantaneous heating and consequent expansion of the air. (See also 
 paper on "Coal Dust as an Explosive Agent." by Dr. R. W. Raymond, 
 Trans. A. I. M. E., 1894.) Experiments made in Germany in 1893 
 show that pulverized fuel may be burned without smoke, and with high 
 economy. The fuel, instead of being introduced into the fire-box in the 
 ordinary manner, is first reduced to a powder by pulverizers of any con- 
 struction. In the place of the ordinary boiler fire-box there is a com- 
 bustion chamber in the form of a closed furnace lined with fire-brick and 
 provided with an air-injector. The nozzle throws a constant stream of 
 fuel into the chamber, scattering it throughout the whole space of the 
 fire-box. When this powder is once ignited, and it is very readily done 
 by first raising the lining to a high temperature by an open fire, the 
 combustion continues in an intense and regular manner under the action 
 of the current of air which carries it in. (Mfrs. Record, April, 1893.) 
 
 Records of tests with the Wegener powdered-coal apparatus, which is 
 now (1900) in use in Germany, are given in Eng. News, Sept. 16, 1897. 
 Illustrated descriptions of different forms of apparatus are given in the 
 author's " Steam Boiler Economy." Coal-dust fuel is now extensively 
 used in the United States in rotary kilns for burning Portland cement. 
 
 Powdered fuel was used in the Crompton rotary puddling-furnace at 
 Woolwich Arsenal, England, in 1873. (Jour. I. & S. I., i. 3873, p. 91.) 
 Numerous experiments on the use of powdered fuel for steam boilers 
 were made in the U. S. between 1895 and 1905, but they were not com- 
 mercially successful. 
 
 Peat or Turf, as usually dried in the air, contains from 25 % to 30% of 
 water, which must be allowed for in estimating its heat of combustion. 
 This water having been evaporated, the analysis of M. Regnault gives, 
 in 100 parts of perfectly dry peat of the best quality: C, 58%; H, 6%; 
 O, 31%; Ash, 5%. In some examples of peat the quantity of ash is 
 greater, amounting to 7% and sometimes to 11%. 
 
 The specific gravity of peat in its ordinry state is about 0.4 or 0.5. 
 It can be compressed by machinery to a much greater density. (Rankine.) 
 
 Clark (Steam-engine, i. 61) sives as the average composition of dried 
 Irish peat: C, 59%; H, 6%; O, 30%; N, 1.25%; Ash, 4%. 
 
 Applying Dulong's formula to this analysis, we obtain for the heating 
 value of perfectly dry peat 10,260 heat-units per pound, and for air- 
 dried peat containing 25% of moisture, after making allowance for 
 evaporating the water, 7,391 heat-units per pound. 
 
 A paper on Peat in the U. S., by M. R. Campbell, will be found in 
 Mineral Resources of the U. S. (U. S. Geol. Survey) for 1905, p. 1319. 
 
 Sawdust as Fuel. The heating power of sawdust is naturally the 
 same per pound as that of the wood from which it is derived, but if 
 allowed to get wet it is more like spent tan (which see below). The 
 conditions necessary for burning sawdust are that plenty of room should 
 be given it in the furnace, and sufficient air supplied on the surface of 
 the mass, preferably by means of a fan-blast. The same applies to shav- 
 ings, refuse lumber, etc. Sawdust is frequently burned in saw-mills, etc., 
 by being blown into the furnace by a fan-blast. 
 
 Wet Tan Bark as Fuel. Tan, or oak bark, after having been used 
 in the processes of tanning, is burned as fuel. The spent tan consists of 
 the fibrous portion of the bark. The principal cause of poor economy 
 in the burning of tan bark besides the difficulty of securing good com- 
 bustion in the furnace, is the amount of heat that is carried away in the 
 shape of superheated steam in the chimney gases. If the bark, after 
 partial drying by compression, were further dried in a rotary drier by 
 waste heat from the chimney gases, there would be an important gain 
 in economy. For calculations showing the advantages of drying, and 
 for illustrations of tan-bark furnaces, see "Steam Boiler Economy." 
 
 D. M. Myers (Trans. A. S. M. E., 1909) describes some experiments 
 on tan as a'boiler fuel. One hundred Ib. of air-dried bark fed to the 
 mill will produce 213 Ib. of spent tan containing 65% moisture. Tak* 
 
MISCELLANEOUS SOLID FUELS. 839 
 
 ing 9500 B.T.U. as the heating value per Ib. of dry tan and 500 F. as the 
 temperature of the chimney gases, the available heat in 1 Ib. of wet tan 
 is 2665 B.T.U. Based on this value as much as 71% efficiency has 
 been obtained in a boiler test with a special furnace, or 1.93 Ib. of 
 water evaporated from and at 212 per Ib. of wet tan. The average 
 heating value of dry hemlock tan, as found by a bomb calorimeter in six 
 tests by Dr. Sherman, is 9504 B.T.U. The composition of dry tan is 
 Ash, 1.42; C, 51.80; H,6.04; O, 40.74. By Dulong's formula the heating 
 value would be 8152 B.T.U. 
 
 Straw as Fuel. (Eng'g Mechanics, Feb. 1893, p. 55.) Experiments 
 in Russia showed that winter-wheat straw, dried at 230 F., had the 
 following composition, C, 46.1; H, 5.6; N, 0.42: O, 43.7; Ash, 4.1. Heat- 
 ing value in British thermal units: dry straw, 6290; with 6% water. 
 5770; with 10% water, 5448. With straws of other grains the heating 
 value of dry straw ranged from 5590 for buckwheat to 6750 for flax. 
 
 Clark (S. E., vol. 1, p. 62) gives the mean composition of wheat and 
 barley straw as C, 36; H, 5; O, 38; N, 0.50; Ash, 4.75; Water, 15.75, the 
 two straws varying less than 1 % . The heating value of straw of this 
 composition, according to Dulong's formula, and deducting the heat 
 lost in evaporating the water, is 5155 heat-units. Clark erroneously 
 gives it as 8144 heat-units. 
 
 Bagasse as Fuel in Sugar Manufacture. Bagasse is the name given 
 to refuse sugar-cane, after the juice has been extracted. Prof. L. A. 
 Becuel, in a paper read before the Louisiana Sugar Chemists' Associa- 
 tion, in 1892, says: " With tropical cane containing 12.5% woody fibre, a 
 juice containing. 16. 13% solids, and 83.87% water, "bagasse of, say, 66% 
 and 72% mill extraction has the following percentage composition: 
 
 66% bagasse: Woody Fibre, 37; Combustible Salts, 10; Water, 53. 
 
 72% bagasse: Woody Fibre, 45; Combustible Salts, 9; Water, 46. 
 
 "Assuming that the woody fibre contains 51% carbon, the sugar and 
 other combustible matters an average of 42.1%, and that 12,906 units 
 of heat are generated for every pound of carbon consumed, the 66% 
 bagasse is capable of generating 297,834 heat-units per 100 Ib. as against 
 345,200, or a difference of 47,366 units in favor of the 72% bagasse. 
 
 "Assuming the temperature of the waste gases to be 450 F., that of 
 the surrounding atmosphere and water in the bagasse at 86 F., and the 
 quantity of air necessary for the combustion of one pound of carbon at 
 24 Ib., the lost heat will be as follows: In the waste gases, heating air 
 from 86 to 450F., and in vaporizing the moisture, etc., the 66 % bagasse 
 will require 112,546 heat-units, and 116,150 for the 72% bagasse. 
 
 "Subtracting these quantities from the above, we find that the 66% 
 bagasse will produce 185,288 available heat-units per 100 Ib., or nearly 
 24 % less than the 72 % bagasse, which gives 229,050 units. Accordingly 
 one ton of cane of 2000 Ib. at 66% mill extraction will produce 680 Ib. 
 bagasse, equal to 1,259,958 available heat-units, while the same cane at 
 72% extraction will produce 560 Ib. bagasse, equal to 1,282,680 units. 
 
 "A similar calculation for the case of Louisiana cane containing 10% 
 woody fiore, and 16% total solids in the juice, assuming 75% mill ex- 
 traction, shows that bagasse from one ton of cane contains 1,573,956 
 heat-units, from which 561,465 have to be deducted, which makes such 
 bagasse worth on an average nearly 92 Ib. coal per ton of cane ground. 
 
 "It appears that with the best boiler plants, those taking up all the 
 available heat generated, by using this heat economically the bagasse 
 can be made to supply all the fuel required by our sugar-houses." 
 
 The figures below are from an article by Samuel Vickess (The Engineer, 
 Chicago, April 1, 1903). 
 
 When canes with 12% fibre are ground, the juice extractions and 
 liquid left in the residual bagasse are generally as follows: 
 
 With 
 
 Per Cent of Normal 
 Juice Extracted on 
 Weight of Cane. 
 
 Per Cent of Liquid 
 Left in Bagasse on 
 Weight" of Bagasse. 
 
 Double crushing 
 
 70 
 62 
 72 
 76 
 
 82 
 
 60 
 68 
 57 
 50 
 
 50 
 
 Single crushing 
 
 Crusher and double crushing 
 
 Triple Crushing . 
 
 Crusher and triple crushing with 
 saturation 
 
840 
 
 FUEL. 
 
 The value of bagasse as a fuel depends upon the amount of woody 
 fibre it contains, and the amount of combustible matter (sucrose, 
 glucose, and gums), held in the liquid it retains. 100 Ib. cane with 
 triple crushing gives 76 Ib. juice, and 24 Ib. bagasse, which consists of 12 
 Ib. fibre and 12 Ib. juice. The 12 Ib. of juice contains 16% or 1.92 Ib. 
 sucrose, 0.5% or 0.06 Ib. glucose, 2.5% other organic matter and 1% or 
 0.12 Ib. ash, making a total of 20% or 2.4 Ib. of solid matter, and 80% 
 or 9.6 Ib. of water. Reducing these figures to quantities corresponding 
 to 1 Ib. of bagasse, and multiplying by the heating values of the several 
 substances as given by Stohlmann, viz.: fibre, 7461; sucrose, 6957; 
 glucose, 6646; organic matter, 7461, we find the heating value of the com- 
 bustible in 1 Ib. of bagasse to be 4397 B.T.U. This is the gross heating 
 value which would be obtained in a calorimeter in which the products 
 of combustion were cooled to the temperature of the atmosphere. To 
 find approximately the heat available for generating steam in a boiler 
 we may assume that 10 Ib. of air is used in burning each pound of ba- 
 gasse, that the atmospheric temperature is 82 and the flue gas tempera- 
 ture 462, and that in addition to the 0.4 Ib. water per Ib. bagasse half 
 of the remaining 0.6 Ib. is oxygen and hydrogen in proportions which 
 form water, making 0.7 Ib. water w r hich escapes in the flue gas as super- 
 heated steam. The heat lost in the flue gases per pound of bagasse is 
 10 X 0.24 X (462 - 82) + 0.7 [(212 - 82) + 970 + 0.5 (462 - 212)] = 1770 
 B.T.U. , which subtracted from 4397 leaves 2627 B.T.U. as the net or 
 available heating value, which is equivalent to an evaporation of 2.7 Ib. 
 of water from and at 212. Mr. Vickess states that in practice 1 Ib. of 
 such green bagasse evaporates 2 to 21/4 Ib. from feed water at 100 
 into steam at 90 Ib. pressure. This is equivalent to from 2.31 to 2.59 
 Ib. from and at 212. 
 
 E. W. Kerr, in Bulletin No. 117 of the Louisiana Agricultural Experi- 
 ment Station, Baton Rouge, La., gives the results of a study of many 
 different forms of bagasse furnaces. An equivalent evaporation of 2 1/4 
 Ib. of steam from and at 212 was obtained from 1 Ib. of wet bagasse of 
 a net calorific value of 3256 B.T.U. This net value is that calculated 
 from the analysis by Dulong's formula, minus the heat required to 
 evaporate the moisture and to heat the vapor to the temperature of the 
 escaping chimney gases, 594 F. The approximate composition of 
 bagasse of 75% extraction is given as 51% free moisture, and 28% of 
 water combined with 21 % of carbon in the fibre and sugar. For the 
 best results the bagasse should be burned at a high rate of combustion, 
 at least 100 Ib. per sq. ft of grate per hour. Not more than 1.5 Ib. of 
 bagasse per sq. ft. of heating surface per hour should be burned under 
 ordinary conditions, and not less than 1.5 boiler horse-power should be 
 provided per ton of cane per 24 hours. 
 
 For illustrations of bagasse furnaces see " Steam Boiler Economy." 
 
 LIQUID FUEL. 
 
 Products of the Distillation of Crude Petroleum. 
 
 Crude American petroleum of sp. gr. 0.800 may be split up by fractional 
 distillation as follows (" Robinson's Gas and Petroleum Engines "): 
 
 Temp, of 
 Distillation 
 Fahr. 
 
 Distillate. 
 
 Per- 
 cent- 
 ages. 
 
 Specific 
 Gravity. 
 
 Flashing 
 Point. 
 Deg. F. 
 
 113 
 
 Rhigolene. I 
 
 traces. 
 
 590 to .625 
 
 
 113 to 140 
 140 to 158 
 
 Chymogene. J 
 Gasoline (petroleum spirit) . 
 
 1.5 
 
 .636 to .657 
 
 
 158 to 248 
 248 
 to 
 
 Benzine, naphtha C.benzolene 
 ( Benzine, naphtha B 
 \ Benzine naphtha A 
 
 10. 
 2.5 
 2. 
 
 .680 to .700 
 .714 to .718 
 .725 to .737 
 
 14 
 '"32 " 
 
 347 
 
 ( Polishing oils 
 
 
 
 
 338 and ) 
 
 Kerosene (lamp-oil) 
 
 50. 
 
 802 to .820 
 
 100 to 122 
 
 upwards. J 
 482 ' 
 
 Lubricating oil 
 
 15. 
 
 .850 to .915 
 
 230 
 
 
 
 2 
 
 
 
 
 Residue and Loss 
 
 16. 
 
 
 
LIQUID FUEL. 
 
 841 
 
 Lima Petroleum, produced at Lima, Ohio, is ol a dark green color, 
 very fluid, and marks 48 Baume at 15 C. (sp. gr., 0.792). 
 
 The distillation in fifty parts, each part representing 2% by volume, 
 gave the following results: 
 
 Sp. Per Sp. Per Sp. Per Sp. Per Sp. 
 cent. 
 50 l 
 
 52] 
 
 to ! 
 
 58 t 
 60 
 62 
 64 
 
 Per Sp. Per 
 
 cent. Gr. cent. Gr. cent: Gr. 
 
 2 0.680 18 0.720 34 0.764 
 
 .728 36 .768 
 
 .730 38 
 
 .735 40 
 
 .740 42 
 
 .742 44 
 
 .746 46 
 
 .683 20 
 
 .685 22 
 
 .690 24 
 
 .694 26 
 
 .698 28 
 
 .700 30 
 
 .706 32 
 
 .760 48 
 
 .772 
 .778 
 .782 
 .788 
 .792 
 .800 
 
 RETURNS. 
 
 Gr. 
 
 .802 
 
 .806 
 
 .800 
 .804 
 .808 
 .812 
 
 cent. 
 68 0, 
 70 , 
 72 
 73 
 76 , 
 78 
 82 
 86 
 
 Gr. 
 
 ,820 
 ,825 
 .830 
 .830 
 .810 
 .820 
 .818 
 .816 
 
 cent. 
 
 88 
 90 
 
 92) 
 to [ 
 100 J 
 
 * 
 
 Gr. 
 0.815 
 .815 
 
 1 
 
 1 
 
 
 16 per cent naphtha, 70 Baume. 6 per cent parafflne oil. 
 68 per cent burning oil. 10 per cent residuum. 
 
 The distillation started at 23 C., this being due to the large amount of 
 naphtha present, and when 60% was reached, at a temperature of 310 C. 
 the hydrocarbons remaining in the retort were dissociated, when gases 
 escaped, lighter distillates were obtained, and, as usual in such cases, the 
 temperature decreased from 310 C. down gradually to 200 C., until 
 75% of oil was obtained, and from this point the temperature remained 
 constant until the end of the distillation. Therefore these hydrocarbons 
 in statu moriendi absorbed much heat. (Jour. Am. Chem. Soc.) 
 
 There is not a good agreement between the character of the materials 
 designated gasoline, kerosene, etc., and the temperature of distillation 
 and densities employed in different places. The following table shows 
 one set of values that is probably as good as any. 
 
 Name. 
 
 Boiling 
 Point. 
 
 Specific 
 Gravity. 
 
 Density at 
 59 F. 
 
 Petroleum, ether 
 
 F. 
 104-158 
 
 650-0.660 
 
 Baume. 
 85-80 
 
 Gasoline 
 
 158-176 
 
 .660- .670 
 
 80-78 
 
 Naphtha C 
 
 176-212 
 
 .670- 707 
 
 78-68 
 
 Naphtha B 
 
 212-248 
 
 .707- .722 
 
 68-64 
 
 Naphtha A 
 
 248-302 
 
 .722- .737 
 
 64-60 , 
 
 Kerosene 
 
 302-572 . 
 
 .753- .864 
 
 56-32 
 
 Gasoline is different from a simple substance with a fixed boiling 
 point, and therefore theoretical calculations on the heat of combustion, 
 air necessary, and conditions for vaporizing or carbureting air are of 
 little value. (C. E. Lucke.) 
 
 Value of Petroleum as Fuel. Thos. Urquhart, of Russia (Proc. 
 Inst. M. E., Jan., 1889), gives the following table of the theoretical 
 evaporative power of petroleum in comparison with that of coal, as 
 determined by Messrs. Favre and Silbermann: 
 
 
 Specific 
 Gravity 
 
 Cherh. Comp. 
 
 Heating 
 power, 
 
 Theoret. 
 Evap., 
 Lb. of 
 
 Fuel. 
 
 790 T7I 
 
 
 British 
 
 Water per 
 
 
 
 
 Thermal 
 
 Ib. Fuel, 
 
 
 Water 
 = 1.000 
 
 C. 
 
 H. 
 
 0. 
 
 Units. 
 
 from and 
 
 
 
 
 
 
 
 at 212 F. 
 
 Penna. heavy crude oil .... 
 Caucasian light crude oil . . 
 
 0.886 
 0.884 
 
 84.9 
 86.3 
 
 13.7 
 13.6 
 
 1.4 
 0.1 
 
 20.736 
 22,027 
 
 21.48 
 22.79 
 
 Caucasian heavy crude oil . 
 
 0.938 
 
 86.6 
 
 12.3 
 
 1.1 
 
 20,138 
 
 20.85 
 
 Petroleum refuse 
 
 0.928 
 
 87.1 
 
 11.7 
 
 1.2 
 
 19,832 
 
 20.53 
 
 Good English coal 
 
 1.380 
 
 80.0 
 
 5.0 
 
 8.0 
 
 14,112 
 
 14.61 
 
 In experiments on Russian railways with petroleum as fuel Mr. 
 Urquhart obtained an actual efficiency equal to 82 % of the theoretical 
 
842 
 
 FUEL. 
 
 heating-value. The petroleum is fed to the furnace by in cans of a 
 spray-injector driven by steam. An induced current of air is carried in 
 around the injector-nozzle, and additional air is supplied at the bottom 
 of the furnace. 
 
 Beaumont, Texas, oil analyzed as follows (Eng. News, Jan. 30, 1902) : 
 C, 84.60; H, 10.90; S, 1.63; O, 2.87. Sp. gr. ; 0.92; flash point, 142 F.; 
 burning point, 181 F. ; heating value per lb., by oxygen calorimeter, 
 19,060 B.T.U. A test of a horizontal tubular boiler with this oil, by 
 J. E. Den ton gave an efficiency of 78.5%. As high as 82 % has been re- 
 ported for California oil. 
 
 Bakersfield, Cal., oil: Sp. gr. 16 Baume; Moisture, 1%; Sulphur, 
 0.5%. B.T.U. per lb., 18,500. 
 
 Redondo, Cal., oil. six lots: Moisture, 1.82 to 2.70%; Sulphur, 2.17 to 
 2.60%; B.T.U. per lb., 17,717 to 17,966. Kilowatt-hours generated per 
 barrel (334 lb.) of oil in a 5000 K.W. plant, using water-tube boilers, 
 and reciprocating engines and generators having a combined efficiency of 
 90.2 to 94.75% (boiler economy and steam-rate of engine not stated). 
 2000 K.W. load, 237.3; 3000 K.W., 256.7; 5000 K.W., 253.4; variable 
 load, 24 hours, 243.8. (C. R. Weymouth, Trans. A. S. M. E., 1908.) 
 
 The following table shows the relative values of petroleum and coal. 
 It is based on the following assumed data: B.T.U. per lb. of oil, 19,000; 
 sp. gr., 0.90 =7.57 lb. per gal ; 1 barrel = 42 gal. =315 lb. 
 
 Coal, B.T.U. 
 per lb. 
 
 1 lb. oil 
 = lb. coal. 
 
 1 barrel oil 
 = lb. coal. 
 
 1 ton coal 
 = barrels oil. 
 
 10,000 
 11,000 
 12,000 
 13,000 
 14,000 
 15,000 
 
 .9 
 
 .727 
 .583 
 .462 
 .357 
 .267 
 
 598 
 544 
 499 
 460 
 427 
 399 
 
 3.34 
 3.68 
 4.01 
 4.34 
 4.68 
 5.01 
 
 From this table we see that if coal of a heating value of only 10,000 
 B.T.U. per lb. costs $3.34 per ton, and coal of 14,000 B.T.U. per lb. costs 
 $4.68 per ton, then the price of oil will have to be as low as $1 a barrel 
 to compete with coal; or, if the poorer coal is $3.34 and the better coal 
 $4.68 per ton, then oil will be the cheaper fuel if it is below $1 per barrel. 
 
 Heating Values of California Fuel Oils. 
 
 (R. "W. Fenn, Eng. News, May 13, 1909.) . 
 
 Degree 
 
 Baume. 
 
 at 
 P 
 
 i! 
 
 i 
 
 |! 
 
 offfl 
 
 c'> 
 '5 g 
 
 CO 
 
 |! 
 
 fr 
 
 IS 
 
 10 
 12 
 14 
 16 
 
 18 
 20 
 22 
 24 
 26 
 
 1.000 
 0.986 
 0.972 
 0.959 
 0.947 
 0.934 
 0.922 
 0.910 
 0.899 
 
 150 
 346 
 341 
 336 
 332 
 327 
 323 
 319 
 315 
 
 18,380 
 18,500 
 18,620 
 18,740 
 18,860 
 18,980 
 19,100 
 19,220 
 19.340 
 
 6442 
 6394 
 6345 
 6302 
 6257 
 6212 
 6173 
 6133 
 6093 
 
 28 
 30 
 32 
 34 
 36 
 38 
 40 
 42 
 44 
 
 0.887 
 0.875 
 0.865 
 0.854 
 0.844 
 0.835 
 0.825 
 0.816 
 0.806 
 
 311 
 307 
 303 
 299 
 296 
 293 
 289 
 286 
 283 
 
 19,460 
 19,580 
 19,700 
 19,820 
 19,940 
 20,050 
 20,150 
 20,250 
 20,350 
 
 6051 
 6008 
 5973 
 5935 
 5901 
 5865 
 5827 
 5789 
 5751 
 
 Fuel Oil Burners. A great variety of burners are on the market, 
 most of them based on the principle of using a small jet of steam at the 
 boiler pressure to inject the oil into the furnace, in the shape of finely 
 divided spray, and at the same time to draw in the air supply and mix it 
 intimately with the oil. So far as economy of oil is concerned these 
 burners are all of about equal value, but their successful operation de- 
 pends on the construction of the furnace. This should have a large 
 combustion chamber, entirely surrounded with fire brick, and the 
 jet should be so directed that it will strike a fire-brick surface and re- 
 bound before touching the heating surface of the boiler. Burners 
 
ALCOHOL AS FUEL. 843 
 
 using air at high pressure, 40 Ib. per sq. in., without steam, have been 
 used with advantage. Lower pressures have been found not sufficient 
 to atomize the oil. Mechanical atomizers have now (1915) largely 
 replaced steam jet oil burners. See "Steam Boiler Economy." 
 
 When boilers are forced, with a combustion chamber too small to 
 allow the oil spray to be completely burned in it before passing to the 
 boiler surface, dense clouds of smoke result, with a deposit of lampblack 
 or soot. 
 
 Crude Petroleum vs. Indiana Block Coal for Steam-raising at 
 the South Chicago Steel Works. (E. C. Potter, Trans. A. I. M. E., 
 xvii. 807.) With coal, 14 tubular boilers 16 ft. X 5 ft. required 25 men 
 to operate them; with fuel oil, 6 men were required, a saving of 19 men 
 at $2 per day, or $38 per day. 
 
 For one week's work 2731 barrels of oil were used, against 848 tons of 
 coal required for the same work, showing 3.22 barrels of oil to be equiva- 
 lent to 1 ton of coal With oil at 60 cents per barrel and coal at $2.15 
 per ton, the relative cost of oil to coal is as $1.93 to $2.15. No evapora- 
 tion tests were made 
 
 Petroleum as a Metallurgical Fuel. C. E. Felton (Trans. A. I. 
 M. E., xvii. 809) reports a series of trials with oil as fuel hi steel-heating 
 and open-hearth steel-furnaces, and in raising steam, with results as 
 follows: 1. In a run of six weeks the consumption of oil, partly refined 
 (the paraffine and some of the naphtha being removed) , in heating 14- 
 inch ingots in Siemens furnaces was about 6 1/2 gallons per ton of blooms. 
 2. In melting in a 30-ton open-hearth furnace 48 gallons of oil were used 
 per ton of ingots. 3. In a six weeks' trial with Lima oil from 47 to 54 
 gallons of oil were required per ton of ingots. 4. In a six months' trial 
 with Siemens heating-furnaces the consumption of Lima oil was 6 gal- 
 lons per ton of ingots. Under the most favorable circumstances, 
 charging hot ingots and running full capacity, 4 1/2 to 5 gallons per ton 
 were required. 5. In raising steam in two 100-H.P. tubular boilers, the 
 feed- water being supplied at 160 F., the average evaporation was about 
 12 pounds of water per pound of oil, the best 12 hours' work being 16 
 pounds. 
 
 Specifications for the Purchase of Fuel Oil. The U. S. government 
 specifications for the purchase of fuel oil (1914) contain the following 
 requirements : 
 
 The oil should not have been distilled at a temperature high enough 
 to burn it, nor at a temperature so high that flecks of carbonaceous mat- 
 ter begin to separate. 
 
 It should not flash below 140 F., in a closed Abel-Pensky or Pensky- 
 Martins tester. 
 
 The specific gravity should range from 0.85 to 0.96 at 59 F. 
 
 It should flow readily, at ordinary atmospheric temperatures and 
 under a head of 1 ft. of oil, through a 4-in. pipe 10 ft. in length. 
 
 It should not congeal nor become too sluggish to flow at 32 F. 
 
 It should have a calorific value of not less than 18,000 B.T.U. per Ib. 
 A bonus is to be paid or a penalty deducted as the fuel oil delivered 
 is above or below the standard. 
 
 It should be rejected if it contains more than 2% water, more than 
 1 % sulphur, or more than a trace of sand, clay or dirt. 
 
 ALCOHOL AS FUEL. 
 
 Denatured alcohol is a grain or ethyl alcohol mixed with a denaturant 
 in order to make it unfit for beverage or medicinal purposes. Under acts 
 of Congress of June 7, 1906, and March 2, 1907, denatured alcohol 
 became exempt from internal revenue taxation, when used in the 
 industries. 
 
 The Government formulae for completely denatured alcohol are: 
 
 1. To every 100 gal. of ethyl or grain alcohol (of not less than 180% 
 proof) there shall be added 10 gal. of approved methyl or wood alcohol 
 and % gal. of approved benzine. (180% proof = 90% alcohol, 10% 
 water, by volume.) 
 
 2. To every 100 gal. of ethyl alcohol (of not less than 180% proof) 
 there shall be added 2 gal. of approved methyl alcohol and Yi gal. of 
 approved pyridin (a petroleum product) bases. 
 
844 
 
 FUEL. 
 
 Methyl alcohol, benzine and pyridin used as denaturants must con- 
 form to specifications of the Internal Revenue Department. 
 
 The alcohol which it is proposed to manufacture under the present 
 law is ethyl alcohol, C^HsOH. This material is seldom, if ever, obtained 
 pure, it being generally diluted with water and containing other alco- 
 hols when used for engines. 
 
 SPECIFIC GKAVITY OF ETHYL ALCOHOL AT 60 P. COMPARED WITH 
 WATER AT 60. (Smithsonian Tables.) 
 
 Sp. Gr. 
 
 Per cent Al- 
 cohol. 
 
 Sp. Gr. 
 
 Per cent Al- 
 cohol. 
 
 Sp. Gr. 
 
 Per cent Al- 
 cohol. 
 
 Weight. 
 
 Vol. 
 
 Weight. 
 
 Vol. 
 
 Weight. 
 
 Vol. 
 
 0.834 
 .832 
 .830 
 .828 
 
 85.8 
 86.6 
 87.4 
 88.1 
 
 90.0 
 90.6 
 91.2 
 91.8 
 
 0.826 
 .824 
 .822 
 .820 
 
 88.9 
 89.6 
 90.4 
 91.1 
 
 92.3 
 92.9 
 93.4 
 94.0 
 
 0.818 
 .816 
 .814 
 .812 
 
 91.9 
 92.6 
 93.3 
 94.0 
 
 94.5 
 95.0 
 95.5 
 96.0 
 
 The heat of combustion of ethyl alcohol, 94% by volume, as deter- 
 mined by the calorimeter, is 11,900 B.T.U. per Ib. a little more than 
 half that of gasoline (Lucke). Favre and Silbermann obtained 12,913 
 B.T.U for absolute alcohol. Dulong's formula for C 2 H 6 OH gives 
 13,010 B.T.U. 
 
 The products of complete combustion of alcohol are HzO and COz. 
 Under certain conditions, with an insufficient supply of air, acetic acid is 
 formed, which causes rusting of the parts of an alcohol engine. This 
 may be prevented by addition to the alcohol of benzol or acetylene. 
 
 With any good small stationary engine as small a consumption as 0.70 
 Ib. of gasoline, or 1.16 Ib. of alcohol per brake H.P. hour may .reasonably 
 be expected under favorable conditions (Lucke) . 
 
 References. H. Diederichs, Intl. Marine Eng'g, July, 1906; Machy., 
 Aug., 1906. C. E. Lucke and S. M. Woodward, Farmer's Bulletin, No. 
 277. U. S. Dept. of Agriculture, 1907. Eng. Rec., Nov. 2, 1907. T. L. 
 White, Eng. Mag., Sept., 1908. 
 
 VAPOR PRESSURE OF SATURATION FOR VARIOUS LIQUIDS, IN 
 
 MILLIMETERS OF MERCURY. 
 
 (To convert into pounds per sq. in., multiply by 0.01934; to convert 
 into inches of mercury, multiply by 0.03937.) 
 
 Tem- 
 pera- 
 ture. 
 
 Pure 
 Ethyl 
 Alco- 
 hol. 
 
 Pure 
 Methyl 
 Alco- 
 hol. 
 
 Water. 
 
 Gaso- 
 line. 
 
 Tem- 
 pera- 
 ture. 
 
 Pure 
 Ethyl 
 Alco- 
 hol. 
 
 Pure 
 Methyl 
 Alco- 
 hol. 
 
 Water. 
 
 Gaso- 
 line. 
 
 0* 
 5 
 10 
 15 
 
 20 
 25 
 30 
 
 32 
 41 
 50 
 59 
 68 
 77 
 86 
 
 12 
 17 
 24 
 32 
 44 
 59 
 78 
 
 30 
 40 
 54 
 71 
 94 
 123 
 159 
 
 5 
 
 9 
 13 
 17 
 
 24 
 32 
 
 99 
 115 
 133 
 154 
 179 
 210 
 251 
 
 35* 
 40 
 45 
 50 
 55 
 60 
 65 
 
 95 
 104 
 113 
 122 
 131 
 140 
 149 
 
 103 
 134 . 
 172 
 220 
 279 
 350 
 437 
 
 204 
 259 
 327 
 409 
 508 
 624 
 761 
 
 42 
 55 
 71 
 92 
 117 
 149 
 187 
 
 301 
 360 
 422 
 493 
 561 
 648 
 739 
 
 VAPOR TENSION OF ALCOHOL AND WATER, AND DEGREE OF SATURATION 
 OF AlR WITH THESE VAPORS. 
 
 Temp., 
 Degs. F. 
 
 Vapor Tension, Inches 
 Mercury. 
 
 1 Pound of Air Contains in Saturated 
 Condition, in Pounds. 
 
 At 28.95 Inches. 
 
 At 26.05 Inches. 
 
 Alcohol 
 Vapor. 
 
 Water 
 Vapor. 
 
 Alcohol. 
 Vapor. 
 
 Water. 
 Vapor. 
 
 Alcohol 
 Vapor. 
 
 Water. 
 Vapor. 
 
 u 50 
 59 
 68 
 77 
 86 
 104 
 122 
 
 0.950 
 1.283 
 1.723 
 2.325 
 3.090 
 5.270 
 8.660 
 
 0.359 
 0.500 
 0.687 
 0.925 
 1.240 
 2.162 
 3.620 
 
 0.055 
 0.075 
 0.104 
 0.144 
 0.200 
 0.390 
 0.827 
 
 0.008 
 0.011 
 0.016 
 0.022 
 0.031 
 0.063 
 0.135 
 
 0.061 
 0.084 
 0.117 
 0.162 
 0.227 
 0.450 
 1.002 
 
 0.009 
 0.013 
 0.018 
 0.025 
 0.036 
 0.072 
 0.164 
 
. 
 
 FUEL GAS. 843 
 
 FUEL GAS. 
 
 The following notes are extracted from a paper by W. J. Taylor on 
 "The Energy of Fuel" (Trans. A. I. M. E., xviii. 205): 
 
 Carbon Gas. In the old Siemens producer, practically all the heat 
 of primary combustion that is, the burning of solid carbon to carbon 
 monoxide, or about 30% of the total carbon energy was lost, as little 
 or no steam was used in the producer, and nearly all the sensible heat of 
 the gas was dissipated in its passage from the producer to the furnace, 
 which was usually placed at a considerable distance. 
 
 Modern practice has improved on this plan, by introducing steam 
 with the air blown into the producer, and by utilizing the sensible heat of 
 the gas in the combustion-furnace. It ought to be possible to oxidize 
 one out of every four Ibs. of carbon with oxygen derived from water- 
 vapor. The thermic reactions in this operation are as follows: 
 
 Heat-units. 
 4 Ibs. C burned to CO (3 Ibs. gasified with air and 1 Ib. with 
 
 water) develop 17,600 
 
 1 5 Ibs. of water (which furnish 1.33 Ibs. of oxygen to combine 
 
 with 1 Ib. of carbon) absorb by dissociation 10,333 
 
 The sas consisting of 9.333 Ibs. CO, 0.167 Ib. H, and 13.39 Ibs. N, 
 
 heated 600, absorbs 3,748 
 
 Leaving for radiation and loss . 3,519 
 
 17,600 
 
 The steam which is blown into a producer with the air is almost all con r 
 densed into finely-divided water before entering the fuel, and conse- 
 quently is considered as water in these calculations. 
 
 The 1.5 Ibs. of water liberates : 167 Ib. of hydrogen, which is delivered 
 to the gas, and yields in combustion the same heat that it absorbs in the 
 producer by dissociation. According to this calculation, therefore, 60% 
 of the heat of primary combustion is theoretically recovered by the dis- 
 sociation of steam, and, even if all the sensible heat of the gas be counted, 
 with radiation and other minor items, as loss, yet the gas must carry 
 4 X 14,500 - (3748 + 3519) = 50,733 heat-units, or 87% of the calo- 
 rific energy of the carbon. This estimate shows a loss in conversion of 
 13% without crediting the gas with its sensible heat, or charging it with 
 the heat required for generating the necessary steam, or taking into 
 account the loss due to oxidizing some of the carbon to CO2. In good 
 producer-practice the proportion of CO2 in the gas represents from 4% 
 to 7% of the C burned to CO2, but the extra heat of this combustion should 
 be largely recovered in the dissociation of more water-vapor, and there- 
 fore does not represent as much loss as it would indicate. As a con- 
 veyer of energy, this gas has the advantage of carrying 4.46 Ibs less 
 nitrogen than would be present if the fourth pound of coal had been 
 gasified with air; and in practical working the use of steam reduces tha 
 amount of clinkering in the producer. 
 
 Anthracite Gas. In anthracite coal there is a volatile combustible 
 varying in quantity from 1.5% to over 7%. The amount of energy 
 derived from the coal is shown in the following theoretical gasification 
 made with coal of assumed composition: Carbon, 85%; vol. HC, 5%; ash, 
 10%- 80 Ibs carbon assumed to be burned to CO; 5 Ibs. carbon burned 
 to COa; three fourths of the necessary oxygen derived from air, and one 
 fourth from water. 
 
 r- Products. % 
 
 Process. Pounds. Cubic Feet. Anal, by Vol. 
 
 80 Ibs. C burned to CO 186.66 25 29-24 33.4 
 
 5 Ibs. C burned to CO 2 18.33 157.64 2.0 
 
 5 Ibs. vol. HC (distilled) 5.00 116.60 1.6 
 
 120 Ibs. oxygen are required, of 
 which 30 Ibs. from H 2 O liber- 
 ate H 3.75 712.50 9.4 
 
 90 Ibs. from air are associated 
 with N 301.05 4064.17 53.6 
 
 614.79 7580.15 100.0 
 
846 FUEL. 
 
 Energy in the above gas obtained from 100 Ibs. anthracite: 
 
 186. 66 Ibs. CO 807,304 heat-units. 
 
 5.00 " CH 4 117,500 
 
 3.75 " H 232,500 " 
 
 1,157,304 
 
 Total energy in gas per Ib 2,248 " 
 
 Total energy in 100 Ibs. of coal 1,349,500 " 
 
 Efficiency of the conversion 86%. 
 
 The sum of CO and H exceeds the results obtained in practice. The 
 sensible heat of the gas will probably account for this discrepancy and 
 therefore, it is safe to assume the possibility of delivering at least 82% 
 of the energy of the anthracite. 
 
 Bituminous Gas. A theoretical gasification of 100 Ibs of coal, con- 
 taining 55% of carbon and 32% of volatile combustible (which is above 
 the average of Pittsburgh coal), is made in the following table. It is 
 assumed that 50 Ibs. of C are burned to CO and 5 Ibs. to CO2; one fourth 
 of the O is derived from steam and three fourths from air; the heat value 
 of the volatile combustible is taken at 20,000 heat-units to the pound. 
 In computing volumetric proportions all the volatile hydrocarbons, 
 fixed as well as C9ndensing, are classed as marsh-gas, since it is only by 
 some such tentative assumption that even an approximate idea of the 
 volumetric composition can be formed. The energy, however, is calcu- 
 lated from weight: 
 
 , : Prod ucts . 
 
 Process. Pounds. Cubic Feet. Anal, by Vol. 
 
 50 Ibs. C burned to CO 116.66 1580.7 27.8 
 
 5 Ibs. C burned to CO 2 18.33 157.6 2.7 
 
 32 Ibs. vol. HC (distilled) 32 . 00 746 . 2 13.2 
 
 80 Ibs. O are required, of which 20 
 Ibs., derived from H2O, liber- 
 ate H 2.5 475.0 8.3 
 
 60 Ibs. O, derived from air, are as- 
 sociated with N 200.70 2709.4 47.8 
 
 370.19 5668.9 99.8 
 
 Energy in 116.66 Ibs. CO 504,554 heat-units. 
 
 " 32.00 Ibs. vol. HC 640,000 
 
 2.50 Ibs. H 155,000 
 
 1,299,554 
 
 Energy in coal 1,437,500 
 
 Per cent of energy delivered in gas 90.0 
 
 Heat-units m 1 Ib. of gas 3,484 
 
 Water-gas. Water-gas is made in an intermittent process, by blow- 
 Ing up the fuel-bed of the producer to a high state of incandescence (and 
 in some cases utilizing the resulting gas, which is a lean producer-gas), 
 then shutting off the air and forcing steam through the fuel, which dis- 
 sociates the water into its elements of oxygen and hydrogen, the former 
 combining with the carbon of the coal, and the latter being liberated. 
 
 This gas can never play a very important part in the industrial field, 
 owing to the large loss of energy entailed in its production, yet there are 
 places and special purposes where it is desirable, even at a great excess 
 in cost per unit of heat over producer-gas; for instance, in small high- 
 temperature furnaces, where much regeneration is impracticable, or 
 where the "blow-up" gas can be used for other purposes instead of being 
 wasted. 
 
 The reactions and energy required in the production of 1000 feet of 
 water-gas, composed, theoretically, of equal volumes of CO and H, are as 
 follows: 
 
 500 cubic feet of H weigh 2 . 635 Ibs. 
 
 500 cubic feet of CO weigh 36 . 89 
 
 Total weight of 1000 cubic feet 39 . 525 Ibs. 
 
 Now, as CO is composed of 12 parts C to 16 of O', the weight of C in 
 36.89 Ibs. is 15.81 Ibs. and of O 21.08 Ibs. When this oxygen is derived 
 
FUEL GAS. 
 
 847 
 
 from water it liberates, as above, 2.635 Ibs. of hydrogen. The heat de- 
 veloped and absorbed in these reactions (roughly, as we will not take 
 into account the energy required to elevate the coal from the tempera- 
 ture of the atmosphere to, say, 1800) is as follows: Heat-units 
 2.635 Ibs. H. absorb in dissociation from water 2.635 X 62,000 = 163,370* 
 
 15.81 Ibs. C burned to CO develops 15.81 X 4400 = 69,564 
 
 Excess of heat-absorption over heat-development = 93,806 
 
 If this excess could be made up from C burnt to CO 2 without loss by 
 radiation, we would only have to burn an additional 4.83 Ibs. C to supply 
 this heat, and we could then make 1000 feet of water-gas from 20.64 Ibs. 
 of carbon (equal 24 Ibs. of 85% coal). This would be the perfection of 
 
 gas-making, as the gas would contain really the same energy as the coal; 
 but instead, we require in practice more than double this amount of coal 
 and do not deliver more than 50% of the energy of the fuel in the gas, 
 because the supporting heat is obtained in an indirect way and with 
 imperfect combustion. Besides this, it is not often that the sum of CO 
 and H exceed 90%, the balance being CO2 and N. But water-gas should 
 be made with much less loss of energy by burning the "blow-up" (pro- 
 ducer) gas in brick regenerators, the stored-urj heat of which can be 
 returned to the producer by the air used in blowing-up. 
 
 The following table shows what may be considered average volumetric 
 analyses, and the weight and energy of 1000 cubic feet, of the four types 
 of gases used for heating and illuminating purposes: 
 
 
 Natural 
 Gas. 
 
 Coal- 
 gas. 
 
 Water- 
 gas. 
 
 Producer-gas. 
 
 Anthra. 
 
 Bitu. 
 
 CO. 
 
 0.50 
 2.18 
 92.6 
 0.31 
 0.26 
 3.61 
 0.34 
 
 6.0 
 46.0 
 40.0 
 4.0 
 0.5 
 1.5 
 0.5 
 1.5 
 32.0 
 735,000 
 
 45.0 
 45.0 
 2.0 
 
 27.0 
 12.0 
 1.2 
 
 27.C 
 12.0 
 2.5 
 0.4 
 2.5 
 56.2 
 0.3 
 
 H 
 
 CH t 
 
 C 2 H 4 
 
 COa. . . 
 
 4.0 
 2.0 
 0.5 
 1.5 
 
 45.6 
 322,000 
 
 2.5 
 57.0 
 0.3 
 
 N 
 
 O 
 
 Vapor . ... 
 
 Pounds in 1000 cubic feet 
 
 45.6 
 1,100,000 
 
 65.6 
 137,455 
 
 65.9 
 156,917 
 
 Heat-units in 1000 cubic feet 
 
 Natural Gas in Ohio and Indiana. 
 
 (Enq. and M. J., April 21, 1894.) 
 
 
 Fos- 
 toria, 
 O. 
 
 Find- 
 
 Ia o y ' 
 
 St. 
 Mary's, 
 O. 
 
 Muncie, 
 Ind. 
 
 Ander- 
 son, 
 Ind. 
 
 Koko- 
 mo, 
 Ind. 
 
 Mar- 
 ion, 
 Ind. 
 
 Hydrogen 
 
 1.89 
 
 1.64 
 
 1.94 
 
 2.35 
 
 1.86 
 
 1.42 
 
 1.20 
 
 Marsh-gas 
 
 92.84 
 
 93.35 
 
 93.85 
 
 92.67 
 
 93.07 
 
 94.16 . 
 
 93.57 
 
 Olefiant gas 
 
 .20 
 
 .35 
 
 .20 
 
 .25 
 
 .47 
 
 .30 
 
 .15 
 
 Carbon monoxide . 
 Carbon dioxide 
 Oxygen 
 
 .55 
 .20 
 .35 
 
 .41 
 .25 
 .39 
 
 .44 
 .23 
 .35 
 
 .45 
 .25 
 .35 
 
 .73 
 .26 
 .42 
 
 .55 
 
 .29 
 .30 
 
 .60 
 .30 
 .55 
 
 Nitrogen .... 
 
 3.82 
 
 3.41 
 
 2.98 
 
 3.53 
 
 3.02 
 
 2.80 
 
 3.42 
 
 Hydrogen sulphide 
 
 .15 
 
 .20 
 
 .21 
 
 .15 
 
 .15 
 
 .18 
 
 .20 
 
 Natural Gas as a Fuel for Boilers. J. M. Whitham (Trans. A. S. 
 /. E., 1905) reports the results of several tests of water-tube boilers with 
 natural gas. The following is a condensed statement of the results : 
 
 Kind of Boiler. | Cook Vertical. | Heine. | Cahall Vert. 
 
 Rated H.P. of boilers 
 H.P. developed 
 
 1500 
 
 1642 
 
 1500 
 1507 
 
 200 
 155 
 
 200 
 218 
 
 200 
 
 258 
 
 300 
 340 
 
 300 
 260 
 
 Temperature at chimney 
 Gas pressure at burners, oz. 
 Cu. ft. of gas per boiler. . 
 H.P.-hour 
 
 521 
 6.9 
 
 44.9* 
 
 494 
 6.4 
 
 41.0* 
 
 386 
 46. Of 
 
 450 
 40. 7f 
 
 465 
 38. 3t 
 
 406 
 4.8 
 
 42.3 
 
 374 
 7 to 30 
 
 34 
 
 Boiler efficiency, % 
 
 72.7 
 
 
 65.8 
 
 
 74.9 
 
 
 
 *Reduced to 4 oz. press, and 62 F. fReduced to atmos. press, and 32 F. 
 
848 
 
 FUEL. 
 
 Six tests by Daniel Ashworth on 2-flue horizontal boilers gave cu. ft. of 
 gas per boiler H.P. hour, 58.0; 59.7; 67.0; 63.0; 74.0; 47.0. 
 
 On the first Cook boiler test, the chimney gas, analyzed by the Orsat 
 apparatus, showed 7.8 CO2; 8.05 O; 0.0 CO; 84.15 N. This shows an 
 excessive air supply. 
 
 White versus Blue Flame. Tests were made with the air supply throt- 
 tled at the burners, so as to produce a white flame, and also unthrottled, 
 producing a blue flame with the following results: 
 
 Pressure of gas at burners, oz 
 
 4 
 
 
 6 
 
 
 8 
 
 
 Kind of flame 
 
 White 
 
 Blue 
 
 White 
 
 Blue 
 
 White 
 
 Blue 
 
 Boiler H.P.made per 250-H.P. boiler 
 Cu. ft. of gas (at 4 oz. and 60 F.) per 
 H.P. hour 
 
 247 
 41 
 
 213 
 
 41 
 
 297 
 41.6 
 
 271 
 
 M 9 
 
 255 
 49 
 
 227 
 43 1 
 
 Chimney temperature 
 
 436 
 
 503 
 
 478 
 
 511 
 
 502 
 
 508 
 
 Average of 6 tests White, 266 H.P., 43.6 cu. ft.; Blue, 237 H.P., 
 43.8 cu. ft., showing that the economy is the same with each flame, but 
 the capacity is greatest with the white flame. Mr. Whitham's principal 
 conclusions from these tests are as follows: 
 
 (1) There is but little advantage possessed by one burner over another. 
 
 (2) As good economy is made with a blue as with a white or straw flame, 
 and no better. 
 
 (3) Greater capacity may be made with a straw-white than with a blue 
 flame. 
 
 (4) An efficiency as high as from 72 to 75 per cent in the use of gas is 
 seldom obtained under the most expert conditions. 
 
 (5) Fuel costs are the same under the best conditions with natural gas 
 at 10 cents per 1000 cu. ft. and semi-bituminous coal at $2.87 per ton of 
 2240 Ibs. 
 
 (6) Considering the saving of labor with natural gas, as compared with 
 hand-firing of coal, in a plant of 1500 H.P., and coal at $2 per ton of 2240 
 Ibs., gas should sell for about 10 cents per 1000 cu. ft, 
 
 ANALYSES OF NATURAL GAS. 
 
 Illuminants 
 
 Carbonic oxide 
 
 Hydrogen 
 
 Marsh gas. 
 
 Ethane 
 
 Carbonic acid 
 
 Oxygen 
 
 Nitrogen 
 
 B.T.U. per cu. ft. at 60 F. and 
 14.7 Ibs. barometer 
 
 0.45 
 
 0.00 
 
 0.20 
 
 81.05 
 
 17.60 
 
 0.00 
 
 0.15 
 
 0.55 
 
 1030 
 
 0.15 
 
 0.00 
 
 0.30 
 
 83.20 
 
 15.55 
 
 0.20 
 
 0.10 
 
 0.50 
 
 1020 
 
 0.50 
 
 0.15 
 
 0.25 
 
 83.40 
 
 15.40 
 
 0.00 
 
 0.00 
 
 0.30 
 
 1026 
 
 1.6 
 1.8 
 
 0.3 
 
 81.9 
 
 13.2 
 
 0.0 
 
 0.4 
 
 0.8 
 
 1098 
 
 The first three analyses are of the gas from nine wells in Lewis Co., 
 W. Va.; the last is from a mixture from fields in three states supplying 
 Pittsburg, Pa., used in the tests of the Cook boiler. 
 
 Producer-gas from One Ton of Coal. 
 
 (W. H. Blauvelt, Trans. A. I. M. E., xviii, 614.) 
 
 Analysis by Vol . 
 
 Per 
 
 Cent. 
 
 Cubic Feet. 
 
 Lbs. 
 
 
 Equal to 
 
 
 CO 
 
 25 3 
 
 33 213 84 
 
 2451.20 
 
 1050.51 
 
 Ibs. C + 1400. 7 Ibs 
 
 
 
 H 
 
 9.2 
 
 12,077.76 
 
 63.56 
 
 63.56 
 
 H. 
 
 
 CH4 
 
 3.1 
 
 4,069.68 
 
 174.66 
 
 174.66 
 
 CH 4 . 
 
 
 C2H4 
 
 8 
 
 1,050 24 
 
 77.78 
 
 77.78 
 
 C2H 4 . 
 
 
 CO2 
 
 3.4 
 
 4,463.52 
 
 519.02 
 
 141.54 
 
 C + 377. 44 Ibs 
 
 O 
 
 N (by difference) 
 
 58.2 
 
 76,404.96 
 
 5659.63 
 
 7350.17 
 
 Air. 
 
 
 
 100.0 
 
 131,280.00 
 
 8945.85 
 
 
 
 
FUEL GAS. 
 
 849 
 
 Calculated upon this basis, the 131,280 ft. of gas from the ton of coal 
 contained 20,311,162 B.T.U., or 155 B.T.U. per cubic ft., or 2270 B. T.U, 
 per Ib. 
 
 The composition of the coal from which this gas was made was as 
 follows: Water, 1.26%; volatile matter, 36.22%; fixed carbon, 57.98%; 
 sulphur, 0.70%; ash, 3.78%. One ton contains 1159.6 Ibs. carbon and 
 724.4 Ibs. volatile combustible, the energy of which is 31,302,200 B.T.U. 
 Hence, in the processes of gasification and purification there was a loss of 
 35.2% of the energy of the coal. 
 
 The composition of the hydrocarbons in a soft coal is uncertain and 
 quite complex; but the ultimate analysis of the average coal shows that 
 it approaches quite nearly to the composition of CH 4 (marsh-gas). 
 
 Mr. Blauvelt emphasizes the following points as highly important in 
 soft-coal producer-practice: 
 
 Fii 
 
 the air before being used. To prevent these sources of loss, the pr< 
 should be placed so as to lose as little as possible of the sensible heat of 
 the gas, and prevent condensation of the hydrocarbon vapors. A high 
 fuel-bed should be carried, keeping the producer cool on top, thereby 
 preventing the breaking-down.of the hydrocarbons and the deposit of 
 soot, as well as keeping the carbonic acid low. 
 
 Second. That a producer should be blown with as much steam mixed 
 with the air as will maintain incandescence. This reduces the percentage 
 of nitrogen and increases the hydrogen, thereby greatly t enriching the gas. 
 The temperature of the producer is kept down, diminishing the loss of heat 
 by radiation through the walls, and in a large measure preventing clinkers. 
 
 The Combustion of Producer-gas. (H. H. Campbell, Trans. A. I. 
 M. E., xix, 128.) The combustion of the components of ordinary pro- 
 ducer-gas may be represented by the following formulEe: 
 
 C 2 H 4 4- 60 = 2C0 2 +2H 2 0; 2H -f O = H 2 O; 
 CH 4 + 4 O = CO 2 + 2 H 2 O; CO + O = CO 2 . 
 
 AVERAGE COMPOSITION BY VOLUME OF PRODUCER-GAS: A, MADE WITH 
 OPEN GRATES, NO STEAM IN BLAST; B, OPEN GRATES, STEAM-JET IN 
 BLAST. 10 SAMPLES OF EACH. 
 
 002. O. C 2 H4 CO. H. CH 4 . N. 
 
 A min 3.6 0.4 0.2 20.0 5.3 3.0 58.7 
 
 A max 5.6 0.4 0.4 24.8 8.5 5.2 64.4 
 
 A average 4.84 0.4 0.34 22.1 6.8 3.74 61.78 
 
 B min 4.6 0.4 0.2 20.8 6.9 2.2 57.2 
 
 B max 6.0 0.8 0.4 24. 9.8 3.4- 62. 
 
 B average 5.3 0.54 0.36 22.74 8.37 2.56 60.13 
 
 The coal used contained carbon 82%, hydrogen 4.7%. 
 The following are analyses of products of combustion: 
 
 C0 2 . O. CO. CH 4 . H. N. 
 
 Minimum 15.2 0.2 trace. trace. trace. 80.1 
 
 Maximum 17.2 1.6 2.0 0.6 2.0 83.6 
 
 Average 16.3 0.8 0.4 0.1 0.2 82.2 
 
 Proportions of Gas Producers and Scrubbers. (F. C. Tryon, Power, 
 Dec. 1, 1908.) Small inside diameter means excessive draft through the 
 fire. If a fire is forced, as will be necessary with too small an inside diam- 
 eter, the results will be clinkers and blow-holes or chimneys through the 
 fire bed, with excess CO 2 and weak gas; clinkers fused to the lining, and 
 burning out of grates. If sufficient steam is used to keep down the ex- 
 cessive heat, the result is likely to be too much hydrogen in the gas, with 
 the attendant engine troubles. 
 
 The lining should never be less than 9 in. thick even in the smaller sizes, 
 and a 100-H.P., or larger, producer should have at least 12 in. of generator 
 lining. The lining next to the fire bed should be of the best quality of 
 refractory material. A good lining consists of a course of soft common 
 bricks put in edgewise next to the steel shell of the generator, laid in 
 Portland cement; then a good firebrick 6 in. thick laid inside to fit the 
 circle, the bricks being dipped as laid in a fine grouting of ground firebrick. 
 
 If we take H/4 Ibs. of coal per H.P.-hour as a fair average and 10 Ibs, of 
 
850 
 
 FUEL. 
 
 coal per hour per squaie foot of internal fuel-bed cross-section, with 9 in. 
 of refractory lining up to 100 H.P. and at least 12 in. of lining on larger 
 sizes, the generator will give good gas without forcing and without excess- 
 ive heat in the zone of complete combustion. A 200-H.P. producer on 
 this basis consumes 250 Ibs. of coal at full load, and at 10 Ibs. per sq. ft. 
 internal area 25 sq. ft. will be necessary. With a 12-in. lining the outside 
 diameter will be 92 in. 
 
 Practice has shown that the depth of the fuel bed should never be less 
 than the inside diameter up to 6 ft.; above this size the depth can be 
 adjusted as experience indicates the best working results. Assuming for 
 a 200-H.P. producer 18 in. for the ashpit below the grate, 12 in. for the 
 thickness of the grate and the ashes to protect it, 68 in. depth of fuel bed, 
 24 in. above the fuel to the gas outlet, the height will be 10 ft. 4 in. to the 
 top of the generator; above this the coal-feeding hopper, say 32 in. high, 
 is mounted; this makes the height over all 13 ft. 
 
 The wet scrubber of a gas producer should be of ample size to cool the 
 gas to atmospheric temperature and wash out most of the impurities. 
 A good rule is to make its diameter three-fourths that of the inside diam- 
 eter of the generator and the height one and one-half times the height of 
 the generator shell. For a 100-H.P. producer, 4 ft. inside diam., the wet 
 scrubber should be 3 ft. inside diam., and if the generator shell is 8 ft. 
 6 in. high, the scrubber should be 12 ft. 9 in. high. When filled with the 
 proper amount of baffling and scrubbing material (coke is commonly 
 used), the scrubber will have space for about 30 cu. ft. of gas. A 100-H.P. 
 gas engine using 12,000 B.T.U. per H.P.-hour will use 160 cu. ft. of 125- 
 B.T.U. gas per minute. The wet scrubber will therefore be emptied 51/3 
 times every minute, and would require about 8 Va gallons of water per 
 minute; if the diameter of the scrubber were reduced one-third the vol- 
 ume of water necessary to cool and scrub the gas would have to be doubled. 
 Gas must be cooled below 90 F. to enable it to give up the impurities it 
 carries in suspension, and even lower than this to condense its moisture. 
 
 A separate dry scrubber with two compartments should always be pro- 
 vided and the piping between the two scrubbers so arranged that the gas 
 can be turned into either part of the dry scrubber at will. The dry 
 scrubber should be equal in area to the inside of the generator, and the 
 depth of each part should be sufficient to accommodate at least 2 cu. ft. 
 of scrubbing material and give 1 cu. ft. of space next to the outlet. Oil- 
 soaked excelsior is a good scrubbing material and should be packed as 
 closely as possible. 
 
 Taking as the standard the dimensions above stated for the different 
 parts of a producer-gas plant, a list of dimensions for different horse-power 
 capacities would be about as in the following table. 
 
 DIMENSIONS OF GAS PRODUCERS AND SCRUBBERS. 
 
 H.P. 
 
 Producers. 
 
 Wet Scrub- 
 bers. 
 
 Dry Scrubbers. 
 
 Inside 
 Diam. 
 
 Out- 
 side 
 Diam. 
 
 Height. 
 
 Diam. 
 
 Height. 
 
 
 Diam. 
 
 Height. 
 
 25 
 35 
 50 
 60 
 75 
 100 
 125 
 150 
 175 
 200 
 
 in, 
 24 
 28 
 34 
 37 
 ' 42 
 48 
 54 
 58 
 63 
 68 
 
 in. 
 42 
 46 
 52 
 55 
 60 
 72 
 78 
 82 
 87 
 92 
 
 ft. in. 
 6 6 
 6 10 
 7 4 
 7 7 
 8 
 8 6 
 9 6 
 9 10 
 10 3 
 10 8 
 
 in. 
 18 
 21 
 26 
 28 
 32 
 36 
 41 
 44 
 48 
 51 
 
 ft. in. 
 9 9 
 10 3 
 11 
 11 5 
 12 
 12 9 
 14 3 
 14 9 
 15 5 
 16 
 
 Single.. . 
 . . do .... 
 
 in. 
 24 
 28 
 34 
 37 
 42 
 48 
 52 
 58 
 63 
 68 
 
 ft. in. 
 3 
 3 
 6 
 6 
 6 
 7 
 7 
 7 6 
 7 6 
 7 6 
 
 Double . 
 ...do.... 
 ...do.... 
 ...do.... 
 ...do.... 
 ...do.... 
 ...do.... 
 ...do.... 
 
 The inside diameter of the producers corresponds to the formula 
 H.P. = 6.25d 2 . 
 
GAS PRODUCERS. 
 
 851 
 
 Gas Producer Practice. The following notes on gas producers are 
 condensed from the catalogue of the Morgan Construction Co. 
 
 The Morgan Continuous Gas Producer is made in the following sizes: 
 
 Diam. inside of lining, ft 6 8 10 12 
 
 Area of gas-making surface, sq. ft. . . . 28 50 78.5 113 
 
 24-hour capacity with good coal, tons 4 7 10 15 
 
 Diam. of outlet, in 20 27 33 40 
 
 The best coal to buy for a producer in any locality is that which by 
 analysis or calorimeter test shows the most heat units for a dollar. It 
 rarely pays to buy gas coal unless it can be had at a moderate cost over the 
 ordinary steam bituminous grade. For very high temperature melting 
 operations a fairly high percentage of volatile matter is necessary to give a 
 luminous flame and intensify the radiation from the roof of the furnace. 
 Freely burning gas coals are the most easily gasified, and the capacity of 
 the producer to handle these coals is twice as great as when a slaty, dirty 
 coal, high in ash and sulphur, is used. It is usually best to use "run-of- 
 mine" coal, crushed at the mine to pass a 4-in. ring. It never pays to use 
 slack coal, for it cuts down the capacity by choking the blast, which has 
 to be run at high pressure to get through the fire, overheating the gas and 
 lowering the efficiency of the producer. 
 
 There is always a certain amount of CO2 formed, even in the best practice; 
 in fact, it is inevitable, and if kept within proper limits does not constitute 
 a net loss of efficiency, especially with very short gas flues, because the 
 energy of the fuel so burned is represented in the sensible heat or tem- 
 perature of the gas, and results in delivering a hot gas to the furnace. 
 The best result is at about 4% CO2, a gas temperature between 1100 and 
 1200 F., and flues less than 100 ft. long. 
 
 The amount of steam required to blow a gas producer is from 33% to 
 40% of the weight of the fuel gasified. If 30 Ibs. of steam is called a 
 standard horse-power, we have therefore to provide about 1 H.P. of steam 
 for every 80 Ibs. of coal gasified per hour or for every ton of coal gasified in 
 24 hours. 
 
 In the original Siemens air-blown producer about 70% of the whole gas 
 was inert and 30% combustible. Then with the advent of steam-blown 
 producers the dilution was reduced to about 60%, with 40% combustible. 
 Now, under the system of automatic feed, uniform conditions, perfect 
 distribution and adjustment of the steam blast here presented, we are able 
 to reduce the nitrogen to 50% and sometimes less. 
 
 In the best practice the volume of gas from the producer is now reduced 
 to about 60 cu. ft. per pound of coal, of which 30 cu. ft. are nitrogen. 
 These volumes are measured at 60 F. 
 
 The temperature of the gas leaving the producer under best modern 
 conditions is about 1200 F. It can be run cooler than this, but not much, 
 except at a sacrifice of both quantity and quality. At this temperature, 
 the sensible heat carried by the gas is 1200 X 0.35 (average specific heat) = 
 420 B.T.U. per pound. As one pound of good gas is about 16 cu. ft. and 
 carries about 16 X 180 = 2880 heat units at normal temperature, we see 
 that the sensible heat carried away represents about one-seventh, or over 
 14% of the combustive energy, which is much too large a percentage to lose 
 whenever it can be utilized by using the gas at the temperature at which 
 it is made. 
 
 Capacity of Producers. The capacity of a gas producer is a varying 
 quantity, dependent upon the construction of the producer and upon the 
 quality of the coal supplied to it. The point is, not to push the producer so 
 hard as to burn up the gas within it; also to avoid blowing dust through 
 into the flues. These two limitations in a well-constructed automatically 
 fed gas producer occur at about the same rate of gasification, namely, 
 at about 10 Ibs. per sq. ft. of surface per hour with bituminous coal carry- 
 ing 10% of ash and 1 1/3 % of sulphur. With gas coal, having high volatile 
 percentage and low ash, this rate can be safely increased to 12 Ibs. and in 
 some cases to 15 Ibs. per sq. ft. At 10 Ibs. per sq. ft., the capacity of a 
 gas producer 8 ft. internal diameter is 500 Ibs. per hour, which with gas 
 coals may be increased to a maximum of about 700 Ibs. It frequently 
 happens that the cheapest coal available is of such quality that neither 
 of these figures can be reached, and the gasification per sq. ft. has to be cut 
 down to 6 or 7 Ibs. per hour to get the best results. 
 
852 
 
 FUEL 
 
 Flues. It is necessary to provide large flue capacity and to carry the 
 full area right up to the furnace ports, which latter may be slightly reduced 
 to give the gas a forward impetus. Generally speaking, the net area of a 
 flue should not be less than Vie of the area of the gas-making surface in the 
 producers supplying it. Or it may be stated thus: The carrying capa- 
 city of a hot gas flue is equivalent to 200 Ibs. of coal per hour per sq. ft. of 
 section. 
 
 Loss of Energy in a Gas Producer. The total loss from all sources in the 
 gasification of fuel in a gas producer under fairly good conditions, when 
 the gas is used cold or when its sensible heat is not utilized, ranges between 
 20% and 25%, which under very bad conditions may be increased to 60%. 
 The loss under favorable conditions, using the gas hot, is reduced to as 
 low as 10%,. which also includes the heat of the steam used in blowing. 
 
 Test of a Morgan Producer. The following is the record of a test made 
 in Chicago by Robert W. Hunt & Co. The coal used was Illinois " New 
 Kentucky" run-of-mine of the following analysis: 
 
 Fixed carbon, 50.87; volatile matter, 37.32; moisture, 5.08; ash (1.12 
 sulphur) ,6.73. The average of all the gas analyses by volume is as follows : 
 
 CO, 24.5; H, 17.8; CH 4 and C 2 H 4 , 6.8; total combustibles, 49.1%; CO 2 , 
 3.7; O, 0.4; N, 46.8; total non-combustibles, 50.9%. 
 
 Average depth of fuel bed, 3 ft. 4 in. Average pressure of steam on 
 blower, 4.7 Ibs. per sq. in. Analysis of ash: combustible, 4.66%; non- 
 combustible, 95.34%. Percentage of fuel lost in the ash, 4.66 X 6.73 * 
 100 = 0.3%. 
 
 High Temperature Required for Production of CO. In an ordinary 
 coal fire, with an excess of air CO2 is produced, with a high temperature. 
 When the thickness of the coal bed is increased so as to choke the air sup- 
 ply CO is produced, with a decreased temperature. It appears, however, 
 that if the temperature is greatly lowered, CO2 instead of CO will be pro- 
 duced notwithstanding the diminished air supply. Herr Ernst (Eng'g, 
 April 4, 1893) holds that the oxidation of C begins at 752 F., and that COz 
 is then formed as the main product, with only a small amount of CO, 
 whether the air be admitted in large or in small quantities. When the 
 rate of combustion is increased and the temperature rises to 1292 F. the 
 chief product is CO2 even when the exhaust gases contain 20% by volume 
 of COs, which is practically the maximum limit, proving that all the 
 oxygen has been consumed. Above 1292 F. the proportion of CO rapidly 
 increases until 1823 F. is reached, when CO is exclusively produced. 
 
 Experiments reported by J. K. Clement and H. A. Grine in Bulletin No. 
 393 of the U. S. Geological vSurvey, 1909, show that with the rate of flow 
 of gas and the depth of fuel bed which obtain in a gas producer a temper- 
 ature of 1100 C. (2012 F.) or more is required for the formation of 90% 
 CO gas from CO 2 and charcoal, and 1300 (2372 F.) for the same percen- 
 tage from CO 2 and coke, and from CO 2 and anthracite coal. With a tem- 
 perature 100 C. (180 F.) lower than these the resultant gas will contain 
 about 50% CO. It follows that the temperature of the fuel bed of the gas 
 producer must be at least 1300 C. in order to yield the highest possible 
 percentage of CO. 
 
 The Mond Gas Producer is described by H. A. Humphrey in Proc. Inst. 
 C. E., vol. cxxix, 1897. The producer, which is combined with a by-prod- 
 uct recovery plant, uses cheap bituminous fuel and recovers from it 90 
 Ibs. of sulphate of ammonia per ton, and yields a gas suitable for gas 
 engines and all classes of furnace work. The producer is worked at a much 
 lower temperature than usual, due to the large quantity of superheated 
 steam introduced with the air r amounting to more than twice the weight 
 of the fuel. The gas containing the ammonia is passed through an absorb- 
 ing apparatus, and treated so that 70% of the original nitrogen of the fuel 
 is recovered. The result of a test showed that for every ton of fuel about 
 2.5 tons of steam and 3 tons of air are blown through the grate, the mixture 
 being at a temperature of about 480 F. The greater part of this steam 
 passes through the producer undecomposed, its heat being used in a 
 regenerator to furnish fresh steam for the producer. More than 0.5 ton 
 of steam is decomposed in passing through the hot fuel, and nearly 4.5 tons 
 of gas are produced from a ton of coal, equal to about 160,000 cu. ft. at 
 ordinary atmospheric temperature. The gas has a calorific power of 81 % 
 of that of the original fuel. Mr. Humphrey gives the following table 
 Showing the relative value of different gases. 
 
FUEL GAS. 
 
 853 
 
 
 i 
 
 
 fl 
 
 M 
 
 
 /I 
 
 , 
 
 
 "."S 
 
 , 
 
 !"*< 
 
 fcjj^. 
 
 I . 
 
 
 
 1 
 
 Volume per cent. 
 
 |p 
 
 J 
 
 2 00 
 
 Ill 
 
 II 
 
 ti . 
 
 *| 
 
 
 * M o 
 
 C 
 
 S**" 1 " 
 S * S 
 
 03 +i 
 
 ^8 
 
 o.s 
 
 ^2 
 
 
 J31 
 
 m 
 
 
 
 I s 
 
 5 
 
 s 3 
 
 Hydrogen (H) 
 
 24 8 
 
 8 6 
 
 18 73 
 
 20.0 
 
 56.9 
 
 48 
 
 22 
 
 Marsh gas (CH 4 ) 
 
 2 3 
 
 2 4 
 
 31 
 
 
 22 6 
 
 39 5 
 
 67 
 
 C W H2^ gases . 
 
 nil 
 
 nil 
 
 31 
 
 4 or?) 
 
 3 
 
 3.8 
 
 6 
 
 Carbonic oxide (CO) 
 
 13 2 
 
 24 4 
 
 25 07 
 
 21 
 
 8.7 
 
 7.5 
 
 0.6 
 
 Nitrogen (N) . . 
 
 46 8 
 
 59 4 
 
 48 98 
 
 49 5 
 
 5 8 
 
 5 
 
 3 
 
 Carbonic acid (CO2) 
 
 12 9 
 
 5 2 
 
 6 57 
 
 5 
 
 3.0 
 
 nil 
 
 6 
 
 Total volume 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 Total combustible gases 
 
 40 3 
 
 35 4 
 
 44 42 
 
 45 
 
 91.2 
 
 98 8 
 
 95 6 
 
 Theoretical. 
 
 
 
 
 
 
 
 
 Air required for combustion .... 
 
 112.4 
 
 101.4 
 
 113.2 
 
 154.0 
 
 410.0 
 
 581.0 
 
 806.0 
 
 Calorific value per cu. ft., ) 
 in Ib. C. units j 
 
 85.9 
 
 74.7 
 
 88.9 
 
 115.3 
 
 284.0 
 
 381.0 
 
 495.8 
 
 Do., B.T.U. per cu. ft 
 
 154.6 
 
 134.5 
 
 160.0 
 
 207.5 
 
 511.2 
 
 658.8 
 
 892.4 
 
 Do., per litre, gram C. units . . . 
 
 1,374 
 
 1,195 
 
 1,432 
 
 1,845 
 
 4,544 
 
 6,096 
 
 7,932 
 
 NOTE. Where the volume per cent does not add up to 100 the slight 
 difference is due to the presence of oxygen. 
 
 The following is the analysis 9f gas' made in a Mond producer at the 
 works of the Solvay Process Co. in Detroit, Mich. (Mineral Industry, vol. 
 viii, 1900): CO 2 , 14.1; O, 0.3; N, 42.9; H, 25.9; CH 4 , 4.1; CO, 12.7. Com- 
 bustible, 42.7%. Calories per litre, 1540, --= 173 B.T.U. per cu. ft. 
 
 Relative Efficiencies of Different Coals in Gas Producer and 
 Engine Tests. The following is a condensed statement of the principal 
 results obtained in the gas-producer tests of the U. S. Geological Survey 
 t St. Louis in 1904. (R. H. Fernald, Trans. A. S. M. #., 1905.) 
 
 
 B.t.u. 
 
 Pounds per elec- 
 trical H.P. hour 
 
 
 B.t.u. 
 
 Pounds per elec- 
 trical H.P. hour 
 
 
 per 
 
 at switchboard. 
 
 
 per 
 
 at switchboard. 
 
 Sample. 
 
 Ib. 
 
 
 Sample. 
 
 Ib. 
 
 
 
 
 
 
 
 
 
 bus- 
 tible. 
 
 Coal 
 as 
 fired. 
 
 Dry 
 
 coal. 
 
 Com- 
 bus- 
 tible. 
 
 
 bus- 
 tible. 
 
 Coal 
 as 
 fired. 
 
 Dry 
 coal. 
 
 Com- 
 bus- 
 tible. 
 
 Ala. No. 2... 
 
 14820 
 
 1.71 
 
 .64 
 
 .53 
 
 Ky.No. 3.. 
 
 14650 
 
 2.05 
 
 1.91 
 
 .72 
 
 Colo. No. 3... 
 
 13210 
 
 2.14 
 
 .71 
 
 .58 
 
 Mo. No. 2.. 
 
 14280 
 
 1.94 
 
 1.71 
 
 .43 
 
 111. No. 3 
 
 14560 
 
 1.93 
 
 .79 
 
 .60 
 
 Mont. No. 1 
 
 13580 
 
 2.54 
 
 2.25 
 
 .98 
 
 111. No. 4 
 
 14344 
 
 2.01 
 
 .76 
 
 .57 
 
 N.Dak.No.2 
 
 12600 
 
 3.80 
 
 2.29 
 
 2.05 
 
 Ind.No. 1.... 
 
 14720 
 
 2.17 
 
 .93 
 
 .71 
 
 Texas No. 1 
 
 12945 
 
 3.34 
 
 2.22 
 
 .88 
 
 Ind.No.2.... 
 
 14500 
 
 1.68 
 
 .55 
 
 39 
 
 Texas No. 2 
 
 12450 
 
 2.58 
 
 1.71 
 
 .52 
 
 Okla.No. 1... 
 
 14800 
 
 1.92 
 
 .83 
 
 66 
 
 W.Va.No.l 
 
 15350 
 
 1.60 
 
 1.57 
 
 .48 
 
 Okla.No.4... 
 
 13890 
 
 1.57 
 
 .43 
 
 .17 
 
 W.Va.No.4 
 
 15600 
 
 1.32 
 
 1.29 
 
 .17 
 
 Iowa No. 2. . . 
 
 13950 
 
 2.07 
 
 .73 
 
 .30 
 
 W.Va.No.7 
 
 15800 
 
 1.53 
 
 1.50 
 
 .40 
 
 Kan. No. 5... 
 
 15200 
 
 1.69 
 
 .62 
 
 .43 
 
 Wyo.No.2 
 
 13820 
 
 2.28 
 
 2.07 
 
 .60 
 
 The gas was made in a Taylor pressure producer rated at 250 H.P. Its 
 inside diam. was 7 ft., area of fuel bed 38.5 sq. ft., height of casing 15 ft.; 
 rotative ash table; centrifugal tar extractor. The engine was a 3-cylinder 
 
851 FUEL. 
 
 vertical Westinghouse, 19 in. diam., 22 in. stroke, 200 r.p.m., rated at 
 235 B.H.P. Comparing the results of the W. Va. No. 7 coal, the best 
 on the list, with the North Dakota coal, the one which gave the poorest 
 results, the heat values per Ib. combustible of the coals are as 1 to 0.808; 
 reciprocal, 1 to 1.24; the Ibs. combustible per E. H. P. hour as 1 to 1.75, 
 and Ibs. coal as fired per E. H. P. hour as 1 to 2.88. The relative thermal 
 efficiencies of the engine with the two coals are as 2.05 to 1.17, or as 1 to 
 0.578. The analyses by volume of the dry gas obtained from the two 
 coals was: 
 
 C0 2 O CO H CH 4 N Total 
 
 combustible. 
 
 W. Va 10.16 0.24 15.82 11.16 3.74 5888 30.72 
 
 N. Dak 8.69 0.23 20.90 14.33 4.85 51.00 40.08 
 
 The dry-gas analysis shows the North Dakota gas to be by far the best ; 
 its much lower result in the engine test is due to the smaller quantity of 
 gas produced per Ib. of coal, which was 22.7 cu. ft. per Ib. of coal as fired, 
 as compared with 70.6 cu. ft. for the W. Va. coal, measured at 62 F. and 
 14.7 Ib. absolute pressure. 
 
 Use of Steam in Producers and in Boiler-furnaces. (R. W. Ray- 
 mond, Trans. A. I. M. E. t xx, 635.) No possible use of steam can cause 
 a gain of heat. If steam be introduced into a bed of incandescent carbon 
 't is decomposed into hydrogen and oxygen. 
 
 The heat absorbed by the reduction of one pound of steam to hydrogen 
 is much greater in amount than the heat generated by the union of the 
 oxygen thus set free with carbon, forming either carbonic oxide or car- 
 bonic acid. Consequently, the effect of steam alone upon a bed of incan- 
 descent fuel is to chill it. In every water-gas apparatus, designed to 
 produce by means of the decomposition of steam a fuel-gas relatively 
 Free from nitrogen, the loss of heat in the producer must be compensated 
 by some reheating device. 
 
 This loss may be recovered if the hydrogen of the steam is subsequently 
 burned, to form steam again. Such a combustion of the hydrogen is 
 contemplated, in the case of fuel-gas, as secured in the subsequent use of 
 that gas. Assuming the oxidation of H to be complete, the use of steam 
 will cause neither gain nor loss of heat, but a simple transference, the 
 heat absorbed by steam decomposition being restored by hydrogen com- 
 bustion. In practice, it may be doubted whether this restoration is ever 
 complete. But it is certain that an excess of steam would defeat the 
 reaction altogether, and that there must be a certain proportion of steam, 
 which permits the realization of important advantages, without too great 
 a net loss in heat. 
 
 The advantage to be secured (in boiler furnaces using small sizes of 
 anthracite) consists principally in the transfer of heat from the lower 
 side of the fire, where it is not wanted, to the upper side, where it is 
 wanted. The decomposition of the steam below cools the fuel arid the 
 grate-bars, whereas a blast of air alone would produce, at that point, 
 intense combustion (forming at first CO2), to the injury of the grate, the 
 fusion of part of the fuel, etc. 
 
 Gas Analyses by Volume and by Weight. To convert an analysis 
 of a mixed gas by volume into analysis by weight: Multiply the percentage 
 of each constituent gas by its relative density, viz: CO2 by 11, O by 8, 
 CO and N each by 7, and divide each product by the sum of the products. 
 Conversely, to convert analysis by weight into analysis by volume, divide 
 the percentage by weight of each gas by its relative density, and divide 
 each Quotient by the sum of the quotients. 
 
 Gas-fuel for Small Furnaces. E. P. Reichhelm (Am. Mack., Jan. 
 10, 1895) discusses the use of gaseous fuel for forge fires, for drop-forging, 
 in annealing-ovens and furnaces for melting brass and copper, for case- 
 hardening, muffle-furnaces, and kilns. Under ordinary conditions, in 
 such furnaces he estimates that the loss by draught, radiation, and the 
 heating of space not occupied by work is, with coal, 80%, with petro- 
 leum 70%, and with gas above the grade of producer-gas 25%. He 
 gives the following table of comparative cost of fuels, as used in these 
 furnaces: 
 
ACETYLENE AND CALCIUM CAKfilDE. 
 
 855 
 
 Kind of Gas. 
 
 "i 2 ! 
 
 E.S 3 
 SSS 
 |1 
 
 No. of Heat- 
 units in Fur- 
 naces f after 
 Deducting 
 25 % Loss. 
 
 Average Cost 
 per 1000 Ft. 
 
 Co?t of 1,000,- 
 000 Heat- 
 units Ob- 
 tained in, 
 Fiirnar.es. 
 
 Natural 
 
 1,000,000 
 675,000 
 646,000 
 690,000 
 313,000 
 377,000 
 185,000 
 150,000 
 306,365 
 
 750,000 
 506,250 
 484,500 
 517,500 
 234,750 
 282,750 
 138,750 
 112,500 
 229,774 
 
 
 
 Coal-gas 20 candle-power 
 
 $1.25 
 1.00 
 .90 
 .40 
 .45 
 .20 
 .15 
 .15 
 
 $2.46 
 2.06 
 .73 
 .70 
 .59 
 .44 
 .33 
 .65 
 .73 
 .73 
 
 
 Gasolene gas 20 candle-power 
 
 
 \Vater-gas from, bituminous coal 
 
 Water-gas and producer-gas mixed 
 Producer-gas . 
 
 Naphtha-gas, fuel 21/2 gals, per 1000 ft. . 
 
 Coal, $4 per ton, per 1,000,000 heat-units 
 Crude petroleum, 3 cts. per gal., per 1,( 
 
 utilized 
 
 )00,000 heat-units 
 
 Mr. Reichhelm gives the following figures from practice in melting 
 brass with coal and with naphtha converted into gas: 1800 Ibs. of metal 
 require 1080 Ibs. of coal, at $4.65 pei ton, equal to $2.51, or, say, 15 cents 
 per 100 Ibs. Mr,. T.'s report: 2500 Ibs. of metal require 47 gals, of naphtha, 
 at 6 cents per gal., equal to $2.82, or, say, 111/4 cents per 100 Ibs. 
 
 Blast-Furnace Gas. The waste-gases from iron blast furnaces 
 were formerly utilized only for heating the blast in the hot-blast ovens and 
 for raising steam for the blowing-engine pumps, hoists and other auxiliary 
 apparatus. Since the introduction of gas engines for blowing and other 
 purposes it has been found that there is a great amount of surplus gas 
 available for other uses, so that a large power plant for furnishing electric 
 current to outside consumers may easily be run by it. H. Freyn, in r <* 
 paper presented before the Western Society of Engineers (Eng. Rec., 
 Jan. 13, 1906), makes an elaborate calculation for the design of such a 
 plant in connection with two blast furnaces of a capacity of 400 tons of 
 pig iron each per day. Some of his figures are as follows: The two fur- 
 naces would supply 4,350,000 cu. ft. of gas per hour, of 90 B.T.U. average 
 heat value per cu. ft. The hot-blast stoves would require 30% of this, or 
 1,305,000 cu. ft.; the gas-blowing engines 720,000 cu. ft.; pumps, hoists 
 and lighting machinery, 120,000 cu. ft.; gas-cleaning machinery, 120,000 
 cu. ft.; losses in piping, 48,000 cu. ft.; leaving available for outside uses, in 
 round numbers, 2,000,000 cu. ft. per hour. At the rate of 100 cu. ft. of gas 
 per brake H.P. hour this would supply engines of 20,000 H.P., but assum- 
 ing that on account of irregular working of the furnaces only half this 
 amount would be available for part of the time, a 10,000-H.P. plant could 
 be run with the surplus gas of the two furnaces. Taking into account the 
 cost of the plant, figured at $61.60 per B.H.P., interest, depreciation, 
 labor, etc-., the annual cost of producing one B.H.P., 24 hours a day, is 
 $17.88, no value being placed on the blast-furnace gas, and 1 K.W. hour 
 would cost 0.295 cent, which is far below the lowest figure ever reached 
 with a steam-engine power plant. 
 
 Blast-furnace gas is composed of nitrogen, carbon dioxide and carbon 
 monoxide, the latter being the combustible constituent. An analysis 
 reported in Trans. A.I.M.E., xyii, 50, is, by volume, CO2, 7.08; CO, 27.80; 
 O, 0.10; N, 65.02. The relative proportions of COa and CO vary con- 
 siderably with the conditions of the furnace. 
 
 ACETYLENE AND CALCIUM CARBIDE. 
 
 Acetylene, C2H2, contains 12 parts C and 1 part H, or 92.3% C,7.7% H. 
 It is described as follows in a paper on Calcium Carbide and Acetylene 
 by J. M. Morehead (Am. Gas Light Jour., July 10, 1905. Revised, 
 
 Acetylene is a colorless and tasteless gas. When pure it has a sweef 
 etheral odor, but in the commercial form it carries small percentages of 
 phosphoreted and sulphureted hydrogen which give it a pungent odor. 
 
856 FtJEL. 
 
 Pure acetylene is -without toxic or physiological effect. It may be in- 
 haled or swallowed with impunity. One cu. ft. requires 11.91 cu. ft. of 
 air for its complete combustion. Its specific gravity is 0.92, air being 1. 
 It is the nearest approach to gaseous carbon, and it possesses a higher 
 candle power and flame temperature than any other known substance, 
 240 candles for 5 cu. ft., 4078 F. when burned in air, 7878 F. in oxygen. 
 Its ignition temperature with air is 804 F., with oxygen 782 F. It is 
 soluble in its own volume of water, and in varying proportions in ether, 
 alcohol, turpentine, and acetone. The solubility increases with pressure. 
 It liquefies under a pressure of 700 Ibs. per sq. in. at 70 F. The pres- 
 sure necessary for liquefaction varies directly with the temperature up 
 to 98, which is its critical temperature, beyond which it is impossible 
 to liquefy the gas at any pressure. 
 
 When calcium carbide is brought into contact with water, the calcium 
 robs the water of its oxygen and forms lime and thus frees the hydrogen, 
 which combines with the carbon of the carbide to form acetylene. 
 Sixty-four Ibs. of calcium carbide combine with thirty-six Ibs. of water 
 and produce twenty-six Ibs. of acetylene and 74 Ibs. of pure slacked 
 lime. [The chemical reaction is CaC2 + 2H 2 O = C2H2 + Ca(OH) 2 .] 
 
 Chemically pure calcium carbide will yield at 70 F. and 30 in. mer- 
 cury 5.83 cu. ft. acetylene per pound of carbide. Commercially pure 
 carbide is guaranteed to yield 5 cu. ft. of acetylene per pound, and 
 usually exceeds the guarantee by a few per cent. The reaction between 
 calcium carbide and water, and the subsequent slacking of the calcium 
 oxide produced, give rise to considerable heat. This heat from one pound 
 of chemically pure calcium carbide amounts to sufficient to raise the 
 temperature of 4.1 Ibs. of water from the freezing to the boiling point. 
 
 There are two types of generators; one in which a varying quantity of 
 water is dropped on to the carbide, the other in which the carbide is 
 dropped into a large excess of water. Owing to the large amount of heat 
 generated by the reaction, and the susceptibility of the acetylene to 
 heat, the first, or dry type, is* confined to lamps and to small machines. 
 
 Acetylene produces 1475 B.T.U. per cubic foot (at 70 F. and 30 in.), 
 as compared with 1000 for natural gas and 600 for coal or water gas. 
 At the present state of development of the acetylene industry and the 
 calcium carbide manufacture, this gas will not compete with coal gas or 
 water gas, or with electricity as supplied in our cities. 
 
 The explosive limits of acetylene and air are from 3 % acetylene and 
 97% air to 24% acetylene and 76% air, the point of maximum explo- 
 sibility being 7.7% acetylene and 92.3% air. 
 
 The combustion of acetylene requires theoretically 2 % volumes of 
 oxygen for 1 volume of acetylene. In autogenous welding and other 
 oxy-acetylene processes, however, a consid?rable part of the necessary 
 oxygen is taken from the air, and hence only from 1.25 to 1.75 cubic feet 
 of oxygen per cubic foot of acetylene need be supplied. 
 
 Of the 1475 heat units contained in a cubic foot of acetylene, 227 are 
 endothermic energy, which it is believed is higher than that for any 
 other substance. The balance of the energy is derived from the com- 
 bination of the carbon and hydrogen of the acetylene with oxygen, as 
 is the case with other combustible gases. 
 
 Due to the extraordinary endothermic energy of acetylene the gas 
 will explode of itself if it is ignited while at a pressure slightly in excess 
 of 15 Ibs. to the square inch. The compression, storage, use and trans- 
 portation of unabsorbed acetylene at pressures in excess of this figure 
 are forbidden by the fire, police, insurance and transportation authorities 
 in practically all cities. Danger of explosion from compressed acetylene 
 is removed and the use of compressed acetylene is rendered safe and 
 feasible for motor car, yacht, railroad train and all other portable uses 
 by absorbing the acetylene in acetone, which is itself absorbed in turn 
 in asbestos, Keisselgour or other non-inflammable substances. 
 
 Calcium carbide was discovered on May 4, 1892, at the plant of the 
 Willson Aluminum Co., in North Carolina. It is a crystalline body, 
 hard, brittle and varying in color from almost black to brick red. Its 
 specific gravity is 2.26. A cubic foot of crushed carbide weighs 138 Ibs., 
 and in weight, color and most of its physical characteristics is about 
 like granite. If broken hot, the fracture shows a handsome, bluish 
 purple iridescence and the crystals are apt to be quite large. 
 
ACETYLENE AND CALCIUM CARBIDE. 857 
 
 Calcium carbide, CaC2, contains 62.5% Ca and 37.5% C. It is in- 
 soluble in most acids and in all alkalies; it is non-inflammable, infusible, 
 non-explosive, unaffected by jars, concussions or time, and, except for 
 the property of giving off acetylene when brought in contact with water, 
 it is an inert and stable body. It is made by the reduction in an electric 
 arc furnace of a mixture of finely pulverized and intimately mixed cal- 
 cium oxide or quicklime and carbon in the shape of coke (CaO + 3C = 
 CaC2 + CO). The furnaces employ from 12,000 to 15,000 electric H.P. 
 each and produce from 50 to 75 tons per day. The output is crushed to 
 different sizes and it is sold in steel drums for $70 per ton at the works. 
 
 The entire use for calcium carbide is for the production of acetylene. 
 [Wohler, in 1862, obtained calcium carbide by heating an alloy of cal- 
 cium and zinc together with carbon to a very high temperature.] 
 
 Acetylene Generators and Burners. Lewes classifies acetylene 
 generators under four types: (1) Those in which water drips or flows 
 slowly on a mass of carbide; (2) those in which water rises, coming in 
 contact with a mass of carbide; (3) those in which water rises, coming in 
 contact with successive layers of carbide; (4) those in which the carbide 
 is dropped or plunged into an excess of water. He shows that the first 
 two classes are dangerous; that some generators of the third-class, are 
 good, 1)ut that those of the fourth are the best. 
 
 Of the various burners used for acetylene, those of the Naphey type 
 are among the most satisfactory. Two tubes leading from the base of 
 the burner are so adjusted as to cause two jets of flame to impinge upon 
 each other at some little distance from the nozzles, and mutually to 
 splay each other out into a flat flame. The tips of the nozzles, usually 
 of steatite, are formed on the principle of the Bunsen burner, insuring a 
 thorough mixture of the acetylene with enough air to give the best 
 illumination. (H. C. Biddle, Cal Jour, of Tech., 1907.) 
 
 Acetylene gas is an endothermic 'compound. In its formation heat is 
 absorbed, and there resides in the acetylene molecule the power of spon- 
 taneously decomposing and liberating this heat if it is subjected to a 
 temperature or pressure beyond the capacity of its unstable nature to 
 withstand. (Thos. L. White, Eng. Mag., Sept., 1908.) Mr. White 
 recommends the use of acetylene for carbureting the alcohol used ir. 
 alcohol motors for automobiles. 
 
 The Acetylene Blowpipe. (Machy., July, 1907.) The acetylene 
 is produced in a generator and stored in a tank at a pressure of 2.2 to 3 
 Ibs. per sq. in. The oxygen is compressed in a tank at about 150 Ibs. 
 pressure. The acetylene is conveyed to the burner through a 1-in. pipe 
 with one Y%-\n branch leading to each blowpipe connection. The oxygen 
 is conveyed through 2/g-in. pipe with ^-in. branches. The blowpipe is 
 of brass, made on the injector principle. As acetylene is so rich in car- 
 bon containing 92.3 % it is possible, when mixed with air in a Bunsen 
 burner, to. obtain 3100 F., and when combined with oxygen, 6300 F., 
 which is the hottest flame known as a product of combustion, and nearly 
 equals the electric arc. This is about 1200 higher than the oyx- 
 hydrogen blowpipe flame. 
 
 In lighting the blowpipe, the acetylene is first turned on full; then the 
 oxygen is added until the flame is only a single cone. At the apex of this 
 cone is a temperature of 6300 F. In welding, this point is held from % 
 to ^t in. distant from the metal to be welded. Too much acetylene pro- 
 duces two cones and a white color ; an excess of oxygen is indicated by a 
 violet tint. 
 
 Theoretically, 2 y<i volumes of oxygen are required for complete com- 
 bustion of 1 volume of acetylene. Practically, however, with the blow- 
 pipe, the best welding results are obtained with 1.7 volumes of oxygen to 
 1 volume of acetylene. The acetylene is, therefore, not completely 
 burned with the blowpipe, according to the reaction: 
 
 2C 2 H 2 (4 vol.) -f- 5O 2 . (10 vol.) = 4CO 2 + 2H 2 O, 
 but it is incompletely burned according to the reaction: 
 C 2 H 2 (2 vol.) -f- O 2 (2 vol.) = 2CO + H 2 . 
 
 The Theory and Practice of Oxy-Acetylene Welding is described in an 
 illustrated article by J. F. Springer in Indust. Eng'g., Oct., 1909. 
 The Levoisite process of making oxygen (99.9 % pure) , used in acety- 
 
858 
 
 ILLUMINATING - GAS. 
 
 lene welding, is described by Max Mauran in Met. and Chem. Eng'g., 
 June, 1914. 
 
 IGNITION TEMPERATURE OP GASES. 
 
 Mayer and Munch (Bericht der deutscher Gesellschaft, xxvi, 2241) give 
 the following: 
 
 " ' CH 4 ,667C. 1233 F. 
 
 C2He, 616 1141 
 
 C 3 H 8 , 547 1017 
 
 C2H2, 580 1076 
 
 CaHe, 504 939 
 
 Marsh-gas, 
 
 Ethane, 
 
 Propane, 
 
 Acetylene, 
 
 Propylene, 
 
 French 
 1022 
 
 Very different figures are given by other authorities. 
 Commission obtained for hydrogen 1071 F.; CH 4 , 1436; , 
 
 CO, 1202; CO in presence of a large quantity of CO2, 1292 F. Vivian 
 Lewes gives for the ignition temperature of cannel coal 668 F.; bi- 
 tuminous, 766, semi-bituminous 870 F. W. S. Hutton gives for 
 anthracite, 925 F. 
 
 ILLUMINATING-GAS. 
 
 Coal-gas is made by distilling bituminous coal in retorts. The* retort 
 is usually a long horizontal semi-cylindrical or a shaped chamber, holding 
 from 160 to 300 Ibs. of coal. The retorts are set in "benches" of from 
 3 to 9, heated by one fire, which is generally of coke. The vapors distilled 
 from the coal are converted into a fixed gas by passing through the retort, 
 which is heated almost to whiteness. 
 
 The gas passes out of the retort through an "ascension-pipe" into a 
 long horizontal pipe called the hydraulic main, where it deposits a por- 
 tion of the tar it contains; thence it goes into a condenser, a series of iron 
 tubes surrounded by cold water, where it is freed from condensable vapors, 
 as ammonia-water, then into a washer, where it is exposed to jets of 
 water, and into a scrubber, a large chamber partially filled with trays 
 made of wood or iron, containing coke, fragments of brick or paving- 
 Atones, which are wet with a spray of water. By the washer and scrubber 
 the gas is freed from the last portion of tar and ammonia and from some 
 of the sulphur compounds. The gas is then finally purified from sulphur 
 compounds by passing it through lime or oxide of iron. The gas is drawn 
 from the hydraulic main and forced through the washer, scrubber, etc., 
 by an exhauster or gas pump. 
 
 The kind of coal used is generally caking bituminous, but as usually 
 this coal is deficient in gases of high illuminating power, there is added to 
 it a portion of cannel coal or other enricher. 
 
 The following table, abridged from one in Johnson's Cyclopedia, shows 
 the analysis, candle-power, etc., of some gas-coals and enrichers: 
 
 Gas-ooals, etc. 
 
 Vol. Matter. 
 
 Fixed Garb. 
 
 ^ 
 
 II 
 $S 
 
 o^ 
 
 Coke per 
 ton of 2240 
 Ibs. 
 
 !~'i 
 2 >> 
 
 5-* 
 
 Ibs. 
 
 bush. 
 
 Pittsburgh Pa 
 
 36.76 
 36.00 
 37.50 
 40.00 
 43.00 
 46.00 
 53.50 
 
 51.93 
 58.00 
 56.90 
 53.30 
 40.00 
 41.00 
 44.50 
 
 7.07 
 6.00 
 5.60 
 6.70 
 17.00 
 13.00 
 2.00 
 
 Vo',642 
 10,528 
 10,765 
 9800 
 13,200 
 15,000 
 
 
 
 
 
 Westmoreland, Pa 
 Sterling, O 
 
 16.62 
 18.81 
 20.41 
 34.98 
 42.79 
 28.70 
 
 1544 
 1480 
 1540 
 1320 
 1380 
 1056 
 
 40 
 36 
 36 
 32 
 32 
 44 
 
 6420 
 3993 
 2494 
 2806 
 4510 
 
 Despard, W. Va 
 
 
 Petonia, W. Va 
 
 Grahamite, W. Va 
 
 The products of the distillation of 100 Ibs. of average gas-coal are about 
 as follows. They vary according to the quality of coal and the tempera- 
 ture of distillation. 
 
 Coke, 64 to 65 Ibs.; tar, 6.5 to 7.5 Ibs.; ammonia liquor, 10 to 12 Ibs.; 
 purified gas, 15 to 12 Ibs.; impurities and loss, 4.5% to 3.5%. 
 The composition of the gas by volume ranges about as follows ; Hydro- 
 
ILLUMINATING^ GAS. 859 
 
 gen, 38% to 48%; carbonic oxide, 2% to 14%; marsh-gas (Methane, 
 CH 4 ), 43% to 31%; heavy hydrocarbons (CwH 2 w, ethylene, propylene, 
 benzole vapor, etc.), 7.5% to 4.5%; nitrogen, 1% to 3%. 
 
 In the burning of the gas the nitrogen is inert: the hydrogen and car- 
 bonic oxide give heat but no light. The luminosity of the flame is due to 
 the decomposition by heat of the heavy hydrocarbons into lighter hydro- 
 carbons and carbon, the latter being separated in a state of extreme 
 subdivision. By the heat of the flame this separated carbon is heated to 
 intense whiteness, and the illuminating effect of the flame is due to the 
 light of incandescence of the particles of carbon. 
 
 The attainment of the highest degree of luminosity of the flame de- 
 pends upon the proper adjustment of the proportion of the heavy hydro- 
 carbons (with due regard to their individual character) to the nature or 
 the diluent mixed therewith. 
 
 Investigations of Percy F. Frankland show that mixtures of ethylene 
 and hydrogen cease to have any luminous effect when the proportion of 
 ethylene does not exceed 10% of the whole. Mixtures of ethylene and 
 carbonic oxide cease to have any luminous effect when the proportion of 
 the former does not exceed 20%, while all mixtures of ethylene and 
 marsh-gas have more or less luminous effect. The luminosity of a mix- 
 ture of 10% ethylene and 90% marsh-gas being equal to about 18 candles, 
 and that of one of 20% ethylene and 80% marsh-gas about 25 candles. 
 The illuminating effect of marsh-gas alone, when burned in an argand 
 burner, is by no means inconsiderable. 
 
 For further description, see the treatises on gas by King, Richards, 
 and Hughes; also Appleton's Cyc. Mech., vol. i. p. 900. 
 
 Water-gas. Water-gas is obtained by passing steam through a bed 
 of coal, coke, or charcoal heated to redness or beyond. The steam is 
 decomposed, its hydrogen being liberated and its oxygen burning the 
 carbon of the fuel, producing carbonic-oxide gas. The chemical reaction 
 is, C + H 2 O = CO + 2 H, or 2 C + 2 H 2 O = C + CO 2 + 4 H, followed 
 by a splitting up of the CO 2 , making 2 CO + 4 H. By weight the normal 
 gas CO + 2 H is composed of C + O + H = 28 parts CO and 2 parts H, 
 
 12 + 16 + 2 
 
 or 93.33% CO and 6.67% H; by volume it is composed of equal parts of 
 carbonic oxide and hydrogen. Water-gas produced as above described 
 has great heating-power, but no illuminating-power. It may, however, 
 be used for lighting by causing it to heat to whiteness some solid sub- 
 stance, as is done in the Welsbach incandescent light. 
 
 An illuminating-gas is made from water-gas by adding to it hydro- 
 carbon gases or vapors, which are usually obtained from petroleum or 
 some of its products. A history of the development of modern illumi- 
 nating water-gas processes, together with a description of the most recent 
 forms of apparatus, is given by Alex. C. Humphreys, in a paper on " Water- 
 gas in the United States," read before the Mechanical Section of the 
 British Association for Advancement of Science, in 1889. After describ- 
 ing many earlier patents, he states that success in the manufacture of 
 water-gas may be said to date from 1874, when the process of T. S. C. 
 Lowe was introduced. All the later most successful processes are the 
 modifications of Lowe's, the essential features of which were "an apparatus 
 consisting of a generator and superheater internally fired; the super- 
 heater being heated by the secondary combustion from the generator, 
 the heat so stored up in the loose brick of the superheater being used, in 
 the second part of the process, in the fixing or rendering permanent of the 
 hydrocarbon gases; the second part of the process consisting in the 
 passing of steam through the generator fire, and the admission of oil or 
 hydrocarbon at some point between the fire of the generator and the 
 loose filling of the superheater." 
 
 The water-gas process thus has two periods: first the " blow," during 
 which air is blown through the bed coal in the generator, and the par- 
 tially burned gaseous products are completely burned in the superheater, 
 giving up a great portion of their heat to the fire-brick work contained 
 in it, and then pass out to a chimney; second, the "run" during which the 
 air blast is stopped, the opening to the chimney closed, and steam is 
 blown through the incandescent bed of fuel. The resulting water-gas 
 passing into the carburetting chamber in the base of the superheater is 
 there charged with hydrocarbon vapors, or spray (such as naphtha and 
 other distillates or crude oil) , and passes through the superheater, where 
 
860 
 
 ILJAJMINATING- GAS. 
 
 the hydrocarbon vapors become converted into fixed illuminating gases. 
 From the superheater the combined gases are passed, as in the coal-gas 
 process, through washers, scrubbers, etc., to the gas-holder. In this 
 case, however, there is no ammonia to be removed. 
 
 The specific gravity 01 water-gas increases with the increase of the 
 heavy hydrocarbons which give illuminating power. The following 
 figures, taken from different authorities, are given by F. H. Shelton in a 
 paper on " Water-gas," read before the Ohio Gas Light Association, in 
 1894: 
 
 Candle-power.... 19.5 20.22.5 24. 25.426.3 28.3 29.6 .30 to 31. 9 
 Sp. gr. (Air = l).. .571 .630 .589 .60 to .67 .64 .602 .70 .65 .65 to .71 
 
 Analyses of Water-gas and Coal-gas Compared. 
 
 The following analyses are taken frorn a report of Dr. Gideon E. 
 Moore on the Granger Water-gas, 1885: 
 
 
 Composition by Vol. 
 
 Composition by Weight. 
 
 Water-gas. 
 
 Coal- 
 gas. 
 Heidel- 
 berg. 
 
 Water-gas. 
 
 Coal- 
 gas. 
 
 Wor - [ Lake, 
 cester. | 
 
 Wor- 
 cester. 
 
 Lake. 
 
 Nitrogen . ... 
 
 2.64 
 0.14 
 0.06 
 11.29 
 0.00 
 1.53 
 28.26 
 18.88 
 37.20 
 
 3.85 
 0.30 
 0.01 
 12.80 
 0.00 
 2.63 
 23.58 
 20.95 
 35.88 
 
 2.15 
 3.01 
 0.65 
 2.55 
 1.21 
 1.33 
 8.88 
 34.02 
 46.20 
 
 0.04402 
 0.00365 
 0.00114 
 0.18759 
 
 0.06175 
 0.00753 
 0.00018 
 0.20454 
 
 0.04559 
 0.09992 
 0.01569 
 0.05389 
 0.03834 
 0.07825 
 0.18758 
 0.41087 
 0.06987 
 
 Carbonic acid 
 
 Oxygen 
 
 Ethylene 
 
 Propylene 
 
 Benzole vapor . . 
 
 0.07077 
 0.46934 
 0.17928 
 0.04421 
 
 0.11700 
 0.37664 
 0.19133 
 0.04103 
 
 Carbonic oxide 
 
 Marsh-gas ...... 
 
 
 
 100.00 
 
 100.00 
 
 100.00 
 
 1 .00000 
 
 1 .00000 
 
 1 .00000 
 
 Density: Theory 
 
 0.5825 
 0.5915 
 
 0.6057 
 0.6018 
 
 0.4580 
 
 
 
 
 Practice . . . 
 
 
 
 
 
 
 
 
 
 B.T.U.fromlcu.ft.: 
 Water liquid 
 
 650.1 
 597.0 
 
 688.7 
 646.6 
 
 642.0 
 577.0 
 
 
 
 
 vapor 
 
 
 
 
 
 
 
 
 Flame-temperature, F . . . 
 
 5311.2 
 
 5281.1 
 
 5202.9 
 
 
 
 
 Average candle-power 
 
 22.06 
 
 26.31 
 
 
 
 
 
 The heating- values (B.T.U.) of the gases are calculated from the 
 analysis by weight, by using the multipliers given below (computed 
 from results of J. Thomsen), and multiplying tha result by the weight 
 Of 1 cu. ft. of the gas at 62 F., and atmospheric pressure. 
 
 The flame- temperatures (theoretical) are calculated on the assumption 
 Of complete combustion of the gases in air, without excess of air. 
 
 The candle-power was determined by photometric tests, using a pres- 
 sure of l/2-in. water-column, a candle consumption of 120 grains of sper- 
 maceti per hour, and a meter rate of 5 cu. ft. per hour, the result being 
 corrected for a temperature at 62 F. and a barometric pressure of 30 in. 
 It appears that the candle-power may be regulated at the pleasure of the 
 person in charge of the apparatus, the range of candle-power being from 
 20 to 29 candles, according to the manipulation employed. 
 
 Calorific Equivalents of Constituents of Illuminating-gas. 
 
 Heat-units from 1 Ib. Heat-units from 1 Ib. 
 
 Water Water Water Water 
 
 Liquid. Vapor. Liquid. Vapor. 
 
 Ethylene 21,524.4 20,134.8 Carbonic oxide . 4,395.6 4,395.6 
 
 Propylene. .. .21,222.0 19,834.2 Marsh-gas 24,021.0 21,592.8 
 
 Benzole vapor .18,954.0 17,847.0 Hydrogen 61 .524.0 51 804,0 
 
ILLUMINATING- GAS. 
 
 861 
 
 Efficiency of a Water-gas Plant. The practical efficiency of an 
 illuminating water-gas setting is discussed in a paper by A. G. Glasgow 
 (Proe. Am. Gaslight Assn., 1890) from which the following is abridged: 
 
 The results refer to 1000 cu. ft. of unpurifiedcarburetted gas, reduced to 
 60 F. The total anthracite charged per 1000 cu. ft. of gas was 33.4 Ibs., 
 ash and unconsumed coal removed, 9.9 Ibs., leaving total combustible 
 consumed, 23.5 Ibs., which is taken to have a fuel-value of 14,500 B.T.U. 
 per pound, or a total of 340,750 heat-units. 
 
 
 
 Com- 
 posi- 
 tion by 
 Vol. 
 
 Weight 
 
 KxTcu. 
 Ft. 
 
 Com- 
 posi- 
 tion by 
 W'ht. 
 
 Specific 
 Heat. 
 
 I. Carburetted Water-gas. . 
 
 CO 2 + H 2 S 
 C M H 2 . ... 
 CO 
 CH 4 
 H... 
 
 3.8 
 14.6 
 28.0 
 17.0 
 35.6 
 
 .465842 
 1.139968 
 2.1868 
 .75854 
 .1991464 
 
 0.09647 
 .23607 
 .45285 
 .15710 
 .04124 
 
 0.02088 
 .0872H 
 .11226 
 .09314 
 .14041 
 
 
 N 
 
 1.0 
 
 .078596 
 
 .01627 
 
 .00397 
 
 
 
 100.0 
 
 4.8288924 
 
 1.00000 
 
 .45786 
 
 
 CO 2 
 CO... 
 
 3.5 
 
 43.4 
 
 .429065 
 3.389540 
 
 .1019 
 .8051 
 
 .02205 
 .19958 
 
 II. Uncarburetted gas 
 
 H 
 
 51.8 
 
 .289821 
 
 .0688 
 
 .23424 
 
 
 N 
 
 1.3 
 
 .102175 
 
 .0242 
 
 .00591 
 
 
 
 100.0 
 
 4.210601 
 
 1.0000 
 
 .46178 
 
 
 CO 2 ... 
 
 17.4 
 
 2.133066 
 
 .2464 
 
 .05342 
 
 III. Blast products escap- 
 
 o 
 
 3.2 
 
 .2856096 
 
 .0329 
 
 .00718 
 
 ing from superheater . . 
 
 N 
 
 79.4 
 
 6.2405224 
 
 .7207 
 
 .17585 
 
 
 
 100.0 
 
 8.6591980 
 
 1.0000 
 
 .23645 
 
 
 CO 2 ... 
 
 9.7 
 
 1.189123 
 
 .1436 
 
 .031075 
 
 
 CO 
 
 17.8 
 
 1.390180 
 
 .1680 
 
 .041647 
 
 IV. Generator blast-gases. . 
 
 N 
 
 72.5 
 
 5.698210 
 
 .6884 
 
 .167970 
 
 
 
 100.0 
 
 8.277513 
 
 1.0000 
 
 .240692 
 
 The heat-energy absorbed by the apparatus is 23.5 X 14,500 = 340,750 
 heat-units = A. Its disposition is as follows* 
 J3, the energy of the CO produced; 
 
 C, the energy absorbed in the decomposition of the steam; 
 
 D, the difference between the sensible heat of the escaping iauminating- 
 gases and that of the entering oil; 
 
 E, the heat carried off by the escaping blast products; 
 
 F, the heat lost by radiation from the shells; 
 
 G t the heat carried away from the shells by convection (air-currents); 
 
 //, the heat rendered latent in the gasification of the oil; 
 
 7, the sensible heat in the asn and unconsumed coal recovered from 
 the generator. 
 
 The heat equation lsA=B+C+D+E+F+G+H+I: A 
 
 280 
 being known. A comparison of the CO in Tables I and II show that j^ t 
 
 or 64.5% of the volume of carburetted gas, is pure water-gas, distributed 
 thus: CO 2 , 2.3%; CO, 28.0%; H, 33.4%; N, 0.8%; = 64.5%. 1 Ib. of CO 
 at 60 F. = 13,531 cu. ft. CO per 1000 cu. ft. of gas = 280 + 13.531 
 = 20.694 Ibs. Energy of the CO = 20.694 X 4395.6 = 91,043 heat- 
 units = B. 1 Ib. of H at 60 F. = 189.2 cu. ft. H per M of gas = 334 
 * 189.2 = 1.7653 Ibs. Energy of the H per Ib. (according to Thomsen, 
 considering the steam generated by its combustion to be condensed to 
 water at 75 F.) = 61,524 B.T.U. In Mr. Glasgow's experiments the 
 steam entered the generator at 331 F.; the heat required to raise the 
 product of combustion of 1 Ib. of H, viz., 8.98 Ibs. H 2 O, from water at 75 
 to steam at 331 must therefore be deducted from Thomsen's figure, or 
 61,524 - (8.98 X 1140.2) = 51,285 B.T.U. per Ib. of H. Energy of 
 the H, then, is 1.7653 X 51,285 = 90,533 heat-units = C. The best 
 
shell of the apparatus gave figures for the amount of heat lost by radia- 
 tion = 12,454 heat-units = F, and by 
 
 S62 ILLUMINATING-GAS. 
 
 lost due to the sensible heat in the illuminating-gases, their temperature 
 being 1450 F., and that of the entering oil 235 F., is 48.29 (weight) 
 X.45786 (sp. heat) X 1215 (rise of temperature) = 26,864 heat-units = D. 
 
 (The specific heat of the entering oil is approximately that of the 
 issuing gas.) 
 
 The heat carried off in 1000 cu. ft. of the escaping blast products is 
 86.592 (weight) X .23645 (sp. heat) X 1474 (rise of temp.) = 30,180 
 heat-units: the temperature of the escaping blast gases being 1550 F., 
 and that of the entering air 76 F. But the amount of the blast gases, 
 by registration of an anemometer, checked by a calculation from the 
 analyses of the blast gases, was 2457 cubic feet for every 1000 cubic feet 
 of carburetted gas made. Hence the heat carried off per M. of carburetted 
 gas is 30,180 X 2.457 = 74,152 heat-units = E. 
 
 Experiments made by a radiometer covering four square feet of the 
 
 he amount of heat lost by radia- 
 convection = 15,696 heat-units 
 
 
 The heat rendered latent by the gasification of the oil was found by 
 taking the difference between all the heat fed into the carburetter and 
 superheater and the total heat dissipated therefrom to be 12,841 heat- 
 units = H. The sensible heat in the ash and unconsumed coal is 9.9 Ibs. 
 X 1500 X .25 (sp. ht.) = 3712 heat-units = /. 
 
 The sum of all the items B+C+D+E+F+G+H+I = 
 327,295 heat-units, which subtracted from the heat-energy of the com- 
 bustible consumed, 340,750 heat-units, leaves 13,455 heat-units, or 4 per 
 cent unaccounted for. 
 
 Of the total heat-energy of the coal consumed, or 340,750 heat-units, 
 the energy wasted is the sum of items D, E : F, G, and 7, amounting to 
 132,878 heat-units, or 39 per cent; the remainder, or 207,872 heat-units, 
 or 61 per cent, being utilized. The efficiency of the apparatus as a heat 
 machine is therefore 61 per cent. 
 
 Five gallons, or 35 Ibs. of crude petroleum, were fed into the carburetter 
 per 1000 cu. ft. of gas made; deducting 5 Ibs. of tar recovered, leaves 
 30 Ibs. X 20,000 = 600,000 heat-units as the net heating- value of the 
 petroleum used. Adding this to the heating-value of the coal, 340,750 
 B.T.U., gives 940,750 heat-units, of which there is found as heat-energy 
 in the carburetted gas, as in the table below, 764,050 heat-units, or 81 
 per cent, which is the commercial efficiency of the apparatus, i.e., the 
 ratio of the energy contained in the finished product to the total energy 
 of the coal and oil consumed. 
 
 The heating-power per M. cu. ft. of 
 the carburetted gas is 
 CO 2 38.0 
 C 3 H 6 *146.0x. 117220x21222.0=363200 
 CO 280.0 x. 078100 x 4395.6= 96120 
 CH 4 170.0 x. 044620x24021.0- 1822 10 
 H 356.0 x. 005594x61524.0 =122520 
 N 10.0 
 
 1000.0 764050 
 
 The heating-power per M. of the 
 un carburetted gas is 
 CO 2 35.0 
 CO 434.0 x. 0781 00 x 4395.6=148991 
 H 518.0X. 005594X61524.0- 178277 
 N 13.0 
 
 1000.0 327268 
 
 The candle-power of the gas is 31, or 6.2 candle-power per gallon of oil 
 used. The calculated specific gravity is .6355, air being 1. 
 
 For description of the operation of a modern carburetted water-gas 
 plant, see paper by J. Stelfox, Eng'g, July 20, 1894, p. 89. 
 
 Space Required for a Water-gas Plant. Mr. Shelton, taking 15 
 modern plants of the form requiring the most floor-space, figures the 
 average floor-space required per 1000 cubic feet of daily capacity as 
 follows: 
 
 Water-gas Plants of Capacity Require an Area of Floor-space for each 
 in 24 hours of 1000 cu. ft. of about 
 
 100,000 cubic feet 4 square feet. 
 
 200,000 " " 3.5 
 
 400,000 " " 2.75 " 
 
 600,000 " " 2 to 2.5 sq. ft. 
 
 7 to 10 million cubic feet 1.25 to 1.5 sq. ft. 
 
 The heating- value of the illuminants C n H 2n is assumed to equal that 
 
ILLUMINATING-GAS. 863 
 
 These figures include scrubbing and condensing rooms, but not boiler 
 and engine rooms. In coal-gas plants of the most modern and compact 
 forms one with 16 benches of 9 retorts each, with a capacity of 1,500,000 
 cubic feet per 24 hours, will require 4.8 sq. ft. of space per 1000 cu. ft. 
 of gas, and one of 6 benches of 6 retorts each, with 300,000 cu. ft. capacity 
 per 24 hours, will require 6 sq. ft. of space per 1000 cu. ft. The storage- 
 room required for the gas-making materials is: for coal-gas, 1 cubic foot 
 of room for every 232 cubic feet of gas made; for water-gas made from 
 coke, 1 cubic foot of room for every 373 cu. ft. of gas made; and for 
 water-gas made from anthracite, 1 cu. ft. of room for every 645 cu. ft. of 
 gas made. 
 
 The comparison is still more in favor of water-gas if the case is con- 
 sidered of a water-gas plant added as an auxiliary to an existing coal- 
 gas plant ; for, instead of requiring further space for storage of coke, part 
 of that already required for storage of coke produced and not at once 
 sold can be cut off, by reason of the water-gas plant creating a constant 
 demand for more or less of the coke so produced. 
 
 Mr. Shelton gives a calculation showing that a water-gas of 0.625sp. gr. 
 would require gas-mains eight per cent greater in diameter than the same 
 quantity coal-gas of 0.425 sp. gr. if the same pressure is maintained at the 
 holder. The same quantity may be carried in pipes of the same diam- 
 eter if the pressure is increased in proportion to the specific gravity. 
 With the same pressure the increase of candle-power about balances the 
 decrease of flow. With five feet of coal-gas, giving, say, eighteen candle- 
 power, 1 cubic foot equals 3.6 candle-power; with water-gas of 23 candle- 
 power, 1 cubic foot equals 4.6 candle-power, and 4 cubic feet gives 18.4 
 candle-power, or' more than is given by 5 cubic feet of coal-gas. Water- 
 gas may be made from oven-coke or gas-house coke as well as from an- 
 thracite coal. A water-gas plant may be conveniently run in connection 
 with a coal-gas plant, the surplus retort coke of the latter being used as 
 the fuel of the former. 
 
 In coal-gas making it is impracticable to enrich tne gas to over twenty 
 candle-power without causing too great a tendency 10 smoke, but water- 
 gas of as high as thirty candle-power is quite common. A mixture of 
 coal-gas and water-gas of a higher C.P. than 20 can be advantageously 
 distributed. 
 
 Fuel- value of Illuminating-gas. E. G. Love (School of Mines 
 Qtly, January, 1892) describes F. W. Hartley's calorimeter for determin- 
 ing the calorific power of gases, and gives results obtained in tests of the 
 carbureted water-gas made by the municipal branch of the Consoli- 
 dated Co. of New York. The tests were made from time to time during 
 the past two years, and the figures give the heat-units per cubic foot at 
 60 F. and 30 'inches pressure: 715, 692, 725, 732, 691, 738, 735, 703, 734, 
 730, 731, 727. Average, 721 heat-units. Similar tests of mixtures of 
 coal- and water-gases made by other branches of the same company give 
 694, 715, 684, 692, 727, 665, 695, and 686 heat-units per foot, or an 
 average of 694.7. The average of all these tests was 710.5 heat-units, 
 and this we may fairly take as representing the calorific power of the 
 illuminating gas of New York. One thousand feet of this gas, costing 
 $1.25, would therefore yield 710,500 heat-units, which would be equiva- 
 lent to 568,400 heat-units for $1.00. 
 
 The common coal-gas of London, with an illuminating power of 16 to 
 17 candles, has a calorific power of about 668 units per foot, and costs 
 from 60 to 70 cents per thousand. 
 
 The product obtained by decomposing steam by incandescent carbon, 
 as effected in the Motay process, consists of about 40% of CO, and a 
 little over 50% of H. 
 
 This mixture would have a heating-power of about 300 units per cubic 
 foot, and if sold at 50 cents per 1000 cubic feet would furnish 600,000 units 
 for $1.00, as compared with 568,400 units for $1.00 from illuminating gas 
 at $1.25 per 1000 cubic feet. This illuminating-gas if sold at $1.15 per 
 thousand would therefore be a more economical heating agent than the 
 fuel-gas mentioned, at 50 cents per thousand, and be much more advan- 
 tageous than the latter, in that one main, service, and meter could be used 
 to furnish gas for both lighting and heating. 
 
 A large number of fuel-gases tested by Mr. Love gave from 184 to 470 
 heat-units per foot, with an average of 309 units. 
 
 Taking the cost of heat from illuminating-gas at tlie lowest figure given 
 
864 
 
 ILLUMINATING-GAS . 
 
 by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, 
 equal to coai at $40 per ton of 2000 Ibs., the coal having a, calorific power 
 of only 12,000 heat-units per pound, or about 83% of that of pure carbon. 
 600,000: (12,000 X 2000) :: $1 : $40. 
 
 FLOW OF GAS IN PIPES. 
 
 The rate of flow of gases of different densities, the diameter of pipes 
 required, etc., are given in King's Treatise on Coal Gas, vol. ii, 374, aa 
 follows: 
 
 If d = diameter of pipe in inches, 
 Q = quantity of gas in cu. ft. per 
 
 hour, 
 
 I = length of pipe in yards, /, 
 
 h = pressure in inches of water, 
 s = specific gravity of gas, air 
 being 1, 
 
 Moiesworth gives Q = 1000 y 
 
 J. P. Gill, Am. Gas-light Jour., 1894, gives Q = 1291 
 
 (1350)2/i' 
 
 (1350)2^ ' 
 = 1350(^2 
 
 = 1350 V~ 
 
 291 \ - 
 
 ' S 
 
 -,- - d") 
 
 This formula is said to be based on experimental data, and to make 
 allowance for obstructions by tar, water, and other bodies tending to check 
 the flow of gas through the pipe. 
 
 King's formula translated into the form of the common formula for the 
 flow of compressed air 9r steam in pipes, Q = c */(PI P2) d*>/wL, in 
 which Q = cu. ft. per min., PI p* = difference in pressure in Ibs. per 
 sq. in; w = density in Ibs. per cu. ft., L = length in ft., d = diam. in ins., 
 gives 56.6 for the value of the coefficient c, which is nearly the same as that 
 commonly used (60) in calculations of the flow of air in pipes. For values 
 of c based on Darcy's experiments on flow of water in pipes see Flow of 
 Steam. 
 
 An experiment made by Mr. Clegg, in London, with a 4-in. pipe, 6 miles 
 long, pressure 3 in. of water, specific gravity of gas 0.398, gave a discharge 
 into the atmosphere of 852 cu. ft. per hour., after a correction of 33 cu. ft. 
 was made for leakage. 
 
 Substituting this value, 852 cu. ft., for Q in the formula Q = C Vd 5 ft -4- si, 
 we find C, the coefficient, = 997, which corresponds nearly with the formula 
 given by Moiesworth. 
 
 Wm. Cox (Am. Mach., Mar. 20, 1902) gives the following formula for 
 flow of gas in long pipes. 
 
 Q _ 3000 
 
 
 Q= discharge in cu. ft. per hour at atmospheric pressure; d = diam. 
 of pipe in ins.; p t = initial and p% = terminal absolute pressure, Ibs. per 
 sq. in.; I = length of pipe in feet, L = length in miles. For Pi 2 p 2 2 
 may be substituted (PI + p 2 ) (Pi . 2). The specific gravity of "the 
 gas is assumed to be 0.65, air being 1. For fluids of any other sp. gr., 
 s, multiply the coefficients 3000 or 41.3 by V0.65/S. For air, s = 1, the 
 coefficients become 2419 and 33.3. J. E. Johnson Jr.'s formula for air, 
 page 619, translated into the same notation as Mr. Cox's, makes the coeffU 
 cients 2449 and 33.5. 
 
 Services for Lamps. (Moiesworth.) 
 
 Lamps. 
 
 Ft. from 
 Main. 
 
 Require 
 Pipe-bore. 
 
 Lamps. 
 
 Ft . from 
 Main. 
 
 Require 
 Pipe-bore. 
 
 2 
 
 40 
 
 3 'gin. 
 
 15 
 
 130 
 
 1 in. 
 
 4 . 
 
 40 
 
 1/2 in. 
 
 20... 
 
 150 
 
 11/4 in. 
 
 6 
 
 50 
 
 5/8 i n - 
 
 25 
 
 180 
 
 1 1/9 in. 
 
 to 
 
 too 
 
 3/4 in. 
 
 30 
 
 200 
 
 1 3/4 in. 
 
 
 
 
 
 
 
 (In cold climates no service less than 3/ 4 in. shouH te used,) 
 
FLOW OF GAS IN PIPES. 
 
 865 
 
 Factors for Reducing Volumes of Gas to Equivalent Volumes at 
 60 F. and 30-inches Barometer. 
 
 (Multiply the observed volume by the factor to obtain the 
 equivalent volume.) 
 
 d^ 
 
 Barometer. 
 
 II 
 
 HQ 
 
 30.0 
 
 29.8 
 
 29.6 
 
 29.4 
 
 29.2 
 
 29.0 
 
 28.8 
 
 28.6 
 
 28.4 
 
 28.2 
 
 28.0 
 
 -30 
 
 2095 
 
 1 2014 
 
 1934 
 
 1853 
 
 1772 
 
 1692 
 
 1611 
 
 1530 
 
 1450 
 
 1 1369 
 
 1 1288 
 
 -25 
 
 .1956 1.1876 
 
 .1796 
 
 .1716 
 
 .1637 
 
 .1557 
 
 .1476 
 
 .1398 
 
 .1318 
 
 .1238 
 
 .1159 
 
 -20 
 
 18201 1741 
 
 1662 
 
 1583 
 
 1505 
 
 1426 
 
 1347 
 
 1268 
 
 1189 
 
 1111 
 
 1032 
 
 -15 
 
 .1687 1.1609 
 
 .1531 
 
 .1453 
 
 .1375 
 
 .1297 
 
 .1219 
 
 .1141 
 
 .1064 
 
 .0986 
 
 .0908 
 
 -10 
 
 .15571.1480! .1403 
 
 .1326 
 
 .1249 
 
 .1172 
 
 .1095 
 
 .1018 
 
 .0941 
 
 .0863 
 
 .0786 
 
 - 5 
 
 .14301.1354 .1277 
 
 .1201 
 
 .1125 
 
 .1049 
 
 .0973 
 
 .0896 
 
 .0820 
 
 .0744 
 
 .0668 
 
 
 
 .13061.1230! .1155 
 
 .1079 
 
 .1004 
 
 .0929 
 
 .0853 
 
 .0778 
 
 .07031 .0627 
 
 .0552 
 
 5 
 
 .1184; 1.1 109 .1035 
 
 .0960 
 
 .0885 
 
 .0811 
 
 .0736 
 
 .0662 
 
 .0587 
 
 .0513 
 
 .0438 
 
 10 
 
 .10651.0991 .0917 
 
 .0843 
 
 .0770 
 
 .0696 
 
 .0622 
 
 .0548 
 
 .0474 
 
 .0401 
 
 .0327 
 
 15 
 
 .09481.0875 .0802 
 
 .0729 
 
 .0656 
 
 .0585 
 
 .0510 
 
 .0437 
 
 .0364 
 
 1.0291 
 
 .0218 
 
 20 
 
 .0834 
 
 1.0762 .0689 
 
 .0617 
 
 .0545 
 
 .0473 
 
 .0401 
 
 .0328 
 
 .0256 
 
 1.0184 
 
 .0112 
 
 25 
 
 .0722 
 
 1.0651 
 
 .0579 
 
 .0508 
 
 .0436 
 
 .0365 
 
 .0293 
 
 .0222 
 
 .0150 
 
 1.0079 
 
 .0007 
 
 30 
 
 .0613 
 
 1.0542 .0471 
 
 .0401 
 
 .0330 
 
 .0259 
 
 .0188 
 
 .0118 
 
 .0047 
 
 0.9976 
 
 0.9905 
 
 35 
 
 .0506 
 
 1.0435 .0365 
 
 .0295 
 
 .0225 
 
 .0155 
 
 .0085 
 
 .0015 
 
 0.9945 
 
 .9875 
 
 .9805 
 
 40 
 
 .0400 
 
 1.0331! .0261 
 
 .0192 
 
 .0123 
 
 .0053 
 
 0.9984 
 
 0.9915 
 
 .9845 
 
 .9776 
 
 .9707 
 
 45 
 
 .0297 1.0229J .0160 
 
 1.0091 
 
 .0023 
 
 0.9954 
 
 .9885 
 
 .9817 
 
 .9748 
 
 .9679 
 
 .9611 
 
 50 
 
 .01961.0128 .0060 
 
 0.9992 
 
 0.9924 
 
 .9856 
 
 .9788 
 
 .9720 
 
 .9652 
 
 .9584 
 
 .9516 
 
 55 
 
 .0097 1.00300.9962 
 
 .9895 
 
 .9828 
 
 .9761 
 
 .9693 
 
 .9626 
 
 .9559 
 
 .9491 
 
 .9424 
 
 60 
 
 .00000.99331 .9867 
 
 .9800 
 
 .9733 
 
 .9667 
 
 .9600 
 
 .9533 
 
 .9467 
 
 .9400 
 
 .9333 
 
 65 
 
 0.9905 
 
 .9838 .9772 
 
 .9706 
 
 .9640 
 
 .9574 
 
 .9508 
 
 .9442 
 
 .9376 
 
 .9310 
 
 .9244 
 
 70 
 
 .9811 
 
 .9746 .9680 
 
 .9615 
 
 .9550 
 
 .9484 
 
 .9419 
 
 .9353 
 
 .9288 
 
 .9223 
 
 .9157 
 
 75 
 
 .9719 
 
 .9655 .9590 
 
 .9525 
 
 .9460 
 
 .9395 
 
 .9331 
 
 .9266 
 
 .9201 
 
 .9136 
 
 .9071 
 
 80 
 
 .9629 
 
 .9565 .9501 
 
 .9437 
 
 .9373 
 
 .9308 
 
 .9244 
 
 .9180 
 
 .9116 
 
 .9052 
 
 .8987 
 
 85 
 
 .9541 
 
 .94773 .9414 
 
 .9350 
 
 .9286 
 
 .9223 
 
 .9159 
 
 .9096 
 
 .9032 
 
 .8968 
 
 .8905 
 
 90 
 
 .9454 
 
 .9391 
 
 .9328 
 
 .9265 
 
 .9202 
 
 .9139 
 
 .9076 
 
 .9013 
 
 .8950 
 
 .8887 
 
 .8824 
 
 95 
 
 .9369 
 
 .9306 
 
 .9244 
 
 .9181 
 
 .9119 
 
 .9056 
 
 .8994 
 
 .8931 
 
 .8869 
 
 .8807 
 
 .8744 
 
 100 
 
 .9285 
 
 .9223 
 
 .9161 
 
 .9099 
 
 .9037 
 
 .8976 
 
 .8914 
 
 .8852 
 
 .8790 
 
 .8728 
 
 .8666 
 
 105 
 
 .9203 
 
 .9141 
 
 .9080 
 
 .9019 
 
 .8957 
 
 .8896 
 
 .8835 
 
 .8773 
 
 .8712 
 
 .8651 
 
 .8589 
 
 110 
 
 .9122 
 
 .9061 
 
 .9000 
 
 .8940 
 
 .8879 
 
 .8818 
 
 .8757 
 
 .8696 
 
 .8636 
 
 .8575 
 
 .8514 
 
 115 
 
 .9043 
 
 .8982 
 
 .8922 
 
 .8862 
 
 .8801 
 
 .8741 
 
 .8681 
 
 .8621 
 
 .8560 
 
 .8500 
 
 .8440 
 
 120 
 
 .8965 
 
 .8905 
 
 .8845 
 
 .8785 
 
 .8726 
 
 .8666 .8606 
 
 .8546 
 
 .8486 
 
 .8427 
 
 .8367 
 
 Formula: Equivalent volume = observed volume X . . ' > X ^r 
 
 ~~ 
 
 Maximum Supply of Gas through Pipes in cu. ft. per Hour, 
 Specific Gravity being taken at 0.45, calculated from the 
 Formula Q = 1000 \/d*ti TsL ( Moles worth .) 
 
 LENGTH OF PIPE = 10 YARDS. 
 
 Diameter of 
 
 Pressure by the Water-gage in Inches. 
 
 Inches. 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 1.0 
 
 , : '= 
 
 n/4 
 
 1V 2 
 
 26 
 73 
 149 
 260 
 411 
 843 
 
 37 
 
 103 
 211 
 368 
 581 
 1192 
 
 46 
 126 
 258 
 451 
 711 
 1460 
 
 53 
 
 145 
 298 
 521 
 821 
 1686 
 
 59 
 162 
 333 
 582 
 918 
 1886 
 
 64 
 187 
 365 
 638 
 1006 
 2066 
 
 70 
 192 
 394 
 689 
 1082 
 2231 
 
 74 
 205 
 422 
 737 
 1162 
 2385 
 
 79 
 218 
 447 
 781 
 1232 
 2530 
 
 83 
 230 
 471 
 823 
 1299 
 2667 
 
 (Continued on p. 866) 
 
ILLUMINATING- GAS. 
 
 Maximum Supply of Gas through Pipes in cu. ft. per Hour, 
 Specific Gravity being taken at 0.45, calculated from the 
 Formula Q = 1000 \/&h 4- si. (Molesworth.) (Continued) 
 
 LENGTH OF PIPE = 100 YARDS. 
 
 Diam. 
 of Pipe, 
 Inches. 
 
 Pressure by the Water-gage in Inches. 
 
 e.i 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.75 
 
 1.0 
 
 1.25 
 
 1.5 
 
 2 
 
 2.5 
 
 3 /4 
 
 23 
 
 32 
 
 42 
 
 46 
 
 51 
 
 63 
 
 73 
 
 81 
 
 89 
 
 103 
 
 115 
 
 1 
 
 47 
 
 67 
 
 82 
 
 94 
 
 105 
 
 129 
 
 149 
 
 167 
 
 183 
 
 211 
 
 236 
 
 M/4 
 
 82 
 
 116 
 
 143 
 
 165 
 
 184 
 
 225 
 
 260 
 
 291 
 
 319 
 
 368 
 
 412 
 
 1V> 
 
 130 
 
 184 
 
 225 
 
 260 
 
 290 
 
 356 
 
 411 
 
 459 
 
 503 
 
 581 
 
 649 
 
 2 
 
 267 
 
 377 
 
 462 
 
 533 
 
 596 
 
 730 
 
 843 
 
 943 
 
 1033 
 
 1193 
 
 1333 
 
 IVi 
 
 466 
 
 659 
 
 807 
 
 932 
 
 1042 
 
 1276 
 
 1473 
 
 1647 
 
 1804 
 
 2083 
 
 2329 
 
 3 
 
 735 
 
 1039 
 
 1270 
 
 1470 
 
 1643 
 
 2012 
 
 2323 
 
 2598 
 
 2846 
 
 3286 
 
 3674 
 
 3V 2 
 
 1080 
 
 1528 
 
 1871 
 
 2161 
 
 2416 
 
 2958 ! 3416 
 
 3820 
 
 4184 
 
 4831 
 
 5402 
 
 4 
 
 1508 
 
 2133 
 
 2613 
 
 3017 
 
 3373 
 
 4131 I 4770 
 
 5333 
 
 5842 
 
 6746 
 
 7542 
 
 LENGTH OF PIPE = 1000 YARDS. 
 
 Diam. 
 of Pipe, 
 Inches. 
 
 Pressure by the Water-gage in Inches. 
 
 0.5 
 
 0.75 
 
 1.0 
 
 1.5 
 
 2.0 
 
 . 2.5 
 
 3.0 
 
 > 
 
 f 
 
 5 
 6 
 
 33 
 
 92 
 189 
 329 
 520 
 1067 
 1863 
 2939 
 
 41 
 113 
 231 
 403 
 636 
 1306 
 2282 
 3600 
 
 47 
 130 
 267 
 466 
 735 
 1508 
 2635 
 4157 
 
 58 
 159 
 327 
 571 
 900 
 1847 
 3227 
 5091 
 
 67 
 184 
 377 
 659 
 1039 
 2133 
 3727 
 5879 
 
 75 
 205 
 422 
 737 
 1162 
 2385 
 4167 
 6573 
 
 82 
 226 
 462 
 807 
 1273 
 2613 
 4564 
 7200 
 
 LENGTH OF PIPE = 5000 YARDS. 
 
 Diameter of 
 Pipe in 
 Inches. 
 
 Pressure by the Water-gage in Inches. 
 
 1.0 
 
 1.5 
 
 2.0 
 
 2.5 
 
 3.0 
 
 2 
 
 119 
 
 146 
 
 169 
 
 189 
 
 207 
 
 3 
 
 329 
 
 402 
 
 465 
 
 520 
 
 569 
 
 4 
 
 675 
 
 826 
 
 955 
 
 1067 
 
 1168 
 
 5 
 
 1179 
 
 1443 
 
 1667 
 
 1863 
 
 2041 
 
 6 
 
 1859 
 
 2277 
 
 2629 
 
 2939 
 
 3220 
 
 7 
 
 2733 
 
 3347 
 
 3865 
 
 4321 
 
 4734 
 
 8 
 
 3816 
 
 4674 
 
 5397 
 
 6034 
 
 6610 
 
 9 
 
 5123 
 
 6274 
 
 7245 
 
 8100 
 
 8873 
 
 10 
 
 6667 
 
 8165 
 
 9428 
 
 10541 
 
 11547 
 
 12 
 
 10516 
 
 12880 
 
 14872 
 
 16628 
 
 18215 
 
 Mr. A. C. Humphreys says his experience goes to show that these 
 tables give too small a flow, but it is difficult to accurately check the 
 tables, on account of the extra friction introduced by rough pipes, 
 bends, etc. For bends, one rule is to allow 1/42 of an inch pressure for 
 each right-angle bend. 
 
 Where there is apt to be trouble from frost it is well to use no service 
 of less diameter than 3/ 4 in., no matter how short it may be. In ex- 
 tremely cold climates this is now often increased to 1 in., even for a 
 single lamp. The best practice in tUe U. S. now condemns any service 
 less than 3/ 4 in. 
 
STEAM. 867 
 
 STEAM. 
 
 The Temperature of Steam in contact with water depends upon 
 the pressure under which it is generated. At the ordinary atmospheric 
 pressure (14.7 Ib. pej sq. in.) its temperature is 212 F. As the pressure 
 is increased, as by the steam being generated in a closed vessel, its tem- 
 perature, and that of the water in its presence, increases. 
 
 Saturated Steam is steam of the temperature due to its pressure 
 not superheated. 
 
 Superheated Steam is steam heated to a temperature above that due 
 to its pressure. 
 
 Dry Steam is steam which contains no moisture. It may be either 
 saturated or superheated. 
 
 Wet Steam is steam containing intermingled moisture, mist, or 
 spray. It has the same temperature as dry saturated steam of the same 
 pressure. 
 
 Water introduced into the presence of superheated steam will flash 
 into steam until the temperature of the steam is reduced to that due its 
 pressure. Water in the presence of saturated steam has the same 
 temperature as the steam. Should cold water be introduced, lowering 
 the temperature of the whole mass, some of the steam will be con- 
 densed, reducing the pressure and temperature of the remainder, until 
 equilibrium is established. 
 
 Total Heat of Saturated Steam (above 32 F.). According to Marks 
 and Davis, the formula for total heat of steam, based on researches 
 by Henning, Knoblauch, Linde and Klebe, is H = 1150.3 + 0.3745 (t - 
 212) - 0.000550 (t - 212)2, in which H is the total heat in B.T.U. above 
 water at 32 F. and t is the temperature Fahrenheit. 
 
 Latent Heat of Steam. The latent heat, or heat of vaporization, is 
 obtained by subtracting from the total heat at any given temperature 
 the heat of the liquid, or total heat above 32 in water of the same tem- 
 perature. 
 
 The total heat in steam (above 32) includes three elements: 
 
 1st. The heat required to raise the temperature of the water to the 
 temperature of the steam. 
 
 2d. The heat required to evaporate the water at that temperature, 
 called internal latent heat. 
 
 3d. The latent heat of volume, or the external work done by the steam 
 in making room for itself against the pressure of the superincumbent at- 
 mosphere (or surrounding steam if inclosed in a vessel) . 
 
 The sum of the last two elements is called the latent heat of steam. 
 
 Heat required to Generate 1 Ib. of Steam from water at 32 F. 
 
 Heat-units. 
 
 Sensible heat, to raise the water from 32 to 212 = 180.0 
 
 Latent heat, 1, of the formation of steam at 212 = 897 . 6 
 
 2, of expansion against the atmospheric 
 pressure, 2116.4 Ib. per sq. ft. X 
 26.79 cu. ft. = 55,786 foot-pounds -4- 
 
 778= 72.8 
 
 970.4 
 
 Total heat above 32 F 1150 . 4 
 
 The Heat-Unit, or British Thermal Unit. The old definition of 
 the heat-unit (Rankine), viz., the quantity of heat required to raise the 
 temperature of 1 Ib. of water 1 F., at or near its temperature of maxi- 
 mum density (39.1 F.), is now (1909) no longer used. Peabody defines 
 it as the heat required to raise a pound of water from 62 to 63 F., and 
 Marks and Davis as i/igo of the heat required to raise 1 Ib. of water from 
 32 to 212 F. By Peabody 's definition the heat required to raise 1 Ib. of 
 water from 32 to 212 is 180.3 instead of 180 units, and the heat of va- 
 porization at 212 is 969.7 instead of 970.4 units. 
 
 Specific Heat of Saturated Steam. When a unit weight of saturated 
 steam is increased in temperature and in pressure, the volume decreasing 
 so as to just keep it saturated, the specific heat is negative, and decreases 
 as temperature increases. (See Wood, Thermodynamics, p. 147; Pea- 
 body, Thermodynamics, p. 93.) 
 
868 
 
 'STEAM. 
 
 Absolute Zero. The value of the absolute zero has been variously 
 given as from 459.2 to 460.66 degrees below the Fahrenheit zero. Marks 
 and Davis, comparing the results of Berthelot (1903) , Buckingham, 1907, 
 and Ross-Innes, 1908, give as the most probable value 459.64 F. 
 The value 460 is close enough for all engineering .calculations. 
 
 The Mechanical Equivalent of Heat. The value generally accepted, 
 based on Rowland's experiments, is 778 ft.-lb. Marks and Davis give 
 the value 777.52 standard ft.-lb., based on later experiments, and on the 
 value of (7 = 980.665 cm. per sec. 2 , = 32.174 ft. per sec. 2 , fixed by inter- 
 national agreement (1901). [With this value of g and the mean gram- 
 calorie being taken as equivalent to 4.1834 X 10 7 dyne-centimeters, the 
 equivalent of 1 B.T.U. is 777.54 ft.-lb.] These values of the absolute 
 zero and of the mechanical equivalent of heat have been used by Marks 
 and Davis in the computation of their steam tables. In refined in- 
 vestigations involving the value of the mechanical equivalent of heat 
 the value of g for the latitude in which the experiments are made must 
 be considered. 
 
 Marks and Davis give the value of the mean gram-calorie as 4.1834 
 joules, which is equivalent to 777.54 ft.-lb. = 1 B.T.U. Goodenough, 
 taking 1 mean calorie = 4.184 joules, gives 1 mean B.T.U. = 777.64 
 ft.-lb. 
 
 Pressure of Saturated Steam. Holborn and Henning, Zeit. des 
 Ver. deutscher Ingenieure, Feb. 20, 1909, report results of measurements 
 of the pressures of saturated steam at temperatures ranging from 50 to 
 200 C. (112 to 392 F.). Their values agree closely with those ob- 
 tained in 1905 by Knoblauch, Linde and Klebe. From a table in the 
 article giving pressures for each degree from to 200 C., the following 
 values have been transformed into English measurements (Eng. Digest, 
 April, 1909). 
 
 Deg. F. 
 
 Lb. per sq. 
 in. 
 
 Deg. F. 
 
 Lb. per sq. 
 
 in. 
 
 Deg. F. 
 
 Lb. per sq. 
 in. 
 
 32 
 68 
 100 
 
 0.0885 
 0.3386 
 0.9462 
 
 150 
 200 
 250 
 
 3.715 
 11.527 
 29.819 
 
 300 
 350 
 400 
 
 66.972 
 134.508 
 248.856 
 
 Volume of Saturated Steam. The values of specific volumes of satu- 
 rated steam are computed by Clapeyron's equation (Marks and Davis's 
 Tables), which gives results remarkably close to those found in the ex- 
 periments of Knoblauch, Linde and Klebe. 
 
 Goodenough's Steam Tables. (Properties of Steam and Ammonia, 
 John Wiley & Sons, 1915.) These tables are based on the same original 
 data as those of Marks and Davis, and on some later ones. They adopt 
 the same definition of the thermal unit, the mean B.T.U. or i/iso of 
 the heat required to raise the temperature of 1 Ib. of water from 32 
 to 212 F. The differences between the figures given in the two sets 
 of tables are in general small ; the most important being that the latent 
 heat of steam at 212 F. is given as 971.7 B.T.U. instead of 970.4, the 
 figure given by Marks and Davis. A comparison of some figures from 
 the two tables is given on p. 869, Goodenough's values being given in 
 the upper lines (G), and Marks and Davis's in the lower lines (M), 
 only the digits which differ from those in the upper lines being given. 
 
 Properties of Saturated Steam at High Temperatures. (From G. A. 
 Goodenough's Properties of Steam and Ammonia, 1915.) 
 
 Temp. 
 
 o F 
 
 Pressure 
 Lb. per 
 Sq. in. 
 
 Volume of 
 1 Lb., 
 Cu. ft. 
 
 Weight of 
 1 Cu. ft., 
 Lb. 
 
 Heat of 
 Liquid 
 B.T.U. 
 
 Heat of 
 Vapor, 
 B.T.U. 
 
 Latent 
 Heat, 
 B.T.U. 
 
 600 
 620 
 640 
 660 
 680 
 700 
 706.3 
 
 1540 
 1784 
 2057 
 2361 
 2699 
 3075 
 3200 
 
 0.272 
 0.226 
 0.186 
 0.151 
 0.118 
 0.080 
 0.048 
 
 3.68 
 4.43 
 5.38 
 6.60 
 8.5 
 12.5 
 20.90 
 
 604.5 
 633 
 664 
 700 
 745 
 820 
 921 
 
 1164.2 
 1151 
 1134 
 1112 
 1080 
 1018 
 921 
 
 488.9 
 452 
 409 
 358 
 290 
 171 
 
 
STEAM 
 
 869 
 
 Properties of Saturated Steam. 
 
 Comparison of Goodenough and Marks and Davis (see p. 868.) 
 
 
 Abso- 
 lute 
 Pres- 
 sure. 
 
 Tem- 
 pera- 
 ture 
 
 o p 
 
 Total Heat 
 Above 32. 
 
 Latent 
 Heat. 
 
 Vol- 
 ume, 
 Cu.Ft. 
 in 
 1 Lb. 
 
 Weight 
 of 
 1 Cu.Ft. 
 
 Entropy. 
 
 In 
 
 Water. 
 
 In 
 Steam. 
 
 Water. 
 
 Vapor- 
 ization. 
 
 G. 
 
 0.0887 
 
 32 
 
 
 
 1073.0 
 
 1073.0 
 
 3296 
 
 0.000304 
 
 
 
 2.1826 
 
 M. 
 
 '* 
 
 " 
 
 " 
 
 .4 
 
 .4 
 
 4 
 
 M 
 
 " 
 
 32 
 
 G. 
 
 0.949 
 
 100 
 
 68.00 
 
 1104.6 
 
 1036.6 
 
 350.3 
 
 0.002855 
 
 0.1296 
 
 1.8523 
 
 M. 
 
 11 
 
 " 
 
 7.97 
 
 3.6 
 
 5.6 
 
 .8 
 
 1 
 
 5 
 
 05 
 
 G. 
 
 14.7 
 
 212 
 
 180 
 
 1151.7 
 
 97f.7 
 
 26.81 
 
 0.03730 
 
 0.3120 
 
 1.4469 
 
 M. 
 
 
 " 
 
 " 
 
 0.4 
 
 0.4 
 
 .79 
 
 2 
 
 18 
 
 47 
 
 G. 
 
 50 
 
 281 
 
 249.8 
 
 1175.6 
 
 925.9 
 
 8.53 
 
 0.1173 
 
 0.4108 
 
 1.2501 
 
 M. 
 
 " 
 
 
 50.1 
 
 3.6 
 
 3.5 
 
 
 5 
 
 13 
 
 468 
 
 G. 
 
 100 
 
 327.8 
 
 297.9 
 
 1188.4 
 
 890.5 
 
 4.442 
 
 0.2251 
 
 0.4736 
 
 1.1309 
 
 M. 
 
 " 
 
 
 8.3 
 
 6.3 
 
 88.0 
 
 29 
 
 8 
 
 43 
 
 277 
 
 G. 
 
 150 
 
 358.5 
 
 329.8 
 
 1194.7 
 
 864.9 
 
 3.020 
 
 0.3311 
 
 0.5131 
 
 1.0573 
 
 M. 
 
 " 
 
 " 
 
 30.2 
 
 3.4 
 
 3.2 
 
 12 
 
 20 
 
 42 
 
 50 
 
 G. 
 
 200 
 
 381.9 
 
 354.5 
 
 1198.5 
 
 844.0 
 
 2.292 
 
 0.4364 
 
 0.5426 
 
 1.0030 
 
 M. 
 
 11 
 
 " 
 
 .9 
 
 .1 
 
 3,2 
 
 
 
 70 
 
 37 
 
 19 
 
 G. 
 
 250 
 
 401.1 
 
 374.9 
 
 1200.6 
 
 825.8 
 
 1.846 
 
 0.542 
 
 0.5663 
 
 0.9595 
 
 M. 
 
 " 
 
 " 
 
 5.2 
 
 1.5 
 
 6.3 
 
 50 
 
 1 
 
 76 
 
 600 
 
 G. 
 
 300 
 
 417.5 
 
 392.4 
 
 1201.9 
 
 809.4 
 
 1.545 
 
 0.647 
 
 0.5863 
 
 0.9229 
 
 M. 
 
 " 
 
 M 
 
 .7 
 
 4.1 
 
 11.3 
 
 51 
 
 5 
 
 78 
 
 51 
 
 G. 
 
 400 
 
 444.8 
 
 422.0 
 
 1202.5 
 
 780.6 
 
 1.162 
 
 0.860 
 
 0.6190 
 
 0.8631 
 
 M. 
 
 " 
 
 " 
 
 " 
 
 8. 
 
 6. 
 
 70 
 
 ** 
 
 210 
 
 80 
 
 G. 
 
 500 
 
 467.2 
 
 446.6 
 
 1201.7 
 
 755.0 
 
 0.928 
 
 1.077 
 
 0.6455 
 
 0.8146 
 
 M. 
 
 " 
 
 .3 
 
 8. 
 
 10. 
 
 62. 
 
 30 
 
 80 
 
 80 
 
 220 
 
 G. 
 
 600 
 
 486.5 
 
 468.0 
 
 1199.8 
 
 731.8 
 
 0.770 
 
 1.30 
 
 0.6679 
 
 0.7735 
 
 M. 
 
 " 
 
 .6 
 
 9. 
 
 210. 
 
 41. 
 
 60 
 
 2 
 
 700 
 
 830 
 
 Volume of Superheated Steam. Linde's equation (1905), 
 
 pv = 0.5962 T - p (1 + 0.0014 p) 
 
 in which p is in Ib. per sq. in., v is in cu. ft. and T is the absolute 
 temperature on the Fahrenheit scale, has been used in the computation 
 of Marks and Davis's tables. 
 
 Specific Heat of Superheated Steam. Mean specific heats from the 
 temperature of saturation to various temperatures at several pressures 
 English and metric units. Knoblauch and Jakob (from Peabody's 
 Tables). 
 
 Kg. per 
 sq. cm. 
 Lb. per 
 sq. in. . 
 Temp., 
 sat.C. 
 Temp., 
 sat. F. 
 
 1 
 14.2 
 99 
 210 
 
 2 
 28.4 
 120 
 248 
 
 4 
 56.9 
 143 
 289 
 
 6 
 85.3 
 158 
 316 
 
 8 
 113.3 
 169 
 336 
 
 10 
 142.2 
 179 
 350 
 
 12 
 170.6 
 187 
 368 
 
 14 
 199.1 
 194 
 381 
 
 16 
 227.5 
 200 
 392 
 
 18 
 256.0 
 206 
 403 
 
 20 
 284.4 
 211 
 412 
 
 F. 
 212 
 302 
 392 
 482 
 572 
 662 
 752 
 
 o r~* 
 
 100 
 150 
 200 
 250 
 300 
 350 
 
 0.463 
 .462 
 .462 
 .463 
 .464 
 .468 
 
 
 
 
 
 
 
 
 
 
 
 0.478 
 .475 
 .474 
 .475 
 .477 
 
 0.515 
 .502 
 .495 
 .492 
 .492 
 
 
 
 
 
 
 
 
 
 0.530 
 .514 
 .505 
 .503 
 
 0.560 
 .532 
 .517 
 .512 
 
 0.597 
 .552 
 .530 
 .522 
 
 0.635 
 .570 
 .541 
 .529 
 
 0.677 
 .588 
 .550 
 536 
 
 
 
 
 0.609 
 .561 
 543 
 
 0.635 
 .572 
 550 
 
 0.664 
 .585 
 557 
 
 .473 
 
 .481 
 
 .494 .504 
 
 .512 
 
 .520 
 
 .526 
 
 .531 
 
 .537 
 
 .542 
 
 .547 
 
870 
 
 STEAM. 
 
 Properties of Superheated Steam. See the table on page 875, con- 
 densed from Marks and Davis's tables. 
 
 The Specific Density of Gaseous Steam, that is, steam considerably 
 superheated, is 0.622, that of air being 1. That is to say, the weight of a 
 cubic foot of gaseous steam is about five-eighths of that of a cubic foot of 
 air, of the same pressure and temperature. 
 
 The density or weight of a cubic foot of gaseous steam is expressible by 
 the same formula as that of air, except that the multiplier or coefficient 
 is less in proportion to the less specific density. Thus, 
 
 1.684 p 
 +460' 
 
 n= 
 
 +460 
 
 in which D is the weight of a cubic foot, p the total pressure per square 
 inch and t the temperature Fahrenheit. (Clark's "Steam-engine.) 
 
 H. M. Prevost Murphy (Eng. News, June 18, 1908) shows that the 
 specific density is not a constant, but varies with the temperature, and 
 
 n OQS*/ 
 that the correct value is 0.6113 + ^ / 
 
 ooO t 
 
 The Rationalization of Regnault's Experiments on Steam. 
 
 (J. McFarlane Gray, Proc. Inst. M. E., July, 1889.) The formulae con- 
 structed by Regnault are strictly empirical, and were based entirely on 
 his experiments. They are therefore not valid beyond the range of tem- 
 peratures and pressures observed. 
 
 Mr. Gray has made a most elaborate calculation, based not on experi- 
 ments but on fundamental principles of thermodynamics, from which he 
 deduces formulae for the pressure and total heat of steam, and presents 
 tables calculated therefrom which show substantial agreement with 
 Regnault's figures. He gives the following examples of steam-pressures 
 calculated for temperatures beyond the range of Regnault's experiments. 
 
 Temperature. 
 
 Pounds per 
 Sq. In. 
 
 Temperature. 
 
 Pounds per 
 Sq. In. 
 
 C. 
 
 Fahr. 
 
 C. 
 
 Fahr. 
 
 230 
 240 
 250 
 260 
 280 
 300 
 320 
 
 446 
 464 
 482 
 500 
 536 
 572 
 608 
 
 406.9 
 488.9 
 579.9 
 691.6 
 940.0 
 1261.8 
 1661.9 
 
 340 
 360 
 380 
 400 
 415 
 427 
 
 644 
 680 
 716 
 752 
 779 
 800.6 
 
 2156.2 
 2742.5 
 3448.1 
 4300.2 
 5017.1 
 5659.9 
 
 These pressures are higher than those obtained by Regnault's 
 formula, which gives for 415 C. only 4067.1 Ibs. per square inch. 
 
 Available Energy in Expanding Steam. Rankine Cycle. (J. B. 
 Stanwood, Power, June 9, 1908.) A simple formula for finding, with the 
 aid of the steam and entropy tables, the available energy per pound ol 
 steam in B.T.U. when it is expanded adiabatically from a higher to a 
 lower pressure is: 
 
 U = H - Hi + T (Ni - N). 
 
 U available B.T.U. in 1 Ib. of expanding steam; H and Hi total heat 
 in 1 Ib. steam at the tw9 pressures; T = absolute temperature at the 
 lower pressure; N Ni, difference of entropy of 1 Ib. of steam at the two 
 pressures. 
 
 EXAMPLE. Required the available B.T.U. in 1 Ib. steam expanded 
 from 100 Ibs. to 14.7 Ibs. absolute. H = 1186.3; Hi = 1150.4; T = 672; 
 N = 1.602; Ni = 1.756. 35.9 + 103.5 = 138.4. 
 
 Efficiency of the Cycle. Let the steam be made from feed-water at 
 212. Heat required = 1186.3 180 1006.3; efficiency = 138.4 * 
 1006.3 = 0.1375. 
 
 Rankine Cycle. This efficiency is that of the Rankine cycle, which 
 assumes that the steam is expanded adiabatically to the exhaust pres- 
 sure and temperature, and that the feed-water from which the steam is 
 made is introduced into the system at the temperature of the exhaust. 
 Carnot Cycle. The Carnot ideal cycle, which assumes that all the 
 heat entering the system enters at the highest temperature, and in which 
 the efficiency is (Ti - T 2 ) + Ti, gives (327.8 - 212) + (327.8 + 460) = 
 0.1470 and the available energy in B.T.U. = 0.1470 X 1006.3 = 147.9 B.T.U. 
 
$71 
 Properties of Saturated Steam. 
 
 (Condensed from Marks and Davis's Steam Tables and Diagrams, 1909, 
 by permission of the publishers, Longmans, Green & Co.) 
 
 2 
 
 d" 
 
 
 Total Heat 
 
 ^ni 
 
 Ug 
 
 
 O 
 
 4 
 
 
 iP 
 
 . . 
 
 above 32 F . 
 
 *r"i 
 
 
 
 53 
 
 I 
 
 I 
 
 M J 
 
 |f 
 
 3-f 
 
 1 $ 
 
 1 3 
 
 |2 
 
 33 
 
 ~| 
 
 ^ 
 
 s . 
 
 
 0) ^ 
 
 S 
 
 L> '^ 
 
 -2 "3 
 
 i ^ 
 
 r fl 
 
 Is 
 
 >^ 
 
 >>o 
 
 2 
 
 1^ 
 
 B 
 
 o> -i> 
 
 5 $ 
 
 |*5 
 
 
 Q)>- M 
 
 j.s! 
 
 f 
 
 ft * 
 
 KS 
 
 82 
 
 > 
 
 4^ 
 
 H 
 
 +-> QJ 
 
 .5 W 
 
 S w 
 
 J*P 
 
 >__ 
 
 6si 
 
 W 
 
 K 
 
 29.74 
 
 0.0886 
 
 32 
 
 0.00 
 
 1073.4 
 
 1073.4 
 
 3294 
 
 0.000304 
 
 0.0000 
 
 2.1832 
 
 29.67 
 
 0.1217 
 
 40 
 
 8,05 
 
 1076.9 
 
 1068.9 
 
 2438 
 
 0.000410 
 
 0.0162 
 
 2.1394 
 
 29.56 
 
 0.1780 
 
 50 
 
 18.08 
 
 1081.4 
 
 1063.3 
 
 1702 
 
 0.000587 
 
 0.0361 
 
 2.0865 
 
 29.40 
 
 0.2562 
 
 60 
 
 28.08 
 
 1085.9 
 
 1057.8 
 
 1208 
 
 0.000828 
 
 0.0555 
 
 2.0358 
 
 29.13 
 
 0.3626 
 
 70 
 
 38.06 
 
 1090.3 
 
 1052.3 
 
 871 
 
 0.001148 
 
 0.0745 
 
 1.9868 
 
 28.39 
 
 0.505 
 
 80 
 
 48.03 
 
 1094.8 
 
 1046.7 
 
 636.8 
 
 0.001570 
 
 0.0932 
 
 1 .9398 
 
 28.50 
 
 0.696 
 
 90 
 
 58.00 
 
 1099.2 
 
 1041.2 
 
 469.3 
 
 0.002131 
 
 0.1114 
 
 1 .8944 
 
 28.00 
 
 0.946 
 
 100 
 
 67.97 
 
 1103.6 
 
 1035.6 
 
 350.8 
 
 0.002851 
 
 0.1295 
 
 1.8505 
 
 27.88 
 
 1 
 
 101.83 
 
 69.8 
 
 1104.4 
 
 1034.6 
 
 333.0 
 
 0.00300 
 
 0.1327 
 
 1.8427 
 
 25.85 
 
 2 
 
 126.15 
 
 94.0 
 
 1115.0 
 
 1021.0 
 
 173.5 
 
 0.00576 
 
 0.1749 
 
 1.7431 
 
 23.81 
 
 3 
 
 141.52 
 
 109.4 
 
 1121.6 
 
 1012.3 
 
 118.5 
 
 0.00845 
 
 0.2008 
 
 1.6840 
 
 21.78 
 
 4 
 
 153.01 
 
 120.9 
 
 1126.5 
 
 1005.7 
 
 90.5 
 
 0.01107 
 
 0.2198 
 
 .6416 
 
 19.74 
 
 3 
 
 162.28 
 
 130.1 
 
 1130.5 
 
 1000.3 
 
 73.33 
 
 0.01364 
 
 0.2348 
 
 1.6084 
 
 17.70 
 
 6 
 
 170.06 
 
 137.9 
 
 1133.7 
 
 995.8 
 
 61.89 
 
 0.01616 
 
 0.2471 
 
 .5814 
 
 15.67 
 
 7 
 
 176.85 
 
 44.7 
 
 1136.5 
 
 991.8 
 
 53.56 
 
 0.01867 
 
 0.2579 
 
 .5582 
 
 13.63 
 
 8 
 
 182.86 
 
 50.8 
 
 1139.0 
 
 988.2 
 
 47.27 
 
 0.02115 
 
 0.2673 
 
 .5380 
 
 11.60 
 
 9 
 
 188.27 
 
 56.2 
 
 1141.1 
 
 985.0 
 
 42.36 
 
 0.02361 
 
 0.2756 
 
 .5202 
 
 9.56 
 
 10 
 
 193.22 
 
 61.1 
 
 1143.1 
 
 982.0 
 
 38.38 
 
 0.02606 
 
 0.2832 
 
 .5042 
 
 7.52 
 
 11 
 
 197.75 
 
 65. Z 
 
 1144.9 
 
 979.2 
 
 35.10 
 
 0.02849 
 
 0.2902 
 
 .4895 
 
 5.49 
 
 12 
 
 201 .96 
 
 69.9 
 
 1146.5 
 
 976.6 
 
 32.36 
 
 0.03090 
 
 0.2967 
 
 .4760 
 
 3.45 
 
 13 
 
 205.87 
 
 73.8 
 
 1148.0 
 
 974.2 
 
 30.03 
 
 0.03330 
 
 0.3025 
 
 .4639 
 
 1.42 
 
 14 
 
 209.55 
 
 77.5 
 
 1149.4 
 
 971.9 
 
 28.02 
 
 0.03569 
 
 0.3081 
 
 .4523 
 
 Ibs. 
 
 
 
 
 
 
 
 
 
 
 gage. 
 
 14.70 
 
 212 
 
 80.0 
 
 1150.4 
 
 970.4 
 
 26.79 
 
 0.03732 
 
 0.3118 
 
 .4447 
 
 0.3 
 
 15 
 
 213.0 
 
 81.0 
 
 1150.7 
 
 969.7 
 
 26.27 
 
 0.03806 
 
 0.3133 
 
 .4416 
 
 1.3 
 
 16 
 
 216.3 
 
 84.4 
 
 1152.0 
 
 967.6 
 
 24.79 
 
 0.04042 
 
 0.3183 
 
 .4311 
 
 2.3 
 
 17 
 
 219.4 
 
 87.5 
 
 1153.1 
 
 965.6 
 
 23.38 
 
 0.04277 
 
 0.3229 
 
 .4215 
 
 3.3 
 
 18 
 
 222.4 
 
 90.5 
 
 1154.2 
 
 963.7 
 
 22.16 
 
 0.04512 
 
 0.3273 
 
 .4127 
 
 4.3 
 
 19 
 
 225.2 
 
 93.4 
 
 1155.2 
 
 961.8 
 
 21.07 
 
 0.04746 
 
 0.3315 
 
 .4045 
 
 5.3 
 
 20 
 
 228.0 
 
 96.1 
 
 1156.2 
 
 960.0 
 
 20.08 
 
 0.04980 
 
 0.3355 
 
 .3965 
 
 6.3 
 
 21 
 
 230.6 
 
 98.8 
 
 1157.1 
 
 958.3 
 
 19.18 
 
 0.05213 
 
 0.3393 
 
 .3887 
 
 7.3 
 
 22 
 
 233.1 
 
 201.3 
 
 1158.0 
 
 956.7 
 
 18.37 
 
 0.05445 
 
 0.3430 
 
 .3811 
 
 8.3 
 
 23 
 
 235.5 
 
 203.8 
 
 1158.8 
 
 955.1 
 
 17.62 
 
 0.05676 
 
 0.3465 
 
 .3739 
 
 9.3 
 
 24 
 
 237.8 
 
 206.1 
 
 1159.6 
 
 953.5 
 
 16.93 
 
 0.05907 
 
 0.3499 
 
 .3670 
 
 10.3 
 
 25 
 
 240.1 
 
 208.4 
 
 1160.4 
 
 952.0 
 
 16.30 
 
 0.0614 
 
 0.3532 
 
 .3604 
 
 11.3 
 
 26 
 
 242.2 
 
 210.6 
 
 1161.2 
 
 950 r 6 
 
 15.72 
 
 0.0636 
 
 0.3564 
 
 .3542 
 
 12.3 
 
 27 
 
 244.4 
 
 212.7 
 
 1161.9 
 
 949.2 
 
 15.18 
 
 0.0659 
 
 0.3594 
 
 .3483 
 
 13.3 
 
 28 
 
 246.4 
 
 214.8 
 
 1162.6 
 
 947.8 
 
 14.67 
 
 0.0682 
 
 0.3623 
 
 .3425 
 
 14.3 
 
 29 
 
 248.4 
 
 216.8 
 
 1163.2 
 
 946.4 
 
 14.19 
 
 0.0705 
 
 0.3652 
 
 .3367 
 
 15.3 
 
 30 
 
 250.3 
 
 18.8 
 
 1163.9 
 
 945.1 
 
 13.74 
 
 0.0728 
 
 0.3680 
 
 .3311 
 
 16.3 
 
 31 
 
 252.2 
 
 20.7 
 
 1164.5 
 
 943.8 
 
 13.32 
 
 0.0751 
 
 0.3707 
 
 .3257 
 
 17.3 
 
 32 
 
 254.1 
 
 22.6 
 
 1165.1 
 
 942.5 
 
 12.93 
 
 0.0773 
 
 0.3733 
 
 .3205 
 
 18.3 
 
 33 
 
 255.8 
 
 24.4 
 
 1165.7 
 
 941.3 
 
 12.57 
 
 0.0795 
 
 0.3759 
 
 .3155 
 
 19.3 
 
 34 
 
 257.6 
 
 26.2 
 
 1166.3 
 
 940.1 
 
 12.22 
 
 0.0818 
 
 0.3784 
 
 .3107 
 
 20.3 
 
 35 
 
 259,3 
 
 27.9 
 
 1166.8 
 
 938.9 
 
 11.89 
 
 0.0841 
 
 0.3808 
 
 .3060 
 
 21.3 
 
 36 
 
 261,0 
 
 29.6 
 
 1167.3 
 
 937.7 
 
 11.58 
 
 0.0863 
 
 0.3832 
 
 .3014 
 
 22.3 
 
 37 
 
 262.6 
 
 31.3 
 
 1167.8 
 
 936.6 
 
 11.29 
 
 0.0886 
 
 0.3855 
 
 .2969 
 
 23.3 
 
 38 
 
 264.2 
 
 32.9 
 
 1168.4 
 
 935.5 
 
 11.01 
 
 0.0908 
 
 0.3877 
 
 .2925 
 
 24.3 
 
 39 
 
 265.8 
 
 34.5 
 
 1168.9 
 
 934.4 
 
 10.74 
 
 0.0931 
 
 0.3899 
 
 .2882 
 
 25.3 
 
 40 
 
 267.3 
 
 36.1 
 
 1169.4 
 
 933.3 
 
 10.49 
 
 0.0953 
 
 0.3920 
 
 .2841 
 
 
 41 
 
 268.7 
 
 37.6 
 
 1169.8 
 
 932.2 
 
 10.25 
 
 0.0976 
 
 0.3941 
 
 .2800 
 
 27.3 
 
 42 
 
 270.2 
 
 39.1 
 
 1170.3 
 
 931.2 
 
 10.02 
 
 0.0998 
 
 0.3962 
 
 1.2759 
 
 28.3 
 
 43 
 
 271.7 
 
 40.5 
 
 1170.7 
 
 930.2 
 
 9.80 
 
 0.1020 
 
 0.3982 
 
 1.2720 
 
 29.3 
 
 44 
 
 273.1 
 
 42.0 
 
 1171.2 
 
 929.2 
 
 9.59 
 
 0.1043 
 
 0.4002 
 
 1.2681 
 
 30.3 
 
 45 
 
 274.5 
 
 43.4 
 
 1171.6 
 
 928.2 
 
 9.39 
 
 0.1065 
 
 0.4021 
 
 1.2644 
 
872 
 
 Properties of Saturated Steam. (Continued.) 
 
 a* 
 
 gd 
 
 
 Total Heat 
 
 ^J5> 
 
 
 
 0) 
 
 4, * 
 
 1? 
 
 B 
 
 II 
 
 above 32 F. 
 
 || 
 
 "8 
 
 53 
 
 
 
 
 -^ 
 
 5 
 <$ .^ 
 
 *& 
 |J 
 
 !] 
 
 II 
 
 0) .Jj 
 
 a> 2 
 
 1 ^ 
 
 aT S 
 
 g c3 
 3 
 
 .?> 
 
 || 
 
 II 
 
 3^ 
 
 M 
 
 OJ^H 
 
 "5 a 
 
 "5 Si 
 
 "^3 ii D 
 
 "o-Scc 
 
 'Sjit 
 
 c 
 
 
 O 
 
 <J 
 
 H 
 
 ^ 
 
 W 
 
 H 
 
 > 
 
 ^ 
 
 H 
 
 W 
 
 31.3 
 
 46 
 
 275.8 1244.8 
 
 1172.0 
 
 927.2 
 
 9.20 
 
 0.1087 
 
 0.4040 
 
 1.2607 
 
 32.3 
 
 47 
 
 277.2 
 
 246.1 
 
 1172.4 
 
 926.3 
 
 9.02 
 
 0.1109 
 
 0.4059 
 
 .2571 
 
 33.3 
 
 48 
 
 278.5 
 
 247.5 
 
 1172.8 
 
 925.3 
 
 8.84 
 
 0.1131 
 
 0.4077 
 
 .2536 
 
 34.3 
 
 49 
 
 279.8 
 
 248.8 
 
 1173.2 
 
 924.4 
 
 8.67 
 
 0.1153 
 
 0.4095 
 
 .2502 
 
 35.3 
 
 50 
 
 281.0 
 
 250.1 
 
 1173.6 
 
 923.5 
 
 8.51 
 
 0.1175 
 
 0.4113 
 
 .2468 
 
 36.3 
 
 51 
 
 282.3 
 
 251.4 
 
 1174.0 
 
 922.6 
 
 8.35 
 
 0.1197 
 
 0.4130 
 
 .2432 
 
 37.3 
 
 52 
 
 283.5 
 
 252.6 
 
 1174.3 
 
 921.7 
 
 8.20 
 
 0.1219 
 
 0.4147 
 
 .2405 
 
 38.3 
 
 53 
 
 284.7 
 
 253.9 
 
 1174.7 
 
 920.8 
 
 8.05 
 
 0.1241 
 
 0.4164 
 
 .2370 
 
 39.3 
 
 54 
 
 285.9 
 
 255.1 
 
 1175.0 
 
 919.9 
 
 7.91 
 
 0.1263 
 
 0.4180 
 
 .2339 
 
 40.3 
 
 55 
 
 287.1 
 
 256.3 
 
 1175.4 
 
 919.0 
 
 7.78 
 
 0.1285 
 
 0.4196 
 
 .2309 
 
 41.3 
 
 56 
 
 288.2 
 
 257.5 
 
 1175.7 
 
 918.2 
 
 7.65 
 
 0.1307 
 
 0.4212 
 
 .2278 
 
 42.3 
 
 57 
 
 289.4 
 
 258.7 
 
 1176.0 
 
 917.4 
 
 7.52 
 
 0.1329 
 
 0.4227 
 
 .2248 
 
 43.3 
 
 58 
 
 290.5 
 
 259.8 
 
 1176.4 
 
 916.5 
 
 7.40 
 
 0.1350 
 
 0.4242 
 
 .2218 
 
 44.3 
 
 59 
 
 291.6 
 
 261.0 
 
 1176.7 
 
 915.7 
 
 7.28 
 
 0.1372 
 
 0.4257 
 
 .2189 
 
 45.3 
 
 60 
 
 292.7 
 
 262.1 
 
 1177.0 
 
 914.9 
 
 7.17 
 
 0.1394 
 
 0.4272 
 
 .2160 
 
 46.3 
 
 61 
 
 293.8 
 
 263.2 
 
 1177.3 
 
 914.1 
 
 7.06 
 
 0.1416 
 
 0.4287 
 
 .2132 
 
 47.3 
 
 62 
 
 294.9 
 
 264.3 
 
 1177.6 
 
 913.3 
 
 6.95 
 
 0.1438 
 
 0.4302 
 
 .2104 
 
 48.3 
 
 63 
 
 295.9 
 
 265.4 
 
 1177.9 
 
 912.5 
 
 6.85 
 
 0.1460 
 
 0.4316 
 
 .2077 
 
 49.3 
 
 64 
 
 297.0 
 
 266.4 
 
 1178.2 
 
 911.8 
 
 6.75 
 
 0.1482 
 
 0.4330 
 
 .2050 
 
 50.3 
 
 65 
 
 293.0 
 
 267.5 
 
 1178.5 
 
 911.0 
 
 6.65 
 
 0.1503 
 
 0.4344 
 
 .2024 
 
 51.3 
 
 66 
 
 29?. 
 
 268.5 
 
 1178.8 
 
 910.2 
 
 6 56 
 
 0.1525 
 
 0.4358 
 
 1998 
 
 52.3 
 
 67 
 
 300.0 
 
 269.6 
 
 1179.0 
 
 909.5 
 
 6.47 
 
 0.1547 
 
 0.4371 
 
 .1972 
 
 53.3 
 
 68 
 
 301.0 
 
 270.6 
 
 1179.3 
 
 908.7 
 
 6.38 
 
 0.1569 
 
 0.4385 
 
 .1946 
 
 54.3 
 
 69 ' 
 
 302.0 
 
 271.6 
 
 1179.6 
 
 908.0 
 
 6.29 
 
 0.1590 
 
 0.4398 
 
 .1921 
 
 55.3 
 
 70 
 
 302.9 
 
 272.6 
 
 1179.8 
 
 907.2 
 
 6.20 
 
 0.1612 
 
 0.4411 
 
 .1896 
 
 56.3 
 
 71 
 
 303.9 
 
 273.6 
 
 1180.1 
 
 906.5 
 
 6.12 
 
 0.1634 
 
 0.4424 
 
 .1872 
 
 57.3 
 
 72 
 
 304.8 
 
 274.5 
 
 1180.4 
 
 905.8 
 
 6.04 
 
 0.1656 
 
 0.4437 
 
 .1848 
 
 58.3 
 
 73 
 
 305.8 
 
 275.5 
 
 1180.6 
 
 905.1 
 
 5.96 
 
 0.1678 
 
 0.4449 
 
 .1825 
 
 59.3 
 
 74 
 
 306.7 
 
 276.5 
 
 1180.9 
 
 904.4 
 
 5.89 
 
 0.1699 
 
 0.4462 
 
 .1801 
 
 60.3 
 
 75 
 
 307.6 
 
 277.4 
 
 1181.1 
 
 903.7 
 
 5.81 
 
 0.1721 
 
 0.4474 
 
 .1778 
 
 61.3 
 
 76 
 
 308.5 
 
 278.3 
 
 1181.4 
 
 903.0 
 
 5.74 
 
 0.1743 
 
 0.4487 
 
 .1755 
 
 62.3 
 
 77 
 
 309.4 
 
 279.3 
 
 1181.6 
 
 902.3 
 
 5.67 
 
 0.1764 
 
 0.4499 
 
 .1730 
 
 63.3 
 
 78 
 
 310.3 
 
 280.2 
 
 1181.8 
 
 901.7 
 
 5.60 
 
 0.1785 
 
 0.4511 
 
 .1712 
 
 64.3 
 
 79 
 
 311.2 
 
 281.1 
 
 1182.1 
 
 901.0 
 
 5.54 
 
 0.1808 
 
 0.4523 
 
 .1687 
 
 65.3 
 
 80 
 
 312.0 
 
 282.0 
 
 1182.3 
 
 900.3 
 
 5.47 
 
 0.1829 
 
 0.4535 
 
 .1665 
 
 66.3 
 
 81 
 
 312.9 
 
 282.9 
 
 1182.5 
 
 899.7 
 
 5.41 
 
 0.1851 
 
 0.4546 
 
 .1644 
 
 67.3 
 
 82 
 
 313.8 
 
 283.8 
 
 1182.8 
 
 899.0 
 
 5.34 
 
 0.1873 
 
 0.4557 
 
 .1623 
 
 68.3 
 
 83 
 
 314.6 
 
 284.6 
 
 1183.0 
 
 898.4 
 
 5.28 
 
 0.1894 
 
 0.4568 
 
 1602 
 
 69.3 
 
 84 
 
 315.4 
 
 285.5 
 
 1183.2 
 
 897.7 
 
 5.22 
 
 0.1913 
 
 0.4579 
 
 .'1581 
 
 70.3 
 
 85 
 
 316.3 
 
 286.3 
 
 1183.4 
 
 897.1 
 
 5.16 
 
 0.1937 
 
 0.4590 
 
 .1561 
 
 71.3 
 
 86 
 
 317.1 
 
 287.2 
 
 1183.6 
 
 896.4 
 
 5.10 
 
 0.1959 
 
 0.4601 
 
 .1540 
 
 72.3 
 
 87 
 
 317.9 
 
 288.0 
 
 1183.8 
 
 895.8 
 
 5.05 
 
 0.1980 
 
 0.4612 
 
 .1520 
 
 73.3 
 
 88 
 
 318.7 
 
 288.9 
 
 1184.0 
 
 895.2 
 
 5.00 
 
 0.2001 
 
 0.4623 
 
 .1500 
 
 74.3 
 
 89 
 
 319.5 
 
 289.7 
 
 1184.2 
 
 894.6 
 
 4.94 
 
 0.2023 
 
 0.4633 
 
 .1481 
 
 75.3 
 
 90 
 
 320.3 
 
 290.5 
 
 1184.4 
 
 893.9 
 
 4.89 
 
 0.2044 
 
 4644 
 
 .1461 
 
 76.3 
 
 91 
 
 321.1 
 
 291.3 
 
 1184.6 
 
 893.3 
 
 4.84 
 
 0.2065 
 
 0.4554 
 
 .1442 
 
 77.3 
 
 92 
 
 321.8 
 
 292.1 
 
 1184.8 
 
 892.7 
 
 4.79 
 
 0.2087 
 
 0.4664 
 
 .1423 
 
 78.3 
 
 93 
 
 322.6 
 
 292.9 
 
 1185.0 
 
 892.1 
 
 4.74 
 
 0.2109 
 
 0.4674 
 
 1404 
 
 79.3 
 
 94 
 
 323.4 
 
 293.7 
 
 1185.2 
 
 891.5 
 
 4.69 
 
 0.2130 
 
 0.4684 
 
 .1385 
 
 80.3 
 
 95 
 
 324.1 
 
 294.5 
 
 1185.4 
 
 890.9 
 
 4.65 
 
 0.2151 
 
 0.4694 
 
 1367 
 
 81.3 
 
 96 
 
 324.9 
 
 295.3 
 
 1185.6 
 
 890.3 
 
 4.60 
 
 0.2172 
 
 0.4704 
 
 .1348 
 
 82.3 
 
 97 
 
 325.6 
 
 296.1 
 
 1185.8 
 
 889.7 
 
 4.56 
 
 0.2193 
 
 0.4714 
 
 .1330 
 
 83.3 
 
 98 
 
 326.4 
 
 296.8 
 
 1186.0 
 
 889.2 
 
 4.51 
 
 0.2215 
 
 0.4724 
 
 .1312 
 
 84.3 
 
 99 
 
 327.1 
 
 297.6 
 
 1186.2 
 
 888.6 
 
 4.47 
 
 0.2237 
 
 0.4733 
 
 .1295 
 
 85.3 
 
 100' 
 
 327.8 
 
 298.3 
 
 1186.3 
 
 888.0 
 
 4.429 
 
 0.2258 
 
 0.4743 
 
 .1277 
 
 87.3 
 
 102 
 
 329.3 
 
 299.8 
 
 1186.7 
 
 886.9 
 
 4.347 
 
 0.2300 
 
 0.4762 
 
 .1242 
 
 89.3 
 
 104 
 
 330.7 
 
 301.3 
 
 1187.0 
 
 885.8 
 
 4.268 
 
 0.2343 
 
 0.4780 
 
 .1208 
 
Properties of Saturated Steam. (Continued.) 
 
 873 
 
 a? . 
 
 8"d 
 
 
 Total Heat 
 
 1^4. 
 
 
 . 
 
 o 
 
 i, 
 
 d 
 
 
 
 above32F. 
 
 ^.8 
 
 "8 
 
 ^3 
 
 
 
 I 
 
 k 
 
 $ o 1 
 1^ 
 
 il 
 
 1 | 
 
 1 ^ 
 
 ^ 
 
 o? B 
 
 *o g 
 
 *^rr> 
 
 s 
 
 ' 
 
 II 
 
 8>? 
 
 
 ftl 
 
 2*5 
 
 o^5 
 
 1^'S 
 
 O 
 
 J3 
 
 |j 
 
 11 
 
 3.Q 
 
 JBi-i 
 
 gjpn 
 
 "*"* > 
 
 S c) 
 
 -^ II D 
 
 |.SoQ 
 
 K^f^ 
 
 ~c^ 
 
 a o 
 
 6^ 
 
 < 
 
 H 
 
 fl td 
 
 M 
 
 5 W 
 
 w 
 
 
 * 
 
 W 
 
 W 
 
 91.3 
 
 106 
 
 332.0 
 
 302.7 
 
 1187.4 
 
 884.7 
 
 4.192 
 
 0.2336 
 
 0.4798 
 
 .117 
 
 93.3 
 
 108 
 
 333.4 
 
 304.1 
 
 1187.7 
 
 883.6 
 
 4.118 
 
 0.2429 
 
 0.4816 
 
 .114 
 
 95.3 
 
 110 
 
 334.8 
 
 305.5 
 
 1188.0 
 
 882.5 
 
 4.047 
 
 0.2472 
 
 0.4834 
 
 .110 
 
 97.3 
 
 112 
 
 336. 1 
 
 306.9 
 
 1188.4 
 
 881.4 
 
 3.978 
 
 0.2514 
 
 0.4852 
 
 .107 
 
 99.3 
 
 114 
 
 337.4 
 
 308.3 
 
 1188.7 
 
 880.4 
 
 3.912 
 
 0.2556 
 
 0.4869 
 
 .104 
 
 101.3 
 
 116 
 
 338.7 
 
 309.6 
 
 1189.0 
 
 879.3 
 
 3.848 
 
 0.2599 
 
 0.4886 
 
 .101 
 
 103.3 
 
 118 
 
 340.0 
 
 311.0 
 
 1189.3 
 
 878.3 
 
 3.786 
 
 0.2641 
 
 0.4903 
 
 .098 
 
 105.3 
 
 120 
 
 341.3 
 
 312.3 
 
 1189.6 
 
 877.2 
 
 3.726 
 
 0.2683 
 
 0.4919 
 
 .095 
 
 107.3 
 
 122 
 
 342.5 
 
 313.6 
 
 1189.8 
 
 876.2 
 
 3.668 
 
 0.2726 
 
 0.4935 
 
 .092 
 
 109.3 
 
 124 
 
 343.8 
 
 314.9 
 
 1190.1 
 
 875.2 
 
 3.611 
 
 0.2769 
 
 0.4951 
 
 .089 
 
 111.3 
 
 126 
 
 345.0 
 
 316.2 
 
 1190.4 
 
 874.2 
 
 3.556 
 
 0.2812 
 
 0.4967 
 
 .086 
 
 113.3 
 
 128 
 
 346.2 
 
 317.4 
 
 1190. 7 
 
 873.3 
 
 3.504 
 
 0.2854 
 
 0.4982 
 
 .083 
 
 115.3 
 
 130 
 
 347.4 
 
 318.6 
 
 1191.0 
 
 872.3 
 
 3.452 
 
 0.2897 
 
 0.4998 
 
 .080 
 
 117.3 
 
 132 
 
 348.5 
 
 319.9 
 
 1191.2 
 
 871.3 
 
 3 402 
 
 0.2939 
 
 0.5013 
 
 .078 
 
 119.3 
 
 134 
 
 349.7 
 
 321.1 
 
 1191.5 
 
 870.4 
 
 3.354 
 
 0.2981 
 
 0.5028 
 
 .075 
 
 121.3 
 
 136 
 
 350.8 
 
 322.3 
 
 1191.7 
 
 869.4 
 
 3.308 
 
 0.3023 
 
 0.5043 
 
 .072 
 
 123.3 
 
 138 
 
 352.0 
 
 323.4 
 
 1192.0 
 
 868.5 
 
 3.263 
 
 0.3065 
 
 0.5057 
 
 .070 
 
 125.3 
 
 140 
 
 353. 1 
 
 324.6 
 
 1192.2 
 
 867.6 
 
 3.219 
 
 0.3107 
 
 0.5072 
 
 .067 
 
 127.3 
 
 142 
 
 354.2 
 
 325.8 
 
 1192.5 
 
 866.7 
 
 3.175 
 
 0.3150 
 
 0.5086 
 
 .064 
 
 129.3 
 
 144 
 
 355.3 
 
 326.9 
 
 1192.7 
 
 865.8 
 
 3.133 
 
 0.3192 
 
 0.5100 
 
 .062 
 
 131.3 
 
 146 
 
 356.3 
 
 328.0 
 
 1192.9 
 
 864.9 
 
 3.092 
 
 0.3234 
 
 0.5114 
 
 .059 
 
 133.3 
 
 148 
 
 357.4 
 
 329.1 
 
 1193.2 
 
 864.0 
 
 3.052 
 
 0.3276 
 
 0.5128 
 
 .057 
 
 135.3 
 
 150 
 
 358.5 
 
 330.2 
 
 1193.4 
 
 863.2 
 
 3.012 
 
 0.3320 
 
 0.5142 
 
 .055 
 
 137.3 
 
 152 
 
 359.5 
 
 331.4 
 
 1193.6 
 
 862.3 
 
 2.974 
 
 0.3362 
 
 0.5155 
 
 .052 
 
 139.3 
 
 154 
 
 360.5 
 
 332.4 
 
 1193.8 
 
 861.4 
 
 2.938 
 
 0.3404 
 
 0.5169 
 
 .050 
 
 141.3 
 
 156 
 
 361.6 
 
 333.5 
 
 1194.1 
 
 860.6 
 
 2.902 
 
 0.3446 
 
 0.5182 
 
 .047 
 
 143.3 
 
 158 
 
 362.6 
 
 334.6 
 
 1194.3 
 
 859.7 
 
 2.868 
 
 0.3488 
 
 0.5195 
 
 .045 
 
 145.3 
 
 160 
 
 363.6 
 
 335.6 
 
 1194.5 
 
 858.8 
 
 2.834 
 
 0.3529 
 
 0.5208 
 
 .043 
 
 147.3 
 
 162 
 
 364.6 
 
 336.7 
 
 1194.7 
 
 858.0 
 
 2.801 
 
 3570 
 
 0.5220 
 
 .040 
 
 149.3 
 
 164 
 
 365.6 
 
 337.7 
 
 1194.9 
 
 857.2 
 
 2.769 
 
 0.3612 
 
 0.5233 
 
 .038 
 
 151.3 
 
 166 
 
 366.5 
 
 338.7 
 
 1195.1 
 
 856.4 
 
 2.737 
 
 0.3654 
 
 0.5245 
 
 .036 
 
 153.3 
 
 168 
 
 367.5 
 
 339.7 
 
 1195.3 
 
 855.5 
 
 2.706 
 
 0.3696 
 
 0.5257 
 
 .034 
 
 155.3 
 
 170 
 
 368.5 
 
 340.7 
 
 1195.4 
 
 854.7 
 
 2.675 
 
 0.3738 
 
 0.5269 
 
 .032 
 
 157.3 
 
 172 
 
 369.4 
 
 341.7 
 
 1195.6 
 
 853.9 
 
 2.645 
 
 0.3780 
 
 0.5281 
 
 .030 
 
 159.3 
 
 174 
 
 370.4 
 
 342.7 
 
 1195.8 
 
 853.1 
 
 2.616 
 
 0.3822 
 
 0.5293 
 
 .027 
 
 161.3 
 
 176 
 
 371.3 
 
 343.7 
 
 1196.0 
 
 852.3 
 
 2.588 
 
 0.3864 
 
 0.5305 
 
 .025 
 
 163.3 
 
 178 
 
 372.2 
 
 344.7 
 
 1196.2 
 
 851.5 
 
 2.560 
 
 0.3906 
 
 0.5317 
 
 .023 
 
 165.3 
 
 180 
 
 373.1 
 
 345.6 
 
 1196.4 
 
 850.8 
 
 2.533 
 
 0.3948 
 
 0.5328 
 
 .021 
 
 167.3 
 
 182 
 
 374.0 
 
 346.6 
 
 1196.6 
 
 850.0 
 
 2.507 
 
 0.3989 
 
 0.5339 
 
 .019 
 
 169.3 
 
 184 
 
 374.9 
 
 347.6 
 
 1196.8 
 
 849.2 
 
 2.481 . 
 
 0.4031 
 
 0.5351 
 
 .017 
 
 171.3 
 
 186 
 
 375.8 
 
 348.5 
 
 1196.9 
 
 848.4 
 
 2.455 
 
 0.4073 
 
 0.5362 
 
 .015 
 
 173.3 
 
 183 
 
 376.7 
 
 349.4 
 
 1197.1 
 
 847.7 
 
 2.430 
 
 0.4115 
 
 0.5373 
 
 .013 
 
 175.3 
 
 190 
 
 377.6 
 
 350.4 
 
 1197.3 
 
 846.9 
 
 2.406 
 
 0.4157 
 
 0.5384 
 
 .Oil 
 
 177.3 
 
 192 
 
 378.5 
 
 351.3 
 
 1197.4 
 
 846.1 
 
 2.381 
 
 0.4199 
 
 0.5395 
 
 .009 
 
 179.3 
 
 194 
 
 379.3 
 
 352.2 
 
 1197.6 
 
 845.4 
 
 2.358 
 
 0.4241 
 
 0.5405 
 
 .007 
 
 181.3 
 
 196 
 
 380.2 
 
 353.1 
 
 1197.8 
 
 844.7 
 
 2.335 
 
 0.4283 
 
 0.5416 
 
 .005< 
 
 183.3 
 
 198 
 
 381.0 
 
 354.0 
 
 1197.9 
 
 843.9 
 
 2.312 
 
 0.4325 
 
 0.5426 
 
 .0031 
 
 185.3 
 
 200 
 
 381.9 
 
 354.9 
 
 1198.1 
 
 843.2 
 
 2.290 
 
 0.437 
 
 0.5437 
 
 .001 
 
 190.3 
 
 205 
 
 384.0 
 
 357.1 
 
 1198.5 
 
 841.4 
 
 2.237 
 
 0.447 
 
 0.5463 
 
 0.997 
 
 195.3 
 
 210 
 
 386.0 
 
 359.2 
 
 1198.8 
 
 839.6 
 
 2.187 
 
 0.457 
 
 0.5488 
 
 0.992 
 
 200.3 
 
 215 
 
 388.0 
 
 361.4 
 
 1199.2 
 
 837.9 
 
 2.138 
 
 0.468 
 
 0.5513 
 
 0.988 
 
 205.3 
 
 220 
 
 389.9 
 
 363.4 
 
 1199.6 
 
 836.2 
 
 2.091 
 
 0.478 
 
 0.5538 
 
 0.984 
 
 210.3 
 
 225 
 
 391.9 
 
 365.5 
 
 1199.9 
 
 834.4 
 
 2.046 
 
 0.489 
 
 0.5562 
 
 0.979 
 
 215.3 
 
 230 
 
 393.8 
 
 367.5 
 
 1200.2 
 
 832.8 
 
 2.004 
 
 0.499 
 
 0.5586 
 
 0.975 
 
 220.3 
 
 235 
 
 395.6 
 
 369.4 
 
 1200.6 
 
 831.1 
 
 1.964 
 
 0.509 
 
 0.5610 
 
 0.971 
 
 225.3 
 
 240 
 
 397.4 
 
 371.4 
 
 1200.9 
 
 829.5 
 
 1.924 
 
 0.520 
 
 0.5633 
 
 0.967 
 
 230.3 
 
 245 
 
 399.3 
 
 373.3 
 
 1201.2 
 
 827.9 
 
 1.887 
 
 0.530 
 
 0.5655 
 
 0.963 
 
874 
 
 Properties of Saturated Steam. (Continued.) 
 
 " 
 
 tfd 
 
 
 Total Heat 
 
 ^ ' 
 
 
 
 0) 
 
 D, 
 
 S 
 
 1^ 
 
 oT-tJ 
 
 above 32 F. 
 
 ^ 
 
 fe'o 
 
 PH-! 
 
 *5 
 
 I 
 
 ^ 
 
 gCQ 
 
 
 
 
 S n 
 
 g 
 
 0*^ 
 
 ~ s" 
 
 *o 
 
 S 
 
 *| 
 
 ^1 
 
 ll 
 
 | 1 
 
 -2 ^ 
 
 1 ^ 
 
 rj.fi 
 
 l 
 
 a' 
 
 Ij 
 
 3J 
 
 ~J2 
 
 aJi 
 
 rt eg 
 
 rt J* 
 
 S^'c 
 
 G 
 
 .5P^-> 
 
 " 
 
 
 0^ 
 
 J^ 
 
 H 
 
 5 S 
 
 -5 8 
 
 5 II|D 
 
 g.-co 
 
 | fe 
 
 1 
 
 c o 
 W 
 
 235.3 
 
 250 
 
 401.1 
 
 375.2 
 
 1201.5 
 
 826.3 
 
 1.850 
 
 0.541 
 
 0.5676 
 
 0.9600 
 
 245.3 
 
 260 
 
 404.5 
 
 378.9 
 
 1202.1 
 
 823.1 
 
 1.782 
 
 0.561 
 
 5719 
 
 9525 
 
 255.3 
 
 270 
 
 407.9 
 
 382.5 
 
 1202.6 
 
 820.1 
 
 .718 
 
 0.582 
 
 5760 
 
 0.9454 
 
 265.3 
 
 280 
 
 411.2 
 
 386.0 
 
 1203.1 
 
 817. f 
 
 .658 
 
 0.603 
 
 0.5800 
 
 0.9385 
 
 275.3 
 
 290 
 
 414.4 
 
 389.4 
 
 1203.6 
 
 814.2 
 
 .602 
 
 0.624 
 
 0.5840 
 
 9316 
 
 285.3 
 
 300 
 
 417.5 
 
 392.7 
 
 1204.1 
 
 811.3 
 
 .551 
 
 0.645 
 
 5878 
 
 0.9231 
 
 295.3 
 
 310 
 
 420.5 
 
 395.9 
 
 1204.5 
 
 808.5 
 
 .502 
 
 0.666 
 
 0.5915 
 
 0.9187 
 
 305.3 
 
 320 
 
 423.4 
 
 399.1 
 
 1204.9 
 
 805.8 
 
 .456 
 
 0.687 
 
 0.5951 
 
 0.9125 
 
 315.3 
 
 330 
 
 426.3 
 
 402.2 
 
 1205.3 
 
 803.1 
 
 .413 
 
 0.708 
 
 0.5986 
 
 9065 
 
 325.3 
 
 340 
 
 429.1 
 
 405.3 
 
 1205.7 
 
 800.4 
 
 .372 
 
 0.729 
 
 0.6020 
 
 9006 
 
 335.3 
 
 350 
 
 431.9 
 
 408.2 
 
 1206.1 
 
 797.8 
 
 .334 
 
 0.750 
 
 0.6053 
 
 0.8949 
 
 345.3 
 
 360 
 
 434.6 
 
 411.2 
 
 1206.4 
 
 795.3 
 
 .298 
 
 0.770 
 
 0.6085 
 
 0.8894 
 
 355.3 
 
 370 
 
 437.2 
 
 414.0 
 
 1206.8 
 
 792.8 
 
 .264 
 
 0.791 
 
 0.6116 
 
 0.8840 
 
 365.3 
 
 380 
 
 439.8 
 
 416.8 
 
 1207.1 
 
 790.3 
 
 .231 
 
 0.812 
 
 0.6147 
 
 0.8788 
 
 375.3 
 
 390 
 
 442.3 
 
 419.5 
 
 1207.4 
 
 787.9 
 
 .200 
 
 0.833 
 
 0.6178 
 
 0.8737 
 
 385.3 
 
 400 
 
 444.8 
 
 422 
 
 1208 
 
 786 
 
 .17 
 
 0.86 
 
 0.621 
 
 0.868 
 
 435.3 
 
 450 
 
 456.5 
 
 435 
 
 1209 
 
 774 
 
 .04 
 
 0.96 
 
 0.635 
 
 844 
 
 485.3 
 
 500 
 
 467.3 
 
 448 
 
 1210 
 
 762 
 
 0.93 
 
 1.08 
 
 0.648 
 
 0.822 
 
 535.3 
 
 550 
 
 477.3 
 
 459 
 
 1210 
 
 751 
 
 0.83 
 
 1.20 
 
 0.659 
 
 0.801 
 
 585.3 
 
 600 
 
 486.6 
 
 469 
 
 1210 
 
 741 
 
 0.76 
 
 1.32 
 
 0.670 
 
 0.783 
 
 Properties of Superheated Steam, Marks & Davis and Goodenough 
 Compared. 
 
 v = volume, cu. ft. per lb.; h = total heat above 32 F.; n = entropy. 
 
 The figures in the upper lines are from Marks and Davis 's tables, 
 those in the lower lines (the differing digits only being given) are inter- 
 polated from Goodenough 's tables, in which the figures are for steam 
 of given temperatures, not even degrees of superheat. 
 
 Abso- 
 lute 
 Pres- 
 sure. 
 
 Temp. 
 
 Sat. 
 Steam. 
 
 Superheat, Degrees Fahrenheit. 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 400 
 
 500 
 
 20 
 
 228.0 
 
 V 21.69 
 
 23.25 
 
 24.80 
 
 26.33 
 
 27.85 
 
 29.37 
 
 32.39 
 
 35.40 
 
 
 
 8 
 
 3 
 
 .77 
 
 .29 
 
 1 
 
 1 
 
 1 
 
 30 
 
 
 
 h 1179.9 
 
 1203.5 
 
 1227.1 
 
 1250.6 
 
 1274.1 
 
 1297.6 
 
 1344.8 
 
 1392.2 
 
 
 
 7.3 
 
 6.0 
 
 9.8 
 
 3.5 
 
 7.0 
 
 300.7 
 
 8.5 
 
 7.0 
 
 
 
 n K7652 
 
 1.7961 
 
 1.8251 
 
 1.8524 
 
 1.8781 
 
 1.9026 
 
 1.9479 
 
 1.9893 
 
 
 
 86 
 
 8000 
 
 92 
 
 64 
 
 823 
 
 69 
 
 530 
 
 956 
 
 100 
 
 327.8 
 
 V 4.79 
 
 5.14 
 
 5.47 
 
 5.80 
 
 6.12 
 
 6.44 
 
 7.07 
 
 7.69 
 
 
 
 " 
 
 3 
 
 6 
 
 .79 
 
 
 
 1 
 
 3 
 
 4 
 
 
 
 h 1213.8 
 
 1239.7 
 
 1264.7 
 
 1289.4 
 
 1313.6 
 
 1337.8 
 
 1385.9 
 
 1434.1 
 
 
 
 5.9 
 
 42.5 
 
 8.3 
 
 93.6 
 
 8.7 
 
 43.7 
 
 93.6 
 
 43.9 
 
 
 
 n 1.6358 
 
 1.6658 
 
 1.6933 
 
 1.7188 
 
 1.7428 
 
 1.7656 
 
 1.8079 
 
 1.8468 
 
 
 
 84 
 
 91 
 
 74 
 
 235 
 
 84 
 
 720 
 
 159 
 
 566 
 
 200 
 
 381.9 
 
 V 2.49 
 
 2.68 
 
 2.86 
 
 3.04 
 
 3.21 
 
 3.38 
 
 3.71 
 
 
 
 
 .50 
 
 9 
 
 5 
 
 2 
 
 .18 
 
 4 
 
 .66 
 
 
 
 
 h 1229.8 
 
 1257.1 
 
 1282.6 
 
 1307.7 
 
 1332.4 
 
 1357.0 
 
 1405.9 
 
 
 
 
 I 
 
 8.0 
 
 5.7 
 
 12.7 
 
 9.0 
 
 65.1 
 
 16.8 
 
 
 
 
 n 1.5823 
 
 1.6120 
 
 1.6385 
 
 1.6632 
 
 1.6862 
 
 1.7082 
 
 1.7493 
 
 
 
 
 09 
 
 5 
 
 411 
 
 76 
 
 922 
 
 156 
 
 596 
 
 
 
 300 
 
 417.5 
 
 v 1.69 
 
 1.83 
 
 1.96 
 
 2.09 
 
 2.21 
 
 2.33 
 
 2.55 
 
 
 
 
 
 2 
 
 4 
 
 6 
 
 .18 
 
 .29 
 
 
 
 
 
 
 h 1240.3 
 
 1268.2 
 
 1294.0 
 
 1319.3 
 
 1344.3 
 
 1369.2 
 
 1418.6 
 
 
 
 
 35.0 
 
 5.9 
 
 5.2 
 
 23.3 
 
 51.0 
 
 78.1 
 
 31.5 
 
 
 
 
 n 1.5530 
 
 1.5824 
 
 1.6082 
 
 1.6323 
 
 1.6550 
 
 1.6765 
 
 1.7168 
 
 
 
 
 458 
 
 784 
 
 76 
 
 44 
 
 94 
 
 829 265 
 
 
STEAM. 
 
 875 
 
 Properties of Superheated Steam. 
 
 (Condensed from Marks and Davis's Steam Tables and Diagrams.) 
 v = specific volume in cu. ft. per lb., h = total heat, from water at 
 32 F. in B.T.U. per lb., n = entropy, from water at 32. 
 
 W 0> 
 
 a 
 
 g^o? 
 b 
 
 if 
 
 Degrees of Superheat. 
 
 
 
 20 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 400 
 
 500 
 
 20 
 
 228 
 
 v20.08 
 
 20.73 
 
 21.69 
 
 23.25 
 
 24.80 
 
 26.33 
 
 27.85 
 
 29.37 
 
 32.39 
 
 35.40 
 
 
 
 h 1156.2 
 
 1165.7 
 
 1179.9 
 
 1203.5 
 
 1227.1 
 
 1250.6 
 
 1274.1 
 
 1297.6 
 
 1344.8 
 
 1392.2 
 
 
 
 n 1 . 7320 
 
 1.7456 
 
 1.7652 
 
 1.7961 
 
 1.8251 
 
 1.8524 
 
 1.8781 
 
 1.9026 
 
 1.9479 
 
 1.9893 
 
 40 
 
 267.3 
 
 v 10.49 
 
 10.83 
 
 11.33 
 
 12.13 
 
 12.93 
 
 13.70 
 
 14.48 
 
 15.25 
 
 16.78 
 
 18.30 
 
 
 
 h 1169 4 
 
 1179.3 
 
 1194.0 
 
 1218.4 
 
 1242.4 
 
 1266.4 
 
 1290.3 
 
 1314.1 
 
 1361.6 
 
 1409.3 
 
 
 
 n 1.6761 
 
 1.6895 
 
 1.7089 
 
 1.7392 
 
 1.7674 
 
 1.7940 
 
 1.8189 
 
 1.8427 
 
 1.8867 
 
 1.9271 
 
 60 
 
 292.7 
 
 v7.17 
 
 7.40 
 
 7.75 
 
 8.30 
 
 8.84 
 
 9.36 
 
 9.89 
 
 10.41 
 
 11.43 
 
 12.45 
 
 
 
 h 1177.0 
 
 1187.3 
 
 1202.6 
 
 1227.6 
 
 1252.1 
 
 1276.4 
 
 1300.4 
 
 1324.3 
 
 1372.2 
 
 1420.0 
 
 
 
 n 1.6432 
 
 1.6568 
 
 1.6761 
 
 1 . 7062 
 
 1.7342 
 
 1.7603 
 
 1.7849 
 
 1 081 
 
 1.8511 
 
 1.8908 
 
 89 
 
 312.0 
 
 v5.47 
 
 5.65 
 
 5.92 
 
 6.34 
 
 6.75 
 
 7.17 
 
 7.56 
 
 7>5 
 
 8.72 
 
 9 49 
 
 
 
 h 1182.3 
 
 1193.0 
 
 1208.8 
 
 1234.3 
 
 1259.0 
 
 1283.6 
 
 1307.8 
 
 1331.9 
 
 1379.8 
 
 1427.9 
 
 
 
 11 1.6200 
 
 1.6338 
 
 1.6532 
 
 1.6833 
 
 1.7110 
 
 1.7368 
 
 1.7612 
 
 1.7840 
 
 1.8265 
 
 1.8658 
 
 100 
 
 327.8 
 
 v4.43 
 
 4.58 
 
 4.79 
 
 5.14 
 
 5.47 
 
 5.80 
 
 6.12 
 
 6.44 
 
 7.07 
 
 7.69 
 
 
 
 h 1186.3 
 
 1197.5 
 
 1213.8 
 
 1239.7 
 
 1264.7 
 
 1289.4 
 
 1313.6 
 
 1337.8 
 
 1385.9 
 
 1434.1 
 
 
 
 n 1.6020 
 
 1.6160 
 
 1.6358 
 
 1.6658 
 
 1.6933 
 
 1.7188 
 
 1.7428 
 
 1.7656 
 
 1.8079 
 
 1.8468 
 
 120 
 
 341.3 
 
 v3.73 
 
 3.85 
 
 4.04 
 
 4.33 
 
 4.62 
 
 4.89 
 
 5.17 
 
 5.44 
 
 5.96 
 
 6.48 
 
 
 
 h 1189.6 
 
 1201.1 
 
 1217.9 
 
 1244.1 
 
 1269.3 
 
 1294.1 
 
 1318.4 
 
 1342.7 
 
 1391.0 
 
 1439.4 
 
 
 
 n 1.5873 
 
 1.6016 
 
 1.62(6 
 
 1.6517 
 
 1.6789 
 
 1.7041 
 
 1.7280 
 
 1.7505 
 
 1.7924 
 
 1.831 
 
 (40 
 
 353.1 
 
 v3.22 
 
 3.32 
 
 3.49 
 
 3.75 
 
 4.00 
 
 4.24 
 
 4.48 
 
 4.71 
 
 5.16 
 
 5.61 
 
 
 
 h 1192.2 
 
 1204.3 
 
 1221.4 
 
 1248.0 
 
 1273.3 
 
 1298.2 
 
 1322.6 
 
 1346.9 
 
 1395.4 
 
 1443.8 
 
 
 
 n 1.5747 
 
 1.5894 
 
 1.6096 
 
 1.6395 
 
 1 .6666 
 
 1.6916 
 
 1.7152 
 
 1.7376 
 
 1 . 7792 
 
 1.8177 
 
 160 
 
 363.6 
 
 v2.83 
 
 2.93 
 
 3.07 
 
 3.30 
 
 3.53 
 
 3.74 
 
 3.95 
 
 4.15 
 
 4.56 
 
 4.95 
 
 
 
 h 1194.5 
 
 1207.0 
 
 1224.5 
 
 1251.3 
 
 1276.8 
 
 1301.7 
 
 1326.2 
 
 1350.6 
 
 1399.3 
 
 1447.9 
 
 
 
 n 1.5639 
 
 1.5789 
 
 1.5993 
 
 1.6292 
 
 K6561 
 
 1.6810 
 
 1.7043 
 
 1.7266 
 
 1.7680 
 
 1.8063 
 
 180 
 
 373.1 
 
 v2.53 
 
 2.62 
 
 2.75 
 
 2.96 
 
 3.16 
 
 3.35 
 
 3.54 
 
 3.72 
 
 4.09 
 
 4.44 
 
 
 
 h 1196.4 
 
 1209.4 
 
 1227.2 
 
 1254.3 
 
 1279.9 
 
 1304.8 
 
 1329.5 
 
 1353.9 
 
 1402.7 
 
 1451.4 
 
 
 
 n 1.5543 
 
 1.5697 
 
 1.5904 
 
 1.6201 
 
 1.6468 
 
 1.6716 
 
 1.6948 
 
 1.7169 
 
 1.7581 
 
 1.7962 
 
 200 
 
 381.9 
 
 v2.29 
 
 2.37 
 
 2.49 
 
 2 68 
 
 2.86 
 
 3.04 
 
 3.21 
 
 3.38 
 
 3.71 
 
 4.03 
 
 
 
 h 1198.1 
 
 1211. 6 
 
 1229.8 
 
 1257.1 
 
 1282.6 
 
 1307.7 
 
 1332.4 
 
 1357.0 
 
 1405.9 
 
 1454.7 
 
 
 
 n 1.5456 
 
 1.5614 
 
 1.5823 
 
 1.6120 
 
 1.6385 
 
 1 .6632 
 
 1.6862 
 
 1.7082 
 
 1.7493 
 
 1.7872 
 
 220 
 
 389.9 
 
 v2.09 
 
 2.16 
 
 2.28 
 
 2.45 
 
 2.62 
 
 2.78 
 
 2.94 
 
 3.10 
 
 3.40 
 
 3.69 
 
 
 
 h 1199.6 
 
 1213.6 
 
 1232.2 
 
 1259.6 
 
 1285.2 
 
 1310.3 
 
 1335.1 
 
 1359.8 
 
 1408.8 
 
 1457.7 
 
 
 
 n .5379 
 
 1.5541 
 
 1.5753 
 
 1.6049 
 
 1.6312 
 
 1 .6558 
 
 1.6787 
 
 1.7005 
 
 1.7415 
 
 1.7792 
 
 240 
 
 397.4 
 
 v .92 
 
 1.99 
 
 2.09 
 
 2.26 
 
 2.42 
 
 2.57 
 
 2.71 
 
 2.85 
 
 3.13 
 
 3.40 
 
 
 
 h 200.9 
 
 1215.4 
 
 1234.3 
 
 1261.9 
 
 1287.6 
 
 1312.8 
 
 1337.6 
 
 1362.3 
 
 1411 5 
 
 1460.5 
 
 
 
 n .5309 
 
 1.5476 
 
 1.5690 
 
 1.5985 
 
 1.6246 
 
 1.6492 
 
 1 .6720 
 
 1.6937 
 
 1.7344 
 
 1.7721 
 
 260 
 
 404.5 
 
 v .78 
 
 1.84 
 
 1.94 
 
 2.10 
 
 2.24 
 
 2.39 
 
 2.52 
 
 2.65 
 
 2.91 
 
 3.16 
 
 
 
 h 202.1 
 
 1217.1 
 
 1236.4 
 
 1264 1 
 
 1289.9 
 
 1315.1 
 
 1340.0 
 
 1364.7 
 
 1414.0 
 
 1463.2 
 
 
 
 n .5244 
 
 1.5416 
 
 1.5631 
 
 1.5926 
 
 1.6186 
 
 1.6430 
 
 1.6658 
 
 1.6874 
 
 1.7280 
 
 1.7655 
 
 280 
 
 411.2 
 
 v .66 
 
 1.72 
 
 1.81 
 
 1.95 
 
 2.09 
 
 2.22 
 
 2.35 
 
 2.48 
 
 2.72 
 
 2.95 
 
 
 
 h 203.1 
 
 1218.7 
 
 1238.4 
 
 1266.2 
 
 1291 .9 
 
 1317.2 
 
 1342.2 
 
 1367.0 
 
 1416.4 
 
 1465. 7 
 
 
 
 n .5185 
 
 1 . 5362 
 
 1.5580 
 
 1.5873 
 
 1.6133 
 
 1.6375 
 
 1.6603 
 
 1.6818 
 
 1.7223 
 
 1 7597 
 
 300 
 
 417.5 
 
 v .55 
 
 J.60 
 
 1.69 
 
 1.83 
 
 1.96 
 
 2.09 
 
 2.21 
 
 2.33 
 
 2.55 
 
 2.77 
 
 
 
 h 204.1 
 
 1220.2 
 
 1240.3 
 
 1268.2 
 
 1294.0 
 
 1319.3 
 
 1344.3 
 
 1369.2 
 
 1418.6 
 
 1468.0 
 
 
 
 n .5129 
 
 1.5310 
 
 1.5530 
 
 1.5824 
 
 1 .6082 
 
 1.6323 
 
 1.6550 
 
 1.6765 
 
 1.7168 
 
 1.7541 
 
 350 
 
 431.9 
 
 v .33 
 
 1.38 
 
 1.46 
 
 1.58 
 
 1.70 
 
 1.81 
 
 1.92 
 
 2.02 
 
 2.22 
 
 2.41 
 
 
 
 h 206.1 
 
 1223.9 
 
 1244.6 
 
 1272.7 
 
 1298.7 
 
 1324.1 
 
 1349.3 
 
 1374.3 
 
 1424.0 
 
 1473.7 
 
 
 
 n .5002 
 
 1.5199 
 
 1.5423 
 
 1.5715 
 
 1.5971 
 
 1.6210 
 
 1 .6436 
 
 1.6650 
 
 1 . 7052 
 
 1.7422 
 
 400 
 
 444.8 
 
 v .17 
 
 1.21 
 
 1.28 
 
 1.40 
 
 1.50 
 
 1.60 
 
 1.70 
 
 1.79 
 
 1.97 
 
 2.14 
 
 
 
 h 207.7 
 
 1227.2 
 
 1248.6 
 
 1276.9 
 
 1303.0 
 
 1328.6 
 
 1353.9 
 
 1379.1 
 
 1429.0 
 
 1478.9 
 
 
 
 n .4894 
 
 1.5107 
 
 1.5336 
 
 1.5625 
 
 1.5880 
 
 1.6117 
 
 1.6342 
 
 1.6554 
 
 1.6955 
 
 1.7323 
 
 450 
 
 456.5 
 
 v .04 
 
 1.08 
 
 1.14 
 
 1.25 
 
 1.35 
 
 1.44 
 
 1.53 
 
 1.61 
 
 1.77 
 
 1.93 
 
 
 
 h1209 
 
 1231 
 
 1252 
 
 1281 
 
 1307 
 
 1333 
 
 1358 
 
 1383 
 
 1434 
 
 1484 
 
 
 
 n 1.479 
 
 1.502 
 
 1.526 
 
 1.554 
 
 1.580 
 
 1.603 
 
 1.626 
 
 1.647 
 
 1.687 
 
 1.723 
 
 $00 
 
 467.3 
 
 vO.93 
 
 0.97 
 
 1.03 
 
 1.13 
 
 1.22 
 
 1.31 
 
 1.39 
 
 1.47 
 
 1.62 
 
 1.76 
 
 
 
 h 1210 
 
 1233 
 
 1256 
 
 1285 
 
 1311 
 
 1337 
 
 1362 
 
 1388 
 
 1438 
 
 1489 
 
 
 
 n 1.470 
 
 1.496 
 
 1.519 
 
 1.548 
 
 1.573 
 
 1.597 
 
 1.619 
 
 1.640 
 
 1.679 
 
 1.713 
 
876 
 
 STEAM. 
 
 FLOW OF STEAM. 
 
 Flow of Steam through a Nozzle. (From Clark on the Steam- 
 engine.) The flow of steam of a greater pressure into an atmosphere of a 
 less pressure increases as the difference of pressure is increased, until the 
 external pressure becomes only 58% of .the absolute pressure in the boiler. 
 The flow of steam is neither increased nor diminished by the fall of the ex- 
 ternal pressure below 58%, or about 4/ 7 of the inside pressure, even to 
 the extent of a perfect "vacuum. In flowing through a nozzle of the best 
 form, the steam expands to the external pressure, and to the volume aue to 
 this pressure, so long as it is not less than 58% of the internal pressure. 
 For an external pressure of 58%, and for lower percentages, the ratio of 
 expansion is 1 to 1 .624. 
 
 When steam of varying initial pressures is discharged into the atmos- 
 phere the atmospheric pressure being not more than 58% of the initial 
 pressure the velocity of outflow at constant density, that is, supposing the 
 initial density to be maintained, is given by the formula V = 3.5953 V&' 
 V = velocity in feet per second, as for steam of the initial density; 
 h = the height in feet of a column of steam of the given initial pressure, 
 the weight of which is equal to the pressure on the unit of base. 
 
 The lowest initial pressure to which the formula applies, when the steam 
 is discharged into the atmosphere at 14.7 Ibs. per sq. in., is (14.7 X 100/58) 
 = 25.37 Ibs. per sq. in. 
 
 From the contents of the table below it appears that the velocity of out- 
 flow into the atmosphere, of steam above 25 Ibs. per sq. in. absolute pres- 
 sure, increases very slowly with the pressure, because the density, and the 
 weight to be moved, increase with the pressure. An average of 900 ft. per 
 sec. may, for approximate calculations, be taken for the velocity of out- 
 flow as for constant density, that is, taking the volume of the steam at the 
 initial volume. For a fuller discussion of this subject see "Steam Tur- 
 bines, page 1085- 
 
 Outflow of Steam into the Atmosphere. External pressure per 
 square inch, 14.7 Ibs. absolute. Ratio of expansion in nozzle. 1.624. 
 
 
 i 
 
 
 
 <g . 
 
 feS* 
 
 
 . a . 
 
 'o 
 
 fc 
 
 ,* 
 
 bsolute Initial 
 Pressure per 
 square inch. 
 
 elocity of Out- 
 flow as at Co 
 stant Density 
 
 ctual Velocity 
 Outflow Ex- 
 panded. 
 
 ischarge per 
 square inch 
 Orifice per mil 
 
 orse-power pe 
 sq. in. of Orifi 
 if H.P. = 30 It 
 per hour. 
 
 bsolute Initial 
 Pressure per 
 square inch. 
 
 elocity of Out- 
 flow as at Co 
 stant Density 
 
 ctual Velocity 
 Outflow Ex- 
 panded. 
 
 ischarge per 
 square inch of 
 Orifice per mi 
 ute. 
 
 orse-power pe 
 sq. in. of Orifi 
 if H.P. = 30 It 
 per hour. 
 
 < 
 
 > 
 
 < 
 
 Q 
 
 H 
 
 < 
 
 > 
 
 ^ 
 
 Q 
 
 M 
 
 Ibs. 
 
 feet 
 p. sec. 
 
 feet 
 per sec . 
 
 Ibs. 
 
 H.P. 
 
 Ibs. 
 
 feet 
 p. sec. 
 
 feet 
 per sec. 
 
 Ibs. 
 
 H.P. 
 
 25.37 
 
 863 
 
 1401 
 
 22.81 
 
 45.6 
 
 90 
 
 895 
 
 1454 
 
 77.94 
 
 155.9 
 
 30 
 
 867 
 
 1408 
 
 26.84 
 
 53.7 
 
 100 
 
 898 
 
 1459 
 
 86.34 
 
 172.7 
 
 40 
 
 874 
 
 1419 
 
 35.18 
 
 70.4 
 
 115 
 
 902 
 
 1466 
 
 98.76 
 
 197.5 
 
 50 
 
 880 
 
 1429 
 
 44.06 
 
 88.1 
 
 135 
 
 906 
 
 1472 
 
 115.61 
 
 231.2 
 
 60 
 
 885 
 
 1437 
 
 52.59 
 
 105.2 
 
 155 
 
 910 
 
 1478 
 
 132.21 
 
 264.4 
 
 70 
 
 889 
 
 1444 
 
 61.07 
 
 122.1 
 
 165 
 
 912 
 
 1481 
 
 140.46 
 
 280.9 
 
 75 
 
 891 
 
 1447 
 
 65.30 
 
 130.6 ' 
 
 215 
 
 919 
 
 1493 
 
 181.58 
 
 363.2 
 
 Rateau's Formula. A. Rateau, in 1895-6, made experiments with 
 converging nozzles 0.41, 0.59 and 0.95 in. diam., on steam of pressures from 
 1.4 to 170 Ibs. per sq. in. In his paper read at the Intl. Eng'g. Congress at 
 Glasgow (Ena. Rec., Oct. 16, 1901) he gives the following formula, appli- 
 cable when the final pressure, absolute, is less than 58% of the initial. 
 Pounds per hour per sq. in. area of orifice = 3.6 P (16.3 0.96 log P). 
 P absolute pressure, Ibs. per sq. in. 
 
 Napier's Approximate Rule. Flow in pounds per second = ab- 
 solute pressure X area in square inches * 70. This rule gives results 
 
FLOW OF STEAM. 
 
 877 
 
 whfrh closely correspond with those in the above table, and with results 
 computed by Rateau's formula, as shown below. 
 
 Abs. press., Ibs. 
 
 per sq. in ....... 25.37 40 60 75 100 135 165 215 
 
 Discharge per m in. , 
 
 by table, Ibs.... 22.81 35.18 52.59 65.30 86.34 115.61 140.46 181.58 
 By Rateau's for- 
 
 mula % 22.76 35.43 52.49 65.25 86.28 115.47 140.28 181.39 
 
 By Napier's rule. 21.74 34.29 51.43 64.29 85.71 115.71 141.43 184.29 
 
 Flow of Steam in Pipes. The commonly accepted formula for 
 
 flow of air, steam or gas in pipes is W = c 
 
 w (p * ~ 
 
 d " 
 
 in which 
 
 W = the weight in pounds per minute, pi and p* = initial and final 
 pressures in pounds per square inch, w = density in pounds per cubic 
 foot, d = internal diameter of the pipe in inches, and L = length in 
 feet, and c an experimental coefficient, which varies with the diameter 
 of the pipe. It varies also with the velocity and with the smoothness 
 of the pipe, but there are no authentic data for the amount of the 
 variations due to these causes. For the derivation of the formula, see 
 Ency. Brit., llth ed., vol. xiv, p. 67, also "Steam," 1913 edition, 
 published by the Babcock & Wilcox Co. 
 
 The value of the coefficient c, as deduced by G. H. Babcock from 
 
 : 
 
 study of published experiments, is 87 
 
 3.6/d 
 
 It is probably as 
 
 Si, 
 
 " 
 
 learly correct as can be derived from the few experimental records that 
 are available. For the different standard sizes of lap welded pipe the 
 value of c computed from Babcock's formula are as below: 
 
 VALUES OF c FOR STANDARD SIZES OF LAP-WELDED PIPE. 
 
 Size, 
 In. 
 
 "1/2 
 
 , 3/4 
 
 H/4 
 H/2 
 
 21/2 
 
 31/2 
 
 Inter. 
 Diam., 
 In. 
 
 c 
 
 Size, 
 
 In. 
 
 Inter. 
 Diam., 
 In. 
 
 e 
 
 Size, 
 In. 
 
 Inter. 
 Diam., 
 In. 
 
 c 
 
 0.622 
 0.824 
 1 .049 
 1.380 
 1.610 
 2.067 
 2.469 
 3.068 
 3.548 
 
 33.4 
 37.5 
 41.3 
 45.8 
 48.4 
 52.5 
 55.5 
 59.0 
 61 .3 
 
 4 
 4V, 
 
 6 
 7 
 8 
 9 
 10 
 11 
 
 4.026 
 4.506 
 5.047 
 6.065 
 7.023 
 7.981 
 8.941 
 10.02 
 11 .00 
 
 63.2 
 64.8 
 66.5 
 68.7 
 70.7 
 72.2 
 73.4 
 74.5 
 75.5 
 
 12 
 13 
 14 
 15 
 17O.D. 
 18O.D. 
 20 O.D. 
 22 O.D. 
 24 O.D. 
 
 12.00 
 13.25 
 14.25 
 15.25 
 16.214 
 17.182 
 19.182 
 21.25 
 23.25 
 
 76.3 
 77. 1 
 77.7 
 78.2 
 78.7 
 79.1 
 79.8 
 80.4 
 81.0 
 
 The table, page 878, calculated from the formula with the above 
 values of c gives the flow of steam in pounds per minute for a drop of 
 1 Ib. pressure per 1000 ft. of length. For any other ratio of drop to 
 length multiply the figures in the table by the factors given below. 
 
 FACTORS FOR CORRECTION OF TABLE OF FLOW OF STEAM. 
 Drop Ib. per 
 
 1000ft. 14 K 2 346 8 10 15 20 25 
 
 Factor 0.5 0.707 1.414 1.732 2 2.45 2.83 3.16 3.87 4.47 5 
 
 For Flow of Steam at low pressures, see Heating and Ventilation, 
 page 699. 
 
 Flow of Steam in Long Pipes. Ledoux's Formula. In the flow 
 of steam or other gases in long pipes, the volume and the velocity are 
 increased as the drop in pressure increases. Taking this into account a 
 correct formula for flow would be an exponential one. Ledoux gives 
 
 699 
 
 .5/ 
 
 \/ 
 
 Y 
 
 - T: - r-s; , his notation being reduced to English meas- 
 pi 1 ** 4 pz 
 
 Mines, 1S92; Trans. A. S. M. E., xx., 365; Power, June, 
 
 ures. (Annales des . . . ., 
 
 1907.) See Johnson's formula for flow of air, page 619. 
 
878 
 
 m 
 
 STEAM. 
 
 iA CN <N CO * NO 
 
 tN""! 
 
 o ----2as?S3|=S9||i|=sii 
 
 ^00 
 
 CNiAO<N-^-ONiAOTj-TfTj-cnNOONONNO<NiA^ 
 
 7 ii 
 
 o =ss?3ss|Rasg|||||g|| 
 
 O'S 
 
 TGOONO lAt^ fSiA\O '^Tj-miAiAfN 
 
 II II 
 
 a s 
 
 >tN> H !}-_ rs J^ TJ- 
 
 jq 
 
 ^-CAt^sO'A' >ANOcoOcOOONCA<NvO ^OO 
 
 g* 
 
 O <N iA 00 <Arn CO rf ON 00 ON ONO " NO O t^ ^lA t^ ON 
 CNCsJcn 
 
 6% 
 
 <SOOt^iAiAA CO OOOiAO 
 
 H 
 
 fN<N 
 
 i 
 
 |2^5S?3?=5:3R5<.**N-^*i.* 
 
 Li 
 
 *$ 
 
 o - =2S*K8ftSftg3!8s8!ii 
 
 ^'1 
 
 SSS3SsSasR8S!ss,o,*^ N o. 
 
 II 
 a 
 
 ^~^~f^2^=i 
 
 t>, 
 
 ^S 
 <Ng 
 
 fx^iAO^OoO^t'OO 
 
 5 
 
 O (N CO NO ON CO CO TT O O iA Tf^- 00 ON <N ON ^ "1- ^1- iA 
 
 ^ 
 
 8 
 
 i5lsgSS5feSS!QS?S_^-^oo,a,o.^^ 
 
 l 
 
 O CO lA 00 CN t^ CO 00 NO ON 1^ Tj- iA fN COCOOO ACNO 
 fNcOiAr^OTTOOcoOvOcoOONOOfNON 
 (NcOCO'^-AiAt>.OCN 
 
 ci 
 
 5SiSSSSS95S5588!8$SSSo.**_^ 
 
 5 ii 
 
 <N 
 
 O CN CO -3- sO A <N ON ON ^- CO O ON O CO f> fN NO 
 <N<NCO>ANOoOO ^NO^OO'A 
 
 c8 ^ 
 
 3SlpsliSllsii5llasas22a 
 
 <j^ 5 
 
 
 Ml* 
 
 QQQQQ 
 
 ;J< 5^ ^ ^ > ddddd 
 
FLOW OF STEAM. 
 
 879 
 
 Carrying Capacity of Eitra Heavy Steam Pipes. 
 
 (Power Specialty Co.) 
 
 _ 
 
 rt 
 
 200 
 
 150 
 
 100 
 
 50 
 
 _ 
 
 S S e 
 
 200 
 
 150 
 
 100 
 
 50 
 
 J*oS 
 
 5 |-S 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 J'o.S 
 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 ill 
 
 l-g " 
 
 Pounds of steam per 
 
 1|| 
 
 jj * 
 
 Pounds of steam per 
 
 2k, 
 
 <5'w.S 
 
 hour. 
 
 a 
 
 -< 2 .~ 
 
 hour. 
 
 1 
 
 0.71 
 
 1210 
 
 872 
 
 618 
 
 362 
 
 6 
 
 25.93 
 
 40800 
 
 31600 
 
 22600 
 
 13210 
 
 I 1/4 
 
 1.27 
 
 2000 
 
 1555 
 
 1105 
 
 646 
 
 7 
 
 34.47 
 
 54600 
 
 42250 
 
 30000 
 
 17600 
 
 1 V2 
 
 1.75 
 
 2750 
 
 2140 
 
 1525 
 
 894 
 
 8 
 
 44.18 
 
 69500 
 
 54000 
 
 38400 
 
 22450 
 
 2 
 
 2.93 
 
 4610 
 
 3590 
 
 2550 
 
 1525 
 
 9 
 
 58.42 
 
 92000 
 
 71500 
 
 50800 
 
 29800 
 
 21/2 
 
 4.20 
 
 6610 
 
 5150 
 
 3660 
 
 2140 
 
 10 
 
 74.66 
 
 117300 
 
 91500 
 
 65000 
 
 38100 
 
 
 6.56 
 
 10300 
 
 8050 
 
 5720 
 
 3450 
 
 11 
 
 90.76 
 
 142800 
 
 111500 
 
 79200 
 
 46300 
 
 31/2 
 
 8.85 
 
 13900 
 
 10820 
 
 7720 
 
 4520 
 
 12 
 
 108.43 
 
 170500 
 
 133000 
 
 94750 
 
 55400 
 
 
 11.44 
 
 18000 
 
 14000 
 
 10000 
 
 5850 
 
 14 
 
 153.94 
 
 242000 
 
 188200 
 
 133900 
 
 78600 
 
 41/2 
 
 14.18 
 
 22300 
 
 17350 
 
 12320 
 
 7230 
 
 16 
 
 176.71 
 
 277500 
 
 216200 
 
 153800 
 
 90500 
 
 
 18.19 
 
 28610 
 
 22250 
 
 15800 
 
 9300 
 
 18 
 
 226.98 
 
 357000 
 
 278000J197500 
 
 115700 
 
 The quantities in the above table are based on the following velocities: 
 
 Steam superheated degrees F. 50 100 150 200 250 
 
 Velocity, ft. per min 8000 8500 8950 9450 9900 10450 
 
 Resistance to Flow by Bends, Valves, etc. (From Briggs on 
 Warming Buildings by Steam.) The resistance at the entrance to a 
 tube when no special bell-mouth is given consists of two parts. The 
 head v* * 20 is expended in giving the velocity of flow; and the head 
 0.505 v z -*- 2 g in .overcoming the resistance of the mouth of the tube 
 Hence the whole loss of head at the entrance is 1.505 v 2 *- 2g. This resist- 
 ance is equal to the resistance of a straight tube of a length equal to about 
 60 times its diameter. The loss at each sharp right-angled elbow is the 
 same as in flowing through a length of straight tube equal to about 40 
 times its diameter. For a globe steam stop-valve the resistance is 
 taken to be I 1 /a times that of the right-angled elbow. 
 
 Sizes of Steam-pipes for Stationary Engines. An old common 
 rule is that steam-pipes supplying engines should be of such size that the 
 mean velocity of steam in them does not exceed 6000 feet per minute, in 
 order that the loss of pressure due to friction may not be excessive The 
 velocity is calculated on the assumption that the cylinder is filled at each 
 stroke. In modern practice with large engines and high pressures, this 
 rule gives unnecessarily large and costly pipes. For such engines the 
 allowable drop in steam pressure should be assumed and the diameter 
 calculated by means of the formulae given above. 
 
 An article in Power, May, 1893, on proper area of supply-pipes for 
 engines gives a table showing the practice of leading builders. To facili- 
 tate comparison, all the engines have been rated in horse-power at 40 
 pounds mean effective pressure. The table contains all the varieties of 
 simple engines, from the slide-valve to the Corliss, and it appears that 
 there is no general difference in the sizes of pipe used in the different types. 
 The averages selected from this table are as follows: 
 
 DIAMETERS OF CYLINDERS CORRESPONDING TO VARIOUS SIZES OF 
 STEAM-PIPES BASED ON PISTON-SPEED OF ENGINE OF 600 FT. PER 
 MINUTE, AND ALLOWABLE MEAN VELOCITY OF STEAM IN PIPE OF 
 4000, 6000, AND 8000 FT. PER MINUTE. (STEAM ASSUMED TO BE 
 ADMITTED DURING FULL STROKE.) 
 
 Diam. of pipe, inches . . 2 
 
 Vel. 4000 5.2 
 
 Vel. 6000 6.3 
 
 Vel. 8000 7.3 
 
 Horse-power, approx. . . 20 
 
 Diam. of pipes, inches . 7 
 
 Vel. 4000 18.1 20.7 
 
 Vel. 6000 22.1 25.3 
 
 Vel. 8000 25.6 29.2 
 
 Horse-power, approx. . . 245 320 
 
 Formula. Area of pipe = A^ 
 
 mean velocity of steam in pipe 
 For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, 
 
 2 V2 
 
 3 
 
 3V2 
 
 4 
 
 4V2 
 
 5 
 
 6 
 
 6.5 
 
 7.7 
 
 9.0 
 
 10.3 
 
 11.6 
 
 12.9 
 
 15.5 
 
 7.9 
 
 9.5 
 
 11.1 
 
 12.6 
 
 14.2 
 
 15.8 
 
 19.0 
 
 9.1 
 
 10.9 
 
 12.8 
 
 14.6 
 
 16.4 
 
 18.3 
 
 21.9 
 
 31 
 
 45 
 
 62 
 
 80 
 
 100 
 
 125 
 
 180 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 20.7 
 
 23.2 
 
 25.8 
 
 28.4 
 
 31.0 
 
 33.6 
 
 36.1 
 
 25.3 
 
 28.5 
 
 31.6 
 
 34.8 
 
 37.9 
 
 41.1 
 
 44.3 
 
 29.2 
 
 32.9 
 
 36.5 
 
 40.2 
 
 43.8 
 
 47.5 
 
 51.1 
 
 320 
 
 406 
 
 500 
 
 606 
 
 718 
 
 845 
 
 981 
 
 Area 
 
 of cy] 
 
 Linder X 
 
 piston-speed . 
 
880 
 
 STEAM. 
 
 and 8000 ft. per min., area of pipe = respectively 0.15, 0.10, and 0.075< 
 area of cylinder. Diam. of pipe-respectively 0.3873, 0.3162, -and 0.2739X 
 diam. of cylinder. The reciprocals of these are 2. 582,3. 162and3. 651. 
 
 The first line in the above table may be used for proportioning exhaust 
 pipes, in which a velocity not exceeding 4000 ft. pe* minute is advisable. 
 The last line, apprpx. H.P. of engine, is based on the velocity of 60CO ft. 
 per min. in the pipe, using the corresponding diameter of piston, and 
 taking H.P. = 1/2 (diam. of piston in inches) 2 . 
 
 Sizes of Steam-pipes for Marine Engines. In marine-engine 
 practice the steam-pipes are generally not as large as in stationary practice 
 for the same sizes of cylinder. Seaton gives the following rules: 
 
 Main Steam-pines should be of such size that the mean velocity of flow 
 does not exceed 8000 ft. per min. 
 
 In large engines, 1000 to 2000 H.P., cutting off at less than half stroke, 
 the steam-pipe may be designed for a mean velocity of 9000 ft., and 
 10,000 ft. for still larger engines. 
 
 In small engines and engines cutting off later than half stroke, a velocity 
 of less than 8000 ft. per minute is desirable. 
 
 Taking 8100 ft. per min. as the mean velocity, S speed of piston in feet 
 per min., and D the diameter of the cylinder, 
 
 Diam. of main steam-pipe* v D 2 S * 8100 =>!> V& + 90. 
 
 Stop and Throttle Valves should have a greater area of passages than the 
 area of the main steam-pipe, on account of the friction through the cir- 
 cuitous passages. The shape of the passages should be designed so as to 
 avoid abrupt changes of direction and of velocity of flow as far as possible. 
 
 Area of Steam Ports and Passages 
 
 Area of piston X speed of piston in ft. per min. __ (Diam.)2 X speed 
 6000 7639 
 
 Opening of Port to Steam. To avoid wire-drawing during admission 
 the area of opening to steam should be such that the mean velocity of 
 flow does not exceed 10,000 ft. per min. To avoid excessive clearance 
 the width of port should be as short as possible, the necessary area being 
 obtained by length (measured at right angles to the line of travel of the 
 valve). In practice this length is usually 0.6 to 0.8 of the diameter of 
 the cylinder, but in long-stroke engines it may equal or even exceed the 
 diameter. 
 
 Exhaust Passages and Pipes. The area should be such that the mean 
 velocity of the steam should not exceed 6000 ft. per min., and the area 
 should be greater if the length of the exhaust-pipe is comparatively long. 
 The area of passages from cylinders to receivers should be such that the 
 velocity will not exceed 5000 ft. per min. 
 
 The following table is computed on the basis of a mean velocity of flow 
 of 8000 ft. per min. for the main steam-pipe, 10,000 for opening to steam, 
 and 6000 for exhaust. A = area of piston, D its diameter. 
 STEAM AND EXHAUST OPENINGS. 
 
 Piston- 
 speed, 
 
 Diam. of 
 Steam-pipe 
 
 Area of 
 Steam-pipe 
 
 Diam. of 
 
 Exhaust 
 
 Area of 
 Exhaust 
 
 Opening 
 to Steam 
 
 ft. per min. 
 
 ^ D. 
 
 + A. 
 
 * >. 
 
 4- A. 
 
 *- A. 
 
 300 
 
 0.194 
 
 0.0375 
 
 0.223 
 
 0.0500 
 
 0.03 
 
 400 
 
 0.224 
 
 0.0500 
 
 0.258 
 
 0.0667 
 
 0.04 
 
 500 
 
 0.250 
 
 0.0625 
 
 0.288 
 
 0.0833 
 
 0.05 
 
 600 
 
 0.274 
 
 0.0750 
 
 0.316 
 
 0.1000 
 
 0.06 
 
 700 
 
 0.296 
 
 0.0875 
 
 0.341 
 
 0.1167 
 
 0.07 
 
 800 
 
 0.316 
 
 0.1000 
 
 0.365 
 
 0.1333 
 
 0.08 
 
 900 
 
 0.335 
 
 0.1125 
 
 0.387 
 
 0.1500 
 
 0.09 
 
 1000 
 
 0.353 
 
 0.1250 
 
 0.400 
 
 0.1667 
 
 0.10 
 
 proportioning Steam-Pipes for Minimum Total Loss by Radiation 
 ana Friction. For a given size of pipe and quantity of steam to be 
 carried the loss of pressure due to friction is calculated by formulae given 
 above, or taken from the tables. The work of friction, being converted 
 into heat, tends to dry or superheat the steam, but its influence is usually 
 so small that it may be neglected. The loss of heat by radiation tends to 
 destroy the superheat and condense some of the steam into water. For 
 
FLOW OF STEAM. 
 
 881 
 
 weU-covered steam-pipes this loss may be estimated at about 0.3 
 B.T.U. per sq. ft. of external surface of the pipe per hour per degree of 
 difference of temperature between that of the steam and that of the 
 surrounding atmosphere (see Steam-pipe Coverings, p. 584). 
 
 A practical problem in power-plant design is to find the diameter of 
 pipe to carry a given quantity of steam with a minimum total loss of 
 available energy due to both radiation and friction, considering also the 
 money loss due to interest and depreciation on the value of the pipe 
 and covering as erected. Each case requires a separate arithmetical 
 computation, no formula yet being constructed to fit the general case. 
 An approximate method of solution, neglecting the slight gain of heat by 
 the steam from the work of friction, and assuming that the water con- 
 densed by radiation of heat is removed by a separator and lost, is as fol- 
 lows: Calculate the amount of steam required by the engine, in pounds 
 per minute. From a steam pipe formula or table find the several drops 
 of pressure, in Ibs. per sq. in., in pipes of different assumed diameters, for 
 the given quantity of steam and the given length of pipe. Compute from 
 a theoretical indicator diagram of steam expanding in the engine the loss 
 of available work done by 1 Ib. of steam, due to the several drops already 
 found, and the corresponding fraction of 1 Ib. of steam that will have to 
 be supplied to make up for this loss of work. State this loss as equiva- 
 lent to so many pounds of steam per 1000 Ibs. of steam carried. Calcu- 
 late the loss in Ibs. of steam condensed by radiation in the pipes of the 
 different diameters, per 1000 Ibs. carried. Add the two losses together 
 for each assumed size of pipe, and by inspection find which pipe gives the 
 lowest total loss. The money loss due to cost and depreciation may also 
 be figured approximately in the same unit of Ibs. of steam lost per 1000 
 Ibs. carried, by taking the cost of the covered pipe, assuming a rate of 
 interest and depreciation, finding the annual loss in cents, then from the 
 calculated value of steam, which depends on the cost of fuel, find the 
 equivalent quantity of steam which represents this money loss, and 
 the equivalent Ibs. of steam per 1000 Ibs. carried. This is to be added to 
 the sum of the louses due to friction and radiation, and it will be found to 
 modify somewhat the conclusion as to the diameter of pipe and the drop 
 which corresponds to a minimum total loss. 
 
 Instead of determining the loss of available work per pound of steam 
 from theoretical indicator diagrams, it may be computed approximately 
 on the assumption, based on the known characteristics of the engine, 
 that its efficiency is a certain fraction of that of an engine working between 
 the same limits of temperature on the ideal Carnot cycle, as shown in 
 the table below, and from the efficiency thus found, compared with the 
 efficiency at the given initial pressure less the drop, the loss of work may 
 be calculated. 
 AVAILABLE MAXIMUM THERMAL EFFICIENCY OF STEAM EXPANDED 
 
 BETWEEN THE GIVEN PRESSURES AND 1 LB. ABSOLUTE, BASED ON 
 
 THE CARNOT CYCLE. (E = Ti - Tz) * Ti. 
 
 Initial Pressure 
 less than Maxi- 
 mum, Lbs. 
 
 Maximum Initial Absolute Pressures. 
 
 100 
 
 125 | 150 
 
 175 | 200 
 
 225 | 250 
 
 275 I 300 
 
 Maximum Thermal Efficiency. 
 
 o 
 
 0.287 
 .286 
 .284 
 .280 
 .272 
 
 0.302 
 .301 
 .299 
 .296 
 .290 
 
 0.314 
 .313 
 .312 
 .309 
 .304 
 
 0.324 
 .323 
 .322 
 .320 
 .316 
 
 0.333 
 .332 
 .331 
 .329 
 .326 
 
 0.341 
 .340 
 .339 
 .337 
 .335 
 
 0.348 
 .347 
 .346 
 .345 
 .342 
 
 0.354 
 .354 
 .353 
 .352 
 .349 
 
 0.360 
 .359 
 .359 
 .358 
 .356 
 
 2. . 
 
 5 
 
 10. . 
 
 20 
 
 This table shows that if the initial steam pressure is lowered from 
 100 Ibs. to 80 Ibs., the efficiency of the Carnot cycle is reduced from 
 0.287 to 0.272, or over 5%, but if steam of 300 Ibs. is lowered to 280 Ibs. 
 the efficiency is reduced only from 0.360 to 0.356 or 1.1%. With high- 
 pressure steam, therefore, much greater loss of pressure by friction of 
 steam pipes, valves and ports is allowable than with steam of low pressure. 
 
 Theoretically the loss of efficiency due to drop in pressure on account 
 of friction of pipes should be less than that indicated in the above table, 
 since the work of friction tends to superheat the steam, but practically 
 most, if not all, of the superheating is lost by radiation. 
 
882 
 
 STEAM. 
 
 By a method of calculation somewhat similar to that above outlined, 
 the following figures were found, in a certain case, of the cost per day 
 of the transmission of 50,000 Ibs. of steam per hour a distance of 1000 
 feet, with 100 Ibs. initial pressure. 
 
 Diameter of Pipe. 
 
 6 in. 
 
 7 in. 
 
 8 in. 
 
 10 in. 
 
 12m. 
 
 1. Interest, etc., 12% per annum. . 
 2. Condensation 
 
 $0.39 
 1.51 
 
 $0.46 
 1.76 
 
 $0.53 
 2.01 
 
 $0.66 
 2.51 
 
 $0.84 
 3.02 
 
 3. Friction 
 
 86 
 
 38 
 
 19 
 
 06 
 
 0.02 
 
 
 
 
 
 
 
 Total per day 
 
 $2.76 
 
 $2.60 
 
 $2.73 
 
 $3.23 
 
 $3.88 
 
 STEAM-PIPES. 
 
 Bursting-tests of Copper Steam-pipes. (From Ileport of Chief 
 Engineer Melville, U. S. N., for 1892.) Some tests were made at the 
 New York Navy Yard which show the unreliability of brazed seams in 
 copper pipes. Each pipe was 8 in. diameter inside and 3 ft. 1 5/g in. long. 
 Both ends were closed by ribbed heads and the pipe was subjected to a 
 hot-water pressure, the temperature being maintained constant at 371 F. 
 Three of the pipes were made of No. 4 sheet copper (Stubs gauge) and the 
 fourth was made of No. 3 sheet. 
 
 The following were the results, in Ibs. per sq. in., of bursting-pressure: 
 
 Pipe number 1 2 3 4 4' 
 
 Actual bursting-strength. . 835 785 950 1225 1275 
 Calculated " 1336 1336 1569 1568 1568 
 
 Difference 501 551 619 343 293 
 
 The tests of specimens cut from the ruptured pipes show the injurious 
 action of heat upon copper sheets; and that, while a white heat does not 
 change the character of the metal, a heat of only slightly gieater degree 
 causes it to lose the fibrous nature that it has acquired in rolling, and a 
 serious reduction in its tensile strength and ductility results. 
 
 A Failure of a Brazed Copper Steam-pipe on the British steamer 
 Prodano was investigated by Prof. J. O. Arnold. He found that the 
 brazing was originally sound, but that it had deteriorated by oxidation 
 of the zinc in the brazing alloy by electrolysis, which was due to the 
 presence of fatty acids produced by decomposition of the oil used in the 
 engines. A full account of the investigation is given in The Engineer, 
 April 15, 1898. 
 
 -Reinforcing Steam-pipes. (Eng., Aug. 11, 1893.) In the Italian 
 Navy copper pipes above 8 in. diam. are reinforced by wrapping them with 
 a close spiral of copper or Delta-metal wire. Two or three independent 
 spirals are used for safety in case one wire breaks. They are wound at a 
 tension of about 11/2 tons per sq. in. 
 
 Materials for Pipes and Valves for Superheated Steam. (M. W. 
 Kellogg, Trans. A. S. M. E., 1907.) The latest practice is to do away 
 with fittings entirely on high-pressure steam lines and put what are known 
 as "nozzles" on the piping itself. This is accomplished by welding 
 wrought-steel pipe on the side of another section, so as to accomplish 
 the same result as a fitting. In this way rolled or cast steel flanges and a 
 Rockwood or welded joint can be used. This method has three distinct 
 advantages: 1. The quality of the metal used. 2. The lightening of the 
 entire work. 3. The doing away with a great many joints. 
 
 As a general average, at least 50% of the joints can be left out; some- 
 times the proportion runs up as high as 70%. 
 
 Above 575 F. the limit of elasticity in cast iron is reached with a 
 pressure varying from 140 to 175 pounds. Under such conditions the 
 material is strained and does not resume its former shape, eventually 
 showing surface cracks which increase until the pipe breaks. [This state- 
 ment concerning cast iron does not seem to agree with the one on page 
 464, to the effect that no diminution in its strength takes place under 
 900 F.I 
 
 Tests by Bach on cast steel show that at 572 F. the reduction in break- 
 ing strength amounts only to 1.1% and at 752 F. to about 8', ( . 
 
 The effect of temperature on nickel is similar to that on cast steel and 
 in consequence this material is very suitable for use in connection with 
 
STEAM-PIPES. 883 
 
 superheated steam. Bach recommends that bronze alloys be 
 done away with for use on steam lines above a temperature of about 
 390 F. 
 
 The old-fashioned screwed joint, no matter how well made, is not 
 suitable for superheated steam work. 
 
 In making up a joint, the face of all flanges or pipe where a joint is made 
 should be given a fine tool finish and a plane surface, and a gasket should 
 be used. The best results have been obtained with a corrugated soft 
 Swedish steel gasket with "Smooth-on" applied, and with the McKim 
 gasket, which is of copper or bronze surrounding asbestos. On super- 
 heated steam lines a corrugated copper gasket will in time pit out iu 
 some part of the flange nearly through the entire gasket. 
 
 Specifications for pipes and fittings for superheated steam service were 
 published by Crane Co., Chicago, in the Valve World, 1907. 
 
 Riveted Steel Steam-pipes have been used for high pressures. See 
 paper on A Method of Manufacture of Large Steam-pipes, by Chas. H. 
 Manning, Trans. A. S. M. E., vol. xv. 
 
 Valves in Steam-pipes. Should a globe-valve on a steam-pipe have 
 the steam-pressure on top or underneath the valve is a disputed question. 
 With the steam-pressure on top, the stuffing-box around the valve-stem 
 cannot be repacked without shutting off steam from the whole line of 
 pipe; on the other hand, if the steam-pressure is on the bottom of the 
 valve it all has to be sustained by the screw-thread on the valve-stem, 
 and there is danger of stripping the thread. 
 
 A correspondent of the American Machinist, 1892, says that it is a very 
 uncommon thing in the ordinary globe- valve to have the thread give out, 
 but by water-hammer and merciless screwing the seat will be crushed 
 down quite frequently. Therefore with plants where only one boiler is 
 used he advises placing the valve with the boiler-pressure underneath it. 
 On plants where several boilers are connected to one main steam-pipe 
 he would reverse the position of the valve, then when one of the valves 
 needs repacking the valve can be closed and the pressure in the boiler 
 whose pipe it controls can be reduced to atmospheric by lifting the safety- 
 valve. The repacking can then be done without interfering with the 
 operation of the other boilers of the plant. 
 
 He proposes also the following other rules for locating valves: Place 
 valves with the stems horizontal to avoid the formation of a water-pocket. 
 Never put the junction-valve close to the boiler if the main pipe is above 
 the boiler, but put it on the highest point of the junction-pipe. If the other 
 plan is followed, the pipe fills with water whenever this boiler is stopped 
 and the others are running, and breakage of the pipe may cause serious 
 results. Never let a junction-pipe run into the bottom of the main pipe, 
 but into the side or top. Always use an angle- valve where convenient, 
 as there is more room in them. Never use a gate valve under high pressure 
 unless a by-pass is used with it. Never open a blow-off valve on a boiler 
 a little and then shut it; it is sure to catch the sediment and ruin the 
 valve; throw it well open before closing. Never use a globe-valve on an 
 indicator-pipe. For water, always use gate or angle valves or stop-cocks 
 to obtain a clear passage. Buy if possible valves with renewable disks. 
 Lastly, never let a man go inside a boiler to work, especially if he is to 
 hammer on it, unless you break the joint between the boiler and the 
 valve and put a plate of steel between the flanges. 
 
 The " Steam-Loop " is a system of piping by which water of con- 
 densation in steam-pipes is automatically returned to the boiler. In its 
 simplest form it consists of three pipes, which are called the riser, the 
 horizontal, and the drop-leg. When the steam-loop is used for returning 
 to the boiler the water of condensation and entrainment from the steam- 
 pipe through which the stearn flows to the cylinder of an engine, the riser 
 is generally attached to a separator; this riser empties at a suitable 
 height into the horizontal, and from thence the water of condensation is 
 led into the drop-leg, which is connected to the boiler, into which the 
 water of condensation is fed as soon as the hydrostatic pressure in the 
 drop-leg in connection with the steam-pressure in the pipes is sufficient to 
 overcome the boiler-pressure. The action of the device depends on the 
 following principles: Difference of pressure may be balanced by a water- 
 column; vapors or liquids tend to flow to the point of lowest pressure; 
 rate of flow depends on difference of pressure and mass; decrease of static 
 pressure in a steam-pipe or chamber is proportional to rate of conden- 
 
884 
 
 STEAM. 
 
 sation; In a steam-current water will be carried or swept along rapidly 
 by friction. (Illustrated in Modern Mechanism, p. 807. Patented by 
 J. H. Blessing, Feb. 13, 1372, Dec. 28, 1883.) Mr. Blessing thus describes 
 the operation of the loop in Eng. Review, Sept., 1907. 
 
 The heating system is so arranged that the water of condensation from 
 the radiators gravitates towards some low point and thence isled into the 
 top of a receiver. After this is done it is found that owing to friction 
 caused by the velocity of the steam passing through the different pipes 
 and condensation due to radiation, the steam pressure in the small drip 
 receiver is much less than that in the boiler. This difference will deter- 
 mine the height, or the length of the loop, that must be employed so that 
 the water will gravitate through it into the boiler; that is to say, if there is 
 10 Ibs. difference in pressure, the descending leg of the loop should extend 
 about 30 feet above the water-level in the boiler, since a column of water 
 2.3 ft. is equal to 1 Ib. pressure, and a difference in pressure of 10 Ibs. 
 would require a column 23 ft. high. If we make the loop 30 feet high 
 we shall have an additional length of 7 ft. with which to overcome fric- 
 tion. The water, after it reaches the top of the loop, composed of a 
 larger section of pipe, will flow into the boiler through the descending 
 leg with a velocity due to the extra 7 ft. added to the discharging leg. 
 
 Loss from an Uncovered Steam-pipe. (Bjorling on Pumping- 
 engines.) The amount of loss by condensation in a steam-pipe carried 
 down a deep mine-shaft has been ascertained by actual practice at the 
 Clay Cross Colliery, near Chesterfield, where there is a pipe 712 in. internal 
 diam., 1100 ft. long. The loss of steam by condensation was ascertained 
 by direct measurement of the water deposited in a receiver, and was found 
 to be equivalent to about 1 Ib. of coal per'I.H.P. per hour for every 100 ft. 
 of steam-pipe; but there is no doubt that if the pipes had been in the up- 
 cast shaft, and well covered with a good non-conducting material, the loss 
 would have been less. (For Steam-pipe Coverings, see p. 584, ante.) 
 
 Condensation in an Underground Pipe Line. (W. W. Christie, 
 Eng. Rec., 1904.) A length of 300 ft. of 4-in. pipe, enclosed in a box 
 of li/4-in. planks, 10 ins. square inside, and packed with mineral wool, 
 was laid in a trench, the upper end being 1 ft. and the lower end 5 ft. below 
 the surface. With 80 Ibs. gauge pressure in the pipe the condensation 
 was equivalent to 0.275 B.T.U. per minute per sq. ft. of pipe surface 
 when the outside temperature was 31 F., and 0.222 per min. when the 
 temperature was 62 F. 
 
 Steam Receivers on Pipe Lines. (W. Andrews, Steam Eng'g, Dec. 
 10, 1902.) In the four large power houses in New York City, with 
 an ultimate capacity of 60,000 to 100,000 H.P. each, the largest steam 
 mains are not over 20 ins. in diameter. Some of the best plants have 
 pipes which run from the header to the engine two sizes smaller than that 
 called for by the engine builders. These pipes before reaching the engine 
 are carried into a steel receiver, w r hich acts also as a separator. This ' 
 receiver has a cubical capacity of three times that of the high-pressure 
 cylinder and is placed as close as possible to the cylinder. The pipe from 
 the receiver to the cylinder is of the full size called for by the engine 
 builder. The objects of this arrangement are: First, to have a full supply 
 of steam to the throttle; second, to provide a cushion near the engine on 
 which the cut-off in the steam chest may be spent, thereby preventing 
 vibrations from being transmitted through the piping system; and 
 third, to produce a steady and rapid flow of steam in one direction only, 
 by having a small pipe leading into the receiver. The steam flows 
 rapidly enough to make good the loss caused during the first quarter of 
 the stroke. Plants fitted up in this way are successfully running where 
 the drop in steam pressure is not greater than 4 Ibs., although the engines 
 are 500 ft. away from the boilers. 
 
 Equation of Pipes. F9r determining the number of small sized 
 pipes that are equal in carrying capacity to one of greater size the table 
 given under Flow of Air, page 625, is commonly used. It is based on the 
 equation N = ^ds + di 6 , in which N is the number of smaller pipes of 
 diameter d\ equal in capacity to one pipe of diameter d. A more 
 accurate equation, based on Unwin's formula for flow of fluids, is N = 
 
 - 1+ 3 ' 6 ; (d and di in inches). For d= 2di, the first formula giv 
 3.6 
 
THE STEAM-BOILER. 
 
 885 
 
 JV = 5.7, and the second N = 6.15, an unimportant difference, but for 
 d = 8di, the first gives N = 181 and the second N = 274, a considerable 
 difference. (G. F. Gebhardt, Power, June, 1907). 
 
 Identification of Power House Piping by Different Colors. (W. 
 
 H. Bryan, Trans. A. S. M. E., 1908.) In large power plants the multi^ 
 piicity of pipe lines carrying different fluids causes confusion and may 
 lead to danger by an operator opening a wrong valve. It has therefore 
 become customary to paint the different lines of different colors. The 
 paper gives several tables showing color schemes that have been adopted 
 in different plants. The following scheme, adopted at the New York 
 Edison Co.'s Waterside Station, is selected as an example. 
 
 Pipe Lines. 
 
 Colors of Pipe. 
 
 Bands, Cou- 
 plings, Valves, 
 etc. 
 
 Steam, high pressure to engines, boiler 
 cross-overs leaders and headers 
 
 Black 
 Buff 
 Orange 
 Orange 
 Green 
 
 Slate 
 Dark Brown 
 
 Blue 
 Maroon 
 
 Green 
 Slate 
 Blue 
 Vermilion 
 Brown 
 Brown 
 Brown 
 Black 
 
 Brass 
 Black 
 Red 
 Black 
 Black 
 
 Red 
 Blue 
 
 Red 
 Same 
 
 Red 
 Black 
 Black 
 Same 
 Black 
 Green 
 Red 
 Same 
 
 All other steam lines 
 
 Steam exhaust 
 
 Steam, drips including traps 
 
 
 Blow-offs, drips from water columns 
 
 Drains from crank pits 
 
 Cold water to primary heaters and 
 
 
 Hot-water mains, primary heaters to 
 pumps, and cooling-water returns. . . . 
 Air pump discharge to hot well . 
 
 Cooling water pumps to engines 
 
 Fire lines 
 
 Cylinder oil high pressure 
 
 
 Engine oil . 
 
 
 
 THE STEAM-BOILER. 
 
 The Horse-power of a Steam-boiler. The term horse-power has 
 two meanings in engineering: First, an absolute unit or measure of the rate 
 of work, that is, of the work done in a certain definite period of time, by 
 a source of energy, as a steam-boiler, a waterfall, a current of air or water, 
 or by a prime mover, as a steam-engine, a water-wheel, or a wind-mill. 
 The value of this unit, whenever it can be expressed in foot-pounds of 
 energy, as in the case of steam-engines, water-wheels, and waterfalls, is 
 33,000 foot-pounds per minute. In the case of boilers, where the work 
 done, the conversion of water into steam, cannot be expressed in foot- 
 pounds of available energy, the usual value given to the term horse-power 
 is the evaporation of 30 Ibs. of water of a temperature of 100 F. into 
 steam at 70 Ibs. pressure above the atmosphere. Both of these units are 
 arbitrary; the first, 33,000 foot-pounds per minute, first adopted by James 
 Watt, being considered equivalent to the power exerted by a good London 
 draught-horse, and the 30 Ibs. of water evaporated per hour being con- 
 sidered to b^ the pfparn reauirement per indicated horse-power of an 
 average engine (in 1876). 
 
 The Committee of Judges of the Centennial Exhibition, 1876, in report- 
 ing the trials of competing boilers at that exhibition adopted the unit, 
 30 Ib. of water evaporated into dry steam per hour from feed-water at 
 100 P., and under a pressure of 70 Ib. per square inch above the atmos- 
 phere, these conditions being considered by them to represent fairly 
 average practice. 
 
 The A. S. M. E. Committee on Boiler Tests, 1884, accepted the same 
 unit, and defined it as equivalent to 34.5 Ib. evaporated per hour from a 
 
886 THE STEAM-BOILER. 
 
 feed-water temperature of 212 into steam at the same temperature. 
 The committee of 1899 adopted 34.5 Ib. per hour, from and at 212, as 
 the unit of commercial horse-power, and it was reaffirmed in the Boiler 
 Code of the Power Test Committee, 1915. Using the figures for 
 total heat of steam given in Marks and Davis's steam tables (1909), 
 34 Yi Ib. from and at 212, is equivalent to 33,479 B.T.U. per hour, or to 
 an evaporation of 30.018 Ib. from 100 feed- water temperature into 
 steam at 70 Ib. pressure. 
 
 The second definiti9n of the term horse-power is an approximate meas- 
 ure of the size, capacity, value, or "rating" of a boiler, engine, water- 
 wheel, or other source or conveyer of energy, by which measure it may be 
 described, bought and sold, advertised, etc. No definite value can be 
 given to this measure, which varies largely with local custom or indivi- 
 dual opinion of makers and users of machinery. The nearest 
 approach to uniformity which can be arrived at in the term "horse- 
 power,' ' used in this sense, is to say that a boiler, engine, water-wheel, 
 or other machine, "rated" at a certain horse-power, should be capable 
 of steadily developing that horse-power for a long period of time under 
 ordinary conditions of use and practice, leaving to local custom, to the 
 judgment of the buyer and seller, to written contracts of purchase and 
 sale, or to legal decisions upon such contracts, the interpretation of 
 what is meant by the term "ordinary conditions of use and practice." 
 (Trans. A. 5. M. ?., vol. vii, p. 226.) 
 
 Contracts for power-plant apparatus should specify the leading 
 dimensions of the apparatus and its rated capacity. If a specific 
 guarantee of capacity is made, either working or maximum capacity, 
 the operating conditions under which the guarantee is to be met should 
 be clearly set forth; such, for example, as steam pressure, speed, vacuum, 
 quality of fuel, force of draft, etc. Likewise if a contract contains a 
 guarantee of economy all the conditions should be fully specified. 
 
 The commercial rating of capacity determined on for power-plant 
 apparatus, whether for the purpose of contracts for sale or otherwise, 
 should be such that a sufficient reserve capacity beyond the rating 
 is available to meet the contingencies of practical operation ; such con- 
 tingencies, for example, as the loss of steam pressure and capacity due 
 to cleaning fires, inferior coal, oversight of the attendants, sudden de- 
 mand for an unusual output of steam or power, etc. 
 
 The Committee of 1899 says: A boiler rated at any stated capacity 
 should develop that capacity when using the best coal ordinarily sold in 
 the market where the boiler is located ,when fired by an ordinary fireman, 
 without forcing the fires, while exhibiting good economy; and further, the 
 boiler should develop at least one-third more than the stated capacity 
 when using the same fuel and operated by the same fireman, the full 
 draught being employed and the fires being crowded; the available draught 
 at the damper, unless otherwise understood, being not less than 1/2 inch 
 water column. 
 
 Unit of Evaporation. (Abbreviation, U. E.) It is the custom to 
 reduce results of boiler-tests to the common standard of the equivalent 
 evaporation from and at the boiling-point at atmospheric pressure, or 
 " from and at 212 F." This unit of evaporation, or one pound of water 
 evaporated from and at 212, is equivalent to 970.4 British thermal 
 units. 1 B.T.U. = the mean quantity of heat 'equired to raise 1 Ib. of 
 water 1 F. between 32 and 212. 
 
 Measures for Comparing the Duty of Boi ers. The measure of 
 the efficiency of a boiler is the number of pounds >f water evaporated per 
 pound of combustible (coal less moisture and ash), the evaporation 
 being reduced to the standard of "from and ai 212." 
 
 The measure of the capacity of a boiler is the amount of " boiler horse- 
 power" developed, a horse-power being defined as the evaporation of 
 34.5 Ib. per hour from and at 212. 
 
 The measure of relative rapidity of steaming of boilers is the number 
 of pounds of water evaporated from and at 212 per hour per square 
 foot of water-heating surface. 
 
 The measure of relative rapidity of combustion of fuel in boiler- 
 furnaces is the number of pounds of coal burned per hour per square 
 foot of grate-surface, 
 
STEAM-BOILER PROPORTIONS. 887 
 
 STEAM-BOILER PROPORTIONS. 
 
 Proportions of Grate and Heating Surface required for a given 
 Horse-power. The term horse-power here means capacity to evap- 
 orate 34.5 Ib. of water from and at 212 F. 
 
 Average proportions for maximum economy for land boilers fired with 
 good anthracite coal (ordinary hand firing) : 
 
 Heating surface per horse-power 11 . 5 sq. ft. 
 
 Grate surface per horse-power 1/3 
 
 Ratio of heating to grate surface 34 . 5 
 
 Water evap'd from and at 212 per sq. ft. H.S. per hr . . . 3 Ib. 
 
 Combustible burned per H.P. per hour. . 3 
 
 Coal with 1/6 refuse, Ib. per H.P. per hour 3.6 
 
 Combustible burned per sq. ft. grate per hour 9 
 
 Coal with 1/6 refuse, Ib. per sq. ft. grate per hour 10.8 
 
 Water evap'd from and at 212 per Ib. combustible. ... 11.5 
 Water evap'd from and at 212 per Ib. coal (i/e refuse) . 9.6 
 Heating-surface. For maximum economy with any kind of fuel a 
 boiler should be proportioned so that at least one square foot of heating- 
 surface should be given for every 3 IDS. of water to be evaporated from 
 and at 212 F. per hour. Still more liberal proportions are required if a 
 portion of the heating-surface has its efficiency reduced by: 1. Tendency 
 of the heated gases to short-circuit, that is, to select passages of least 
 resistance and now through them with high velocity, to the neglect of 
 other passages. 2. Deposition of soot from smoky fuel. 3. Incrusta- 
 tion. If the heating-surfaces are clean, and the heated gases pass over 
 it uniformly, little if any increase in economy can be obtained by increasing 
 the heating-surface beyond the proportion of 1 sq. ft. to every 3 Ibs. of 
 water to be evaporated, and with all conditions favorable but little 
 decrease of economy will take place if the proportion is 1 sq. ft. to every 
 4 Ibs. evaporated; but in order to provide for driving of the boiler beyond 
 its rated capacity, and for possible decrease of efficiency due to the causes 
 above named, it is better to adopt 1 sq. ft. to 3 Ibs. evaporation per hour 
 as the minimum standard proportion. 
 
 Where economy may be sacrified to capacity, as where fuel is very 
 cheap, it is customary to proportion the heating-surface much less liber- 
 ally. The following table shows approximately the relative results that 
 may be expected with different rates of evaporation, with anthracite coal. 
 
 Lbs. water evapor'd from and at 21 2 per sq.ft. heating-surf ace per hour: 
 2 2.5 3 3.5 4 5 6 7 8 9 10 
 
 Sq. ft. heating-surface required per horse-power: 
 17.3 13.8 11.5 9.8 8.6 6.8 5.8 4.9 4.3 3.8 3.5 
 
 Ratio of heating to grate surface if 1/3 sq. ft. of G.S. is required per H.P.: 
 52 41.4 34.5 29.4 25.8 20.4 17.4 13.7 12.9 11.4 10.5 
 
 Probable relative economy: 
 100 100 100 95 90 85 80 75 70 65 60 
 
 Probable temperature of chimney gases, degrees F.: 
 450 450 450 518 585 652 720 787 855 922 990 
 
 The relative economy will vary not only with the amount of heating- 
 surface per horse-power, but with the efficiency of that heating-surface as 
 regards its capacity for transfer of heat from the heated gases to the water, 
 which will depend on its freedom from soot and incrustation, and upon the 
 circulation of the water and the heated gases. 
 
 With bituminous coal the efficiency will largely depend upon the 
 thoroughness with which the combustion is effected in the furnace. 
 
 The efficiency with any kind of fuel will greatly depend upon the amount 
 of air supplied to the furnace in excess of that' required to support com- 
 bustion. With strong draught and thin fires this excess may be great, 
 causing a serious loss of economy. The subject is further discussed below. 
 
 Measurement of Heating-surface. The usual rule is to consider as 
 heating-surface all the surfaces that are surrounded by water on one side 
 and by flame or heated gases on the other, using the external instead of 
 the internal diameter of tubes, for greater convenience in calculation, 
 external diameters of boiler-tubes usually being made in even inches or 
 half inches. This method, however, is inaccurate, for the true heating- 
 surface of a tube is the side exposed to the hot gases, the inner surface in a 
 fire-tube boiler and the outer surface in a water-tube boiler. The re- 
 
888 
 
 THE STEAM-BOILER. 
 
 Distance to the passage of heat from the hot gases on one side of a tube or 
 plate to the water on the other consists almost entirely of the resistance to 
 the passage of the heat from the gases into the metal, the resistance of the 
 metal itself and that of the wetted surface being practically nothing. 
 See paper by C. W. Baker, Trans. A. S. M. E., vol. xix. 
 
 RULE for finding the heating-surface of vertical tubular boilers: Multiply 
 the circumference 9f the fire-box (in inches) by its height above the grate; 
 multiply the combined circumference of all the tubes by their length, and 
 to these two products add the area of the lower tube-sheet; from this sum 
 subtract the area of all the tubes, and divide by 144: the quotient is the 
 number of square feet of heating-surface. 
 
 RULE for finding the heating-surface of horizontal tubular boilers: Take 
 the dimensions in inches. Multiply two-thirds of the circumference of the 
 shell by its length; multiply the sum of the circumferences of all the tubes 
 by their common length; to the sum pi these products add two thirds of 
 the area of both tube-sheets; from this sum subtract twice the combined 
 area of all the tubes; divide the remainder by 144. to obtain the result in 
 square feet. 
 
 RULE for finding the square feet of heating-surface in tubes: Multiply 
 the number of tubes by the diameter of a tube in inches, by its length in 
 feet, and by 0.2618. 
 
 Horse-power, Builder's Rating. Heating-surface per Horse- 
 power. It is a general practice among builders to furnish about 10 
 square feet of heating-surface per horse-power, but as the practice is not 
 uniform, bids and contracts should always specify the amount of heating- 
 surface to be furnished. Not less than one-third square foot of grate-sur- 
 face should be furnished per horse-power with ordinary chimney draught, 
 not exceeding 0.3 in. of water column at the damper, for anthracite coal, 
 and for poor varieties of soft coal high in ash, with ordinary furnaces. A 
 smaller ratio of grate surface may be allowed for high grade soft coal and 
 for forced draught. 
 
 Horse-power of Marine and Locomotive Boilers. The term horse- 
 power is not generally used in connection with boilers in marine practice, 
 or with locomotives. The boilers are designed to suit the engines, and 
 are rated by extent of grate and heating-surface only. 
 
 Grate-surface. The amount of grate-surface required per horse- 
 power, and the proper ratio of heating-surface to grate-surface are ex- 
 tremely variable, depending chiefly upon the character of the coal and 
 upon the rate of draught. With good coal, low in ash, approximately 
 equal results may be obtained with large grate-surface and light draught 
 and with small grate-surface and strong draught, the total amount of coal 
 burned per hour being the same in both cases. With good bituminous 
 coal, like Pittsburgh, low in ash, the best results apparently are obtained 
 with strong, draught and high rates of combustion, provided the grate- 
 surfaces are cut down so that the total coal burned per hour is not too great 
 for the capacity of the heating-surface to absorb the heat produced. 
 
 With coals high in ash, especially if the ash is easily fusible, tending to 
 choke the grates, large grate-surface and a slow rate of combustion are 
 required, unless means, such as shaking grates, are provided to get rid of 
 the ash as fast as it is made. The amount of grate-surface required per " 
 horse-power under various conditions may be estimated as follows: 
 
 
 Si? 
 ^J. 
 . ScsT'eS 
 
 03 O .j m O 
 
 ^ ta ftO 
 
 Lbs. Coal 
 per H.P. 
 per hour. 
 
 Pounds of Coal burned per square 
 foot of Grate per hour. 
 
 8 
 
 10 
 
 12 
 
 15 
 
 20 | 25 
 
 30 | 35 | 40 
 
 Sq. Ft. Grate per H.P. 
 
 .09 
 .10 
 .10 
 .11 
 .12 
 .13 
 .14 
 .17 
 
 .25 
 
 Good coal and 
 boiler, 
 
 Fair coal or boiler, 
 
 Poor coal or boiler, 
 
 Lignite and poor 
 boiler, 
 
 )10 
 [ 9 
 ( 8.61 
 
 R 
 
 H 
 
 ( 6 - 9 
 
 M 
 
 {3.45 
 
 3.45 
 3.83 
 4. 
 4.31, 
 4.93 
 5. 
 5.75 
 6.9 
 
 10. 
 
 .43 
 .48 
 .50 
 .54 
 .62 
 .63 
 .72 
 .86 
 
 1.25 
 
 .35 
 
 .38 
 .40 
 .43 
 .49 
 .50 
 .58 
 .69 
 
 1.00 
 
 .28 
 .32 
 .33 
 .36 
 .41 
 .42 
 .48 
 .58 
 
 .83 
 
 .23 
 .25 
 .26 
 .29 
 .33 
 .34 
 .38 
 .46 
 
 .67 
 
 .17 
 .19 
 .20 
 .22 
 .24 
 .25 
 .29 
 .35 
 
 .50 
 
 .14 
 .15 
 .16 
 
 .17 
 .20 
 .20 
 .23 
 .28 
 
 .40 
 
 .11 
 .13 
 .13 
 .14 
 .17 
 .17 
 .19 
 .23 
 
 .33 
 
 .10 
 .11 
 .12 
 .13 
 .14 
 .15 
 .17 
 .22 
 
 .29 
 
PERFORMANCE OF BOILERS. 889 
 
 In designing a boiler for a given set of conditions, the grate-surface 
 should be made as liberal as possible, say sufficient for a rate of combus- 
 tion of 10 Ibs. per square foot of grate for anthracite, and 15 Ibs. per square 
 foot for bituminous coal, and in practice a portion of the grate-surface 
 may be bricked over if it is found that the draught, fuel, or other condi- 
 tions render it advisable. 
 
 Proportions of Areas of Flues and other Gas-passages. Rules 
 are usually given making the area of gas-passages bear a certain ratio to 
 the area of the grate-surface; thus a common rule for horizontal tubular 
 boilers is to make the area over the bridge wall 1/7 of the grate-surface, 
 the flue area 1/8, and the chimney area 1/9. 
 
 For average conditions with anthracite coal and moderate draught, say 
 a rate of combustion of 12 Ibs. coal per square foot of grate per hour, and a 
 ratio of heating to grate surface of 30 to 1, this rule is as good as any, but 
 it is evident that if the draught were increased so as to cause a rate of com- 
 bustion of 24 Ibs., requiring the grate-surface to be cut down to a ratio of 
 60 to 1, the areas of gas-passages should not be reduced in proportion. 
 The amount of coal burned per hour being the same under the changed 
 conditions, and there being no reason why the gases should travel at a 
 higher velocity, the actual areas of the passages should remain as before, 
 but the ratio of the area to the grate-surface would in that case be 
 doubled. 
 
 Mr. Barrus states that the highest efficiency with anthracite coal is 
 obtained when the tube area is 1/9 to 1/10 of the grate-surface, and with 
 bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of 
 combustion, such as 10 to 12 Ibs. per square foot of grate per hour, and 12 
 square feet of heating-surface allowed to the horse-power. 
 
 The tube area should be made large enough not to choke the draught 
 and so lessen the capacity of the boiler; if made too large the gases are apt 
 to select the passages of least resistance and escape from them at a high 
 velocity and high temperature. 
 
 This condition is very commonly found in horizontal tubular boilers 
 where the gases go chiefly through the upper rows of tubes; sometimes 
 also in vertical tubular boilers, where the gases are apt to pass most rapidly 
 through the tubes nearest to the center. It may to some extent be 
 remedied by placing retarders in those tubes in which the gases travel the 
 quickest. 
 
 Air-passages through Grate-bars. The usual practice is, air- 
 opening = 30% to 50% of area of the grate; the larger the better, to avoid 
 stoppage of the air-supply by clinker; but with coal free from clinker much 
 smaller air-space may be used without detriment. See paper by F. A. 
 Scheffler, Trans. A. S. M . E., vol. xv, p. 503. 
 
 Distance .from Dead Plate to Shell in Horizontal Tubular Boiler 
 Settings. Rules of the Department of Smoke Inspection, Chicago, 
 1912. 
 
 Diameter of shell, in 72 66 60 54 48 42 36 
 
 Dead plate to shell, in. . . 42 40 38 36 34 32 30 
 
 The department has required that all boilers be set higher than has 
 formerly been the practice in order to provide greater combustion 
 space and to allow the installation of proper furnaces. . 
 PERFORMANCE OF BOILERS. 
 
 The performance of a steam-boiler comprises both its capacity for gener- 
 ating steam and its economy of fuel. Capacity depends upon size, both of 
 grate-surface and of heating-surface, upon the kind of coal burned, upon the 
 draught, and also upon the economy. Economy of fuel depends upon the 
 completeness with which the coal is burned in the furnace, on the proper 
 regulation of the air-supply to the amount of coal burned, and upon the 
 thoroughness with which the boiler absorbs the heat generated in the 
 furnace. The absorption of heat depends on the extent of heating-sur- 
 face in relation to the amount of coal burned or of water evaporated, upon 
 the arrangement of the gas-passages, and upon the cleanness of the sur- 
 faces. The capacity of a boiler may increase with increase of economy 
 when this is due to more thorough combustion of the coal or to better regu- 
 lation of the air-supply, 9r it may increase at the expense of economy 
 when the increased capacity is due to overdriving, causing an increased 
 loss of heat in the chimney gases. The relation of capacity to economy 
 is therefore a complex one, depending on many variable conditions. 
 
890 THE STEAM-BOILER. 
 
 A formula expressing the relation between capacity, rate of driving, 
 or evaporation per square foot of heating-surface, to the economy, or 
 evaporation per pound of combustible is given on page 893. 
 
 Selecting the highest results obtained at different rates of driving with 
 anthracite coal in the Centennial tests (in 1876) and the highest results 
 with anthracite reported by Mr. Barrus in his book on Boiler Tests, the 
 author has plotted two curves showing the maximum results which may 
 be expected with anthracite coal, the first under exceptional conditions 
 such as obtained in the Centennial tests, and the second under the best 
 conditions of ordinary practice. (Trans. A. S. M. E., xviii, 354). 
 From these curves the following figures are obtained. 
 
 Lbs. water evaporated from and at, 212 per sq. ft. heating-surface 
 per hour: 
 
 1.6 1.7 2 2.6 3 3.5 4 4.5 5 6 7 8 
 Lbs. water evaporated from and at 212 per Ib. combustible: 
 Centennial... 11.8 11.9 12.0 12.1 12.05 12 11.85 11.7 11.5 10.85 9.8 8.5 
 
 Barrus 11.4 11.5 11.55 11.6 11.6 11.5 11.2 10.9 10.6 9.9 9.2 8.5 
 
 Avg. Cent'l 12.0 11.6 11.2 10.8 10.4 10.0 9.6 8.8 8.0 7.2 
 
 The figures in the last line are taken from a straight line drawn as nearly 
 as possible through the average of the plotting of all the Centennial tests. 
 The poorest results are far below these figures. It is evident that no for- 
 mula can be constructed that will express the relation of economy to rate oi 
 driving as well as do the three lines of figures given above. 
 
 'For semi-bituminous and bituminous coals the relation of economy tc 
 the rate of driving no doubt follows the same general law that it does with 
 anthracite, i.e., that beyond a rate of evaporation of 3 or 4 Ibs. per sq. ft. oi 
 heating-surface per hour there is a decrease of economy, but the figures 
 obtained in different tests will show a wider range between maximum and 
 average results on account of the fact that it is more difficult with bitumi- 
 nous than with anthracite coal to secure complete combustion in the 
 furnace. 
 
 The amount of the decrease in economy due to driving at rates exceeding 
 4 Ibs. of water evaporated per square foot of heating-surface per hour 
 differs greatly with different boilers, and with the same boiler it may diffei 
 with different settings and with different coal. The arrangement and size 
 of the gas-passages seem to have an important effect upon the relation oi 
 economy to rate of driving. 
 
 A comparison of results obtained from different types of boilers leads to 
 the general conclusion that the economy with which different types oi 
 boilers operate depends much more upon their proportions and the con- 
 ditions under which they work, than upon their type; and, moreover, 
 that when the proportions are correct, and when the conditions are favor- 
 able, the various types of boilers give substantially the same economic 
 result. 
 
 Conditions of Fuel Economy in Steam-boilers. 1. That the boiler 
 has sufficient heating surface to absorb from 75 to 80% of all the heat 
 generated by the fuel. 2. That this surface is so placed, and the gas pas- 
 sages so controlled by baffles, that the hot gases are forced to pass uni- 
 formly over the surface, not being short-circuited. 3. That the furnace is 
 of such a kind, and operated in such a manner, that the fuel is completely 
 burned in it, and that no unburned gases reach the heating surface of the 
 boiler. 4. That the fuel is burned with the minimum supply of air re- 
 quired to insure complete combustion, thereby avoiding the carrying of an 
 excessive quantity of heated air out of the chimney. 
 
 There are two indices of high economy. 1. High temperature, ap- 
 proaching 3000 F. in the furnace, combined with low temperature, below 
 600 F., in the flue. 2. Analysis of the flue gases showing between 4 ynd 
 8% of free oxygen. Unfortunately neither of these indices is available 
 to the ordinary fireman; he cannot distinguish by the eye any temperature 
 above 2000, and he cannot know whether or not an excessive amount oi 
 oxygen is passing through the fuel. The ordinary haphazard way of firing 
 therefore gives an average of about 10% lower economy than can be 
 obtained when the firing is controlled, as it is in many large plants, by re- 
 cording furnace pyrometers, or by continuous gas analysis, or by both- 
 Low CO2 in the flue gases may indicate either excessive air supply in the 
 furnace, or leaks of air into the setting, or deficient air supply with the 
 presence qf CO, and, therefore imperfect combustion. The latter, if exces- 
 
PERFORMANCE OF BOILERS. 891 
 
 sive, is indicated by low furnace temperature. The analysis for CO2 should 
 be made both of the gas sampled just beyond the furnace and of the gas 
 sampled at the flue. Diminished CO 2 in the latter indicates air-leakage. 
 
 Less than 4% of free oxygen in the gases is usually accompanied with 
 CO, and it therefore indicates imperfect combustion from deficient air, 
 supply. More than 8% means excessive air supply and corresponding 
 waste of heat. 
 
 Air Leakage or infiltration of air through the firebrick setting is a 
 common cause of poor economy. It may be detected by analysis as above 
 Stated, and should be prevented by stopping all visible cracks in the brick- 
 work, and by covering it with a coating impervious to air. 
 
 Autographic CO2 Recorders are used in many large boiler plants for 
 the continuous recording of the percentage of carbon dioxide in the gases. 
 When the percent age of CO 2 is between 12 and 16.it indicates good fur- 
 nace conditions, when below 12 the reverse. 
 
 Continuous Records are an important element in securing maximum 
 economy in modern boiler plants. They include records of coal and 
 water consumption, of draft at the furnace and the chimney, of the 
 analyses of the gases, of the flue temperature, and of the steam de- 
 livered. For description of steam flow meters and other recording 
 apparatus see Steam Boiler Economy. 2d edition. 
 
 Efficiency of a Steam-boiler. The efficiency of a boiler is the 
 percentage of the total heat generated by the combustion of the fuel 
 which is utilized in heating the water and in raising steam. With anthra- 
 cite coal the heating-value of the combustible portion is very nearly 
 14,800 B.T.U. per lb., equal to an evaporation from and at 212 of 14,800 
 * 970 = 15.26 Ibs. of water. A boiler which when tested with anthra- 
 cite coal shows an evaporation of 12 Ibs. of water per lb. of combustible, 
 has an efficiency of 12 -s- 15.26 = 78.6%, a figure which is approximated, 
 but scarcely ever quite reached, in the best practice. With bituminous 
 coal it is necessary to have a determination of its heating-power made 
 by a coal calorimeter before the efficiency of the boiler using it can be 
 determined, but a close estimate may be made from the chemical analysis 
 of the coal. (See Coal.) 
 
 The difference between the efficiency obtained by test and 100% is 
 the sum of the numerous wastes of heat, the chief of which is the necessary 
 loss due to the temperature of the chimney-gases. If we tyave an analysis 
 and a calorimetric determination of the heating-power of the coal (properly 
 sampled), and an average analysis of the chimney-gases, the amounts 
 of the several losses may be determined with approximate accuracy by 
 the method described below. 
 
 Data given: 
 
 1. ANALYSIS OF THE COAL. 2. ANALYSIS OF THE DRY CHIMNEY- 
 Cumberland Semi-bituminous. GASES, BY WEIGHT. 
 
 Carbon . 80.55 C. O. N. 
 
 Hydrogen 4.50 CO 2 = 13.6 = 3.71 9.89 
 
 Oxygen ... 2.70 CO = 0.2 = 0.09 0.11 
 
 Nitrogen 1.08 O = 11.2= 11.20 
 
 Moisture 2.92 N = 75.0=.. 75.00 
 
 Agh c 05 
 
 100.0 3.80 21.20 75.00 
 100.00 
 
 Heating-value of the coal by Dulong's formula, 14,243 heat-units. 
 The gases being collected over water, the moisture in them is not deter- 
 mined. 
 
 3. Ash and refuse as determined by boiler-test, 10.25, or 2% more than 
 that found by analysis, the difference representing carbon in the ashes 
 Obtained in the boiler-test. 
 
 4. Temperature of external atmosphere, 60 F. 
 
 5. Relative humidity of air, 60%, corresponding (see air tables) to 
 0.007 lb. of vapor in each lb. of air. 
 
 6. Temperature of chimney-gases, 560 F. 
 Calculated results: 
 
 The carbon in the chimney-gases being 3.8% of their weight, the total 
 weight of dry gases per lb. of carbon burned is 100 -*- 3.8 = 26.32 Ibs. 
 Since the carbon burned is 80.55 - 2 = 78.55% of the weight of the coal, 
 the weight of the dry gases per lb. of coal is 26.32 X 78.55 -f- 100 = 
 20.67 Ibs. 
 
892 THE STEAM-BOILER, 
 
 Each pound of coal furnishes to the dry chimney-gases 0.7855 lb. C, 
 and 0.0108 N, a total of 0.7963, say 0.80 lb. This subtracted from 
 20.67 Ibs. leaves 19.87 Ibs. as the quantity of dry air (not including 
 moisture) which enters the furnace per pound of coal, not counting the 
 air required to burn the available hydrogen, that is, the hydrogen 
 minus one-eighth of the oxygen chemically combined in the coal. Each 
 lb. of coal burned contained 0.045 lb. H, which requiras 0.045 X 8 = 
 0.36 lb. O for its combustion. Of this, 0.027 lb. is furnished by the coal 
 itself, leaving 0.333 lb. to come from the air. The quantity of air 
 needed to supply this oxygen air containing 23 % by weight of oxygen) 
 is 0.333 -r- 0.23 = 1.45 lb., which added to "the 19.87 Ibs. already found 
 gives 21.32 Ibs. as the quantity of dry air supplied to the furnace per 
 lb. of coal burned. 
 
 The air carried in as vapor is 0.0071 lb. for each lb. of dry air, or 21.3 
 X 0.0071 = 0.15 lb. for each lb. of coal. Each lb. of coaj contained 
 0.029 lb. of moisture, which was evaporated and carried into the 
 chimney-gases. The 0.045 lb. of H per lb. of coal when burned formed 
 0.045 X 9 = 0.405 lb. of H 2 O. 
 
 From the analysis of the chimney-gas it appears that 0.09 -^ 3.80 = 
 2.37% of the carbon in the coal, or 0.0237 X 0.7855 = 0.0186 lb. C 
 per lb. of coal, was burned to CO instead of to COz. 
 
 We now have the data for calculating the various losses of heat, as 
 follows, for each pound of coal burned: 
 
 Heat- Per cent of 
 units. Heat-value 
 
 of the Coal. 
 
 20.67 Ibs. dry gas X (560 - 60) X sp. heat 0.24 = 
 
 2480.4 
 
 17.41 
 
 0.15 lb. vapor in air X (560 - 60) X sp. ht. 0.46 --= 
 
 34.5 
 
 0.24 
 
 0.029 lb. moist, in coal heated from 60 to 212 = 
 
 4.4 
 
 0.03 
 
 0.029 lb. evap. from and at 212; 0.029 X 970 = 
 
 28.1 
 
 0.20 
 
 0.029 lb. steam (heated 212 to 560) X 348X 0.46 = 
 
 4.6 
 
 0.03 
 
 0.405 lb. H 2 O from H in coal X (152 + 970 + 
 
 
 
 348 X 0.46) 
 
 519.2 
 
 3.65 
 
 0.0186 lb. C burned to CO; loss by incomplete 
 
 
 
 combustion, 0.0186 X (14,6QO - 4450) 
 
 188.8 
 
 1.33 
 
 0.02 lb. carbon lost in ashes: 0.02 X 14,600 
 
 292.0 
 
 2.05 
 
 Radiation and unaccounted for, by difference = 
 
 676.1 
 
 4.75 
 
 4228.1 29.69 
 
 Utilized in making steam, equivalent evapora- 
 tion 10.37 Ibs. from and at 212 perlb. of coal = 10,014.9 70.31 
 
 14,243.0 100.00 
 
 The heat lost by radiation from the boiler and furnace is not easily 
 determined directly, especially if the boiler is enclosed in brickwork, or 
 is protected by non-conducting covering. It is customary to estimate 
 the heat lost by radiation by difference, that is, to charge radiation with 
 all the heat lost which is not otherwise accounted for. One method of 
 determining the loss by radiation is to block off a portion of the grate- 
 surface and build a small fire on the remainder, and drive this fire with 
 just enough draught to keep up the steam-pressure and supply the heat 
 lost by radiation without allowing any steam to be discharged, weighing 
 the coal consumed for this purpose during a test of several hours' dura- 
 tion. 
 
 Estimates of radiation by difference are apt to be greatly in error, as 
 in this difference are accumulated all the errors of the analyses of the 
 coal and of the gases. An average value of the heat lost by radiation 
 from a boiler set in brickwork is about 3 % . When several boilers are in 
 a battery and enclosed in a boiler-house the loss by radiation may be very 
 much less, since much of the heat radiated from the boiler is returned to 
 it in the air supplied to the furnace, which is taken from the boiler-room. 
 An important source of error in making a "heat balance" such as the 
 one above given, especially when highly bituminous coal is used, may be 
 due to the non-combustion of part of the hydrocarbon gases distilled from 
 the coal immediately after firing, when the temperature of the furnace may 
 be reduced below the point of ignition of the gases. Each pound of hydro- 
 gen which escapes burning is equivalent to a loss of heat in the furnace of 
 
PERFORMANCE OF BOILERS. 893 
 
 62,000 heat-units. Another source of error, especiallywith bituminous slack 
 coal nigii in moisture, is due to the formation of water-gas, CO + H, by the 
 decomposition of the water, and the consequent absorption of heat, this 
 water-gas escaping unburned on account of the choking of the air supply 
 when fine fresh coal is supplied to the fire. 
 
 In analyzing the chimney-gases by the usual method the percentages of 
 the constituent gases are obtained by volume instead of by weight. To 
 reduce percentages by volume to percentages by weight, multiply the per- 
 centage by volume of each gas by its specific gravity as compared with air, 
 and divide each product by the sum of the products. 
 
 Instead of using the percentages by weight of the gases, the percentage 
 by volume may be used directly to find the weight of gas per pound of 
 carbon by the formula given below. 
 
 If O, CO, CO2, and N represent the percentages by volume of oxygen, 
 carbonic oxide, carbonic acid, and nitrogen, respectively, in the gases of 
 combustion: 
 
 Lb. of air required to burn ) = 3 . 032 N ^ 
 one pound of carbon J CO2 + CO 
 
 N 
 Ratio Of total air to the theoretical requirement = j^_~ 3 782 (O - 1/2 CO)* 
 
 Lb. of air per pound \ __ j Lb. of air per pound ) v j Per cent of car- [ 
 of coal i t of carbon j A | bon in coal \ 
 
 11CO 2 +80+7(CO+N) 
 Lb. dry gas produced per pound of carbon = 37CO 4- CO) 
 
 Relation of Boiler Efficiency to the Rate of Driving, Air Supply, 
 etc. In the author's Steam Boiler Economy (p. 294) a formula is de- 
 veloped showing the efficiency that may be expected, when the com- 
 bustion of the coal is complete, under different conditions. The 
 formula is 
 
 Ba_ K- tcf 970 
 
 __ _ 
 
 ~E^~~ K (1 + RS/W) K (K - tcf) S ' 
 
 K = heating value per Ib. of combustible; Ea= actual evaporation from 
 and at 212 per Ib. of combustible; E p = possible evaporation = K * 
 970; t elevation of the temperature of the water in the boiler above 
 the atmospheric temperature; c specific heat of the chimney gases, 
 taken at 0.24;/ = weight of flue gases per Ib. of combustible; S square 
 feet of heating surface; W = pounds of water evaporated per hour; 
 W/S = rate of driving; R= radiation loss, in units of evaporation per 
 sq. ft. of heating-surface per hour; a is a coefficient found by experiment; 
 it may be called a coefficient of inefficiency of the boiler, and it depends 
 on and increases with the resistance to the passage of heat through the 
 metal, soot or scale on the metal, imperfect combustion, short-circuiting, 
 air leakage, or any other defective condition, not expressed in terms in 
 the formula, which may tend to lower the efficiency. Its value is between 
 200 and 400 when records of tests show high efficiency, and above 400 for 
 lower efficiencies. 
 
 The coefficient a is a criterion of performance of a boiler when all the 
 other terms of the formula are known as the results of a test. By trans- 
 position its value is 
 
 f K-tcf 1 . C*f* W 
 
 L970 (1 + RS/W) a \ ' (K- tcf) S 
 
 On the diagram below (Fig. 159), with abscissas representing rates of 
 driving and ordinates representing efficiencies are plotted curves showing 
 the relation of the efficiency to rate of driving for values of a= 100 to 
 400 and values of f from 20 to 35. together with a broken line showing 
 the maximum efficiencies obtained by six boilers at the Centennial Exhi- 
 bition, and other lines showing the poor results obtained from five other 
 boilers. The curves are also based on the following values, K = 14.800; 
 c = 0.24; = 300 (except one curve, t = 250); R = 0.1. 
 
 An inspection of the curves shows the following. 1. The maximum 
 Centennial results all lie below the curve / = 20, a = 200, by 2 to 4%, 
 but they follow the general direction of the curve. This curve may 
 
894 
 
 THE! SiEAM-B OILER. 
 
 therefore be taken as representing the maximum possible boiler per- 
 formance with anthracite coal, as the results obtained in 1876 have never 
 been exceeded with anthracite. 
 
 2. With/ = 20 and a = 200 the efficiency for maximum performance, 
 according to the curve, is a little less than 82% at 2 Ibs. evaporation pel 
 sq. ft. of heating-surface per hour, but it decreases very slowly at hignei 
 rates, so that it is 80% at 31/2 Ibs., and 76% at 5S/ 4 Ibs. 
 
 With a = 200 and / greater than 20, the efficiency has a lower maxi- 
 mum, reaches the maximum at a lower rate of driving, and falls off 
 rapidly as the rate increases, the more rapidly the higher the value of /. 
 showing excessive air supply to be a potent cause of low economy. 
 
 12 3 4 5 6 *7 
 
 Lbs. of Water EvaporatecLfrom and at 212 F. per s<j. ft. of; Heating Surface per Hour 
 FIG. 359. 
 
 3. An increase in the value of a from 200 to 400 with / = 20 is much 
 less detrimental to efficiency than an increase in / from 20 to 30. 
 
 In the diagram, Fig. T60, are plotted, together with the curve for/ = 20, 
 a= 200, t = 300, and K = 15,750, marked R = 0.1, a straight line, R = 0, 
 showing the theoretical maximum efficiency when there is no loss by 
 radiation, Jand the plottings of the results of two series of tests, one of a 
 Thornycroft boiler, with W/S from 1.24 to 8.5, and the other of a Babcock 
 & Wilcox marine b9iler with W/S from 5.18 to 13.67, together with the 
 maximum Centennial tests. The calculated value of a in all these tests 
 except one ranged from 191 to 454, the highest values being those show- 
 ing the largest departure from the curve R = 0.1. The one exception 
 is the Thornycroft test showing over 86% efficiency; this gives a value 
 of a = 57, which indicates an error in the test, as such a low value is far 
 below the lowest recorded in any other test. 
 
 In the second edition of Steam Boiler Economy (page 316), there is 
 developed a modification of the efficiency formula, so that it takes 
 
PERFORMANCE OF BOILERS. 
 
 895 
 
 account, in addition to the other variables, of hydrogen and moisture in 
 the coal and of incomplete combustion. It is 
 
 E a _ Ki - tcfi 970.4 fli c2/i 2 W_ 
 
 Wp~ K+(1RS/W) K~ K (Ki - tcfi) ~S" 
 The notation is the same as in the original formula except that Ki 
 
 K - 101.5 C 
 
 
 - 970 - 4 (- 09 
 
 ) in which c H and 
 
 pj- * 
 C_/O -p \-s\Jz 
 
 M are respectively the percentages of carbon, hydrogen and moisture 
 in the coal, and CO and CO 2 percentages by volume of the dry flue 
 gases, and f\ - /+ 0.28H + 0.03 M. 
 
 Computing the results of six series of boiler tests, 47 tests in all, 
 which have given high efficiencies, the value of i is found to average 
 about 200. Values from 1 60 to 240 may be obtained in duplicate tests 
 
 1 2 3 ' 4 5 6 7 8 9 10 11 12 13 14 
 Lbs. of Water Evaporated from and at 212 F per s<j. ft. o Heating Surface per Hour 
 
 PIG. 160. 
 
 in which all the conditions, as far as known, are identical, the dif- 
 ference between individual and average values being probably due to 
 errors. Values above 300, if not due to errors, represent defective per- 
 formance which may be due to short-circuiting or to unclean heating 
 surfaces. 
 
 Effect of Quality of Coal upon Efficiency. Calculations have been 
 made, using the formula given above, of the theoretical efficiencies 
 obtainable from five different kinds of coal and an average fuel oil, the 
 analyses of which are given below, on the assumption of complete com- 
 bustion with 20% excess air supply, fli = 200, t = 300, c = 0.24 aiid rates 
 of driving W/S from 1 to 14 Ib. The results are shown in the table. 
 ANALYSES OF FUELS. 
 
 Anthracite 
 Dry and Free 
 from Ash. 
 
 Semi-bitum. 
 
 Pittsburgh 
 Ash and 
 Sul. Free. 
 
 Illinois 
 
 Lignite. 
 
 California 
 Fuel Oil. 
 
 C 94.3 
 H 2.3 
 O 2.4 
 N 1.0 
 
 B.T.U. per 
 Ib. 15,000 
 
 Moist. 1.7 
 N.S.Ash 4.6 
 C 85.0 
 H 4.5 
 O 3.2 
 
 14,950 
 
 Moist. 2.0 
 C 83.0 
 H 5.5 
 8.0 
 
 N 1.0 
 
 14,908 
 
 Moist. 10.8 
 C 61.0 
 H 4.2 
 9.6 
 N 1.2 
 Ash, SI 3. 2 
 
 10,640 
 
 Moist.27.0 
 C 47.4 
 H 3.3 
 12.0 
 N 1.0 
 
 8,250 
 
 0.2 
 84.9 
 11.9 
 1.9 
 S 1.1 
 
 19,600 
 
 RELATION OF EFFICIENCY TO QUALITY OF COAL. 
 
 Rate of 
 Driving, W/S. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 Anthracite 
 
 81.85 
 80.41 
 79.78 
 78.28 
 75.83 
 78.78 
 
 84.56 
 82.96 
 82.30 
 80.59 
 77.76 
 81.61 
 
 Ef 
 84.71 
 83.00 
 82.34 
 80.44 
 77.51 
 82.01 
 
 ficienc 
 84.16 
 82.38 
 81.71 
 79.64 
 76.52 
 81.74 
 
 es 
 82.39 
 80.42 
 79.76 
 77.34 
 73.98 
 80.52 
 
 80.25 
 78.10 
 77.45 
 74.71 
 70.90 
 78.97 
 
 77.95 
 75.64 
 75.01 
 71.93 
 67.79 
 77.26 
 
 75.59 
 73.12 
 72.48 
 69.09 
 64.62 
 75.48 
 
 73.19 
 70.54 
 69.92 
 66.20 
 61.40 
 73.58 
 
 Semi-bitum 
 
 Pittsburgh bitum . . 
 Illinois 
 
 Lignite 
 
 Fuel Oil 
 
896 
 
 THE STEAM-BOILER. 
 
 Effect of Imperfect Combustion and Excess Air Supply. Taking 
 a Pittsburgh bituminous coal, having a composition, free from sul- 
 phur and ash, of 83 C, 5.5 H, 8 O, 1.5 N, and 2 Moisture, and a heating 
 value of 14,908 B.T.U. per Ib. fuel = 15,222 B.T.U. per Ib. combustible, 
 and assuming it to be burned with different quantities of air, as in the 
 table below, we may compute the weight of air supplied per pound of 
 fuel and per pound of carbon, and the analysis by volume of the gases, 
 giving results as follows: 
 
 Case. 
 
 Per 
 Cent 
 of C 
 Burned 
 to CO. 
 
 Per 
 Cent 
 Excess 
 Air. 
 
 Dry 
 Gas 
 per Ib. 
 Fuel 
 = / 
 
 Dry 
 Gas 
 per Ib. 
 Car- 
 bon. 
 
 Analysis of Dry Gas by Volume. 
 
 C0 2 . 
 
 CO. 
 
 O. 
 
 N. 
 
 (1) 
 
 
 
 
 
 
 5 
 
 10 
 20 
 
 
 20 
 50 
 100 
 
 20 
 
 
 
 11.60 
 13.83 
 17.16 
 22.72 
 11.36 
 13.23 
 11.12 
 10.65 
 
 13.98 
 16.66 
 20.67 
 27.37 
 13.69 
 15.93 
 13.40 
 12.83 
 
 18.45 
 15.30 
 12.18 
 9.10 
 17.85 
 15.18 
 17.21 
 15.88 
 
 
 
 
 
 0.94 
 0.80 
 1.92 
 3.97 
 
 
 3.56 
 7.09 
 10.57 
 
 3.12 
 
 
 
 81.55 
 81.14 
 80.73 
 80.33 
 81.21 
 80.90 
 80.87 
 80.15 
 
 (2). . 
 
 (3) 
 
 (4) . . 
 
 A 
 
 B 
 
 C 
 D 
 
 H 2 O in gases per Ib. fuel = 0.09 H + 0.01 M, in all cases = 0,515 Ib. 
 Case (1) is an ideal but not a practicable case, since it is not possible 
 in practice to burn all the C to CO2 without excess of air. Cases 
 (2), (3), (4), A and B are all within the range of ordinary practice 
 (which sometimes shows 200% or more excess air) and cases C and D 
 represent either the condition of too heavy firing and choked air supply, 
 or the condition existing for a minute or two after firing of fine moist 
 slack coal, which temporarily chokes the air supply and causes the for- 
 mation of a great volume of smoky gas. 
 
 Cases 2 and A represent the best possible practice, reached only 
 when all conditions are most favorable. 
 
 Applying the formula given above, we take K= 14,908; i = 300; 
 c = 0.24; R = 0.1; a\ = 200; /= the values given in the table; K\ and 
 J\ = values given by the formulae in the preceding paragraph, and 
 W/S different values from 0.5 to 14, and obtain the theoretical efficiencies 
 given below: 
 
 THEORETICAL EFFICIENCIES WITH PITTSBURGH COAL UNDER DIF- 
 FERENT CONDITIONS. 
 
 Case 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 ^ 
 
 B 
 
 c 
 
 D 
 
 Per cent C to CO. 
 
 
 
 
 
 
 
 
 
 5 
 
 5 
 
 10 
 
 20 
 
 Per cent excess air 
 
 
 
 20 
 
 50 
 
 100 
 
 
 
 20 
 
 
 
 
 
 W/S = 
 
 Efficiencies, Per Cent. 
 
 0.5 
 
 74.76 
 
 73.68 
 
 72.05 
 
 68.97 
 
 72.53 
 
 71.61 
 
 69.77 
 
 65.79 
 
 1 
 
 81.13 
 
 79.78 
 
 77.7.3 
 
 73.72 
 
 78,69 
 
 77.54 
 
 76.23 
 
 71.34 
 
 2 
 
 84.06 
 
 82.30 
 
 79.60 
 
 73.90 
 
 81.53 
 
 80.02 
 
 78.98 
 
 73.87 
 
 3 
 
 84,49 
 
 82.34 
 
 79.02 
 
 71.72 
 
 81.91 
 
 80.09 
 
 79.35 
 
 74.16 
 
 4 
 
 84.24 
 
 81.71 
 
 77.79 
 
 68.91 
 
 81.64 
 
 79.50 
 
 79.09 
 
 73.85 
 
 6 
 
 83.03 
 
 79.76 
 
 74.65 
 
 62.60 
 
 80.43 
 
 77.65 
 
 77.91 
 
 72.64 
 
 8 
 
 81.47 
 
 77.45 
 
 71.17 
 
 55.87 
 
 78.87 
 
 75.48 
 
 76.39 
 
 71.11 
 
 10 
 
 79.77 
 
 75.01 
 
 67.55 
 
 49.20 
 
 77.17 
 
 73.15 
 
 74.74 
 
 69.45 
 
 12 
 
 77.99 
 
 72.48 
 
 63.86 
 
 42.37 
 
 75.41 
 
 70.76 
 
 73.02 
 
 67.72 
 
 14 
 
 76.16 
 
 69.92 
 
 60.12 
 
 35.48 
 
 73.58 
 
 68.32 
 
 71.27 
 
 65.97 
 
 The figures in the table show the great falling off in efficiency at high 
 rates of driving when the air supply is excessive, and the necessity of 
 gas analysis (or of a CO2 or an oxygen indicator) if high efficiencies are 
 to be obtained at high rates of driving. 
 
 The Straight-line Formula for Efficiency . An examination of the 
 curves plotted from the table given above shows that when the rate of 
 driving is in excess of 3 Ib. per sq. ft. of heating surface per hour, and 
 the effect of the radiation loss is therefore of small importance, the 
 curves become approximately straight lines, the formula of which is 
 
PERFORMANCE OF BOILERS. 
 
 897 
 
 E = E max - C(W/S - 3), in which E is the efficiency at any rate of 
 driving above W/S = 3, E max is the efficiency when W/S = 3, and C 
 is a constant which depends on the quality of the coal and on the 
 furnace conditions. Taking from the above table the efficiencies at 
 W/S = 3 and W/S = 14 and calculating the value of C in the above 
 equation of a straight line between these points, we obtain the following 
 formulae for efficiency for the several cases named: 
 
 Cases. 
 
 Per Cent 
 C to CO 2 
 
 Per Cent 
 Excess Air. 
 
 Formula. 
 
 2 
 3 
 
 A 
 B 
 C 
 D 
 
 
 
 
 
 5 
 5 
 10 
 20 
 
 
 
 20 
 50 
 100 
 
 20 
 
 
 
 E 
 E 
 E 
 E 
 E 
 E 
 E 
 E 
 
 = 84.5 - 0.76(W/S 
 = 82.3 - \.\3(W/S 
 = 79.0 - \.72(W/S 
 = 71.7 - 3.39(W/S 
 = 81.9 - 0.76(W/S 
 = 80.1 - \.07(W/S 
 = 79.4 - 0.74(W/S 
 = 74.2 - 0.75(W/S 
 
 1 1 1 I 1 1 1 1 
 
 The efficiencies calculated by these formulae in every case in which 
 W/S is between 3 and 14 are slightly lower than those calculated from 
 the complex formula, but in no case is the difference as great as 1%. 
 It must be noted that all the efficiencies are theoretical 9nes, based on 
 the assumptions that there are no leaks of air into the boiler setting, no 
 loss due to unburned hydrocarbons, and no short circuiting or deposit 
 of soot on the tubes. In cases 1, A, C and D, in which there is no excess 
 air supply, there would in practice be probably some loss from unburned 
 hydrocarbons. 
 
 The straight line formulae obtained from the figures in the table 
 showing the relation of quality of coal to efficiency, assuming complete 
 combustion and 20% excess air supply, are 
 
 Anthracite E= 84.7- 1.05(1*75-3 
 
 Semi-bituminous E = 83 . - 1 . 13 ( W/S - 3 
 
 Pittsburgh bituminous E = 82 . 3 1 . 13 ( W/S - 3 
 
 Illinois bituminous J57 = 80 . 4 1 . 29(W/S - 3 
 
 Lignite E = 77.5- l.4Q(W/S- 3 
 
 Fuel oil E = 82.0 - 0.77(W/S - 3) 
 
 Efficiencies Obtained in Practice. In the best modern practice, 
 under the most favorable furnace conditions, the highest figures in 
 the above tables have almost been reached. A few tests with fuel oil 
 have shown figures slightly higher than those given above. The best 
 record yet obtained with coal is that of the ten best out of the sixteen 
 tests at the Delray station of the Detroit Edison Co., reported by D. 
 S. Jacobus in Trans. A. S. M. E., 1911. A straight line drawn through 
 j the plotting of these tests corresponds to the formula 
 
 =81- 1.33 (W/S- 3). 
 
 No account is taken in the above calculation of any loss due to un- 
 
 ! consumed hydrogen or hydrocarbons, nor of absorption of heat by 
 
 I decomposition of moisture in the coal by the reaction C + H2O = 2H 
 
 f CO. Serious losses may be due to these causes if the air supply is 
 
 ! deficient and the furnace temperature low from, the firing of a thick 
 
 j layer of fresh and moist coal, or if the combustible gases are chilled by 
 
 ? the surface of the boiler to a temperature below that of ignition. No 
 
 , account, either, has been taken of the loss due to moisture in the air, 
 
 which loss is usually not over 0.5%, but may reach 2% with excessive 
 
 air supply of high temperature and humidity. 
 
 The highest efficiencies are obtained with low rates of driving, say 
 3 to 4 Ib. evaporated from and at 212 per sq. ft. of heating surface 
 per hour. With higher rates of driving high efficiencies can be obtained 
 only when the air supply is carefully regulated according to the in- 
 dications of gas analyses, when the coal is nearly dry, when it is fed at 
 a regular rate by a mechanical stoker, and when the gases from the 
 coal are completely burned in a large fire-brick combustion chamber 
 before they are chilled by the comparatively cool surfaces of the boiler. 
 Modern practice tends to extremely large combustion chambers. 
 
 K~ U 
 
898 THE STEAM-BOILER* 
 
 With water-tube boilers of the Babcock & Wilcox type the tubes are 
 often placed 12 feet or more above the grate bars. In the Stirling 
 boilers of the Detroit Edison Co. the combustion chambers are over 
 25 ft. high. 
 
 The range of efficiency between the highest possible and that which 
 may be found in ordinary practice is very large. While 80 per cent 
 efficiency is possible with anthracite and semi-bituminous coals, and 
 with bituminous coals containing not over 3% moisture and not over 
 35% volatile matter in the combustible, it is difficult to get over 65% 
 with Illinois coals, high in volatile matter and in moisture, even with 
 mechanical stokers and with gas analysis. With ordinary hand- 
 firing the average efficiency is apt to be at least 15 % lower than these 
 figures. For numerous records of boiler tests under various conditions, 
 with a discussion of the results, see "Steam Boiler Economy," 2d 
 edition. 
 
 Maximum Boiler Efficiencies at Different Rates of Driving. The 
 ten best tests of the large boilers of the Detroit Edison Co., reported 
 by D. S. Jacobus in Jour. A. S. M. E., Nov., 1911, with rates of driving 
 from 3.24 to 7.29 Ib. water evaporated from and at 212 per sq. ft. of 
 heating surface per hour gave efficiencies which are represented (within 
 1%) by the formula E = 81 - 1.33 (R - 3), in which E is the efficiency 
 per cent and R the rate of driving. Eight tests of Babcock & Wilcox 
 marine boilers built for the U. S. war- vessels Cincinnati and Wyoming 
 (Indust. Eng'g, March, 1911), at rates of driving from 8.42 to 14.76 
 Ib. correspond within 3% with the .formula E = 80 - 1.43 (R - 3). 
 The Detroit tests were made with bituminous coal, low in moisture, 
 containing about 30% volatile matter, with mechanical stokers and 
 very large combustion chambers. The marine boiler tests were made . 
 with semi-bituminous coal containing about 20% volatile matter, with 
 hand-firing. These tests establish a world's record for boiler efficiencies. 
 The formulse give the following efficiencies for the several rates of 
 driving named, the first being used for rates of driving of 3 to 7 Ib. and 
 tfee second for rates of 7 to 15 Ib. 
 
 R = 3 4 5 6 7 8 10 12 14 15 
 
 E = 81 79.7 78.3 77.0 75.7 72.9 70.0 67.1 64.3 62.8 
 
 Some High Bates of Evaporation. Eng'g, May 9, 1884, p. 415. 
 
 Locomotive. Torpedo-boat. 
 
 Water evap. per sq. f t. H . S . per hour . 12 . 57 13 . 73 12 .54 20 . 74 
 Water evap. per Ib. fuel from and at 
 
 212 8.22 8.94 8.37 7.04- 
 
 Thermal units transf'd per sq. ft. of 
 
 H.S 12,142 13,263 12,113 20,034 
 
 Efficiency . , 0.586 0.637 0.542 0.468 
 
 It is doubtful if these figures were corrected for moisture in the steam. 
 BOILERS USING WASTE GASES. 
 
 Steam-boilers Fired with Waste Gases from Puddling and Heat- 
 ing-Furnaces. The Iron Age, April 6, 1893, contains a report of a 
 number of tests of steam-boilers utilizing the waste heat from puddling 
 and heating-furnaces in rolling-mills. The following principal data are 
 selected: in Nos. 1,2, and 4 the boiler is a Babcock & Wilcox water- tube 
 boiler, and in No. 3 it is a plain cylinder boiler, 42 in. diam. and 26 ft. 
 long. No. 4 boiler was connected with a heating-furnace, the others 
 with puddling furnaces. 
 
 No. 1 No. 2 No. 3 No. 4 
 
 Heating-surface, sq. ft 1026 1196 143 1380 
 
 Grate-surface, sq. ft 19 . 9 13 . 6 13 . 6 16 . 7 
 
 Ratio H.S. to G.S 52 '87.2 10.5 82.8 
 
 Water evap. per hour, Ibs 3358 2159 1812 3055 
 
 Water evap. per sq. ft. H.S. per hr. Ibs. .. 3.3 1.8 12. 7 2.2 
 Water evap. per Ib. coal from and at 212 5.9 6. 24 3. 76 6.31 
 Water evap. per Ib. combustible from 
 
 and at 212 7.20 4.31 8.34 
 
 In No. 2, 1.38 Ib. of iron were puddled per Ib. of coal. 
 
 In No. 3, 1.14 Ib. of iron were puddled per Ib. of coal. 
 
 No. 3 shows that an insufficient amount of heating-surface was 
 provided for the amount of waste heat available. 
 
EULES FOB CONDUCTING BOILER TESTS. 
 
 899 
 
 Water-tube Boilers using Blast-furnace Gases. D. S. Jacobus 
 (Trans. A. /. M. E., xvii, 50) reports a test of a water-tube boiler using 
 blast-furnace gas as fuel. The heating-surface was 2535 sq. ft. It 
 developed 328 H.P., or 5.01 Ib. of water from and at 212 per sq. ft. of 
 heating-surface per hour. Some of the principal data obtained were as 
 follows: Calorific value of 1 Ib. of the gas, 1413 B.T.U., including the 
 effect, of its initial temperature, which was 650 F. Amount of air used 
 to burn 1 Ib. of the gas = 0.9 Ib. Chimney draught, 11/3 in. of water. 
 Area of gas inlet 300 sq. in. ; of air inlet, 100 sq. in. Temperature of the 
 chimney gases, 775 F. Efficiency of the boiler calculated from the 
 temperatures and analyses of the gases at exit and entrance, 61 %. The 
 average analyses were as follows, hydrocarbons being included in the 
 nitrogen : 
 
 
 At Entrance. 
 
 At Exit. 
 
 At Entrance. 
 
 At Exit. 
 
 CO 2 . 
 
 10 69 
 
 26 37 
 
 7 08 
 
 18 64 
 
 o . ' : 
 
 11 
 
 3 05 
 
 10 
 
 2 96 
 
 CO 
 
 26.71 
 
 1.78 
 
 27 80 
 
 1 98 
 
 Nitrogen 
 C in CO 2 
 
 62.48 
 2.92 
 
 68.80 
 7 19 
 
 65.02 
 
 76.42 
 
 C in CO 
 
 11.45 
 
 0.76 
 
 
 
 Total C 
 
 14.37 
 
 7.95 
 
 
 
 RULES FOR CONDUCTING BOILER TESTS. 
 
 Object of an Evaporation Test. The principal object of an 
 evaporation test of a steam-boiler is to find out how many pounds 
 of water it evaporates under a certain set of conditions in a given 
 time and how many pounds of coal are required to effect this evapo- 
 ration. The test may be made for one or more of several purposes, ( 
 viz: 
 
 1. To determine whether or not the stipulations of a contract 
 between the seller and the buyer of a boiler (or of an appendage to 
 tl>9 boiler, such as a furnace) have been performed. 
 
 2. To determine the relative economy of different kinds of fuel, of 
 different kinds of furnaces, or of different methods of driving. 
 
 3. To determine whether or not the boilers, as ordinarily run under 
 the every-day conditions of the plant, are operated as economically 
 as they should be. 
 
 4. To determine, in case the boilers either fail to furnish easily the 
 quantity of steam desired, or else furnish it at what is supposed to be 
 an excessive cost for fuel, whether any additional boilers are needed 
 or whether some change in the conditions of running is a sufficient 
 remedy for the difficulty. 
 
 For the first of the above-named purposes, it is necessary that the 
 test should be made with every precaution to insure accuracy, such 
 as those described in the Code of the Committee of the American 
 Society of Mechanical Engineers,* which is printed in abridged form 
 below. 
 
 INSTRUCTIONS REGARDING TESTS IN GENERAL. 
 (Code of 1915). 
 
 OBJECT. 
 
 Ascertain the specific object of the test, and keep this in view not 
 only in the work of preparation, but also during the progress of the 
 test. 
 
 If questions of fulfillment of contract are involved, there should be 
 
 * Trans. A.S.M.E., 1915. Reprinted in pamphlet form by the 
 Society. The first committee of the society on boiler-tests reported 
 in 1885, the second in 1899. In 1909 a committee on Tests of Power 
 Plant Apparatus was appointed; its preliminary report was published 
 In 1912. and its final reoort in 1915. 
 
900 THE STEAM-BOILER. 
 
 a clear understanding between all the parties, preferably in writing, 
 as to the operating conditions which should obtain during the trial,' 
 the methods of testing to be followed, corrections to be made in case 
 the conditions actually existing during the test differ from those 
 specified, and all other matters about which dispute may arise, unless 
 these are already expressed in the contract itself, 
 
 PREPARATIONS. 
 
 Dimensions Measure the dimensions of the principal parts of 
 the apparatus to be tested, so far as they bear on the objects in view, 
 or determine them from working drawings. Notice the general 
 features of the apparatus, both exterior and interior, and make sketches, 
 if needed, to show unusual points of design. 
 
 The areas of the heating surfaces of boilers and superheaters to be 
 found are those of surfaces in contact with the fire or hot gases. 
 The submerged surfaces in boilers at the mean water level should 
 be considered as water-heating surfaces, and other surfaces which 
 are exposed to the gases as superheating surfaces. 
 
 Examination of Plant. Make a thorough examination of the phys- 
 ical condition of all parts of the plant or apparatus which concern 
 the object in view, and record the conditions found. 
 
 In boilers examine for leakage of tubes and riveted or other metal 
 joints. Note the condition of brick furnaces, grates and baffles. 
 Examine brick walls and cleaning doors for air leaks, either by shut- 
 ting the damper and observing the escaping smoke or by candle- 
 flame test. Determine the condition of heating surfaces with refer- 
 ence to exterior deposits of soot and interior deposits of mud or scale. 
 
 If the object .of the test is to determine the highest efficiency or 
 capacity obtainable, any physical defects, or defects of operation. 
 tending to make the result unfavorable should first be remedied; all 
 fouled parts being cleaned, and the whole put in first-class condition. 
 If, on the other hand, the object is t9 ascertain the performance under 
 existing conditions, no such preparation is either required or desired. 
 
 Precautions against Leakage. In steam tests make sure that there 
 is no leakage through blow-offs, drips, etc., or any steam or water con- 
 nections, which would in any way affect the results. All such con- 
 nections should be blanked off, or satisfactory assurance should be 
 obtained that there is leakage neither out nor in. 
 
 Apparatus and Instruments. See that the apparatus and instru- 
 ments are substantially reliable, and arrange them in such a way 
 as to obtain correct data. 
 
 Weighing Scales. For determining the weight of coal, oil, water, etc., 
 ordinary platform scales serve every purpose. Too much depend- 
 ence, however, should not be placed upon their reliability without 
 first calibrating them by the use of standard weights, and carefully 
 examining the knife-edges, bearing plates, and ring suspensions, 
 to see that they are all in good order. 
 
 For testing locomotives and some classes of marine boilers, wh< 
 room is lacking, sacks or bags are sometimes required to facilitate 
 the handling of coal, the sacks being weighed at the time of filling. 
 
 /* SAMPLING AND DRYING COAL. 
 
 Select a representative shovelful from each barrow-load as it is 
 drawn from the coal-pile or other source of supply, and store the 
 samples in a cool place in a covered metal receptacle. When all 
 the coal has thus been sampled, break up the lumps, thoroughly mix 
 the whole quantity, and finally reduce it by the process of repeated 
 shin 
 
 - -, - , ly 
 
 filled and preserved for subsequent determinations of moisture, calorific 
 value, and chemical composition. 
 
 When the sample lot of coal has been reduced by quartering to 
 
RULES FOR CONDUCTING BOILER TESTS. 901 
 
 8av 100 Ibs., a portion weighing say 15 to 20 Iba. should be with- 
 drawn for the purpose of immediate moisture determination. This 
 is placed in a shallow iron pan and dried on the hot iron boiler flue 
 for at least 12 hours, being weighed before and after drying on scales 
 reading to quarter ounces. 
 
 The moisture thus determined is approximately reliable for an- 
 thracite and semi-bituminous coals, but not for coals containing much 
 inherent moisture. For such coals, and for all absolutely reliable 
 determinations the method to be pursued is as follows: 
 Take one of the samples contained in the glass jars, and subject it 
 to a thorough air drying, by spreading it in a thin layer and exposing 
 it for several hours to the atmosphere of a warm room, weighing it 
 before and after, thereby determining the quantity of surface moisture 
 it contains. Then crush the whole of it by running it through an 
 ordinary coffee mill or other suitable crusher adjusted so as to pro- 
 duce somewhat coarse grains (less than Vie in.), thoroughly mix the 
 crushed sample, select from it a portion of from 10 to 50 grams 
 (say MOZ. to 2 oz.), weigh it in a balance which will easily show a 
 * variation as small as 1 part in 1000, and dry it for one hour in an 
 air or sand bath at a temperature between 240 and 280 F. Weigh 
 it and record the loss, then heat and weigh again until the minimum 
 weight has been reached. The difference between the original and 
 the minimum weight is the moisture in the air-dried coal. The 
 sum of the moisture thus found and that of the surface moisture 
 is the total moisture. 
 
 If a larger drying oven is available the moisture may be deter- 
 mined by heating one of the glass jars full of coal, the cover being 
 removed, at a temperature between 240 and 280 F. until it reaches 
 the minimum weight. 
 
 SAMPLING STEAM. 
 
 Construct a sampling pipe or nozzle made of y 2 -m. iron pipe and 
 insert it in the steam main at a point where, the entrained moisture 
 is likely to be most thoroughly mixed. The inner end of the pipe, 
 which should extend nearly across to the opposite side of the main, 
 should be closed and the interior portion perforated with not less 
 than twenty Vg-m. holes equally distributed from end to end and 
 preferably drilled in irregular or spiral rows, with the first hole not 
 less than half an inch from the wall of the pipe. 
 The sampling pipe should not be placed near a point where water may 
 
 pocket or where such water may affect the amount of moisture 
 
 contained in the sample. 
 
 RULES FOR CONDUCTING EVAPORATIVE TESTS OF BOILERS. 
 OBJECT AND PREPARATIONS. 
 
 Determine the object of the test, take the dimensions, note the 
 physical conditions, examine for leakages, install the testing appli- 
 ances, etc., as pointed out in the general instructions and make prep- 
 arations for the test accordingly. 
 
 Determine the character of fuel to be used. For tests of maximum 
 efficiency or capacity of the boiler to compare with other boilers, 
 the coal should be of some kind which is commercially regarded as 
 a standard for the locality where the test is made. 
 
 A coal selected for maximum efficiency and capacity tests should 
 be the best of its class, and especially free from slagging and unusual 
 clinker-forming impurities. 
 
 For guarantee and other tests with a specified coal containing not 
 more than a certain amount of ash and moisture, the coal selected 
 should not be higher in ash and in moisture than the stated amounts 
 
902 
 
 THE STEAM-BO1LEK. 
 
 because any increase is liable to reduce the efficiency and capacity 
 more than the equivalent proportion of such increase. 
 
 OPERATING CONDITIONS. 
 
 Determine what the operating conditions and method of firing 
 should be to conform to the object in view, and see that they prevail 
 throughout the trial, as nearly as possible. 
 
 DURATION. 
 
 The duration of tests to determine the efficiency of a hand-fired 
 boiler should be at least ten consecutive hours. In case the rate of 
 combustion is less than 25 Ibs. per sq. ft. of grate per hour the tests 
 should be continued for such a time as may be required to burn a total 
 of 250 Ibs. of coal per square foot of grate. Tests of longer^duration 
 than 10 hours are advisable in order to obtain greater accuracy. 
 
 In the case of a boiler using a mechanical stoker, the duration, 
 where practicable, should be at least 24 hours. If the stoker is of 
 a type that permits the quantity and condition of the fuel bed at 
 beginning and end of the test to be accurately estimated, the dura- 
 tion may be reduced to 10 hours, or such time as may be required 
 to bum the total of 250 Ibs. per square foot. 
 
 STARTING AND STOPPING. 
 
 The conditions regarding the temperature of the furnace and 
 boiler, the quantity and quality of the live coal and ash on the grates, 
 the water level, and the steam pressure, should be as nearly as pos- 
 sible the same at the end as at the beginning of the test. 
 
 To secure the desired equality of conditions with hand-fired boilers, 
 the following method should be employed: 
 
 The furnace being well heated by a preliminary run, burn the fire low* 
 and thoroughly clean it. leaving enough live coal spread evenly 
 over the grate (say 2 to 4 ins.),* to serve as a foundation for the 
 new fire. Note quickly the thickness of the coal bed as nearly as 
 it can be estimated or measured, also the water level, f the steam 
 pressure, and the time, and record the latter as the starting time. 
 Fresh coal should then be fired from that weighed for the test, the ash-pit 
 thoroughly cleaned and the regular work of the test proceeded with. 
 
 Before the end of the test the tire should again be burned low 
 and cleaned in such a manner as to leave the same amount of live 
 coal on the grate as at the start. When this condition is reached, 
 observe quickly the water level, t the steam pressure, and the 
 time, and record the latter as the stopping time. If the water 
 level is lower than at the beginning, a correction should be made 
 by computation, rather than by feeding additional water. Finally 
 remove the ashes and refuse from the ashpit. 
 
 In a plant containing several boilers where it is not practicable 
 to clean them simultaneously, the fires should be cleaned one after 
 the other as rapidly as may be, and each one after cleaning charged 
 with enough coal to maintain a thin fire in good working condition. 
 After the last fire is cleaned and in working condition, burn all 
 the fires low (say 4 to 6 ins.), note quickly the thickness of each, 
 also the water levels, steam pressure, and time, which last is taken 
 as the starting time. Likewise when the time arrives for closing 
 the test, the fires should be quickly cleaned one by one, and when 
 this work is completed they should all be burned low the same 
 as at the start and the various observations made as noted. 
 
 * 1 to 2 ins. for small anthracite coals. 
 
 t Do not blow down the water-glass column for at least one hour 
 before these readings are taken. An erroneous indication may other- 
 wise be caused by a change of temperature and density of the water 
 within the column and connecting pipe. 
 
RULES FOR CONDUCTING BOILER TESTS. 903 
 
 In the case of a large boiler having several furnace doors requiring 
 the fire to be cleaned in sections one after the other, the above 
 directions pertaining to starting and stopping in a plant of several 
 boilers may be followed. 
 To obtain the desired equality of conditions of the fire when a 
 
 mechanical stoker other than a chain grate is used, the procedure 
 
 should be modified where practicable as follows: 
 
 Regulate the coal feed so as to burn the fire to the low condition 
 required for cleaning. Shut off the coal-feeding mechanism and 
 fill the hoppers level full. Clean the ash or dump plate, note quickly 
 the depth and condition of the coal on the grate, the water level, 
 the steam pressure, and the time, and record the latter as the 
 starting time. Then start the coal-feeding mechanism, clean the 
 ashpit, and proceed with the regular work of the test. 
 
 When the time arrives for the close of the test, shut off the coal- 
 feeding mechanism, fill the hoppers and burn the fire to the same 
 low point as at the beginning. When this condition is reached, 
 note the water level, the steam pressure, and the time, and record 
 the latter as the stopping time. Finally clean the ash plate and 
 haul the ashes. 
 
 In the case of chain-grate stokers, the desired operating conditions 
 should be maintained for half an hour before starting a test and 
 for a like period before its close, the height of the stoker gate or 
 throat plate and the speed of the grate being the same during both 
 these periods. 
 
 EECOEDS. 
 
 Half-hourly readings of the instruments are usually sufficient. If 
 there are sudden and wide fluctuations, the readings in such cases 
 should be taken every fifteen minutes, and in some instances oftener. 
 The coal should be weighed and delivered to the firemen in portions 
 sufficient for one hour's run, thereby ascertaining the degree of 
 uniformity of firing. An ample supply of coal should be maintained 
 at all times, but the quantity on the floor at the end of each hour 
 should be as small as practicable, so that the same may be readily 
 estimated and deducted from the total weight. 
 
 The records should be such as to ascertain also the consumption 
 of feed-water each hour, and thereby determine the degree of uni- 
 formity of evaporation. 
 
 QUALITY OF STEAM. 
 
 If the boiler does not produce superheated steam the percentage 
 of moisture in the steam should be determined -by the use of a throttling 
 or separating calorimeter. If the boiler has superheating surface, 
 the temperature of the steam should be determined by the use of 
 a thermometer inserted in a thermometer well. 
 
 SAMPLING AND DRYING COAL. 
 
 During the progress of the test the coal should be regularly sampled 
 for the purpose of analysis and determination of moisture. 
 
 ASHES AND REFUSE. 
 
 The ashes and refuse withdrawn from the furnace and ash-pit 
 daring the progress of the test and at its close should be weighed so 
 far as possible in a dry state. If wet, the amount of moisture should 
 be ascertained and allowed for, a sample being taken and dried for 
 this purpose. This sample may serve also for analysis and the deter- 
 mination of unburned carbon. 
 
 CALORIFIC TESTS AND ANALYSES OF COAL. 
 
 The quality of the fuel should be determined by calorific tests and 
 Analyses of the coal sample above ivferml tO- 
 
904 THE STEAM-BOILER. 
 
 ANALYSES OF FLUE GASES. 
 
 For approximate determinations of the composition of the flue 
 gases, the Orsat apparatus, or some modification thereof, should 
 be employed. If momentary samples are obtained the analyses 
 should be made as frequently as possible, say every 15 to 30 minutes, 
 depending on the skill of the operator, noting at the time the sample 
 is drawn the furnace and firing conditions. If the sample drawn 
 is a continuous one, the intervals may be made longer. 
 
 SMOKE OBSERVATIONS. 
 
 In tests of bituminous coals requiring a determination of the amount 
 of smoke produced, observations should be made regularly through- 
 out the trial at intervals of five minutes (or if necessary every minute) , 
 noting at the same time the furnace and firing conditions. For tests 
 of furnaces, methods of firing, or smoke prevention devices, observations 
 every 10 or 15 seconds, continued during an hour, are advisable. 
 
 CALCULATION OF RESULTS. 
 
 (a) Corrections for Quality of Steam. When the percentage of moisture 
 is less than 2 per cent it is sufficient merely to deduct the percentage 
 from the weight of water fed, in which case the factor of correction 
 for quality is 
 
 _ % moisture 
 100 
 
 When the percentage is greater than 2 per cent, or if extreme accu- 
 racy is required, the factor of correction is 
 
 - 
 
 H-h 
 
 in which P is the proportion of moisture, H the total heat of 1 Ib. 
 of saturated steam, hi the heat in water at the temperature of satu- 
 rated steam, and h the heat in water at the feed temperature. 
 
 When the steam is superheated the factor of correction for quality 
 of steam is 
 
 H s -h 
 
 H-h 
 
 in which H s is the total heat of 1 Ib. of superheated steam of the 
 observed temperature and pressure. 
 
 (6) Correction for Live Sleam, if any, used for Aiding Combustion. The 
 quantity of steam or power, if any, used for producing blast, inject- 
 ing fuel, or aiding combustion should be determined and recorded in 
 the table of data and results. 
 
 (c) Equivalent Evaporation. The equivalent evaporation from and 
 at 212 is obtained by multiplying the weight of water evaporated, 
 corrected for moisture in steam, by the "factor of evaporation." 
 The latter equals 
 
 H-h 
 970.4 
 
 in which H and h are respectively the total heat of saturated steam 
 and of the feed-water entering the boiler. 
 
 The "factor of evaporation" and the "factor of correction for 
 quality of steam" may be combined into one expression in the 
 case of superheated steam as follows : 
 H s -h 
 "970.4* 
 
 (d) Efficiency. The "efficiency of boiler, furnace and grate" is the 
 relation between the heat absorbed per pound of coal fired, and 
 the calorific value of 1 Ib. of coal. 
 
 The "efficiency based on combustible" is the relation between 
 
 
RULES FOR CONDUCTING BOILER TESTS. 905 
 
 the heat absorbed per pound of combustible burned, and the 
 calorific value of 1 Ib. of combustible. This expression of efficiency 
 furnishes a means for comparing the results of different tests, 
 when the losses of unburned coal due to grates, cleanings, etc., are 
 eliminated. 
 
 The "combustible burned" is determined by subtracting from 
 the weight of coal supplied to the boiler, the moisture in the coal, 
 the weight of ash and unburned coal withdrawn from the furnace 
 and ash-pit, and the weight of dust, soot, and refuse, if any, with- 
 drawn from the tubes, flues, and combustion chambers, including ash 
 carried away in the gases,, if any, determined from the analyses of 
 coal and ash. The "combustible" used for determining the cal- 
 orific value is the weight of coal less the moisture and ash found by 
 analysis. 
 
 The "heat absorbed" per pound of coal or combustible is cal- 
 culated by multiplying the equivalent evaporation from and at 
 212 per pound of coal or combustible by 970.4. 
 
 CHART. 
 
 In trials having for an object the determination and exposition, 
 of the complete boiler performance, the entire log of readings and 
 data should be plotted on a chart and represented graphically. 
 
 Data and Results of Evaporative Test.* 
 
 1. Test of boiler located at 
 
 2. Number and kind of boilers 
 
 3. Kind of furnace 
 
 4. Grate surface (width length ) sq. ft. 
 
 5. Water heating surface sq. ft. 
 
 6. Superheating surface sq. ft. 
 
 7 Total heating surface sq. ft. 
 
 e. Distance from center of grate to nearest heating 
 
 surface ft. 
 
 DATE, DURATION, ETC. 
 
 8. Date 
 
 9. Duration hrs. 
 
 10. Kind and size of coal 
 
 AVERAGE PRESSURES, TEMPERATURES, ETC. 
 
 11. Steam pressure by gage Ibs. per sq. in. 
 
 12. Temperature of steam, if superheated degs. 
 
 13. Temperature of feed- water entering boiler degs. 
 
 14. Temperature of escaping gases leaving boiler degs. 
 
 15. Force of draft between damper and boiler ins. 
 
 c. Draft in furnace ins. 
 
 d. Draft or blast in ash-pit ins. 
 
 16. State of weather 
 
 a. Temperature of external air degs. 
 
 &. Temperature of air entering ash-pit degs. 
 
 c. Relative humidity of air entering ash-pit degs 
 
 17. 
 
 QUALITY OF STEAM 
 
 Percentage of moisture in steam or degrees of super- 
 heating % or degs. 
 
 18. Factor of correction for quality of steam % or degs. 
 
 TOTAL QUANTITIES. 
 
 19. Total weight of COP! as fired Ibs. 
 
 20. Percentage of moisture in coal as fired- per cent . 
 
 21. Total weight of dry coal fired Ibs. 
 
 * This table contains the principal items of the table in the Code 
 of 1915 of the A.S.M.E. Committee on Power Tests. 
 
906 
 
 THE STEAM-BOILER. 
 
 22. Total ash, clinkers, and refuse (dry) ................. Ibs. 
 
 23. Total combustible burned (.Item 21 Item 22) ....... Ibs. 
 
 24. Percentage pf ash and refuse in dry coal ............. per cent. 
 
 25. Total weight of water fed to boiler .................. Ibs. 
 
 26. Total water evaporated, corrected for quality of steam 
 
 (Item 25 X Item 18) ................................ Ibs. 
 
 27. Factor of evaporation based on temperature of water 
 
 entering boiler .................................. 
 
 28. Total equivalent evaporation from and at 212 (Item 
 
 26 X Item 27) .................................. Ibs. 
 
 HOURLY QUANTITIES AND RATES. 
 
 29. Dry coal per hour ................................. Ibs, 
 
 30. Dry coal per square foot of grate surface per hour ..... Ibs. 
 
 31. Water evaporated per hour, corrected for quality of 
 
 steam ........................................ . . Ibs. 
 
 32. Equivalent evaporation per hour from and at 212. . . . Ibs. 
 
 33. Equivalent evaporation per hour from and at 212 per 
 
 square foot of water-heating surface ............... Ibs. 
 
 CAPACITY. 
 
 34. Evaporation per hr. from and at 212 (same as Item 32) Ibs. 
 
 a. Boiler horse-power developed (Item 34 + 34 >/2) ... Bl. H.P. 
 
 35. Rated capacity per hour, from and at 212 ........... Ibs. 
 
 a. Rated boiler horse-p9wer ...................... Bl. H.P. 
 
 36. Percentage of rated capacity developed .............. per cent. 
 
 ECONOMY. 
 
 37. Water fed per pound of coal as fired (Item 25 -5- Item 19) Ibs. 
 
 38. Water evaporated per pound of dry coal (Item 26 -5- 
 
 Item 21) ........ ............................... Ibs. 
 
 39. Equivalent evaporation from and at 212 per pound of 
 
 coal as fired (Item 28 -j- Item 19) ................. Ibs. 
 
 40. Equivalent evaporation from and at 212 per pound of 
 
 dry coal (Item 28 -f- Item 21) ..................... Ibs. 
 
 41. Equivalent evaporation from and at 212 per pound of 
 
 combustible (Item 28 -* Item 23) .................. Ibs. 
 
 EFFICIENCY. 
 
 42. Calorific value of 1 Ib. of dry coal by calorimeter ...... B.T.U. 
 
 43. Calorific value of 1 Ib. of combustible by calorimeter. . B.T.U. 
 
 44. Efficiency of boiler, furnace and grate ................ per cent. 
 
 Item 40X970. 4 
 ~~Item 42 
 
 45. Efficiency based on combustible ...................... per cent. 
 
 ^ Item 41X970. 4 
 Item 43 
 
 COST OF EVAPORATION. 
 
 46. Cost of coal per ton of . . . .Ibs. delivered in boiler room, dollars. 
 
 47. Cost of coal required for evaporating 1000 Ibs. of water 
 
 under observed conditions ........................ dollars. 
 
 48. Cost of coal required for evaporating 1000 Ibs. of water 
 
 from and at 212 ...... . ......................... dollars. 
 
 SMOKE DATA. 
 
 49. Percentage of smoke as observed .................... per cent. 
 
 FIRING DATA. 
 
 50. Kind of firing, whether spreading, alternate, or coking 
 
 a. Average interval between times of leveling or 
 
 breaking up ................................ min. 
 
EXILES FOR CONDUCTING BOILER TESTS. 
 
 ANALYSES AND HEAT BALANCE. 
 
 907 
 
 51. Analysis of dry gases by volume. 
 
 a. Carbon dioxide (COa) per cent. 
 
 b. Oxygen (O) per cent. 
 
 c. Carbon monoxide (CO) per cent. 
 
 d. Hydrogen and hydrocarbons per cent. 
 
 e. Nitrogen, by difference (N). per cent. 
 
 As Fired. 
 
 Dry Coal. 
 
 Combustible. 
 
 52. Proximate analysis of coal 
 
 a. Moisture 
 
 b. Volatile Matter 
 
 c. Fixed carbon 
 
 d. Ash 
 
 100% 100% 100% 
 
 e. Sulphur, separately determined, referred to dry coal . per cent. 
 
 53. Ultimate analysis of dry coal. 
 
 a. Carbon (C) per cent. 
 
 b. Hydrogen (H) per cent. 
 
 c. Oxygen (O) per cent. 
 
 d. Nitrogen (N) per cent. 
 
 e. Sulphur <S) per cent. 
 
 /. Ash per cent. 
 
 54. Analysis of ash and refuse, etc 
 
 55. Heat balance, based on dry coal and com- 
 
 bustible. 
 
 a. Heat absorbed by the boiler (Item 40 
 
 or 41 X 970.4) : 
 
 b. Loss due to evaporation of moisture 
 
 in coal 
 
 C. Loss due to heat carried away by 
 steam formed by the burning of 
 hydrogen 
 
 d. Loss due to heat carried away in the 
 
 dry flue gases 
 
 e. Loss due to carbon monoxide ... 
 
 /. Loss due to combustible in ash and 
 
 refuse 
 
 g. Loss due to heating moisture in air. 
 h. Loss due to unconsumed hydrogen 
 
 and hydrocarbons, to radiation, 
 
 and unaccounted for 
 
 i. Total calorific value of 1 Ib. of dr; 
 
 coal or combustible. (Items 4: 
 
 and 43) 
 
 Dry Coal. 
 
 B.T.U. 
 
 Per cent. 
 
 100 
 
 If it is desired that the heat balance be based on coal "as fired," or 
 on combustible burned, the items in the first column are multiplied by 
 ( 100 -Item 20) -^- 100 for coal as fired or by 100 -T- (100 - Item 55 /, 
 per cent) for combustible. 
 
 PRINCIPAL DATA AND RESULTS OF BOILER TEST. 
 
 1. Grate surface (width length ) , sq. ft. 
 
 2. Total heating surface sq. ft. 
 
 3. Date 
 
 4. Duration hra. 
 
 5. Kind and size of coal 
 
908 THE STEAM-BOILER. 
 
 6. Steam pressure by gage. . ~. Ibs. per sq. in. 
 
 7. Temperature of feed water entering boiler degs. 
 
 8. Percentage of nioisture in steam or number of degrees 
 
 of superheating % or deg. 
 
 9. Percentage of moisture in coal per cent. 
 
 10. Dry coal consumed per hour Ibs. 
 
 11. Dry coal consumed per square foot of grate surface per 
 
 hour Ibs. 
 
 12. Equivalent evaporation per hour from and at 212 .... Ibs. 
 
 13. Equivalent evaporation per hour from and at 212 per 
 
 square foot of heating surface Ibs. 
 
 14. Rated capacity per hour, from and at 212 Ibs. 
 
 15. Percentage of rated capacity developed per cent 
 
 16. Equivalent evaporation from and at 212 per pound 
 
 of dry coal Ibs. 
 
 17. Equivalent evaporation from and at 212 per pound 
 
 of combustible Ibs. 
 
 18. Calorific value of 1 Ib. of dry coal by calorimeter B.T.U. 
 
 19. Calorific value of 1 Ib. of combustible by calorimeter. . B.T.U. 
 
 20. Efficiency of boiler, furnace and grate per cent. 
 
 21. Efficiency based on combustible per cent. 
 
 FACTORS OF EVAPORATION. 
 
 The figures in the table on the next four pages are calculated from the 
 formula F =(# h) * 970.4, in which H is the total heat above 32 of 
 1 Ib. of steam of the observed pressure, h the total heat above 32 of the 
 feed-water, and 970.4 the heat of vaporization, or latent heat, of steam at 
 212 F. The values of these total heats and of the latent heat are those 
 given in Marks and Davis's steam tables. 
 
 The factors are given for every 3 of feed -water temperature between 
 32 and 212, and for every 5 or 10 Ibs. steam pressure within the ordinary 
 working limits of pressure. Intermediate values correct to the third 
 decimal place may easily be found by interpolation. 
 
 The factors in the table are for dry saturated steam only. 
 
 STRENGTH OF STEAM-BOILERS. VARIOUS RULES FOR 
 CONSTRUCTION. 
 
 There is a great lack of uniformity in the rules prescribed by different 
 writers and by legislation governing the construction of steam-boilers. 
 In the United States, boilers for merchant vessels must be constructed 
 according to the rules and regulations prescribed by the Board of Super- 
 vising Inspectors of Steam Vessels; in the U. S. Navy, according to rules 
 of the Navy Department, and in some cases according to special acts of 
 Congress. On land, in some States, such as Massachusetts and Ohio, 
 and in some cities in other States, the construction of boilers is governed 
 by local laws; but in many places there are no laws upon the subject, 
 and boilers are constructed according to the idea of individual en- 
 gineers and boiler-makers. In recent years, however, there has been a 
 great improvement in this matter. The wide publication of the 
 Massachusetts boiler rules, the activity of the American Boiler Manu- 
 facturers' Association, of the American Society for Testing Materials, 
 and the work of a committee of the American Society of Mechanical 
 Engineers, which completed its "Boiler Code" in 1915 (issued in pam- 
 
 hlet form by the Society), have all tended to bring about a great 
 egree of uniformity in the materials and the methods of boiler con- 
 struction. The matter on the following pages consists chiefly of ex- 
 tracts from the Massachusetts rules and the A. S. M. E. Boiler Code, 
 and is condensed from a fuller treatment of the subject in the second 
 edition of the author's " Steam Boiler Economy." 
 
 Materials Used in Boilers. For the shells, tubes, rivets and braces 
 the material now in almost universal use is a special kind of soft opeii- 
 hearth steel, low in sulphur and phosphorus and of a tensile strength 
 not exceeding 65,000 Ib. per sq. in. for shell plates and not exceeding 
 55,000 Ib. per sq. in. for rivets. 
 
 Cast iron is used for fire-doors,, grate-bars, manhole and handhole 
 
 (Continued on p. 913.) 
 
FACTOES OF EVAPORATION. 
 
 909 
 
 Lbs 
 Gauge press. .0.3 
 Abs. press. ... 15. 
 
 10.3 
 25. 
 
 20.3 
 35. 
 
 30.3 
 45. 
 
 40.3 
 55. 
 
 50.3 
 65. 
 
 60.3 
 75. 
 
 70.3 
 85. 
 
 80.3 
 95. 
 
 85.3 
 100 
 
 Feed 
 water. 
 
 Factors of Evaporation. 
 
 212 F. 
 
 1.0003 
 
 1.0103 
 
 1.0169 
 
 1.0218 
 
 1 .0258 
 
 1 .0290 
 
 1.0316 
 
 1 .0340 
 
 1 .0361 
 
 1.0370 
 
 209 
 
 34 
 
 34 
 
 1.0200 
 
 50 
 
 89 
 
 1.0321 
 
 47 
 
 71 
 
 92 
 
 1.0401 
 
 206 
 
 65 
 
 65 
 
 31 
 
 81 
 
 1 .032^ 
 
 52 
 
 79 
 
 1.0402 
 
 I .0423 
 
 32 
 
 203 
 
 % 
 
 96 
 
 62 
 
 1.0312 
 
 51 
 
 83 
 
 1.0410 
 
 33 
 
 54 
 
 63 
 
 200 
 
 1.0127 
 
 I .0227 
 
 93 
 
 43 
 
 82 
 
 1.0414 
 
 41 
 
 64 
 
 85 
 
 94 
 
 197 
 
 58 
 
 58 
 
 1 .0324 
 
 74 
 
 1.0413 
 
 45 
 
 72 
 
 95 
 
 1.0516 
 
 1 .0525 
 
 194 
 
 89 
 
 89 
 
 55 
 
 1.0405 
 
 44 
 
 76 
 
 1 0503 
 
 1.0526 
 
 47 
 
 56 
 
 191 
 
 1 .0220 
 
 1 .0320 
 
 86 
 
 36 
 
 75 
 
 1 .0507 
 
 34 
 
 57 
 
 78 
 
 87 
 
 188 
 
 51 
 
 51 
 
 .0417 
 
 67 
 
 1.0506 
 
 38 
 
 65 
 
 88 
 
 1.0609 
 
 1.0618 
 
 185 
 
 82 
 
 82 
 
 48 
 
 98 
 
 37 
 
 69 
 
 96 
 
 1.0619 
 
 40 
 
 49 
 
 182 
 
 1.0313 
 
 1.0413 
 
 79 
 
 1 .0529 
 
 68 
 
 1 .0600 
 
 1 .0627 
 
 50 
 
 71 
 
 80 
 
 179 
 
 44 
 
 44 
 
 .0510 
 
 60 
 
 99 
 
 31 
 
 58 
 
 81 
 
 1 .0702 
 
 1.0711 
 
 176 
 
 75 
 
 75 
 
 41 
 
 91 
 
 1.0630 
 
 62 
 
 89 
 
 1.0712 
 
 33 
 
 42 
 
 173 
 
 1.0406 
 
 1.0506 
 
 72 
 
 1 .0622 
 
 61 
 
 93 
 
 1 .0720 
 
 43 
 
 64 
 
 73 
 
 170 
 
 37 
 
 37 
 
 1.0603 
 
 53 
 
 . 92 
 
 1.0724 
 
 51 
 
 74 
 
 95 
 
 1 .0804 
 
 167 
 
 68 
 
 63 
 
 34 
 
 84 
 
 1.0723 
 
 55 
 
 82 
 
 .0805 
 
 1.0826 
 
 35 
 
 164 
 
 99 
 
 99 
 
 65 
 
 1.0715 
 
 54 
 
 86 
 
 1.0812 
 
 36 
 
 57 
 
 66 
 
 161 
 
 1 .0530 
 
 1.0630 
 
 96 
 
 45 
 
 85 
 
 1.0817 
 
 43 
 
 67 
 
 88 
 
 97 
 
 158 
 
 61 
 
 61 
 
 1 .0727 
 
 76 
 
 1.0816 
 
 47 
 
 74 
 
 98 
 
 1.0919 
 
 1 .0928 
 
 155 
 
 92 
 
 92 
 
 58 
 
 1.0807 
 
 46 
 
 78 
 
 1.0905 
 
 1 .0929 
 
 50 
 
 59 
 
 152 
 
 1 .0623 
 
 1.0723 
 
 89 
 
 38 
 
 77 
 
 1.0909 
 
 36 
 
 60 
 
 80 
 
 90 
 
 149 
 
 54 
 
 54 
 
 .0820 
 
 69 
 
 1.0908 
 
 40 
 
 67 
 
 91 
 
 1.1011 
 
 1.1021 
 
 146 
 
 85 
 
 85 
 
 51 
 
 1.0900 
 
 39 
 
 71 
 
 98 
 
 1.1022 
 
 42 
 
 52 
 
 143 
 
 1.0715 
 
 1.0815 
 
 81 
 
 31 
 
 70 
 
 1.1002 
 
 1.1029 
 
 52 
 
 73 
 
 82 
 
 140 
 
 46 
 
 46 
 
 .0912 
 
 62 
 
 1.1001 
 
 33 
 
 60 
 
 83 
 
 1.1104 
 
 1.1113 
 
 137 
 
 77 
 
 77 
 
 43 
 
 93 
 
 32 
 
 64 
 
 91 
 
 1.1114 
 
 35 
 
 44 
 
 134 
 
 1.0808 
 
 1.0908 
 
 74 
 
 1.1023 
 
 63 
 
 95 
 
 1.1121 
 
 45 
 
 66 
 
 75 
 
 131 
 
 39 
 
 39 
 
 1.1005 
 
 54 
 
 93 
 
 1.1125 
 
 52 
 
 76 
 
 97 
 
 1.1206 
 
 128 
 
 70 
 
 70 
 
 36 
 
 85 
 
 1.1124 
 
 56 
 
 83 
 
 1.1207 
 
 1.1227 
 
 37 
 
 125 
 
 1.0901 
 
 1.1001 
 
 67 
 
 1.1116 
 
 55 
 
 87 
 
 1.1214 
 
 38 
 
 58 
 
 68 
 
 122 
 
 31 
 
 31 
 
 97 
 
 47 
 
 86 
 
 1.1218 
 
 45 
 
 69 
 
 89 
 
 98 
 
 119 
 
 62 
 
 62 
 
 1.1128 
 
 78 
 
 1.1217 
 
 49 
 
 76 
 
 99 
 
 1.1320 
 
 1.1329 
 
 116 
 
 93 
 
 93 
 
 59 
 
 .1209 
 
 48 
 
 80 
 
 1 . 1306 
 
 1.1330 
 
 51 
 
 60 
 
 113 
 
 1.1024 
 
 1.1124 
 
 90 
 
 39 
 
 79 
 
 1.1310 
 
 37 
 
 61 
 
 82 
 
 91 
 
 110 
 
 55 
 
 55 
 
 .1221 
 
 70 
 
 .1309 
 
 41 
 
 68 
 
 92 
 
 1.1412 
 
 1.1422 
 
 107 
 
 86 
 
 86 
 
 52 
 
 1.1301 
 
 40 
 
 72 
 
 99 
 
 1.1423 
 
 43 
 
 53 
 
 104 
 
 1.1116 
 
 1.1216 
 
 82 
 
 32 
 
 71 
 
 1.1403 
 
 1.1430 
 
 53 
 
 74 
 
 83 
 
 101 
 
 47 
 
 47 
 
 1.1313 
 
 63 
 
 1.1402 
 
 34 
 
 61 
 
 84 
 
 1.1505 
 
 1.1514 
 
 98 
 
 78 
 
 78 
 
 44 
 
 93 
 
 33 
 
 65 
 
 91 
 
 1.1515 
 
 36 
 
 45 
 
 95 
 
 1 . 1209 
 
 1.1309 
 
 75 
 
 1.1424 
 
 63 
 
 95 
 
 .1522 
 
 46 
 
 66 
 
 76 
 
 92 
 
 40 
 
 40 
 
 1.1406 
 
 55 
 
 94 
 
 1.1526 
 
 53 
 
 77 
 
 97 
 
 1.1607 
 
 89 
 
 71 
 
 71 
 
 37 
 
 86 
 
 .1525 
 
 57 
 
 84 
 
 .1608 
 
 .1628 
 
 37 
 
 86 
 
 1.1301 
 
 1.1401 
 
 67 
 
 .1518 
 
 56 
 
 88 
 
 .1615 
 
 38 
 
 59 
 
 68 
 
 83 
 
 32 
 
 32 
 
 98 
 
 48 
 
 87 
 
 1.1619 
 
 46 
 
 69 
 
 90 
 
 99 
 
 80 
 
 63 
 
 63 
 
 .1529 
 
 78 
 
 1.1618 
 
 50 
 
 76 
 
 1.1700 
 
 1.1721 
 
 1.1730 
 
 77 
 
 94 
 
 94 
 
 60 
 
 1.1609 
 
 48 
 
 80 
 
 1.1707 
 
 31 
 
 51 
 
 61 
 
 74 
 
 1.1425 
 
 1.1525 
 
 91 
 
 40 
 
 79 
 
 1.1711 
 
 38 
 
 62 
 
 82 
 
 92 
 
 71 
 
 55 
 
 55 
 
 1.1621 
 
 71 
 
 1.1710 
 
 42 
 
 69 
 
 92 
 
 1.1813 
 
 .1822 
 
 68 
 
 86 
 
 86 
 
 52 
 
 1.1702 
 
 41 
 
 73 
 
 1.1800 
 
 1.1823 
 
 44 
 
 53 
 
 65 
 
 1.1517 
 
 1.1617 
 
 83 
 
 33 
 
 72 
 
 1.1804 
 
 30 
 
 54 
 
 75 
 
 84 
 
 62 
 
 48 
 
 48 
 
 1.1714 
 
 63 
 
 1.1803 
 
 35 
 
 61 
 
 85 
 
 .1906 
 
 .1915 
 
 59 
 
 79 
 
 79 45 
 
 94 
 
 33 
 
 65 
 
 92 
 
 1.1916 
 
 37 
 
 46 
 
 56 
 
 1.1610 
 
 1.17IO| 76 
 
 1.1825 
 
 64 
 
 96 
 
 .1923 
 
 47 
 
 67 
 
 77 
 
 53 
 
 41 
 
 41 
 
 1.1807 
 
 56 
 
 95 
 
 1.1927 
 
 54 
 
 78 
 
 98 
 
 1.2008 
 
 50 
 
 72 
 
 72 
 
 38 
 
 87 
 
 1.1926 
 
 58 
 
 85 
 
 .2009 
 
 1 .2029 
 
 39 
 
 47 
 
 1.1703 
 
 1.1803 
 
 69 
 
 1.1918 
 
 57 
 
 89 
 
 .2016 
 
 40 
 
 60 
 
 70 
 
 44 
 
 34 
 
 34 
 
 .1900 
 
 49 
 
 88 
 
 1.2020 
 
 47 
 
 71 
 
 91 
 
 1.2101 
 
 41 
 
 65 
 
 65 
 
 31 
 
 80 
 
 .2019 
 
 51 
 
 78 
 
 .2102 
 
 1.2122 
 
 32 
 
 38 
 
 96 
 
 96 
 
 62 
 
 1.2011 
 
 50 
 
 82 
 
 1.2109 
 
 33 
 
 53 
 
 63 
 
 35 
 
 1.1827 
 
 1.1927 
 
 93 
 
 42 
 
 81 
 
 1.2113 
 
 40 
 
 64 
 
 84 
 
 94 
 
 32 
 
 58 
 
 58 
 
 1.2024 
 
 73 
 
 1.2113 
 
 44 
 
 71 
 
 95 
 
 1.2216 
 
 1.2225 
 
THE STEAM-BOILER. 
 
 Lbs. 
 Gauge press. 90.3 
 Abs. press. . 105. 
 
 95.3 
 110. 
 
 100.3 
 115. 
 
 105.3 
 120. 
 
 110.3 
 125. 
 
 115.3 
 130. 
 
 120.3 
 135. 
 
 125.3 
 140. 
 
 130.3 
 145. , 
 
 135.3 
 150. 
 
 140 3 
 155. 
 
 Feed 
 water. 
 
 Factors of Evaporation. 
 
 212 F. 
 
 1.0379 
 
 1.0387 
 
 1 .0396 
 
 1.0404 
 
 1.0411 
 
 1.0418 
 
 1 .0425 
 
 1.0431 
 
 1.0437 
 
 1.0443 
 
 1 . 0449 
 
 209 
 
 1.0410 
 
 1.0419 
 
 1 .0427 
 
 35 
 
 42 
 
 49 
 
 56 
 
 62 
 
 68 
 
 74 
 
 80 
 
 206 
 
 41 
 
 50 
 
 58 
 
 66 
 
 73 
 
 81 
 
 87 
 
 93 
 
 99 
 
 1.0505 
 
 1.0511 
 
 203 
 
 72 
 
 81 
 
 89 
 
 97 
 
 1.0504 
 
 1.0512 
 
 1.0518 
 
 1.0524 
 
 1.0530 
 
 36 
 
 43 
 
 200 
 
 1.0504 
 
 1.0512 
 
 1 .0520 
 
 1 .0528 
 
 35 
 
 43 
 
 49 
 
 55 
 
 61 
 
 67 
 
 74 
 
 197 
 
 35 
 
 43 
 
 51 
 
 59 
 
 66 
 
 74 
 
 80 
 
 86 
 
 92 
 
 98 
 
 1.0605 
 
 194 
 
 66 
 
 74 
 
 82 
 
 90 
 
 97 
 
 1 .0605 
 
 1.0611 
 
 1.0617 
 
 1 .0623 
 
 1.0629 
 
 36 
 
 191 
 
 97 
 
 1 .0605 
 
 1.0613 
 
 1 .0621 
 
 1.0629 
 
 36 
 
 42 
 
 48 
 
 54 
 
 60 
 
 67 
 
 188 
 
 1.0628 
 
 36 
 
 44 
 
 52 
 
 60 
 
 67 
 
 73 
 
 79 
 
 85 
 
 91 
 
 98 
 
 185 
 
 59 
 
 67 
 
 75 
 
 83 
 
 91 
 
 98 
 
 1 .0704 
 
 1.0710 
 
 1 0716 
 
 1.0722 
 
 1.0729 
 
 182 
 
 90 
 
 98 
 
 1 .0706 
 
 1.0714 
 
 1 .0721 
 
 1 .0729 
 
 35 
 
 41 
 
 47 
 
 53 
 
 60 
 
 179 
 
 1.0721 
 
 1.0729 
 
 37 
 
 45 
 
 52 
 
 60 
 
 66 
 
 72 
 
 78 
 
 84 
 
 91 
 
 176 
 
 52 
 
 60 
 
 68 
 
 76 
 
 83 
 
 91 
 
 97 
 
 1.0803 
 
 1.0809 
 
 1.0815 
 
 1.0822 
 
 173 
 
 82 
 
 91 
 
 99 
 
 1.0807 
 
 1.0814 
 
 1.0822 
 
 1.0828 
 
 34 
 
 40 
 
 46 
 
 53 
 
 170 
 
 1.0813 
 
 1 .0822 
 
 1 .0830 
 
 38 
 
 45 
 
 53 
 
 59 
 
 65 
 
 71 
 
 77 
 
 83 
 
 167 
 
 44 
 
 53 
 
 61 
 
 69 
 
 " 76 
 
 84 
 
 90 
 
 96 
 
 1 .0902 
 
 1.0908 
 
 1.0914 
 
 164 
 
 75 
 
 84 
 
 92 
 
 1.0900 
 
 1 .0907 
 
 1.0914 
 
 1 .0921 
 
 1.0927 
 
 33 
 
 39 
 
 45 
 
 161 
 
 1.0906 
 
 1.0914 
 
 1.0923 
 
 31 
 
 38 
 
 45 
 
 52 
 
 58 
 
 64 
 
 70 
 
 76 
 
 158 
 
 37 
 
 45 
 
 54 
 
 62 
 
 69 
 
 76 
 
 82 
 
 89 
 
 95 
 
 1.1001 
 
 1.1007 
 
 155 
 
 68 
 
 76 
 
 85 
 
 93 
 
 1.1000 
 
 1.1007 
 
 1.1013 
 
 1.1020 
 
 1.1026 
 
 32 
 
 38 
 
 152 
 
 99 
 
 1.1007 
 
 1.1015 
 
 1.1024 
 
 31 
 
 38 
 
 44 
 
 51 
 
 57 
 
 63 
 
 69 
 
 149 
 
 1 . 1030 
 
 38 
 
 46 
 
 55 
 
 62 
 
 69 
 
 75 
 
 81 
 
 88 
 
 94 
 
 1.1100 
 
 146 
 
 61 
 
 69 
 
 77 
 
 86 
 
 93 
 
 1.1100 
 
 1.1106 
 
 1.1112 
 
 1.1119 
 
 1.1125 
 
 31 
 
 143 
 
 92 
 
 1.1100 
 
 1.1108 
 
 1.1116 
 
 1.1124 
 
 31 
 
 37 
 
 43 
 
 49 
 
 56 
 
 62 
 
 140 
 
 1.1123 
 
 31 
 
 39 
 
 47 
 
 54 
 
 62 
 
 68 
 
 74 
 
 80 
 
 86 
 
 93 
 
 137 
 
 53 
 
 62 
 
 70 
 
 78 
 
 85 
 
 93 
 
 99 
 
 1.1205 
 
 1.1211 
 
 1.1217 
 
 1.1224 
 
 134 
 
 84 
 
 93 
 
 1.1201 
 
 1.1209 
 
 1.1216 
 
 1.1223 
 
 1.1230 
 
 36 
 
 42 
 
 48 
 
 54 
 
 131 
 
 1.1215 
 
 1.1223 
 
 32 
 
 40 
 
 47 
 
 54 
 
 60 
 
 67 
 
 73 
 
 79 
 
 85 
 
 128 
 
 46 
 
 54 
 
 62 
 
 71 
 
 78 
 
 85 
 
 91 
 
 98 
 
 1.1304 
 
 1.1310 
 
 1.1316 
 
 125 
 
 77 
 
 85 
 
 93 
 
 1.1302 
 
 1.1309 
 
 1.1316 
 
 1.1322 
 
 1.1328 
 
 35 
 
 41 
 
 47 
 
 122 
 
 1.1308 
 
 1.1316 
 
 1.1324 
 
 32 
 
 40 
 
 47 
 
 53 
 
 59 
 
 65 
 
 71 
 
 78 
 
 119 
 
 39 
 
 47 
 
 55 
 
 63 
 
 70 
 
 78 
 
 84 
 
 90 
 
 96 
 
 1.1402 
 
 1.1409 
 
 116 
 
 69 
 
 78 
 
 86 
 
 94 
 
 1.1401 
 
 1.1408 
 
 1.1415 
 
 1.1421 
 
 1.1427 
 
 33 
 
 39 
 
 113 
 
 1.1400 
 
 1.1408 
 
 1.1417 
 
 1.1425 
 
 32 
 
 39 
 
 45 
 
 52 
 
 58 
 
 64 
 
 70 
 
 110 
 
 31 
 
 39 
 
 47 
 
 56 
 
 63 
 
 70 
 
 76 
 
 82 
 
 89 
 
 95 
 
 1.1501 
 
 T07 
 
 62 
 
 70 
 
 78 
 
 87 
 
 94 
 
 1.1501 
 
 1.1507 
 
 1.1513 
 
 1.1519 
 
 1.1526 
 
 32 
 
 104 
 
 92 
 
 1.1501 
 
 1.1509 
 
 1.1517 
 
 1.1525 
 
 32 
 
 38 
 
 44 
 
 50 
 
 56 
 
 63 
 
 101 
 
 1.1523 
 
 32 
 
 40 
 
 48 
 
 55 
 
 63 
 
 69 
 
 75 
 
 81 
 
 87 
 
 93 
 
 98 
 
 54 
 
 62 
 
 71 
 
 79 
 
 86 
 
 93 
 
 1.1600 
 
 1.1606 
 
 1.1612 
 
 1.1618 
 
 1.1624 
 
 95 
 
 85 
 
 93 
 
 1.1602 
 
 1.1610 
 
 1.1617 
 
 1 . 1624 
 
 30 
 
 37 
 
 43 
 
 49 
 
 55 
 
 92 
 
 1.1616 
 
 1.1624 
 
 32 
 
 41 
 
 48 
 
 55 
 
 61 
 
 67 
 
 74 
 
 80 
 
 86 
 
 89 
 
 47 
 
 55 
 
 63 
 
 71 
 
 79 
 
 86 
 
 92 
 
 98 
 
 1.1704 
 
 1.1711 
 
 1.1717 
 
 86 
 
 78 
 
 86 
 
 94 
 
 1.1702 
 
 1.1710 
 
 1.1717 
 
 1.1723 
 
 1.1729 
 
 35 
 
 41 
 
 48 
 
 83 
 
 1.1708 
 
 1.1717 
 
 1.1725 
 
 33 
 
 40 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 80 
 
 39 
 
 47 
 
 56 
 
 64 
 
 71 
 
 78 
 
 85 
 
 91 
 
 97 
 
 1.1803 
 
 1.1809 
 
 77 
 
 70 
 
 78 
 
 86 
 
 95 
 
 1.1802 
 
 1.1809 
 
 1.1815 
 
 1.1822 
 
 1.1828 
 
 34 
 
 40 
 
 74 
 
 1.1801 
 
 1.1809 
 
 1.1817 
 
 1.1826 
 
 33 
 
 40 
 
 46 
 
 52 
 
 59 
 
 65 
 
 71 
 
 71 
 
 32 
 
 40 
 
 48 
 
 56 
 
 64 
 
 71 
 
 77 
 
 83 
 
 89 
 
 96 
 
 1.1902 
 
 68 
 
 62 
 
 71 
 
 79 
 
 87 
 
 94 
 
 1 . 1902 
 
 1.1908 
 
 1.1914 
 
 1.1920 
 
 1.1926 
 
 33 
 
 65 
 
 93 
 
 1.1902 
 
 1.1910 
 
 1.1918 
 
 1.1925 
 
 33 
 
 39 
 
 45 
 
 51 
 
 57 
 
 63 
 
 62 
 
 1.1924 
 
 32 
 
 41 
 
 49 
 
 56 
 
 63 
 
 70 
 
 76 
 
 82 
 
 88 
 
 94 
 
 59 
 
 55 
 
 63 
 
 72 
 
 80 
 
 87 
 
 94 
 
 1.2000 
 
 1.2007 
 
 1.2013 
 
 1.2019 
 
 1.2025 
 
 56 
 
 86 
 
 94 
 
 1.2002 
 
 1.2011 
 
 1.2018 
 
 1.2025 
 
 31 
 
 38 
 
 44 
 
 50 
 
 56 
 
 53 
 
 1.2017 
 
 1.2025 
 
 33 
 
 42 
 
 49 
 
 56 
 
 62 
 
 68 
 
 75 
 
 81 
 
 87 
 
 50 
 
 48 
 
 56 
 
 64 
 
 73 
 
 80 
 
 87 
 
 93 
 
 99 
 
 1.2106 
 
 1.2112 
 
 1 2118 
 
 47 
 
 79 
 
 87 
 
 95 
 
 1.2104 
 
 1.2111 
 
 1.2118 
 
 1.2124 
 
 1.2130 
 
 37 
 
 43 
 
 49 
 
 44 
 
 1.2110 
 
 1.2118 
 
 1.2126 
 
 35 
 
 42 
 
 49 
 
 55 
 
 61 
 
 68 
 
 74 
 
 80 
 
 41 
 
 41 
 
 49 
 
 57 
 
 66 
 
 73 
 
 80 
 
 86 
 
 92 
 
 99 
 
 1.2205 
 
 1.2211 
 
 38 
 
 72 
 
 80 
 
 88 
 
 97 
 
 1.2204 
 
 1.2211 
 
 1.2217 
 
 1.2223 
 
 1.2230 
 
 36 
 
 42 
 
 35 
 
 1.2203 
 
 1.2211 
 
 1.2219 
 
 1.2228 
 
 35 
 
 42 
 
 48 
 
 55 
 
 61 
 
 67 
 
 73 
 
 32 
 
 34 
 
 42 
 
 51 
 
 59 
 
 66 
 
 73 
 
 79 
 
 86 
 
 92 
 
 98 
 
 1.2304 
 
FACTORS Of EVAPORATION. 
 
 911 
 
 Lbs. 
 augepress.145.3 
 bs. piess .160. 
 
 150.3 
 165. 
 
 155.3 
 170. 
 
 160.3 
 175. 
 
 165.3 
 180. 
 
 170.3 
 185. 
 
 175.3 
 190. 
 
 180.3 
 195. 
 
 185.3 
 200. 
 
 190.3 
 205. 
 
 195.3 
 210 
 
 Feed 
 water. 
 
 Factors of Evaporation. 
 
 212 F. 
 
 1.0454 
 
 1.0460 
 
 1.0464 
 
 1.0469 
 
 1 .0474 
 
 1 .0478 
 
 1.0483 
 
 1.0487 
 
 1.0492 
 
 1.0496 
 
 1.0499 
 
 209 
 
 86 
 
 91 
 
 95 
 
 1.0500 
 
 1 .0505 
 
 1 .0509 
 
 1.0514 
 
 1.0519 
 
 1.0523 
 
 1.0527 
 
 1.0530 
 
 206 
 
 1.0517 
 
 1 .0522 
 
 1.0526 
 
 31 
 
 36 
 
 40 
 
 45 
 
 50 
 
 54 
 
 58 
 
 61 
 
 203 
 
 .. 48 
 
 53 
 
 57 
 
 62 
 
 67 
 
 71 
 
 77 
 
 81 
 
 85 
 
 89 
 
 92 
 
 200 
 
 79 
 
 84 
 
 88 
 
 93 
 
 98 
 
 1.0602 
 
 1 .0608 
 
 1.0612 
 
 1.0616 
 
 1.0620 
 
 1.0623 
 
 197 
 
 1.0610 
 
 1.0615 
 
 1.0619 
 
 1.0624 
 
 1.0629 
 
 33 
 
 39 
 
 . 43 
 
 47 
 
 51 
 
 54 
 
 194 
 
 41 
 
 46 
 
 50 
 
 55 
 
 60 
 
 64 
 
 70 
 
 74 
 
 78 
 
 82 
 
 85 
 
 191 
 
 72 
 
 77 
 
 81 
 
 86 
 
 91 
 
 95 
 
 1.0701 
 
 1.0705 
 
 1 . 0709 
 
 1.0713 
 
 1.0716 
 
 188 
 
 1.0703 
 
 I .0708 
 
 1.0712 
 
 1.0717 
 
 1.0722 
 
 1 .0727 
 
 32 
 
 36 
 
 40 
 
 44 
 
 47 
 
 185 
 
 34 
 
 39 
 
 43 
 
 48 
 
 53 
 
 58 
 
 63 
 
 67 
 
 71 
 
 75 
 
 78 
 
 182 
 
 65 
 
 70 
 
 74 
 
 79 
 
 84 
 
 88 
 
 94 
 
 98 
 
 1.0802 
 
 1.0806 
 
 1.0809 
 
 179 
 
 96 
 
 1.0801 
 
 1 .0805 
 
 1.0810 
 
 1.0815 
 
 1.0819 
 
 1.0825 
 
 1 0829 
 
 33 
 
 37 
 
 40 
 
 176 
 
 1 .0827 
 
 32 
 
 36 
 
 41 
 
 46 
 
 50 
 
 56 
 
 60 
 
 64 
 
 68 
 
 71 
 
 173 
 
 58 
 
 63 
 
 67 
 
 72 
 
 77 
 
 81 
 
 87 
 
 91 
 
 95 
 
 9<i 
 
 *.0902 
 
 170 
 
 89 
 
 94 
 
 98 
 
 1 .0903 
 
 1.0908 
 
 1.0912 
 
 1.0917 
 
 1 0922 
 
 1.0926 
 
 1.0930 
 
 33 
 
 167 
 
 1 .0920 
 
 1.0925 
 
 1 .0929 
 
 34 
 
 39 
 
 43 
 
 48 
 
 53 
 
 57 
 
 61 
 
 64 
 
 164 
 
 51 
 
 56 
 
 60 
 
 65 
 
 70 
 
 74 
 
 79 
 
 84 
 
 88 
 
 92 
 
 95 
 
 161 
 
 81 
 
 87 
 
 91 
 
 96 
 
 1.1001 
 
 1.1005 
 
 1.1010 
 
 1 1014 
 
 1.1019 
 
 1 . 1023 
 
 1 . 1026 
 
 ,158 
 
 1.1012 
 
 1.1018 
 
 1 . 1022 
 
 1 . 1027 
 
 32 
 
 36 
 
 41 
 
 45 
 
 49 
 
 54 
 
 57 
 
 155 
 
 43 
 
 48 
 
 53 
 
 58 
 
 . 63 
 
 67 
 
 72 
 
 76 
 
 80 
 
 85 
 
 88 
 
 152 
 
 74 
 
 79 
 
 83 
 
 89 
 
 94 
 
 98 
 
 1.1103 
 
 1.1107 
 
 1.1111 
 
 1.1115 
 
 1.1119 
 
 149 
 
 1.1105 
 
 1.1110 
 
 1.1114 
 
 1.1120 
 
 1.1125 
 
 1.1129 
 
 34 
 
 38 
 
 42 
 
 46 
 
 49 
 
 146 
 
 36 
 
 41 
 
 45 
 
 50 
 
 56 
 
 60 
 
 65 
 
 69 
 
 73 
 
 77 
 
 80 
 
 143 
 
 67 
 
 72 
 
 76 
 
 81 
 
 86 
 
 91 
 
 96 
 
 1.1200 
 
 1.1204 
 
 1 . 1208 
 
 1.1211 
 
 ,140 
 
 98 
 
 1.1203 
 
 1.1207 
 
 1.1212 
 
 1.1217 
 
 1.1221 
 
 1.1227 
 
 31 
 
 35 
 
 39 
 
 42 
 
 137 
 
 1.1229 
 
 34 
 
 38 
 
 43 
 
 48 
 
 52 
 
 58 
 
 62 
 
 66 
 
 70 
 
 73 
 
 134 
 
 59 
 
 65 
 
 69 
 
 74 
 
 79 
 
 83 
 
 88 
 
 92 
 
 97 
 
 1.1301! 1.1304 
 
 131 
 
 90 
 
 95 
 
 1.1300 
 
 1.1305 
 
 1.1310 
 
 1.1314 
 
 1.1319 
 
 1.1323 
 
 1 . 1327 
 
 32 
 
 35 
 
 128 
 
 1.1321 
 
 1.1326 
 
 30 
 
 36 
 
 41 
 
 45 
 
 50 
 
 54 
 
 58 
 
 62 
 
 66 
 
 125 
 
 52 
 
 57 
 
 61 
 
 66 
 
 72 
 
 76 
 
 - 81 
 
 85 
 
 89 
 
 93 % 
 
 122 
 
 83 
 
 88 
 
 92 
 
 97 
 
 1.1402 
 
 1.1407 
 
 1.1412 
 
 1.1416 
 
 1.1420 
 
 1.1424 
 
 1.1427 
 
 119 
 
 1.1414 
 
 1.1419 
 
 1.1423 
 
 1.1428 
 
 33 
 
 37 
 
 43 
 
 47 
 
 51 
 
 55 
 
 58 
 
 116 
 
 45 
 
 50 
 
 54 
 
 59 
 
 64 
 
 68 
 
 73 
 
 78 
 
 82 
 
 86 
 
 89 
 
 113 
 
 75 
 
 81 
 
 85 
 
 90 
 
 95 
 
 99 
 
 1.1504 
 
 1.1508 
 
 1.1512 
 
 I.bl5 
 
 1.1520 
 
 no 
 
 1.1506 
 
 1.1511 
 
 1.1515 
 
 1.1521 
 
 1.1526 
 
 1 . 1 530 
 
 35 
 
 39 
 
 43 
 
 47 
 
 50 
 
 107 
 
 37 
 
 42 
 
 46 
 
 51 
 
 57 
 
 61 
 
 66 
 
 70 
 
 74 
 
 78 
 
 81 
 
 104 
 
 68 
 
 73 
 
 77 
 
 82 
 
 87 
 
 92 
 
 97 
 
 1.1601 
 
 1.1605 
 
 1.1609 
 
 1.1612 
 
 101 
 
 99 
 
 1.1604 
 
 1.1608 
 
 1.1613 
 
 1.1618 
 
 1.1622 
 
 1.1627 
 
 32 
 
 36 
 
 40 
 
 43 
 
 98 
 
 1.1629 
 
 35 
 
 39 
 
 44 
 
 49 
 
 53 
 
 58 
 
 62 
 
 67 
 
 71 
 
 74 
 
 95 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 84 
 
 89 
 
 93 
 
 97 
 
 1.1701 
 
 1.1705 
 
 92 
 
 91 
 
 96 
 
 1.1700 
 
 1.1705 
 
 1.1711 
 
 1.1715 
 
 1.1720 
 
 1.1724 
 
 1 . 1 728 
 
 32 
 
 35 
 
 89 
 
 1.1722 
 
 1.1727 
 
 31 
 
 36 
 
 42 
 
 46 
 
 51 
 
 .55 
 
 59 
 
 63 
 
 66 
 
 86 
 
 53 
 
 58 
 
 62 
 
 67 
 
 72 
 
 76 
 
 82 
 
 86 
 
 90 
 
 94 
 
 97 
 
 83 
 
 84 
 
 89 
 
 93 
 
 98 
 
 1.1803 
 
 1.1807 
 
 1.1812 
 
 1.1817 
 
 1.1821 
 
 1.1825 
 
 1.1828 
 
 80 
 
 1.1814 
 
 1.1820 
 
 1.1824 
 
 1.1829 
 
 34 
 
 38 
 
 43 
 
 47 
 
 52 
 
 56 
 
 59 
 
 77 
 
 45 
 
 50 
 
 54 
 
 60 
 
 65 
 
 69 
 
 74 
 
 78 
 
 82 
 
 86 
 
 90 
 
 74 
 
 76 
 
 81 
 
 85 
 
 90 
 
 96 
 
 1.1900 
 
 1.1905 
 
 1.1909 
 
 1.1913 
 
 1.1917 
 
 1.1920 
 
 71 
 
 1.1907 
 
 1.1912 
 
 1.1916 
 
 1.1921 
 
 1.1926 
 
 31 
 
 36 
 
 40 
 
 44 
 
 48 
 
 51 
 
 68 
 
 38 
 
 43 
 
 47 
 
 52 
 
 57 
 
 61 
 
 67 
 
 71 
 
 75 
 
 79 
 
 82 
 
 65 
 
 69 
 
 74 
 
 78 
 
 83 
 
 88 
 
 92 
 
 97 
 
 1.2002 
 
 1.2006 
 
 1.2010 
 
 1.2013 
 
 62 
 
 99 
 
 1 .2005 
 
 1 .2009 
 
 1.2014 
 
 1.2019 
 
 1.2023 
 
 1.2028 
 
 32 
 
 36 
 
 41 
 
 44 
 
 59 
 
 1.2030 
 
 35 
 
 40 
 
 45 
 
 50 
 
 54 
 
 59 
 
 63 
 
 67 
 
 72 
 
 75 
 
 56 
 
 61 
 
 66 
 
 70 
 
 76 
 
 81 
 
 85 
 
 90 
 
 94 
 
 98 
 
 1.2102 
 
 1.2106 
 
 53 
 
 92 
 
 97 
 
 1.2101 
 
 1.2107 
 
 1.2112 
 
 1.2116 
 
 1.2121 
 
 1.2125 
 
 1.2129 
 
 33 
 
 36 
 
 50 
 
 1.2123 
 
 1.2128 
 
 32 
 
 37 
 
 43 
 
 47 
 
 52 
 
 56 
 
 60 
 
 64 
 
 67 
 
 47 
 
 54 
 
 59 
 
 63 
 
 68 
 
 74 
 
 78 
 
 83 
 
 87 
 
 91 
 
 95 
 
 98 
 
 44 
 
 85 
 
 90 
 
 94 
 
 1.2200 
 
 1.2205 
 
 1.2209 
 
 1.2214 
 
 1.2218 
 
 1.2222 
 
 1.2226 
 
 1.2229 
 
 41 
 
 1.2216 
 
 1.2221 
 
 1.2225 
 
 31 
 
 36 
 
 40 
 
 45 
 
 49 
 
 53 
 
 57 
 
 60 
 
 38 
 
 47 
 
 52 
 
 56 
 
 62 
 
 67 
 
 71 
 
 76 
 
 80 
 
 84 
 
 88 
 
 91 
 
 35 
 
 78 
 
 83 
 
 88 
 
 93 
 
 98 
 
 1.2302 
 
 1.2307 
 
 1.2311 
 
 1.2315 
 
 1.2320 
 
 1.2323 
 
 32 
 
 1.2309 
 
 1.2315 
 
 1.2319 
 
 1.2324 
 
 1.2329 
 
 33 
 
 38 
 
 42 
 
 46 
 
 51 
 
 54 
 
912 
 
 THE STEAM-BOILER. 
 
 Lbs. 
 Gauge press. 200.3 
 Abs. press. . .215. 
 
 205. 
 220. 
 
 J 210.. 
 225. 
 
 5 215J 
 230. 
 
 220.: 
 
 235. 
 
 J 225.3 
 240. 
 
 230.3 
 245. 
 
 235.3 
 250. 
 
 240.3 
 255. 
 
 245.) 
 260. 
 
 250.3 
 265. 
 
 Feed 
 water. 
 
 Factors of Evaporation. 
 
 212 F. 
 
 1 .0503 
 
 .0507 
 
 .051C 
 
 1.0513 
 
 1.0517 
 
 1.0520 
 
 1.0523 
 
 1.0527 
 
 1.0529 
 
 1.0533 
 
 1.0535 
 
 209 
 
 34 
 
 38 
 
 41 
 
 44 
 
 
 52 
 
 55 
 
 58 
 
 60 
 
 64 
 
 66 
 
 206 
 
 65 
 
 69 
 
 72 
 
 75 
 
 79 
 
 83 
 
 86 
 
 89 
 
 91 
 
 95 
 
 97 
 
 203 
 
 96 
 
 1 .0600 
 
 1.0603 
 
 1.0606 
 
 1.0611 
 
 1.0614 
 
 1.0617 
 
 1 .0620 
 
 1.0622 
 
 1.0626 
 
 1.0629 
 
 200 
 
 1.0627 
 
 31 
 
 34 
 
 37 
 
 42 
 
 45 
 
 48 
 
 51 
 
 53 
 
 57 
 
 60 
 
 197 
 
 58 
 
 62 
 
 65 
 
 68 
 
 73 
 
 76 
 
 79 
 
 82 
 
 84 
 
 88 
 
 91 
 
 194 
 
 89 
 
 93 
 
 96 
 
 1 0700 
 
 1 0704 
 
 1 0707 
 
 1 0710 
 
 1.0713 
 
 1 0715 
 
 1 0719 
 
 1 0722 
 
 191 
 
 1 .0720 
 
 .0724 
 
 1 .0727 
 
 31 
 
 35 
 
 38 
 
 41 
 
 44 
 
 46 
 
 50 
 
 53 
 
 188 
 
 51 
 
 55 
 
 58 
 
 62 
 
 66 
 
 69 
 
 72 
 
 75 
 
 78 
 
 81 
 
 84 
 
 185 
 
 82 
 
 86 
 
 89 
 
 93 
 
 97 
 
 1.0800 
 
 1 .0803 
 
 .0806 
 
 1 .0809 
 
 1.0812 
 
 1.0815 
 
 182 
 
 1.0813 
 
 1.0817 
 
 1.0820 
 
 1 .0823 
 
 1.0828 
 
 31 
 
 34 
 
 37 
 
 39 
 
 43 
 
 46 
 
 179 
 
 44 
 
 48 
 
 51 
 
 54 
 
 59 
 
 62 
 
 65 
 
 68 
 
 70 
 
 74 
 
 77 
 
 176 
 
 75 
 
 79 
 
 82 
 
 86 
 
 90 
 
 93 
 
 96 
 
 99 
 
 1 .0901 
 
 1 .0905 
 
 1.0908 
 
 173* 
 
 1 .0906 
 
 1.0910 
 
 1.0913 
 
 1.0916 
 
 1.0921 
 
 1 .0924 
 
 1.0927 
 
 I .0930 
 
 32 
 
 36 
 
 39 
 
 170 
 
 37 
 
 41 
 
 44 
 
 47 
 
 51 
 
 55 
 
 58 
 
 61 
 
 63 
 
 67 
 
 69 
 
 167 
 
 68 
 
 72 
 
 75 
 
 78 
 
 82 
 
 86 
 
 89 
 
 92 
 
 94 
 
 98 
 
 1.1001 
 
 164 
 
 99 
 
 1.1003 
 
 1.1006 
 
 1.1009 
 
 1.1013 
 
 1.1016 
 
 .1019 
 
 1.1023 
 
 1.1025 
 
 1.1029 
 
 31 
 
 161 
 
 1 . 1030 
 
 34 
 
 37 
 
 40 
 
 44 
 
 47 
 
 50 
 
 54 
 
 56 
 
 60 
 
 62 
 
 158 
 
 61 
 
 65 
 
 68 
 
 71 
 
 75 
 
 78 
 
 81 
 
 85 
 
 87 
 
 91 
 
 93 
 
 155 
 
 92 
 
 96 
 
 99 
 
 1.1102 
 
 1.1106 
 
 1.1109 
 
 1.1112 
 
 1.1115 
 
 1.1118 
 
 1.1122 
 
 1.1124 
 
 152 
 
 1.1123 
 
 1.1127 
 
 1.1130 
 
 33 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 53 
 
 55 
 
 149 
 
 54 
 
 58 
 
 61 
 
 64 
 
 68 
 
 71 
 
 74 
 
 77 
 
 80 
 
 83 
 
 86 
 
 146 
 
 84 
 
 89 
 
 92 
 
 95 
 
 99 
 
 1.1202 
 
 1.1205 
 
 .1208 
 
 1.1211 
 
 1.1214 
 
 1.1217 
 
 143 
 
 1.1215 
 
 1.1219 
 
 1.1223 
 
 1.1226 
 
 1.1230 
 
 33 
 
 36 
 
 39 
 
 42 
 
 45 
 
 48 } 
 
 140 
 
 46 
 
 50 
 
 53 
 
 56 
 
 61 
 
 64 
 
 67 
 
 70 
 
 72 
 
 76 
 
 79 
 
 137 
 
 77 
 
 81 
 
 84 
 
 87 
 
 92 
 
 95 
 
 98 
 
 1.1301 
 
 1.1303 
 
 1 . 1307 
 
 1.1310 
 
 134 
 
 1.1308 
 
 1.1312 
 
 .1315 
 
 1.1318 
 
 1 . 1322 
 
 1 . 1326 
 
 1 . 1329 
 
 32 
 
 34 
 
 38 
 
 40 
 
 131 
 
 39 
 
 43 
 
 46 
 
 49 
 
 53 
 
 56 
 
 59 
 
 62 
 
 65 
 
 69 
 
 71 
 
 128 
 
 70 
 
 74 
 
 77 
 
 80 
 
 84 
 
 87 
 
 90 
 
 93 
 
 96 
 
 1.1400 
 
 1.1402 ' 
 
 125 
 
 1.1400 
 
 1.1405 
 
 1.1408 
 
 1.1411 
 
 1.1415 
 
 1.1418 
 
 1.1421 
 
 1.1424 
 
 1.1427 
 
 30 
 
 33 
 
 122 
 
 31 
 
 35 
 
 39 
 
 42 
 
 46 
 
 49 
 
 52 
 
 55 
 
 58 
 
 61 
 
 64 i 
 
 119 
 
 62 
 
 66 
 
 69 
 
 72 
 
 77 
 
 80 
 
 83 
 
 86 
 
 88 
 
 92 
 
 95 
 
 116 
 
 93 
 
 97 
 
 1.1500 
 
 1.1503 
 
 1.1507 
 
 1.1511 
 
 1.1514 
 
 1.1517 
 
 1.1519 
 
 1.1523 
 
 1.1525 : 
 
 113 
 
 1.1524 
 
 1.1528 
 
 31 
 
 34 
 
 38 
 
 41 
 
 44 
 
 48 
 
 50 
 
 54 
 
 56 
 
 110 
 
 55 
 
 59 
 
 62 
 
 65 
 
 69 
 
 72 
 
 75 
 
 78 
 
 81 
 
 85 
 
 87 
 
 107 
 
 85 
 
 90 
 
 93 
 
 96 
 
 1.1600 
 
 1.1603 
 
 1.1606 
 
 1.1609 
 
 1.1612 
 
 1.1615 
 
 1.1618 
 
 104 
 
 1.1616 
 
 1 . 1620 
 
 1.1624 
 
 1.1627 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 101 
 
 47 
 
 51 
 
 54 
 
 57 
 
 61 
 
 65 
 
 68 
 
 71 
 
 73 
 
 77 
 
 80 
 
 98 
 
 78 
 
 82 
 
 85 
 
 88 
 
 92 
 
 95 
 
 98 
 
 1.1702 
 
 1 . 1 704 
 
 1.1708 
 
 1.1710 
 
 95 
 
 1.1709 
 
 1.1713 
 
 1.1716 
 
 .1719 
 
 1.1723 
 
 1.1726 
 
 1.1729 
 
 32 
 
 35 
 
 39 
 
 41 
 
 92 
 
 39 
 
 44 
 
 47 
 
 50 
 
 54 
 
 57 
 
 60 
 
 63 
 
 66 
 
 69 
 
 72 
 
 89 
 
 70 
 
 75 
 
 78 
 
 81 
 
 85 
 
 88 
 
 91 
 
 94 
 
 97 
 
 1.1800 
 
 1.1803 
 
 86 
 
 1.1801 
 
 1.1805 
 
 1.1808 
 
 1.1812 
 
 1.1816 
 
 1.1819 
 
 .1822 
 
 1.1825 
 
 1.1827 
 
 31 
 
 34 
 
 83 
 
 32 
 
 36 
 
 39 
 
 42 
 
 46 
 
 50 
 
 53 
 
 56 
 
 58 
 
 62 
 
 64 
 
 80 
 
 63 
 
 67 
 
 70 
 
 73 
 
 77 
 
 80 
 
 83 
 
 87 
 
 89 
 
 93 
 
 95 
 
 77 
 
 94 
 
 98 
 
 1.1901 
 
 1.1904 
 
 .1908 
 
 1.1911 
 
 .1914 
 
 1.1917 
 
 1.1920 
 
 1.1924 
 
 1.1926 
 
 74 
 
 1.1924 
 
 .1929 
 
 32 
 
 35 
 
 39 
 
 42 
 
 45 
 
 48 
 
 51 
 
 54 
 
 57 
 
 71 
 
 55 
 
 59 
 
 63 
 
 66 
 
 70 
 
 73 
 
 76 
 
 79 
 
 82 
 
 85 
 
 88 
 
 68 
 
 86 
 
 90 
 
 93 
 
 96 
 
 .2001 
 
 1.2004 
 
 .2007 
 
 .2010 
 
 1.2012 
 
 1.2016 
 
 1.2019 
 
 65 
 
 1.2017 
 
 .2021 
 
 1.2024 
 
 1.2027 
 
 31 
 
 35 
 
 38 
 
 41 
 
 43 
 
 47 
 
 49 
 
 62 
 
 48 
 
 52 
 
 55 
 
 58 
 
 62 
 
 65 
 
 68 
 
 72 
 
 74 
 
 78 
 
 80 
 
 59 
 
 79 
 
 83 
 
 86 
 
 89 
 
 93 
 
 96 
 
 99 
 
 .2102 
 
 1.2105 
 
 1.2109 
 
 1.2111 
 
 56 
 
 1.2110 
 
 .2114 
 
 1.2117 
 
 .2120 
 
 .2124 
 
 1.2127 
 
 .2130 
 
 33 
 
 36 
 
 40 
 
 42 
 
 53 
 
 41 
 
 45 
 
 48 
 
 51 
 
 55 
 
 58 
 
 61 
 
 64 
 
 67 
 
 70 
 
 73 
 
 50 
 
 71 
 
 76 
 
 79 
 
 82 
 
 86 
 
 89 
 
 92 
 
 95 
 
 98 
 
 1.2201 
 
 1.2204 
 
 47 
 
 1.2202 
 
 .2207 
 
 1.2210 
 
 .2213 
 
 .2217 
 
 .2220 
 
 .2223 
 
 .2226 
 
 .2229 
 
 32 
 
 35 
 
 44 
 
 34 
 
 38 
 
 41 
 
 44 
 
 48 
 
 51 
 
 54 
 
 57 
 
 60 
 
 63 
 
 66 
 
 41 
 
 65 
 
 69 
 
 72 
 
 75 
 
 79 
 
 82 
 
 85 
 
 88 
 
 91 
 
 94 
 
 97 
 
 38 
 
 
 .2300 
 
 1.2303 
 
 .2306 
 
 .2310 
 
 1.2313 
 
 .2316 
 
 2319 
 
 1.2322 
 
 1.2325 
 
 1.2328 
 
 35 
 
 1 2327 
 
 31 
 
 34 
 
 37 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 57 
 
 59 
 
 32 
 
 58 
 
 62 
 
 65 
 
 68 
 
 72 
 
 /5 
 
 78 
 
 82 
 
 84 
 
 88 
 
 90 
 
STRENGTH OF STEAM-BOILERS* 913 
 
 plates, headers of water-tube boilers (for pressures under 160 lb.), mud 
 drums (not exceeding 18 in. diameter), and nozzles for pipe attach- 
 ments, but there is a tendency to substitute rolled or forged steel for all 
 these purposes except grate-bars. 
 
 Quality of Steel. (A. S. M. E. Boiler Code, 1915.) 
 
 FLANGE. FIREBOX. 
 
 Plates 3/4 in. thick 
 
 and under . . . 12 0. 25% 
 Plates over s/ 4 in. 
 thick ...... 0.12 0.30 
 
 Manganese ............. 0.30 0.60% 0.30 0.50 
 
 PhoT^>n j Acid ---- Not ver 0.05 Not over ........... 0.04 
 
 Phosphorus J Basic Not over 04 Not over ........... 035 
 
 Sulphur ........... > .Not over 0.05 Not over ........... 0.04 
 
 Copper .............. Not over ........... 0.05 
 
 Tensile strength, lb. per sq. in. . . . 55,00065,000 55,00063,000 
 
 Yield point, min., lb. per sq. in. . . 0.5 tens. str. 0.5 tens. str. 
 
 . 1,500,000 1,500,000 
 
 Elongation in 8-m., mm., per cent ^^-^ - Tens, str. 
 
 For material over 3/4 in. in thickness a deduction of 0.5 from the 
 percentage of elongation shall be made for each increase of 1/8 in. in 
 thickness above 3/ 4 in., to a minimum of 20%. 
 
 Cold bending and quonch bending tests are also required, and for fire- 
 box steel a homogeneity test (see page 507). 
 
 Rivet steel: Tensile strength, 45,000-55,000, Elongation in 8 in. 
 1,500,000 -T- tensile strength, but need not exceed 30%. Stay bolt steel, 
 T. S., 50,000-60,000. 
 
 Queiich-bend Tests. The test specimen, when heated to a light 
 cherry red as seen in the dark (not less than 1200 F.), and quenched 
 at once in water the temperature of which is between 80 and 90, shall 
 bend through 180 without cracking on the outside of the bent portion, 
 as follows: For material 1 in. or under in thickness, flat on itself; for 
 material over I in. in thickness, around a pin of a diameter equal to 
 the thickness. 
 
 Boiler tubes are now generally made of soft steel, but charcoal iron 
 tubes are still preferred by some users. 
 
 Shells; Water and Steam Drums. The cylindrical structure, in- 
 cluding the ends, of a fire-tube boiler, is usually called the shell. The 
 cylinder superposed on the tubes of a water-tube boiler is called a" 
 water and steam drum. Shells of marine boilers of the Scotch type 
 have been built of diameters as large as 16 ft. Water and steam drums 
 of water-tube boilers are rarely made of greater diameter than 42 in. 
 
 The thickness of shell for a given pressure is found from the common 
 formula for safe strength of thin cylinders, 
 
 P = 2 1 Tf *dF; whence t=PdF + 2Tf. 
 
 P = safe working pressure; T = tensile strength of plate, both in lb. 
 per sq. in., t = thickness of plate in inches: / = ratio of the strength of a 
 riveted joint to that of the solid plate; F = factor of safety allowed; and 
 d = diameter of shell or drum in inches. 
 
 The value taken for T is commonly that stamped on the plates by the 
 manufacturer, / is taken from tables of strength of riveted joints or is 
 computed, and F must be taken at a figure not less than is prescribed 
 by local or State laws, or, in the case of marine boilers, by the rules 
 of the U. S. Board of Supervising Inspectors, and may be more than this 
 figure if a greater margin of safety is desired. 
 
 Strength of Circumferential Seam. Safe working pressure P = 
 4tT f + dF; t = PdF + 4:Tf, notation as above. The strength of a 
 shell against rupture on a circumferential line is twice that against 
 rupture on a longitudinal line, therefore single riveting is sufficient 
 on the circumferential seams while double, triple or quadruple rivet- 
 ing is used for the longitudinal seams. 
 
 Thickness of Plates; Riveting. (Mass. Boiler Rules, 1910). The 
 longitudinal joints of a boiler, the shell or drum of which exceeds 36 in. 
 diameter, shall be of butt and double strap construction; if it does not 
 
914 
 
 THE STEAM-BOILER. 
 
 exceed 36 in. lap-riveted construction may be used, the maximum 
 pressure on such shells being 100 Ib. per sq. in. 
 
 Minimum thickness of plates in flat-stayed surfaces, 5/ie in. 
 
 The ends of stay bolts shall be riveted over or upset. 
 
 Rivets shall be of sufficient length to completely fill the rivet holes 
 and form a head equal in strength to the body of the rivet. 
 
 Rivets shall be machine driven wherever possible, with sufficient 
 pressure to fill the rivet holes, and shall be allowed to cool and shrink 
 under pressure. 
 
 Rivet holes shall be drilled full size with plates, butt straps and 
 heads bolted in position; or they may be punched not to exceed 1/4 in. 
 less than full size for plates over 5/ 16 in. thick, and 1/8 in. or less for 
 plates not exceeding 5/i 6 in. thick, and then drilled or reamed to full 
 size with plates, butt straps and heads bolted up in position. 
 
 The longitudinal joints, of horizontal return-tubular boilers shall be 
 located above the fire-line of the setting. 
 
 The thickness of plates in a shell or drum shall be of the same gage. 
 Minimum thickness of shell plates (Mass. Rules and A. S. M. E. Code) : 
 Diam. 36 in. or under, 1/4 in.; over 36 to 54 in., 5/16 in.; over 54 to 72 
 in., 3/ 8 m.; over 72 in., 1/2 in. 
 
 Minimum thickness of butt straps: 
 
 Straps, in . | 1/4 
 
 Plates, in. U/4 to 11/32 3/ 8 to !3/ 32 7/ 16 to l5/ 32 l/ 2 to 9/ 16 5/ 8 to 3/ 4 7/ 8 1 to U/8 UA 
 
 6/16 
 
 Vl6 I V2 |5/8 
 
 3/4 I VS 
 
 Minimum thickness of tube sheets: 
 
 Diam. of tube 
 sheet, in . . 
 
 42 or under 
 
 Over 42 to 54 
 
 Over 54 to 72 
 
 Over 72 
 
 Thickness, in 
 
 3/8 
 
 7/16 
 
 V2 
 
 9/16 
 
 Convex or Bumped Heads. Minimum thickness of convex heads, 
 t = i/id F P -T- T- d = diameter in inches; F = 5 = factor of safety; P = 
 working pressure, Ib. per sq. in. ; T = tensile strength stamped on the 
 head. 
 
 When a convex head has a manhole opening the thickness is to be 
 increased not less than i/g in. 
 
 When the head is of material of the same quality and thickness as 
 that of the shell, the head is of equal strength with the shell when the 
 radius of curvature of the head equals the diameter of the shell, or when 
 the rise of the curve = 0.134 diam. of shell. 
 
 [The A. S. M. E. Boiler Code specifies a higher factor of safety, 5.5, 
 and adds l/g in. to the thickness, making the formula t = 2.75 PR/T 
 + l/g in., R being the radius to which the head is dished, in inches. 
 When R is less than 0.8 d the thickness shall be at least that found by 
 the formula when R = 0.8 d. Dished heads with the pressure on the 
 convex side are allowed a maximum working pressure equal to 60% 
 of that for heads of the same dimensions with the pressure on the 
 concave side. When the dished head has a manhole opening the thick- 
 ness as found by these rules shall be increased by not less than i/g in. 
 The corner radius of a dished head shall be not less than iy 2 in. nor 
 more than 4 in., and not less than 0.03#. A manhole opening in a 
 dished head shall be flanged to a depth not less than three times the 
 thickness of the head measured from the outside.] 
 
 Efficiency of Riveted Joints. (Mass. Boiler Rules, 1910.)* 
 X = efficiency = ratio of strength of unit length of riveted joint to 
 
 the strength of the same length of a solid plate. 
 T = tensile strength of the material, in pounds per square inch. 
 t = thickness of plate, in inches. 
 b = thickness of butt strap, in inches. 
 
 JP = pitch of rivets, in inches, on the row having the greatest pitch, 
 d = diameter of rivet, after driving, in inches. 
 a = cross-section of rivet after driving, in square inches, 
 s = strength of rivet in single shear, in pounds per square inch. 
 S = strength of rivet in double shear, in pounds per square inch. 
 
 * The same rules are given hTthe A. S. M. E. Boiler Code of 1914, 
 which was modeled on the Massachusetts Rules. 
 
STRENGTH OF STEAM-BOILERS. 915 
 
 c - crushing strength of rivet, in pounds per square inch. 
 n = number of rivets in single shear in a length of joint equal to P. 
 2V = number of rivets in double shear in the same length of joint. 
 For single-riveted lap joints: 
 
 A - strength of solid plate = PtT. 
 
 B = strength of plate between rivet holes = (P d)tT. 
 
 C shearing strength of one rivet = nsa. 
 
 D = crushing strength of plate in front of one rivet = dtc. 
 
 ~K C* T) 
 
 X = -r or or , whichever is least. 
 A A A 
 
 For double-riveted lap joints: 
 
 A and B as above, C and D to be taken for two rivets. 
 X = B, C, or D (whichever is least) divided by A. 
 For butt and double strap joint, double-riveted: 
 A = strength of solid plate = PtT. 
 B = strength of plate between rivet holes in the outer row = 
 
 (P - d)tT. 
 C = shearing strength of two rivets in double shear, plus shearing 
 
 strength of one rivet in single shear = NSa -\- nsa. 
 D = strength of plate between rivet holes in the second row, plus 
 the shearing strength of one rivet in single shear in the outer 
 row = (P - 2d)tT + nsa. 
 
 E = strength of plate between rivet holes in the second row, plus 
 the crushing strength of butt strap in front of one rivet in 
 the outer row = (P - 2d)tT + dbc. 
 
 F = crushing strength of plate in front of two rivets, plus the 
 crushing strength of butt strap in front of one rivet = 
 Ndtc + 7idbc. 
 G = crushing strength of plate in front of two rivets, plus the 
 
 shearing strength of one rivet in single shear = Ndtc + nsa. 
 X = B, C, D, E, F, or G (whichever is least) divided by A. 
 For butt and double strap joint, triple-riveted: 
 
 The same as for double-riveted, except that four rivets instead oi 
 
 two are taken for N in computing C, F, and G. 
 For butt and double strap joint, quadruple-riveted: 
 A, B, and D the same as for double-riveted joints. 
 C = shearing strength of eight rivets in double shear and three 
 
 rivets in single shear = NSa + nsa. 
 
 E = strength of plate between rivet holes in the third row (the 
 outer row being the first) plus the shearing strength in single 
 shear of two rivets in the second row and one rivet in the 
 outer row = (P 4d)tT -f- nsa. 
 
 F = strength of plate between rivet holes in the second row, plus 
 the crushing strength of butt strap in front of one rivet in 
 the outer row = (P - 2d)tT + dbc. 
 
 G = strength of plate between rivet holes in the third row, plus 
 the crushing strength of butt strap in front of two rivets 
 in the second row and one rivet in the outer row = 
 
 (P -4d)tT + ndbc. 
 
 H - crushing strength of plate in front of eight rivets, plus the 
 crushing strength of butt strap in front of three rivets = 
 Ndtc + ndbc. 
 
 I = crushing strength of plate in front of eight rivets, plus the 
 shearing strength in single shear of two rivets in the second 
 row and one in the outer row = Ndtc + nsa. 
 X= B, C, D, E, F, G, H, or / (whichever is least) divided by A. 
 The Massachusetts Rules allow the crushing strength of mild steel to 
 be taken at 95,000 Ib. per sq. in. The maximum shearing strength of 
 rivets, in Ib. per sq. in. of cross-section, is taken as follows: 
 In single shear, iron, 38,000; steel, 42,000. 
 In double shear, iron, 70,OOO; steel, 78,000. 
 The A. S. M. Boiler Code also allows 95,000 Ib. per sq. in. for 
 ing strength, but for shearing strength gf rivets allows: 
 In single shear, iron 38,000; steel 44,000. 
 In double shear, iron 76,000; steel 88,000. 
 
916 THE STEAM-BOILER. 
 
 Allowable Stresses on Braces and Staybolts. (Massachusetts Rules.) 
 The maximum allowable stress per square inch net cross-sectional 
 area of stays and stay bolts shall be as follows: Weldless mild steel, 
 head to head or through stays, 8000 lb., 9000 lb.; diagonal or crow- 
 foot stays, 7500 lb., 8000 lb.; mild steel or wrought-iron stay bolts 
 6500 lb., 7000 lb. The first figure in each case is for size up to 1 1/4 
 in. diameter or equivalent area, the second for size over 1 1/4 in. or 
 equivalent area. 
 
 The A. S. M. E. Boiler Code allows for welded stays 6000 lb. per sq. 
 in.; for unwelded stays (a) 7500; (&) 9500; (c) 8500. (a) less than 20 
 diameters long, screwed through plates with ends riveted over; (6) 
 lengths between supports not exceeding 120 diameters; (c) exceeding 120 
 diameters. 
 
 Allowable Pressure on Staybolted Surfaces. The U. S. Supervising 
 Inspectors' rule (for steamboat service) is: 
 
 P = W + S 2 
 
 P = allowable pressure, lb. per sq. in., 5 = maximum pitch in inches, 
 t = thickness in sixteenths of an inch, k = 112 for plates up to 7/ie in., 
 and 120 for plates over 7/ 16 in. 
 
 The A. S. M. E. Boiler Code gives the same formula with the follow- 
 ing values of the constants: For stays screwed through plates with 
 ends riveted over, plates jnot over 7/ 16 in. thick, C 112; over 7/i 6 in. 
 thick, C = 120; for stays screwed through plates and fitted with single 
 nuts outside of plate, C = 135; for stays fitted with inside nuts and 
 outside washers, the diameters of washers not less than 0.4 S and 
 thickness not less than t, C = 175. 
 
 Staybolts. Staybolts in water-legs are subject not only to longi- 
 tudinal stress due to the boiler pressure, and to corrosion, but also to 
 bending stress caused by relative motions of the outer and inner sheets 
 of the furnace or waterleg due to the variations in temperature to 
 which the two are subjected. A staybolt usually fails by transverse 
 fracture close to the outer sheet, which is supposed to be due to the 
 fact that the fire-box sheet is generally thinner than the outer sheet, and 
 therefore holds the end of the stay less rigidly. Staybolts are some- 
 times drilled with a small hole at one end through which water will be 
 blown out as soon as a fracture extends far enough across the section 
 to reach the hole, thus calling attention to the failure of the stay. A 
 better form is one in which the hole extends the whole length of the stay. 
 The inner portion of the stay is turned to i/g in. smaller diameter than 
 the ends, in order to make the stay more flexible and diminish the 
 chances of fracture. 
 
 Tube Spacing in Horizontal Tubular Boilers. In modern practice 
 the tubes are arranged in vertical and horizontal rows (not staggered 
 as in earlier practice), with not less than 1 in. space between adjacent 
 tubes, not less than 2 in. between the two central vertical rows, and 
 not less than 2 Y^ in. between the shell and the nearest tube. In boilers 
 60 in. diameter and larger a manhole is put in the front head beneath 
 the central rows of tubes. 
 
 Tubes and Tube Holes. (Mass. Boiler Rules) . Tube holes shall be 
 drilled full size, or they may be punched not to exceed ^ in. less than 
 the full size, and then drilled, reamed or finished full size with a rotating 
 cutter. The edge of tube holes shall be chamfered to a radius of about 
 1/16 in. A fire-tube boiler shall have the ends of the tubes substantially 
 beaded. The ends of all tubes, suspension tubes and nipples shall be 
 flared not less than 1/8 in. over the diameter of the tube hole on all 
 water-tube boilers and superheaters, and shall project through the tube 
 sheets or headers not less than 1/4 in. nor more than 1/2 in. Separately 
 fired superheaters shall have the tube ends protected by refractory ma- 
 terial where they connect with drums or headers. 
 
 Holding Power of Expanded Tubes. (The Locomotive, Sept., 1893.) 
 Tubes 3 in. external diameter, 0.109 in. thick were expanded in a 
 3/g-in. plate by rolling with a Dudgeon expander, without the pro- 
 jecting part being flared or beaded. Stress was applied to draw the 
 tubes out of the plates. The observed stress which caused yielding 
 was, in three specimens, 6500, 5000 and 7500 lb. Two other specimens 
 were flared so that the diameter of the extreme end of the tube pro- 
 
STRENGTH OF STEAM-BOILERS. 
 
 917 
 
 jecting 3/i6 in. beyond the plate was 3.2 in., the diameter of the tube 
 where it entered the plate being 3.1 in. The observed stress which 
 caused the yielding of . these specimens was 21,000 and 19.500 Ib. 
 The Locomotive estimates that the factor of safety of the plain rolled 
 tubes is nearly 4 and that of the flared tubes about 15 against the stress 
 to which they are subjected in a boiler at 100 Ib. gage pressure. It is 
 considered that the tubes act as stays for that portion of the flat head 
 that is within two inches of the upper row of tubes, and that the seg- 
 ment above this (except that portion that lies with 3 in. of the shell) re- 
 quires to be braced, 
 
 Size of Boiler Tubes. The following table gives the dimensions of 
 the tubes commonly used in stoam-boilers, together with their calculated 
 surface per foot of length, and the length per square foot of surface, 
 internal and external: 
 
 Dimensions of Standard Boiler Tubes 
 
 .i A 
 
 
 1 
 
 
 
 55 
 
 J. 9 * 
 
 t_, ** v 
 
 
 
 
 
 External D 
 ameter, Ii 
 
 Standard 
 Thickness 
 In. 
 
 11 
 
 lij 
 
 Length per 
 Sq. ft. of 
 Inside 
 Surface. 
 
 Outside Su] 
 face per Fc 
 of Length 
 Sq. ft. 
 
 .1 
 
 Internal 
 Area, Sq. 
 
 External 
 Area, Sq. 
 
 2 
 
 0.095 
 
 1.810 
 
 0.4738 
 
 2.110 
 
 0.5236 
 
 .910 
 
 0.0179 
 
 0.0218 
 
 21/4 
 
 .095 
 
 2.060 
 
 .5393 
 
 .854 
 
 .5890 
 
 .698 
 
 .0231 
 
 .0276 
 
 
 .109 
 
 2.282 
 
 .5974 
 
 .674 
 
 .6545 
 
 .528 
 
 .0284 
 
 .0341 
 
 23/4 
 
 .109 
 
 2.532 
 
 .6629 
 
 .508 
 
 .7199 
 
 .389 
 
 .0350 
 
 .0412 
 
 3 
 
 .109 
 
 2.782 
 
 .7283 
 
 .373 
 
 .7854 
 
 .273 
 
 .0422 
 
 .0491 
 
 31/4 
 
 .120 
 
 3.010 
 
 .7880 
 
 .269 
 
 .8508 
 
 .175 
 
 .0494 
 
 .0576 
 
 3V 2 
 
 .120 
 
 3.260 
 
 .8535 
 
 .172 
 
 .9163 
 
 .091 
 
 .0580 
 
 .0668 
 
 3V4 
 
 .120 
 
 3.510 
 
 .9189 
 
 .088 
 
 .9817 
 
 .018 
 
 .0672 
 
 .0767 
 
 4 
 
 .134 
 
 3.732 
 
 ' .9770 
 
 .024 
 
 1 .0472 
 
 0.955 
 
 .0760 
 
 .0873 
 
 Flues Subjected to External Pressure. The rules of the U. S. Board 
 of Supervising Inspectors, Steamboat Inspection Service, 1909, give tile 
 following rules for flues subjected to external pressure only: 
 
 Plain lap-welded flues 7 to 13 in. diameter. 
 
 Furnaces. The tensile- strength of steel used in the construction of ' 
 corrugated or ribbed furnaces shall not exceed 67,000, and be not less 
 than 54,000 Ib. ; and in all other furnaces the minimum tensile strength 
 shall not be less than 58,000, and the maximum not more than 67,000 
 Ib. The minimum elongation in 8 inches shall be 20%. 
 
 All corrugated furnaces having plain parts at the ends not ex- 
 ceeding 9 inches m length (except flues especially provided for), when 
 new, and made to practically true circles, shall be allowed a steam 
 pressure in accordance with the formula P = C X T + D. 
 
 P = pressure in Ib. per sq. in., T = thickness in inches, C = a con- 
 stant, as below. 
 
 Leeds suspension bulb furnace. . . C = 17,000, T not less than 5/i 6 in. 
 
 Morison corrugated type C = 15,600, T not less than 5/ 16 in. 
 
 Fox corrugated type C = 14,000, T not less than 5/16 jn. 
 
 Purves type, rib projections C = 14,000, T not less than 7/i 6 in. 
 
 Brown corrugated type C = 14,000, T not less than 5/ 16 in. 
 
 Type having sections 18 ins. long C = 10,000, T not less than 7/ie in. 
 
 Limiting dimensions from center of the corrugations or projecting 
 ribs, and of their depth, are given for each furnace. 
 
 Working Pressure on Boilers with Triple Riveted Joints. A triple 
 riveted double butt and strap joint, carefully designed, may be made 
 to have an efficiency something higher than 85 per cent. Good boiler 
 plate steel may be considered to have a tensile strength of 55,000 Ib. 
 per sq. in. Taking these figures and a iactor of safety of 5, we have 
 safe working pressure 
 
 2T_tf _ 2 X 55, OOP 5< 1X0.85 _ 187001 
 dF = 5d d ' 
 
 from which the following table is calculated. 
 
918 
 
 THE STEAM-BOILER. 
 
 Safe Working Pressure for Shells with Joints of 85% Efficiency. 
 
 Thickness, In. . . 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 V2 
 
 9/16 
 
 5/8 
 
 n/18 
 
 3/4 
 
 13/16 
 
 V8 
 
 15/16 
 
 1 
 
 Diameter, In. 
 24 
 
 IP5 
 
 747 
 
 
 
 
 
 
 
 
 
 
 
 
 30 .. 
 
 156 
 
 195 
 
 734 
 
 
 
 
 
 
 
 
 
 
 
 36... 
 
 no 
 
 16? 
 
 195 
 
 777 
 
 760 
 
 
 
 
 
 
 
 
 
 42 
 
 
 139 
 
 167 
 
 195 
 
 773 
 
 750 
 
 
 
 
 
 
 
 
 48... 
 
 
 1?? 
 
 146 
 
 170 
 
 195 
 
 719 
 
 743 
 
 
 
 
 
 
 
 54 
 
 
 108 
 
 no 
 
 151 
 
 173 
 
 195 
 
 716 
 
 738 
 
 
 
 
 
 
 60 
 
 
 
 117 
 
 136 
 
 156 
 
 175 
 
 195 
 
 714 
 
 733 
 
 
 
 
 
 66 .. 
 
 
 
 106 
 
 174 
 
 147 
 
 159 
 
 177 
 
 195 
 
 71? 
 
 730 
 
 
 
 
 72 
 
 
 
 
 114 
 
 130 
 
 146 
 
 16? 
 
 179 
 
 195 
 
 711 
 
 ??7 
 
 
 
 78 
 
 
 
 
 
 170 
 
 135 
 
 150 
 
 165 
 
 180 
 
 195 
 
 710 
 
 775 
 
 
 84... 
 
 
 
 
 
 
 175 
 
 139 
 
 153 
 
 167 
 
 181 
 
 195 
 
 209 
 
 223 
 
 90 
 
 
 
 
 
 
 117 
 
 130 
 
 143 
 
 156 
 
 169 
 
 18? 
 
 195 
 
 708 
 
 96 
 
 
 
 
 
 
 
 121 
 
 134 
 
 146 
 
 158 
 
 170 
 
 183 
 
 195 
 
 Shells of externally fired boilers are rarely made over 9/ 16 in. thick. 
 
 Pressures Allowed on Boilers. (Mass. Boiler Rules.) The pressure 
 allowed on a boiler constructed wholly of cast iron shall not exceed 
 25 Ib. per sq. in. 
 
 The pressure allowed on a boiler the tubes of which are secured to 
 cast-iron headers shall not exceed 160 Ib. per sq. in. 
 
 The maximum pressure to be allowed on a shell or drum of a boiler 
 shall be determined from the minimum thickness of the shell plates, the 
 lowest tensile strength stamped on the plates by the manufacturer, the 
 efficiency of the longitudinal joint or of the ligament between the tube 
 holes, whichever is least, the inside diameter of the outside course, and 
 a factor of safety not less than five. 
 
 The lowest factor of safety to be used for boilers the shells or drums 
 of which are exposed to the products of combustion, and the longi- 
 tudinal joints of which are lap riveted, shall be as follows: 5 for boiler j 
 not over 10 years old; 5.5 for boilers over 10 and not over 15 years old; 
 5.75 for boilers over 15 and not over 20 years old; 6 for boilers over 20 
 years old. The lowest factor of safety to be used for boilers the longi- 
 tudinal joints of which are of butt and double strap construction is 4.5 
 
 A hydrostatic test is to be applied if in the judgment of the in- 
 spector or of the insurance company it is advisable. The maximum 
 pressure in a hydrostatic test shall not exceed 1 1 A times the maximum 
 allowable working pressure, except that twice the maximum allowable 
 working pressure may be applied on boilers permitted to carry not 
 over 25 Ib. pressure, or on pipe boilers. 
 
 Fusible Plugs. (A. S. M. E. Code.) Fusible plugs, if used, shall be 
 filled with tin with a melting point between 400 and 500 P. The least 
 diameter of fusible metal shall be not lessithan ^ in., except for maximum 
 allowable working pressures of over 175 Ib. per sq. in. or when it is 
 necessary to place a fusible plug in a tube, in which case the least 
 diameter, of fusible metal shall be not less than 3/g in. 
 
 Steam-domes. Steam-domes or drums were formerly almost uni- 
 versally used on horizontal boilers, but their use is now generally discon- 
 tinued, as they are considered a useless appendage to a steam-boiler, and 
 unless properly designed and constructed are an element of weakness. 
 
 IMPROVED METHODS OF FEEDING COAL. 
 
 Mechanical Stokers. (William R. Roney, Trans. A. S. M. E., vol. 
 xii.) Mechanical stokers have been used in England to a limited extent 
 since 1785. In that year one was patented by James Watt. (See D. K. 
 Clark's Treatise on the Steam-engine.) 
 
 After 1840 many styles of mechanical stokers were patented in England, 
 but nearly all were variations and modifications of the two forms of 
 stokers patented by John Jukes in 1841 and by E. Henderson in 1843. 
 i The Jukes stoker consisted of longitudinal fire-bars, connected by 
 
IMPROVED METHODS OF FEEDING COAL. 919 
 
 links, so as to form an endless chain. The small coal was delivered from 
 a hopper on the front of the boiler, on to the grate, which, slowly movirfg 
 from front to rear, gradually advanced the fuel into the furnace and 
 discharged the ash and clinker at the back. 
 
 The Henderson stoker consists primarily of two horizontal fans revolv- 
 ing on vertical spindles, which scatter the coal over the fire. 
 
 The first American stoker was the Murphy stoker, brought out in 
 1878. It consists of two coal magazines placed in the side walls of the 
 boiler furnace, and extending back from the boiler front 6 or 7 feet. In 
 the bottom of these magazines are rectangular iron boxes, which are 
 moved from side to side by means of a rack and pinion, and serve to 
 push the coal upon the grates, which incline at an angle of about 35 
 from the inner edge of the coal magazines, forming a V-shaped recep- 
 tacle for the burning coal. The grates are composed of narrow parallel 
 bars, so arranged that each alternate bar lifts about an inch at the lower 
 end, while at the bottom of the V, and filling the space between the ends 
 of the grate-bars, is placed a cast-iron toothed bar, arranged to be 
 turned by a crank. The purpose of this bar is to grind the clinker com- 
 ing in contact with it. Over this V-shaped receptacle is sprung a fire- 
 brick arch. 
 
 In the Roney mechanical stoker the fuel to be burned is dumped into a 
 hopper on the boiler front. Set in the lower part of the hopper is a 
 "pujher," which, by a vibratory motion, gradually forces the fuel over 
 the 'dead-plate" and on the grate. The grate-bars in their normal con- 
 dition form a series of steps. Each bar is capable of a rocking motion 
 through an adjustable angle. All the grate-bars are coupled together by 
 a "rocker-bar." A variable back-and-forth motion being given to the 
 "rocker-bar," through a connecting-rod, the grate-bars rock in unison, 
 now forming a series of steps, and now approximating to an inclined 
 plane, with the grates partly overlapping, like shingles on a roof. When 
 the grate-bars rock forward the fire will tend to work down in a body. 
 But before the coal can move too far the bars rock back to the stepped 
 position, checking the downward motion. The rocking motion is slow, 
 being from 7 to 10 strokes per minute, according to the kind of coal. 
 This alternate starting and checking motion is continuous, and finally 
 lands the cinder and ash on the dumping-grate below. 
 
 The Hawley Down-draught Furnace. A foot or more above the 
 ordinary grate there is carried a second grate, composed of a series of 
 water-tubes, opening at both ends into steel drums or headers, through 
 which water is circulated. The coal is fed on this upper grate, and as it 
 is partially consumed falls through it upon the lower grate, where the 
 combustion is completed in the ordinary manner. The draught through 
 the coal on the upper grate is downward through the coal and the grate. 
 The volatile gases are therefore carried down through the bed of coal, 
 where they are thoroughly heated, and are burned in the space beneath, 
 where they meet the excess of hot air drawn through the fire on the lower 
 grate. In tests in Chicago, from 30 to 45 Ib. of coal were burned per 
 square foot of grate upon this system, with good economical results. 
 (See catalogue of the Hawley Down-draught Furnace Co., Chicago.) 
 
 The Chain Grate Stoker, made by Jukes in 1841, is now (1909) widely 
 used in the United States. It is made by the Babcock & Wilcox Co., 
 Green Engineering Co., and others. 
 
 Under-feed Stokers. Results similar to those that may be obtained 
 with downward draught are obtained by feeding the coal at the bottom 
 of the bed, pushing upward the coal already on the bed which has had 
 its volatile matter distihed from it. The volatile matter of the freshly 
 fired coal then has to pass through a body of ignited coke, where it 
 meets a supply of hot air. (See circular of The Underfeed Stoker Co., 
 Chicago.) 
 
 The Taylor Gravity Stoker is a combination of an underfeed stoker 
 containing two horizontal rows of pushers with an inclined or step grate 
 through which air is blown by a fan. 
 
 The Riley Stoker is an underfeed stoker with a single horizontal row 
 of pushers in combination with moving grate-bars, and moving pushers 
 at the rear of the furnace for continuously dumping the refuse. 
 
920 
 
 THE STEAM-BOILEK 
 
 SMOKE PREVENTION. 
 
 The following article was contributed by the author to a " Report on 
 Smoke Abatement," presented by a committee to the Syracuse Cham- 
 ber of Commerce, published by the Chamber in 1907. 
 
 Smoke may be made in two ways: (1) By direct distillation of tarry 
 condensible vapors from coal without burning; (2) By the partial burn- 
 ing or splitting up of hydrocarbon gases, the hydrogen burning and the 
 carbon Deing left unburned as smoke or soot. These causes usually act 
 conjointly. 
 
 The direct cause of smoke is that the gases distilled from the coal are 
 not completely burned in the furnace before coming in contact with the 
 surface of the boiler, which chills them below the temperature of ignition. 
 
 The amount and quality of smoke discharged from a chimney may 
 vary all the vyay from a dense cloud of jet-black smoke, which may be 
 ' carried by a light wind for a distance of a mile or more before it is finally 
 dispersed into the atmosphere, to a thin cloud, which becomes invisible 
 a few feet from the chimney. Often the sanje chimney will for a few 
 minutes immediately after firing give off a dense black cloud and then a 
 few minutes later the smoke will have entirely disappeared. 
 
 The quantity and density of smoke depend upon many variable causes. 
 Anthracite coal produces no smoke under any conditions of furnace. Semi- 
 bituminous, containing 12.5 to 25% of volatile matter in the combustible 
 part of the coal, will give off more or less smoke, depending on the con- 
 ditions under which it is burned, and bituminous coal, containing from 
 25 to 50% of volatile matter, will give off great quantities of smoke with 
 all of the usual old-style furnaces, even with skillful firing, and this smoke 
 can only be prevented by the use of special devices, together with proper 
 methods of firing the fuel and of admission of air. 
 
 Practically the whole theory of smoke production and prevention may 
 be illustrated by the flame of an ordinary gas burner or gas stove. 
 When the gas is turned down very low every particle of gas, as it emerges 
 from the burner, is brought in contact with a sufficient supply of hot air to 
 effect its complete and instantaneous combustion, with a pale blue or 
 almost invisible flame. Turn on the gas a little more and a white flame 
 appears. The gas is imperfectly burned in the center of the flame. Par- 
 ticles of carbon ha^e been separated which are heated to a white heat. 
 If a cold plate is brought in contact with the white flame, these carbon 
 particles are deposited as soot. Turn on the gas still higher, and it burns 
 with a dull, smoky flame, although it is surrounded with an unlimited 
 quantity of air. Now, carry this smoky flame into a hot fire-brick or 
 porcelain chamber, where it is brought in contact with very hot air, and 
 it will be made smokeless by the complete burning of the particles. 
 
 We thus see: (1) That smoke may be prevented from forming if each 
 particle of gas, as it is made by distillation from coal, is immediately 
 mixed thoroughly with hot air, and (2) That even if smoke is formed 
 by the absence of conditions for preventing it, it may afterwards be 
 burned if it is thoroughly mixed with air at a sufficiently high temperature. 
 It is easy to burn smoke when it is made in small quantities, but when 
 made in great volumes it is difficult to get the hot air mixed with it unless 
 special apparatus is used. In boiler firing the formation of smoke must 
 be prevented, as the conditions do not usually permit of its being burned. 
 The essential conditions for preventing smoke in boiler fires may be 
 enumerated as follows: 
 
 1. The gases must be distilled from the coai at a uniform rate. 
 
 2. The gases, when distilled, must be brought into intimate mixture 
 with sufficient hot air to burn them completely. 
 
 3. The mixing should be done in a fire-brick chamber. 
 
 4. The gases should not be allowed to touch the comparatively cold 
 surfaces of the boiler until they are completely burned. This means that 
 the gases shall have sufficient space and time in which to burn before they 
 are allowed to come in contact with the boiler surface. 
 
 Every one of these four conditions is violated in the ordinary method 
 of burning coal under a steam boiler. (1) The coal is fired intermittently 
 and often in large quantities at a time, and the distillation proceeds at so 
 rapid a rate that enough air cannot be introduced into the. furnace to burn 
 the gas. (2) The piling of fresh coal on the grate in itself chokes the air 
 
SMOKE PREVENTION. 921 
 
 supply. (3) The roof of the furnace is the cold shell, or tubes, of the 
 boiler, instead of a fire-brick arch, as it should be, and the furnace is not of 
 a sufficient size to allow the gases time and space in which to be thoroughly 
 mixed with the air supply. 
 
 In order to obtain the 'conditions for preventing: smoke it is necessary: 
 (I) That the coal be delivered into the furnace in small quantities at a 
 time. (2) That the draught be sufficient 'o carry enough air into the 
 furnace to burn the gases as fast as they are distilled. (3) That the air 
 itself be thoroughly heated either by passing through a bed of white-hot 
 coke or by passing' through channels in hot brickwork, or by contact with 
 hot fire-brick surfaces. (4) That the gas and the air be brought into 
 the most complete and intimate mixture, so that each paiticle of carbon 
 it the gas meets, before it escapes from the furnace, its necessary supply 
 ol air. (5) That the flame produced by the burning shall be completely 
 extinguished by the burning of every particle of the carbon into invisible 
 carbon dioxide. 
 
 If a white flame touches the surface of a boiler,' it is apt to deposit 
 soot and to produce smoke. A white flame itself is the visible evidence 
 of incomplete combustion. 
 
 The first remedy for smoke is to 9btain anthracite coal. If this is not 
 commercially practicable, then obtain, if possible, coal with the smallest 
 amount of volatile matter. Coal of from 15 to 25% of volatile matter 
 makes much less smoke than coals containing higher percentages. Pro- 
 vide a proper furnace for burning coal. Any furnace is a proper furnace 
 which secures the conditions named in the preceding paragraphs. Next, 
 compel the firemen to follow instructions concerning the method of 
 firing. 
 
 It is impossible with coal containing over 30% of volatile matter and 
 with a water-tube boiler, with tubes set close to the grate and vertical 
 gas passages, as in an anthracite setting, to prevent smoke even by the 
 . most skillful firing. This style of setting for a water-tube boiler should 
 be absolutely condemned. A Dutch oven setting, or a longitudinal 
 setting with fire-brick baffle walls, is highly recommended' as a smoke- 
 preventing furnace, but with such a furnace it is necessary to use con- 
 siderable skill in firing. 
 
 Mechanical mixing of the gases and the air by steam jets is sometimes 
 successful in preventing smoke, but it is not a universal preventive, 
 especially when the coal is very high in volatile matter, when the firing 
 is done unskillfully, or when the boiler is being driven beyond its normal 
 capacity. It is essential to have sufficient draught to burn the coal prop- 
 erly and this draught may be obtained either from a chimney or a fan. 
 There is no especial merit in forced draught. except that it enables a larger 
 quantity of coal to be burned and the boiler to be driven harder in case 
 of emergency, and usually the harder the boiler is driven, the more 
 difficult it is to suppress smoke. 
 
 Down-draught furnaces and mechanical stokers of many different kinds 
 are successfully used for smoke prevention, and when properly designed 
 and installed and handled skillfully, and usually at a rate not beyond 
 that for which they are designed, prevent all smoke. If these appliances 
 are found giving smoke, it is always due either to overdriving or to un- 
 skillful handling. It is necessary, however, that the design of these 
 stokers be suited to the quality of the coal and the quantity to be burned, 
 and great care should be taken to provide a sufficient size of furnace with 
 a fire-brick roof and means of introducing air to make them completely 
 'successful. 
 
 Burning Illinois Coal without Smoke. (L. P. Breckenridge, 
 ' Bulletin No. 15 of the Univ. of 111. Eng'g Experiment Station, 1907.) 
 Any fuel may be burned economically and without smoke if it is 
 mixed with the proper amount of air at a proper temperature. The 
 boiler plant of the University of Illinois consists of nine units aggregating 
 2000 H.P. Over 200 separate tests have been made. The following is a 
 condensed statement of the results in regard to smoke prevention. 
 
 Boilers Nos. 1 and 2. Babcock & Wilcox. Chain-grate stoker. Usual 
 vertical baffling. Can be run without smoke at from 50 to 120 % of rated 
 capacity. 
 
 No. 3. Stirling boiler. Chain-grate stoker. Usual baffling and com- 
 
922 THE STEAM-BOILER. 
 
 bustion arches. Can be run without smoke at capacities of 50 to 
 
 140%. 
 
 No. 4. National water-tube. Chain-grate stoker. Vertical baffling 
 No smoke at capacities of 50 to 120%. With the Murphy furnace it was 
 smokeless except when cleaning fires. 
 
 No. 5. Babcock & Wilcox. Roney stoker. Vertical baffling Nearly 
 smokeless (maximum No. 2 on a chart in which 5 represents black smoke) 
 up to 100% of rating, but cannot be run above 100% without objection- 
 able smoke. 
 
 No. 6. Babcock & Wilcox. Roney stoker. Horizontal tile-roof baf- 
 fling. Can be run without smoke at capacities of 50 to 100% of rating. 
 
 N9S. 7 and 8. Stirling, equipped with Stirling bar-grate stoker. Usual 
 baffling and combustion arches. Can be run without smoke at 50 to 
 140% of rating. 
 
 No. 9. Heine boiler. Chain-grate stoker. Combustion arch and tile- 
 roof furnace. Can be run without smoke at capacities of 50 to 140%. 
 It is almost impossible to make smoke with this setting under any con- 
 dition of operation. As much as 46 Ibs. of coal per sq. ft. of grate surface 
 has been burned without smoke. 
 
 Conditions of Smoke Prevention. Bulletin No. 373 of the U. S. 
 Geological Survey, 1909 (188 pages), contains a report of an extensive 
 research by D. T. Randall and J. T. Weeks on The Smokeless Combustion 
 of Coal in Boiler Plants. A brief summary of the conclusions reached is 
 as follows: 
 
 Smoke prevention is both possible and economical. There are many 
 types of furnaces and stokers that are operated smokelessly. 
 
 Stokers or furnaces must be set so that combustion will be complete 
 before the gases strike the heating surfaces of the boiler. When partly 
 burned gases at a temperature of say 2500 F. strike the tubes of a 
 boiler at say 350 F., combustion may be entirely arrested. 
 
 The most economical hand-fired plants are those that approach most 
 nearly to the continuous feed of the mechanical stoker. The fireman is ' 
 so variable a factor that the ultimate solution of the problem depends on 
 the mechanical stoker in other words, the personal element must be 
 eliminated. 
 
 A well designed and operated furnace will burn many coals without 
 smoke up to a certain number of pounds per hour, the rate varying with 
 different coals.' If more than this amount is burned, the efficiency will 
 decrease and smoke will be made, owing to the lack of furnace capacity 
 to supply air and mix gases. 
 
 High volatile matter in the coal gives low efficiency, and vice versa. 
 When the furnace was forced the efficiency decreased. 
 
 With a hand-fired furnace the best results were obtained when firing 
 was done most frequently, with the smallest charge. 
 
 Small sizes of coal burned with less smoke than large sizes, but developed 
 lower capacities. 
 
 Peat, lignite, and sub-bituminous coal burned readily in the tile-roofed 
 furnace and developed the rated capacity, with practically no smoke. 
 
 Coals which smoked badly gave efficiencies three to five per cent lower 
 than the coals burning with little smoke. 
 
 Briquets were found to be an excellent form for using slack coal in a 
 hand-fired plant. 
 
 In the average hand-fired furnace washed coal burns with lower effi- 
 ciency and makes more smoke than raw coal. Moreover, washed coal 
 offers a means of running at high capacity, with good efficiency, in a 
 well-designed furnace. 
 
 Forced draught did not burn coal any more efficiently than natural 
 draught. It supplied enough air for high rates of combustion, but as the 
 capacity of the boiler increased, the efficiency decreased and the per- 
 centage of black smoke increased. 
 
 Fire-brick furnaces of sufficient length and a continuous, or nearly 
 continuous, supply of coal and air to the fire make it possible to burn 
 most coals efficiently and without smoke. 
 
 Coals containing a large percentage of tar and heavy hydrocarbons 
 are difficult to burn without smoke and require special furnaces ancj 
 than ordinary care in firing. 
 
. 
 
 FORCED COMBUSTION IN STEAM-BOILERS. 923 
 FORCED COMBUSTION IN STEAM-BOILERS. 
 
 For the purpose of increasing the amount of steam that can be gener- 
 ated by a boiler of a given size, forced draught is of great importance. 
 It is universally used in the locomotive, the draught being obtained by a 
 steam-jet in the smoke-stack. It is now largely used in ocean steamers, 
 especially in ships of war, and to a small extent in stationary boilers. 
 Economy of fuel is generally not attained by its use, its advantages be- 
 ing confined to the securing of increased capacity from a boiler of a 
 given bulk, weight, or cost. 
 
 There are three different modes of using the fan for promoting com- 
 bustion: 1, blowing direct into a closed ash-pit; 2, exhausting the gases 
 by the suction of the fan ; 3, forcing air into an air-tight boiler-room 
 or stoke-hold. Each of these three methods has its advantages and dis- 
 advantages. 
 
 In the use of the closed ash-pit the blast-pressure frequently forces 
 the gases of combustion from the joint around the furnace doors in so 
 great a quantity as to affect both the efficiency of the boiler and the 
 health of the firemen. 
 
 The chief defect of the second plan is the great size of the fan required 
 to produce the necessary exhaustion, on account of the higher exit tem- 
 perature enlarging the volume of the waste gases. 
 
 The third method that of forcing cold air by the fan into an air-tight 
 boiler-room the closed stoke-hold system though it overcame the 
 difficulties in working ^belonging to the two forms first tried, has serious 
 defects of its own, as it cannot be worked, even with modern high-class 
 boiler-construction, much, if at all, above the power of a good chimney 
 draught, in most boilers, without damaging them. (J. Howden, Proc. 
 Eng'g Congress at Chicago, in 1893.) 
 
 In 1880 Mr. Howden designed an arrangement intended to overcome 
 the defects of both the closed ash-pit and the closed stoke-hold systems. 
 
 An air-tight chamber is placed on the front end of the boiler and sur- 
 rounding the furnaces. This reservoir, which projects from 8 to 10 
 inches from the end 9f the boiler, receives the air under pressure, which 
 is passed by valves into the ash-pits and over the fires in proportions 
 suited to the kind of fuel and the rate of combustion. The air used above 
 the fires is admitted to a space between the outer and inner furnace- 
 doors, the inner having perforations and an air-distributing box through 
 which the air passes under pressure. By means of the balance of pres- 
 sure above and below the fires all tendency of the fire to blow out at 
 the door is removed. 
 
 A feature of the system is the combination of the heating of the air of 
 combustion by the waste gases with the controlled and regulated admis- 
 sion of air to the furnaces. This arrangement is effected most conve- 
 niently by passing the hot fire-gases after they leave the boiler through 
 stacks of vertical tubes enclosed in the uptake, their lower ends being 
 immediately above the smoke-box doors. Installations on Howden's 
 system have been arranged for a rate of combustion to give an average 
 of from 18 to 22 I.H.P. per square foot of fire-grate with fire-bars from 
 5 to 5 y z ft. in length. It is believed that with suitable arrangement of 
 proportions even 30 I.H.P. per square foot can be obtained. 
 
 For an account of uses of exhaust-fans for increasing draught, see 
 paper by W. R. Roney, Trans. A. S. M. E., vol. xv. 
 
 Calculations for Forced Draft. In designing a forced draft installa- 
 tion the principal data needed are: 1, The maximum number of pounds 
 of coal that will have to be burned per hour at the most rapid rate of 
 driving, when the efficiency of the boiler, furnace and grate is lowest; 
 2, the number of pounds of air used per pound of coal. If C, H and O 
 are respectively the carbon, hydrogen and oxygen in 1 Ib. of coal, then 
 the number of pounds of air required, theoretically, for complete com- 
 bustion is 34.56(C/3 -f H + O/8). With mechanical stokers and CO 2 
 apparatus for control of the air supply 50% excess air supply is ample, 
 but with ordinary hand-firing the actual air supply may be 100% or 
 more in excess, In the author's " Steam Boiler Economy," 2d ed. 1915, 
 p. 242, there is given a calculation of the number of cubic feet of air 
 per minute required per boiler horsepower developed, giving results as 
 follows: 
 
924 
 
 THE STEAM-BOtLEU. 
 
 Cvstc FEET OF Am PEH MINUTE AT 70 6 F. PEE BOILER HORSEPOWER. 
 
 Semi- East. West. 
 Fuel Anth. bit. Bitu. Bitu. Lignite Oil 
 
 Air* 50% excess .11,52 11.30 10.99 11.86 13.63 11.13 
 
 Air 100% excess 15.36 15.07 14.65 15.82 16.17 14.84 
 
 Note that these figures are based not upon the rated horse-power of 
 the boiler, but upon that actually developed, which may be far m excess 
 of the rated power. For induced draft the figures given should be 
 multiplied by (T+ 460) -i- 530, in which T is the temperature of the 
 gases to be handled by the induced draft fan. 
 
 FUEL ECONOMIZERS. 
 
 Economizers for boiler plants are usually made of vertical cast-iron 
 tubes contained in a long rectangular chamber of brickwork. The feed- 
 water enters the bank of tubes at one end, while the hot gases enter the 
 chamber at the other end and travel in the opposite direction to the 
 water. The tubes are made of cast iron because it is more non-corrosive 
 than wrought iron or steel when exposed to gases of combustion at low 
 temperatures. An automatic scraping device is usually provided for 
 the purpose of removing dust from the outer surface of the tubes. 
 
 The amount of saying of fuel that may be made by an economizer 
 varies greatly according to the conditions of operation. With a given 
 quantity of chimney gases to be passed through it, its economy will be 
 greater '(1) the higher the temperature of these gases; (2) the lower the 
 temperature of the water fed into it ; and (3) the greater the amount of its 
 heating surface. From (1) it is seen that an economizer will save more 
 fuel if added to a boiler that is overdriven than if added to one driven at 
 a nominal rate. From (2) it appears that less saving can be expected 
 from an economizer in a power plant in which the feed-water is heated by 
 exhaust steam from auxiliary engines than when the feed-water entering 
 it is taken directly from the condenser hot-well. The amount of heat- 
 ing surface that should be used in any given case depends not only on 
 the saving of fuel that may be made, but also on the cost of coal, and on 
 the annual C9sts of maintenance, including interest, depreciation, etc. 
 
 The following table shows the theoretical results possibly attainable 
 from economizers under the conditions specified. It is assumed that the 
 coal has a heating value of 15,000 B.T.U. per Ib. of combustible; that it 
 is completely burned in the furnace at a temperature of 2500 F. ; that 
 the boiler gives efficiencies ranging from 60 to 75 % according to the rate 
 of driving; and that sufficient economizer surface is provided to reduce 
 the temperature of the gases in all cases to 300 F. Assuming the specific 
 heat of the gases to be constant, and neglecting the loss of heat by radi- 
 ation, the temperature of the gases leaving the boiler and entering the 
 economizer is directly proportional to (100- % of boiler efficiency), 
 and the combined efficiency of boiler and economizer is (2500 300) 
 -T- 2500 = 88%, which corresponds to an evaporation of (15.000 -f- 970) 
 X 0.88 = 13.608 Ib. from and at 212 per Ib. of combustible; or as- 
 suming the feed-water enters the economizer at 100 F. and the boiler 
 makes steam of 150 Ib. absolute pressure, to an evaporation of 11.729 
 Ib. under these conditions. Dividing this figure into the number of 
 heat units utilized by the economizer per Ib. of combustible gives the 
 heat-units added to the water, from which, by reference to a steam 
 table, the temperature may be found. With these data we obtain the 
 results given in the table below. 
 
 Boiler Efficiency, per cent. 
 
 60 
 
 65 
 
 70 
 
 75 
 
 B.T.U. absorbed by boiler per Ib. combustible 
 g 'p u jjj chimney gases leaving boiler 
 
 9000 
 6000 
 1000 
 300 
 4200 
 28 
 9.278 
 4.330 
 448 
 70 
 
 9750 
 5250 
 875 
 300 
 3450 
 23 
 10.051 
 3.557 
 389 
 65.7 
 
 10500 
 4500 
 750 
 300 
 2700 
 18 
 10.824 
 2.884 
 327 
 60 
 
 11250 
 3750 
 625 
 300 
 1950 
 13 
 1 1 .598 
 2.010 
 265 
 52 
 
 Estimated temp, of gases leaving boiler 
 
 Estimated temp of gases leaving economizer . . 
 
 J3 T u saved by economizer 
 
 Efficiency gained by economizer per cent 
 
 Equivalent water evap. per Ib. comb, in boiler 
 B.T.U. saved by econ. equivalent to evap. of Ib 
 Temp of water leaving economizer . ... 
 
 Efficiency of the economizer, per cent 
 
ECONOMIZEES. 
 
 925 
 
 Equation of the Economizer. Let W '=* Ib. of water evaporated 
 by the boiler, under actual conditions of feed-water temperature and 
 steam pressure, per Ib. of combustible; G = Ib. of flue-gas per Ib. 
 combustible; Ti and T 2 = temperatures of gas entering and leaving 
 the economizer; ti and fa = temperatures of water entering and leaving 
 the economizer; then assuming no loss by radiation and leakage, and 
 taking the specific heat of the gas at 0.24 and that of the water at 1, 
 
 j. U.<s4Cr ., _, . ZTVT' T 1 \ 
 
 fa ll |Tf- (jfl 22) = f (2 1 12), 
 
 in which F has the values in the following table for given values of 
 W and G. 
 
 10 
 
 I 
 
 F =0.24 G/W. 
 
 G = 18 
 
 0.54 
 
 0.48 
 
 0.43 
 
 0.39 
 
 0.36 
 
 21 
 
 0.63 
 
 0.56 
 
 0.50 
 
 0.46 
 
 0.42 
 
 24 
 
 0.72 
 
 0.64 
 
 0.58 
 
 0.52 
 
 0.48 
 
 27 
 
 0.81 
 
 0.72 
 
 0.65 
 
 0.59 
 
 0.54 
 
 30 
 
 0.90 
 
 0.80 
 
 0.72 
 
 0.65 
 
 0.60 
 
 Ti is usually fixed by the operating conditions of the boiler, and ti 
 by the condenser and feed-water heater conditions. 
 
 Taking Ti at 800, 700 and 600, corresponding values of F at 0.49, 
 0.39 and 0.36, and ti = 100, 
 
 100 
 
 300, then fa = 0.43(500) -f- 100 =315 
 250, 0.39(450) + 100 =266 
 
 220, 0.36(380) + 100 =237 
 
 the 
 
 0.43(800- T 2 );let 
 0.39(700- T 2 ); 
 0.36(600- T 2 ); 
 
 The mean temperature difference between the flue gas and 
 water, 
 
 t = TI + r 2 fa+ h Ti-fa + T 2 -u 
 
 22 2 
 
 For the three cases given tm = 343, 292, 242. 
 
 If w = Ib. of water heated by the economizer per hour from t\ to fa, 
 S = sq. ft. of economizer surface, and C = heat-units transmitted per 
 square foot of surface per hour per degree of mean temperature dif- 
 ference, then w(fa ti) = SCtm. The value of C is given by manu- 
 facturers as ranging between 2 and 4 for different conditions of practice. 
 It probably increases in some proportion to the increase of tm, but no 
 records of experiments have been published from which the law of this 
 increase may be determined. 
 
 Amount of Heating Surface. The Fuel Economizer Co. says: We 
 have found in practice that by allowing 4 sq . ft. of heating surface per 
 boiler H.P. (34 Yi Ib. evap. from and at 212 = 1 H.P.) we are able to 
 raise the feed-water 60 F. for every 100 reduction in the temperature, 
 the gases entering the economizer at 450 to 600. With gases at 600 
 to 700 we have allowed a heating surface of 4 }/% to 5 sq. ft. per H.P., 
 and for every 100 reduction in temperature .of the gases we have 
 obtained about 65 rise in temperature of the water; the feed-water 
 entering at 60 to 120. With 5000 sq . ft. of boiler-heating surface (plain 
 cylinder boilers) developing 1000 H.P. we should recommend 5 sq. ft. of 
 economizer surface per boiler H. P. developed, or an economizer of about 
 500 tubes, and it should heat the feed-water about 300. 
 
 Heat Transmission in Economizers. (Carl S. Dow, Indust. Eng'g, 
 April, 1909.) The rate of heat transmission (C) per sq. ft. per hour per 
 degree of difference between the average temperatures of the gases and 
 the water passing through the economizer varies with the mean tem- 
 perature of the gas about as follows: Gas, 600, C= 3.25; gas 500, 
 C = 3; gas 400, C = 2.75; gas 300, C = 2.25. 
 
 Calculation of the Saving made by an Economizer. The usual 
 method of calculating the saving of fuel by an economizer when the 
 boiler and the economizer are tested together as a unit is by the formula 
 (Hi - h) -v- (Hz - /i), in which h is the total heat above 32 of 1 Ib. of 
 
926 
 
 THE STEAM-BOILER. 
 
 water entering, Hi the total heat of 1 Ib. of water leaving the economizer, 
 and 7/2 the total heat above 32 of 1 Ib. of steam at the boiler pressure. 
 If h = 100, Hi = 210, Hz = 1200, then the saving according to the for- 
 mula is (210 - 100) ~ 1100 = 10%. This is correct if the saving is 
 defined as the ratio of the heat absorbed by the economizer to the total 
 heat absorbed by the boiler and economizer together, but it is not 
 correct if the saving is defined as the saving of fuel made by running the 
 combined unit as compared with running the boiler alone making the 
 same quantity of steam from feed-water at the low temperature, so as to 
 cause the boiler to furnish Hz h heat-units per Ib. instead of Hz Hi. 
 In this case the boiler is called on to do more work, and in doing it it may 
 be overdriven and work with lower efficiency. 
 
 In a test made by F. G. Gasche, in Kansas City in 1897, using Mis- 
 souri coal analyzing moisture 7.58; volatile matter, 36.69; fixed carbon, 
 35.02; ash, 15.69; sulphur, 5.12, he obtained an evaporation of 5.17 Ib. 
 from and at 212 per Ib. of coal with the boiler alone, and when the 
 boiler and economizer were tested together the equivalent evaporation 
 credited to the boiler was 5.55, to the economizer 0.72, and to the com- 
 bined unit 6.27, the saving by the combined unit as compared with the 
 boiler alone being (6.27 - 5.17) -4- 6.27 = 17.5%, while the saving of 
 heat shown by the economizer in the combined test is only (6.27 
 5.55) -f- 6.27 = 11.5%, or as calculated by Mr. Gasche from the formula 
 (Hi - h) -=- (Hz - h), (172.1 - 39.3) ^ (1181.8 -i- 39.3) = 11.6%. 
 
 The maximum saving of fuel which may be made by the use of an 
 economizer when attached to boilers that are working with reasonable 
 economy is about 15 % . Take the case of a condensing engine iising 
 steam of 125 Ib. gage pressure, and with a hot-well or feed-water 
 temperature of 100 P. The economizer may be expected under the 
 best conditions to raise this temperature about 170 or to 270. Then 
 h= 68, Hi = 239, H 2 =1190. (Hi- h).+l(Hz - ft) = 171 -r- 1122 = 15.24%. 
 
 If the boilers are not working with fair economy on account of being 
 overdriven, then the saving made by the addition of an economizer may 
 be much greater. 
 
 Test of a Large Economizer. (R. D. Tomlinson, Power, Feb., 1904.) 
 Two tests were made of one of the sixteen Green economizers at the 
 74th St. Station of the Rapid Transit Railway, New York City. Four 
 520-H.P. B. & W. boilers were connected to the economizer. It had 512 
 tubes, 10 ft. long, 49/ 16 in. external diam.; total heating surface 6760 sq. 
 ft., or 3.25 sq. ft. per rated H.P. of the boilers. Draught area through 
 economizer, 3 sq. in. per H. P. The stack for each 16 boilers and four 
 economizers was 280 ft. high, 17 ft. internal diam. The first test was 
 made with the boilers driven at 94% of rating, the second at 113%. 
 The results are given below, the figures of the second test being in 
 parentheses. 
 
 Water entering economizer 96 (93.5) ; leaving 200 (203.8) ; rise 
 104 (110.3). 
 
 Gases entering economizer 548 (603) ; leaving 295 (325) ; drop 253 
 (278). 
 
 Steam, gage pressure, 166 (165). Total B. T.U. per Ib. from feed 
 temp. 1132 (1134). 
 
 Saving of heat by economizer, per cent, 9.17 (9.73). 
 
 Reduction of draught in passing through economizer, in. of water, 
 0.16 (0.23). 
 
 Results from Seven Tests of Sturtevant Economizers (Catalogue of 
 B. F. Sturtevant Co.) 
 
 Plants 
 Tested. 
 
 Gases 
 Entering. 
 Deg. F. 
 
 Gases 
 Leaving. 
 Deg. F. 
 
 Water 
 Entering. 
 Deg. F. 
 
 Water 
 Leaving. 
 Deg. F. 
 
 Increase in 
 Tempera- 
 ture. 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 
 650 
 575 
 
 470 
 500 
 460 
 440 
 525 
 
 275 
 290 
 230 
 240 
 200 
 220 
 225 
 
 180 
 160 
 130 
 110 
 90 
 120 
 180 
 
 340 
 320 
 260 
 230 
 230 
 236 
 320 
 
 160 
 160 
 130 
 120 
 140 
 116 
 140 
 
INCRUSTATION AND CORROSION. 927 
 
 Explosions of Economizers. Explosions of economizers are rare, 
 but their possibility should be recognized and guarded against. They 
 may occur from over-pressure, due to closing of the outlet valve or 
 other causes, which may be prevented by means of a safety valve. 
 When the gas inlet damper is closed there is a possibility that it may 
 leak combustible gas into the economizer flue, making an explosive 
 mixture which might be ignited by a lighted torch. The headers or 
 tubes may be weakened by internal or external corrosion, and a rup- 
 ture might occur at the normal working pressure. This should be 
 guarded against by annual inspection and hydraulic test at 50 per 
 cent in excess of the working pressure. 
 
 THERMAL STORAGE. 
 
 In Druitt Halpin's steam storage system (Industries and Iron, Mar. 22. 
 1895) he employs only sufficient boilers to supply the mean demand, and 
 storage tanks sufficient to supply the maximum demand. These latter 
 not being subjected to the fire suffer but little deterioration. The boilers 
 working continuously at their most economical rate have their excess of 
 energy during light load stored up in the water of the tank, from wliich 
 it may be drawn at will during heavy load. He proposes that the boilers 
 and tanks shall work under a pressure of 265 Ibs. per square inch when 
 fully charged, which corresponds to a temperature of 406 F., and that 
 the engines be worked at 130 Ibs. per square inch, which corresponds to 
 347 F. The total available heat stored when the reservoirs are charged 
 is that due to a range of 59. The falling in temperature of 141/4 Ibs. of 
 water from 407- to 347 will yield 1 Ib. of steam. To allow for radia- 
 tion of loss and imperfect working, this may be taken at 16 Ibs. of water, 
 per pound of steam. The steam consumption per effective H.P. maybe 
 taken at 18 Ibs. per hour in condensing and 25 Ibs. per hour in non-con- 
 densing engines. The storage-room per effective H.P. by this method 
 would, therefore, be (16 X 18) -^ 62.5= 4.06 cu. ft. for condensing and 
 (16 X 25) -5- 62.5 = 6.4 cu. ft. for non-condensing engines. 
 
 Gas storage, assuming that illuminating gas is used, would require 
 about 20 cu. ft. of storage room per effective H.P. hour stored, and if 
 ordinary fuel gas were stored it would require about four times this 
 capacity. In water storage 317 cu. ft. would be required at an elevation 
 of 100 ft. to store one H.P. hour, so that of the three methods of storing 
 energy the thermal method is by far the most economical of space. 
 
 In the steam storage method the boiler is completely filled with water 
 and the storage tank nearly so. The two are in free communication by 
 means of pipes, and a constant circulation of water is maintained between 
 the two, but the steam for the engines is taken only from the top of the 
 storage tank through a reducing valve. 
 
 In the feed storage system, the excess of energy during light load Is 
 stored in the tank as before, but the boilers are not completely filled. In 
 this system the strain is taken exclusively from the boilers, the super- 
 heated water of the storage tanks being used during heavy load as feed- 
 water to the boilers. 
 
 A third method is a combination of these two. In the "combined" 
 feed and steam storage system the pressure in boiler and storage tank is 
 equalized by connecting the steam spaces in both by pipe, and the steam 
 for the engines is, therefore, taken from both. In other words they work 
 in parallel. 
 
 INCRUSTATION AND CORROSION. 
 
 Incrustation or Scale. Incrustation (as distinguished from mere 
 sediments due to dirty water, which are easily blown out, or gathered 
 up, by means of sediment-collectors) is due to the presence of salts in the 
 feed-water (carbonates and sulphates of lime and magnesia for the most 
 part), which are precipitated when the water is heated, and form hard 
 deposits upon the boiler-plates. (See Impurities in Water, p. 720, ante.) 
 
 Where the quantity of these salts is not very large (12 grains per 
 gallon, say) scale preventives may be found effective. The chemical 
 preventives either form with the salts other salts soluble in hot water; 
 or precipitate them in the form of soft mud, which does not adhere to 
 the plates, and can be washed out from time to time. The selection of 
 the chemical must depend upon the composition of the water, an4 it 
 should, be introduced regularly with the feed, 
 
928 THE STEAM-BOILER. 
 
 EXAMPLES. Sulphate-of-lime scale prevented by carbonate of soda: 
 The sulphate of soda produced is soluble in water; and the carbonate of 
 lime falls down in grains, does not adhere to the plates, and may there- 
 fore be blown out or gathered into sediment-collectors. The chemical 
 reaction is: 
 
 Sulphate of lime + Carbonate of soda = Sulphate of soda -{-Carbonate of lime 
 CaSO* Na 2 CO 3 Na 2 SO 4 CaCO 3 
 
 Where the quantity of salts is large, scale preventives are not of much 
 use. Some other source of supply must be sought, or the bad water 
 purified before it is allowed to enter the boilers. The damage done to 
 boilers by unsuitable water is enormous. 
 
 Pure water may be obtained by collecting rain, or condensing steam 
 by means of surface condensers. The water thus obtained should be 
 mixed with a little bad water, or treated with a little alkali, as undiluted, 
 pure water corrodes iron; or, after each periodic cleaning, the bad water 
 may be used for a day or two to put a skin upon the plates. 
 
 Carbonate of lime and magnesia may be precipitated either by heat- 
 ing the water or by mixing milk of lime (Porter-Clark process) with it, 
 the water being then filtered. 
 
 Corrosion may be produced by the use of pure water, or by the presence 
 of acids in the water, caused perhaps in the engine-cylinder by the ac- 
 tion of high-pressure steam upon the grease, resulting in the production 
 of fatty acids. Acid water may be neutralized by the addition of lime. 
 
 Amount of Sediment which may collect in a 100-H. P. steam-boiler, 
 evaporating 3000 Ibs. of water per hour, the water containing different 
 amounts of impurity in solution provided that no water is blown off: 
 'Grains of solid impurities per U. S. gallon; 
 
 5 10 20 30 40 50 60 70 80 90 100 
 
 Equivalent parts per 100,000: 
 
 8.57 17.14 34.28 51.42 68.56 85.71 102.85 120 137.1 154.3 171.4 
 Sediment deposited in 1 hour, pounds: 
 
 0.257 0.514 1.028 1.542 2.056 2.571 3.085 3.6 4.11 4.63 5.14 
 In one day of 10 hours, pounds: 
 
 2.57 5.14 10.28 15.42 20.56 25.71 30.85 36.0 41.1 46.3 . 51.4 
 In one week of 6 days, pounds: 
 15.43 30.85 61.7 92.55 123.4 154.3 185.1 216.0 246.8 277.6 308.5 
 
 If a 100-H.P. boiler has 1200 sq. ft. heating-surface, one week's running 
 without blowing off, with water containing 100 grains of solid matter per 
 gallon in solution, would make a scale nearly 0.02 in. thick, if evenly depos- 
 ited all over the heating-surface, assuming the scale to have a sp. gr. of 
 2.5 = 156 Ibs. Der cu. ft.; 0.02 X 1200 X 156 X Vi2 = 312 Ibs. 
 
 Effect of Scale on Boiler Efficiency. The following statement, 
 or a similar one, has been published and republished for 40 years or more 
 by makers of "boiler compounds," feed-water heaters and water : puri- 
 fying apparatus, but the author has not been able to trace it to its original 
 source:* 
 
 " It has been estimated that scale 1/50 of an inch thick requires the 
 burning of 5 per cent of additional fuel: scale 1/25 of an inch thick 
 requires 10 per cent more fuel; Vie of an inch of scale requires 
 cent additional fuel; I/a of an inch, 30 per cent., and 1/4 of an inch, bt> per 
 cent." 
 
 The absurdity of the last statement may be shown by a simple caicti 
 Mion. Suppose a clean boiler is giving 75% efficiency with a furnace 
 temperature of 2400 F. above the atmospheric temperature, Neglectn 
 the radiation and assuming a constant specific heat for the gases, the 
 temperature of the chimney gases will be 600. A certain amount 
 fuel and air supply will furriish 100 Ibs. of gas. In the boiler with 1/4 iru 
 
 * A committee of the Am. Ky. Mast. Mechs. Assn. in 1872 quoted 
 from a paper by Dr. Jos. G. Rodgers before the Am. Assn. for Adv. of 
 Science (date not stated): "It has been demonstrated [how and by 
 whom not stated] that a scale Vie in. thick requires the expenditure of 
 15% more fuel As the scale thickens the ratio increases; thus when it 
 is V4 in. thick, 60% more is required," 
 
INCRUSTATION AND CORROSION. 929 
 
 scale 66% more fuel will make 66 Ibs. more gas. As the extra fuel does 
 no work in evaporating water, its heat must all go into the chimney 
 gad. We have then in the chimney gases 
 
 100 Ibs. at 600 F., product 60,000 
 66 Ibs. at 2400 F., product 158,400 ... 
 
 ^^ ^lo,4(JU 
 
 which divided by 166 gives 1370 above atmosphere as the temperature 
 of the chimney gas, or more than enough to make the flue connection and 
 damper red hot. (Makers of boiler compounds, etc., please copy.) 
 
 Another writer says: "Scale of Vie inch thickness will reduce boiler 
 efficiency Vs, and the reduction of efficiency increases as the square of 
 the thickness of the scale." 
 
 This is still more absurd, for according to it if Vie in. scale reduces the 
 efficiency i/g, then 3/ 16 in. will reduce it 9/s, or to below zero. 
 
 From a series of tests of locomotive tubes covered with different thick- 
 nesses of scale up to Vs in. Prof. E. C. Schmidt (Bull. No. 11 Univ. of 
 111. Experiment Station, 1907) draws the following conclusions: 
 
 1. Considering scale 9f ordinary thickness, say varying up to Vs inch, 
 the loss in heat transmission due to scale may vary in individual cases 
 from insignificant amounts to as much as 10 or 12 per cent. 
 
 2. The loss increases somewhat with the thickness of the scale. 
 
 3. The mechanical structure of the scale is of as much or more impor- 
 tance than the thickness in producing this loss. 
 
 4. Chemical composition, except in so far as it affects the structure 
 of the scale, has no direct influence on its heat-transmitting qualities. 
 
 In 1896 the author made a test of a water-tube boiler at Aurora. 111., 
 which had a coating of scale about 1/4 in. thick throughout its whole 
 heating surface, arid obtained practically the same evaporation as in 
 another test, a few days later, after the boiler had been cleaned. This 
 is only one case, but the result is not unreasonable when it is known 
 that the scale was very soft and porous, and was easily removed from the 
 tubes by scraping. 
 
 Prof. R. C. Carpenter (Am. Electrician, Aug., 1900) says: So far as I am 
 able to determine by tests, a lime scale, even of great thickness, has no 
 appreciable effect on the efficiency of a bpiler, as in a test which was 
 conducted by myself the results were practically as good when the boiler 
 was thickly covered with lime scale as when perfectly clean. . . . Ob- 
 servations and experiments have shown that any scale porous to water 
 has little or no detrimental effect on economy of the boiler. There 
 is, I think, good philosophy for this statement; the heating capacity is 
 affected principally by the rapidity with which the heated gases will 
 surrender heat, as the water and the metal have capacities for absorbing 
 heat more than a hundred times faster than the air will surrender heat. 
 
 A thin film of grease, being impermeable to water, keeps the latter 
 from contact with the metal and generally produces disastrous results. 
 It is much more harmful than a very thick scale of carbonate of lime. 
 
 Boiler-scale Compounds. The Bavarian Steam-boiler Inspection 
 Assn. in 1885 reported as follows: 
 
 Generally the unusual substances in water can be retained in soluble 
 form or precipitated as mud by adding caustic soda or lime. This is 
 especially desirable when the boilers have small interior spaces. 
 
 It is necessary to have a chemical analysis of the water in order to fully 
 determine the kind and quantity of the preparation to be used for the 
 above purpose. 
 
 All secret compounds for removing boiler-scale should be avoided. 
 (A list of 27 such compounds manufactured and sold by German firms is 
 then given which have been analyzed by the association.) 
 
 Such secret preparations are either nonsensical or fraudulent, or 
 contain either one of the two substances recommended by the association 
 for removing scale, generally soda, which is colored to conceal its presence, 
 and sometimes adulterated with useless or even injurious matter. 
 
 These additions as well as giving the compound some strange, fanciful 
 name, are meant simply to deceive the boiler owner and conceal from him 
 the fact that he is buying colored soda or similar substances, for which 
 he is paying an exorbitant price. 
 
 Kerosene and other Petroleum Oils: Foaming, Kerosene ha? 
 been recom mended as a scale preventive. See paper by k. F, 
 
930 THE STEAM-BOILER. 
 
 ffrans. A. S. M. E., ix. 247)^ The Am. Mach~' May 22, 1890,~says: 
 Kerosene used in moderate quantities will not make the boiler foam; 
 it is recommended and used for loosening the scale and for preventing the 
 formation of scale. The presence of oil in combination with other im- 
 purities increases the tendency of many boilers to foam, as the oil with the 
 impurities impedes the free escape of steam from the water surface. 
 The use of common oil not only tends to cause foaming, but is dangerous 
 otherwise. The grease appears to combine with the impurities of the 
 water, and when the boiler is at rest this compound sinks to the plates 
 and clings to them in a loose, spongy mass, preventing the water from 
 coming in contact with the plates, and thereby producing overheating, 
 which may lead to an explosion. Foaming may also be caused by forcing 
 the fire, or by taking the steam from a point over the furnace or where 
 the ebullition is violent ; the greasy and dirty state of new boilers is another 
 good cause for foaming. Kerosene should be used at first in small quan- 
 tities, the effect carefully noted, and the quantity increased if necessary 
 for obtaining the desired results. 
 
 R. C. Carpenter (Trans. A. S. M. E., vol. xi) says: The boilers of the 
 State Argicultural College at Lansing, Mich., were badly incrusted with 
 a hard scale. It was fully 3/ 8 in. thick in many places. The first appli- 
 cation of the oil was made while the boilers were being but little used, 
 by inserting a gallon of oil, filling with water, heating to the boiling-point 
 and allowing the water to stand in the boiler two or three weeks before 
 removal. By this method fully one-half the scale was removed during 
 the warm season and before the boilers were needed for heavy firing. 
 The oil was then added in small quantities when the boiler was in actual 
 use. For boilers 4 ft. in diam. and 12 ft. long the best results were 
 obtained by the use of 2 qts. for each boiler per week, and for each boiler 
 6 ft. in diam. 3 qts. per week. The water used in the boilers has the fol- 
 lowing analysis: CaCO 3 , 206 parts in a million; MgCOs, 78 parts; Fe 2 CO 3 , 
 22 parts; traces of sulphates and chlorides of potash and soda. Total 
 solids, 325 parts in 1,000,000. 
 
 Petroleum Oils heavier than kerosene have been used with good re- 
 sults Crude oil should never be used. The more volatile oils it contains 
 make explosive gases, and its tarry constituents are apt to form a spongy 
 Incrustation. 
 
 Removal of Hard Scale. When boilers are coated with a hard scale 
 difficult to remove the addition of 1/4 lb. caustic soda per horse-power, 
 and steaming for some hours, according to the thickness of the scale, just 
 before cleaning, will greatly facilitate that operation, rendering the scale 
 soft and loose. This should be done, if possible, when the boilers are not 
 otherwise in use. (Steam.) 
 
 Corrosion in Marine Boilers. (Proc. Inst. M. E., Aug., 1884.) 
 The investigations of the Committee on Boilers served to show that the 
 internal corrosion of boilers is greatly due to the combined action of air 
 and sea-water when under steam, and when not under steam to the com- 
 bined action of air and moisture upon the unprotected surfaces of the 
 metal. There are other deleterious influences at work, such as the corro- 
 sive action of fatty acids, the galvanic action of copper and brass, and the 
 Inequalities of temperature; these latter, however, are considered to be of 
 minor importance. 
 
 Of the several methods recommended for protecting the internal sur- 
 faces of boilers, the three found most effectual are: First, the formation 
 of a .thin layer of hard scale, deposited by working the boiler with sea- 
 water- second, the coating of the surfaces with a thin wash of Portland 
 cement particularly wherever there are signs of decay; third, the use of 
 tine slabs suspended in the water and steam spaces. 
 
 As to general treatment for the preservation of boilers when laid up 
 In the reserve, either of the two following methods is adopted. First, 
 the boilers are dried as much as possible by airing-stoves, after which 
 2 to 3 cwt of quicklime is placed on trays at the bottom of the boiler and 
 Dn the tubes. The boiler is then closed and made as air-tight as possible, 
 inspection is made every six months, when if the lime be found slacked 
 t is renewed. Second, the boilers are filled with sea or fresh water, 
 saving added soda to it in the proportion of 1 lb. to every 100 or 120 Ibs. 
 >f water The sufficiency of the saturation can be tested by introducing: 
 
 $ piece of clean new iron and leaving it in tne boiler for ten or twelve 
 
INCKUSTATION AND CORROSION. 931 
 
 hours: if it shows signs of rusting, mure &oda should be added. It is 
 essential that the boilers be entirely filled, to the complete exclusion of 
 air. 
 
 Mineral oil has for many years been exclusively used for internal 
 lubrication of engines, with the view of avoiding the effects of fatty acid, 
 as this oil does not readily decompose and possesses no acid properties. 
 
 Of all the preservative methods adopted in the British service the use 
 of zinc properly distributed and fixed has been found the most effectual 
 in saving the iron and steel surfaces from corrosion, and also in neutral- 
 izing by its own deterioration the hurtful influences met with in water as 
 ordinarily supplied to boilers. The zinc slabs now used in the navy 
 boilers are 12 in. long, 6 in. wide, and ^ in. thick; this size being found 
 convenient for general application. The amount of zinc used in new 
 boilers at present is one slab of the above size for every 20 I.H.P., or 
 about 1 sq. ft. of zinc surface to 2 sq. ft. of grate surface. Rolled zinc is 
 found the most suitable for the purpose. Especial care must be taken 
 to insure perfect metallic contact between the slabs and the stays or 
 plates to which they are attached. The slabs should be placed in such 
 positions that all the surfaces in the boiler are protected. Each slab 
 should be periodically examined to see that its connection remains per- 
 fect, and to renew any that may have decayed; this examination is 
 usually made at intervals not exceeding three months. Under ordinary 
 circumstances of working these zinc slabs may be expected to last in fit 
 condition from 60 to 90 days, immersed in hot sea-water; but in new 
 boilers they at first decay more rapidly. The slabs are generally 
 secured by means of iron straps 2 in. X 3 /8 in., and long enough to 
 reach the nearest stay, to which the strap is attached by screw-bolts. 
 
 To promote the proper care of boilers when not in use the following 
 order has been issued to the French Navy by the Government: On board 
 all ships in the reserve, as well as those which are laid up, the boilers will 
 be completely filled with fresh water. In the case of large boilers with 
 large tubes there will be added to the water a certain amount of milk of 
 lime, or a solution of soda. In the case of tubulous boilers with small 
 tubes milk of lime or soda may be added, but the solution will not be 
 so strong as in the case of the larger tube, so as to avoid any danger of 
 contracting the effective area by deposit from the solution; but the 
 strength of the solution will be just sufficient to neutralize any acidity of 
 the water. (Iron Age, Nov. 2, 1893.) 
 
 Use of Zinc. : Zinc is often used in boilers to prevent the corrosive 
 action of water on the metal. The action appears to be an electrical 
 one, the iron being one pole of the battery and the zinc being the other. 
 The hydrogen goes to the iron shell and escapes as a gas into the steam. 
 The oxygen goes to the zinc. 
 
 On account of this action it is generally believed that zinc will always 
 prevent corrosion, and that it cannot be harmful to the boiler or tank. 
 Some experiences go to disprove this belief, and in numerous cases zinc 
 has not only been of no use, but has even been harmful. In one case a 
 tubular boiler had been troubled with a deposit of scale consisting chiefly 
 of organic matter and lime, and zinc was tried as a preventive. The 
 beneficial action of the zinc was so obvious that its continued use was 
 advised, with frequent opening of the boiler and cleaning out of detached 
 scale until all the old scale should be removed and the boiler become 
 clean. Eight or ten months later the water-supply was changed, it be- 
 ing now obtained from another stream supposed to be free from lime 
 and to contain only organic matter. Two or three months after its 
 introduction the tubes and shell were found to be coated with an ob- 
 stinate adhesive scale, composed of zinc oxide and the organic matter 
 or sediment of the water used. The deposit had become so heavy in 
 places as to cause overheating and bulging of the plates over the fire. 
 (The Locomotive.) 
 
 Effect of Deposit on the Fire-surface of Flues. (Rankine.) An 
 external crust of a carbonaceous kind is often deposited from the flame 
 and smoke of the furnaces in the flues and tubes, and if allowed to accu- 
 mulate, seriously impairs the economy of fuel. It is removed from time 
 to time by means of scrapers and wire brushes. The accumulation of 
 this crust is the probable cause of the fact that in some steamships the 
 consumption of coal per I.H.P. per hour goes on gradually increasing 
 
932 THE STEAM-BOILER. 
 
 until it reaches one and a half times its original amount, and sometimes 
 more. 
 
 Dangerous Steam-boilers discovered by Inspection. Tlje Hartford 
 Steam-boiler Inspection and Insurance Co. reported in The Locomotive 
 the following summary of defects in boilers discovered by its inspectors 
 in the year 1912: 
 
 Number of visits of inspection made 183,519 
 
 Total number of boilers examined 337,178 
 
 Number found uninsurable 977 
 
 Whole 
 Nature of Defects Number Dangerous 
 
 Cases of sediment or loose scale 26,299 1,553 
 
 Cases of adhering scale 40,336 1,436 
 
 Cases of grooving 2,700 252 
 
 Cases of internal corrosion 15,403 
 
 Cases of external corrosion 10,411 895 
 
 Cases of defective bracing 1,391 
 
 Cases of defective staybolting 1,712 345 
 
 Settings defective 8,119 768 
 
 Fractured plates and heads 3,288 510 
 
 Burned plates 4,965 517 
 
 Laminated plates 445 55 
 
 Cases of defective riveting 1,816 405 
 
 Cases of leakage around tubes 10,159 1,607 
 
 Cases of defective tubes or flues 11,488 4,780 
 
 Cases of leakage at seams 5,304 401 
 
 Water-gages defective 3,663 816 
 
 Blow-offs defective 4,429 1,398 
 
 Cases of low water , 447 151 
 
 Safety-valves overloaded 1,349 380 
 
 Safety-valves defective 1,534 419 
 
 Pressure-gages defective 6,765 568 
 
 Boilers without pressure-gages 633 102 
 
 Miscellaneous defects 2,268 420 
 
 Total 164,924 18,932 
 
 The above-named company publishes annually a summary like the 
 above, and also a classified list of boiler-explosions, compiled chiefly from 
 newspaper reports, showing that from 200 to 300 explosions take place in 
 the United States every year, killing from 200 to 300 persons, and in- 
 juring from 300 to 450. The lists are not pretended to be complete, and 
 may include only a fraction of the actual number of explosions. 
 
 Steam-boilers as Magazines of Explosive Energy. Prof. R. H. 
 Thurston (Trans. A. S. M. E., vol. vi), in a paper with the above title, 
 presents calculations showing the stored energy in the hot water and 
 steam of various boilers. Concerning the plain tubular boiler of average 
 form and dimensions he says: It is 60 in. in diameter, containing 66 
 3-in. tubes, and is 15 ft. long. It has 850 sq . ft. of heating and 30 sq . ft. of 
 
 erate surface; is rated at 60 H.P., but is oftener driven lip to 75; weighs 
 500 lb., and contains nearly its own weight of water, but only 21 lb. 
 of steam when under a pressure of 75 lb. per sq. in., which is below its 
 safe allowance. It stores 52,000,000 foot-pounds of energy, of which 
 but 4 % is in the steam, and this is enough to drive the boiler just about 
 one mile into the air, with an initial velocity of nearly 600 ft. per second. 
 
 SAFETY-VALVES. 
 
 Calculation of Weight, etc., for Lever Safety-valves. 
 
 Let W = weight of ball at end of lever; w = weight of lever itself; V = 
 weight of valve and spindle, all in pounds; L = distance between ful- 
 crum and center of ball; I = distance between fulcrum and center of 
 valve; g = distance between fulcrum and center of gravity of lever, all in 
 inches; A = area of valve, in sq. in.; P = pressure of steam, in lb. per 
 set. in., at which valve will open. 
 
SAFETY-VALVES. 933 
 
 Then PA X I - W X L + w X g + V X I; 
 
 whence P = (WL + wg + VI) -h Al; W = (PAl - wg - VI) -J- L; L = 
 (PAZ - w0 - VO - W. 
 
 EX\MPLE. Diameter of valve, 4 in. ; distance from fulcrum to'center 
 of bail, 36 in. ; to center of valve, 4 in. ; to center of gravity of lever, 
 15 y. in.; weight of valve and spindle, 3 lb.; weight of lever, 7 lb.; re- 
 quired the weight of ball to make the blowing-off pressure 80 lib. per sq. 
 in. ; area of 4-in. valve = 12.566 sq. in. Then 
 
 = PAl -wg -VI = 80 X 12.566 X 4 - 7 X 151/2 - 3 X 4 = 1Qg 4 ^ 
 L, 36 
 
 By the rules of the U.S. Supervising Inspectors of Steam Vessels the 
 use of lever safety-valves is prohibited on all boilers built for steam 
 vessels after June' 30, 1906. 
 
 A method for calculating the size of safety-valve is given in The Loco- 
 motive July, 1892, based on the assumption that the actual opening 
 should be sufficient to discharge all the steam generated by the boiler. 
 Napier's rule for flow of steam is taken, viz., flow through aperture of one 
 sq. in. in Ibs. per second = absolute pressure -s- 70, or in Ibs. per hour = 
 51.43 X absolute pressure. 
 
 If the angle of the seat is 45, the area of opening in sq. in. = circum- 
 ference of the disk X the lift X 0.71, 0.71 being the cosine of 45; or 
 diameter of disk X lift X 2.23. 
 
 Spring-loaded Safety-Valves. 
 
 Spring-loaded safety-valves to be used on U. S. merchant vessels must 
 conform to the rules prescribed by the Board of Supervising Inspectors, 
 and on vessels for the U. S. Navy to specifications made by the Bureau 
 of Steam Engineering, U. S. N. Valves to be used on stationary boilers 
 must conform in many cases to the special laws made by various states. 
 Few of these rules are on a logical basis, in that they take no account of 
 the lift of the valve, and it is quite clear that the rate of steam discharge 
 through a safety-valve depends upon the area of opening, which varies 
 with the circumference of the valve and the lift. Experiments made by 
 the Consolidated Safety Valve Co. showed that valves made by the differ- 
 ent manufacturers and employing various combinations of springs with 
 different designs of valve lips and huddling chambers give widely different 
 lifts. Lifts at popping point of different makes of safety-valves, at 200 
 Ibs. pressure, are as follows: 
 
 4-in. stationary valves, in., 0.031, 0.056, 0.064, 0.082, 0.094, 0.094, 0.137. 
 
 Av. 0.079 in. 
 3V2-in. locomotive valves, in., 0.040, 0.051, 0.065, 0.072, 0.076-, 0.140 ins. 
 
 Av. 0.074 in. 
 
 United States Supervising Inspectors' Rule (adopted in 1904). A = 
 0.2074 W /P. A = area of safety valve in sq. in. per sq. ft. of grate 
 surface; W = Ibs. of water evaporated per sq. ft. of grate surface per 
 hour; P = boiler pressure, absolute, Ibs. per sq. in. This rule assumes 
 a lift of 1/32 of the nominal diameter, and 75% of the flow calculated by 
 Napier's rule. This 75% corresponds nearly to the cosine of 45, or 0.707. 
 
 Massachusetts Rule of 1909. A = 770 W/P, in which W = Ibs. evapo- 
 rated per sq. ft. of grate per second; A and P as above. This is the 
 same as the U. S. rule with a 3.2% larger constant. 
 
 Philadelphia Rule. A = 22.5 G -f- (P + 8.62). A = total area of 
 valve or valves, sq. in.; G = grate area, sq. ft.; P = boiler pressure 
 (gauge). This rule came from France in 1868. It was recommended 
 to the city of Philadelphia by a committee of the Franklin Institute, 
 although the committee "had not found the reasoning upon which the 
 rule had been based." 
 
 Philip G. Darling (Trans. A. S. M. E., 1909) commenting on the above 
 rules says: The principal defect of these rules is that they assume that 
 valves of the same nominal size have the same capacity, and they rate 
 them the same without distinction, in spite of the fact that in actual prac- 
 tice some have but one-third of the capacity of others. There are other 
 .defects, such as varying the assumed lift as the valve diameter, while in 
 
934 
 
 THE STEAM-BOILER. 
 
 reality with a given design the lifts are more nearly the same in the dif- 
 ferent sizes, not varying nearly as rapidly as the diameters. And 
 further than this, the actual lifts assumed for the larger valves are 
 nearly double the actual average obtained in practice. The direct con- 
 clusion is that existing rules and statutes are not safe to follow. 
 
 Rules of the A. S. M. E. Boiler Code Committee. In 1914 the Com- 
 mittee had several conferences with the principal safety-valve manu- 
 facturers of the country and an agreement was finally reached on the 
 rules given in condensed form below. The discharging capacity of a 
 valve is based on Napier's rule with a coefficient of discharge of 0.96. 
 The formula being W = 3600 X 3.1416 XDLX 0.96 X 0.707 X P/7Q 
 or W = 109.66 D L P pounds per hour for a 45 bevel seat valve. 
 For flat seat valves the factor 0.707 is omitted and the formula becomes 
 W = 155.11 DLP pounds per hour. The following table is calcu- 
 lated from the first formula. 
 
 Discharge Capacities of Direct Spring-Loaded Pop Safety-Valves with 
 45 Bevel Seats. Pounds per Hour. 
 
 A 
 
 Diam. 1 in. 
 
 Diam. 1^ in. 
 
 Diam. 2 in. 
 
 Diam. 2y 2 in. 
 
 m 
 S.8. 
 
 Lift, in. 
 
 rh-Q 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 cs 
 
 0.02 
 
 0.04 
 
 0.05 
 
 0.03 
 
 0.05 
 
 0.06 
 
 0.04 
 
 0.06 
 
 0.07 
 
 0.04 
 
 0.06 
 
 0.08 
 
 15 
 
 65 
 
 131 
 
 163 
 
 ~l46 
 
 245 
 
 293 
 
 261 
 
 391 
 
 456 
 
 326 
 
 488 
 
 651 
 
 25 
 
 87 
 
 174 
 
 218 
 
 196 
 
 326 
 
 392 
 
 349 
 
 523 
 
 610 
 
 435 
 
 653 
 
 871 
 
 50 
 
 142 
 
 284 
 
 354 
 
 320 
 
 532 
 
 639 
 
 568 
 
 851 
 
 994 
 
 710 
 
 1064 
 
 1419 
 
 75 
 
 197 
 
 393 
 
 492 
 
 443 
 
 738 
 
 886 
 
 787 
 
 1181 
 
 1377 
 
 984 
 
 1475 
 
 1968 
 
 100 
 
 252 
 
 503 
 
 629 
 
 566 
 
 944 
 
 1133 
 
 1007 
 
 1510 
 
 1761 
 
 1258 
 
 1887 
 
 2516 
 
 125 
 
 307 
 
 613 
 
 767 
 
 689 
 
 1149 
 
 1379 
 
 1224 
 
 1836 
 
 2145 
 
 1532 
 
 2299 
 
 3064 
 
 150 
 
 362 
 
 723 
 
 904 
 
 813 
 
 1355 
 
 1625 
 
 1438 
 
 2158 
 
 2529 
 
 1806 
 
 2710 
 
 3613 
 
 175 
 
 416 
 
 833 
 
 1040 
 
 936 
 
 1561 
 
 1872 
 
 1664 
 
 2497 
 
 2913 
 
 2081 
 
 3121 
 
 4161 
 
 200 
 
 471 
 
 941 
 
 1178 
 
 1060 
 
 1766 
 
 2119 
 
 1884 
 
 2826 
 
 3296 
 
 2354 
 
 3532 
 
 4709 
 
 225 
 
 526 
 
 1052 
 
 1315 
 
 1183 
 
 1972 
 
 2366 
 
 2104 
 
 3154 
 
 3680 
 
 2629 
 
 3944 
 
 5258 
 
 250 
 
 581 
 
 1161 
 
 1451 
 
 1307 
 
 2177 
 
 2613 
 
 2322 
 
 3484 
 
 4064 
 
 2903 
 
 4355 
 
 5807 
 
 275 
 
 635 
 
 1271 
 
 1589 
 
 1430 
 
 2383 
 
 2860 
 
 2542 
 
 3813 
 
 4448 
 
 3177 
 
 4766 
 
 6355 
 
 300 
 
 698 
 
 1397 
 
 1746 
 
 3155 
 
 2589 
 
 3107 
 
 2762 
 
 4143 
 
 4832 
 
 3452 
 
 5177 
 
 6903 
 
 Capacities of Safety-Valves. Continued. 
 
 ri 
 
 Diam. 3 in. 
 
 Diam. 3 y 2 in. 
 
 Diam. 4 in. 
 
 Diam. 4^ in. 
 
 SP 
 
 Lift, in. .,-. 
 
 *S 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 Min. 
 
 Int. 
 
 Max. 
 
 0:2 
 
 0.05 
 
 0.08 
 
 0.10 
 
 0.06 
 
 0.09 
 
 0.11 
 
 0.07 
 
 0.10 
 
 0.12 
 
 0.08 
 
 0.11 
 
 0.13 
 
 IT 
 
 489 
 
 782 
 
 977 
 
 684 
 
 1026 
 
 1254 
 
 912 
 
 1303 
 
 1564 
 
 1173 
 
 1613 
 
 1906 
 
 25 
 
 653 
 
 1046 
 
 1307 
 
 914 
 
 1372 
 
 1676 
 
 1219 
 
 1742 
 
 2090 
 
 1568 
 
 2156 
 
 2547 
 
 50 
 
 1064 
 
 1703 
 
 2129 
 
 1490 
 
 2235 
 
 2732 
 
 1987 
 
 2839 
 
 3406 
 
 2555 
 
 3513 
 
 4151 
 
 75 
 
 1475 
 
 2361 
 
 2951 
 
 2066 
 
 3099 
 
 3788 
 
 2754 
 
 3935 
 
 4722 
 
 3542 
 
 4870 
 
 5756 
 
 100 
 
 1887 
 
 3019 
 
 3774 
 
 2642 
 
 3963 
 
 4843 
 
 3522 
 
 5032 
 
 6038 
 
 4529 
 
 6227 
 
 7358 
 
 125 
 
 2299 
 
 3677 
 
 4596 
 
 3218 
 
 4826 
 
 5899 
 
 4290 
 
 6128 
 
 7354 
 
 5516 
 
 7583 
 
 8963 
 
 150 
 
 2710 
 
 4335 
 
 5419 
 
 3794 
 
 5690 
 
 6954 
 
 5058 
 
 7226 
 
 8670 
 
 6503 
 
 8940 
 
 10566 
 
 175 
 
 3121 
 
 4993 
 
 6242 
 
 4369 
 
 6553 
 
 8010 
 
 5824 
 
 8320 
 
 9984 
 
 7490 
 
 10298 
 
 12173 
 
 200 
 
 3532 
 
 5b5l 
 
 7064 
 
 4946 
 
 7418 
 
 9068 
 
 6593 
 
 9420 
 
 11305 
 
 8475 
 
 11655 
 
 13773 
 
 225 
 
 3944 
 
 6310 
 
 7890 
 
 5521 
 
 8280 
 
 10120 
 
 7361 
 
 10514 
 
 12616 
 
 9465 
 
 13013 
 
 15383 
 
 250 
 
 4355 
 
 6968 
 
 8708 
 
 6097 
 
 9143 
 
 11175 
 
 8130 
 
 11614 
 
 13938 
 
 10448 
 
 14366 
 
 16980 
 
 275 
 
 4766 
 
 7620 
 
 9533 
 
 6672 
 
 10005 
 
 12333 
 
 8895 
 
 12707 
 
 15248 
 
 11438 
 
 15728 
 
 18585 
 
 300 
 
 5177 
 
 8280 
 
 10358 
 
 7248 
 
 10875 
 
 13290 
 
 9668 
 
 13807 
 
 16568 
 
 12428 
 
 17088 
 
 20195 
 
 Safety-Valve Requirements. Each boiler shall have two or more 
 safety-valves, except a boiler for which one safety-valve 3-in. size or 
 smaller is required by these Rules. 
 
 The safety-valve capacity for each boiler shall be such that the 
 safety-valve or valves will discharge all the steam that can be generated 
 
SAFETY-VALVES. 935 
 
 bv the boiler without allowing the pressure to rise more than 6% above 
 the maximum allowable working pressure, or more than 6 % above the 
 highest pressure to which any valve is set. 
 
 One or more safety-valves on every boiler shall be set at or below 
 the maximum allowable working pressure. The remaining valves may 
 be set within a range of 3% above the maximum allowable working 
 pressure but the range of setting of all of the valves on a boiler shall 
 not exceed 10% of the highest pressure to which any valve is set. 
 
 Safety-valves shall be of the direct spring-loaded pop type. The 
 vertical lift of the valve disk may be made any amount desired up to a 
 maximum of 0.15 in. The diameter measured- at the inner edge of the 
 valve seat shall be not less than 1 in. or more than 4 ^ in. 
 
 Each safety-valve shall have plainly stamped or cast on the body: 
 (a) The name or trade-mark of the manufacturer, (b) The nominal 
 diameter with the words " Bevel Seat" or " Flat Seat." (c) The steam 
 pressure at which it is set to blow, (rf) The lift of the valve disk from 
 its seat, measured immediately after the sudden lift due to the pop. 
 (e) The weight of steam discharged in pounds per hour at the pressure 
 for which it is set to blow. 
 
 The minimum capacity of a safety-valve or valves to be placed on a 
 boiler shall be determined on the basis of 6 Ib. of steam per hour per 
 sq. ft. of boiler heating surface for water tube boilers, and 5 Ib. for all 
 other types of power boilers, and upon the relieving capacity marked 
 on the valves by the manufacturer, provided such marked capacity 
 does not exceed that given in the table, in which case the minimum 
 safety-valve capacity shall be determined on the basis of the maximum 
 relieving capacity given in the table for the particular size of valve and 
 working pressure for which it was constructed. The heating surface 
 shall be computed for that side of the boiler surface exposed to the 
 products of combustion, exclusive of the superheating surface. 
 
 Valves 1 M in. diam. with lifts 0.03, 0.04 and 0.05 in. give a discharge 
 for 0.04-in. lift the same as that of a 1-in. valve with 0.05-in. lift; with 
 0.03-in. lift 25% less and with 0.05-in. lift 25% greater. 
 
 The discharge capacity of a fl?t seat valve is 1.41 times that of a 
 45 bevel seat valve of the same diameter and lift. 
 
 Safety-Valves for Locomotives. A Committee of theAmerican Railway 
 Master Mechanics Association presented a report on safety-valves in 
 1912, giving the following formula for 45 bevel seat valves: D L P = 
 0.036 H, in which D = total of the diameters of the inner edge of 
 the seats of the valves required; L = vertical lift in inches; P = 
 absolute pressure, Ib. per sq. in. ; H = total heating surface of boiler, 
 sq. ft. (superheating surface not included). Every locomotive should 
 be equipped with not less than two and not more than three safety- 
 valves, the size to be determined by the formula. The valves are to 
 be set as follows: The first at boiler pressure, second 2 Ib. in excess, 
 third 3 Ib. in excess of the second. Manufacturers should be required 
 to stamp on the valve the lift in inches as determined by actual test. 
 
 The formula corresponds to the discharge calculated by Napier's 
 rule with a coefficient of flow of 0.973 and an evaporation of 4 Ib. per 
 square foot of heating surface per hour. It is evident that safety- 
 valve? proportioned according to this formula will have a relieving 
 capacity much less than the evaporative capacity of locomotive 
 boilers with large fire-boxes and short flues. The Consolidated Safety 
 Valve Co. suggests the formula D L P = Ci Hi + Cz Hz in which Hi is 
 fire-box and Hz flue heating-surface, sq. ft., and Ci and Cz are constants 
 to be determined by experiment. Ci being considerably larger than 2. 
 
 Unequal expansion of safety-valve parts under steam temperatures 
 tends to cause leakage, and as this temperature effect becomes more 
 serious in the large sizes the manufacturers do not recommend the use 
 of valves larger than 4 1/2 ins. If greater relieving capacity be required 
 it is the best practice to use duplex valves or additional single valves. 
 
 For an extended discussion on safety-valves, see Trans, A. 5. M. E,, 
 
936 
 
 THE STEAM-BOILER. 
 
 THE INJECTOR. 
 
 Equation of the Injector. 
 
 Let S be the number of pounds of steam used; 
 
 W the number of pounds of water lifted and forced Into the boiler; 
 h the height in feet of a column of water, equivalent to the absolute 
 
 pressure in the boiler; 
 
 h Q the height in feet the water is lifted to the injector; t 
 t\ the temperature of the water before it enters the injector; 
 tz the temperature of the water after leaving the injector; 
 H the total heat above 32 F. in one pound of steam in the boiler, 
 
 L the work in friction and the equivalent lost work due to radiation 
 
 and lost heat; 
 
 778 the mechanical equivalent of heat. 
 Then 
 
 - = ,- 
 
 / <o 
 
 An equivalent formula, neglecting Who + L as small, is 
 
 or 
 
 d 778J H-(t*-32) . 
 
 3.1851 p] 
 
 [H -(2- 32)] d -0.1851 p' 
 In which d = weight of 1 cu. ft. of water at temperature t z ; p = absolute 
 pressure of steam, Ibs. per sq. in. 
 
 The rule for finding the proper sectional area for the narrowest part of 
 the nozzles is given as follows by Rankine, S. E., p. 477: 
 
 Area in square inches = 
 
 cubic feet per hour gross feed-water 
 800 Vpressure in atmospheres 
 
 An important condition which must be fulfilled in order that the injec- 
 tor will work is that the supply of water must be sufficient to condense 
 the steam. As the temperature of the supply or feed-water is higher, 
 the amount of water required for condensing purposes will be greater. 
 
 The table below gives the calculated value of the maximum ratio of 
 water to the steam, and the values obtained on actual trial, also the 
 highest admissible temperature of the feed-water as shown by theory 
 and the highest actually found by trial with several injectors. 
 
 Gauge- 
 pres- 
 sure, 
 pounds 
 per 
 sq. in. 
 
 Maximum Ratio Water 
 to Steam. 
 
 Gauge- 
 pres- 
 sure, 
 pounds 
 per 
 sq. in. 
 
 Maximum Temperature 
 of Feed-Water. 
 
 Calculated 
 from 
 Theory. 
 
 Actual Ex- 
 periment. 
 
 Theoreti- 
 cal. 
 
 Experimental 
 Results. 
 
 0) 
 
 . bo 
 f*o' 
 
 ill 
 
 H. * 
 
 T3 
 
 .8, 
 
 <%o' 
 
 z 
 
 Oi ocs 
 
 H 2 
 
 5 
 
 H. 
 
 P. 
 
 M. 
 
 S. 
 
 H. 
 
 P. 
 
 M. 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 
 36.5 
 25.6 
 20.9 
 17.87 
 16.2 
 14.7 
 13.7 
 12.9 
 12.1 
 11.5 
 
 30.9 
 22.5 
 19.0 
 15.8 
 13.3 
 11.2 
 12.3 
 11.4 
 
 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 120 
 150 
 
 
 
 
 
 132 
 134 
 134 
 132 
 131 
 130 
 130 
 131 
 132* 
 132* 
 134* 
 121* 
 
 19.9 
 17.2 
 15.0 
 14.0 
 11.2 
 11.7 
 11.2 
 
 21.5 
 19.0 
 15.86 
 13.3 
 12.6 
 12.9 
 
 142 
 132 
 126 
 120 
 114 
 109 
 105 
 99 
 95 
 87 
 77 
 
 173 
 162 
 156 
 150 
 143 
 139 
 134 
 129 
 125 
 117 
 107 
 
 135 
 
 120 
 
 130 
 
 140 
 
 113 
 
 125 
 
 14J* 
 141* 
 
 115 
 
 iis 
 
 123 
 123 
 122 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * Temperature of delivery above 212. Waste- valve closed. 
 H, Hancock inspirator; P, Park injector; M, Metropolitan injector; 
 S, Sellers 1876 injector. 
 
THE INJECTOR. 937 
 
 Efficiency of the Injector. Experiments at Cornell University 
 described by Prof. R. C. Carpenter, in Cassier's Magazine, Feb., 1892 
 show that the injector, when considered merely as a pump, has an exceed- 
 ingly low efficiency, the duty ranging from 161,000 to 2,752,000 undei 
 different circumstances of steam and delivery pressure. Small direct- 
 acting pumps, such as are used for feeding boilers, show a duty of from 
 4 to 8 million ft.-lbs., and the best pumping-engines from 100 to 140 mil- 
 lion. When used for feeding water into a boiler, however, the injector 
 has a thermal efficiency of 100%, less the trifling loss due to radiation, 
 since all the heat rejected passes into the water which is carried into the 
 boiler. 
 
 The loss of work in the injector due to friction reappears as heat which 
 is carried into the boiler, and the heat which is converted into useful 
 work in the injector appears in the boiler as stored-up energy. 
 
 Although the injector thus has a perfect efficiency as a boiler-feeder, it 
 is not the most economical means for feeding a boiler, since it can draw 
 only cold or moderately warm water, while a pump can feed water which 
 has been heated by exhaust steam which would otherwise be wasted. 
 
 Performance of Injectors. In Am. Mack., April 13, 1893, are a 
 number of letters from different manufacturers of injectors in reply to the 
 question: "What is the best performance of the injector in raising or 
 lifting water to any height? " Some of the replies are tabulated below. 
 
 W. Sellers & Co. 25.51 Ibs. water delivered to boiler per ib. of steam; 
 temperature of water, 64; steam pressure, 65 Ibs. 
 
 Schaeffer & Budenberg 1 gal. water delivered to boiler for 0.4 to 
 0.8 Ib. steam. 
 
 injector will lift by suction water of 
 
 140 F. 136 to 133 122 to 118 113 to 107 
 
 If boiler pres. is 30 to 60 Ibs. 60 to 90 Ibs. 90 to 120 Ibs. 120tol501bs, 
 If the water is not over 80 F., the injector will force against a pres- 
 sure 75 Ibs. higher than that of the steam. 
 
 Hancock Inspirator Co.: 
 
 Lift in feet 22 22 22 11 
 
 Boiler pressure, absolute, Ibs 75.8 54.1 95.5 75.4 
 
 Temperature of suction 34.9 35.4 47.3 53. 2 a 
 
 Temperature of delivery 134 117.4 173.7 131.1 
 
 Water fed per Ib. of steam. Ibs 11.02 13.67 8.18 13.3 
 
 The theory of the injector is discussed in Wood's, Peabody's, and 
 Rontgen's treatises on Thermodynamics. See also "Theory and Practice 
 of the Injector," by Strickland L. Kneass, New York, 1910. 
 
 Boiler-feeding Pumps. Since the direct-acting pump, commonly 
 used for feeding boilers, has a very low efficiency, or less than one-tenth 
 that of a good engine, it is generally better to use a pump driven by belt 
 from the main engine or driving shaft. The mechanical work needed to 
 feed a boiler may be estimated as follows: If the combination of boilei 
 and engine is such that half a cubic foot, say 32 Ibs. of water, is needed 
 per horse-power, and the boiler-pressure is 100 Ibs. per sq. in., then the 
 work of feeding the quantity of water is 100 Ibs. X 144 sq. in. X 1/2 ft.- 
 Ib. per hour = 120 ft.-lbs. per min. = 120/33,000 = .0036 H.P., or less 
 than Vio of 1% of the power exerted by the engine. If a direct-acting 
 pump, which discharges its exhaust steam into the atmosphere, is used 
 for feeding, and it has only Vio the efficiency of the main engine, then the 
 steam used by the pump will be equal to nearly 4% of that generated by 
 the boiler. 
 
 The low efficiency of boiler-feeding pumps, and of other small auxiliary 
 steam-driven machinery, is, however, of no importance if all the exhaust 
 steam from these pumps is utilized in heating the feed-water. 
 
 The following table by Prof. D. S. Jacobus gives the relative steam 
 consumption of steam and power pumps and injector, with and with- 
 out heater, as used upon a boiler with 80 Ibs. gauge-pressure, the pump 
 having a duty of 10,000,000 ft.-lbs. per 100 Ibs. of coal when no heater 
 Is used; the injector heating the water from 60 to 150 F. 
 
 Direct-acting pump feeding water at 60, without a heater ] .000 
 
 Injector feeding water at 150, without a heater 0.985 
 
 Injector feeding water through a heater in which it is heated from 
 
 150 to 200 0.938 
 
938 
 
 THE STEAM-BOILER. 
 
 Direct-acting pump feeding water through a heater, in which it Is 
 
 heated from 60 to 200 . 879 
 
 Geared pump, run from the engine, feeding water through a heater, 
 in which it is heated from 60 to 200 .868 
 
 Gravity Boiler-feeders. If a closed tank be placed above the level 
 of the water in a boiler and the tank be filled or partly filled with water, 
 then on shutting off the supply to the tank, admitting steam from the 
 boiler to the upper part of the tank, so as to equalize the steam-pressure 
 in the boiler and in the tank, and opening a valve in a pipe leading from 
 the tank to the boiler, the water will run into the boiler. An apparatus 
 of this kind may be made to work with practically perfect efficiency as a 
 boiler-feeder, as an injector does, when the feed-supply is at ordinary 
 atmospheric temperature, since after the tank is emptied of water and the 
 valves in the pipes connecting it with the boiler are closed the conden- 
 sation of the steam remaining in the tank will create a vacuum which will 
 lift a fresh supply of water into the tank. The only loss of energy in the 
 cycle of operations is the radiation from the tank and pipes, which may 
 be made very small by proper covering. 
 
 When the feed-water supply is hot, such as the return water from a 
 heating system, the gravity apparatus may be made to work by having 
 two receivers, one at a low level, which receives the returns or other 
 feed-supply, and the other at a point above the boilers. A partial vacuum 
 being created in the upper tank, steam-pressure is applied above the 
 water in the lower tank by which it is elevated into the upper. The 
 operation of such a machine may be made automatic by suitable arrange- 
 ment of valves. 
 
 FEED-WATER HEATERS. 
 
 Percentage of Saving for Each Degree of Increase in Temperature 
 of Feed-water Heated by Waste Steam. 
 
 Initial 
 Temp, 
 of 
 Feed. 
 
 Steam Pressure in Boiler, Ibs. per sq. in. above Atmosphere. 
 
 Initial 
 Temp. 
 
 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 32 
 
 .0872 
 
 .0861 
 
 .0855 
 
 .0851 
 
 .0847 
 
 .0844 
 
 .0841 
 
 .0839 
 
 .0837 
 
 .0835 
 
 .0833 
 
 32 
 
 40 
 
 .0878 
 
 .0867 
 
 .0861 
 
 .0856 
 
 .0853 
 
 .0850 
 
 .0847 
 
 .0845 
 
 .0843 
 
 .0841 
 
 .0839 
 
 40 
 
 50 
 
 .0886 
 
 .0875 
 
 .0868 
 
 .0864 
 
 .0860 
 
 .0857 
 
 .0854 
 
 .0852 
 
 .0850 
 
 .0848 
 
 .0846 
 
 50 
 
 60 
 
 .0894 
 
 .0883 
 
 .0876 
 
 .0872 
 
 .0867 
 
 .0864 
 
 .0862 
 
 .0859 
 
 .0856 
 
 .0855 
 
 .0853 
 
 60 
 
 70 
 
 0902 
 
 .0890 
 
 .0884 
 
 .0879 
 
 .0875 
 
 .0872 
 
 .0869 
 
 .0867 
 
 .0864 
 
 .0862 
 
 .0860 
 
 70 
 
 80 
 
 .0910 
 
 .0898 
 
 .0891 
 
 .0887 
 
 .0883 
 
 .0879 
 
 .0877 
 
 .0874 
 
 .0872 
 
 .0870 
 
 .0868 
 
 60 
 
 90 
 
 .0919 
 
 0907 
 
 .0900 
 
 .0895 
 
 .0888 
 
 0887 
 
 .0884 
 
 .0883 
 
 .0879 
 
 .0877 
 
 .0875 
 
 90 
 
 100 
 
 .0927 
 
 .0915 
 
 .0908 
 
 .0903 
 
 .0899 
 
 .0895 
 
 .0892 
 
 .0890 
 
 .0887 
 
 .0885 
 
 .0883 
 
 100 
 
 110 
 
 .0936 
 
 .0923 
 
 .0916 
 
 .0911 
 
 .0907 
 
 .0903 
 
 .0900 
 
 .0898 
 
 .0895 
 
 .0893 
 
 .0891 
 
 110 
 
 120 
 
 .0945 
 
 .0932 
 
 .0925 
 
 .0919 
 
 .0915 
 
 .0911 
 
 .0908 
 
 .0906 
 
 .0903 
 
 .0901 
 
 .0899 
 
 120 
 
 130 
 
 .0954 
 
 0941 
 
 .0934 
 
 .0928 
 
 .0924 
 
 .0920 
 
 .0917 
 
 .0914 
 
 .0912 
 
 .0909 
 
 .0907 
 
 130 
 
 140 
 
 .0963 
 
 .0950 
 
 .0943 
 
 .0937 
 
 .0932 
 
 .0929 
 
 .0925 
 
 .0923 
 
 .0920 
 
 .0918 
 
 .0916 
 
 140 
 
 150 
 
 .0973 
 
 .0959 
 
 .0951 
 
 0946 
 
 .0941 
 
 .0937 
 
 .0934 
 
 .0931 
 
 .0929 
 
 .0926 
 
 .0924 
 
 150 
 
 160 
 
 .0982 
 
 .0968 
 
 .0961 
 
 0955 
 
 .0950 
 
 .0946 
 
 .0943 
 
 .0940 
 
 .0937 
 
 .0935 
 
 .0933 
 
 160 
 
 170 
 
 0992 
 
 .0978 
 
 .0970 
 
 .0964 
 
 .0959 
 
 .0955 
 
 .0952 
 
 .0949 
 
 .0946 
 
 .0944 
 
 .0941 
 
 170 
 
 180 
 
 .1002 
 
 .0988 
 
 .0981 
 
 .0973 
 
 .0969 
 
 .0965 
 
 .0961 
 
 .0958 
 
 .0955 
 
 .0953 
 
 .0951 
 
 180 
 
 190 
 
 .1012 
 
 .0998 
 
 .0989 
 
 .0983 
 
 .0978 
 
 .0974 
 
 .0971 
 
 .0968 
 
 .0964 
 
 .0962 
 
 .0960 
 
 190 
 
 200 
 
 .1022 
 
 .1008 
 
 .0999 
 
 0993 
 
 0988 
 
 .0984 
 
 .0980 
 
 .0977 
 
 .0974 
 
 .0972 
 
 .0969 
 
 200 
 
 210 
 
 .1033 
 
 .1018 
 
 .1009 
 
 .1003 
 
 .0998 
 
 .0994 
 
 .0990 
 
 .0987 
 
 .0984 
 
 .0981 
 
 .0979 
 
 210 
 
 220 
 
 
 .1029 
 
 .1019 
 
 .1013 
 
 .1008 
 
 .1004 
 
 .1000 
 
 .0997 
 
 .0994 
 
 .0991 
 
 .0989 
 
 220 
 
 230 
 
 
 .1039 
 
 .1031 
 
 .1024 
 
 .1018 
 
 .1012 
 
 .1010 
 
 .1007 
 
 .1003 
 
 .1001 
 
 .0999 
 
 230 
 
 240 
 
 
 .1050 
 
 .1041 
 
 .1034 
 
 .1029 
 
 .1024 
 
 .1020 
 
 .1017 
 
 .1014 
 
 .1011 
 
 .1009 
 
 240 
 
 250 
 
 
 .1062 
 
 .1052 
 
 .1045 
 
 .1040 
 
 .1035 
 
 .1031 
 
 .1027 
 
 .1025 
 
 .1022 
 
 .1019 
 
 250 
 
 An approximate rule for the conditions of ordinary practice is that a 
 saving of 1% is made by each increase of 11 in the temperature of the 
 feed-water. This corresponds to 0.0909% per degree. 
 
 The calculation of saving is made as follows: Boiler-pressure, 100 Ibs. 
 gauge; total heat in steam above 32 = 1185 B.T.U. Feed-water, original 
 temperature 60?, final temperature 209 F. Increase in heat-units, 150. 
 
FEED-WATER HEATERS. 939 
 
 Heat-units above 32 in feed- water of original temperature =28. Heat- 
 units in steam above that in cold feed-water, 1185 28 = 1157. Saving 
 by the feed-water heater = 150/1157 = 12.96%. The same result is 
 obtained by the use of the table. Increase in temperature 150 X 
 tabular figure 0.0864 = 12.96%. Let total heat of 1 Ib. of steam at the 
 boiler-pressure = H ' total heat of 1 Ib. of feed-water before entering the 
 heater = hi, and after passing through the heater = fo; then the saving 
 
 made by the heater is ^ _ ^ 
 
 Strains Caused by Cold Feed-water. A calculation is made In 
 The Locomotive of March, 1893, of the possible strains caused in the sec- 
 tion of the shell of a boiler by cooling it by the injection of cold feed- 
 water. Assuming the plate to be cooled 200 F., and the coefficient of 
 expansion of steel to be 0.0000067 per degree, a strip 10 in. long would 
 contract 0.013 in., if it were free to contract. To resist this contraction, 
 assuming that the strip is firmly held at the ends and that the modulus 
 of elasticity is 29,000,000, would require a force of 37,700 Ibs. per sq. in. 
 Of course this amount of .strain cannot actually take place, since the strip 
 is not firmly held at the ends, but is allowed to contract to some extent 
 by the elasticity of the surrounding metal. But, says The Locomotive, 
 we may feel pretty confident that in the case considered a longitudinal 
 strain of somewhere in the neighborhood of 8,000 or 10,000 Ibs. per sq. in. 
 may be produced by the feed- water striking directly upon the plates; 
 and this, in addition to the normal strain produced by the steam-pressure, 
 is quite enough to' tax the girth-seams beyond their elastic limit, if the 
 feed-pipe discharges anywhere near them. Hence it is not surprising that 
 the girth-seams develop leaks and cracks in 99 cases out of every 100 in 
 which the feed discharges directly upon the fire-sheets. 
 
 Capacity of Feed-water Heaters. (W. R. Billings, Eng. Rec., 
 Feb., 1898.) Closed feed-water heaters are seldom provided with 
 sufficient surface to raise the feed temperature to more than 200. The 
 rate of heat transmission may be measured by the number of British 
 thermal units which pass through a square foot of tubular surface in one 
 hour for each degree of difference in temperature between the water and 
 the steam. One set of experiments gave results as below: 
 
 Difference between 
 final temperatures 
 of water and 
 steam 
 
 5 F 67 B.T.U. 
 
 6 
 
 8 
 11 
 15 
 
 18 
 
 79 
 
 89 
 
 .114 
 
 , 129 
 
 .139 
 
 Transmitted in one 
 hour by each sq. ft. 
 of surface for each 
 degree of average 
 difference in temper- 
 atures. 
 
 Even with the rate of transmission as low as 67 B.T.U. the water was 
 still 5 from the temperature of the steam. At what rate would the heat 
 have been transmitted if the water could have been brought to within 
 2 of the temperature of the steam, or to 210 when the steam is at 212? 
 
 For commercial purposes feed-water heaters are given a H.P. rating 
 which allows about one-third of a square foot of surface per H.P. a 
 boiler H.P. being 30 Ibs. of water per hour. If the figures given in the 
 table above are accepted as substantially correct, a heater which is to 
 raise 3000 Ibs. of water per hour from 60 to 207, using exhaust steam 
 at 212 as a heating medium, should have nearly 84 sq. ft. of heating 
 surface or nearly a square foot of surface per H.P. That feed-water 
 heaters do not carry this amount of heating surface is well known. 
 
 Calculation of Surface of Heaters and Condensers. (H. L. Hep- 
 burn, Power, April, 1902.) Let W = Ibs. of water per hour; A = area of 
 surface in sq. ft.; Ts = temperature. of the steam; / = initial tempera- 
 ture of the water; F = final temperature of the water; S = Ibs. of steam 
 per hour; H = B.T.U. above 32 F. in 1 Ib. of steam; N = B.T.U. in 
 L Ib. of condensed steam; U = B.T.U. transmitted per sq. ft. per hr. per 
 deg. of mean difference of temperature between the steam and the water. 
 
 Then A U = W log e ^ ~ p , for heaters. 
 
 
 H N Ts I 
 
 A U M S -= j- x logg -^ = , for condensers. 
 
 r L 2s "" f 
 
940 
 
 THE STEAM-BOILER, 
 
 The value of U varies widely according to the condition of the surface 
 whether clean or coated with grease or scale, and also with the velocity 
 of the water over the surfaces. Values of 300 to 350 have been obtained 
 in experiments with corrugated copper tubes, but ordinary heaters give 
 much lower values. From the experiments of Loring and Emery on the 
 U. S. S. Dallas, Mr. Hepburn finds U = 192. Using this value he finds 
 the number of square feet of heating surface required per 1000 Ibs. of 
 feed-water per hour to be as follows, the temperature of the entering 
 water being 60 F. 
 
 Steam Temperature, 212. 
 
 Steam 25 in. Vacuum. 
 
 F 
 
 S 
 
 F 
 
 S 
 
 F 
 
 S 
 
 F 
 
 S 
 
 194 
 196 
 198 
 200 
 202 
 
 11.11 
 11.73 
 12.44 
 13.20 
 14.17 
 
 204 
 206 
 208 
 210 
 212 
 
 15.34 
 
 16.85 
 18.93 
 22.52 
 Infinite 
 
 90 
 95 
 100 
 105 
 110 
 
 2.38 
 3.03 
 3.76 
 4.62 
 5.65 
 
 115 
 120 
 125 
 130 
 133 
 
 6.78 
 8.60 
 11.15 
 16.25 
 Infinite 
 
 F = final temperature of feed-water, S = sq. ft. of surface. From this 
 table it is seen that if 30 Ibs, of water per hour is taken to equal 1 H.P. 
 and a feed-water heater is made with 1/3 sq. ft. per H.P., it may be ex- 
 pected to heat the feed-water from 60 to something less than 194, or ii 
 made with 1/2 sq. ft. per H.P. it may heat the water to 204 F. 
 
 For a further discussion of this subject, see Heat, pages 587 to 591. 
 
 Proportions of Open Type Feed-water Heaters. C. L. Hubbard 
 (Practical Engineer, Jan. 1, 1909) gives the following: 
 
 Exhaust heaters should be proportioned according to the quality of 
 the water to be used, the size being increased with the amount of mud 
 or scale-producing properties which the water contains regardless of the 
 quantity of water to be heated. The general proportions of an open 
 heater will depend somewhat upon the arrangement of the trays or pans, 
 but an approximation of the size of shell for a cylindrical heater is as 
 follows: A = H -4- aL; L = H * a A ; in which A =-- sectional area of shell 
 in sq. ft.; L = length of shell in linear ft.; H = total weight of water to 
 be heated per hour divided by the weight of steam used per horse-power 
 per hour by the engine; a 2.15 for very muddy water, 6.0 for slightly 
 muddy water, and 8.0 for clear water. 
 
 The pan or tray surface varies according to the quality of the water, 
 both as regards the amount of mud and the scale-making ingredients. 
 The surface in square feet for each 1000 Ibs. of water heated per hour 
 may be taken as follows, for the vertical and horizontal types respectively: 
 
 Very bad water 8.5 and 9 . 1 
 
 Medium muddy water 6 and 6.5 
 
 Clear and little scale 2 and 2 . 2 
 
 The space between the pans is made not less than 0.1 the width for 
 rectangular and 0.25 the diameter for round pans. Under ordinary 
 circumstances it is not cust9mary to use more than six pans in a tier, 
 in order to obtain a low velocity over each pan. The size of the storage 
 or settling chamber in the horizontal type varies from 0.25 to 0.4 of the 
 volume of the shell, depending on the quality of the water; 0.33 is about 
 the average. In the case of vertical heaters, this varies from 0.4 to 0.6 
 of the volume of the shell. Filters occupy from 10 to 15% of the volume 
 of the shell in the horizontal type and from 15 to 20% in the vertical. 
 
 Open versus Closed Feed-water Heaters. (W. E. Harrington, St. 
 Rwy. Jour., July 22, 1905.) There still exists some difference of opinion 
 as to the relative desirability of open or closed type of feed-water heater, 
 but the degree of perfection which the open heater has attained has elimi- 
 nated formerly objectionable features. The chief objection which attended 
 the early use of the open heater, namely, that the oil from the exhaust 
 steam was carried into the boiler, did much to discourage its more general 
 adoption. This objection does not hold good against the better designs 
 of open heaters now on the market. There are thousands of installations 
 in which the open heater is now being used where no difficulty is experi- 
 enced from the contamination of the feed-water by oil. The perfection of 
 oil separators for use in the exhaust steam connection to the heater has 
 rendered this possible. 
 
STEAM SEPARATORS. 
 
 941 
 
 STEAM SEPARATORS. 
 
 If moist steam flowing at a high velocity in a pipe has its direction 
 suddenly changed, the particles of water are by their momentum pro- 
 jected in their original direction against the bend in the pipe or wall of 
 the chamber in which the change of direction takes place. By making 
 proper provision for drawing off the water thus separated the steam may 
 be dried to a greater or less extent. For long steam-pipes a large drum 
 should be provided near the engine for trapping the water condensed in 
 the pipe. A drum 3 ft. diameter, 15 ft. high, has given good results in 
 separating the water of condensation of a steam-pipe 10 in. diameter 
 and 800 ft. long. 
 
 Efficiency of Steam Separators. Prof. R. C. Carpenter, in 1891, 
 made a series of tests of six steam separators, furnishing them with 
 steam containing different percentages of moisture, and testing the 
 quality of steam before entering and after passing the separator. A 
 condensed table of the principal results is given below. 
 
 Make of 
 Separator. 
 
 Test with Steam of about 10% 
 of Moisture. 
 
 Tests with Varying Moisture. 
 
 Quality 
 of Steam 
 before. 
 
 Quality 
 of Steam 
 after. 
 
 Efficiency, 
 per cent. 
 
 Quality of 
 Steam 
 before. 
 
 Quality of 
 Steam after. 
 
 Av'ge 
 Effi- 
 ciency. 
 
 B 
 A 
 D 
 C 
 E 
 F 
 
 87.0% 
 90.1 
 89.6 
 90.6 
 88.4 
 88.9 
 
 98.8% 
 98.0 
 95.8 
 93.7 
 90.2 
 92.1 
 
 90.8 
 80.0 
 59.6 
 33.0 
 15.5 
 28.8 
 
 66.1 to 97.5% 
 51.9 " 98 
 72.2 " 96.1 
 67.1 " 96.8 
 68.6 " 98.1 
 70.4 " 97.7 
 
 97.8 to 99% 
 97.9 99.1 
 95.5 98.2 
 .93.7 98.4 
 79.3 98.5 
 84.1 97.9 
 
 87.6 
 76.4 
 71.7 
 63.4 
 36.9 
 28.4 
 
 Conclusions from the tests were: 1. That no relation existed between 
 the volume of the several separators and their efficiency. 2. No marked 
 decrease in pressure was shown by any of the separators, the most being 
 1.7 Ibs. in E. 3. Although changed direction, reduced velocity, and per- 
 haps centrifugal force are necessary for good separation, still some means 
 must be provided to lead the water out of the current of the steam. The 
 high efficiency obtained from B and A was largely due to this feature. In 
 B the interior surfaces are corrugated and thus catch the water thrown 
 out of the steam and readily lead it to the bottom. In A, as so on as the 
 water falls or is precipitated from the steam, it comes in contact with the 
 perforated diaphragm through which it runs into the space below, where 
 it is not subjected to the action of the steam. Experiments made by 
 Prof. Carpenter on a "Stratton" separator in 1894 showed that>the 
 moisture in the steam leaving the separator was less than 1% when that 
 in the steam supplied ranged from 6% to 21%. 
 
 Experiments by Prof. G. F. Gebhardt (Power, May 11, 1909) on six 
 separators of different makes led to the following conclusions: (1) The 
 efficiency of separation decreases as the velocity of the steam increases. 
 (2) The efficiency increases as the percentage of moisture in the enter- 
 ing steam increases. (3) The drop in pressure increases rapidly with the 
 increase in velocity. The six separators are described as follows: 
 
 U: 2-in. vertical; no baffles; current reversed once. 
 
 V: 4-in. horizontal with single baffle plate of the fluted type; current 
 reversed once. 
 
 W: 4-in. vertical with two baffle plates of the smooth type; current 
 reversed once. 
 
 X: 3-in. horizontal f several fluted baffle plates; no reversal of current. 
 
 Y: 6-in. vertical; centrifugal type; current reversed once. 
 
 Z: 3-in. horizontal; current reversed twice; steam impinges on hori- 
 zontal fluted baffle during reversal. 
 
 The efficiency is defined as the ratio of the water removed from the 
 steam by the separator to the water injected into the dry steam for the 
 purpose of the test. With steam at 100 Ibs. pressure containing 10% 
 water, the efficiencies, taken from plotted curves, were as follows: 
 
 U V W X Y Z 
 
 At 2000 ft. per min 64 69 86 88 79 66 
 
 At 3000 ft. per min 37 45 80 60 61 48 
 
942 THE STEAM-BOILER. 
 
 DETERMINATION OF THE MOISTURE IN STEAM STEAM 
 CALORIMETERS. 
 
 In all boiler-tests it is important to ascertain the quality of the steam, 
 i.e., 1st, whether the steam is "saturated" or contains the quantity of 
 heat due to the pressure according to standard experiments; 2d, whether 
 the quantity of heat is deficient, so that the steam is wet; and 3d, whether 
 the heat is in excess and the steam superheated. The best method of 
 ascertaining the quality of the steam is undoubtedly that employed by a 
 committee which tested the boilers at the American Institute Exhibition 
 of 1871-2, of which Prof. Thurston was chairman, i.e., condensing all the 
 water evaporated by the boiler by means of a surface condenser, weighing 
 the condensing water, and taking its temperature as it enters ana as it 
 leaves the condenser; but this plan cannot always be adopted. 
 
 A substitute for this method is the barrel calorimeter, which with careful 
 operation and fairly accurate instruments may generally be relied on to 
 give results within two per cent of accuracy (that is, a sample of steam 
 which gives the apparent result of 2% of moisture may contain anywhere 
 between and 4%). This calorimeter is described as follows: A sample 
 of the steam is taken by inserting a perforated l/2-inch pipe into and 
 through the main pipe near the boiler, and led by a hose, thoroughly 
 felted, to a barrel, holding preferably 400 Ibs. of water, which is set upon 
 a platform scale and provided with a cock or valve for allowing the water 
 to flow to waste, and with a small propeller for stirring the water. 
 
 To operate the calorimeter the barrel is filled with water, the weight 
 and temperature ascertained, steam blown through the hose outside the 
 barrel until the pipe is thoroughly warmed, when the hose is suddenly 
 thrust into the water, and the propeller operated until the temperature 
 of the water is increased to the desired point, say about 110 usually. 
 The hose is then withdrawn quickly, the temperature noted, and the 
 weight again taken. 
 
 An error of 1/10 of a pound in weighing the condensed steam, or an 
 error of 1/2 degree in the temperature, will cause an error of over 1 % in 
 the calculated percentage of moisture. See Trans. A . S. M. E., vi, 293. 
 
 The calculation of the percentage of moisture is made as below ; 
 
 Q = quality of the steam, dry saturated steam being unity. 
 H = total heat of 1 Ib. of steam at the observed pressure. 
 T = total heat of 1 Ib. of water at the temperature of steam of the 
 
 observed pressure. 
 
 h = total heat of 1 Ib. of condensing water, original. 
 hi = total heat of 1 Ib. of condensing water, final. 
 W = weight of condensing water, corrected for water-equivalent of 
 
 the apparatus. 
 
 w = weight of the steam condensed. 
 Percentage of moisture = 1 Q. 
 
 If Q is greater than unity, the steam is superheated, and the degrees of 
 superheating = 2.0833 (H - T) (Q - 1). 
 
 Difficulty of Obtaining a Correct Sample. Experiments by Prof. 
 D. S. Jacobus (Trans. A. S. M. E., xvi, 1017), show that it is practically 
 impossible to obtain a true average sample of the steam flowing in a pipe. 
 For accurate determinations all the steam made by the boiler should be 
 passed through a separator, the water separated should be weighed a-nd 
 a calorimeter test made of the steam just after it has passed the separator. 
 Coil Calorimeters. Instead of the open barrel in which the steam 
 is condensed, a coil acting as a surface-condenser may be used, which is 
 placed in the barrel, the water in coil and barrel being weighed separately. 
 For a description of an apparatus of this kind designed by the author, 
 which he has found to give results with a probable error not exceeding 
 1/2 per cent of moisture, see Trans. A. S. M. E., vi, 294. This calorimeter 
 may be used continuously, if desired, instead of intermittently. In this 
 case a continuous flow of condensing water into and out of the barrel 
 must be established, and the temperature of inflow and outflow and of 
 tne condensed steam read at short intervals of time 
 
DETEKMINATION OF THE MOISTUBE IN STEAM. 943 
 
 Throttling Calorimeter. For percentages of moisture not exceed- 
 ing 3 per cent the throttling calorimeter is most useful and convenient 
 and remarkably accurate. In this instrument the steam which reaches 
 it in a i/2-inch pipe is throttled by an orifice 1/J6 inch diameter; opening 
 into a chamber which has an outlet to the atmosphere. The steam in 
 this chamber has its pressure reduced nearly or quite to the pressure of the 
 atmosphere, but the total heat in the steam before throttling causes the 
 steam in the chamber to be superheated more or less according to whether 
 the steam before throttling was dry or contained moisture. The only 
 observations required are those of the temperature and pressure of the 
 steam on each side of the orifice. 
 
 The author's formula for reducing the observations of the throttling 
 calorimeter is as follows (Experiments on Throttling Calorimeters, Am. 
 
 Mach., Aug. 4, 1892): w = 100 X H ^ h ~ ^ (T ~ Q, in which w = 
 
 percentage of moisture in the steam; H = total heat, and L= latent 
 heat of steam in the main pipe ; h = total heat due the pressure in 
 the discharge side of the calorimeter, = 1150.4 at atmospheric pressure; 
 K = specific heat of superheated steam ; T = temperature of the 
 throttled and superheated steam in the calorimeter; t = temperature due 
 to the pressure in the calorimeter, = 212 at atmospheric pressure. 
 
 Taking K at 0.46 and the pressure in the discharge side of the calo- 
 rimeter as atmospheric pressure, the formula becomes 
 
 = 100 X 
 
 H- 1150.4 - 0.46 (T - 212) 
 
 From this formula the following table is calculated: 
 MOISTURE IN STEAM DETERMINATIONS BY THROTTLING CALORIMETER. 
 
 Degree of 
 Super- 
 heating 
 T - 212. 
 
 Gauge-pressures. 
 
 5 | 10 | 20 | 30 | 40 | 50 
 
 60 
 
 70 
 
 75 
 
 80 | 85 | 90 
 
 Per Cent of Moisture in Steam. 
 
 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 
 Dif. p. deg.. . 
 
 0.51 
 0.01 
 
 0.90 
 0.39 
 
 1.54 
 1.02 
 0.51 
 0.00 
 
 2.06 
 1.54 
 1.02 
 0.50 
 
 2.50 
 1.97 
 1.45 
 0.92 
 0.39 
 
 2.90 
 2.36 
 1.83 
 1.30 
 0.77 
 0.24 
 
 3.24 
 2.71 
 2.17 
 1.64 
 1.10 
 0.57 
 0.03 
 
 3.56 
 3.02 
 2.48 
 1.94 
 1.40 
 0.87 
 0.33 
 
 3.71 
 3.17 
 2.63 
 2.09 
 1.55 
 1.01 
 0.47 
 
 3.86 
 3.32 
 2.77 
 2.23 
 1.69 
 1.15 
 0.60 
 0.06 
 
 3.99 
 3.45 
 2.90 
 2.35 
 1.80 
 1.26 
 0.72 
 0.17 
 
 .0544 
 
 4.13 
 3.58 
 3.03 
 2.49 
 1.94 
 1.40 
 0.85 
 0.31 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .0503 
 
 .0507 
 
 .0515 
 
 .0521 
 
 .0526 
 
 .0531 
 
 .0535 
 
 
 
 .0539 
 
 .0541 
 
 .0542 
 
 .0546 
 
 Degree of 
 Super- 
 heating 
 T - 212. 
 
 Gauge-pressures. 
 
 100 | 110 | 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 j 190 | 200 I 250 
 
 Per Cent of Moisture in Steam. 
 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 110 
 
 4.39 
 3.84 
 3.29 
 2.74 
 2.19 
 1.64 
 1.09 
 0.55 
 0.00 
 
 4.63 
 4.08 
 3.52 
 2.97 
 2.42 
 1.87 
 1.32 
 0.77 
 0.22 
 
 4.85 
 4.29 
 3.74 
 3.18 
 2.63 
 2.08 
 1.52 
 0.97 
 0.42 
 
 5.08 
 4.52 
 3.96 
 3.41 
 2.85 
 2.29 
 1.74 
 1.18 
 0.63 
 0.07 
 
 5.29 
 4.73 
 4.17 
 3.61 
 3.05 
 2.49 
 1.93 
 1.38 
 0.82 
 0.26 
 
 5.49 
 4.93 
 4.37 
 3.80 
 3.24 
 2.68 
 2.12 
 1.56 
 1.00 
 0.44 
 
 5.68 
 5.12 
 4.56 
 3.99 
 3.43 
 2.87 
 2.30 
 1.74 
 1.18 
 0.61 
 0.05 
 
 5.87 
 5.30 
 4.74 
 4.17 
 3.61 
 3.04 
 2.48 
 1.91 
 1.34 
 0.78 
 0.21 
 
 6.05 
 5.48 
 4.91 
 4.34 
 3.78 
 3.21 
 2.64 
 2.07 
 1.50 
 0.94 
 0.37 
 
 6.22 
 5.65 
 5.08 
 4.51 
 3.94 
 3.37 
 2.80 
 2.23 
 1.66 
 1.09 
 0.52 
 
 6.39 
 5.82 
 5.25 
 4.67 
 4.10 
 3.53 
 2.96 
 2.38 
 1.81 
 1.24 
 0.67 
 0.10 
 
 7.16 
 6.58 
 6.00 
 5.41 
 4.83 
 4.25 
 3.67 
 3.09 
 2.51 
 1.93 
 1.34 
 0.76 
 .0581 
 
 
 
 
 
 
 
 
 
 
 Dif. p. deg. . . 
 
 .0549 
 
 .0551 
 
 .0554 
 
 .0556 
 
 .0559 
 
 .0561 
 
 .0564 
 
 .0566 
 
 .0568 
 
 .0570 
 
 .0572 
 
 Separating Calorimeters. For percentages of moisture beyond the 
 range of the throttling calorimeter the separating calorimeter is used, 
 
944 CHIMNEYS. 
 
 which is simply a steam separator on a small scale. An improved form 
 of this calorimeter is described by Prof. Carpenter in Power, Feb., 1893. 
 
 For fuller information on various kinds of calorimeters, see papers by 
 Prof. Peabody, Prof. Carpenter, and Mr. Barrus in Trans. A. S< M. E. t 
 vols. x, xi, xii, 1889 to 1891; Appendix to Report of Com. on Boiler Tests, 
 A. S. M. E., vol. vi, 1884; Circular of Schaeffer & Budenberg, N. Y., 
 "Calorimeters, Throttling and Separating." 
 
 Identification of Dry Steam by Appearance of a Jet. Prof. 
 Denton (Trans. A. S. M. E., vol. x) found that jets of steam show un- 
 mistakable change of appearance to the eye when steam varies less than 
 1% from the condition of saturation in the direction of either wetness 
 or of superheating. 
 
 If a jet of steam flow from a boiler into the atmosphere under circum- 
 stances such that very little loss of heat occurs through radiation, etc., 
 and the jet be transparent close to the orifice, or be even a grayish-white 
 color, the steam may be assumed to be so nearly dry that no portable 
 condensing calorimeter will be capable of measuring the amount of water 
 in the steam. If the jet be strongly white, the amount of water may be 
 roughly judged up to about 2%, but beyond this only a calorimeter can 
 determine -the exact amount of moisture. 
 
 A common brase pet-cock may be used as an orifice, but it should, if 
 possible, be set into the steam-drum of the boiler and never be placed 
 further away from the latter than 4 feet, and then only when the inter- 
 mediate reservoir or pipe is well covered. 
 
 Usual Amount of Moisture in Steam Escaping from a Boiler. 
 In the common forms of horizontal tubular land boilers and water-tube 
 boilers with ample horizontal drums, and supplied with water free from 
 substances likely to cause foaming, the moisture in the steam does not 
 generally exceed 2% unless the boiler is overdriven or the water-level is 
 carried too high. 
 
 CHIMNEYS. 
 
 Chimney Draught Theory. The commonly accepted theory of 
 chimney draught, based on Peclet's and Rankine's hypotheses (Rankine, 
 S E.), is discussed by Prof. De Volson Wood, Trans. A, S. M. E., vol. xi. 
 
 Peclet represented the law of draught by the formula 
 
 in which h is the "head," defined as such a height of hot gases as, if added 
 to the column of gases in the chimney, would produce the 
 same pressure at the furnace as a column of outside air, of 
 the same area of base, and a height equal to that of the 
 chimney; 
 
 u is the required velocity of gases in the chimney; 
 G a constant to represent the resistance to the passage of air 
 
 through the coal; 
 
 I the length of the flues and chimney; 
 m the mean hydraulic depth or the area of a cross-section divided 
 
 by the perimeter; 
 
 / a constant depending upon the nature of the surfaces over 
 which the gases pass, whether smooth, or sooty and rough. 
 Rankine's formula (Steam Engine, p. 288),. derived by giving certain 
 values to the constants (so-called) in Peclet's formula, is 
 
 ^( 0.0807^ , x 
 
 u=^ - (H-H-Hs-i)* 
 
 lo(o.084 ) 
 
 in which H - t^Wrfthe eyjn^eet^ 
 
 T,= absolute temperature of the gases in the chimney; 
 T 2 = absolute temperature of the external air. 
 
CHIMNEYS. 
 
 945 
 
 Prof. Wood derives from this a still more complex formula which gives 
 the height of chimney required for burning a given quantity of coal per 
 second, and from it he calculates the following table, showing the height 
 of chimney required to burn respectively 24, 20, and 16 Ibs. of coal per 
 square foot of grate per hour, for the several temperatures of the chimney 
 gases given. 
 
 Outside Air. 
 
 _L 
 
 520 
 absolute or 
 I59F. 
 
 Chimney Gas. 
 
 Coal per sq. ft. of grate per hour, Ibs. 
 
 T i 
 Absolute. 
 
 Temp. 
 Fahr. 
 
 24 
 
 20 
 
 16 
 
 Height H, feet. 
 
 700 
 800 
 1000 
 1100 
 1200 
 1400 
 1600 
 2000 
 
 239 
 339 
 539 
 639 
 739 
 939 
 1139 
 1539 
 
 250.9 
 172.4 
 149.1 
 148.8 
 152.0 - 
 159.9 
 168.8 
 206.5 
 
 157.6 
 115.8 
 100.0 
 98.9 
 100.9 
 105.7 
 111.0 
 132.2 
 
 67.8 
 55.7 
 48.7 
 48.2 
 49.1 
 51.2 
 53.5 
 63.0 
 
 Rankine's formula gives a maximum draught when ^ = 21/12*2, or 
 622 F., when the outside temperature is 60. Prof. Wood says: "This 
 result is not a fixed value, but departures from theory in practice do not 
 affect the result largely. There is, then, in a properly constructed chimney 
 properly working, a temperature giving a maximum draught,* and that 
 temperature is not far from the value given by Rankine, although in 
 special cases it may be 50 or 75 more or less." 
 
 All attempts to base a practical formula for chimneys upon the theoret- 
 ical formula of Peclet and Rankine have failed on account of the impos- 
 sibility of assigning correct values to the so-called "constants" G and /. 
 (See trans. A. S. M. E., xi, 984.) 
 
 Force or Intensity of Draught. The force of the draught is equal 
 to the difference between the weight of the column of hot gases inside of 
 the chimney and the weight of a column of the external air of the same 
 height. It is measured by a draught-gauge, usually a U-tube partly 
 filled with water, one leg connected by a pipe to the interior of the flue, 
 and the other open to the external air. 
 
 If D is the density of the air outside, d the density of the hot gas inside, 
 
 in Ibs. per cubic foot, h the height of the chimney in feet, and 0.192 the 
 
 factor for converting pressure in Ibs. per sq. ft. into inches of water column, 
 
 then the formula for the force of draught expressed in inches of water is, 
 
 F = 0.192/1 (D - d). 
 
 The density varies with the absolute temperature (see Rankine). 
 
 d= ^0.084; D = 0.0807 , 
 
 Tl T 2 
 
 where T O is the absolute temperature at 32 F., = 493, TI the absolute 
 temperature of the chimney gases and r 2 that of the external air. Sub- 
 stituting these values the formula for force of draught becomes 
 
 ,.0.192 ft 
 
 - il^l) -ft ( 7 -M - - 5 ). 
 
 T2 Tl J \ T 2 Tl / 
 
 * Much confusion to students of the theory of chimneys has resulted 
 from their understanding the words maximum draught to mean maxi- 
 mum intensity or pressure of draught, as measured by a draught-gauge. 
 It here means maximum quantity or weight of gases passed up the 
 chimney. The maximum intensity is found only with maximum tem- 
 perature, but after the temperature' reaches about 622 F. the density of 
 the gas decreases more rapidly than its velocity increases, so that the 
 weight is a maximum about 622 F,, as shown by Rankine. W. K. 
 
946 
 
 CHIMNEYS. 
 
 To find the maximum intensity of draught for any given chimney, the 
 heated column being 600 F., arid the external air 60, multiply the height 
 above grate in feet by 0.0073, and the product is the draught in inches 
 of water. 
 
 Height of Water Column Due to Unbalanced Pressure in Chimney 
 10O Feet High.' (The Locomotive, 1884.) 
 
 ' S o! 
 
 Temperature of the External Air Barometer, 14.7 Ibs. per sq. in. 
 
 |l| 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 H o 
 
 
 
 
 
 
 
 
 
 
 
 
 200 
 
 0.453 
 
 0.419 
 
 0.384 
 
 0.353 
 
 0.321 
 
 0.292 
 
 0.263 
 
 0.234 
 
 0.209 
 
 0.182 
 
 0.157 
 
 220 
 
 .488 
 
 .453 
 
 .419 
 
 .388 
 
 .355 
 
 .326 
 
 .298 
 
 .269 
 
 .244 
 
 .217 
 
 .192 
 
 240 
 
 .520 
 
 .488 
 
 .451 
 
 .421 
 
 .388 
 
 .359 
 
 .330 
 
 .301 
 
 .276 
 
 .250 
 
 .225 
 
 260 
 
 .555. 
 
 .528 
 
 .484 
 
 .453 
 
 .420 
 
 .392 
 
 .363 
 
 .334 
 
 .309 
 
 .282 
 
 .257 
 
 280 
 
 .584 
 
 .549 
 
 .515 
 
 .482 
 
 .451 
 
 .422 
 
 .394 
 
 .365 
 
 .340 
 
 .313 
 
 .288 
 
 300 
 
 .611 
 
 .576 
 
 .541 
 
 .511 
 
 .478 
 
 .449 
 
 .420 
 
 .392 
 
 .367 
 
 .340 
 
 .315 
 
 320 
 
 .637 
 
 .603 
 
 .568 
 
 .538 
 
 .505 
 
 .476 
 
 .447 
 
 .419 
 
 .394 
 
 .367 
 
 .342 
 
 340 
 
 .662 
 
 .638 
 
 .593 
 
 .563 
 
 .530 
 
 .501 
 
 .472 
 
 .443 
 
 .419 
 
 .392 
 
 .367 
 
 360 
 
 .687 
 
 .653 
 
 .618 
 
 .588 
 
 .555 
 
 .526 
 
 .497 
 
 .468 
 
 .444 
 
 .417 
 
 .392 
 
 380 
 
 .710 
 
 .676 
 
 .641 
 
 .611 
 
 .578 
 
 .549 
 
 .520 
 
 .492 
 
 .467 
 
 .440 
 
 .415 
 
 400 
 
 .732 
 
 .697 
 
 .662 
 
 .632 
 
 .598 
 
 .570 
 
 .541 
 
 .513 
 
 .488 
 
 .461 
 
 .436 
 
 420 
 
 .753 
 
 .718 
 
 .684 
 
 .653 
 
 .620' 
 
 .591 
 
 .563 
 
 .534 
 
 .509 
 
 .482 
 
 .457 
 
 440 
 
 .774 
 
 .739 
 
 .705 
 
 .674 
 
 .641 
 
 .612 
 
 .584 
 
 .555 
 
 .530 
 
 .503 
 
 .478 
 
 460 
 
 793 
 
 .758 
 
 .724 
 
 694 
 
 660 
 
 .632 
 
 603 
 
 574 
 
 549 
 
 522 
 
 497 
 
 480 
 
 .810 
 
 .776 
 
 .741 
 
 .710 
 
 .678 
 
 .649 
 
 .620 
 
 .591 
 
 .566 
 
 .540 
 
 .515 
 
 500 
 
 .829 
 
 .791 
 
 .760 
 
 .730 
 
 .697 
 
 .669 
 
 .639 
 
 .610 
 
 .586 
 
 .559 
 
 .534 
 
 For any other height of chimney than 100 ft. the height of water column 
 is found by simple proportion, the height of water column being directly 
 proportioned to the height of chimney. 
 
 The calculations have been made for a chimney 100 ft. high, with 
 various temperatures outside and inside of the flue, and on the supposition 
 that the temperature of the chimney is uniform from top to bottom. 
 This is the basis on which all calculations respecting the draught-power 
 of chimneys have been made by Rankine and other writers, but it is very 
 far from the truth in most cases. The difference will be shown by com- 
 paring the reading of the draught-gauge with the table given. In one 
 case a chimney 122 ft. high showed a temperature at the base of 320, 
 and at the top of 230. 
 
 Box, in his "Treatise on Heat," gives the following table: 
 
 DRAUGHT POWERS OF CHIMNEYS, ETC., WITH THE INTERNAL AIR AT 552 
 AND THE EXTERNAL AIR AT 62, AND WITH THE DAMPER NEARLY 
 CLOSED. 
 
 sf- 
 
 -u.S ^ 
 
 Theoretical Velocity 
 in feet per second. 
 
 It 
 
 di 
 
 Theoretical Velocity 
 in feet per second. 
 
 til 
 
 |s 
 
 Cold Air 
 
 Hot Air 
 
 111 
 
 3'~ 03 
 
 Cold Air 
 
 Hot Air 
 
 w g 
 
 O 8*0 
 
 Entering. 
 
 at Exit. 
 
 *6 
 
 PH 
 
 Entering. 
 
 at Exit. 
 
 10 
 
 0.073 
 
 17.8 
 
 35.6 
 
 80 
 
 0.585 
 
 50.6 
 
 101.2 
 
 20 
 
 0.146 
 
 25.3 
 
 50.6 
 
 90 
 
 0.657 
 
 53.7 
 
 107.4 
 
 30 
 
 0.219 
 
 31.0 
 
 62.0 
 
 100 
 
 0.730 
 
 56.5 
 
 113.0 
 
 40 
 
 0.292 
 
 35.7 
 
 71.4 
 
 120 
 
 0.876 
 
 62.0 
 
 124.0 
 
 50 
 
 0.365 
 
 40.0 
 
 80.0 
 
 150 
 
 1.095 
 
 69.3 
 
 138.6 
 
 60 
 
 0.438 
 
 43.8 
 
 87.6 
 
 175 
 
 1.277 
 
 74.3 
 
 149.6 
 
 70 
 
 0.511 
 
 47.3 . 
 
 94.6 
 
 200 
 
 1.460 
 
 80.0 
 
 160.0 
 
CHIMNEYS. 
 
 947 
 
 Bate of Combustion Due to Height of Chimney. Trowbridge's 
 "Heat and Heat Engines" gives the following figures for the heights of 
 chimney for producing certain rates of combustion per sq. ft. of grate. 
 They may be approximately true for anthracite in moderate and large 
 sizes, but greater heights than are given in the table are needed to secure 
 the given rates of combustion with small sizes of anthracite, and for 
 bituminous coal smaller heights will suffice if the coal is reasonably free 
 from ash 5% or less. 
 
 Height, 
 feet. 
 
 I 
 
 Lbs. of 
 Coal per 
 Sq. Ft. of 
 
 Grate. 
 
 7.5 
 8.5 
 9.5 
 10.5 
 
 Height, 
 feet. 
 
 45 
 50 
 55 
 60 
 65 
 
 Lbs. of 
 Coal per 
 Sq. Ft. of 
 
 Grate. 
 
 Height, 
 feet. 
 
 12.4 
 13.1 
 13.8 
 14.5 
 15.1 
 
 70 
 75 
 80 
 85 
 90 
 
 Lbs. of 
 Coal per 
 Sq. Ft. of 
 
 Grate. 
 
 15.8 
 16.4 
 16.9 
 17.4 
 18.0 
 
 Height, 
 feet. 
 
 Lbs. of 
 Coal per 
 Sq. Ft. of 
 
 Grate. 
 
 95 
 100 
 105 
 110 
 
 18.5 
 19.0 
 19.5 
 20.0 
 
 W. D. Ennis (Eng. Mag., Nov., 1907), gives the following as the force 
 of draught required for burning No. 1 buckwheat coal: 
 
 Draught, in. of water 0.3 0.45 0.7 1.0 
 
 Lbs. coal per sq. ft. grate per hour 10 15 20 25 
 
 Thurston's rule for rate of combustion effected by a giyen height of 
 chimney (Trans. A. S. M. E., xi, 991) is: Subtract 1 from twice the square 
 root of the height, and the result is the rate of combustion in pounds per 
 square foot of grate per hour, for anthracite. Or rate = 2 V/i 1, in 
 which h is the height in feet. This rule gives the following: 
 
 h = 50 60 70 80 90 100 110 125 150 175 200 
 - 1 = 13.14 14.49 15.73 16.8917.97 19 19.9721.3623.4925.4527.28 
 
 The results agree closely with Trowbridge's table given above. In 
 practice the high rates of combustion for high chimneys given by the 
 formula are not generally obtained, for the reason that with high chimneys 
 there are usually long horizontal flues, serving many boilers, and the 
 friction and the interference of currents from the several boilers are apt to 
 cause the intensity of draught in the branch flues leading to each boiler 
 to be much less than that at the base of the chimney. The draught of 
 each boiler is also usually restricted by a damper and by bends in the gas- 
 passages. In a battery of several boilers connected to a chimney 150 ft. 
 high, the author found a draught of 3/ 4 -inch water-column at the boiler 
 nearest the chimney, and only i/4-inch at the boiler farthest away. The 
 first boiler was wasting fuel from too high temperature of the chimney- 
 gases, 900, having too large a grate-surface for the draught, and the last 
 boiler was working below its rated capacity and with poor economy, on 
 account of insufficient draught. 
 
 The effect of changing the length of the flue leading into a chimney 
 60 ft. high and 2 ft. 9 in. square is given in the following table, from Box 
 on "Heat": 
 
 Length of Flue in 
 feet. 
 
 Horse-power. 
 
 Length of Flue in 
 feet. 
 
 Horse-power. 
 
 50 
 100 
 200 
 400 
 600 
 
 107.6 
 100.0 
 85.3 
 70.8 
 62.5 
 
 800 
 1,000 
 1,500 
 2,000 
 3,000 
 
 56.1 
 51.4 
 43.1. 
 38.2 
 31.7 
 
 and 
 
 The temperature of the gases in this chimney was assume^ to be 552 F., 
 id that or the atmosphere 62. 
 
948 SIZE OF CHIMNEYS. 
 
 High Chimneys not Necessary. Chimneys above 150 ft. in height I 
 are very costly, and their increased cost is rarely justified by increased effi- 
 ciency. In recent practice it has become somewhat common to build two 
 or more smaller chimneys instead of one large one. A notable example i 
 is the Spreckels Sugar Refinery in Philadelphia, where three separate 
 chimneys are used for one boiler-plant of 7500 H.P. The three chimneys 
 are said to have cost several thousand dollars less than a single chimney 
 of their combined capacity would have cost. Very tall chimneys have 
 been characterized by one writer as "monuments to the folly of their 
 builders." 
 
 Heights of Chimney required for Different Fuels. The minimum 
 height necessary varies with the fuel, wood requiring the least, then good 
 bituminous coal, and fine sizes of anthracite the greatest. It also varies 
 with the character of the boiler the smaller and more circuitous the 
 gas-passages the higher the stack required ; also with the number of boilers, 
 a single boiler requiring less height than several that discharge into a 
 horizontal flue. No general rule can be given. 
 
 C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following heights 
 have been found to give good results in plants of moderate size, and to 
 produce sufficient draught to force the boilers from 20 to 30 per cent 
 above their rating: 
 
 With free-burning bituminous coal, 75 feet; with anthracite of medium 
 and large size, 100 feet: with slow-burning bituminous coal, 120 feet; with 
 anthracite pea coal, 130 feet; with anthracite buckwheat coal, 150 feet. 
 For plants of 700 or 800 horse-power and over, the chimney should not 
 be less than 150 feet high regardless of the kind of coal to be used. 
 
 SIZE OF CHIMNEYS. 
 
 The formula given below, and the table calculated therefrom for chim- 
 neys up to 96 in. diameter and 200 ft. high, were first published by the 
 author in 1884 (Trans. A. S. M. E., vi, 81). They have met with much 
 approval since that date by engineers who have used them, and have been 
 frequently published in boiler-makers' catalogues and elsewhere. The 
 table is now extended to cover chimneys up to 12 ft. diameter and 300 ft. 
 high. The sizes corresponding to the given commercial horse-powers 
 are believed to be ample for all cases in which the draught areas through 
 the boiler-flues and connections are sufficient, say not less than 20% 
 greater than the area of the chimney, and in which the draught between 
 the boilers and chimney is not checked by long horizontal passages and 
 right-angled bends. 
 
 Note that the figures in the table correspond to a coal consumption of 5 Ibs. 
 of coal per horse-power per hour. This liberal allowance is made to cover 
 the contingencies of poor coal being used, and of the boilers being driven 
 beyond their rated capacity. In large plants, with economical boilers 
 and engines, good fuel and other favorable conditions, which will reduce 
 the maximum rate of coal consumption at any one time to less than 5 it 
 per H.P. per hour, the figures in the table may be multiplied by the ratio 
 of 5 to the maximum expected coal consumption per H.P. per hour. 
 Thus, with conditions which make the maximum coal consumption only 
 2.5 Ibs. per hour, the chimney 300 ft. high X 12 ft. diameter should be 
 sufficient for 6155 X 2 = 12,310 horse-power. The formula is based on 
 the following data: 
 
 1. The draught power of the chimney varies as the square root of the 
 height. 
 
 2. The retarding of the ascending gases by friction may be considered 
 as equivalent to a diminution of the area of the chimney, or to a lining or 
 the chimney by a layer of gas which has no velocity. The thickness of 
 this lining is assumed to be 2 inches for all chimneys, or the diminution 
 of area equal to the perimeter X 2 inches (neglecting the overlapping ol 
 the corners of the lining). Let D = diameter in feet, A = area, and E = 
 effective area in square feet: 
 
 8 D 2 /"~~ 
 
 For square chimneys, E = D 8 jy "* A ~~ 3 Am 
 
 For round chimneys, E = ^ (l) 2 - ^j\ = A - 0.591 ^A. 
 
i CHIMNEYS. 949 
 
 For simplifying calculations, the coefficient of VA may be taken as 0.6 
 for both square and round chimneys, and the formula becomes 
 
 E - A - 0.6 VI. 
 
 3 The power varies directly as this effective area E. 
 
 4. A chimney should be proportioned so as to be capable of giving 
 sufficient draught to cause the boiler to develop much more than its rated 
 power, in case of emergencies, or to cause the combustion of 5 Ibs. of fuel 
 per rated horse-power of boiler per hour. 
 
 5 The power of the chimney varying directly as the effective area, /</, 
 and' as the square root of the height, H, the formula for horse-power of 
 boiler for a given size of chimney will take the form H.P. = CE Vf/, in 
 which C is a constant, the average value of which, obtained by plotting 
 the results obtained from numerous examples in practice, the author 
 finds to be 3.33. 
 
 The formula for horse-power then is 
 
 H.P. = 3.33 E V#, or H.P. = 3.33 (A - 0.6 VI) Vff. 
 
 If the horse-power of boiler is given, to find the size of chimney, the 
 height being assumed, 
 
 E = 0.3 H.P. ^ V// ; = A - 0.6 VI. 
 
 For round chimneys, diameter of chimney = diam. of E -H 4". 
 For square chimneys, side of chimney = V# + 4". 
 
 If effective area E is taken in square feet, the diameter m inches is d = 
 13 54 V# + 4", and the side of a square chimney in inches is s = 
 
 V 
 
 If 
 
 ' /03HP\ 
 
 f horse-power is given and area assumed, the height // = ^ ^ - J 
 
 An approximate formula for chimneys above 1000 H.P. is H.P. = 
 2.5 D 2 V//. This gives the H.P. somewhat greater than the figures in 
 the table. 
 
 In proportioning chimneys the height should first be assumed, with due 
 consideration of the heights of surrounding buildings or hills near to the 
 proposed chimney, the length of horizontal flues, the character of coal to 
 be used, etc. ; then the diameter required for the assumed height and horse- 
 power is calculated by the formula or taken from the table. 
 
 For Height of Chimneys see pages 947 and 948. No formula for 
 height can be given which will be satisfactory for different classes of coal, 
 kinds and amounts of ash, styles of grate-bars, etc. A formula in " Ingeni- 
 eurs Taschenbuch," translated into English measures, is ft = 0.216 R 2 + 6d. 
 h= height in ft; R = Ibs. coal burned per sq. ft. of grate per hour; d = 
 diam. in ft. This formula gives an insufficient height for small sizes of 
 anthracite, and a height greater than is necessary for free-burning bitu- 
 minous coal low in ash. 
 
 The Protection of Tall Chimney-shafts from Lightning. C. 
 Molyneux and J. M. Wood (Industries, March 28, 1890) recommend for 
 tall chimneys the use of a coronal or heavy band at the top of the chimney, 
 with copper points 1 ft. in height at intervals of 2 ft. throughout the cir- 
 cumference. The points should be gilded to prevent oxidation. The 
 most approved form of conductor is a copper tape about 8/4 in. by 1/8 in. 
 thick, weighing 6 ozs. per ft. If iron is used it should weigh not less than 
 21/4 Ibs. per ft. There must be no insulation, and the copper tape should 
 be fastened to the chimney with holdfasts of the same material, to pre- 
 vent voltaic action. An allowance for expansion and contraction should 
 be made, say 1 in. in 40 ft. Slight bends in the tape, not too abrupt, 
 answer the purpose. For an earth terminal a plate of metal at least 3 ft. 
 sq. and Vie in. thick should be buried as deep as possible in a damp spot. 
 The plate should be of the same metal as the conductor, to which it 
 should be soldered. The best earth terminal is water, and when a deep 
 well or other large body of water is at hand, the conductor should be 
 carried down into it. Right-angled bends in the conductor should b 
 avoided. No bend in it should be over 30. 
 
950 
 
 SIZE OF CHIMNEYS. 
 
 IM3I + 
 
 
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 -oo ommoo TI^C 
 
 OO 
 
 u-\OO OOmO Ot^ 
 
 O^ T ' O r^s t^CM 
 
 ^ 
 
 \Oxo r 
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 f^ ^-msi 
 
 , .^i rnr^r^c 
 OorvjTj- vo oo . 
 
 ~- . _ <VJ (Nl 
 
 oo<2 p^^2r 
 
 OvOOOT 
 
 vi r^ m 
 
 f>t>.OOaO 
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 o ' ' (S CM 
 
 
 r^. \O ^ - OO 
 m i> -n- m o 
 
 sd !>.' O f^ so 
 
 r^sO O^ m fA 
 t^ r>. o N_ oo 
 
 O >o (N oo 
 T^mm 
 
 O f*i OO 
 
 Sf^r^ 
 
 O OO in rA 
 
 t>.r>iOv-- 
 
 .2 w 
 Q.2 
 
 oo -T r^ OfAv 
 tMs(s tnc^ 
 
 ofsoo-^- oorsjoo -rorgT 
 pt>.r>oQ 
 
CHIMNEYS. 
 
 951 
 
 Velocity of Gas in Chimneys. The velocity of the heated gas, Teased 
 on the chimney porportions given in the table, may be found from the 
 following data: 
 
 A = Lb. coal per hour = boiler horsepower X 5 ; 
 B = Lb. gas per lb. coal = say 20 Ib.;' 
 
 C = Cu. ft. of gas per Ib. Of gas = 12.4 X (temp, of gas + 460) -f- 492; 
 
 -= 25 cu. ft. for 532 F. = 500 cu. ft. 
 per lb. coal; 
 
 A X B X C 1 
 V = Velocity of gas. feet per second = 
 
 chimney area (JqTftT 
 
 Based on a gas temperature of 532 F., 5 lb. coal per hour per rated 
 H.P., and 20 lb. gas per lb. of coal we have 
 
 Cu. ft. gas per second per lb. of coal per hour = 0.1389; 
 
 Cu. ft. gas per second per boiler horse-power = 0.6944; 
 and the velocities in feet per second, based on the effective areas given 
 in the table, corresponding to different heights of chimney are: 
 
 Height, ft. . 
 Velocity, ft. 
 per sec.. . 
 
 50 
 
 16 3 
 
 60 
 17 8 
 
 70 
 19 4 
 
 80 
 ?0 7 
 
 90 
 
 77 
 
 100 
 
 73 7 
 
 110 
 74 3 
 
 125 
 75 Q 
 
 150 
 
 78 3 
 
 175 
 30 6 
 
 200 
 3? 7 
 
 225 
 34 7 
 
 250 
 36 6 
 
 300 
 40 1 
 
 Chimney Table for Oil Fuel. (C. R. Weymouth, Journal A. S. M.E. t 
 October, 1912.) Conditions: Sea level; atmospheric temperature, 
 80 F. ; draught at chimney side of damper, 0.30 in. ; excess air, less than 
 50 % , assumed 50 % for calculations of efficiency and chimney dimensions ; 
 temperature of gases leaving chimney, 500 F. ; boiler efficiency, 73 % ; 
 actual boiler horse-power, 150 per cent of rated; lb. gas per actual 
 boiler H.P.,54.6; height of chimney above pointpf draught measurement. 
 12 ft. less than tabulated height. When building conditions permit 
 select chimneys of least height in table for minimum cost of chimney. 
 Chimney capacities stated are maximum for continuous load equally 
 divided on all boilers. For large plants or swinging load, reduce capacity 
 10 to 20%. Breeching 20% in excess of stack area; length not exceed- 
 ing 10 chimney diameters. 
 
 Size of Chimneys for Oil Fuel 
 
 
 
 Height in Feet above Boiler Room Floor. 
 
 
 Area, 
 Sq. ft. 
 
 80 | 90 | 100 | 110 
 
 120 | 130 
 
 140 
 
 150 | 160 
 
 
 
 Actual Horse-power = 1 50 Per cent of Rated. 
 
 . 
 
 1.77 
 
 63 
 
 75 
 
 84 91 
 
 96 
 
 101 
 
 104 
 
 108 
 
 110 
 
 24 
 
 3.14 
 
 123 
 
 148 
 
 166| 180 
 
 191 
 
 201 
 
 208 
 
 215 
 
 221 
 
 30 
 
 4.91 
 
 206 
 
 249 
 
 280 304 
 
 324 
 
 340 
 
 354 
 
 366 
 
 377 
 
 36 
 
 7.07 
 
 312 
 
 379 
 
 427 466 
 
 497 
 
 523 
 
 545 
 
 564 
 
 58! 
 
 42 
 
 9.62 
 
 443 
 
 539 
 
 609| 665 
 
 711 
 
 749 
 
 782 
 
 810 
 
 830 
 
 48 
 
 12.57 
 
 599 
 
 729 
 
 827 
 
 904 
 
 967 
 
 1,020 
 
 1,070 
 
 1,110 
 
 1,145 
 
 54 
 
 15.90 
 
 779 
 
 951 
 
 1,080 
 
 1,180 
 
 1,270 
 
 1,340 
 
 1,400 
 
 1,460 
 
 1,500 
 
 60 
 
 19.64 
 
 985 
 
 1,200 
 
 1,370 
 
 1,500 
 
 1,610 
 
 1,710 
 
 1,790 
 
 1,860 
 
 1,920 
 
 66 
 
 23.76 
 
 1,220 
 
 1,490 
 
 1,700 
 
 1,860 
 
 2,000 
 
 2,120 
 
 2,220 
 
 2,310 
 
 2,390 
 
 72 
 
 28.27 
 
 1,470 
 
 1,810 
 
 2,060 
 
 2,260 
 
 2,430 
 
 2,580 
 
 2.710 
 
 2,820 
 
 2,910 
 
 78 
 
 33.18 
 
 1,750 
 
 2,150 
 
 2,460 
 
 2,710 
 
 2,910 
 
 3,000 
 
 3.250 
 
 3,380 
 
 3,500 
 
 84 
 
 38.49 
 
 2,060 
 
 2,530 
 
 2,900 
 
 3,190 
 
 3,440 
 
 3,650 
 
 3,840 
 
 4,000 
 
 4,150 
 
 96 
 
 50.27 
 
 2,750 
 
 3,390 
 
 3,880 
 
 4,290 
 
 4,630 
 
 4,920 
 
 5,180 
 
 5,400 
 
 5,610 
 
 108 
 
 63.62 
 
 3,550 
 
 4,380 
 
 5,020 
 
 5,550 
 
 6,000 
 
 6,390 
 
 6,730 
 
 7,030 
 
 7,300 
 
 120 
 
 78.54 
 
 4.440 
 
 5,490 
 
 6,310 
 
 6,990 
 
 7.560 
 
 8,060 
 
 8,490 
 
 8,890 
 
 9,240 
 
 132 
 
 95.03 
 
 5,450 
 
 6,740| 7,760 
 
 8,600 
 
 9,310 
 
 9,930 
 
 10,500 
 
 11,000:11.400 
 
 144 
 
 113.1 
 
 6,550 
 
 8,1 20i 9,350 
 
 10.400 
 
 11,200 
 
 12,000 
 
 12,700 
 
 13.300! 13.800 
 
 156 
 
 132.7 
 
 7,760 
 
 9,630 11,100 
 
 12, 300 113,400 
 
 14,300 
 
 15,100 
 
 15.800 16,500 
 
 168 
 
 153.9 
 
 9,060 
 
 I1,300;i3,000 
 
 14.400 15.700 
 
 16,800 
 
 17,700 
 
 18,600 19.400 
 
 180 
 
 176.7 
 
 10.500 
 
 13,000 15.100 
 
 16,700 18,200 
 
 19,50020,600 
 
 21,60022,600 
 
 In using the above table it must be noted that the conditions upon 
 which it is based are aU fairly good. With unskilful handling of oil 
 
952 CHIMNEYS. 
 
 fuel the excess air is apt to be much more than 50% and the efficiency 
 much less than 73%. In that case the actual horse-power developed 
 by a given size of chimney may be much less than the figure given in 
 the table 
 
 DRAUGHT OF CHIMNEYS 100 FT. HIGH OIL FUEL. 
 
 Temp. "of gases enter- 
 ing chimney 300 400 500 600 700 
 
 Net chimney draught, inches of water 
 f 60 F. 0.367 0.460 0.534 0.593 0.642 
 
 Temp, of outside air. \ 80 0.325 0.417 0.490 0.550 0.599 
 
 [100 0.284 0.377 0.451 0.510 0.559 
 
 . The net draught is the theoretical draught due to the difference in 
 weight of atmospheric air and chimney gases at the stated temperatures, 
 multiplied by a coefficient, 0.95, for temperature drop in stack, and by 
 6/6 as a correction for friction. For high altitudes the draught varies 
 directly as the normal barometer. For other heights than 100 feet 
 (measured above the level of entrance of the gases) the draught varies 
 as the square root of the height. 
 
 Chimneys with Forced Draught. When natural, or chimney, draught 
 only is used, the function of the chimney is 1, to produce such a dif- 
 ference of pressure, or intensity of draught, between the bottom of the 
 chimney and the ash-pit as will cause the flow of the required quantity 
 of air through the grate-bars and the fuel bed, and the flow of the gases 
 of combustion through the gas passages, the damper and the breeching; 
 ai^d 2, to convey the gases above the tops of surrounding buildings and 
 to such a height that they will not become a nuisance. With forced 
 draught the blower produces the difference of pressure, and the only use 
 of the chimney is that of conveying the gases to a place where they will 
 cause no inconvenience; and in that case the height of the chimney may 
 ")e much less than that of a chimney for natural draught. 
 
 With oil or natural gas for fuel, the resistance of the grates and of the 
 Aiiel bed is eliminated, and the height of the chimney may be much less 
 than that of one desired for coal firing. When oil or gas is substituted 
 for coal, and the chimney is a high one, it may be necessary to restrict 
 its draught power by a damper or other means, in order to prevent its 
 creating too greata negative pressure in the furnace and thereby too great 
 an admission of air, which will cause a decrease in efficiency. 
 
 The Largest Chimney in the World, in 1908, is that of the Montana 
 smelter, at Great Falls, Mont. Height 506 ft. Internal diam. at top 
 50 ft. Built of Custodis radial brick. Designed to remove 4,000,000 cu. 
 ft. of gases per minute at an average temperature of 600 F. Erected on 
 top of a hill 500 ft. above the city, and 246 ft. above the floor of the fur- 
 naces, which are about 2000 ft. distant. Designed for a wind pressure of 
 331/3 IDS. per sq. ft. of projected area; bearing pressure limited to 21 tons 
 per sq. ft. at any section. Foundation: 111 ft. max. diam., 221/2 ft. deep; 
 bearing pressure on bottom (shale rock) 4.83 tons per sq. ft.; octagonal 
 outside, 103 ft. across at bottom, 81 ft. at top. with inner circular open- 
 ing 47 ft.- diam. at bottom, 64 ft. at top; made of 1 cement, 3 sand, 5 
 crushed slag. Four flue openings in the base, each 15 ft. wide, 36 ft. 
 high. The stack proper consists of an octagonal base, 46 ft. in height, 
 which has a taper of 8%, and above this a circular barrel, the first 180 ft. 
 above the base having a taper of 7%, the next 100 ft. of 4%, and the 
 remaining 180 ft. to the cap 2%. 
 
 The chimney wall varies from 66 in. at the base to 181/8 in. at the top 
 by uniform decrements of 2 in. per section, excepting at the section imme- 
 diately above the top of the base, where the thickness decreases from 60 in. 
 to 54 in. The outside diameters of the stack are 781/2 ft. at the base, 
 53 ft. 9 in. at the base of the cap; the inside diameters range from 661/2 ft. 
 at the foundation line to 50 ft. at the top. The chimney is lined with 4- 
 inch acid-proof brick, laid in sections carried on corbels from the main 
 shell. A description of the methods of design and of erection of the 
 Great Falls chimney is given in Eng. Rec.> Nov. 28, 1908. 
 
CHIMNEYS. 
 
 Some Tall Brick Chimneys (1895). 
 
 953 
 
 
 
 i 
 
 Outside 
 Diameter. 
 
 Capacity by the 
 Author's 
 Formula. 
 
 
 
 5 
 
 
 
 
 Pounds 
 
 
 9 
 
 g 
 
 
 
 H. P. 
 
 Coal 
 
 
 I- 
 
 o 
 
 G 
 t i 
 
 3 
 
 tt 
 
 D, 
 
 
 per 
 Hour. 
 
 1. Hallsbruekner Hfltte, 
 
 
 
 
 
 
 
 Saxony 
 
 460 
 
 15 7' 
 
 33' 
 
 16' 
 
 13 221 
 
 66,105 
 
 2 Townsend's Glasgow 
 
 454 
 
 
 32 
 
 
 
 
 3. Tennant's, Glasgow 
 4. Dobson & Barlow, Bol- 
 
 435 
 
 13' 6" 
 
 40 
 
 
 9,795 
 
 48,975 
 
 ton ling 
 
 367 1/2 
 
 13' 2" 
 
 33' 10" 
 
 
 8,245 
 
 41,225 
 
 5. Fall River Iron Co., Bos- 
 
 350 
 
 11 
 
 30 
 
 21 
 
 5,558 
 
 27,790 
 
 6. Clark Thread Co., New- 
 
 
 
 
 
 
 
 ark N J 
 
 335 
 
 11 
 
 28' 6" 
 
 14 
 
 5,435 
 
 27,175 
 
 7. Merrimac Mills, Lowell, 
 
 
 
 
 
 
 
 Mass 
 
 282' 9" 
 
 12 
 
 
 
 5,980 
 
 29,900 
 
 8. Washington Mills, Law- 
 
 250 
 
 10 
 
 
 
 3,839 
 
 19,195 
 
 9. Amoskeag Mills, Man- 
 chester N H 
 
 250 
 
 10 
 
 
 
 3,839 
 
 19,195 
 
 10. Narragansett E. L. Co., 
 
 238 
 
 14 
 
 
 
 7,515 
 
 37,575 
 
 1 1 . Lower Pacific Mills, Law- 
 
 
 
 
 
 
 
 rence Mass 
 
 214 
 
 8 
 
 
 
 2,248 
 
 11,240 
 
 12. Passaic Print Works, 
 
 
 
 
 
 
 
 
 200 
 
 9 
 
 
 
 2,771 
 
 13,855 
 
 13. Edison Station Brooklyn, 
 Two each . . . 
 
 150 
 
 50" x 120" 
 
 
 each 
 
 1,541 
 
 7,705 
 
 
 NOTES ON THE ABOVE CHIMNEYS. 1. This chimney is situated near 
 Freiberg at an elevation of 219 ft. above that of the foundry works, so 
 that its total height above the sea will be 7113/ 4 ft. The furnace-gases 
 are conveyed across river to the chimney on a bridge, through a pipe 
 3227 ft. long. It is built of brick, and cost about $40,000. Mfr. & Bldr. 
 
 2. Owing to the fact that it was struck by lightning, and somewhat 
 damaged, as a precautionary measure a copper extension subsequently 
 was added to it, making its entire height 488 feet. 
 
 1, 2, 3, and 4 were built of these great heights to remove deleterious 
 gases from the neighborhood, as well as for draught for boilers. 
 
 5 The structure rests on a solid granite foundation, 55 X 30 feet, and 
 16 feet deep. In its construction there were used 1,700,000 bricks, 
 2000 tons of stone, 2000 barrels of mortar, 1000 loads of sand, 1000 barrels 
 of Portland cement, and the estimated cost is $40,000. It is arranged for 
 two flues, 9 feet 6 inches by 6 feet, connecting with 40 boilers, which are 
 to be run in connection with four triple-expansion engines of 1350 horse- 
 power each. 
 
 6. It has a uniform batter of 2.85 ins. to every 10 ft. Designed for 
 21 boilers of 200 H.P. each. It is surmounted by a cast-iron coping 
 which weighs six tons, and is composed of 32 sections bolted together 
 by inside flanges so as to present a smooth exterior. The foundation 
 is 40 ft. square and 5 ft. deep. Two qualities of brickf were used; the 
 outer portions were of the first quality North River, and the backing up 
 was of good quality New Jersey brick. Every twenty feet in vertical 
 measurement an iron ring, 4 ins. wide and 3/ 4 to 1/2 in. thick, placed edge- 
 wise, was built into the walls about 8 ins. from the outer circle As the 
 chimney starts from the base it is double. The outer wall is 5 ft. 2 ins. 
 in thickness, and inside of this is a second wall 20 ins. thick arid spaced 
 
954 CHIMNEYS. 
 
 off about 20 ins. from main wall. From the interior surface of the main 
 wall eight buttresses are carried, nearly touching this inner or main flue 
 wall in order to keep it in line should it tend to sag. The interior wall, 
 starting with the thickness described, is gradually reduced until a height 
 of about 90 ft. is reached, when it is diminished to 8 inches.^. At 165 ft. 
 it ceases, and the rest of the chimney is without lining. The total weight 
 of the chimney and foundation is 5000 tons. It was completed in Sep- 
 tember, 1888. 
 
 7. Connected to 12 boilers, with 1200 sq. ft. of grate. Draught 1 9/i 6 ins. 
 
 8. Connected to 8 boilers, 6 ft. 8 in. diam. X 18 ft. Grate 448 sq. ft. 
 
 9. Connected to 64 Manning vertical boilers, total grate surface 1810 
 sq. ft. Designed to burn 18,000 Hxs. anthracite per hour. 
 
 10. Designed for 12,000 H.P. of engines; (compound condensing). 
 
 11. Grate-surface 434 square feet; H.P. of boilers about 2500. 
 
 13. Eight boilers (water-tube) each 450 H.P.; 12 engines, each 300 
 H.P. For the first 60 feet the exterior wall is 28 ins. thick, then 24 ins. for 
 20 ft., 20 ins. for 30 ft., 16 ins. for 20 ft., and 12 ins. for 20 ft. The inte- 
 rior wall is 9 ins. thick of fire-brick for 50 ft., and then 8 ins. thick of red 
 brick for the next 30 ft. Illustrated in Iron Age, Jan. 2, 1890. 
 
 A number of the above chimneys are illustrated in Power, Dec., 1890. 
 
 More Recent Brick Chimneys (1909). Heller & Merz Co., Newark, 
 N. J. 350 ft. high, inside diam., 8 ft. Outside diam., top 9 ft. 10 1/4 in., 
 bottom 27 ft. 61/2 in. Outside taper 5.2 in 100. Outer shell 7Vs in. at 
 the top, 38 in. at the bottom. Custodis radial brick laid in mortar of 
 1 cement, 2 lime, 5 sand. The changes in thickness are made by 2-in. 
 offsets on the inside every 20 ft. Iron band 3 1/2 X 5 /i6 in., three courses 
 below the top. Lined with 4 in. of special brick to resist acids. The 
 lining is sectional, being carried on corbels projecting from the shell every 
 20 ft. An air space of 2 ins. is left between the lining and the shell. 
 The lining bricks are laid in a mortar made of silicate of soda and white 
 asbestos wool, tempered to the consistency of fire-clay mortar. This 
 mortar is acid-proof, and its binding power, which is considerable in 
 comparison to that of fire-clay mortar, is unaffected by temperatures up 
 to 2000 F. (Eng. News, Feb. 15, 1906.) Supported on 324 piles driven 
 60 ft. to solid rock, and covering an area 45 ft. square. Total cost $32,000. 
 The standard Custodis radial brick is 4*/2 in. thick and 6 1/2 in. wide; 
 radial lengths are 4, 51/2, 7i/s, 85/s and 105/sins. The smallest size has 
 six vertical perforations, 1 in. square, and the largest fifteen. 
 
 Eastman Kodak Co., Rochester, N. Y. Height 366 ft.; internal diam. 
 at top 9 ft. 10 ins., at bottom 20 ft. 10 ins.; outside diam., top 11 ft., bottom 
 27 ft. 10 ins. Radial brick, with 4-in. acid-resisting brick lining. 
 
 Some notable tall chimneys built by the Alphonse Custodis Chimney 
 Construction Co. are: Dolgeville, N. Y., 6 X 175 ft.; Camden, N. J., 7 X 210 
 ft.; Newark, N. J., 8 X 350 ft.; Rochester, N. Y., 9 X 366 ft.; Constable 
 Hook, N. J., 10 X 365 ft.; Providence. R. I.. 16 X 308 ft.: Garfield. Utah. 
 30 X 300 ft. ; Great Falls Mont., 50 X 506 ft. 
 
 Interior Stack of the Equitable Building, New York City (Eng. 
 News, Nov. 12, 1914). The stack is 11 ft. outside diam., 596 ft. high, 
 made of steel plates 5/16 in. thick. It is supported on the. steelwork of 
 the building at every other story. It has a 2-in. lining of J. & M. 
 Vitribestos, alternate layers of plain and corrugated asbestos board 
 coated with a supposedly vitrified compound. The rated H.P. of this 
 chimney, taking 10 ft. 7 in. as the inside diameter, is 6710, equivalent 
 to the burning of 33,550 Ib. of coal per hour. 
 
 Stability of Chimneys. Chimneys must be designed to resist the 
 maximum force of the wind in the locality in which they are built. A 
 general rule for diameter of base of brick chimneys, approved by many 
 years of practice in England and the United States, is to make the diam- 
 eter of the base one-tenth of the height. If the chimney is square of 
 rectangular, make the diameter of the inscribed circle of the base one- 
 tenth of the height. The "batter" or taper of a chimney should be 
 from I/in to 1/4 inch to the foot on each side. The brickwork should be 
 one brick (8 or 9 inches) thick for the first 25 feet from the top, increasing 
 1/2 brick (4 or 41/2 inches) for each 25 feet from the top downwards, 
 the inside diameter exceeds 5 feet, the top length should be 11/2 bricks; 
 and if under 3 teet. it may be 1/2 brick for ten feet.. 
 
 (From The Locomotive, 1884 ami 1886.) For chimneys of four feet in 
 
STABILITY OF CHIMNEYS. 955 
 
 diameter and one hundred feet high, and upwards, the best form is cir- 
 cular witn a straignt oatter on me outside. 
 
 Chimneys of any considerable height are not built up of uniform 
 thickness from top to bottom, nor with a uniformly varying thickness of 
 wall, but the wall, heaviest of course at the base, is reduced by a series 
 of steps. 
 
 Where practicable the load on a chimney foundation should not exceed 
 two tons per square foot in compact sand, gravel, or loam. Where a 
 solid rock-bottom is available for foundation, the load may be greatly 
 increased. If the rock is sloping, all unsound portions should be removed, 
 and the face dressed to a series of horiz9ntal steps, so that there shall IDO 
 no tendency to slide after the structure is finished. 
 
 All boiler-chimneys of any C9nsiderable size should consist of an outer 
 stack of sufficient strength to give stability to the structure, and an inner 
 stack or core independent of the outer one. This core is by many engineers 
 extended up to a height of but 50 or 60 feet from the base of the chimney, 
 but the better practice is to run it up the whole height of the chimney: it 
 may be stopped off, say, a couple of feet below the top, and the outer shell 
 contracted to the area of the core, but the better way is to run it up to 
 about 8 or 12 inches of the top and not C9ntract the outer shell. But 
 under no circumstances should the core at its upper end be built into or 
 connected with the outer stack. This has been done in several instances 
 by bricklayers, and the result has been the expansion of the inner core 
 which lifted the top of the outer stack squarely up arid cracked, the brick- 
 work. 
 
 For a height of 100 feet we would make the outer shell in three steps, the 
 first 20 feet high, 16 inches thick, the second 30 feet high, 12 inches thick, 
 the third 50 feet high and 8 inches thick. These are the minimum 
 thicknesses admissible for chimneys of this height, and the batter should 
 be not less than 1 in 36 to give stability. The core should also be built 
 In three steps, each of which may be about one-third the height of tha 
 chimney, the lowest 12 inches, the middle 8 inches, and the upper step 
 4 inches thick. This will insure a good sound core. The top of a chimney 
 may be protected by a cast-iron cap; or perhaps a cheaper and equally 
 good plan is to lay the ornamental part in some good cement, and plaster 
 the top with the same material. 
 
 C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following 
 approximate method may be used for determining the thickness of walls. 
 If the inside diameter at the tpp is less than 3 ft. the walls may be 4 ins. 
 thick for the first 10 ft., and increased 4 ins. for each 25 ft. downward. 
 If the inside diameter is more than 3 ft. and less than 5 ft., begin with a 
 wall 8 ins. thick, increasing 4 ins. for each 25 ft. downward. If the diam- 
 eter is over 5 ft., begin with a 12-in. wall, increasing below the first 10 ft. 
 as before. The lining or core may be 4 ins. thick for the first 20 ft. from 
 the top, 8 ins. for the next 30 ft., 12 ins. for the next 40 ft., 16 ins. for 
 the next 50 ft., and 20 ins. for the next 50 ft. .Using this method for an 
 outer wall 200 ft. high and assuming a cubic foot of brickwork to weigh 
 130 Ibs., it gives a maximum pressure of 8.2 tons per sq. ft. of section at 
 the base; while a lining 190 ft. high would have a maximum pressure of 
 8.6 tons per sq. ft. The safe load for brickwork may be taken at from 
 8 to 10 tons per sq. ft., although the strength of best pressed brick will run 
 much higher. 
 
 James B. Francis, in a report to the Lawrence Mfg. Co. in 1873 (Eng. 
 News, Aug. 28, 1880), concerning the probable effects of wind on that 
 company's chimney as then constructed, says: 
 
 The stability of the chimney to resist the force of the wind depends 
 mainly on the weight of its outer shell, and the width of its base. The 
 cohesion of the mortar may add considerably to its strength; but it is too 
 uncertain to be relied upon. The inner shell will add a little to the 
 stability, but it may be cracked by the heat, and its beneficial effect, if 
 any, is too uncertain to be taken into account. 
 
 The effect of the joint action of the vertical pressure due to the weight 
 of the chimney, and the horizontal pressure due to the force of the wind is 
 to shift the center of pressure at the base of the chimney, from the axis 
 toward one side, the extent of the shifting depending on the relative 
 magnitude of the two forces. If the center of pressure is brought too near 
 the side of the chimney, it will crush the brickwork ou that side, and the 
 
955 CHIMNEYS. 
 
 chimney will fall. A line drawn through the center of pressure, perpen- 
 dicular to the direction of the wind, must leave an area of brickwork 
 between it and the side of the chimney, sufficient to support half the weight 
 of the chimney: the other half of the weight being supported by the brick- 
 work on the windward side of the line. 
 
 Different experimenters on the strength of brickwork give very different 
 results. Kirkaldy found the weights which caused several kinds of 
 bricks, laid in hydraulic lime mortar and in Roman and Portland cements, 
 to fail slightly, to vary from 19 to 60 tons (of 2000 Ibs.) per sq. ft. If 
 we take in this case 25 tons per sq. ft. as the weight that would cause it 
 to begin to fail, we shall not err greatly. 
 
 Rankine, in a paper printed in the transactions of the Institution of 
 Engineers, in Scotland, for 1867-68, says: "It had previously been ascer- 
 tained by observation of the success and failure of actual chimneys, and 
 especially of those which respectively stood and fell during the violent 
 storms of 1856, that, in order that a round chimney may be sufficiently 
 stable, its weight should be such that a pressure of wind, of about 55 Ibs. per 
 sq. ft. of a plane surface, directly facing the wind, or 27V2 Ibs. per sq. ft.' 
 of the plane projection of a cylindrical surface, . . . shall not cause the 
 resultant pressure at any bed-joint to deviate from the axis of the 
 chimney by more than one-quarter of the outside diameter at that 
 joint." 
 
 Steel Chimneys are largely used, especially for tall chimneys of iron- 
 works, from 150 to 300 feet in height. The advantages claimed are: 
 greater strength and safety; smaller space required; smaller cost, by 
 30 to 50 per cent, as compared with brick chimneys; avoidance of infiltra- 
 tion of air and consequent checking of the draught, common in brick 
 chimneys. They are usually made cylindrical in shape, with a wide curved 
 flare for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is 
 provided, to which the chimney is riveted, and the plate is secured to a 
 massive foundation by holding-down bolts. No guys are used. 
 
 Design of Self-supporting Steel Chimneys. John D. Adams 
 (Eng. News, July 20, 1905) .gives a very full discussion of the design of steel 
 chimneys, from which the following is adapted. The bell-shaped bottom 
 of the chimney is assumed to occupy one-seventh of the total height, and 
 the point of maximum strain is taken to be at the top of this bell portion. 
 Let D = diam. in inches, H = height in feet, T = thickness in inches, 
 S = safe tensile stress, Ibs. per sq. in. The general formula for moment 
 of resistance of a hollow cylinder is M = 1/32 it (D*- Z)i 4 ) S/D. When 
 the thickness is a small fraction of the diameter this becomes approxi- 
 mately M = 0.7854 D Z TS. 
 
 With steel plate of 60,000 Ibs. tensile strength, riveting of 0.6 efficiency, 
 and a factor of safety of 4, we have S = 9000 pounds per sq. in., and the 
 safe moment of resistance = 7070 D Z T. 
 
 The effect of the wind upon a cylinder is equal to the wind pressure 
 multiplied by one-half the diametral plane, and taking the maximum 
 wind pressure at 50 Ibs. per sq. ft., we get 
 
 Total wind pressure = 50 X 1/12 D X 1/2 X */iR = 25 DH/14. 
 
 The distance of the center of pressure above the top of the bell por- 
 tion = 3/7 H, multiplied by the total wind pressure, gives us the bend- 
 ing moment due to the wind, 
 
 inch-pounds, 25 DH/14 X 8/7 H X 12 = 9.184 DH*. 
 
 Equating the bending and the resisting moment we have T = 0.0013 
 
 With this formula the maximum thickness of plates was calculated 
 for different sizes of chimneys, as given in the table on p. 957. 
 
 In tlie above formula, no attention has been paid to the weight of the 
 steel in the stack above the bell portion, which weight has a tendency 
 to decrease the tension on the windward side and increase the com- 
 pression on the ieeward side of the stack. A column of steel 150 ft. 
 high would exert a pressure of approximately 500 Ib. per sq. in., which, 
 with steel of 60,000 Ib. tensile strength, is less than 1 % of the ultimate 
 strength, and may safely be neglected. 
 
 From the table'it appears that a chimney 12 X 120 ft. requires, as far 
 as fracture by bending of a tubular section is concerned, a thickness of 
 but little over i/g in. In designing a stack of such extreme proportions 
 
SIZE OF CHIMNEYS. 
 
 057 
 
 as 12 X 120 ft., there are other factors besides bending to take Into con- 
 sideration that ordinarily could be neglected. For instance, such a stack 
 should be provided with stiffening angles, or else made heavier, to guard 
 against lateral flattening. Ordinarily, however, the strength of the 
 chimney determined as a tubular section will be the prime factor in deter- 
 mining the maximum thickness of plates. 
 
 THICKNESS OP BASE-RING PLATES OF SELF-SUPPORTING STEEL STACKS. 
 
 For normal wind pressure of 50 Ibs. per sq. ft. on half the diametral plane 
 
 Diameter of Stack in feet. 
 
 Sl > 5 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 8.5 
 
 9 
 
 9.5 
 
 10 
 
 11 
 
 12 
 
 70 
 
 80 
 90 
 100 
 110 
 120 
 130 
 140 
 150 
 160 
 170 
 180 
 190 
 200 
 210 
 220 
 230 
 240 
 250 
 
 0.152 
 0.198 
 0.224 
 0.310 
 0.375 
 0.446 
 0.523 
 0.607 
 0.696 
 
 .133 
 .182 
 .219 
 .271 
 328 
 .390 
 .458 
 .531 
 .609 
 .693 
 
 .106 
 .139 
 .175 
 .217 
 .262 
 .312 
 .366 
 .425 
 .487 
 .555 
 .626 
 .702 
 
 
 
 
 1 ... 
 
 
 
 
 .116 
 
 .146 
 .181 
 .218 
 .260 
 .305 
 .354 
 .406 
 .462 
 .522 
 '.585 
 .652 
 
 -.099 
 .125 
 .155 
 .187 
 .223 
 .262 
 .303 
 .348 
 .396 
 .447 
 .501 
 .559 
 .620 
 .682 
 
 
 
 
 
 
 
 
 .111 
 .135 
 .164 
 .195 
 .228 
 .265 
 .305 
 .346 
 .391 
 .439 
 .489 
 .542 
 .596 
 .655 
 .717 
 
 
 
 
 
 
 
 .127 
 .154 
 .183 
 .215 
 .250 
 .286 
 .326 
 .368 
 .413 
 .460 
 .510 
 .562 
 .617 
 .674 
 .734 
 
 .120 
 .146 
 .173 
 .203 
 .236 
 .271 
 .308 
 .348 
 .390 
 .434 
 .481 
 .531 
 .582 
 .637 
 .693 
 .752 
 
 
 
 
 
 .138 
 .164 
 .193 
 .223 
 .257 
 .292 
 .330 
 .370 
 .411 
 .456 
 .503 
 .552 
 .603 
 .657 
 .713 
 
 .131 
 .156 
 .183 
 .212 
 .244 
 .277 
 .313 
 .351 
 .391 
 .433 
 .478 
 .524 
 .573 
 .624 
 .677 
 
 .119 
 .142 
 .166 
 .193 
 .222 
 .252 
 .285 
 .319 
 .356 
 .394 
 .434 
 .476 
 .521 
 .567 
 .615 
 
 'J30' 
 .153 
 .180 
 .203 
 .231 
 .261 
 .293 
 .326 
 .361 
 .398 
 .437 
 .477 
 .520 
 .564 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Foundation. Neglecting the increase of wind area due to the flare 
 at the base of the chimney, which has but a very small turning effect, 
 if all dimensions be taken in feet, we have 
 
 Total wind pressure = i/ 2 D X H X 50 = 25 DH; lever-arm =* l/ 2 H; 
 hence, turning moment = 12.5 DH 2 . 
 
 Let d = diameter and h = height of foundation. For average con- 
 ditions h =s 0.4 d, then volume of foundation = 0.7854 d z h, and for 
 concrete at 150 Ibs. per cu. ft., weight of foundation = W = 0.7854 d*h 
 X 150 = 47.124 d>. 
 
 The stability of the foundation or the tendency to resist overturning 
 is equal to the weight of the foundation multiplied by its radius or 1/2 Wd 
 = 23.562 d*. Applying a factor of safety of 21/2, which is indicated by 
 current practice, gives safe stability = 9.425 d 4 . Equating this to the 
 overturning moment we obtain d= 1.07 <\JDH 2 , in which all dimensions 
 are in feet. 
 
 Anchor-bolts. The holding power of the bolts depends on three 
 factors: the number of bolts, the diameter of the bolt circle, and the 
 diameter of the bolts. The number of bolts is largely conventional and 
 may ^e selected so as not to necessitate bolts of too large a diameter. The 
 diameter of the bolt circle is also more or less arbitrary. The bolts will 
 be stretched and therefore strained, in proportion to their distance from 
 the ttxis of turning, assuming, as we must, that the cast-iron ring at the 
 base of the chimney is rigid. The leverage at which any bolt acts is also 
 directly proportional to its distance from the axis of turning. Therefore, 
 since the effectiveness of any one bolt, as regards overturning, depends 
 upon the strain in that bolt, multiplied by its leverage, it is evident that 
 the effectiveness of any bolt varies as the square of its distance from the 
 axis of turning. If we lay out, say, 12 or 24 bolts equidistant on a circle 
 and :,dd all the squares of these distances, we will find that we may con- 
 sider the total as though the bolts were all placed at a distance of 3/ 8 
 the diameter of the bolt circle from the axis of turning, which is the tan- 
 gent to the bolt circle. 
 
 Let & SB diameter of bolt in inches, n = number of bolts, diameter 
 
958 
 
 CHIMNEYS. 
 
 of bolt circle 
 
 Take safe working stress at 8000 pounds per sq. 
 
 inch. Then resistance to overturning^ = 0.7854 b 2 X 8000 X 2/ 3 d x 3/ 8 X 
 N = 6283 b*Nd/4. Equating this to the turning moment, 12.5 DH*, 
 gives v = 0.0257 H\/^7~d for 12 bolts, 0.0222 H\/D/d for 18 bolts, 
 and 0.0182 H VD/d for 24 bolts. 
 
 Reinforced Concrete Chimneys began extensively to come into use 
 in the United States in 1901. Some hundreds of them are now (1909) 
 in use. The following description of the method of construction of these 
 chimneys is condensed from a circular of the Weber Chimney Co., Chicago. 
 
 The foundation is comparatively light and made of concrete, consisting 
 of 1 cement, 3 sand, and 5 gravel or macadam. The steel reenforcement 
 consists of two networks usually made of T steel of small size. The bars 
 for the lower network are placed diagonally and the bars for the second 
 network (about 4 to 6 ins. above .the first one) run parallel to the sides. 
 The vertical bars, forming the reenforcement of the chimney itself, also 
 go down into the foundation and a number of these bars are bent in order 
 to secure an anchorage for the chimney. 
 
 f The chimney shaft consists of two parts, the lower double shell and the 
 single shell above, which are united at the offset. The inside shell is 
 usually 4 ins. thick, while the thickness of the outer shell depends on the 
 height and varies from 6 to 12 ins. The single shell is from 4 to 10 ins. 
 thick. The height of the double shell depends upon the purpose of the 
 chimney, nature and heat of the gases, etc. 
 
 Between the two shells in the lower part there is a circular air space 4 
 ins. in width. An expansion joint is provided where the two shells unite. 
 
 The concrete above the ground level consists of one part Portland 
 cement and three parts of sand. No gravel or macadam is used. 
 
 The bending forces caused by wind pressure are taken up by the vertical 
 steel reenforcement. The resistance of the concrete itself against tension 
 is not considered in calculation. 
 
 The vertical T bars are from 1 X 1 X Vs to 1 1/ 2 XI 1/2 X 1/2 in., the weight 
 and number depending upon the dimensions of the chimney. The bars 
 are from 16 to 30 ft. long and overlap .not less than 24 ins. They are 
 placed at regular intervals of 18 ins. and encircled by steel rings bent to 
 the desired circle. 
 
 The following is a list of some of the tallest concrete chimneys that 
 have been built of their respective diameters: Butte, Mont., 350 X 18 
 ft.; Seattle, Wash., 278 X 17 ft.; Portland, Ore., 230 X 12 ft.; Lawrence, 
 Mass., 250 X 11 ft.; Cincinnati, Ohio, 200 X 10 ft.; Worcester, Mass, 
 220 X 9 ft.; Atlanta, Ga., 225 X 8 ft.; Chicago. 175 X 7 ft.; Rockville, 
 Conn., 175 X 6 ft.; Seymour, Ind., 150 X 5 ft.; lola, Kans., 143 X 4 ft.; 
 St. Louis, Mo., 130 X 3 ft. 4 in.; Dayton, Ohio, 94 X 3 ft. 
 
 Sizes of Foundations for Steel Chimneys. 
 
 (Selected from circular of Phila. Engineering Works.) 
 HALF-LINED CHIMNEYS. 
 
 Diameter, clear, feet 3456 
 
 Height, feet 100 100 150 150 
 
 Least diam. foundation.. 15'9" 16' 4" 20'4" 21'10' 
 Least depth foundation.. 6' 6' 9' 
 
 Height, feet 125 200 200 
 
 Least diam. foundation 18'5" 23'8" 25' 
 
 Least depth foundation 7' 
 
 Weight of Sheet-iron Smoke-stacks per Foot 
 (Porter Mfg. Co.) 
 
 150 
 22'7" 
 9' 
 250 
 29'8" 
 12' 
 
 9 
 
 150 
 23'8" 
 10' 
 275 
 33'6" 
 12' 
 
 11 
 
 150^ 
 
 10' 
 300 
 36' 
 14' 
 
 Diam. 
 inches. 
 
 Thick- 
 ness. 
 W. G. 
 
 Weight 
 per ft. 
 
 Diam. 
 inches. 
 
 Thick- 
 ness. 
 W. G. 
 
 Weight 
 per ft. 
 
 Diam. 
 inches. 
 
 Thick- 
 ness. 
 W. G. 
 
 Weight 
 per ft. 
 
 10 
 12 
 14 
 16 
 20 
 22 
 24 
 
 No. 16 
 
 7.20 
 8.66 
 9.58 
 11.68 
 13.75 
 15.00 
 16.25 
 
 26 
 28 
 30 
 10 
 12 
 14 
 16 
 
 No ; 16 
 No 14 
 
 17.50 
 18.75 
 20.00 
 9.40 
 11.11 
 13.69 
 15.00 
 
 20 
 22 
 24 
 26 
 28 
 30 
 
 No ; 14 
 
 18.33 
 20.00 
 21.66 
 23.33 
 25.00 
 26.66 
 
 : --^.^m 
 
THE STEAM ENGINE. 
 
 959 
 
 THE STEAM-ENGINE. 
 
 Expansion of Steam. Isothermal and Adiabatic. According to 
 Mariotte's law, the volume of a perfect gas, the temperature being kept 
 constant, varies inversely as its pressure, or p i/v; pv = a constant. The 
 curve constructed from this formula is called the isothermal curve, or 
 curve of equal temperatures, and is a common or rectangular hyperbola. 
 The expansion of steam in an engine is not isothermal, since the temper- 
 ature decreases with increase of volume, but its expansion curve approxi- 
 mates the curve of pv = a constant. The relation of the pressure and 
 volume of saturated steam, as deduced from Regnault's experiments, and 
 as given in steam tables, is approximately, according to Rankine (S. E., 
 p. 403), for pressures not exceeding 120 Ibs., p cc 1/vii, or p oc -y~is or pv^ = 
 pfli-0626a constant. Zeuner has found that the exponent 1.0646 gives a 
 closer approximation. 
 
 When steam expands in a closed cylinder, as in an engine, according to 
 Rankine (S. E., p. 385), the approximate law of the expansion is p oc 1/vV*. 
 orpc-y~9' or pv l ' m = a constant. The curve constructed from this 
 formula is called the adiabatic curve, or curve of no transmission of heat. 
 
 Peabody (Therm., p. 112) says: "It is probable that this equation was 
 obtained by comparing the expansion lines on a large number of indicator- 
 diagrams. . . . There does not appear to be any good reason for using an 
 exponential equation in this connection, . . . and the action of a lagged 
 steam-engine cylinder is far from being adiabatic. . . . For general pur- 
 poses the hyperbola is the best curve for comparison with the expansion 
 curve of an indicator-card. ..." Wolff and Denton, Trans. A. S. M. E. t 
 ii, 175, say: " From a number of cards examined from a variety of steam- 
 engines in current use, we find that the actual expansion line varies between 
 the 10/9 adiabatic curve and the Mariotte curve." 
 
 Prof. Thurston (Trans. A.S. M. E.,i\, 203) says he doubts if the exponent 
 ever becomes the same in any two engines, or even in the same engine 
 at different times of the day and under varying conditions of the day. 
 
 Expansion of Steam according to Mariotte's Law and to the 
 Adiabatic Law. (Trans. A. S. M. E., ii, 156.) Mariotte's law pv = 
 
 vn 1 
 
 PIVI; values calculated from formula = -5 (1 + hyp log R), in which 
 
 Pi K 
 
 R = v<i -*- vi, Pi absolute initial pressure, P m = absolute mean pressure, 
 v\ = initial volume of steam in cylinder at pressure pi, vz = final volume 
 of steam at final pressure. Adiabatic law: pv* pivi: values calcu- 
 
 lated from formula - 
 
 10 R l - 
 
 Ratio 
 of Ex- 
 pansion 
 R. 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 Ratio 
 of Ex- 
 pansion 
 R. 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 Ratio 
 of Ex- 
 pansion 
 R. 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 Mar. 
 
 Adiab. 
 
 Mar. 
 
 Adiab. 
 
 Mar. 
 
 Adiab. 
 
 1.00 
 
 1.000 
 
 1.000 
 
 3.7 
 
 0.624 
 
 0.600 
 
 6. 
 
 0.465 
 
 0.438 
 
 1.25 
 
 .978 
 
 .976 
 
 3.8 
 
 .614 
 
 .590 
 
 6.25 
 
 .453 
 
 .425 
 
 1.50 
 
 .937 
 
 .931 
 
 3.9 
 
 .605 
 
 .580 
 
 6.5 
 
 .442 
 
 .413 
 
 2' 75 
 
 .891 
 
 .881 
 
 4. 
 
 .597 
 
 .571 
 
 6.75 
 
 .431 
 
 .403 
 
 
 .847 
 
 .834 
 
 4.1 
 
 .588 
 
 .562 
 
 7. 
 
 .421 
 
 .393 
 
 2.2 
 
 .813 
 
 .798 
 
 4.2 
 
 .580 
 
 .554 
 
 7.25 
 
 .411 
 
 .383 
 
 2.4 
 
 .78! 
 
 .765 
 
 4.3 
 
 .572 
 
 .546 
 
 7.5 
 
 .402 
 
 .374 
 
 2.5 
 
 .766 
 
 .748 
 
 4.4 
 
 .564 
 
 .538 
 
 7.75 
 
 .393 
 
 .365 
 
 2.6 
 
 .752 
 
 .733 
 
 4.5 
 
 .556 
 
 .530 
 
 8. 
 
 .385 
 
 .357 
 
 2.8 
 
 .725 
 
 .704 
 
 4.6 
 
 .549 
 
 .523 
 
 8.25 
 
 .377 
 
 .349 
 
 3. 
 
 .700 
 
 .678 
 
 4.7 
 
 .542 
 
 .516 
 
 8.5 
 
 .369 
 
 .342 
 
 3.1 
 
 .688 
 
 .666 
 
 4.8 
 
 .535 
 
 .509 
 
 8.75 
 
 .362 
 
 .335 
 
 3.2 
 
 .676 
 
 .654 
 
 4.9 
 
 .528 
 
 .502 
 
 9. 
 
 .355 
 
 .328 
 
 3.3 
 
 .665 
 
 .642 
 
 5 
 
 .522 
 
 .495 
 
 9.25 
 
 .349 
 
 .321 
 
 3.4 
 
 .654 
 
 .630 
 
 5.25 
 
 .506 
 
 .479 
 
 9.5 
 
 .342 
 
 .315 
 
 35 
 
 .644 
 
 .620 
 
 5.5 
 
 .492 
 
 .464 
 
 9.75 
 
 .336 
 
 .309 
 
 3.6 
 
 .634 
 
 .610 
 
 5.75 
 
 .478 
 
 .450 
 
 10. 
 
 .330 
 
 .303 
 
960 
 
 THE STEAM-ENGINE. 
 
 Mean Pressure of Expanded Steam. For calculations of engine 
 it is generally assumed that steam expands according to Mariotte's law, 
 the curve of the expansion line being a hyperbola. The mean pressure. 
 measured above vacuum, is then obtained Irom the formula 
 
 P M -H 1 + hy P' gfi . or P m =P t (1 + hyp log *). 
 
 in which P m is the absolute mean pressure, p\ the absolute initial pressure 
 taken as uniform up to the point of cut-off, P t the terminal pressure, and 
 R the ratio of expansion. If I = length of stroke to the cut-off, L = total 
 stroke. 
 
 l + hy plo g ft 
 = -- 
 
 Mean and Terminal Absolute Pressures. Mariotte's Law. The 
 
 values in the following table are based on Mariotte's law, except those 
 in the last column, which give the mean pressure of superheated steam, 
 which, according to Rankine, expands in a cylinder according to the 
 law p<xv~*%. These latter values are calculated from the formula 
 
 = - - . R~iis may be found by extracting the square root 
 
 of four times. From the mean absolute pressures given deduct the mean 
 
 ti 
 back pressure (absolute) to obtain the mean effective pressure. 
 
 Rate 
 of 
 Expan- 
 sion. 
 
 Cut- 
 off. 
 
 Ratio of 
 Mean to 
 Initial 
 Pressure. 
 
 Ratio of 
 Mean to 
 Terminal 
 Pressure. 
 
 Ratio of 
 Terminal 
 to Mean 
 Pressure. 
 
 Ratio of 
 Initial 
 to Mean 
 Pressure. 
 
 Ratio of 
 Mean to 
 Initial 
 Dry Steam. 
 
 30 
 
 28 
 
 0.033 
 0.036 
 
 0.1467 
 0.1547 
 
 4.40 
 4.33 
 
 0.227 
 0.231 
 
 6.82 
 6.46 
 
 0.136 
 
 26 
 
 0.038 
 
 0.1638 
 
 4.26 
 
 0.235 
 
 6.11 
 
 
 24 
 
 0.042 
 
 0.1741 
 
 4.18 
 
 0.239 
 
 5.75 
 
 
 22 
 
 0.045 
 
 0.1860 
 
 4 09 
 
 0.244 
 
 5 38 
 
 
 20 
 18 
 
 0.050 
 0.055 
 
 0.1998 
 2161 
 
 4.00 
 3 89 
 
 0.250 
 256 
 
 5.00 
 4 63 
 
 0.186 
 
 16 
 
 0.062 
 
 0.2358 
 
 3 77 
 
 0.265 
 
 4.24 
 
 
 15 
 
 0.066 
 
 0.2472 
 
 3.71 
 
 0.269 
 
 4.05 
 
 
 14 
 
 0.071 
 
 0.2599 
 
 3 64 
 
 275 
 
 3 85 
 
 
 J3.33 
 13 
 
 0.075 
 0.077 
 
 0.2690 
 2742 
 
 3.59 
 3 56 
 
 0.279 
 280 
 
 3.72 
 3 65 
 
 0.254 
 
 12 
 
 0.083 
 
 0.2904 
 
 3 48 
 
 287 
 
 3 44 
 
 
 11 
 
 0.091 
 
 0.3089 
 
 3.40 
 
 0.294 
 
 3.24 
 
 
 10 
 9 
 8 
 7 
 
 0.100 
 0.111 
 0.125 
 0.143 
 
 0.3303 
 0.3552 
 0.3849 
 0.4210 
 
 3.30 
 3.20 
 3.08 
 2 95 
 
 0.303 
 0.312 
 0.321 
 339 
 
 3.03 
 2.81 
 2.60 
 2 37 
 
 0.314 
 
 '"o.m" 
 
 6.66 
 6.00 
 
 0.150 
 0.166 
 
 0.4347 
 4653 
 
 2.90 
 2 79 
 
 0.345 
 360 
 
 2.30 
 2 15 
 
 0.417 
 
 5.71 
 
 0.175 
 
 0.4807 
 
 2 74 
 
 364 
 
 2 08 
 
 
 5.00 
 4.44 
 
 0.200 
 0.225 
 
 0.5218 
 0.5608 
 
 2.61 
 2 50 
 
 0.383 
 400 
 
 .92 
 
 78 
 
 0.506 
 
 4.00 
 3.63 
 
 0.250 
 0.275 
 
 0.5965 
 6308 
 
 2.39 
 2 29 
 
 0.419 
 437 
 
 .68 
 58 
 
 0.582 
 
 3.33 
 3.00 
 
 0.300 
 0.333 
 
 0.6615 
 6995 
 
 2.20 
 2 10 
 
 0.454 
 476 
 
 .51 
 43 
 
 0.6 8 
 
 2.86 
 2.66 
 
 0.350 
 375 
 
 0.7171 
 7440 
 
 2.05 
 98 
 
 0.488 
 505 
 
 .39 
 
 34 
 
 0.707 
 
 2.50 
 2.22 
 2.00 
 .82 
 .66 
 .60 
 .54 
 .48 
 
 0.400 
 0.450 
 0.500 
 0.550 
 0.600 
 0.625 
 0.650 
 0.675 
 
 0.7664 
 0.8095 
 0.8465 
 0.8786 
 0.9066 
 0.9187 
 0.9292 
 0.9405 
 
 .91 
 .80 
 .69 
 .60 
 .51 
 .47 
 .43 
 .39 
 
 0.523 
 0.556 
 0.591 
 0.626 
 0.662 
 0.680 
 0.699 
 0.718 
 
 .31 
 .24 
 .18 
 .14 
 .10 
 .09 
 .07 
 .06 
 
 0.756 
 0.800 
 0.840 
 0.874 
 0.900 
 
 "'6;926'" 
 
THE STEAM-ENGINE. 
 
 961 
 
 Calculation of Moan Effective Pressure, Clearance and Com- 
 pression Considered, In the above tables no account is taken of 
 
 clearance, which in actual 
 
 ___ I ___ ^ steam-engines modifies the 
 
 ratio of expansion and the 
 mean pressure ; nor of com- 
 pression and back-pressure, 
 which diminish the mean 
 effective pressure. In the 
 following calculation these 
 elements are considered. 
 
 L = length of stroke, I = 
 length before cut-off, x = 
 length of compression part of 
 stroke, c = clearance, pi = 
 initial pressure, p& back 
 pressure, p c = pressure of 
 clearance steam at end of 
 compression. All pressures 
 are absolute, that is, measured 
 from a perfect vacuum. 
 
 Area of ABCD = Pl (l + c) (l 4- hyp log j^) ; 
 B = pi,(L-x); 
 
 C - Pec (l + hyp log ^ =p b (x+c) (l + hyp log ^p); 
 = (Pi-Pe) c = pi 
 Area of A = ABCD-(B-f C4- D) 
 
 - \Pb (L-x)+pb (z + c) (l + hyp log *-^ + plC -p b ( X -4-c)] 
 ) (l + hyp log ^^ 
 
 - pb [(L -x) + (x + c) hyp log l -pic. 
 
 Mean effective pressure - 
 
 area of A 
 
 EXAMPLE. Let L = l, 2 = 0.25, rr = 0.25, c = 0.1, 
 Area A = 60 (0.25 + 0.1) (l + hyp log ~^\ 
 
 Ibs., p& = 2 Ibs. 
 
 - 2 [(1-0.25) +0.35 hyp log ^yl -60X0 1. 
 
 = 21 (1 4- 1.145) -2 [0.75 + 0.35 X 1.2531 - 6 
 
 = 45.045 - 2.377 - 6 = 36.668 = mean effective pressure. 
 
 The actual indicator-diagram generally shows a mean pressure con- 
 siderably less than that due to the initial pressure and the rate of expan- 
 sion. The causes of loss of pressure are: 1. Friction in the stop-valves 
 and steam-pipes. 2. Friction or wire-drawing of the steam during 
 admission and cut-off, due chiefly to defective valve-gear and contracted 
 steam-passages. 3. Liquefaction during expansion. 4. Exhausting 
 before the engine has completed its stroke. 5. Compression due to early 
 closure of exhaust. 6. Friction in the exhaust-ports, passages, am} 
 pipes, 
 
962 THE STEAM-ENGINE. 
 
 Re-evaporation during expansion of the steam condensed during admis- 
 sion, and valve-leakage after cut-off, tend to elevate the expansion line 
 of the diagram and increase the mean pressure. 
 
 If the theoretical mean pressure be calculated from the initial pressure 
 and the rate of expansion on the supposition that the expansion curve 
 follows Mariotte's law, pv = a constant, and the necessary corrections 
 are made for clearance and compression, the expected mean pressure in 
 practice may be found by multiplying the calculated results by the factor 
 (commonly called the "diagram factor") in the following table according 
 to Seaton. 
 
 Particulars of Engine. Factor. 
 
 Expansive engine, special valye-gear, or with a sepa- 
 
 rate cut-off valve, cylinder jacketed ............. 0.94 
 
 Expansive engine having large ports, etc., and good 
 
 ordinary valves, cylinders jacketed .............. 0.9 to 0.92 
 
 Expansive engines with the ordinary valves and gear 
 
 as in general practice, and unjacketed ........... . 8 to . 85 
 
 Compound engines, with expansion valve to h.p. 
 cylinder; cylinders jacketed, and with large ports, 
 etc ..... ...................................... . 9 to . 91 
 
 Compound engines, with ordinary slide-valves, cylin- 
 
 ders jacketed, and good ports, etc ............... . 8 to . 85 
 
 Compound engines as in general practice in the 
 merchant service, with early cut-off in both cylin- 
 ders, without jackets and expansion- valves ....... . 7 to . 8 
 
 Fast-running engines of the type and design usually 
 
 fitted in war-ships ............................ . 6 to . 8 
 
 If no correction be made for clearance and compression, and the engine 
 Is in accordance with general modern practice, the theoretical mean 
 pressure may be multiplied by 0.96, and the product by the proper factor 
 in the table, to obtain the expected mean pressure. 
 
 Given the Initial Pressure and the Average Pressure, to Find the 
 Ratio of Expansion and the Period of Admission. 
 
 P = initial absolute pressure in Ibs. per sq. in.; 
 
 p = average total pressure during stroke in Ibs. per sq. in.; 
 
 L = length of stroke in inches; 
 
 I = period of admission measured from beginning of stroke; 
 
 c = clearance in inches ; 
 
 R = actual ratio of expansion = , . ....... (1) 
 
 R 
 To find average pressure p, taking account of clearance, 
 
 p = P(E + c) + P(l + c)hyplogg-Pc 
 
 L 
 whence pL + Pc=P (I + c) (1 + hyp log R) ; 
 
 (3) 
 
 Given p and P, to find R and I (by trial and error). There being two 
 unknown quantities R and I, assume one of them, viz., the period of 
 admission i, substitute it in equation (3) and solve for R. Substitute this 
 
 value of R in the formula (1), or I = =r-^ c, obtained from formula 
 
 K 
 
 d), and find I. If the result is greater than the assumed value of I, 
 then the assumed value of the period of admission is too long; if less, the 
 assumed value is too short. Assume a new value of I, substitute it ir 
 formula (3) as before, and continue by this method of trial and error till 
 the required values of R a.nd I are obtained. 
 
THE STEAM-ENGINE. 
 
 963 
 
 EXAMPLE. P=70, p = 42.78, L = 
 I = 21 in. 
 
 P r . 42.78 
 
 60 In., c =3 in., to find I. Assume 
 
 hyp log R 
 hyp log R 
 
 -1 = 
 
 70 
 
 X 60 -f 3 
 
 l+c 21 + 3 
 
 = 0.653, whence R = 1.92. 
 L + c 
 
 -1 = 1.653- 1 0.653; 
 
 which Is greater than the assumed value, 21 inches. 
 Now assume I = 15 inches: 
 42.78 v 
 
 hyp log R = 
 
 70 
 
 - X 60 -f 3 
 
 15 + 3 
 
 1 = 1.204, whence R 3.5; 
 
 P C - c= r-^ -3 = 18 -3 = 15 inches, the value assumed. 
 
 K o.O 
 
 Therefore R = 3.5, and 1 = 15 inches. 
 
 Period of Admission Required for a Given Actual Ratio of Expansion: 
 
 1 J-^-c, in inches (4) 
 
 K 
 
 100 + p. ct. clearance 
 percentage of stroke, 1= 5 p. ct. clearance . (5) 
 
 K 
 
 In percen 
 Terminal 
 Pressure 
 
 _ . .sure at any other Point of the Expansion. Let L\ = length of 
 stroke up to the given point. 
 
 Pressure at the given point = 
 
 Li + c 
 
 (7) 
 
 Mechanical Energy of Steam Expanded Adiabatically to Various 
 ressures. The figures in the following table are taken from a chart 
 nstructed by R. M. Neilson in Power, Mar. 16, 1909. The pressures 
 e absolute, IDS per sq. in. 
 
 3*5) 
 
 2 I 15 
 
 
 
 20 
 
 25 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 170 
 
 200 
 
 250 
 
 "a? ^ 
 
 E 
 
 Mechanical Energy, Thousands of Foot-Pounds per Lb. of Steam. 
 
 15 
 12 
 
 10 
 8 
 6 
 4 
 2 
 1 
 
 
 12 
 22 
 34 
 49 
 68 
 100 
 131 
 
 17 
 
 29 
 39 
 50 
 64 
 85 
 116 
 147 
 
 29.5 
 41 
 50.5 
 62 
 76 
 95.5 
 128 
 157.5 
 
 55.5 
 66.5 
 75.5 
 86.5 
 101 
 120 
 151 
 181.5 
 
 77.5 
 88 
 97 
 109 
 123 
 142 
 171 
 200.5 
 
 94.5 
 104 
 113 
 124 
 138 
 157 
 186.5 
 215 
 
 107 
 116 
 125 
 136 
 150 
 168 
 197.5 
 225 
 
 116.5 
 126 
 135.5 
 147 
 160 
 177.5 
 207 
 234.5 
 
 121 
 135 
 144 
 155 
 
 168.5 
 186 
 215 
 
 243 
 
 136.5 
 145 
 154 
 165.5 
 179.5 
 196 
 224 
 250.5 
 
 !46 
 154.5 
 163.5 
 174.5 
 188 
 204.5 
 232.5 
 260.5 
 
 160 
 168.5 
 176 
 186 
 199 
 216 
 244 
 270.5 
 
 Measures for Comparing the Duty of Engines. Capacity is meas- 
 ured in horse-powers, expressed by the initials, H.P.: 1 H.P. = 33,000 
 ft.-lbs. per minute, =550 ft.-lbs. per second, = 1,980,000 ft.-lbs. per hour. 
 1 ft.-lb. = a pressure of 1 Ib. exerted through a space of 1 ft. 
 
 Economy is measured, 1, in pounds of coal per horse-power per hour; 
 2, in pounds of steam per horse-power per hour. The second of these 
 measures is the more accurate and scientific, since the enerine uses steam 
 and not coal, and it is independent of the economy of the boiler. A still 
 more accurate measure is the heat units per minute (or per hour) per 
 horse-power. 
 
964 
 
 THE STEAM-ENGINE. 
 
 In gas-engine tests the common measure is the number of cubic feet 
 of gas (measured at atmospheric pressure) per horse-power, but as all gas 
 is not of the same quality, it is necessary for comparison of tests to give 
 the analysis of the gas. When the gas for one engine is made in one 
 gas-producer, then the number of pounds of coal used in the producer per 
 hour per horse-power of the engine is a measure of economy. Since 
 different coals vary in heating value, a more accurate measure is the 
 number of heat units required per horse-power per hour. 
 
 Economy, or duty of an engine, is also measured in the number of foot- 
 pounds of work done per pound of fuel. As 1 horse-power is equal to 
 1,980,000 ft.-lbs. of work in an hour, a duty of 1 Ib. of coal per H.P. per 
 hour would be equal to 1,980,000 ft.-lbs. per Ib. of fuel; 2 Ibs. per H.P. 
 per hour equals 990,000 ft.-lbs. per Ib. of fuel, etc. 
 
 The duty of pumping-engines is expressed by the number of foot- 
 pounds of work done per 100 Ibs. of coal, per 1000 Ibs. of steam, or per 
 million heat units, 
 
 When the duty of a pumping-engine is given, in ft.-lbs. per 100 Ibs. of 
 coal, the equivalent number of pounds of fuel consumed per horse-power 
 per hour is found by dividing 198 by the number of millions of foot-pounds 
 of duty. Thus a pumping-engine giving a duty of 99 millions is equiva- 
 lent to 198/99 = 2 Ibs. of fuel per horse-power per hour. 
 
 Efficiency Measured in Thermal Units per Minute. The efficiency 
 of an engine is sometimes expressed in terms of the number of thermal 
 units used by the engine per minute for each indicated horse-power, instead 
 of by the number of pounds of steam used per hour. 
 
 The heat chargeable to an engine per pound of steam is the difference 
 between the total heat in a pound of steam at the boiler-pressure and that 
 in a pound of the feed-water entering the boiler. In the case of con- 
 densing engines, suppose we have a temperature in the hot-well of 100 F., 
 corresponding to a vacuum of 28 in. of mercury; we may feed the water 
 into the boiler at that temperature. In the case of a non-condensing 
 engine, by using a portion of the exhaust steam in a good feed-water 
 heater, at a pressure a trifle above the atmosphere (due to the resistance 
 of the exhaust passages through the heater), we may obtain feed-water 
 at 212. One pound of steam used by the engine then would be equivalent 
 to thermal units as follows: 
 
 Gauge pressure 50 75 100 125 150 175 200 
 
 Absolute pressure. ...65 90 115 140 165 190 215 
 Total heat in steam above 32: 
 
 1178.5 1184.4 1188.8 1192.2 1195.0 1197.3 1199.2 
 
 Subtracting 68 and 180 heat-units, respectively, the heat above 32 in 
 feed-water of 100 and 212 F. f we have 
 
 Heat given by boiler per pound of steam: 
 
 'Feed at 100.. ,.1110.5 1116.4 1120.8 1124.2 1127.0 1129.3 1131.2 
 Feed at 212 998.5 1004.4 1008.8 1012.2 1015.0 1017.3 1019.2 
 
 Thermal units per minute used by an engine for each pound of steam 
 used per indicated horse-power per hour: 
 
 Feed at 100. . . . 18.51 18.61 18.68 18.74 18.78 18.82 18.85 
 Feed at 212 16.64 16.76 16.78 16.87 16.92 16.96 16.99 
 
 EXAMPLES. A triple-expansion engine, condensing, with steam at 
 175 Ibs. gauge, and vacuum 28 in., uses 13 Ibs. of water per I. H.P. per hour, 
 and a high-speed non-condensing engine, with steam at 100 Ibs. gauge, 
 uses 30 Ibs. How many thermal units per minute does each consume? 
 
 Ans. 13 X 18.82 = 244.7, and 30 X 16.78 = 503.4 thermal units 
 per minute. 
 
 A perfect engine converting all the heat-energy of the steam into 
 work would require 33,000 ft.-lbs. 777.54 = 42.44 thermal units per 
 minute per indicated horse-power. This figure, 42.44, therefore, divided 
 by the number of thermal units per minute per I. H.P. consumed by an 
 engine, gives its efficiency as compared with an ideally perfect engine. 
 In the examples above, 42.44 divided by 244.7 and by 503.4 gives 
 J7.34% and 8.43% efficiency, respectively. 
 
ACTUAL EXPANSIONS. 
 
 965 
 
 ACTUAL, EXPANSIONS 
 
 With Different Clearances and Cut-offs 
 
 Computed by A. F. Nagle. 
 
 
 Per Cent of Clearance. 
 
 Cut- 
 
 
 off. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 .01 
 
 100.00 
 
 50.5 
 
 34.0 
 
 25.75 
 
 20.8 
 
 17.5 
 
 15.14 
 
 13.38 
 
 12.00 
 
 10.9 
 
 10 
 
 .02 
 
 50.00 
 
 33.67 
 
 25.50 
 
 20.60 
 
 17.33 
 
 15.00 
 
 13.25 
 
 11.89 
 
 10.80 
 
 9.91 
 
 9.17 
 
 (H 
 
 33 33 
 
 25 25 
 
 20 40 
 
 17 16 
 
 14 86 
 
 13 12 
 
 11 78 
 
 10 70 
 
 9 82 
 
 9 08 
 
 8 46 
 
 .04 
 
 25.00 
 
 20.20 
 
 17.00 
 
 14.71 
 
 13.00 
 
 11.66 
 
 10.60 
 
 9.73 
 
 9.00 
 
 8.39 
 
 7.86 
 
 .05 
 
 20.00 
 
 16.83 
 
 14.57 
 
 12.87 
 
 11.55 
 
 10.50 
 
 9.64 
 
 8.92- 
 
 8.31 
 
 7.79' 
 
 7.33 
 
 .06 
 
 16.67 
 
 14.43 
 
 12.75 
 
 11.44 
 
 10.40 
 
 9.55 
 
 8.83 
 
 8.23 
 
 7.71 
 
 7.27 
 
 6.88 
 
 ,07 
 
 14.28 
 
 12.62 
 
 11.33 
 
 10.30 
 
 9.46 
 
 8.75 
 
 8.15 
 
 7.64 
 
 7.20 
 
 6.81 
 
 6.47 
 
 .08 
 
 12.50 
 
 11.22 
 
 10.2 
 
 9.36 
 
 8.67 
 
 8.08 
 
 7.57 
 
 7.13 
 
 6.75 
 
 6.41 
 
 6.11 
 
 .09 
 
 11.11 
 
 10.10 
 
 9.27 
 
 8.58 
 
 8.00 
 
 7.50 
 
 7.07 
 
 6.69 
 
 6.35 
 
 6.06 
 
 5.79 
 
 .10 
 
 10.00 
 
 9.18 
 
 8.50 
 
 7.92 
 
 7.43 
 
 7.00 
 
 6.62 
 
 6.30 
 
 6.00 
 
 5.74 
 
 5.50 
 
 .11 
 
 9.09 
 
 8.42 
 
 7.84 
 
 7.36 
 
 6.93 
 
 6.56 
 
 6.24 
 
 5.94 
 
 5.68 
 
 5.45 
 
 5.24 
 
 .12 
 
 8.33 
 
 7.78 
 
 7.29 
 
 6.86 
 
 6.50 
 
 6.18 
 
 5.89 
 
 5.63 
 
 5.40 
 
 5.19 
 
 5.00 
 
 .14 
 
 7.14 
 
 6.73 
 
 6.37 
 
 6.06 
 
 5.78 
 
 5.53 
 
 5.30 
 
 5.10 
 
 4.91 
 
 4.74 
 
 4.58 
 
 .16 
 
 6.25 
 
 5.94 
 
 5.67 
 
 5.42 
 
 5.20 
 
 5.00 
 
 4.82 
 
 4.65 
 
 4.50 
 
 4.36 
 
 4.23 
 
 .20 
 
 5.00 
 
 4.81 
 
 4.64 
 
 4.48 
 
 4.33 
 
 4.20 
 
 4.08 
 
 3.96 
 
 3.86 
 
 3.76 
 
 3.67 
 
 .25 
 
 4.00 
 
 3.88 
 
 3.77 
 
 3.68 
 
 3.58 
 
 3.50 
 
 3.42 
 
 3.34 
 
 3.27 
 
 3.21 
 
 3.14 
 
 30 
 
 3 33 
 
 3.26 
 
 3.19 
 
 3.12 
 
 3.06 
 
 3.00 
 
 2.94 
 
 2.90 
 
 2.84 
 
 2.80 
 
 ?, 75 
 
 40 
 
 2 50 
 
 2 46 
 
 2 43 
 
 2 40 
 
 2 36 
 
 2 33 
 
 2 30 
 
 2 28 
 
 2 25 
 
 2 22 
 
 ? 20 
 
 .50 
 
 2.00 
 
 .98 
 
 .96 
 
 .94 
 
 .92 
 
 .90 
 
 .89 
 
 .88 
 
 .86 
 
 .85 
 
 .83 
 
 60 
 
 .67 
 
 .66 
 
 .65 
 
 .64 
 
 .63 
 
 .615 
 
 .606 
 
 .597 
 
 .588 
 
 .580 
 
 571 
 
 70 
 
 43 
 
 42 
 
 42 
 
 41 
 
 .41 
 
 .400 
 
 .395 
 
 .390 
 
 .385 
 
 .380 
 
 375 
 
 .80 
 
 .25 
 
 .25 
 
 .244 
 
 .241 
 
 .238 
 
 .235 
 
 .233 
 
 .230 
 
 .227 
 
 .224 
 
 .222 
 
 .90 
 
 .111 
 
 .11 
 
 .109 
 
 .108 
 
 .106 
 
 .105 
 
 .104 
 
 .103 
 
 .102 
 
 .101 
 
 .100 
 
 1.00 
 
 .00 
 
 .00 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 .000 
 
 Relative Efficiency of 1 Ib. of Steam with and without Clearance; 
 
 back pressure and compression not considered. 
 
 P (I + c) + P (I + c) hyp log R - PC 
 
 KL 
 t p = l; L = 100; I = 25; c = 7. 
 
 Mean total pressure p = ' 
 et P = 1; L = 100; I = 25; c 
 32 + 32 hyp log - 
 
 32 + 32X 1.207-7 
 100 
 
 = 0.636. 
 
 100 
 
 f the clearance be added to the stroke, so that clearance becomes 
 zero, the same quantity of steam being used, admission / being then 
 = I + c = 32, and stroke L +.c = 107, 
 
 PI-- 
 
 32 + 32 hyp log - 
 107 
 
 32X^207 
 
 The work of one stroke = pi(L + c) = 0.660 X 107 = 70.6. The 
 amount of the clearance 7 being added to both admission and the 
 stroke, the same quantity of steam will do more work than when the 
 clearance is 7 in the ratio 706 : 636, or 1 1 % more, 
 
 Back Pressure Considered. If backpressure =0.10ofP,thisamount 
 has to be subtracted from p and p\ giving p = 0.536, pi = 0.560, the 
 work of a given quantity of steam used without clearance being greater 
 than when clearance is 7% in the ratio (560 X 1.07) : 536, or 12% more. 
 
 Effect of Compression. By early closure of the exhaust, so that a 
 portion of the exhaust-steam is compressed into the clearance-space, 
 much of the loss due to clearance may be avoided. If expansion is con- 
 tinued down to the back pressure, if the back pressureis uniform through- 
 out the exhaust-stroke, and if compression begins at such point that the 
 
966 
 
 THE STEAM-ENGINE. 
 
 exhaust-steam remaining in the cylinder is compressed to the initial 
 pressure at the end of the back stroke, then the work of compression of the 
 exhaust-steam equals the work done during expansion by the clearance- 
 steam. The clearance-space being filled by the exhaust-steam thus com- 
 pressed, no new steam is required to fill the clearance-space for the next 
 forward stroke, and the work and efficiency of the steam used in the 
 cylinder are just the same as if there were no clearance and no compression. 
 When, however, there is a drop in pressure from the final pressure of the 
 expansion, or the terminal pressure, to the exhaust or back pressure (the 
 usual case), the work of compression to the initial pressure is greater than 
 the work done by the expansion of the clearance-steam, so that a loss of 
 efficiency results. In this case a greater efficiency can be attained by 
 inclosing for compression a less quantity of steam than that needed to fill 
 the clearance-space with steam of the initial pressure. (See Clark, 
 S. E., p. 399, et seq.; also F. H. Ball, Trans. A. S. M. E., xiv, 1067.) It is 
 shown by Clark that a somewhat greater efficiency is thus attained 
 whether or not the pressure of the steam be carried down by expansion 
 to the back exhaust-pressure. 
 
 Cylinder-condensation may have considerable effect upon the best 
 point of compression, but it has not yet (1893) been determined by 
 experiment. (Trans. A. S. M. E., xiv, 1078.) 
 
 Clearance in L.OW- and High-speed Engines. (Harris Tabor, Am. 
 Mach., Sept. 17, 1891.) The construction of the high-speed engine is 
 such, with its relatively short stroke, that the clearance must be much 
 larger than in the releasing-valve type. The short-stroke engine is, 
 of necessity, an engine with large clearance, which is aggravated when 
 variable compression is a feature. Conversely, the engine with releasing- 
 valve gear is, from necessity, an engine of slow rotative speed, where 
 great power is obtainable from long stroke, and small clearance is a 
 feature in its construction. In one case the clearance will vary from 
 8% to 12% of the piston-displacement, and in the other from 2% to 3%. 
 In the case of an engine with a clearance equaling 10% of the piston- 
 displacement the waste room becomes enormous when considered in con- 
 nection with an early cut-off. The system of compounding reduces the 
 waste due to clearance in proportion as the steam is expanded to a lower 
 pressure. The farther expansion is carried through a train of cylinders 
 the greater will be the reduction of waste due to clearance. This is shown 
 from the fact that the high-speed, engine, expanding steam much less than 
 the Corliss, will show a greater gain when changed from simple to com- 
 pound than its rival under similar conditions. 
 
 Cylinder-condensation. Rankine, S. E., p. 421, says: Conduction 
 of heat to and from the metal of the cylinder, or to and from liquid water 
 contained in the cylinder, has the effect of lowering the pressure at the 
 beginning and raising it at the end of the stroke, the lowering effect being 
 on the whole greater than the raising effect. In some experiments the 
 quantity of steam wasted through alternate liquefaction and evaporation 
 in the cylinder has been found to be greater than the quantity which 
 performed the work. 
 
 Percentage of Loss by Cylinder-condensation, taken at Cut-off. 
 
 (From circular of the Ashcroft Mfg. Co. on the Tabor Indicator, 1889.) 
 
 Percentage of 
 Stroke com- 
 pleted at 
 Cut-ofif. 
 
 Per cent of Feed-water ac- 
 counted for by the Indicator. 
 
 Per cent of Feed-water due 
 to Cylinder-condensation. 
 
 Simple 
 Engines. 
 
 Compound 
 Engines, 
 h.p. cyl. 
 
 Triple-ex- 
 pansion 
 Engines, 
 h.p. cyl. 
 
 Simple 
 Engines. 
 
 Compound 
 Engines, 
 h.p. cyl. 
 
 Triple-ex- 
 pansion 
 Engines, 
 h.p. cyl. 
 
 , 5 
 10 
 15 
 20 
 
 , 30 
 1 40 
 50 
 
 58 
 66 
 71 
 
 74 
 78 
 
 82 
 86 
 
 
 
 42 
 34 
 29 
 26 
 22 
 18 
 14 
 
 
 
 74 
 76 
 
 78 
 82 
 85 
 88 
 
 
 26 
 24 
 22 ' 
 18 
 15 
 12 
 
 
 78 
 80 
 84 
 87 
 90 
 
 22 
 20 
 16 
 13 
 iO 
 

 CYLINDER CONDENSATION. 
 
 967 
 
 Theoretical Compared with Actual Water-consumption, Single- 
 cylinder Automatic Cut-off Engines. (From the catalogue of the 
 Buckeye Engine Co.) The following table has been prepared on the 
 basis of the pressures that result in practice with a constant boiler-pressure 
 of 80 Ibs. and different points of cut-off, with Buckeye engines and others 
 with similar clearance. Fractions are omitted, except in the percentage 
 column, as the degree of accuracy their use would seem to imply is not 
 attained or aimed at. 
 
 Cut-off 
 
 Mean 
 Effective 
 
 Total 
 Terminal 
 
 Indicated 
 Rate, Ibs. 
 
 Assumed. 
 
 Product 
 
 Part of 
 
 
 
 
 
 of Cols. 
 
 Stroke. 
 
 Jr ressure. 
 Ibs. per 
 sq. in. 
 
 Ibs. per 
 sq. in. 
 
 I.H.P. per 
 hour. 
 
 Act'lRate. 
 
 % Loss. 
 
 1 and 6. 
 
 0.10 
 
 18 
 
 11 
 
 20 
 
 32 
 
 58 
 
 5.8 
 
 0.15 
 
 27 
 
 15 
 
 19 
 
 27 
 
 41 
 
 6.15 
 
 0.20 
 
 35 
 
 20 
 
 19 
 
 25 
 
 31.5 
 
 6.3 
 
 0.25 
 
 42 
 
 25 
 
 20 
 
 25 
 
 25 
 
 6.25 
 
 0.30 
 
 48 
 
 30 
 
 20 
 
 24 
 
 21.8 
 
 6.54 
 
 0.35 
 
 53 
 
 35 
 
 21 
 
 25 
 
 19 
 
 6.65 
 
 0.40 
 
 57 
 
 38 
 
 22 
 
 26 
 
 16.7 
 
 6.68 
 
 0.45 
 
 61 
 
 43 
 
 23 
 
 27 
 
 15 
 
 6.75 
 
 0.50 
 
 64 
 
 48 
 
 24 
 
 27 
 
 13.6 
 
 6.8 
 
 It will be seen that while the best indicated economy is when the cut-off 
 Is about at 0.15 or 0.20 of the stroke, giving about 30 Ibs. M.E.P., and a 
 terminal 3 or 4 Ibs. above atmosphere, when we come to add the per- 
 centages due to a constant amount of. unindicated loss, as per sixth 
 column, the most economical point of cut-off is found to be about 0.30 of 
 the stroke, giving 48 Ibs. M.E.P. and 30 Ibs. terminal pressure. This 
 showing agrees substantially with modern experience under automatic 
 cut-off regulation. 
 
 The last column shows that the actual amount of cylinder condensation 
 is nearly a constant quantity, increasing only from 5.8% of the cylinder 
 volume at 0.10 cut-off to 6.8% at 0.50 cut-off. 
 
 Experiments on Cylinder-condensation. Experiments by Major 
 Thos. English (Eng'g, Oct. 7, 1887, p. 386) with an engine 10 X 14 in., 
 jacketed in the sides but not on the ends, indicate that the net initial 
 condensation (or excess of condensation over re-evaporation) by the 
 clearance surface varies directly as the initial density of the steam, and 
 inversely as the square root of the number of revolutions per unit of time. 
 The mean results gave for the net initial condensation by clearance-space 
 per sq. ft. of surface at one rev. per second 6.06 thermal units in the engine 
 when run non-condensing and 5.75 units when condensing. 
 
 G. R. Bodmer (Eng'g, March 4, 1892, p. 299) says: Within the ordinary 
 limits of expansion desirable in one cylinder the expansion ratio has 
 practically no influence on the amount of condensation per stroke, which 
 for simple engines can be expressed by the following formula for the 
 weight of water condensed [per minute, probably; the original does not 
 
 state]: W = CJ T ~ . where T denotes the mean admission temper- 
 
 L $N* 
 
 ature, t the mean exhaust temperature, S clearance-surface (square feet)t 
 N the number of revolutions per second, L latent heat of steam at the 
 mean admission temperature, and C a constant for any given type of 
 engine. 
 
 Mr. Bodmer found from experimental data that for high-pressure non- 
 jacketed engines C = about 0.11, for condensing non-jacketed engines 
 0.085 to 0.11, for condensing jacketed engines 0.085 to 0.053. The 
 figures for jacketed engines apply to those jacketed in the. usual way, 
 and not at the ends. 
 
 C varies for different engines of the same class, but is practically con- 
 stant for any given engine. For simple high-pressure non-jacketed 
 engines it was found to range from 0.1 to 0.112. 
 
 Applying Mr, Bodmer's formula to the case of a Corliss non-jacketed 
 
968 
 
 THE STEAM ENGINE. 
 
 non-condensing engine, 4-ft. stroke, 24 in. diam., 60 revs, per min., initial 
 ressure 90 Ibs. gauge, exhaust pressure 2 Ibs., we have T - t = 112, 
 = 1, L = 880, S = 7 sq. ft.; and, taking C = 0.112 and W= Ibs. 
 water condensed per minute, 
 
 pr 
 
 M 
 
 W = 
 
 0.09 Ib. per 
 
 minute, or 5.4 Ibs. per hour. If the steam used per I.H.P. per hour 
 nS c ? r ,K ing to the dia gm is 20 Ibs., the actual water consumption is 
 25.4 Ibs., corresponding to a cylinder condensation of 27%. 
 
 INDICATOR-DIAGRAM OF A SINGLE-CYLINDER ENGINE. 
 
 Definitions. The Atmospheric Line, AB, is a line drawn by the pencil 
 of the indicator when the connections with the engine are closed and both 
 
 sides of the piston 
 
 -=-K are open to the 
 
 atmosphere. 
 
 The Vacuum Line, 
 OX, is a reference 
 line usually drawn 
 about 14.7 pounds 
 by scale below the 
 atmospheric line. 
 
 The Clearance 
 Line, OF, is a refer- 
 ence line drawn at a 
 distance from the 
 end of the diagram 
 equal to the same 
 per cent of its length 
 as the clearance and 
 B waste room is of the 
 piston-displacement . 
 -X The Line of Boiler- 
 
 pressure, JK, is 
 
 tic. 162. drawn parallel to the 
 
 atmospheric line, and at a distance from it by scale equal to the boiler- 
 pressure shown by the gauge. 
 
 The Admission Line, CD, shows the rise of pressure due to the admission 
 of steam to the cylinder by opening the steam-valve. 
 
 The Steam Line, DE, is drawn when the steam-valve is open and steam 
 is being admitted to the cylinder. 
 
 The Point of Cut-off, E, is the point where the admission of steam is 
 stopped by the closing of the valve. It is often difficult. to determine 
 the exact point at which the cut-off takes place. It is usually located 
 where the outline of the diagram changes its curvature from convex to 
 concave. 
 
 The Expansion Curve, EF, shows the fall in pressure as the steam in the 
 cylinder expands doing work. 
 
 The Point of Release, F, shows when the exhaust-valve opens. 
 The Exhaust Line, FG, represents the change in pressure that takes 
 place when the exhaust-valve opens. 
 
 The Back-pressure Line, GH, shows the pressure against which the 
 piston acts during its return stroke. 
 
 The Point of Exhaust Closure, H, is the point where the exhaust-valve 
 closes. It cannot be located definitely, as the change in pressure is at first 
 due to the gradual closing of the valve. 
 
 The Compression Curve, HC, shows the rise in pressure due to the com- 
 pression of the steam remaining in the cylinder after the exhaust-valve 
 has closed. 
 
 The Mean Height of the Diagram equals its area divided by its length. 
 The Mean Effective Pressure is the mean net pressure urging the piston 
 forward = the mean height X the scale of the indicator-spring. 
 
 To find the Mean Effective Pressure from the Diagram. Divide the 
 length, LB, into a number, say 10, equal parts, setting off half a part at 
 L, half a part at B, and nine other parts between; erect ordinates perpen- 
 dicular to the atmospheric line at the points of division of LB, cutting 
 the diagram; add together the lengths of these ordinates intercepted 
 
INDlCAtOK-DIAGUAMS. 
 
 969 
 
 between the upper and lower lines of the diagram and divide by their 
 number. This gives the mean height, which multiplied by the scale of 
 the indicator-spring gives the M.E.P. Or find the area by a planimeter, 
 or other means (see Mensuration, p. 56), and divide by the length LB 
 to obtain the mean height. 
 
 The Initial Pressure is the pressure acting on the piston at the beginning 
 of the stroke. 
 
 The Terminal Pressure is the pressure above the line of perfect vacuum 
 that would exist at the end of the stroke if the steam had not been released 
 earlier. It is found by continuing the expansion-curve to the end of the 
 diagram. 
 
 A single indicator card shows the pressure exerted by the steam at 
 each instant on one side of the piston; a card taken simultaneously from 
 the opposite end of the engine shows the pressure exerted on the other 
 nrte. By superposing these cards the pressure or tension on the piston 
 
 I may be determined. The pressure or pull on the crank pin at any 
 
 itant is the pressure or tension in the rod modified by the angle of the 
 
 innecting rod and by the effect of the inertia of the reciprocating parts. 
 
 Dr discussion of this subject see Klein's "High-speed Steam Engine," 
 
 so papers by S. A. Moss, Trans. A. S. M. E., 1904, and by F. W. Holl- 
 
 ann, in Power,- April 6, 1909. 
 
 Errors of Indicators. The most common error is that of the spring, 
 which may vary from its normal rating; the error may be determined by 
 oper testing apparatus and allowed for. But after making this correc- 
 
 >n, even with the best work, the results are liable to variable errors 
 
 lich may amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., 
 
 310; Denton, Trans. A. S. M. E., xi, 329; David Smith, U. S. N., Proc. 
 *'g Congress, 1893, Marine Division. 
 
 . ther errors of indicator diagrams are those due to inaccuracy of the 
 straight-line motion of the indicator, to the incorrect design or position 
 of the "rig" or reducing motion, to long pipes between the indicator and 
 the engine, to throttling of these pipes, to friction or lost motion in the 
 indicator mechanism, and to drum-motion distortion. For discussion of 
 the last named see Power, April, 1909. For methods of testing indicators, 
 see paper by D. S. Jacobus, Trans. A. S. M. E., 1898. 
 
 Indicator "Rigs," or Reducing-motions; Interpretation of Diagrams 
 for Errors of Steam-distribution, etc. For these see circulars of manu- 
 facturers of Indicators; also works on the Indicator. 
 
 Pendulum Indicator Rig. Power (Feb., 1893) gives a graphical 
 representation of the errors in indicator-diagrams, caused by the use of 
 incorrect forms of the pendulum rigging. It 
 is shown that the "brumbo" pulley on the 
 pendulum, to which the cord is attached, 
 does not generally give as good a reduction 
 as a simple pin attachment. When the end 
 of the pendulum is slotted, working in a pin 
 on the crosshead, the error is apt to be con- 
 siderable at both ends of the card. With a 
 vertical slot in a plate fixed to the cross- 
 head, and a pin on the pendulum working in 
 this slot, the reduction is perfect, when the 
 cord is attached to a pin on the pendulum, 
 a slight error being introduced if the brumbo 
 pulley is used. With the connection be- 
 tween the pendulum and the crosshead made 
 by means of a horizontal link, the reduction 
 
 whk 
 
 1 
 
 strai 
 
 FIG. 163. 
 
 is nearly perfect, if the construction is such that the connecting link 
 vibrates equally above and below the horizontal, and the cord is attached 
 by a pin. If the link is horizontal at mid-stroke a serious error is intro- 
 duced, which is magnified if a brumbo pulley also is used. The adjoin- 
 ing figures show the two forms recommended. 
 
 The Manograph, for indicating engines of very high speed, invented 
 by Prof. Hospitalier, is described by Howard Greene in Power, June, 1907. 
 It is made by Carpentier, of Paris. A small mirror is tilted upward and 
 downward by a diaphragm which responds to the pressure variations in 
 the cylinder, and the same mirror is rocked from side to side by a reducing 
 mechanism which is geared to the engine and reproduces the reciprocations 
 
D70 fHE STEAM-ENGINE. 
 
 of the engine piston on a smaller scale. A beam of light is reflected by 
 the mirror to the ground-glass screen, and this beam, by the oscillations 
 of the mirror, is made to traverse a path corresponding to that of the 
 pencil point of an ordinary indicator. The diagram, therefore, is made 
 continuously but varies with varying conditions in the cylinder. 
 
 A plate-holder carrying a photographic dry plate can be substituted for 
 the ground -glass screen, and the diagram photographed, the exposure 
 required varying from half a second to three seconds. By the use of 
 special diaphragms and springs the effects of low pressures and vacuums 
 can be magnified, and thus the instrument can be made to show with 
 remarkable clearness the action of the valves of a gas engine on the suction 
 and exhaust strokes. 
 
 The Lea Continuous Recorder, for recording the steam consumption 
 of an engine, is described by W. H. Booth in Power, Aug. 31, 1909. It 
 comprises a tank into which flows the condensed steam from a condenser, 
 a triangular notch through which the water flows from the tank, and a 
 mechanical device through which the variations in the level of the water 
 In the tank are translated into the motion of a pencil, which motion is 
 made proportionate to the quantity flowing, and is recorded on paper 
 moved by clockwork. 
 
 INDICATED HORSE-POWER OF ENGINES, SINGLE-CYLINDER. 
 
 Indicated Horse-power, I.H.P. = , 
 
 oo,000 
 
 in which P = mean effective pressure in Ibs. per sq. in.; L = length of 
 stroke in feet; a = area of piston in square inches. For accuracy, one 
 half of the sectional area of the piston-rod must be subtracted from the 
 area of the piston if the rod passes through one head, or the whole area of 
 the rod if it passes through both heads; n = No. of single strokes per min. 
 2 X No. of revolutions of a double-acting engine. 
 
 n~ r> 
 
 I.H.P. =^-7:7^ in which *S = piston speed in feet per minute. 
 00,000 
 
 I.H.P. = = = - 0000238 PLd*n = 0.0000238 P&S, 
 
 In which d = diam. of cyl. in inches. (The figures 238 are exact, since 
 7854 * 33 = 23.8 exactly.) If product of piston-speed X mean effec- 
 tive pressure = 42,017, then the horse-power would equal the square of 
 the diameter in inches. 
 
 Handy Rule for Estimating the Horse-power of a Single-cylinder 
 Engine. Square the diameter and divide by 2. This is correct whenever 
 the product of the mean effective pressure and the piston-speed = 1/2 
 of 42,017, or, say, 21,000, viz., when M.E.P. = 30 and S = 700; when 
 M.E.P. = 35 and S = 600; when M.E.P. = 38.2 and S = 550; and when 
 M.E.P. = 42 and S = 500. These conditions correspond to those of 
 ordinary practice with both Corliss engines and shaft-governor high-speed 
 engines. 
 
 Given Horse-power, Mean Effective Pressure, and Piston-speed, 
 to find Size of Cylinder. 
 
 , .. ^. , ./I.H. 
 
 Area = -- - - Diameter = 205 y ps 
 
 33,000 X I.H.P ^. , ./I.H.P. 
 
 -- - - = 
 
 Brake Horse-power is the actual horse-power of the engine as measured 
 at the fly-wheel by a friction-brake or dynamometer. It is the indicated 
 horse-power minus the friction of the engine. 
 
 Electrical Horse-power is the power in an electric current, usually 
 measured in kilowatts, translated into horse-power. 1 H.P. = 33,000 
 ft. Ibs. per min.; 1 K.W.= 1.3405 H.P.; 1 H.P. = 0.746 kilowatts, or 
 746 watts. 
 
 EXAMPLE. A 100-H.P. engine, with a friction loss of 10% at rated 
 load, drives a generator whose efficiency is 90%, furnishing current to a 
 motor of 90% effy., through a line whose loss is 5%. I.H.P. = 
 B.H.P. = 90; E.H.P. at generator 81, at end of line 76.95. H.P, delivered 
 by motor 69.26. 
 
INDICATED HORSE-POWER OP ENGINES. 
 
 971 
 
 Table for Roughly Approximating the Horse-power of a Com- 
 pound Engine from the Diameter of its Low-pressure Cylinder. 
 
 The indicated horse-power of an engine being 42 017' in which P=* 
 
 mean effective pressure per sq. in., s = piston-speed 'in ft. per min., and 
 d = diam. of cylinder in inches; if s = 600 ft. per min., which is approxi- 
 mately the speed of modern stationary engines, and P = 35 Ibs., which is 
 an approximately average figure, for the M.E.P. of single-cylinder engines, 
 and of compound engines referred to the low-pressure cylinder, then 
 I.H.P. = i/2^ 2 ; hence the rough-and-ready rule for horse-power given 
 above: Square the diameter in inches and divide by 2. This applies to 
 triple and quadruple expansion engines as well as to single cylinder and 
 compound. For most economical loading, the M.E.P. referred to the 
 low-pressure cylinder of compound engines is usually not greater than 
 that of simple engines; for the greater economy is obtained by a greater 
 number of expansions of steam of higher pressures, and the greater the 
 number of expansions for a given initial pressure the lower the mean 
 effective pressure. The following table gives approximately the figures 
 of mean total and effective pressures for the different types of engines, 
 together with the factor by which the square of the diameter is to be 
 multiplied to obtain the horse-power at most economical loading, for a 
 piston-speed of 600 ft. per minute. 
 
 
 Type of Engine. 
 
 - 
 
 d H o 
 
 SB'S 
 
 Ill 
 
 mi 
 
 53 O> 
 
 US 
 
 o> X 
 
 Non-condensing. 
 
 Single Cylinder . . 
 Compound 
 
 100 
 120 
 
 5. 
 7 5 
 
 20 
 16 
 
 0.522 
 402 
 
 52.2 
 48 2 
 
 15.5 
 15.5 
 
 36.7 
 32.7 
 
 600 
 
 0.524 
 467 
 
 Triple 
 
 160 
 
 10. 
 
 16 
 
 .330 
 
 52.8 
 
 15.5 
 
 37.3 
 
 n 
 
 .533 
 
 Quadruple 
 
 200 
 
 12.5 
 
 16 
 
 .282 
 
 56.4 
 
 15.5 
 
 40.9 
 
 " 
 
 .584 
 
 Condensing Engines. 
 
 Single Cylinder.. 
 Compound 
 
 100 
 120 
 
 10. 
 15 
 
 10 
 
 8 
 
 0.330 
 
 247 
 
 33.0 
 29 6 
 
 2 
 
 2 
 
 31.0 
 27 6 
 
 600 
 
 0.443 
 390 
 
 Triple 
 
 160 
 
 20. 
 
 8 
 
 .200 
 
 32.0 
 
 2 
 
 30 
 
 M 
 
 .429 
 
 Quadruple 
 
 200 
 
 25. 
 
 8 
 
 .169 
 
 33.8 
 
 2 
 
 31.8 
 
 " 
 
 .454 
 
 For any other piston-speed than 600 ft. per min., multiply the figurei 
 in the last column by the ratio of the piston-speed to 600 ft. 
 
 Horse-power Constant of a given Engine for a Fixed Speed 
 product of its area of piston in square inches, length of stroke in feet 
 
 and number of single strokes per minute divided by 33,000, or ' 
 
 oo.UUU 
 
 C. The product of the mean effective pressure as found by the dia- 
 gram and this constant is the indicated horse-power. 
 
 Horse-power Constant of any Engine of a given Diameter of 
 Cylinder, whatever the length of stroke, = area of piston -H 33,000 = square 
 of the diameter of piston in inches X 0.0000238. A table of constants 
 derived from this formula is given on page 973. 
 
 The constant multiplied by the piston-speed in feet per minute and 
 by the M.E.P. gives the I.H.P. 
 
 Table of Engine Constants for Use in Figuring Horse-power. 
 "Horse-power constant" for cylinders from 1 inch to 60 inches in diam- 
 eter, advancing by 8ths. for one foot of piston-speed per minute and one 
 pound of M.E.P. Find the diameter of the cylinder in the column -at the 
 side. If the diameter contains no fraction the constant will be found in 
 the column headed Even Inches. If the diameter is not in even inches, 
 follow the line horizontally to the column corresponding to the required 
 fraction. The constants multiplied by the piston-speed and by the 
 M.E.P. give the horse-power. 
 
"972 
 
 THE STEAM-ENGINE. 
 
 Engine Constants, Constant X Piston Speed X M.E.P. *=H.P. 
 
 Diam.o 
 Cylin- 
 der. 
 
 Even 
 Inches. 
 
 + 1/8 
 
 + 1/4 
 
 + 3/8 
 
 + 1/2 
 
 + 5/8 
 
 + 3/4 
 
 + 7/8 
 
 1 
 
 .0000238 
 
 .0000301 
 
 .0000372 
 
 .0000450 
 
 .0000535 
 
 .0000628 
 
 .0000729 
 
 .0000837 
 
 2 
 
 .0000952 
 
 .0001074 
 
 .0001205 
 
 .0001342 
 
 .0001487 
 
 .0001640 
 
 .0001800 
 
 .0001967 
 
 3 
 
 .0002142 
 
 .0002324 
 
 .0002514 
 
 .0002711 
 
 .0002915 
 
 .0003127 
 
 .0003347 
 
 .0003574 
 
 4 
 
 .0003808 
 
 .0004050 
 
 .0004299 
 
 .0004554 
 
 .0004819 
 
 .0005091 
 
 .0005370 
 
 .0005656 
 
 5 
 
 .0005950 
 
 .0006251 
 
 .0006560 
 
 .0006876 
 
 .0007199 
 
 .0007530 
 
 .0007869 
 
 .0008215 
 
 6 
 
 .0008568 
 
 .0008929 
 
 .0009297 
 
 .0009672 
 
 .0010055 
 
 .0010445 
 
 .0010844 
 
 .0011249 
 
 7 
 
 .0011662 
 
 .0012082 
 
 .0012510 
 
 .0012944 
 
 .0013387 
 
 .0013837 
 
 .0014295 
 
 .0014759 
 
 8 
 
 .0015232 
 
 .0015711 
 
 .0016198 
 
 .0016693 
 
 .0017195 
 
 .0017705 
 
 .0018222 
 
 .0018746 
 
 9 
 
 .0019278 
 
 .0019817 
 
 .0020363 
 
 .0020916 
 
 .0021479 
 
 .0022048 
 
 .0022625 
 
 .0023209 
 
 10 
 
 .0023800 
 
 .0024398 
 
 .0025004 
 
 .0025618 
 
 .0026239 
 
 .0026867 
 
 .0027502 
 
 .0028147 
 
 11 
 
 .0028798 
 
 .0029456 
 
 .0030121 
 
 .0030794 
 
 .0031475 
 
 .0032163 
 
 .0032859 
 
 .0033561 
 
 12 
 
 .0034272 
 
 .0034990 
 
 .0035714 
 
 .0036447 
 
 .0037187 
 
 .0037934 
 
 .0038690 
 
 .0039452 
 
 13 
 
 .0040222 
 
 .0040999 
 
 .0041783 
 
 .0042576 
 
 .0043375 
 
 .0044182 
 
 .0044997 
 
 .0045819 
 
 14 
 
 .0046648 
 
 0047484 
 
 .0048328 
 
 .0049181 
 
 .0050039 
 
 .0050906 
 
 .0051780 
 
 .0052661 
 
 15 
 
 .0053550 
 
 0054446 
 
 .0055349 
 
 .0056261 
 
 .0057179 
 
 .0058105 
 
 .0059039 
 
 .0059979 
 
 16 
 
 .0060928 
 
 0061884 
 
 .0062847 
 
 .0063817 
 
 .0064795 
 
 .0065780 
 
 .0066774 
 
 .0067774 
 
 17 
 
 0068782 
 
 0069797 
 
 .0070819 
 
 .0071850 
 
 .0072887 
 
 .0073932 
 
 .0074985 
 
 .0076044 
 
 18 
 
 0077112 
 
 0078187 
 
 .0079268 
 
 .0080360 
 
 .0081452 
 
 .0082560 
 
 .0083672 
 
 .0084791 
 
 19 
 
 0085918 
 
 0087052 
 
 0088193 
 
 0089343 
 
 .0090499 
 
 .0091663 
 
 .0092835 
 
 .0094013 
 
 20 
 
 0095200 
 
 0096393 
 
 0097594 
 
 0098803 
 
 .0100019 
 
 .0101243 
 
 .0102474 
 
 .0103712 
 
 21 
 
 0104958 
 
 0106211 
 
 0107472 
 
 0108739 
 
 .0110015 
 
 .0111299 
 
 .0112589 
 
 .0113886 
 
 22 
 
 0115192 
 
 0116505 
 
 0117825 
 
 0119152 
 
 .0120487 
 
 .0121830 
 
 .0123179 
 
 .0124537 
 
 23 
 
 0125902 
 
 0127274 
 
 0128654 
 
 0130040 
 
 .0131435 
 
 .0132837 
 
 .0134247 
 
 .0135664 
 
 24 
 
 0137088 
 
 0138519 
 
 0139959 
 
 0141405 
 
 .0142859 
 
 .0144321 
 
 .0145789 
 
 .0147266 
 
 25 
 
 0148750 
 
 0150241 
 
 0151739 
 
 0153246 
 
 .0154759 
 
 .0156280 
 
 .0157809 
 
 .0159345 
 
 26 
 
 0160888 
 
 0162439 
 
 0163997 
 
 0165563 
 
 0167135 
 
 .0168716 
 
 .0170304 
 
 .0171899 
 
 27 
 
 0173502 
 
 0175112 
 
 0176729 
 
 0178355 
 
 .0179988 
 
 .0181627 
 
 .0183275 
 
 .0184929 
 
 28 
 
 0186592 
 
 0188262 
 
 0189939 
 
 0191624 
 
 0193316 
 
 .0195015 
 
 .0196722 
 
 0198436 
 
 29 
 
 0200158 
 
 0201887 
 
 0203634 
 
 0205368 
 
 0207119 
 
 .0208879 
 
 .0210645 
 
 0212418 
 
 30 
 
 0214200 
 
 0215988 
 
 0217785 
 
 0219588 
 
 0221399 
 
 .0223218 
 
 .0225044 
 
 0226877 
 
 31 
 
 0228718 
 
 0230566 
 
 0232422 
 
 0234285 
 
 0236155 
 
 .0238033 
 
 .0239919 
 
 0241812 
 
 32 
 
 0243712 
 
 0245619 
 
 0247535 
 
 0249457 
 
 0251387 
 
 .0253325 
 
 .0255269 
 
 0257222 
 
 33 
 
 0259182 
 
 0261149 
 
 0263124 
 
 0265106 
 
 0267095 
 
 .0269092 
 
 .0271097 
 
 0273109 
 
 34 
 
 0275128 
 
 0277155 
 
 0279189 
 
 0281231 
 
 0283279 
 
 .0285336 
 
 .0287399 
 
 0289471 
 
 35 
 
 0291550 
 
 0293636 
 
 0295729 
 
 0297831 
 
 0299939 
 
 .0302056 
 
 .0304179 
 
 0306309 
 
 36 
 
 0308448 
 
 0310594 
 
 0312747 
 
 0314908 
 
 0317075 
 
 .0319251 
 
 .0321434 
 
 0323624 
 
 37 
 
 0325822 
 
 0328027 
 
 0330239 
 
 0332460 
 
 0334687 
 
 .0336922 
 
 .0339165 
 
 0341415 
 
 38 
 
 0343672 
 
 0345937 
 
 0348209 
 
 0350489 
 
 0352775 
 
 .0355070 
 
 0357372 
 
 .0359681 
 
 39 
 
 0361998 
 
 0364322 
 
 0366654 
 
 0368993 
 
 8371339 
 
 .0373694 
 
 0376055 
 
 .0378424 
 
 40 
 
 0380800 
 
 0383184 
 
 0385575 
 
 0387973 
 
 0390379 
 
 .0392793 
 
 0395214 
 
 .0397642 
 
 41 
 
 0400078 
 
 0402521 
 
 0404972 
 
 0407430 
 
 0409895 
 
 .0412368 
 
 0414849 
 
 .0417337 
 
 42 
 
 0419832 
 
 0422335 
 
 0424845 
 
 0427362 
 
 0429887 
 
 0432420 
 
 0434959 
 
 .0437507 
 
 43 
 
 0440062 
 
 0442624 
 
 0445194 
 
 0447771 
 
 0450355 
 
 0452947 
 
 0455547 
 
 .0458154 
 
 44 
 
 0460768 
 
 0463389 
 
 0466019 
 
 0468655 
 
 0471299 
 
 0473951 
 
 0476609 
 
 .0479276 
 
 45 
 
 0481950 
 
 0484631 
 
 0487320 
 
 0490016 
 
 0492719 
 
 0495430 
 
 0498149 
 
 .0500875 
 
 46 
 
 0503608 
 
 0506349 
 
 0509097 
 
 0511853 
 
 0514615 
 
 0517386 
 
 0520164 
 
 .0522949 
 
 47 
 
 0525742 
 
 0528542 
 
 0531349 
 
 0534165 
 
 0536988 
 
 0539818 
 
 0542655 
 
 .0545499 
 
 48 
 
 0548352 
 
 0551212 
 
 0554079 
 
 0556953 
 
 0559835 
 
 0562725 
 
 0565622 
 
 .0568526 
 
 49 
 
 0571438 
 
 0574357 
 
 0577284 
 
 0580218 
 
 0583159 
 
 0586109 
 
 0589065 
 
 .0592029 
 
 50 
 
 0595000 
 
 0597979 
 
 0600965 
 
 0603959 
 
 0606959 
 
 0609969 
 
 0612984 
 
 .0616007 
 
 51 
 
 0619038 
 
 0622076 
 
 0625122 
 
 0628175 
 
 0632235 
 
 0634304 
 
 0637379 
 
 .0640462 
 
 52 
 
 0643552 
 
 0646649 
 
 0649753 
 
 0652867 
 
 0655987 
 
 0659115 
 
 0662250 
 
 .0665392 
 
 53 
 
 0668542 
 
 0671699 
 
 0674864 
 
 0678036 
 
 0681215 
 
 0684402 
 
 0687597 
 
 .0690799 
 
 54 
 
 0694008 
 
 0697225 
 
 0700449 
 
 0703681 
 
 0705293 
 
 0710166 
 
 0713419 
 
 .0716681 
 
 55 , 
 
 0719950 
 
 0724226 
 
 0726510 
 
 0729801 
 
 0733099 
 
 0736406 
 
 0739719 
 
 .0743039 
 
 56 
 
 0746368 
 
 0749704 
 
 0753047 
 
 0756398 
 
 0759755 
 
 0763120 
 
 0766494 
 
 .0769874 
 
 57 
 
 0773262 
 
 0776657 
 
 0780060 
 
 0783476 
 
 0786887 
 
 0790312 
 
 0793745 
 
 .0797185 
 
 58 
 
 0800632 
 
 0804087 
 
 0807549 
 
 0811019 
 
 0814495 
 
 0817980 
 
 0821472 
 
 .0824971 
 
 59 
 
 0828478 
 
 0831992 
 
 0835514 
 
 0839043 
 
 0842579 
 
 0846123 
 
 .0849675 
 
 .0853234 
 
 60 
 
 0856800 
 
 0860374 
 
 0863955 
 
 0867543 
 
 0871139 
 
 0874743 
 
 .0878354 
 
 .0881973 
 
INDICATED HORSE-POWER OF ENGINES. 
 
 973 
 
 Horse-power per Pound Mean Effective Pressure. 
 
 Formula, Area in sq. in. X piston-speed -5- 33,000. 
 
 Diam of 
 Cylinder, 
 inches. 
 
 Speed of Piston in feet per minute. 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 900 
 
 4 
 
 .0381 
 
 .0762 
 
 .1142 
 
 .1523 
 
 .1904 
 
 .2285 
 
 .2666 
 
 .3046 
 
 .3427 
 
 41/2 
 
 .0482 
 
 .0964 
 
 .1446 
 
 .1928 
 
 .2410 
 
 .2892 
 
 .3374 
 
 .3856 
 
 .4338 
 
 5 
 
 .0595 
 
 .1190 
 
 .1785 
 
 .2380 
 
 .2975 
 
 .3570 
 
 .4165 
 
 .4760 
 
 .5355 
 
 31/2 
 
 .0720 
 
 .1440 
 
 .2160 
 
 .2880 
 
 .3600 
 
 .4320 
 
 .5040 
 
 .5760 
 
 .6480 
 
 6 
 
 .0857 
 
 .1714 
 
 .2570 
 
 .3427 
 
 .4284 
 
 .5141 
 
 .5998 
 
 .6854 
 
 .7711 
 
 61/2 
 
 .1006 
 
 .2011 
 
 .3017 
 
 .4022 
 
 .5028 
 
 .6033 
 
 .7039 
 
 .8044 
 
 .9050 
 
 7 
 
 .1166 
 
 .2332 
 
 .3499 
 
 .4665 
 
 .5831 
 
 .6997 
 
 .8163 
 
 .9330 
 
 .0496 
 
 71/2 
 
 .1339 
 
 .2678 
 
 .4016 
 
 .5355 
 
 .6694 
 
 .8033 
 
 .9371 
 
 .0710 
 
 .2049 
 
 8 
 
 .1523 
 
 .3046 
 
 .4570 
 
 .6093 
 
 .7616 
 
 .9139 
 
 .0662 
 
 .2186 
 
 .3709 
 
 81/2 
 
 .1720 
 
 .3439 
 
 .5159 
 
 .6878 
 
 .8598 
 
 .0317 
 
 .2037 
 
 .3756 
 
 .5476 
 
 9 
 
 .1928 
 
 .3856 
 
 .5783 
 
 .7711 
 
 .9639 
 
 .1567 
 
 .3495 
 
 .5422 
 
 .7350 
 
 91/2 
 
 .2148 
 
 .4296 
 
 .6444 
 
 .8592 
 
 1.0740 
 
 .2888 
 
 .5036 
 
 .7184 
 
 .9532 
 
 10 
 
 .2380 
 
 .4760 
 
 .7140 
 
 .9520 
 
 1.1900 
 
 .4280 
 
 .6660 
 
 .9040 
 
 2.1420 
 
 11 
 
 .2880 
 
 . .5760 
 
 .8639 
 
 1.1519 
 
 1.4399 
 
 .7279 
 
 2.0159 
 
 2.3038 
 
 2.5818 
 
 12 
 
 .3427 
 
 .6854 
 
 .0282 
 
 1.3709 
 
 1.7136 
 
 2.0563 
 
 2.3990 
 
 2.7418 
 
 3.0845 
 
 13 
 
 .4022 
 
 .8044 
 
 .2067 
 
 1 .6089 
 
 2.0111 
 
 2.4133 
 
 2.8155 
 
 3.2178 
 
 3.6200 
 
 14 
 
 .4665 
 
 .9330 
 
 .3994 
 
 1.8659 
 
 2.3324 
 
 2.7989 
 
 3.2654 
 
 3.7318 
 
 4.1983 
 
 15 
 
 .5355 
 
 .0710 
 
 .6065 
 
 2.1420 
 
 2.6775 
 
 3.2130 
 
 3.7485 
 
 4.2840 
 
 4.8195 
 
 16 
 
 .6093 
 
 .2186 
 
 .8278 
 
 2.4371 
 
 3.0464 
 
 3.6557 
 
 4.2650 
 
 4.8742 
 
 5.4835 
 
 17 
 
 .6878 
 
 .3756 
 
 2.0635 
 
 2.7513 
 
 3.4391 
 
 4.1269 
 
 4.8147 
 
 5.5026 
 
 6.1904 
 
 18. 
 
 .7711 
 
 .5422 
 
 2.3134 
 
 3.0845 
 
 3.8556 
 
 4.6267 
 
 5.3978 
 
 6.1690 
 
 6.9401 
 
 19 
 
 .8592 
 
 .7184 
 
 2.5775 
 
 3.4367 
 
 4.2959 
 
 5.1551 
 
 6.0143 
 
 6.8734 
 
 7.7326 
 
 20 
 
 .9520 
 
 .9040 
 
 2.8560 
 
 3.8080 
 
 4.7600 
 
 5.7120 
 
 6.6640 
 
 7.6160 
 
 8.5680 
 
 21 
 
 .0496 
 
 2.0992 
 
 3.1488 
 
 4.1983 
 
 5'. 2479 
 
 6.2975 
 
 7.3471 
 
 8.3966 
 
 9.4462 
 
 22 
 
 .1519 
 
 2.3038 
 
 3.4558 
 
 4.6077 
 
 5.7596 
 
 6.9115 
 
 8.0634 
 
 9.2154 
 
 10.367 
 
 23 
 
 .2590 
 
 2.5180 
 
 3.7771 
 
 5.0361 
 
 6.2951 
 
 7.5541 
 
 8.8131 
 
 10.072 
 
 11.331 
 
 24 
 
 .3709 
 
 2.7418 
 
 4.1126 
 
 5.4835 
 
 6.8544 
 
 8.2253 
 
 9.5962 
 
 10.967 
 
 12.338 
 
 25 
 
 .4875 
 
 2.9750 
 
 4.4625 
 
 5.9500 
 
 7.4375 
 
 8.9250 
 
 10.413 
 
 11.900 
 
 13.388 
 
 26 
 
 .6089 
 
 3.2178 
 
 4.8266 
 
 6.4355 
 
 8.0444 
 
 9.6534 
 
 11.262 
 
 12.871 
 
 14.480 
 
 27 
 
 .7350 
 
 3.4700 
 
 5.2051 
 
 6.9401 
 
 8.6751 
 
 10.410 
 
 12.145 
 
 13.880 
 
 15.615 
 
 28 
 
 .8659 
 
 3.7318 
 
 5.5978 
 
 7.4637 
 
 9.3296 
 
 1 1 . 196 
 
 13.061 
 
 14.927 
 
 16.793 
 
 29 
 
 2.0016 
 
 4.0032 
 
 6.0047 
 
 8.0063 
 
 10.008 
 
 12.009 
 
 14.011 
 
 16.013 
 
 18.014 
 
 30 
 
 2.1420 
 
 4.2840 
 
 6.4260 
 
 8.5680 
 
 10.710 
 
 12.852 
 
 14.994 
 
 17.136 
 
 19.278 
 
 31 
 
 2.2872 
 
 4.5744 
 
 6.8615 
 
 9.1487 
 
 11.436 
 
 13.723 
 
 16.010 
 
 18.297 
 
 20.585 
 
 32 
 
 2.4371 
 
 4.8742 
 
 7.3114 
 
 9.7485 
 
 12.186 
 
 14.623 
 
 17.060 
 
 14.497 
 
 21.934 
 
 33 
 
 2.5918 
 
 5.1836 
 
 7.7755 
 
 10.367 
 
 12.959 
 
 15.551 
 
 18.143 
 
 20.735 
 
 23.326 
 
 34 
 
 2.7513 
 
 5.5026 
 
 8.2538 
 
 11.005 
 
 13.756 
 
 16.508 
 
 19.259 
 
 22.010 
 
 24.762 
 
 35 
 
 2.9155 
 
 5.8310 
 
 8.7465 
 
 11.662 
 
 14.578 
 
 17.493 
 
 20.409 
 
 23.324 
 
 26.240 
 
 36 
 
 3.0845 
 
 6.1690 
 
 9.2534 
 
 12.338 
 
 15.422 
 
 18.507 
 
 21.591 
 
 24.676 
 
 27.760 
 
 37 
 
 3.2582 
 
 6.5164 
 
 9.7747 
 
 13.033 
 
 16.291 
 
 19.549 
 
 22.808 
 
 26.066 
 
 29.324 
 
 38 
 
 3.4367 
 
 6.8734 
 
 10.310 
 
 13.747 
 
 17.184 
 
 20.620 
 
 24.057 
 
 27.494 
 
 30.930 
 
 39 
 
 3.6200 
 
 7.2400 
 
 10.860 
 
 14.480 
 
 18.100 
 
 2 .720 
 
 25.340 
 
 28.960 
 
 32.580 
 
 40 
 
 3.8080 
 
 7.6160 
 
 11.424 
 
 15.232 
 
 19.040 
 
 22.848 
 
 26.656 
 
 30.464 
 
 34.272 
 
 41 
 
 4.0008 
 
 8.0016 
 
 12.002 
 
 16.003 
 
 20.004 
 
 24.005 
 
 28.005 
 
 32.006 
 
 36.007 
 
 42 
 
 4.1983 
 
 8.3866 
 
 12.585 
 
 16.783 
 
 20.982 
 
 25.180 
 
 29.378 
 
 33.577 
 
 37.775 
 
 43 
 
 4.4006 
 
 8.8012 
 
 13.202 
 
 17.602 
 
 22.003 
 
 26.404 
 
 30.804 
 
 35.205 
 
 39.606 
 
 44 
 
 4.6077 
 
 9.2154 
 
 13.823 
 
 18.431 
 
 23.038 
 
 27.646 
 
 32.254 
 
 36.861 
 
 4 .469 
 
 45 
 
 4.8195 
 
 9.6390 
 
 14.459 
 
 19.278 
 
 24.098 
 
 28.917 
 
 33.737 
 
 38.556 
 
 43.376 
 
 46. 
 
 5.0361 
 
 10.072 
 
 15.108 
 
 20.144 
 
 25.180 
 
 30.216 
 
 35.253 
 
 40.289 
 
 45.325 
 
 47 
 
 5.2574 
 
 10.515 
 
 15.772 
 
 21 .030 
 
 26.287 
 
 31.545 
 
 36.802 
 
 42.059 
 
 47.317 
 
 48 
 
 5.4835 
 
 10.967 
 
 16.451 
 
 21.934 
 
 27.418 
 
 32.901 
 
 38.385 
 
 43.868 
 
 49.352 
 
 49 
 
 5.7144 
 
 11.429 
 
 17.143 
 
 22.858 
 
 28.572 
 
 34.286 
 
 40.001 
 
 45.715 
 
 51.429 
 
 50 
 
 .9:00 
 
 11.900 
 
 17.850 
 
 23.800 
 
 29.750 
 
 35.700 
 
 41.650 
 
 47.600 
 
 3.550 
 
 5! 
 
 .1904 
 
 12.381 
 
 18.571 
 
 24.762 
 
 30.952 
 
 37.142 
 
 43.333 
 
 49.523 
 
 5.713 
 
 52 
 
 .4355 
 
 12.871 
 
 19.307 
 
 25.742 
 
 32.178 
 
 38.613 
 
 45.049 
 
 1.484 
 
 7.920 
 
 53 
 
 .6854 
 
 13.371 
 
 20.056 
 
 26.742 
 
 33.427 
 
 40.113 
 
 46.798 
 
 3.483 
 
 60.169 
 
 54 
 
 .9401 
 
 13.880 
 
 20.820 
 
 27.760 
 
 34.700 
 
 41.640 
 
 48.581 
 
 5.521 
 
 2.461 
 
 55 
 
 7.1995 
 
 14.399 
 
 2 .599 
 
 28.798 
 
 35.998 
 
 43.197 
 
 50.397 
 
 7.596 
 
 4.796 
 
 56 
 
 7.4637 
 
 14.927 
 
 22.391 
 
 29.855 
 
 37.318 
 
 44.782 
 
 52.246 
 
 9.709 
 
 7.173 
 
 57 
 
 7.7326 
 
 15.465 
 
 23.198 
 
 30.930 
 
 38.663 
 
 46.396 
 
 54.128 
 
 1.861 
 
 9.597 
 
 58 
 
 8.0063 
 
 16.013 
 
 24.019 
 
 32.025 
 
 40.032 
 
 48.038 
 
 56.044 
 
 4.051 
 
 2.054 
 
 59 
 
 8.2848 
 
 16.570 
 
 24.854 
 
 33.139 
 
 41.424 
 
 49.709 
 
 57.993 
 
 6.278 
 
 4.563 
 
 60 
 
 8.5680 
 
 17.136 
 
 25.704 
 
 34.272 
 
 42.840 
 
 51.408 
 
 59.976 
 
 8.544 
 
 7.112 
 
974 
 
 THE STEAM-ENGINE. 
 
 Nominal Horse-power. The term "nominal horse-power "originated 
 in -the time of Watt, and was used to express approximately the power 
 of an engine as calculated from its diameter, estimating the mean pressure 
 in the cylinder at 7 Ibs. above the atmosphere. It has long been obsolete. 
 
 Horse-power Constant of a given Engine for Varying Speeds = 
 product of its area of piston and length of stroke divided by 33,000. 
 This multiplied by the mean effective pressure and by the number of 
 jingle strokes per minute is the indicated horse-power. 
 
 To draw the Clearance-line on the Indicator-diagram, the ac- 
 
 tual clearance not being known. The clearance-line may be obtained 
 approximately by drawing a straight line, cbad, across the compression 
 
 FIG. 164. 
 
 curve, first having drawn OX parallel to the atmospheric line and 14.7 
 Ibs. below. Measure from a the distance ad, equal to cb, and draw YO 
 perpendicular to OX through d; then will TB divided by AT be the per- 
 centage of clearance. The clearance may also be found from the expan- 
 sion-line by constructing a rectangle efhg, and drawing a diagonal gj 
 to intersect the line XO. This will give the point 0, and by erecting a 
 perpendicular to XO we obtain a clearance-line OY. 
 
 Both these methods for finding the clearance require that the expan- 
 sion and compression curves be hyperbolas. Prof. Carpenter (Power, 
 Sept., 1893) says that with good diagrams the methods are usually very 
 accurate, and give results which check substantially. 
 
 The Buckeye Engine Co., however, says that, as the results obtained are 
 seldom correct, being sometimes too little, but more frequently too much, 
 and as the indications from the two curves seldom agree, the operation 
 has little practical value, though when a clearly defined and apparently 
 undistorted compression curve exists of sufficient extent to admit of the 
 application of the process, it may be relied on to give much more correct 
 results than the expansion curve. 
 
 To draw the Hyperbolic Curve on the Indicator-diagram. Select 
 
 any point / in the actual curve, and 
 from this point draw a line perpen- 
 dicular to the line JB, meeting the 
 latter in the point J. The line JB 
 may be the line of boiler-pressure, 
 but this is not material; it may be 
 drawn at any convenient height near 
 the top of the diagram and parallel 
 to the atmospheric line. From J 
 draw a diagonal to K, the latter 
 point being the intersection of the 
 _ vacuum and clearance lines; from 7 
 FIG. 165. draw IL parallel with the atmos- 
 
 pheric line. From L, the point of 
 Intersection of the diagonal JK and the horizontal line /, draw the verti- 
 
WATER-CONSUMPTION OF ENGINES. 975 
 
 <al line LM. The point M is the theoretical point of cut-off, and LM the 
 cut-off line. Fix upon any number of points 1, 2, 3, etc., on the line JB, 
 and from these points draw diagonals to K. From the intersection of these 
 diagonals with LM draw horizontal lines, and from 1,2, 3, etc., vertical 
 lines. Where these lines meet will be points in the hyperbolic curve. 
 
 Theoretical Water-consumption calculated from the Indicator- 
 card. The following method is given by Prof. Carpenter (Power, 
 Sept., 1893): p mean effective pressure, I = length of stroke in feet, 
 a = area of piston in square inches, a *- 144 = area in square feet, c = 
 percentage of clearance to the stroke, b = percentage of stroke at point 
 where water rate is to be computed, n = number of strokes per minute, 
 60 n = number per hour, w weight of a cubic foot of steam having a 
 pressure as shown by the diagram corresponding to that at the point where 
 water rate is required, w' = that corresponding to pressure at end 01 
 compression. 
 
 Number of cubic feet per stroke =1 (-jr^) TTT' 
 
 ponding weight of steam per stroke in Ibs. = 1 1 10Q C ) rrg w. 
 olume of clearance = 
 
 eight of steam in clearance =- 
 
 
 
 14,4UO 
 
 Total weight of 1 _ 7 /&+ c\ wa _ Icaw' la ,,. , * 
 
 steam per stroke J ~~ 6 V 100 / 144 14,400 ~ 14,400 U "*" ' w ~ cw J' 
 
 Total weight of steam ) 60 nla ... . .. 
 
 from diagram per hour) = 14^00 [(6 + c) w ~ cw] ' 
 
 The indicated horse-power is plan *- 33,000. Hence the steam-con- 
 sumption per hour per indicated horse-power is 
 
 33.000 - 
 
 Changing the formula to a rule, we have: To find the water rate from 
 the indicator diagram at any point in the stroke. 
 
 RULE. To the percentage of the entire stroke which has been com- 
 pleted by the piston at the point under consideration add the percentage 
 of clearance. Multiply this result by the weight of a cubic foot of steam, 
 having a pressure of that at the required point. Subtract from this the 
 product of percentage of clearance multiplied by weight of a cubic foot 
 of steam having a pressure equal to that at the end of the compression. 
 Multiply this result by 137.50 divided by the mean effective pressure.* 
 
 NOTE. This method applies only to points in the expansion curve 
 or between cut-off and release. 
 
 The beneficial effect of compression in reducing the water-consumption 
 of an engine is clearly shown by the formula. If the compression is 
 carried to such a point that it produces a pressure equal to that at the 
 point under consideration, the weight of steam per cubic foot is equal, 
 and w = w'. In this case the effect of clearance entirely disappears, and 
 the formula becomes 137.5 (bw) -f- p. 
 
 In case of no compression, w' becomes zero, and the water-rate = 
 137.5 [(& + c) w] + p. 
 
 Prof. R. C. Carpenter (Sibley Jour, of Eng'g, Dec., 1910) states that 
 tests of engines show that economy is really decreased by high com- 
 pression. Armand Duchesne (Power, Jan. 10, 1911) gives as a reason 
 for this that the steam undergoing compression is superheated and 
 the work of compressing the superheated steam is greater than the work 
 which it gives out later when it is in the condition of saturated steam. 
 
 * For compound or triple-expansion engines read: divided by the 
 equivalent mean effective pressure, on the supposition that all work is 
 done in one cylinder. 
 
976 
 
 THE STEAM ENGINE. 
 
 Prof. Denton (Trans. A. S. M. E., xiv, 1363) gives the following tabl 
 of theoretical water-consumption for a perfect Mariotte expansion with 
 steam at 150 Ibs. above atmosphere, and 2 Ibs. absolute back pressure: 
 
 Ratio of Expansion, r. 
 
 M.E.P., Ibs. per sq. in. 
 
 Lbs. of Water per hour 
 per horse-power, W . 
 
 10 
 
 52.4 
 
 9.68 
 
 15 
 
 38.7 
 
 8.74 
 
 20 
 
 30.9 
 
 8.20 
 
 25 
 
 25.9 
 
 7.84 
 
 30 
 
 22.2 
 
 7.63 
 
 35 
 
 19.5 
 
 7.45 
 
 The difference between the theoretical water-consumption found by the 
 formula and the actual consumption as found by test represents "water 
 not accounted for by the indicator," due to cylinder condensation, leak- 
 age through ports, radiation, etc. 
 
 Leakage of Steam. Leakage of steam, except in rare instances, has 
 so little effect upon the lines of the diagram that it can scarcely be 
 detected. The only satisfactory way to determine the tightness of an 
 engine is to take it when not in motion, apply a full boiler-pressure to 
 the valve, placed in a closed position, and to the piston as well, which 
 is blocked for the purpose at some point away from the end of the stroke, 
 and see by the eye whether leakage occurs. The indicator-cocks provide 
 means for bringing into view steam which leaks through the steam- 
 valves, and in most cases that which leaks by the piston, and an opening 
 
 made in the exhaust-pipe or observations at the atmospheric escape- 
 pipe, are generally sufficie 
 exhaust-valves. 
 
 pipe, are generally sufficient to determine the fact with regard to the 
 
 The steam accounted for by the indicator should be computed for both 
 the cut-off and the release points of the diagram. If the expansion-line 
 departs much from the hyperbolic curve a very different result is shown 
 at one point from that shown at the other. In such cases the extent of 
 the loss occasioned by cylinder condensation and leakage is indicated in a 
 much more truthful manner at the cut-off than at the release. (Tabor 
 Indicator Circular.) 
 
 COMPOUND ENGINES. 
 
 Compound, Triple- and Quadruple-expansion Engines. A com- 
 pound engine is one having two or more cylinders, and in which the steam 
 after doing work in the first or high-pressure cylinder completes its 
 expansion in the other cylinder or cylinders. 
 
 The term "compound" is commonly restricted, however, to engines in 
 which the expansiqn takes place in two stages only high and low 
 pressure, the terms triple-expansion and quadruple-expansion engines 
 being used when the expansion takes place respectively in three and 
 four stages. The number of cylinders may be greater than the number 
 of stages of expansion, for constructive reasons; thus in the compound or 
 two-stage expansion engine the low-pressure stage may be effected in two 
 cylinders so as to obtain the advantages of nearly equal sizes of cylinders 
 and of three cranks at angles of 120. In triple-expansion engines there 
 are frequently two low-pressure cylinders, one of them being placed 
 tandem with the high-pressure, and the other with the intermediate 
 cylinder, as in mill engines with two cranks at 90. In the triple-expan- 
 sion engines of the steamers Camvania and Lucania, with three cranks at 
 120, there were five cylinders, two high, one intermediate, and two low, 
 the high-pressure cylinders being tandem with the low. 
 
 Advantages of Compounding. -The advantages secured by divid- 
 ing the expansion into two or more stages arc twofold: 1. Reduction 
 of wastes of steam by cylinder-condensation, clearance, and leakage; 
 2. Dividing the pressures on the cranks, shafts, etc., in large engines so 
 as to avoirt excessive pressures and consequent friction. The diminished 
 
COMPOUND ENGINES. 
 
 977 
 
 loss by cylinder-condensation is effected by decreasing the range of tem- 
 perature of the metal surfaces of the cylinders, or the difference of tempera- 
 ture of the steam at admission and exhaust. When high-pressure steam 
 is admitted into a single-cylinder engine a large portion is condensed by 
 the comparatively cold metal surfaces; at the end of the stroke and during 
 the exhaust the water is re-evaporated, but the steam so formed escapes 
 into the atmosphere or into the condenser, doing nowork; while if it is 
 taken into a second cylinder, as in a compound engine, it does work. 
 The steam lost in the first cylinder by leakage and clearance also does 
 work in the second cylinder. Also, if there is a second cylinder, the 
 temperature of the steam exhausted from the first cylinder is higher than 
 if there is only one cylinder, and the metal surfaces therefore are not 
 cooled to the same degree. The difference in temperatures and in pres- 
 sures corresponding to the work of steam of 150 Ibs. gauge-pressure ex- 
 panded 20 times, in one, two, and three cylinders, is shown in the 
 following table, by W. H. Weightman, Am. Mack., July 28, 1892: 
 
 
 Single 
 Cyl- 
 inder. 
 
 Compound 
 Cylinders. 
 
 Triple-expansion 
 Cylinders. 
 
 teter of cylinders, in. . 
 Area ratios 
 
 60 
 
 33 
 1 
 
 61 
 3.416 
 
 28 
 1 
 
 46 
 2.70 
 
 61 
 
 4.740 
 
 Expansions . 
 
 20 
 
 5 
 
 4 
 
 2.714 
 
 2.714 
 
 2.714 
 
 Initial steam-pressures 
 absolute pounds 
 Mean pressures, pounds. . . 
 
 165 
 32.96 
 
 165 
 86.11 
 
 33 
 19.68 
 
 165 
 121.44 
 
 60.8 
 44.75 
 
 22.4 
 16.49 
 
 Mean effective pressures, 
 
 
 
 
 
 
 
 pounds . . 
 
 28.96 
 
 53.11 
 
 15.68 
 
 60.64 
 
 22.35 
 
 12.49 
 
 Steam temperatures into 
 
 
 
 
 
 
 
 cylinders 
 
 366 
 
 366 
 
 259.9 
 
 366 
 
 293.5 
 
 234.1 
 
 Steam temperatures out 
 of the cylinders 
 
 184.2 
 
 259.9 
 
 184.2 
 
 293.5 
 
 234.1 
 
 184.2 
 
 Difference in temperatures 
 
 181.8 
 
 106.1 
 
 75.7 
 
 72.5 
 
 59.4 
 
 49.9 
 
 "Woolf " and Receiver Types of Compound Engines. The 
 
 compound steam-engine, consisting of two cylinders, is reducible to two 
 forms, 1, in which the steam from the h.p. cylinder is exhausted direct 
 into the l.p. cylinder, as in the Woolf engine; and 2, in which the steam 
 from the h.p. cylinder is exhausted into an intermediate reservoir, whence 
 the steam is supplied to, and expanded in, the l.p. cylinder, as in the 
 " receiver-engine. " 
 
 If the steam be cut off in the first cylinder before the end of the stroke, 
 the total ratio of expansion is the product of the two ratios of expansion; 
 that is, the product of the ratio of expansion in the first cylinder, into the 
 ratio of the volume of the second to that of the first cylinder. 
 
 Thus, let the areas of the first and second cylinders be as 1 to 31/2, the 
 strokes being equal, and let the steam be cut off in the first at 1/2 stroke; 
 then 
 
 Expansion in the 1st cylinder 1 to 2 
 
 Expansion in the 2d cylinder 1 to 31/2 
 
 Total or combined expansion, the product of the two ratios 1 to 7 
 
 Woolf Engine, without Clearance Ideal Diagrams. The 
 
 diagrams of pressure of an ideal Woolf engine are shown in Fig. 166, as' 
 they would be described by the indicator, according to the arrows. In 
 these diagrams pq is the atmospheric line, mn the vacuum line, cd the 
 admission line, dg the hyperbolic curve of expansion in the first cylinder, 
 and gh the consecutive expansion-line of back pressure for the return- 
 Btroke of the first piston, and of positive pressure for the steam-stroke 
 of the second piston. At the point h, at the end of the stroke of the 
 second piston, the steam is exhausted into the condenser, and the pressure 
 falls to the level of perfect vacuum, mn. 
 
978 
 
 THE STEAM-ENGINE. 
 
 d *_( 
 
 P 
 
 The diagram of the second cylinder, below gh, is characterized by the 
 absence of any specific period of admission; the whole of the steam-line 
 
 gh being expansional, generated by the, 
 expansion of the initial body of steam 
 contained in the first cylinder into Urn 
 seconc i When the return-stroke is 
 completed, the whole of the steam 
 transferred from the first is shut into 
 the second cylinder. The final pres- 
 sure and volume of the steam in the 
 second cylinder are the same as if the 
 whole of the initial steam had been 
 admitted at once into the second cylin- 
 der, and then expanded to the end of 
 the stroke in the manner of a single- 
 cylinder engine. The net work of the 
 steam is also the same, according to 
 both distributions. 
 
 Receiver-engine, without Clear- 
 ance Ideal Diagrams. In the 
 AT ideal receiver-engine the pistons of the 
 
 mAGRAMs two cylinders are connected to cranks 
 
 -DIAGRAMS. at right angleg tQ each Qther Qn the 
 
 same shaft. The receiver takes the steam exhausted from the first cylin- 
 der and supplies it to the second, in which the steam is cut off and then 
 expanded to the end of the stroke. On the assumption that the initial 
 pressure in the second cylinder is equal to the final pressure in the first, 
 and of course equal to the pressure in the receiver, the volume cut off in 
 the second cylinder must be equal to the volume of the first cylinder, for 
 the second cylinder must admit as much steam at each stroke as is dis- 
 charged from the first cylinder. 
 
 In Fig. 167, cd is the line of admission and kg the exhaust-line for the 
 first cylinder; and dg is the expansion-curve and pq the atmospheric line. 
 
 iftfi 
 
 ^60 Ibs. 
 
 FIG. 167. RECEIVER-ENGINE, 
 IDEAL, INDICATOR-DIAGRAM. 
 
 FIG. 168. RECEIVER ENGINE, IDEAL 
 DIAGRAMS REDUCED AND COMBINED. 
 In the region below the exhaust-line of the first cylinder, between it and 
 the line of perfect vacuum, ol, the diagram of the second cylinder is 
 formed: hi, the second line of admission, coincides with the exhaust-line 
 hg of the first cylinder, showing in the ideal diagram no intermediate 
 fall of pressure, and ik is the expansion-curve. The arrows indicate 
 the order in which the diagrams are formed. 
 
 In the action of the receiver-engine, the expansive working of the 
 steam, though clearly divided into two consecutive stages, is, as in the 
 Woolf engine, essentially continuous from the point of cut-off in the first 
 cylinder to the end of the stroke of the second cylinder, where it is 
 delivered to the condenser; and the first and second diagrams may be 
 placed together and combined to form a continuous diagram. For this 
 purpose take the second diagram as the basis of the combined diagram, 
 namely, hiklo, Fig. 168. The period of admission, hi, is one-third of the 
 stroke, and as the ratios of the cylinders areas 1 to 3, hi is also the propor- 
 
COMPOUND ENGINES. 
 
 979 
 
 ism 
 con 
 
 P 
 
 by 
 
 il length of the first diagram as applied to the second. Produce oh up- 
 ards, and set off oc equal to the total height of the first diagram above the 
 vacuum-line; and, upon the shortened base hi, and the height he, complete 
 the first diagram with the steam-line cd and the expansion line di. 
 
 It is shown by Clark (S. E., p. 432 et seq.) in a series of arithmetical calciu. 
 lations, that the receiver-engine is an elastic system of compound engine, in 
 which considerable latitude is afforded for adapting the pressure in the re- 
 ceiver to the demands of the second cylinder, without considerably dimin- 
 ishing the effective work of the engine. In the Woolf engine, on the* 
 contrary, it is of much importance that the intermediate volume of space 
 " ween the first and second cylinders, which is the cause of an interme- 
 
 te fall of pressure, should be reduced to the lowest practicable amount. 
 
 Supposing that there is no loss of steam in passing through the engine, 
 cooling and condensation, it is obvious that whatever steam passes 
 through the first cylinder must also find its way through the second 
 cylinder. By varying, therefore, in the receiver-engine, the period of 
 admission in the second cylinder, and thus also the V9lume of steam ad- 
 mitted for each stroke, the steam will be measured into it at a higher 
 pressure and of a less bulk, or at a lower pressure and of a greater bulk; 
 the pressure and density naturally adjusting themselves to the volume 
 that the steam from the receiver is permitted to occupy in the second 
 cylinder. With a sufficiently restricted admission, the pressure in the 
 receiver may be maintained at the pressure of the steam as exhausted 
 from the first cylinder. On the contrary, with a wider admission, the 
 pressure in the receiver may fall or "drop" to three-fourths or even one- 
 half of the pressure of the exhaust steam from the first cylinder. 
 
 (For a more complete discussion of the action of steam in the Woolf 
 and receiver engines, see Clark on the Steam-engine.) 
 
 Combined Diagrams of Compound Engines. The only way of 
 making a correct combined diagram from the indicator-diagrams of 
 the several cylinders 
 in a compound engine 
 is to set off all the 
 diagrams on the same 
 horizontal scale of vol- 
 umes, adding the 
 clearances to the cyl- 
 inder capacities prop- 
 er. When this is 
 attended to, the suc- 
 cessive diagrams fall 
 exactly into their right 
 places relatively to one 
 another, and would 
 compare properly with 
 any theroretical ex- 
 pansion-curve, (Prof. 
 A. B. W. Kennedy, 
 Proc. Inst. M. E., Oct., 
 1886.) 
 
 This method of com- 
 bining diagrams is 
 commonly adopted, 
 but there are objec- 
 tions to its accuracy, 
 since the whole quan- 
 tity of steam con- FIG. 169. 
 sumed in the first cylinder at the end of the stroke is not carried forward 
 to the second, but a part of it is retained in the first cylinder for com- 
 pression. For a method of combining diagrams in which compression 
 is taken account of, see discussions by Thomas Mudd and others, in Proc. 
 Inst. M. E., Feb., 1887, p. 48. The usual method of combining diagrams 
 is also criticised by Frank H. Ball as inaccurate and misleading (Am. 
 Mach., April 12, 1894; Trans. A. S. M. E., xiv, 1405, and xv, 403). 
 
 Figure 169 shows a combined diagram of a quadruple-expansion engine, 
 drawn according to the usual method, that is, the diagrams are first 
 reduced in length to relative scales that correspond with the relative 
 
980 
 
 THE STEAM-ENGINE. 
 
 piston-displacement of the three cylinders. Then the diagrams are 
 placed at such distances from the clearance-line of the proposed combined 
 diagram as to represent correctly the clearance in each cylinder. 
 
 Proportions of Cylinders in Compound Engines. Authorities 
 differ as to the proportions by volume of the high and lo_w pressure 
 cylinders v and F._ Thus Grashof gives V *- v = 0.85 Vr; Hrabak, 
 0.90 v^; Werner, VV; and Rankine, ^/r 2 , r being the ratio of expansion. 
 Busley makes the ratio dependent on the boiler-pressure thus: 
 
 Lbs. per sq. in 60 90 105 120 
 
 V -*- v =3 4 4.5 5 
 
 (See Seaton's Manual, p. 95, etc., for analytical method; Sennett, p. 496, 
 etc.; Clark's Steam-engine, p. 445, etc.; Clark's Rules, Tables, Data, p. 849, 
 etc.) 
 
 Mr. J. McFarlane Gray states that he finds the mean effective pressure 
 in th6 compound engine reduced to the low-pressure cylinder to be approx- 
 imately the square root of 6 times the boiler-pressure. 
 
 Ratio of Cylinder Capacity in Compound Marine Engines. (Sea- 
 ton.) The low-pressure cylinder is the measure of the power of a com- 
 pound engine, for so long as the initial steam-pressure and rate of expansion 
 are the same, it signifies very little, so far as total power only is concerned, 
 whether the ratio between the low and high pressure cylinders is 3 or 
 4; but as the power developed should be nearly equally divided between 
 the two cylinders, in order to get a good and steady working engine, 
 there is a necessity for exercising a considerable amount of discretion 
 in fixing on the ratio. 
 
 In choosing a particular ratio the objects are to divide the power evenly 
 and to avoid as much as possible "drop" and high initial strain. [Some 
 writers advocate drop in the high-pressure cylinder making it smaller 
 Mian is the usual practice and making the cylinder ratio as high as 6 or 7.] 
 
 If increased economy is to be obtained by increased boiler-pressures 
 the rate of expansion should vary with the initial pressure, so that the 
 pressure at which the steam enters the condenser should remain constant. 
 In this case, with the ratio of cylinders constant, the cut-off in the high- 
 pressure cylinder will vary inversely as the initial pressure. 
 
 Let R be the ratio of the cylinders; r the rate of expansion; PI the 
 initial pressure: then cut-off in high-pressure cylinder =* R -* r\ r varies 
 with pi, so that the terminal pressure p n is constant, and consequently 
 r = PI-*- p n ; therefore, cut-off in high-pressure cylinder = R X p n -*- pi. 
 
 Ratios of Cylinders as Found in Marine Practice. The rate of 
 expansion may be taken at one-tenth of the boiler-pressure (or about one- 
 twelfth the absolute pressure), to work economically at full speed. There- 
 fore, when the diameter of the low-pressure cylinder does not exceed 
 100 inches, and the boiler-pressure 70 Ibs., the ratio of the low-pressure 
 to the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 Ibs., 
 3.75; for 90 Ibs., 4.0; for 100 Ibs., 4.5. If these proportions are adhered 
 to, there will be no need of an expansion-valve to either cylinder. If, 
 however, to avoid "drop," the ratio be reduced, an expansion-valve 
 should be fitted to the high-pressure cylinder. 
 
 Where economy of steam is not of first importance, but rather a large 
 power, the ratio of cylinder capacities may with advantage be decreased, 
 so that with a boiler-pressure of 100 Ibs. it may be 3.75 to 4. 
 
 In tandem engines there is no necessity to' divide the work equally. 
 The ratio is generally 4, but when the steam-pressure exceeds 90 Ibs. 
 absolute 4.5 is better, and for 100 Ibs. 5.0. 
 
 When the power requires that the l.p. cylinder shall be more than 100 in. 
 diameter, it should be divided in two cylinders. -In this case the ratio of the 
 combined capacity of the two l.p. cylinders to that of the h.p. may be 
 3.0 for 85 Ibs. absolute, 3.4 for 95 Ibs., 3.7 for 105 Ibs., and 4.0 for 115* Ibs. 
 
 Receiver Space in Compound Engines should be from 1 to 1.5 times 
 the capacity of the high-pressure cylinder, when the cranks are at an 
 angle of from 90 to 120. When the cranks are at 180 or nearly this, 
 the space may be very much reduced. In the case of triple-compound 
 engines, with cranks at 120, and the intermediate cylinder leading the 
 high-pressur^ a very small receiver will do. The pressure in the receiver 
 should never exceed half the boiler-pressure. (Seaton.) 
 
COMPOUND ENGINES, 981 
 
 Formula for Calculating the Expansion and the Work of Steam 
 in Compound Engines. 
 
 (Condensed from Clark on the " Steam-engine. ") 
 
 a = area of the first cylinder in square inches; 
 ~' = area of the second cylinder in square inches; 
 
 = ratio of the capacity of the second cylinder to that of the first ; 
 = length of stroke in feet, supposed to be the same for bpth cylinders; 
 = period of admission to the first cylinder in feet, excluding clearance; 
 = clearance at each end of the cylinders, in feet; 
 = length of the stroke plus the clearance, in feet; 
 = period of admission plus the clearance, in feet; 
 = length of a given part of the stroke of the second cylinder, in feet; 
 = total initial pressure in the first cylinder, in Ibs. per square inch, 
 
 supposed to be uniform during admission; 
 P f = total pressure at the end of the given part of the stroke s; 
 p = average total pressure for the whole stroke; 
 R = nominal ratio of expansion in the first cylinder, or L -*- l\ 
 R f = actual ratio of expansion in the first cylinder, or L' *- l'\ 
 R" actual combined ratio of expansion, in the first and second cylin- 
 ders together; 
 n = ratio of the final pressure in the first cylinder to any intermediate 
 
 fall of pressure between the first and second cylinders; 
 N ratio of the volume of the intermediate space in the Woolf engine, 
 
 ,-; 
 
 reckoned up to, and including the clearance of, the second pis- 
 ton, to the capacity of the first cylinder plus its clearance. The 
 value of N is correctly expressed by the actual ratio of the 
 
 volumes as stated, on the assumption that the intermediate space 
 is a vacuum when it receives the exhaust-steam from the first 
 cylinder. In point of fact, there is a residuum of unexhausted 
 steam in the intermediate space, at low pressure, and the value 
 of N is thereby practically reduced below the ratio here stated, 
 
 = whole net work in one stroke, in foot-pounds. 
 atio of expansion in the second cylinder: 
 
 In the Woolf engine, 
 (n-l)r 
 
 In the receiver-engine, - 
 
 Total actual ratio of expansion = product of the ratios of the three 
 consecutive expansions, in the first cylinder, in the intermediate space, 
 and in the second cylinder, 
 
 In the Woolf engine, R' (r j- t -f #); 
 In the receiver-engine, r -771 or rR f . 
 Combined ratio of expansion behind the pistons ^ - rR' = R". 
 
 Work done in the two cylinders for one stroke, with a given cut-off 
 and a given combined actual ratio of expansion: 
 
 Woolf engine, w = aP [l'(l + hyp log R") -c]; 
 Receiver engine, w = aP ll f (1 + hyp log R") -c (l-l- ^r )1 
 when there is no intermediate fall of pressure. 
 
982 THE STEAM-ENGINE. 
 
 When there is an intermediate fall, when the pressure falls to 3/ 4f 2/ 
 1/2 of the final pressure in the 1st cylinder, the reduction of work is 0.2%, 
 1.0%, 4.6% of that when there is no fall. 
 
 Total work in the two cylinders of a receiver-engine, for one stroke 
 for any intermediate fall of pressure, 
 
 EXAMPLE. Let a = I sq. in., P = 63 Ibs., I' = 2.42 ft , n = 4 R" = 
 5.969, c = 0.42 ft., r = 3, R' = 2.653; 
 
 w = l X 63 [2.42 (5/4 hyp log 5.969) -.42 (l + - -)1 =421.55 ft .-Ibs. 
 
 L \ 4 /s ^.DOo / J 
 
 Calculation of Diameters of Cylinders of a compound condensing 
 engine of 2000 H.P. at a speed of 700 feet per minute, with 100 Ibs. boiler- 
 pressure. 
 
 100 Ibs. gauge-pressure = 115 absolute, less drop of 5 Ibs. between 
 boiler and cylinder = 110 Ibs. initial absolute pressure Assuming 
 terminal pressure in l.p. cylinder = 6 Ibs., the total expansion of steam 
 i i both cylinders = 110 -*- 6 = 18.33. Hyp log 18.33 = 2.909. Back 
 pressure in l.p. cylinder, 3 Ibs. absolute. 
 
 The following formulae are used in the calculation of each cylinder: 
 
 (1) Area of cylinder "/ v X . 3 f' OQO . 
 
 M.E.P. X piston-speed 
 
 (2) Mean effective pressure = mean total pressure - back pressure. 
 
 (3) Mean total pressure = terminal pressure X (1 + hyp log R). 
 
 (4) Absolute initial pressure = absolute terminal pressure X ratio of 
 expansion. 
 
 First calculate the area of the low-pressure cylinder as if all the work 
 were done in that cylinder. 
 
 From (3), mean total pressure = 6 X (1 + hyp log 18.33) = 23.454 
 Ibs. 
 
 From (2), mean effective pressure = 23.454 3 = 20.454 Ibs. 
 
 From (1). area of cylinder = ?' = 4610 sq.ins. = 76.6ins. diam. 
 
 If half the work, or 1000 H.P.', is done in the l.p. cylinder the M.E.P. 
 will be half that found above, or 10.227 Ibs., and the mean total pressure 
 10.227+ 3 = 13.227 Ibs. 
 
 From (3), 1 + hyp log R = 13.227- -s- 6 = 2.2045. 
 
 Hyp log R = 1.2045, whence R in l.p. cyl. = 3.335. 
 
 From (4), 3.335 X 6 = 20.01 Ibs. initial pressure in l.p. cyl. and ter- 
 minal piessure in h.p. cyl., assuming no drop between cylinders. 
 
 110 * 20.01 = 18.33 -4- 3.335 = 5.497, Rin h.p. cyl. 
 
 From (3), mean total pres. in h.p. cyl. = 20.01 X (1 + hyp log 5.497) 
 
 From (2), 54.11 - 20.01 = 34.10, M.E.P. in h.p. cyl. 
 
 i nnn v 33 nnn 
 From (1), area of h.p. cyl. = ""p* 34 1" =1382 sq. ins. = 42 ins. diam. 
 
 Cylinder ratio = 4610 -f- 1382 = 3.336. 
 
 The area of the h.p. cylinder may be found more directly by dividing 
 the area of the l.p. cyl. by the ratio of expansion in that cylinder. 4610 
 v- 3.335 = 1382 sq.ins. 
 
 In the above calculation no account is taken of clearance, of com- 
 pression, of drop between cylinders, nor of area of piston-rods. It also 
 assumes that the diagram in each cylinder is the full theoretical diagram, 
 with a horizontal steam-line and a hyperbolic expansion line, with no 
 allowance for rounding of the corners. To make allowance for these, 
 the mean effective pressure in each cylinder must be multiplied by a 
 diagram factor, or the ratio of the area of an actual diagram of the class 
 of engine considered, with the given initial and terminal pressures, to the 
 area of the theoretical diagram. Such diagram factors will range from 
 0.6 to 0.94, as in the table on p. 962. 
 
 Best Ratios of Cylinders. The question what is the best ratio of 
 areas of the two cylinders of a compound engine is still (1901) a disputed 
 one, but there appears to be an increasing tendency in favor of large 
 
TRIPLE-EXPANSION ENGINES. 983 
 
 ratios, even as great as 7 or 8 to 1, with considerable terminal drop in 
 the high-pressure cylinder. A discussion of the subject, together with a 
 description of a, new method of drawing theoretical diagrams of multiple- 
 expansion engines, taking into consideration drop, clearance, and com- 
 pression will be found in a paper by Bert C. Ball, in Trans. A. S. M. E., 
 Ed, 1092. 
 
 TRIPLE-EXPANSION ENGINES. 
 
 Proportions of Cylinders. H. H. Suplee, Mechanics, Nov., 1887, 
 gives the following method of proportioning cylinders of triple-expansion 
 engines: 
 
 As in the case of compound engines the diameter of the low-pressure 
 cylinder is first determined, being made large enough to furnish the entire 
 power required at the mean pressure due to the initial pressure and 
 expansion ratio given; and then this cylinder is given only pressure enough 
 to perform one-third of the work, and the other cylinders are proportioned 
 so as to divide the other two-thirds between them. 
 
 Let us suppose that an initial pressure of 150 Ibs. is used and that 
 900 H.P. is to be developed at a piston-speed of 800 ft. per min., and that 
 an expansion ratio of 16 is to be reached with an absolute back-pressure 
 of 2 Ibs. 
 
 The theoretical M.E.P. with an absolute initial pressure of 150 + 14.7 =* 
 164.7 Ibs. initial at 16 expansions is 
 
 P (1 + hyp log 16) _ ? 3.7726 = 3g 83> 
 
 16 16 
 
 less 2 Ibs. back pressure, = 38.83 - 2 = 36.83. 
 
 In practice only about 0.7 of this pressure is actually attained, so that 
 36.83 x 0.7 = 25.781 Ibs. is the M.E.P. upon which the engine is to be 
 proportioned. 
 
 To obtain 900 H.P. we must have 33,000 X 900 = 29,700,000 Toot- 
 pounds, and this divided by the mean pressure (25.78) and by the speed 
 in feet (800) will give 1440 sq. in. as the area of the l.p. cylinder, about 
 equivalent to 43 in. diam. 
 
 Now as one-third of the work is to be done in the l.p. cylinder, the 
 M.E.P. in it will be 25.78 * 3 = 8.59 Ibs. 
 
 The cut-off in the high-pressure cylinder is generally arranged to cut off 
 at 0.6 of the stroke, and so the ratio of the h.p. to the l.p. cylinder is equal 
 to 16 X 0.6 = 9.6, and the h.p. cylinder will be 1440 -* 9.6 = 150 sg. 
 in. area, or about 14 in. diameter, and the M.E.P. in the h.p. cylinder is 
 equal to 9.6 X 8.59 == 82.46 Ibs. 
 
 If the intermediate cylinders made a mean size between the other two, 
 . its size would be determined by dividing the area of the l.p. cylinder by 
 the square root of the ratio between the low and the high; but in practice 
 this is found to give a result too large to equalize the stresses, so that 
 instead the area of the int. cylinder is found by dividing the area of the 
 l.p. piston by 1.1 times the square root of the ratio of l.p. to h.p. cylinder, 
 which in this case is 1440 * (1.1 V^6) = 422.5 sq.in., or a little more 
 than 23 in. diam. 
 
 The choice of expansion ratio is governed by the initial pressure, and is 
 generally chosen so that the terminal pressure in the l.p. cylinder shall be 
 about 10 Ibs. absolute. 
 
 Formulae for Proportioning Cylinder Areas of Triple-Expansion 
 Engines. The following formulae are based on the method of first 
 finding the cylinder areas that would be required if an ideal hyperbolic dia- 
 gram were obtainable from each cylinder, with no clearance, compression, 
 wire-drawing, drop by free expansion in receivers, or loss by cylinder 
 condensation, assuming equal work to be done in each cylinder, and 
 then dividing the areas thus found by a suitable diagram factor, such as 
 those given on page 962, expressing the ratio which the area of an actual 
 diagram, obtained in practice from an engine of the type under consider- 
 ation, bears to the ideal or theoretical diagram. It will vary in different 
 classes of engine and in different cylinders of the same engine, usual 
 values ranging from 0.6 to 0.9. When any one of the three stages of 
 expansion takes place in two cylinders, the combined area of these 
 cylinders equals the area found by the formulae. 
 
984 
 
 THE STEAM-ENGINE. 
 
 NOTATION. 
 
 Pi = initial pressure in the high-pressure cylinder. 
 Pt = terminal pressure in the low-pressure cylinder. 
 #5 = back pressure in the low-pressure cylinder. 
 
 Pt = term, press, in h.p. cyl. and initial press, in intermediate cyl. 
 
 p-3= term, press, in int. cyl. and initial press, in l.p. cyl. 
 
 Ri, Ri, Rz, ratio of exp. in h.p. int. and l.p. cyls. 
 
 R = total ratio of exp. = Ri x Rz X Rz- 
 
 P = M.E.P. of the combined ideal diagram, referred to the l.p. cyL 
 
 Pi, P 2 , P 3 = M.E.P. in the h.p., int., and l.p. cyls. 
 
 // P = horse-power of the engine = PLA S N -4- 33,000. 
 
 L = length of stroke in feet ; N = number of single strokes per niin. 
 
 Ai, A 2 , Az, areas (sq. ins.) of h.p. int. and l.p. cyls. (ideal). 
 
 W = work done in one cylinder per foot of stroke. 
 
 r-z = ratio of A 2 to A\; r 3 = ratio of Az to Ai. 
 
 Fi, F 2 , F 3 , diagram factors of h.p. int. and l.p. cyl. 
 
 Ci, 2, a 3 , areas (actual) of h.p. int. and l.p. cyl. 
 
 Formulae. 
 
 (1) R = p l -^ p t . 
 
 (2) P = p t (1 + hyp log R) - p bf 
 
 " Ps = V3 P. 
 
 Hyp log # 3 = (Ps - Pt+ Pb) -* Pf 
 
 (5) RiRz = R -5- Rz; Ri = Rz = ^RiRz. 
 
 (6) ps = p t X Rs. 
 
 S7) P2 P3 X #2. 
 8) pi = pz X Ri. 
 9) P 2 = pz (hyp log fl 2 ) fe= PzRs. 
 
 10) Pi = p2 (hyp log ^i) = P 2 ^2. 
 
 11) W = 11,000 HP -5- LN, 
 
 12) Ai = W + Pi; At = W + P z 
 
 13) r 2 = ^2 -* Ai = Pi -4- P 2 = I 
 
 14) 01 = 
 
 <3) 
 (4) 
 
 ^3 = W 
 i or #2; rs 
 
 * Ai Pi ~- P 8 . 
 
 From these formulae the figures in the following tables have been 
 calculated: 
 THEORETICAL MEAN EFFECTIVE PRESSURES, CYLINDER RATIOS, ETC., 
 
 OF TRIPLE-EXPANSION ENGINES. 
 Back pressure, 3 Ibs. Terminal pressure, 8 Ibs. (absolute). 
 
 Pi. 
 
 If. 
 
 P. 
 
 P 3 . 
 
 Rz. 
 
 Ri, Rt, 
 
 Or T2. 
 
 Ps. 
 
 P2. 
 
 P 2 . 
 
 Pi. 
 
 r, 
 
 120 
 140 
 160 
 180 
 200 
 220 
 240 
 
 15 
 17.5 
 20 
 22.5 
 25 
 27.5 
 30 
 
 26.66 
 27.90 
 28.97 
 29.91 
 30.75 
 31.51 
 32.21 
 
 8.89 
 9.30 
 9.66 
 9.97 
 10.25 
 10.50 
 10.74- 
 
 .626 
 .712 
 .790 
 .861 
 .928 
 .990 
 2.049 
 
 3.037 
 3.197 
 3.343 
 3.477 
 3.601 
 3.718 
 3.826 
 
 13.01 
 13.70 
 14.32 
 14.89 
 15.42 
 15.91 
 16.39 
 
 39.51 
 43.79 
 47.86 
 51.77 
 55.54 
 59.16 
 62.72 
 
 14.45 
 15.92 
 17.29 
 18.55 
 19.76 
 20.90 
 22.00 
 
 43.89 
 50.89 
 57.76 
 64.52 
 71.16 
 77.69 
 84.16 
 
 4.939 
 5.472 
 5.980 
 6.471 
 6.942 
 7.397 
 7.839 
 
 THEORETICAL MEAN EFFECTIVE PRESSURES, CYLINDER RATIOS, ETC., 
 
 OF TRIPLE-EXPANSION ENGINES. 
 Back pressure, 3 Ibs. Terminal pressure, 10 Ibs. (absolute). 
 
 Pi. 
 
 R. 
 
 P. 
 
 P 3 . 
 
 R 3 . 
 
 Ri, Rt, 
 or rz. 
 
 Pa. 
 
 pz. 
 
 P 2 . 
 
 Pi. 
 
 T3. 
 
 120 
 140 
 160 
 180 
 200 
 220 
 240 
 
 8 
 
 16 
 18 
 20 
 22 
 24 
 
 31.85 
 33.39 
 34.73 
 35.90 
 36.96 
 37.91 
 38.78 
 
 10.62 
 11.13 
 11.58 
 11.97 
 12.32 
 12.64 
 12.93 
 
 .436 
 .511 
 .580 
 .643 
 .702 
 .757 
 .809 
 
 2.890 
 3.044 
 3.182 
 3.310 
 3.428 
 3.538 
 3.642 
 
 14.36 
 15.11 
 15.80 
 16.43 
 17.02 
 17.57 
 18.09 
 
 41.50 
 45.99 
 50.28 
 54.38 
 58.34 
 62.15 
 65.88 
 
 15.24 
 16.82 
 18.29 
 19.66 
 20.97 
 22.20 
 23.38 
 
 44.04 
 51.20 
 58.20 
 65.09 
 71.88 
 78.54 
 85.15 
 
 4.148 
 4.600 
 5.027 
 5.439 
 5.834 
 6.215 
 6.587 
 
 Given the required H.P. of an engine, its speed and length of stroke, 
 
TRIPLE-EXPANSION ENGINES. 
 
 985 
 
 a,nd the assumed diagram factors Fi. F 2 , Fs for the three cylinders, tne 
 areas of the cylinders may be found by using formula (11), (12), and 
 (14), and the values of Pi, Pz, and Ps in the above table. 
 
 A Common Rule for Proportioning the Cylinders of multiple- 
 expansion engines is: for two-cylinder compound engines, the cylinder 
 ratio is the square root of the number of expansions, and for triple- 
 expansion engines the ratios of the high to the intermediate and of the 
 intermediate to the low are each equal to the cube root of the number of 
 expansions, the ratio of tht high to the low being the product of the two 
 ratios, that is, the square of the cube root of the number of expansi9ns. 
 Applying this rule to the pressures above given, assuming a terminal 
 pressure (absolute) of 10 Ibs. and 8 Ibs. respectively, we have, for triple- 
 expansion engines: 
 
 Boiler- 
 pressure 
 (Absolute) . 
 
 Terminal Pressure, 10 Ibs. 
 
 Terminal Pressure, 8 Ibs. 
 
 No. of Ex- 
 pansions. 
 
 Cylinder Ratios, 
 areas. 
 
 Nc. of Ex- 
 pansions. 
 
 Cylinder Ratios, 
 areas. 
 
 130 
 140 
 150 
 160 
 
 13 
 14- 
 15 
 16 
 
 1 to 2.35 to 5. 53 
 1 to 2. 41 to 5.81 
 1 to 2. 47 to 6. 08 
 1 to 2. 52 to 6. 35 
 
 161/4 
 171/2 
 
 20 83/4 
 
 1 to 7.53 to 6. 42 
 1 to 2. 60 to 6. 74 
 1 to 2. 66 to 7. 06 
 1 to 2. 71 to 7.37 
 
 The ratio of the diameters is the square root of the ratios of the areas, 
 and the ratio of the diameters of the first and third cylinders is the same 
 as the ratio of the areas of first and second. 
 
 Seaton, in his Marine Engineering, says: When the pressure of steam 
 employed exceeds 115 Ibs. absolute, it is advisable to employ three 
 cylinders, through each of which the steam expands in turn. The ratio 
 of the low-pressure to high-pressure cylinder in this system should be 5, 
 when the steam-pressure is 125 Ibs.. absolute; when 135 Ibs., 5.4; when 
 145 Ibs., 5.8; when 155 Ibs., 6.2; when 165 Ibs., 6.6. The ratio of low- 
 pressure to intermediate cylinder should be about one-half that between 
 low-pressure and high-pressure, as given above. That is, if the ratio 
 of l.p. to h.p. is 6, that of l.p. to int. should be about 3, and consequently 
 that of int. to h.p. about 2. In practice the ratio of int. to h.p. is nearly 
 2.25, so that the diameter of the int. cylinder is 1.5 that of the h.p. The 
 introduction of the triple-compound engine has admitted of ships being 
 propelled at higher rates of speed than formerly obtained without exceed- 
 ing the consumption of fuel of similar ships fitted with ordinary com- 
 pound engines; in such cases the higher power to obtain the speed has been 
 developed by decreasing the rate of expansion, the low-pressure cylin- 
 der being only 6 times the capacity of the high-pressure, with a working 
 pressure of 170 Ibs. absolute. It is now a very general practice to make 
 the diameter of the low-pressure cylinder equal to the sum of the diameters 
 of the h.p. and int. cylinders; hence, 
 
 Diameter of int. cylinder =1.5 diameter of h.p. cylinder; 
 Diameter of l.p. cylinder = 2.5 diameter of h.p. cylinder. 
 
 In this case the ratio of l.p. to h.p. is 6.25; the ratio of int. to h.p. is 2.26; 
 and ratio of l.p. to int. is 2.78. 
 
 Ratios of Cylinders for Different Classes of Engines. (Proc. Inst. 
 M. E., Feb., 1887, p. 36.) As to the best ratios for the cylinders in a 
 triple engine there seems to be great difference of opinion. Considerable 
 latitude, however, is due to the requirements of the case, inasmuch as 
 it would not be expected that the same ratio would be suitable for an 
 economical land engine, where the space occupied and the weight were of 
 minor importance, as in a war-ship, where the conditions were reversed. 
 In the land engine, for example, a theoretical terminal pressure of about 
 7 Ibs. above absolute vacuum would probably be aimed at, which would 
 give a ratio of capacity of high pressure to low pressure of 1 to 8 Viz or 1 to 
 9; whilst in a war-ship a terminal pressure would be required of 12 to 13 
 Ibs. which would need a ratio of capacity of 1 to 5; yet in both these 
 instances the cylinders were correctly proportioned and suitable to the 
 requirements of the case. It is obviously unwise, therefore, to introduce 
 any hard-and-fast rule. 
 
 Types of Three-stage Expansion Engines, 1. Three cranks at 
 
THE STEAM-ENGINE. 
 
 120 (leg. 2. Two cranks with 1st and 2d, cylinders tandem. 3. Two 
 cranks with 1st and 3d cylinders tandem. The most common type is the 
 first, with cylinders arranged in the sequence high, intermediate, low. 
 
 Sequence of Cranks. Mr. Wyllie (Proc. Inst. M. E., 1887) favors 
 the sequence high, low, intermediate, while Mr. Mudd favors high, inter- 
 mediate, low. The former sequence, high, low, intermediate, gave an 
 approximately horizontal exhaust-line, and thus minimizes the range of 
 temperature and the initial load; the latter sequence high, intermediate, 
 low, increased the range and also the load. 
 
 Mr. Morrison, in discussing the question of sequence of cranks, pre- 
 sented a diagram showing that with the cranks arranged in the sequence 
 high, low, intermediate, the mean compression into the receiver was 
 19V2 per cent of the stroke; with the sequence high, intermediate, low, 
 it was 57 per cent. 
 
 In the former case the compression was just what was required to keep 
 the receiver-pressure practically uniform ; in the latter case the compression 
 caused a variation in the receiver-pressure to the extent sometimes of 
 22V2 Ibs. 
 
 Velocity of Steam tjirough Passages in Compound Engines. 
 (Proc. Inst. M. E., Feb., 1887.) In the SS. Para, taking the area of the 
 cylinder multiplied by the piston-speed in feet per second and dividing 
 by the area of the port the velocity of the initial steam through the high- 
 pressure cylinder port would be about 100 feet per second; the exhaust 
 would be about 90. In the intermediate cylinder the initial steam had 
 a velocity of about 180, and the exhaust of 120. In the low-pressure 
 cylinder, the initial steam entered through the port with a velocity of 250, 
 and in the exhaust-port the velocity was about 140 feet per second. 
 
 A Double-tandem Triple-expansion Engine, built by Watts, 
 Campbell & Co., Newark, N. J., is described in Am. Mack., April 26, 1894. 
 It is two three-cylinder tandem engines coupled to one shaft, cranks at 
 90, cylinders 21, 32 and 48 by 60 in. stroke, 65 revolutions per minute, 
 rated H.P. 2000; fly-wheel 28 ft. diameter, 12 ft. face, weight 174,000 
 bs.; main shaft 22 in. diameter at the swell; main journals 19 X 38 in.; 
 ^rank-pins 91/2 X 10 in.; distance between center lines of two engines 
 24 ft. 7 1/2 in.; Corliss valves, with separate eccentrics for the exhaust- 
 calves of the l.p. cylinder. 
 
 QUADRUPLE-EXPANSION ENGINES. 
 
 H. H. Suplee (Trans. A. S. M. E., x, 583) states that a study of 14 
 different quadruple-expansion engines, nearly all intended to be operated 
 at a pressure of 180 Ibs. per sq. in., gave average cylinder ratios of 1 to 2, 
 to 3.78, to 7.70, or nearly in the proportions 1, 2, 4, 8. 
 
 If we take the ratio of areas of any two adjoining cylinders as the fourth 
 root of the number of expansions, the ratio of the 1st to the 4th will be 
 the cube of the fourth root. On this basis the ratios of areas for different 
 pressures and rates of expansion will be as follows: 
 
 Gauge- 
 pressures. 
 
 Absolute 
 Pressures. 
 
 Terminal 
 Pressures. 
 
 Ratio of 
 Expansion. 
 
 Ratios of Areas 
 of Cylinders. 
 
 
 
 !12 
 
 14.6 
 
 : 1 95 : 3 81 : 7 43 
 
 160 
 
 175 
 
 10 
 8 
 SI2 
 
 17.5 
 21.9 
 16.2 
 
 : 2. 05: 4. 18: 8.55 
 : 2.16: 4.68: 10.12 
 : 2.01 : 4 02: 8.07 
 
 180 
 
 195 
 
 '8 
 
 19.5 
 24.4 
 
 : 2.10: 4.42: 9.28 
 : 2 22 : 4 94 : 10 98 
 
 200 
 220 
 
 215 
 235 
 
 P 
 
 ,1 
 
 h 
 
 17.9 
 21.5 
 26.9 
 19.6 
 23.5 
 29.4 
 
 : 2. 06: 4. 23: 8.70 
 : 2.15: 4.64: 9.98 
 : 2.28: 5.19: 11.81 
 : 2. 10: 4. 43: 9.31 
 : 2.20: 4.85: 10.67 
 : 2.33: 5.42: 12.62 
 
 Seaton says: When the pressure of steam employed exceeds 190 Ibs. 
 absolute, four cylinders should be employed, with tag steam expanding 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 987 
 
 through each successively; and the ratio of l.p. to h.p. should be at least 
 7.5, and if economy of fuel is of prime .consideration it should be 8; then 
 the ratio of first intermediate to h.p. should be 1.8, that of second inter- 
 mediate to first int. 2, and that of l.p. to second int. 2.2. 
 
 .in a paper read before the North East Coast Institution of Engineers 
 and Shipbuilders, 1890, William Russell Cummins advocates the use of a 
 four-cylinder engine with four cranks as being more suitable for high 
 speeds than the three-cylinder three-crank engine. The cylinder ratios, 
 he claims, should be designed so as to obtain equal initial loads in each 
 cylinder. The ratios determined for the triple engine are 1, 2.04, 6.54, 
 and for the quadruple, 1, 2.08, 4.46, 10.47. He advocates long stroke,, 
 high piston-speed, 100 revolutions per minute, and 250 Ibs. boiler-pressure, 
 unjacketed cylinders, and separate steam and exhaust valves. 
 
 ECONOMIC PERFORMANCE OF STEAM-ENGINES. 
 
 Economy of Expansive Working under Various Conditions, Single 
 Cylinder. 
 
 (Abridged from Clark on the Steam Engine.) 
 
 1. SINGLE CYLINDERS WITH SUPERHEATED STEAM, NON-CONDENSING. 
 Inside cylinder locomotive, cylinders and steam-pipes enveloped by the 
 hot gases in the smoke-box. Net boiler pressure 100 Ibs.; net maximum 
 pressure in cylinders 80 Ibs. per sq. in. 
 
 Cut-off, per cent 20 25 30 35 40 50 60 70 80 
 
 Actual ratio of expan- 
 sion 3.91 3.31 2.87 2.53 2.26 1.86 1.59 1.39 1.23 
 
 Water per I.H.P. per 
 
 hour, Ibs 18.5 19.4 20 21.2 22.2 24.5 27 30 33 
 
 2. SINGLE CYLINDERS WITH SUPERHEATED STEAM, CONDENSING. - 
 The best results obtained by Him, with a cylinder 233/ 4 x 67 in. and steam 
 superheated 150 F., expansion ratio 33/4 to 41/2, total maximum pressure 
 in cylinder 63 to 69 Ibs., were 15.63 and 15.69 Ibs. of water per I.H.P. per 
 hour. 
 
 3. SINGLE CYLINDERS, NOT STEAM-JACKETED, CONDENSING. The best 
 result is from a Corliss-Wheelock engine 18 X 48 in.; cut-off, 12.5%; 
 actual expansion ratio, 6.95; maximum absolute pressure in cylinder 
 104 Ibs.; steam per I.H.P. hour, 19.58 Ibs. Other engines, with lowei 
 steam pressures, gave a steam consumption as high as 26.7 Ibs. 
 
 Feed-water Consumption of Different Types of Engines. The 
 following tables are taken from the circular of the Tabor Indicator (Ash- 
 croft Mfg. Co., 1889). In the first of the two columns under Feed-water 
 required, in the tables for .simple engines, the figures are obtained by 
 computation from nearly perfect indicator diagrams, with allowance 
 lor cylinder condensation according to the table on page 936, but without 
 .allowance for leakage, with back-pressure in the non-condensing table 
 taken at 16 Ibs. above zero, and in the condensing table at 3 Ibs. above zero. 
 The compression curve is supposed to be hyperbolic, and commences at 
 0.91 of the return-stroke, with a clearance of 3% of the piston-displace- 
 ment. 
 
 Table No. 2 gives the feed-water consumption for jacketed compound- 
 condensing engines of the best class. The water condensed in the jackets 
 is included in the quantities given. The ratio of areas of the two cylinders 
 is as 1 to 4 for 120 Ibs. pressure: the clearance of each cylinder is 3% 
 and the cut-off in the two cylinders occurs at the same point of stroke. 
 The initial pressure in the l.p. cylinder is 1 Ib. per sq. in. below the back- 
 pressure of the h.p. cylinder. The average back-pressure of the whole 
 stroke in the l.p. cylinder is 4.5 Ibs. for 10% cut-off; 4.75 Ibs. for 20% 
 cut-off; and 5 Ibs. for 30% cut-off. The steam accounted tor by the 
 indicator at cut-off in the h.p. cylinder (allowing a small amount for leak- 
 age) is 0.74 at 10% cut-off, 0.78 at 20%, and 0.82 at 30% cut-off. Tbe 
 loss by condensation between the cylinders is such that the steam ac- 
 counted for at cut-off in the l.p. cylinder, expressed in proportion of that 
 shown at release in the h.p. cylinder, is 0.85 at 10% cut-off, 0.87 at 20% 
 cut-off, and 0.89 at 30% cut-off. 
 
988 
 
 THE STEAM-ENGINE. 
 
 TABLE No. 1. 
 
 FEED-WATER CONSUMPTION, SIMPLE ENGINES. 
 NON-CONDENSING ENGINES. CONDENSING ENGINES. 
 
 
 A 
 
 
 Feed-water Re- 
 
 
 * 
 
 
 Feed- water Re- 
 
 
 o 
 
 JS 
 
 quired per I.H.P. 
 per Hour. 
 
 
 1 
 
 J 
 
 quired per I.H.P. 
 per Hour. 
 
 
 
 2? 
 
 
 
 
 
 
 
 i 
 
 3 
 
 J4 
 
 A"Sfi . 
 
 
 1 
 
 1 
 
 M 
 
 41* 
 
 
 M 
 
 
 
 o v 
 
 S 3 yj 
 
 
 
 
 o 
 
 G 
 
 ^ g 3 M 
 
 
 i 
 
 PH 
 
 o >-3 
 
 O c3 JS c3 
 
 
 d 
 
 M 
 
 o ^ 
 
 ^ 1-3 
 
 td 
 o 
 
 
 
 o 
 
 IJ 
 
 1 ^ 
 
 ! 
 
 8 
 
 
 
 w 
 
 605 ,S 
 
 3 
 
 on . 
 
 8 
 
 K5-S 
 
 ^o^ 2 
 
 5 
 
 CO . 
 
 ' 
 
 *5"5 
 
 'S -w 
 
 u 
 
 5 
 
 & 
 
 
 ||li 
 
 vJ 
 
 g 
 
 & 
 
 1 
 
 |'? CO 
 
 111! 
 
 
 
 3? 
 
 a 
 
 a~- 
 
 sS^ 
 
 i 
 
 !S -" 
 
 d 
 
 a 12 . 
 
 
 l* 
 
 
 
 
 
 t-l 
 
 
 1 
 
 
 
 V 
 
 S a 
 
 S 
 
 g&flcj 
 
 o^.S.S 
 
 <o 
 
 w a 
 
 o 
 
 a 
 
 W)=3 
 
 o^'"" 1 
 
 
 80 
 
 16.07 
 
 27.61 
 
 29.88 
 
 
 80 
 
 29.72 
 
 17.30 
 
 18.89 
 
 
 90 
 
 19.76 
 
 25.43 
 
 27.43 
 
 
 90 
 
 33.41 
 
 17.15 
 
 18.70 
 
 
 100 
 
 23.45 
 
 23.90 
 
 25.73 
 
 
 100 
 
 37.10 
 
 17.02 
 
 18.56 
 
 / 
 
 80 
 
 32.02 
 
 24.04 
 
 25.68 
 
 / 
 
 80 
 
 38.28 
 
 17.60 
 
 19.09 
 
 20 5 
 
 90 
 
 37.47 
 
 23.00 
 
 24.57 
 
 15 
 
 90 
 
 42.92 
 
 17.45 
 
 18.91 
 
 ( 
 
 100 
 
 42.92 
 
 22.25 
 
 23.77 
 
 
 100 
 
 47.56 
 
 17.32 
 
 18.74 
 
 / 
 
 80 
 
 43.97 
 
 24.71 
 
 26.29 
 
 / 
 
 80 
 
 45.63 
 
 18.27 
 
 19.69 
 
 30 j 
 
 90 
 
 50.73 
 
 23.91 
 
 25.38 
 
 20 j 
 
 90 
 
 51.08 
 
 18.14 
 
 19.51 
 
 I 
 
 100 
 
 57.49 
 
 23.27 
 
 24.68 
 
 
 100 
 
 56.53 
 
 18.02 
 
 19.36 
 
 
 80 
 
 53.25 
 
 25.76 
 
 27.17 
 
 t 
 
 80 
 
 57.57 
 
 19.91 
 
 21.25 
 
 
 90 
 
 61.01 
 
 25.03 
 
 26.35 
 
 30 j 
 
 90 
 
 64.32 
 
 19.78 
 
 21.06 
 
 
 too 
 
 68.76 
 
 24.47 
 
 25.73 
 
 
 100 
 
 71.08 
 
 19.67 
 
 20.93 
 
 
 80 
 
 60.44 
 
 26.99 
 
 28.38 
 
 
 80 
 
 66.85 
 
 21.36 
 
 22.56 
 
 
 90 
 
 68.96 
 
 26.32 
 
 27.62 
 
 
 90 
 
 74.60 
 
 21.24 
 
 22.41 
 
 
 100 
 
 77.48 
 
 25.78 
 
 26.99 
 
 
 100 
 
 82.36 
 
 21.13 
 
 22.24 
 
 TABLE No. 2 
 FEED-WATER CONSUMPTION FOR COMPOUND CONDENSING ENGINES. 
 
 Cut-off 
 per cent. 
 
 Initial Pressure above 
 Atmosphere. 
 
 Mean Effective Press. 
 
 Feed-water 
 Required 
 per I.H.P. per 
 Hour, Ib. . 
 
 h.p.Cyl.,lb.|l.p.Cyl.,lb. 
 
 h.p.Cyl.,lb.|l.p.Cyl.,lb. 
 
 ! 
 
 80 
 100 
 120 
 
 4.0 
 7.3 
 11.0 
 
 11.67 
 15.33 
 
 18.54 
 
 2.65 
 3.87 
 5.23 
 
 16.92 
 15.00 
 13.86 
 
 I 
 
 80 
 100 
 120 
 
 4.3 
 8.1 
 12.1 
 
 26.73 
 33.13 
 39.29 
 
 5.48 
 7.56 
 9.74 
 
 14.60 
 13.67 
 13.09 
 
 i 
 
 80 
 100 
 120 
 
 4.6 
 8.5 
 11.7 
 
 37.61 
 46.41 
 56.00 
 
 7.48 
 10.10 
 12.26 
 
 14.99 
 14.21 
 13.87 
 
 Sizes and Calculated Performances of Vertical High-speed 
 EngineSo Thfc following tables are taken from an old circular, describ- 
 ing: the engines made by the Lake Erie Engineering Works, Buffalo, N. Y. 
 The engines are fair representatives of the type largely used for driving 
 dynamos directly without belts. The tables were calculated by E F 
 Williams, designer of the engines. They are here somewhat abridged to 
 save space. 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 089 
 
 Simple Engines Non-condensing. 
 
 li 
 
 T:- 
 
 rt W 
 
 Is 
 
 Q'~ 
 
 71/2 
 81/2 
 JOV 2 
 
 l>l/ 2 
 16 
 18 
 
 22 
 241/2 
 27 
 
 
 
 .2 
 cT 
 
 rX 
 
 2 
 
 DQ 
 
 Revs, per 
 Minute. 
 
 H.P.w 
 
 cutting 
 at 1/5 str 
 
 ten 
 off 
 oke. 
 
 H.P. when 
 cutting off 
 at 1/4 stroke. 
 
 H.P. when 
 cutting off 
 at 1/3 stroke 
 
 Dimen- 
 sions of 
 Wheels, 
 dia. face 
 
 Steam-pipe, 
 ins. 
 
 Exhaust- 
 pip*. 1 
 
 70 
 Ibs. 
 
 80 
 Ibs. 
 
 90 
 Ibs. 
 
 70 
 
 Ibs. 
 
 80 
 Ibs. 
 
 90 
 
 Ibs. 
 
 70 
 Ibs. 
 
 80 
 Ibs. 
 
 90 
 
 Ibs. 
 
 Ft. 
 
 In. 
 
 10 
 12 
 14 
 16 
 18 
 20 
 24 
 28 
 32 
 34 
 
 370 
 318 
 277 
 246 
 222 
 181 
 158 
 138 
 120 
 112 
 
 20 
 27 
 41 
 53 
 66 
 95 
 119 
 179 
 221 
 269 
 
 25 
 32 
 49 
 64 
 80 
 115 
 144 
 216 
 267 
 325 
 
 30 
 39 
 60 
 77 
 96 
 138 
 173 
 26 1 
 322 
 392 
 
 26 
 34 
 52 
 67 
 84 
 120 
 151 
 227 
 281 
 342 
 
 31 
 
 41 
 62 
 81 
 100 
 144 
 181 
 272 
 336 
 409 
 
 36.5 
 
 36 
 
 47 
 71 
 93 
 116 
 166 
 208 
 313 
 386 
 470 
 
 42 
 
 32 
 41 
 63 
 82 
 102 
 146 
 183 
 276 
 340 
 414 
 
 37 
 
 48 
 74 
 96 
 120 
 172 
 215 
 324 
 400 
 487 
 
 43 
 56 
 85 
 
 Hi 
 
 198 
 248 
 373 
 460 
 560 
 
 4 
 
 41/9 
 
 5'9" 
 6'8" 
 
 71/2 
 8'4" 
 10 
 
 n'8" 
 
 13' 4" 
 
 14' 2* 
 
 4 
 
 61/2 
 
 :i 
 
 15 
 19 
 28 
 34 
 41 
 
 18 
 
 31/2 
 4 
 
 % 
 
 6 
 
 7 
 8 
 
 3 
 31/2 
 
 4V2 
 
 6 
 7 
 8 
 9 
 10 
 
 M.E.P.,lb3. ... 
 Ratio of exp.... 
 
 Term'! press, 
 (about), Ibs. . 
 Cyl. cond'n, %- 
 Steam per I. H. P. 
 hour, Ibs 
 
 2.4 
 
 29 
 
 35 
 
 30.5 
 
 37 
 
 43.5 
 
 50 
 
 Note. The 
 nominal-power 
 rating of the en- 
 gines is at 80 Ibs. 
 gauge pressure, 
 steam cut-off at 
 1/4 stroke. 
 
 5 
 
 4 
 
 3 
 
 17.9 
 26 
 
 32.9 
 
 20 
 26 
 
 30 
 
 22.3 
 26 
 
 27.4 
 
 22.4 
 24 
 
 31.2 
 
 25 
 24 
 
 29.0 
 
 27.6 
 24 
 
 27.9 
 
 29.8 
 21 
 
 32 
 
 33.3 
 21 
 
 31.4 
 
 36.8 
 21 
 
 30 
 
 Compound Engines Non-condensing High-pressure Cylinder 
 and Receiver Jacketed. 
 
 Diam. 
 
 Cylinder, 
 inches. 
 
 Stroke, inches. 
 
 Revolutions per 1 
 Minute. | 
 
 H.P., cutting off 
 at 1/4 Stroke 
 in h.p. Cylinder. 
 
 H.P., cutting off 
 at 1/3 Stroke 
 in h.p. Cylinder. 
 
 H.P., cutting off 
 at 1/2 Stroke 
 in h.p. Cylinder. 
 
 Cyls. 
 31/s: 1. 
 
 Cy!s. 
 4i/ 2 : 1. 
 
 Cyls. 
 3l/ 3 : 1. 
 
 Cyls. 
 4i/ 2 : 1. 
 
 Cyls. 
 31/ 3 : 1. 
 
 Cyk 
 
 41/ 2 : *. 
 
 cm 
 
 W 
 
 Pk 
 
 w 
 
 ti 
 ^ 
 
 80 
 Ibs. 
 
 90 
 
 Ibs. 
 
 130 
 Ibs. 
 
 150 
 Ibs. 
 
 80 
 
 Ibs. 
 
 90 
 
 Ibs. 
 
 130 
 
 Ibs. 
 
 150 
 Ibs. 
 
 80 
 
 Ibs. 
 
 90 
 
 Ibs. 
 
 130 
 Ibs. 
 
 150 
 Iba. 
 
 53/4 
 63/ 8 
 73 /4 
 
 J0 2 V 2 
 
 ir /2 
 
 18 
 20 
 
 241/ 2 
 281/2 
 
 61/2 
 7 1/2 
 
 uv, 
 
 !?$ 
 
 l81/ 2 
 
 2% 
 
 I? 1 * 
 
 12 
 131/2 
 16l /2 
 
 gV2 
 
 281/.> 
 
 ^ 
 
 43 
 52 
 60 
 
 10 
 12 
 14 
 16 
 18 
 20 
 24 
 28 
 32 
 34 
 42 
 48 
 
 370 
 
 318 
 277 
 246 
 222 
 185 
 158 
 138 
 120 
 112 
 93 
 80 
 
 7 
 9 
 14 
 18 
 26 
 32 
 43 
 57 
 74 
 94 
 138 
 180 
 
 15 
 19 
 
 28 
 37 
 53 
 65 
 88 
 118 
 152 
 194 
 285 
 374 
 
 19 
 24 
 36 
 47 
 68 
 84 
 112 
 151 
 194 
 249 
 365 
 477 
 
 32 
 40 
 60 
 
 78 
 112 
 139 
 186 
 249 
 321 
 412 
 603 
 789 
 
 23 
 29 
 43 
 57 
 81 
 100 
 135 
 180 
 232 
 297 
 436 
 570 
 
 31 
 39 
 
 58 
 76 
 109 
 135 
 181 
 242 
 312 
 400 
 587 
 767 
 
 35 
 45 
 67 
 87 
 125 
 154 
 206 
 277 
 357 
 457 
 670 
 877 
 
 46 
 59 
 87 
 114 
 164 
 202 
 271 
 363 
 468 
 601 
 880 
 1151 
 
 44 
 56 
 83 
 109 
 156 
 192 
 258 
 346 
 446 
 572 
 838 
 1096 
 
 55 
 70 
 104 
 136 
 195 
 241 
 323 
 433 
 558 
 715 
 1048 
 1370 
 
 64 
 81 
 121 
 158 
 226 
 279 
 374 
 502 
 647 
 829 
 1215 
 1589 
 
 79 
 101 
 159 
 196 
 231 
 346 
 464 
 623 
 803 
 1030 
 1508 
 1973 
 
 Mean eff. pressure, Ibs.. 
 Ratio of expansion 
 
 Cyl. condensation, % . . 
 Ter. pres. (abt.), Ibs... 
 Loss from expanding 
 below atmosphere, % 
 St.perl.H.P.hour.lbs. 
 
 3.3 
 
 6.8 
 
 8.7 
 
 14.4 
 
 10.4 
 
 14.0 
 
 16 
 
 21 
 
 20 
 
 25 
 
 29 
 
 36 
 
 131/2 
 
 181/4 
 
 101/4 
 
 133/4 
 
 63/ 4 
 
 91/4 
 
 14 
 
 7.3 
 
 34 
 55 
 
 14 
 7.7 
 
 15 
 42 
 
 16 
 7.9 
 
 17. 
 47 
 
 16 
 9 
 
 3 
 
 29 
 
 12 
 9.2 
 
 5 
 33.3 
 
 12 
 10.4 
 
 
 27.7 
 
 13 
 10.5 
 
 
 
 28.7 
 
 13 
 12 
 
 
 
 25.4 
 
 10 
 14 
 
 
 30 
 
 10 
 15.5 
 
 
 26.2 
 
 11 
 14.6 
 
 
 21 
 
 It 
 
 17.8 
 
 
 
 20 
 
990 
 
 THE STEAM-ENGINE. 
 
 Compound Engines Condensing Steam-jacketed. 
 
 Diam. 
 Cylinder, 
 inches. 
 
 Stroke, inches. 
 
 t-c 
 0) 
 
 ft 
 
 GO 
 | 
 
 "3 "5 
 
 11 
 
 rt 
 
 370 
 318 
 277 
 246 
 222 
 185 
 158 
 138 
 120 
 112 
 93 
 80 
 
 H.P. when 
 cutting off at 
 1/4 Stroke 
 inh.p. Cylinder. 
 
 H.P. when 
 cutting off at 
 1/3 Stroke 
 inh.p. Cylinder. 
 
 H.P. when 
 cutting off at 
 1/2 Stroke 
 inh.p. Cylinder. 
 
 Ratio, 
 3V3: 1. 
 
 Ratio, 
 4: 1. 
 
 Ratio, 
 31/s: 1. 
 
 Ratio, 
 4: 1. 
 
 Ratio, 
 31/3: 1. 
 
 Ratio, 
 4: 1. 
 
 fc 
 W 
 
 ^ 
 
 w 
 
 ^ 
 
 H-i 
 
 80 
 Ibs. 
 
 110 
 
 Ibs. 
 
 115 
 
 Ibs. 
 
 125 
 
 Ibs. 
 
 80 
 
 Ibs. 
 
 110 
 
 Ibs. 
 
 115 
 
 Ibs. 
 
 125 
 
 Ibs. 
 
 80 
 
 Ibs. 
 
 110 
 Ibs. 
 
 115 
 Ibs. 
 
 125 
 Ibs. 
 
 106 
 134 
 200 
 261 
 374 
 462 
 619 
 830 
 1070 
 1373 
 2012 
 2632 
 
 6 
 
 61/2 
 8V4 
 
 91/2 
 11 
 
 12V2 
 14 
 17 
 19 
 21 
 26 
 30 
 
 61/2 
 7l /2 
 
 101/2 
 
 131/2 
 151/2 
 
 181/2 
 201/ 2 
 221/2 
 2 f/2 
 
 12 
 131/2 
 |6 V2 
 
 If /2 
 281/ 2 
 
 ? 8 i/2 
 
 43 
 52 
 60 
 
 10 
 12 
 14 
 16 
 18 
 20 
 24 
 28 
 32 
 34 
 42 
 48 
 
 44 
 56 
 83 
 109 
 156 
 192 
 258 
 346 
 446 
 572 
 838 
 1096 
 
 59 
 76 
 112 
 147 
 210 
 260 
 348 
 467 
 602 
 772 
 1131 
 1480 
 
 53 
 67 
 100 
 131 
 187 
 231 
 310 
 415 
 535 
 686 
 1006 
 1316 
 
 62 
 78 
 116 
 152 
 218 
 269 
 361 
 484 
 624 
 801 
 1174 
 1534 
 
 55 
 70 
 104 
 136 
 195 
 241 
 323 
 433 
 558 
 715 
 1048 
 1370 
 
 70 
 90 
 133 
 174 
 250 
 308 
 413 
 554 
 .714 
 915 
 1341 
 1757 
 
 68 
 87 
 129 
 169 
 242 
 298 
 400 
 536 
 691 
 887 
 1299 
 1699 
 
 75 
 95 
 141 
 185 
 265 
 327 
 439 
 588 
 758 
 972 
 1425 
 1863 
 
 70 
 90 
 133 
 174 
 250 
 308 
 413 
 554 
 714 
 915 
 1341 
 1757 
 
 97 
 123 
 183 
 239 
 343 
 423 
 568 
 761 
 981 
 1258 
 1844 
 2411 
 
 95 
 120 
 179 
 234 
 335 
 414 
 555 
 744 
 959 
 1230 
 1801 
 2356 
 
 Mean eff . press., Ibs 
 Ratio of expansion 
 
 Cyl. condensation, %. . . 
 St. per I.H.P. hour, Ibs. 
 
 20 
 
 27 
 
 24 
 
 28 
 
 25 
 
 32 
 
 31 
 
 34 
 
 32 
 
 44 
 
 43 
 
 48 
 
 131/2 
 
 161/4 
 
 10 
 
 121/4 
 
 63/4 
 
 81/4 
 
 18 I 18 
 17.3)16.6 
 
 20 
 16.6 
 
 20 
 15.2 
 
 15 
 17.0 
 
 15 
 16.4 
 
 18 
 16.3 
 
 18 
 15.8 
 
 12 
 17.5 
 
 12 
 17.0 
 
 14 
 16.8 
 
 14 
 16.C 
 
 Triple-expansion Engines, Non-condensing Receiver only 
 Jacketed. 
 
 Diameter 
 Cylinders, 
 inches. 
 
 I 
 o 
 r, 
 
 1 
 
 1 
 
 Horse-power 
 when cutting 
 off at 42% of 
 Stroke in First 
 
 Horse-power 
 when cutting 
 off at 50% of 
 Stroke in First 
 
 Horse-power 
 when cutting 
 off at 67% of 
 Stroke in First 
 
 
 oT 
 
 
 Cylinder. 
 
 Cylinder. 
 
 Cylinder. 
 
 
 
 
 n 
 
 O 
 
 
 
 
 
 
 
 H.P. 
 
 T.P. 
 
 L.P. 
 
 
 0)*jH 
 
 180 Ibs. 
 
 200 Ibs. 
 
 180 Ibs. 
 
 200 Ibs. 
 
 180 Ibs. 
 
 200 Ibs. 
 
 
 
 
 'Jl 
 
 PH 
 
 
 
 
 
 
 
 43/4 
 
 71/2 
 
 12 
 
 10 
 
 370 
 
 55 
 
 64 
 
 70 
 
 84 
 
 95 
 
 108 
 
 5V2 
 
 81/2 
 
 131/7 
 
 12 
 
 318 
 
 70 
 
 81 
 
 90 
 
 106 
 
 120 
 
 137 
 
 61/2 
 
 
 J61/ ? 
 
 14 
 
 277 
 
 104 
 
 121 
 
 133 
 
 158 
 
 179 
 
 204 
 
 71/2 
 
 12 
 
 19 
 
 16 
 
 246 
 
 136 
 
 158 
 
 174 
 
 207 
 
 234 
 
 267 
 
 9 
 
 141/ 2 
 
 221/3 
 
 18 
 
 222 
 
 195 
 
 226 
 
 250 
 
 296 
 
 335 
 
 382 
 
 10 
 
 16 
 
 25 
 
 ZO 
 
 185 
 
 241 
 
 279 
 
 308 
 
 366 
 
 414 
 
 471 
 
 111/2 
 
 18 
 
 281/2 
 
 24 
 
 158 
 
 323 
 
 374 
 
 413 
 
 490 
 
 555 
 
 632 
 
 13 
 
 22 
 
 33l/ ? 
 
 28 
 
 138 
 
 433 
 
 502 
 
 554 
 
 657 
 
 744 
 
 848 
 
 15 
 
 241/ 2 
 
 38 
 
 32 
 
 120 
 
 558 
 
 647 
 
 714 
 
 847 
 
 959 
 
 1093 
 
 17 
 
 27 
 
 43 
 
 34 
 
 112 
 
 715 
 
 829 
 
 915 
 
 1089 
 
 1230 
 
 1401 
 
 20 
 
 33 
 
 52 
 
 42 
 
 93 
 
 1048 
 
 1215 
 
 1341 
 
 1592 
 
 1801 
 
 2053 
 
 231/ 2 
 
 38 
 
 60 
 
 48 
 
 80 
 
 1370 
 
 1589 
 
 1754 
 
 2082 
 
 2356 
 
 2685 
 
 Mean eff. press., Ibs 
 
 25 
 
 29 
 
 32 
 
 38 
 
 43 
 
 49 
 
 No. of expansions 
 
 
 
 
 
 
 
 16 
 
 13 
 
 10 
 
 Cyl. condensation, % 
 
 14 
 
 12 
 
 10 
 
 Steam p. I.H.P.p.hr., Ibs. 
 
 20.76 
 
 19J6 
 
 19.25 
 
 17.00 
 
 17.89 
 
 17.20 
 
 Lbs.coalat81b.evap.,lbs. 
 
 2.59 
 
 2.39 
 
 2.40 
 
 2.12 
 
 2.23 
 
 2.15 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 991 
 Triple-expansion Engines Condensing Steam- jacketed. 
 
 
 
 IH 
 
 Horse- 
 
 Horse- 
 
 Horse- 
 
 Horse- 
 
 Diameter 
 Cylinders, 
 inches. 
 
 g 
 
 1 
 
 * 
 
 lutions p 
 lute. 
 
 power when 
 cutting off 
 at 1/4 Stroke 
 in First Cyl. 
 
 power when 
 cutting off 
 at 1/3 Stroke 
 in First Cyl. 
 
 power when 
 cutting off 
 at 1/2 Stroke 
 in First Cyl. 
 
 power when 
 cutting off 
 at 3/4 Stroke 
 in First Cyl. 
 
 AH 
 
 fl| 
 
 PH 
 
 2 
 
 o.a 
 ^ 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 W 
 
 
 ^ 
 
 CO 
 
 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 43/ 4 
 
 ?!/> 
 
 12 
 
 10 
 
 370 
 
 35 
 
 42 
 
 48 
 
 44 
 
 53 
 
 59 
 
 57 
 
 72 
 
 84 
 
 81 
 
 97 
 
 110 
 
 51/J 
 
 !/> 
 
 131/9 
 
 12 
 
 318 
 
 45 
 
 53 
 
 62 
 
 56 
 
 67 
 
 76 
 
 73 
 
 92 
 
 107 
 
 104 
 
 123 
 
 140 
 
 6l/o 
 
 101/9 
 
 161/9 
 
 14 
 
 277 
 
 67 
 
 79 
 
 92 
 
 83 
 
 100 
 
 112 
 
 108 
 
 137 
 
 159 
 
 154 
 
 183 
 
 208 
 
 71/2 
 
 12 
 
 19 
 
 16 
 
 246 
 
 87 
 
 103 
 
 120 
 
 109 
 
 131 
 
 147 
 
 141 
 
 180 
 
 208 
 
 201 
 
 239 
 
 272 
 
 9 
 
 141/9 
 
 221/9 
 
 18 
 
 222 
 
 125 
 
 148 
 
 172 
 
 156 
 
 187 
 
 211 
 
 203 
 
 257 
 
 299 
 
 289 
 
 343 
 
 390 
 
 10 
 
 16 
 
 25 
 
 20 
 
 185 
 
 154 
 
 183 
 
 212 
 
 192 
 
 7.3 1 
 
 7.60 
 
 250 
 
 317 
 
 368 
 
 356 
 
 423 
 
 481 
 
 1U/9 
 
 18 
 
 281/9 
 
 24 
 
 158 
 
 206 
 
 245 
 
 284 
 
 258 
 
 310 
 
 348 
 
 335 
 
 426 
 
 494 
 
 477 
 
 568 
 
 645 
 
 13 
 
 22 
 
 331/9 
 
 28 
 
 138 
 
 277 
 
 329 
 
 381 
 
 346 
 
 415 
 
 467 
 
 450 
 
 571 
 
 663 
 
 640 
 
 761 
 
 865 
 
 15 
 
 241/9 
 
 38 
 
 32 
 
 120 
 
 357 
 
 424 
 
 491 
 
 446 
 
 535 
 
 602 
 
 580 
 
 736 
 
 854 
 
 825 
 
 981 
 
 1115 
 
 n 
 
 27 
 
 43 
 
 34 
 
 112 
 
 458 
 
 543 
 
 629 
 
 572 
 
 686 
 
 777. 
 
 744 
 
 944 
 
 1095 
 
 1058 
 
 1258 
 
 1430 
 
 20 
 
 33 
 
 52 
 
 42 
 
 93 
 
 670 
 
 796 
 
 922 
 
 838 
 
 1006 
 
 1131 
 
 1089 
 
 1383 
 
 1605 
 
 1551 
 
 1844 
 
 2096 
 
 231/2 
 
 38 
 
 60 
 
 .48 
 
 80 
 
 877 
 
 1041 
 
 1206 
 
 1096 
 
 1316 
 
 1480 
 
 1424 
 
 1808 
 
 2099 
 
 2028 
 
 2411 
 
 2740 
 
 Mean eff. press., Ibs 
 
 16 
 
 19 
 
 22 
 
 20 
 
 24 
 
 27 
 
 26 
 
 33 
 
 38.3 
 
 37 
 
 44 
 
 50 
 
 No. of expansions 
 
 26.8 
 
 20.1 
 
 13.4 
 
 8 9 
 
 Cyl. condensation, % . . 
 
 
 
 
 
 19 
 
 19 
 
 19 
 
 16 
 
 16 
 
 16 
 
 12 
 
 12 
 
 12 
 
 8 
 
 8 
 
 8 
 
 St. p. I.H.P. p. hr., Ibs.. 
 
 14 7 
 
 n 9 
 
 13 3 
 
 14 3 
 
 13 9 
 
 13 2 
 
 14 3 
 
 13 6 
 
 13 
 
 15 7 
 
 14 9 
 
 14 7 
 
 Coal at 8 Ibs. evap., Ibs- 
 
 1.8 
 
 1.73 
 
 1.66 
 
 1.78 
 
 1.7 
 
 41.65 
 
 1.78 
 
 1.70 
 
 1.62 
 
 1.96 
 
 1.86 
 
 1.72 
 
 The Willans Law. Total Steam Consumption at Different Loads. 
 
 Mr. Willans found with his engine that when the total steam consump- 
 tion at different loads was plotted as ordinates, the loads being abscissas, 
 the result would be a straight inclined line cutting the axis of ordinates at 
 some distance above the origin of coordinates, this distance representing 
 the steam consumption due to cylinder condensation at zero load. This 
 statement applies generally to throttling engines, and is known as the 
 Willans law. It applies also approximately to automatic cut-off engines 
 of the Corliss, and probably of other types, up to the most economical 
 load. In Mr. Barrus's book there is a record of six tests of a 16 X 42-in. 
 Corliss twin-cylinder non-condensing engine, which gave results as follows: 
 
 I.H.P... 37 100 146 222 250* 287 342 
 
 Feed-water per I.H.P. hour. 73.63 38.28 31.47 25.83 25.0* 25.39 25.91 
 
 Total feed-water per hour... 2724 3825 4595 5734 6250 7287 8861 
 
 * Interpolated from the plotted curve. 
 
 The first five figures in the last line plot in a straight line whose equa- 
 tion is y = 2122 -I- 16.55 H.P., and a straight line through the plotted 
 position of the last two figures has the equation y = 28.62 H.P. 927. 
 These two lines cross at 253 H.P., which is the most economical load, the 
 water rate being 24.96 Ibs. and the total feed 6314 Ibs. . The figure 2122 
 represents the constant loss due to cylinder condensation, which is just 
 over one-third of the total feed-water at the most economical load. 
 
 In Geo. H. Barrus's book on "Engine Tests " there is a diagram of 
 condensation and leakage in tight or fairly tight simple engines using sat- 
 urated steam. The average curve drawn through the several observations 
 shows the condensation and leakage to be about as follows for different 
 percentages of cut-off: 
 
 Cut-off, % of stroke = 1 5 10 15 20 
 
 Condens. and leakage, % = p. . . 60 43 35 29 
 c = IX p -4- (100 - p) = 7.5 7.5 8 8.2 
 
 25 30 35 42 
 24 20 17 15 
 
 7.9 7.5 7.2 7.4 
 
 The figures in the last line represent the condensation and leakage as 
 a percentage of the volume of the stroke of the piston, that is, in the same/ 
 
992 THE STEAM-ENGINE. 
 
 terms as the first line, instead of as a percentage of the total steam sup- 
 plied, in which terms the figures of the second line afe expressed. They 
 indicate that the amount of cylinder condensation is nearly a constant 
 quantity for a given engine with a given steam pressure and speed, what- 
 ever may be the point of cut-off. 
 
 Economy of Engines under Varying Loads. (From Prof. W. C. 
 Unwin's lecture before the Society of Arts, London, 1892.) The general 
 result of numerous trials with large engines was that with a constant load an 
 indicated horse-power should be obtained with a consumption of 11/2 Ibs. 
 of coal per I.H.P. for a condensing engine, and 13/4 Ibs. for a non-conden- 
 sing engine, corresponding to about 13/4 Ibs. to 2 1/8 Ibs. per effective H. P. 
 
 In electric-lighting stations the engines work under a very fluctuating 
 load, and the results are far more unfavorable. An excellent Willans 
 non-condensing engine, which on full-load trials worked with under 
 2 Ibs. per effective H.P. hour, in the ordinary daily working of the station 
 used 71/2 Ibs. in 1886, which was reduced to 4.3 Ibs. in 1890 and 3.8 Ibs. in 
 1891 . Probably in very f ew cases were the engines at electric-light stations 
 working under a consumption of 41/2 Ibs. per effective H.P. hour. In the 
 case of small isolated motors working with a fluctuating load, still more 
 extravagant results were obtained. 
 
 At electric-lighting stations the load factor, viz., the ratio of the average 
 load to the maximum, is extremly small, and the engines worked under 
 very unfavorable conditions, which largely accounted for the excessive 
 fuel consumption at these stations. 
 
 In steam-engines the fuel consumption has generally been reckoned on 
 the indicated horse-power. At full-powet trials this w r as satisfactory 
 enough, as the internal friction is then usually a small fraction of the total. 
 
 Experiment has, however, shown that the internal friction is nearly 
 constant, and hence, when the engine is lightly loaded, its mechanical 
 efficiency is greatly reduced. At full load small engines have a mechan- 
 ical efficiency of 0.8 to 0.85, and large engines might reach at least 0.9, 
 but if the internal friction remained constant this efficiency would be 
 much reduced at low powers. Thus, if an engine working at 100 I.H.P. 
 had an efficiency of 0.85, then when the I.H.P. fell to 50 the effective H.P. 
 would be 35 H.P. and the efficiency only 0.7. Similarly, at 25 H.P. the 
 effective H.P. would be 10 and the efficiency 0.4. 
 
 Experiments on a Corliss engine at Creusot gave the following results: 
 
 Effective power at full load 1.0 0.75 0.50 0.25 0.125 
 
 Condensing, mechanical efficiency . 82 0.79 0.74 . 63 . 48 
 
 Non-condensing, mechanical efficiency. . 86 0.83 . 78 . 67 . 52 
 
 Steam Consumption of Engines of Various Sizes. W. C. Unwin 
 (Cassier's Magazine, 1894) gives a table showing results of 49 tests of 
 engines of different types. In non-condensing simple engines, the steam 
 consumption ranged from 65 Ibs. per hour in a 5-horse-power engine to 22 
 Ibs. in a 134-H.P. Harris-Corliss engine. In non-condensing compound 
 engines, the only type tested was the Willans, which ranged from 27 Ibs. 
 in a 10-H.P. slow-speed engine, 122 ft. per minute, with steam-pressure 
 of 84 Ibs., to 19.2 Ibs. in a 40-H.P. engine, 401 ft. per minute, with steam- 
 pressure 165 Ibs. A Willans triple-expansion non-condensing engine, 
 39 H.P., 172 Ibs. pressure, and 400 ft. piston speed per minute, gave a 
 consumption of 18.5 Ibs. In condensing engines, nine tests of simple 
 engines gave results ranging only from 18.4 to 22 Ibs. In compound- 
 condensing engines over 100 H.P., in 13 tests the range is from 13.9 to 
 20 Ibs. In three triple-expansion engines the figures are 11.7, 12.2, and 
 12.45 Ibs., the lowest being a Sulzer engine of 360 H.P. In marine com- 
 pound engines, the Fusiyama and Colchester, tested by Prof. Kennedy, 
 gave steam C9nsumption of 21.2 and 21.7 Ibs.; and the Meteor and Tartar 
 triple-expansion engines gave 15.0 and 19.8 Ibs. 
 
 Taking the most favorable results which can be regarded as not excep- 
 tional it appears that in test trials, with constant and full load, the ex- 
 penditure of steam and coal is about as follows: 
 
 Ibs. Per I.H.P. hour. Per Effective H.P. hr. 
 Kind of Engine. Co ^ " steam,' 'Coal, Steam,' 
 
 Non-condensing 1.80 16.5 2.00 18.0 
 
 Condensing 1.50 13,5 1.75 15. 9 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 993 
 
 These may be regarded as minimum values, rarely surpassed by the 
 most efficient machinery, and only reached with very good machinery in 
 the favorable conditions of a test trial. 
 
 Small Engines and Engines with Fluctuating Loads are usually 
 very wasteful of fuel. The following figures, illustrating their low ^econ- 
 omy, are given by Prof. Unwin, Cassiw's Magazine, 1894. Small engines 
 in workshops in Birmingham, Eng. 
 
 Probable I.H.P. at full 
 load 
 
 Average I.H.P. during 
 observation 
 
 Coal per I.H.P. per hour 
 
 during observation, Ibs. 36.0 
 
 12 45 
 
 60 
 
 2.96 7.37 8.2 
 
 45 
 8.6 
 
 75 60 60 
 23.64 19.08 20.08 
 
 21.25 22.61 18.13 11.68 9.53 8.50 
 
 It is largely to replace such engines as the above that power will be 
 distributed from central stations. 
 
 Tests at Royal Agricultural Society's'show at Plymouth, Eng. Engi- 
 neering, June 27, 1890. 
 
 Rated 
 H.P. 
 
 Com- 
 pound or 
 Simple. 
 
 Diam. of 
 Cylinders. 
 
 Stroke, 
 ins. 
 
 Max. 
 
 Steam- 
 pressure. 
 
 Per Brake H.P. 
 per hour. 
 
 3 
 
 ce - o 
 a 
 
 h.p. 
 
 l.p. 
 
 Coal. 
 
 Water. 
 
 5 
 3 
 2 
 
 simple 
 compound 
 simple 
 
 7 
 3 
 
 41/2 
 
 "6" 
 
 10 
 6 
 
 7V2 
 
 75 
 110 
 
 75 
 
 12.12 
 4.82 
 11.77 
 
 78.1 Ibs. 
 42.03 " 
 89 9 " 
 
 6. lib. 
 8.72 " 
 7.64" 
 
 Steam-consumption, of Engines at Various Speeds. (Profs. Den- 
 ton and Jacobus, Trans. A. S. M. E., x, 722.) 17 X 30 in. engine, 
 non-condensing, fixed cut-off, Meyer valve. (From plotted diagrams.) 
 
 Revs, per min . . 
 1/8 cut-off, Ibs. . . 
 1/4 cut-off, Ibs. . . 
 1/2 cut-off, Ibs. . . 
 
 8 12 16 20 
 39 35 32 30 
 39 34 31 29.5 
 39 36 34 33 
 
 24 
 
 29.3 
 
 29 
 
 32 
 
 32 
 
 29 
 
 28.4 
 30.8 
 
 40 
 
 28.7 
 
 28 
 
 29.8 
 
 28.5 
 27.5 
 29.2 
 
 56 72 88 
 
 28.3 28 27.7 
 
 27.1 26.3 25.6 
 
 28.8 28.7 
 
 Steam-consumption of same engine ; fixed speed, 60 revs, per minute. 
 
 Varying cut-off compared with throttling-engine for same horse-powe r 
 and boiler-pressures: 
 Cut-off, fraction 
 
 of stroke 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 
 
 Steam, 90 Ibs.. . 29 27.5 27 27 27.2 27.8 28.5 
 
 Steam, 60 Ibs.. . 39 34.2 32.2 31.5 31.4 31.6 32.2 34.1 36.5 39 
 
 Throttling-engine, 7/ 8 cut-off, for corresponding horse-powers. 
 Steam, 90 Ibs.. . 42 37 33.8 31.5 29.8 , 
 Steam, 60 Ibs 50.1 49 46.8 44.6 41 ... 
 
 Some of the principal conclusions from this series of tests are as follows: 
 
 1. There is a distinct gain in economy of steam as the speed increases 
 for 1/2, i/s, and 1/4 cut-off at 90 Ibs. pressure. The loss in economy for 
 about 1/4 cut-off is at the rate of 1/1? Ib. of water per I.H.P. per hour for each 
 decrease of a revolution per minute from 86 to 26 revolutions, and at the 
 rate of 5/ 8 ib. of water below 26 revolutions. Also, at all speeds the 1/4 
 cut-off is more economical than either the 1/2 or 1/8 cut-off. 
 
 2. At 90 Ibs. boiler-pressure and above 1/3 cut-oftVto produce a given 
 H.P. requires about 20% less steam than to cut off at 7/ 8 stroke and regu- 
 late by the throttle. 
 
 3. For the same conditions with 60 Ibs. boiler-pressure, to obtain, by 
 throttling, the same mean effective pressure at 7/g cut-off that is obtained 
 by cutting off about 1/3, requires about 30% more steam than for the 
 latter condition. 
 
 Capacity and Economy of Steam Fire Engines. (Eng. News, 
 Mar. 28, 1895.) Tests of fire engines by Dexter Brackett for the Board 
 of Fire Commissioners, Boston, Mass, are tabulated on p. 994. 
 
994 
 
 THE STEAM-ENGINE. 
 
 Results of Tests of Steam Fire Engines. 
 
 No. of 
 engine. 
 
 Boiler heating 
 Surface. 
 
 s 
 
 03 - 
 
 sL 
 
 J-sl 
 
 c8 "O 
 
 y 
 
 fiisi 
 
 ^ &<s 
 
 Av. steam 
 pressure. 
 
 A v. water 
 pressure. 
 
 |j_ 
 
 *-"o"ai 
 
 18 
 
 tJ 0>t4-4 
 
 IP.O 
 
 Av. water 
 pumped per 
 min, 1 
 
 , 
 
 101 
 
 Ibs. 
 191 
 
 Ibs. 
 2 26 
 
 Ibs. 
 90 2 
 
 Ibs. 
 143 2 
 
 7 619 800 
 
 galls. 
 549 
 
 1 
 
 
 184 
 
 
 92 3 
 
 124 
 
 9*632*700 
 
 499 
 
 2 . 
 
 85 
 
 191 
 
 2 66 
 
 78 4 
 
 123 3 
 
 5900 000 
 
 535 
 
 3... 
 
 74 
 
 141 6' 
 
 3 57 
 
 75 7 
 
 113 8 
 
 5' 882' 000 
 
 482 
 
 4 
 
 86 5 
 
 138 4 
 
 2 88 
 
 71 5 
 
 136 4 
 
 8*112 900 
 
 459 
 
 5 
 
 86 
 
 163 7 
 
 
 102 7 
 
 121 2 
 
 8*736*300 
 
 449 
 
 5... 
 
 
 103 3 
 
 5 87 
 
 72 1 
 
 119 6 
 
 14 026 000 
 
 545 
 
 6 
 
 86 
 
 181 6 
 
 3 45 
 
 92 7 
 
 143 
 
 9*678*400 
 
 536 
 
 7 .. 
 
 112 
 
 117 3 
 
 4 94 
 
 68 8 
 
 119 2 
 
 10*201*600 
 
 596 
 
 8... 
 
 140 5 
 
 172 1 
 
 3 51 
 
 101 3 
 
 112 8 
 
 7*758*300 
 
 910 
 
 9 
 
 174 
 
 142 5 
 
 4 49 
 
 76 5 
 
 111 5 
 
 7*187*400 
 
 482 
 
 10 .. 
 
 225 
 
 91 1 
 
 4 22 
 
 59 
 
 102 1 
 
 6*482*100 
 
 419 
 
 10... 
 
 
 151 4 
 
 4 10 
 
 87 8 
 
 126 8 
 
 7*993*400 
 
 564 
 
 11.... 
 
 229 
 
 148 4 
 
 3 76 
 
 74 7 
 
 128 1 
 
 7 265 000 
 
 572 
 
 
 
 
 
 
 
 
 
 Nos. 1, 2, 3 and 4, Amoskeag engines; Nos. 5, 6, 7 and 8, Clapp & 
 Jones; Nos. 9, 10, 11, Silsby. . The engines all show an exceedingly high 
 rate of combustion, and correspondingly low boiler efficiency and pump 
 duty. 
 
 Economy Tests of High-speed Engines. (F. W. Dean and A. C. 
 Wood, Jour. A.S.M. E., June, 1908.) S9me of these engines had been In 
 service for a long time, and therefore their valves may not have been in 
 the best condition. The results may be taken as fairly representing the 
 economy of average engines of the type, under usual working conditions. 
 The engines were all non-condensing. The 16 X 15-in. engine was 
 vertical, the others horizontal. They were all direct-connected to gen- 
 erators. 
 
 No. of Test. 
 Size of engine, ins 
 
 Hours in service 
 
 Revs, per min 
 
 Valves ; . . . . 
 
 Generator, K.W 
 
 Steam per I.H.P.-hr. 
 Steam per K.W.-hr . . 
 
 1 
 
 15 X H 
 
 15,216 
 
 240 
 
 Iflat 
 
 100 
 
 37.2,t 36.2* 
 60.2, 58.4 
 
 2 
 
 16X15 
 20,000 
 240 
 Iflat 
 2-50 
 
 36.7,t 35.8 
 61.0 59.7 
 
 3 
 
 14 X 12 
 
 28,644 
 300 
 
 1 flat 
 
 2-40 
 
 31.7,f 32.0 
 57.1, 57.4 
 
 4 
 
 16XM 
 
 719 
 
 270 
 
 4 flat 
 
 125 
 
 37.5,* 36 7 
 54.9, 54.7 
 
 No. of Test. 
 Size of engine, ins. . . 
 
 Hours in service 
 
 Revs, per min 
 
 Valves 
 
 Generator, K.W 
 
 Steam per I.H.P.-hr.. 
 Steam per K.W.-hr. . . 
 
 5 
 
 18X18 
 
 32,000 
 
 220 
 
 1 piston 
 
 150 
 
 39.3, f 34.7,* 29.51 
 61.8, 51.8, 43.4 
 
 15X 16 
 5,600 
 250 
 
 1 piston 
 
 100 
 
 36.3,* 33.6 
 55.2, 49.4 
 
 7 
 
 12 X 18 
 
 10,800 
 
 190 
 
 f 2 flat inlet 
 \ 2 Corliss exh. 
 
 44.0, t 36.7, 34.1 
 79.3, 60.5, 53.7 
 
 * 3/4 load ; f V2 load ; $ 1 1/4 load ; 1 1/2 load ; the others full load. 
 
 Some of the conclusions of the authors from the results of these tests 
 are as follows: 
 
 The performances of the perfectly balanced flat valve engines are so 
 relatively poor as to disqualify them, unless this type of valve can be made 
 with some mechanism by which wear will not increase leakage. The four 
 valve engines, which were built to be more economical than single-valve 
 
ECONOMIC PERFORMANCE OF STEAM ENGINES. 995 
 
 engines, have utterly failed in their object. The duplication of valves 
 used in both four-valve engines simply increased the opportunity for leak- 
 age. The most economical result was obtained from a piston valve engine, 
 No. 5, heavily loaded. With the lighter loads that are comparable the 
 fiat valve engine, No. 3, surpassed No. 5 in economy. The Hat valve 
 engines give a flatter load curve than the piston valve engines. Compar- 
 ing the results of the flat valve engines, the most economical results \\ere 
 obtained from engine No. 3, which had a valve which automatically takes 
 up wear, and if it does not cut, must maintain itself tight for long periods. 
 
 From the results we are justified in thinking that most high-speed en- 
 gines rapidly deteriorate in economy. On the contrary, slower running 
 Corliss or gridiron valve engines improve in economy for some time and 
 then maintain the economy for many years. It is difficult to see that 
 the speed is the cause of this, and it must depend on the nature of the 
 valve. 
 
 The steam consumption of small single-valve high-speed engines non- 
 condensing, is not often less than 30 Ibs. per I.H.P. per hour. Two Water- 
 town engines, 10 X 12 tested by J. W. Hill for the Philadelphia Dept. of 
 Public Works in 1904, gave respectively 30.67 and 29.70 Ibs. at full load, 
 61.8 and 63.9 I.H.P., and 28.87 and 29.54 Ibs. at approximately half-load, 
 37.63 and 36.36 I.H.P. 
 
 High Piston-speed in Engines. (Proc. Inst. M. E., July, 1883, p. 
 321.) The torpedo boat is an excellent example of the advance towards 
 high speeds, and shows what can be accomplished by studying lightness 
 and strength in combination. In running at 22 1/2 knots an hour, an engine 
 with cylinders of 16 in. stroke will make 480 revolutions per minute, which 
 gives 1280 ft. per minute for piston-speed; and it is remarked that engines 
 running at that high rate work much more smoothly than at lower speeds, 
 and that the difficulty of lubrication diminishes as the speed increases. 
 
 A High-speed Corliss Engine. A Corliss engine, 20 X 42 in., has 
 been running a wire-rod mill at the Trenton Iron Co.'s works since 1877, at 
 160 revolutions or 1120 ft. piston-speed per minute (Trans. A. S. M. E., ii, 
 72). A piston-speed of 1200 ft. per min. has been realized in locomotive 
 practice. 
 
 The Limitation of Engine-speed. (Chas. T. Porter, in a paper on the 
 Limitation of Engine-speed, Trans. A. S. M. E., xiv, 806.) The practical 
 limitation to high rotative speed in stationary reciprocating steam-engines 
 is not found in the danger of heating or of excessive wear, nor, as is gen^ 
 erally believed, in the centrifugal force of the fly-wheel, nor in the tendency 
 to knock in the centers, nor in vibration. He gives two objections to very 
 high speeds: First, that "engines ought not to be run as fast as they can 
 be; " second, the large amount of waste room in the port, which is required 
 for proper steam distribution. In the important respect of economy of 
 steam, the high-speed engine has thus far proved a failure. Large gain 
 was looked for from high speed, because the loss by condensation on a 
 given surface would be divided into a greater weight of steam, but this 
 expectation has not been realized. For this unsatisfactory result we have 
 to lay the blame chiefly on the excessive amount of waste room. The 
 ordinary method of expressing fhe amount of waste room in the percentage 
 added by it to the total piston displacement, is a misleading one. It 
 should be expressed as the percentage which it adds to the length of 
 steam admission. For example, if the steam is cut off at 1/5 of the stroke, 
 
 7c added by the waste room to the total piston displacement means 
 40% added to the volume of steam admitted. Engines of four, five and 
 six feet stroke may properly be run at from 700 to 800 ft. of piston travel 
 per minute, but for ordinary sizes, says Mr. Porter, 600 ft. per minute 
 should be the limit. 
 
 British High-speed Engines. (John Davidson, Power, Feb. 9, 1909.) 
 
 The following figures show the general practice of leading builders: 
 
 J.H.P. 50 100 200 500 750 1000 1500 2000 
 
 Revs, per min.. 
 
 600-700 550-600 500 350-375 325 250 200 160-180 
 Piston speed, ft. per min. 
 
 600 650 675 750 775 800 900 1000 
 
 Rapid strides have been made during the last few years, despite the 
 
996 
 
 THE STEAM-ENGINE. 
 
 competition of the steam turbine. The single-acting type (Brotherhood, 
 Willans and others) has been superseded by double-acting engines with 
 forced lubrication. There is less wear in a high-speed than in a low-speed 
 engine. A 500-H.P. 3-crank engine after running 7 years, 12 hours per 
 day and 300 days per year, showed the greatest wear to be as follows: 
 crank pins, 0.003 in.; main bearings, 0.003 in.; eccentric sheaves, 0.015 in.; 
 crosshead pins, 0.005 in. All pins, where possible, are of steel, case- 
 hardened. High-speed engines have at least as high economy and effi- 
 ciency as any other type of engine manufactured. A triple-expansion 
 mill engine, with steam at 175 Ibs., vacuum 26 ins., superheat 100 F. t 
 gave results as shown below, [figures taken from curves in the original]. 
 
 Fraction of full 
 
 load 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 
 
 Lbs. steam per 
 
 I.H.P. hour.. 12.7 11.85 11.4 11.1 10.9 10.S 10.75 10.75 10.8 11.0 
 Lbs. steam per 
 
 B.H.P.hour.. 16.0 14.8 13.7 12.9 12.4 12.05 11.85 11.8 11,8 11.8 
 
 Owing to the fprced lubrication and throttle-governing, the economical 
 performance at light loads is relatively much better than in slow-speed 
 engines. The piston valves render the use of superheat practicable. 
 At 200 superheat the saving in steam consumption of a triple-expansion 
 engine is 26%. [A curve of the relation of superheat to saving shows 
 that the percentage of saving is almost uniformly 1.4% for each additional 
 10 from to 160 of superheat.] 
 
 The method of governing small high-speed engines is by means of a 
 plain centrifugal governor fixed to the crank shaft and acting directly 
 on a throttle. Several makers use a governor which at light loads acts 
 by throttling, and at heavy loads by altering the expansion in the high- 
 pressure cylinder. The crank-shaft governor used in America has been 
 found impracticable for high speeds, except perhaps for small engines. 
 
 Advantage of High Initial and Low Back Pressure. The theoretical 
 advantage due to the use of high steam pressure and low back pressure 
 or high vacuum is shown in the following table, which gives the effi- 
 ciencies of an ideal engine operating on the Rankine cycle with different 
 initial and back pressures, using dry saturated steam. The method 
 of calculating the Rankine cycle efficiency, and a table showing the 
 efficiencies with superheated steam will be found under Steam Turbines, 
 page 1089. 
 
 Rankine Cycle Efficiencies Saturated Steam. 
 
 Initial 
 Pressure, 
 Absolute, 
 Lb. 
 
 Vacuum, In. of Mercury. 
 
 
 
 26 
 
 27 
 
 28 
 
 28.5 | 29 
 
 Efficiencies, Per Cent. 
 
 100... 
 
 13.9 
 16.7 
 18.7 
 19.4 
 20.0 
 
 23.6 
 25.9 
 27.4 
 28.0 
 28.6 
 
 24.8 
 27.0 
 28.5 
 29.1 
 29.7 
 
 26.3 
 28.4 
 29.9 
 30.5 
 31.0 
 
 27-. 4 
 29.4 
 30.9 
 31.4 
 32.0 
 
 28.9 
 30.8 
 32.2 
 32.7 
 33.2 
 
 150 
 
 200 ... 
 
 225 
 
 250 
 
 In practice the efficiencies given in the above table cannot be reached 
 on account of the imperfection of the engine and its losses due to 
 cylinder condensation, leakage, radiation and friction. The relative 
 advantages of high pressure and low back pressure are probably pro- 
 portional to the figures in the table, provided the expansion is divided 
 into two or more stages at pressures above 100 Ib. The possibility of 
 obtaining very high vacua is limited by the temperature of the con- 
 densing water available and by the imperfections of the air pump. 
 The use of high initial pressures is limited by the safe working pressure 
 of the boiler and engine. 
 

 
 EC 
 
 ECONOMIC PERFORMANCE OF STEAM-ENGINES. 997 
 
 Comparison of the Economy of Compound and Single-cylinder Corliss 
 Condensing Engines, each expanding about Sixteen Times. (D. S. 
 
 Jacobus, Trans., A. S. M. E., xii, 943.) 
 
 The engines used in obtaining comparative results are located at 
 Stations I and II of the Pawtucket Water Co. 
 
 The tests show that the compound engine is about 30% more economical 
 than the single-cylinder engine. The dimensions of the two engines are 
 as follows: Single 20 X 48 ins.; compound 15 and 301/8 X 30 ins. The 
 steam used per I.H.P. hour was: single 20.35 Ibs., compound 13.73 Ibs. 
 
 Both of the engines are steam-jacketed, practically on the barrels only, 
 with steam at full boiler-pressure, viz., single 106.3 Ibs., compound 127.5 Ibs. 
 
 The steam-pressure in the case of the compound engine is 127 Ibs., or 
 21 Ibs. higher than for the single engine. If the steam-pressure be raised 
 this amount in the case of the single engine, and the indicator-cards be 
 increased accordingly, the consumption for the single-cylinder engine 
 would be 19.97 Ibs. per hour per horse-power. 
 
 Two-cylinder vs. Three-cylinder Compound Engine. A Wheelock 
 triple-expansion engine, built for the Merrick Thread Co., Holyoke, Mass., 
 is constructed so that the intermediate cylinder may be cut out of the 
 circuit and the high-pressure and low-pressure cylinders run as a two- 
 cylinder compound, using the same conditions of initial steam-pressure 
 and load. The diameters of the cylinders are 12, 16, and 24 13/33 ins., the 
 stroke of the first two being 36 ins. and that of the low-pressure cylinder 
 48 ins. The results of a test reported by S. M. Green and G. I. Rockwood, 
 Trans. A. S. M. E., vol. xiii, 647, are as follows: In Ibs. of dry steam used 
 per I.H.P. per hour, 12 and 2413/32 in. cylinders only used, two tests 13.06 
 and 12,76 Ibs. .average 12.91. All three cylinders used, two tests 12.67 
 and 12.90 Ibs., average 12.79. The difference is only 1%, and would 
 indicate that more than two cylinders are unnecessary in a compound 
 engine, but it is pointed out by Prof. Jacobus, that the conditions of the 
 test were especially favorable for the two-cylinder engine, and not rela- 
 tively so favorable for the three cylinders. The steam-pressure was 142 
 Ibs. and the number of expansions about 25. (See also discussion on 
 the Rockwood type of engine, Trans. A. S. M. E., vol. xvi.) 
 
 Economy of a Compound Engine. (D. S. Jacobus, Trang.A.S.M.E., 
 1903.) A Rice & Sargent engine, 20 and 40 X 42 ins., was tested with 
 steam about 149 Ibs., vacuum 27.3 to 28.8 ias. or 0.82 to 1.16 Ibs. abso- 
 lute. r.D.m. 120 to 122. with results as follows: 
 
 I.H.P 1004 853 820 627 491 340 
 
 Water per I.H.P. per hr... 12.75 12.33 12.55 12.10 13.92 14.58 
 B.T.U. per I.H.P. per min. 231.8 226.3 229.9 222.7 256.8 267.7 
 
 The Lentz Compound Engine is described in The Engineer (London), 
 July 10, 1908. It is the latest development of the reciprocating engine 
 with four double-seated poppet valves to each cylinder, each valve op^ 
 crated by a separate eccentric mounted on a lay-shaft driven by bevel- 
 gearing from the main shaft. The throw of the high-pressure steam 
 eccentrics is varied by slide-blocks which are caused to slide along the lay- 
 shaft by the action of a centrifugal inertia governor, which is also mounted 
 on the lay-shaft. No elastic packing is used in the engine, the piste n-rod 
 stuffing box being fitted with ground cast-iron rings, and the valve stems 
 being provided with grooves and ground to fit long bushings to 0.001 in. 
 Two tests of a Lentz engine built in England, 141/2 and 243/ 4 by 271/3 in., 
 gave results as follows: 
 
 Saturated steam, 170 Ibs., vacuum 26 in., I.H.P. 366, steam per I.H.P. 
 per hour 12.3 Ibs. Steam 170 Ibs. superheated 150 F., vac. 26 in., I.H.P. 
 366, steam per I.H.P. per hour, 10.4 Ibs. Revs, ner min. in both cases 
 167. Piston speed 767 ft. per min. Engines are built for speeds up to 
 900 ft. per min., and up to 350 r.p.m. The Lentz engine is built in the 
 United States by the Erie City Iron Works. 
 
 The Stumpf Uniflow Engine is a single cylinder engine with a very 
 long piston and with exhaust ports in the middle of the cylinder which 
 are uncovered as the piston travels beyond them. The inlet ports are 
 at the ends. The exhaust steam therefore does not have to flow back 
 to the ends of the cylinder in order to escape, and the cooling of the 
 ends and of the ports is thereby avoided. It is claimed that this single 
 cylinder engine gives a steam economy equal to that of a compound 
 engine. Uniflow engines are built by Ames Iron Works, Oswego, N.Y. 
 
998 
 
 THE STEAM-ENGINE. 
 
 Steam Consumption of Sulzcr Compound and Triple-expansion 
 Engines with Superheated Steam. 
 
 The figures in the table below were furnished to the author in 1902 
 by Sulzer Bros., Winterthur, Switzerland. Results of official tests: 
 
 Saturated Steam. 
 
 
 Superheated Steam. 
 
 
 
 . 
 
 
 
 r 
 
 
 
 
 . 
 
 
 
 
 
 3 
 
 -! 
 
 
 
 r' ^ 
 
 
 1 1 
 
 fo 
 
 
 
 *"" M 
 
 
 OO 
 
 
 
 
 
 
 O o 
 
 C .f. 
 
 
 
 l| 
 
 dg" 
 
 |l 
 
 * 
 
 1^ . 
 
 0) 
 
 a 
 
 'Sb 
 
 CC W 
 
 d| 
 
 S 
 
 gU 
 
 ri 
 
 gfi t 
 
 *SCL 
 
 Q> 
 
 
 \A 
 
 0) W^ 
 
 c 
 
 *sfi 
 
 0) 
 
 
 
 w 
 
 <D W^ 
 
 Sr 
 
 Hw 
 
 > M 
 
 
 W 1 "*^ 
 
 H 
 
 
 HoQ 
 
 > 
 
 
 00^^ 
 
 130 
 
 356 
 
 26.4 
 
 850 
 
 13.30 
 
 A | 
 
 132 
 122 
 
 428 
 482 
 
 26.4 
 26.6 
 
 842 
 1719 
 
 12.05 
 12.42 
 
 136 
 
 357 
 
 28 
 
 481 
 
 13.00 
 
 ) 
 
 135 
 
 547 
 
 28 
 
 515 
 
 11.32 
 
 134 
 
 356 
 
 28 
 
 750 
 
 13.10 
 
 [ B H 
 
 132 
 
 533 
 
 27.8 
 
 788 
 
 11.52 
 
 135 
 
 356 
 
 27.6 
 
 1078 
 
 14.10 
 
 i ( 
 
 134 
 
 546 
 
 27.2 
 
 1100 
 
 11.88 
 
 130 
 
 358 
 
 28.2 
 
 1076 
 
 14.10 
 
 
 132 
 
 496 
 
 28.3 
 
 1071 
 
 11.73 
 
 129 
 
 358 
 
 28 
 
 1316 
 
 14.50 
 
 [ c i 
 
 136 
 
 527 
 
 * 
 
 1021 
 
 15.37 
 
 190 
 
 397 
 
 27.2 
 
 2880 
 
 11.28 
 
 D 
 
 188 
 
 606 
 
 28 
 
 2860 
 
 8.97 
 
 196 
 
 381 
 
 26.2 
 
 3040 
 
 11.57 
 
 E 
 
 189 
 
 613 
 
 27 ' 
 
 2908 
 
 9.41 
 
 Superheated Steam. 
 
 ) ( 
 
 127 
 
 655 
 
 27.2 
 
 788 
 
 9.91f 
 
 135 1 557 
 
 26.4 
 
 519 
 
 10.80f \ F G^ 
 
 127 
 
 664 
 
 27.2 
 
 797 
 
 9.68f 
 
 135 1 554 
 
 26.4 
 
 347 
 
 10.35tl) 1 
 
 128 
 
 572 
 
 27.1 
 
 788 
 
 10.70f 
 
 A 
 B 
 C 
 D 
 
 E 
 F 
 G 
 
 Normal, H.P. 
 1500 to 1800 
 
 800 to 1000 
 
 950 to 1150 
 3000 triple expan. 
 3000 triple expan. 
 
 400 to 500 
 1000 to 1200 
 
 Cylinders, In. R.P.M. 
 
 30.5 & 49.2 X 59.1 83 
 
 24 & 40.4 X 51.2 83 
 
 26 & 42.3 X 51.2 86 
 
 32 1/4, 47 1/4, & 58 X 59 85 
 
 34, 49, & 61 X 51 83.5 
 
 17.7 & 30.5 X 35.4 110 
 
 26.9 & 47.2 X 66.9 65 
 
 * Non-condensing, t With intermediate superheating. Tempera- 
 ture of steam at entrance to low-pressure cylinder, 307 to 349 F. 
 
 Test of a Non-condensing Engine with Superheated Steam. Prof. 
 J. A. Moyer reports in Power, Dec. 2, 1913, the following results of tests 
 of a simple Lentz horizontal engine, cylinder, 191/32 in. X 2015/16 in. 
 stroke, 207 to 211 r.p.m. Steam pressure, absolute, 170.1 to 171.9 Ib. 
 Back pressure, to 0.34 in. of mercury. 
 
 Indicated horse-power ... . 162 . 7 227 . 6 282 . 1 322 . 5 
 
 Steam per I. H.P. hour, Ib 17.25 15.78 15.24 15.48 
 
 Superheat, deg. F 98.3 139.4 141.5 159.7 
 
 Saving of Steam due to Superheating. The following figures are 
 given by Power Specialty Co., makers of the Foster superheater. 
 
 A 3300 horse-power Lentz cross-compound engine having 37 i/2-in. 
 and 63-in. cylinders, 55-in. stroke, at Charlottenburg, Germany, with* 
 192-lb. gage pressure, 26-in. vacuum, 107 revs, per min., gave the follow- 
 ing steam consumption: 
 
 Temp, 
 of 
 
 Steam. 
 
 Super- 
 heat. 
 
 Load. 
 
 V4 
 
 V2 
 
 3 /4 
 
 Vi 
 
 V4 
 
 570 
 660 
 
 185F. 
 275 F. 
 
 Steam per I.H.P. hr., Ib . . . . 
 Steam per I.H.P. hr., Ib. . . . 
 
 11.1 
 
 10.6 
 
 10.1 
 9.7 
 
 9.5 
 9.0 
 
 9.2 
 8.8 
 
 9.7 
 9.2 
 
 The saving in steam effected by superheating 100 degrees, as com- 
 pared with saturated steam, is, approximately, for steam turbines, 
 10 per cent; triple-expansion engines, 12 per cent; compound engines, 
 14 per cent; simple engines, 18 per cent and over. 
 
ECi 
 
 ECONOMIC PEEFORMANCE OF STEAM-ENGINES. 999 
 
 Tests of Buckeye engines, simple, 12 X 16 in., and compound, 10 and 
 '1/2 X 16 in., with steam at 100 to 110 Ib. pressure, gave the following: 
 
 Engine. 
 
 Per 
 Cent of 
 Rated 
 Load. 
 
 Degrees of Superheat. 
 
 
 
 50 
 
 100 
 
 150 
 
 200 
 
 Lb. Steam per I.H.P. Hr. 
 
 Simple, non-condensing 
 Simple, non-condensing 
 
 30 
 50 
 100 
 100 
 100 
 
 35 
 31.5 
 
 28.5 
 
 28 
 25 ..5 
 24.0 
 
 24 
 22 
 20 
 17.5 
 14 
 
 21.5 
 19 
 18 
 15.5 
 12.5 
 
 19.5 
 17.5 
 17.5 
 14.6 
 11.5 
 
 Simple non-condensing 
 
 Compound, non-condensing 
 
 Compound, condensing 
 
 18 
 
 16.5 
 
 Steam Consumption of Different Types of Engines. 
 
 Tests of a Ridgway 4- valve non-condensing engine, 19 X 18 in., at 
 200 r.p.m. and 100 Ib. pressure, are reported in Power, June, 1909, as 
 
 7.9 
 
 9.75 
 
 10.50 
 
 11.80 
 
 follows: 
 
 Load 1/4 1/2 V4 Full H/4 
 
 Steam per I.H.P. hour. ... 30.7 24.4 23.2 23.8 | 25.4 
 
 The best result obtained at 130 Ib. pressure was 21.6 Ib.; at 115 Ib. 
 pressure, 22.6 Ib. ; and at 85 Ib. pressure, 24.3 Ib. Maintained economy 
 In this type of engine is dependent upon reduction of unnecessary over- 
 travel, properly fitted valves, valves which do not span a wide arc, close 
 approach of the movement of the valves to that of a Corliss engine, and 
 good materials. 
 
 The probable steam consumption of condensing engines of different 
 types with different pressures of steam is given in a set of curves by 
 R. H. Thurston and L. L. Brinsmade, Trans. A. S. M. E., 1897, from 
 which curves the following approximate figures are derived. 
 
 Steam pressure, absolute, Ibs. per sq. in. 
 
 250 
 Ideal Engine 
 
 (Rankine cycle) 
 Quadruple Exp. 
 
 Wastes 20% 
 Triple Exp. 
 
 Wastes 25% 
 Compound. 
 
 Wastes 33% 
 Simple Engine. 
 
 Wastes 50% 14.00 15.00 15.80 
 
 The same authors give the records of tests of a three-cylinder engine 
 at Cornell University, cylinders 9, 16 and 24 ins., 36-in. stroke, first as a 
 triple-expansion engine; second, with the intermediate cylinder omitted, 
 making a compound engine with a cylinder ratio of 7 to 1 : and third, 
 omitting the third cylinder, making a compound engine with a ratio of 
 a little over 3 to 1. The boiler pressure in the first case was 119 Ibs.. 
 in the second 115, and in the third 117 Ibs. Charts are given showing 
 the steam consumption per I.H.P. and per B.H.P. at different loads, 
 from which the following figures are taken. 
 
 Indicated Horse-power 40 60 80 100 110 120 130 
 
 Steam consumption per I.H.P. per hour. 
 
 Triple Exp 19.1 16.7 15.3 14.2 13.7 13.8 14.4 
 
 Comp. 7 to 1 . . 19.6 18.2 17.0 16.3 16. 15.8 15.8 
 
 Comp. 3 to 1 19.7 18.4 18.1 18.5 
 
 Steam consumption per B.H.P. hour. 
 
 Triple Exp 30.5 23.0 19.6 17.1 16.2 16.2 16.7 
 
 Comp. 7 to 1 26.2 21.7 19.3 18.7 18.5 18.4 18.5 
 
 Comp. 3 to 1 23.4 20.6 20. 20 
 
 The most economical performance was as follows: 
 
 Triple Comp. 7 to 1 ComD. 3 to 1 
 
 Indicated Horse-power 112.7 130.0 67.7 
 
 Steam per I.H.P. hour 13.68 15.8 18.03 
 
 400 
 
 6.95 
 
 8.75 
 
 9.25 
 
 10.50 
 
 14.00 
 
 300 
 
 7.5 
 
 9.15 
 
 9.95 
 
 11.25 
 
 15.00 
 
 200 
 8.45 
 10.50 
 11.15 
 12.70 
 16.80 
 
 150 
 9.20 
 11.60 
 12.30 
 13.90 
 18.40 
 
 100 75 50 
 
 10.50 11.40 12.9 
 
 13.0 14.0 15.8 
 
 14.0 15.1 16.7 
 
 15.6 16.9 18.S 
 
 20.4 22.7 25.2 
 
1000 THE STEAM-ENGINE. 
 
 A test of a 7500-#.P. engine, at the 59th St. Station of the Interborough 
 Rapid Transit Co., New York, is reported in Power, Feb., 1906. It is a 
 double cross compound engine, with horizontal h.p. and vertical l.p. 
 cylinders. With steam at 175 Ibs. gauge and vacuum 25.02 ins., 75 r.p.m. 
 it developed 7365 I.H.P., 5079 K.W. at switchboard. Friction and elec- 
 trical losses 417.3 K.W. Dry steam per K.W. hour 17.34 Ibs.; per I.H.P. 
 hour, 11. 96 Ibs. 
 
 A test of a Fleming; 4-valve engine, 15 and 40.5 in. diam., 27-in. stroke, 
 positive-driven Corliss valves, fly-wheel governor, is reported by B. T. 
 Allen in Trans. A. S. M. E., 1903. The following: results were obtained. 
 The speed was above 150 r.p.m. and the vacuum 26 in. 
 
 Fraction of full load about 1/6 5/8 Vio Full load 1.1 
 
 Horse-power 87.1 321.5 348.3 501.6 553.5 
 
 Steam per I:H.P. hour 14.42 13.59 12.33 12.66 12.7 
 
 Relative Economy of Compound Non-condensing Engines 
 under Variable Loads. F. M. Rites, in a paper on the Steam Dis- 
 tribution in a Form of Single-acting Engine (Trans. A.S.M. E., xiii, 537), 
 discusses an engine designed to meet the following problem: Given an 
 extreme range of conditions as to load or steam-pressure, either or both, 
 to fluctuate together or apart, violently or with easy gradations, to 
 construct an engine whose economical performance should be as good as 
 though the engine were specially designed for a momentary condition 
 the adjustment to be complete and automatic. In the ordinary non-con- 
 densing compound engine with light loads -the high-pressure cylinder is 
 frequently forced to supply all the power and in addition drag along with 
 it the low-pressure piston, whose cylinder indicates negative work. Mr. 
 Rites shows the peculiar value of a receiver of predetermined volume 
 which acts as a clearance chamber for compression in the high-pressure 
 cylinder. The Westinghouse compound single-acting engine is designed 
 upon this principle. The following results of tests of one of these engines 
 rated at 175 H.P. for most economical load are given: 
 
 WATER RATES UNDER VARYING LOADS, LBS. PER H.P. PER HOUR. 
 
 Horse-power 210 170 140 115 100 80 50 
 
 Non-condensing 22.6 21.9 22.2 22.2 22.4 24.6 28.8 
 
 Condensing 18.4 18.1 18.2 18.2 18.3 18.3 20.4 
 
 Efficiency of Non-condensing Compound Engines. (W. Lee 
 
 Church, Am. Mach., Nov. 19, 1891.) The compound engine, non-con- 
 densing, at its best performance will exhaust from the low-pressure cylin- 
 der at a pressure 2 to 6 pounds above atmosphere. Such an engine will 
 be limited in its economy to a very short range of power, for the reason 
 that its valve-motion will not permit of any great increase beyond its 
 rated power, and any material decrease below its rated power at once 
 brings the expansion curve in the low-pressure cylinder below atmos- 
 phere. In other words, decrease of load tells upon the compound engine 
 somewhat sooner, and much more severely, than upon the non-compound 
 engine. The loss commences the moment the expansion line crosses a 
 line parallel to the atmospheric line, and at a distance above it repre- 
 senting the mean effective pressure necessary to carry the frictional load 
 of the engine. When expansion falls to this point the low-pressure 
 cylinder becomes an air-pump over more or less of its stroke, the power 
 to drive which must come from the high-pressure cylinder alone. Under 
 the light loads common in many industries the low-pressure cylinder is 
 thus a positive resistance for the greater portion of its stroke. A careful 
 study of this problem revealed the functions of a fixed intermediate 
 clearance, always in communication with the high-pressure cylinder, 
 and having a volume bearing trie same ratio to that of the high-pressure 
 cylinder that the high-pressure cylinder bears to the low-pressure. Engines 
 laid down on these lines have fully confirmed the judgment of the de- 
 signers. The effect of this constant clearance is to supply sufficient steam 
 to the low-pressure cylinder under light loads to hold its expansion curve 
 up to atmosphere, and at the same time leave a sufficient clearance volume 
 in the high-pressure cylinder to permit of governing the engine on its 
 compression under light loads. 
 
 Tests of two non-condensing Corliss engines by G. H. Barrus are re- 
 ported in Power, April 27, 1909. The engines were built by Rice & 
 Sargent, One is a simple engine 22 X 30, and the other a tandern j 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1001 
 
 compound 22 and 36 X 36 ins. Both engines are jacketed in both 
 heads, and the compound engine has a reheating receiver with 0.6 sq. ft. 
 o{ brass pipes per rated H.P. (600). The guarantees were: compound 
 engine, not to exceed 19 Ibs. of steam per I. H.P. per hour, with 130 Ibs. 
 steam pressure and 1 Ib. back pressure in the exhaust pipe, and the 
 simple engine not to exceed 23 Ibs. The friction load, engine run with 
 the brushes off the generator and the field not excited, was not to exceed 
 4V2 H.P. in either engine. The results were: compound engine, 99.2 
 r.p.m., .608.3 H.P.; 18.33 Ibs. steam per I. H.P. per hour; friction load 
 3.8% of 600 H.P.; simple engine, 98.5 r.p.m.; 306.2 LH.P.; 20.98 Ibs. per 
 I.H.P. per hour; friction 3.6% of 300 H.P. 
 
 A single-cylinder engine 12 X 12 ins., made by the Buffalo Forge Co., 
 was tested by Profs. Reeve and Allen. (EL World, May 23, 1903.) 
 Some of the results were: 
 
 I.H.P 16.39 37.20 56.00 69.00 74.10 81.4 89.3 125.9* 86.42f 
 
 Water-rate... 52.3 35.3 33.3 31.9 30.6 34.6 33.1 27.6 27.5 
 
 * Steam pressure 125 Ibs. gauge, all the other tests 80 Ibs. t Con- 
 densing, other tests all non-condensing. 
 
 Effect of Water contained in Steam on the Efficiency of the 
 Steam-engine. .(From a lecture by Walter C. Kerr, before the Franklin 
 Institute, 1891.) Standard writers make little mention of the effect 
 of entrained moisture on the expansive properties of steam, but by 
 common consent rather than any demonstration they seem to agree that 
 moisture produces an ill effect simply proportional to the percentage 
 amount of its presence. That is, 5% moisture will increase the water rate 
 of an engine 5%. 
 
 Experiments reported in 1893 by R. C. Carpenter and L. S. Marks, 
 Trans. A. S. M. E., xy, in which water in varying quantity was intro- 
 duced into the steam-pipe, causing the quality of the steam to range from 
 99% to 58% dry, showed that throughout the range of qualities used the 
 consumption of dry steam per indicated horse-power per hour remains 
 practically constant, and indicated that the water was an inert quantity, 
 doing neither good nor harm. 
 
 Influence of Vacuum and Superheat on Steam Consumption. (Eng. 
 Digest, Mar., 1909.) Herr Roginsky ("Die Turbine") discusses the 
 economies effected by the use of superheat and high vacuums. 
 
 In a certain triple-expansion engine, working under good average 
 conditions, there was found a saving of approximately 6% for each 10% 
 increase in vacuum beyond 50%. 
 
 The Batulli-Tumlirz formula for superheated steam is: p (v + a) = RT. 
 in which p = steam pressure in kgs. per sq. meter, v = cubic meters in 
 1 kg. of superheated steam at pressure p t a = 0.0084, R = 46.7, and 
 T = absolute temperature in deg. C. 
 
 Using this expression, it is found that, neglecting the fuel used for 
 superheating, for each 10 C. of superheat at pressures ranging from 
 100 to 185 Ibs. per sq. in. there is an average increase of volume of 2.8%. 
 The work done by the expansion of superheated steam, as shown by 
 diagrams, is about 1.6% less for 10 of superheating, so that the net 
 saving for each 10 of superheat is 2.8 1.6 = 1.2%, approx. (0.66% 
 for each 10 F.). 
 
 Rateau's formula for the steam consumption (K) per H.P.-hr. of an 
 ideal steam turbine, in which the steam expands from pressure p\ to pa, in 
 
 K = 0.85 (6.95 - 0.92 log p 2 ) /(log P! - log p 2 \ 
 
 K being in kilograms and p\ and pz in kgs. per sq. meter. From this 
 formula the following table is calculated, the values being transformed 
 into British units. 
 
 Lbs. per 
 sq. in. 
 
 Lbs. Steam 
 at 50% 
 Vacuum. 
 
 Reduction of Steam Consumption (%) by 
 using a Vacuum of 
 
 60% 
 
 70% 
 
 80% 
 
 90% 
 
 ?5% 
 
 184.9 
 156.5 
 128 
 99.6 
 
 11.11 
 11.75 
 12.57 
 13.84 
 
 5. 
 
 5.8 
 6.6 
 7.6 
 
 11.1 
 11.8 
 12.9 
 
 14.4 
 
 18. 1\ 
 19.3 
 20.5 
 22. 
 
 27.8 
 28.8 
 20.8 
 33.3 
 
 34.6 
 36.4 
 38.5 
 40.6 
 
1002 
 
 THE STEAM-ENGINE. 
 
 From the entropy diagram it is seen that in expanding from pressures 
 in excess of 100 Ibs. per sq.in. down to 1.42 Ibs. absolute, approximately 
 1 % more work is performed for every 10 F. of superheat. The effect of 
 increasing the degree of vacuum is summed up in the following table: 
 
 Increasing 
 the 
 Vacuum from 
 
 Decreases Steam Consumption. 
 
 in Reciprocating 
 Engines. 
 
 in Steam 
 Turbines. 
 
 50% to 60% 
 50% to 70% 
 50% to 80% 
 50% to 90% 
 50% to 95% 
 
 5.8% 
 11.6% 
 17.3% 
 23.1% 
 26.0% 
 
 6.2% 
 12.6% 
 20.0% 
 30.1% 
 
 37.4% 
 
 In the last case (from 50% to 95%) the decrease in steam consumption 
 Is 44% greater for a steam turbine than for a reciprocating engine. 
 
 The following results of tests of a compound engine using superheated 
 steam are reported in Power, Aug., 1905. The cylinders were 21 and 
 36 X 36 ins. The steam pressure was about 117 Ibs. gauge. R.p.m. 100, 
 vacuum 26.5 ins. 
 
 Test No 1 
 
 Indicated H.P 481 
 
 Superheat of steam 
 
 entering h.p. cyl. . . 253 F 
 B.T.U. supplied per 
 
 I.H.P. per min 198.2 
 
 B.T.U. theoretically 
 
 required. Rankine 
 
 cycle 142.4 
 
 Efficiency ratio 0.72 
 
 Thermal efficiency % 21.39 
 Lbs. steam per I.H.P. 
 
 hour 9.098 9.267 8.886 8.585 8.682 8.742 
 
 The Practical Application of Superheated Steam is discussed in a 
 paper by G. A. Hutchinson in Trans. A. S. M. E. t 1901. Many different 
 forms of superheater are illustrated. 
 
 Some results of tests on a 3000-H.P., four-cylinder, vertical, triple-ex- 
 pansion Sulzer engine, using steam from Schmidt independently fired 
 superheaters, are as follows. (Eng. Rec. t Oct. 13, 1900.) 
 
 2 
 
 461 
 
 3 
 347 
 
 4 
 145 
 
 5 
 333 
 
 6 
 
 258 
 
 242* 
 
 221 
 
 202 
 
 232 
 
 210 
 
 201.7 
 
 197.6 
 
 192.1 
 
 194.0 
 
 194.0 
 
 142.5 
 0.71 
 21.02 
 
 130.2 
 0.66 
 21.46 
 
 128.0 
 0.67 
 22.07 
 
 126.0 
 0.65 
 21.86 
 
 128.5 
 0.66 
 21.86 
 
 Tests Using Steam. 
 
 Highly Superheated. 
 
 Mod- 
 erately 
 Super- 
 heated 
 
 Saturated. 
 
 Initial pressure in h.p. cyl. 
 (absolute) Ibs . 
 
 187.3 
 
 582 
 2,900 
 9.64 
 
 477 
 
 195.5 
 
 585 
 2,779 
 .9.67 
 482 
 
 188.4 
 
 614 
 2,868 
 9.56 
 479 
 
 190.3 
 
 531 
 
 2,850 
 10.29 
 447 
 
 194.6 
 
 381 
 2,951 
 11.77 
 438 
 
 195.9 
 
 381 
 2,999 
 11.75 
 435 
 
 Temp, of steam in valve 
 chest deg. F ... 
 
 Total I.H.P 
 
 Lbs. steam per I.H.P. hour 
 Watt hours per Ib. of coal. 
 
 The saving due to the use of highly superheated steam is (482-438) * 
 482 = 9.1%. 
 
 Tests of a 4000-H.P. double-compound engine (Van den Kerchove, of 
 Brussels) with superheated steam are reported in Power, Dec. 29, 1908. 
 The cylinders are 34 1/4 and 60 ins., stroke 5 ft. Ratio of areas 2.97. The 
 following are the principal results, the first figures given being for the full- 
 load test, and the second (in parentheses) for the half-load test. Steam 
 pressure at drier, 136.5 Ibs. (137.9). R.p.m. 84.3 (84.06). Temp, of 
 steam entering engine 519 F. (498), leaving l.p. cyl. 121.5 (121.5). 
 Vacuum in condenser, ins., 27.5 (27). I.H.P. 3776 (2019). Steam per 
 I.H.P. hour, Ibs., 9.62 (9.60). 
 
 The saving due to the use of superheated steam is reported in numerous 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1003 
 
 tests as being all the way from less than 10% to more than 40%. The 
 greater saving is usually found with engines that are the most inefficient 
 with saturated steam, such as single-cylinder engines with light loads, in 
 which the cylinder condensation is excessive. 
 
 R. P. Bolton (Eng. Mag., May, 1907) states that tests of superheated 
 steam in locomotives, by the Prussian Railway authorities in 1904, with 
 50, 104 and 158 F. superheat, showed a saving of water respectively 
 of 2.5, 10 and 16%, and a saving of coal of 2, 7 and 12%. Mr. Bolton's 
 paper concludes with a long list of references on the subject of super- 
 heated steam. A paper by J. R. Bibbins in Elec. Jour., March, 1906, gives 
 a series of charts showing the saving made by different degrees of super- 
 heating in different types of engines, including steam turbines. 
 
 For description of the Foster superheater, see catalogue of the Power 
 Specialty Co., New York. 
 
 The Wolf (French) semi-portable compound engine of 40 H.P. with 
 superheater and reheater, the engine being mounted on the boiler, is 
 reported by R. E. Mathot, Power, July, 1906, to have given a steam 
 consumption as low as 9.9 IDS. per I. H.P. hour, and 10.98 Ibs. per B.H.P. 
 hour. The steam pressure in the boiler was 172.6 Ibs., and was super- 
 heated initially to 657 F., and reheated to 361 before entering the l.p. 
 cylinder. This is a remarkable record for a small engine. 
 
 A testfof a Rice & Sargent cross-compound horizontal engine 16 and 
 28X42 ins., with superheated steam, is reported by D. S. Jacobus in 
 Trans. A. S. M. E. , 1904. The steam pressure at the throttle was 140 Ibs. 
 gauge, the superheating was 350 to 400, and the vacuum 25 to 26 ins., 
 r.p.m. 102. In three tests with superheated and one with saturated, 
 steam the results were: 
 
 I.H.P. developed ! . . . .474.5 420.4 276.8 406.7 
 
 Water consumption per I. H.P. hour 9.76 9.56 "9.70 13.84 
 
 Coal consumption per I.H.P. hour 1.265 1.257 1.288 1.497 
 
 B.T.U. per min. per I.H.P 205.0 203.7 208.8 248.2 
 
 Temp, of steam entering h.p. cyl 634 659 672 
 
 Temp, of steam leaving h.p. cyl 346 331 288 262 
 
 Temp, of steam entering l.p. cyl 408 396 354 269 
 
 Temp, of steam leaving l.p. cyl 135 141 117 
 
 Performance of a Quadruple Engine. O. P. Hood (Trans. A. S, 
 M. E., 1906) describes a test of a high-duty air compressor, with four 
 steam cylinders, 14.5, 22, 38 and 54 in. diam., 48-in. stroke. The clearr 
 ances were respectively 6, 5.7, 4.4 and 3.5%. R.p.m. 57. Steam pressure, 
 gauge, near throttle, 242.8 Ibs., in 1st. receiver 120.7 Ibs., in 2d, 30.8 Ibs., 
 in 3d, vac., 1.24 ins. Moisture in steam near throttle, 5.74%. Steam 
 in No. 1 receiver, dry; in No. 2, 17 superheat; in No. 3, 9 superheat. 
 The engine has poppet valves on the h.p. cylinder and Corliss valves on 
 the other cylinders. The feed-water heaters are four in number, in series, 
 on the Nordberg system; No. 1 receives its steam from the exhaust of 
 No. 4 cylinder; No. 2 from the jacket of No. 4 cyl.; No. 3 from the jackets 
 of No. 3 cylinder and No. 3 reheater; No. 4 from the jacket of No. 2 
 cylinder. The reheaters are supplied with steam from the boilers. The 
 temperatures of steam and water were as follows: Temperatures of steam: 
 Fed to No. 1 engine, 403; leaving receivers, No. 1, 351; No. 2, 291; 
 No. 3, 216. Exhaust entering preheater, 114. Temperature corre- 
 sponding to condenser pressure, 109.6. Temperatures of water: Fed to 
 preheater, 93; fed to heaters, No. 1, 114; No. 2, 173; No..3. 202; No. 4, 
 269; leaving heater No. 4 as boiler feed, 334. 
 
 The principal results of the test are as follows: 
 
 Cylinder 1 2 3 4 
 
 I.H.P. developed in steam cylinders 181.47 256.96 275.71 275.56 
 
 I.H.P. used in the cylinders 220.04 222.12 226.20 214.84 
 
 Total indicated horse-power, steam cylinders 989.7 
 
 Total horse-power used in air cylinders 883.2 
 
 Total indicated horse-power of auxiliaries 11.0 
 
 Horse-power representing friction of the 
 
 machine 95.5 
 
 Per cent of friction 9.65% 
 
 Mechanical efficiency engine and compressor 90.35% 
 
 Heat consumed by engine per hour per I.H.P., 10,157 B.T.U. ; per 
 B.H.P., 11,382 B.T.U. Equivalent standard coal consumption per 
 
1004 THE STEAM-ENGINE. 
 
 hour assuming 10,000 B.T.U. imparted to the boiler per pound coal, per 
 I.H.P., 1,016 IDS.; per B.H.P., 1,138 Ibs. Dry steam per hour per 
 I.H.P., 11.23 Ibs.; per B.H.P., 12.58 Ibs. Heat units consumed per 
 minute, per I.H.P., 169.29 B.T.U. ; per B.H.P., 189.70 B.T.U. 
 
 Efficiency of Carnot cycle between the temperature of incoming 
 
 steam and that corresponding to pressure in the condenser... 34.0 % 
 
 Actual heat efficiency attained by this engine 25.05% 
 
 Relative efficiency compared with Carnot cycle 73.69% 
 
 Relative efficiency compared with Rankine'cycle 88.2 % 
 
 Duty, ft.-lbs. per million B.T.U. supplied 194,930,000 
 
 This engine establishes a new low record for the heat consumed per hour 
 per I.H.P., being 9% lower than that used by the Wild wood pumping 
 engine reported in 1900. (See Pumping Engines.) 
 
 The Use of Reheaters in the receivers of multiple-expansion engines is 
 discussed by R. H. Thurston in Trans. A.S.M.E., xxi, 893. He shows that 
 such receivers improve the economy of an engine very little unless they 
 are also superheaters; in which case marked economy may be effected 
 by the reduction of cylinder condensation. The larger the amount of 
 cylinder condensation and the greater the losses, exterior and interior, 
 the greater the effect of any given amount of superheating. The same 
 statement will hold of the use of reheaters: the more wasteful the engine 
 without them and the more effectively they superheat, the larger the 
 gain by their use. A reheater should be given such area of heating surface 
 as will insure at least moderate superheating. 
 
 Influence of the Steam-jacket. Tests of numerous engines with 
 and without steam-jackets show an exceeding diversity of results, ranging 
 all the way from 30% saying down to zero, or even in some cases showing 
 an actual loss. The opinions of engineers at this date (1894) is also as 
 diverse as the results, but there is a tendency towards a general belief 
 that the jacket is not as valuable an appendage to an engine as was for- 
 merly supposed. An extensive rtsum& of facts and opinions on the steam- 
 jacket is given by Prof. Thurston in Trans. A. S. M. E., xiv, 462. See 
 also Trans. A. S. M. E. t xiv, 873 and 1340; xiii, 176; xii, 426 and 1340; 
 and Jour. F. I., April, 1891, p. 276. The following are a few statements 
 selected from these papers. 
 
 /The results of tests reported by the research committee on steam-jackets 
 appointed by the British Institution of Mechanical Engineers in 1886, 
 indicate an increased efficiency due to the use of the steam-jacket of from 
 1% to over 30%, according to varying circumstances. 
 
 Professor Unwin considers that "in all cases and "on all cylinders the 
 jacket is useful; provided, of course, ordinary, not superheated, steam is 
 used; but the advantages may diminish to an amount not worth the in- 
 terest on extra cost." 
 
 Professor Cotterill says: Experience shows that a steam-jacket is advan- 
 tageous, but the amount to be gained will vary according to circumstances. 
 In many cases it may be that the advantage is small. Great caution is 
 necessary in drawing conclusions from any special set of experiments on 
 the influence of jacketing. 
 
 In the Pawtucket pumping-engine, 15 and 30 1/8 X 30 in., 50 revs, per 
 min., steam-pressure 125 Ibs. gauge, cut-off i/4in h.p. and 1/3 in l.p. cylinder, 
 the barrels only jacketed, the saving by the jackets was from 1% to 4%. 
 
 The superintendent of the Holly Mfg. Co. (compound pumping-engines) 
 says: "In regard to the benefits derived from steam-jackets on our steam- 
 cylinders, I am somewhat of a skeptic. From data taken on our own 
 engines and tests made I am yet to be convinced that there is any practical 
 value in the steam-jacket." 
 
 Professor Schrooter from his work on the triple-expansion engines at 
 Augsburg, and frlm the results of his tests of the jacket efficiency on a 
 small engine of the Sulzer type in his own laboratory, concludes: (1) The 
 value of the jacket may vary within very wide limits, or even become 
 negative. (2) The shorter the cut-off the greater the gain by the use of a 
 jacket. (3) The use of higher pressure in the jacket than in the cylinder 
 produces an advantage. The greater this difference the better. (4) The 
 high-pressure cylinder may be left unjacketed without great loss, but the 
 other should always be jacketed. 
 
 The test of the Laketon triple-expansion pumping-engine showed a gain 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1005 
 
 of 8.3 % by the use of the jackets, but Prof. Denton points out (Trans. 
 A. S. M. E., xiv, 1412) that all but 1.9% of the gain was ascribable to the 
 greater range of expansion used with the jackets. 
 
 Test of a Compound Condensing Engine with and without Jackets 
 at different Loads. (R. C. Carpenter, Trans. A. S. M. E., xiv, 428.) 
 Cylinders 9 and 16 in. X 14 in. stroke; 112 Ibs. boiler- pressure; rated 
 capacity 100 H.P.; 265 revs, per min. Vacuum, 23 in. From the results 
 of several tests curves are plotted, from which the following principal 
 figures are taken. 
 
 Indicated HP.. 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 1 10 
 
 120 
 
 125 
 
 Steam per I.H.P. per hr. 
 With jackets, Ibs 
 Without jackets, Ibs.. . 
 
 22.6 
 
 21.4 
 
 20.3 
 
 19 6 
 22 
 
 19 
 ?0 5 
 
 18.7 
 19 6 
 
 18.6 
 19 ? 
 
 18.9 
 19 1 
 
 19.5 
 19 3 
 
 20.4 
 20 1 
 
 21.0 
 
 Saving by jacket. % ... 
 
 
 
 
 10 9 
 
 7 3 
 
 4 6 
 
 3 1 
 
 1 
 
 -1 
 
 -1 5 
 
 
 This table gives a clue to the great variation in the apparent saving 
 due to the steam-jacket as reported by different experimenters. With 
 this particular engine it appears that when running at its most econom- 
 ical rate of 100 H.P., without jackets, very little saving is made by use 
 of the jackets. When running light the jacket makes a considerable 
 saving, but when overloaded it is a detriment. 
 
 At the load which corresponds to the most economical rate, with no 
 steam in jackets, or 100 H.P., the use of the jacket makes a saving of 
 only 1%; but at a load of 60 H.P. the saving by use of the jacket is 
 about 11%, and the shape of the curve indicates that the relative ad- 
 vantage of the jacket would be still greater at lighter loads than 60 H.P. 
 
 The Best Economy of the Piston Steam-Engine at the Advent of 
 the Steam Turbine is the subject of a paper by J. E. Denton at the 
 International Congress of Arts and Sciences, St. Louis, 1904. (Power 
 Oct. 26, 1905.) Prof. Denton says: 
 
 During the last two years the following records have been established: 
 
 (1) With an 850 : H.P. Rice & Sargent compound Corliss engine, running 
 at 120 r.p.m., having a 4 to 1 cylinder ratio, clearances of 4% and 7% 
 live jackets on cylinder heads and live steam in reheater, Prof. Jacobus 
 found for 600 H.P. of load, with 150 Ibs. saturated steam, 28.6 ins. vacuum, 
 and 33 expansions, 12.1 Ibs. of water per I.H.P., with a cylinder-conden- 
 sation loss of 22%, and a jacket consumption of 10.7% of the total steam 
 consumption. 
 
 (2) With a 250-H.P. Belgian poppet-valve compound engine, 126 r.p.m. 
 with 2.97 to 1 cylinder ratio, clearances of 4%, steam-chest jackets on 
 barrels and head, and no reheater, Prof. Schroter, of Munich, found with 
 117 H.P. of load, 130 Ibs. saturated steam, 27.6 ins. of vacuum, and 32 ex- 
 pansions, 11.98 Ibs. of water per H.P. per hour, with a cylinder-condensa- 
 tion loss of 23.5%, and a jacket consumption of 7% of the total steam 
 consumption in the high cylinder jacket and 7% in the low jacket. 
 
 ( 3 ) With the Westinghouse twin compound combined poppet-valve 
 and Corliss-valve engine, at the New York Edison plant, running 76 r p m 
 with 5.8 to 1 cylinder ratio, clearances of 10.5% and 4%, without jackets 
 or reheater, Messrs. Andrew, Whitham and Wells found for the full load 
 
 if 5400 H.P 185 Ibs. steam pressure, 27.3 ins. vacuum, and 29 expan- 
 sions^l 1.93 Ibs. of water per I.H.P. per hour, with an initial condensation 
 
 These facts show that the minimum water consumption of the compound 
 engine of the present date, using saturated steam, is not dependent upon 
 any particular cylinder ratio and clearance nor upon any system of jacket- 
 ing, but that tne essential condition is the use of a ratio of expansion 
 ai about 30, above which the cylinder-condensation loss is liable to prevail 
 over the influence of the law of expansion. The conclusion appears 
 warranted, therefore, that if this ratio of expansion is secured with any 
 the current cylinder and clearance ratios, and with any existing system 
 of jackets and reheaters, or without them, a water consumption of 12 4 Ibs 
 horse-power is possible, and that a variation of 04 Ib. below or above 
 igure may occur by the accidental favorable, or unfavorable, jacket 
 ad cylinder-wall expenses which are beyond the control of the designer 
 Compound Piston Engine Economy vs. that of Steam Turbine. In order 
 to compare the economy of the piston engine with that of the steam tur- 
 
1006 THE STEAM-ENGINE. 
 
 bine, we must use the water consumption per brake horse-power, since no 
 indicator card is possible from the turbine; and furthermore, we must use 
 the average water consumption for the range of loads to which engines are 
 subject in practice. 
 
 In all of the public turbine tests to date, with one exception the output 
 was measured through the electric power of a dynamo whose efficiency is 
 not given for the range of loading employed, so that the average brake 
 horse-power is not known. This exception is the Dean and Main test of 
 a 600-H.P. Westinghouse-Parsons turbine using saturated steam at 150 Ibs. 
 pressure, and a 28-in. vacuum. We may compare the results of this test 
 with that of the 850-H.P. Rice & Sargent and of the 250-H.P. Belgian 
 engine, by assuming that the power absorbed by friction in these en- 
 gines is 3 % of the indicated load plus the power shown by friction cards 
 taken with the engine unloaded. The latter showed 5% of the rated 
 power in the R.& S. engine and 8 % in the Belgian engine. The results are : 
 Per cent of full load 41 75 100 125 Avg. 85% 
 
 Lbs. Water per Brake H.P. Hour. 
 
 600-H.P. Turbine 13.62 13.91 14.48 16.05 14.51 
 
 800-H. P. Comp. Engine 13.78 13.44 13.66 17.36 14.56 
 
 250 H.P. Belgian Engine 15.10 14.15 13.99 15.31 14.64 
 
 These figures show practical equality in economy of the types of engines. 
 The full report of the Van den Kerchove Belgian engine is given in Power, 
 June, 1903. 
 
 For large-sized units Prof. Denton compares the Elberfeld test of a 
 Parsons turbine at the full load of 1500 electric H.P., allowing 5% for 
 attached air pump, 95% for generator efficiency, with the 5400-H.P. 
 Westinghouse compound engine at the New York Edison station, whose 
 friction at full load was found to be 4%. The turbine with 150 Ibs. steam 
 and 28 ins. vacuum required 13.08 Ibs. of saturated steam per B.H.P. 
 hour, a gain of 4% over the 600-H.P. turbine. The engine with 18.5 Ibs. 
 boiler pressure gave 12.5 Ibs. per B.H.P. hour. Crediting the turbine 
 with the possible influence of the difference in size and steam pressure, 
 there is again practical equality in economy between it and the piston 
 engine. 
 
 Triple-expansion Pumping Engines. The triple-expansion engine has 
 failed to supplant the compound for electric light and mill service, be- 
 cause the gain in fuel economy due to its use was not sufficient to over- 
 come its higher first cost, depreciation, etc. It is, however, almost uni- 
 versally used in" marine practice, and also in large-sized pumping engines. 
 Prof. Denton says: Pumping engines in the United States have been de- 
 veloped in x the triple-expansion fly- wheel type to a degree of economy 
 superior to that afforded by any compound mill or electric engine, and, 
 for saturated steam, superior to that of the pumping engines of any other 
 country. This is because their slow speed permits of greater benefit 
 from jackets and reheaters and of less losses from wire-drawing and back 
 pressure. These causes, together with the greater subdivision of the range 
 of expansion, have resulted in records made between 1894 and 1900 of 
 11.22, 11.26 and 11.05 Ibs. of saturated steam per I.H.P., with 175 Ibs. 
 steam pressure and from 25 to 33 expansions, in the cases of the Leavitt, 
 Snow and Allis pumping engines, respectively, the corresponding heat 
 consumption being by different dispositions of the jacket drainage, 204, 
 208 and- 212 thermal units per I.H.P. minute; while later the Allis pump, 
 with 185 Ibs. steam pressure, has lowered the record to 10.33 Ibs. of satu- 
 rated steam per I.H.P., with 196 B.T.U. per H.P. minute. 
 
 Gain from Superheating. In the Belgian compound engine above de- 
 scribed, with steam at 130 Ibs., vacuum 27. 6 ins., the average consumption 
 of saturated steam, between 45 and ]25% of load, was 12.45 Ibs. per 
 I.H.P. hour, or 225 B.T.U. per I.H.P. minute. With steam superheated 
 224 F. the average consumption for the same loads was 10.09 Ibs. per 
 I.H.P. hour, computed to be equivalent to 209 B.T.U. per H.P. minute, 
 a gain due to superheating of 7%. With steam supei heated 307 and 
 the load about 80% of rating the water consumption \\as 8.99 Ibs. per 
 I.H.P. hour, equivalent to 192 B.T.U. per H.P. minute. The same load 
 with saturated steam requires 221 B.T.U., showing a gain due to super- 
 heating of 13%. 
 .The best performance reported for superheated steam used in the tur- 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1007 
 
 bine is that of Brown & Boveri Parsons, Frankfort, 4000-H.P. machine, 
 which, with 183 Ibs. gauge pressure and 190 F. superheat, afforded 10.28 
 Ibs. per B.H.P. hour, assuming a generator efficiency of 0.95. Reckoning 
 from the feed temperature of its vacuum of 27.5 ins., the heat consumption 
 is 214 B.T.U. per H.P. minute. 
 
 The heat consumption of the 250-H.P. Belgian compound engine per 
 B.H.P. hour at the highest superheating of 307 F. is 220 B.T.U. The 
 turbine, therefore, probably holds the record for brake horse-power econ- 
 omy over the piston engine for superheated steam by a margin of about 
 3%, although had the compound engine been of the same horse-ppwer as 
 the turbine, so that its friction load would be only 8% of its power instead 
 of the 13% here allowed, it would have excelled the turbine in brake 
 horse-power economy by a margin of about 2.5%. 
 
 The Sulphur-dioxide 'Addendum. If the expansion in piston engines 
 could continue until the pressure of 1 pound was attained before exhaust 
 occurred, considerable more work could be obtained from the steam. 
 This cannot be done, for two reasons: first, because the low cylinder would 
 have to be about five times greater in volume, which is commercially 
 impracticable; and, second, because the velocity of exit through the 
 largest exhaust ports possible is so great that the frictional resistance of 
 the steam makes the back pressure from 1 to 3 pounds higher than the 
 condenser pressure in the best engines of ordinary piston speed. 
 
 All the work due to this extra expansion can be obtained by exhausting 
 the steam at 6 Ibs. pressure against a nest of tubes containing sulphur 
 dioxide which is thereby boiled to a vapor at about 170 Ibs. pressure. 
 
 Professor Josse, of Berlin, has perfected this sulphur-dioxide system 
 of improvement, and reliable tests have shown that if cooling water of 
 65 is available, and to the extent of about twice the quantity usually em- 
 ployed for condensing steam under 28 ins. of vacuum, a sulphur-dioxide 
 cylinder of about half the size of the high-pressure cylinder of a com- 
 pound engine will do sufficient work to improve the best economy of 
 such engines at least 15%. The steam turbine expands its steam to the 
 pressure of its exhaust chamber, and as unlimited escape ports can bo 
 provided from this chamber to a condenser, it follows that the turbine 
 can practically expand its steam to the pressure of the condenser. There- 
 fore a steam turbine attached to a piston engine to operate with the latter's 
 exhaust should effect the same saving as the sulphur-dioxide cylinder. 
 
 Standard Dimensions of Direct-connected Generator Sets. From 
 a report by a committee of the A. S. M. E., 1901. 
 
 Capacity of unit, K.W 25 35 50 75 100 150 200 
 
 Revolutions per minute 310 300 290 275 260 225 200 
 
 Armature bore, center crank engines. .. 4 4 41/2 51/2 678 
 Armature bore, side-crank engines 41/2 51/2 61/2 71/2 81/210 11 
 
 The diameter of the engine shaft at the armature fit is 0.001 in. 
 greater than the bore, for bores up to and including 6 ins., and 0.012 
 in. greater for bores 6 1/2 ins. and larger. 
 
 Dimensions of Some Parts of Large Engines in Electric Plants. 
 The Electrical World, Sept. 27, 1902, gives a table of dimensions of 
 the engines in the five large power stations in New York City at that 
 date. The following figures are selected from the table. 
 
 Name of station 
 
 Metro- 
 politan. 
 
 Manhat- 
 tan. 
 
 Kings- 
 bridge. 
 
 Rapid 
 Transit. 
 
 Edison. 
 
 Type of engine . ... 
 
 Vert. 
 Cross- 
 
 Double, 
 2 hor. 
 
 Vert. 
 Cross- 
 
 Double 
 2 hor. 
 
 3 Cyl. Vert. 
 
 
 Comp. 
 
 2 vert. 
 Cyls. 
 
 Comp. 
 
 2 vert. 
 Cyls. 
 
 
 Rated H.P.. . 
 Cylinders, (60" stroke) 
 Piston rods, diam., in. 
 Crank pins 
 
 4500 
 46, 86 in. 
 9, 10 
 14 X 14 
 
 8000 
 44, 88 in. 
 8 
 18 X 18 
 
 4500 
 46, 86 in. 
 9, 10 
 14 X 14 
 
 8900 
 42, 86 in. 
 8, 10 
 20 X 18 
 
 5200 
 43l/2,2-75J/"in. 
 9 
 22 & 16 X 14 
 
 Wrist pins 
 
 14 X 14 
 
 12 X 12 
 
 14 X 14 
 
 12 X 12 
 
 14 X H 
 
 Shaft length 
 max. diam 
 bearings 
 
 27 ft. 4 in. 
 37 in. 
 34 X 60 
 
 25 ft. 3 in. 
 37 in. 
 34 X60 
 
 27ft. 
 39 in. 
 34 X60 
 
 25 ft. 3 in. 
 37 in. 
 34 X60 
 
 35 ft. 
 293/8 in. 
 26 X 60 
 
1008 
 
 THE STEAM-ENGINE. 
 
 The shafts are hollow, with a 16-in. hole, except the Edison which has 
 10 in. The speed of all the engines is 75 r.p.m., or 750 ft. per min. The 
 crank-pins of the Manhattan and Rapid Transit engines each are at- 
 tached to two connecting-rods, side by side,"hor. and vert., each rod hav- 
 ing a bearing 9 in. long on the pin. The crank-pins of the Edison en- 
 gine are 16 in. diam. for the side-cranks, and 22 in. for the center-crank. 
 
 The four 8000-horse-power engines in the Manhattan station, new in 
 1902, were replaced in 1914-15, although still as good as new, by four 
 30,000 K.W. steam turbines occupying the same space. The turbines 
 will have a water rate 30 per cent lower than the engines. (Power, 
 April 27, 1915.) 
 
 Some Large Rolling-Mill Engines. 
 
 
 Cylinders. 
 
 
 (^ 
 
 tf 
 
 Type. 
 
 8.3 
 
 pu^ 
 
 Fly-wheel. 
 
 Location. 
 
 Builders. 
 
 Diam. 
 Ft. 
 
 Wt. 
 Lbs. 
 
 44 & 82 X60 
 
 65 
 
 Cross-C . 
 
 140 
 
 24 
 
 150,000 
 
 Republic I. & S. 
 
 Filer & 
 
 
 
 
 
 
 
 Co., Youngs- 
 
 Stowell. 
 
 
 
 
 
 
 
 town, Ohio. 
 
 
 46 & 80X60 
 
 80 
 
 Tandem. 
 
 150 
 
 24 
 
 110.000 
 
 Carnegie S. Co., 
 
 Wiscon- 
 
 
 
 
 
 
 
 Donora, Pa. 
 
 sin Eng. 
 
 
 
 
 
 
 
 
 Co. 
 
 52 & 90X60. 
 
 
 Tandem 
 
 
 25 
 
 250,000 
 
 Carnegie S. Co., 
 
 Wm. Tod 
 
 
 
 
 
 
 
 Youngstown, 
 
 Co. 
 
 
 
 
 
 
 
 Ohio. 
 
 
 2 each 
 42 & 70 X54 
 
 
 Double. 
 Tandem. 
 
 150 
 
 none 
 
 Carnegie S. Co., 
 S. Sharon, Pa. 
 
 Allis 
 Chal- 
 
 
 
 
 
 
 
 mers Co. 
 
 
 
 
 
 
 Carnegie S. 
 
 
 
 
 
 
 
 Co., Du- 
 
 Mackin- 
 
 
 
 
 
 
 quesne, Pa. 
 
 tosh, 
 
 2 each . . 
 
 60 
 
 Double. 
 
 150 
 
 none 
 
 Jones & 
 
 Hemp- 
 
 44 & 70X60 
 
 
 Tandem. 
 
 
 
 Laughlin 
 
 hill & 
 
 
 
 
 
 
 Steel Co., 
 
 Co. 
 
 
 
 
 
 
 Aliquippa,Pa. 
 
 
 Some details: Main bearings, No. 1, 25 X 431/2 in.; No. 2, 30 X 52 in.; 
 No. 3, 30 X 60 in. Shaft diam. at wheel pit, No. 1, 26 in.; No. 3, 36 in. 
 Crank pins, No. 1, h.p. 14 X 14; l.p., 14 X 23 in.; No. 2, 18 X 18 in. 
 Crosshead pins, No. 1, 12 X 14; No. 2, 16 X 20 in. No. 4 is a reversing 
 engine, with the Marshall gear. No. 5 is a reversing engine with piston 
 valves below the cylinders. 
 
 Counterbalancing Engines. Prof. Unwin gives the formula for 
 
 counterbalancing vertical engines: Wi = Wzr/p, (1) 
 
 in which W\ denotes the weight of the balance weight and p the radius to 
 its center of gravity, W 2 the weight of the crank-pin and half the weight of 
 the connecting-rod, and r the length of the crank. For horizontal engines: 
 
 Wi = 2/3 (Wz + TF 3 ) r/p to 3/4 (Wz + TF 3 ) r/p (2) 
 
 In which TF 3 denotes the weight of the piston, piston-rod, cross-head, and 
 the other half of the weight of the connecting-rod. 
 
 The American Machinist, commenting on these formulae, says: For 
 horizontal engines formula (2) is often used; formula (1) will give a coun- 
 terbalance too light for vertical engines. We should use formula (2) for 
 computing the counterbalance for both horizontal and vertical engines, 
 excepting locomotives, in which the counterbalance should be heavier. 
 
 For an account of experiments on counterbalancing large engines, with 
 a method of recording vibrations, see paper by D. S. Jacobus, Trans. 
 A. S. M. #., 1905. 
 
 Preventing Vibrations of Engines. Many suggestions have been 
 made for remedying the vibration and noise attendant on the working 
 of the big engines which are employed to run dynamos. A plan which has 
 given great satisfaction is to build hair-felt into the foundations of the 
 engine. An electric company has had a 90-horse-power engine removed 
 from its foundations, which were then taken up to the depth of 4 feet. A 
 
COMMERCIAL ECONOMY COSTS OF POWER. 1009 
 
 layer of felt 5 inches thick was then placed on the foundations and run 
 tip 2 feet on all sides, and on the top of this the brickwork was built up. 
 Safety Valve. 
 
 Steam-engine Foundations Embedded in Air. In the sugar- 
 refinery of Claus Spreckels, at Philadelphia, Pa., the engines are distrib- 
 uted practically all over the buildings, a large proportion of them being 
 on upper floors. Some are bolted to iron beams or girders, and are con- 
 sequently innocent of all foundation. Some of these engines ran noise- 
 lessly and satisfactorily, while others produced more or less vibration and 
 rattle. To correct the latter the engineers suspended foundations from 
 the bottoms of the engines, so that, in looking at them from the lower 
 floors, they were literally hanging in the air. Iron Age, Mar. 13, 1890. 
 
 COMMERCIAL, ECONOMY. COSTS OF POWER. 
 
 The Cost of Steam Power is an exceedingly variable quantity. The 
 principal items to be considered in estimating total annual cost are: load 
 factor ; hours run per year ; percentage of full load at different hours of 
 the day ; cost and quality of fuel ; boiler efficiency and steam consumption 
 of engines at different loads ; cost of water and other supplies ; cost of 
 labor, first cost of plant, depreciation, repairs, interest, insurance and taxes. 
 
 In figuring depreciation not only should the probable life of the several 
 parts of the plant, such as buildings, boilers, engines, condensers, etc., be 
 considered, but also the possibility of part of the plant, or the whole of it, 
 depreciating rapidly in value on account of obsolescence of the machinery 
 or of changes in the conditions of the business. 
 
 When all of the heat in the exhaust steam from engines and pumps, in- 
 cluding water of condensation, is used for heating purposes the fuel cost of 
 steam-engine power may be practically nothing, since the exhaust contains 
 all of the heat in the steam delivered to the engine except from 5 to 10 
 per cent which is converted into work, and a trifling amount lost by 
 radiation. 
 
 Most Economical Point of Cut-off in Steam-engines. (See paper 
 by Wolff and Denton, Trans. A. S. M. E., vol. ii, p. 147-281; also, Ratio 
 of Expansion at Maximum Efficiency, R. H. Thurston, vol. ii, p. 128.) 
 The problem of the best ratio of expansion is not one of economy of con- 
 sumption of fuel and economy of cost of boiler alone. The question of in- 
 terest on cost of engine, depreciation of value of engine, repairs of engine, 
 etc., enters as well; for as we increase the rate of expansion, and thus, 
 within certain limits fixed by the back-pressure and condensation of 
 steam, decrease the amount of fuel required and cost of boiler per unit of 
 work, we have to increase the dimensions of the cylinder and the size 
 of the engine, to attain the required power. 
 
 Type of Engine to be used where Exhaust-steam is needed for 
 Heating. In many factories more or less of the steam exhausted from 
 the engines is utilized for boiling, drying, heating, etc. Where all the 
 exhaust-steam is so used the question of economical use of steam in the 
 engine itself is eliminated, and the high-pressure simple engine is entirely 
 suitable. Where only part of the exhaust-steam is used, and the quantity 
 so used varies at different times, the question of adopting a simple, a 
 condensing, or a compound engine becomes more complex. This problem 
 is treated by C. T. Main in Trans. A. S. M. E., vol. x, p. 48. He shows 
 that the ratios of the volumes of the cylinders in compound engines should 
 vary according t9 the amount of exhaust-steam that can be used for 
 heating. A case is given in which three different pressures of steam are 
 required or could be used, as in a worsted dye-house: the high or boiler 
 pressure for the engine, an intermediate pressure for crabbing, and low- 
 pressure for boiling, drying, etc. If it did not make too much compli- 
 cation of parts in the engine, the boiler-pressure might be used in the high- 
 pressure cylinder, exhausting into a receiver from which steam could be 
 taken for running small engines and crabbing, the steam remaining in the 
 receiver passing into the intermediate cylinder and expanded there to 
 from 5 to 10 Ibs. above the atmosphere and exhausted into a second 
 receiver. From this receiver is drawn the low-pressure steam needed for 
 drying, boiling, warming mills, etc., the steam remaining in the receiver 
 passing into the condensing cylinder. 
 
 Cost of Steam-power. (Chas. T. Main, Trans. A. S. M. E., x, 48.) 
 Estimated costs in New England in 1888, per horse-power, using com- 
 
1010 
 
 THE STEAM-ENGINE. 
 
 pound condensing, and non-condensing engines, and based on engines 
 of 1000 H.P. are as follows: 
 
 Compound Condens- Non-con- 
 Engine. ing Engine, densing 
 
 1. Cost engine and piping, complete $25.00 . 
 
 2. Engine-house 8.00 
 
 3. Engine foundations 7.00 
 
 4. Total engine plant 40.00 
 
 5. Depreciation, 4% on total cost, l 60 
 
 6. Repairs, 2% on total cost 0.80 
 
 7. Interest, 5% on total cost 2.00 
 
 8. Taxation, 1.5% on 3/ 4 cost 45 
 
 9. Insurance on engine and house 165 
 
 Total of lines 5, 6, 7, 3, 9 5.015 
 
 10. 
 
 11. Cost boilers, feed-pumps, etc 9.33 
 
 12. Boiler-house 2.92 
 
 13. Chimney and flues 6. XI 
 
 Total boiler-plant 18.36 
 
 14. 
 
 15. Depreciation, 5% on total cost 0.918 
 
 16. Repairs, 2% on total cost 0.367 
 
 17. Interest, 5% on total cost 0.918 
 
 18. Taxation, 1.5% on 3/ 4 cost 0.207 
 
 19. Insurance, 0.5% on total cost 0.092 
 
 20. Total of lines 15 to 19 2.502 
 
 21. Coal used per I.H.P. per hour, Ibs. . . 1.75 
 
 22. Cost of coal per I.H.P. per day of 10 1/4 cts. 
 
 hours at $5.00 per ton t>f 2240 Ibs. . . . 4.00 
 
 23. Attendance of engine per day 0.60 
 
 24. Attendance of boilers per day 0.53 
 
 25. Oil, waste, and supplies, per day . . . 0.25 
 
 Total daily expense 5.38 
 
 26. 
 
 27. Yearly running expense, 308 days, per 
 
 I.H.P. : . '. P . . $16.570 
 
 28. Total yearly expense, lines 10. 20, 
 
 and 27 24.087 
 
 29. Total yearly expense per I.H.P. for 
 
 power if 50% of exhaust-steam is 
 
 used for heating 12.597 
 
 30. Total if all exhaust-steam is used for 
 
 heating 8.624 
 
 33.00 
 
 1.32 
 
 0.66 
 
 1.65 
 
 0.371 
 
 0.138 
 
 4.139 
 
 24.80_ 
 
 1.240 
 0.496 
 1.240 
 0.279 
 0.124 
 
 3.379 
 
 2.50 
 
 cts. 
 5.72 
 0.40 
 0.75 
 0.22 
 
 7.09 
 
 $21.837 
 29.355 
 
 14.907 
 7.916 
 
 Engine. 
 
 $17.50 
 7.50 
 4.50 
 
 29.50 
 
 1.18 
 
 0.59 
 
 1.475 
 
 0.332 
 
 0.125 
 
 3.702 
 
 5.00 
 8.00 
 
 29.00 
 
 1.450 
 0.580 
 1.450 
 0.326 
 0.145 
 
 3.951 
 3.00 
 
 cts. 
 6.86 
 0.35 
 0.90 
 0.20 
 
 8.31 
 
 When exhaust-steam or a part of the receiver-steam is used for heating, 
 or if part of the steam in a condensing engine is diverted from the con- 
 denser, and used for other purposes than power, the value of such steam 
 should be deducted from the cost of the total amount of steam generated 
 in order to arrive at the cost properly chargeable to power. The figures 
 in lines 29 and 30 are based on an assumption made by Mr. Main of losses 
 of heat amounting to 25% between the boiler and the exhaust-pipe, an 
 allowance which is probably too large. 
 
 See also two papers by Chas. E. Emery on "Cost of Steam Power," 
 Trans. A. S. M. E., vol. xii, Nov., 1883, and Trans. A. 1. E. E., vol. x, 
 
 a c'ost of Coal for Steam-power. The following table shows the 
 amount and the cost of coal per day and per year for various horse-powers 
 from 1 to 1000, based on the assumption of 4 Ibs. of coal being used per 
 
COMMERCIAL ECONOMY COSTS OF POWER. 1011 
 
 hour per horse-power. It is useful, among other things, in estimating the 
 saving that may be made in fuel by substituting more economical boilers 
 and engines for those already in use. Thus with coal at $3.00 per ton of 
 2000 ibs., a saving of $9000 per year in fuel may be made by replacing a 
 steam plant of 1000 H.P., requiring 4 Ibs. of coal per hour per horse-power, 
 with one requiring only 2 Ibs. 
 
 
 Coal Consumption, at 4 Ibs. 
 
 
 
 
 
 per H.P. hour; 10 hours a 
 day; 300 days per Year. 
 
 $2 per 
 Short 
 
 $3 per 
 
 Short 
 
 $4 per 
 Short 
 
 
 
 
 
 
 Ton. 
 
 Ton. 
 
 Ton. 
 
 1 
 
 Lbs. 
 
 Long Tons. 
 
 Short 
 Tons. 
 
 
 
 
 e 
 
 
 
 
 
 
 Cost in 
 
 Cost in 
 
 Cost In 
 
 1 
 
 Per 
 
 Per 
 
 Per 
 
 VOQ T 
 
 Per 
 
 Per 
 
 Y- 
 
 Dollars. 
 
 Dollars. 
 
 Dollars. 
 
 
 Day. 
 
 Day. 
 
 lear. 
 
 Day. 
 
 r. 
 
 Day. 
 
 Yr. 
 
 Day. 
 
 Yr. 
 
 Day. 
 
 Yr. 
 
 1 
 
 40 
 
 0.0179 
 
 53.57 
 
 0.02 
 
 6 
 
 0.04 
 
 12 
 
 0.06 
 
 18 
 
 0.08 
 
 24 
 
 10 
 
 400 
 
 0.1786 
 
 53.57 
 
 0.20 
 
 60 
 
 0.40 
 
 120 
 
 0.60 
 
 180 
 
 0.80 
 
 240 
 
 25 
 
 1,000 
 
 0.4464 
 
 133.92 
 
 0.50 
 
 150 
 
 1.00 
 
 300 
 
 1.50 
 
 450 
 
 2.00 
 
 600 
 
 50 
 
 2,000 
 
 0.8928 
 
 267.85 
 
 1.00 
 
 300 
 
 2.00 
 
 600 
 
 3.00 
 
 900 
 
 4.00 
 
 1,200 
 
 75 
 
 3,000 
 
 1 .3393 
 
 401.78 
 
 1.50 
 
 450 
 
 3.00 
 
 900 
 
 4.50 
 
 1,350 
 
 6.00 
 
 1,800 
 
 100 
 
 4,000 
 
 1.7857 
 
 535.71 
 
 2.00 
 
 600 
 
 4.00 
 
 1,200 
 
 6.00 
 
 1.800 
 
 8.00 
 
 2,400 
 
 150 
 
 6,000 
 
 2.6785 
 
 803.56 
 
 3.00 
 
 900 
 
 6.00 
 
 1,800 
 
 9.00 
 
 2,700 
 
 12.00 
 
 3,600 
 
 200 
 
 8,000 
 
 3.5714 
 
 1,071.42 
 
 4.00 
 
 1,200 
 
 8.00 
 
 2,400 
 
 12.00 
 
 3,600 
 
 16.00 
 
 4,800 
 
 250 
 
 10,000 
 
 4.4642 
 
 1,339.27 
 
 5.00 
 
 1,500 
 
 10. CO 
 
 3,000 
 
 15.00 
 
 4.500 
 
 20.00 
 
 6,000 
 
 300 
 
 12,000 
 
 5.3571 
 
 1,607.13 
 
 6.00 
 
 1,800 
 
 12.00 
 
 3,600 
 
 18.00 
 
 5,400 
 
 24.00 
 
 7,200 
 
 350 
 
 14,000 
 
 6.2500 
 
 1,874.98 
 
 7.00 
 
 2,100 
 
 14.00 
 
 4,200 
 
 21.00 
 
 6,200 
 
 28.00 
 
 8,400 
 
 400 
 
 16,000 
 
 7.1428 
 
 2,142.84 
 
 8.00 
 
 2,400 
 
 16.00 
 
 4,800 
 
 24.00 
 
 7,200 
 
 32.00 
 
 9600 
 
 450 
 
 18,000 
 
 8.0356 
 
 2,410.69 
 
 9.00 
 
 2,700 
 
 18.00 
 
 5,400 
 
 27.00 
 
 8,100 
 
 36.00 
 
 10^800 
 
 500 
 
 20.000 
 
 8.9285 
 
 2,678.55 
 
 10.00 
 
 3,000 
 
 20.00 
 
 6,000 
 
 30.00 
 
 9,000 
 
 40.00 
 
 12,000 
 
 600 
 
 24,000 
 
 10.7142 
 
 3,214.26 
 
 12.00 
 
 3,600 
 
 24.00 
 
 7,200 
 
 36.00 
 
 10,800 
 
 48.00 
 
 14,400 
 
 700 
 
 28,000 
 
 12.4999 
 
 3,749.97 
 
 14.00 
 
 4,200 
 
 28,00 
 
 8,400 
 
 42.00 
 
 11,600 
 
 56.00 
 
 16,800 
 
 800 
 
 32,000 
 
 14.2856 
 
 4,285.68 
 
 16.00 
 
 4,800 
 
 32.00 
 
 9,600 
 
 48.00 
 
 12,400 
 
 64.00 
 
 19,200 
 
 900 
 
 36,000 
 
 16.0713 
 
 4,821.39 
 
 18.00 
 
 5,400 
 
 36.00 
 
 10,800 
 
 54.00 
 
 14,200 
 
 72.00 
 
 21,600 
 
 1000 
 
 40,000 
 
 17.8570 
 
 5,357.10 
 
 20.00 
 
 6,000 
 
 40.00 
 
 12,000 
 
 60.00 
 
 18,000 
 
 80.00 
 
 24,000 
 
 It is usual to consider that a factory working 10 hours a day requires 
 101/2 hours coal consumption on account of the coal used in banking or 
 in starting the fires, and that there are 306 wprking days in the year. For 
 these conditions multiply the costs given in the table by 1.071. For 
 24 hours a day 365 days in the year, multiply them by 2.68. For other 
 rates of coal consumption than 4 Ibs. per H.P. hour, the figures are to be 
 modified proportionately. 
 
 Relative Cost of Different Sizes of Steam-engines. 
 
 (From catalogue of the Buckeye Engine Co., Part III.) 
 
 Horse-power.. . . 
 Cost per H. P., $ 
 
 50 
 20 
 
 75 
 171/2 
 
 100 
 16 
 
 125 
 15 
 
 150 
 
 141/2 
 
 200 
 131/2 
 
 250 
 13 
 
 300 
 
 123/4 
 
 350 
 
 12.5 
 
 400 
 12.6 
 
 500 
 12.8 
 
 600 
 131/4 
 
 700 
 14 
 
 800 
 15 
 
 Power Plant Economies. (H. G. Stott, Trans. A. I. E. E., 190G.) 
 The table on the following page gives an analysis of the heat losses found 
 in a year's operation of one of the most efficient plants in existence. 
 
 The following notes concerning power-plant economy are condensed 
 from Mr. Stott's paper. 
 
 Item 1. B.T.U.per Ib. of coal. The coal is bought and paid for on 
 the basis of the B.T.U, found by a bomb calorimeter, 
 
1012 THE STEAM-ENGINE. 
 
 AVERAGE LOSSES IN THE CONVERSION OF 1 LB. OF COAL INTO ELECTRICITY,, 
 
 B.T.U. % B.T.U. % 
 
 1. 
 
 B.T.U. per Ib. of coal supplied 14,150 100.0 
 
 
 
 2. 
 
 Loss in ashes 
 
 340 
 
 2.4 
 
 3. 
 
 Loss to stack 
 
 3,212 
 
 22.7 
 
 4. 
 5. 
 
 Loss in boiler radiation and air leakage 
 Returned by feed-water heater 441 3.1 
 
 1,131 
 
 8.0 
 
 6. 
 
 Returned by economizer 960 6.8 
 
 
 
 7. 
 
 Loss in pipe radiation 
 
 28 
 
 0.2 
 
 8. 
 
 Delivered to circulator 
 
 223 
 
 1.6 
 
 9. 
 
 Delivered to feed purnp 
 
 203 
 
 1.4 
 
 10. 
 
 Loss in leakage and high-pressure drips 
 
 152 
 
 1.1 
 
 11. 
 
 Delivered to small auxiliaries 
 
 51 
 
 0.4 
 
 12. 
 
 Heating _. 
 
 31 
 
 0.2 
 
 13. 
 
 Loss in engine friction 
 
 111 
 
 0.8 
 
 14. 
 
 Electrical losses 
 
 36 
 
 0.3 
 
 15. 
 
 Engine radiation losses 
 
 28 
 
 0.?. 
 
 16. 
 
 Rejected to condenser 
 
 8,524 
 
 60.1 
 
 17. 
 
 To house auxiliaries 
 
 29 
 
 0.2 
 
 15,551 109.9 14,099 99.6 
 14,099 99.6 
 
 Delivered to bus bar 1,452 10.3 
 
 Item 3. The chimney loss is very large, due to admitting too much air 
 to the combustion chamber. This loss can be reduced about half by the 
 use of a CO2 recorder and proper management of the fire. 
 
 Item 4. This loss is largely due to infiltration of air into the brick 
 setting. It can be saved by having an air-tight sheet-iron casing enclosing 
 a magnesia lining outside of the brickwork. 
 
 Item 5. All auxiliaries should be driven by steam, so that their exhaust 
 may be utilized in the feed-water heater. 
 
 Item 6. In all cases where the load factor exceeds 25% the investment 
 in economizers will be justified. 
 
 Item 7. The pipes are covered with two layers of covering, each about 
 1.5 in. thick. 
 
 Item 10. The high-pressure drips can be returned to the boiler, so 
 practically all the loss under this heading is recoverable. 
 
 Item 13. Recent tests of a 7500-H.P. reciprocating engine show a 
 mechanical efficiency of 93.65%, or an engine friction of 6.35%. The 
 engine is lubricated by the flushing system. 
 
 Item 16. The maximum theoretical efficiency of an engine working 
 between 175 Ibs. gauge and 28 ins. vacuum is 
 
 (Ti - T 2 ) -f- Ti = (837 - 560) -^ 837 = 33%. 
 
 The actual best efficiency of this engine is 17 Ibs. per K.W.-hour = 16.7% 
 thermal efficiency: dividing by 0.98, the generator efficiency, gives the net 
 thermodynamic efficiency of the engine, = 17%. The difference between 
 the theoretical and the actual efficiency is 33 - 17 = 16%, of which 6.35% 
 is due to engine friction, and the balance. 9.65%, is due to cylinder con- 
 densation, incomplete expansion, and radiation. [Some of this difference 
 is due to the fact that the engine does not work on the Carnot cycle, in 
 which the heat is all received at the highest temperature, and part of this 
 loss might be saved by the Nordberg feed-water heating system. There 
 may also be a slight loss from leakage. W.K.J Superheated steam, to 
 such an extent as to insure dry steam at the point 01 cut-off in the low- 
 pressure cylinder, might save 5 or 6%. 
 
 The present type 01 power plant using reciprocating engines can be im- 
 proved in efficiency as follows: Reduction of stack losses, 12%; boiler 
 radiation and leakage, 5%; by superheating, 6%; resulting in a net in- 
 crease of thermal efficiency of the entire plant of 4.14% and bringing the 
 total from 10.3 to 14.44%. 
 
 The Steam Turbine. The best results from the steam turbine up to 
 date show that its economy on dry saturated steam is practically equal 
 to that of the reciprocating engine, and that 200 J superheat reduces its 
 steam consumption 13.5%. The shape of the economy curve is much 
 
c< 
 
 iOMMERCIAL ECONOMY COSTS OF POWER. 1013 
 Maintenance and Operation Costs of Different Types of Plant. 
 
 
 Recip- 
 rocating 
 Engines. 
 
 Steam 
 Turbines 
 
 Recip- 
 rocating 
 Engines 
 and 
 Steam 
 Turbines. 
 
 Gas- 
 Engine 
 Plant. 
 
 Gas 
 
 Engines 
 and 
 Steam 
 Turbines. 
 
 MAINTENANCE. 
 1. Engine room mechan- 
 ical 
 
 2.57 
 
 0.51 
 
 1.54 
 
 2.57 
 
 1.54 
 
 2. Boiler room or pro- 
 ducer room 
 
 4 61 
 
 4 30 
 
 3.52 
 
 1.15 
 
 1.95 
 
 3. Coal- and ash-han- 
 dling apparatus . . . 
 4. Electrical apparatus 
 OPERATION. 
 5. Coal; and ash-han- 
 dling labor 
 
 0.58 
 1.12 
 
 2 26 
 
 0.54 
 1.12 
 
 2.11 
 
 0.44 
 1.12 
 
 1.74 
 
 0.29 
 1.12 
 
 1.13 
 
 0.29 
 1.12 
 
 1.13 
 
 6. Removal of ashes 
 7. Dock rental 
 
 1.06 
 0.74 
 
 0.94 
 0.74 
 
 0.80 
 0.74 
 
 0.53 
 0.74 
 
 0.53 
 0.74 
 
 8. Boiler-room labor. . . . 
 9. Boiler- room oil.waste, 
 
 7.15 
 0.17 
 
 6.68 
 0.17 
 
 5.46 
 0.17 
 
 1.79 
 
 0.17 
 
 3.03 
 0.17 
 
 10 Coal 
 
 61 30 
 
 57 30 
 
 46.87 
 
 26.31 
 
 25.77 
 
 1 1 . Water 
 
 7.14 
 
 0.71 
 
 5.46 
 
 3.57 
 
 2.14 
 
 12. Engine-room me- 
 chanical labor 
 13. Lubrication 
 14. Waste, etc 
 
 6.71 
 1.77 
 30 
 
 1.35 
 0.35 
 0.30 
 
 4.03 
 1.01 
 0.30 
 
 6.71 
 1.77 
 0.30 
 
 4.03 
 1.06 
 0.30 
 
 15. Electrical labor 
 
 2 52 
 
 2 52 
 
 2 52 
 
 2.52 
 
 2.52 
 
 
 
 
 
 
 
 Relative cost of mainte- 
 nance and operation . . 
 
 100.00 
 
 79.64 
 
 75.72 
 
 50.67 
 
 46.32 
 
 Relative investment in 
 per cent 
 
 100.00 
 
 82.50 
 
 77.00 
 
 100.00 
 
 91.20 
 
 
 
 
 
 
 
 flatter [from 3300 to 8000 K. W. the range of steam consumption is between 
 14.6 and 15.0 Ibs. per K.W.-hour], so that the all-day efficiency would be 
 considerably better than that of the reciprocating engine, and the cost 
 would be about 33% less for the combined steam motor and electric 
 generator. 
 
 High-pressure Reciprocating Engine with Low-pressure Turbine. The 
 reciprocating engine is more efficient than the turbine in the higher pres- 
 sures, while the turbine can expand to lower pressures and utilize the gain 
 of full expansion. The combination of the two would therefore be more 
 efficient than a turbine alone. 
 
 The Gas Engine. The best result up to date obtained from gas pro- 
 ducers and gas engines is about as follows: Loss in producer and auxiliaries, 
 20%; in jacket water, 19%; in exhaust gases, 30%; in engine friction, 
 6.5%; in electric generator, 0.5%. Total losses, 76%. Converted into 
 electric energy, 24%. Only one important objection can be raised to this 
 motor, that its range of economical load is practically limited to between 
 50% and full load. This lack of overload capacity is probably a fatal 
 defect for the ordinary railway power plant acting under a violently 
 fluctuating load, unless protected by a large storage-battery. 
 
 At light loads the economy of gas and liquid fuel engines fell off even 
 more rapidly than in steam-engines. The engine friction was large and 
 nearly constant, and in some cases the combustion was also less perfect 
 at light loads. At the Dresden Central Station the gas-engines were kept 
 working at nearly their full power by the use of storage-batteries. The 
 results of some experiments are given below: 
 
1014 THE STEAM-ENGINE. 
 
 Brake-load, per Gas-engine, cu. ft. 
 cent of full of Gas per Brake 
 
 Petroleum Eng., 
 Lbs. of Oil per 
 
 Petroleum Eng., 
 Lbs. of Oil per 
 
 Power. 
 
 H.P. per hour. 
 
 B.H.P. per hr. 
 
 B.H.P. per hr. 
 
 100 
 
 22.2 
 
 0.96 
 
 0.88 
 
 75 
 
 23.8 
 
 1.11 
 
 0.99 
 
 59 
 
 28.0 
 
 1.44 
 
 1.20 
 
 20 
 
 40.8 
 
 2.38 
 
 1.82 
 
 121/2 
 
 66.3 
 
 4.25 
 
 3.07 
 
 
 Combination of Gas Engines and Turbines. A steam turbine unit can 
 be designed to take care of 100% overload -for a few seconds. If a plant 
 were designed with 50% of its normal capacity in gas engines and 50% 
 in steam turbines, any fluctuations in load likely to arise in practice could 
 be. taken care of. By utilizing the waste heat of the gas engine in econ- 
 omizers and superheaters there can be saved approximately 37% of this 
 waste heat, to make steam for the turbines. The average total thermal 
 efficiency of such a combination plant would be 24.5%. This combina- 
 tion offers the possibility of producing the kilowatt-hour for less than one- 
 half its present cost. 
 
 The table on p. 1013 shows the distribution of estimated relative main- 
 tenance and operation costs of five different types of plant, the total cost 
 of current with the reciprocating engine plant being taken at 100. 
 
 Storing Heat in Hot Water. (See also p. 927.) There is no satisfac- 
 tory method for equalizing the load on the engines and boilers in electric- 
 light stations. Storage-batteries have been used, but they are expensive 
 in first cost, repairs, and attention. Mr. Halpin, of London, proposes to 
 store heat during the day in specially constructed reservoirs. As the 
 water in the boilers is raised to 250 Ibs. pressure, it is conducted to cylin- 
 drical reservoirs resembling English horizontal boilers, and stored there 
 for use when wanted. In this way a comparatively small boiler-plant 
 can be used for heating the water to 250 Ibs. pressure all through the 
 twenty-four hours of the day, and the stored water may be drawn on at 
 any time, according to the magnitude of the demand. The steam-engines 
 are to be worked by the steam generated by the release of pressure from 
 this water, and the valves are to be arranged in such a way that the steam 
 shall work at 130 Ibs. pressure. A reservoir 8 ft. in diameter and 30 ft. 
 long, containing 84,000 Ibs. of heated water at 250 Ibs. pressure, would 
 supply 5250 Ibs. of steam at 130 Ibs. pressure. As the steam consump- 
 tion of a condensing electric-light engine is about 18 Ibs. per horse-power 
 hour, such a reservoir would supply 286 effective horse-power hours. In 
 1878, in France, this method of storing steam was used on a tramway. 
 M. Francq, the engineer, designed a smokeless locomotive to work by 
 steam-power supplied by a reservoir containing 400 gallons of water at 
 220 Ibs. pressure. The reservoir was charged with steam from a stationary 
 boiler at one end of the tramway. 
 
 An installation of the Rateau low-pressure turbine and regenerator 
 system at the rolling mill of the International Harvester Co., in Chicago, 
 is described in Power, June, 1907. The regenerator is a cylindrical shell 
 11 1/2 ft. diam., 30 ft. long, containing six large elliptical tubes perforated 
 with many 3/ 4 _in. holes through which exhaust steam from a reversing 
 blooming-mill engine enters the water contained in the shell. A large 
 steam pipe leads from the shell to the turbine. A series of tests of the 
 combination was made, giving results as follows: The 42 X 60 in. blooming 
 mill engine developed 820 I. H.P. on the average, with a water rate of 64 
 Ibs. per I. H.P. hour. It delivered its exhaust, averaging a little above at- 
 mospheric pressure, to the regenerator, at an irregular rate corresponding 
 to the varying work of the rolling-mill engine. The regenerator furnished 
 steam to the turbine, which in four different tests developed 444, 544, 
 727 and 869 brake H.P. at the turbine shaft, with a steam consumption 
 of 47.7, 37.1, 30.7 and 33.7 Ibs. of steam per B.H.P. hour at the turbine. 
 Had the turbine been of sufficient capacity to use all the exhaust of the 
 mill engine, 1510 H.P. might have been delivered at the switchboard, 
 which added to the 820 of the mill engine would make 2330 H.P. for 
 52,400 Ibs. of steam, or a steam' rate of 22,5 Ibs. per H,P. liour for tne 
 .combination, 
 
EULES FOR CONDUCTING ENGINE TESTS. 1015 
 
 UTILIZING THE SUN'S HEAT AS A SOURCE OF POWER. 
 
 John Ericsson, 1868-1875, experimented on "solar engines," in which 
 reflecting surfaces concentrated the sun's rays at a central point causing 
 them to boil water. A large motor of this type was built at Pasadena, 
 Cal., in 1898. The rays were concentrated upon a water heater through 
 which ether or sulphur dioxide was pumped in pipes, and utilized in a 
 vapor engine. The apparatus was commercially unsuccessful on account 
 of variable weather conditions. Eng. News, May 13, 1909, describes the 
 solar heat systems of F. Shuman and of H. E. Willsie and John Boyle, Jr. 
 
 In the Shuman invention a tract of land is rolled level, forming a shallow 
 trough. This is lined with asphaltum pitch and covered with about 
 3 ins. of water. Over the water about Vie in. of paraffine is flowed, leaving 
 between this and a glass cover about 6 ins. of dead air space. It is esti- 
 mated that a power plant of this type to cover a heat-absorption area of 
 160,000 sq. ft., or nearly four acres, would .develop about 1000 H.P. 
 Provision is made for storing hot water in excess of the requirements of 
 a low-pressure turbine during the day, to be utilized for running the 
 turbine during the period when there is no absorption of heat. The 
 heated water is run from the heat absorber to the storage tank, thence 
 to the turbine, through a condenser and back to the heat absorber. The 
 water enters the thermally insulated storage tank, or the turbine, at about 
 202 F. With a vacuum of 28 ins. in the condenser, the boiling-point of 
 the water is reduced to 102, and as it enters the turbine nearly 10% 
 explodes into steam. Mr. Shuman estimates that a 1000-H.P. plant built 
 upon his plan would cost about $40,000. 
 
 The Willsie and Boyle plant also utilizes the indirect system of absorb- 
 ing solar heat and storing the hot water in tanks. This hot water cir- 
 culates in a boiler containing some volatile liquid, and the vapor generated 
 is used to operate the engine, is condensed, and returned to the boiler 
 to be used again. Mr. Willsie compares the cost per H.P.-hour in a 
 400-H.P. steam-electric and solar-electric power plant, and finds that the 
 steam plant would have to obtain its coal for $0.66 a ton to compete with 
 the sun power plant in districts favorable to the latter. 
 
 RULES FOR CONDUCTING TESTS FOR RECIPROCATING 
 STEAM-ENGINES. 
 
 (Abstract of the 1915 Code of the Power Test Committee of the 
 Am. Soc. M. E.) 
 
 The code for steam engine tests applies to tests for determining 
 the performance of the engine alone (including reheaters and jackets, 
 if any) apart from that of steam-driven auxiliaries which are neces- 
 sary to its operation. For tests of engine and auxiliaries combined, 
 and tests of multiple expansion engines from which steam is with- 
 drawn Jf or heating feed water or otherwise, refer to the Code for Com- 
 plete Steam Power Plants. 
 
 OBJECT AND PREPARATIONS. 
 
 ^ Determine the object of the test, take the dimensions, and note 
 the physical conditions, not only of the engine, but of all parts of 
 the plant that are concerned in the determinations, examine for 
 leakages, install the testing appliances, etc., and prepare for the 
 test accordingly . 
 
 The determination of the heat and steam consumption of an engine 
 by feed-water test requires the measurement of the various supplies 
 of water fed to the boiler; that of the water wasted by separators 
 and drips on the main steam line, that of steam used for other purposes 
 than the main engine cylinders, and that of water and steam which 
 escape by leakage of the boiler and piping; all of these last being de- 
 ducted from the total feed water measured. 
 
 Where a surface condenser is provided and the steam consumption 
 is determined from the water discharged by the air pump, no such 
 measurement of drips and leakage is required, but assurance must 
 be had that all the steam passing into the cylinders finds -its way 
 
1016 THE STEAM-ENGINE. 
 
 into the condenser. If the condenser leaks, the defects causing 
 such leakage should be remedied, or suitable correction should be 
 made. 
 
 When no other method is available the steam consumption may 
 be determined by the use of a steam meter, bearing in mind the caution 
 that it should be calibrated under the exact conditions of use. 
 
 The steam consumed by steam-driven auxiliaries which are re- 
 quired for the operation of the engine should be included in the total 
 steam from which the heat consumption is calculated and the quan- 
 tity of steam thus used should be determined and reported. 
 
 OPERATING CONDITIONS. 
 
 Determine what the operating conditions should be to conform 
 to the object in view, and see that they prevail throughout the trial. 
 
 DURATION. 
 
 A test for steam or heat consumption, with substantially constant 
 load, should be continued for such time as may be necessary to obtain 
 a number of successive hourly records, during which the results are 
 reasonably uniform. For a test involvirg the measurement of feed- 
 water for this purpose, five hours' duration is sufficient. Where a 
 surface condenser is used, and the measurement is that of the water 
 discharged by the air pump, the duration may be somewhat shorter. 
 In this case, successive half-hourly records may be compared and the 
 time correspondingly reduced. 
 
 When the load varies widely at different times of the day, the 
 duration should be such as to cover the entire period of variation. 
 
 STARTING AND STOPPING. 
 
 The engine and appurtenances having been set to work and thor- 
 oughly heated under the prescribed conditions of test (except in cases 
 where the object is to obtain the performance under working condi- 
 tions) note the water levels in the boilers and feed reservoir, take the 
 time and consider this the starting time. Then begin the measure- 
 ments and observations and carry them forward until the end of the 
 period determined on. When this time arrives, the water levels and 
 steam pressure should be brought as near as practicable to the same 
 points as at the start. This being done, again note the time and 
 consider it the stopping time of the test. If there are differences in 
 the water levels, proper corrections are to be applied. 
 
 Where a surface condenser is used, the collection of water dis- 
 charged by the air pump begins at the starting time, and the water 
 is thereafter^measured or weighed until the end of the test. 
 
 RECORDS. 
 
 Half-hourly readings of the instruments are sufficient, excepting 
 where there are wide fluctuations. A set of indicator diagrams should 
 be obtained at intervals of 15 or 20 minutes, and often er if the nature 
 of the test makes it necessary. Mark on each card the cylinder and 
 the end on which it was taken, also the time of day. Record on one 
 card of each set the readings of the steam pressure and vacuum gages. 
 These records should be subsequently entered on the general log, 
 together with the areas, pressures, lengths, etc., measured from the 
 diagrams, when these are worked up. 
 
 CALCULATION OF RESULTS. 
 
 Dry Steam. The quantity of dry steam consumed is determined 
 by deducting the moisture, if any, found by the calorimeter test 
 from the total amount of feed-water (the latter being corrected 
 for leakages and other losses) or from the amount of air-pump dis- 
 charge, as the case may be. If the steam is superheated, no cor- 
 rection is to be made for the superheat. 
 
 Heat Consumption. The number of heat-units consumed by the 
 engine is found by multiplying the weight of feed-water consumed, 
 
RULES FOR CONDUCTING STEAM-ENGINE TESTS. 1017 
 
 corrected for moisture in the steam, if any, and for plant leakages 
 and other exterior losses, by the total heat of I Ib. of steam (sat- 
 urated or superheated) less the heat in 1 Ib. of water at the tem- 
 perature corresponding to the pressure in the exhaust pipe near 
 the engine. 
 
 Indicated Horse-power. In a single double-acting cylinder the indi- 
 cated horse-power is found by using the formula 
 
 PLAN 
 33,000* 
 
 in which P represents the average mean effective pressure in pounds 
 per square inch measured from the indicator diagrams, L the length 
 of stroke in feet, A the area of the piston less 9ne-half the area 
 of the piston rod, or the mean area of the rod if it passes through 
 both cylinder heads, in square inches, and N the number of single 
 strokes per minute. 
 
 Brake Horse-power. The brake horse-power is found by multiplying 
 the net pressure or weight in pounds on the brake arm (the gross 
 weight minus the weight when the brake is entirely free from the 
 pulley) in pounds, the circumference of the circle whose radius 
 is the horizontal distance between the center of the shaft and the 
 bearing point at the end of the brake arm in feet, and the number 
 of revolutions of the brake shaft per minute; and dividing the 
 product by 33,000. 
 
 Electrical Horse-power. The electrical horse-power of a direct-con- 
 nected generator is found by dividing the output at the terminals 
 expressed in kilowatts, by the decimal 0.7457. With alternating 
 current generators the net output is to be used, this being the total 
 output less that consumed for excitation and for separately-driven 
 ventilating fans. 
 
 Efficiency. The thermal efficiency, that is, the percentage of the 
 total heat consumption which is converted into work, is found 
 by dividing the quantity 2546.5, which is the B.T.U. equivalent 
 of one H. P. -hour, by the number of heat-units actually consumed 
 per H! P. -hour. 
 
 The Rankine cycle efficiency is found by dividing the heat con- 
 sumption of an ideal engine conforming to the Rankine cycle by 
 the actual heat consumption. 
 
 Steam Accounted for by Indicator Diagrams at Points Near Cut-off 
 and Release. The steam accounted for, expressed in pounds per 
 I.H.P. per hour, may be found by using the formula 
 
 IJOOrKC + E) W c - (H + E} W h ], 
 
 in which 
 
 M.E.P. = mean effective pressure; 
 
 C = proportion of direct stroke completed at points on ex- 
 pansion line near cut-off or release; 
 E = proportion of clearance; 
 H = proportion of return stroke uncompleted at point on 
 
 compression line just after exhaust closure; 
 W c = weight of 1 cu. ft. steam at pressure shown at cut-off or 
 
 release point; 
 
 W n = weight of 1 cu. ft. steam at pressure shown at compres- 
 sion point. 
 
 In multiple expansion engines the mean effective pressure to be 
 used in the above formula is the aggregate M.E.P. referred to the 
 cylinder under consideration. In a compound engine the aggregate 
 M.E.P. for the h.p. cylinder is the sum of the actual M.E.P. of 
 the h.p. cylinder and that of l.p. cylinder multiplied by the cyl- 
 inder ratio. Likewise the aggregate M.E.P. for the l.p. cylinder 
 is the sum of the actual M.E.P. of the l.p. cylinder and the M.E.P. 
 of the h.p. cylinder divided by the cylinder ratio. 
 
 The relation between the weight of steam shown by the indicator 
 at any point in the expansion line and the weight of the mixture 
 of steam and water in the cylinder, may be represented graphically 
 by plotting on the diagram a saturated steam curve showing the 
 
1018 THE STEAM-ENGINE. 
 
 total consumption per stroke (including steam retained at com- 
 pression) and comparing the abscissae of this curve with the absciss* 
 of the expansion line, both measured from the line of no clearance. 
 Cut-off and Ratio of Expansion. To find the percentage of cut-off, 
 or what may best be termed the "commercial cut-off," the fol- 
 lowing rule should be observed: 
 
 Through the point of maximum pressure during admission 
 draw a line parallel to the atmospheric .line. Through a 
 point on the expansion line where the cut-off is complete, 
 draw a hyperbolic curve. The intersection of these two lines 
 is the point of commercial cut-off, and the proportion of cut-off 
 is found by dividing the length measured on the diagram 
 up to this point by the total length. 
 
 To find the ratio of expansion divide the volume corresponding 
 to the piston displacement, including clearance, by the volume of 
 the steam at the commercial cut-off, including clearance. 
 
 In a multiple expansion engine, the ratio of expansion is found 
 by dividing the volume of the l.p. cylinder, including clearance, 
 by the volume of the h.p. cvlinder at the commercial cut-off, in- 
 cluding clearance. 
 
 DATA AND RESULTS. 
 
 The data and results should be reported in accordance with the 
 form given herewith, adding lines for data not provided for, or omitting 
 those not required, as may conform to the object in view. If the 
 principal data and results pertaining to steam consumption only are 
 desired, the subjoined abbreviated table may be used. 
 
 DATA AND RESULTS OF STEAM-ENGINE TEST 
 Code of 1915. 
 
 1. Test of engine located at 
 
 To determine 
 
 Test conducted by , 
 
 DIMENSIONS, ETC. 
 
 2. Type of engine (simple or multiple expansion). 
 
 3. Class of service (mill, marine, electric, etc.) . . . 
 
 4. Auxiliaries (steam or electric driven) . 
 
 5. Rated power of engine 
 
 1st 2d 3d 
 
 6. Diameter of cylinders in! 
 
 7. Stroke of pistons ft 
 
 (a) Diameter of piston-rod, each end, 
 
 in : 
 
 8. Clearance (average) in per cent of piston 
 
 displacement 1 to 
 
 9. H. P; constant 1 Ib. 1 rev H.P . 
 
 (a) Cylinder ratio (based on net pis- 
 ton displacement 1 to 
 
 10. Capacity of generator or other apparatus 
 
 consuming power of engine H.P 
 
 DATE AND DURATION. 
 
 11. Date ' 
 
 12. Duration hr. 
 
 AVERAGE PRESSURES AND TEMPERATURES. 
 
 13. Pressure in steam pipe near throttle, by gage Ibs. per sq, in. 
 
 14. Barometric pressure ins. 
 
 15. Pressure in 1st receiver, by gage Ibs. per sq. in. 
 
 16. Pressure in 2d receiver, by gage Ibs. per sq. in. 
 
 17. Vacuum in condenser ins. 
 
 18. Pressure in jackets and reheaters . . . Ibs. per sq. in. 
 
 19. Temperature of steam near throttle, if superheated degs. 
 
 20. Temperature corresponding to pressure in exhaust pipe 
 
 near engine 
 
I RULES FOR CONDUCTING STEAM-ENGINE TESTS. 1019 
 
 QUALITY OF STEAM. 
 
 ; 21. Percentage of moisture in steam near throttle, or degrees 
 
 of superheating % or deg. 
 
 TOTAL QUANTITIES. 
 
 Water fed to boilers, from main supply Ibs. 
 
 Water fed to boilers from additional supplies Ibs. 
 
 Total water fed to boilers Ibs. 
 
 Total condensed steam from surface condenser (corrected 
 for condenser leakage) Ibs. 
 
 26. Total dry steam consumed (Item 24 to 25 less moisture 
 
 in steam) - Ibs. 
 
 HOURLY QUANTITIES. 
 
 27. Water fed to boilers from main supply per hour Ibs. 
 
 2S. Water fed to boilers from additional supplies per hour. . Ibs. 
 
 29. Total water fed to boilers or drawn from surface con- 
 
 denser per hour Ibs. 
 
 30. Total -dry steam consumed for all purposes per hour 
 
 (Item 26 ~ Item 12) Ibs. 
 
 31. Steam consumed per hour for all purposes foreign to the 
 
 main engine (including drips and leakage of plant) . . . Ibs. 
 
 32. Dry stearn consumed by engine per hour (Item 30 
 
 Item 31) Ibs. 
 
 33. Heat units consumed by engine per hour (Item 32 X 
 
 total heat of steam per Ib. above exhaust temperature 
 
 of Item 20) B.T.U. 
 
 INDICATOR DIAGRAMS. 
 
 lstCyl.2dCyl. 3d Cyl. 
 
 34. Commercial cut-off in per cent of stroke, 
 
 per cent 
 
 35. Initial pressure above atmosphere 
 
 Ibs. per sq. in 
 
 36. Back pressure at lowest point above or 
 
 below atmosphere Ibs. per sq. in 
 
 37. Mean effective pressure Ibs. per sq. in 
 
 38. Aggregate M.E.P. referred to each cyl- 
 
 inder Ibs. per sq. in . . , f 
 
 39. Steam accounted for per I.H.P.-hr. at 
 
 point on expansion line shortly after 
 
 cut-off Ibs 
 
 40. Stearn accounted for per I.H.P.-hr. at 
 
 point on expansion line just before 
 release Ibs. . 
 
 SPEED. 
 
 41. Revolutions per minute R.P.M. 
 
 42. Piston speed per minute ft. 
 
 (a) Variation of speed between no load and full load . per cent. 
 
 (b) Momentary fluctuation of speed on suddenly 
 
 changing from full load to half load per cent. 
 
 43. Indicated H.P. developed, whole engine. I.H.P. 
 
 (a) I.H.P. developed by 1st cylinder I.H.P. 
 
 (b) I.H.P. developed by 2d cylinder I.H.P. 
 
 (c) I.H.P. developed by 3d cylinder I.H.P. 
 
 44. Brake H.P B.H.P. 
 
 45. Friction of engine (Item 43 Item 44) H.P. 
 
 (a) Friction expressed in percentage of I.H.P. (Item 
 
 45 -4- Item 43 X 100) per cent. 
 
 (&) Indicated H.P. with no load, at normal speed. . . . I.H.P. 
 
1020 THE STEAM-ENGINE. 
 
 ECONOMY RESULTS. 
 
 46. Dry steam consumed by engine per I.H.P. per hr Ibs. 
 
 47. Dry steam consumed by engine per brake H.P.-hr Ibs. 
 
 48. Percentage of steam consumed by engine accounted for 
 
 by indicator at point near cut-off per cent. 
 
 49. Percentage of steam consumed near release per cent. 
 
 50. Heat-units consumed by engine per I. H.P.-hr. (Item 
 
 33 -r- Item 43) B.T.U. 
 
 51. Heat-units consumed by engine per brake H.P.-hr. (Item 
 
 33 -=- Item 44) B.T.U. 
 
 52. Heat-units consumed per H.P.-hr. by ideal engine, 
 
 based on Rankine cycle B.T.U. 
 
 EFFICIENCY RESULTS. 
 
 53. Thermal efficiency of engine referred to I.H.P. (2546.5 -4- 
 
 Item 50) per cent. 
 
 54. Thermal efficiency of engine referred to Brake H.P. 
 
 (2546.5 -i- Item 51) per cent. 
 
 65. Efficiency of engine based on Rankine cycle referred to 
 
 I.H.P. (Item 52 4- Item 50) per cent. 
 
 56. Efficiency of engine referred to Brake H.P. (Item 52 -r- * 
 
 Item 51) per cent. 
 
 WORK DONE PER HEAT-UNIT. 
 
 57. Foot-pounds of net work per B.T.U. consumed by 
 
 engine (1,980,000 -r- Item 51) ft.-lbs. 
 
 SAMPLE DIAGRAMS. 
 
 58. Sample diagrams from each cylinder 
 
 NOTE: For an engine driving an electric generator the form should 
 be enlarged to include the electrical data, embracing the average 
 voltage, number of amperes each phase, number of watts, number 
 of watt-hours, average power factor, etc.; and the economy results 
 based on the electric output embracing the heat-units and steam 
 consumed per electric H.P. per hour and per kw.-hr., together with 
 the efficiency of the generator. 
 
 Likewise, in a marine engine having a shaft dynamometer, the 
 form should include the data obtained from this instrument, in which 
 case the Brake H.P. becomes the Shaft H.P. 
 
 PRINCIPAL DATA AND RESULTS OF RECIPROCATING ENGINE TEST. 
 
 1. Dimensions of cylinders 
 
 2. Date 
 
 3. Duration hrs. 
 
 4. Pressure in steani pipe near throttle by gage Ibs. per sq. in. 
 
 5. Pressure in receivers Ibs. per sq. in. 
 
 6. Vacuum in condenser ins. 
 
 7. Percentage of moisture in steam near throttle or 
 
 number of degrees of superheating / % or deg. 
 
 8. Net steam consumed per hour Ibs. 
 
 9. Mean effective pressure in each cylinder. . Ibs. per sq. in. 
 
 10. Revolutions per minute R.P.M. 
 
 11. Indicated horse-power developed H.P. 
 
 12. Steam consumed per I.H.P. per hr Ibs. 
 
 13. Steam accounted for at- cut-off each cylinder Ibs. 
 
 14. Heat consumed per I.H.P. per hr B.T.U. 
 
DIMENSIONS OP PARTS OF ENGINES. 
 
 1021 
 
 DIMENSIONS OF PARTS OF ENGINES. 
 
 The treatment of this subject by the leading authorities on the steam- 
 engine is very unsatisfactory, being a confused mass of rules and for- 
 mulae based partly upon theory and partly upon practice. The practice 
 of builders shows an exceeding diversity of opinion as to correct dimen- 
 sions. The treatment given below is chiefly the result of a study of the 
 works of Rankine, Seaton, Unwin, Thurston, Marks, and Whitham, and 
 is largely a condensation of a series of articles by the author published 
 in the American Machinist, in 1894, with many alterations and much 
 additional matter. 
 
 (Two notable papers on the subject, however, have appeared: 1, Cur- 
 rent Practice in Engine Proportions, by Prof. John H. Barr, 1897; and 
 2, Current Practice in Steam-engine Design, by Ole N. Trooien, 1909. 
 Both of these are abstracted on pages 1039 and 1040.) 
 
 Cylinder. (Whitham) Length of bore = stroke 4- breadth of pis- 
 ton-ring i/8-to 1/2 in.; length between heads = stroke + thickness of 
 piston -f sum of clearances at both ends ; thickness of piston = breadth 
 of ring -f- thickness of flange on one side to carry the ring + thickness 
 of follower-plate. 
 
 Thickness of flange or follower. . . 3 /g to 1/2 in. 3/ 4 in. 1 in. 
 
 For cylinder of diameter 8 to 10 in. 36 in. 60 to 100 in. 
 
 Clearance of Piston. (Seaton.) The clearance allowed varies with 
 the size of the engine from i/g to 3/g m - f r roughness of castings and 
 1/16 to i/s in. for each working joint. Naval and other very fast-running 
 engines have a larger allowance. In a vertical direct-acting engine the 
 parts which wear so as to bring the piston nearer the bottom are three, 
 viz., the shaft journals, the crank-pin brasses, and piston-rod gudgeon- 
 brasses. 
 
 Thickness of Cylinder. In the earlier editions of this book eleven 
 formulae, from seven different authorities, were given for thickness of 
 cylinders and they were applied to six engines, the dimensions of which 
 are given in the following table. 
 
 DIMENSIONS, ETC., OF ENGINES. 
 
 Indicated horse-pow'er 
 
 I.H P 
 
 50 
 
 450 
 
 1250 
 
 Diam. of cyl., in 
 
 D 
 
 10 
 
 30 
 
 50 
 
 Stroke, feet. 
 
 L 
 
 1 2 
 
 2V 2 5 
 
 4 8 
 
 Revs, per min 
 
 T 
 
 250 . 125 
 
 130 65 
 
 90 45 
 
 Piston speed, ft. per min 
 
 s 
 
 500 
 
 650 
 
 700 
 
 Area of piston, sq. in. . . . 
 
 OL 
 
 78 54 
 
 706 86 
 
 1963 5 
 
 Mean effective pressure 
 
 M E P. 
 
 42 
 
 32 3 
 
 30 
 
 Max. total unbalanced pressure. 
 Max. total pressure per sq. in. . . 
 
 P 
 P 
 
 7854 
 100 
 
 70,686 
 100 
 
 196.350 
 100 
 
 The thickness of the cylinders of these engines, according to the 
 eleven formulae, ranges for engines 1 and 2 from 0.33 to 1.13 in., for 
 3 and 4 from 0.99 to 2.00 in., and for 5 and 6 from 1.56 to 3.00 in. 
 The averages of the eleven are, for 1 and 2, 0.76 in.; for 3 and 4, 1.48 
 in.; for 5 and 6, 2.26 in. 
 
 The average corresponds nearly to the formula t = 0.00037 Dp -}- 0.4 
 in. A convenient approximation is t = 0.0004 Dp -f 0.3 in., which gives 
 for 
 
 Diameters 10 20 30 40 50 60 in. 
 
 Thicknesses . 70 1 . 10 1 . 50 1 . 90 2 . 30 2 . 70 in. 
 
 The last formula corresponds to a tensile strength of cast iron of 
 12,500 lb., with a factor of safety of 10 and an allowance of 0.3 in. for 
 reboring. 
 
 Thickness of Cylinder and Its Connections for Marine Engines. 
 
 (Seaton.) D = the diam. of the cylinder in inches; p = load on the 
 safety-valves in lb. per sq. in. ; /, a constant multiplier, = thickness of 
 barrel + 0.25 in. 
 
1022 THE STEAM-ENGINE. 
 
 Thickness of metal of cylinder barrel or liner, not to be less thai* 
 PXD + 3000 when of cast iron.* 
 
 Thickness of cylinder-barrel = p X D -~ 5000 + O.G in. 
 Thickness of liner = 1.1 X / 
 
 Thickness of liner when of steel = p X D -5- 0000 + 0.5 in. 
 Thickness of metal of steam-ports = 0.6 X /. 
 Thickness of metal valve-box sides = 0.65 X /. 
 Thickness of metal of valve-box covers = 0.7 X /. 
 
 cylinder bottom =1.1 X /, if single thickness. 
 
 = 0.65 X/. if double 
 covers =1.0 X/, if single 
 = 0.6 X/, if double 
 cylinder flange =1.4 x/. 
 
 cover-flange =1.3 X/. 
 valve-box flange = 1.0 X/. 
 door-flange =0.9 X /. 
 
 face over ports =1.2 X/. 
 
 " = 1.0 X/, when there is a false- 
 
 face. 
 false-face =0.8 X /, when cast iron. 
 
 = 0.6 X /, when steel or bronze. 
 
 Cylinder-heads. Applying six different formulae to the engines of 10, 
 30, and 50 inches diameter, with maximum unbalanced steam-pressure 
 of 100 Ib. per sq. in., we have 
 
 For cylinder 10 in. diam., 0.35 to 1,15 in.; for 30 in. diam., 0.90 to 
 1.75 in. ; for 50-in. diam., 1.50 to 2.75 in. The averages are respectively 
 0.65, 1.38, and 2.10 in. 
 
 The average is expressed by the formula t = 0.00036 Dp -{- 0.31 inch. 
 
 Web-stiffened Cylinder-covers. Seaton objects to webs for 
 stiffening cast-iron cylinder-covers as a source of danger. The strain on 
 one web is one of tension, and if there should be a nick r defect in the 
 outer edge of the web the sudden application of strain is apt to start 
 a crack. He recommends that high-pressure cylinders over 24 in. and 
 low-pressure cylinders over 40 in. diam. should have their covers cast 
 hollow, with two thicknesses of metal. The depth of the cover at the 
 middle should be about 1/4 the diam. of the piston for pressures of 80 Ib. 
 and upwards, and that of the low-pressure cylinder-cover of a com- 
 pound engine equal to that of the high-pressure cylinder. Another 
 rule is to make the depth at the middle^not less than 1.3 times the 
 diameter of the piston-rod. In the British Navy the cylinder-covers 
 are made of steel castings, 3/4 to 1 1/4 in. thick, generally cast without 
 webs, stiffness being obtained by their form, which is often a series of 
 corrugations. 
 
 Cylinder-head Bolts. Diameter of bolt-circle for cylinder-head = 
 diameter of cylinder + 2 X thickness of cylinder + 2 X diameter of bolts. 
 The bolts should not be more than 6 in. apart (Whitham). 
 
 Marks gives for number of bolts b = 0.7854 Dip -=- 5000 c, in which 
 c = area of a single bolt, p = boiler-pressure in Ib. per sq. in.; 5000 Ib. 
 is taken as the safe strain per sq. in. on the nominal area of the bolt. 
 
 Thurston says: Cylinder flanges are made a little thicker than the 
 cylinder, and usually of equal thickness with the flanges of the heads. 
 Cylinder-bolts should be so closely spaced as not to allow springing of the 
 flanges and leakage, say, 4 to 5 times the thickness of the flanges. Their 
 diameter should be proportioned for a maximum stress of not over 4000 
 to 5000 Ib. per square inch. 
 
 If D = diameter of cylinder, p = maximum steam-pressure, b = 
 number of bolts, s = size or diameter of each bolt, and. 5000 Ib. be 
 allowed per sq. in. of actual area at the root of the thread, 0.7854 D?p = 
 3927 &s2; whence 652 = 0.0002 D*p. 
 
 b = 0.0002 5^; s = 0.01414 D A [?. For the three engines we have: 
 
 * When made of exceedingly good material, at least twice melted, 
 the thickness may be 0.8 of that given by the above rules. 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1023 
 
 Diameter of cylinder, inches 10 30 50 
 
 Diameter of bolt-circle, approx 13 35 57,5 
 
 Circumference of circle, approx 40.8 110 180 
 
 Minimum no. of bolts, circ. -T- 6 7 18 30 
 
 Diam of bolts, s = 0.01414 D+f 3/ 4 in. 1 . 00 1 . 29 
 
 The diameter of bolt for the 10-inch cylinder is 0.54 in. by the formula, 
 but 3/4 inch is as small as should be taken, on account of possible over- 
 strain by the wrench in screwing up the nut. 
 
 The Piston. Details of Construction of Ordinary Pistons. (Seaton.) 
 Let D be the diameter of the piston in inches, p the effective pressure 
 per square inch on it, x a constant multiplier, found as follows: 
 
 x = (D + 50) X VP~+ 1. 
 The thickness of front of piston near the b9ss = 0.2 X x. 
 
 rim 
 back 
 
 boss around the rod 
 flange inside packing-ring 
 
 at edge 
 packing-ring 
 junk- ring at edge 
 
 inside packing-ring 
 at bolt-holes 
 
 metal around piston edge 
 breadth of packing-ring 
 depth of piston at center 
 lap of junk-ring on the piston 
 space between piston body and packing-ring = 0.3 
 diameter of junk-ring bolts =0.1 
 
 = 0.17 X x. 
 = 0.18 X x. 
 = 0.3 X x. 
 = 0.23 X x. 
 = 0.25 X x. 
 = 0.15 X x. 
 
 - 0.23 X x. 
 = 0.21 X x. 
 
 0.35 X X. 
 
 0.25 X*. 
 = 0.63 X x. 
 = 1.4 X x. 
 = 0.45 X x. 
 X x. 
 X x +0.25 in. 
 
 pitch of junk-ring bolts = 10 diameters. 
 
 number of webs in the piston = (D -f 20) -5- 12. 
 
 thickness of webs in the piston = 0.18 X x. 
 
 Marks gives the approximate rule: Thickness of pist9n-head 
 m which I = length of stroke, and D = diameter of cylinder in inches. 
 Whitham says: In a horizontal engine the rings support the piston, or at 
 least a part of it, under ordinary conditions. The pressure due to the 
 weight of the piston upon an area equal to 0.7 the diameter of the 
 cylinder X breadth of ring-face, should never exceed 200 Ib. per sq. in. 
 He also gives a formula much used in this country: Breadth of ring- 
 face = 0.15 X diameter of cylinder. 
 For our engines we have diameter = ....... 10 30 50 
 
 Thickness of piston-head. 
 Marks, 'i/lD; long stroke ............ 3.31 5.48 7.00 
 
 Marks, 'f/lD'; short stroke ............ 3 . 94 6.51 
 
 Seaton, depth at center =\Ax ........ 4.20 9.80 
 
 Seaton, breadth of ring = 0.63 x ....... 1 . 89 4 . 41 
 
 Whitham, breadth of ring = 0. 15 D ____ 1 . 50 4 . 50 
 
 8 .32 
 15.40 
 
 6 . 93 
 
 7 . 50 
 
 Diameter of Piston Packing-rings. These are generally turned, 
 before they are cut, about 1/4 inch diameter larger than the cylinder, 
 for cylinders up to 20 inches diameter, and then enough is cut out of the 
 rings to spring them to the diameter of the cylinder. For larger -cylin- 
 ders the rings are turned proportionately larger. Seaton recommends 
 an excess of 1 %. of the diameter of the cylinder. 
 
 A theoretical paper on Piston Packing Rings of Modern Steam En- 
 gines by O. C. Reymann will be found in Jour. Frank. Inst., Aug., 1897. 
 
 Cross-section of the Rings. The thickness is commonly made 
 1/30 of the diam. of cyl. + i/g inch, and the width = thickness + i/ginch. 
 For an eccentric ring the mean thickness may be the same as for a ring 
 of uniform thickness, and the minimum thickness = 2/3 the maximum. 
 
 A circular issued by J. H. Dunbar, manufacturer of packing-rings, 
 Youngstown, Ohio, says: Unless otherwise ordered, the thickness of 
 rings will be made equal to 0.03 X their, diameter. This thickness has 
 been found to be satisfactory in practice. It admits of the ring being 
 
1024 THE STEAM-ENGINE. 
 
 made about 3/i 6 in. to the foot larger than the cylinder, and has, when 
 new, a tension of about two pounds per inch of circumference, which is 
 ample to prevent leakage if the surface of the ring and cylinder are 
 smooth. 
 
 As regards the width of rings, authorities "scatter" from very narrow 
 to very wide, the latter being fully ten times the former. For instance, 
 Unwin gives W = 0.014 d + 0.08. Whitham's formula is W = 0.15 d. 
 In both formulae W is the width of the ring in inches, and d the diameter 
 of the cylinder in inches. Un win's formula makes the width of a 20-in, 
 ring W = 20 X 0.014 -f 0.08 = 0.36 in., while Whitham's is 20 X 0.15 = 
 3 in. for the same diameter of ring. There is much less difference in the 
 practice of engine-builders in this respect, but there is still room for a 
 standard width of ring. It is believed that for cylinders over 16 in. 
 diameter 8/4 in. is a popular and practical width, and 1/2 in. for cylinders 
 of that size and under. 
 
 Fit of Piston-rod into Piston. (Seaton.) The most convenient 
 and reliable practice is to turn the piston-rod end with a shoulder of i/ie 
 inch for small engines, and i/s inch for large ones, make the taper 3 in. to 
 the foot until the section of the rod is three-fourths of that of the body, 
 then turn the remaining part parallel ; the rod should then fit into the 
 piston so as to leave i/g in. between it and the shoulder for large pistons 
 and 1/16 in. for small. The shoulder prevents the rod from splitting the 
 piston, and allows of the rod being turned true after long wear without 
 encroaching on the taper. 
 
 The piston is secured to the rod by a nut, and the size of the rod should 
 be such that the strain on the section at the bottom of the thread does 
 not exceed 5500 Ib. per sq. in. for iron, 7000 Ib. for steel. The depth 
 of this nut need not exceed the diameter which would be found by allow- 
 ing these strains. The nut should be locked to prevent its working 
 loose. 
 
 Diameter of Piston-rods. Taking d = diam. of piston-rod, D = 
 diam. of piston, I = length of stroke, p = maximum unbalanced pres- 
 sure, Ib. per_sq. in., Unwin gives, for iron rods, d = 0.0167 D\/p; steel, 
 0.0144 D^/p. Marks gives: (1) d = 0.0179 Z>Vp"for iron; (2) 0.0105 
 ZVp for steel; and (3) d = 0.0390 ^DU^p for iron; (4) 0.0352 ffDH*p 
 for steel. Deduce the diameter of the rod by (1) or (2) and if this 
 diameter is less than 1/12? then use (3) or (4). Applying these four 
 formulae to the six engines and taking the average results, we have the 
 following : 
 
 Diameter of Piston-rods. 
 
 Diameter of Cylinder, inches 
 
 1 
 
 
 
 3 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 Stroke, inches 
 
 12 
 
 24 
 
 30 
 
 60 
 
 48 
 
 96 
 
 Diam. of rod, average for iron 
 " " average for steel 
 
 1.49 
 1.33 
 
 1.82 
 1.59 
 
 4.30 
 3.83 
 
 5.26 
 4.52 
 
 7.11 
 6.33 
 
 8.74 
 7.46 
 
 An empirical formula which gives results approximating the above 
 averages is d" = c\/Dlp, the values of c being for short stroke engines, 
 iron, 0.0145; steel, 0.0129; and for long stroke engines, iron, 0.0126, 
 steel, 0.0108. 
 
 The calculated results for this formula, for the six engines, are, re- 
 spectively: 
 
 Iron 1.59 1.95 4.35 5.36 7.11 8.73 
 
 Steel 1.31 1.67 3.87 4.58 6.32 7.48 
 
 In considering an expansive engine, p, the effective pressure, should be 
 taken as the absolute working pressure, or 15 Ib. above that to which 
 the boiler safety-valve is loaded ; for a compound engine the value of p 
 for the high-pressure piston should be taken as the absolute pressure, 
 less 15 Ib., or the same as the load on the safety-valve; for the medium- 
 pressure the load may be taken as that due to half the absolute boiler- 
 pressure; and for the low-pressure cylinder the pressure to which the 
 escape- valve is loaded + 15 Ib., or the maximum absolute pressure 
 which can be got in the receiver, or about 25 Ib. It is an advantage to 
 make all the rods of a compound engine alike, and this is now the rule. 
 
 Piston-rod Guides. The thrust on the guide, when the connecting- 
 
DIMENSIONS OF PARTS OF ENGINES. 1025 
 
 rod is at its maximum angle with the line of the piston-rod, is found from 
 the formula: Thrust = total load on piston X tangent of maximum angle 
 of connecting-rod = p tan 0. ' This angle, 9, is the angle whose sine = 
 half stroke of piston -~ length of connecting-rod. 
 
 Ratio of length of connecting-rod to stroke . . 2 21/2 3 
 
 Maximum angle of connecting-rod with line 
 
 of piston-rod .......................... 14 29' 11 33' 9 36' 
 
 Tangent of the angle ....................... 0.258 0.204 0.169 
 
 Secant of the angle .................. ...... 1.0327 1.0206 1 .014 
 
 Thurston says: The rubbing surfaces of guides are so proportioned 
 that if V be their relative velocity in feet per minute, and p be the in- 
 tensity of pressure on the guide hi Ib. per sq. in., pV < 60,000 and 
 pV> 40,000. 
 
 The lower is the safer limit; but for marine and stationary engines it 
 is allowable to take p = 60,000 -s- V. According to Rankine, for loco- 
 
 motives, p = -TTo/ where p is the pressure in Ib. per sq. in. and V 
 
 the velocity of rubbing in feet per minute. This includes the sum of 
 all pressures forcing the two rubbing surfaces together. 
 
 Some British builders of portable engines restrict the pressure between 
 the guides and cross-heads to less than 40, sometimes 35 Ib. per sq. in. 
 
 For a mean velocity of 600 feet per minute, Prof. Thurston's formulae 
 give, p < 100, p > 66.7; Rankine's gives p = 72.2 Ib. per sq. in. 
 
 Whitham gives, 
 
 A = area of slides in square inches = - -==. = P - 
 
 p Q \/n 2 - 1 p Q Vn 2 - I 
 
 in which P = total unbalanced pressure, pi = pressure per square inch 
 on piston, d = diameter of cylinder, p = pressure allowable per square 
 inch on slides, and n = length of connecting-rod -j- length of crank. 
 This is equivalent to the formula, A = P tan 6 ~ po. For n = 5, p\ = 
 100 and p a = 80, A = 0.2004 d 2 . For the three engines 10, 30, and 50 in. 
 diam., this would give for area of slides, A = 20, 180, and 500 sq. in., 
 respectively. Whitham says: The normal pressure on the slide may be 
 as high as 500 Ib. per sq. in., but this is when there is good lubrication 
 and freedom from dust. Stationary and marine engines are usually 
 designed to carry 100 Ib. per sq. in., and the area in this case is reduced 
 from 50% to 60% by grooves. In locomotive engines the pressure 
 ranges from 40 to 50 Ib. per sq. in. of slide, on account of the inaccessi- 
 bility of the slide, dirt, cinder, etc. 
 
 The Connecting-rod. Ratio of length of connecting-rod to length of 
 stroke. Experience has led generally to the ratio of 2 or 2 1/2 to 1, the 
 latter giving a long and easy-working rod, the former a rather short, but 
 yet a manageable one (Thurston) . Whitham gives the ratio of from 2 
 to 4 1/2 and Marks from 2 tcL.4. 
 
 Dimensions of the Connecting-rod. The calculation of the diameter 
 of a connecting-rod on a theoretical basis, considering it as a strut sub- 
 ject to both compressive and bending stresses, and also to stress due to 
 its inertia, in high-speed engines, is quite complicated. See Whitham, 
 Steam-engine Design, p. 217; Thurston, Manual of S. E., p. 100. 
 
 Applying seven formulae given by different authorities to the six 
 engines the average diameters (at the middle of the rod) are given 
 below : 
 
 Diameter of Connecting-rods. 
 
 Diameter of Cylinder, inches 
 
 1 
 
 
 
 3 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 Stroke, inches 
 
 12 
 
 24 
 
 30 
 
 60 
 
 48 
 
 96 
 
 Length of connecting-rod 1 
 
 30 
 
 60 
 
 75 
 
 150 
 
 120 
 
 240 
 
 Diameter of rod, inches 
 
 2.24 
 
 2.26 
 
 6.38 
 
 6.27 
 
 10.52 
 
 10.26 
 
 The average figures show but little difference in diameter between 
 long- and short-stroke engines; this is what might be expected, for while 
 the connecting-rod, considered simply as a column, would require an 
 Increase of diameter for an increase of length, the load remaining the 
 
1026 THE STEAM-ENGINE. 
 
 same, yet in an engine generally the shorter the connecting-rod the 
 greater the number of revolutions, and consequently the greater the 
 strains due to inertia. The influences tending to increase the diameter 
 therefore tend to balance each other, and to render the diameter to 
 some extent independent of the length. The_average figures correspond 
 nearly to the simple formula d = 0.021 D\/p. The diameters of rod for 
 the three diameters of engine by this formula are, respectively, 2.10, 
 6.30, and 10.50 in. Since the total pressure on_the piston P = 0.7854 
 D*p, the formula is equivalent to d = 0.0237 \/~P. 
 
 Seaton and Sennett give the diameter at the necks of a connecting- 
 rod = 0.9 the dianv at the middle. Whitham gives it as 1.0 to 1.1 the 
 diam. of the piston-rod. 
 
 Connecting-rod Ends. For a connecting-rod end of the marine 
 type, where the end is secured with two bolts, each bolt should be pro- 
 portioned for a safe tensile strength equal to two-thirds of the maximum 
 pull or thrust in the connecting-rod. 
 
 The cap is to be proportioned as a beam loaded with the maximum 
 pull of the connecting-rod, and supported at both ends. The calcula- 
 tion should be made for rigidity as well as strength, allowing a maximum 
 deflection of Vioo inch. For a strap^and-key connecting-rod end the 
 strap is designed for tensile strength, considering that two-thirds of the 
 |)ull on the connecting-rod may come on one arm. At the point where 
 the metal is slotted for the key and gib, the straps must be thickened to 
 make the cross-section equal to that of the remainder of the strap. Be- 
 tween the end of the strap and the slot the strap is liable to fail in double 
 shear, and sufficient metal must be provided at the end to prevent such 
 failure. 
 
 The breadth of the key is generally one-fourth of the width of the 
 strap, and the length, parallel to the strap, should be such that the cross- 
 section will have a shearing strength equal to the tensile strength of the 
 section of the strap. The taper of the key is generally about 5/8 inch 
 to the foot. 
 
 Tapered Connecting-rods. In modern high-speed engines it is cus- 
 tomary to make the connecting-rods of rectangular instead of circular 
 section, the sides being parallel, and the depth increasing regularly from 
 the cross-head end to the crank-pin end. According to Grashof, the 
 bending action on the rod due to its inertia is greatest at 6/ 1( ) the length 
 from the cross-head end, and, according to this theory, that is the point 
 at which the section should be greatest, although in practice the section 
 is made greatest at the crank-pin end. 
 
 Professor Thurston furnished the author with the following rule for 
 tapered connecting-rods of rectangular section: Take the section as com- 
 puted by the formula d" = 0.1 A/ 'DL\/~p~+ 3/4 for a circular section, 
 and for a rod 4/3 the actual length, placing the computed section at 
 2/3 the length from the small end, and carrying the taper straight 
 through this fixed section to the large end. This brings the computed 
 section at the surge point and makes it heavier than the rod for which 
 a tapered form is not required. 
 
 Taking the above formula, multiplying L by 4/3. and changing it to I 
 
 in inches, it becomes d = 1/30 V-DJ \/P~+ 3 /4 in. Taking a rectangular 
 section of the same area as the round section whose diameter is rf, 
 and making the depth of the section h = twice the thickness t, we have 
 
 0.7854 d* = hi = 2 &, whence t = 0.627; d = 0.0209 V Dl\/l) + 0.47in., 
 which is the formula for the thickness or distance between the parallel 
 sides of the rod. Making the depth at the cross-head end = 1.5 t, and 
 at 2/3 the length = 2 t, the equivalent depth at the crank end is 2.25 t. 
 Applying the formula to the short-stroke engines of our examples, we have 
 
 Diameter of cylinder, inches 
 
 10 
 
 30 
 
 50 
 
 Stroke, inches . 
 
 12 
 
 30 
 
 48 
 
 Length of connecting-rod 
 
 30 
 
 75 
 
 120 
 
 Thickness t - 0209 "V ' Dl VP+ 47 = 
 
 1.61 
 
 3.60 
 
 5.59 
 
 
 2.42 
 
 5.41 
 
 8.39 
 
 Depth at crank end, 21/42 
 
 3.62 
 
 8.11 
 
 12.58 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1027 
 
 The thicknesses t, found by the formula t = 0.0209 V Dl\/P + 0.47, 
 agree closely with the more simple formula t = 0.01 D\/~p + 0.60 in., the 
 thicknesses calculated by this formula being respectively 1.6, 3.6, and 
 5.6 in. 
 
 The Crank-Pin. A crank-pin should be designed (1) to avoid heat- 
 ing, (2) for strength, (3) for rigidity. The heating of a crank-pin 
 depends on the pressure on its rubbing surface, and on the coefficient 
 of friction, which latter varies greatly, according to tile effectiveness of 
 the lubrication. It also depends upon the facility with which the heat 
 produced may be carried away : thus it appears that locomotive crank- 
 pins may be prevented to some degree from overheating by the cooling 
 action of the air through which they pass at a high speed. 
 
 Marks states as a general law, within reasonable limits as to pressure 
 and speed of rubbing, the longer a bearing is made, for a given pressure 
 and number of revolutions, the cooler it will work; and its diameter has 
 no effect upon its heating. 
 
 Whitham recommends for pressure per square inch of projected area, 
 for naval engines 500 pounds, for merchant marine engines 400 pounds, 
 for paddle-wheel engines 800 to 900 pounds. 
 
 Thurston says the pressure on a steel crank-pin should, in the steam- 
 engine, never exceed 1000 or 1200 pounds per square inch. He gives 
 the formula for length of a steel pin, in inches. 
 I = PR + 600,000, 
 
 in which P and R are the mean total load on the pin in pounds, and the 
 number of revolutions per minute. For locomotives, the divisor may be 
 taken as 500,000. Pins so proportioned, if well made and well lubri- 
 cated, may always be depended upon to run cool; if not well formed, 
 perfectly cylindrical, well finished, and kept well oiled, no crank-pin 
 can be relied upon. It is assumed above that good bronze or white- 
 metal bearings are used. 
 
 By calculating lengths of iron crank-pins for the engines 10, 30, and 
 50 inches diametor, long and short stroke, by the formulae given by dif- 
 ferent writers, it is found that there is a great difference in the results, 
 so that one formula in certain cases gives a length three times as great 
 as another. 
 
 The average of the calculated lengths of iron crank-pins for the 
 several cases by five formulae are given in the table below, together 
 with the calculated lengths by two formulee for steel. 
 
 Length of Crank-pins. 
 
 Diameter of cylinder ... D 
 
 10 
 
 250 
 50 
 7,854 
 42 
 3,299 
 2.72 
 
 W 2 
 
 ' 
 
 7,854 
 42 
 3,299 
 1.36 
 
 30 
 
 % 
 
 450 
 70,686 
 32.3 
 22,832 
 9.86 
 
 30 
 
 65 
 
 450 
 70,686 
 32.3 
 22,832 
 4.93 
 
 50 
 4 
 90 
 1,250 
 196,350 
 30 
 58,905 
 17.12 
 
 50 
 8 
 45 
 
 1.250 
 196,350 
 30 
 58,905 
 8.56 
 
 Stroke L (ft ) 
 
 Revolutions per minute ... R 
 
 Horse-power . s I.H.P. 
 
 Maximum pressure Ibs. 
 
 
 Mean pressure P. 
 
 Length of crank-pin, average for iron. . 
 
 Unwin, best steel, I =0.1 I.H.P. -=-r 
 Thurston, steel, I = P R + 600,000 
 
 0.83 
 1.37 
 
 0.42 
 0.69 
 
 3.0 
 4.95 
 
 1.5 
 
 2.47 
 
 5.21 
 
 8.84 
 
 2.61 
 
 4.42 
 
 The calculated lengths for the long-stroke engines are too low to pre- 
 vent excessive pressures. See "Pressures on the Crank-pins," below. 
 
 The Strength of the Crank-pin is determined substantially as is that 
 of the crank. In overhung cranks the load is usually assumed as 
 carried at the middle of the pin, and, equating its moment with that of 
 the resistance of the pin, 
 
 l/ 2 PI 
 
 and d= 
 
 5.1 PI 
 
 in which d 
 
 _ diameter of pin in inches, P maximum load on the 
 
 piston, t = the maximum allowable stress on a square inch of the metal. 
 For iron it may be taken at 9000 Ibs, For steel the diameters found by 
 this formula may be reduced 10%. (Thurston.) 
 
1028 
 
 THE STEAM-ENGINE. 
 
 Unwin gives the same formula in another form, viz.: 
 
 the last form to be used when the ratio of length to diameter is assumed, 
 For wrought iron, t = 6000 to 9000 Ibs. per sq. in., 
 
 -\/5.1/="o.0947 to 0.0827; ^ / 57l7i = 0.0291 to 0.0238. 
 For steel, t = 9000 to 13,000 Ibs. per sq. in., 
 
 <y5JL/i = 0,0827 to 0.0723: V5.1# = 0.0238 to 0.0194, 
 Marks, calculating the diameter for rigidity, gives 
 d = 0.066 
 
 = 0.945 
 
 + LN; 
 
 p = maximum steam-pressure in pounds per square inch, D = diameter 
 of cylinder in inches, L = length of stroke in feet, N = number of single 
 strokes per minute. He says there is no need of an investigation of the 
 strength of a crank-pin, as the condition of rigidity gives a great excess 
 of strength. 
 
 Marks's formula is based upon the assumption that the whole load 
 may be concentrated at the outer end, and cause a deflection of 0.01 in. 
 at that point. It is serviceable, he says, for steel and for wrought iron 
 alike. 
 
 Using t.he average lengths of the crank-pins already found, we have 
 the following for our six engines : 
 
 Diameter of Crank-pins. 
 
 
 10 
 
 10 
 
 30 
 
 30 
 
 50 
 
 50 
 
 Stroke ft.. . 
 
 J 
 
 2 
 
 21/0 
 
 5 
 
 4 
 
 8 
 
 
 2.72 
 
 1.36 
 
 986 
 
 4.93 
 
 17.12 
 
 fi ( >6 
 
 
 2 29 
 
 1 82 
 
 7 34 
 
 5 82 
 
 12 40 
 
 9 84 
 
 Marks, d = 0.066 ^p^F 2 
 
 1.39 
 
 0.85 
 
 6.44 
 
 3.78 
 
 12.41 
 
 7.39 
 
 Pressures on the Crank-pins. - If we take the mean pressure upon 
 the crank-pin = mean pressure on piston, neglecting the effect of the 
 varying angle of the connecting-rod, we have the following, using the 
 average lengths already found, and the diameters according to Unwin 
 and Marks: 
 
 Engine No 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 
 
 
 
 
 Diameter of cylinder inches .... 
 
 10 
 
 10 
 
 30 
 
 30 
 
 50" 
 
 50 
 
 Stroke, feet 
 
 1 
 
 2 
 
 2V2 
 
 5 
 
 4 
 
 8 
 
 
 3,299 
 
 3,299 
 
 22,832 
 
 22,832 
 
 58,905 
 
 58,905 
 
 Projected area of pin, Unwin 
 
 6 23 
 
 2 36 
 
 72.4 
 
 28.7 
 
 2!2 3 
 
 84 2 
 
 Projected area of pin Marks 
 
 3 78 
 
 1 16 
 
 63 5 
 
 18 6 
 
 212 5 
 
 63 3 
 
 Pressure per square inch, Unwin 
 Pressure per square inch, Marks 
 
 530 
 873 
 
 1,398 
 2,845 
 
 315 
 360 
 
 7% 
 1,228 
 
 277 
 277 
 
 700 
 930 
 
 The results show that the application of the formulae for length and 
 diameter of crank-pins give quite low pressures per square inch of pro- 
 jected area for the short-stroke high-speed engines of the larger sizes, but 
 too high pressures for all the other engines. It is therefore evident that 
 after calculating the dimensions of a crank-pin according to the formulae 
 given, the results should be modified, if necessary, to bring the pressure 
 per square inch down to a reasonable figure. 
 
 In order to bring the pressures down to 500 pounds per square inch, 
 we divide the mean pressures by 500 to obtain the projected area, or 
 
DIMENSIONS OF PARTS OF ENGINES. 1029 
 
 product of length by diameter. Making I = 1.5 d for engines Nos. 1, 
 2, 4, and 6, the revised table for the six engines is as follows: 
 
 Engine No 1 2 3 4 5 6 
 
 Length of crank-pin, inches. . 3.15 3.15 9.86 8.37 17.12 13.30 
 Diameter of crank-pin 2 . 10 2.10 7 . 34 5 . 58 12 ..40 8 . 87 
 
 Crosshead-pin or Wrist-pin. Seaton says the area, calculated by 
 multiplying the diameter of the journal by its length, should be such 
 that the pressure does not exceed 1200 Ib. per sq. in., taking the maxi- 
 mum load on the piston as the total pressure on the pin. 
 
 For small engines with the gudgeon shrunk into the jaws of the con- 
 necting-rod, and working in brasses fitted into a recess in the piston-rod 
 end and secured by a wrought-iron cap and two bolts, Seaton gives: 
 
 Diameter of gudgeon = 1 . 25 X diam. cf piston-rod, 
 
 Length of gudgeon = 1 . 4 X diam. of piston-rod. 
 
 If the pressure on the section, as calculated by multiplying length by 
 diameter, exceeds 1200 Ibs. per sq. in., this length should be increased. 
 
 J. B. Stanwood, in his "Ready Reference" book, gives for length of 
 crosshead-pin 0.25 to 0.3 diam. of piston, and diam. =0.18 to 0.2 
 diam. of piston. Since he gives for diam. of piston-rod 0.14 to 0.17 
 diam. of piston, his dimensions for diameter and length of crosshead-pin 
 are about 1.25 and 1.8 diam. of piston-rod respectively. Taking the 
 maximum allowable pressure at 1200 Ibs. per sq. in. and making the 
 length of the crosshead-pin = 4/ 3 of its diameter, we have d= v 'p ~- 40, 1 = 
 Vp-*. 30, in which P= maximum total load on piston in Ibs., d = diam. 
 and 1= length of pin in inches. For the engines of our example we haves 
 
 Diameter of piston, inches 10 30 50 
 
 Maximum load on piston, Ibs 7854 70,686 196,350 
 
 Diameter of crosshead-pin, inches. .... 2. 22 6 . 65 11 . 08 
 
 Length of crosshead-pin, inches - 2.96 8.86 14.77 
 
 Stanwood's rule gives diameter, ins. ... 1.8 to 2 5 . 4 t :> 6 9.0 to 10 
 Stanwood's rule gives length, inches. . . 2.5 to 3 7.5 to 9 12.5 to 15 
 Stanwood's largest dimensions give 
 
 pressure per sq. in., Ibs 1309 1329 1309 
 
 These pressures are greater than the maximum allowed by Seaton. 
 
 The Crank-arm. The crank-arm is to be treated as a lever, so that 
 If ais the thickness in adirection parallel to the shaft-axis and b its breadth 
 at a section x inches from the crank-pin center, then, bending moment 
 M at that section = Px, P being the thrust of the connecting-rod, and 
 / the safe strain per square inch r 
 
1030 
 
 THE STEAM-ENGINE. 
 
 The crank-eye or boss into which the pin is fitted should bear the same 
 relation to the pin that the bos does to the shaft. 
 
 The diameter of the shaft-end onto which th^ crank is fitted should 
 be 1.1 X diameter of shaft. 
 
 Tnurston says: Tne empirical proportions adopted by builders will 
 commonly be found to tali well within tne calculated safe margin. 
 Tne.se proportions are, from the practice of successful designers, about 
 as follows: 
 
 The hub is 1.75 to 1.8 times the least diameter of that part of the 
 shaft carrying full load; the eye is 2.0 to 2.25 tne diameter of the inserted 
 portion of tne pin and their depths are, for the hub, 1.0 to 1.2 the 
 diameter of snaft, anc* for tne eye, 1.25 to 1.5 the diameter of pin. The 
 web is made vj.7 to 0.75 the widtn of the adjacent hub or eye, and is 
 given a depth of 0.5 to 0.6 that of the adjacent hub or eye. 
 
 Tne cranK-shaft is usually enlarged at the seat of the crank to about 
 1.1 its diameter at the journal. The size should be nicely adjusted to 
 allow for the shrinkage or forcing on of the crank. A difference of 
 diameter of 0.2 % will usually suffice. 
 
 Tne formulae given by different writers for crank-arms practically 
 agree, since they all consider the crank as a beam loaded at one end and 
 fixed at the other. The relation of breadth to thickness may vary 
 according to the taste of the designer. Calculated dimensions for our 
 six engines are as follows: 
 
 Dimensions of Crank-arms. 
 
 Diam of cylinder ins. 
 
 10 
 
 10 
 
 30 
 
 30 
 
 50 
 
 50 
 
 Stroke S ins 
 
 12 
 
 24 
 
 30 
 
 60 
 
 48 
 
 96 
 
 Max. pressure on pin P 
 (approx ) Ibs 
 
 7854 
 
 7854 
 
 70,686 
 
 70,686 
 
 196,350 
 
 196,350 
 
 Diam crank-pin d 
 
 2.10 
 
 2.10 
 
 7.34 
 
 5.58 
 
 12.40 
 
 8.87 
 
 Dv^ff J-T\/ ' D 
 
 
 
 
 
 
 
 (a'= 4.69, 5. 09 and 5. 22).... 
 Length of boss, 0.8 D 
 Thickness of boss, 0.4 D 
 Diam. of boss, 1.8 D 
 Length crank-pin eye, 0.8 d 
 Thickness of crank-pin eye, 
 4d 
 
 2.74 
 
 2.19 
 1.10 
 4.93 
 1.76 
 
 0.88 
 
 3.46 
 
 2.77 
 1.39 
 6,23 
 1.76 
 
 0.88 
 
 7.70 
 
 6 16 
 3.08 
 13.86 
 5.87 
 
 2.94 
 
 9.70 
 
 7.76 
 3.88 
 17.46 
 4.46 
 
 2.23 
 
 12.55 
 
 10.04 
 5.02 
 22.59 
 9.92 
 
 4.46 
 
 15.82 
 
 12.65 
 6.32 
 28.47 
 7.10 
 
 3.55 
 
 Max. mom. T at distance 
 V2*S r V2> from center of 
 
 37 149 
 
 80 661 
 
 
 788 149 
 
 1 848 439 
 
 3 479,322 
 
 7,871,671 
 
 Thickness of crank-arm a = 
 75 D 
 
 2.05 
 
 2 60 
 
 5.78 
 
 7.28 
 
 9.41 
 
 11.87 
 
 Greatest breadth, 
 
 
 
 
 
 
 
 b = V6 T * 9000 a 
 Min. mom. TO at distance 
 d from center of pin= Pd. 
 Least breadth, 
 
 3.48 
 16,493 
 
 4.55 
 16,493 
 
 9.54 
 
 528,835 
 
 13.0 
 394,428 
 
 15.7 
 2,434,740 
 
 21.0 
 1,741,625 
 
 & 1= V6 T + 9000 a 
 
 2.32 
 
 2.06 
 
 7.81 
 
 6.01 
 
 13.13 
 
 9.89 
 
 The Shaft. Twisting Resistance. From the general formula 
 for torsion, we have: T = -^ d*S = 0.19635 d?S, whence d = ^I^-L T ^ 
 
 in which T = torsional moment in inch-pounds, d = diameter in inches, 
 and ,S = the shearing resistance of the material, Ib. per sq. in. 
 
 If a constant force P were applied to the crank-pin tangentially to its 
 
 path, the work done in foot-pounds per minute would be 
 
 P X L X 2rr X R + 12 = 33,000 X I.H.P., 
 
 in which L = length of crank in inches, and R = revs, per min., and the 
 
 mean twisting moment T = l.H.P. -*- H X 63,025. Therefore 
 
 T -T- S = ^321,427 l.H.P. -* ^^'. 
 
DIMENSIONS OF PARTS OP ENGINES. 
 
 1031 
 
 This may take the form 
 
 d = ^I.H.P.X FIR, or d = a S/I.H.P. + R t 
 
 in which F and a are factors that depend on the strength of the material 
 and on the factor of safety. Taking S at 45,000 pounds per square inch 
 for wrought iron, and at 60,000 for steel, we have, for simple twisting by 
 a uniform tangential force, 
 Factor of safety =568 10 56810 
 
 Iron F = 35.7 42.8 57.1 71.4 a = 3.3 3.5 3.85 4.15 
 
 Steel F= 26.8 32.1 42.8 53.5 a = 3.0 3.18 3.5 3.77 
 
 Unwin, taking for safe working strength of wrought iron 9000 Ibs., 
 steel 13,500 Ibs., and cast iron 4500 Ibs., gives a = 3.294 for wrought 
 iron, 2.877 for steel, and 4.15 for cast iron. Thurston, for crank-axles 
 of wrought iron, gives a = 4.15 or more. 
 
 Seaton says: For wrought iron, /, the safe strain per square inch, should 
 not exceed 9000 Ibs., and when the shafts are more than 10 inches diameter, 
 8000 Ibs. Steel, when made from the ingot and of good materials, will 
 admit of a stress of 12,000 Ibs. for small shafts, and 10,000 Ibs. for those 
 above 10 inches diameter. 
 
 The difference in the allowance between large and small shafts is to com- 
 pensate for the defective material observable in the heart of large shaft- 
 ing, owing to the hammering failing to affect it. 
 
 The formula d = a -\/I.H.P. -4- R assumes the tangential force to be 
 uniform and that it is the only acting force. For engines, in which the 
 tangential force varies with the angle between the crank and the connect- 
 ing-rod, and with the variation in steam-pressure in the cylinder, and also 
 is influenced by the inertia of the reciprocating parts, and in which also 
 the shaft may be subjected to bending as well as torsion, the factor 
 a must be increased, to provide for the maximum tangential force and 
 for bending. 
 
 Seaton gives the following table showing the relation between the 
 maximum and mean twisting moments of engines working under various 
 conditions, the momentum of the moving parts being neglected, which is 
 allowable: 
 
 
 
 Max. 
 
 
 Description of Engine. 
 
 Steam Cut-off 
 at 
 
 Twist 
 Divided 
 by 
 
 Cube 
 Root 
 
 of the 
 
 
 
 Mean 
 Twist. 
 
 Ratio. 
 
 * 
 
 
 Moment. 
 
 
 Single-crank expansive . 
 
 0.2 
 
 2.625 
 
 
 .38 
 
 
 0.4 
 
 2 125 
 
 
 29 
 
 i i< 
 
 0.6 
 
 
 .835 
 
 
 .22 
 
 * 
 
 8 
 
 
 698 
 
 
 20 
 
 Two-cylinder expansive, cranks at 90 . 
 
 
 0.2 
 
 
 .616 
 
 
 .17 
 
 . i 
 
 
 0.3 
 
 
 .415 
 
 
 .12 
 
 
 
 
 0.4 
 
 
 .298 
 
 
 .09 
 
 * " 
 
 
 0.5 
 
 
 .256 
 
 
 .08 
 
 i 
 
 
 0.6 
 
 
 .270 
 
 
 .08 
 
 ' " 
 
 
 0.7 
 
 
 .329 
 
 
 .10 
 
 
 
 
 0.8 
 
 
 .357 
 
 
 .11 
 
 Three-cylinder compound, cranks 120. 
 Three-cylindercompound.l.p. cranks op 
 oosite one another, and h.p. midway 
 
 i 
 
 h.p. 0.5, l.p.0.66 
 
 
 .40 
 .26 
 
 
 .12 
 
 .08 
 
 For the engines we are considering it will be a very liberal allowance for 
 ratio of maximum to mean twisting moment if we take it as equal to the 
 ratio of the maximum to the mean pressure on the piston. The factor a, 
 then, in the formula for diameter of the shaft will be multiplied by the cube 
 
 root of this ratio, or 
 
 
 
 ^~ = 1 .49 
 
 for the 10. 30, and 50-in. engines, respectively. Taking a = 3.5, which 
 corresponds to a shearing strength of 60,000 a.nd a factor of safety of 8 for 
 
1032 
 
 THE STEAM-ENGINE. 
 
 steel, or to 45,000 and a factor of 6 for iron, we have for the new coeffi- 
 cient ai in the formula d\ a\ y'l.H.P. -*- R, the values 4.69, 5.08, and 
 5.22 from which we obtain the diameters of shafts of the six engines as 
 follows: 
 
 Engine No 1 2 3 4 5 6 
 
 Diam. of cyl 10 10 30 30 50 50 
 
 Horse-power, I.H.P 50 50 450 450 1250 " 1250 
 
 Revs, per min., R 250 125 130 65 90 45 
 
 Diam. of shaft d = 2.743.46 7.67 9.7012.5515.82 
 
 These diameters are calculated for twisting only. When the shaft is 
 also subjected to bending strain the calculation must be modified as 
 below: 
 
 Resistance to Bending. The strength of a circular-section shaft 
 to resist bending is one-half of that to resist twisting. If B is the bending 
 moment in inch-lbs., and d the diameter of the shaft in inches, 
 
 B = 2 X ^' and d = 
 
 / is the safe strain per square inch of the material of which the shaft is 
 composed, and its value may be taken as given above for twisting (Seaton). 
 
 Equivalent Twisting Moment. When a shaft is subject to both 
 twisting and bending simultaneously, the combined strain on any section 
 of it may be measured by calculating what is called the equivalent twisting 
 moment; that is, the two strains are. so combined as to be treated as a 
 twisting strain only of the same magnitude and the size of shaft calculated 
 accordingly. Rankine gave the following solution of the combined action 
 of the two strains. 
 
 If T = the twisting moment, and B = the bending moment on a section 
 of a shaft, then the equivalent twisting moment T\ = B+ v/ ^ 2 + T 2 . 
 
 The two principal strains vary throughout the revolution, and the 
 maximum equivalent twisting moment can only be obtained accurately 
 by a series of calculations of bending and twisting moments taken at 
 fixed intervals, and from them constructing a curve of strains. 
 
 Considering the engines of our examples to have overhung cranks, the 
 maximum bending moment resulting from the thrust of the connecting- 
 rod on the crank-pin will take place when the engine is passing its centers 
 (neglecting the effect of the inertia of the reciprocating parts), and it will 
 be the product of the total pressure on the piston by the distance between 
 two parallel lines passing through the centers of the crank-pin and of the 
 shaft bearing, at right angles to their axes; which distance is equal to 
 1/2 length of crank-pin bearing + length of hub 4- 1/2 length of shaft- 
 bearing + any clearance that may be allowed between the crank and the 
 two bearings. For our six engines we may take this distance as equal 
 to 1/2 length of crank-pin + thickness of crank-arm + 1.5 X the diam- 
 eter of the shaft as already found by the calculation for twisting. The 
 calculation of diameter is then as below: 
 
 Engine No. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Diam. of cyl., in.... 
 Horse-power . 
 
 10 
 50 
 
 10 
 50 
 
 30 
 450 
 
 30 
 450 
 
 50 
 1250 
 
 50 
 
 1250 
 
 Revs, per rain 
 Max. press, on pis,P 
 Leverage,* L in 
 Bd.mo.P=in.-lb 
 Twist, mom. T .... 
 Equiv. twist morn. 
 
 250 
 7,854 
 6.32 
 49,637 
 47,124 
 
 125 
 
 7,854 
 7.94 
 62,361 
 94,248 
 
 130 
 70,686 
 22.20 
 1,569,222 
 1,060,290 
 
 65 
 70,686 
 26.00 
 1,837,836 
 2,120,580 
 
 90 
 196,350 
 36.80 
 7,225,680 
 4,712,400 
 
 45 
 
 196,350 
 42.25 
 8,295,788 
 9,424,800 
 
 Ti= B+ Vj32 +r2 
 (approx.) 
 
 118,000 
 
 175,000 
 
 3,463,000 
 
 4,647,000 
 
 15,840,000 
 
 20,850,000 
 
 * Leverage = distance between centers of crank-pin and shaft bearing 
 - 1/2 Z + 2.25d. 
 
 Having already found the diameters, on the assumption that the shafts 
 were subjected to a twisting moment T only, we may find the . 
 
DIMENSIONS OF PAHTS OF ENGINES. 1033 
 
 for resisting combined bending and twisting by multiplying the diameters 
 already found by the cube roots of the ratio T\ -* T, or 
 
 1.40 1.27 1.46 1.34 1.64 1.36 
 Giving correqted diameters di = 3.84 4.3911.3512.99 20.58 21.52 
 
 By plotting these results, using the diameters of the cylinders for abscis- 
 sas and diameters of the shafts for ordinates, we find that for the long- 
 stroke engines the results lie almost in a straight line expressed by the 
 formula, diameter of shaft = 0.43 X diameter of cylinder; for the short- 
 stroke engines the line is slightly curved, but does not diverge far from a 
 straight line whose equation is, diameter of shaft = 0.4 diameter of 
 cylinder. Using these two formulas, the diameters of the shafts will be 
 4.0, 4.3, 12.0, 12.9, 20.0, 21.5. 
 
 J. B, Stanwood, in Engineering, June 12, 1891, gives dimensions of 
 shafts of Corliss engines in American practice for cylinders 10 to 30 in. 
 diameter. The diameters range from 415/16 to 1415/ie, following precisely 
 the equation, diameter of shaft = 1/2 diameter of cylinder Vie inch. 
 
 Fly-wheel Shafts. Thus far we have considered the shaft as resist- 
 ing the force of torsion and the bending moment produced by the pressure 
 on the crank-pin. In the case of fly-wheel engines the shaft on the 
 opposite side of the bearing from the crank-pin has to be designed with 
 reference to the bending moment caused by the weight of the fly-wheel, 
 the weight of the shaft itself, and the strain of the belt. For engines 
 in which there is an outboard bearing, the weight of fly-wheel and shaft 
 being supported by two bearings, the point of the shaft at which the 
 bending moment is a maximum may be taken as the point midway 
 between the two bearings or at the middle of the fly-wheel hub, and the 
 amount of the moment is the product of the weight supported by one of 
 the bearings into the distance from the center of that bearing to the 
 middle point of the shaft. The shaft is thus to be treated as a beam 
 supported at the ends and loaded in the middle. In the case of an over- 
 hung fly-wheel, the shaft having only one bearing, the point of maximum 
 moment should be taken as the middle of the bearing, and its amount is 
 very nearly the product of half the weight of the fly-wheel and the shaft 
 into the distance of the middle of its hub from the middle of the bear- 
 ing. The bending moment should be calculated and combined with the 
 twisting moment as above shown, to obtain the equivalent twisting 
 moment, and the diameter necessary at the point of maximum moment 
 calculated therefrom. 
 
 In the case of our six engines we assume that the weights of the fly- 
 wheels, together with the shaft, are double the weight of fly-wheel rim 
 
 d?s 
 obtained from the formula T7= 785,400 ff2 ^ 2 (given under Fly-wheels); 
 
 that the shaft is supported by an outboard bearing, the distance between 
 the two bearings being 2 1/2, 5, and 10 feet for the 10-in., 30-in., and 50-in. 
 engines, respectively. The diameters of the fly-wheels are taken such 
 that their rim velocity will be a little less than 6000 feet per minute. 
 
 Engine No 1 2 3 4 5 6 
 
 Diam. of cyl., inches 10 10 30 30 50 50 
 
 Diam. of fly-wheel, ft. ... 7.5 15 14.5 29 21 42 
 
 Revs, per min 250 125 130 65 90 45 
 
 Half wt. fly-wheel and 
 
 shaft, Ibs 268 536 5,968 11,936 26,384 52,769 
 
 Lever arm for maximum 
 
 moment, in 15 15 30 30 60 60 
 
 Maximum bending mo- 
 ment, in.-lbs 4020 8040 179,040 358,080 1,583,070 3,166,140 
 
 As these are very much less than the bending moments calculated from 
 the pressures- on the crank-pin, the diameters already found are sufficient 
 for the diameter of the shaft at the fly-wheel hub. 
 
 In the case of engines with heavy band fly-wheels and with long fly- 
 wheel shafts it is of the utmost importance to calculate the diameter of 
 the shaft with reference to the bending moment due to the weight of the 
 fly-wheel and the shaft. 
 
 B. H. Coffey (Power, October, 1892) gives the formula for combined 
 bending jmd twisting resistance, Ti = 0.196 d*S, in which T\ = B + 
 2 ; r being the maximum, not the mean twisting moment; and 
 
1034 
 
 THE STEAM-ENGINE. 
 
 finds empirical working values for 0.196 S as below. He says: Four 
 points should be considered in determining this value: First, the nature 
 of the material; second, the manner of applying the loads, with shock 
 or otherwise; third, the ratio of the bending moment to the torsional 
 moment the bending moment in a revolving shaft produces reversed 
 strains in the material, which tend to rupture it; fourth, the size of the 
 section. Inch for inch, large sections are weaker than small ones. He 
 puts the dividing line between large and small sections at 10 in. diameter, 
 and gives the following safe values of S X 0.196 for steel, wrought iron, 
 and cast iron, for these conditions. 
 
 VALUE OF S X 0.196. 
 
 Ratio. 
 
 Heavy Shafts 
 with Shock. 
 
 Light Shafts 
 with Shock. 
 Heavy Shafts 
 No Shock. 
 
 Light Shafts 
 No Shock. 
 
 B to T. 
 
 Steel. 
 
 Wro't 
 Iron. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Wro't 
 Iron. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Wro't 
 Iron. 
 
 Cast 
 Iron. 
 
 3 to 10 or less 
 
 1045 
 941 
 855 
 
 784 
 
 880 
 785 
 715 
 655 
 
 440 
 393 
 358 
 328 
 
 1566 
 1410 
 1281 
 1176 
 
 1320 
 1179 
 1074 
 984 
 
 660 
 589 
 537 
 492 
 
 2090 
 1882 
 1710 
 1568 
 
 1760 
 1570 
 1430 
 1310 
 
 880 
 785 
 715 
 655 
 
 3 to 5 or less 
 
 1 to 1 or less 
 
 B greater than T. . . 
 
 Mr. Coffey gives as an example of improper dimensions the fly-wheel 
 shaft of a 1500 H.P. engine at Willimantic, Conn., which broke while the 
 engine was running at 425 H.P. The shaft was 17 ft. 5 in. long between 
 centers of bearings, 18 in. diam. for 8 ft. in the middle, and 15 in. diam. 
 for the remainder, including the bearings. It broke at the base of the 
 fillet connecting the two large diameters, or 561/2 in. from the center of 
 the bearing. He calculates the mean torsional moment to be 446,654 
 inch-pounds, and the maximum at twice the mean; and the total weight 
 on one bearing at 87,530 Ibs., which, multiplied by 561/2 in., gives 
 4,945,445 in.-lbs. bending moment at the fillet. Applying the formula 
 Ti = B+^/B* + T z , gives for equivalent twisting moment 9,971,045 in.- 
 lbs. Substituting this value in the f9rmula T\ = 0.196/ScZ 3 gives for S 
 the shearing strain 15,070 Ibs. persq. in., or if the metal had a shearing 
 strength of 45,000 lb., a factor of safety of only 3. Mr. Coffey considers 
 that 6000 lb. is all that should be allowed for S under these circum- 
 stances. This would give d = 20.35 in. If we take from Mr. Coffey's 
 table a value of 0.196 5 = 1100, we obtain cP = 9000 nearly, or d = 20.8 
 in. instead of 15 in., the actual diameter. 
 
 Length of Shaft-bearings. There is as great- a difference of opinion 
 among writers, and as great a variation in practice concerning length of 
 journal-bearings, as there is concerning crank-pins. The length of a 
 journal being determined from considerations of its heating, the observa- 
 tions concerning heating of crank-pins apply also to shaft-bearings, and 
 the formulee for length of crank-pins to avoid heating may also be used, 
 using for the total load upon the bearing the resultant of all the pres- 
 sures brought upon it, by the pressure on the crank, by the weight of the 
 fly-wheel, and by the pull of the belt. After determining this pressure, 
 however, we must resort to empirical values for the so-called constants 
 of the formulae, really variables, which depend on the power of the 
 bearing to carry away heat, and upon the quantity of heat generated, 
 which latter depends on the pressure, on the number of square feet of 
 rubbing surface passed over in a minute, and upon the coefficient of 
 friction. This coefficient is an exceedingly variable quantity, ranging 
 from 0.01 or less with perfectly polished journals, having end-play, and 
 lubricated by a pad or oil-bath, to 0.10 or more with ordinary oil-cup 
 lubrication. 
 
 Thurston says that the maximum allowable mean- intensity of pressure 
 may be, for all cases, computed by his formula for journals, I - PV + 
 60,000 d, or by Rankine's, I = P(V 20) 4- 44,800 d, in which P is the 
 mean total pressure in pounds, V the velocity of rubbing surface in feet 
 per minute, and d the diameter of the shaft in inches. It must be borne 
 in mind, he says, that the friction work on the main bearing next the crank 
 is the sum of that due the action of the piston on the pin and that due 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1035 
 
 that portion of the weight of wheel and shaft and of pull of the belt which 
 is carried there. The outboard bearing carries practically only the 
 latter two parts of the total. The crank-shaft journals will be made 
 longer on one side, and perhaps shorter on the other, than that of the 
 crank-phi, in proportion to the work falling upon each, i.e., to their 
 respective products of mean total pressure, speed of rubbing surfaces, and 
 coefficients of friction. 
 
 Unwin says: Journals running at 150 revolutions per minute are often 
 only one diameter long. Fan shafts running 150 revolutions per minute 
 have journals six or eight diameters long. The ordinary empirical mode 
 of proportioning the length of journals is to make the length proportional 
 to the diameter, and to make the ratio of length to diameter increase 
 with the speed. For wrQught-iron journals: 
 
 Revs.permin. = 50 100 150 200 250 500 1000 Z/d 0.004 fl + 1. 
 Length + diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0. 
 
 Cast-iron journals may have l + d = 9/ 10 , and steel journals Z-s-cf = li/4, 
 of the above values. 
 
 Unwin gives the following, calculated from the formula I = . 4 H.P. -r- r r 
 in which r is the crank radius in inches, and H.P. the horse-power trans- 
 mitted to the crank-pin. 
 
 THEORETICAL JOURNAL LENGTH IN INCHES. 
 
 Load on 
 Journal in 
 Pounds. 
 
 Revolutions of Journal per minute. 
 
 50 
 
 100 
 
 200 
 
 300 
 
 500 
 
 1000 
 
 1,000 
 2,000 
 4,000 
 5,000 
 10,000 
 15,000 
 20,000 
 30,000 
 40,000 
 50.000 
 
 0.2 
 0.4 
 0.8 
 1.0 
 2. 
 3. 
 4. 
 6. 
 8. 
 10. 
 
 0.4 
 0.8 
 1.6 
 
 4! 
 6. 
 8. 
 12. 
 16. 
 20. 
 
 0.8 
 1.6 
 3.2 
 4. 
 8. 
 12. 
 16. 
 24. 
 32. 
 40. 
 
 1.2 
 
 2.4 
 4.8 
 6. 
 12. 
 18. 
 24. 
 36. 
 
 2. 
 4. 
 8. 
 10. 
 20. 
 30. 
 40. 
 
 4. 
 8. 
 16. 
 20. 
 40. 
 
 
 
 
 
 
 
 
 Applying six different formulae to our six engines, we have: 
 
 Engine No . 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 
 
 
 
 
 Diam. cyl 
 
 10 
 
 10 
 
 30 
 
 30 
 
 50 
 
 50 
 
 Horse-power 
 
 50 
 
 50 
 
 450 
 
 450 
 
 1 250 
 
 1 250 
 
 Revs per min 
 
 250 
 
 125 
 
 130 
 
 65 
 
 90 
 
 45 
 
 Mean pressure on crank-pin = S 
 Half wt. of fly-wheel and shaft = Q. . . . 
 Resultant pressure on bearing 
 
 3,299 
 268 
 
 3,299 
 536 
 
 23,185 
 5,968 
 
 23,185 
 11,936 
 
 58,905 
 26,470 
 
 58,905 
 52,940 
 
 V^+5-Bj. 
 
 Diam. of shaft journal 
 
 3,310 
 3 84 
 
 3,335 
 4 39 
 
 23,924 
 11 35 
 
 26,194 
 12 99 
 
 64,580 
 20 58 
 
 79,200 
 21 52 
 
 Length of shaft journal: 
 Marks, 2 = 0.0000325 /#i#(/=0.10) 
 Whitham,Z = 0.00005 15 fR 1 R(f =0.10) 
 Thurston, Z = PFn- (60,000 d) 
 Rankine, l=P(V+20) + (44,800 d).. . 
 Unwin, Z=(0. 004/2+ 1) d. ... 
 
 5.38 
 4.27 
 3.61 
 5.22 
 7 68 
 
 2.71 
 2.15 
 1.82 
 2.78 
 6 59 
 
 20.87 
 16.53 
 14.00 
 21.70 
 17 25 
 
 11.07 
 8.77 
 7.43 
 10.85 
 16 36 
 
 37.78 
 29.95 
 25.36 
 35.16 
 27 99 
 
 23.17 
 18.35 
 15.55 
 22.47 
 25 39 
 
 Unwin, Z = 0.4H.P.-*-r 
 
 3 33 
 
 1 60 
 
 12 00 
 
 6 00 
 
 20 83 
 
 10 42 
 
 
 
 
 
 
 
 
 Average 
 
 4.92 
 
 2.99 
 
 17.05 
 
 10.00 
 
 29.54 
 
 19.22 
 
 If we divide the mean resultant pressure on the bearing by the pro- 
 jected area, that is, by the product of the diameter and length of the 
 journal, using the greatest and smallest lengths out Of the seven lengths 
 
1036 
 
 THE STEAM-ENGINE. 
 
 for each journal given above, we obtain the pressure per square inch 
 upon the bearing, as follows: 
 
 Engine No 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 
 
 
 
 
 Press, per sq. in., shortest journal 
 Longest journal 
 
 259 
 112 
 
 455 
 115 
 
 176 
 97 
 
 336 
 123 
 
 151 
 83 
 
 353 
 145 
 
 Average journal 
 
 175 
 
 254 
 
 124 
 
 202 
 
 106 
 
 191 
 
 Journal of length = diam 
 
 
 173 
 
 
 155 
 
 
 175 
 
 Many of the formulas give for the long-stroke engines a length of journal 
 less than the diameter, but such short journals are rarely used in practice. 
 The last line in the above table has been calculated on the supposition 
 that the journals of the long-stroke engines are made of a length equal 
 to the diameter. 
 
 In the dimensions of Corliss engines given by J. B. Stanwood (Eng., 
 June 12, 1891), the lengths of the journals for engines of diam. of cyl. 
 10 to 20 in. are the same as the diam. of the cylinder, and a little more 
 than twice the diam. of the journal. For engines above 20 in. diam. of 
 cyl. the ratio of length to diam. is decreased so that an engine of 30 in. 
 diam. has a journal 26 in. long, its diameter being 1415/16 in. These 
 lengths of journal are greater than those given by any of the formulae 
 above quoted. 
 
 There thus appears to be a hopeless confusion in the various formulae 
 for length of shaft journals, but this is no more than is to be expected 
 from the variation in the coefficient of friction, and in the heat-conducting 
 power of journals in actual use, the coefficient varying from 0.10 (or 
 even 0.16 as given by Marks) down to 0.01, according to the condition 
 of the bearing surfaces and the efficiency of lubrication. Thurston's 
 
 formula, I = 
 
 reduces to the form I = 0.000004363 PR, in which 
 
 P = mean total load on journal, and R = revolutions per minute. This 
 is of the same form as Marks's and Whitham's formulae, in which, if /, the 
 coefficient of friction, be taken at 0.10, the coefficients of PR are, respec- 
 tively, 0.0000065 and 0.00000515. Taking the mean of these three 
 formulae, we have I = 0.0000053 PR, if / = 0.10 or I = 0.000053 fPR 
 for any other value of /. The author believes this to be as safe a formula 
 as any for length of journals, with the limitation that if it brings a result 
 of length of journal less than the diameter, then the length should be 
 made equal to the diameter. Whenever, with/ = 0.10 it gives a length 
 which is inconvenient or impossible of construction on account of limited 
 space, then provision should be made to reduce the value of the coefficient 
 of friction below 0.10 by means of forced lubrication, end play, etc., and 
 to carry away the heat, as by water-cooled journal-boxes. The value of 
 P should be taken as the resultant of the mean pressure on the crank, 
 and the load brought on the bearing by the weight of the shaft, fly-wheel, 
 
 etc., as calculated by the formula already given, viz., Ri = ^Q 2 + 2 for 
 horizontal engines, and Ri = Q 4- S for vertical engines. 
 
 For our six engines the formula I = 0.0000053 PR gives, with the 
 limitation for the long-stroke engines that the length shall not be less 
 than the diameter, the following: 
 Engine No ............. 1 2 
 
 Length of journal ....... 4.39 4.39 
 
 Pressure per square inch 
 
 on journal ............ 196 173 
 
 Crank-shafts with Center-crank 
 
 center-crank engines, one of the crank-arms, and its adjoining journal, 
 called the after journal, usually transmit the power of the engine to the 
 work to be done, and the journal resists both twisting and bending mo- 
 ments, while the other journal is subjected to bending moment only. 
 For the after crank- journal the diameter should be calculated the same 
 as for an overhung crank, using the formula for combined bending and 
 twisting moment, T\ = B + \/ B* + T2, in which Ti is the equivalent 
 twisting moment, B the bending moment, and T the twisting moment. 
 This value of T\ is -to be used in the formula, diameter = tyliTTTIS. The 
 
 3 
 
 16.48 
 
 4 
 12.99 
 
 5 
 
 30.80 
 
 6 
 
 21.52 
 
 128 155 102 171 
 
 and Double-crank Arms. In 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1037 
 
 bending moment is taken as the maximum load on piston multiplied Dy 
 one-f9urth of the length of the crank-shaft between middle points of the 
 two journal bearings, if the center is midway between the bearings, or 
 by one-half the distance measured parallel to the shaft from the middle 
 of the crank-pin to the middle of the after bearing. This supposes the 
 crank-shaft to be a beam loaded at its middle and supported at the ends, 
 but Whitham would make the bending moment only one-half of this, 
 considering the shaft to be a beam secured or fixed at the ends, with a 
 point of contraflexure one-fourth of the length from the end. The first 
 supposition is the safer, but since the bending moment will in any case 
 be much less than the twisting moment, the resulting diameter will be 
 but little greater than if Whitham's supposition is used. For the for- 
 ward journal, which is subjected to bending moment only, diameter of 
 
 shaft = ^/10.2 BIS, in which B is the maximum bending moment and 
 S the safe shearing strength of the metal per square inch. 
 
 For our six engines, assuming them to be center-crank engines, and 
 considering the crank-shaft to be a beam supported at the ends and 
 loaded in the middle, and assuming lengths between centers of shaft 
 bearings as given below, we have: 
 
 Length of^ shaft, 
 
 
 
 
 
 
 
 assumed, in., L. . 
 
 20 
 
 24 
 
 48 
 
 60 
 
 76 
 
 96 
 
 Max. press, on 
 
 
 
 
 
 
 
 crank-pin, P 
 Max. bending mo- 
 
 7,854 
 
 7,854 
 
 70,686 
 
 70,686 
 
 196,350 
 
 196,350 
 
 ment, B =1/4 PL, 
 Twisting mom., T 
 
 39,270 
 47,124 
 
 49,637 
 94,248 
 
 848,232 
 1,060,290 
 
 1,060,290 
 2,120,580 
 
 3,729,750 
 4,712,400 
 
 4,712,400 
 9,424,800 
 
 Equiv. twist, mom. 
 
 
 
 
 
 
 
 B + ^B 2 + T 2 ... 
 Diam. of after jour. 
 
 101,000 
 
 156,000 
 
 2,208,000 
 
 3,430,000 
 
 9,740,000 
 
 15,240,000 
 
 - 4/5.1 Ti 
 
 3QO 
 
 4 AH 
 
 ni ^ 
 
 i -j nn 
 
 
 
 d V 8000 " 
 
 . vo 
 
 .OU 
 
 . \j 
 
 \j .UU 
 
 18.25 
 
 21 .20 
 
 Diam. of forw. jour., 
 
 
 
 
 
 
 
 d iV 10 - 2jB 
 
 3Afl 
 
 3QQ 
 
 1 A 00 
 
 
 
 
 dl V 8000 
 
 .DO 
 
 . yy 
 
 lu.zo 
 
 1 1 . 16 
 
 16.82 
 
 18. 18 
 
 The lengths of the journals would be calculated in the same manner as 
 in the case ot overhung cranks, by the formula I = 0.000053 fPR, in 
 which P is the resultant of the mean pressure due to pressure of steam op 
 the piston, and the load of the fly-wheel, shaft, etc., on each of the two 
 bearings. Unless the pressures are equally divided between the twc 
 bearings, the calculated lengths of the two will be different; but it is 
 usually customary to make them both of the same length, and in no casb 
 to make the length less than the diameter. The diameters also are usually 
 made alike for the two journals, using the largest diameter found by 
 calculation. 
 
 The crank-pin for a center crank should be of the same length as for 
 an overhung crank, since the length is determined from considerations 
 of heating, and not of strength. The diameter also will usually be the 
 same, since it is made great enough to make the pressure per square inch 
 on the projected area (product of length by diameter) small enough to 
 allow of free lubrication, and the diameter so calculated will be greater 
 than is required for strength. 
 
 Crank-shaft with Two Cranks coupled at 90. If the whole 
 power of the engine is transmitted through the after journal of the after 
 crank-shaft, the greatest twisting moment is equal to 1.414 times the 
 maximum twisting moment due to the pressure on one of the crank-pins. 
 If T = the maximum twisting moment produced by the steam-pressure 
 on one of the pistons, then 2 7 i, the maximum twisting moment on the 
 after part of the crank-shaft, and on the line-shaft produced, when each 
 crank makes an angle of 45 with the center line of the engine, is 1.414 T. 
 Substituting this value in the formula for diameter to resist simple 
 torsion, viz.. d = ^5.1 T -r S, we have d = ^5.1 X 1.414 T -r S t or 
 
1038 THE STEAM-ENGINE. 
 
 d = 1.932 ty T/S, in which T is the maximum twisting moment pro- 
 duced by one of the pistons, d = diameter in inches, and S = safe 
 working shearing strength of the material. For the forward journal of 
 the after crank, and the after journal of the forward crank, the torsional 
 moment is that due to the pressure of steam on the forward piston only, 
 and for the forward journal of the forward crank, if none of the power 
 of the engine is transmitted through it, the torsional moment is zero, and 
 its diameter is to be calculated for bending moment only. 
 
 For Combined Torsion and Flexure. Let B^ = bending moment 
 on either journal of the forward crank due to maximum pressure on 
 forward piston, B 2 = bending moment on either journal of the after crank 
 due to maximum pressure on after piston, T\ = maximum twisting 
 moment on after journal of forward crank, and Tz = maximum twisting 
 moment on after journal of after crank, due to pressure on the after 
 piston. 
 
 Then equivalent twisting moment on after journal of forward crank 
 Bi + Vtfi* -}- T 7 ! 2 . 
 
 On forward journal of after crank = _ _ 
 
 On after journal of after crank = J5 2 -f ^B<?+ (T\+ 7 7 2 ) 2 . 
 
 These values of equivalent twisting moment are to be used in the 
 
 formula for diameter of journals d = \J5.l T/S. For the forward 
 
 Journal of the forward crank-shaft d = ^10.2 Bi/S. 
 
 It is customary to make the two journals of the forward crank of one 
 diameter, viz., that calculated for the after journal. 
 
 For a Three-cylinder Engine with cranks at 120, the greatest 
 twisting moment on the after part of the shaft, if the maximum pressures 
 on the three pistons are equal, is equal to twice the maximum pressure on 
 any one piston, and it takes place when two of the cranks make angles 
 of 30 with the center line, the third crank being at right angles to it. 
 (For demonstration, see Whitham's "Steam-engine Design," p. 252.) 
 For combined torsion and flexure the same method as above given for 
 two -crank engines is adopted for the first two cranks; and for the 
 third, or after crank, if all the power of the three cylinders is transmitted 
 through it, we have the equivalent twisting moment on the forward 
 
 Journal = B a -f ^B + (Ti + r 2 ) 2 , and on the after journal = B 3 + 
 
 (Ti + T 2 + 7 7 3 )2, B 3 and T s being respectively the bending and 
 twisting moments due to the pressure on the third piston. 
 
 Crank-shafts for Triple-expansion Marine Engines, according to 
 an article in The Engineer, April 25, 1890, should be made larger than the 
 formulae would call for, in order to provide for the stresses due to the 
 racing of the propeller in a sea-way, which can scarcely be calculated. 
 A kind of unwritten law has sprung up for fixing the size of a crank- 
 shaft, according to which the diameter of the shaft is made about 0.45 D, 
 where D is the diameter of the high-pressure cylinder. This is for solid 
 shafts. When the speeds are high, as in war-ships, and the stroke short, 
 the formula becomes 0.4 D, even for hollow shafts. 
 
 The Valve-stem or Valve-rod. The valve-rod should be designed 
 to- move the valve under the most unfavorable conditions, which are when 
 the stem acts bv thrusting, as a long column, when the valve is unbalanced 
 (a balanced valve may become unbalanced bv the joint leaking) and when 
 it is imperfectly lubricated. The load on the valve is the product of the 
 area into the greatest unbalanced pressure upon it per square inch, and 
 the coefficient of friction may be as high as 20%. The product of this 
 coemcient and the load is the force necessary to move the valve, which 
 equals the maximum thrust on the valve-rod. From this force the 
 diameter of the valve-rod may be calculated by the usual formula for 
 columns. An empirical formula given by Seaton is: Diam. of rod = 
 d = \/lbp/F, in which 7 = length, and b = breadth of valve, in inches; 
 p = maximum absolute pressure on the valve in Ib. per sq. in., and 
 F a coemcient whose values are, for iron: long rod 10,000, short 12,000; 
 for steel: long rod 12,000, short 14,500. 
 
 Whitham gives the short empirical rule: Diam. of valve-rod = 1/30 
 diam. of cyl. = 1/3 diam. of piston-rod. 
 
DIMENSIONS OF PARTS OF ENGINES. 1039 
 
 The Eccentric. Diarn. of eccentric-sheave = 2.4 X throw of eccen- 
 tric + 1.2 X diam. of shaft. D = diam. of valve rod (Seaton). 
 
 Breadth of the sheave at the shaft ...... = 1.15 X D + 0.65 in. 
 
 Breadth of the sheave at the strap ...... = D + 0.6 in. 
 
 Thickness of metal around the shaft. . . . = 0.7 X D + 0.5 in. 
 
 Thickness of metal at circumference. . . . = 0.6 X D -j- 0.4 in. 
 
 Breadth of key ....................... =0.7 X D + 0.5 in. 
 
 Thickness of key ..................... = 0.25 X D + 0.5 in. 
 
 Diam. of bolts connecting parts of strap. = 0.6 X D -f 0.1 in. 
 
 THICKNESS OF ECCENTRIC-STRAP. 
 
 When of bronze or malleable cast iron : 
 
 Thickness of eccentric-strap at the middle. . . = 0.4 X D + 0.6 in. 
 Thickness of eccentric-strap at the sides ..... =0.3 X ) + 0.5 in. 
 
 When of wrought iron or cast steel : 
 
 Thickness of eccentric-strap at the middle. . . = 0.4 X D + 0.5 in. 
 Thickness of eccentric-strap at the sides ..... = 0.27 X D + 0.4 in. 
 
 The Eccentric-rod. The diameter of the eccentric-rod in the body 
 and at the eccentric end may be calculated in the same way as that of 
 the connecting-rod, the length being taken from center of strap to 
 center of pin. Diameter at the link end = 0.8 D + 0.2 in. 
 
 This is for wrought iron ; no reduction in size should be made for steel. 
 
 Eccentric-rods are often made of rectangular section. 
 
 Reversing-gear should be so designed as to have more than sufficient 
 strength to withstand the strain of both the valves and their gear at the 
 same time under the most unfavorable circumstances; it will then have 
 the stiffness requisite for good working. 
 
 Assuming the work done in reversing the link-motion, W, to be only 
 that due to overcoming the friction of the valves themselves through their 
 whole travel, then, if T be the travel of valves in inches, for a compound 
 engine 
 
 f l x b x P\ _L. T ( I L X 61 X PI\ 
 
 _ ?. f l 
 ~12\ 
 
 li, b it and PI being length, breadth, and maximum steam-pressure 
 valve of the second cylinder; and for an expansive engine 
 
 To provide for the friction of link-motion, eccentrics, and other gear, 
 and for abnormal conditions of the same, take the work at one and a half 
 times the above amount. 
 
 To find the strain at any part of the gear having motion. when reversing, 
 divide the work so found by the space moved through by that part in 
 feet; the quotient is the strain in pounds; the size may be found from the 
 ordinary rules of construction for any of the parts of the gear. (Seaton.) 
 
 Current Practice in Engine Proportions, 1897. (Compare pages 1021 
 to 1039.) A paper with this title by Prof. John H. Barr, in Trans. 
 A. S. M. E., xviii, 737, gives the results of an examination of the propor- 
 tions of parts of a great number of single-cylinder engines made by 
 different builders. The engines classed as low speed (L. S.) are Corliss 
 
 la speed or 200 to 300 revs, per i 
 are expressed in formulas of rational form with empirical coefficients, 
 and are here abridged as follows (dimensions in inches): 
 
 Thickness of Shell, L. S. only. t = CD + B; D = diam. of piston in 
 in. ; B = . 3 in. ; C varies from 04 to . 06, mean =- . 05. 
 
 Flanges and Cylinder-heads. l to 1 . 5 X thickness of shell, mean 1 . 2. 
 
 Cylinder-head Studs. No studs less than 3/4 in. nor greater than 13/gin. 
 diam. Least number, 8, for 10 in. diam. Average number = 0.7D. 
 Average diam. = D /40 -f i/ 2 in 
 
 Ports and Pipes. a= area" of port (or pipe) in sq. in.: A = area of 
 piston, sq. m.; V = mean piston-speed, ft. per min.: a '= AV 1C, in which 
 C=mean velocity of steam through the port or pipe in ft. per min. 
 
1040 THE STEAM-ENGINE. 
 
 Ports, H. S. (same ports for steam as for exhaust). C = 4500 to 
 6500, mean 5500. For ordinary piston-speed of 600 ft. per min. a = 
 KA; K = 0.09 to 0.13, mean 0.11. 
 
 melnT 09 S ' ~~ = 500 t0 9000 ' mean 6800; K " ' 8 tO ' 10 ' 
 
 Exhaust-ports, L. S. = 4000 to 7000, mean 5500; # = 0.10 to 0.125, 
 mean u . 1 1 . 
 
 'x s - T ? = 580 to 70 ' mean 65 - Tf d = diam - of 
 
 D = diam. of piston, d = . 29 D to . 32 D, mean . 30 D. 
 
 ' S ' G = 5000 to 8000, mean 6000; d = 0". 27 to 0.35 D; 
 
 = ' 33 t0 
 28 tO 47 ' mean 38 ; d = ' 35 to 
 
 7meo' ' ~ 
 
 y^V 9 ' ~~ F = face * D = Diameter. F = CD. H. S.: C - 
 0. meanO.46. L. S.:<7 - 0.25 toO. 45, mean 0.32. 
 -rods. ~d = diam. of rod; D = diam. of piston; L = stroke, in.: 
 = DL H g . ,_ 12 to Q 175 mean L 
 
 0.13, mean 0.11. 
 
 Connecting-rods. H. S. (generally 6 cranks loner, rectangular section): 
 Breadth; h = height of section; Li = length of connecting-rod; 
 
 D = diam. of piston; & = C^DLi; C = 0.045 to 0.07, mean 0.057; 
 n, => Kb; K = 2.2 to 4, mean 2.7. L. S. (generally 5 cranks long, cir- 
 cular sections only): C = 0.082 to 0.105. mean 0.092. 
 
 Cross-head Slides. Maximum pressure in Ibs. per sq. in. of shoe, due 
 to the vertical component of the force on the connecting-rod. H. S.: 
 10.5 to 38, mean 27. L. S.: 29 to 58, mean 40. 
 
 Cross-head Pins. I = length; d = diam.; projected area = a = dl 
 CA; A = area of piston; I = Kd. H. S.: C = 0.06 to 0.11, mean 0.08; 
 K = 1 to 2, mean 1.25. L. S.: C = 0.054 to 0.10, mean 0.07; K = 1 to 
 1 .*5, mean 1 . 3. 
 
 Crank-pin. H. P. = horse-power of engine; L= length of stroke; 
 
 1 = length of pin; I = C X H.P. /L+ B; d = diam. of pin; A = area of 
 piston; dl = KA. H. S.: C = 0.13 to 0.46, mean 0.30; B = 2.5 in.; 
 K = 0.17 to 0.44, mean 0.24. L. S.: C = 0.4 to 0.8, mean 0.6; B = 
 
 2 in.; K = 0.065 to 0.115, mean 0.09. _ 
 
 Crank-shaft Main Journal. d= C ^/H.P.-J- N; d= diam.; Z = length; 
 N = revs, per min.; projected area = MA; A = area of piston. H. S.: 
 (7 = 6.5 to 8.5, mean 7.3; l = Kd; K = 2 to 3, mean 2.2; M = 0.37 to 
 0.70, mean 0.46. L. S.: C = 6'to 8, mean 6.8; K= 1.7 to 2.1, mean 
 1.9; M = 0.46 to 0.64, mean 0.56. 
 
 Piston-speed. H. S.: 530 to 660, mean 600; L. S.: 500 to 850, mean 
 600. 
 
 Weight of Reciprocating Parts (piston, piston-rod, cross-head, and one- 
 half of connecting-rod). W = CD 2 *- LN Z \ D = diam. of piston; 
 L = length of stroke, in.; AT = revs, per min. H. S. only: C = 1,200,000 
 to 2,300,000, mean 1,860,000. 
 
 Belt-surface per I HfP. S = C X H.P. + B; S = product of width of 
 belt in feet by velocity of belt in ft. per min. H. S.: C = 21 to 40, mean 
 28; 5 = 1800. L. S.; S = CX H.P., C = 30 to 42, mean = 35. 
 
 Fly-wheel (H. S. only). Weight of rim in Ibs.: W = C X H.P.-*- 
 DrW 3 ; Di = diam. of wheel in in.; C = 65 X 10 10 to 2 X 10 12 mean = 
 12 X 10", or 1,200,000,000,000. 
 
 Weight of Engine per I.H.P. in Ibs., including flv-wheel. W = 
 C X H.P. H. S.: C= 100 to 135, mean 115. L. S.: "C = 135 to 240, 
 mean 175. 
 
 Current Practice in Steam-engine Design, 1909. (Ole N. Trooien, 
 Bull. Univ'y of Wis., No. 252; Am. Mach., April 22, 1909.) Practice in 
 prop9rtioning standard steam-engine parts has settled down to certain 
 definite values, which have by long usage been found to give satisfactory 
 results. These values can readily be expressed in formulas showing the 
 relation between the more important factors entering the problem of 
 design. 
 
 These formulae may be considered as partly rational and partly em- 
 
DIMENSIONS OF PAKTS OP ENGINES. 1041 
 
 pirical; rational in the sense that the variables enter in the same manner 
 as in a strict analysis, and empirical in the sense that the constants, 
 instead of being obtained from assumed working strength, bearing 
 pressures etc., are derived from actual practice and include elements 
 whose values are not accurately known but which have been found safe 
 and economical. 
 
 The following symbols of notation are used in the formulas given: 
 D = diameter of piston. A = area of piston. L = length of stroke. 
 7> = unit steam pressure, taken as 125 Ibs. per sq. in. above exhaust as 
 a standard pressure. H.P. = rated horse-power. N = revs, per min. 
 Cand K, constants, and tf = diam. and Z = length of unit under consider- 
 ation. All dimensions in inches. 
 
 The commercial point of cut-off is taken at 1/4 of the stroke. H. S., 
 high-speed engines. L. S., low-speed, or long-stroke engines. 
 
 Piftton Rod d = C ^DL. H. S.: (7 = 0.15 (min., 0.125; max., 
 0.187): L. S.: C = 0.114 (min., 0.1; max., 0.156). 
 
 Winder. Thickness of wall in ins. CD 4-0.28. C =0.054 
 (min., 0.035; max.. 0.072). Clearance volume 5 to 11% for H.S. engines, 
 and from 2 to 5% for Corliss eneines. 
 
 Stud BoUs. Number =0.72 D for H. S. (0.65 D for Corliss.) Diam. 
 in ins. = 0.04D -1-0.375. 
 
 Ratio (C) of Stroke to Cylinder Diameter (L /DV For N > 200, 
 C = 1.07 (min.. 0.82; max., 1.55): for N = 110 to 200, C = 136 (min., 
 1 . 03: max., 1 . 88) ; for AT < 110 (Corliss engines), C = (L - 8) /D = 1 . 63 
 (min., 1.15; max., 2.4). 
 
 Piston. Width of face in ins. = CD + 1. Mean value of C = 0.32 
 for H. S, (0,26 for Corliss). Thickness of shell = thickness of cylinder 
 wall X 0.6 (0.7 for Corliss). 
 
 Piston Speeds. H. S., 605 ft. per min. (min. 320; max., 920)- Corliss, 
 592 ft. per min. (min., 400; max., 800). 
 
 Cross-head. Area of shoes in sq. ins. =0.53 A (min., 0.37; max., 
 0.72). 
 
 Cross-head Pin. Diameter = . 25 D (min., 0.17; max., 0.28). 
 Length for H.S. = diam. X 1.25 (min., I; max., 1.5); for Corliss = 
 diam. X 1.43 (min., 1; max., 1.9). _ 
 
 Connecting-rods. Breadth for H. S. =0.073 ^L C D (min., 0.55; max., 
 0.094). Height = breadth X 2.28 (min., 1.85; max., 3). For L. S., diam. 
 of circular rod =0.092 ^L C D (min., 0.081; max., 0.104). L c = length 
 
 center to center of bearings. 
 
 Crank-pin. Diam. for H.S. center-crank engines *= . 4 D (min., 
 0.28; max., 0.526). Diam. for side-crank Corliss = 0.27 D (min.," 
 0.21; max., 0.32). Length for H. S. = diam. X0.87 (min., 0.66; 
 max., 1.25). Length for Corliss = diam. X 1.14 (min., 1; max., 1.3). 
 
 Main Journals of Crank-shaft. For H. S. center-crank engines, diam. 
 = 6.6 ^H.P./iV (min., 5.4; max., 8.2). For Corliss, diameter = 7^2 
 (min., 6.4; max., 8). 
 
 ... 
 
 Fly-wheels. Total weight in pounds for H.S. up to 175 H.P. 
 = 1 300,000,000,000 H.P. /DrW 3 , where Di = diam. of wheel in ins. 
 (min., 660,000,000,000; max., 2,800,000,000,000). For larger H.S. 
 engines, weight = (C X H.P. /Z>i 2 A 73 ) 4- 1000, where C = 720,000,000,000 
 (min., 330,000,000,000; max., 1,140,000,000,000). For Corliss engines, 
 weight = (C X H.P. /DW 3 ) -K, where C = 890,000,000,000 (min., 625,- 
 000,000,000; max., 1,330,000,000,000), and # = 4000 (min., 2,800; max., 
 6000). Diam. in ins.= 4.4X length of stroke. 
 
 Belt Surface per I. H.P. Square feet of belt surface per minute (S) 
 for H. S. = H.P. X 26.5 (min., 10; max., 55). For Corliss engines, 
 S = 1000 + (21 X H.P.) (min., 18.2; max., 35). 
 
 Velocity of Wheel Rim. For H. S. 70 ft. per sec. (min., 48; max., 
 70); for Corliss, 68 ft. per sec. (min., 40; max., 68). 
 
 Weight of Reciprocating Parts (Piston + piston rod + crosshead + 1/2 
 connecting-rod). Weight in Ibs. W = (D 2 /ZJV 2 ) X 2,000,000 (min., 
 1,370,000; max., 3,400,000). Balance weight opposite crank-pin = 
 
 'Weight of engine per I.H.P. Lbs. per I. H.P. for belt-connected H. S. 
 
1042 THE STEAM-ENGINE. 
 
 engines = H.P. X 82 (min., 52; max., 120). Do., for Corliss = H.P. 
 X 1^2 (min., 102; max., 164). 
 
 Shafts and Bearings of Engines. (James Christie, Proc. 
 Engrs. Club of Phila., 1898.) The dimensions are determined by two 
 independent considerations: 1. Sufficient size to prevent excessive 
 deflection or torsional yield. 2. To provide sufficient wearing surface; 
 to prevent excessive wear of journals. Usually, when the first condi- 
 tion is preserved, the other is provided for. When the bearings are 
 flexible, and excessive deflection within the limit of ordinary safety 
 affects nothing external to the bearings, considerable deflection can be 
 tolerated. When bearings are rigid, or deflection may derange external 
 mechanism, for example, an overhung crank, then the deflection 
 must be more restricted. The effect of deflection is to concentrate 
 pressure on the ends of journals, rendering the apparent bearing surface 
 Inefficient. 
 
 In direct-driven electric generators a deflection of 0.01 in. per foot of 
 length has caused much trouble from hot bearings. I have proportioned 
 such shafts so that the deflection will not exceed one-half this extent. 
 
 In some shafts, especially those having an oscillating movement, 
 torsional elasticity is a prime consideration, and the limits can be known 
 only by experience. Reuleaux says: "Limit the torsional yield to 0.1 
 degree per foot of length." This in some cases can be readily tolerated; 
 in others, it has proved excessive. I have adopted the following as a 
 general guide: Permissible twist per foot of length = 0.10 degree for 
 easy service, without severe fluctuation of load ; 0.075 degree for fluctu- 
 ating loads suddenly applied ; 0.050 degree f9r loads suddenly reversed. 
 
 Sufficiency of wearing surface and the limitation of pressure per unit 
 of surface are determined by several conditions: 1. Speed of movement. 
 2. Character of material. 3. Permissible wear of journals or bearings. 
 4. Constancy of pressure in one direction. 5. Alternation of the direction 
 of pressure. 
 
 Taking the product of pressure per sq. in. of surface in Ibs., and speed 
 of movement in ft. per min., we obtain a quantity, which we can term 
 the permissible foot-pounds per minute for each sq. in. of wearing surface. 
 This product varies in good practice under various conditions from 
 50,000 to 500,000 ft.-lbs. per min. For instance, good practice, in later 
 years, has largely increased the area of crosshead slide surfaces. For 
 crossheads having maximum speed of 1000 feet per minute, the pressure 
 per inch of wearing surface should not exceed 50 pounds, giving 50,000 
 ft.-lbs. per min.; whereas crank-pins of the requisite grade of steel, with 
 good lining metal in the boxes and efficient lubrication, will endure 
 200,000 ft.-lbs. per min. satisfactorily, and more than double this when 
 speeds are very high and the pressure intermittent. On main shafts, 
 with pressures constant in one direction, it is advisable not to exceed 
 50,000 ft.-lbs. per min. for heavily loaded shafts at low velocity. This 
 may be increased to 100,000 for lighter loads and higher velocities. It 
 can be inferred, therefore, that the product of speed and pressure cannot 
 be used, in any comprehensive way, as a rational basis for proportioning 
 wearing surfaces. The pressure per unit of surface must be reduced as the 
 speed is increased, but not in a constant ratio. A g9od example of 
 journals severely tested are the recent 110,000-pound freight cars, which 
 bear a pressure of 400 Ibs. per sq. in. of journal bearing, and at a speed 
 of ten miles per hour make about 60,000 foot-pounds per minute. . 
 
 Calculating the Dimensions of Bearings. (F. E. Cardullo, Mach'y, 
 Feb"., 1907.) The durability of the lubricating film is affected in great 
 measure by the character of the load that the bearing carries. When the 
 load is unvarying in amount and direction, as in the case of a shaft carry- 
 ing a heavy bandwheel, the film is easily ruptured. In those cases where 
 the pressure is variable in amount and direction, as in railway journals 
 and crank-pins, the film is much more durable. When the journal only 
 rotates through a small arc, as with the wrist-pin of a steam-engine, the 
 circumstances are most favorable. It has been found that when all other 
 circumstances are exactly similar, a car journal will stand about twice 
 the unit pressure that a fly-wheel journal will. A crank-pin, since the 
 load completely reverses every revolution, will stand three times, and a 
 wrist-Din will stand four times the unit pressure that the fly-wheel journal 
 
DIMENSIONS OF PARTS OF ENGINES. 1043 
 
 The amount of pressure that commercial oils will endure at low speeds 
 without breaking down varies from 500 to 1000 Ibs. per sq. in., where the 
 load is steady. It is not safe, however, to load a bearing to this extent, 
 since it is only under favorable circumstances that the film will stand this 
 pressure without rupturing. On this account, journal bearings should 
 not be required to stand more than two-thirds of this pressure at slow 
 speeds, and the pressure should be reduced when the speed increases. 
 The approximate unit pressure which a bearing will endure without 
 seizing is p = PK -*- (DN + A') (1). p = allowable pressure in Ibs. per 
 sq. in. of projected area, D = diam. of the bearing in ins., N = r.p.m. 
 and P and K depend upon the kind of oil, manner of lubrication, etc. 
 
 P is the maximum safe unit pressure for the given circumstances, at a 
 very slow speed. In ordinary cases, its value is 200 for collar thrust 
 bearings, 400 for shaft bearings, 800 for car journals, 1200 for crank-pins, 
 and 1600 for wrist-pins. In exceptional circumstances, these values 
 may be increased by as much as 50%, but only when the workmanship 
 is of the best, the care the most skillful, the bearing readily accessible, 
 and the oil of the best quality, and unusually viscous. In the great units 
 of the Subway power plant in New York, the value of P for the crank- 
 
 The factor K depends upon the method of oiling, the rapidity of cool- 
 ing, and the care which the journal is likely to get. It will have about 
 the following values: Ordinary work, drop-feed lubrication, 700; first- 
 class care, drop-feed lubrication, 1000; force-feed lubrication or ring- 
 oiling 1200 to 1500; extreme limit for perfect lubrication and air-cooled 
 bearings, 2000. The value 2000 is seldom used, except in locomotive 
 work where the rapid circulation of the air cools the journals. Higher 
 values than this may only be used in the case of water-cooled bearings. 
 
 In case the bearing is some form of a sliding shoe, the quantity 240 V 
 should be substituted for the quantity DN, V being the velocity of rubbing 
 in feet per second. There are a few cases where a unit pressure sufficient 
 to break down the oil film is allowable, such as the pins of punching and 
 shearing machines, pivots of swing bridges, etc, 
 
 In general, the diameter of a shaft or pin is fixed from considerations of 
 
 strength or stiffness. Having obtained the proper diameter, we must 
 
 next make the bearing long enough so that the unit pressure shall not 
 
 exceed the required value. This length may be found by the equation: 
 
 L = (W + PK) X (N +K/D) ...... (2) 
 
 where L is the length of the bearing in ins., W the load upon it in lbs. ( 
 and P, K, N, and D are as before. 
 
 A bearing may give poor satisfaction because it is too long, as well as 
 because it is too short. Almost every bearing is in the condition of a 
 loaded beam, and therefore it has some deflection. 
 
 Shafts and crank-pins must not be made so long that they will allow 
 the load to concentrate at any point. A good rule for the length is to 
 
 make the ratio of length to diameter about equal to VsV. This 
 quantity may be diminished by from 10 to 20% in the case of crank-pins 
 and increased in the same proportion in the case of shaft bearings, but 
 it is not wise to depart too far from it. In the case of an engine making 
 100 r.p.m., the bearings would be by this rule from 11/4 to 11/2 diams. in 
 length. In the case of a motor running at 1000 r.p.m., the bearings 
 would be about 4 diams. long. 
 
 The diameter of a shaft or pin must be such that it will be strong and 
 stiff enough to do its work properly. In order to design it for strength 
 and stiffness, it is first necessary to know its length. This may be assumed 
 tentatively from the equation 
 
 K. ...... . (3) 
 
 The diameter may then be found by any of the standard equations for 
 the strength of shafts or pins given in the different works on machine 
 design. [See The Strength of the Crank-pin, page 1027.] The length is 
 then recomputed from formula No. 2, taking this new value if it does 
 not differ materially from the one first assumeoU If it does, and espe- 
 cially if it is greater than the assumed length, take the mean .value of the 
 assumed and computed lengths, and try again. 
 . EXAMPLE. We will take the case of the crank-pin of an engine with a 
 
1044 THE STEAM-ENGINE. 
 
 20-in. cylinder, running at 80 r.p.m., and having a maximum unbalanced 
 steam pressure of 100 Ibs. per sq. in. The total steam load on the piston 
 is 31,400 pounds. P is taken at 1200, and K as 1000. We will therefore 
 obtain for our trial length: 
 
 L = (20X 31 ,400 X ^80) -s- ( 1200X1000) = 4. 7, or say 43/4 ins. 
 In order that the deflection of the pin shall not be sufficient to destroy 
 the lubricating film we have 
 
 which limits the deflection to 0.003 in. This gives D= 3.85 or say 37/s 
 ins. With this diameter, formula No. 2 gives L = 8.9, say 9 ins. 
 
 The mean of this value and the one obtained before is about 7 ins. 
 Substituting this in the equation for the diameter, we get 5 1/4 ins. sub- 
 stituting this new diameter in equation No. 2 we have L = 7.05, say 
 
 Probably most good designers would prefer to take about half an inch 
 off the length of this pin, and add it to the diameter, making it 53/ 4 X61/2 
 inches, and this will bring the ratio of the length to the diameter nearer 
 
 ~ 
 
 Engine-frames or Bed-plates. No definite rules for the design 
 of engine-frames have been given by authors of works on the steam- 
 engine. The proportions are left to the designer who uses "rule of 
 thumb " or copies from existing engines. F. A. Halsey (Am. Mach., 
 Feb. 14, 1895) has made a comparison of proportions of the frames of 
 horizontal Corliss engines of several builders. The method of comparison 
 is to compute from the measurements the number of square inches in the 
 smallest cross-section of the frame, that is, immediately behind the 
 pillow btock, also to compute the total maximum pressure upon the piston, 
 and to divide the latter quantity by the former. The result gives the 
 number of pounds pressure upon the piston allowed for each square inch 
 of metal in the frame. He finds that the number of Ibs. per sq. in. of 
 smallest section of frame ranges from 217 for a 10 X 30 in. engine up to 
 575 for a 28 X 48 in. A 30 X 60 in. engine shows 350 Ibs., and a 32-in. 
 engine which has been running for many years shows 667 Ibs. Generally 
 the strains increase with the size of the engine, and more cross-section of 
 metal is allowed with relatively long strokes than with short ones. 
 
 From the above Mr. Halsey formulates the general rule that in engines 
 of moderate speed, and having strokes up to 1 1/2 times the diameter of the 
 cylinder, the load per square inch of smallest section should be for a 10-in. 
 engine 300 ibs., which figure should be increased for larger bores up to 500 
 Ibs. for a 30-in. cylinder of the same relative stroke. For high speeds or 
 for longer strokes the load per square inch should be reduced. 
 
 FLY-WHEELS. 
 
 The function of a fly-wheel is to store up and to restore the periodical 
 fluctuations of energy given to or taken from an engine or machine, and 
 thus to keep approximately constant the velocity of rotation. Eankine 
 
 calls the quantity -^-=r the coefficient of fluctuation of speed or of un- 
 
 Z Ji/Q 
 
 steadiness, in which E is the mean actual energy, and A/7 the excess 
 of energy received or of work performed, above the mean, during a 
 given interval. The ratio of the periodical excess or deficiency of energy 
 A" to the whole energy exerted in one period or revolution General 
 Morin found to be from i/e to 1/4 for single-cylinder engines using expan- 
 sion; the shorter the cut-off ^he higher the value. For a pair of engines 
 with cranks coupled at 90 the value of the ratio is about 1/4, and for 
 three engines with cranks at 120, 1/12 of its value for single-cylinder 
 engines. For tools working at intervals, such as punching, slotting and 
 plate-cutting machines, coining-presses, etc., &E is nearly equal to the 
 whole work performed at each operation. 
 
 A fly-wheel reduces the coefficient to a certain fixed amount, being 
 
 2 lilQ 
 
 about 1/32 for ordinary machinery, and 1/50 or Veo for machinery for fine 
 purposes. 
 
FLY-WHEELS. 1045 
 
 If m be the reciprocal of the intended value of the coefficient of fluc- 
 tuation of speed, A# the fluctuation of energy, / the moment of inertia 
 
 of the fly-wheel alone, and a its mean angular velocity, / = 2 As 
 
 the rim of a fly-wheel is usually heavy in comparison with the arms, 
 / may be taken to equal VFr 2 , in which W = weight of rim in pounds, and 
 
 r the radius of the wheel; then W = ^~ = -^~ , if v be the velocity 
 
 of the rim in feet per second. The usual mean radius of the fly-wheel 
 in steam-engines is from three to five times the length of the crank. The 
 ordinary values of the product mg, the unit of time being the second, lie 
 between 1000 and 2000 feet. (Abridged from Rankine, S. E., p. 62.) 
 Thurston gives for engines with automatic valve-gear W = 250,000 
 
 , in which A = area of piston in square inches, S = stroke in feet, 
 
 p = mean steam-pressure in Ibs. per sq. in., R = revolutions per minute, 
 D = outside diameter of wheel in feet. Thurston also gives for ordinary 
 forms of non-condensing engine with a ratio of expansion between 3 and 
 
 5 t w = jL, in which a ranges from 10,000,000 to 15,000,000, averaging 
 
 12,000,000. For gas-engines, in which the charge is fired with every 
 revolution, the American Machinist gives this latter formula, with a 
 doubled, or 24,000,000. Presumably, if the charge is fired every other 
 revolution, a should be again doubled. 
 
 Rankine ("Useful Rules and Tables," p. 247) gives ^=475,000 
 ASx) 
 
 VD*R* ' ia whicil V is the variation of speed, per cent of the mean speed. 
 Thurston's first rule above given corresponds with this if we take V = 1.9. 
 
 Hartnell (Proc. InsL M. E., 1882, 427) says: The value of V, or the 
 variation permissible in portable engines, should not exceed 3% with an 
 ordinary load, and 4% when heavily loaded. In fixed engines, for ordi- 
 nary purposes, V = 2 1/2 to 3%. For good governing or special purposes, 
 such as cotton-spinning, the variation should not exceed 11/2 to 2%. 
 
 F. M. Rites (Trans. A. S. M. E., xiv, 100) develops a new formula for 
 
 C X I H P 
 weight of rim, viz., W = 32 ' , and weight of rim per horse-power 
 
 , in which C varies from 10,000,000,000 to 20,000,000,000; also 
 
 using the latter value of C, he obtains for the energy of the fly-wheel 
 M& = W (3.14) 2 Z> 2 /? 2 = CX H.P. (3.14) 2 D 2 /? 2 = 850,000 H.P. F1 
 
 2 64.4 3600 = WD* X 64 . 4 X 3600 R 
 
 wheel energy per H.P. = 850,000 -s- R. 
 
 The limit of variation of speed with such a weight of wheel from excess 
 of power per fraction of revolution is less than 0.0023. 
 
 The value of the constant C given by Mr. Rites was derived from 
 practice of the Westinghouse single-acting engines used for electric- 
 lighting. For double-acting engines in ordinary service a value of C 
 5,000,000,000 would probably be ample. 
 
 From these formulas it appears that the weight of the fly-wheel for a 
 given horse-power should vary inversely with the cube of the revolutions 
 and the square of the diameter. 
 
 J. B. Stanwood (Eng'g, June 12, 1891) says: Whenever 480 feet is the 
 lowest piston-speed probable for an engine of a certain size, the fly-wheel 
 weight for that speed approximates closely to the formula 
 
 W = 700,000 (Ps -f- D 2 # 2 . 
 
 W = weight in pounds, d = diameter of cylinder in inches, s = stroke 
 in inches, D = diameter of wheel in feet, R = revolutions per minute, 
 corresponding to 480 feet piston-speed. 
 
 In a Ready Reference Book published by Mr. Stanwood, Cincinnati; 
 1892, he gives the same formula, with coefficients as follows: For slide- 
 valve engines, ordinary duty, 350,000: same, electric lighting, 700,000; 
 for automatic high-speed engines, 1,000,000; for Corliss engines, ordinary 
 duty 700,000, electric lighting 1,000,000. 
 
1046 
 
 THE STEAM-ENGINE. 
 
 Thurston's formula above given, W = aAS -j- R*D* w ith a =12,000,000 
 if reduced to terms of d and s in ins., becomes W = 785,400 d"s -H R^D*. 
 If we reduce it to terms of horse-power, we have I.H.P. = 2 ASPR + 
 33,000, in which P = mean effective pressure. Taking this at 40 Ibs., 
 we obtain W = 5,000,000,000 I.H.P. -=- RW*. If mean effective pres- 
 sure = 30 Ibs., then W = 6,666,000,000 I.H.P. -=- jR3)2. 
 
 Emil Theiss (Am. Mach., Sept. 7 and 14, 1893) gives the following 
 values of d, the coefficient of steadiness, which is the reciprocal of what 
 Rankine calls the coefficient of fluctuation: 
 For engines operating 
 
 Hammering and crushing machinery d = 5 
 
 Pumping and shearing machinery d = 20 to 30 
 
 Weaving and paper-making machinery d = 40 
 
 Milling machinery d = 50 
 
 Spinning machinery d = 50 to 100 
 
 Ordinary driving-engines (mounted on bed- 
 plate) , belt transmission d = 35 
 
 Gear-wheel transmission d = 50 
 
 Mr. Theiss's formula for weight of fly-wheel in pounds is W = i X 
 d X I H P 
 V2 v *' wnere ^ * s tne coefficient of steadiness, V the mean velocity 
 
 of the fly-wheel rim in feet per second, n the number of revolutions per 
 minute, i = a coefficient obtained by graphical solution, the values of 
 which for different conditions are given in the following table. In 
 the lines under "cut-off," p means "compression to initial pressure," 
 and O "no compression." 
 
 VALUES OF i. SINGLE-CYLINDER NON-CONDENSING ENGINES. 
 
 Piston- 
 speed, ft. 
 per min. 
 
 Cut-off, 1/6. 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, 1/2. 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 242,010 
 208,200 
 168,590 
 162,070 
 
 O 
 
 Comp. 
 P 
 220,760 
 188.510 
 165.210 
 
 
 
 Comp. 
 P 
 
 
 
 200 
 400 
 600 
 800 
 
 272,690 
 240,810 
 194,670 
 158,200 
 
 218,580 
 187,430 
 145,400 
 108.690 
 
 209,170 
 179,460 
 1 36.460 
 135,260 
 
 201,920 
 170.040 
 146,610 
 
 193,340 
 174.630 
 
 182.840 
 167,860 
 
 SINGLE-CYLINDER CONDENSING ENGINES. 
 
 Piston- 
 speed, ft. 
 per min. 
 
 Cut-off, 1/8. 
 
 Cut-off, 1/6- 
 
 Cut-off, 1/4. 
 
 Cut-off, .1/3. 
 
 Cut-off, 1/9. 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 O 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 
 
 200 
 
 400 
 600 
 
 265.560 
 194,550 
 148,780 
 
 176,560 
 117,870 
 140,090 
 
 234,160 
 174,380 
 
 173,660 
 118,350 
 
 204,210 
 164,720 
 
 167,140 
 133,080 
 
 189,600 
 174.630 
 
 161,830 
 151,680 
 
 172,690 
 
 156,990 
 
 
 
 TWO-CYLINDER ENGINES, CRANKS AT 90. 
 
 Piston- 
 
 Cut-off, l/e. 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, 1/2. 
 
 speed, ft. 
 
 Comp. 
 
 Q 
 
 Comp. 
 
 o 
 
 Comp. 
 
 Q 
 
 Comp. 
 
 Q 
 
 
 P 
 
 
 P 
 
 
 P 
 
 
 P 
 
 
 200 
 400 
 600 
 
 71,980 
 70,160 
 70.040 
 
 } 
 { Mean 
 [60,140 
 
 59,420 
 57,000 
 57,480 
 
 Mean 
 54,340 
 
 49.272 
 49.150 
 
 40 9?ft 
 
 Mean 
 50,000 
 
 37,920 
 35,000 
 
 1 Mean 
 \ 36,950 
 
 800 
 
 70.040 
 
 J 
 
 60.140 
 
 J 
 
 
 
 
 
 THREE-CYLINDER ENGINES, CRANKS AT 120. 
 
 Piston- 
 speed, ft. 
 per min. 
 
 Cut-off, 1/6. 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, 1/2. 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 
 
 Comp. 
 P 
 
 O 
 
 200 
 800 
 
 33.810 
 30.190 
 
 32.240 
 31,570 
 
 33,810 
 35,140 
 
 35,500 
 33,810 
 
 34,540 
 36,470 
 
 33.450 
 32,850 
 
 35,260 
 33,810 
 
 32.370 
 32.370 
 
 As a mean value of i for these engines we may use 33,810. 
 
FLY-WHEELS. 1047 
 
 Weight of Fly-wheels for Alternating-current Units. (J. Begtrup, 
 Am. Mach., July 10, 1902.) 
 
 In which T7= weight of rim of fly-wheel in pounds, D = mean diameter 
 of rim in feet, W\ = weight of armature in pounds, D\= mean diameter 
 of armature in feet, // = rated horse-power of engine, U = a factor of 
 steadiness, N = number of revolutions per minute, V = maximum 
 instantaneous displacement in degrees, not to exceed 5 degrees divided 
 by the number of poles on the generator, according to the rule of the 
 General Electric Company. 
 
 For simple horizontal engines, length of connecting-rod = 5 cranks, 
 U = 90; (ditto, no account being taken of angularity of connecting-rod, 
 U = 64) ; cross-compound horizontal engines, connecting-rod = 5 cranks, 
 U = 51; ditto, vertical engines, heavy reciprocating parts, unbalanced, 
 U = 78; vertical compound engines, cranks 180 degrees apart, recipro- 
 cating parts balanced, U = 60. 
 
 The small periodical variation in velocity (not angular displacement) 
 can be determined from the following formula: 
 
 387,700,000 HZ 
 
 in which H = rated horse-power, Z = a factor of steadiness, N = revs. 
 per min., D = mean diameter of fly-wheel rim in feet, W= weight of fly- 
 wheel rim in pounds, Di = mean diameter of armature or field in feet, 
 Wi = weight of armature, F = variation in per cent of mean speed. 
 
 For simple engines and tandem compounds, Z = 16; for horizontal 
 cross-compounds, Z = 8.5; for vertical cross-compounds, heavy recip- 
 rocating parts, Z = 12.5; for vertical compounds, cranks opposite, 
 weights balanced, Z 14. F represents here the entire variation, 
 between extremes not variation from mean speed. It generally varies 
 from 0.25% of mean speed to 0.75% evidently a negligible quantity. 
 
 A mathematical treatment of this subject will be found in a paper 
 by J. L. Astrom, in Trans. A. 8. M. E., 1901. 
 
 Centrifugal Force in Fly-wheels. Let W = weight of rim in 
 pounds; R = mean radius of rim in feet; r = revolutions per minute, 
 g = 32.16; v = velocity of rim in feet per second = 2nRr *- 60. 
 
 Centrifugal force of whole rim = F = ^ = *^? r * = 0.000341 WRr*. 
 
 ffK oOUU Q 
 
 The resultant, acting at right angles to a diameter, of half of this force 
 tends to disrupt one half of the wheel from the other half, and is resisted 
 by the section of the rim at each end of the diameter. The resultant of 
 half the radial forces taken at right angles to the diameter is 1 -5- i/V = 
 2/7T of the sum of these forces ; hence the total force F is to be divided by 
 2X2X1. 5708 = 6. 2832 to obtain the tensile strain on the cross-section 
 of the rim, or, total strain on the cross-section = S = 0.00005427 WRr*. 
 The weight IFi of a rim of cast iron 1 inch square in section is 2 nR X 
 3.125 = 19.635/2 pounds, whence strain per square inch of sectional 
 area of rim = Si = 0.0010656 /? 2 r 2 = 0.0002664 D 2 r 2 = 0.0000270 F a , 
 In which D = diameter of wheel in feet, and V is velocity of rim in feet 
 per minute. Si = 0. 0972 v 2 , if v is taken in feet per second. 
 
 For wrought iron: 
 
 .Sj = 0.0011366 # 2 r 2 = 0.0002842 D 2 r 2 = 0.0000288 V 2 . 
 
 For steel: 
 
 Si = 0.0011593 # 2 r 2 = 0.0002901 > 2 r 2 = 0.0000294 V 2 . 
 
 For wood: 
 
 Si = 0.0000888 #V 2 = 0.0000222 >V 2 = 0.00000225 V 2 . 
 The specific gravity of the wood being taken at 0.6 = 37.5 Ibs. per cu. 
 ft., or 1/12 the weight of cast iron. 
 
 EXAMPLE. Required the strain per square inch in the rim of a cast- 
 iron wheel 30 ft. diameter, 60 revolutions per minute. 
 
 Answer. 15 2 X 60 2 X 0.0010656 = 863. 1 Ibs. 
 
 Required the strain per square inch in a cast-iron wheel-rim running 
 a mile a minute. Answer. 0.000027 X 5280 2 = 752.7 Ibs. 
 
1048 THE STEAM-ENGINE. 
 
 In cast-iron fly-wheel rims, on account of their thickness, there is 
 difficulty in securing soundness, and a tensile strength of 10,000 Ibs. 
 per sq. in. is as much as can be assumed with safety. Using a factor of 
 safety of 10 gives a maximum allowable strain in the rim of 1000 Ibs. 
 per sq. in., which corresponds to a rim velocity of 6085 ft. per minute. 
 
 For any given material, as cast iron, the strength to resist centrifugal 
 force depends only on the velocity of the rim, and not upon its bulk or 
 weight. 
 
 Chas. E. Emery (Cass. Mag., 1892) says: It does not appear that fly- 
 wheels of customary construction should be unsafe at the comparatively 
 low speeds now in common use if proper materials are used in con- 
 struction. The cause of rupture of fly-wheels that have failed is usually 
 either the "running away of the engine, such as may be caused by 
 the breaking or slackness of a governor-belt, or incorrect design or de- 
 . fective materials of the fly-wheel. 
 
 Chas. T. Porter (Trans. A.S.M.E., xiv, 808) states that no case of the 
 bursting of a fly-wheel with a solid rim in a high-speed engine is known. 
 He attributes the bursting of wheels built in segments to insufficient 
 strength of the flanges and bolts by which the segments are held together. 
 [The author, however, since the above was written, saw a solid rim fly- 
 wheel of a high-speed engine which had burst, the cause being a large 
 shrinkage hole at the junction between one of the arms and the rim. The 
 wheel was about 6 ft. diam. Fortunately no one was injured by the 
 accident.] (See also Thurston, "Manual of the Steam-engine," Part II, 
 page 413.) 
 
 Diameters of Fly-wheels for Various Speeds. If 6000 feet per 
 minute be the maximum velocity of rim allowable, then 6000 = nRD, 
 in which R = revolutions per minute, and D= diameter of wheel in feet, 
 whence D = 6000 * irR = 1910 -s- R. 
 
 W. H. Boehm, Supt. of the Fly-wheel Dept. of the Fidelity and Casu- 
 alty Co. (Eng. News, Oct. 2, 1902), says: For a given material there is a 
 definite speed at which disruption will occur, regardless of the amount 
 of material used. This mathematical truth is expressed by the formula: 
 
 V = 1.6 VSIW\ 
 
 In which V is the velocity of the rim of the wheel in feet per second at 
 which disruption will occur, W the weight of a cubic inch of the material 
 used, and S the tensile strength of 1 square inch of the material. 
 
 For cast-iron wheels made in one piece, assuming 20,000 Ibs. per sq. 
 in. as the strength of small test bars,- and 10,000 Ibs. per sq. in. in large 
 castings, and applying a factor of safety of 10, V = 1.6 ^1000/0.26 = 
 100 ft. per second for the safe speed. For cast steel of 60,000 Ibs. per 
 sq. in., V = 1.6 Veooo *- 0.28 = 233 ft. per second. This is for wheels 
 made in one piece. If the wheel is made in halves, or sections, the 
 efficiency of the rim joint must be taken into consideration. For belt 
 wheels with flanged and bolted rim joints located between the arms, the 
 joints average only one-fifth the strength of the rim, and no such joint 
 can be designed having a strength greater than one-fourth the strength 
 of the rim. If the rim is thick enough to allow the joint to be reinforced 
 by steel links shrunk on, as in heavy balance wheels, one-third the 
 strength of the rim may be secured in the joint; but this construction can 
 not be applied to belt wheels having thin rims. 
 
 For hard maple, having a tensile strength of 10,500 Ibs. per sq. in., 
 and weighing 0.0283 Ib. per cu. in., we have, using a factor of safety of 
 20, and remembering that the strength is reduced one-half because the 
 wheel is built up of segments, F = 1.6 ^262.5 -*- 0.0283 = 154 ft. per 
 second. The stress in a wheel varies as the square of the speed, and the 
 factor of safety on speed is the square root of the factor of safety on 
 strength. 
 
 Mr. Boehm gives the following table of safe revolutions per minute 
 of cast-iron wheels of different diameters. The flange joint is taken at 
 . 25 of the strength of a wheel with no joint, the pad joint, that is a wheel 
 made in six segments, with bolted flanges or pads on the arms, = 0.50. 
 and the link joint =- 0.60 of the strength of a solid rim. 
 
FLY-WHEELS. 
 
 1049 
 
 SAFE REVOLUTIONS PER MINUTE OF CAST-IRON FLY-WHEELS. 
 
 
 No 
 
 Flange 
 
 Pad 
 
 Link 
 
 
 No 
 
 Flange 
 
 Pad 
 
 Link 
 
 
 joint. 
 
 joint. 
 
 joint. 
 
 joint. 
 
 
 joint. 
 
 joint. 
 
 joint. 
 
 joint. 
 
 Diam. 
 
 
 
 
 
 3iam. 
 
 
 
 
 
 in 
 
 R.P.M. 
 
 R.P.M. 
 
 R.P.M. 
 
 R.P.M. 
 
 in 
 
 R.P.M. 
 
 R.P.M 
 
 R.P.M. 
 
 R.P.M. 
 
 Ft. 
 
 
 
 
 
 Ft. 
 
 
 
 
 
 1 
 
 1910 
 
 955 
 
 1350 
 
 1480 
 
 16 
 
 120 
 
 60 
 
 84 
 
 92 
 
 2 
 
 955 
 
 478 
 
 675 
 
 740 
 
 17 
 
 112 
 
 56 
 
 79 
 
 87 
 
 3 
 
 637 
 
 318 
 
 450 
 
 493 
 
 18 
 
 106 
 
 53 
 
 75 
 
 82 
 
 A 
 
 478 
 
 239 
 
 338 
 
 370 
 
 19 
 
 100 
 
 50 
 
 71 
 
 78 
 
 5 
 
 382 
 
 191 
 
 270 
 
 296 
 
 20 
 
 95 
 
 48 
 
 68 
 
 74 
 
 6 
 
 318 
 
 159 
 
 225 
 
 247 
 
 21 
 
 91 
 
 46 
 
 65 
 
 70 
 
 7 
 
 273 
 
 136 
 
 193 
 
 212 
 
 22 
 
 87 
 
 44 
 
 62 
 
 67 
 
 8 
 
 239 
 
 119 
 
 169 
 
 185 
 
 23 
 
 84 
 
 42 
 
 59 
 
 64 
 
 9 
 
 212 
 
 106 
 
 150 
 
 164 
 
 24 
 
 80 
 
 40 
 
 56 
 
 62 
 
 10 
 
 191 
 
 96 
 
 135 
 
 148 
 
 25 
 
 76 
 
 38 
 
 54 
 
 59 
 
 11 
 
 174 
 
 87 
 
 123 
 
 135 
 
 26 
 
 74 
 
 37 
 
 52 
 
 57 
 
 12 
 
 159 
 
 80 
 
 113 
 
 124 
 
 27 
 
 71 
 
 35 
 
 50 
 
 55 
 
 13 
 
 147 
 
 73 
 
 104 
 
 114 
 
 28 
 
 68 
 
 34 
 
 48 
 
 53 
 
 14 
 
 136 
 
 68 
 
 96 
 
 106 
 
 29 
 
 66 
 
 33 
 
 47 
 
 51 
 
 _L 
 
 128 
 
 64 
 
 90 
 
 99 
 
 30 
 
 64 
 
 32 
 
 45 
 
 49 
 
 The table is figured for a margin of safety on speed of approximately 
 3, which is equivalent to a margin on stress developed, or factor of safety 
 in the usual sense, of 9. (Am. Mack., Nov. 17, 1904.) 
 
 Strains in the Rims of Fly-band Wheels Produced by Centrif- 
 ugal Force. (James B. Stanwood, Trans. A. S. M. E., xiv, 251.) 
 Mr. Stanwood mentions one case of a fly-band wheel where the periphery 
 velocity on a 17 ft. 9 in. wheel is over 7500 ft. per minute. 
 
 In band-saw mills the blade of the saw is operated successfully over 
 wheels 8 and 9 ft. in diameter, at a periphery velocity of 9000 to 10,000 ft. 
 per minute. These wheels are of cast iron throughout, of heavy thick- 
 ness, with a large number of arms. 
 
 In shingle-machines and chipping-machines where cast-iron disks 
 from 2 to 5 ft. in diameter are employed, with knives inserted radially, 
 the speed is frequently 10,000 to 11,000 ft. per minute at the periphery. 
 
 If the rim of a fly-wheel alone be considered, the tensile strain in pounds 
 per square inch of the rim section is T = F 2 /10 nearly, in which V = 
 velocity in feet per second; but this strain is modified by the resistance 
 of the arms, which prevent the uniform circumferential expansion of the 
 rim, and induce a bending as well as a tensile strain. Mr. Stanwood 
 discusses the strains in band-wheels due to transverse bending of a section 
 of the rim between a pair of arms. 
 
 When the arms are lew in number, and of large cross-section, the rim 
 will be strained transversely to a greater degree than with a greater num- 
 ber of lighter arms. To illustrate the necessary rim thicknesses for vari- 
 ous rim velocities, pulley diameters, number of arms, etc., the- following 
 table is given, based upon the formula 
 
 t- 0.475 <!+*. 
 
 ( -jL) 
 
 in which t= thickness of rim in inches, d= diameter of pulley in inches, 
 N = number of arms, V = velocity of rim in feet per second, and F= the 
 greatest strain in pounds per square inch to which any fiber is subjected. 
 The value of F is taken at 0000 ibs. per sq. in. 
 
1050 
 
 THE STEAM-ENGINE. 
 
 THICKNESS OF RIMS IN SOLID WHEELS. 
 
 Diameter of 
 Pulley in 
 inches. 
 
 Velocity of 
 Rim in feet per 
 second. 
 
 Velocity of 
 Rim in feet per 
 minute. 
 
 No. of Arms. 
 
 Thickness in 
 inches. 
 
 24 
 
 50 
 
 3,000 
 
 6 
 
 2/10 
 
 24 
 
 88 
 
 5,280 
 
 6 
 
 15/32 
 
 48 
 
 88 
 
 5,280 
 
 6 
 
 15/18 
 
 108 
 
 184 
 
 11,040 
 
 16 
 
 2V2 
 
 108 
 
 184 
 
 11,040 
 
 36 
 
 1/3 
 
 If the limit of rim velocity for all wheels be assumed to be 88 ft. per 
 second, equal to 1 mile per minute, F = 6000 IDS., the formula becomes 
 
 t = 0.475d -i- 0.672V2 = 0.7 d -J- N*. 
 
 When wheels are made in halves or in sections, the bending strain may 
 be such as to make t greater than that given above. Thus, when the 
 joint comes half way between the arms, the bending action is similar to 
 a beam supported simply at the ends, uniformly loaded, and t is 50% 
 
 greater. Then the formula becomes t = 0.712 d + N*\-^- 2 -TQ), or for a 
 
 fixed maximum rim velocity of 88 ft. per second and F 6000 Ibs., (= 
 1.05d -s- N 2 . In segmental wheels it is preferable t9 have the "joints 
 opposite the arms. Wheels in halves, if very thin rims are to be em- 
 ployed, should have double arms along the line of separation. 
 
 Attention should be given to the proportions of large receiving and 
 tightening pulleys. The thickness of rim for a 48-in. wheel (shown in 
 table) with a rim velocity of 88 ft. per second, is 15/ie in. Many wrecks 
 have been caused by the failure of receiving or tightening pulleys whose 
 rims have been too thin. Fly-wheels calculated for a given coefficient 
 of steadiness are frequently lighter than the minimum safe weight. This 
 is true especially of large wheels. A rough guide to the minimum weight 
 of wheels can be deduced from our formulae. The arms, hub, lugs, etc., 
 usually form from one-quarter to one-third the entire weight of the wheel. 
 
 sectional wheels (joint between arms) t = 1.05 d -* N z . Weight of rim 
 for solid wheels, w = . 57 d 2 b -s- N z , in pounds. Weight of rim in sec- 
 tions wheels with joints between arms, w = 0.86 d?b * A' 2 , in pounds. 
 Total weight of wheel: for solid wheel, W = 0.76 d?b -s- A 72 to 0.86 d z b -*- 
 N 2 , in pounds. For segmental wheels with joint between arms, W = 
 1 .05 d?b -f- N 2 to 1 .3 d?b * N*, in pounds. 
 
 (This subject is further discussed by Mr. Stanwood, in vol. xv, and by 
 Prof. Gaetano Lanza, in vol. xvi, Trans. A. S. M. E.) 
 
 Arms of Fly-wheels and Pulleys. Professor Torrey (Am. Mack* 
 July 30, 1891) gives the following formula for arms of elliptical cross- 
 section of cast-iron wheels: 
 
 W = load in pounds acting on one arm: S = strain on belt in pounds 
 per inch of width, taken at 56 for single and 112 for double belts; v = 
 width of belt in inches; n = number of arms; L = length of arm in feet; 
 b = breadth of arm at hub; d = depth of arm at hub, both in inches; 
 W = Sv + n; b = WL ^ 30 d 2 . The breadth of the arm is its least 
 dimension = minor axis of the ellipse, and the depth the major axis. 
 This formula is based on a factor of safety of 10. 
 
 In using the formula, first assume some depth for the arm, and calcu- 
 late the required breadth to go with it. If it gives too round an arm, 
 assume the depth a little greater, and repeat the calculation. A second 
 trial will almost always give a good section. 
 
 The size of the arms at the hub having been calculated, they may be 
 somewhat reduced at the rim end. The actual amount cannot be cal- 
 culated, as there are too many unknown quantities. However, the depth 
 
FLY-WHEELS. 1051 
 
 and breadth can be reduced about one-third at the rim without danger, 
 and this will give a well-shaped arm. 
 
 Pulleys are often cast in halves, and bolted together. When this is 
 done the greatest care should be taken to provide sufficient .metal in the 
 bolts. This is apt to be the very weakest point in such pulleys. The 
 combined area of the bolts at each joint snould be about 28/100 the 
 cross-section of the pulley at that point. (Torrey.) 
 
 Unwin gives d = . 6337 ^/ BD/n for single belts; 
 
 d = . 798 ^jBD/n for double belts ; 
 
 D being the diameter of the pulley, and B the breadth of the rirn, both in 
 inches. These formulae are based on an elliptical section of arm in which 
 b = 0.4dqrd = 2.56ona width of belt = 4/s the width of the pulley 
 rim, a maximum driving force transmitted by the belt of 56 Ibs. per inch 
 of width for a single belt and 112 Ibs. for a double belt, and a safe working 
 stress of cast iron of 2250 Ibs. per square inch. 
 
 If in Torrey's formula we make 6 = 0.4 c/, it reduces to 
 
 / WL . ., */WL 
 o < 
 
 . V 
 = V 1 
 
 EXAMPLE. Given a pulley 10 feet diameter; 8 arms, each 4 feet long:; 
 face, 36 inches wide; belt, 30 inches: required the breadth and depth of the 
 arm at the hub. According to Unwin, 
 
 d = 0.6337 $ 'BD/n =0.633^/36X 120/8 = 5.16 for single belt, 6 = 2.06; 
 d = 0.798 -yBD/n = 0.798 ^36 X 120/8 = 6.50 for double belt, 6 = 2.60. 
 
 According to Torrey, if we take the formula 6 = WL -f- 30 d 2 and 
 assume d = 5 and 6.5 inches, respectively, for single and double belts, 
 we obtain 6 == 1.08 and 1.33, respectively, or practically only one-half 
 of the breadth according to Unwin, and, since transverse strength is pro- 
 portional to breadth, an arm only one-half as strong. 
 
 Torrey's formula is said to be based on a factor of safety of 10, but this 
 factor can be only apparent and not real, since the assumption that the 
 strain on each arm is equal to the strain on the belt divided by the num- 
 ber of arms, is, to say the least, inaccurate. It would be more nearly 
 correct to say that the strain of the belt is divided among half the number 
 of arms. Unwin makes the same assumption in developing his formula, 
 but says it is only in a rough sense true, and that a large factor of safety 
 must be allowed. He therefore takes the low figure of 2250 Ibs. per square 
 inch for the safe working strength of cast iron. Unwin says that his 
 equations agree well with practice. 
 
 A Wooden-rim Fly-wheel, built in 1891 for a pair of Corliss engines 
 at the Amoskeag Mfg. Co.'s mill, Manchester, N.H., is described by 
 C. H. Manning in Trans. A. S. M. E., xiii, 618. It is 30 ft. diam. and 
 108 in. face. The rim is 12 inches thick, and is built up of 44 courses of 
 ash plank, 2, 3, and 4 inches thick, reduced about 1/2 inch in dressing, 
 set edgewise, so as to break joints, and glued and bolted together. There 
 are two hubs and two sets of arms, 12 in each, all of cast iron. The weights 
 are as follows: 
 
 Weight (calculated) of ash rim 31,855 Ibs. 
 
 Weight of 24 arms (foundry 45,020) 40 349 
 
 Weight of 2 hubs (found ry* 35,030) 31, 394 " 
 
 Counter-weights in 6 arms 664 " 
 
 Total, excluding bolts and screws 104, 262 " 
 
 The wheel was tested at 76 revs, per min., being a surface speed of 
 nearly 7200 feet per minute. 
 
 Wooden Fly-wheel of the Willimantic TJnen Co. (Illustrated in 
 Power, March, 1893.) Rim 28 ft. diam., 110 in. face. The rim is 
 carried upon three sets of arms, one under the center of each belt, with 
 12 arms in each set. 
 
 The material of the rim is ordinary whitewood, 7/ 8 in. in thickness, cut 
 into segments not exceeding 4 feet in length, and either 5 or 8 inches in 
 
1052 
 
 THE STEAM-ENGINE. 
 
 width. These were assembled by building a complete circle 13 inches in 
 width, first with the 8-inch inside and the 5-inch outside, and then beside 
 it another circle with the widths reversed, so as to break joints. Each 
 piece as it was added was brushed over with glue and nailed with three- 
 inch wire nails to the pieces already in position. The nails pass through 
 three and into the fourth thickness. .At the end of each arm four 14- 
 inch b9lts secure the rim, the ends being covered by wooden plugs glued 
 and driven into the face of the wheel. 
 
 Wire-wound Fly-wheels for Extreme Speeds. (Eng'g News, 
 August 2, 1890.) The power required to produce the Mannesmann 
 tubes is very large, varying from 2000 to 10,000 H.P., according to the 
 dimensions of the tube. Since this power is needed for only a short time 
 (it takes only 30 to 45 seconds to convert a bar 10 to 12 ft. long and 4 in. 
 in diameter into a tube), and then some time elapses before the next bar 
 is ready, an engine of 1200 H.P. provided with a large fly-wheel for stor- 
 ing the energy will supply power enough for one set of rolls. These 
 fly-wheels are so large and run at such great speeds that the ordinary 
 method of constructing them cannot be followed. A wheel at the Mannes- 
 mann Works, made in Komotau, Hungary, in the usual manner, broke at 
 a tangential velocity of 125 ft. per second. The fly-wheels designed to 
 hold at more than double this speed consist of a cast-iron hub to which 
 two steel disks, 20 ft. in diameter, are bolted; around the circumference 
 of the wheel thus formed 70 tons of No. 5 wire are wound under a tension 
 of 50 Ibs. In the Mannesmann Works at Landore, Wales, such a wheel 
 makes 240 revolutions a minute, corresponding to a tangential velocity 
 of 15,080 ft. or 2.85 miles per minute. 
 
 THE SLIDE-VALVE. 
 
 Definitions. Travel = total distance moved by the valve. 
 
 Throw of the Eccentric = eccentricity of the eccentric = distance from 
 the center of the shaft to the center of the eccentric disk = 1/2 the travel 
 of the valve. 
 
 Lap of the valve, also called outside lap or steam-lap = distance the 
 outer or steam edge of the valve extends beyond or laps over the steam 
 edge of the port when the valve is in its central position. 
 
 Inside lap, or exhaust-lap = distance the inner or exhaust edge of the 
 valve extends beyond or laps over the exhaust edge of the port when the 
 valve is in its central position. The inside lap is sometimes made zero, 
 or even negative, in which latter case the distance between the edge of 
 the valve and the edge of the port is sometimes called exhaust clearance, 
 or inside clearance. 
 
 Lead of the valve = the distance the steam-port is opened when the 
 engine is on its center and the piston is at the beginning of the stroke. 
 
 Lead-angle = the angle between the position of the crank when the 
 valve begins to be opened and its position when the piston is at the 
 beginning of the stroke. 
 
 The valve is said .to have lead when the steam-port opens before the 
 piston begins its stroke. If the piston begins its stroke before the admis- 
 sion of steam begins, the valve is said to have negative lead, and its amount 
 is the lap of the edge of the valve over the edge of the port at the instant 
 when the piston stroke begins. 
 
 Lap-angle = the angle through which the eccentric must be rotated to 
 cause the steam edge to travel from its central position the distance of 
 the lap. 
 
 Angular advance of the eccentric = lap-angle + lead-angle. 
 
 Linear advance = lap + lead. 
 
 Effect of Lap, Lead, etc., upon the Steam Distribution. Given 
 valve-travel 2 3/ 4 in., lap 3/ 4 in., lead Vie in., exhaust-lap Vs in., required 
 crank position for admission, cut-off, release and compression, and 
 greatest port-opening. (Halsey on Slide-valve Gears.) Draw a circle 
 of diameter fh = travel of valve. From O the center set off Oa = lap 
 and ab = lead, erect perpendiculars Oe, ac, bd; then ec is the lap-angle 
 and cd the lead-angle, measured as arcs. Set off fg = cd, the lead- 
 angle; then Og is the position of the crank for steam admission. Set off 
 2ec + cd from h to i\ then Oi is the crank-angle for cut-off, and fk * fh 
 is the fraction of stroke completed at cut-off. Set off 01 = exhaust* 
 
THE SLIDE-VALVE. 
 
 1053 
 
 lap and draw lm; em is the exhaust-lap angle. Set off hn = ec + cd em, 
 and On is the position of crank at release. Set off fp.= ec + cd + em, 
 and Op is the position of crank for compression, fo -*- fh is the fraction 
 of stroke completed at release, and hq *- hf is the fraction of the return 
 stroke completed when compression begins; Oh, the throw of the eccentric, 
 minus Oa the lap, equals ah the maximum port-opening. 
 
 iCut-off 
 
 FIG. 170. 
 
 If a valve has neither lap nor lead, the line joining the center of the 
 eccentric disk and the center of the shaft being at right angles to the line 
 of the crank, the engine would follow full stroke, admission of steam 
 beginning at the beginning of the stroke and ending at the end of the 
 stroke. 
 
 Adding lap to the valve enables us to cut off steam before the end of 
 the stroke. The eccentric being advanced on the shaft an amount equal 
 to the lap-angle enables steam to be admitted at the beginning of the 
 stroke, as before lap was added, and advancing it a further amount equal 
 to the lead-angle causes steam to be admitted before the beginning of the 
 stroke. 
 
 Having given lap to the valve, and having advanced the eccentric 
 on the shaft from its central position at right angles to the crank, 
 through the angular advance = lap-angle 4- lead-angle, the four events, 
 admission, cut-off, release or exhaust-opening, and compression or exhaust- 
 closure, take place as follows: Admission, when the crank lacks the lead- 
 angle of having reached the center; cut-off, when the crank lacks two 
 lap-angles and one lead-angle of having reached the center. During 
 the admission of steam the crank turns through a semicircle less twice 
 the lap-angle. The greatest port-opening is equal to half the travel of the 
 valve less the lap. Therefore for a given port-opening the travel of the 
 valve must be increased if the lap is increased. When exhaust-lap is 
 added to the valve it delays the opening of the exhaust and hastens its 
 closing by an angle of rotation equal to the exhaust-lap angle, which is 
 the angle through which the eccentric rotates from its middle position 
 
1054 
 
 THE STEAM-ENGINE. 
 
 while the exhaust edge of the valve uncovers its lap. Release then 
 takes place when the crank lacks one lap-angle and one lead-angle minus 
 one exhaust-lap angle of having reached the center, and compression when 
 the crank lacks lap-angle + lead-angle 4- exhaust-lap angle of having 
 reached the center. 
 
 The above discussion of the relative position of the crank, piston, and 
 valve for the different points of the stroke is accurate only with a con- 
 necting-rod of infinite length. 
 
 For actual connecting-rods the angular position of the rod causes a 
 distortion of the position of the valve, causing the events to take place too 
 late in the forward stroke and too early in the return. The correction of 
 this distortion may be accomplished to some extent by setting the valve 
 so as to give equal lead on both forward and return stroke, and by alter- 
 ing the exhaust-lap on one end so as to equalize the release and com- 
 pression. F. A. Halsey, in his Slide-valve Gears, describes a method of 
 equalizing the cut-off without at the same time affecting the equality of 
 the lead. In designing slide-valves the effect of angularity of the con- 
 necting-rod should be studied on the drawing-board, and preferably by 
 the use of a model. 
 
 Sweet's Valve-diagram. To find outside and inside lap of valve 
 for different cut-offs and compressions (see Fig. 171): Draw a circle 
 whose diameter equals travel of valve. Draw diameter BA and con- 
 tinue to A, 1 , so that the length AA 1 bears the same ratio to XA as the 
 
 FIG. 171. Sweet's Valve Diagram. 
 
 length of connecting-rod does to length of engine-crank. Draw small 
 circle K with a radius equal to lead. Lay off AC so that ratio of AC to 
 AB = cut-off in parts of the stroke. Erect perpendicular CD. Draw 
 DL tangent to K\ draw XS perpendicular to DL; XS is then outside lap 
 of valve. 
 
 To find release and compression: If there is no inside lap, draw FE 
 through X parallel to DL. F and E will be position of crank for release 
 and compression. If there is an inside lap, draw a circle about X, in 
 which radius XY equals inside lap. Draw HG tangent to this circle and 
 parallel to DL; then H and G are crank positions for release and for com- 
 pression. Draw HN and MG, then AN is piston position at release and 
 A'M piston position at compression, AB being considered stroke of 
 engine. 
 
 To make compression alike on each stroke it is necessary to increase 
 the inside lap on crank end of valve, and to decrease by the same amount 
 the inside lap on back end of valve. To determine this amount, through 
 M with a radius MM 1 = AA 1 , draw arc MP, from P draw PT perpen- 
 dicular to AB, then TM is the amount to be added to inside lap on crank 
 end, and to be deducted from inside lap on back end of valve, inside lap 
 being XY. 
 
 For the Bilgram Valve-Diagram, see Halsey on Slide-valve Gears. 
 
 The Zeuner Valve-diagram is given in most of the works on the 
 steam-engine, and in treatises on valve-gears, as Zeuner's, Peabody's, and 
 Spangler's. The following paragraphs show how the Zeuner valve-diagram 
 may be employed as a convenient means (1) f9r finding the lap, lead, 
 etc., of a slide-valve when the points of admission, cut-off, and release 
 
THE SLIDE-VALVE. 
 
 1055 
 
 are given; and (2) for obtaining the points of admission, cut-off, release, 
 and compression, etc., when the travel, the laps, and the lead of the valve 
 are given. In working out these two problems, the connecting-rod is 
 supposed to be of infinite length. 
 
 Determination of the Lap, Lead, etc., of a Slide-valve for Given Steam 
 Distribution. Given the points of admission, cut-off , and release, to find 
 the point of compression, the lap, the lead, the exhaust lap, the angular 
 advance, and the port-openings at different fractions of the stroke. 
 
 Draw a straight line A A', Fig. 172, to represent on any scale the travel 
 of the valve, and on it draw a circle, with the center 0, to represent the 
 path of the center of the eccentric. The line and the circle will also repre- 
 sent on a different scale the length of stroke of the piston and the path 
 of the crank-pin. On the circle, which is called the crank circle, mark B, 
 
 Valve , 
 
 (Cut-off 
 
 Center of\ Y 
 Eccentric 
 
 B\Admisson 
 
 FIG. 172. Zeuner's Valve Diagram. 
 
 the position of the crank-pin when admission of steam begins, the direc* 
 tion of motion of the crank being shown by the arrow; C, the position of 
 the crank-pin at cut-off; and L, its position at release. From these points 
 draw perpendiculars BM, CN, and LV t to the line A A'; M, N, and V 
 will then represent the positions of the piston at admission, cut-off, and 
 release respectively, the admission taking place, as shown, before the 
 piston reaches the end of the stroke in the direction OA, and release 
 taking place before the end of the stroke in the direction OA'. 
 
 Bisect the arc BC at D, and draw the diameter DOD' . On DO draw 
 the circle DHOGE, called the valve circle. Draw OB, cutting the valve 
 circle at G; and OC, cutting it at H. Then OG = OH is the lap of the 
 valve, measured on the scale in which OA is the half-travel of the valve. 
 With OG as radius draw the arc GF1I, called the steam-lctp circle, or, for 
 short, the lap circle. 
 
1056 THE STEAM-ENGINE. 
 
 Mark the point E, at which the valve circle cuts the line OA. The 
 distance FE represents the lead of the valve, and BG = AF is the max- 
 imum port-opening. A perpendicular drawn from OA at E will cut the 
 valve circle and tne crank circle at D, since the triangle DEO is a right- 
 angled triangle drawn in the semicircle DEGO. 
 
 Erect the perpendicular FJ, then angle DOJ = AOB is the lead-angle 
 and JOK is the lap-angle, OK being a perpendicular to AA 1 drawn from 
 O. DOK is the sum of the lap and lead angles, that is, the angular 
 advance, by which the eccentric must be set beyond 90 ahead of the 
 crank. Set off KY = KD ; then Y is the position of the center of the 
 eccentric when the crank is in the position OA. 
 
 To find the point of compression, set off D'P = D'L; then P is the 
 point of compression. 
 
 Draw OP and OL. On OB' draw the valve circle ORD'S, cutting 
 OL at R and OP at S. With OR as a radius draw the arc of the exhaust- 
 lap circle, RTS; OR = OS is the exhaust lap. 
 
 The port-opening at any part of the stroke, or corresponding position 
 of the crank, is represented by the radial distances, as EF, DW, and J'X, 
 intercepted between the lap and the valve circles on radii drawn from O. 
 Thus, on the radius OB, the port-opening is zero when steam admission is 
 about to begin; on the radius OA, when the crank is on the dead center 
 the opening is EF, or equal to the lead of the valve; on the radius DO, 
 midway between the point of admission and the point of cut-off, the 
 opening is a maximum DW AF = BG\ on the radius OC it is zero 
 again when steam has just been cut off. 
 
 In like manner the exhaust opening is represented by the radial dis- 
 tances intercepted between the exhaust-lap circle, RR'TS, and the valve 
 circle, ORD'S. On the radius OL it is zero when release begins; on OD' 
 it is TD r , a maximum; and on OP it is zero again when compression begins. 
 
 Determination of the Steam Distribution, etc., for a Given Valve. Given 
 the valve travel, the lap, the lead, and the exhaust lap, to find the maxi- 
 mum port-opening, the angular advance, and the points of admission, 
 cut-off, release, and compression. 
 
 This problem is the reverse of the preceding. Draw AOA' to represent 
 the valve travel on a certain scale, O being the middle point, and on this 
 line on the same scale set off OF = the lap, FE the lead, and OR' = 
 the exhaust lap. AF then will be the maximum port-opening. Draw the 
 perpendiculars OK and ED. DOK is the angular advance. 
 
 Draw the diameter DOD f , and on DO and D'O draw the two valve 
 circles. From 0, the center, with a radius OF, the lap, draw the arc of 
 the steam-lap circle cutting the valve circle in G and H. Through G 
 draw OB, and through H draw OC', B then is the point of admission, 
 and C the point of cut-off. With OR, the exhaust lap, as a radius, draw 
 the arc of the exhaust-lap circle, RTS, cutting the valve circle in R and 
 S. Through R draw OL, and through S draw OP. Then L is the point 
 of release and P the point of compression. Draw the perpendiculars 
 BM, CN, LV, and PP', to find M, N, V, and P', the respective positions 
 on the stroke of the piston when admission, cut-off, release, and com- 
 pression take place. 
 
 Practical Application of Zeuner's Diagram. In problems solved by 
 paeans of the Zeuner diagram, the results obtained on the drawings are 
 relative dimensions or the ratios of the several dimensions to a given 
 dimension the scale of which is known, such as the valve travel, the 
 maximum port-opening, or the length of stroke. In problems similar to 
 the first problem given above, the known dimensions are usually the 
 length of stroke, the maximum port-opening, AF, which is calculated 
 from data of the dimensions of cylinder, the piston speed, and the allow- 
 able velocity of steam through the port. The length of the stroke being 
 represented on a certain scale by AA', the points of admission, cut-off, 
 release, and compression, in fractions of the stroke, are measured respec- 
 tively by A'M , AN, AV, and A'P on the same scale. The actual dimen- 
 sion of the maximum port-opening is represented on a different scale by 
 AF, therefore the actual dimensions of the lap, lead, and exhaust lap are 
 measured respectively by OF, FE, and OR' on the same scale as AF; 
 or, in other words, the lap, lead, and exhaust lap are respectively the 
 f) fl* FF OTf f 
 
 ratios -j-p' -7~p and-7-rp each multiplied by the maximum port-opening. 
 
THE SLIDE-VALVE. 
 
 1057 
 
 In problems similar to the second problem, the actual dimensions of 
 the lap, the lead, the exhaust lap, and the valve travel are all known, 
 and are laid down on the same scale on the line AA', representing the 
 valve travel; and the maximum port-opening is found by the solution of 
 the problem to be AF, measured on the same scale; or the maximum 
 port-opening = 1/2 valve travel minus the lap. Also in this problem 
 A A' represents the known length of stroke on a certain scale, and the 
 points of admission, cut-off, release, and compression, in fractions of the 
 stroke, are represented by the ratios which A'M, AN, AV, and A'P, 
 respectively, bear to AA'. 
 
 Port-opening. The area of port-opening is usually made such that 
 the velocity of the steam in passing through it should not exceed 6000 ft. 
 per min. The ratio of port area to piston area will vary with the piston- 
 speed as follows: 
 Forspeed^iston.J 10Q 200 30Q 400 500 600 700 800 900 1000 12QO 
 
 Port area = piston } 0017 Q33 Q5 Q67 Og3 x 10? 133 15 167 2 
 
 tiled A } 
 
 For a velocity of 6000 ft. per min., 
 
 Port area = sq. of diam. of cyl.X piston speed -s- 7639. 
 
 The length of the port-opening may be equal to or something less thaiv 
 the diameter of the cylinder, and the width = area of port-opening -fr- 
 its length. 
 
 The bridge between steam and exhaust ports should be wide enough 
 to prevent a leak of steam into the exhaust due to overtravel of the 
 valve. 
 
 The width of exhaust port = width of steam port + 1/2 travel of valve 
 + inside lap width of bridge. 
 
 Lead. (From Peabody's Valve-gears.) The lead, or the amount 
 that the valve is open when the engine is on a dead point, varies, with the 
 type and size of the engine, from a very small amount, or even nothing 
 up to 3/ 8 of an inch or more. Stationary-engines running at slow speed 
 may have from 1/64 to Vie inch lead. The effect of compression is to fill 
 the waste space at the end of the cylinder with steam; consequently, 
 engines having much compression need less lead. Locomotive-engines 
 having the valves controlled by the ordinary form of Stephenson link- 
 motion may have a small lead when running slowly and with a long 
 cut-off, but when at speed with a short cut-off the lead is at least 1/4 inch; 
 and locomotives that have valve-gear which gives constant lead com- 
 monly have 1/4 inch lead. The lead -angle is the angle the crank makes 
 with the line of dead points at admission. It may vary from to 8. 
 
 Inside Lead. Weisbach (vol. ii, p. 296) says: Experiment shows 
 that the earlier opening of the exhaust ports is especially of advantage, 
 and in the best engines the lead of the valve upon the side of the exhaust, 
 or the inside lead, is 1/25 to 1/15; i.e., the slide-valve at the lowest or highest 
 position of the piston has made an opening whose height is 1/25 to 1/15 of 
 the whole throw of the slide-valve. The outside lead of the slide-valve 
 or the lead on the steam side, on the other hand, is much smaller, and is 
 often only 1/100 of the whole throw of the valve. 
 
 Effect of Changing Outside Lap, Inside Lap, Travel and 
 Angular Advance. (Thurston.) 
 
 
 Admission. 
 
 Expansion. 
 
 Exhaust. 
 
 Compression. 
 
 Incr. 
 O.L. 
 
 is later, 
 ceases sooner 
 
 occurs earlier, 
 continues longer 
 
 is unchanged 
 
 begins at 
 same point 
 
 Incr. 
 I.L. 
 
 unchanged 
 
 begins as before, 
 continues longer 
 
 occurs later, 
 ceases earlier 
 
 begins sooner, 
 continues longel 
 
 Incr. 
 
 begins sooner, 
 
 begins later, 
 
 begins later, 
 
 begins later, 
 
 T. 
 
 continues longer 
 
 ceases sooner 
 
 ceases later 
 
 ends sooner 
 
 Incr. 
 A.A 
 
 begins earlier, 
 period unaltered 
 
 begins sooner, 
 per. the same 
 
 begins earlier, 
 per. unchanged 
 
 begins earlier, 
 per. the same 
 
1058 
 
 THE STEAM-ENGINE. 
 
 Zeuner gives the following relations (Weisbach-Dubois, vol. ii, p. 307), 
 It S = travel of valve, p = maximum port opening; 
 L = steam-lap, I = exhaust-lap; 
 
 L 
 
 li 
 
 ratio of steam-lap to half travel = ^ , L = X S\ 
 
 r = ratio of exhaust-lap to half travel = 
 
 I 
 
 0.5S 
 
 If a = angle BOG between positions of crank at admission and at 
 cut-off, and ft = angle LOP between positions of crank at release and at 
 
 ,. sin (180 -a) , sin (180 -/3) 
 Bompression, then R = 1/2 3 r, '> r = l /2 3 ; 
 
 Sin 1/2 a Sill 1/2 ft 
 
 Crank-angles for Connecting-rods of Different Lengths. 
 
 FORWARD AND RETURN STROKES. 
 
 Ratio of Length of Connecting-rod to Length of Stroke. 
 
 II 1 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 5 
 
 Infi- 
 nite 
 
 ta ** B 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For. 
 
 cc o 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 or 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ret. 
 
 .01 
 
 10.3 
 
 13.2 
 
 10.5 
 
 12.8 
 
 10.6 
 
 12.6 
 
 10.7 
 
 12.4 
 
 10.8 
 
 12.3 
 
 10.9 
 
 12.1 
 
 11.5 
 
 .02 
 
 14.6 
 
 18.7 
 
 14.9 
 
 18.1 
 
 15.1 
 
 17.8 
 
 15.2 
 
 17.5 
 
 15.3 
 
 17.4 
 
 15.5 
 
 17.1 
 
 16.3 
 
 .03 
 
 17.9 
 
 22.9 
 
 18.2 
 
 22.2 
 
 18.5 
 
 21.8 
 
 18.7 
 
 21.5 
 
 18.8 
 
 21.3 
 
 19.0 
 
 21.0 
 
 19.9 
 
 .04 
 
 20.7 
 
 26.5 
 
 21.1 
 
 25.7 
 
 21.4 
 
 25.2 
 
 21.6 
 
 24.9 
 
 21.8 
 
 24.6 
 
 22.0 
 
 24.3 
 
 23.1 
 
 .05 
 
 23.2 
 
 29.6 
 
 23.6 
 
 28.7 
 
 24.0 
 
 28.2 
 
 24.2 
 
 27.8 
 
 24 4 
 
 27.5 
 
 24.7 
 
 27.2 
 
 25.8 
 
 .10 
 
 33.1 
 
 41.9 
 
 33.8 
 
 40.8 
 
 34.3 
 
 40.1 
 
 34.6 
 
 39.6 
 
 34.9 
 
 39.2 
 
 35.2 
 
 38.7 
 
 36.9 
 
 .15 
 
 41 
 
 51.5 
 
 41.9 
 
 50.2 
 
 42.4 
 
 49.3 
 
 42.9 
 
 48.7 
 
 43.2 
 
 48.3 
 
 43.6 
 
 47.7 
 
 45.6 
 
 .20 
 
 48 
 
 59.6 
 
 48.9 
 
 58.2 
 
 49.6 
 
 57.3 
 
 50.1 
 
 56.6 
 
 50.4 
 
 56.2 
 
 50.9 
 
 55.5 
 
 53.1 
 
 .25 
 
 54.3 
 
 66.9 
 
 55.4 
 
 65,4 
 
 56.1 
 
 64.4 
 
 56.6 
 
 63.7 
 
 57.0 
 
 63.3 
 
 57.6 
 
 62.6 
 
 60.0 
 
 .30 
 
 60.3 
 
 73.5 
 
 61.5 
 
 72.0 
 
 62.2 
 
 71.0 
 
 62 8 
 
 70.3 
 
 63.3 
 
 69.8 
 
 63.9 
 
 69.1 
 
 66.4 
 
 .35 
 
 66.1 
 
 79.8 
 
 67.3 
 
 78.3 
 
 68.1 
 
 77.3 
 
 68.8 
 
 76.6 
 
 69.2 
 
 76.1 
 
 69.9 
 
 75.3 
 
 72.5 
 
 .40 
 
 71.7 
 
 85.8 
 
 73.0 
 
 84.3 
 
 73.9 
 
 83.3 
 
 74.5 
 
 82.6 
 
 75.0 
 
 82.0 
 
 75.7 
 
 81.3 
 
 78.5 
 
 .45 
 
 77 2 
 
 91 5 
 
 78.6 
 
 90.1 
 
 79 6 
 
 89 1 
 
 80 2 
 
 88 4 
 
 80 7 
 
 87 9 
 
 81 4 
 
 87.1 
 
 84 3 
 
 .50 
 
 82.8 
 
 97.2 
 
 84.3 
 
 95.7 
 
 85.2 
 
 94.8 
 
 85.9 
 
 94.1 
 
 86.4 
 
 93.6 
 
 87.1 
 
 92.9 
 
 90.0 
 
 .55 
 
 88.5 
 
 102.8 
 
 89.9 
 
 101.4 
 
 90.9 
 
 100.4 
 
 91.6 
 
 99.8 
 
 92.1 
 
 99.3 
 
 92 9 
 
 98 6 
 
 95.7 
 
 .60 
 
 94.2 
 
 108.3 
 
 95.7 
 
 107.0 
 
 96.7 
 
 106.1 
 
 97.4 
 
 105.5 
 
 98.0 
 
 105.0 
 
 98.7 
 
 104.3 
 
 101.5 
 
 .65 
 
 100.2 
 
 113.9 
 
 101.7 
 
 112.7 
 
 102.7 
 
 111.9 
 
 103.4 
 
 III. 2 
 
 103.9 
 
 110.8 
 
 104.7 
 
 110.1 
 
 107.5 
 
 .70 
 
 106.5 
 
 119.7 
 
 108.0 
 
 118.5 
 
 109.0 
 
 117.8 
 
 109.7 
 
 117.2 
 
 110.2 
 
 116.7 
 
 110.9 
 
 116.1 
 
 113.6 
 
 .75 
 
 113.1 
 
 125.7 
 
 114.6 
 
 124.6 
 
 115.6 
 
 123.9 
 
 116.3 
 
 123.4 
 
 116.7 
 
 123.0 
 
 117.4 
 
 122.4 
 
 120.0 
 
 .80 
 
 120.4 
 
 132 
 
 121.8 
 
 131.1 
 
 122.7 
 
 130.4 
 
 J23.4 
 
 129.9 
 
 123.8 
 
 129.6 
 
 124.5 
 
 129.1 
 
 126.9 
 
 .85 
 
 128.5 
 
 139 
 
 129.8 
 
 138.1 
 
 130.7 
 
 137.6 
 
 131.3 
 
 137.1 
 
 131.7 
 
 136.8 
 
 132.3 
 
 136.4 
 
 134.4 
 
 .90 
 
 138. 1 
 
 146.9 
 
 139.2 
 
 146.2 
 
 139.9 
 
 145.7 
 
 140.4 
 
 145.4 
 
 140.8 
 
 145.1 
 
 141.3 
 
 144.8 143.1 
 
 .95 
 
 150.4 
 
 156.8 
 
 151.3 
 
 156.4 
 
 151.8 
 
 156.0 
 
 152.2 
 
 155.8 
 
 152.5 
 
 155.6 
 
 152.8 
 
 155.3 
 
 154.2 
 
 .96 
 
 153.5 
 
 159.3 
 
 154.3 
 
 158.9 
 
 154.8 
 
 158.6 
 
 155.1 
 
 158.4 
 
 155.4 
 
 158.2 
 
 155.7 
 
 158.0 
 
 156.9 
 
 .97 
 
 157.1 
 
 162.1 
 
 157.8 
 
 161.8 
 
 158.2 
 
 161.5 
 
 158.5 
 
 161.3 
 
 158.7 
 
 161.2 
 
 159.0 
 
 161.0 
 
 160.1 
 
 .98 
 
 161.3 
 
 165.4 
 
 161.9 
 
 165.1 
 
 162.2 
 
 164.9 
 
 162.5 
 
 164.8 
 
 162.6 
 
 164.7 
 
 162.9 
 
 164.5 163.7 
 
 .99 
 
 166.8 
 
 169 7 
 
 167 2 
 
 169 5 
 
 167 4 
 
 169 4 
 
 167 6 
 
 169 3 
 
 167 7 
 
 169 2 
 
 167 9 
 
 169 1 168.5 
 
 1.00 
 
 180 
 
 180 
 
 180 
 
 180 
 
 180 
 
 180 
 
 180 180 
 
 180 
 
 180 
 
 180 
 
 180 
 
 180 
 
 Ratio of Lap and of Port-opening to Valve-travel. The table 
 on page 1059, giving the ratio of lap to travel of valve and ratio of travel 
 to port-opening, is abridged from one given by Buei in Weisbach-Dubois, 
 
THE SLIDE- V At VE. 
 
 1059 
 
 vol. ii. It is calculated from the above formulae. Intermediate values 
 may be found by the formulae, or with sufficient accuracy by interpolation 
 from the figures in the table. By the table on page 1068 the crank-angle 
 may be found, that is, the angle between its position when the engine is 
 on the center and its position at cut-off, release, or compression, when 
 these are known in fractions of the stroke. To illustrate the use of the 
 tables the following example is given by Buel: width of port = 2.2 in.; 
 width of port-opening = width of port +0.3 in.; overtravel = 2.5 in.; 
 length of connecting-rod = 2 1/2 times stroke; cut-off = 0.75 of stroke; 
 release = 0.95 of stroke; lead-angle, 10. From the first table we find 
 crank-angle = 114.6; add lead-angle, making 124.6. From the second 
 table, for angle between admission and cut-off, 125, we have ratio of 
 travel to port-opening = 3.72, or for 124.6 = 3.74, which, multiplied 
 by port-opening 2.5, gives 9.45 in. travel. The ratio of lap to travel, 
 by the table, is 0.2324, or 9.45 X 0.2324 = 2.2 in. lap. For exhaust- 
 lap, we have for release at 0.95, crank-angle = 151.3; add lead-angle 
 10 = 161 .3. From the second table, by interpolation, ratio of lap to 
 travel = 0.0811, and 0.0811 X 9.45 = 0.77 in., the exhaust-lap. 
 
 Lap-angle = 1/2(180 lead-angle crank-angle at cut-off); 
 
 = 1/2(180 - 10 - 114.6) = 27.7. 
 
 Angular advance lap-angle + lead-angle = 27.7 + 10 = 37.7. 
 Exhaust lap-angle = crank-angle at release + lap-angle + lead -angle 180 
 
 = 151. 3+27. 7+10-180 = 9. 
 Crank-angle at com- ) 
 
 pression measured > = 1 80 lap-angle lead-angle exhaust lap-angle 
 on return stroke ) 
 
 = 180-27.7-10-9=133.3; corresponding, by 
 table, to a piston position of .81 of the return stroke; or 
 Crank-angle at compression = 180 (angle at release angle at cut-off) 
 
 + lead-angle 
 = 180 - (151 .3-114. 6) +10= 133.3. 
 
 The positions determined above for cut-off and release are for the 
 forward stroke of the piston. On the return stroke the cut-off will take 
 place at the same angle, 114.6, corresponding by table to 66.6% of the 
 return stroke, instead of 75%. By a slight adjustment of the angular 
 advance and the length of the eccentric-rod the cut-off can be equalized. 
 The width of the bridge should be at least 2.5 + .23 - 2.2 = .55 in. 
 
 Lap and Travel of Valve. 
 
 S'Sfcg 
 
 *o 
 
 i 
 
 ^^" 
 
 *o 
 
 >i 
 
 S*Ste" 
 
 ti 
 
 >i 
 
 IIP 
 
 I'312 
 flf 38 
 
 o Travel 
 
 el of Vab 
 Port-ope 
 
 fill 
 
 o'oO-c 
 ftp^ncj fl 
 
 o Travel 
 
 3S 
 
 C5 
 5| 
 
 ajpL, 
 
 iixl 
 
 3 fl ? 
 
 0-50^3 
 
 d^ 
 
 o Travel 
 
 .2 o 
 
 cs a 
 > o 
 *S tJ 
 
 - 
 
 * c S 
 
 a 
 
 >*-, 
 
 
 
 S * c 
 
 0, 
 
 ft 
 
 * c S 
 
 a 
 
 |*o . 
 
 'i"S.2 
 
 c5 
 
 3 
 
 ^TJ 
 
 ! o 
 
 A 
 
 
 I'c'i J g 
 
 a 
 
 H^ 
 
 "3b*-i ""^ ^ * 
 
 II 
 
 .2^bb 
 
 Slsl 
 
 II 
 
 1| b - 
 
 |ojff! 
 
 ii 
 
 o^ ^ 
 
 
 r 
 
 I' S 
 
 
 y 
 
 |3.a 
 
 |; t 8 ? 
 
 r 
 
 I 5 ' 
 
 30 
 
 0.4830 
 
 58.70 
 
 85 
 
 0.3686 
 
 7.61 
 
 135 
 
 0.1913 
 
 3.24 
 
 35 
 
 .4769 
 
 43.22 
 
 90 
 
 .3536 
 
 6.83 
 
 140 
 
 .1710 
 
 3.04 
 
 40 
 
 .4699 
 
 33.17 
 
 95 
 
 .3378 
 
 6.17 
 
 145 
 
 .1504 
 
 2.86 
 
 45 
 
 .4619 
 
 26.27 
 
 100 
 
 .3214 
 
 5.60 
 
 150 
 
 .1294 
 
 2.70 
 
 50 
 
 .4532 
 
 21.34 
 
 105 
 
 .3044 
 
 5.11 
 
 155 
 
 .1082 
 
 2.55 
 
 55 
 
 .4435 
 
 17.70 
 
 110 
 
 .2868 
 
 4.69 
 
 160 
 
 .0868 
 
 2.42 
 
 60 
 
 .4330 
 
 14.93 
 
 115 
 
 .2687 
 
 4.32 
 
 165 
 
 .0653 
 
 2.30 
 
 65 
 
 .4217 
 
 12.77 
 
 120 
 
 .2500 
 
 4.00 
 
 170 
 
 .0436 
 
 2.19 
 
 70 
 
 .4096 
 
 11.06 
 
 125 
 
 .2309 
 
 3.72 
 
 175 
 
 .0218 
 
 2.09 
 
 75 
 
 .3967 
 
 9.68 
 
 130 
 
 .2113 
 
 3.46 
 
 180 
 
 .0000 
 
 2.00 
 
 80 
 
 3830 
 
 8 55 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
1060 
 
 THE STEAM-ENGINE. 
 
 Relative Motions of Crosshead and Crank. L = length of coru 
 necting-rod, R length of crank, = angle of crank with center line of 
 engine, D = displacement of crosshead from the beginning of its stroke, 
 V = velocity of crank-pin, F t = velocity of piston. 
 
 sin0 (L- 
 
 COS<? 
 
 For /2-1 
 
 From these formulae Mr. A. F. Nagle computes the following: 
 PISTON DISPLACEMENT AND PISTON VELOCITY FOR EACH 10 OF MOTION 
 
 OF CRANK. Length of crank = 1. Length of connecting-rod = 5. 
 
 Piston velocity Fi for vel. of crank-pin = 1. 
 
 Angle 
 of 
 Cr'nk 
 
 10 
 20 
 30 
 40 
 50 
 
 Displacement. 
 
 Velocity. 
 
 Angle 
 of 
 Cr'nk 
 
 Displacement. 
 
 Velocity. 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 0.018 
 0.072 
 0.159 
 0.276 
 0.416 
 
 0.012 
 0.048 
 0.109 
 0.192 
 0.298 
 
 0.207 
 0.406 
 0.587 
 0.742 
 0.865 
 
 
 60 
 70 
 80 
 84 
 90 
 
 0.576 
 0.747 
 0.924 
 1.000 
 1.101 
 
 0.424 
 0.569 
 0.728 
 
 954 
 1.005 
 1.019 
 1.011 
 1.000 
 
 0.778 
 0.875 
 0.950 
 
 'i.'ooo 
 
 0.899 
 
 PERIODS OF ADMISSION, OR CUT-OFF, FOR VARIOUS LAPS 
 AND TRAVELS OF SLIDE-VALVES. 
 
 The two following tables are from Clark on the Steam-engine. In the 
 first table are given the periods of admission corresponding to travels of 
 valve of from 12 in. to 2 in., and laps of from 2 in. to 3/ 8 in., with 1/4 in. 
 and Vs in. of lead. With greater leads than those tabulated, the steam 
 would be cut off earlier than as shown in the table. 
 
 The influence of a lead of S/IQ in. for travels of from l- r >/8 in. to 6 in., 
 and laps of from 1/2 in. to 11/2 i n - a s calculated for in the second table, 
 is exhibited by comparison of the periods of admission in the table, for 
 the same lap and travel. The greater lead shortens the period of admis- 
 sion, and increases the range for expansive working. 
 
 Periods of Admission, or Points of 'Cut-off, for Given Travels and 
 Laps of Slide-valves. 
 
 1M 
 
 -6 
 
 Periods of Admission, or Points of Cut-off, for the 
 following Laps of Valves in inches. 
 
 H 
 
 ! 
 
 A 
 
 2 
 
 l3/ 4 
 
 H/2 
 
 U/4 
 
 1 
 
 7/8 
 
 3/4 
 
 5/8 
 
 VL> 
 
 3/8 
 
 in. 
 12 
 
 1/4 
 
 88 
 
 3 
 
 8 
 
 95 
 
 96 
 
 V 
 
 98 
 
 98 
 
 99 
 
 99 
 
 10 
 
 V4 
 
 82 
 
 87 
 
 89 
 
 92 
 
 95 
 
 96 
 
 97 
 
 98 
 
 98 
 
 99 
 
 8 
 
 V4 
 
 72 
 
 78 
 
 84 
 
 88 
 
 92 
 
 94 
 
 95 
 
 96 
 
 98 
 
 98 
 
 6 
 
 1/4 
 
 50 
 
 62 
 
 71 
 
 79 
 
 86 
 
 89 
 
 91 
 
 94 
 
 96 
 
 97 
 
 51/2 
 
 1/8 
 
 43 
 
 56- 
 
 68 
 
 77 
 
 85 
 
 88 
 
 91 
 
 94 
 
 96 
 
 97 
 
 
 1/8 
 
 32 
 
 47 
 
 61 
 
 72 
 
 82 
 
 86 
 
 89 
 
 92 
 
 95 
 
 97 
 
 41/2 
 
 1/8 
 
 14 
 
 35 
 
 51 
 
 66 
 
 78 
 
 83 
 
 87 
 
 90 
 
 94 
 
 96 
 
 4 
 
 1/8 
 
 
 17 
 
 39 
 
 57 
 
 72 
 
 78 
 
 83 
 
 88 
 
 92 
 
 95 
 
 31/2 
 
 1/8 
 
 
 
 20 
 
 44 
 
 63 
 
 71 
 
 79 
 
 84 
 
 90 
 
 94 
 
 
 1/8 
 
 
 
 
 23 
 
 50 
 
 61 
 
 71 
 
 79 
 
 86 
 
 91 
 
 21/2 
 
 1/8 
 
 
 
 
 
 27 
 
 43 
 
 57 
 
 70 
 
 80 
 
 88 
 
 2 
 
 Vg 
 
 
 
 
 
 
 
 33 
 
 52 
 
 70 
 
 81 
 
 
 
 
 
 
 
THE SLIDE-VALVE. 
 
 1061 
 
 Periods of Admission, or Points of Cut-off, for given Travels and 
 Laps of Slide-valves. 
 
 Constant lead, 5/16- 
 
 Travel. 
 
 
 
 
 I 
 
 ,ap. 
 
 * 
 
 
 
 
 Inches. 
 
 V2 
 
 V8 
 
 3/4 ' 
 
 7/ 8 
 
 1 
 
 U/8 
 
 H/4 
 
 13/8 
 
 1 1/2 
 
 ]5/ 8 
 
 19 
 
 
 
 
 
 
 
 
 
 13/4 
 
 39 
 
 
 
 
 
 
 
 
 
 17/8 
 
 47 
 
 17 
 
 
 
 
 
 
 
 
 2 
 
 55 
 
 34 
 
 
 
 
 
 
 
 
 21/ 8 
 
 61 
 
 42 
 
 14 
 
 
 
 
 
 
 
 21/4 
 
 65 
 
 50 
 
 30 
 
 
 
 
 
 
 
 23/8 
 
 68 
 
 55 
 
 38 
 
 13 
 
 
 
 
 
 
 21/2 
 
 71 
 
 59 
 
 45 
 
 27 
 
 
 
 
 
 
 25/ 8 
 
 74 
 
 63 
 
 49 
 
 36 
 
 12 
 
 
 
 
 
 23/4 
 
 76 
 
 67 
 
 56 
 
 43 
 
 26 
 
 
 
 
 
 27/8 
 
 78 
 
 70 
 
 59 
 
 47 
 
 32 
 
 11 
 
 
 
 
 3 
 
 80 
 
 73 
 
 62 
 
 50 
 
 38 
 
 23 
 
 
 
 
 31/8 
 
 81 
 
 74 
 
 65 
 
 55 
 
 44 
 
 30 
 
 10 
 
 
 
 31/4 
 
 83 
 
 76 
 
 68 
 
 59 
 
 48 
 
 34 
 
 22 
 
 
 
 33/8 
 31/2 
 
 84 
 85 
 
 78 
 80 
 
 71 
 73 
 
 62 
 64 
 
 51 
 53 
 
 40 
 45 
 
 29 
 34 
 
 9 
 20 
 
 
 \i 
 
 <* 
 
 41/ 4 
 
 41/2 
 43/4 
 
 5V3 
 
 86 
 87 
 87 
 88 
 89 
 90 
 92 
 93 
 94 
 95 
 
 81 
 82 
 83 
 84 
 86 
 87 
 89 
 90 
 92 
 93 
 
 75 
 76 
 78 
 79 
 81 
 83 
 85 
 87 
 89 
 91 
 
 66 
 68 
 70 
 72 
 76 
 79 
 81 
 83 
 86 
 88 
 
 57 
 60 
 63 
 66 
 70 
 73 
 76 
 78 
 82 
 85 
 
 49 
 52 
 55 
 58 
 63 . 
 67 
 70 
 73 
 78 
 82 
 
 38 
 42 
 46 
 49 
 56 
 61 
 65 
 67 
 73 
 78 
 
 26 
 32 
 36 
 40 
 47 
 54 
 58 
 62 
 68 
 74 
 
 9 
 19 
 25 
 29 
 37 
 45 
 51 
 56 
 63 
 69 
 
 Platon- valve. The piston-valve is a modified form of the slide- 
 valve. The lap, lead, etc., are calculated in the same manner as for the 
 common slide-valve. The diameter of valve and amount of port-opening 
 are calculated on the basis that the most contracted portion of the steam- 
 passage between the valve and the cylinder should have an area such that 
 the velocity of steam through it will not exceed 6000 ft. per minute. The 
 area of the opening around the circumference of the valve should be ab9ut 
 double the area of the steam-passage, since that portion of the opening 
 that is opposite from the steam-passage is of little effect. 
 
 Setting the Valves of an Engine. The principles discussed above 
 are applicable not only to the designing of valves, but also to adjustment 
 of valves that have been improperly set; but the final adjustment of the 
 eccentric and of the length of the rod depends upon the amount of lost 
 motion, temperature, etc.; and can be effected only after trial. After 
 the valve has been set as accurately as possible when cold, the lead and 
 lap for the forward and return strokes being equalized, indicator diagrams 
 should be taken and the length of the eccentric-rod adjusted, if necessary, 
 to correct slight irregularities. 
 
 To Put an Engine on its Center. Place the engine in a position 
 where the piston will have nearly completed its outward stroke, and 
 opposite some point on the crosshead, such as a corner, make a mark 
 upon the guide. Against the rim of the pulley or crank-disk place a 
 pointer and mark a line with it on the pulley. Then turn the engine over 
 the center until the crosshead is again in the same position on its inward 
 stroke. This will bring the crank as much below the center as it was 
 above it before. With the pointer in the same position as before make 
 a second mark on the pulley rim. Divide the distance between the marks 
 in two and mark the middle point. Turn the engine until the pointer 
 is opposite this middle point, and it will then be on its center. To avoid 
 
1062 THE STEAM-ENGINE. 
 
 the error that may arise from the looseness of crank-pin and wrist-pin 
 bearings, the engine should be turned a little above the center and 
 then be brought up to it, so that the crank-pin will press against the 
 same brass that it does when the first two marks are made. 
 
 Link Motion. Link-motions, of which the Stephenson link is the 
 most commonly used, are designed for two purposes: first, for reversing 
 the motion of the engine, and second, for varying the point of cut-off 
 by varying the travel of the valve. The Stephenson link-motion is a 
 combination of two eccentrics, called forward and back eccentrics, with 
 a link connecting the extremities of the eccentric-rods ; so that by vary- 
 ing the position of the link the valve-rod may be put in direct connec- 
 tion with either eccentric, or may be given a movement controlled in 
 part by one and in part by the other eccentric. When the link is moved 
 by the reversing lever into a position such that the block to which the 
 valve-rod is attached is at either end of the link, the valve receives its 
 maximum travel, and when the link is in mid-gear the travel is the 
 least and cut-off takes place early in the stroke. 
 
 In the ordinary shifting-link with open rods, that is, not crossed, the 
 lead of the valve increases as the link is moved from full to mid-gear, 
 that is, as the period of steam admission is shortened. The variation ot 
 lead is equalized for the front and back strokes by curving the link to 
 the radius of the eccentric-rods concavely to the axles. With crossed 
 eccentric-rods the lead decreases as the link is moved from full .to mid- 
 gear. In a valve-motion with stationary link the lead is constant. 
 (For illustration see Clark's "Steam-engine," vol. ii, p. 22.) 
 
 The linear advance of each eccentric is equal to that of the valve in 
 full gear, that is, to lap + lead of the valve, when the eccentric-rods 
 are attached to the link in such position as to cause the half-travel of 
 the valve to equal the eccentricity of the eccentric. 
 
 The angle between the two eccentric radii, that is, between lines 
 drawn from the center of the eccentric disks to the center of the shaft, 
 j equals 180 less twice the angular advance. 
 
 i Buel, in Appletpn's "Cyclopedia of Mechanics," vol. ii, p. 3 16, discusses 
 the Stephenson link as follows: "The Stephenson link does not give a 
 perfectly correct distribution of steam; the lead varies for different 
 points of cut-off. The period of admission and the beginning of ex- 
 haust are not alike for both ends of the cylinder, and the forward 
 motion varies from the backward. 
 
 "The correctness of the distribution of steam by Stephenson's link- 
 motion depends upon conditions which, as much as the circumstances 
 will permit, ought to be fulfilled, namely: 1. The link should be curved 
 in the arc of a circle whose radius is equal to the length of the eccentric- 
 rod. 2. The eccentric-rods ought to be long, the longer they are in pro- 
 portion to the eccentricity the more symmetrical will the travel of the 
 valve be on both sides of the center of motion. 3. The link ought to be 
 short. Each of its points dascribes a curve in a vertical plane, whose 
 ordinates grow larger the farther the considered point is from the center 
 of the link; and as the horizontal motion only is transmitted to the 
 valve, vertical oscillation will cause irregularities. 4. The link-hanger 
 ought to be long. The longer it is the nearer will be the arc in which 
 the link swings to a straight line, and thus the less its vertical oscillation. 
 If the link is suspended at its center, the curves tkat are described by 
 points equidistant on both sides from the center are not alike, and 
 hence results the variation between the forward and backward gears. 
 If the link is suspended at its lower end, its lower half will have less 
 vertical oscillation and the upper half more. 5. The center from which 
 the link-hanger swings changes its position as the link is lowered or 
 raised, and also causes irregularities. To reduce them to the smallest 
 amount the arm of the lifting-shaft should be made as long as the 
 eccentric-rod, and the center of the lifting-shaft should be placed at 
 the height corresponding to the central position of the center on which 
 the link-hanger swings." 
 
 All these conditions can never be fulfilled in practice, and the variations 
 in the lead and the period of admission can be somewhat regulated in an 
 artificial way, but for one gear only. This is accomplished by giving 
 different lead to the two eccentrics, which difference will be smaller the 
 longer the eccentric-rods are and the shorter the link, and by suspending 
 
THE STEPHENSON LINK-MOTION. 
 
 1063 
 
 the link not exactly on its center line but at a certain distance from it, 
 giving what is called "the offset." 
 
 For application of the Zeuner diagram to link-motion, see Holmes on 
 the Steam-engine, p. 290. See also Clark's Railway Machinery (1855), 
 Clark's Steam-engine, Zeuner's and Auchincloss's Treatises on Slide- 
 valve Gears, and Halsey's Locomotive Link Motion. (See page 1119.) 
 
 The following rules are given by the American Machinist for laying out 
 a link for an upright slide-valve engine. By the term radius of link is 
 meant the radius of the link-arc, ab, Fig. 173, drawn through the center 
 of the slot ; this radius is generally made equal to the distance from the 
 
 Fig. 173. 
 
 center of shaft to center of the link-block pin P when the latter stands 
 midway of its travel. The distance between the centers of the eccentric- 
 rod pins e\ 62 should not be less than 2 1/2 times, and, when space will 
 permit, three times the throw of the eccentric. By the throw we mean 
 twice the eccentricity of the eccentric. The sl9t link is generally sus- 
 pended from the end next to the forward eccentric at a point in the link- 
 arc prolonged. This will give comparatively a small amount of slip to the 
 link-block when the link is in forward gear; but this slip will be increased 
 when the link is in backward gear. This increase of slip is, however, 
 considered of little importance, because marine engines, as a rule, work 
 but very little in the backward gear. When it is necessary that the 
 motion shall be as efficient in backward gear as in forward gear, then the 
 link should be suspended from a point midway between the two eccentric- 
 rod pins; in marine engine practice this point is generally located on the 
 link-arc; for equal cut-offs it is better to move the point of suspension 
 a small amount towards the eccentrics. 
 
 For obtaining the dimensions of the link in inches: Let L denote the 
 length of the valve, 5 the breadth, p the absolute steam-pressure per sq. in., 
 and R a factor of computation used as below; then R = 0.01 *^L XB X p 
 
 RX 1.6 
 RX 0.8 
 72X2.5 
 (RX 0.7) + l/4ih. 
 (RX 0.6) + 1/4 in. 
 (RX 0.8) + 1/4 in. 
 = R + 1/4 in. 
 Diameter of block-pin when secured at both ends . = (R X . 8) + 1/4 io. 
 
 Breadth of the link. 
 
 Thickness T of the bar 
 
 Length of sliding-block 
 
 Diameter of eccentric-rod pins 
 
 Diameter of suspension-rod pin 
 
 Diameter of suspension-rod pin when overhung. . . 
 Diameter of block-pin when overhung. 
 
1064 THE STEAM-ENGINE. 
 
 The length of the link, that is, the distance frcm a to 6, measured on a 
 straight line joining the ends of the link-arc in the slot, should be such 
 as to allow the center of the link-block pin P to be placed in a line with 
 the eccentric-rod pins, leaving sufficient room for the slip of the block. 
 Another type of link frequently used in marine engines is the double-bar 
 link, and this type is again divided into two classes: one class embraces 
 those links which have the eccentric-rod ends as well as the valve-spindle 
 end between the bars, as shown at B (with these links the travel of the 
 valve is less than the throw of the eccentric); the other class embraces 
 those links, shown at C, for which the eccentric-rods are made with fork- 
 ends, so as to connect to studs on the outside of the bars, allowing the 
 block to slide to the end of the link, so that the centers of the eccentric- 
 rod ends and the block-pin are in line when in full gear, making the travel 
 of the valve equal to the throw of the eccentric. The dimensions of these 
 links when the distance between the eccentric-rod pins is 2 1/2 to 23/4 times 
 the throw of eccentrics can be found as follows: 
 
 Depth of bars.. = (R X 1.25)4- Vain. 
 
 Thickness of bars = (R X 0.5 ) -f 1/4 in. 
 
 Diameter of center of sliding-block = R X 1.3 
 
 When the distance between the eccentric-rod pins is equal to 3 or 4 
 times the throw of the eccentrics, then 
 
 Depth of bars = (R X 1 . 25) + 3/ 4 in. 
 
 Thickness of bars = (R X . 5 ) -f 1/4 in. 
 
 All the other dimensions may be found by the first table. These are 
 empirical rules, and the results may have to be slightly changed to suit 
 given conditions. In marine engines the eccentric-rod ends for all 
 classes of links have adjustable brasses. In locomotives the slot-link is 
 usually employed, and in these the pin-holes have case-hardened bushes 
 driven into the pin-holes, and have no adjustable brasses in the ends of 
 the eccentric-rods. The link in B is generally suspended by one of the 
 eccentric-rod pins; and the link in C is suspended by one of the pins in 
 the end of the link, or by one of the eccentric-rod pins. (See note on 
 Locomotive Link Motion, p. 1119.) 
 
 The Walschaerts Valve-gear. Fig. 174. This gear, which was 
 invented, in Belgium, has for many years been used on locomotives in 
 Europe, and it has now (1909) come largely into use in the United States. 
 The return crank Q, which takes the place of an eccentric, through the 
 rod B oscillates the link on the fixed pin F. The block D is raised and 
 lowered in the link by the reversing rod I, operating through the bell- 
 
 FIG. 174. The Walschaerts Valve-gear. , 
 
 crank levers H , H, and the supporting rod G. When the block is in its 
 lowest position the radius rod U has a motion corresponding in direction 
 to that of the rod B ; when the block is at its upper position U moves in 
 an opposite direction to B. The valve-rod E is moved by the combined 
 action of U and a lever T whose lower end is connected through the 
 rod S to the cross-head R. Constant lead is secured by this gear. (The 
 main crank and the return crank should be shown in the cut as inclin- 
 ing to the right to correspond with the position of the cross-hea.<J.) 
 
GOVERNORS. 1065 
 
 Other Forms of Valve-gear, as the Joy, Marshall, Hackworth, 
 Brerame, Walschaerts, Corliss, etc., are described in Clark's Steam- 
 engine, vol. ii. Power, May 11, 1909, illustrates the Stephenson, Gooch, 
 Allen, Polenceau, Marshall, Joy, Waldegg, Walschaerts, Fink, and 
 Baker-Pilliod gears. The design of the Reynolds-Corliss valve-gear is 
 discussed by A. H. Eldridge in Power, Sept., 1893. See also Henthorn 
 on the Corliss Engine. Rules for laying down the center lines of the 
 Joy valve-gear are given in American Machinist, Nov. 13, 1890. For 
 Joy's "Fluid-pressure Reversing- valve," see Eng'g, May 25, 1894. 
 
 GOVERNORS. 
 
 Pendulum or Fly-ball Governor. The inclination of the arms of a 
 revolving pendulum to a vertical axis is such that the height of the point 
 of suspension h above the horizontal plane in which the center of gravity 
 of the balls revolves (assuming the weight of the rods to be small compared 
 with the weight of the balls) bears to the radius r of the circle described 
 by the centers of the balls the ratio 
 
 h _ weight _ w _ gr 
 
 r ~ centrifugal force ~~ wv' 2 ~ v 2 ' 
 gr 
 
 which ratio is independent of the weight of the balls, v being the velocity 
 of the centers of the balls in feet per second. 
 
 If T = number of revolutions of the balls in 1 second, v = 2-nrT = ar, 
 in which a = 'the angular velocity, or 2 vT, and 
 
 0r 2 g 0.8146. 9.775. . 
 
 h = V = 4^' or h - ^- feet = -^ r inches, 
 
 g = 32.16. If N = revs, per minute, h = 35,190 *- N*. 
 
 For revolutions per minute. ... 40 45 50 60 75 
 
 The height in inches will be ... 21.99 17.38 14.08 9.775 6.256 
 
 Number of turns per minute required to cause the arms to take a given 
 angle with the vertical axis: Let I = length of the arm in inches from 
 the center of suspension to the center of gyration, and a the required 
 angle; then 
 
 The simple governor is not isochronous; that is, it does not revolve 
 at a uniform speed in ail positions, the speed changing as the angle of the 
 arms changes. To remedy this defect loaded governors, such as Porter's, 
 are used. From the balls of a common governor whose collective weight 
 is A let there be hung by a pair of links of lengths equal to the pendulum 
 arms a load B capable of sliding on the spindle, having its center of gravity 
 in the axis of rotation. Then the centrifugal force is that due to A alone, 
 and the effect of gravity is that due to A + 2 B; consequently the alti- 
 tude for a given speed is increased in the ratio (A + 2 B) : A, as com- 
 pared with that of a simple revolving pendulum, and a given absolute 
 variation in altitude produces a smaller proportionate variation in speed 
 than in the common governor. (Rankine, S. E., p. 551.) 
 
 For the weighted governor let 1= the length of the arm from the point 
 of suspension to the center of gravity of the ball, and let the length of the 
 suspending-link h = the length of the portion of the arm from the point 
 of suspension of the arm to the point of attachment of the link; G = the 
 weight of one ball, Q = half the weight of the sliding weight, h = the 
 height of the governor from the point of suspension to the plane of revolu- 
 tion of the balls, a = the angular velocity = 2 irT, T being the number of 
 
 revolutions per second ; then a = y/T^ 1 + l) ; fcsJ ^ (* + T ) 
 in feet, or h = ^^(l + ^r ) in inches, N being the number of revo- 
 lutions per minute. 
 
1066 THE STEAM-ENGINE. 
 
 J. H. Barr gives h = (^^)* B + ^ W ,in which B is the combined 
 
 weight of the two balls and W the central weight. 
 
 For various forms of governor see App. Cyl. Mech., vol. ii, 61, and 
 Clark's Steam-engine, vol. ii, p. 65. 
 
 To Change the Speed of an Engine Having a Fly-ball Governor. 
 
 A slight difference in the speed of a governor changes the position of its 
 weights from that required for full load to that required for no load. 
 It is evident therefore that, whatever the speed of the engine, the normal 
 speed of the governor must be that for which the governor was designed; 
 i.e., the speed of the governor must be kept the same. To change the 
 speed' of the engine the problem is to so adjust the pulleys which drive 
 the governor that the engine at its new speed shall drive it just as fast as 
 it was driven at its original speed. In order to increase the engine-speed 
 we must decrease the pulley upon the shaft of the engine, i.e., the driver, 
 or increase that on the governor, i.e., the driven, in the proportion that 
 the speed of the engine is to be increased. 
 
 Fly-wheel or Shaft-governors. At the Centennial Exhibition in 
 1876 there were shown a few steam-engines in which the governors were 
 contained in the fly-wheel or band-wheel, the fly-balls or weights revolving 
 around the shaft in a vertical plane with the wheel and shifting the eccen- 
 tric so as automatically to vary the travel of the valve and the point of 
 cut-off. This form of governor has since come into extensive use, espe- 
 cially for high-speed engines. In its usual form two weights are carried on 
 arms the ends of which are pivoted to two points on the pulley near its 
 circumference, 180 apart. Links connect these arms to the eccentric. 
 The eccentric is not rigidly keyed to the shaft but is free to move trans- 
 versely across it for a certain distance, having an oblong hole which allows 
 of this movement. Centrifugal force causes the weights to fly towards 
 the circumference of the wheel and to pull the eccentric into a position of 
 minimum eccentricity. This force is resisted by a spring attached to 
 each arm which tends to pull the weights towards the shaft and shift the 
 eccentric to the position of maximum eccentricity. The travel of the valve 
 is thus varied, so that it tends to cut off earlier in the stroke as the engine 
 increases its speed. Many modifications of this general form are in use. 
 In the Buckeye and the Mclntosh & Seymour engines the governor shifts 
 the eccentric around on the shaft so as to vary the angular advance. 
 In the Sweet "Straight-line" engine and in some others a single weight 
 and a single spring are used. For discussions of this form of governor 
 see Hartnell, Proc. Inst. M. E., 1882, p. 408; Trans. A. S. M. E., ix, 300; 
 xi, 1081; xiv, 92: xy, 929; Modern Mechanism, p. 399: Whitham's Con- 
 structive Steam Engineering; J. Begtrup, Am. Mach., Oct. 19 and Dec. 14, 
 1893, Jan. 18 and March 1, 1894. 
 
 Mare recent references are: J. Richardson, Proc. Inst. M. E., 1895 
 (includes electrical regulation of steam-engines); A. K. Mansfield, Trans. 
 A. S. M. E., 1894; F. H. Ball, Trans. A. S. M. E., 1896; R. C. Carpenter, 
 Power, May and June, 1898; Thos. Hall, EL World, June 4, 1898; F. M. 
 Rites, Power, July, 1902; E. R. Briggs, Am. Mach., Dec. 17, 1903 
 
 The Rites Inertia Governor, which is the most common form of the 
 shaft governor at this date (1909). has a long bar, usually made heavy at 
 the ends, like a dumb-bell, instead of the usual weights. This is carried 
 on an arm of the fly-wheel by a pin located at some distance from the 
 center line of the bar, and also at some distance from its middle point. 
 To pins located at two other points are attached the valve-rod and the 
 spring. The bar acts both by inertia and by centrifugal force. When 
 the wheel increases its speed the inertia of the bar tends to make it fall 
 behind, and thus to change the relative position of the fly-wheel arm and 
 the bar, and to change the travel of the valve. A small book on " Shaft 
 Governors " (Hill Pub. Co., 1908) describes and illustrates this and many 
 other forms of shaft governors, and gives practical directions for adjusting 
 them. 
 
 Calculation of Springs for Shaft-governors. (Wilson Hartnell, 
 Proc. Tnst. M. E., Aug., 1882.) The springs for shaft-governors may be 
 conveniently calculated as follows, dimensions being in inches: 
 
 Let W = weight of the balls or weights, in pounds: 
 
 n and ra = the maximum and minimum radial distances of the 
 center of the balls or of the centers of gravity of the weights; 
 

 GOVERNORS. 1067 
 
 la and h = the leverages, i.e., the perpendicular distances from the 
 center of the weight-pin to a line in the direction of the centrif- 
 ugal force drawn through the center of gravity of the weights 
 or balls at radii n and rz; 
 
 mi and m^ = the corresponding leverages of the springs; 
 
 Ci and C T 2 = the centrifugal forces, for 100 revolutions per minute, 
 at radii n and rz; 
 
 Pi and P2 = the corresponding pressures on the spring; 
 
 (It is convenient to calculate these and note them down for refer- 
 ence.) 
 
 Cs and C 4 = maximum and minimum centrifugal forces; 
 
 S = mean speed (revolutions per minute); 
 
 Si and Sz = the maximum and minimum number of revolutions 
 per minute; 
 
 Ps and PI = the pressures on the spring at the limiting number 
 of revolutions (Si and 2); 
 
 P 4 Ps = D = the difference of the maximum and minimum 
 pressures on the springs; 
 
 V = the percentage of variation from the mean speed, or the 
 sensitiveness; 
 
 t = the travel of the spring; 
 
 u = the initial extension of the spring; 
 
 v = the stiffness in pounds per inch ; 
 
 w the maximum extension = u + t. . 
 
 The mean speed and sensitiveness desired are supposed to be given, 
 
 fsv sv 
 
 S 1 = S T7^' St^S+TF^' 
 
 It is usual to give the spring-maker the values of P 4 and of v or w. 
 To ensure proper space being provided, the dimensions of the spring should 
 be calculated by the formulas for strength and extension of springs, and 
 the least length of the spring as compressed be determined. 
 
 The governor-power =^2 *X T-X- 
 With a straight centripetal line, the governor-power 
 
 ~V^ X ("IT" 1 )' 
 
 For a preliminary determination of the governor-power it may be taken 
 as equal to this in all cases, although it is evident that with a curved cen- 
 tripetal line it will be slightly less. The difference D must be constant for 
 the same spring, however great or little its initial compression. Let the 
 spring be screwed up until its minimum pressure is P 5 . Then to find the 
 speed Po = P$ + D, 
 
 0.28XnX W-, Ca = .28 X r z X W; 
 
 _*,_* 
 
 t v v 
 
 The speed at which the governor would be isochronous would be 
 
 Suppose the pressure on the spring with a speed of 100 revolutions, at 
 the maximum and minimum radii, was 200 Ibs. and 100 Ibs., respectively, 
 
10G8 
 
 THE STEAM-ENGINE. 
 
 then the pressure of the spring to suit a variation from 95 to 105 revolu- 
 tions will be 100 X (^) 2 = 90 .2 and 200 X (^) 2 = 220 .5 That is, the 
 
 increase of resistance from the minimum to the maximum radius must be 
 220 -90 = 130 Ibs. 
 
 The extreme speeds due to such a spring, screwed up to different 
 pressures, are shown in the following table: 
 
 Revolutions per minute balls shut 
 
 80 
 
 00 
 
 9S 
 
 100 
 
 no 
 
 120 
 
 Pressure on springs balls shut 
 
 64 
 
 81 
 
 90 
 
 100 
 
 121 
 
 M4 
 
 Increase of pressure when balls open fully 
 
 no 
 
 no 
 
 no 
 
 no 
 
 no 
 
 130 
 
 Pressure on springs, balls open fully 
 
 1Q4 
 
 ?n 
 
 ??0 
 
 ?so 
 
 ?*>! 
 
 ?74 
 
 Revolutions per minute, balls open fully 
 
 Q8 
 
 10? 
 
 105 
 
 107 
 
 11? 
 
 117 
 
 Variation per cent of mean speed 
 
 to 
 
 6 
 
 5 
 
 ^ 
 
 1 
 
 _ i 
 
 
 
 
 
 
 
 
 The speed at which the governor would become isochronous is 114. 
 
 Any spring will give the right variation at some speed; hence in experi- 
 menting with a governor the correct spring may be found from any wrong 
 one by a very simple calculation. Thus, if a governor with a spiing 
 whose stiffness is 50 Ibs. per inch acts best when the engine runs at 95, 90 
 
 /90 \ 2 
 being its proper speed, then 50 X ( ^ j =45 Ibs. is the stiffness of spring 
 
 required. 
 
 To determine the speed at which the governor acts best, the spring 
 may be screwed up until the governor begins to "hunt" and then be 
 slackened until it is as sensitive as is compatible with steadiness. 
 
 CONDENSERS, AIR-PUMPS, CIRCULATING-PUMPS, ETC. 
 
 The Jet Condenser. In practice the temperature in the hot-well 
 varies from 110 to 120, and occasionally as much as 130 is maintained. 
 To find the quantity of injection-water per pound of steam to be condensed: 
 Let T\ = temperature of steam at the exhaust pressure; T = temper- 
 ature of the cooling-water; T% = temperature of the water after condensa- 
 tion, or of the hot-well; Q = pounds of the cooling-water per Ib. of steam 
 condensed; then 
 
 prr TT 
 
 Another formula is: Q= 5-, in which W is the weight of steam con- 
 
 K 
 
 densed, H the units of heat given up by 1 Ib. of steam in condensing, and 
 R the rise in temperature of the cooling-water. This is applicable both 
 to jet and to surface condensers. 
 
 Quantity of Cooling-water. The quantity depends chiefly upon 
 Its initial temperature, which in Atlantic practice may vary from 40 in 
 the winter of temperate zone to 80 in subtropical seas. To raise the 
 temperature to 100 in the condenser will require three times as many 
 thermal units in the former case as in the latter, and therefore only one- 
 third as much cooling-water will be required in the former case as in the 
 latter. It is usual to provide pumping power sufficient to supply 40 times 
 the weight of steam for general traders, and as much as 50 times for ships 
 stationed in subtropical seas, when the engines are compound. If the 
 circulating pump is double-acting, its capacity may be 1/53 in the former 
 and 1/42 in the latter case of the capacity of the low-pressure cylinder. 
 (Seaton.) 
 
 The following table, condensed from one given by W. V. Terry in Power, 
 Nov. 30, 1909, shows the amount of circulating water required under 
 different conditions of vacuum, temperature of water entering the con- 
 denser, and drop. The "drop" is the difference between the temperature 
 of steam due to a given vacuum and the temperature of the water leaving 
 the condenser. 
 
CONDENSERS, AIR-PUMPS, ETC, 
 
 1069 
 
 POUNDS OF CIRCULATING WATER PER POUND OP STEAM CONDENSED. 
 
 Vac- 
 uum. 
 Ins. 
 
 Drop. 
 
 D ff 
 
 Injection Water Temperature, Deg. F. 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 85 
 
 90 
 
 29.0 
 
 6 
 
 37.5 
 
 45.7 
 
 58.3 
 
 80.8 
 
 
 
 
 
 
 
 
 12 
 
 47.8 
 
 61.8 
 
 87.5 
 
 
 
 
 
 
 
 
 
 18 
 
 65.7 
 
 95.5 
 
 
 
 
 
 
 
 
 
 28.5 
 
 6 
 
 25.6 
 
 29.2 
 
 33.9 
 
 40.3 
 
 50.0 
 
 65.7 
 
 95.5 
 
 
 
 
 
 12 
 
 30.0 
 
 35.0 
 
 42.0 
 
 52.5 
 
 70.0 
 
 
 
 
 
 
 
 18 
 
 36.2 
 
 43.8 
 
 55.3 
 
 75.0 
 
 
 
 
 
 
 
 28.0 
 
 6 
 
 21.5 
 
 23.9 
 
 26.9 
 
 30.9 
 
 36.3 
 
 43.8 
 
 55.3 
 
 75.0 
 
 
 
 
 12 
 
 24.4 
 
 27.7 
 
 31.8 
 
 37.5 
 
 45.7 
 
 58.3 
 
 80.8 
 
 
 
 
 
 18 
 
 28.4 
 
 32.8 
 
 38.9 
 
 47.8 
 
 61.8 
 
 87.5 
 
 
 
 
 
 27.0 
 
 6 
 
 16.4 
 
 17.8 
 
 19.5 
 
 21.5 
 
 23.9 
 
 27.0 
 
 30.9 
 
 36.2 
 
 43.8 
 
 55.3 
 
 
 12 
 
 18.1 
 
 19.8 
 
 21.9 
 
 24.4 
 
 27.7 
 
 31.8 
 
 37.5 
 
 45.7 
 
 58.3 
 
 80.8 
 
 
 18 
 
 20.3 
 
 22.4 
 
 25.0 
 
 28.4 
 
 32.8 
 
 38.9 
 
 47.8 
 
 61.8 
 
 87.5 
 
 
 26.0 
 
 6 
 
 14.0 
 
 15.0 
 
 16.2 
 
 17.5 
 
 19.1 
 
 21.0 
 
 23.4 
 
 26.3 
 
 30.0 
 
 35.0 
 
 
 12 
 
 15,2 
 
 16.4 
 
 17.8 
 
 19.5 
 
 21.5 
 
 23.9 
 
 26.9 
 
 30.9 
 
 36.3 
 
 43.8 
 
 
 18 
 
 16.8 
 
 18.1 
 
 19.8 
 
 21.9 
 
 24.4 
 
 27.7 
 
 31.8 
 
 37.5 
 
 45.7 
 
 58.3 
 
 Ejector Condensers. For ejector or injector condensers (Bulkley's, 
 Schutte's, etc.) the calculations for quantity of condensing-water is the 
 same as for jet condensers. 
 
 The Barometric Condenser consists of a vertical cylindrical chamber 
 mounted on top of a discharge pipe whose length is 34 ft. above the level 
 of the hot well. The exhaust steam and the condensing water meet in the 
 upper chamber, the water being delivered in such a manner as to expose 
 a large surface to the steam. The external atmosphere maintains a col- 
 umn of water in the tube, as a column of mercury is maintained in a 
 barometer, and no air pump is needed. The Bulkley condenser is the 
 original form of the type. In some modern forms a small air pump draws 
 from the chamber the residue of air which is not drawn out by the de- 
 scending column of water, discharging it into the column below the 
 chamber. 
 
 The Surface Condenser Cooling Surface. In practice, with the 
 compound engine, brass condenser-tubes, 18 B.W.G. thick, 13 Ibs. of 
 steam per sq. ft. per hour, with the cooling-water at an initial temperature 
 of 60, is considered very fair work when the temperature of the feed- 
 water is to be maintained at 120. It has been found that the surface in 
 the condenser may be half the heating surface of the boiler, and under 
 some circumstances considerably less than this. In general practice the 
 following holds good when the temperature of sea-water is about 60: 
 Terminal pres., Ibs., abs. . 30 20 15 121/2 10 8 6 
 Sq. ft. per I.H.P 3 2.50 2.25 2.00 1.80 1.60 1.50 
 
 For ships whose station is in the tropics the allowance should be in- 
 creased by 20%, and for ships which occasionally visit the tropics 10% 
 increase will give satisfactory results. If a ship is constantly employed 
 in cold climates 10% less suffices. (Seaton, Marine Engineering.) 
 
 Whitham (Steam-engine Design, p. 283, also Trans. A.S.M. E., ix, 43] ) 
 
 gives the following: S= ,, _. , in which S = condensing-surface in 
 
 sq. ft.; Ti = temperature Fahr. of steam of the pressure indicated by the 
 vacuum-gauge; t = mean temperature of the circulating water, or the 
 arithmetical mean of the initial and final temperatures: L = latent heat 
 of saturated steam at temperature T\\ k = perfect conductivity of 1 sq. 
 ft. of the metal used for the condensing-surface for a range of 1 F. (or 
 550 B.T.U. per hour for brass, according to Isher wood's experiments); 
 c = fraction denoting the efficiency of the condensing-surface; W = 
 
1070 THE STEAM-ENGINE. 
 
 v 
 
 pounds of steam condensed per hour. From experiments by Loring and 
 Emery, on U.S.S. Dallas, c is found to be 0.323, and ck = 180; making 
 
 the equation B = 180 ^_ t) - 
 
 Whitham recommends this formula for designing engines having inde- 
 pendent circulating-pumps.. When the pump is worked by the main 
 engine the value of S should be increased about 10%. 
 
 Taking Ti at 135 F., and L = 1020, corresponding to 25 in. vacuum, 
 
 and t for summer temperatures at 75, we have: 5=^ 77-77 L =^n = ~TS7r 
 
 LoU (loO to' loU 
 
 Much higher results than those quoted by Whitham are obtained from 
 modern forms of condensers. The literature on the subject of condensers 
 from 1900 to 1909 has been quite voluminous, and much difference of 
 opinion as to rules of proportioning condensers is shown. 
 
 Coefficient of Heat Transference in Condensers. (Prof. E. Josse 
 of Berlin. Condensed from an abstract in Power, Feb. 2, 1909. See also 
 Transmission of Heat from Steam to Water, pages 587 to 5890 
 
 The coefficient U, the number of heat units transferred per hour through 
 1 sq. ft. of metallic condenser wall when the temperature of the steam is 
 1 F. higher than that of the water, can be deduced from the formula 
 l/U = l/Ai + d,L + 1/Az, 
 
 in which \/A\ is the resistance to transmission from steam to metal, 1/Ag 
 the resistance to transmission from metal to water,, and d/L the resistance 
 to transmission of heat through the metal, d being the usual thickness of 
 condenser tubes (1 m.m. or .0393 in.). For this thickness the value of 
 L is fairly well known and may be given as 18,430 for brass, 6,500 for 
 copper, 11,270 for iron, 5740 for zinc, 11,050 for tin and 2660 for alumi- 
 num. The middle term d/L would have the value of 1/18,430 and be of 
 comparatively little importance. 
 
 The term l/Az is the most important and has been investigated with 
 the aid of two concentric tubes, water being sent both through the inner 
 tube and the annular jacket. The values of various experimenters differ 
 greatly. Ser gives the approximate formula__ 
 A - 2 = 510 vY, 
 
 where V is the velocity of water through the tubes in ft. per sec. This 
 velocity is far more important than the material of the condenser tubes 
 and their thickness, and also of greater consequence than the velocity 
 of the steam, about which, or, rather, the term 1/Ai, there is even less 
 agreement. Prof. Josse adopts the figure 3900. The velocity of the 
 steam has its influence, but the whole term does not count for much. 
 For water flowing at the rate of 1 .64 ft. per sec. Josse's formula would be: 
 l/U = 1/3900 -f 1/18,430 + 1/653 = 1/445, 
 
 and U = 445. 
 
 If A i be increased to twice its value U would rise only to 475, and if the 
 tube thickness be doubled U would hardly be affected. An increase, 
 however, in the rate of flow of water from 1.64 to 5 feet per second would 
 raise U to 625. As an increase of the steam flow is undesirable 'the best 
 plan is to accelerate the flow of the circulating water, and by introducing 
 the baffle strips or retarders into his condenser tubes, in order to break the 
 water currents up into vortices, Josse raised the value of U at a velocity of 
 3.28 feet per second from 614 to 922. 
 
 Opinions differ concerning the increase' of U with greater differences of 
 temperature. According to some the heat transferred should increase 
 proportionately to the difference; according to Weiss and others, pro- 
 portionally to the square of the temperature differences. Josse's investi- 
 gations were conducted by placing thermo couples in different portions 
 of the condenser tubes. If the heat transferred increases as a linear 
 function of the difference, then the rise of the temperature in the cool- 
 ing water should follow an exponential law, and it was found to be so. 
 
 Curves showing the relation of the extent of surface to the temperatures 
 Of steam and water show an agreement with the formula 
 
 Surface 
 
 6 j-^ 
 
CONDENSERS, AIR-PUMPS, ETC. 
 
 1071 
 
 where t s is the saturation temperature and c the temperature of the cooling- 
 water at entrance, t being the discharge temperature;. 
 
 Air Leakage. Air passes into the condenser with the exhaust steam, 
 the temperature of the air being that of the steam; the pressure of the 
 mixture will be the sum of the partial stearn pressure and of the partial 
 air pressure. The air must be withdrawn by the air-pump. If the with- 
 drawal takes place at the temperature corresponding to the condenser 
 pressure the partial steam pressure would be equal to the condenser 
 pressure, 'and the pump would have to deal with an enormous air volume. 
 The air temperature should, therefore, be lowered, at the spot where the 
 air is withdrawn, below the saturation temperature of the condenser 
 pressure. 
 
 In steam turbines it is more easy to keep air out than in reciprocating 
 engines. Experiments with a 300-kw. Parsons turbine show that not more 
 than 1/2 Ib. of air was delivered per hour when 6600 Ibs.of steam was used 
 per hour. 
 
 Condenser Pumps. The air and condensed water may either be 
 removed separately, by a so-called dry-air pump, or both together, by 
 a wet-air pump. As dry-air pumps have to deal with high compression 
 ratios, with high vacua and single-stage pumps, the clearances must be 
 small. When the clearance amounts to 5% the vacuum cannot be main- 
 tained at more than 95%, and the clearance must be reduced, or other 
 expedients adopted. Three are mentioned: (1) the air-pump may be 
 built in two stages; (2) the pump may be fitted with an equalizing pipe 
 so that the two sides of the piston are connected near the end of each 
 stroke; the volumetric efficiency is raised by this expedient, but consider- 
 ably more power is absorbed to accomplish the result; (3) with the wet- 
 air pump the clearance space is made to receive the condensed water, 
 which will fill at least part of it. 
 
 Contraflow and Ordinary Flow. Prof. Josse questions the distinction 
 between contraflow and ordinary flow. For the greater portion of the 
 condenser there is a rise of temperature only on the water side; the tem- 
 perature of the steam side remains that of the saturated steam, and the 
 term "contraflow" should, strictly speaking, only be applied if there is a 
 temperature fall in the one direction and a corresponding temperature rise 
 in the opposite direction. As far as the condensation is concerned, it is 
 immaterial in which direction the water flows. The contraflow principle 
 is, however, correct and necessary for the smaller portion of the condenser 
 in which the condensed liquid is cooled together with the air; for the 
 air must be withdrawn from the coldest spot. It seems inadvisable to 
 attempt to direct the flow of the steam on the contraflow principle, as that 
 would obstruct the steam flow and create a pressure difference between 
 different portions of the condenser which would be injurious to the main- 
 tenance of high vacua. 
 
 The Power Used for Condensing Apparatus varies from about 
 1 1/2 to 5% of the indicated power of the main engine, depending on the 
 efficiency of the apparatus, on the degree of vacuum obtained, the tem- 
 perature of the cooling-water, the load on the engine, etc. J. R. Bibbins 
 (Power, Feb., 1905) gives the records of test of a 300-kw. plant from which 
 the following figures are taken. Cooling-water per Ib. of steam 32 to 37 
 Ibs. Vacuum 27.3 to 27.8 ins. Temp, cooling-water 73. Hot-well 102 
 to 105. 
 
 Indicated H.P 
 
 151 
 
 220 
 
 238 
 
 260 
 
 291 
 
 294 
 
 457 
 
 589 
 
 % of total power used . . . 
 
 4.69 
 
 3.51 
 
 3.22 
 
 3.22 
 
 3.08 
 
 2.97 
 
 2.80 
 
 2.47 
 
 % for air cylinder 
 
 1.63 
 
 1.36 
 
 1.27 
 
 1.21 
 
 1.19 
 
 1.09 
 
 0.95 
 
 0.83 
 
 % for water pump 
 
 3.07 
 
 2.14 
 
 1.95 
 
 2.00 
 
 1.90 
 
 1.89 
 
 1.85 
 
 1.52 
 
 Vacuum, ins. of Mercury, and Absolute Pressures. The vacuum 
 as shown by a mercury column is not a direct measure of pressure, but 
 only of the difference between the atmospheric pressure and the absolute 
 pressure in the vacuum chamber. Since the atmospheric pressure varies 
 with the altitude and also with atmospheric conditions, it is necessary 
 when accuracy is desired to give the reading of the barometer as well as 
 that of the vacuum gauge, or preferably to give the absolute pressure in 
 Ibs. per SQ. in. above a perfect vacuum. 
 
1072 
 
 THE STEAM-ENGINE. 
 
 Temperatures, Pressures and Volumes of Saturated Air. (D. B, 
 
 Morison, on the influence of Air on Vacuum in Surface Condensers, 
 Eng'g, April 17, 1908.) 
 
 VOLUME OF 1 LB. OF Am WITH ACCOMPANYING VAPOR. 
 
 & 
 & 
 
 !.* 
 
 2^ 
 
 rt 
 
 Vacuum, ins. of Mercury, and Ibs. absolute. 
 
 24 in., 
 2.947. 
 
 26 in., 
 1.962. 
 
 27 in., 
 1.474. 
 
 28 in., 
 0.9823. 
 
 28.5 in., 
 0.7368. 
 
 28.8 in., 
 0.5894. 
 
 29 in., 
 0.4912. 
 
 50 
 60 
 70 
 80 
 90 
 100 
 110 
 120 
 
 0.17 
 0.25 
 0.36 
 0.50 
 0.69 
 0.94 
 1.26- 
 1.68 
 
 P 
 
 2.78 
 2.70 
 2.59 
 2.45 
 2.26 
 2.01 
 1.69 
 1.27 
 
 V 
 
 68 
 71 
 75 
 81 
 90 
 103 
 125 
 170 
 
 P 
 
 .79 
 .71 
 .60 
 .46 
 .27 
 .02 
 0.70 
 0.28 
 
 V 
 
 105 
 113 
 124 
 137 
 163 
 203 
 304 
 770 
 
 P 
 1.30 
 1.22 
 1.11 
 0.97 
 0.78 
 0.53 
 0.21 
 
 V 
 147 
 158 
 178 
 204 
 260 
 390 
 (a) 
 
 P 
 
 0.81 
 0.73 
 0.62 
 0.48 
 0.29 
 0.042 
 
 V 
 233 
 263 
 315 
 420 
 700 
 (&) 
 
 P 
 0.57 
 0.49 
 0.38 
 0.24 
 0.05 
 
 V 
 336 
 393 
 520 
 832 
 (c) 
 
 P 
 
 0.42 
 0.34 
 0.23 
 0.09 
 
 V 
 450 
 566 
 852 
 
 (d) 
 
 P 
 
 0.32 
 0.24 
 0.13 
 
 V 
 592 
 800 
 1536 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 P = partial pressure of air, Ibs. per sq. in. V = volume of 1 Ib. of 
 air with accompanying vapor, cu. ft. (a) over 1000; (6) nearly 5000; 
 (c) about 4000; (d) over 2000. 
 
 TEMPERATURES AND PRESSURES OF SATURATED AIR. 
 
 Vacuum, Ins. 
 
 Proportions of Air and Steam by Weight. 
 
 with Barom. 
 at 30 in. 
 
 Saturated 
 Steam. 
 
 Air, 0.25. 
 Steam, 1. 
 
 Air, 0.5. 
 Steam, 1. 
 
 Air, 0.75. 
 Steam, 1. 
 
 Air, 1. 
 Steam, 1. 
 
 29 
 28 
 27 
 26 
 25 
 24 
 
 79. 5 F. 
 101.5 
 115 
 126 
 134 
 141 
 
 75 
 96.5 
 110 
 120.2 
 128.4 
 135.2 
 
 71 
 92.4 
 105.6 
 115.5 
 123.5 
 130.3 
 
 67.5 
 88.8 
 1C1.7 
 111.5 
 119 2 
 125.8 
 
 64.5 
 85.3 
 98.6 
 108.3 
 116.2 
 122.3 
 
 From this table it is seen that a temperature of 126 F. corresponds to 
 a 24-in. vacuum if the steam in the condenser has 75% of its weight of 
 air mingled with it, and to a 26-in. vacuum if it is free from air. 
 
 One cubic foot of air measured at 60 F. and atmospheric pressure 
 becomes 10 cii. ft. at 27 in. and 30 cu. ft. at 29 in. vacuum at the same 
 temperature; 10.9 cu. ft. at 105 and 27 in.; 30.5 cu. ft. at 70 F. and 
 29 in. The same cu. ft. of air saturated with water vapor at 70 F. and 
 29 in. becomes 124.3 cu. ft., or 44.9 cu. ft. at 105 and 27 in. vacuum. 
 The temperatures 105 and 70 are about 10% below the temperatures 
 of saturated steam at 27 in. and 29 in. respectively. 
 
 Condenser Tubes are generally made of solid-drawn brass tubes, and 
 tested both by hydraulic pressure and steam. They are usually made of 
 a composition of 68% of best selected copper and 32% of best Silesian 
 spelter. The Admiralty, however, always specify the tubes to be made 
 of 70% of best selected copper and to have 1% of tin in the composition, 
 and test the tubes to a pressure of 300 Ibs. per sq. in. (Seaton.) 
 
 The diameter of the condenser tubes varies from 1/2 in. in small con- 
 densers, when they are very short, to 1 in. in very large condensers and 
 long tubes. In the mercantile marine the tubes are, as a rule, 3/ 4 in. 
 diam. externally, and 18 B.W.G. thick (0.049 inch); and 16 B.W.G. 
 (0 .065), under some exceptional circumstances. In the British Navy the 
 tubes are also, as a rule, 3/ 4 in. diam., and 18 to 19 B.W.G., tinned on 
 both sides: when the condenser is brass the tubes are not required to be 
 tinned. Some of the smaller engines have tubes 5/g in. diam., and 19 
 B. W. G. The smaller the tubes, the larger is the surface which can be 
 put in a certain space. (Seaton.) 
 
 In the merchant service the almost universal practice is to circulate 
 the water through the tubes. 
 
 Whitham says the velocity of flow through the tubes should not be 
 less than 400 nor more than 700 ft. per min. 
 
CONDENSERS, AIR-PUMPS, ETC. 
 
 1073 
 
 Tube-plates are usually made of brass. Rolled-brass tube-plates 
 snould be from 1.1 to 1.5 times the diameter of tubes in thickness, 
 depending on the method of packing. When the packings go completely 
 through the plates, the latter thickness, but when only partly through, 
 the former, is sufficient. Hence, for 3/ 4 _in. tubes the plates are usually 
 7/8 to 1 in. thick with glands and tape-packings, and 1 to 11/4 ins. thick 
 with wooden ferrules. The tube-plates should be secured to their seat- 
 ings by brass studs and nuts, or brass screw-bolts: in fact there must be 
 no wrought iron of any kind inside a condenser. When the tube-plates 
 are of large area it is advisable to stay them by brass rods, to prevent 
 them from collapsing. 
 
 Spacing of Tubes, etc. The holes for ferrules, glands, or india- 
 rubber are usually 1/4 inch larger in diameter than the tubes; but when 
 absolutely necessary the wood ferrules may be only 3/ 32 inch thick. 
 
 The pitch of tubes when packed with wood ferrules is usually 1/4 inch 
 more than the diameter of the ferrule-hole. For example, the tubes are 
 generally arranged zigzag, and the number which may be fitted into a 
 square foot of plate is as follows: 
 
 Pitch of 
 Tubes, 
 In. 
 
 No. in a 
 Sq. Ft. 
 
 Pitch of 
 Tubes, 
 In. 
 
 No. in a 
 Sq. Ft. 
 
 Pitch of 
 Tubes, 
 In. 
 
 No. in a 
 
 Sq. Ft. 
 
 1 Vl6 
 
 H/8 
 
 172 
 150 
 137 
 
 1 5/32 
 13/16 
 1 V32 
 
 128 
 121 
 116 
 
 1 1/4 
 19/32 
 1 5/16 
 
 110 
 106 
 99 
 
 Air-Pump. The air-pump in all condensers abstracts the water con- 
 densed and the air originally contained in the water when it entered the 
 boiler. In the case of jet-condensers it also pumps out the water of con- 
 densation and the air which it contained. The size of the pump is calcu- 
 ' la ted from these conditions, making allowance for efficiency of the pump. 
 
 In surface condensation allowance must be made for the water oc- 
 casionally admitted to the boilers to make up for waste, and the air 
 cpntained in it, also for slight leaks in the joints and glands, so that the 
 air-pump is made about half as large as for jet-condensation. 
 
 Seaton says: The efficiency of a single-acting air-pump is generally 
 taken at 0.5 and that of a double-acting pump at 0.35. When the 
 temperature of the sea is 60, and that of the (jet) condenser is 120, 
 Q being the volume of the cooling-water and q the volume of the con- 
 densed water in cubic feet, and n the number of strokes per minute, 
 
 The volume of the single-acting pump ='2.74 (Q + q) 4- n. 
 
 The volume of the double-acting pump = 4 (Q + q) + n. 
 
 W. H. Booth, in his "Treatise on Condensing Plant," says the 
 volume to be generated by an air-pump bucket should not be less than 
 0.75 cu. ft. per pound. of steam dealt with by the condensing plant. 
 Mr. R. W. Allen has made tests with as little air-pump capacity as 0.5 
 cu. ft. and lie gives 0.6 cu. ft. as a minimum. An Edwards pump with 
 three 14-in. barrels, 12-in. stroke, single-acting, 150 r.p.m., is rated at 
 45,000 Ibs. of steam per hour from a surface condenser, which is equiva- 
 lent to 0.66 cu. ft. per pound of feed-water. 
 
 In the Edwards pump, the base of the pump and the bottom of the 
 piston are conical in shape. The water from the condenser flows by 
 gravity into the space below the piston, which descending projects it' 
 through ports into the space in the barrel above the piston, whence on 
 the ascending stroke of the piston it is discharged through the outlet 
 valves. There are no bucket or foot- valves, and the pump may be run 
 at much higher speeds than older forms of pump. (See Catalogue of 
 the Wheeler Condenser and Engineering Co.) 
 
 The Area through Valve-seats and past the valves should not be 
 less than will admit the full quantity of water for condensation at a 
 velocity not exceeding 400 ft. per minute. In practice the area is gen- 
 erally in excess of this. (Seaton.) 
 
 Area through foot-valves = D 2 X <S -f- 1000 square inches. 
 Area through head-valves = Z> 2 X S_+ 800 square inches. 
 Diameter of discharge-pipe = D X \/S * 35 inches. 
 D = diam. of air-pump in inches, S = its speed in ft. per min. 
 
 James Tribe (Am. Mach., Oct. 8, 1891) gives the following rule for air- 
 
1074 
 
 THE STEAM-ENGINE. 
 
 pumps used with jet-condensers: Volume of single-acting air-pumpdrivea 
 by main engine = volume of low-pressure cylinder in cubic feet, multiplied 
 by 3.5 and divided by the number of cubic feet contained in one pound 
 of exhaust steam of the given density. For a double-acting air-pump the 
 same rule will apply, but the volume of steam for each stroke of the 
 pump will be but one-half. Should the pump be driven independently 
 of the engine, then the relative speed must be considered. Volume of jet- 
 condenser = volume of air-pump X 4. Area of injection valve = vol. of 
 air-pump in cubic inches *- 520. 
 
 The Work done by an Air-pump, per stroke, is a maximum the- 
 oretically, when the vacuum is between 21 and 22 ins. of mercury. As- 
 suming adiabatic compression, the mean effective pressure per stroke 
 
 is P = 3 .46 PI If j - 1 1 1 where p = absolute pressure of the vacuum 
 
 and pz the terminal, or atmospheric, pressure, = 14 .7 Ibs. per sq. in. The 
 horse-power required to compress and deliver 1 cu. ft. of air per minute, 
 measured at the lower pressure, is, neglecting friction, P X 144 -5- 33,000. 
 The following table is calculated from these formulae (R. R. Pratt, Power, 
 Sept.,,7, 1909). 
 
 Vac. in 
 Ins. of 
 Mer- 
 
 Abs. 
 Press., 
 Ins. of 
 Mer- 
 
 P2 
 Pi 
 
 Theo- 
 retic. 
 M.E.P. 
 
 Theo- 
 retic. 
 H.P. 
 
 Vac. in 
 Ins. of 
 Mer- 
 
 Abs. 
 Press., 
 Ins. of 
 Mer- 
 
 P2 
 
 Pi 
 
 Theo- 
 retic. 
 M.E.P. 
 
 Theo- 
 retic. 
 H.P. 
 
 cury. 
 
 cury. 
 
 
 
 
 cury. 
 
 cury. 
 
 
 
 
 29 
 
 1 
 
 30.00 
 
 2.86 
 
 0.0124 
 
 18 
 
 12 
 
 2.50 
 
 6.21 
 
 0.0271 
 
 26 
 
 2 
 
 15.00 
 
 4.05 
 
 0.0177 
 
 16 
 
 14 
 
 2.14 
 
 5.89 
 
 0.0256 
 
 27 
 
 3 
 
 10.00 
 
 4.83 
 
 0.0211 
 
 14 
 
 16 
 
 .87 
 
 5.42 
 
 0.02.36 
 
 26 
 
 4 
 
 7.50 
 
 5.40 
 
 0.0235 
 
 12 
 
 18 
 
 .67 
 
 4.88 
 
 0.0212 
 
 25 
 
 5 
 
 6.00 
 
 5.78 
 
 0.0252 
 
 10 
 
 20 
 
 .50 
 
 4.23 
 
 0.0184 
 
 24 
 
 6 
 
 5.00 
 
 6.05 
 
 0.0264 
 
 8 
 
 22 
 
 .36 
 
 3.52 
 
 4153 
 
 23 
 
 7 
 
 4.28 
 
 6.23 
 
 0.0271 
 
 6 
 
 24 
 
 .25 
 
 2.73 
 
 0.0119 
 
 22 
 
 8 
 
 3.75 
 
 6.33 
 
 0.0276 
 
 4 
 
 26 
 
 .15 
 
 1.88 
 
 0.0082 
 
 21 
 
 9 
 
 3.33 
 
 637 
 
 0.0278 
 
 2 
 
 28 
 
 .07 
 
 0.96 
 
 0.0042 
 
 20 
 
 10 
 
 3.00 
 
 6.36 
 
 0.0277 
 
 1 
 
 29 
 
 .03 
 
 0.49 
 
 002! 
 
 The work done by the air-pump is to compress the saturated mixture 
 if air and water vapor at the condenser pressure to atmospheric pressure 
 and to discharge it into the atmosphere together with the water of 
 condensation (and with the cooling water in the case of jet condensers 
 operated vith an air-pump). The amount of air to be discharged 
 varies with the amount of air in the feed-water and with the leakage of 
 air through the stuffing-boxes. Geo. A. Orrok (Jour. A. S. M. E., 1912, 
 p. 1625) found the volume of air in city water at 52 deg. F. to be over 4 
 per cent; and in feed-water at 187 degrees less than 1 per cent. With 
 turbines of from 5,000 to 20,000 kw. capacity the air discharged by 
 the air-pump at atmospheric pressure and temperature varied from 
 1 cu. ft. per min. with the units in the best condition to 15 or 20 when 
 ordinary leakage was present, or to 30 to 50 when the units were in bad 
 condition. Stodola states that we may ordinarily expect the air to 
 amount to 1.5 to 2.5 cu. ft. per min. for each 1000 kw. capacity. 
 T. C. McBride (Power, July 14, 1908) gives results of tests in which 
 the amount of air varied from 18 to 74 volumes per 10,000 volumes of 
 exhaust steam. C. L. W. Trinks (Proc. Engrs. Soc. of W. Penna., June, 
 1914) gives the weight of air normally expected by builders of air- 
 pumps as 0.25 to 0.50 per cent of the weight of steam. 
 
 W. H. Herschel (Power, June 1, 1915), after quoting the above figures, 
 gives the results of calculations based upon assumed air leakages of 
 20, 40, and 60 volumes of air per 10,000 volumes of steam, corresponding 
 respectively to 0.31, 0.62, and 0.93 per cent of the weight of steam, or 
 approximately to 15, 30, and 45 cu. ft. per min. for every 1000 kw. 
 capacity, the smallest amount being that which may be obtained with 
 stuffing-boxes in the best condition, while the largest value may be 
 reached, or even exceeded, with stuffing-boxes in poor condition. 
 Following are his figures for the extreme conditions: 
 
CONDENSERS, AIR-PUMPS, ETC. 
 
 1075 
 
 TOTAL WORK OF AN AIR-PUMP, INCLUDING DISCHARGE OF COOLING WATER. 
 
 SM^ 
 Hi 
 
 Vacuum, In., Leakage 0.31 %. 
 
 i 
 
 Vacuum, In., Leakage 0.93%. 
 
 29 
 
 28.5 
 
 28 
 
 27 
 
 26 
 
 29 
 
 28.5 
 
 28 
 
 27 | 26 
 
 Temperature of Condenser F. 
 
 Temperature of Condenser F. 
 
 32 
 50 
 60 
 70 
 80 
 
 Ft.-lb 
 32 
 50 
 60 
 70 
 80 
 
 Lb. 
 32 
 50 
 60 
 70 
 80 
 
 63 
 68 
 71 
 76 
 
 Work 
 2150 
 3300 
 4820 
 8220 
 
 71 
 77 
 79 
 83 
 86 
 
 perLb 
 1560 
 2120 
 2740 
 4010 
 7750 
 
 g Wat 
 25.6 
 36.7 
 52.3 
 75.8 
 164.0 
 
 78 
 83 
 86 
 89 
 94 
 
 . Stearr 
 1280 
 1650 
 2000 
 2670 
 3930 
 
 er per 
 21.7 
 30.2 
 37.9 
 52.2 
 70.0 
 
 87 
 92 
 96 
 100 
 104 
 
 iCond 
 1000 
 1210 
 1410 
 1700 
 2110 
 
 Lb. S 
 18.2 
 24.7 
 27.5 
 32.8 
 41 .0 
 
 96 
 100 
 104 
 109 
 111 
 
 ensed 
 840 
 990 
 1120 
 1280 
 1530 
 
 ;eam. 
 15.6 
 19.9 
 22.6 
 25.2 
 31 .8 
 
 32 
 50 
 60 
 70 
 80 
 
 Ft.-lb. 
 32 
 50 
 60 
 70 
 80 
 
 Lb. 
 32 
 50 
 60 
 70 
 80 
 
 55 
 64 
 
 68 
 
 72 
 
 Work 
 3840 
 5760 
 8440 
 13250 
 
 62 
 71 
 75 
 80 
 82 
 
 perLb 
 2880 
 3730 
 4720 
 6610 
 11330 
 
 ig Wat 
 32.8 
 47.3 
 66.0 
 98.8 
 493.0 
 
 68 
 78 
 82 
 86 
 92 
 
 Stearr 
 2380 
 2920 
 3450 
 4410 
 6960 
 
 3r per 
 28.0 
 35.5 
 45.1 
 61.8 
 82.0 
 
 77 
 85 
 88 
 95 
 99 
 
 iCond 
 1840 
 2150 
 2440 
 2850 
 3520 
 
 Lb. St 
 24.5 
 28.6 
 35.7 
 39.6 
 52.0 
 
 77 
 9t 
 96 
 103 
 106 
 
 ensed. 
 1530 
 1760 
 1960 
 2210 
 2560 
 
 earn. 
 21.5 
 24.5 
 27.8 
 30.1 
 38.1 
 
 Coolin 
 32.1 
 55.0 
 89.8 
 164.0 
 
 Coolir 
 42.7 
 70.8 
 123.8 
 494.0 
 
 Most Economical Vacuum for Turbines. Mr. Herschel, taking the 
 air-pump work given in the above table for the several conditions 
 named, an efficiency of 50 per cent for the air-pump, and assuming a 
 turbine working with dry steam 150-lb. gage, without superheat, cal- 
 culates the net work of the turbine in foot-pounds per Ib. of steam 
 with the most economical vacuum for different temperatures of cooling 
 water. He compares the results with those calculated for the same 
 air-pump conditions, but for a turbine using steam of 140 Ib. super- 
 heated 218 F. The results are tabulated below, the vacuum giving 
 the best economy being given in parentheses. The lines marked S are 
 for the superheated steam turbine. It appears that 29 in. vacuum is 
 the most economical only for low temperatures of cooling water, and 
 that the vacuum giving the best economy decreases with increase of 
 leakage and with increasing temperature of the cooling water. 
 
 Temperature of cooling water, F. 32 I 50 | 60 | 70 
 Net Work of Turbine, Ft.-lb. per Lb. of Steam. 
 
 80 
 
 Leakage of (o.31% 
 
 air % 
 weight of ] 
 
 steam. 0.93% 
 
 I 56000(29) I 53700(29) 
 I S. 76200(29) I 73900(29) 
 
 I 52120(28.5) I 50360(28) I 48980(27) 
 I 71620(28.5) I 69080(28.5) | 65240(28) 
 
 52620(29) 150140(28.5) I 48800(28) 
 8.72820(29) | 69640(28.5) 167660(28.5) 
 
 I 47500(27) 
 I 64280(28) 
 
 I 46160(27) 
 I 62060(27) 
 
 Circulating-pump. Let Q be the quantity of cooling-water in 
 cubic feet, n the number of strokes per minute, and S the length of stroke 
 in feet. 
 
 Capacity of circulating-pump = Q * n cubic feet. 
 
 Diameter of circulating-pump = 13.55 ^Q-^-nS inches. 
 
 The clear area through the valve-seats and past the valves should be 
 such that the mean velocity of flow does not exceed 450 feet per minute. 
 The flow through the pipes should not exceed 500 ft. per min, in small 
 pipes and 600 in large pipes. (Seaton.) 
 
 For Centrifugal Circulating-pumps, the velocity of flow in the inlet and 
 outlet pipes should not exceed 400 ft. per min. The diameter of the fan- 
 wheel is from 21/2 to 3 times the diam, of the pipe, and the speed, at H$ 
 periphery 450 to 500 ft. per min. 
 
1076 THE STEAM-ENGINE. 
 
 The Leblanc Condenser (made by the Westinghouse Machine Co.) 
 
 accomplishes the separate removal of water and air by means of a pair ol 
 relatively small turbine-type rotors on a common shaft in a single casing, 
 which is integral with or attached directly to the lower portion of the 
 condensing chamber. The condensing chamber itself is but little more 
 than an enlargement of the exhaust pipe. The injection water is pro- 
 jected downwards through a spray nozzle, and the combined injection 
 water and condensed steam flow downward to a centrifugal discharge 
 pump under a head of 2 or 3 ft., which insures the filling of the pump. 
 The space above the water level in the condensing chamber is occupied 
 by water vapor plus the air which entered with the injection water and 
 with the exhaust steam, and this space communicates with the air-pump 
 through a relatively small pipe. 
 
 The air-pump differs from pumps of the ejector type in that the vanes 
 in traversing the discharge nozzle at high speed constitute a series of 
 pistons, each one of which forces ahead of it a small pocket of air, the 
 high velocity of which effectually prevents its return to the condenser. 
 A small quantity of water is supplied to the suction side of the air-purnp 
 to assist in the performance of its functions. The power required for the 
 pumps is said to approximate 2 to 3 per cent of the power generated by 
 the main engine. 
 
 Feed-pumps for Marine Engines. With surface-condensing 
 engines the amount of water to be fed by the pump is the amount con- 
 densed from the main engine plus what may be needed to supply auxiliary 
 engines and to supply leakage and waste. Since an accident may happen 
 to the surface-condenser, requiring the use of jet-condensation, the pumps 
 of engines fitted with surface-condensers must be sufficiently large to do 
 duty under such circumstances. With jet-condensers and boilers using 
 salt water the dense salt water in the boiler must be blown off at intervals 
 to keep the density so low that deposits of salt will not be formed. Sea- 
 water contains about 1/32 of its weight of solid matter in solution. The 
 boiler of a surface-condensing engine may be worked with safety when 
 the quantity of salt is four times that in sea-water. If Q net quantity 
 of feed-water required in a given time to make up for what is used as 
 steam, n number of times the saltness of ^he water in the boiler is to 
 that of sea-water, then the gross feed-water = nQ -s- (n 1). In order to be 
 capable of filling the boiler rapidly each feed-pump is made of a capacity 
 equal to twice the gross feed-water. Two feed-pumps should be supplied 
 so that one may be kept in reserve to be used while the other is out of 
 repair. If Q be the quantity of net feed-water in cubic feet, I the length 
 of stroke of feed-pump in feet , and n the number of strokes per minute, 
 
 Diameter of each feed-pump plunger in inches = ^550 Q + nl. 
 If W be the net feed-water in pounds, 
 
 Diameter of each feed-pump plunger in inches = ^8.9 W+nl. 
 
 An Evaporative Surface Condenser built at the Virginia Agricul- 
 tural College is described by James H. Fitts (Trans. A.S. M. E., xiv, 690). 
 It consists of two rectangular end chambers connected by a, series of 
 horizontal rows of tubes, each row of tubes immersed in a pan of water. 
 Through the spaces between the surface of the water in each pan and the 
 bottom of the pan above air is drawn by means of an exhaust-fan. At 
 the top of one of the end chambers is an inlet for steam, and a horizontal 
 diaphragm about midway causes the steam to traverse the upper half 
 of the tubes and back through the lower. An outlet at the bottom leads 
 to the air-pump. The passage of air over the water surfaces removes 
 the vapor as it rises and thus hastens evaporation. The heat necessary 
 to produce evaporation is obtained from the steam in the tubes, causing 
 the steam to condense. It was designed to condense 800 Ibs. steam per 
 hour and give a vacuum of 22 in., with a terminal pressure in the cylinder 
 of 20 Ibs. absolute. Results of tests show that the cooling-water required 
 is practically equal in amount to the steam used by the engine. And 
 since the consumption of steam is reduced by the application of a con- 
 denser, its use will actually reduce the total quantity of water required. 
 
 The Continuous Use of Condensing-water is described in a series 
 of articles in Power, Aug.-Dec., 1892. It finds its application in situations 
 where water for condensing purposes is expensive or difficult to obtain. 
 
CONDENSERS, AIR-PTTMPS, ETC. 
 
 1077 
 
 The different methods described include cooling pans on the roof; 
 
 fountains and other spray pipes in ponds, fine spray discharged at an 
 elevation above a pond; trickling the water discharged from the hot-well 
 over parallel narrow metal tanks contained in a large wooden structure, 
 while a fan blower drives a current of air against the films of water falling 
 from the tanks, etc. These methods are suitable for small powers, but 
 for large powers they are cumbersome and require too much space, and 
 are practically supplanted by cooling towers. 
 
 The Increase of Power that may be obtained by adding a condenser 
 giving a vacuum of 26 inches of mercury to a non-condensing engine may 
 
 ..-.-....,.. M * * f j- ffiP"' 
 
 / / / / / / /Ab'sqiut'e Mean Pressure'in Pounds / "7 /// / 
 30J 4/5,0 60 /TO 8fo /90 /1 00/1 1 01 20 1 30 1 40 1 50^160 1 7,0 1 SOxtgO-^OO 
 
 120 60 40 30 24 20 17 15 13 12 11 10 
 
 Per Cent ot Power Gained by Vacuum 
 
 Fig. 175. 
 
 toe approximated by considering it to be equivalent to a net gain of 12 Ibs. 
 mean effective pr essure per sq. in. of piston area. If A = area of piston 
 in sq ins , S = piston speed in ft. per min., then 12 AS 33,000 ** 
 AS -t 2750 = H.P. made available by the vacuum. If the vacuum 
 13 2 Ibs per sq. in. = 27 .9 in. of mercury, then H.P. = AS j 2500. t 
 The saving of steam for a given horse-power will be represented approxi- 
 mately by the shortening of the cut-off when the engine is run with the 
 condenser. Clearance should be included in the calculation. To the 
 mean effective pressure non-condensing, with a given actual cut-off 
 clearance considered, add 3 Ibs. to obtain the approximate mean total 
 pressure, condensing. From tables of expansion of steam find what 
 actual cut-off will give this mean total pressure The difference between 
 this and the original actual cut-off, divided by the latter and by 100, will 
 
 ' 
 
 catalogue of H. R. Worthington) shows 
 
 the percentage of power that may be gained by attaching a condenser 
 to a non-condensing engine assuming that the vacuum is 12 Ibs. per sq. 
 
1078 THE STEAM-ENGINE. 
 
 in. The diagram also shows the mean pressure in the cylinder for a given 
 initial pressure and cut-off, clearance and compression not considered. 
 
 The pressures given in the diagram are absolute pressures above a 
 vacuum. 
 
 To find the mean effective pressure produced in an engine cylinder with 
 90 Ibs. gauge (= 105 Ibs. absolute) pressure, cut-off at 1/4 stroke: find 
 105 in the left-hand or initial-pressure column, follow the horizontal line 
 to the right until it intersects the oblique line that corresponds to the 1/4 
 cut-off, and read the mean total pressure from the row of figures directly 
 above the point of intersection, which in this case is 63 Ibs. From this 
 subtract the mean absolute back pressure (say 3 Ibs. for a condensing 
 engine and 15 Ibs. for a non-condensing' engine exhausting into the 
 atmosphere) to obtain the mean effective pressure, which in this case, for 
 a non-condensing engine, gives 48 Ibs. To find the gain of power by the 
 use of a condenser with this engine, read on the lower scale the figures 
 that correspond in position to 48 Ibs. in the upper row, in this case 25%. 
 As the diagram droes not take into consideration clearance or compression, 
 the results are only approximate. 
 
 Advantage of High Vacuum in Reciprocating Engines. (R. D. 
 Tomli#son, Power, Feb. 23, 1909.) Among the transatlantic liners, 
 the best ships with reciprocating engines are carrying from 26 to -28 and 
 more inches of vacuum. Where the results are looked into, the engineers 
 are required to keep the vacuum system tight and carry all the vacuum 
 they can get, and while it is true that greater benefits can be derived 
 from high vacua in a steam turbine than in a reciprocating engine, it is 
 also true that, where primary heaters are not used, the higher the vacuum 
 carried the greater is the justifiable economy which can be obtained from 
 the plant. 
 
 The Interborough Rapid Transit Company, New York City, changed 
 the motor-driven air-pump and jet-condenser for a barometric type of 
 condenser and increased the vacuum on each of the 8000-H.P. Allis- 
 Chalmers horizontal vertical engines at the 74th Street station from 
 26 to 28 ins., thereby increasing the power on each of the eight units 
 approximately 275 H.P., and the economy of the station was increased 
 nearly in the same ratio. This change was made about seven years ago 
 and the plant is still operating with 28 ins. of vacuum, measured with 
 mercury columns connected to the exhaust pipe at a point just below the 
 exhaust nozzle of the low-pressure cylinders. 
 
 A careful test made on the 59th Street station showed a decrease 
 steam consumption of 8% when the vacuum was raised from 25 to 28 ins. 
 These engines drive 5000-kw. generators. 
 
 The Choice of a Condenser. Condensers may be divided into two 
 general classes: 
 
 First. Jet condensers, including barometric condensers, siphon 
 condensers, ejector condensers, etc., in which the cooling-water mingl~~ 
 with the steam to be condensed. 
 
 Second. Surface condensers, in which the cooling-water is separated 
 from the steam, the cooling- water circulating on one side of this surface 
 and the steam coming into contact with the other. 
 
 In the jet-condenser the steam, as soon as condensed, becomes mixed 
 with the cooling-water, and if the latter should be unsuitable for boiler- 
 feed because of scale-forming impurities, acids, salt, etc., the pure distilled 
 water represented by the condensed steam is wasted, and, if it were 
 necessary to purchase other water for boiler-feeding, this might represent 
 a considerable waste of money. On the other hand, if the cooling- water 
 is suitable for boiler-feeding, or if a fresh supply of good water is easily 
 obtainable, the jet-condenser, because of its simplicity and low cost, is 
 unexcelled. 
 
 Surface condensers are recommended where the cooling-water is un- 
 fitted for boiler-feed and where no suitable and cheap supply of pure 
 boiler-feed is available. 
 
 Where a natural supply of cooling-water, as from a well, spring, lake or 
 river, is not available, a water-cooling tower can be installed and the same 
 cooling-water used over and over. (Wheeler Condenser and Eng. Co.) 
 
 Owing to their great cost as compared with jet-condensers, surface 
 condensers should not be used except where absolutely necessary, i.e., 
 where lack of feed- water for the boiler warrants the extra cost. Of course 
 there are cases, such as at sea, where surface condensers are indispensable. 
 
 1/11 
 he 
 
 in 
 
 vo 
 
 on 
 
 Les 
 
 *d 
 

 COOLING TOWEBS. 1079 
 
 On land, suitable feed-water can always be obtained at some expense, 
 and that cost capitalized makes it a simple arithmetical problem to 
 determine the extra investment permissible in order to be able to return 
 condensed steam as feed-water to the boiler. Unfortunately there is 
 another point which greatly complicates the matter, and one which makes 
 it impossible to give exact figures, viz., the corrosion and deterioration of 
 the condenser tubes themselves, the exact cause of which is not often 
 understood. With clean, fresh water, free from acid, the tubes of a con- 
 denser last indefinitely, but where the cooling-water contains sulphur, 
 as in drainage from coal mines, or sea-water contaminated by sewage, 
 such as harbor water, the deterioration is exceedingly rapid. 
 
 A better vacuum may possibly be obtained from a surface condenser 
 where there is plenty of cooling-water easily handled. The better vacuum 
 is due to the fact that the air-pump will have much less air to handle inas- 
 much as the air carried in suspension by the cooling-water does not have 
 to be extracted as in the case of jet-condensers. Water in open rivers, 
 the ocean, etc., is said to carry in suspension 5% by volume of air. It 
 may be said that except for leakages, which should not exist, the air- 
 pump will have no work to do at all inasmuch as the water will have no 
 opportunity to become aerated. On the other hand, if the cooling-water 
 is limited, these advantages are offset by the fact that a surface condenser 
 cannot heat the cooling-water so near to the temperature of the exhaust 
 steam as can a jet-condenser. (F. Hodgkinson, El. Jour., Aug., 1909.) 
 
 A barometric condenser used in connection with a 15,000-k.w. steam- 
 engine-turbine unit at the 59th St. station of the Rapid Transit Co., New 
 York, contains approximately 25,000 sq. ft. of cooling surface arranged in 
 the double two-pass system of water circulation, with a 30-in. centrifugal 
 circulating pump having a maximum capacity of 30,000 gal. per hour. 
 The dry vacuum pump is of the single-stage type, 12- and 29-in. X 24-in., 
 with Corliss valves on the air cylinder. The condensing plant is capable 
 of maintaining a vacuum within 1.1 in. of the barometer when condensing 
 150,000 Ib. of steam per hour when supplied with circulating water at 70 F. 
 (H. G. Stott, Jour. A.S.M.E., Mar., 1910.) 
 
 Cooling Towers are usually made in the shape of large cylinders of 
 sheet steel, filled with narrow boards or lath arranged in geometrical 
 forms, or hollow tile, or wire network, so arranged that while the water, 
 which is sprayed over them at the top, trickles down through the spaces it 
 is met by an ascending air column. The air is furnished either by disk 
 fans at the bottom or is drawn in by natural draught. In the latter case 
 the tower is made very high, say 60'to 100 ft., so as to act like a chimney. 
 When used in connection with steam condensers, the water produced by 
 the condensation of the exhaust steam is sufficient to compensate for the 
 evaporation in the tower, and none need be supplied to the system. There 
 is, on the contrary, a slight overflow, which carries with it the oil from 
 the engine cylinders, and tends to clean the system of oil that would 
 otherwise accumulate in the hot-well. 
 
 The cooling of water in a pond, spray, or tower goes on in three ways 
 first, by radiation, which is" practically negligible; second, by conduction 
 or absorption of heat by the air, which may vary from one-fifth to one- 
 third of the entire effect; and, lastly, by evaporation. The latter is the 
 chief effect. Under certain conditions the water in a cooling tower can 
 actually be cooled below the temperature of the atmosphere, as water is 
 cooled by exposing it in porous vessels to the winds of hot and dry climates. 
 
 The evaporation of 1 Ib. of water absorbs about 1000 heat units. The 
 rapidity of evaporation is determined, first, by the temperature of the 
 water, and, second, by the .vapor tension in the air in immediate contact 
 with the water. In ordinary air the vapor present is generally in a con- 
 dition corresponding to superheated steam, that is, the air is not saturated. 
 If saturated air be brought into contact with colder water, the cooling 
 of the vapor will cause some of it to be precipitated out of the air; on the 
 other hand, if saturated air be brought into contact with warmer water, 
 , some of the latter will pass into the form of vapor. This is what occurs in 
 the cooling tower, so that the latter is in a large measure independent 
 of climatic conditions; for even if the air be saturated, the rise in tem- 
 perature of the atmospheric air from contact with the hot water in the 
 cooling tower will greatly increase the water-carrying capacity of the air, 
 enabling a large amount of beat to be absorbed through the evaporation 
 
1080 
 
 THE STEAM-ENGINE. 
 
 of the water. The two things to be sought after in coofing-towei design 
 are, therefore, first, to present a large surface of water to the air, and, 
 second, to provide for bringing constantly into contact with this surface 
 the largest possible volume of new air at the least possible expenditure of 
 energy. (Wheeler Condenser and Engineering Co.) 
 
 The great advantage of the cooling tower lies in the fact that large 
 surfaces of water can be presented to the air while the latter is kept in 
 rapid motion. 
 
 Calculation of the Air Supply for a Cooling Tower. Let T\ and T% 
 be the temperatures of the water entering and leaving; t\ temperature 
 of the air supply; z its relative humidity; t2, temperature of the air 
 leaving; mi mz, pounds of moisture in one pound of saturated air at 
 temperatures ti, t-2', e\., e-2, total heat, B.T.U., above 32 F. per pound 
 of water vapor at temperatures ti, t%\ A Ib. of air supplied per Ib. of 
 entering water. All temperatures are in degrees F. 
 
 Then, for each 1 Ib. of water entering the tower the heat (B.T.U.) 
 carried in is: by the water, Ti 32; by the air, 0.2375 A (ti 32) +A m\ e\z. 
 The heat carried out is: by the water, [l-(ra2-rai2)] X (T2-32); by 
 the air, 0.2375 A (tz-32) + A (mz e-2). Neglecting loss by radiation, the 
 heat carried into the tower equals the heat leaving it. Equating these 
 Quantities and solving for A we have: 
 
 Ti - Tz + (mi - miZ) (r 2 -32) 
 
 0.2375 (fa - ti) + 
 From this equation the table on p. 1081 has been calculated. 
 
 Water Evaporated in a Cooling Tower. The following table 
 gives the values of (mzmiz) per pound of air in the cooling-tower formula. 
 Multiplying these values by the number of pounds of air per pound of 
 water for the given conditions, w r i.U give the amount of water evapo- 
 rated, or make-up water required with surface condensers, per pound 
 of the inflowing water. 
 
 Pounds Water Evaporated per Pound of Air. 
 
 
 
 li = 50 
 
 
 
 70 
 
 
 
 80 
 
 
 Ti= 100 
 
 2=0.5 
 
 0.7 
 
 0.9 
 
 0.5 
 
 0.7 
 
 0.9 
 
 0.5 
 
 0.7 
 
 0.9 
 
 ( 92 
 
 * 2 = { 88 
 ( 84 
 
 .02912 
 .02503 
 .02141 
 
 .02761 
 .02352 
 .01990 
 
 .02610 
 .02201 
 .01839 
 
 .02510 
 .02101 
 .01739 
 
 .02198 
 .01789 
 .01427 
 
 .01887 
 .01478 
 .01116 
 
 .02188 
 .01779 
 .01417 
 
 .01748 
 .01339 
 .00977 
 
 .01308 
 .00899 
 .00537 
 
 TI= 110 
 
 
 li = 50 
 
 
 
 70 
 
 
 
 90 
 
 
 ( 102 
 tf-X 98 
 
 / 94 
 
 .04179 
 .03626 
 .03135 
 
 .04028 
 .03475 
 .02984 
 
 .03877 
 .03324 
 .02833 
 
 .03777 
 .03224 
 .02733 
 
 .03465 
 .02912 
 .02421 
 
 .03154 
 .02601 
 .02110 
 
 .03017 
 .02464 
 .01972 
 
 .02402 
 .01848 
 .01357 
 
 .01785 
 .01232 
 .00741 
 
 Ti= 120 
 
 
 ti = 50 
 
 
 
 70 
 
 
 
 90 
 
 
 (112 
 2= J108 
 (104 
 
 .05905 
 .05151 
 .04482 
 
 .05754 
 .05000 
 .04331 
 
 .05603 
 .04845 
 .04180 
 
 .05503 
 .04749 
 .04080 
 
 .05191 
 .04437 
 .03768 
 
 .04880 
 .04126 
 .03457 
 
 .04743 
 .03989 
 .03320 
 
 .04127 
 .03373 
 .02704 
 
 .03511 
 .02757 
 .02088 
 
 Tests of a Cooling Tower and Condenser are reported by J. H. Vail 
 in Trans. A . S. M . E ., 1898. The tower was of the Barnard type, with two 
 chambers, each 12 ft. 3 in. X 18 ft. X 29 ft. 6 in. high, containing gal- 
 vanized-wire mats. Four fans supplied a strong draught to the two cham- 
 bers. The rated capacity of each section was to cool the circulating 
 water needed to condense 12,500 Ibs. of steam, from 132 to 80 F., when 
 the atmosphere does not exceed 75 F. nor the humidity 85%. The fol- 
 lowing is a record of some observations. 
 
 Date, 1898. 
 
 Jan. 
 31. 
 
 Feb. 
 
 June 
 20. 
 
 July. 
 
 Aug. 
 26. 
 
 Nov. 
 4. 
 
 Aug. 2. 
 
 Max. 
 
 Min. 
 
 Temperature atmosphere . 
 Temp, condenser discharge 
 Temp, water from tower.. 
 Heat extracted by tower. . 
 Speed of fans, r.p.m 
 Vacuum, inches 
 
 30 
 110 
 65 
 
 45 
 36 
 
 251/2 
 
 36 
 110 
 84 
 26 
 
 26 
 
 78 
 120 
 84 
 36 
 145 
 25 
 
 96 
 130 
 93 
 37 
 '162 
 241/2 
 
 85 
 '118 
 88 
 30 
 150 
 251/2 
 
 59 
 129 
 92 
 37 
 148 
 25 
 
 103 
 128 
 98 
 32 
 160 
 26 
 
 83 
 106 
 9,0 
 
 21 
 140 
 26 
 
 The quantity of steam condensed or of water circulated is uot stated, 
 
COOLING TOWERS. 
 
 1081 
 
 Pounds of Air per Pound of Circulating Water. 
 
 Outflowing air saturated. 
 
 Ti=100 
 
 i = 
 
 50 
 
 
 
 70 
 
 
 
 80 
 
 
 T 2 *, 
 
 2=0.5 
 
 0.7 
 
 0.9 
 
 0.5 
 
 0.7 
 
 0.9 
 
 0.5 
 
 0.7 
 
 0.9 
 
 (92 
 
 739 
 
 0.767 
 
 0.798 
 
 0.962 
 
 1.044 
 
 .175 
 
 1.144 
 
 1.382 
 
 1.755 
 
 70-^88 
 (84 
 
 0.846 
 0.975 
 
 0.884 
 1 .026 
 
 0.926 
 1.083 
 
 1 .124 
 1 .366 
 
 1 .278 
 1.604 
 
 .482 
 .944 
 
 1.428 
 1.850 
 
 1.831 
 2.598 
 
 2.562 
 4.394 
 
 (92 
 
 80 < 88 
 
 0.508 
 580 
 
 0.527 
 605 
 
 0.547 
 0.632 
 
 0.644 
 0.767 
 
 0.713 
 0.869 
 
 0.800 
 .004 
 
 0.783 
 0.971 
 
 0.939 
 1.239 
 
 1.187 
 1.725 
 
 (84 
 
 0.665 
 
 0.699 
 
 0.737 
 
 0.927 
 
 1.086 
 
 .312 
 
 1.253 
 
 1.751 
 
 2.947 
 
 ( 92 
 
 0.280 
 
 0.287 
 
 0.297 
 
 0.348 
 
 0.382 
 
 0.424 
 
 0.422 
 
 0.496 
 
 0.619 
 
 90^88 
 
 0.313 
 0.356 
 
 0.326 
 0.372 
 
 0.338 
 0.390 
 
 0.409 
 0.491 
 
 0.460 
 0.569 
 
 0.527 
 0.680 
 
 0.514 
 0.655 
 
 0.647 
 JO. 904 
 
 0.888 
 1.500 
 
 T^llO 
 
 /! = 
 
 50 
 
 
 
 70 
 
 
 
 90 
 
 
 ( 102 
 
 710 
 
 729 
 
 0.750 
 
 0.838 
 
 0.898 
 
 0.966 
 
 .135 
 
 1.388 
 
 1.790 
 
 7CK 98 
 
 0.804 
 
 0.829 
 
 0.856 
 
 0.975 
 
 1.056 
 
 1.155 
 
 .406 
 
 1.821 
 
 2.596 
 
 j 94 
 
 0.915 
 
 0.948 
 
 0.983 
 
 1 .144 
 
 1.260 
 
 1 .403 
 
 .796 
 
 2.543 
 
 4.395 
 
 ( 102 
 
 546 
 
 0.561 
 
 0.576 
 
 0.644 
 
 0.688 
 
 0.739 
 
 0.868 
 
 1 .055 
 
 1 .358 
 
 80 < 98 
 
 0.617 
 
 0.636 
 
 0.655 
 
 0.746 
 
 0.807 
 
 0.880 
 
 .071 
 
 1.382 
 
 1.962 
 
 ( 94 
 
 0.700 
 
 0.724 
 
 0.751 
 
 0.873 
 
 0.960 
 
 1.067 
 
 .364 
 
 1 .898 
 
 3.312 
 
 ( 102 
 
 0.383 
 
 0.392 
 
 0.402 
 
 0.449 
 
 0.478 
 
 0.512 
 
 0.600 
 
 0.726 
 
 0.926 
 
 90 K 98 
 
 0.430 
 
 0.442 
 
 0.455 
 
 0.517 
 
 0.558 
 
 0.606 
 
 0.736 
 
 0.942 
 
 1.328 
 
 ( 94 
 
 0.484 
 
 0.501 
 
 0.518 
 
 0.602 
 
 0.659 
 
 0.730 
 
 0.931 
 
 1.311 
 
 2.229 
 
 T!=120 
 
 h = 
 
 50 
 
 
 
 70 
 
 
 
 90 
 
 
 ( 112 
 
 0.651 
 
 0.663 
 
 0.677 
 
 0.732 
 
 0.767 
 
 0.806 
 
 0.394 
 
 1 .007 
 
 1.155 
 
 70^ 108 
 
 0.733 
 
 . 749 
 
 0.766 
 
 0.839 
 
 0.886 
 
 0.939 
 
 1 .061 
 
 1.227 
 
 1 .458 
 
 ( 104 
 
 0.828 
 
 0.849 
 
 0.871 
 
 0.967 
 
 1.031 
 
 1 .104 
 
 .278 
 
 1.530 
 
 1.918 
 
 ( 112 
 
 0.533 
 
 0.544 
 
 0.554 
 
 0.599 
 
 0.627 
 
 0.656 
 
 0.729 
 
 0.820 
 
 0.938 
 
 80^ 108 
 
 0.599 
 
 0.612 
 
 0.625 
 
 0.687 
 
 0.722 
 
 0.764 
 
 0.863 
 
 0.996 
 
 1 .180 
 
 f 104 
 
 0.675 
 
 0.692 
 
 0.710 
 
 0.787 
 
 0.838 
 
 0.896 
 
 1 .037 
 
 1.246 
 
 1.548 
 
 ( 112 
 
 0.416 
 
 0.423 
 
 0.432 
 
 0.468 
 
 0.487 
 
 0.510 
 
 0.565 
 
 0.633 
 
 0.721 
 
 90- 108 
 
 0.465 
 
 0.475 
 
 0.485 
 
 0.531 
 
 0.558 
 
 . 590 
 
 0.666 
 
 0.765 
 
 0.902 
 
 1 104 
 
 0.522 
 
 0.535 
 
 0.548 
 
 0.607 
 
 0.645 
 
 0.688 
 
 0.796 
 
 0.947 
 
 1.178 
 
 Temp. deg.F. . 50 
 
 B. T. U 1081.4 
 
 Temp. deg. F. . . 94 
 
 .. 1101.0 
 
 VALUES OF e\ OR ez. 
 
 70 80 84 
 
 1090.3 1094.8 1096.6 
 
 98 102 104 
 
 1102.7 1104.5 1105.4 
 
 88 92 
 
 1098.3 1100.1 
 
 108 112 
 
 1107.1 1108.9 
 
 Temp. d< 
 B. T. U 
 
 Weight of Water Vapor Mixed with 1 Lb. of Air at Atmospheric 
 Pressure. 
 
 Full Saturation. Values interpolated from table on page 613. 
 
 Deg. 
 F. 
 
 Mois- 
 ture, 
 Ib. 
 
 Deg. 
 
 Mois- 
 ture, 
 Ib. 
 
 Deg. 
 
 Mois- 
 ture. 
 Ib. 
 
 Deg. 
 
 Mois- 
 ture, 
 Ib. 
 
 Deg. 
 
 Mois- 
 ture, 
 Ib. 
 
 32 
 
 0.00374 
 
 54 
 
 0.00874 
 
 76 
 
 0.01917 
 
 98 
 
 0.04002 
 
 120 
 
 0.08099 
 
 34 
 
 .00406 
 
 56 
 
 .00940 
 
 78 
 
 .02054 
 
 100 
 
 .04270 
 
 122 
 
 .08629 
 
 36 
 
 .00439 
 
 58 
 
 .01012 
 
 80 
 
 .02200 
 
 102 
 
 .04555 
 
 124 
 
 .09193 
 
 38 
 
 .00475 
 
 60 
 
 .01089 
 
 82 
 
 .02353 
 
 104 
 
 .04858 
 
 126 
 
 .09794 
 
 40 
 
 .00514 
 
 62 
 
 .01171 
 
 84 
 
 .02517 
 
 106 
 
 .05182 
 
 128 
 
 .10437 
 
 42 
 
 .00555 
 
 64 
 
 .01259 
 
 86 
 
 .02692 
 
 108 
 
 .05527 
 
 130 
 
 .11123 
 
 44 
 
 .00600 
 
 66 
 
 ..01353 
 
 88 
 
 .02879 
 
 110 
 
 .05893 
 
 132 
 
 .11855 
 
 46 
 
 .00648 
 
 68 
 
 .01453 
 
 90 
 
 .03077 
 
 112 
 
 .06281 
 
 134 
 
 .12637 
 
 48 
 
 .00699 
 
 70 
 
 .01557 
 
 92 
 
 .03288 
 
 114 
 
 .06695 
 
 136 
 
 .13473 
 
 50 
 
 .00753 
 
 72 
 
 .01669 
 
 94 
 
 .03511 
 
 116 
 
 .07134 
 
 138 
 
 .14367 
 
 52 
 
 .00812 
 
 74 
 
 .01789 
 
 96 
 
 .03750 
 
 118 
 
 .07601 
 
 140 
 
 .15324 
 
 - 
 
1082 THE STEAM-ENGINE. 
 
 Iwt in the two tests on Aug. 2 the H.P. developed was 900 I.H^P. in the 
 first and 400 in the second, the engine being a tandem compound, Corliss 
 type, 20 and 36 X 42 in., 120 r.p.m. 
 
 J. R. Bibbins (Trans. A.S.M.E., 1909) gives a large amount of informa- 
 tion on the construction and performance of different styles of cooling 
 towers. He suggests a type of combined fan and natural draft tower 
 suited to most efficient running on peak as well as light loads. 
 
 Evaporators and Distillers are used with marine engines for the pur- 
 pose of providing fresh water for the boilers or for drinking purposes. 
 
 Weir's Evaporator consists of a small horizontal boiler, contrived so as 
 to be easily taken to pieces and cleaned. The water in it is evaporated by 
 the steam from the main boilers passing through a set of tubes placed in 
 its bottom. The steam generated in this boiler is admitted to the low- 
 
 Sressure valve-chest, so that there is no loss of energy, and the water con- 
 ensed in it is returned to the main boilers. 
 
 In Weir's Feed-heater the feed-water before entering the boiler is heated 
 up very nearly to boiling-point by means of the waste water and steam 
 from the low-pressure valve-chest of a compound engine. 
 
 ROTARY STEAM-ENGINES STEAM TURBINES. 
 
 Rotary Steam-engines, other than steam turbines, have been invented 
 by the thousands, but not one has attained a commercial success, as regards 
 economy of steam. For all ordinary uses the possible advantages, such 
 as saving of space, to be gained by a rotary engine are overbalanced by 
 its waste of steam. Rotary engines are in use, however, for special pur- 
 poses, such as steam fire-engines and steam feeds for sawmills, in which 
 steam economy is not a matter of importance. 
 
 impulse and Reaction Turbines. A steam turbine of the simplest 
 form is a wheel similar to a water wheel, which is moved by a jet of steam 
 impinging at high velocity on its blades. Such a wheel was designed 
 by Branca, an Italian, in 1629. The De Laval steam turbine, which is 
 similar in many respects to a Pelton water wheel, is of this class. It is 
 known as an impulse turbine. In a book written by Hero, of Alexan- 
 dria, about 150 B.C., there is shown a revolving hollow metal ball, into 
 which steam enters through a trunnion from a boiler beneath, and 
 escapes tangentially from the outer rim through two arms which are 
 bent backwards, so that the steam by its reaction causes the ball to 
 rotate in an opposite direction to that of the escaping jets. This wheel 
 is the prototype of a reaction turbine. In most modern steam turbines 
 both the impulse and reaction principles are used, jets of steam striking 
 blades or buckets inserted in the rim of a wheel, so as to give it a forward 
 impulse, and escaping from it in a reverse direction so as to react upon 
 it. The name impulse wheel, however, is now generally given to wheels 
 like the De Laval, in which the pressure on the two sides of a wheel con- 
 taining the blades is the same, and the name reaction wheel to one in 
 which the steam decreases in pressure in passing through the blades. 
 The Parsons turbine is of this class. 
 
 The De Laval Turbine. The distinguishing features of this turbine 
 are the diverging nozzles, in which the steam expands down to the at- 
 mospheric pressure in non-condensing, and to the vacuum pressure in 
 condensing wheels; a single forged steel disk carrying the blades on its 
 periphery; a slender, flexible shaft on which the wheel is mounted and 
 which rotates about its center of gravity; and a set of reducing gears, 
 usually 10 to 1 reduction, to change the very high speed of the turbine 
 to a moderate speed for driving machinery. Following are the sizes 
 and speeds of some De Laval turbines: 
 
 Horse-power 5 30 100 300 
 
 Revolutions per minute 30,000 20,000 13,000 10,000 
 
 Diam. to center of blades, ins. 3.94 8.86 19.68 29.92 
 
 The number and size of nozzles vary with the size of the turbine. 
 The nozzles are provided with valves, so that for light loads some of 
 them may be closed, and a relatively high efficiency is obtained at light 
 loads. The taper of the nozzles differs for condensing and non-condens- 
 ing turbines. Some turbines are provided with two sets of nozzles, one 
 for condensing and the other for non-condensing operation. 
 
 The disk of the De Laval turbine is not mounted midway between 
 the shaft bearings, but considerably nearer to the spherical bearing 
 
ROTARY STEAM-ENGiNES STEAM TURBINES. 1Q83 
 
 at the governor end. At low speeds the shaft bends, but as the speed 
 increases the gyroscopic action of the disk causes it to rotate in a plane 
 at right angles to an axis through the center of gravity of the shaft 
 and disk. The speed just below that at which this takes place, and at 
 which the vibration of the shaft is greatest, is called the critical speed. 
 It is about 1/5 to 1/8 of the normal speed of the turbine. 
 
 The diameter of the shaft of a De Laval 100-H.P. turbine is 1 in., 
 and that of a 300-H.P. about 15/i 6 in. The teeth of the pinions of 
 the reducing gear are cut in an enlarged section of the shaft. The pitch 
 of the gears is very small, 0.15 in. in the smallest and 0.26 in. in the 
 largest sizes. The shaft is said to be made of 0.60 to 0.80 C steel and 
 the gears of 0.20 C steel. 
 
 The Zolley or Rateau Turbine. The Zolley or Rateau turbines 
 are developments of the De Laval and consist of a number of De Laval 
 elements in series, each succeeding element utilizing the exhaust steam 
 from the preceding. The steam is partly expanded in the first row of 
 nozzles, strikes the first row of buckets and leaves them with practically 
 zero velocity. It is then further expanded through the second row of 
 nozzles, strikes a second row of moving buckets and again leaves them 
 with zero velocity. This process is repeated until the steam is com- 
 pletely expanded. 
 
 The Parsons Turbine. In the Parsons, or reaction type of turbine, 
 there are a large number of rows of blades, mounted on a rotor or revolv- 
 ing drum. Between each pair of rows there is a row of stationary blades 
 attached to the casing, which take the place of nozzles. A set of sta- 
 tionary blades and the following set of moving blades constitute what is 
 known as a stage. The steam expands and loses pressure in both sets. 
 The speed of rotation, the peripheral speed of the blades and the velocity 
 of the steam through the blades are very much lower than in the De Laval 
 turbine. The rotor, or drum, on which the moving blades are carried, 
 Is usually made in three sections of different diameters, the smallest at 
 the high-pressure end where steam is admitted, and the largest at the 
 exhaust end. In each section the radial length of the blades and also 
 their width increase from one end to the other, to correspond with the 
 increased volume of steam. The Parsons turbine is built in the United 
 States by the Westinghouse Machine Co. and by the Allis-Chalmers Co. 
 
 The Westinghouse Double- flow Turbine. For sizes above 5000 K.W. 
 a turbine is built in which the impulse and reaction types are combined. 
 It has a set of non-expanding nozzles, an impulse wheel with two velocity 
 stages (that is two wheels with a set of stationary non-expanding blades 
 between), one intermediate section and two low-pressure sections with 
 Parsons blading. After steam has passed through the impulse wheel 
 and the intermediate section it is divided into two parts, one going to 
 the right and the other to the left hand low-pressure section. There is 
 an exhaust pipe at each end. In this turbine, the end thrust, which has 
 to be balanced in reaction turbines of the usual type, is almost entirely 
 avoided. Other advantages are the reduction in size and weight, due to 
 higher permissible speed; blades and casing are not exposed to high 
 temperatures; reduction of size of exhaust pipes and of length of shaft; 
 avoidance of large balance pistons. 
 
 The Curtis Turbine, made by the General Electric Company, is an 
 impulse wheel of several stages. Steam is expanded in nozzles and 
 enters a set of three or more blades, at least one of which is stationary. 
 The blades are all non-expanding, and the pressure is practically the same 
 on both sides of any row of blades*. In smaller sizes of turbines, only 
 one set of stationary and movable blades is used, but in large sizes there 
 are from two to five sets, each forming a pressure stage, separated by 
 diaphragms containing additional sets of nozzles. The smaller sizes have 
 horizontal shafts, but the larger ones have vertical shafts supported on a 
 step bearing supplied with oil or water under a pressure sufficient to 
 support the whole weight of the shaft and its attached rotating disks. 
 Curtis turbines are made in sizes from 15 K.W. at 3600 to 4000 revs, per 
 minute up to 9000 K.W. at 750 revs, per minute. 
 
 The Spiro Turbine consists of two " herring-bone" helical gear wheels 
 meshed together and revolving in a closely fitting casing. The steam 
 enters through two non-expanding nozzles at mid-length of the gears, 
 expands into the spaces between adjacent gear teeth and escapes at 
 
1084 THE STEAM-ENGINE. 
 
 the outer ends of the teeth when they pass the line of contact between 
 the two rotors. The turbine is made in small sizes, under 100 H.P., 
 and is used non-condensing. Its merits are compactness and simplicity, 
 but it is not economical of steam. 
 
 Mechanical Theory of the Steam Turbine. In the impulse turbine 
 of the De Laval type, with a single disk containing blades at its rim, 
 steam at high pressure enters the smaller end or throat of a tapering 
 nozzle, and, as it passes through the nozzle, is expanded adiabatically 
 down to the pressure in the casing of the turbine, that is to the pressure 
 of the atmosphere, in a non-condensing turbine, or to the pressure of 
 the vacuum, if the turbine is connected to a condenser. The steam 
 thus expanded has its volume and its velocity enormously increased, 
 its pressure energy being converted into energy of velocity. It then 
 strikes tangentially the concave surfaces of the curved blades, and thus 
 drives the wheel forward. In passing through the blades it has its direc- 
 tion reversed, and the reaction of the escaping jet also helps 'to drive the 
 wheel forward. If it were possible for the direction of the jet to be com- 
 pletely reversed, or through an arc of 180, and the velocity of the blade 
 in the direction of the entering jet was one-half the velocity of the jet, 
 then all the kinetic energy due to the velocity of the jet would be con- 
 verted into work on the blade, and the velocity of the jet with reference 
 to the earth would be zero. This complete reversal, however, is impos- 
 sible, since room has to be allowed between the blades for the passage of 
 the steam, and the blades, therefore, are curved through an arc consid- 
 erably less than 180, and the jet on leaving the wheel still has some 
 kinetic energy, which is lost. The velocity of the entering steam jet 
 also is so great that it is not practicable to give the wheel rim a velocity 
 equal to one-half that of the jet, since that would be beyond a safe speed. 
 The speed of the wheel being less than half that of the entering jet, also 
 causes the jet to leave the wheel with some of its energy unutilized. 
 The mechanical efficiency of the wheel, neglecting radiation, friction, and 
 other internal losses, is expressed by the fraction (E^ #2) * EI, in 
 which EI is the kinetic energy of the steam jet impinging on the wheel 
 and Ez that of the steam as it leaves the blades. 
 
 In multiple-stage impulse turbines, the high velocity of the wheel is 
 reduced by causing the steam to pass through two or more rows of 
 blades, which rows are separated by a row of stationary curved blades 
 which direct the steam from the outlet of one row to the inlet of the 
 next. The passages through all the blades, both movable and secondary, 
 are parallel, or non-expanding, so that the steam does not change its 
 pressure in passing through them. The wheel with two rows of movable 
 blades running at half the velocity of a single-stage turbine, or one with 
 three rows at one-third the velocity, causes the same total reduction in 
 velocity as the single-stage wheel; and a greater reduction in the velocity 
 of the wheel can be obtained by increasing the number of rows. It is, 
 therefore, possible by having a sufficient number of rows of blades, or 
 velocity stages, to run a wheel at comparatively slow speed and yet 
 have the steam escape from the last set of blades at a lower absolute 
 velocity than is possible with a single-stage turbine. In the reaction 
 turbine . the reduction of the pressure and its conversion into kinetic 
 energy, or energy of velocity, takes place in the blades, which are made 
 of such shape as to allow the steam to expand while passing through them. 
 The stationary blades also allow of expansion in volume, thus taking 
 the place of nozzles. 
 
 In all turbines, whether of the impulse, reaction, or combination 
 type, the object is to take in steam at high pressure and to discharge it 
 into the atmosphere, or into the condenser, at the lowest pressure and 
 largest volume possible, and with the lowest possible absolute velocity, 
 or velocity with reference to the earth, consistent with getting the steam 
 away from the wheel, and to do this with the least loss of energy in the 
 wheel due to friction of the steam through the passages, to shock due 
 to incorrect shape, or position of the blades, to windage of frictional 
 resistance of the steam in contact with the rotating wheel, or other 
 causes. The minimizing of these several losses is a problem of extreme 
 difficulty which is being solved by costly experiments. 
 
 Heat Theory of the Steam Turbine. The steam turbine may also be 
 considered as a heat engine, the object of which is to take a pound of 
 
NOTARY STEAM-ENGINES STEAM TURBINES. 1085 
 
 steam containing a certain quantity of heat, Hi, transform as great a 
 part of this heat as possible into work, and discharge the remaining part, 
 HZ, into the condenser. The thermal efficiency of the operation is 
 (Hi - HZ) -J- HI, and the theoretical limit of this efficiency is (Ti TZ) 
 i- T 2 , in which Ti is the initial and T 2 the final absolute temperature. 
 
 Referring to temperature entropy dia- 
 gram, Fig. 176, the total heat above 32 F. ff 
 of 1 Ib. of steam at the temperature Ti is J[ 
 represented by the area OACDG and its ^ /I 
 entropy is 0!. Expanding adiabatically to r> Ti d D/ ] 
 TZ part of its heat energy is converted into / 
 work, represented by the area BCDF, I 
 
 while OABFG represents the heat dis- / Ta/ 1 F 
 
 charged into the condenser. The total B/ H 
 
 heat of 1 Ib. of dry saturated steam at TZ / 
 is greater than this by the area EFGH, the 
 fraction FE -5- BE representing moisture in 
 the 1 Ib. of wet steam discharged. If 
 HI = heat units in 1 Ib. of dry steam at the 
 state-point D, and HZ = heat units in 1 Ib. 
 of dry steam at the state-point E, at the 
 temperature Tz, then the energy converted 
 into work =BCDF=Hi -Hz+ (0 2 - 0i) T 2 . 
 This quantity is called the available en- 
 ergy Ea, of 1 Ib. of steam between the 
 
 j 
 
 JG 
 
 temperatures TI and T 2 . ^ , ^ , - 
 
 If the steam is initially wet, as repre- L _!.$ ]J 
 
 sented by the state-point d and entropy L ZlzU-* 
 
 0*, then the work done in adiabatic expan- ^~ 
 
 sion is BCdfB, which is equal to E a = FIG. 176. 
 
 HI -H 2 + (02 - 0i) T 2 - (0i - 0*) (.Ti -Tz). 
 
 The quantity 0! - 0* = (L/T{) (l-x), in which L = latent heat 
 
 of evaporation at the temperature Ti, and x = the moisture in 1 Ib. of 
 
 steam. The values of Hi, HZ, 4>i, 2 , etc., for different temperatures, 
 
 may be taken from steam tables or diagrams. 
 
 If the steam is initially superheated to the temperature T s , as repre- 
 sented by the state-point j, the entropy being < 3 , then the total heat at 
 j is Hi + C (T s - Ti), in which C is the mean specific heat of super- 
 heated steam between T\ and T s . The increase of entropy above 0i 
 is 03 -0! = C loge (Ts/Ti). The energy converted into work is E a = 
 
 Hi - H 2 + (02 - 0l) TZ + [V2 (Ts + TI) - TZ} (03 - 0l) 
 
 Velocity of Steam in Nozzles. Having obtained the total available 
 energy in steam expanding adiabatically between two temperatures, as 
 shown above, the maximum possible flow into a vacuum is obtained 
 
 from the common formula, Energy, in foot-pounds, = 1/2 W/g X V 2 , in 
 which Wis the weight (in this case 1 Ib.), V is the velocity in feet per 
 second, and g = 32.2. As the energy E a is in heat units, it is multi- 
 
 which Wis the weight (in this case 1 Ib.), V is the velocity in feet per 
 second, and g = 32.2. As the energy E a is in heat units 
 plied by 778 to convert it into foot-pounds, and we have 
 
 V = V778X2gE a = 223.8 \/~W a . 
 
 This is the theoretically maximum possible velocity. It cannot be 
 obtained in a short nozzle or orifice, but is approximated in the long 
 expanding nozzles used in turbines. In the throat or narrow section of 
 an orifice, the velocity and the weight of steam flowing per second may 
 be found by Napier's or Bateau's formula, see page 876, or from Gras- 
 hof's formula as given by Moyer, F = AoPiW? -H 60, or A = 60 F -f- 
 PO-97, in which A is the area of the smallest section of the nozzle, 
 sq. in., F is the flow of steam (initially dry saturated) in Ibs. per sec., 
 and P is the absolute pressure, Ibs. per sq. in. This formula is appli- 
 cable in all cases where the final pressure P 2 does not exceed 58 % of the 
 initial pressure. For wet steam the formula becomes F = AoP\wi -v- 
 60 \/~x, Ao = 60 F \/~x -T- PiO.97, in which x is the dryness quality of the 
 inflowing steam, 1 x being the moisture. 
 
 For superheated steam F = ^oPiO-97 (i -f 0.00065 D) -r- 60; A => 
 60 F -i- P^-97 (1 -f 0.00065 D), D being the superheat in degrees F. 
 
1086 
 
 THE STEAM-ENGINE. 
 
 When the final pressure p2 is greater than 0.58 P?., a coefficient is to 
 
 be applied to F in the above formulae, the value of which is most con- 
 
 veniently taken from a curve given by Rateau. The values of this co- 
 
 efficient, c, for different ratios of Pi/Pz, are approximately as follows: 
 
 P 2 -e-Pi= 0.580.60 0.62 0.64 0.66 0.68 0.70 0.720.740.760.78 
 
 C= 1. 0.995 0.985 0.975 0.965 0.955 0.945 0.93 0.91 0.88 0.85 
 
 Pa -7- Pi = 0.800.82 0.84 0.86 0.88 0.90 0.92 0.940.960.981.00 
 
 c= 0.82 0.79 0.76 0.72 0.675 0.625 0.57 0.51 0.42 0.30 0.00 
 
 The quality of steam after adiabatic expansion, xz, is found from the 
 formula xz = (x 1 Li/7 T i + X #2) 7VZ/2, (8) 
 
 in which Q\ and 61 are the entropies of the liquid, LI and Lt the latent 
 heats of evaporation, and Xi and xz the dryness quality, at the initial 
 and final conditions respectively. Curves of steam quality are plotted in 
 an entropy-total heat chart given in Moyer's "Steam Turbines" and 
 also in Marks and Da vis's "Steam Tables and Diagrams." 
 
 The area of the smallest section or throat of the nozzle being found, 
 the area of any section beyond the throat is inversely proportional to the 
 velocity and directly proportional to the specific volume and to the 
 dryness, or Ai/A = V /Vi X Vi/v X XI/X Q , in which A is in the area in 
 sq. ins., V the velocity in ft. per sec., v the volume of 1 Ib. of steam in 
 cu. ft., and x the dryness fraction, the subscript referring to the 
 smallest section and the subscript 1 to any other section. The ratio 
 Ai/Ao for the largest cross section of a properly designed nozzle depends 
 upon the ratio of the initial to the final pressure. Moyer gives it as 
 Ai/A = 0.172 Pi/Pa + 0.70, and for Pi/P 2 greater than 25, Ai/Ao = 0.175 
 
 In practice expanding nozzles are usually made so that an axial sec- 
 tion shows the inner walls in straight lines. The transverse section is 
 usually either a circle or a square with rounded corners. The diver- 
 gence of the walls is about 6 degrees from the axis for the non-condens- 
 ing and as much as 12 degrees for condensing turbines for low vacuums. 
 'Mover gives an empirical formula for the length between the throat and 
 
 'the mouth, L = Vl5 ,4 inches. The De Laval turbine uses a much 
 longer nozzle for mechanical reasons. The entrance to the nozzle above 
 the throat should be well rounded. The efficiency of a well-made nozzle 
 with smooth surfaces as measured by the velocity is about 96 to 97%, 
 corresponding to an energy efficiency of 92 to 94%. 
 
 Speed of the Blades. If VI = peripheral velocity of the blade, 
 Vi = absolute velocity of the steam entering the blades and a the nozzle 
 angle, or angle of the nozzle to the plane of the wheel, then (in impulse 
 turbines with equal entrance and exit angles of the blade with the plane 
 of the wheel) for maximum theoretical efficiency of the blade, V b = 1/2 Vi 
 cos a. The nozzle angle is usually about 20, cos a = 0.940, and the 
 efficiency of a single row of blades is (0.94 - V b / Vi) 4 V b / Vi. 
 
 For Vi = 3000 ft. per sec., the efficiency for different blade speeds is 
 about as follows: 
 
 200 400 600 800 1000 1200 1400 1600 1800 2000 
 23 44 60 72 81 87 89 87 80 71 
 The highest efficiency is obtained when 
 h. V b = about 1/2 V2. It is difficult, for mechan- 
 
 ical reasons, to use speeds much greater than 
 500 ft. per sec., therefore the highest effi- 
 ciencies are often sacrificed in commercial 
 I machines. The blade speeds used in practice 
 vary from 500 to 1200 ft. per sec. For an 
 impulse wheel with more than one row of mov- 
 ing blades in a single pressure stage, efficiency 
 4NV b 
 
 Referring to Fig. 177, if Vi is the absolute 
 direction and velocity of the entering jet, V b 
 the direction and velocity of the blade, the 
 resultant, Vr, is the velocity and direction of the jet relatively to th 
 blade, and the edge of the blade is made tangent to this direction. Also 
 
 . 77 
 
ROTARY STEAM-ENGINES STEAM TURBINES. 1087 
 
 V x , the resultant of V^ and V r ~at the other edge of the blade, is the 
 absolute velocity and direction of the steam escaping from the wheel. 
 If Q is the angle between V r and Vfr, the maximum energy is abstracted 
 from the steam when the angle between V x and VJF, = 90 - 1/2 8, and 
 the efficiency is cos Q + cos2 1/2 @. 
 
 For details of design of blades, and of turbines in general, see Moyer, 
 Foster, Thomas, Stodola and other works on Steam Turbines, also 
 Peabody's "Thermodynamics." Calculations of stages, nozzles, etc., 
 are much facilitated by the use of Peabody's " Steam Tables" and Marks 
 and Davis's "Steam Tables and Diagrams." 
 
 Comparison of Commercial Impulse and Reaction Turbines. (Moyer.) 
 IMPULSE. REACTION. 
 
 1. Few stages. 1. Many stages. 
 
 2. Expansion in nozzles. 2. No nozzles. 
 
 3. Large drop in pressure in a 3. Small drop in pressure in a 
 
 stage. stage. 
 
 4. Initial steam velocities 1000 to 4. All steam velocities low, 300 to 
 
 4000 ft. per sec. 600 ft. per sec. 
 
 5. Blade velocities 400 to 1200 ft. 5. Blade velocities 150 to 400 ft. 
 
 per sec. per sec. 
 
 6. Best efficiency when the blade 6. Best efficiency when the blade 
 
 velocity is nearly half the ini- velocity is nearly equal to 
 
 tial velocity. of steam. the highest velocity of the 
 
 steam. 
 
 Xoss due to Windage (or friction of a turbine wheel rotating in steam). 
 Moyer gives for the friction of a plain disk without blades, F w , and of 
 one row of blades without the disk, F^, in horse-power: 
 
 F w = 0.08 <J2 (M/lOO)* 8 w -J- (1 + 0.00065 D)*, 
 F & -X>.3dl^tt/100)to-*. (1 + 0.00065 D)*, 
 
 in which d = diam. of disk to inner edge of blade, in feet ; u = peripheral 
 velocity of disk, in ft. per sec.: w = density of dry saturated steam at 
 the pressure surrounding the disk, in Ibs. per cu. ft., and D = super- 
 heat in degrees F. The sum of F w and F b is the friction of the disk and 
 blades. For moist sieam the term 1 + 0.00065 D if to be omitted, and 
 the expression multiplied by a coefficient c, whose value is approxi- 
 mately as follows: 
 
 ^fure^nSeam 2 4 6 8 10 12 16 20 24 
 
 Coefficient c. .. 1.01 1.05 1.10 1.16 1.25 1.37 1.65 2.00 2.44 
 At high rotative speeds the rotation loss of a non-condensing turbine 
 with wheels revolving in steam at atmospheric pressure is quite large, 
 and in small turbines it may be as much as 20% of the total output. 
 The loss decreases rapidly with increasing vacuum. In a turbine with 
 more than one stage part of the friction loss of rotation is converted into 
 heat which in the next stage is converted into kinetic energy, thus partly 
 compensating for the loss. 
 
 Efficiency of the Machine. The maximum possible thermodynamic 
 efficiency of a steam turbine, as of any other steam engine, is expressed 
 by the ratio which the available energy between two temperatures bears 
 to the total heat, measured above absolute zero, of the steam at the 
 higher temperature. In the temperature-entropy diagram Fig. 176 it is 
 represented by the ratio of the area BCDF to OACDG. Of this avail- 
 able energy, from 50 to 75 and possibly 80 per cent is obtainable at the 
 shaft of turbines of different sizes and designs. As with steam engines, 
 the highest mechanical and thermal efficiencies are reached only with 
 large sizes and the most expensive designs. The several losses which 
 tend to reduce the efficiency of turbines below the theoretical maximum 
 are- 1, residual velocity, or the kinetic energy due to the velocity of the 
 steam escaping from the turbine; 2, friction and imperfect expansion 
 in the nozzles; 3, windage, or friction due to rotation of the wheel in 
 steam; 4, friction of the steam traveling through the blades; 5, shocks, 
 impacts, eddies, etc., due to imperfect shape or roughness of blades; 6, 
 leakage around the ends of the blades or through clearance spaces; 7, shaft 
 friction: 8, radiation. The sum of all these losses amounts to about 
 25% of the available energy in the largest and best design and 
 or more in small sizes or poor Designs, 
 
1088 
 
 THE STEAM-ENGINE. 
 
 Steam Consumption of Turbines. The steam consumption of any 
 steam turbine is so greatly influenced by the conditions of pressure, 
 moisture or superheat, and vacuum, that it is necessary to know the effect 
 of these conditions on any turbines whose performances are to be com- 
 pared with each other or with a given standard. Manufacturers usually 
 furnish with their guarantees of performance under standard conditions 
 of pressure, superheat and vacuum, a statement or set of curves showing 
 the amount that the steam consumption per K.W.-hour will be increased 
 or diminished by stated variations from these standard conditions. 
 When a test of steam consumption is made under any conditions varying 
 from the standard, the results should be corrected in order to compare 
 them with other tests. Moyer gives the following example of applying 
 corrections to a pair of tests made in 1907, to reduce them both to a steam 
 pressure of 179 Ibs. gauge, 28.5 iris, vacuum, and 100 F. superheat. 
 
 
 7500-K.W. 
 Westing- 
 house- 
 Parsons. 
 
 Correc- 
 tions, 
 per cent. 
 
 9000-K.W. 
 Curtis. 
 
 Correc- 
 tions, 
 per cent. 
 
 Averacre steam pressure 
 
 177.5 
 
 -0 15 
 
 179 
 
 
 
 Average vacuum, ins., referred 
 
 27.3 
 
 -3.36 
 
 29 55 
 
 + 12 39 
 
 Avera.se superheat deg F. . 
 
 95 7 
 
 -0 29 
 
 116 
 
 + 1 28 
 
 Average load on generator K TV. 
 
 9830 5 
 
 
 8070 
 
 
 Steam cons Ibs. per K W.-hr. . 
 
 15.15 
 
 
 13 
 
 
 Net correction, per cent/ 
 
 
 -3.80 
 
 
 + 13.67 
 
 Corr. st. cons., Ibs. per K.W.-hr. 
 
 14.57 
 
 
 14.77 
 
 
 For the 7500-K.W. turbine, the following corrections given by the manu- 
 facturer were used: pressure, 0.1% for each pound; vacuum, 2.8% for 
 each inch; superheat, 7% for each 100 F. For the 9000-K.W. turbine, 
 the following corrections were used: superheat, 8% for 100 F.; vacuum, 
 8% for each inch. 
 
 The results as corrected show that the two turbines would give practi- 
 cally the same economy if tested under uniform conditions. The results 
 are equivalent respectively to 9.58 and 9.72 Ibs. per I. H. P. -hour, as- 
 suming 97% generator efficiency and 91% mechanical efficiency of a 
 steam-engine. 
 
 The proper correction for moisture in a steam turbine test is stated to 
 be a little more than twice the percentage of moisture. There is a large 
 increase in the disk and blade rotation losses when wet steam is used. 
 
 Effect of Vacuum on Steam Turbines. M. R. Bump (Power, June 
 15, 1909) gives the following as the steam consumption per K.W. hour 
 of a 1000 K.W. turbine at full rated load, 175 Ib. gage pressure, 100 
 superheat: 
 
 Vacuum, in.. 29 28 27 26 25 24 23 22 21 
 Steam per 
 K.W. hr. Ib. . 15.35 16.55 17.50 18.55 19.35 20.00 20.6 21.1 21.6 
 
 The gain in economy per inch of vacuum at different vacuums is 
 given as follows in Mech. Engr., Feb. 24, 1906. 
 
 Inches of Vacuum. 
 
 28 
 
 27 
 
 26 
 
 25 
 
 Curtis, per cent gain per inch of vacuum. . 
 Parsons, per cent gain per inch of vacuum 
 
 5.1 
 5.0 
 
 4.8 
 4.0 
 
 4.6 
 3.5 
 
 4.2 
 3.0 
 
 Westi .ghouse- Parsons, per cent gain per 
 
 
 
 
 
 inch of vacuum . 
 
 3 14 
 
 3.05 
 
 2 95 
 
 2 87 
 
 Theoretical per cent gain per inch of vac.. 
 
 5.2 
 
 4.4 
 
 3.7 
 
 3.0 
 
 Tests of Turbines. The following results of tests of turbines are 
 selected from a series of tables in Moyer 's "Steam Turbines." 
 
ROTARY STEAM-ENGINES STEAM TURBINES. 1089 
 
 3^ 
 &* 
 
 Bfe 
 
 < 
 
 o> en 
 
 Ig 
 
 ^ 
 
 *J* 
 
 |1s? 
 
 *-* 
 
 Vacuum, 
 ins. 
 
 ^ 
 
 && 2 
 A A 
 
 g 
 
 jH 
 
 & 
 
 W- 
 < 
 
 S| 
 
 3& 
 
 |l1 
 
 *-* 
 
 a 
 
 SI 
 
 
 
 Si 
 
 S* 
 
 2000 ( 
 C. \ 
 
 555 
 1067 
 2024 
 
 155 
 170 
 166 
 
 204 
 120 
 207 
 
 28.5 
 28.4 
 28.5 
 
 18.09 
 16.31 
 15.02 
 
 300 ( 
 W.-P.j 
 
 233 
 
 461 
 688 
 
 145 
 145 
 140 
 
 4.1 
 
 4.8 
 7.0 
 
 28.0 
 28.0 
 27.2 
 
 15.99 
 13.99 
 15.73 
 
 
 5374 
 
 182 
 
 133 
 
 29.4 
 
 13.15 
 
 
 383 
 
 153 
 
 2 
 
 28.2 
 
 14.15 
 
 
 8070 
 
 179 
 
 116 
 
 7.9.4 
 
 13.00 
 
 
 756 
 
 149 
 
 1 
 
 27.8 
 
 13.28 
 
 
 10186 
 
 176 
 
 147 
 
 29.5 
 
 12.90 
 
 500 
 
 1122 
 
 149 
 
 5 
 
 26.5 
 
 14.32 
 
 
 13900 
 
 198 
 
 140 
 
 29.3 
 
 13.60 
 
 W.-P. 
 
 386 
 
 148 
 
 3 
 
 0.8 
 
 24.94 
 
 1500 ( 
 
 530 
 1071 
 
 145 
 131 
 
 110 
 124 
 
 28.9 
 28.3 
 
 21.58 
 18.24 
 
 
 767 
 1144 
 
 147 
 126 
 
 3 
 
 11 
 
 0.8 
 0.8 
 
 22.10 
 24.36 
 
 P. ) 
 
 1585 
 
 128 
 
 125 
 
 27.5 
 
 17.60 
 
 1 nnn ( 
 
 752 
 
 151 
 
 
 
 27.5 
 
 14.77 
 
 300 ( 
 P. I 
 
 303 
 297 
 
 158 
 161 
 
 
 
 
 26.6 
 
 
 23.15 
 
 34.20 
 
 IUUU ) 
 
 W.-P.| 
 
 1503 
 2253 
 
 147 
 145 
 
 
 
 
 27.0 
 25.2 
 
 13.61 
 15.29 
 
 1000 J 
 
 194 
 
 425 
 
 171 
 144 
 
 47 
 21 
 
 27.7 
 27.6 
 
 31.97 
 
 24.91 
 
 3000 ( 
 W.-P.I 
 
 2295 
 4410 
 
 152 
 144 
 
 102 
 
 87 
 
 26.2 
 26.2 
 
 12.36 
 11.85 
 
 R. 1 
 
 871 
 
 166 
 
 11 
 
 23.6 
 
 24.61 
 
 3OA 
 
 196 
 
 198 
 
 16 
 
 27.4 
 
 15.62 
 
 
 1024 
 
 164 
 
 10 
 
 25.0 
 
 21.98 
 
 J\J(J 
 
 298 
 
 197 
 
 64 
 
 27.4 
 
 14.35 
 
 
 
 
 
 
 
 
 352 
 
 199 
 
 84 
 
 27.2 
 
 13.94 
 
 C., Curtis; P., Parsons; W.-P., Westinghouse-Parsons; R., Rateau; 
 D M De Laval. Note that the figures of steam consumption in the first 
 half of the table are in Ibs. per K.W.-hour; in second half, in Ibs. per Brake 
 H.P.-hour. 
 
 A test of a Westinghouse double-flow turbine at the Williamsburff 
 power station, Brooklyn N. Y., gave the following results (Eng. News, 
 Dec. 30, 1909): Speed, 750 r.p.m.; Steam pressure at throttle, 203.4 Ibs.; 
 Superheat, 80.1 F.; Vacuum, 28.6 ins.; Load, 13,384 K.W.; Steam per 
 K.W.-hour, 14.4. Ibs.; Efficiency of generator, 98%; Windage, 2.0%; 
 Equivalent B. H. P., 18,620; Steam per B. H. P.-hour, 10.3 Ib. 
 
 Efficiency of the Rankine Cycle, and the Rankine Cycle Ratio. 
 
 An ideal engine operating on the Rankine cycle expands the steam 
 adiabatically to the condenser pressure and the exhaust steam heats 
 the feed water to the condenser temperature. It has no clearance nor 
 loss by leakage or radiation. The efficiency of the Rankine cycle is 
 the quotient of the number of heat-units converted into work by the 
 ideal engine per Ib. of steam divided by the difference between the 
 total heat per Ib. of the entering steam and the total heat of 1 Ib. of 
 feed- water at the condenser temperature. 
 
 The Rankine Cycle Ratio is the ratio between the thermal efficiency 
 of an actual engine or turbine and the efficiency of an ideal engine 
 operating on the Rankine cycle between the same temperature and 
 pressure limits as those of the actual engine. 
 
 The available energy of 1 Ib. of steam supplied = heat utilized per 
 Ib. in an ideal engine operating on the Rankine cycle = U = H_ Hz + 
 Tz(Nz - N s ) in which 
 
 H = heat-units per Ib. of the entering steam, whether saturated or 
 superheated. 
 
 H 2 = heat units per Ib. of the exhaust steam. 
 Tz absolute temperature of the exhaust. 
 
 N and Nz = respectively the entropy of the entering and of the 
 exhaust steam. 
 
 If the exhaust steam is superheated (as it roay be in the case of the 
 high-pressure cylinder of a triple expansion engine using highly super- 
 heated steam) U = H s - H 2 - Tz(N b -~ sit). (These formulae may be 
 derived from a study of the aitropy temperature diagram, page 1085.) 
 
 EXAMPLE. A steam curbine operating with 225 Ib. absolute pre,~ 
 sure, 150 superheat, and 28,5 in. vacuum uses 10 Ib. of steam per 
 
1090 
 
 THE STEAM-ENGINE. 
 
 brake horse-power hour. Required the available energy per Ib. steam, 
 the Bankine cycle efficiency and the Rankine cycle ratio. 
 
 H s = 1285.9; H* = 1099.2; Tz = 549.6; h = heat units per Ib. of 
 feed-water at the temperature T 2 = 58. W = Ib. steam per H.P.-hour = 
 10. A = heat equivalent of one H.P.-hour = 1,980,000 -r- 777.54 = 
 2546.5 B.T.U.; JV S = 1.6296; N 2 = 2.0058 W(H S - h) = total heat 
 per H.P.-hour = 10 X (1285.9 - 58) = 12,279 B.T.U. Thermal 
 
 ficiency E = 2546.5 + W(H - h) = 20.74%. Available energy per 
 Ib., U = 1285.9 - 1099.2 + 549.6 (2.0058 - 1.6296) = 393.5 B.T.U. 
 Rankine cycle efficiency ER = U -r- (H s - h) = 393.5 -=- 1227.9 = 32.04%. 
 Rankine cycle-ratio R = E + ER = 20.74 + 32 = 64.7%. 
 
 Factors for Reduction to Equivalent Rankine Efficiency. When 
 engines are tested with different pressures, superheat and vacuum, 
 it is often desirable to reduce the results to a common standard of 
 assumed conditions. The conditions stated in the above example 
 correspond with good modern practice and they probably furnish as 
 good a standard for comparison as any other. The Rankine cycle 
 efficiency ER, for this set of conditions is 32.04% ; the thermal efficiency, 
 for W = 10 Ib. is 20.74 % ; and the ratio E -f- ER is 64.7 %. For another 
 set of conditions, pressure 150 Ib., vacuum 27 in., and dry saturated 
 steam ER is 27.0. The quotient 32.04 -r 27.0 = 1.187, may be used 
 as a factor to reduce the Rankine efficiency, the Rankine cycle ratio, 
 and the steam consumpti9n per H.P.-hour to the equivalent for stand- 
 ard conditions; thus, equivalent E = 27 X 1.187 = 32.04, equivalent R 
 (assuming W= 11.87 and E = 17.48%) = 17.48 X 1.187 = 20.74, and 
 equivalent W = 11.87 -r- 1.187 = 10 Ib., provided the percentage losses 
 due to friction, radiation and leakage are the same for the two condi- 
 tions. The factor is used as a multiplier to obtain the equivalent 
 thermal efficiency and Rankine cycle ratio, and as a divisor to obtain 
 the equivalent steam consumption. The factor may be found also 
 
 32.04 (H s - h), 
 from the equation F = pj -in which H s , h, and U are the 
 
 values for the given set of conditions. The factors computed by this 
 formula and the efficiency of the Rankine cycle for different conditions 
 are given in the table at the top of p. 1091. 
 
 Effect of Increase in Pressure, Vacuum and Superheat on Efficiency. 
 
 Selecting from the table on p. 1091 the figures for Rankine cycle efficiency 
 given in the table below and comparing them by taking differences 
 between consecutive figures in both the horizontal and the vertical rows, 
 we find that the increase of efficiency due to increasing either the pres- 
 sure, the superheat or the vacuum cannot be expressed as a constant 
 percentage, but that it varies with variations in each condition. 
 EFFECT OF VARYING CONDITIONS ON RANKINE CYCLE EFFICIENCY. 
 
 Pressure, 
 Absolute . 
 
 150 
 
 Vacuum, 
 In. 
 
 Superheat. 
 
 
 
 Diff. 
 
 150 
 
 Diff. 
 
 300 
 
 Diff. 
 
 ,27,, 
 28,, 
 ( 29.... 
 
 27.0 
 28.4 
 30.8 
 
 0.5 
 1.4 
 0.6 
 2.4 
 0.6 
 
 27.5 
 29.0 
 31.4 
 
 1.1 
 1.5 
 1.0 
 2.4 
 1.0 
 
 28.6 
 30.0 
 32.4 
 
 1.4 
 2.4 
 
 200 
 
 ,27,, 
 28,, 
 (29.... 
 
 28.5 
 29.9 
 32.2 
 
 0.6 (1.5) 
 1.4 
 0.6 (1.5) 
 
 0.6 (1.4) 
 
 29.1 
 30.5 
 32.8 
 
 1.4 
 
 2.3 
 1.0(1.4) 
 
 30.1 
 31.5 
 33.8 
 
 1.4 
 
 2.3 
 
 (1.4) 
 
 250 
 
 ,27, 
 
 28,, 
 
 (29.... 
 
 29.7 
 31.0 
 33.2 
 
 0.6 (1.2) 
 1.3 
 0.6(1.1) 
 2.2 
 0.6 (1.0) 
 
 30.3 
 31.6 
 33.9 
 
 0.9 (1.2) 
 0.9(1.1) 
 
 31.2 
 32.6 
 34.2 
 
 1.4 
 2.8 
 
 The figures in parentheses show the increase in efficiency due taf 
 
ROTARY STEAM-ENGINES STEAM TURBINES. 1091 
 
 Efficiency of Bankine Cycle, ER (per cent) and Factor JPfor Reduction 
 to Standard Conditions, 
 
 (225 Lb. Absolute Pressure, 150 Superheat, 28.5 In. Vacuum and 
 Rankine Cycle efficiency of 32 per cent being taken as standard.) 
 
 Absolut. 
 Pres- 
 sure, 
 Lb. per 
 Sq. In. 
 
 Vacuum 
 In. 
 Mercury . 
 
 Superheat, Degrees Fahrenheit. . 
 
 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 150 
 
 27 ir 
 
 oo j EiR 
 
 28 ]p 
 28.5 { f* 
 29 |F" 
 
 27.0 
 1.187 
 28.4 
 1.127 
 29.4 
 1.088 
 30.8 
 1.040 
 
 27.1 
 1.182 
 28.5 
 1.122 
 29.6 
 1.083 
 31.0 
 1.035 
 
 27.3 
 1.174 
 28.7 
 1.115 
 29.8 
 1.076 
 31.1 
 1.028 
 
 27.5 
 1.163 
 29.0 
 1.105 
 30.0 
 1.067 
 31.4 
 1.020 
 
 27.8 
 1.150 
 29.3 
 1.094 
 30.3 
 1.057 
 31.7 
 1.011 
 
 28.2 
 1.136 
 29.6 
 1.081 
 30.6 
 1.046 
 32.0 
 1.001 
 
 28.6 
 1.122 
 30.0 
 1.068 
 31.0 
 1.033 
 32.4 
 0.989 
 
 200 
 
 27 { 
 28 ]' 
 28.5 {f- 
 29 {f. 
 
 28.5 
 1.124 
 29.9 
 1.072 
 30.9 
 1.038 
 32.2 
 0.995 
 
 28.6 
 1.119 
 30.0 
 1.067 
 31.0 
 1.033 
 32.3 
 0.990 
 
 28.8 
 1.111 
 30.2 
 1.060 
 31.2 
 1.026 
 32.6 
 0.984 
 
 29.1 
 1.100 
 30.5 
 1.051 
 31.5 
 1.018 
 32.8 
 0.977 
 
 29.4 
 1.090 
 30.8 
 1.041 
 31.8 
 1.009 
 33.1 
 0.968 
 
 29.7 
 1.078 
 31.1 
 1.030 
 32.1 
 0.998 
 33.4 
 0.959 
 
 30.1 
 1.064 
 31.5 
 1.018 
 32.4 
 0.988 
 33.8 
 0.949 
 
 225 
 
 - 
 
 250 
 
 27 {f" 
 28 {? 
 28.5 |f* 
 29 jf* 
 
 29.1 
 1.101 
 30.5 
 1.052 
 31.4 
 1.019 
 32.7 
 0.978 
 
 29.2 
 1.096 
 30.6 
 1.047 
 31.6 
 1.014 
 32.9 
 0.973 
 
 29.5 
 1.087 
 30.8 
 1.040 
 31.8 
 1.008 
 33.1 
 0.967 
 
 29.7 
 1.078 
 31.1 
 1.031 
 32.0 
 1.000 
 33.4- 
 0.960 
 
 30.0 
 1.068 
 31.3 
 1.022 
 32.3 
 0.991 
 33.6 
 0.952 
 
 30.3 
 1.056 
 31.7 
 1.011 
 32.6 
 0.981 
 34.0 
 0.943 
 
 30.7 
 1.044 
 32.0 
 1.000 
 33.0 
 0.971 
 34.3 
 0.934 
 
 27 jf 
 
 78 J E * 
 28 J F 
 
 90 r j ER 
 
 28.5 J F 
 29 j* 
 
 29.7 
 1.079 
 31.0 
 1.033 
 32.0 
 1.002 
 33.2 
 0.963 
 
 29.8 
 1.075 
 31.1 
 1.029 
 32.1 
 0.998 
 33.4 
 0.959 
 
 30.0 
 1.068 
 31.3 
 1.022 
 32.3 
 0.992 
 33.6 
 0.953 
 
 30.3 
 1.059 
 31.6 
 1.014 
 32.6 
 0.984 
 33.9 
 0.946 
 
 30.5 
 1.049 
 31.9 
 1.005 
 32.8 
 0.975 
 34.1 
 0.938 
 
 30.9 
 1.038 
 32.2 
 0.995 
 33.2 
 0.966 
 34.5 
 0.930 
 
 31.2 
 1.026 
 32.6 
 0.984 
 33.5 
 0.956 
 34.8 
 0.920 
 
 increase of 50 Ib. in pressure, the superheat and the vacuum being 
 constant. 
 
 Constant. 
 
 Increase of 
 
 
 Increases 
 
 
 
 
 Efficiency. 
 
 Pressure and vacuum 
 
 j Superheat frc 
 
 >m 
 150 
 
 to 150 
 " 300 
 
 0.5 t 
 0.9 
 
 o 0.6 a 
 1.1 
 
 v. 0.6 
 1.0 
 
 Pressure and 
 
 j Vacuum 
 
 27 
 
 " 28 
 
 1.3 
 
 1.5 
 
 1.4 
 
 Superheat 
 
 1 
 
 28 
 
 " 29 
 
 2.2 
 
 2.4 
 
 2.3 
 
 Superheat and 
 
 j Pressure 
 
 150 
 
 " 200 
 
 1.4 
 
 1.6 
 
 1.5 
 
 vacuum 
 
 1 
 
 200 
 
 " 250 
 
 1.0 
 
 1.2 
 
 1.1 
 
 W. H. Wallis (Eng'g, April 21, 1911) finds as the results of tests of 
 a compound reaction turbine that the percentage reduction of steam 
 consumption by increasing the vacuum from 25 in. to the figures given 
 was as follows: Vacuum, 27 in.; reduction, 71/2%; 28 in., 12%; 28.6 in., 
 
 Steam Consumption and Heat Consumption of the Ideal Engine. 
 
 If the Rankine cycle efficiency is given for a stated set of conditions, 
 
1092 THE STEAM-ENGINE. 
 
 the corresponding theoretical steam consumption per H. P. -hour may be 
 
 For the extreme cases in the table on p. 1090, we have: 
 
 Pres- 
 sure, 
 Lb. 
 
 Vac., 
 In. 
 
 Super- 
 heat. 
 
 ** 
 
 h. 
 
 E s. 
 
 U. 
 
 W. 
 
 H s -h 
 
 W (Hf-h). 
 
 150 
 250 
 
 27 
 29 
 
 
 300 
 
 1193.4 
 1363.5 
 
 82.0 
 44.6 
 
 27.0 
 
 34.8 
 
 299.7 
 459.1 
 
 8.49 
 5.60 
 
 1114.4 
 1318.9 
 
 9461 
 7376 
 
 The figures in the last column, W(H S - h), show the B.T.U. con- 
 sumed (or supplied by the boiler) per H. P. -hour. The number of 
 pounds of steam supplied under the second set of conditions is 33.3 % less 
 than that supplied under the first set, but the saving of heat is only 
 (9461 - 7376)- -v- 9461 = 22%. 
 
 Westinghouse Turbines at the Manhattan 74th Street Station, 
 New York. Each of the 30,000 Kw. cross-compound units consists 
 of two turbines, a high and a low pressure, side by side. Each half 
 drives a generator, the high pressure running 1500 r.p.m. and the low 
 pressure 750, the generators being tied together electrically. The tur- 
 bines are reaction throughout, having no impulse wheel. The h.p. 
 is a single flow machine and the l.p. a double flow. The turbines are 
 to have a vacuum of 97% = 29.1 in. mercury, or 0.442 Ib. per sq. in. 
 absolute. The boilers will run at 215 Ib. pressure, and at peak of the 
 load, twice each day of 24 hours, will run at 300% of rating. Under- 
 feed stokers. Superheat at throttle, 120. (Power, April 27, 1915). 
 
 A Steam Turbine Guarantee. A 22,500-Kw. steam turbine built 
 in 1913 by C. A. Parsons Co., Newcastle, England, for the Common- 
 wealth Edison Co., Chicago, was guaranteed as follows: At 750 r.p.m. 
 200 Ib. pressure by gage, 29 in. vacuum in the condenser 
 
 Load, Kw.. 10,000 15,000 20,000 25,000 
 
 Steam per Kw .-hour, Ib 12.50 11.65 11.25 11.65 
 
 Efficiency of a 5000-Kw. Steam Turbine Generator. (F. W. Ballard, 
 Trans. A. S. M. E., 1914.) A plotted diagram of a series of tests shows 
 that the total steam consumption at different loads follows the Willans 
 straight-line law up to the point of maximum efficiency. The turbine 
 was of the Allis-Chalmers-Parsons type, rated at 5000 Kw., 1800 r.p.m., 
 11,000 volts, A.C. With steam at 225 Ib. gage, superheat 125 F., 
 vacuum 281/2 in., 90% power factor, the steam consumption at 
 different loads was as follows (figures approximate, from the chart) : 
 
 Load, Kw 2,000 4,000 5,000 6,000 6,500 7,000 7,900 
 
 Steam per Kw.- 
 
 hour, Ib 15.5 13.75 13.50 13.20 13.00 13.10 13.30 
 
 Total steam per 
 
 hour, Ib 31,000 55,000 67,500 79,000 85,000 91,500 105,000 
 
 Up to a load of 6500 Kw. the total consumption is 9000 + 12 X 
 Kw. load, nearly. The efficiency ratio on the Rankine cycle was 0.68 
 at 6500 Kw. 
 
 Comparison of Large Turbines and Reciprocating Engines. Moyer 
 gives a set of curves of the steam consumption of a standard 5000-Kw. 
 turbine generator and a 4-cylinder compound reciprocating steam- 
 engine generator, assuming both units, operating under the same con- 
 ditions. The following figures are taken from the curves: 
 
 Load in Kilowatts 3000 4000 5000 6000 7000 7500 
 
 Lb. Steam per Kilowatt-hour. 
 Turbine 16.0 15.5 15.315.25 15.4 15.5 
 
 Reciprocating engine: 
 
 With equal work in cylinders. 18.0 17.4 17.8 19.0 20.8 22.0 
 Unequal work in cylinders. . 18 . 4 17 . 17 . 2 17 . 5 18.4 19.0 
 
EOTAHY STEAM-ENGINES STEAM TTJEBINES. 1093 
 
 Steam Consumption of Small Steam Turbines. Small turbines, 
 from 5 to 200 H.P., are extensively used for purposes where high speed of 
 rotation is not an objection, such as for driving electric generators, cen- 
 trifugal fans, etc., and where economy of fuel is not as important as 
 saving of space, convenience of operation, etc. The steam consump- 
 tion of these turbines varies as greatly as does that of small high-speed 
 steam-engines, according to the design, speed, etc. A paper by Geo. A. 
 Orrok in Trans. A. S. M. E., 1909, discusses the details of several makes 
 of machines. From a curve presented by R. H. Rice in discussion of 
 this paper the following figures are taken showing the steam consumption 
 in Ibs. per B.H.P.-hour of different makes of impulse turbines. 
 
 Type. 
 
 Sturte- 
 vant. 
 
 Terry. 
 
 Bliss. 
 
 Bliss. 
 
 Kerr. 
 
 Curtis. 
 
 Curtis. 
 
 Rated H.P 
 
 20 
 
 50 
 
 100 
 
 200 
 
 150 
 
 50 
 
 200 
 
 S to lPuflload.'; 
 
 11 1/4 load. . . 
 
 72 
 65 
 61 
 58 
 
 59 
 
 49 
 
 46 
 44 
 
 58 
 48 
 43 
 40 
 
 55 
 
 47 
 42 
 39 
 
 52 
 44 
 41 
 39 
 
 44 
 36 
 33 
 31 
 
 32 
 30 
 
 29 
 28 
 
 Dry steam, 150 Ibs. pressure; atmospheric exhaust. 
 
 Mr. Orrok shows that the steam consumption of these turbines largely 
 depends on their peripheral speed. From a set of curves plotted with 
 speed as the base it appears that the steam consumption per B.H.P.-hour 
 ranges about as follows: 
 Peripheral speed, ft. 
 
 per min 5,000 10,000 15,000 20,000 25,000 
 
 Steam per B.H.P.-hour 45 to 70 38 to 60 31 to 52 29 to 45 29 to 40 
 
 Low-Pressure Steam Turbines. Turbines designed to utilize the ex- 
 haust steam from reciprocating engines are used to some extent. For 
 steam at or below atmospheric pressure the turbine has a great advan- 
 tage over reciprocating engines in its ability to expand the steam down 
 to the vacuum pressure, while a reciprocating condensing engine generally 
 does not expand below 8 or 10 Ibs. absolute pressure. In order to ex- 
 pand to lower pressures the low-pressure cylinder would have to be 
 inordinately large, and therefore costly, and the increased loss from 
 cylinder condensation and radiation would more than counterbalance 
 the gain due to greater expansion. 
 
 Mr. Parsons (Proc. Inst. Nav. Arch., 1908) gives the following figures 
 showing that the theoretical economy of the combination of a recipro- 
 cating engine and an exhaust steam turbine is about the same whether 
 the turbine receives its steam at atmospheric pressure or at 7 Ibs. abso- 
 lute, the initial steam pressure in the engine being 200 Ibs. absolute and 
 the vacuum 28 ins. 
 
 Back pressure of engines, Ibs. abs 16 131/2 8 
 
 Initial pressure, turbine, Ibs. abs 15 121/2 7 
 
 'in engine 178 189 218 
 
 in turbine 142 . 131 100 
 
 total 320 320 318 
 
 The following figures, by the General Electric Co., show the percentage 
 over the output of a condensing reciprocating engine that may be made 
 by installing a low-pressure turbine between the engine and the con- 
 denser, the vacuum being 281/2 ins. 
 Inches vacuum at admission 
 
 valve 4 8 12 16 20 24 
 
 PC* cent of work gained ... 26.1 26.5 26.8 26.3 25.3 23.6 20 
 
 It appears that a well-designed reciprocating compound engine work- 
 ing down to about atmospheric pressure is a more efficient machine than 
 a turbine with the same terminal pressure, and that between the atmos- 
 phere and the condenser pressure the turbine is far more economical; 
 therefore a combination of an engine and a turbine can be designed 
 which will give higher economy than either an engine or a turbine work- 
 ing through the whole range of pressure. 
 
 B.T.U. 
 
 utilized per Ib. of steam 
 
1094 THE STEAM-ENGINE. 
 
 When engines are run intermittently, such as rolling-mill and hoisting 
 engines, their exhaust steam may be made to run low-pressure turbines 
 by passing it first into a heat accumulator, or thermal storage system, 
 where it gives up its heat to water, the latter furnishing steam continu- 
 ously to the turbines. (See Thermal Storage, pages 927 and 1014.) 
 
 The following results of tests of a Westinghouse low-pressure turbine 
 are reported by Francis Hodgkinson. 
 
 Steam press.. 
 
 Ib. abs 
 
 
 17.4 
 
 12.4 
 
 11.8 
 
 7.7 
 
 5 
 
 .2 
 
 11.6 
 
 8.7 
 
 6.1 
 
 4.5 
 
 Vacuum, 
 
 ins. 
 
 26.0 
 
 26.0 
 
 27.0 
 
 27.0 
 
 27. 
 
 .0 
 
 27.8 
 
 28.0 
 
 27.9 
 
 28.0 
 
 Brake H 
 
 .P.. 
 
 920 
 
 472 
 
 592 
 
 321 
 
 102 
 
 586 
 
 458 
 
 234 
 
 114 
 
 Steam per 
 B.H.P.-hr., 
 
 Ibs 
 
 
 27.9 
 
 37.1 
 
 29.9 
 
 37.3 
 
 64, 
 
 4 
 
 28.0 
 
 30.4 
 
 38.6 
 
 54.8 
 
 Tests of a 1000-K.W. low-pressure double-flow Westinghouse turbine 
 are reported to have given results as 'follows. (Approximate figures, 
 from a curve.) 
 
 Load, Brake H.P 200 400 600 800 1000 1200 1500 2000 
 
 Pressure at inlet, Ibs. 
 
 abs....- 4.1 5.1 6.1 7.2 8.3 9.4 11.0 13.5 
 
 Steam per ) 2?1/2 in yac> ?5 4? 5 3g 33 3Q 2g 26 . 5 24 . 5 
 
 hour Ibs ) 28 in ' vac ' 62 42 33 29 27 25.5 24.5 22.5 
 
 The total steam consumption per hour followed the Wilians law, 
 being directly proportional to the power after adding a constant for 
 load, viz.: for 27i/2-in. vacuum the total steam consumption per hour 
 was 12,000 Ibs. + 18 X H.P., and for 28-in. vacuum, 9000 Ibs. + 18 X 
 H.P. (approx.). 
 
 The guaranteed steam consumption of a 7000-K.W. Rateau-Smoot 
 low-pressure turbine generator is given in a curve by R. C. Smoot (Power, 
 June 22, 1909), from which the following figures are taken. The admis- 
 sion pressure is taken at 16 Ibs. absolute and the vacuum 281/2 ins. 
 
 K.W. output 1500 2000 3000 4000 5000 6000 7000 
 
 Steam per K.W.-hr., Ib.. .. 40 37 32.5 29.5 27.6 26.2 25.7 
 Over-all efficiency, % 43 47 54 60 65 68 70 
 
 The performance of a combined plant of several reciprocating 2000- 
 K.W. engines and a 7000-K.W. low-pressure turbine is estimated as fol- 
 lows, the engines expanding the steam from 215 to"16 Ibs. absolute, and 
 the turbines from 16 Ibs. to 0.75 Ib., the vacuum being 28.5 ins. with 
 the barometer at 30 ins. 
 
 Engine. Turbine. 
 
 Theoretical steam per K.W.-hour, Ibs 18 17.8 
 
 Steam per K.W.-hr. at switchboard, Ibs 27.7 26.6 
 
 Combined efficiency of engine and dynamo, per cent ... 65 67 
 
 Steam per K.W.-hour for combined plant = 1 -i- (1/27.7 4- 1/26.6) = 
 
 13.6 Ibs. 
 
 The combined efficiency is 66%, representing the ratio of the energy 
 at the switchboard to the available energy of the steam delivered to the 
 engine and expanded down to the condenser pressure, after allowing for 
 all losses in engine, turbine, and dynamo. 
 
 Very little difference is made in the plant efficiency if the intermediate 
 pressure is taken anywhere from 3 or 4 Ibs. below atmosphere to 15 or 
 20 Ibs. above. 
 
 M. B. Carroll (Gen. Elec. Rev., 1909) gives an estimate of the steam 
 consumption of a combined unit of a 1000-K.W. engine and a low-pres- 
 sure turbine. The engine, non-condensing, will develop 1000 H.P., 
 with 32,000 Ibs. of steam per hour. Allowing 8% for moisture in the 
 exhaust, 29,440 Ibs. of dry steam will be available for the turbine, which 
 at 33 Ibs. per K.W.-hour will develop 893 K.W., making a total output of 
 1893 K.W. for 32,000 Ibs. steam, or 16.9 Ibs. per K.W.-hour. The engine 
 alone as a condensing engine will develop 1320 K.W. at 24.2 Ibs. per K.W.- 
 hour. The combined unit therefore develops 573 K.W., or 43.5% more 
 than the condensing engine using the same amount of steam. The 
 maximum capacity of the engine, non-condensing, is 1265 K.W., an<i 
 condensing, 1470 K...W,, and of the combined unit 2500 K.W. 
 
INTERNAL-COMBUSTION ENGINES. 1095 
 
 Tests of a 15,000 K.W. Steam-Engine-Turbine Unit are reported 
 by H. G. Stott and R. J. S. Pigott in Jour. A.S.M.E., Mar., 1910. The 
 steam-engine is one of the 7500 K.W. Manhattan type engines at the 59th 
 St. station of the Rapid Transit Co., New York, with two 42-in. horizontal 
 h.p. and two 86-in. vertical l.p. cylinders, and the turbine, also 7500 K.W., 
 is of the vertical three-stage impulse type. The principal results are sum-, 
 marized as follows: An increase of 100% in the maximum capacity and 
 146% in the economical capacity of the plant; a saving of about 85% of 
 the condensed steam for return to the boilers [it was previously wasted]; 
 an average improvement in economy of 13% over the best high-pressure 
 turbine results, and of 2.5% (between 7500 and 15,000 K.W.) over the re- 
 sults obtained by the engine alone; an average thermal efficiency between 
 6500 and 15,500 K.W. of 20.6%. [This efficiency is not quite equal to 
 that reached by triple-expansion pumping engines. See page 806.] 
 
 Reduction Gear for Steam Turbines. Double spiral reduction gears, 
 usually of a ratio of 1 to 10, are used with the DeLaval turbine to obtain 
 a velocity of rotation suitable for dynamos, centrifugal pumps, etc. G. W. 
 Melville and J. H. McAIpine have designed a similar gear, with the pinion 
 carried in a floating frame supported at a single point between the bear- 
 ings to equalize the strain on the gear teeth, for reducing the speed of 
 large horizontal turbines to suitable speeds for marine propellers. A 
 6000 H.P. gear with reduction from 1500 to 300 r.p.m. has given an effi- 
 ciency of 98.5% (Eng'g, Sept. 17; Eng. News, Oct. 21 and Dec. 30, 1909). 
 
 The Fottinger Transformer or Hydraulic Pinion is an apparatus for 
 reducing the speed of a propeller shaft below the speed of the steam- 
 turbine shaft. It consists of a turbine wheel 9r water motor, mounted 
 on the end of the propeller shaft, and a centrifugal pump mounted on 
 the shaft of the steam turbine. The water is delivered by the pump 
 to the motor and from the motor it passes to a tank and thence to the 
 inlet of the pump. The ratio of reduction is determined by the design 
 of the turbine and pump. The ratios hitherto applied range from 1.2:1 
 to 6:1. Reversing is accomplished by means of a second turbine on 
 the propeller shaft, a valve directing the water to either the ahead or 
 astern turbine as required. Hydraulic pinions transmitting 10,000 
 shaft horse-power have shown an over-all efficiency of about 92 per cent. 
 An illustrated description will be found in Engineering of Sept. 25, 1914. 
 
 HOT-AIR ENGINES. 
 
 Hot-air (or Caloric) Engines. Hot-air engines are used to some 
 extent, but their bulk is enormous compared with their effective power. 
 For an account of the largest hot-air engine ever built (a total failure) see 
 Church's Life of Ericsson. For theoretical investigation, see Rankin'3 
 Steam-engine and Roentgen's Thermodynamics. For description of con- 
 structions, see Appleton's Cyc. of Mechanics and Modern Mechanism, and 
 Babcock on Substitutes for Steam, Trans. A. S. M. E., vii, p. 693. 
 
 Test of a Hot-air Engine (Robinson). A vertical double-cylinder 
 (Caloric Engine Co.'s) 12 nominal H.P. engine gave 20.19 I. H.P. in the 
 working cylinder and 11.38 I. H.P. in the pump, leaving 8.81 net I.H.P.; 
 while the effective brake H.P. was 5.9, giving a mechanical efficiency of 
 67%. Consumption _of. coke, 3.7 Ibs. per brake. H.P. per hour. Mean 
 pressure on pistons 15.37 Ibs. per square inch, and in pumps 15.9 Ibs., the 
 area of working cylinders being twice that of the pumps. The air was 
 supplied about 1160 F. and rejected at end of stroke about 890 F. 
 
 INTERNAL-COMBUSTION ENGINES. 
 
 References. For theory of the internal-combustion engine, see 
 paper by Dugald Clerk, Proc. Inst. C. E., 1882, vol. Ixix; and Van 
 Nostrand's Science Series, No. 62. See also Wood's Thermodynamics; 
 Standard works on gas-engines are " A Text-book on Gas, Air, and Oil 
 Engines," by Bryan Donkin; "The Gas and Oil Engine," by Dugald 
 Clerk; "Internal Combustion Engines," by Carpenter and Diederichs; 
 " Gas Engine Design," by C. E. Lucke; "Gas and Petroleum Engines," 
 by W. Robinson; "The Modern Gas Engine and the Gas Producer," by 
 A. M. Levin, and "The Gas Engine," by C. P. Poole. r * For prac- 
 tical operation cf gas and oil engines, see "The Gas Engine, by 
 F. {I, Jones, and "Tlie Gas Engine Handbook," by , w, 
 
1096 INTERNAL-COMBUSTION ENGINES. 
 
 For descriptions of large gas-engines using blast furnace gas see papers 
 in Proc. Iron and Steel Inst., 1906, and Trans. A. I. M. E., 1906. Many 
 papers on gas-engines are in Trans. A.8.M.E., 1905 to 1909. 
 
 An Internal-combustion Engine is an engine in which combustible 
 gas, vapor, or oil is burned in a cylinder, generating a high temperature 
 and high pressure in the gases of combustion, which expand behind a 
 piston, driving it forward. ^Rotary gas-engines or gas turbines, are still, 
 1915, in the experimental stage.) 
 
 Four-cycle and Two-cycle Gas-Engines. In the ordinary type of 
 single-cylinder gas-engine (for example the Otto) known as a four-cycle 
 engine, one ignition of gas takes place in one end of the cylinder every 
 two revolutions of the fly-wheel, or every two double strokes. The fol- 
 lowing sequence of operations takes place during four consecutive strokes: 
 (a) inspiration of a mixture of gas and air during an entire stroke; (6) 
 compression during the second (return) stroke; (c) ignition at or near the 
 dead-point, and expansion during the third stroke; (d) expulsion of the 
 burned gas during the fourth (return) stroke. Beau de Rochas in 1862 
 laid down the law that there are four conditions necessary to realize the 
 best results from the elastic force of gas: (1) The cylinders should have 
 the greatest capacity with the smallest circumferential surface; (2) the 
 speed should be as high as possible; (3) the cut-off should be as early as 
 possible; (4) the initial pressure should be as high as possible. 
 
 (Strictly speaking four-cycle should be called four-stroke-cycle, but the 
 term four-cycle is generally used in the trade.) 
 
 The two great sources of waste in gas-engines are: 1. The high tempera- 
 ture of the rejected products of combustion; 2. Loss of heat through the 
 cylinder walls to the water-jacket. As the temperature of the water- 
 jacket is increased the efficiency of the engine becomes higher. 
 
 Fig. 178 is an indicator diagram of a four-cycle gas-engine. AB, the 
 lower line, shows the admission of the mixture, at a pressure slightly 
 below the atmosphere on account of the re- 
 sistance of the inlet valve, EC is the com- 
 pression into the clearance space, ignition 
 taking place at C and combustion with 
 increase of pressure continuing from C to D. 
 The gradual termination of the combustion 
 is shown by the rounded corner at D. DE 
 is the expansion line, EF the line of pressure 
 drop as the exhaust valve opens, and FA the 
 w p line of expulsion of the burned gases, the 
 * ^ pressure being slightly above the atmos- 
 A T? T ^ i no B phere on account of the resistance of the 
 
 * IG ' 178> exhaust valve. 
 
 In a two-cycle single-acting engine an explosion takes place with every 
 revolution, or with each forward stroke of the piston. Referring to the 
 diagram Fig. 178 and beginning at E, when the exhaust port begins to 
 open to allow the burned gases to escape, the pressure drops rapidly to F. 
 Before the end of the stroke is reached an inlet port opens, admitting 
 a mixture of gas and air from a reservoir in which it has been compressed. 
 This mixture being under pressure assists in driving the burned gases 
 out through the exhaust port. The inlet port and the exhaust port close 
 early in the return stroke, and during the remainder of the stroke BC 
 the mixture, which may include some of the burned gas, is compressed and 
 the ignition takes place at C, as in the four-cycle engine. 
 
 In one form of the two-cycle engine only compressed air is admitted 
 while the exhaust port is open, the fuel gas being admitted under pressure 
 after the exhaust port is closed. By this means a greater proportion ol 
 the burned gases are swept out of the cylinder. This operation is known 
 as " scavenging." 
 
 Theoretical Pressures and Temperatures in Gas-Engines. Referring 
 to Fig. 178, let P s be the absolute pressure at B, the end of the suction 
 stroke, P c the pressure at C, the end of the compression stroke; P^the 
 maximum pressure at D, when the gases of combustion are at their 
 highest temperature; P e the pressure at E, when the exhaust valve begii 
 to open For the hypothetical case of a cylinder with walls incapable of 
 absorbing or conducting heat, and of perfect and instantaneous combustion 
 
INTEKNAL COMBUSTION ENGINES. lOlJ? 
 
 or explosion of the fuel, ail ideal diagram might be constructed which 
 would have the following characteristics. In a four-cycle engine receiv- 
 ing a charge of air and gas at atmospheric pressure and temperature, 
 the pressure at B, or P s , would be 14.7 Ibs. per sq. in. absolute, and the 
 temperature say 62 F. f or 522 absolute. The pressure at C, or P c , would 
 depend on the ratio V t -i- Vz, V\ being the original volume of the mixture 
 in the cylinder before compression, or the piston displacement plus the 
 volume of the clearance space, and Vz the volume after compression, or 
 the clearance volume, and its value would be P c = P s (Vi/Vz) n . The 
 absolute temperature at the end of compression would be T c = 522 X 
 ( IV F 2 ) n ~\ or it may be found from the formula P S F 5 -H T s = P C V C + T c , 
 the subscripts s and c referring respectively to conditions at the beginning 
 and end of compression. The compression would be adiabatic, and the 
 value of the exponent n would be about the value for air, or 1.406. The 
 work done in compressing the mixture would be calculated by the formula 
 for compressed air (see page 634). The theoretical rise of tempera- 
 ture at the end of the explosion, T x , above the temperature at the end of 
 the compression T c may be found from the formula (T x - T c ) C v = H, 
 in which // is the amount of heat in British thermal units generated by 
 the combustion of the fuel in 1 Ib. of the mixture, and C v the mean specific 
 heat, at constant volume, of the gases of combustion between the tem- 
 peratures T x and T c . Having obtained the temperature, the correspond- 
 
 n 
 
 Ing pressure P x may be found from the formulaP^ = P C X (T x /T c } n ~' i . 
 In like manner the pressure and temperature at the end of expansion, 
 P e and T e , and the work done during expansion, may be calculated by 
 the formula for adiabatic expansion of air. 
 
 The ideal diagram of the adiabatic compression of air, instantaneous 
 heating, and adiabatic expansion, differs greatly from the actual diagram 
 of a gas-engine, and the pressures, temperatures, and amount of work 
 done are different from those obtained by the method described above. 
 In the first place the mixture at the beginning of the compression stroke 
 is usually below atmospheric pressure, on account of the resistance of 
 the inlet valve, in a four-cycle engine, but may be above atmospheric 
 pressure in a two-cycle engine, in which the mixture is delivered from a 
 receiver under pressure. Then the temperature is much higher than 
 that of the atmosphere, since it is heated by the walls of the cylinder 
 as it enters. The compression is not adiabatic, since heat is received 
 from the walls during the first part of the stroke. If the clearance space 
 is small and the pressure and temperature at the end of compression there- 
 fore high, the gas may give up some heat to the walls during the latter 
 part of the stroke. The explosion is not instantaneous, and during its 
 continuance heat is absorbed by the cylinder walls, and therefore neither 
 the temperature nor the pressure found by calculation will be actually 
 reached. Poole states that the rise in temperature produced by com- 
 bustion is from 0.4 to 0.7 of what it would be with instantaneous com- 
 bustion and no heat loss to the cylinder walls. Finally the expansion 
 is not adiabatic, as the gases of combustion, at least during the first part 
 of the expanding stroke, are giving up heat to the cylinder. 
 
 Calculation of the Power of Gas-Engines. If the mean effective pres- 
 sure in a gas-engine cylinder be obtained from an indicator diagram, its 
 power is found by the usual formula for steam-engines, H.P. = PLAN + 
 33,000, in which P is the mean effective pressure in Ibs. per sq. in., L the 
 length of stroke in feet, A the area of the piston in square inches, and N 
 the number of explosion strokes per minute. 
 
 For purposes of design, however, the mean effective pressure either 
 has to be assumed from a knowledge of that found in other engines of 
 the same type and working under the same conditions as those of the 
 design, or it may be calculated from the ideal air diagram and modified 
 by the use of -a coefficient or diagram factor depending on the kind of 
 fuel used and the compression pressure. Lucke gives the following 
 
1098 
 
 INTEKNALr-COMBUSTtON ENGINES. 
 
 factors for four-cycle engines by which the mean effective pressure 
 of a theoretical air diagram is to be multiplied to obtain the actual M.E.P. 
 for the several conditions named. 
 
 Kind of Fuel and Method of Use. 
 
 Compres- 
 sion. 
 Gauge 
 Pressure. 
 
 Factor. 
 Per Cent- 
 
 Kerosene when previously vaporized 
 
 Lb. 
 45-75 
 
 30-40 
 
 Kerosene injected on a hot bulb may be as low as 
 
 
 20 
 
 Gasoline used in carburetor requiring a vacuum 
 
 
 25-40 
 
 Gasoline with but little initial vacuum. 
 
 80-130 
 
 50-30 
 
 Producer gas 
 
 100-160 
 
 56-40 
 
 Coal gas . 
 
 Av. 80 
 
 Av. 45 
 
 Blast-furnace gas 
 
 130-180 
 
 48-30 
 
 Natural gas. 
 
 90-140 
 
 52-40 
 
 Factors for two-cycle engines are about O.S those for four-cycle engines. 
 
 Pressures and Temperatures at end of Compression and at Re- 
 lease. The following tables, greatly condensed from very full tables 
 given by C. P. Poole, show approximately the pressures and tempera- 
 tures that may be realized in practice under different conditions. Poole 
 says that the value of n, the exponent in the formula for compression, 
 ranges from 1.2 to 1.38, these being extreme cases; the values most 
 commonly obtained are from 1.28 to 1.35. The tables for compression 
 pressures and temperatures are based on n = 1.3 and 1.4, on compres- 
 sion ratios or Vi/Va from 3 to 8, on absolute pressures in the cylinder 
 before compression from 13 to 16 Ibs., and on absolute temperatures 
 before compression of 620 to 780 (160 to 320 F.). The release pres- 
 sures and temperatures are based on values of n of 1.29 and 1.32, abso- 
 lute pressures at the end of the explosion from 240 to 360 Ibs. per sq. in., 
 and absolute temperatures at the end of the explosion of 1800 to 3000 F. 
 
 COMPRESSION PRESSURES. 
 
 s d *f 
 
 n= 1.3. 
 
 I C n 
 
 n= 1.34. 
 
 
 
 a o.2 
 
 
 o oi 
 
 
 
 P s =13 
 
 13.5 
 
 14 
 
 15 
 
 16 
 
 J"tf 
 
 P s =13 
 
 13.5 
 
 ,4 
 
 15 
 
 16 
 
 3.00 
 
 54.2 
 
 56.3 
 
 58.4 
 
 62.6 
 
 66.7 
 
 3.00 
 
 56.7 
 
 58.9 
 
 61.0 
 
 65.4 
 
 69.7 
 
 4.00 
 
 78.8 
 
 81.9 
 
 84 9 
 
 90.9 
 
 97.0 
 
 4.00 
 
 83.3 
 
 86.5 
 
 89 7 
 
 96.1 
 
 102.5 
 
 5.00 
 
 105.4 
 
 109.4 
 
 113,5 
 
 121.6 
 
 129.7 
 
 5.00 
 
 112.3 
 
 116.7 
 
 121.0 
 
 129.6 
 
 138.3 
 
 6.00 
 
 133.5 
 
 138.7 
 
 143.8 
 
 154.1 
 
 164.3 
 
 6.00 
 
 143.4 
 
 148.9 
 
 154.5 
 
 165.5 
 
 176.5 
 
 7.00 
 
 163.2 
 
 169.4 
 
 175 7 
 
 188.3 
 
 200.8 
 
 7.00 
 
 176.3 
 
 183.1 
 
 189.9 
 
 203.5 
 
 217.0 
 
 8.00 
 
 194.0 
 
 201.5 
 
 209.0 
 
 223.9 
 
 238.7 
 
 8.00 
 
 210.9 
 
 219.0 
 
 227.1 
 
 243.4 
 
 259.6 
 
 COMPRESSION TEMPERATURES. 
 
 Compres- 
 sion 
 Ratio r c . 
 
 n = 1.3, 
 
 Compres- 
 sion 
 Ratio r c . 
 
 n=1.34. 
 
 T 
 
 1 s 
 
 620 
 
 660 
 
 700 
 
 740 
 
 780 
 
 T s = 
 620 
 
 901 
 993 
 1072 
 1140 
 1201 
 1257 
 
 660 
 
 959 
 1057 
 1141 
 1214 
 1279 
 1338 
 
 700 
 
 740 
 
 780 
 
 1133 
 1250 
 1348 
 1434 
 1512 
 1582 
 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 
 862 
 940 
 1005 
 1061 
 1112 
 1157 
 
 918 
 1000 
 1070 
 1130 
 1183 
 1232 
 
 973 
 1061 
 1134 
 1198 
 1255 
 1306 
 
 1029 
 1122 
 1199 
 1267 
 1327 
 1381 
 
 1084 
 1182 
 1264 
 1335 
 1398 
 1456 
 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 
 1017 
 1122 
 1210 
 1287 
 1357 
 1420 
 
 1075 
 1186 
 1279 
 1361 
 1434 
 1501 
 
INTERNAL-COMBUSTION ENGINES. 
 
 1009 
 
 ABSOLUTE PRESSURES PER SQUARE INCH AT RELEASE. 
 Corresponding to Explosion Pressures commonly obtained. 
 NOTE: The expansipn ratios in the left-hand column are based on 
 the volume behind the piston when the exhaust valve begins to open. 
 
 "w ** 
 
 n e =1.29. 
 
 a 
 _o ^ 
 
 n.-IJ2. 
 
 K "^ 
 
 Value of Pa- 
 
 a-| 
 
 Value of P x 
 
 p4 
 
 240 270 300 330 360 
 
 &# 
 
 240 270 300 330 360 
 
 3.00 
 
 58.2 
 
 65.4 
 
 72.7 
 
 80.0 
 
 87.2 
 
 3 00 
 
 56.3 
 
 63 3 
 
 70.4 
 
 77.4 
 
 84.4 
 
 4.00 
 
 40.1 
 
 45.2 
 
 50.2 
 
 55.2 
 
 60.2 
 
 4.00 
 
 38.5 
 
 43.3 
 
 48.1 
 
 52.9 
 
 57.8 
 
 5.00 
 
 30.1 
 
 33.9 
 
 37.6 
 
 41.4 
 
 45.1 
 
 5 00 
 
 28.7 
 
 32.3 
 
 35.8 
 
 39.4 
 
 43.0 
 
 6.00 
 
 23.8 
 
 26.8 
 
 29.7 
 
 32.7 
 
 35.7 
 
 6.00 
 
 22.5 
 
 25.4 
 
 28.2 
 
 31.0 
 
 33.8 
 
 7.00 
 
 19.5 
 
 21.9 
 
 24.4 
 
 26.8 
 
 29.2 
 
 7 00 
 
 18.4 
 
 20.7 
 
 23.0 
 
 25.3 
 
 27.6 
 
 8.00 
 
 16.4 
 
 18.5 
 
 20.5 
 
 22.6 
 
 24.6 
 
 8.00 
 
 15.4 
 
 17.3 
 
 19.3 
 
 21.2 
 
 23.1 
 
 ABSOLUTE TEMPERATURES AT RELEASE. 
 Corresponding to Explosion Temperatures commonly obtained. 
 
 Expansion 
 Ratio r e . 
 
 n e =1.29. 
 
 Expansion 
 Ratio r e . 
 
 n e =1.32. 
 
 Value of T x 
 1800 2100 2400 2700 3000 
 
 Value of T x 
 1800 2100 2400 2700 3000 
 
 3 00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 
 1309 
 1204 
 1129 
 1070 
 1024 
 985 
 
 1527 
 1405 
 1317 
 1249 
 1194 
 1149 
 
 1745 
 1606 
 1505 
 1427 
 1365 
 1313 
 
 1963 
 1806 
 1693 
 1606 
 1536 
 1477 
 
 2182 
 2007 
 1881 
 1784 
 1706 
 1641 
 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 
 1266 
 1155 
 1075 
 1015 
 966 
 925 
 
 1478 
 1348 
 1255 
 1184 
 1127 
 1079 
 
 1689 
 1540 
 1434 
 1353 
 1288 
 1234 
 
 1900 
 1733 
 1613 
 1522 
 1449 
 1388 
 
 2111 
 1925 
 1792 
 1691 
 1610 
 1542 
 
 Pressures and Temperatures after Combustion. According to 
 Poole, the maximum temperature after combustion may be as high as 
 3000 absolute, F., and the maximum pressure as high as 400 Ibs. per 
 sq. in. absolute; these are high figures, however, the more usual figures 
 being about 2300 and 250 Ibs. Poole gives the following figures for 
 the average rise in pressure, above the pressure at the end of compres- 
 sion, produced by combustion of different fuels, with different ratios of 
 compression. 
 
 AVERAGE PRESSURE RISE IN LBS. PER SQ. IN. PRODUCED BY 
 COMBUSTION. 
 
 4 
 A 
 
 d 
 
 1 
 
 Ilium. Gas 
 650B.T.U.* 
 
 Gasoline. 
 
 o 
 
 0> 
 
 M 
 
 4 
 
 3 
 
 d 
 1 
 
 Natural Gas 
 1000 B.T.U.* 
 
 t o 
 
 eg 
 K 
 
 d 
 
 1 
 
 Producer Gas 
 150B.T.U.* 
 
 .2 
 
 I 
 
 d 
 1 
 
 Blast-Furnace 
 Gas 
 100 B.T.U.* 
 
 4.0 
 4.2 
 4.4 
 4.6 
 4.8 
 5.0 
 
 146 
 156 
 166 
 175 
 185 
 195 
 
 195 
 208 
 221 
 234 
 247 
 260 
 
 168 
 179 
 190 
 202 
 213 
 224 
 
 5.0 
 5.2 
 5.4 
 5.6 
 5.8 
 6.0 
 
 192 
 202 
 211 
 221 
 230 
 240 
 
 6.0 
 6.2 
 6.4 
 6.6 
 6.8 
 7.0 
 
 225 
 234 
 243 
 252 
 261 
 270 
 
 7.0 
 7.2 
 7.4 
 7.6 
 7.8 
 8.0 
 
 211 
 
 218 
 225 
 232 
 239 
 246 
 
 * Per cubic foot measured at 32 F. 
 The following figures are given by Poole as a rough approximate 
 ide to the mean effective pressures iu Ibs. per sq. in. obtained with 
 
1100 
 
 INTERNAL-COMBUSTION ENGINES. 
 
 different fuels and different compression pressures in a four-cycle engine. 
 In a two-cycle engine the mean effective pressure of the pump diagram 
 should be subtracted. The delivery pressure is usually from 4 to 8 Ibs. 
 per sq. in. above the atmosphere, and the corresponding mean effective 
 pressure of the pump about 3.8 to 7. 
 
 PROBABLE MEAN EFFECTIVE PRESSURE. 
 
 SUCTION ANTHRACITE PRODUCER GAS. 
 
 MOND PRODUCER GAS. 
 
 Engine 
 
 Compression Pressure, 
 abs. Ibs. per sq. in. 
 
 Engine 
 H.P. 
 
 Compression Pressure. 
 
 too 
 
 115 
 
 130 
 
 145 
 
 160 
 
 100 
 
 115 
 
 130 
 
 145 
 
 160 
 
 10 
 25 
 50 
 100 
 250 
 500 
 
 55 
 60 
 65 
 70 
 75 
 80 
 
 60 
 65 
 70 
 75 
 80 
 85 
 
 65 
 
 70 
 75 
 
 80 
 85 
 90 
 
 75 
 80 
 85 
 90 
 90 
 
 80 
 85 
 90 
 90 
 
 10 
 25 
 50 
 100 
 250 
 500 
 
 60 
 65 
 65 
 70 
 75 
 
 65 
 65 
 70 
 70 
 75 
 80 
 
 65 
 65 
 70 
 
 75 
 80 
 85 
 
 65 
 
 70 
 75 
 80 
 85 
 90 
 
 75 
 80 
 85 
 90 
 90 
 
 NATURAL AND ILLUMINATING GASES. 
 
 Engine 
 
 Compression Pressure. 
 
 Engine 
 H.P. 
 
 Compression Pressures. 
 
 65 
 
 75 
 
 85 
 
 100 
 
 115 
 
 75 
 
 85 
 
 100 
 
 115 
 
 130 
 
 10 
 25 
 50 
 
 60 
 65 
 70 
 
 65 
 70 
 75 
 
 70 
 75 
 80 
 
 75 
 80 
 90 
 
 85* 
 90 
 
 100 
 250 
 500 
 
 80 
 85 
 
 85 
 90 
 95 
 
 90 
 95 
 100 
 
 95 
 100 
 105 
 
 100 
 105 
 110 
 
 KEROSENE SPRAY. 
 
 GASOLINE VAPOR. 
 
 Engine 
 H.P. 
 
 ^ 
 
 Compression Pressures. 
 
 Engine 
 H.P. 
 
 Compression Pressures. 
 
 65 
 
 75 
 
 85 
 
 100 
 
 115 
 
 65 
 
 70 
 75 
 80 
 85 
 
 75 
 
 85 
 
 80 
 85 
 90 
 95 
 
 100 
 
 85 
 90 
 90 
 95 
 
 
 
 5 
 
 10 
 25 
 50 
 
 50 
 55 
 60 
 65 
 
 55 
 60 
 65 
 70 
 
 60 
 65 
 70 
 75 
 
 65 
 70 
 75 
 80 
 
 70 
 75 
 80 
 85 
 
 5 
 
 10 
 25 
 50 
 
 75 
 80 
 85 
 90 
 
 Sizes of Large Gas Engines. From a table of sizes of the Nu'rnberg 
 gas engine, as built by the Allis-Chalmers Co., the following figures are 
 taken. These figures relate to two-cylinder tandem double-acting engines. 
 
 Diam. cyl., ins 
 Stroke cyl., ins 
 Revs, per min 
 
 18 
 24 
 150 
 
 20 
 24 
 150 
 
 21 
 30 
 125 
 
 22 
 30 
 125 
 
 24 
 
 30 
 125 
 
 24 
 36 
 115 
 
 26 
 36 
 115 
 
 28 
 36 
 115 
 
 30 
 42 
 100 
 
 32 
 42 
 100 
 
 Piston speed, ft. per 
 min 
 
 600 
 
 600 
 
 625 
 
 625 
 
 625 
 
 690 
 
 690 
 
 690 
 
 700 
 
 700 
 
 Rated B.H.P 
 
 260 
 
 320 
 
 370 
 
 405 
 
 490 
 
 545 
 
 630 
 
 740 
 
 855 
 
 985 
 
 Factor C 
 
 Diam., ins 
 Stroke, ins 
 
 0.8 
 
 34 
 
 42 
 
 0.8 
 
 36 
 48 
 
 0.84 
 
 38 
 48 
 
 0.84 
 
 40 
 
 48 
 
 0.85 
 
 42 
 54 
 
 0.95 
 
 44 
 
 54 
 
 0.93 
 
 46 
 54 
 
 0.94 
 
 48 
 60 
 
 0.95 
 
 50 
 60 
 
 0.96 
 
 52 
 62 
 
 Revs, per min . 
 
 100 
 
 92 
 
 92 
 
 92 
 
 86 
 
 86 
 
 86 
 
 78 
 
 78 
 
 78 
 
 Piston speed... 
 
 700 
 
 736 
 
 736 
 
 736 
 
 774 
 
 774 
 
 774 
 
 780 
 
 780 
 
 780 
 
 Rated B.H P. 
 
 1105 
 
 1300 
 
 1460 
 
 1630 
 
 1875 
 
 2080 
 
 2280 
 
 2475 
 
 2720 
 
 2950 
 
 Factor C... 
 
 0.96 
 
 1 
 
 1.01 
 
 1.02 
 
 1.0ft 
 
 1.07 
 
 1 08 
 
 1.07 
 
 1.09 
 
 1 Oft 
 
 The figures "factor C" are the values of C in the equation B.H.P. = 
 C X -D 2 , in which D = diam. of cylinder in ins. For twin-cylinder double- 
 acting engines, multiply the B.H.P. and the value of C by 0.95; for twin- 
 
INTEKNAL-COMBTISTION ENGINES. 
 
 ,1101 
 
 tandem double-acting engines, multiply by 2; for two-cylinder single- 
 acting, or for single-cylinder double-acting engines, divide by 2; for 
 single-acting single-cylinders, divide by 4. The figures for B.H.P. corre- 
 spond to mean effective pressures of about 66, 68, and 70 Ibs. per sq. in. 
 for 20, 40, and 50 in. cylinders respectively if we assume 0.85 as the me- 
 chanical efficiency, or the ratio B.H.P. * I.H.P. 
 
 .Engine Constants for Gas Engines. The following constants for 
 figuring the brake H.P. of gas engines are given in Power, Dec. 7, 1909. 
 They refer to four-stroke cycle single-cylinder engines, single acting; for 
 double-acting engines multiply by 2. Producer gas, 0.000056. Illumi- 
 nating gas, 0.000065. Natural gas, 0.00007. Constant X diam. 2 X stroke 
 in ins. X revs, per min.= probable B.H.P. A deduction should be made 
 for the space occupied by the piston rods, about 5% for small engines up 
 to 10% for very large engines. 
 
 Rated Capacity of Automobile Engines. The standard formula for 
 the American Licensed Automobile Manufacturers Association (called 
 the A. L. A. M. formula) for approximate rating of gasoline engines 
 used in automobiles is Brake H.P. = Diam. 2 X No. of cylinders -* 2.5. 
 It is based on an assumed piston speed of 1000 ft. per min. The following 
 ratings are derived from the formula: 
 
 Bore, ins ......... 2 1/2 3 3 1/2 
 
 Bore, mm ......... 64 76 89 
 
 H. P., 1 cylinder... . 2V2 3.6 4.9 
 
 9.8 
 
 19.6 
 
 29.4 
 
 . ., .. 
 
 H.P., 2 cylinders... 
 H.P., 4 " ... 
 H.P., 6 " ... 
 
 5 
 
 10 
 15 
 
 . 
 7.2 
 
 14.4 
 21.6 
 
 4 
 102 
 
 6.4 
 12.8 
 
 25.6 
 38. 
 
 4V 2 
 114 
 8.1 
 16.2 
 
 ?2 ~: 4 6 
 
 5 
 
 127 
 10 
 20 
 
 5V2 
 140 
 12.1 
 
 24.2 
 
 4 48 
 
 6 
 
 154 
 
 14.4 
 
 28.8 
 
 57.6 
 
 86.4 
 
 A committee of the Institution of Automobile Engineers recommends 
 the following formula: B.H.P. = 0.45 (d + s) (d - 1.18)N, in which 
 d = diam., in., s = stroke, in., N = number of cylinders. The formula 
 was derived from the results of tests of engines in first-class condition 
 on the test bench. For ordinary engines on the road the result should 
 be multiplied by 0.6. (Eng'g, Feb. 10, 1911.) 
 
 The American Power Boat Association's formula for rating 2-cycle 
 engines is H.P. = area of piston X number of cylinders X length of 
 stroke X 1.5. 
 
 Approximate Estimate of the Horse-power of a Gas Engine.. 
 From the formula I.H.P. = PLAN -* 33,000, in which P= mean effective 
 pressure in Ibs. per sq. in., L = length of stroke in ft., A = area of piston 
 in sq. ins., N = No. of explosion strokes per min., we have I.H.P. = Pd 2 5-*- 
 42,017, in which c/ = diam. of piston, and S = piston speed in ft. per min., 
 for an engine in which there are two explosion strokes in each revolution, 
 as in a 4-cycle double-acting, 2-cylinder engine, or a 2-cycle, 2-cylinder, 
 single-acting engine. If the mechanical efficiency is taken at 0.84. then 
 the brake horse power B.H.p. = Pd*S * 50,000. Under average con- 
 ditions the product of P and S is in the neighborhood of 50,000, and in 
 that case B.H.P. = d 2 . -Generally, B.H.P. = CX d 2 , in which C is a 
 coefficient having values as below: 
 
 M.E.P. 
 Lbs. per 
 Sq. In. 
 
 Piston Speed, Ft. per Minute. 
 
 500 600 700 800 900 1000 
 
 Value of C for Two Explosions per Revolution. 
 
 150 
 60 
 70 
 80 
 90 
 100 
 110 
 
 0.50 
 0.60 
 0.70 
 0.80 
 0.90 
 1.00 
 1.10 
 
 0.60 
 0.72 
 0.84 
 0.96 
 1.08 
 1.20 
 1.32 
 
 0.70 
 0.84 
 0.98 
 1.12 
 1.26 
 1.40 
 1.54 
 
 0.80 
 0.96 
 .12 
 .28 
 .44 
 .60 
 .76 
 
 0.90 
 .08 
 .26 
 .44 
 .62 
 .80 
 .98 
 
 1.00 
 1.20 
 1.40 
 1.60 
 1.80 
 2.00 
 2.20 
 
 
 These values of C apply to 4-cylinders, 4-cycle, single-acting, to 2- 
 cyl., 2-cycle, single-acting, and to 1-cyl., 2-cycle double-acting. For 
 single cylinders, 4-cycle, single-acting, divide by 4; for single cylinders, 
 4-cycle, double-acting, or 2-cycle, single-acting, divide by 2. 
 
 Oil and Gasoline Engines. The lighter distillates of petroleum, such 
 as gasoline, are easily vaporized at moderate temperatures, and a gaso- 
 line engine differs from a gas-engine only in having an atomizer attached, 
 
1102 INTERNAL-COMBUSTION ENGINES. 
 
 for spraying a fine jet of the liquid into the air-admission pipe. With 
 kerosene and other heavier distillates, or crude oils, it is necessary to 
 provide some method of atomizing and vaporizing the oil at a high 
 temperature, such as injecting it into a hot vaporizing chamber at the 
 end of the cylinder, or into a chamber heated by the exhaust gases. 
 1 The Diesel Oil Engine. The distinguishing features of the Diesel 
 engine are: It compresses air only, to a predetermined temperature above 
 the firing point of the fuel. This fuel is blown as a cloud of vapor (by 
 air from a separate small compressor) into the cylinder when compres- 
 sion has been completed, ignites spontaneously without explosion, 
 solely by reason of the heat of the air generated by the compression, 
 and burns steadily with no essential rise in pressure. The temperature 
 of gases, developed and rejected, is much lower than with engines of the 
 explosive type. The engine uses crude oil and residual petroleum prod- 
 ucts. Guarantees of fuel consumption are made as low as 8 gallons of 
 oil (not heavier than 19 Baume) for each 100 brake H.P. hour at any 
 load between half and full rated load. 
 
 American Diesel engines are built for stationary purposes, in sizes of 
 120, 170, and 225 H.P. in three cylinders, and in "double units" (six 
 cylinders) of 240, 340 and 450 H.P. See catalogue of the American 
 Diesel Engine Co., St. Louis, 1909. 
 
 Much larger sizes have been built in Europe, where they are also 
 built for marine purposes, including submarines in the French and other 
 navies. For the theory of the Diesel engine see a lecture by Rudolph 
 Diesel, in Zeit. des Ver Deutscher Ing., 1897, trans, in Progressive Age, 
 Dec. 1 and 15, 1897, and paper by E. D. Meier in Jour. Frank. Inst. t 
 Oct. 1898. 
 
 The De La Vergne Oil Engine is described in Eng. News, Jan. 13, 1910. 
 It is a four-cycle engine. After the charge of air is compressed to about 
 200 Ibs. per sq. in., the charge of oil is injected, by a jet of air at about 
 600 Ibs. per sq. in., into a vaporizing bulb at the end of the cylinder. Ig- 
 nition of the oil is caused by the high temperature in this bulb. Average 
 results of tests of an engine developing 128 H.P. showed an oil consump- 
 tion per B.H.P. hour of 0.408 Ib. with Solar fuel oil, and 0.484 Ib. with 
 California crude oil. 
 
 Alcohol Engines. Bulletin No. 392 of the U.S. Geol. Survey (1909,) 
 on Comparisons of Gasolene and Alcohol Tests in Internal Combustion 
 Engines, by R. M. Strong, contains the following conclusions: 
 
 The "low" heat value of completely denatured alcohol will average 
 10,500 B.T.U. per Ib., or 71,900 B.T.U. per gallon. The low heat value 
 of 0.71 to 0.73 sp. gr. gasolene will average 19,200 B.T.U. per Ib., or 
 115,800 B.T.U. per gallon. 
 
 A gasolene engine having a compression pressure of 70 Ibs. but other- 
 wise as well suited to the economical use of denatured alcohol as gasolene, 
 will, when using alcohol, deliver about 10% greater maximum power 
 than when using gasolene. 
 
 When the fuels for which they are designed are used to an equal advan- 
 tage, the maximum B.H.P. of an alcohol engine having a compression 
 pressure of 180 Ibs. is about 30% greater than that of a gasolene engine 
 of the same size and speed having a compression pressure of 70 Ibs. 
 
 Alcohol diluted with water in any proportion, from denatured alcohol, 
 which contains about 10% water, to mixtures containing about as much 
 water as denatured alcohol, can be used in gasolene and alcohol engines if 
 the engines are properly equipped and adjusted. 
 
 When used in an engine having constant compression, the amount of 
 pure alcohol required for any given load increases and the maximum 
 available horse- power of the engine decreases with diminution in the 
 percentage of pure alcohol in the diluted alcohol supplied. The rate of 
 increase and decrease, respectively, however, is such that the use of 
 80% alcohol instead of 90% has but little effect upon the performance; 
 so that if 80% alcohol can be had for 15% less cost than 90% alcohol and 
 could be sold without tax when denatured, it would be more economical 
 to use the 80% alcohol. 
 
 Ignition. The "hot-tube" method of igniting the compressed mixture 
 of gas and air in the cylinder is practically obsolete, and electric systems 
 are used instead, Of these the " make-and-break " and the " jump- 
 Spark " systems are in common use, In the former two insulated contact 
 
INTEKNAIi-COMBUSTiON ENGINES. 1103 
 
 pieces are located in the end of the cylinder, and through them an electric 
 current passes while they are in contact. A spark-coil is included in the 
 circuit, and when the circuit is suddenly broken at the proper time for 
 ignition, by mechanism operated from the valve-gear shaft, a spark is 
 made at the contacts, which ignites, the gas. In the "jump-spark" 
 system two insulated terminals separated about 0.03 in. apart are located 
 in the cylinder, and the secondary or high-tension current of an induction 
 coil causes a spark to jump across the space between them when the 
 circuit of the primary current is closed by mechanism operated by the 
 engine. In some oil engines the mixture of air and oil vapor is ignited 
 automatically by the temperature generated by compression of the vapor, 
 in a chamber at the end of the cylinder, called the vaporizer, which is 
 not water-jacketed and therefore is kept hot by the repeated ignitions. 
 Before starting the engine the vaporizer is heated by a Bunsen burner 
 or other means. 
 
 Timing. By adjusting the cam or other mechanism operated by the 
 valve-gear shaft for causing ignition, the time at which the ignition takes 
 place, with reference to the end of the compression stroke, can be regulated. 
 The mixture is usually ignited before the end of the stroke, the advance 
 depending upon the inflammability of the mixture and on the speed of 
 the engine. A slow-burning mixture requires to be ignited earlier than 
 a rapid-burning one and a high-speed earlier than a slow-speed engine, 
 
 Governing. - Two methods of governing the speed of an engine are 
 in common use, the " hit-and-miss " and the throttling methods. In the 
 former the engine receives its usual charge of air and gas only when the 
 engine is running at or below its normal speed; at higher speeds the ad- 
 mission of the charge is suspended until the engine regains its normal 
 speed. One method of accomplishing this is to interpose between the 
 valve-rod and its cam or other operating mechanism, a push-rod, or 
 other piece, the position of which with reference to the end of the valve- 
 rod is controlled by a centrifugal governor so that it hits the valve-rod if 
 the speed is at or below normal and misses it if the speed is above normal. 
 The hit-and-miss method is economical of fuel, but it involves irregularity 
 of speed, making a large and heavy fly-wheel necessary if reasonable 
 uniformity of speed is desired. The throttling method of regulating is 
 similar to that used in throttling steam engines; the quantity of mixture 
 admitted at each charge being varied by varying the position of a butter- 
 fly valve in the inlet pipe. Cut-off methods of governing are also used, 
 such as varying the time of closing the admission valve during the suction 
 stroke, or varying the time of admission of the gas alone, or " quality 
 regulation." 
 
 Gas and Oil Engine Troubles. The gas engine is subject to a 
 greater number of troubles than the steam engine on account of its greater 
 mechanical complexity and of the variable quality of its operating fluid. 
 Among the causes of troubles are: the variable composition of the fuel; 
 too much or too little air supply; compression ratio not right for the 
 kind of fuel; ignition timer set too late or too early; pre-ignition; back- 
 firing; electrical and mechanical troubles with the igniting system; 
 carbon deposits in the cylinder and on the igniting contacts. For a very 
 full discussion of these and many other troubles and the remedies for 
 them, see Jones on the Gas-Engine. 
 
 Conditions of Maximum Efficiency. The conditions which appear 
 to give the highest thermal efficiency in gas and oil engines are: 1, high 
 temperature of cooling water in the jackets; 2, high pressure at the end 
 of compression; 3, lean mixture; 4, proper timing of the ignition; 5, 
 maximum load. The higher economy of a lean mixture may be due to 
 the fact that high compressions may be used with such a mixture, while 
 with rich mixtures high compression pressures cannot be used without 
 danger of pre-ignition. The effect of different timing on economy is 
 shown in a test by J. R. Bibbins, reported by Carpenter and^)iederichs, of 
 an engine using natural gas of a lower heating value* of 934 B.T.U. per 
 cu. ft., delivering 71 H.P. at 297 revs, per min. The maximum thermal 
 efficiency, 23.3%, was obtained when the timing device was set for igni-- 
 
 * By "lower heating value" is meant the value computed after sub- 
 tracting the latent heat of evaporation of 9 Ibs. of water per pound of 
 hydrogen contained in the gas. bee page 561. 
 
1104 
 
 INTERNAL-COMBUSTION ENGINES. 
 
 tlon 30 in advance of the dead center, while the efficiency with ignition 
 at the center was 19%, and with ignition 55 in advance 17.3%. 
 
 Other things being equal, the hotter the walls of the cylinder the less 
 heat is transferred into them from the hot gases, and therefore the highei 
 the efficiency. Cool walls, however, allow of higher compression without 
 pre-ignition, and high compression is a cause of high efficiency. Cool 
 walls also tend to give the engine greater capacity, since with hot walls 
 the fuel mixture expands more on entering the cylinder, reducing the 
 weight of charge admitted in the suction stroke. 
 
 Heat Losses in the Gas Engine* The difference between the thermal 
 efficiency, which is the proportion of heat converted into work in the 
 engine, and 100%, is the loss of heat, which includes the heat carried away 
 in the jacket water, that carried away in the waste gases, and that lost 
 by radiation. The relative amounts of these three losses vary greatly, 
 depending on the size of the engine and on the amount of water used for 
 cooling. Thurston, in Heat as a Form of Energy, reports a test in which 
 the heat distribution was as follows: Useful work, 17.3%; jacket water, 
 52%; exhaust gas, 16%; radiation, 15%. Carpenter and Diederichs 
 quote the following, showing that the distribution of the heat losses 
 varies with the rate of compression and with the speed. 
 
 Ratio 
 of 
 Com- 
 pres- 
 sion. 
 
 R.p.m. 
 
 M.E.P. 
 
 Ibs. 
 per sq. 
 in. 
 
 Ratio 
 Air to 
 Gas. 
 
 Heat- 
 ing 
 Value 
 of 
 Charge, 
 B.T.U. 
 
 Work 
 done 
 by 1 
 B.T.U., 
 Ft.-lbs. 
 
 Ex- 
 haust 
 Temp. 
 Deg. F. 
 
 Heat Distribution, 
 Per Cent. 
 
 Work. 
 
 Jacket 
 Water. 
 
 Ex- 
 haust. 
 
 2.67 
 
 187 
 
 54.3 
 
 7.11 
 
 18.5 
 
 .140 
 
 1022 
 
 18.0 
 
 51.2 
 
 30.8 
 
 2.67 
 
 247 
 
 51.5 
 
 7.35 
 
 17.4 
 
 141 
 
 1137 
 
 18.1 
 
 45.6 
 
 36.3 
 
 4.32 
 
 187 
 
 69.3 
 
 7.43 
 
 17.0 
 
 190 
 
 867 
 
 24.4 
 
 53.8 
 
 21.8 
 
 4.32 
 
 247 
 
 65.2 
 
 7.40 
 
 16.8 
 
 184 
 
 992 
 
 23.7 
 
 49.5 
 
 26.8 
 
 In the long table of results of tests reported by Carpenter and Diede- 
 richs, figures of the distribution of heat show that of the total heat re- 
 ceived by the engines the heat lost in the jacket water ranged from 25.0 
 to 50.4%, and that lost in the exhaust gases from 55 to 23.4%. 
 
 In small air-cooled gasoline engines, such as those used in some auto- 
 mobile engines, in which the cylinders are surrounded by thin metal 
 ribs to increase the radiating surface, and air is propelled against them 
 by a fan, the air takes the place of the jacket water, and the total loss 
 of heat is that carried away by the air and by the exhaust gases. 
 
 Economical Performance of Gas Engines. The best performance 
 of a gas engine using producer gas (1909) is about 30% better than the 
 best recorded performance of a triple-expansion steam engine, or about 
 0.71 Ib. coal per I.H.P. hour, as compared with 1.06 Ibs. for the steam 
 engine. It is probable that the performance of the combination of a 
 high-pressure reciprocating engine, using superheated steam generated in 
 a well-proportioned boiler supplied with mechanical stokers and an econo- 
 mizer, and a low-pressure steam turbine will ere long reduce the steam 
 engine record to 0.9 Ib. per I.H.P. hour. As compared with an ordinary 
 steam engine, however, the gas engine with a good producer is far more 
 economical than the steam engine. Where gas can be obtained cheaply, 
 such as the waste-gas from blast furnaces, or natural gas, the gas-engine 
 can furnish power much more cheaply than it can be obtained from the 
 same gas burned under a boiler to furnish steam to a steam engine. 
 
 In tests made for the U. S. Geological Survey at the St. Louis Exhibi- 
 tion, 1904, of a 235-H.P. gas engine with different coals, made into gas 
 In the same producer, the best result obtained was 1.12 Ibs. of West 
 Virginia coal per B.H.P. hour, and the poorest result 3.23 Ibs. per B.H.P. 
 hour, with North Dakota lignite. 
 
 A 170-H.P. Crossley (Otto) engine tested in England in 1892, using 
 producer gas, gave a consumption of 0.85 Ib. coal per I.H.P. hour, or a 
 thermal efficiency of engine and producer combined of 21.3%. 
 
 Experiments on a Taylor gas producer using anthracite coal and a 
 
TESTS OF GAS AND OIL ENGINES. 1105 
 
 100-H.P. Otto gas engine showed a consumption of 0.97 Ib. carbon per 
 I.H.P. hour. (Iron Age, 1893.) 
 
 In a table in Carpenter and Diederichs on Internal Combustion Engines 
 the lowest recorded coal consumption per B.H.P. hour is 0.71 Ib., with 
 a Tangye engine and a suction gas producer, using Welsh anthracite coal. 
 Other tests show figures ranging from 0.74 Ib. to 1.95, the last with a 
 Westingnouse 500-H.P. engine and a Taylor producer using Colorado 
 bituminous coal. 
 
 In the same book are given the following figures of the thermal efficiency 
 on brake H.P. with different gas and liquid fuels. Illuminating gas, 
 6 tests, 16.1 to 31.0%; natural gas, 4 tests, 16.1 to 29.0%; coke-oven gas, 
 1 test, 27.5%; Morid gas, 1 test, 23.7%; blast-furnace gas, Stests, 20.4 to 
 28.2%; gasoline, 8 tests, 10.2 to 28%; kerosene, Diesel engine, 3 tests, 
 25. 8 to 31.9%; kerosene, other engines, 8 tests, 9.2 to 19.7%; crude oil, 
 Diesel engine, 1 test, 28.1%; alcohol, 4 tests, 21.8 to 32.7%. 
 
 Tests of Diesel engines operating centrifugal pumps in India are 
 reported in Eng. News, Nov. 25, 1909. Using Borneo petroleum residue 
 of 0.934 sp. gr., and a fuel value of 18,600 B.T.U. per Ib., an average of 
 151 B.H.P. during a season, for a total of 6003 engine hours, was obtained 
 with a consumption of 0.462 Ib. of fuel per B.H.P. hour, or one B.H.P. 
 for about 8600 B.T.U. per hour, equal to a thermal efficiency of 29.5%. 
 The pump efficiency at maximum lift of 14 to 16 ft. was 70%, and the 
 fuel consumption per water H.P. hour at the same lift was 0.7 Ib. 
 
 Utilization of Waste Heat from Gas Engines. The exhaust gases 
 from a gas engine may be used to heat air by passing them across a nest 
 of tubes through which air is flowing. A design of this kind, for heating 
 the Ives library building, New Haven, Conn., by Harrison Engineering 
 Co., New York, is illustrated in Heat, and Vent. Mag., Jan., 1910. 
 
 The waste heat might also be used in a boiler to generate steam at or 
 below atmospheric pressure, for use in a low pressure steam turbine. On 
 account of the comparatively low temperature of the exhaust gases, 
 however, the boiler would require a much greater extent of heating sur- 
 face for a given capacity than a boiler with an ordinary coal-fired furnace. 
 
 RULES FOR CONDUCTING TESTS OF GAS AND OIL 
 ENGINES. 
 
 (Abstract from the A. S. M. E. Code of 1915.) 
 
 Object and Preparations. 
 
 Determine the object, take the dimensions, note the physical condi- 
 tion of the engine and its appurtenances, install the testing appliances, 
 etc., as explained in the general instructions, and make preparations 
 for the test accordingly. 
 
 Operating Conditions. 
 
 Determine what the operating conditions should be to conform 
 to the object in view, and see that they prevail throughout the trial. 
 
 Duration. 
 
 The test of a gas or oil engine with substantially constant load 
 should be continued for such time as may be necessary to obtain a 
 number of successive records covering periods of half an hour or less 
 during which the results are found to be uniform. In such cases a 
 duration of three to five hours is sufficient for all practical purposes. 
 
 Starting and Stopping. 
 
 The engine having been set to work under the prescribed condi- 
 tions, the test is begun at a certain predetermined time by commencing 
 to weigh the oil, or measure the gas, as the case may be, and taking 
 other data concerned; after which the regular measurements and 
 observations are carried forward until the end. 
 
 Calorific Tests and Analyses. 
 
 The quality of the oil or gas should be determined by calorific tests 
 and analyses made on representative samples. 
 
1106 INTERNAL-COMBUSTION ENGINES. 
 
 Calculation of Results. 
 
 The ascertained volume of gas is reduced to the equivalent volume at 
 a temperature of 60 deg. and at atmospheric pressure of 30 in. 
 
 The number of heat units consumed by the engine is found by mul- 
 tiplying the heat units per Ib. of oil or per cu. ft. of gas (higher value), 
 as determined by calorimeter test, by the total weight of oil in Ib. or 
 volume of dry gas in cu. ft. consumed. 
 
 The indicated horse-power, brake horse-power, and efficiency are 
 computed by the same methods as those explained in the Steam Engine 
 Code. 
 
 Heat Balance. 
 
 The various quantities showing the distribution of heat in the heat 
 balance are computed in the following manner: 
 
 The heat converted into work per I.H.P.-hour (2546.5 B.T.U.) is 
 found by dividing the work representing 1 H.P., or 1,980,000 ft.-lb., 
 per hour by the number of ft.-lb. representing 1 B.T.U., or 777.5. 
 
 The heat rejected in the cooling water is obtained by multiplying 
 the weight of water supplied by the number of degrees rise of tem- 
 perature, and dividing the product by the indicated horse-power. 
 
 The heat rejected in the -dry exhaust gases per I.H.P.-hr. is found 
 by multiplying the weight of these gases per I.H.P.-hr. by the sensible 
 heat of the gas reckoned from the temperature of the air hi the room 
 and by its specific heat. The weight of the dry exhaust gases per 
 I.H.P.-hr. is the product of the weight of fuel per I.H.P.-hr. by the 
 weight of the dry gatees per Ib. of fuel. The latter is the product of 
 the proportion of carbon in 1 Ib. of fuel by the weight of the dry gases 
 per Ib. of carbon, which may be found by the formula 
 
 _n_CO2 + 8 O + 7 (CO +JN)__ 
 
 3 (CO 2 + CO) ~ 
 
 in. which CO 2 , O, CO, and N are percentages of the dry exhaust gases 
 by volume. 
 
 When the weight of air supplied per Ib. of fuel is determined the 
 weight of dry gas per pound of fuel may be found by the formula 
 
 1 + Ib. air per Ib. fuel - 9 H 
 in which H te the proportion of hydrogen in 1 Ib. of fuel. 
 
 The heat lost in the moisture formed by the burning of hydrogen 
 in the fuel gas is found by multiplying the total heat of 1 Ib. of super- 
 heated steam at the temperature of the exhaust gases, reckoning from 
 the temperature of the air in the room, by the proportion of the 
 hydrogen in the fuel as determined from the analysis, and multiplying 
 the result by 9. 
 
 The heat lost in superheating the moisture contained in the gas 
 and air is determined by multiplying the difference between the 
 temperature of the exhaust gases and that of the gas and air by the 
 average specific heat of superheated steam for the range of temperature 
 and pressure. 
 
 The heat lost through incomplete combustion is obtained by analyz- 
 ing the exhaust gases and computing the heat of the unburned products 
 wlu'ch would have been produced by their combustion. 
 
 The above rules do not apply to engines with hit-and-miss governors. 
 
 Data and Results. 
 
 The data and results should be reported in accordance with the 
 form given herewith, adding lines for data not provided for, or omitting 
 those not required, as may conform to the object in view. If a shorter 
 form is desired, items designated by letters of the alphabet may be 
 omitted. Unless otherwise indicated, the items should be the aver- 
 ages of the data. 
 
 DATA AND RESULTS OF GAS OR OIL ENGINE TEST. 
 
 Code of 1915. 
 
 1. Test of engine, located at 
 
 To determine 
 
 Test conducted by 
 
TESTS OF GAS AND OIL ENGINES. 1107 
 
 Dimensions, Etc. 
 
 2. Type of engine, whether oil or gas 
 
 3. Class of engine, (mill, marine, motor for vehicle, pumping, or 
 
 other) 
 
 (a) Number of strokes of piston for one cycle, and class of cycle. 
 (6) Method of ignition 
 
 (c) Single or double acting 
 
 (d) Arrangement of cylinders 
 
 (e) Vertical or horizontal 
 
 5. Diameter of working cylinders in. 
 
 6. Stroke of pistons ft. 
 
 4. Rated power H.P 
 
 Date, Duration, Etc. 
 
 7. Date, r- 
 
 8. Duration hr. 
 
 9. Kind of oil or gas 
 
 Average Pressure and Temperature. 
 
 10. Pressure of gas near meter in. 
 
 11. Temperature of gas near meter deg. 
 
 (a) Temperature of cooling water, inlet 
 
 (&) Temperature of cooling water, outlet 
 
 (c) Temperature of air by dry-bulb thermometer .... 
 
 (d) Temperature of air by wet-bulb thermometer .... 
 
 (e) Temperature of exhaust gases at cylinder 
 
 Total Quantities. 
 
 12. Gas or oil consumed cu. ft. or Ib. 
 
 13. Moisture in gas, in per cent by weight, referred to dry gas per cent 
 
 14. Equivalent dry gas at 60 deg. and 30 in cu. ft. 
 
 (a) Air supplied in cu. ft 
 
 15. Cooling water supplied to jackets Ib. 
 
 (a) Water or steam fed to cylinder ' 
 
 16. Calorific value of oil per Ib., or of dry gas per cu. ft. at 
 
 60 deg. and 30 in. by calorimeter test (higher value) . .B.T.U. 
 
 Hourly Quantities. 
 
 17. Gas or oil consumed per hour cu.ft.orlb. 
 
 18. Equivalent dry gas per hour at 60 deg. and 30 in cu. ft. 
 
 19. Cooling water supplied per hour Ib. 
 
 20. Heat units consumed per hour (Item 16 X Item 18) B.T.U. 
 
 Analyses. 
 
 21-24. Analysis of oil: C; H; O; S; moisture 
 
 25-30. Analysis of Fuel Gas by Volume: CO2; CO; O; H; 
 
 CH 4 ; C n H m ; N by difference 
 
 31-34. Analysis of Exhaust Gases by Volume: CO2; CO; 
 
 O; N 
 
 Indicator Diagrams. 
 
 35. Pressure in Ib. per sq. in. above atmosphere Ib. 
 
 (a) Maximum pressure 
 
 (&) Pressure at beginning of stroke . . 
 
 (c) Pressure at end of expansion .... 
 
 (d) Exhaust pressure at lowest point 
 
 36. Mean effective pressure in Ib. per sq. in 
 
 Speed. 
 
 37. Revolutions per minute rev, 
 
 38. Average number of explosions or firing strokes per 
 
 minute . 
 
 
 (a) Variation of speed between no load and full load . . rev, 
 
 (b) Momentary fluctuation of speed on suddenly 
 
 changing from full load to half load * 
 
1108 LOCOMOTIVES. 
 
 Power. 
 
 39. Indicated horse-power I.H.P. 
 
 40. Brake horse-power br. H.P. 
 
 41 Friction horse-power by difference (Item 39 - Item 40)* fr.-H.P. 
 
 (a) Friction horse-power by friction diagrams 
 
 42. Percentage of indicated horse-power lost in friction 
 
 Item 41 per cent 
 
 Economy Results. 
 
 43. Heat units consumed by engine per J.H.P.-hourf B.T.U. 
 
 44. Heat units consumed by engine per B.H.P.-hour 
 
 45. Pounds of oil or cubic feet of dry gas at 60 deg. and .'50 
 
 in. consumed per I.H.P. hour Ib. cu. ft. 
 
 46. Pounds of oil or cubic feet of dry gas per B.H.P.-hour. . 
 
 Efficiency. 
 
 47. Thermal efficiency referred to indicated horse-power . . . per cent 
 
 48. Thermal efficiency referred to brake horse-power 
 
 Work Done per Heat Unit. 
 
 49. Ft.-lb. of net work per B.T.U. consumed (1,980,000 ~ 
 
 Item 40) ft.-lb. 
 
 HEAT BALANCE. 
 
 50. Heat balance, based on B.T.U. per I.H.P. per hour 
 
 B.T.U. Per cent 
 
 (a) Heat converted into work 2546 .5 
 
 (&) Heat rejected in cooling water * 
 
 (c) Heat rejected in the dry exhaust gases 
 
 (d) Heat lost due to moisture formed by 
 
 burning of hydrogen 
 
 (e) Heat lost in superheating moisture in 
 
 gas and air 
 
 (/) Heat lost by incomplete combustion 
 
 (0) Heat unaccounted for, including radia- 
 tion 
 
 (h) Total heat consumed per I.H.P.-hr., 
 
 same as Item 43 
 
 Sample Diagrams. 
 
 51. Sample indicator diagrams from each cylinder and if 
 
 possible a stop-motion light-spring diagram showing 
 inlet and exhaust pressures 
 
 LOCOMOTIVES. 
 
 Resistance of Trains. Resistance due to Speed. Various formulae 
 and tables for the resistance of trains at different speeds on a straight 
 level track have been given by different writers. Among these are 
 the following: 
 
 By D. L. Barnes, Eng. Mag., June, 1894: 
 
 Speed, miles per hour 50 60 70 80 90 100 
 
 Resistance, pounds per gross ton . . 12 12 . 4 13 . 5 15 17 20 
 
 By Engineering News, March 8, 1894: 
 
 Resistance in Ibs. per ton of 2000 Ibs. = 1/4 v + 2. 
 
 Speed 5 10 15 20 25 30 35 40 50 60 70 80 90 100 
 
 Resistance. 3 1/4 4.5 53/ 4 7 81/4 9.5 103/ 4 12 14.5 17 19.5 22 24.5 27 
 
 * In two cycle engines this includes the power required for compres- 
 sion. 
 
 t If these results, in the case of a gas engine, are based on the low 
 value of the heat of combustion that fact should be so stated. 
 
LOCOMOTIVES. 1109 
 
 This formula seems to be more generally accepted than the others. 
 It gives results too small, however, below 10 miles an hour. At starting, 
 the resistance is about 17 Ibs. per ton, dropping to 4 or 5 Ibs. at 5 miles 
 an hour. 
 
 By Baldwin Locomotive Works: 
 
 Resistance in Ibs. per ton of 2000 Ibs. = 3 + v *- 6. 
 
 Speed.. .5 10 15 20 2530 35 40 45 50 55 60 70 80 90 100 
 Resistance. 3.8 4.7 5.5 6.3 7.2 8 8.8 9.7 10.5 11.3 12.2 13 14.7 16.3 18 19.7 
 
 The resistance due to speed varies with the condition of the track, the 
 number of cars in a train, and other conditions. 
 
 For tables showing that the resistance varies with the area exposed to 
 the resistance and friction of the air per ton of loads, see Dashiell, Trans. 
 A. S. M. E., vol. xiii. p. 371. 
 
 P. H. Dudley (Bulletin International Ry. Congress, 1900, p. 1734) 
 shows that the condition of the track is an important factor of train 
 resistance which has not hitherto been taken account of. The resist- 
 ance of heavy trains on the N. Y. Central R. R. at 20 miles an hour is 
 only about 31/2 Ibs. per ton on smooth 80-lb. 5i/8-m. rails. The resist- 
 ance of an 80-car freight train, 60,000 Ibs. per car, as given by indicator 
 cards, at speeds between 15 and 25 miles per hour, is represented by the 
 formula R = 1 + 1/8 V, in which R = resistance in Ibs. per ton and 
 V = miles per hour. These values are much below the average and 
 should not be used in estimating the hauling power needed. 
 
 New Formulas for Re-nstance. The Amer. Locomotive Co. (Bulletin 
 No. 1001, Feb., 1910) states that the figures obtained from the old formulae 
 for train resistance are much too high foj* modern loaded freight cars 
 of 40 to 50 tons capacity, and in some instances too low for very light 
 or empty cars. The best data available show that the resistance varies 
 from about 2.5 to 3 Ibs. per ton- (of 2000 Ibs.) for 72-ton cars (including 
 weight of empty car) to 6 to 8 Ibs. for 20-ton cars. From speeds between 
 5 to 10 and 30 to 35 miles an hour, the resistance of freight cars is prac- 
 tically constant. The resistance of the engine and tender is figured 
 separately, and is composed of the following factors: (a) Engine friction = 
 22.2 Ibs. per ton, or 1.11% of the weight on drivers. (6) Head air resist- 
 ance = cross-sectional area (taken at 120 sq. ft.) X 0.002 V 2 , V being 
 the speed in miles per hour, (c) Resistance due to weight on engine 
 trucks and trailing wheels, and t9 the tender, the same per ton as that 
 due to the cars, (d) Grade resistance = 20 Ibs. per ton for each per 
 cent of grade, (e) Curve resistance, which varies with the wheel-base 
 of the locomotive, and is taken as 0.4 + cD Ibs. per ton, in which D is 
 the degree of the curve and c a constant whose value is, 
 For wheel-base, ft. 5 6 7 8 9 12 13 15 16- 20 
 Value of c 0.380 .415 .460 .485 .520 .625 .660 .730 .765 .905 
 
 The sum of these resistances is to be deducted from the tractive force of 
 the locomotive to obtain the available tractive force for overcoming tht 
 resistance of the cars. (See Tractive Force, below.) The maximum 
 tractive force is taken for low speeds at 85% of that due to the boiler 
 pressure; for piston speeds over 250 ft. per min. this is to be multiplied 
 by a speed factor to obtain the actual force. Speed factors and percent- 
 ages of maximum horse-power corresponding to different piston speeds 
 are given below. S = piston speed, ft. per min., F = speed factor, 
 p = % of maximum H.P. 
 
 S 250 300 350 400 450 500 550 600 650 700 750 
 
 F 1.00 .954 .908 .863 .817 .772 .727 .680 .636 .592 .550 
 
 P 60.469.177.283.789.093.596.898.799.7 100 100 
 
 S... . 800 850 900 950 1000 1100 1200 1300 1400 1500 1600 
 
 F 0.517 .487 .460 .435 .412 .372 .337 .307 .283 .261 .241 
 
 P 100 100 100 100 100 9997.896.895.7 94.793.5 
 
 The resistance of freight cars, according to experiments on the Penna. 
 R.R., varies with the weight in tons per car as follows: 
 
 Tons per car 10 20 25 30 40 50 60 70 72 
 
 Resistance, Ibs. per ton 
 
 13.10 7.84 6.62 5.78 4.66 3.94 3.44 3.06 3.00 
 
1110 LOCOMOTIVES. 
 
 From plotted curves of resistances of trains of empty and loaded cars 
 the following figures are derived. R = resistance in IDS. per ton. 
 
 Wt. loaded, tons.., 75 70 65 60 55 50 
 
 Wt. empty, tons 21 20.3 19.5 18.6 17.6 165 
 
 Per cent of loaded wt 28 29 30 31 32 33 
 
 R loaded 2.90 3.07 3.24 3.43 3.65 3.90 
 
 R empty 5.63 5.82 6.00 6.26 6.50 6.85 
 
 Wt. loaded, tons 45 40 35 30 25 20 15 
 
 Wt. empty, tons 15.3 14.0 12.6 11.1 9.5 7.8 6.0 
 
 Percent of loaded wt.... 34 35 36 37 38 39 40 
 
 R loaded 4.18 4.40 4.74 5.07 5.44 5.91 6.40 
 
 R empty 7.26 7.65 8.05 8.45 9.05 9.60 10.3 
 
 'the resistance of passenger cars is derived from the formula R = 5.4 + 
 0.002(7 - 15)2+ 100 ^ (V + 2). V in miles per hour, R = resistance 
 in Ibs. per ton (2000 Ibs.) H.P. = horse-power per ton. 
 
 V = 5 10 15 20 25 30 35 
 
 R= 5.89 5.51 5.42 5.46 5.60 5.85 6.20 
 
 H.P. = 0.079.147 .217 .291 .374 .469 .578 
 
 F=.., 40 45 50 60 70 80 90 
 
 R = 6.65 7.20 7.85 9.4511.4513.8516.65 
 
 H.P.= 709 .864 1.047 1.515 2.135 2.95 4.00 
 
 Resistance of Electric Railway Cars and Trains. W. J. Davis, Jr. 
 (Street Ry. Jour., Dec. 3, 1904), gives as a result of numerous experiments 
 the following formulae: 
 
 (A) For light open platform street cars, 8 tons to 20 tons; maximum 
 speed, 30 miles per hour; cross-section, 85 sq. ft. 
 
 O ^ V2 
 
 R = 6 + 0.11V + ^|^- [l-f-0.1 (n- 1)J. 
 
 (B) For standard interurban electric cars, 25 tons to 40 tons; maximum 
 speed, 60 m.p.h.; cross section, 100 sq. ft. 
 
 R = 5-fO.lSF-f O.SFV^fl-f 0.1 (n - 1)}. 
 
 (C) For heavy interurban electric cars, or steam passenger coaches, 
 40 tons to 50 tons; maximum speed, 75 m.p.h.; crosss-ection, 110 sq. ft. 
 
 R = 4 + 0.13 V + 0.33 FV? 7 [1 -f 0.1 (n - 1)]. 
 
 (D) For heavy freight trains, cars weighing 45 tons loaded; maximum 
 speed, 35 m.p.h.; average cross-section, 110 sq. ft. 
 
 R = 3.5 +0. 13 V-f- 0.385 V^/T(l+ 0.1 (n - 1)]. 
 
 R = resistance in Ibs. per ton of 2000 Ibs., V= speed in miles per hour 
 T = weight of train in tons, n = number of cars in train, including lead- 
 ing motor car. The cross-section includes the space bounded by the wheels 
 between the top of rails and the body. 
 
 Resistance due to Grade. The resistance due to a grade of 1 ft. per 
 mile is, per ton of 2000 Ibs., 2000 X 1/5280 = 0.3788 Ib. per ton, or if 
 R g = resistance in Ibs. per ton due to grade and G = ft. per mile R g = 
 0.3788 G. 
 
 If the grade is expressed as a percentage of the length, the resistance is 
 20 Ibs. per ton for each per cent of grade. 
 
 Resistance due to Curves. Mr. G. R. Henderson in his book entitled 
 "Locomotive Operation" gives the resistance due to curvature at 0.7 
 Ib. per ton of 2000 Ibs. per degree of the curve. (For definition of 
 degrees of a railroad curve see p. 54.) For locomotives, this factor is 
 sometimes doubled, making the resistance in Ibs. per ton = 0.7 c for cars 
 and 1.4 c for locomotives, c being the number of degrees. 
 
 The Baldwin Locomotive Works take the approximate resistance due 
 to each degree of curvature as that due to a straight grade of 1 1/2 ft. per 
 mile. This corresponds to R c 0.5682 c. 
 
 The Amer. Locomotive Co. takes 0.8 Ib. per ton per degree of curva- 
 ture for the resistance of cars on curves. 
 
LOCOMOTIVES. HH 
 
 For mine cars, with short wheel-bases and wheels loose on the axles, 
 experiments quoted by the Baldwin Locomotive Works, 1904, lead to the 
 formula, Resistance due to curvature, in pounds, = 0.20 X wheel-base X 
 weight of loaded cars in pounds, * radius of curve in feet. 
 
 Resistance due to Acceleration. This may be calculated by the ordi- 
 nary formula (see page 529), or reduced to common railroad units, and 
 including the rotative energy of wheels and axles, which increases the 
 effect of the weight of the cars by an equivalent of about 5%, we have 
 
 p = 70 ^ =95.6 ? = 70 V ** ~ Fl * , where P= the accelerating force in 
 
 o t o 
 
 pounds per ton,. V = the velocity in miles per hour, S = the distance 
 In feet, and t = the time in seconds in which the acceleration takes 
 place. Fi and Vi = the smaller and greater velocities, respectively, 
 in miles per hour, for a change of speed. 
 
 Total Resistance. The total resistance in Ibs. per ton of 2000 Ibs. due 
 to speed, to grade, to curves, and to acceleration is the sum of the resist- 
 ances calculated above. 
 
 The Baldwin Locomotive Works in their "Locomotive Data' take the 
 total resistance on a straight level track at slow speeds at from 6 to 10 Ibs. 
 per ton, and in a communication printed in the fourth edition (1898) of 
 this Pocket-book, p. 1076, say: "We know that in some cases, for in- 
 stance in mine construction, the frictional resistance has been shown to 
 be as much as 60 Ibs. per ton at slow speed. The resistance should be 
 approximated to suit the conditions of each individual case, and the 
 increased resistance due to speed added thereto." 
 
 Resistance due to friction. In the above formulae no account has been 
 taken of the resistance due to the friction of rhe working parts. This is 
 rather an obscure subject. Mr. Henderson estimates the percentage of 
 the indicated power consumed by friction to be 0.15 V + c, where 
 V = speed in miles per hour and c =- a constant, whose value may 
 vary from 2 to 8, the latter figure being the safest to use for heavy work 
 at slow speeds. Ordinarily 8% of the indicated power is consumed by 
 internal resistance under these conditions. Professor Goss gives the 
 following formula, obtained from tests at the Purdue locomotive testing 
 laboratory: 
 
 Let d = diameter of cylinder: S = stroke of piston; D = diameter of 
 drivers, all in inches. Then the internal friction = 3.8d 2 /Z), in pounds 
 at the circumference of the drivers. 
 
 Concerning the effect of increasing speed on tractive force, Mr. Render- 
 son says (1906): 
 
 From a number of tests and information from various roads and au- 
 thorities it seems as if, for ordinary simple engines, the coefficient 0.8 
 
 in the equation Actual tractive force = >s could be modified in ac- 
 
 cordance with the speed in order to obtain the actual tractive force at 
 various speeds about as follows: 
 
 Revs, per min. = 20 40 60 80 100 120 140 160 
 
 Coefficient = . 80 0.80 0.80 0.70 0.61 0.53 0.46 0.40 
 
 Revs, per min. = 180 200 220 240- 260 280 300 320 340 
 
 Coefficient = 0.35 0.31 0.28 0.26 0.24 0.23 0.21 0.20 0.19 
 
 Efficiency of the Mechanism of a locomotive. Frank C.Wagner 
 (Proc. A. A. A. S.j 1900, p. 140) gives an account of some dynamometer 
 tests 4 which indicate that in ordinary freight service the power used to 
 drive the locomotive and tender and to overcome the friction of the 
 mechanism is from 10% to 35% of the total power developed in the steam- 
 cylinder. In one test the weight of the locomotive and tender was 16% 
 of the total weight of the train, while the power consumed in the loco- 
 motive and tender was from 30% to 33% of the indicated horse-power. 
 
 Adhesion. The limit of the hauling capacity of a locomotive is the 
 adhesion due to the weight on the driving wheels. Holmes gives the 
 adhesion, in English practice, as equal to 0.15 of the load on the driving 
 wheels in ordinary dry weather, but only 0.07 in damp weather or when 
 the rails are greasy. In American practice it is generally taken as from 
 Vi to 1/5 of the load on the drivers. 
 
1112 
 
 LOCOMOTIVES. 
 
 Tractive Force of a Locomotive. Single Expansion. 
 Let F = indicated tractive force in Ibs. 
 
 p = average effective pressure in cylinder in Ibs. per sq. in. 
 S = stroke of piston in inches. 
 d = diameter of cylinders in inches. 
 D = diameter of driving-wheels in inches. Then 
 _ 4 7cd z pS _ (J 2 pS 
 
 4 nD D 
 
 The average effective pressure can be obtained from an indicator* 
 diagram, or by calculation, when the initial pressure and ratio of expan- 
 sion are known, together with the other properties of the valve-motion. 
 The subjoined table from Auchincloss gives the proportion of mean 
 effective pressure to boiler-pressure above atmosphere for various pro- 
 portions of cut-off. 
 
 Stroke, 
 Cut-off at 
 
 M.E.P. 
 
 (Boiler- 
 pres. =1). 
 
 Stroke, 
 Cut-off at 
 
 M.E.P. 
 
 (Boiler- 
 pres. = 1). 
 
 Stroke, 
 Cut-off at 
 
 M.E.P. 
 
 (Boiler- 
 pres. = 1). 
 
 0.1 
 
 0.15 
 
 0.333 = 1/3 
 
 0.5= 1/2 
 
 0.625 = 5/ 8 
 
 0.79 
 
 .125 = l/ 8 
 
 .2 
 
 .375 = 3/ 8 
 
 .55 
 
 ' .666 = 2/3 
 
 .82 
 
 .15 
 
 .24 
 
 .4 
 
 .57 
 
 .7 
 
 .85 
 
 .175 
 
 .28 
 
 .45 
 
 .62 
 
 .75 = 3/4 
 
 .89 
 
 .2 
 
 .32 
 
 .5 = l/ 2 
 
 .67 
 
 .8 
 
 .93 
 
 .25 = 1/4 
 
 .4 
 
 .55 
 
 .72 
 
 .875 = 7/8 
 
 .98 
 
 .3 
 
 .46 
 
 
 
 
 
 These values were deduced from experiments with an English locomo- 
 tive by Mr. Gooch. As diagrams vary so much from different" causes, 
 this table will only fairly represent practical cases. It is evident that 
 the cut-off must be such that the boiler will be capable of supplying 
 sufficient steam at the given speed. 
 
 We can, however, allow for wire drawing to the steam chest and drop in 
 pressure due to expansion, and internal friction by writing the formula: 
 
 8 Pd 2 S 
 Actual Tractive Force = '- ^ - , d, S, and D being as before and P 
 
 representing boiler pressure in Ibs. per sq. in. 
 
 Compound Locomotives. The Baldwin Locomotive Works give the fol- 
 lowing formulae for compound engines of the Vauclain four-cylinder type: 
 , C*S X 2/3 P , c*S X 1/4 P 
 ~~D~~ ~D~ 
 
 T tractive force in Ibs. C= diam. of high-pressure cylinder in ins. 
 c= diam. of low-pressure cylinder in ins. P= boiler-pressure in Ibs. 
 S= stroke of piston in ins. Z>= diam. of driving-wheels in ins. 
 
 For a two-cylinder or cross-compound engine it is only necessary to con- 
 sider the high-pressure cylinder, allowing a sufficient decrease in boiler 
 pressure to compensate for the necessary back-pressure. The formula is 
 
 D 
 
 The above formulae are for speeds of from 5 to 10 miles an hour, or 
 less; above that the capacity 9f the boiler limits the cut-off which can be 
 used, and the available tractive force is rapidly reduced as the speed 
 increases. _ For a full discussion of this, see page 375 of Henderson's 
 " Locomotive Operation." 
 
 The Size of Locomotive Cylinders is usually taken to be such that 
 the engine will just overcome the adhesion of its wheels to the rails under 
 favorable circumstances. 
 
 The adhesion is taken by a committee of the Am. Ry. Master Mechan- 
 ics' Assn. as 0.25 of the weight on the drivers fop passenger engines, 0.24 
 for freight, and 0.22 for switching engines; and the mean effective pres- 
 sure in the cylinder, when exerting the maximum tractive force, is taken 
 at 0.85 of the boiler-pressure. 
 
LOCOMOTIVES. 
 
 1113 
 
 Let W = weight on drivers in Ibs.; P = tractive force In Ibs., = say 
 0.25 W; pi = boiler-pressure in Ibs. per sq. in.; p = mean effective 
 pressure, = 0.85 p\\ d = diam. of cylinder, 8 = length of stroke, and 
 D = diam. of driving-wheels, all in inches. Then 
 
 4ff X 0.8 
 
 Whence 
 
 Von Borries's rule for the diameter of the low-pressure cylinder of a 
 compound locomotive is d- = 2 ZD -f- ph, in which d= diameter of l.p. 
 cylinder in inches; D = diameter of driving-wheel in inches; p = mean 
 effective pressure per sq. in., after deducting .internal machine friction; 
 h = stroke of piston in inches; Z = tractive force required, usually 0.14 
 to 0.16 of the adhesion. 
 
 The value of p depends on the relative volume of the two cylinders, 
 and from indicator experiments may be taken as follows: 
 
 ri*cc rt TTnm-nA Ratio of Cylinder pin percent of p for Boiler-pres' 
 
 Volumes. Boiler-pressure, sure of 176 Ibs. 
 Large-tender eng's. 1 : 2 or 1 : 2.05 42 74 
 
 Tank-engines 1 : 2 or 1 : 2.2 40 71 
 
 Horse-power of a Locomotive. For each cylinder the horse-powei 
 is H.P. = pLaN *- 33,000, in which p = mean effective pressure, L = 
 stroke in feet, a = area of cylinder = 1/4 ?rd 2 , N = number of single 
 strokes per minute, LN = piston speed, ft. per min. Let M = speed of 
 train in miles per hour, S = length of stroke in inches, and D = diam- 
 eter of driving-wheel in inches. Then LN = MX8&X2S + xD. 
 Whence for the two cylinders the horse-power is 
 
 xD X 33,000 
 
 375 D 
 
 REVOLUTIONS PER MINUTE FOR VARIOUS DIAMETERS OF WHEELS 
 AND SPEEDS. 
 
 Miles per Hour. 
 
 Diameter 
 of Wheel. 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 50 in. 
 
 67 
 
 134 
 
 201 
 
 268 
 
 336 
 
 403 
 
 470 
 
 538 
 
 56 in. 
 
 60 
 
 120 
 
 180 
 
 240 
 
 300 
 
 360 
 
 420 
 
 480 
 
 60m. 
 
 56 
 
 112 
 
 168 
 
 224 
 
 280 
 
 336 
 
 392 
 
 448 
 
 62 in. 
 
 54 
 
 108 
 
 162 
 
 217 
 
 271 
 
 325 
 
 379 
 
 433 
 
 66 in. 
 
 51 
 
 102 
 
 153 
 
 204 
 
 255 
 
 306 
 
 357 
 
 408 
 
 68 in. 
 
 49 
 
 99 
 
 148 
 
 198 
 
 247 
 
 296 
 
 346 
 
 395 
 
 72 in. 
 
 47 
 
 93 
 
 140 
 
 187 
 
 233 
 
 279 
 
 326 
 
 373 
 
 78 in. 
 
 43 
 
 86 
 
 129 
 
 172 
 
 215 
 
 258 
 
 301 
 
 344 
 
 80 in. 
 
 42 
 
 84 
 
 126 
 
 168 
 
 210 
 
 252 
 
 294 
 
 336 
 
 84 in. 
 
 40 
 
 80 
 
 120 
 
 160 
 
 200 
 
 240 
 
 280 
 
 320 
 
 90 in. 
 
 37 
 
 75 
 
 112 
 
 150 
 
 186 
 
 224 
 
 261 
 
 299 
 
 The Size of Locomotive Boilers. (Forney's Catechism of the Loco- 
 motive.) They should be proportioned to the amount of adhesive 
 weight and to the speed at which the locomotive is intended to work. 
 Thus a locomotive with a great deal of weight on the driving-wheels 
 could pull a heavier load, would have a greater cylinder capacity than 
 one with little adhesive weight, would consume more steam, and there- 
 fore should have a larger boiler. 
 
 The weight and dimensions of locomotive boilers are in nearly all 
 cases determined by the limits of weight and space to which they are 
 necessarily confined. It may be stated generally that within these limits 
 Q locomotive boiler cannot be made too large. In other words, boilers for 
 
1114 
 
 LOCOMOTIVES. 
 
 locomotives should ahyays be made as large as is possible under the 
 conditions that determine the weight and dimensions of the locomotives. 
 (See also Holmes on the Steam-engine, pp. 371 to 377 and 383 to 389 
 and the Report of the Am. Ry. M. M. Ass'n. for 1897, pp. 218 to 232.) ' 
 Holmes gives the following from English practice: 
 
 Evaporation, 9 to 12 Ibs. of water from and at 212. 
 
 Ordinary rate of combustion, 65 Ibs. per sq. ft. of grate per hour. 
 
 Ratio of grate to heating surface, 1 : 60 to 90. 
 
 Heating surface per Ib. of coal burnt per hour. 0.9 to 1.5 sq. ft 
 Mr. Henderson states the approximate heating surface needed per 
 indicated horse-power as follows: 
 
 Compound Locomotives 2 square feet. 
 
 Simple Locomotives (cut-off 1/2 stroke or less) 2 1/3 square feet. 
 
 Simple Locomotives (cut-off 1/2 to 3/ 4 stroke) 2 2/3 square feet. 
 
 Simple Locomotives (full stroke) 3 square feet. 
 
 For the ratio of heating surface to grate area the Master Mechanics 
 Ass'n Committee of 1902 advised as below: 
 
 Fuel. 
 
 Passenger. 
 
 Freight. 
 
 Simple. 
 
 Com- 
 pound. 
 
 Simple. 
 
 Com- 
 pound . 
 
 
 65 to 90 
 50 to 65 
 40 to 50 
 
 35 to 40 
 28 to 35 
 
 75 to 95 
 60 to 75 
 35 to 60 
 
 30 to 35 
 
 24 to 30 
 
 70 to 85 
 45 to 70 
 35 to 45 
 
 30 to 35 
 25 to 30 
 
 65 to 85 
 50 to 65 
 45 to 50 
 
 40 to 45 
 30 to 40 
 
 
 Slow burning bituminous 
 
 Bituminous slack and free burning. . 
 
 Low grade bituminous, lignite and 
 slow burning anthracite 
 
 
 A. E. Mitchell, (Eng'g News, Jan. 24, 1891) says: Square feet of boiler- 
 heating surface for bituminous coal should not be less than 4 times the 
 square of the diameter in inches of a cylinder 1 inch larger than the 
 cylinder to be used. One tenth of this should be in the fire-box. On 
 anthracite locomotives more heating-surface is required in the fire-box, on 
 account of the larger grate-area required, but the heating-surface of the 
 flues should not be materially decreased. 
 
 Wootten's Locomotive. (Clark's Steam-engine; see also Jour. 
 Frank. Inst. 1891, and Modern Mechanism, p. 485.) J. E. Wootten 
 designed and constructed a locomotive boiler for the combustion of an- 
 thracite and lignite, though specially for the utilization as fuel of the 
 waste produced in the mining and preparation of anthracite. The special 
 feature of the engine is the fire-box, which is made of great length and 
 breadth, extending clear over the wheels, giving a grate-area of from 
 64 to 85 sq. ft. The draught diffused over these large areas is so gentle 
 as not to lift the fine particles of the fuel. A number of express-engines 
 having this type of boiler are engaged on the fast trains between Phila- 
 delphia and Jersey City. The fire-box shell is 8 ft. 8 in. wide and 10 ft. 
 5 in. long; the fire-box is 8 X 91/2 ft., making 76 sq. ft. of grate-area. 
 The grate" is composed of bars and water-tubes alternately. The regular 
 types of cast-iron shaking grates are also used. The height of the fire- 
 box is only 2 ft. 5 in. above the grate. The grate is terminated by a 
 bridge of fire-brick, beyond which a combustion-chamber, 27 in. long, 
 leads to the flue-tubes, about 184 in number, 13/4 in. diam. The cylin- 
 ders are 21 in. diam., with a stroke of 22 inches. The driving-wheels, 
 four-coupled, are 5 ft. 8 in. diam. The engine weighs 44 tons, of which 
 29 tons are on driving wheels. The heating-surface of the fire-box is 
 135 sq. ft., that of the flue-tubes is 982 sq. ft.: together, 1117 sq. ft., or 
 14.7 times the grate-area. Hauling 15 passenger-cars, weighing with 
 passengers 360 tons, at an average speed of 42 miles per hour, over ruling 
 gradients of 1 in 89, the engine consumes 62 Ibs, of fuel per mile, of 
 34 Vl Iks, per sq, ft, of grate per hour, 
 
LOCOMOTIVES. 
 
 1115 
 
 Grate-surface, Smoke-stacks, and Exhaust-nozzles for Ix>como- 
 motives. A. E. Mitchell, Supt. of Motive Power of the Erie R. R., says 
 (1895) that some roads use the same size of stack, 131/2 in. diam. at 
 throat, for all engines up to 20 in. diam. of cylinder. 
 
 The area of the orifices in the exhaust-nozzles depends on the quantity 
 and quality of the coal burnt, size of cylinder, construction of stack, 
 and the condition of the outer atmosphere. It is therefore impossible 
 to give rules for computing the exact diameter of the orifices. All that 
 can be done is to give a rule by which an approximate diameter can be 
 found. The exact diameter can only be found by trial. Our experi- 
 ence leads us to believe that the area of each orifice in a double exhaust- 
 nozzle should be equal to 1/400 part of the grate-surface, and for single 
 nozzles 1/200 of the grate-surface. These ratios have been used in finding 
 the diameters of the nozzles given in the following table. The same 
 sizes are often used for either hard or soft coal-burners. [These sizes are 
 small at the present day (1909) as locomotives have enormously in- 
 creased in size.] 
 
 
 
 
 
 Double 
 
 Single 
 
 Size of 
 Cylinders, 
 in inches. 
 
 Grate-area 
 for Anthra- 
 cite Coal, in 
 sq. in, 
 
 Grate-area 
 for Bitumin- 
 ous Coal, in 
 sq. in. 
 
 Diameter 
 of Stacks, 
 in inches. 
 
 Nozzles. 
 
 Nozzles. 
 
 Diam. of 
 Orifices, in 
 
 Diam. of 
 Orifices, in 
 
 
 
 
 
 inches. 
 
 inches. 
 
 12x20 
 
 1591 
 
 1217 
 
 91/2 
 
 2 
 
 213/16 
 
 13x20 
 
 1873 
 
 1432 
 
 101/2 
 
 21/8 
 
 3 
 
 14x20 
 
 2179 
 
 1666 
 
 111/4 
 
 25/ie 
 
 3V4 
 
 15x22 
 
 2742 
 
 2097 
 
 121/2 
 
 29/i 6 
 
 311/16 
 
 16x24 
 
 3415 
 
 2611 
 
 14 
 
 27/8 
 
 41/16 
 
 17x24 
 
 3856 
 
 2948 
 
 15 
 
 3Vl6 
 
 45/16 
 
 18x24 
 
 4321 
 
 3304 
 
 153/4 
 
 31/4 
 
 - 45/g 
 
 19x24 
 
 4810 
 
 3678 
 
 161/2 
 
 37/16 
 
 413/ie 
 
 20x24 
 
 5337 
 
 4081 
 
 171/2 
 
 35/8 
 
 51/16 
 
 Exhaust-nozzles in Locomotive Boilers. A committee of the 
 Am. Ry. Master Mechanics' Ass'n. in 1890 reported that they had, after 
 two years of experiment and research, come to the conclusion that, 
 owing to the great diversity in the relative proportions of cylinders and 
 boilers, together with the difference in the quality of fuel, any rule which 
 does not recognize each and all of these factors would be worthless. 
 
 The committee was unable to devise any plan to determine the size 
 of the exhaust-nozzle in proportion to any other part of the engine or 
 boiler. The conditions desirable are: That it must create draught 
 enough on the fire to make steam, and at the same time impose the least 
 possible amount of work on the pistons in the shape of back pressure. 
 It should be large enough to produce a nearly uniform blast without 
 lifting or tearing the fire, and be economical in its use of fuel. The 
 Annual Report of the Association for 1896 contains interesting data on 
 this subject. 
 
 Much important information regarding stacks and exhaust nozzles is 
 embodied in the tests at Purdue University, reported to the Master 
 Mechanics' Ass'n. in 1896 and in the tests reported in the American 
 Engineer in 1902 and 1903. 
 
 Fire-brick Arches in Locomotive Fire-boxes. A committee of 
 the Am. Ry. Master Mechanics' Ass'n. in 1890 reported strongly in favor 
 of the use of brick arches in locomotive fire-boxes. They say: It is the 
 unanimous opinion of all who use bituminous coal and brick arch, that 
 it is most efficient in consuming the various gases composing black 
 smoke and by impeding and delaying their passage through the tubes, 
 and mingling and subjecting them to the heat of the furnace, greatly 
 lessens the volume ejected, and intensifies combustion, and does not in 
 the least check but rather augments draught, with the consequent saving 
 of fuel and increased steaming capacity that might be expected from 
 such results, This in particular when used in connctioa with extension 
 front, 
 
1116 WCOMOTIVES. 
 
 Arches now (1009) ate not quite so much in favor, largely on account 
 of the difficulty and delay caused to workmen when flues must be calked, 
 as occurs frequently in bad water districts, and some of their former 
 advocates are now omitting them altogether. 
 
 Economy of High Pressures. Tests of a Schenectady locomotive 
 with cylinders 16 X 24 ins., at the Purdue University locomotive testing 
 plant, gave results as follows: (Eng. Digest, Mar., 1909; Bull. No. 26, Univ. 
 of 111. Expt. Station). 
 
 Boiler pressure, Ibs. per sq. in. 120 140 160 180 200 220 240 
 Steam per 1 H.P. hour, Ibs. 29.1 27.7 26.6 26. 25.5 25.1 24.7 
 Coal per 1 H.P. hour, Ibs. 4 3.77 3.59 3.50 3.43 3.37 3.31 
 
 In the same series of tests the economy of the boiler at different rates of 
 driving and different pressures was determined, the results leading to the 
 formula E = 11.305 0.221 H, in which E = Ibs. evaporated from and 
 at 212" per Ib. of Youghiogheny coal, and H the equivalent evaporation 
 per sq. ft. of heating surface per hour, with an average error for any 
 pressure which does not exceed 2.1%. 
 
 Leading American Types of Locomotive for Freight and 
 Passenger Service 
 
 1. The eight-wheel or '* American" passenger type, having four coupled 
 driving-wheels and a four-wheeled truck in front. 
 
 2. The "ten-wheel" type, for mixed traffic, having six coupled drivers 
 and a leading four-wheel truck. 
 
 3. The "Mogul" freight type, having six coupled driving-wheels and 
 a pony or two-wheel truck in front. 
 
 4. The "Consolidation" type, for heavy freight service, having eight 
 coupled driving-wheels and a pony truck in front. 
 
 Besides these there is a great variety of types for special conditions of 
 service, as four-wheel and six-wheel switching-engines, without trucks; 
 the Forney type used on elevated railroads, with four coupled wheels 
 under the engine and a four-wheeled rear truck carrying the water-tank 
 and fuel; locomotives for local and suburban service with four coupled 
 driving-wheels, with a two-wheel truck front and rear, or a two-wheel 
 truck front and a four-wheel truck rear, etc. "Decapod" engines for 
 heavy freight service have ten coupled driving-wheels and a two-wheel 
 truck in front, 
 
 O OA n O O O OB 
 
 O O OB O O O h F 
 
 O O O Oc O O O o 
 
 o o n on o on o OH 
 
 Classification of Locomotives (Penna. R. R. Co., 1900). Class A, 
 two pairs of drivers and no truck. Class B, three pairs of drivers and no 
 truck. Class C, four pairs of drivers and no truck. Class D, two pairs of 
 drivers and four-wheel truck. Class E, two pairs of drivers, four-wheel 
 truck, and trailing wheels. Class F, three pairs of driving-wheels and 
 two-wheel truck. Class G, three pairs of drivers and four-wheel truck. 
 Class H, four pairs of drivers and two-wheel truck. Class A is com- 
 monly called a "four-wheeler"; B, a "six-wheeler"; D, an "eight- 
 wheeler," or "American" type; E, "Atlantic" type; F, "Mogul"; 
 G s "ten- wheeler"; H, "Consolidation." 
 
 Modern Classification. The classes shown above, lettered A, B, C, 
 etc., are commonly represented respectively by the symbols 0-4-0; 
 0-6-0; 0-8-0, 4-4-0; 4-4-2, 2-6-0; 4-6-0; 2-8-0; the first figure being 
 the number of wheels in the truck, the second the driving-wheels, and the 
 tbird the trailers. Other types are the "Pacific," 4-6-2; the "Prairie," 2-6-2; 
 
LOCOMOTIVES. 
 
 1117 
 
 and the "Santa Fe," 2-10-2. Engines on the Mallet system, with two 
 locomotive engines under one boiler, are classified 0-8-8-0, 2-6-6-2, etc. 
 
 Formulae for Curves. (Baldwin Locomotive Works.) 
 Approximate Formula for Radius. Approximate Formula for Swing, 
 
 R - 0.7646 W + 2 P. ' (T - TF) T -H 2 S - R. 
 
 R =- radius of min. curve in feet. 
 P play of driving-wheels in 
 
 decimals of 1 ft. 
 W = rigid wheel-base in feet. 
 
 W = rigid wheel-base. 
 T = total wheel-base. 
 R = radius of curve. 
 S = swing on each side of centre. 
 
 Steam-distribution for High-speed Locomotives. 
 
 (C. H. Quereau, Eng'g News, March 8, 1894. 
 
 Balanced Valves. Mr. Philip Wallis, in 1886, when Engineer of Tests 
 for the C., B. & Q. R. R., reported that while 6 H.P. was required to 
 work unbalanced valves at 40 miles per hour, for the balanced valves 
 2.2 H.P. only was necessary. 
 
 [Later tests were reported by the Master Mechanics' Committee in 1896. 
 Unbalanced valves required from 3/ 4 to 2 1/2 per cent of the I. H.P. for 
 their motion, balanced valves from 1/3 to 1/2 as much, and piston valves 
 about 1/5 or I/G. Generally in balanced valves, the area of balance = 
 area of exhaust port + area of two bridges 4- area of one steam port.J 
 
 Effect of Speed on Average Cylinder-pressure. Assume that a locomo- 
 tive has a train in motion, the reverse lever is placed in the running 
 notch, and the track is level; by what is the maximum speed limited? 
 The resistance of the train and the load increase, and the power of the 
 locomotive decreases with increasing speed till the resistance and power 
 are equal, when the speed becomes uniform. The power of the engine 
 depends on the average pressure in the cylinders. Even though the 
 cut-off and boiler-pressure remain the same, this pressure decreases as 
 the speed increases; because of the higher piston-speed and more rapid 
 valve-travel the steam has a shorter time in which to enter the cylinders 
 at the higher speed. The following table, from indicator-cards taken 
 from a locomotive at varying speeds, shows the decrease of average 
 pressure with increasing speed: 
 
 Miles per hour 46 51 51 
 
 Speed, revolutions 224 248 248 
 
 Average pressure per sq. in.: 
 
 Actual 51.5 44.0 47.3 
 
 . 
 Calculated ....... T 46l5 
 
 53 
 
 258 
 
 43.0 
 
 44.7 
 
 54 
 263 
 
 41.3 
 
 43.8 
 
 57 
 
 277 
 
 42.5 
 41.6 
 
 60 
 
 292 
 
 66 
 321 
 
 37.3 36.3 
 39.5 35.9 
 
 The "average pressure calculated" was figured on the assumption that 
 the mean effective pressure W9uld decrease in the same ratio that the 
 speed increased. The main difference lies in the higher steam-line at 
 the lower speeds, and consequent higher expansion-line, showing that 
 more steam entered the cylinder. The back pressure and compression- 
 lines agree quite closely for all the cards, though they are slightly better 
 for the slower speeds. That the difference is not greater may safely be 
 attributed to the large exhaust-ports, passages, and exhaust tip, which 
 is 5 in. diameter. These are matters of great importance for high speeds. 
 
 Boiler-pressure. Assuming that the train resistance increases as the 
 speed after about 20 miles an hour is reached, that an average of 50 Ibs. 
 per sq. in. is the greatest that can be realized in the cylinders of a given 
 engine at 40 miles an hpur. and that this pressure furnishes just sufficient 
 power to keep the train at this speed, it follows that, to increase the 
 speed to 50 miles, the mean effective pressure must be increased in the 
 same proportion. To increase the capacitv for speed of any locomotive 
 its power must be increased, and at least by as much as the speed is to 
 ue increased. One way to accomplish this is to increase the boiler- 
 
1118 LOCOMOTIVES. 
 
 pressure. That this is generally realized, is shown by the increase In 
 boiler-pressure in the last ten years. For twenty-three single-expansion 
 locomotives described in the railway journals this year the steam-pres- 
 sures are as follows: 3, 160 Ibs.; 4, 165 Ibs.; 2, 170 Ibs.; 13 180 Ibs.- 
 1, 190 Ibs. 
 
 Valve-travel. An increased average cylinder-pressure may also be 
 obtained by increasing the valve-travel without raising the boiler- 
 pressure, and better results will be obtained by increasing both. The 
 longer travel gives a higher steam-pressure in the cylinders, a later 
 exhaust-opening, later exhaust-closure, and a larger exhaust-opening 
 all necessary for high speeds and economy. I believe that a 20-in. 
 port and 6i/2-in. (or even 7-in.) travel could be successfully used for 
 high-speed engines, and that frequently by so doing the cylinders could 
 be economically 'reduced and the counter-balance lightened. Or, better 
 still, the diameter of the drivers increased, securing lighter counterbal" 
 ance and better steam-distribution. 
 
 Size of Drivers. Economy will increase with increasing diameter of 
 drivers, provided the work at average speed does not necessitate a cut-off 
 longer than one fourth the stroke. The piston-speed of a locomotive 
 with 62-in. drivers at 55 miles per hour is the same as that of one with 
 68-in. drivers at 61 miles per hour. 
 
 Steam-ports. The length of steam-ports ranges from 15 in. to 23 in., 
 and has considerable influence on the power, speed, and economy of the 
 locomotive. In cards from similar engines the steam-line of the card 
 from the engine with 23-in. ports is considerably nearer boiler-pressure 
 than that of the card from the engine with 171/4-in. ports. That the 
 higher steam-line is due to the greater length of steam-port there is little 
 room for doubt. The 23-in. port produced 531 H.P. in an 18i/ 2 -in. 
 cylinder at a cost of 23.5 Ibs. of water per I. H.P. per hour. The 171/4 
 in. port, 424 H.P., at the rate of 22.9 Ibs. of water, in a 19-in. cylinder. 
 
 Allen Valves. There is considerable difference of opinion as to the 
 advantage of the Allen ported-valve. (See Eng. News, July 6, 1893.) 
 
 A Report on the advantage of Allen valves was made by the Master 
 Mechanics' Committee of 1896. 
 
 Speed of Railway Trains. In 1834 the average speed of trains on 
 the Liverpool and Manchester Railway was 20 miles an hour; in 1838 it 
 was 25 miles an hour. But by 1840 there were engines on the Great 
 Western Railway capable of running 50 miles an hour with a train and 
 80 miles an hour without. (Trans. A. S. M. E., vol. xiii, 363.) 
 
 The limitation to the increase of speed of heavy locomotives seems at 
 present to be the difficulty of counterbalancing the reciprocating parts. 
 The unbalanced vertical component of the reciprocating parts causes 
 the pressure of the driver on the rail to vary with every revolution. 
 Whenever the speed is high, it is of considerable magnitude, and its 
 change in direction is so rapid that the resulting effect upon the rail is 
 not inappropriately called a "hammer blow." Heavy rails have been 
 kinked, and bridges have been shaken to their fall under the action of 
 heavily balanced drivers revolving at high speeds. The means by 
 which the evil is to be overcome has not yet been made clear. See 
 paper by W. F. M. Goss, Trans. A. S. M. E., vol. xvi. 
 
 Much can be accomplished, however, by carefully designing and 
 proportioning the counter-balance in the wheels and by using light, but 
 strong, reciprocating parts. Pages 41-74 of "Locomotive Operation," 
 gives complete rules and results. 
 
 Balanced compound locomotives, with 4 cylinders, the adjacent pis- 
 tons and crossheads being connected 180 apart have also done much 
 to reduce the disturbance of the moving parts. 
 
 Engine No. 999 of the New York Central Railroad ran a mile in 32 
 seconds equal to 112 miles per hour, May 11, 1893. 
 
 Speed in) _ circum. of driving-wheels in in. X no. of rev, per min. X 60 
 hour ) 63,360 
 
 = diam., of driving-wheels in in. X no. of rev. per min. X.003 
 
 (approximate, giving result 8/ 10 of 1 per cent too great). 
 Performance of a High-speed Locomotive. The Baldwin com- 
 pound locomotive No. 1027, on the Phila. & Atlantic City Ry., in 1897 
 made a record as follows: 
 
LOCOMOTIVES. 
 
 1119 
 
 For the 52 days the train ran, from July 2d to August 31st, the average 
 time consumed on the run of 551/2 miles from Camden to Atlantic City 
 was 48 minutes, equivalent to a uniform rate of speed from start to stop 
 Of 69 miles per hour. On July 14th the run from Carnden to Atlantic 
 City was made in 461/2 min., an average of 71.6 miles per hour for the total 
 distance. On 22 days the train consisted of 5 cars and on 30 days it was 
 made up of 6, the weight of cars being as follows: combination car, 57,200 
 Ibs.; coaches, each, 59,200 Ibs.; Pullman car, 85,500 Ibs. 
 
 The general dimensions of the locomotive are as follows: cylinders, 
 13 and 22 X 26 in.; height of drivers, 841/4 in.; total wheel-base, 26 ft. 
 7 in.; driving-wheel base, 7 ft. 3 in.; length of tubes, 13 ft.; diameter of 
 boiler, 583/4 in.; diameter of tubes, 13/ 4 in.; number of tubes, 278; length 
 of fire-box, 1137/gin.; width of fire-box, 96 in.; heating-surface of fire- 
 box, 136.4 sq. ft.; heating-surface of tubes, 1614.9 sq. ft.; total heating- 
 surface, 1835.1 sq. ft.; tank capacity, 4000 gallons; boiler-pressure, 
 200 Ibs. per sq. in.; total weight of engine and tender, 227,000 Ibs.; 
 weight on drivers (about), 78,600 Ibs. 
 
 Fuel Efficiency of American Locomotives. Prof. W. M. Goss, as 
 a result of a series of tests run on the Purdue locomotive, finds the dis- 
 position of the heat developed by burning coal in a locomotive fire-box 
 to be on the average ab9ut as shown in the following table: 
 
 Absorbed by steam in the boiler, 52 %; by the superheater, 5 %; 
 total, 57 %. Losses: In vaporizing moisture in the coal, 5 %; discharge 
 of CO., 1 %; high temperature of the products of combustion, 14 %; 
 unconsumed fuel in the form of front-end cinders, 3 % ; cinders or sparks 
 passed out of the stack, 9 %; unconsumed fuel in the ash, 4 %; radia- 
 tion, leakage of steam and water, etc., 7 %. Total losses, 43 %. 
 
 It is probable that these losses are considerably less than the losses 
 which are experienced in the average locomotive in regular railway 
 service. -*- (Bulletin No. 402, U.S. Geol. Survey, 1909.) 
 
 Locomotive Link Motion. Mr. F. A. Halsey, in his work on " Loco- 
 motive Link Motion," 1898, shows that the Iocati9n of the eccentric-rod 
 pins back of the link-arc and the angular vibrations of the eccentric- 
 rods introduce two errors in the motion which are corrected by the 
 angular vibration of the connecting-rod and by locating the saddle-stud 
 back of the link-arc. He holds that it is probable that the opinions of 
 the critics of the locomotive link motion are mistaken ones, and that it 
 comes little short of all that can be desired for a locomotive valve motion. 
 The increase of lead from full to mid gear and the heavy compression at 
 mid gear are both advantages and not defects. The cylinder problem of 
 a locomotive is entirely different from that of a stationary engine. With 
 the latter the problem is to determine the size of the cylinder and the dis- 
 tribution of steam to drive economically a given load at a given speed. 
 With locomotives the cylinder is made of a size which will start the 
 heaviest train which the adhesion of the locomotive will permit, and the 
 problem then is to utilize that cylinder to the best advantage at a greatly 
 increased speed, but under a greatly reduced mean effective pressure. 
 
 Negative lead at full gear has been used in the recent practice of some 
 railroads. The advantages claimed are an increase in the power of the 
 engine at full gear, since positive lead offers resistance to the motion of 
 the piston; easier riding; reduced frequency of hot bearings; and a 
 slight gain in fuel economy. Mr. Halsey gives the practice as to lead on 
 several roads as follows, showing great diversity: 
 
 
 Full Gear 
 Forward, in. 
 
 Full Gear 
 Back, in. 
 
 Reversing 
 Gear, in. 
 
 New York, New Haven & 
 Hartford 
 
 1/16 POS. 
 
 1/4 neg. 
 
 1/4 pos. 
 
 Majne Central 
 
 o 
 
 1/4 neg. 
 
 
 Illinois Central . . . . 
 
 1/32 POS. 
 
 
 abt 3/ 16 
 
 Lake Shore 
 
 1/16 neg. 
 
 9/64 neg. 
 
 *Yl6 pos. 
 
 Chicago Great Western 
 Chicago & Northwestern 
 
 
 3/16 neg. 
 
 
 
 3 /16 to 9/16 
 1/4 pos 
 
 
 
 
 
1120 
 
 LOCOMOTIVES. 
 
 DIMENSIONS OF SOME LARGE AMERICAN 
 LOCOMOTIVES, 1893 AND 1904. 
 
 Of the four locomotives described in the table on the next page the 
 first two were exhibited at the Chicago Exposition in 1893. The dimen- 
 sions are from Engineering News, June, 1893. The first, or Decapod 
 engine, has ten-coupled driving-wheels. It is one of the heaviest and 
 most powerful engines built up to that date for freight service. The 
 second is a simple engine, of the standard American 8-wheel type, 4 
 driving-wheels, and a 4- wheel truck in front. This engine held the 
 world's record for speed in 1893 for short distances, having run a mile 
 in 32 seconds. 
 
 The other two engines formed part of the exhibit of the Baldwin 
 Locomotive Works at the St. Louis Exposition in 1904. The Santa Fe 
 type engine has five pairs of driving-wheels, and a two-wheeled truck at 
 the front and at the rear. It is equipped with Vauclain tandem com- 
 pound cylinders. 
 
 Dimensions of Some American Locomotives. 
 
 (Baldwin Loco. Wks. 1904-8.) 
 
 
 i 
 
 Boilers. 
 
 Tubes. 
 
 Heating 
 Surface. 
 
 Driving 
 Wheels 
 
 Weight, Ibs. 
 
 11 
 
 gS 
 
 Ba 
 
 J 
 
 N,. 
 
 | 
 
 1) 
 
 X 
 
 * 
 
 Diam., 
 
 on 
 
 Total 
 
 
 1 
 
 QQ 
 
 <A g 
 
 a 
 
 <* 
 
 
 S' s 
 
 1 
 
 1* 
 
 1* 
 
 ins. 
 
 Drivers 
 
 Engine 
 
 
 
 
 
 
 
 ft. in. 
 
 
 
 
 
 
 1 
 
 150 
 
 42 
 
 9 
 
 97 
 
 2 
 
 11 7 
 
 41 
 
 586 
 
 37 
 
 44,420 
 
 52,720 
 
 2 
 
 160 
 
 50 
 
 14.6 
 
 160 
 
 2 
 
 10 6 
 
 75 
 
 873 
 
 48 
 
 72,150 
 
 84,650 
 
 3 
 
 200 
 
 60 
 
 25 9 
 
 287 
 
 2 
 
 11 7 
 
 133 
 
 1733 
 
 69 
 
 83,680 
 
 124,420 
 
 4 
 
 200 
 
 62 
 
 30 
 
 272 
 
 2 
 
 16 1 
 
 136 
 
 2279 
 
 68 
 
 112,000 
 
 159,000 
 
 5 
 
 200 
 
 76 
 
 37.2 
 
 298 
 
 2V4 
 
 13 10 
 
 200 
 
 2414 
 
 51 
 
 164,000 
 
 179,500 
 
 6 
 
 200 
 
 68 
 
 35 
 
 306 
 
 21/4 
 
 14 6 
 
 195 
 
 2593 
 
 56 
 
 166,000 
 
 186,000 
 
 7 
 
 7.00 
 
 66 
 
 49.5 
 
 273 
 
 21/4 
 
 18 10 
 
 190 
 
 3015 
 
 79 
 
 101,420 
 
 193,760 
 
 8 
 
 200 
 
 70 
 
 53 5 
 
 318 
 
 21/4 
 
 19 
 
 195 
 
 3543 
 
 79 
 
 144,600 
 
 209,210 
 
 9 
 
 210 
 
 70 
 
 55 
 
 303 
 
 21/4 
 
 21 
 
 190 
 
 3772 
 
 74 
 
 151,290 
 
 230,940 
 
 10 
 
 225 
 
 78 
 
 58.5 
 
 463 
 
 21/ 4 
 
 19 
 
 210 
 
 5155 
 
 57 
 
 237,800 
 
 267,800 
 
 11 
 
 200 
 
 84 
 
 68.4 
 
 401 
 
 2V4 
 
 21 
 
 232 
 
 4941- 
 
 57 
 
 394,150 
 
 425,900 
 
 Type and cylinder size: 1, Mogul, 13 X 18; 2, Mogul, 16 X 20; 3, Am- 
 erican, 18 X 24; 4, 10-wheel balanced compound, 16 X 26 and 26 X 28; 
 5, Consolidation, 22 X 28; 6, Consolidation, 23 and 35 X 32; 7, Atlantic, 
 15 and 25 X 26; 8, Prairie, 17 and 28 X 28; 9, Pacific, 22 X 28; 10, Deca- 
 pod, 19 and 32 X 32; 11, Mallet, two each 26 and 40 X 30. 
 
 The Mallet Compound Locomotive. The Mallet articulated loco- 
 motive consists principally of two sets of engines flexibly connected un- 
 der one boiler; the rear, which is a high-pressure engine of two cylinders, 
 fixed rigid with the boiler and receiving the steam direct from the dome. 
 The front or low-pressure engine, also provided with two cylinders, is 
 capable of lateral movement to adjust itself to the curvature of the road 
 on the same general principle as a radial truck. The high-pressure 
 engine exhausts into a receiver flexibly connecting the cylinders of the 
 two sets of engines, from which the low-pressure engine receives its 
 steam supply and is exhausted from the latter through a flexible pipe 
 to the stack. Each cylinder has its independent valve and gear con- 
 nected to and operated with a common reversing rigging. By this 
 means the tractive power can be doubled over that of the ordinary 
 engine for a given weight of rail with a substantial saving in fuel. 
 (See paper by C. J. Mellin, Trans. A. S. M. E., 1909.) 
 
 This type of locomotive is adapted to a wider range of service than per- 
 haps any other design. It was originally intended for narrow-gage roads 
 of light construction, necessitating sharp curves and steep grades, in com- 
 bination with light rails. The characteristics of this design are flexibility 
 and uniform distribution of weight combined with the use of two separate 
 engines which would not slip at the same time, and the total weight carried 
 on the drivers, giving great tractive power. The first engine of this rhi ,^s 
 
LARGE AMERICAN LOCOMOTIVES 
 
 1121 
 
 
 Baldwin. 
 N.Y., L.E. 
 &W.R.R. 
 Decapod 
 Freight. 
 
 N.Y. C. & 
 H.R.R. 
 Empire 
 State 
 Express. 
 No. 999. 
 
 Baldwin. 
 Santa Fe 
 Type 
 2-10-2 
 Freight. 
 
 Baldwin. 
 Pacific 
 Type 4-6-2 
 Passenger. 
 
 Running-gear: 
 
 Driving-wheels, diam. . 
 Truck ' . . 
 Journals, driving-axles 
 truck- 
 tender- 
 Wlieel-base: 
 Driving 
 Total engine 
 
 50 in. 
 30 " 
 9 XlOin. 
 5 X10" 
 41/ 2 X 9 " 
 
 18ft. 10 in. 
 27 " 3 " 
 
 86 in. 
 40 " 
 9 X 121/2 in. 
 61/4X10 " 
 4l/ 8 X 8 " 
 
 8ft. 6 in. 
 23" 11 " 
 
 57 in. 
 29 1/4 & 40" 
 
 11 X12" 
 61/ 2 XIO" 
 71/ 2 X12"* 
 
 19 ft, 9 in. 
 35 " 11 " 
 
 77 in. 
 33 1/2 & 45" 
 10X12 in. 
 6X10 " 
 8X12 " * 
 
 13 ft. 4 in. 
 33 " 4 " 
 
 tender. 
 
 16 " 8 " 
 
 15 "2 1/9 ' 
 
 
 
 eng. and tender. . 
 Wt. in working-order: 
 
 On drivers 
 
 53 " 4 " 
 1700001bs 
 
 47 " 81/ 8 " 
 84 000 Ibs 
 
 66ft. Oin. 
 234 580 Ibs 
 
 62' 83/ 4 " 
 141 290 
 
 On truck-wheels 
 Engine, total 
 
 29,500 " 
 192,500 " 
 
 40^000 " ' 
 124000 " 
 
 52,660 " 
 287,240 " 
 
 81 [230 
 222,520 
 
 Tender 
 
 117,500 " 
 
 so'ooo " 
 
 
 
 Eng. and tend., loa'ded 
 Cylinders: 
 h.p. (2) 
 
 310,000 " 
 16X28 in. 
 
 204,000 " 
 19X24 in 
 
 450,000 " 
 19X32 in. 
 
 357,000 
 22X28 in. 
 
 l.p. (2) ' 
 
 27X28 " 
 
 
 32X32 " 
 
 22X28 " 
 
 Piston-rod, diam 
 
 4 in. 
 
 33/ 8 in 
 
 
 
 Connecting-rod, 1'gth. . 
 
 9 / 87/ 16 " 
 
 8ft. 1 1/2 in 
 
 
 
 Steam-ports 
 
 28 1/2X2 in. 
 
 H/2X18 in. 
 
 293/4X15/8" 
 
 307/8X11/2" 
 
 Exhaust-ports 
 
 281/2X8 " 
 
 23/4X18 " 
 
 and 13/4" 
 293/4X63/4" 
 
 307/ 8 X3" 
 
 Valves, out. lap, h.p. 
 out. lap, l.p. . . . 
 
 7/8 in. 
 
 5/ 8 " 
 
 1 in. 
 
 7/8 in. 
 3/4 " 
 
 1 in. 
 
 " in. lap h.p . 
 
 
 1/10 in 
 
 neg 1/4 in 
 
 rie** Vie" 
 
 in . lap, l.p. . . 
 
 
 
 neg 3/8 " 
 
 
 max. travel . . . 
 lead, h.p. 
 
 6 in. 
 1/16 in. 
 
 5l/ 2 in. 
 
 6 in. 
 " 
 
 6 in. 
 3/32 in 
 
 lead, l.p 
 
 5 /16 " 
 
 
 l/ 8 " 
 
 
 Boiler. Type 
 
 Straight 
 
 \Vagon top 
 
 \Vagon to 
 
 Straight 
 
 Diam. barrel inside 
 Thickness of plates . . . 
 Height from rail to 
 center line 
 Length of smoke-box 
 
 6ft. 21/2 in. 
 3/4 in. 
 
 8ft.O in. 
 
 5 " 77/ 8 " 
 
 4ft. 9 in. 
 9/16 in. 
 
 7ft. 11 1/2 in. 
 
 4 " 8 
 
 783/4 in. 
 7/8 &1 Vl6" 
 
 70 in. 
 H/1G in. 
 
 Working pressure 
 
 180 Ibs. 
 
 190 Ibs 
 
 225 Ibs. 
 
 
 Firebox. type 
 
 Wootten 
 
 Buchanan 
 
 
 
 Length inside 
 
 lO' 119/ie" 
 
 9ft 63/8 in 
 
 108 in 
 
 108 in. 
 
 
 8ft. 2 V in 
 
 3 " 47/8 " 
 
 78 " 
 
 66 
 
 Depth at front 
 
 4 " 6 " 
 
 6 " li/4 " 
 
 80 1/4 in 
 
 68 
 
 Thickness side plates. . 
 back plate . . 
 crown-sheet, 
 tube sheet.. . 
 Grate-area 
 
 5 /l6in. 
 5 /16 " 
 3/8 " 
 V2 " 
 89 6 sq ft 
 
 5 /16 in. 
 5 /16 " 
 3/8" 
 V2 " 
 30 7 sq ft 
 
 781/4 ' 
 3/8 ' 
 3/8 ' 
 3/8 ' 
 9 /16 ' 
 
 64 
 
 3/8 
 3/8 
 3/8 
 
 1/2 
 
 Stay-bolts, 1 1/8 in . 
 
 pitch 41/4 in 
 
 4 in 
 
 58 5 sq ft 
 
 49 5 sq ft. 
 
 Tubes iron 
 
 
 268 
 
 391 
 
 245 
 
 Pitch 
 
 23/4 in 
 
 
 
 
 Diam., outside 
 Length 
 
 11 ft. 11 in. 
 
 2 in. 
 12ft in 
 
 21/4 in. 
 20ft 
 
 2 1/4 in. 
 20ft 
 
 Heating-surface : 
 
 Tubes, exterior 
 Fire-box 
 
 2,208.8 ft. 
 234 3 " 
 
 1,697 sq.ft. 
 233 " 
 
 4,586 sq.ft. 
 210 " 
 
 2,874 sq.ft. 
 179 " 
 
 Miscellaneous: 
 
 Exhaust-nozzle, diam 
 
 5 in 
 
 3 1/2 in 
 
 
 
 Stack, smal'st diam. . . 
 
 1 ft. 6 in. 
 
 1 ft. 3 1/4 in. 
 
 
 
 height from 
 rail to top 
 
 15 ft. 6l/ 2 in. 
 
 14ft. 10 in. 
 
 
 
 ' Back truck journals. 
 
1122 
 
 LOCOMOTIVES^ 
 
 was built about 1887, and in 1909 there were approximately 500 running in 
 Europe. They are now extensively in use in the United States for the 
 heaviest service. The largest locomotive yet built is described in Eng. 
 News, April 29, 1909. It was built by the Baldwin Locomotive Works 
 for use on the heavy grades of the Southern Pacific R.R. The principal 
 dimensions areas follows: Cylinders, 26 and 40 X 30 ins.; valves, balanced 
 piston; boiler (steel): diameter, 84 ins.; thickness, 13/ 16 and 27/ 32 ins.; work- 
 ing pressure, 200 Ibs. per sq. in.; fuel, oil; fire-tubes, 401, 2i/4ins. dia. X 
 21 ft.; firebox: length, 126 ins., width, 781/4 ins., depth, front, 751/2 ins., 
 depth, back, 701/2 ins.; water spaces, 5 ins.; grate area, 68.4 sq. ft.; 
 feed-water heater: length, 63 ins., tubes, 401, 21/4 ins. dia.; heating sur- 
 face: firebox, 232 sq. ft., fire-tubes, 4941 sq. ft., feed-water heater tubes, 
 1220 sq. ft.; smokebox superheater, 655 sq. ft.; wheels: driving (16), 
 57 ins. O. dia., main journals, 11X12 ins., other journals, 10 X 12 ins.; 
 truck (4), 301/2 ins. dia., journals, 6 X 10 ins.; tender (8), 331/2 ins. dia., 
 journals, 6X 11 ins.; wheelbase: driving, 39 ft. 4 ins., rigid, 15 ft., total 
 engine, 56 ft. 7 ins., total engine and tender, 83 ft. 6 ins.; length over all, 
 93ft. 61/2 ins.; weight: on drivers, 394,150 Ibs., on front truck, 14,500 Ibs., 
 on back truck, 17,250 Ibs., total engine 425,900 Ibs., total engine and 
 tender 596,000 Ibs.; tender: water tank capy., 9000 gals., oil tank capy., 
 2850 gals. 
 
 Indicated Water Consumption of Single and Compound Loco- 
 motive Engines at Varying Speeds. 
 
 C. H. Quereau, Eng'g News, March 8, 1894. 
 
 Two-cylinder Compound. 
 
 Single-expansion . 
 
 Revolutions. 
 
 Speed, 
 miles per 
 hour. 
 
 Water per 
 I.H.P. per 
 hour. 
 
 Revolu- 
 tions. 
 
 Miles per 
 Hour. 
 
 Water. 
 
 100 to 150 
 150 to 200 
 200 to 250 
 250 to 275 
 
 21 to 31 
 31 to 41 
 41 to 51 
 51 to 56 
 
 18.33 Ibs. 
 18. 9 Ibs. 
 19.7 Ibs. 
 21.4 Ibs. 
 
 151 
 219 
 253 
 307 
 321 
 
 31 
 45 
 52 
 63 
 66 
 
 21.70 
 20.91 
 20.52 
 20.23 
 20.01 
 
 It appears that the compound engine is the more economical at low 
 speeds, -the economy decreasing as the speed increases, and that the 
 simple engine increases in economy with increase of speed within ordinary 
 limits, becoming more economical than the compound at speeds of more 
 than 50 miles per hour. 
 
 The C., B. & Q. two-cylinder compound, which was about 30% less 
 economical than simple engines of the same class when tested in passenger 
 service, has since been shown to be 15% more economical in freight 
 service than the best single-expansion engine, and 29% more economical 
 than the average record of 40 simple engines of the same class on the 
 same division. 
 
 The water rate is also affected by the cut-off; the following table gives 
 what we should consider very good results in practice, though better 
 (i.e. lower results) have occasionally been obtained. (G. R. Henderson, 
 1906.) 
 
 Cut-off per cent of stroke 10 
 
 Lbs. water per I.H.P. hour simple. . 26 
 Lbs. water per I.H.P. hour compound . . 
 
 Cut-off per cent of stroke 60 
 
 Lbs. water per I.H.P. hour simple. . . 24 
 Lbs. water perl H.P. hour compound 181/2 
 
 Indicator-tests of a Locomotive at High Speed. (Locomotive 
 Eng'g, June, 1893.) - Cards were taken by Mr. Angus SiiiHair on the , 
 noUve drawing tlie Empire State Express, 
 
 20 
 
 30 
 
 40 
 
 50 
 
 23 
 
 22 
 
 22 
 
 23 
 
 
 18 
 
 18 
 
 18 
 
 70 
 
 80 
 
 90 
 
 100 
 
 26 
 
 29 
 
 33 
 
 38 
 
 19l/ 2 
 
 201/ 2 
 
 221/2 
 
 25 
 
LOCOMOTIVES. 1123 
 
 RESULTS OF INDICATOR-DIAGRAMS. 
 Miles Miles 
 
 Card No. Revs, per hour. I.H.P. 
 
 1 160 37.1 648 
 
 2 260 60.8 728 
 
 3 190 44 551 
 
 4 250 58 891 
 
 5 260 60 960 
 
 6 298 69 983 
 
 Card No. Revs, per hour. I.H.P. 
 
 7 304 70.5 977 
 
 8 296 68.6 972 
 
 9 300 69.6 1,045 
 
 10 304 70.5 1,059 
 
 11 340 78.9 1,120 
 
 12 310 71.9 1,026 
 
 The locomotive was of the eight-wheel type, built by the Schenectady 
 Locomotive Works, with 19 X 24 in. cylinders, 78-in. drivers, and a 
 large boiler and fire-box. Details of important dimensions are as fol- 
 lows: Heating-surface of fire-box, 150.8 sq. ft.; of tubes, 1670.7 sq. ft.; 
 of boiler, 1821.5 sq. ft. Grate area, 27.3 sq. ft. Fire-box: length, 
 8 ft.; width, 3 ft. 47/ 8 in. Tubes, 268; outside diameter, 2 in. Ports: 
 steam, 18 X 1 1/4 in.; exhaust, 18X23/ 4 in. Valve-travel, 51/2 in. 
 Outside lap, 1 in. ; inside lap, 1/54 in. Journals: driving-axle, 8 1/2 X 10 1/2 
 in. ; truck-axle, 6 X 10 in. 
 
 The train consisted of four coaches, weighing, with estimated load, 
 340,000 Ibs. The locomotive and tender weighed in working order 200,- 
 000 Ibs., making the total weight of the train about 270 tons. During 
 the time that the engine was first lifting the train into speed diagram 
 No. 1 was taken. It shows a mean cylinder-pressure of 59 Ibs. Accord- 
 ing to this, the power exerted on the rails to move the train is 6553 Ibs., 
 or 24 Ibs. per ton. The speed is 37 miles an hour. When a speed of 
 nearly 60 miles an hour is reached the average cylinder-pressure is 
 40.7 Ibs., representing a total traction force of 4520 Ibs., without mak- 
 ing deductions for internal friction. If we deduct 10% for friction, it 
 leaves 15 Ibs. per ton to keep the train going at the speed named. Cards 
 6, 7, and 8 represent the work of keeping the train running 70 miles an 
 hour. They were taken three miles apart, when the speed was almost 
 uniform. The average cylinder-pressure for the three cards is 47.6 Ibs. 
 Deducting 10% again for friction, this leaves 17.6 Ibs. per ton as the 
 power exerted in keeping the train up to a velocity of 70 miles. 
 Throughout the trip 7 Ibs. of water were evaporated per Ib. of coal. 
 The work of pulling the train from New York to Albany was done on a 
 coal consumption of about 3 Vs Ibs. per H. P. per hour. The highest 
 power recorded was at the rate of 1120 H.P. 
 
 Locomotive-testing Apparatus at the Laboratory of Purdue Uni- 
 versity. (W. F. M. Goss, Trans. A. S. M. E., vol. xiv, 826.) The 
 locomotive is mounted with its drivers upon supporting wheels which 
 are carried by shafts turning in fixed bearings, thus allowing the engine 
 to be run without changing its position as a whole. Load is supplied by 
 four friction-brakes fitted to the supporting shafts and offering resistance 
 to the turning of the supporting wheels. Traction is measured by a 
 dynamometer attached to the draw-bar. The boiler is fired in the 
 usual way, and an exhaust-blower above the engine, but not in pipe 
 connection with it, carries off all that may be given out at the stack. 
 
 A Standard Method of Conductincj Locomotive-tests is given in a report by 
 a Committee of the A.S.M.E. in vol. xiv of the Transactions, page 1312 
 
 Locomotive Tests of the Penna. R. B. Co. Eight locomotives were 
 tested in the dynamometer testing plant built by the P. R. R. Co. at 
 the St. Louis Exhibition in 1903. Among the principal results obtained 
 and conclusions derived are the following: 
 
 BOILER PERFORMANCE. 
 Coal per sq. ft. grate per hour, Ibs. 
 
 20 40 60 80 100 120 
 
 Equiv. evap. per sq. ft. H. S. per hour 
 
 3-5 5-7.5 7-10 8.2-12 10.4-14 11.4-15.3 
 Coal per sq. ft. H. S. per hour 
 
 0.6 0.8 1.0 1.2 1.4 . 1.6 1.8 
 
 Equiv. evap. per Ib. dry coal 
 
 10-11.5 9-10.5 8.2-9.7 7.7-9.1 7.1-8.5 6.6-8.1 6.2-7.7 
 Equiv. evap. per sq. ft. H. S. per hour 
 
 4 6 8 10 32 14 
 
 Equiv. evap. per Ib. dry coal 
 
 9.7-12.1 8.8-11.3 7.8-10.5 6.8-9.6 5.8-8.8 5.5-8 
 
1124 
 
 LOCOMOTIVES,, 
 
 The coal used In these tests was a semi-bituminous, containing 16.25% 
 volatile combustible, 7.00% ash and 0.90% moisture. 
 
 The maximum boiler capacity ranged from 81/2 to more than 16 Ibs. 
 or water evaporated per hour per sq. ft. of heating surface. Little or no 
 advantage was found in the use of Serve or ribbed tubes. 
 
 The boiler efficiency decreases as the rate of power developed increases. 
 
 Furnace losses due to excess air are no greater with large grates properly 
 fired than with smaller ones. The boilers with small grates were inferior 
 in capacity to those with la'ge grates. 
 
 No special advantage is derived from large fire-box heating surface; the 
 tube heating surface is effective in absorbing heat not taken up by the 
 fire-box. 
 
 ENGINE PERFORMANCE. 
 
 Maximum I.H.P., four freight locomotives, 1041, 1050, 1098, 1258 
 
 Maximum I.H.P., four passenger locomotives, 816, 945, 1*622, 1641 
 
 
 Kind of Locomotive. 
 
 Simple 
 Freight. 
 
 Com- 
 pound 
 Freight. 
 
 Com- 
 pound 
 Passen- 
 ger. 
 
 Minimum water per I.H.P. hour 
 
 23.67 
 23.83 
 28.95 
 
 20.26 
 22.03 
 25.31 
 
 18.86 
 21.39 
 24.41 
 
 Water per I.H.P. hr. at maximum. load 
 
 Water per I.H.P. hr. at max. consumption. .. 
 
 The steam consumption of simple locomotives operating at all speeds 
 and cut-offs commonly employed on the road falls between the limits 
 of 23.4 and 28.3 Ibs. per I.H.P. hour; compound locomotives between 
 18.6 and 27 Ibs.; and with superheating the minimum steam consumption 
 was reduced to 16.6 Ibs. of superheated steam. 
 
 Comparing a simple and a compound locomotive, the simple enerine 
 used 40% more steam than the compound at 40 revs, per min., 27% more 
 at 80 revs., and only 7% more at 160 revs, per min. 
 
 The frictional resistance of the engines showed an extreme variation 
 ranging from 6 to 38% of the indicated horse-power. The frictional 
 losses increased rapidly at speeds in excess of 160 revs, per min. It 
 appears that the matter of machine friction is closely related to that of 
 lubrication. With oil lubrication a stress at the draw-bar of approxi- 
 mately 500 Ibs. is required to overcome the friction of each coupled axle, 
 while with grease the required force is from 800 to 1100 Ibs. 
 
 The lowest figures for dry coal consumed per dynamometer H.P. hour 
 were approximately as follows: 
 Revs, per min 40 80 
 
 Compound freight engine, { oVp^ 500 foQ 5 
 Compound passenger engine, { DH^P. .*.' '.' 600 
 
 A complete report of the St. Louis locomotive tests is contained in a 
 k>ok of 734 pages and over 800 illustrations, published by the Penna. R.R. 
 Co., Philadelphia, 1906. See also pamphlet on Locomotive Tests, pub- 
 lished by Amer. Locomotive Co., New York, 1906, and Trans. A.S. M. E. t 
 vii, 610. 
 
 Weights and Prices of Locomotives, 1885 and 1905. 
 (Baldwin Loco. Wks.) 
 
 160 
 
 3.25 
 
 800 
 
 2.3 
 
 900 
 
 240 
 
 3.0 
 1000 
 
 Type. 
 
 W'gt 
 
 Price 
 
 Price 
 per 
 Ib. 
 
 
 
 Type. 
 
 W'ght 
 
 Price 
 
 Price 
 per 
 Ib. 
 
 American. . . . 
 Mogul 
 
 80,857 
 72,800 
 85,000 
 92,400 
 
 $6,695 
 6,662 
 7.583 
 7,888 
 
 $ 0828 
 .0912 
 .0892 
 .0854 
 
 American 
 Atlantic 
 
 102,000 
 187,200 
 227,000 
 156,000 
 192,460 
 
 $9,410 
 15,750 
 15,830 
 13,690 
 14,500 
 
 $.092 
 .083 
 .070 
 .088 
 .075 
 
 Ten wheel. . . 
 Consolidation 
 
 Pacific 
 
 Ten wheel 
 Consolidation . 
 
LOCOMOTIVES. 
 
 1125 
 
 The price per pound is figured from the weight of the engine in working 
 order, without the tender. 
 
 Depreciation of Locomotives. (Baldwin Loco. Wks.) It is suggested 
 that for the first five years the full second-hand value of the locomotive 
 (75% of first cost) be taken; for the second five years 85% of this value; 
 for the third five years, 70% ; after 15 years, 50% of the second-hand value; 
 and after 20 years, and as long as the engine remains in use, 25% of the 
 first cost. 
 
 The Average Train Loads of 14 railroads increased from 229 tons of 
 2000 Ibs. in 1895 to 385 tons in 1904. On the Chicago, Milwaukee & St. 
 Paul Ry. the average load increased from 152 tens in 1895 to 281 tons in 
 1903, and on the Lake Shore & Michigan Southern Ry. from 318 tons in 
 1895 to 615 tons in 1903. In the same time the average cost of transpor- 
 tation per ton mile on the C., M. & St. P. Ry. decreased from 0.67 to 0.58 
 cent; and on the L. S. & M. S. Ry. increased from 0.39 to 0.41 cent, the 
 decrease in cost due to heavier train loads being offset by higher cost for 
 labor and material. 
 
 Tractive Force of Locomotives, 1893 and 1905. 
 
 (Baldwin Loco. Wks.) 
 
 Passenger, 1893. 
 
 Weight 
 on 
 Driver. 
 
 Trac- 
 tive 
 Force. 
 
 Passenger, 1905. 
 
 Weight 
 on 
 Driver. 
 
 Trac- 
 tive 
 Force. 
 
 American, single-ex. 
 American, comp 
 
 75,210 
 83,860 
 
 17,270 
 12,900 
 
 Atlantic, comp. .. . 
 Atlantic, single-ex. 
 
 101,420 
 103,600 
 
 22,180 
 23,800 
 
 American, single-ex.. 
 American, comp .... 
 Ten- wheel type, com. 
 
 64,560 
 78,480 
 93,850 
 
 15,550 
 14,050 
 16,480 
 
 15,250 
 
 Pacific, single-ex. . 
 Pacific, single-ex. . 
 Atlantic, single-ex. 
 
 141,290 
 114,890 
 80,930 
 
 29,910 
 25,610 
 21,740 
 
 24,648 
 
 
 
 
 
 
 
 Freight, 1893. 
 
 
 
 Freight, 1905. 
 
 
 
 Consolidation, comp. 
 Ten-wheel, s'gle-ex.. 
 Mogul, single-ex 
 Decapod, compound 
 
 120,600 
 101,000 
 91,340 
 172,000 
 
 21,190 
 23,310 
 21,030 
 35,580 
 
 Sante Fe type, comp. 
 3onsol., 2-cyl. comp.. 
 3onsol., single-ex.. .. 
 3onsol., single-ex.... 
 Consol., single-ex. . . . 
 
 234,580 
 166,000 
 151,490 
 171,560 
 165,770 
 
 62,740 
 40,200 
 40,150 
 44,080 
 45,170 
 
 
 
 25,277 
 
 
 
 46,468 
 
 
 
 
 
 
 
 Waste of Fuel in Locomotives. In American practice economy 
 of fuel is necessarily sacrificed to obtain greater economy due to heavy 
 train-loads. D. L. Barnes, in Eng. Mag., June, 1894, gives a diagram 
 showing the reduction of efficiency of boilers due to high rates of com- 
 bustion, from which the following figures are taken: 
 
 Lbs. of coal per sq. ft. of grate per hour. . . 12 
 Per cent efficiency of boiler 80 
 
 80 
 67 
 
 120 
 59 
 
 160 
 51 
 
 200 
 43 
 
 A rate of 12 Ibs. is given as representing stationary-boiler practice, 40 
 Ibs. English locomotive practice, 120 Ibs. average American, and 200 
 Ibs. maximum American, locomotive practice. 
 
 Pages 473 and 475 of Henderson's "Locomotive Operation" giv* 
 diagrams of evaporation per Ib. of various kinds of coal for different 
 rates of combustion per sq. ft. grate area and heating surface. 
 
 Advantages of Compounding. Report of a Committee of the 
 American Railway Master Mechanics' Association cm Compound Loco, 
 motives (Am, Mack., July 3, 1890) gives the following summary of the 
 advantages gained by compounding: (a) It has achieved a saving in the 
 fuel burnt averaging 18% at reasonable boiler-pressures, with encourag- 
 in? possibilities of further improvement in pressure and in fuel and water 
 economy. (6) It has lessened the amount of water (dead weight) to bt 
 
1126 LOCOMOTIVES* 
 
 hauled, so that (c) the tender and its load are materially reduced In 
 weight, (d) It has increased the possibilities of speed far beyond 60 
 miles per hour, without unduly straining the motion, frames, axles, 01 
 axle-boxes of the engine, (e) It has increased the haulage-power at 
 full speed, or, in other words, has increased the continuous H.P. devel- 
 oped, per given weight of engine and boiler. (/) In some classes has 
 increased the starting-power, (g) It has materially lessened the slide- 
 valve friction per H.P. developed, (h) It has equalized or distributed 
 the turning force on the crank-pin, over a longer portion of its path, 
 which, of C9urse, tends to lengthen the repair life of the engine, (i) In 
 the two-cylinder type it has decreased the oil consumption, and has even 
 done so in the Woolf four-cylinder engine, (j) Its smoother and steadier 
 draught on the fire is favorable to the combustion of all kinds of soft 
 coal; and the sparks thrown being smaller and less in number, it lessens 
 the risk to property from destruction by fire, (k) These advantages 
 arid economies are gained without having to improve the man handling 
 the engine, less being left to his discretion (or careless indifference) than 
 in the simple engine. (I) Valve- motion, of avery ^comotive type, can 
 be used in its best working and most effective position, (m) A wider 
 elasticity in locomotive design is permitted; as, if desired, side-rods can 
 be dispensed with, or articulated engines of 100 tons weight, with inde- 
 pendent trucks, used for sharp curves on mountain service, as suggested 
 by Mallet and Brunner. 
 
 Of 27 compound locomotives in use on the Phila. and Reading Rail- 
 road (in 1892), 12 are in use on heavy mountain grades, and are designed 
 to be the equivalent of 22 X 24 in. simple consolidations; 10 are in some- 
 what lighter service and correspond to 20 X 24 in. consolidations; o are 
 in fast passenger service. The monthly coal record shows: 
 
 Gain in Fuel 
 Class of Engine. No Economy. 
 
 Mountain locomotives. . . . . . 12 25% to 30% 
 
 Heavy freight service 10 12% to 17% 
 
 Fast passenger 5 9% to 11 % 
 
 (Report of Com. A. R. M. M. Assn. 1892.) For a description of the 
 various types of compound locomotive, with discussion of their relative 
 merits, see paper by A. Von Borries, of Germany, the Development of 
 the Compound Locomotive, Trans. A. S. M. E., 1893, vol. xiv, p. 1172. 
 
 As a rule compounds cost considerably more for repairs, and require 
 ^ better class of engineers and machinists to obtain satisfactory results. 
 (Henderson.) 
 
 Balanced Compound Locomotives, There are two high-pressure 
 cylinders placed between the frames and two low-pressure cylinders 
 outside. The inside crank shaft has cranks 90 apart, and each outside 
 crank pin is 180 from the inside crank pin on the same side, so that the, 
 engine on each side is perfectly balanced. The balanced piston valve is 
 so made that high-pressure steam may be admitted to the low-pressure 
 cylinder for starting. See circular of the Baldwin Loco. Wks., No. 62, 1907. 
 
 Superheating in Locomotives. (R. R. Age Gazelle, Nov. 20, 1908.) 
 Superheating steam in locomotives has been found to effect a saving of 
 10 to 15% in the fuel consumption of a locomotive, and 8 to 12% of the 
 water used, or with the same fuel to increase the horse-power and the 
 tractive force. The Baldwin Locomotive Works builds a superheater in 
 the smoke-box, where it utilizes part of the heat of the waste gases in 
 drying the steam and superheating it 50 to 100 F. The heating surface 
 of the superheater is from 12 to 22% of the heating surface in the tubes and 
 fire-box of the boiler. It is recommended to use a boiler pressure of about 
 160 Ibs. when a superheater is used, and to have cylinders of larger dimen- 
 sions than when ordinary steam of 200 Ibs. pressure is used. For an illus- 
 trated and historical description of the use of superheating in locomotives, 
 see paper by H. H. Vaughan, read before the Am. Ry. Mast. Mechs.' Assn., 
 Eng. News, June 22, 1905. 
 
 Counterbalancing Locomotives. Rules for counterbalancing, 
 adopted by different locomotive-builders, are quoted in a paper by Prof. 
 Lanza (Trans. A. *S. M. E., x, 302.) See also articles on Counterbalan- 
 cing Locomotives, in R. R. & Eng. Jour., March and April, 1890; Trans. 
 A. . M . E., vol. xvi, 305; and Trans. Am c Ry. Master Mechanics' Assru 
 
LOCOMOTIVES. 1127 
 
 1897. W. E. Dalby's book on the "Balancing of Engines" (Longmans, 
 Green & Co., 1902) contains a very full discussion of this subject. See 
 also Henderson's "Locomotive Operation" (The Railway Age, 1904). 
 
 Narrow-gauge Railways in Manufacturing Works. A tramway 
 of 18 inches gauge, several miles in length, is in the works of the Lan- 
 cashire and Yorkshire Railway. Curves of 13 feet radius are used. 
 The locomotives used have the following dimensions (Proc. Inst. M. E.. 
 July, 1888): The cylinders are 5 in. in diameter with 6 in. stroke, and 
 2 ft. 31/4 in. centre to centre. Wheels 161/4 in. diameter, the wheel-base 
 2 ft. 9 in.; the frame 7 ft. 4*/4 in. long, and the extreme width of the 
 engine 3 feet. Boiler, of steel, 2 ft. 3 in. outside diam. and 2 ft. long 
 between tube-plates, containing 55 tubes of 13/ 8 in. outside diam.; fire- 
 box, of iron and cylindrical, 2 ft. 3 in. long and 17 in. inside diam. Heat- 
 ing-surface 10.42 sq. ft. in the fire-box and 36.12 in the tubes, total 46.54 
 sq. ft.; grate-area, 1.78 sq. ft.; capacity of tank, 261/2 gallons; working- 
 pressure, 170 Ibs, per sq. in. tractive power, say, 1412 Ibs., or 9.22 Ibs. per 
 fb. of effective pressure per sq. in., on the piston. Weight, empty, 2.80 
 tons; full and in working order, 3.19 tons. 
 
 For description of a system of narrow-gauge railways for manufac- 
 tories, see circular of the C. W. Hunt Co., New York, 
 
 Light Locomotives. For dimensions of light locomotives used for 
 mining, etc., arid for much valuable information concerning them, see 
 catalogue of H. K. Porter Co., Pittsburgh. 
 
 Petroleum-burning Locomotives. (From Clark's Steam-engine.) 
 The combustion of petroleum refuse in locomotives has been success- 
 fully practised by Mr. Thos. Urquhart, on the Grazi and Tsaritsin Rail- 
 way, Southeast Russia. Since November, 1884, the whole stock of 143 
 locomotives under his superintendence has been fired with petroleum 
 refuse. The oil is injected from a nozzle through a tubular opening in 
 the back of the fire-box, by means of a jet of steam, with an induced 
 current of air. 
 
 A brickwork cavity or "regenerative or accumulative combustion, 
 chamber" is formed in the fire-box, into which the combined current 
 breaks as spray against the rugged brickwork slope. In this arrange- 
 ment the brickwork is maintained at a white heat, and combustion is 
 complete and smokeless. The form, mass, and dimensions of the brick- 
 work are the most important elements in such a combination. 
 
 Compressed air was tried instead of steam for injection, but no appre- 
 ciable reduction in consumption of fuel was noticed. 
 
 The heating-power of petroleum refuse is given as 19,832 heat-units, 
 equivalent to the evaporation of 20.53 Ibs. of water from and at 212 F., 
 or to 17.1 Ibs. at 81/2 atmospheres, or 125 Ibs. per sq. in., effective pres- 
 sure. The highest evaporative duty was 14 Ibs. of water under 81/2 
 atmospheres per Ib. of the fuel, or nearly 82% efficiency. 
 
 There is no probability of any extensive use of petroleum as fuel for 
 locomotives in the United States, on account of the unlimited supply of 
 coal and the comparatively limited supply of petroleum. Texas and 
 California oils are now (1902) used in locomotives of the Southern Pacific 
 Railway and the Santa Fe System. 
 
 Self-propelled Railway Cars. The use of single railway cars con- 
 taining a steam or gasolene motor has become quite common in Europe. 
 For a description of different systems see a paper on European Railway 
 Motor Cars by B. D. Gray in Trans A. S. M. E., 1907. 
 
 Tireless Locomotive. The principle of the Francq locomotive is 
 that it depends for the supply of steam on its spontaneous generation 
 from a body of heated water in a reservoir. As steam is generated and 
 drawn off the pressure falls; but by providing a sufficiently large volume 
 of water heated to a high temperature, at a pressure correspondingly 
 high, a margin of surplus pressure may be secured, and means may tmif 
 be provided for supplying the required quantity of steam for the trip. 
 
 The fireless locomotive designed for the service of the Metropolitan 
 Railway of Paris has a cylindrical reservoir having segmental ends, 
 about S^ft. 7 in. in diameter, 261/4 ft. in length, with a capacity of about 
 620 cubic feet. Four-fifths of the capacity is occupied by water, which 
 3 heated by the aid of a powerful jet of steam supplied from stationary 
 boilers. The water is heated until equilibrium is established between 
 the boilers and the reservoir. The temperature is raised to about 390 F. t 
 corresponding to 225 Ibs. per sq. in. The steam from the reservoir it 
 
1128 
 
 LOCOMOTIVES 
 
 passed through a reducing-valve, by which the steam is reduced to the 
 required pressure. It is then passed through a tubular superheater 
 situated within the receiver at the upper part, and thence through the 
 Ordinary regulator to the cylinders. The exhaust-steam is expanded to 
 a low pressure, in order to obviate noise of escape. In certain cases the 
 exhaust-steam is condensed in closed vessels, which are only in part 
 filled with water. 
 
 In working off the steam from a pressure of 225 Ibs. to 67 Ibs., 53G 
 cubic feet of water at 390 F. is sufficient for the traction of the trains, 
 for working the circulating-pump for the condensers, for the brakes, 
 and for electric-lighting of the train. At the stations the locomotive 
 takes from 2200 to 3300 Ibs. of steam nearly the same as the weight 
 of steam consumed during the run between two consecutive charging 
 stations. There is 210 cubic feet of condensing water. Taking the 
 initial temperature at 60 F., the temperature rises to about 180 F. 
 after the longest runs underground. 
 
 The locomotive has ten wheels, on a base 24 ft long, of which six are 
 coupled. 41/2 ft. in diameter. The extreme wheels are on radial axles. 
 The cylinders are 231/2 in. in diameter, with a stroke of 231/2 in. 
 
 The engine weighs, in working order, 53 tons, of which 36 tons are on 
 the coupled wheels. The speed varies from 15 miles to 25 miles per hour. 
 The trams weigh about 140 tons. 
 
 Compressed-air Locomotives. A compressed-air locomotive con- 
 sists essentially of a storage tank mounted upon driving wheels, with two 
 engines similar to those of a steam locomotive. One or more reservoirs or 
 storage tanks are located on the line, from which the locomotive tank is 
 charged. These reservoirs are usually riveted steel cylinders, designed 
 for about 1000 Ibs. working pressure; but sometimes seamless steel cylinders 
 of small diameter, designed for a working pressure of 2000 Ibs. or upwards, 
 are used. The customary maximum pressure in the locomotive tank is 
 800 Ibs. gauge, and the working pressure in the cylinders is from 130 to 
 140 Ibs. The following table is condensed from one in a circular of the 
 Baldwin Locomotive Works, No. 46, 1904. 
 
 See account of the Mekarski compressed-air locomotives, page 652 ante. 
 
 DIMENSIONS AND TRACTIVE POWER OF FOUR COUPLED COMPRESSED-AIR 
 LOCOMOTIVES HAVING Two STORAGE TANKS. 
 
 Class 
 
 4-4-C 
 
 4-6-C 
 
 4-8-C 
 
 4-10-C 
 
 4-1 2-C 
 
 4-16-C 
 
 4-18-C 
 
 
 
 
 
 
 
 
 
 Cylinders, inches .... 
 Diam. of drivers 
 Wheel base 
 
 5X10 
 22" 
 4f 0" 
 
 6X10 
 24" 
 4' 3" 
 
 7X12 
 24" 
 4' 6" 
 
 8X14 
 26" 
 5' V f 
 
 9X14 
 28" 
 
 y y, 
 
 11X14 
 
 28" 
 
 y 6" 
 
 12X16 
 30" 
 6' 0" 
 
 Approx. weight, Ibs.. 
 Inside dia. of tanks. . 
 Aggregate tank vol., 
 cu. ft 
 
 10,000 
 26" 
 
 75 
 
 14,000 
 28* 
 
 100 
 
 18,000 
 30" 
 
 130 
 
 23,000 
 32" 
 
 170 
 
 27,000 
 34" 
 
 200 
 
 37,000 
 38" 
 
 280 
 
 44,00$ 
 40* 
 
 320 
 
 App. height 
 
 4 y 
 
 4 10" 
 
 y o" 
 
 y 4 
 
 5' 8" 
 
 6' 0* 
 
 d 4* 
 
 App. width ever 
 tanks . . 
 
 4' 10* 
 
 y 2" 
 
 y 6" 
 
 y 10* 
 
 & y i 
 
 7' 0* 
 
 7 4* 
 
 App. width over cyl- 
 
 Gauge 
 +24" 
 
 Gauge 
 +26" 
 
 Gauge 
 +27" 
 
 Gauge 
 +28" 
 
 Gauge 
 +30" 
 
 Gauge 
 +32" 
 
 Gauge 
 + 33" 
 
 App. length over 
 
 12' 0" 
 
 If 0" 
 
 15' 0" 
 
 17' 0" 
 
 18' 0" 
 
 2(X 0" 
 
 20 7 6' 
 
 t,Full stroke 
 ' g 3/4 Stroke cut-off 
 o V2 Stroke cut-off 
 PL, l/ 4 Stroke cut-off 
 
 1350 
 1290 
 940 
 510 
 
 1785 
 1700 
 1240 
 670 
 
 2915 
 2780 
 2025 
 1100 
 
 4100 
 3900 
 2840 
 1540 
 
 4820 
 4580 
 3345 
 1815 
 
 7200 
 6860 
 4995 
 2710 
 
 9140 
 8705 
 6340 
 3440 
 
 Draw-bar pull on any grade= tractive power - (.0075 + % of grade) 
 X weight of engine. 
 
 Working pressure in cylinders 140 Ibs.; tank storage pressure, 800 Ibs. 
 
 Other sizes of engines are 51/2X 10 in., 6X12 in., and 8 X12in., 24-in, 
 item, of drivers; 9X14 in., 26-in. drivers, and 10 X 14 in.. 28-in. drivers. . 
 
COMPRESSED-AIK LOCOMOTIVES. 
 
 1129 
 
 CUBIC FEET OF Am, AT ^DIFFERENT STORAGE PRESSURES, REQUIRED TO 
 HAUL ONE TON ONE MILE AT HALF STROKE CUT-OFF, WITH 20, 30 
 AND 40 LBS. FRICTIONAL RESISTANCE PER TON. (Baldwin Loco. Wks.) 
 
 Storage pressure 
 Cylinder working 
 pressure 
 
 
 600 
 130 
 
 700 
 135 
 
 800 
 140 
 
 
 600 
 130 
 
 700 
 135 
 
 800 
 140 
 
 
 600 
 130 
 
 700 
 135 
 
 800 
 140 
 
 
 
 
 
 
 Grade. 
 
 R 
 
 V 
 
 V 
 
 V 
 
 R 
 
 V 
 
 V 
 
 V 
 
 R 
 
 V 
 
 V 
 
 V 
 
 1.74 
 2.23 
 2.73 
 1 70 
 
 Level 
 
 20.0 
 31.2 
 
 42.4 
 64.8 
 87.2 
 109 6 
 
 1.16 
 
 1.81 
 2.47 
 1 7ft 
 
 0.99 
 1.56 
 2.12 
 1 74 
 
 0.87 
 1.36 
 1.85 
 7 8S 
 
 30.0 
 41.2 
 52.4 
 74 8 
 
 1.74 
 2.40 
 3.05 
 
 4 15 
 
 1.50 
 2.05 
 2.61 
 ^ 73 
 
 1.31 
 1.79 
 
 2.28 
 3 76 
 
 40.0 
 51.2 
 62.4 
 84 8 
 
 2.33 
 2.98 
 3.64 
 4 94 
 
 1.99 
 2.56 
 3.11 
 
 4 ?4 
 
 1/2% 
 
 1% 
 
 2% 
 
 3% 
 
 5.08 
 6 39 
 
 4.35 
 5 48 
 
 3.81 
 4 79 
 
 97.2 
 119 6 
 
 5.67 
 6 97 
 
 4.86 
 5 97 
 
 4.25 
 5 7^ 
 
 107.2 
 129 6 
 
 6.25 
 7 56 
 
 5.35 
 6 47 
 
 4.69 
 5.67 
 6.64 
 
 4%.. 
 
 5% 
 
 132.0 
 
 7.69 
 
 6.60 
 
 5.77 
 
 142.0 
 
 8.27 
 
 7.09 
 
 6.20 
 
 152.0 
 
 8.86 
 
 7.60 
 
 
 R= resistance per ton of 2240 Ibs. in pounds. V = cubic feet of air. 
 
 Air Locomotives with Compound Cylinders and Atmospheric Interheater^ 
 are built by H. K. Porter Co. The air enters the high-pressure cylinder 
 at 250 Ibs. gauge pressure and is expanded down to 50 Ibs., overcoming 
 resistance, while the temperature drops about 140 F. This loss of heat 
 is practically all restored in the atmospheric interheater, which is a 
 cylindrical reservoir filled with brass tubes located in the passage-way 
 from the high- to the low-pressure cylinder. The air enters the low- 
 pressure cylinder at 50 Ibs. gauge and a temperature within 10 or 20 of 
 that of the surrounding atmosphere. The exhaust is used to induce a 
 draught of atmospheric air through the tubes of the interheater. This 
 combination permits of expanding the air from 250 Ibs. down to atmos- 
 phere without unmanageable refrigeration. 
 
 The following calculation shows the relative economy of a single- cylinder 
 locomotive using air at 150 Ibs. and of a compound using air at 250 Ibs. 
 in the high-pressure and 50 Ibs. in the low-pressure cylinder, non-expan- 
 sive working being assumed in both cases. 
 
 11.2 cu. ft. of free air at 150 Ibs. gauge and atmospheric temperature 
 would fill a cylinder of 1 cu. ft. capacity, and in moving a piston of 1 sq. 
 ft. area one foot would develop 144 X 150 = 21,600 ft. Ibs. of energy. 
 
 11.2 cu. ft. of free air at 250 Ibs. gauge if used in a cylinder 0.623 sq. ft. 
 area and 1 ft. stroke would develpp 0.623 X 144 X 250= 22,425 ft. Ibs. 
 
 If expanded in two cylinders with a ratio of 4 to 1 the energy developed 
 would be 0.623 X 144 X 200 plus 4 X 0.623 X 144 X 50 = 35,880 ft. Ibs., if 
 the heat is restored between the two cylinders. Gain by compounding 
 with interheating, over simple cylinders with 150 Ibs. initial pressure, 
 35,880 ^ 21,600 = 1.66. 
 
 . These results are about the best that can be obtained with either 
 simple or compound locomotives, as any improvement due to expansive 
 working just about balances the losses due to clearance and initial refrig- 
 eration. The work done per cubic foot of free air in the two systems is: 
 with simple cylinders, 21,600 * 11.2 = 1840 ft. Ibs.; with compound 
 cylinders and atmospheric interheater, 35,880 -* 11.2 = 3205 ft.' Ibs. 
 
 The above calculations have been practically confirmed by actual 
 tests which show 1900 ft. Ibs. of work per cubic foot of free air with the 
 simple locomotive and 3000 ft. Ibs. with the compound, the gain due to 
 expansive working and the losses due to internal friction being some- 
 what greater in the compound than in the simple machine. 
 
 In the operation of compressed-air locomotives the air compressor is 
 generally delivering compressed air at a pressure fluctuating between 
 30 and 1000 Ibs. per sq. in. into the storage reservoir, and it requires an 
 average of about 12,000 ft. Ibs. per cubic foot of free air to compress and 
 deliver it at these pressures. The efficiency of the two systems then is: 
 1900 -4- 12000 = 16% for the simple locomotive, and 3000 -*- 12000 = 
 25% for the compound with atmospheric mterheater. 
 
SHAFTING. 
 
 SHAFTING. 
 
 (See also TORSIONAL STRENGTH; also SHAFTS OF STEAM ENGINES.) 
 For shafts subjected to torsion only, let d = diam. of the shaft in ins., 
 P = a force in Ibs. applied on a lever arm at a distance = a ins. from 
 the axis, S = shearing resistance at the outer fiber, in Ibs. per sq. in., then 
 
 If R = revolutions per minute, then the horse-power transmitted = 
 
 Pa27cR nd*S X2xR RSd* . 
 
 33,000X12 16X33,000X12 321,000' 
 
 3 /321,OOOH.'pT_ A 3 /CXH.P. 
 
 " V " RS = V W~ 
 
 In practice, empirical values are given to S and to the coefficients 
 K = S/5.1and C = 321,000/5, according to the factor of safety assumed, 
 depending on the material, on whether the shaft is subjected to steady, 
 fluctuating, bending, or reversed strains, on the distance between bear- 
 ings, etc. Kimball and Barr (Machine Design) state that the following 
 factors of safety are indicated by successful practice: For head shafts, 
 15; for line shafts carrying pulleys, 10; for small short shafts, counter- 
 shafts, etc., 7. For steel shafting the allowable stress, S, for the above 
 factors would be about 4000, 6000 and 8500 Ibs. respectively, whence 
 
 8 i > 
 
 t/ 80 ^' P ' ; 
 
 for head shafts d= i/ p " ; for line shafts d= i/ p ; for short 
 shafts d = 
 
 /QO TT T> 
 
 7dS U..V. 
 
 VR 
 
 Jones & Laughlin Steel Co. gives the following for steel shafts: 
 
 Turned. Cold-rolled. 
 
 For simply transmitting power ) 
 
 and short countershafts, bear-J H.P. = d z R * 50 H.P = d 3 R -* 40 
 
 ings not more than 8 ft. apart ) 
 As second movers, or line shafts, I TT -p ^ar> . on u r> MT> , 7n 
 
 bearings 8 ft. apart } H ' P ' = d R * 
 
 As prime movers or head shafts! 
 
 carrying mairi driving pulley I TT r> _ ,731? . 10 * w T> _ ^ao inn 
 
 or gear, well supported by\ a "^'~ aK ' 
 
 bearings J 
 
 Jones & Laughlins give the following notes: Receiving and transmit- 
 ting pulleys should always be placed as close to bearings as possible; 
 and it is good practice to frame short "headers" between the main tie- 
 beams of a mill so as to support the main receivers, carried by the head 
 shafts, with a bearing close to each side as is contemplated in the for- 
 mulae. But if it is preferred, or necessary, for the shaft to span the full 
 width of the "bay" without intermediate bearings, or for the pulley to 
 be placed away from the bearings towards or at the middle of the bay, 
 the size of the shaft must be largely increased to secure the stiffness 
 necessary to support the load without undue deflection. 
 
 Diameter of_sh_aft D to carry load at center of bays from 2 to 12 ft. 
 
 span, D = t/- d 4 , in which d is the diameter derived from the formula 
 
 for head shafts, c = length of bay in inches, and Ci= distance in inches 
 between centers of bearings in accordance with the formula for horse- 
 
SHAFTING. 
 
 1131 
 
 power of head shafts. (Jones & Laughlin Steel Co.) 
 different diameters d are as follows: 
 
 Values of c\ for 
 
 d Cj 
 
 d c, 
 
 d GI 
 
 d d 
 
 d c\ 
 
 d Cj 
 
 1 to 13/8 15 
 
 213/10 25 
 
 3 15/ie & 4 37 
 
 51/4 & SS/g 55 
 
 63/8 71 
 
 73/8 88 
 
 Ul/16 & l 3 /4 16 
 
 27/8 to 3 26 
 
 43/16 40 
 
 51/2 57 
 
 61/2 73 
 
 71/2 95 
 
 H3/16 & 17/8 17 
 
 3 l/s to 3 1/4 28 
 
 41/4 41 
 
 55/ 8 59 
 
 65/8 75 
 
 75/s 93 
 
 1 15/16 to 2 l/s 18 
 
 33/8 30 
 
 47/ie & 41/2 44 
 
 53/4 61 
 
 63/4 77 
 
 73/4 96 
 
 23/16 & 2 1/4 19 
 25/16 to 27/ifl 20 
 21/2 to 25/8 24 
 
 37/ie & 31/2 31 
 39/ 16 &35/ 8 33 
 3 11/ie & 3 3/4 34 
 
 43/4 47 
 413/16 49 
 5 51 
 
 57/ 8 63 
 6 65 
 61/8 67 
 
 67/8 79 
 7 81 
 71/8 84 
 
 77/8 99 
 8 101 
 81/2 112 
 
 '2H/16 & 23/4 22 
 
 37/ 8 36 
 
 5V8 52 
 
 61/4 69 
 
 71/4 86 
 
 9 123 
 
 Should the load be applied near one end of the span or bay instead of 
 at the center, multiply the fourth power of the diameter of the shaft 
 required to carry the load at the center of the span or bay by the prod- 
 uct of the two parts of the shaft when the load is near one end, and 
 divide this product by the product of the two parts of the shaft when 
 the load is carried at the center. The fourth root of this quotient will 
 be the diameter required. 
 
 The shaft in a line which carries a receiving-pulley, or which 'carries a 
 transmitting-pulley to drive another line, should always be considered a 
 head-shaft, and should be of the size given by the rules for shafts carrying 
 main pulleys or gears. 
 
 The greatest admissible distance between bearings of shafts subject to 
 no transverse strain except from their own weight is for cold-rolled. shafts, 
 
 L = <y 330,608 X D 2 , and for turned shafts, L t = -^319,586 X D 2 . D = 
 diam. and L = length of shaft, in inches. These formulae are based on 
 an allowable deflection at the center of Vso in. per foot of length, weight 
 of steel 490 Ibs. per cu. ft., and modulus of elasticity = 29,000,000 for 
 turned and 30,000,000 for cold-rolled shafting. [In deriving these formulae 
 the weight of the shaft has been taken as a concentrated instead of a dis- 
 tributed load, giving additional safety.] 
 
 Kimball and Barr say that the lateral deflection of a shaft should not 
 exceed 0.01 in. per foot of length, to insure proper contact at the bear- 
 ings. For ordinary small shafting they give_the following as the allow- 
 
 able distance between the hangers: L = 7 ^d?, for shaft without pulleys; 
 L = 5 -\J d?, for shaft carrying pulleys. (L in ft., d in ins.) 
 
 Deflection of Shafting. (Pencoyd Iron Works.) For continuous 
 iine-shafting it is considered good practice to limit the deflection to a 
 maximum of 1/100 of an inch per foot of length. The weight of bare shaft- 
 ing in pounds = 2.6 d 2 L = W, or when as fully loaded with pulleys as is 
 customary in practice, and allowing 40 Ibs. per inch of width for the 
 vertical pull of the belts, experience shows the load in pounds to be about 
 13 d 2 L = W. Taking the modulus of transverse elasticity at 26,000,000 
 Ibs., we derive from authoritative formulae the following: 
 
 L = -^ 873 d*, d -- 
 L = -x/175d 2 , d 
 
 ' LV873, for bare shafting; 
 
 /LV175, for shafting carrying pulleys, etc. , 
 
 L being the maximum distance in feet between bearings for continuous 
 shafting subjected to bending stress alone, d = diam. in inches. 
 
 The torsional stress is inversely proportional to the velocity of rota- 
 tion, while the bending stress will not be reduced in the same ratio. It 
 is therefore impossible to write a formula covering the whole problem 
 and sufficiently simple for practical application, but the following rules 
 are correct within the range of velocities usual in practice. 
 
 For continuous shafting so proportioned as to deflect not more than 
 
1132 
 
 SHAFTING, 
 
 1/100 of an Inch per foot of length, allowance being made for the weaken- 
 ing effect of key-seats, 
 
 d = ^50 H.P. -*- R, L = ^720 d* t for bare shafts; 
 
 d = ^70 H.P. -*- R, L = ^140 d 2 , for shafts carrying pulleys, etc. 
 
 d = diam. in inches, L = length in feet, R = revs, per min. 
 
 The following are given by J. B. Francis as the greatest admissible dis- 
 tances between the bearings of continuous steel shafts subject to no trans- 
 verse strain except from their own weight, as would be the case were the 
 power given off from the shaft equal on all sides, and at an equal distance 
 from the hanger-bearings. 
 
 Diam. of shaft, in. ...23 45 67 8 9 
 
 Dist. bet. bearings, ft. 15.9 18.2 20.0 21.6 22.9 24.1 25.2 26.2 
 
 These conditions, however, do not usually obtain in the transmission of 
 power by belts and pulleys, and the varying circumstances of each case 
 render it impracticable to give any rule which would be of value for 
 universal application. 
 
 For example, the theoretical requirements would demand that the 
 bearings be nearer together on those sections of shafting where most 
 power is delivered from the shaft, while considerations as to the location 
 and desired contiguity of the driven machines may render it impracti- 
 cable to separate the driving-pulleys by the intervention of a hanger at 
 the theoretically required location. (Joshua Rose.) 
 
 Horse-Power Transmitted by Cold-rolled Steel Shafting at Different 
 Speeds as Prime Movers or Head Shafts Carrying Main Driving 
 Pulley or Gear, well Supported by Bearings. 
 
 Formula H.P. = <f 3 JR -^ 100. 
 
 Revolutions per minute. 
 
 Revolutions per minute. 
 
 Diam. 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 Diam. 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 n/2 
 
 3.4 
 
 6.7 
 
 10.1 
 
 13.5 
 
 16.9 
 
 27/8 
 
 24 
 
 48 
 
 72 
 
 95 
 
 119 
 
 19/16 
 
 3.8 
 
 7.6 
 
 11.4 
 
 15.2 
 
 19.0 
 
 215/16 
 
 25 
 
 51 
 
 76 
 
 101 
 
 127 
 
 > 5 /8 
 
 4.3 
 
 8.6 
 
 12.8 
 
 17.1 
 
 21 
 
 3 
 
 27 
 
 54 
 
 81 
 
 108 
 
 135 
 
 1 n /16 
 
 4.8 
 
 9.6 
 
 14.4 
 
 19.2 
 
 24 
 
 3V8 
 
 31 
 
 61 
 
 91 
 
 122 
 
 152 
 
 13/4 
 
 5.4 
 
 10.7 
 
 16.1 
 
 21 
 
 27 
 
 33/ie 
 
 32 
 
 65 
 
 97 
 
 129 
 
 162 
 
 1 !3/i6 
 
 5.9 
 
 11.9 
 
 17.8 
 
 24 
 
 30 
 
 31/4 
 
 34 
 
 69 
 
 103 
 
 137 
 
 172 
 
 17/8 
 
 6.6 
 
 13.1 
 
 19.7 
 
 26 
 
 33 
 
 33/8 
 
 38 
 
 77 
 
 115 
 
 154 
 
 192 
 
 115/16 
 
 7.3 
 
 14.5 
 
 22 
 
 29 
 
 36 
 
 37/i 6 
 
 41 
 
 81 
 
 122 
 
 162 
 
 203 
 
 2 
 
 8.0 
 
 16.0 
 
 24 
 
 32 
 
 40 
 
 3V2 
 
 43 
 
 86 
 
 128 
 
 171 
 
 214 
 
 2Vl6 
 
 8.8 
 
 17.6 
 
 26 
 
 35 
 
 44 
 
 39/16 
 
 45 
 
 90 
 
 136 
 
 180 
 
 226 
 
 2V8 
 
 9.6 
 
 19.2 
 
 29 
 
 38 
 
 48 
 
 35/s 
 
 48 
 
 95 
 
 143 
 
 190 
 
 238 
 
 23/16 
 
 10.5 
 
 21 
 
 31 
 
 42 
 
 52 
 
 3U/16 
 
 50 
 
 100 
 
 150 
 
 200 
 
 251 
 
 21/4 
 
 11.4 
 
 23 
 
 34 
 
 45 
 
 57 
 
 33/4 
 
 55 
 
 105 
 
 158 
 
 211 
 
 264 
 
 25/16 
 
 12.4 
 
 25 
 
 37 
 
 49 
 
 62 
 
 37/8 
 
 58 
 
 116 
 
 174 
 
 233 
 
 291 
 
 23/8 
 
 13.4 
 
 27 
 
 40 
 
 54 
 
 67 
 
 315/ 16 
 
 61 
 
 122 
 
 183 
 
 244 
 
 305 
 
 27/16 
 
 14.5 
 
 29 
 
 43 
 
 58 
 
 72 
 
 4 
 
 64 
 
 128 
 
 192 
 
 256 
 
 320 
 
 21/2 
 
 15.6 
 
 31 
 
 47 
 
 62 
 
 78 
 
 43/16 
 
 74 
 
 147 
 
 221 
 
 294 
 
 367 
 
 29/16 
 
 16.8 
 
 34 
 
 50 
 
 67 
 
 84 
 
 41/4 
 
 77 
 
 154 
 
 230 
 
 307 
 
 383 
 
 25/8 
 
 18.1 
 
 36 
 
 54 
 
 72 
 
 90 
 
 47/16 
 
 88 
 
 175 
 
 263 
 
 350 
 
 438 
 
 211/16 
 
 19.4 
 
 39 
 
 58 
 
 77 
 
 97 
 
 4V2 
 
 91 
 
 182 
 
 273 
 
 365 
 
 456 
 
 23/4 
 
 21 
 
 41 
 
 62 
 
 83 
 
 104 
 
 43/4 
 
 107 
 
 214 
 
 322 
 
 429 
 
 537 
 
 213/16 
 
 22 
 
 44 
 
 67 89 
 
 111 
 
 5 
 
 125 
 
 250 
 
 375 
 
 500 
 
 625 
 
 For H.P. transmitted by turned steel shafts, as prime movers, etc., 
 
 Cold-rolled Turned 
 1.43 1.11 
 
 . 
 
 multiply the figures by 0.8. 
 For sha 
 
 .. 
 
 hafts, as second movers or line shafts, ) 
 bearings 8 ft. apart, multiply by J 
 
 For simply transmitting power, short counter- 
 shafts, etc., bearings not over 8 ft. apart, multi- 
 ply by 
 
 2.50 
 
SHAFTING. 
 
 1133 
 
 The horse-power is directly proportional to the number of revolutions 
 per minute. 
 
 SPEED OF SHAFTING. Machine shops 120 to 240 
 
 Wood-working 250 to 300 
 
 Cotton and woollen mills . . 300 to 400 
 
 Flange Couplings. The bolts should be designed so that theii 
 combined resistance to a torsional moment around the axis of the shaft 
 is at least as great as the torsional strength of the shaft itself; and the 
 bolts should be accurately fitted so as to distribute the load evenly 
 among them. Let D = diam. of the shaft, d = diam. of the bolts, 
 r = radius of bolt circle, in inches, n = number of bolts, S = allowable shear- 
 ing stress per sq. in., then ;rd 3 *$f-r-16 = i/4 nd z rS, whence d= 0.5 V'DVCw)- 
 Kimball and Barr give n = 3 +D/2, but this number may be modified for 
 convenience in spacing, etc. 
 
 Effect of Cold Boiling. Experiments by Prof. R. H. Thurston in 
 1902 on hot-rolled and cold-rolled steel bars (Catalogue of Jones & 
 Laughlin Steel Co.) showed that the cold-rolled steel in tension had its 
 elastic limit increased 15 to 97%; tensile strength increased 20 to 45%; 
 ductility decreased 40 to 69%. In transverse tests the resistance in- 
 creased 11 to 30% at the elastic limit and 13 to 69% at the yield point. 
 In torsion the resistance at the yield point increased 31 to 64%, and at 
 the point of fracture it decreased 4 to 10%. The angle of torsion at 
 the elastic limit increased 59 to 103%, while the ultimate angle de- 
 creased 19 to 28%. Bars turned from 13/4 in. diam. to various sizes 
 down to 0.35 in. showed that the change in quality produced by cold 
 rolling extended to the center of the bar. The maximum strength of 
 the cold-rolled bar of full size was 82,200 Ibs. per sq. in., and that of the 
 smallest bar 73,600 Ibs. In the hot-rolled steel bars the maximum 
 strength of the full-sized bar was 62,900 Ibs. and that of the smallest bar 
 58,600 Ibs. per sq. in. 
 
 Hollow Shafts. Let d be the diameter of a solid shaft, and d t d 2 the 
 external and internal diameters of a hollow shaft of the same material. 
 
 Then the shafts will be of equal torsional strength when d 3 = - J ^ - 
 
 a\ 
 
 A 10-inch holtow shaft with internal diameter of 4 inches will weigh 16% 
 less than a solid 10-inch shaft, but its strength will be only 2.56% less. 
 If the hole were increased to 5 inches diameter the weight would be 
 25% less than that of the solid shaft, and the strength 6.25% less. 
 
 Table for Laying Out Shafting. The table on the next page 
 (from the Stevens Indicator, April, 1892) is used by Wm. Sellers & Co. to 
 facilitate the laying out of shafting. 
 
 The wood-cuts at the head of this table show the position of the hangers 
 and position of couplings, either for the case of extension in both direc- 
 tions from a Central head-shaft or extension in one direction from that 
 head -shaft. 
 
 Sizes of Collars for Shafting, Wm. Sellers & Co., Am. Mack. Jan. 28, 
 1897. D, diam. of collar; T, thickness; d, diam. of set screw; I, length. 
 All in inches. 
 
 LOOSE COLLARS. 
 
 Shaft 
 
 D 
 
 T 
 
 d 
 
 I 
 
 Shaft 
 
 D 
 
 T 
 
 d 
 
 I 
 
 Shaft 
 
 D 
 
 t 
 
 d 
 
 H/4 
 
 11/2 
 1 5 /8 
 l3/ 4 
 
 13/4 
 17/8 
 
 21/4 
 25/8 
 23/4 
 
 3/4 
 13/16 
 15/16 
 
 U/16 
 
 H/8 
 
 7/16 
 7/16 
 
 7/16 
 7/16 
 
 V2 
 5/8 
 
 5/16 
 3/8 
 7/16 
 7/16 
 9 /16 
 9/16 
 
 21/4 
 2V2 
 23/4 
 
 31/4 
 
 3V2 
 
 33/8 
 33/4 
 4 
 41/2 
 47/8 
 53/ie 
 
 13/16 
 H/4 
 15/16 
 17/16 
 15/8 
 13/4 
 
 5/8 
 5/8 
 
 5/8 
 5/8 
 3/4 
 
 3/4 
 
 5/8 
 11/16 
 H/16 
 13/16 
 13/16 
 15/16 
 
 4 
 
 41/2 
 
 51/2 
 6 
 
 513/16 
 67/16 
 615/ie 
 71 /2 
 
 17/8 
 17/8 
 
 n/ 8 
 
 2 
 
 3/4 
 
 3/4 
 3/4 
 3/4 
 3/4 
 
 FAST COLLARS. 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 13/16 
 U/4 
 13/8 
 11/2, 
 
 U/2 
 13/4 
 
 2V4 
 
 2 
 
 2V4 
 25/8 
 
 1/2 
 1/2 
 1/2 
 9/16 
 
 2V2 
 23/4 
 
 3V4 
 
 31/4 
 35/8 
 
 4V4 
 
 9 /16 
 5/8 
 H/16 
 U/16 
 
 31/2 
 4 
 
 41/2 
 
 45/8 
 53/8 
 6 
 7 
 
 7/8 
 15 /16 
 
 H/8 
 
 51/2 
 6 
 61/2 
 
 ^/8 
 81/4 
 
 93/ 4 
 
1134 
 
 SHAFTING. 
 
 m 
 
 J l! 
 
 eaqonr 
 
 ffj&fl ?5l l^5f |l 
 
 saqoui 
 'q^Sua^j 
 
 
 sui 'xog jo *sui 
 -j'eag jo t^Siia r j 
 
 
 00 
 
 
 11 
 
 'c 2 S *-" =1 
 
 ~ & " C ' ^ ^ 
 
 " 
 
 cK 
 
 !i!li' - 
 
 - 
 
 Distance from Center of Bearing to End of Shaft for Coupling. See B, Figs. 1, 2, an 
 
 !H5 
 
 .S y * . *N *^ p^ 
 
 
 
 USE OF TABLE. Look for size of first shaft i 
 under the head of Size of first shaft, and in the top 1 
 Size of second shaft, find the size of the shaft to be 
 intersection gives the length R this added to the le 
 Irom center to center of bearing, and in cases simil 
 length C, gives the length of the first shaft, thus as in 
 length ; Fig. 2, C + A + S length. 
 
 {3W ^^rt M S 
 
 * S 2" S 
 
 NO 
 
 s"||i| s | RS f 
 
 Ir> 
 
 s?5 | s |_ 
 
 
 1 % 
 
 affslls 
 
 ! * N 
 ! ^T 
 
 asassssl 
 
 
 
 * 
 
 slaaafaftf 
 
 1 ^M 
 
 ^(Nf^csr^r^ 
 
 
 C<1 M W 
 
 .& 
 
 c* ^ N 
 
 w" 
 
 5 
 
 __ tsr^j 
 
 ^ 
 
 ;? 2 ;? p*~d 
 
 
 N 
 
 
 43 ** w c 
 
 r>l 
 
 c^> ** N rt n> ^ J; 
 
 g bo $ 
 
 " 
 
 If-fjj fjsfjj 
 
 S 
 
 ~ "Illil 
 
 Nominal 
 Size of 
 2d Shaft. 
 
 IN? . 
 ' $ s : 
 
 ^^mi.L^H. 
 
 Ij 
 
 "OTS - 
 
 "W^-O S f ' 
 
 N N 00 *< * *< 00-C 00 H * 00 M N 1 
 
 H* is* i"^f5"^rt^J9 ^*^"e<r^r^H~rr 
 
 it ^ T IA lf\ sC fN l>00 O (Nl r^ T m vO tx 
 
 
 
PULLEYS. 1135 
 
 PULLEYS. 
 
 ft = breadth of arm at hub 
 
 Proportions of Pulleys. (See also Fly-wheels, page 1049.) Let 
 n = number of arms, D = diameter of pulley, S = thickness of belt, 
 t = thickness of rim at edge, T = thickness in middle, B = width of rim, 
 = width of belt, h = breadth of arm at hub, hi = breadth of arm at 
 rim, e thickness of arm at hub, e\ = thickness of arm at rim, c = 
 amount of crowning; dimensions in inches. 
 
 Unwin. Reuleaux. 
 
 B = width of rim. 9/ 8 (p + o .4) % P to 5/4 # 
 
 t = thickness at edge of rim 0.75+0 .005 D { ( ^ to V?ft 
 
 T = thickness at middle of rim ... 2t+ c 
 
 For single /BD 
 
 belts = 0.6337V IT R n 
 
 1/ ' a. _ -i_ 
 For double . 3 /BD /4in< "*" 4 * 20~n 
 belts = 0.798 y T 
 
 hi = breadth of arm at rim 2/ 3 h O.Sh 
 
 e thickness of arm at hub A h .5 h 
 
 ei = thickness of arm at rim .4 hi .5 hi 
 
 n = number of arms, for a single set 3 + ^^7) */2 ( 5 + ^-g ) 
 
 {B for sin.-arrr> 
 pulleys. 
 2 B for double, 
 arm pulleys. 
 
 M = thickness of metal in hub htoS/ih 
 
 c = crowning of pulley 1/24 B 
 
 The number of arms is really arbitrary, and may be altered if necessary, 
 (Unwin.) 
 
 Pulleys with two or three sets of arms may be considered as two or three 
 separate pulleys combined in one, except that the proportions of the arms 
 should be .8 or .7 that of single-arm pulleys. (Reuleaux.) 
 
 EXAMPLE. Dimensions of a pulley 60 in. diam., 16 in. face, for double 
 belt 1/2 in. thick. 
 
 Solution by n h hi e e\ t T L M c 
 
 Unwin 9 3.792.531.521.010.651.9710.73.80.67 
 
 Reuleaux 4 5.0 4.0 2.5 2.0 1.25 16 5 
 
 The following proportions are given in an article in the Amer. Machinist 
 authority not stated: 
 
 h = .0625 D + .5 in., hi = .04 D + .3125 in., e = .025 D + .2 
 In., ei = .016 D + .125 in. 
 
 These give for the above example: h = 4.25 in., hi = 2.71 in., e = 
 1.7 in., ei = 1 .09 in. The section of the arms in all cases is taken as 
 elliptical. 
 
 The following solution for breadth of arm is proposed by the author: 
 Assume a belt pull of 45 Ibs. per inch of width of a single belt, that the 
 whole strain is taken in equal proportions on one-half of the arms, and that 
 the arm is a beam loaded at one end and fixed at the other. We have 
 the formula for a beam of elliptical section fP = .0982 Rbd z +1, in which 
 P = the load, R = the modulus of rupture of the cast iron, b = breadth, 
 d = depth, and I = length of the beam, and/ = factor of safety. Assume 
 a modulus of rupture of 36,000 Ibs., a factor of safety of 10, and an addi- 
 tional allowance for safety in taking I = 1/2 the diameter of the pulley 
 instead of 1/2 D less the radius of the hub. 
 
 Take d = h, the breadth of the arm at the hub, and 6 = e 0.4 h 
 
 the thickness. We then have fP - 10 X -^^ = 900 - = 3535xo - 4/i3 - 
 
 n 1/2 D 
 
 ' QOO 7? D *V 7? 7) 
 
 whence h = i/ = 0.633\/ , which is practically the same as 
 
 v oooo n, V' ?i 
 
 the value reached by Unwin from a different set of assumptions. 
 
1136 
 
 PtILLEYS. 
 
 Relation of Belt Width to Pulley Pace. (Am. Mach., Feb. 11, 
 1915.) Carl G. Barth recommends that the relation between the face 
 of the pulley and the belt be expressed by the formula F 1 3/j 8 B + 3/g 
 in., in which F and B are the widths respectively of the pulley face 
 and belt, both in inches. If the limits of design make it impractical 
 to use the dimension given by the equation, the following equation 
 may be substituted: F = 1 3/ 32 B + 3/ 16 in. 
 
 Convexity of Pulleys. Authorities differ. Morin gives a rise equal 
 to 1/10 of the face; Molesworth, 1/24; others from i/g to Vge- Scott A. 
 Smith says the crown should not be over 1/8 inch for a 24-inch face. 
 Pulleys for shifting belts should be " straight," that is, without crowning. 
 Mr. Barth uses the formula H = 0.03125 F 2 /3, in which H is the height 
 of crown and F the width of face in inches. 
 
 CONE OB STEP PULLEYS. 
 
 To find the diameters for the several steps of a pair of cone-pulleys: 
 
 1. Crossed Belts. Let D and d be the diameters of two pulleys 
 connected by a crossed belt, L = the distance between their centers, 
 and = the angle either half of the belt makes with a line joining the 
 
 centers of the pulleys: then total length of belt =(D+c?) ~ + (D + d) ^~ 
 
 f 2 L cos p. fl ** angle whose sine is . L Cos p= i/L 2 ( ? j ' 
 
 The length of the belt is constant when D + d is constant; that is, in a 
 pair of step-pulleys the belt tension will be uniform when the sum of the 
 diameters of each opposite pair of steps is constant. Crossed belts are 
 seldom used for cone-pulleys, on account of the friction between the 
 rubbing parts of the belt. 
 
 To design a pair of tapering speed-cones, so that the belt may fit 
 equally tight in all positions: When the belt is crossed, use a pair of equal 
 and similar cones tapering opposite ways. 
 
 2. Open Belts. When the belt is uncrossed, use a pair of equal 
 and similar conoids, tapering opposite ways, and bulging in the middle, 
 according to the following formula: Let L denote the distance between 
 the axes of the conoids; R the radius of the larger end of each; r the radius 
 of the smaller end; then the radius in the middle, r , is found as follows: 
 
 R + r (R - r) 2 
 2 6.28L 
 
 (Rankine.) 
 
 If DO = the diameter of equal steps of a pair of cone-pulleys, D and 
 d = the diameters of unequal opposite steps, and L = distance between 
 
 the axes, DO 
 
 D+d (D - d) 2 
 2 12. 566 L' 
 
 If a series of differences of radii of the steps, R r, be assumed, then 
 for each pair of steps - = r\> ' ~ T r , and the radii of each may 
 
 A O .ZO Li 
 
 be computed from their half sum and half difference, as follows: 
 
 R + r R - r 
 
 R 
 
 R+r R r 
 2 2 ; 
 
 2 2 
 
 A. J. Frith (Trans. A. S. M. E., x, 298) shows the following application 
 of Rankine's method: If we had a set of cones to design, the extreme 
 diameters of which, including thickness of belt, were 40 ins. and 10 ins., 
 and the ratio desired 4, 3, 2, and 1, we would make a table as follows, 
 L being 100 ins.: 
 
 Trial 
 Sum of 
 D+ d 
 
 Ratio. 
 
 Trial Diams. 
 
 Values of 
 (D-d)s 
 
 Amount 
 to be 
 Added. 
 
 Corrected Values. 
 
 D | d 
 
 12.56 L 
 
 D 
 
 d 
 
 50 
 50 
 50 
 50 
 
 4 
 3 
 
 2 
 
 40 
 37.5 
 33.333 
 25 
 
 10 
 12.5 
 16.666 
 25 
 
 0.7165 
 
 .4975 
 .2212 
 .0000 
 
 0.0000 
 .2190 
 .4953 
 .7165 
 
 40 
 37.7190 
 33.8286 
 25.7165 
 
 10 
 12.7190 
 17.1619 
 25.7165 
 
 The above formulae, are approximate, and they do not give satisfactory 
 
CONE AND S?t> PULLEYS. 1137 
 
 results when the difference of diameters of opposite steps is large and 
 when the axes of the pulleys are near together, giving a large belt-angle. 
 Two more accurate solutions of the problem, one by a graphical method, 
 and another by a trigonometrical method derived from it, are given by 
 C. A. Smith (Trans. A. S. M. E. x, 269). These were copied in earlier 
 editions of this Pocket-book, but are now replaced by formulae derived 
 from a graphical solution by Burmester (" Lehrbuch der Kinematic"; 
 Mach'y Reference Series, No. 14, 1908), which give results far more 
 accurate than are required in practice. 
 
 In all cases 0.8 of the thickness of the belt should be subtracted from 
 che calculated diameter to obtain the actual diameter of the pulley. 
 This should be done because the belt drawn tight around the pulleys is 
 not the same length as a tape-line measure around them. (C. A. Smith.) 
 
 Using Burmester's diagram the author has devised an algebraic solu- 
 tion of the problem (Indust. Eng., June, 1910) which leads to the follow- 
 ing equations: 
 
 Let L = distance between the centers. 
 
 TO = radius of the steps of equal diameter on the two cones. 
 r, f r 2 = radii of any pair of steps. 
 a = 0.79057 L - TO. 
 
 If r, is given, r 2 = Vi.25 L 2 - (0.79057 L - r + rj) 2 - 0.79057 L + r . 
 If the ratio TZ -* r t is given, let r^r\ = c: r 2 = cr\. 
 
 We then have a + cr t = VRZ ( a + ri )2 f which reduces to 
 
 (1 + c 2 ) rj2 + 2 a (1 + c) r t = 1.25 L 2 - 2 a 2 , a quadratic equation, In 
 which a = 0.79057 L r . Substituting the value of a we have 
 
 (l + ct)rkH-(1.58ll -2 r ) (l+c)rt = 3.16228Z,r - 2r 2 , 
 in which L, r and c are given and r t is to be found. 
 
 Let L = 100, c = 4, r = 12.858 as in Mr. Frith's example, page 1136. 
 
 Then 17ri 2 + 10ar t , = 12,500 -8764.62, from which r t =5.001, r 2 =20.004. 
 
 If c = 3, r, = 6.304, r 2 = 18.912. If c = 2, rj = 8.496, r 2 = 16.992. 
 
 Checking the results by the approximate formula for length of belt. 
 page 1148, viz, Length = 2 L + * (r t + r 2 ) + (r 2 - n) 2 -* L, we have 
 for c = 1, 200 + 80.79 + = 280.79 
 
 2, 2004-80.07 + 0.72 = 280.79 
 
 3, 200+ 79.22+ 1.59 = 280.81 
 
 4, 200+ 78.56 + 2.25 = 280.81 
 The maximum difference being only 1 part in 14,000. 
 
 J. J. Clark (Indust. Eng., Aug., 1910) gives the following solution: 
 Using the same notation as above, 
 
 ir(c+l)ri2icro .................. (1). 
 
 ^|f)=2,ro ............ ....... (2) 
 
 s-(r a -r,) -*!,* .......................... (3) 
 
 The quadratic equation (1) gives the value of ri with an approximation 
 to accuracy sufficient for all practical purposes. If greater accuracy is for 
 any reason desired it may be obtained by (2) and (3), using in (3) the values 
 of r, and r 2 , = cr lt already found from (1). Taking n = 3.1415927, the re- 
 sult will be correct to the seventh figure. 
 
 Speeds of Shaft with Cone Pulleys. If S speed (revs, per min.) 
 of the driving shaft, 
 
 si, s 2 , s 3 , s n = speeds of the driven shaft, 
 Z>i, Z>2, Z>3, D n = diameters of the pulleys on the driving cone, 
 
 di, dz, ds, d n =diams. of corresponding pulleys on the driven cone, 
 SDi^s^; SDz =szdz t etc. 
 Si/S = D l /d l = r i; s n /S = D n /d n , = r n . 
 The speed of the driving shaft being constant, the several speeds of 
 
1138 BELTING* 
 
 the driven shaft are proportional to the ratio of the diameter of the 
 driving pulley to that of the driven, or to D/d. 
 
 Speeds in Geometrical Progression. If it is desired that the speed 
 ratios shall increase by a constant percentage, or in geometrical progres- 
 sion, thenr 2 /r l rz/r 2 = r n /r n _ l = c, a constant. 
 
 EXAMPLE. If the speed ratio of the driven shaft at its lowest speed, 
 to the driving shaft be 0.76923, and at its highest speed 2.197, the speeds 
 being in geometrical progression, what is the constant multiplier if w=5? 
 Log 2.197 = 0.341830 
 Log 0.76923 = 1.886056 
 
 0.455774 
 
 Divide by n- !,= 4, 0.113943 = log of 1.30. 
 
 If Dz/dz = 1, then Dt/di = 1 -s- 1.3 = 0.769; Z> 3 d 3 = 1.30; ZVct* 
 l.u<); X/5/(*5 ==s 2.197* 
 
 BELTING. 
 
 Theory of Belts and Bands. A pulley is driven by a belt by means 
 of the friction between the surfaces in contact. Let T\ be the tension on 
 the driving side of the belt, Tz the tension on the loose side; then ,= T\ 
 ITa, is the total friction between the band and the pulley, which is 
 equal to the tractive or driving force. Let / = the coefficient of friction, 
 6 the ratio of the length of the arc of contact to the length of the radius, 
 a = the angle of the arc of contact in degrees, e = the base of the Nape- 
 rian logarithms = 2.71828, m= the modulus of the common logarithms = 
 0.434295. The following formulae are derived by calculus (Rankine's 
 Mach'y and Mill work, p. 351; Carpenter's Exper. Eng'g, p. 173): 
 
 AjL pf&~ To Ti . To Ti * Ti n p'~f&\ 
 
 T* ' l2 ~ e fe' 1/1 l2 ~~ e fd - 
 T! _ T 2 = Ti (1 - e~f e ) = Ti (1 - 10 ~f em ) => Ti (1 - lO" ' 00758 /^) I 
 
 _1 = 1() 0.00758> ; Ti a Tz 
 
 If the arc of contact between the band and the pulley expressed in 
 turns and fractions of a turn = n, 6 = 2*n; ef e = lo 2 - 7288 -/"; that is, ef 6 is 
 the natural number corresponding to the common logarithm 2.7288/n. 
 
 The value of the coefficient of friction /depends on the state and mate- 
 rial of the rubbing surfaces. For leather oelts on iron pulleys, Morin 
 found / = .56 when dry, .36 when wet, .23 when greasy, and .15 
 when oily. In calculating the proper mean tension for a belt, the smallest 
 value, / = .15, is to be taken if there is a probability of the belt becom- 
 ing wet with oil. The experiments of Henry R. Towne and Robert 
 Briggs, however (Jour. Frank. Inst., 1868), show that such a state of 
 lubrication is not of ordinary occurrence; and that in designing machinery 
 we may in most cases safely take / = .42. Reuleaux takes / = .25. 
 Later writers have shown that the coefficient is not a constant quantity, 
 but is extremely variable, depending on the velocity of slip, the condition 
 of the surfaces, and even on the weather. 
 
 The following table shows the values of the coefficient 2.7288 /, by 
 which n is multiplied in the last equation, corresponding to different 
 values of /; also the corresponding values of various ratios among the 
 forces, when the arc of contact is half a circumference: 
 
 /=0.15 0.25 0.42 0.56 
 
 88/=0.4 
 
 2.7288/=0.41 0.68 1.15 1.53 
 Let = TT and n = 1/2, then 
 
 Ti -* T 2 = 1 .603 2.188 3.758 5.821 
 
 Ti -* S = 2.66 1.84 1.36 1.21 
 
 -* 2S= 2.16 1.34 0.86 0.71 
 
BELTING. 1139 
 
 Tn ordinary practice it is usual to assume Tz = S; Ti = 2 5; T\ + Tz -5- 
 25 = 1.5. This corresponds to / = 0.22 nearly. 
 
 For a wire rope on cast iron / may be taken as .15 nearly; and if the 
 groove of the pulley is bottomed with gutta-percha, .25. (Rankine.) 
 
 Centrifugal Tension of Belts. When a belt or band runs at a high 
 velocity, centrifugal force produces a tension in addition to that existing 
 when the belt is at rest or moving at a low velocity. This centrifugal 
 tension diminishes the effective driving force. 
 
 Rankine says: If an endless band, of any figure whatsoever, runs at a 
 given speed, the centrifugal force produces a uniform tension at each 
 cross-section of the band, equal to the weight of a piece of the band whose 
 length is twice the height from which a heavy body must fall in oraer 
 to acquire the velocity of the band. (See Cooper on Belting, p. 101.) 
 If T c = centrifugal tension; 
 
 V velocity in feet per second; 
 
 g= acceleration due to gravity = 32.2; 
 
 W= weight of a piece of the belt 1 ft. long and 1 sq. In. sectional 
 
 area, - 
 Leather weighing 56 Ibs. per cubic foot gives W = 56 + 144 = .388. 
 
 T c =- WV* * g =- 0.388 V 2 + 32.2 = .01272. 
 
 Belting Practice. Handy Formulae for Belting. Since in the 
 practical application of the above formulae the value of the coefficient of 
 friction must be assumed, its actual value varying within wide limits 
 (15% to 135%), and since the values of T\ and Tz also are fixed arbi- 
 trarily, it is customary in practice to substitute for these theoretical 
 formulae more simple empirical formula and rules, some of which are 
 given below. 
 
 Let d=diam. of pulley in inches; *d= circumference; 
 
 V velocity of belt in ft. per second; v = vel. in ft. per minute; 
 a = angle of the arc of contact: 
 
 L = length of arc of contact in feet == irda * (12 X 360); 
 F=tractive force per square inch of sectional area of belt; 
 w = width in inches; t = thickness; 
 S = tractive force per inch of width = F X t; 
 r.p.m. = revs. per minute; r.p.s. = revs, per second = r.p.m. -s- 60. 
 
 v= j2 X r.p.m.; = .2618 d X r.p.m. 
 
 Svw SVw Swd X r.p.m. 
 Horse-power, H.P. =5^ = -^ - 126050 -- 
 
 If F= working tension per square inch =275 Ibs., and t= 7/32 inch, 
 - 60 Ibs. nearly, then 
 
 H.P.= -^ =0.109 Vw = .000476 wd X r.p.m. = wa * T *' m ' - (1) 
 
 If F = 180 Ibs. per square inch, and t = Va inch, S = 30 Ibs., then 
 H.P. = ~ =0.055 Vw =0.000238 wd X r.p.m. = ^^g'' (2) 
 
 If the working strain is 60 Ibs. per inch of width, a belt 1 inch wide 
 traveling 550 ft. per minute will transmit 1 horse-power. If the working 
 strain is 30 Ibs. per inch of width, a belt 1 inch wide traveling 1100 ft. 
 per minute will transmit 1 horse-power. Numerous rules are given by 
 different writers on belting which vary between these extremes. A rule 
 commonly used is: 1 inch wide traveling 1000 ft. per min. = 1H.P. 
 
 H ' P - = l?^ =0 - 067w = - 000262 ^ Xr -P- m -= !E ^F 1 *- (3) 
 
 This corresponds to a working strain of 33 Ibs. per inch of width. 
 
 Many writers give as safe practice for single belts in good condition a 
 working tension of 45 Ibs. per inch of width. This gives 
 
 H.P. = ^| = 0.08187^=0. 000357 ^ X r.p.m. = ^^ . (4 ) 
 
1140 
 
 BELTING. 
 
 For double belts of average thickness, some writers say that the trans- 
 mitting efficiency is to that of single belts as 10 to 7, which would give 
 
 H.P. = = 0.1169 Vw = 0.00051 wd X r.p.m. = Wd *' m ' (5) 
 
 (1) For S = 60 Ibs. per inch wide; 
 
 (2) " 8 = 30 " 
 
 (3) " S = 33 " 
 
 (4) s = 45 " 
 
 (5) " S = 64.3" 
 
 Other authorities, however, make the transmitting power of double belts 
 twice that of single belts, on the assumption that the thickness of a double 
 belt is twice that of a single belt. 
 
 Rules for horse-power of belts are sometimes based on the number of 
 square feet of surface of the belt which pass over the pulley in a minute. 
 Sq. ft. per min. = wv * 12. The above formulae translated into this 
 form give: 
 
 H.P. = 46 sq. ft. per minute. 
 
 H.P. = 92 " 
 
 H.P. = 83 " 
 
 H.P. = 61 
 
 H.P. =- 43 ' (double belt). 
 
 The above formulae are all based on the supposition that the arc of con- 
 tact is 180. For other arcs, the transmitting power is approximately 
 proportional to the ratio of the degrees of arc to 180. 
 
 Some rules base the horse-power on the length of the arc of contact in 
 
 feet. Since L - 
 
 and H.P. 
 
 12 X 360 
 we obtain by substitution H.P. 
 
 33000 " 33000 X 12 X r - P ' m ' X 180* 
 
 Sw 
 
 X L X r.p.m., and the five for- 
 
 H.P. = 
 
 (4); 
 
 muise then take the following form for the several values of S: 
 
 _wL X r.p.m. wL X r.p.m. wL X r.p.m wL X r.p.m. 
 
 275 '".' " 550 UJI 500 367 
 
 TT T /j T-I i- i^v wL X r.p.m. ,_,. 
 
 H.P. (double belt) = ^^ (5). 
 
 ^o/ 
 
 None of the handy formulae take into consideration the centrifugal 
 tension of belts at high velocities. When the velocity is over 3000 ft. 
 per minute the effect of this tension becomes appreciable, and it should 
 be taken account of, as in Mr. Nagle's formula, which is given below. 
 
 Horse-power of a Leather Belt One Inch wide. (Nagle.) 
 
 Formula: H.P. = CVtw (S - 0.012 V) -5- 550. 
 
 For/ = 0.40, a = 180, C = 0.715, w = 1. 
 
 *i 
 
 Laced Belts, S = 275. 
 
 u 
 
 -S 
 
 Riveted Belts, S = 400. 
 
 ft 
 
 Thickness in inches = t. 
 
 fc 
 
 P, 
 
 Thickness in inches = t. 
 
 L 
 
 1/7 
 
 1/6 
 
 3/16 
 
 7/32 
 
 1/4 
 
 5/16 
 
 1/3 
 
 o . 
 "a if 
 > 
 
 7/32 
 
 1/4 
 
 5/16 
 
 1/3 
 
 3/8 
 
 7/16 
 
 1/2 
 
 10 
 
 0.51 
 
 0.59 
 
 0.63 
 
 0.73 
 
 0.84 
 
 1.05 
 
 1.18 
 
 15 
 
 1.69 
 
 1.94 
 
 2.42 
 
 2.58 
 
 2.91 
 
 3.39 
 
 3.87 
 
 15 
 
 0.75 
 
 0.88 
 
 1.00 
 
 1.16 
 
 1.32 
 
 1.66 
 
 1.77 
 
 20 
 
 2.24 
 
 2.57 
 
 3.21 
 
 3.42 
 
 3.85 
 
 4.49 
 
 5.13 
 
 20 
 
 .00 
 
 1.17 
 
 1.32 
 
 1.54 
 
 1.75 
 
 2.19 
 
 2.34 
 
 25 
 
 2.79 
 
 3.19 
 
 3.98 
 
 4.25 
 
 4.78 
 
 5.57 
 
 6.37 
 
 25 
 
 .23 
 
 1.43 
 
 1.61 
 
 1.88 
 
 2.16 
 
 2.69 
 
 2.86 
 
 30 
 
 3.31 
 
 3.79 
 
 4.74 
 
 5.05 
 
 5.67 
 
 6.62 
 
 7.58 
 
 30 
 
 .47 
 
 1.72 
 
 1.93 
 
 2.25 
 
 2.58 
 
 3.22 
 
 3.44 
 
 35 
 
 3.82 
 
 4.37 
 
 5.46 
 
 5.83 
 
 6.56 
 
 7.65 
 
 8.75 
 
 35 
 
 .69 
 
 1.97 
 
 2.22 
 
 2.59 
 
 2.96 
 
 3.70 
 
 3.94 
 
 40 
 
 4.33 
 
 4.95 
 
 6.19 
 
 6.60 
 
 7.42 
 
 8.66 
 
 9.90 
 
 40 
 
 .90 
 
 2.22 
 
 2.49 
 
 2.90 
 
 3.32 
 
 4.15 
 
 4.44 
 
 45 
 
 4.85 
 
 5.49 
 
 6.86 
 
 7.32 
 
 8.43 
 
 9.70 
 
 10.98 
 
 45 
 
 2.09 
 
 2.45 
 
 2.75 
 
 3.21 
 
 3.67 
 
 4.58 
 
 4.89 
 
 50 
 
 5.26 
 
 6.01 
 
 7.51 
 
 8.02 
 
 9.02 
 
 10.52 
 
 12.03 
 
 50 
 
 2.27 
 
 2.65 
 
 2.98 
 
 3.48 
 
 3.98 
 
 4.97 
 
 5.30 
 
 55 
 
 5.68 
 
 6.50 
 
 8.12 
 
 8.66 
 
 9.74 
 
 11.36 
 
 13.00 
 
 55 
 
 2.44 
 
 2.84 
 
 3.19 
 
 3.72 
 
 4.26 
 
 5.32 
 
 5.69 
 
 60 
 
 6.09 
 
 6.96 
 
 8.70 
 
 9.28 
 
 10.43 
 
 12.17 
 
 13.91 
 
 60 
 
 2.58 
 
 3.01 
 
 3.38 
 
 3.95 
 
 4.51 
 
 5.64 
 
 6.02 
 
 65 
 
 6.45 
 
 7.37 
 
 9.22 
 
 9.83 
 
 11.06 
 
 12.90 
 
 14.75 
 
 65 
 
 2.71 
 
 3.16 
 
 3.55 
 
 4.14 
 
 4.74 
 
 5.92 
 
 6.32 
 
 70 
 
 6.78 
 
 7.75 
 
 9.69 
 
 10.33 
 
 11.62 
 
 13.56 
 
 15.50 
 
 70 
 
 2.81 
 
 3.27 
 
 3.68 
 
 4.29 
 
 4.91 
 
 6.14 
 
 6.54 
 
 75 
 
 7.09 
 
 8.11 
 
 10.13 
 
 10.84 
 
 12.16 
 
 14.18 
 
 16.21 
 
 75 
 
 2.89 
 
 3.37 
 
 3.79 
 
 4.42 
 
 5.05 
 
 6.31 
 
 6.73 
 
 80 
 
 7.36 
 
 8.41 
 
 10.51 
 
 11.21 
 
 12.61 
 
 14.71 
 
 16.81 
 
 80 
 
 2.94 
 
 3.43 
 
 3.86 
 
 4.50 
 
 5.15 
 
 6.44 
 
 6.86 
 
 85 
 
 7.58 
 
 8.66 
 
 10.82 
 
 11.55 
 
 13.00 
 
 15.16 
 
 17.32 
 
 85 
 
 2.97 
 
 3.47 
 
 3.90 
 
 4.55 
 
 5.20 
 
 6.50 
 
 6.93 
 
 90 
 
 7.74 
 
 8.85 
 
 11.06 
 
 11.80 
 
 13.27 
 
 15.48 
 
 17.69 
 
 90 
 
 2.97 
 
 3.47 
 
 3.90 
 
 4.55 
 
 5.20 
 
 6.50 
 
 6.93 
 
 100 
 
 7.96 
 
 9.10 
 
 11.37 
 
 12.13 
 
 13.65 
 
 15.92 
 
 18.20 
 
 The H.P. becomes a maximum 
 
 The H.P. becomes a maximum at 
 
 at 87, 41 ft. per sec. = 5245ft. p. min. 
 
 105.4 ft. per sec. = 6324 ft. per min. 
 
BELTING. 
 
 1141 
 
 In the above table the angle of subtension, a, is taken at 180. 
 
 Should it be ....... 
 
 Multiply above 
 values by ..... . 
 
 100 C 
 .70 
 
 110* 
 .75 
 
 120< 
 
 130' 
 .83 
 
 140< 
 .87 
 
 150' 
 -.91 
 
 160 ( 
 .94 
 
 170' 
 ,.97 
 
 180< 
 
 200 
 1.05 
 
 A. F. Nagle's Formula (Trans. A. S: M. E., vol. ii, 1881, p. 91. 
 Tables published in 1882). 
 
 550 /' 
 
 C = 1 - io-- 00758 -fc : t = thickness in inches; 
 
 a = degrees of belt contact; v = velocity in feet per second; 
 / = coefficient of friction; S= stress upon belt per square Inch. 
 
 w = width in inches: 
 
 Taking S at 275 Ibs. per sq. in. for laced belts and 400 Ibs. per sq. in, 
 for lapped and riveted belts, the formula becomes 
 
 H.P.= CVtw(0.50 - 0.0000218 F 2 ) for laced belts: 
 H.P. = C Vtw (0 .727 - .0000218 V 2 ) for riveted belts. 
 VALUES OF C= 1 - 10-0-00758 fa. (NAGLE.) 
 
 Degrees of contact = a. 
 
 j = coeuicient 
 of friction. 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 
 
 200 
 
 0.15 
 
 0.210 
 
 0.230 
 
 0.250 
 
 0.270 
 
 0.288 
 
 0.307 
 
 0.325 
 
 0.342 
 
 0.359 
 
 0.376 
 
 0.408 
 
 .20 
 
 .270 
 
 .295 
 
 .319 
 
 .342 
 
 .364 
 
 .386 
 
 .408 
 
 .428 
 
 .448 
 
 .467 
 
 .503 
 
 .25 
 
 .325 
 
 .354 
 
 .381 
 
 .407 
 
 .432 
 
 .457 
 
 .480 
 
 .503 
 
 .524 
 
 .544 
 
 .582 
 
 .30 
 
 .376 
 
 .408 
 
 .438 
 
 .467 
 
 .494 
 
 .520 
 
 .544 
 
 .567 
 
 .590 
 
 .610 
 
 .649 
 
 .35 
 
 .423 
 
 .457 
 
 .489 
 
 .520 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 .646 
 
 .667 
 
 .705 
 
 .40 
 
 .467 
 
 .502 
 
 .536 
 
 .567 
 
 .597 
 
 .624 
 
 .649 
 
 .673 
 
 .695 
 
 .715 
 
 .753 
 
 .45 
 
 .507 
 
 .544 
 
 .579 
 
 .610 
 
 .640 
 
 .667 
 
 .692 
 
 .715 
 
 .737 
 
 .757 
 
 .792 
 
 .50 
 
 .543 
 
 .582 
 
 .617 
 
 .649 
 
 .679 
 
 .705 
 
 .730 
 
 .753 
 
 .772 
 
 .792 
 
 .826 
 
 .55 
 
 .578 
 
 .617 
 
 .652 
 
 .684 
 
 .713 
 
 .739 
 
 .763 
 
 .785 
 
 .805 
 
 .822 
 
 .853 
 
 .60 
 
 .610 
 
 .649 
 
 .684 
 
 .715 
 
 .744 
 
 .769 
 
 .792 
 
 .813 
 
 .832 
 
 .848 
 
 .877 
 
 1.00 
 
 .792 
 
 .825 
 
 .853 
 
 .877 
 
 .897 
 
 .913 
 
 .927 
 
 .937 
 
 .947 
 
 .956 
 
 .969 
 
 The following table gives a comparison of the formulae already given 
 for the case of a belt one inch wide, with arc of contact 180. 
 
 Horse-power of a Belt One Inch wide, Arc of Contact 180. 
 
 COMPARISON OF DIFFERENT FORMULAE. 
 
 .2 
 v 
 
 *? 
 
 .3 a' 
 
 $z 
 
 i 
 
 Form. I 
 H.P. = 
 
 Form .2 
 H.P. = 
 
 Form. 3 
 H.P. = 
 
 Form. 4 
 H.P. = 
 
 Form. 5 
 double 
 belt 
 
 Nagle's Form. 
 7/32-in- single 
 
 sff 
 
 's ft 
 
 d 
 
 wv 
 
 .wv 
 
 wv 
 
 wv 
 
 H.P.= 
 
 belt. 
 
 >*** 
 
 "53^ 
 !><" 
 
 -*2 
 
 550 
 
 1100 
 
 1000 
 
 733 
 
 wv 
 513 
 
 Laced. 
 
 Riv't'd 
 
 10 
 
 600 
 
 50 
 
 1.09 
 
 0.55 
 
 0.60 
 
 0.82 
 
 1.17 
 
 0.73 
 
 1.14 
 
 70 
 
 1200 
 
 100 
 
 2.18 
 
 1.09 
 
 1.20 
 
 1.64 
 
 2.34 
 
 1.54 
 
 2.24 
 
 30 
 
 1800 
 
 150 
 
 3.27 
 
 1.64 
 
 1.80 
 
 2.46 
 
 3.51 
 
 2.25 
 
 3.31 
 
 40 
 
 2400 
 
 200 
 
 4.36 
 
 2.18 
 
 2.40 
 
 3.27 
 
 4.68 
 
 2.90 
 
 4.33 
 
 50 
 
 3000 
 
 250 
 
 5.45 
 
 2.73 
 
 3.00 
 
 4.09 
 
 5.85 
 
 3.48 
 
 5.26 
 
 60 
 
 3600 
 
 300 
 
 6.55 
 
 3.27 
 
 3.60 
 
 4.91 
 
 7.02 
 
 3.95 
 
 6.09 
 
 70 
 
 4200 
 
 350 
 
 7.63 
 
 3.82 
 
 4.20 
 
 5.73 
 
 8.19 
 
 4.29 
 
 6.78 
 
 80 
 
 4800 
 
 400 
 
 8.73 
 
 4.36 
 
 4.80 
 
 6.55 
 
 9.36 
 
 4.50 
 
 7.36 
 
 90 
 
 5400 
 
 450 
 
 9.82 
 
 4.91 
 
 5.40 
 
 7.37 
 
 10.53 
 
 4.55 
 
 7.74 
 
 100 
 
 6000 
 
 500 
 
 10.91 
 
 5.45 
 
 6.00 
 
 8.18 
 
 11.70 
 
 4.41 
 
 7.96 
 
 110 
 
 6600 
 
 550 
 
 
 
 
 
 
 4.05 
 
 7.97 
 
 120 
 
 7200 
 
 600 
 
 
 
 
 
 
 3.49 
 
 7.75 
 
 
 
 
 
 
 Width of Belt for a Given Horse-power. The width of belt 
 required for any given horse-power may be obtained by transposing the 
 
1142 
 
 BELTING. 
 
 formulae for horse-power so as to give the value of w. Thus: 
 
 From formula (1), w --. H *=- ^ 7 H P '- 2101 H P ' - 275 H ' P - 
 
 From formula (2), w = 
 From formula (3) , w = 
 From formula (4), w- 
 From formula (5),*iy = 
 
 v V d X r.p.m. L Xr.p.m." 
 
 1100 H.P.^ 18. 33 H.P. = 4202 H.P. ^530 H.P. . 
 v V dX r.p.m. LXr.p.m." 
 
 1000 H.P. = 16 .67 H.P. = 3820 H.P. ^ 500 H.P. , 
 v V d X r.p.m."" L x r.p.m. 
 
 733 H.P. = 12 .22 H.P. = 2800 H.P. _ 360 H.P. 
 
 v V dx r.p.m. L xr.p.m/ 
 
 513 H.P. 8. 56 H.P. 1960 H.P. _ 257 H.P 
 
 L Xr.p.m.* 
 
 v V d Xr.p.m. _,,..., ___ 
 
 Many authorities use formula (1) for double belts and formula (2) or 
 (3) for single belts. 
 
 To obtain the width by Nagle's formula, u> = 
 
 F2) . 
 
 divide the given horse-power by the figure in the table corresponding to 
 the given thickness of belt and velocity in feet per second. 
 
 The formula to be used in any particular case is largely a matter of judg- 
 ment. A single belt proportioned according to formula (1), if tightly 
 stretched, and if the surface is in good condition, will transmit the horse- 
 power calculated by the formula, but one so proportioned is objectionable, 
 first, because it requires so great an initial tension that it is apt to stretch, 
 slip, and require frequent restretching and relacing; and second, because 
 this tension will cause an undue pressure on the pulley-shaft, and therefore 
 an undue loss of power by friction. To avoid these difficulties, formula 
 (2), (3), or (4), or Mr. Nagle's table, should be used; the latter especially 
 in cases in which the velocity exceeds 4000 ft. per min. 
 
 The following are from the notes of the late Samuel Webber. (Am. 
 Mach. May 11, 1909.) 
 
 Good oak-tanned leather from the back of the hide weighs almost 
 exactly one avoirdupois ounce for each one-hundredth of an inch in thick- 
 ness, in a piece of leather one foot square, so that 
 
 
 Lbs. 
 
 P 1t sq ' 
 
 Approx. 
 Thick- 
 ness. 
 
 Actual 
 Thick- 
 ness. 
 
 Vel. per 
 Inch for 
 1 H.P. 
 
 Safe Strain 
 per Inch 
 Width. 
 
 Single belt..... 
 
 16 oz. 
 
 1/0 in. 
 
 16 in 
 
 625ft 
 
 52 8 Ib-? 
 
 Light double 
 
 24 " 
 
 1/4 " 
 
 24 " 
 
 417 " 
 
 78.1 " 
 
 Medium 
 
 28 " 
 
 5 /16 " 
 
 0.28 " 
 
 357 " 
 
 92.5 " 
 
 Standard 
 
 33 " 
 
 Vq " 
 
 33 " 
 
 303 " 
 
 109 " 
 
 3-oly 
 
 45 " 
 
 & - 
 
 0.45 " 
 
 222 " 
 
 148 " 
 
 The rule for velocity per inch width for 1 H.P. is: 
 
 Multiply the denominator of the fraction expressing the thickness of 
 the belt in inches by 100, and divide it by the numerator; 
 
 Good, well-calendered rubber belting made with 30-ounce duck and 
 new (i. e.. not reclaimed vulcanized) rubber will be as follows: 
 
 Nomenclature. 
 
 Approximate 
 Thickness. 
 
 Safe Working 
 Strain for 1 Inch 
 Width. 
 
 Velocity per Inch for 
 for 1 H.P. 
 
 }* 
 
 6 
 
 l ? 
 
 0.18h 
 0.24 ' 
 0.30 ' 
 0.35 ' 
 0.40 
 0.45 4 
 
 i. 
 
 45 pounds 
 65 " 
 85 " 
 105 
 125 
 145 " 
 
 735 ft. p 
 508" 
 388" 
 314" 
 264" 
 218" 
 
 er mm. 
 
 M 
 M 
 
 The thickness of rubber belt does not necessarily govern the strength, 
 but the weight of duck does, and with 30-ounce duck, the safe working 
 strains are as above. 
 
 Belt Factors. W. W. Bird (Jour. Worcester Polyt. Inst., Jan. 1910.) 
 
 The factors given in the table below, for use in the formula H.P. =* 
 
 vw + F,tp. which F is an empirical factor, are based on the following 
 
 assumptions: A belt of single thickness will stand a stress on | the tight 
 
 *For double Jbelts, 
 
BELTING. 
 
 1143 
 
 side, Ti, of 60 Ibs. per inch of width, a double belt 105 Ibs., and a 
 triple belt 150 Ibs., and have a fairly long life, requiring only occasional 
 taking up; the ratio of tensions Ti/Tz should not exceed 2 on small, 
 2. 5 on 'medium and 3 on large pulleys ; the creep (travel of the belt 
 relative to the surface of te pulley due to the elasticity of the belt 
 and not to slip) should not exceed 1% this requires that the differ- 
 ence m tensions T\ - Tz should not be greater than 40 ibs. per Inch of 
 width for single, 70 for double and 100 for triple belts. 
 
 Pulley diam, 
 
 Under 
 8 in. 
 
 8 to 
 36 in. 
 
 Over 
 3ft. 
 
 Under 
 14 in. 
 
 14 to 
 60 in. 
 
 Over 
 
 5ft. 
 
 Under 
 21 in. 
 
 21 to 
 84 in. 
 
 Over 
 7ft. 
 
 Belt thick- 
 ness. 
 
 Single. 
 
 S'gle. 
 
 S'gle. 
 
 Dbl. 
 
 Dbl. 
 
 Dbl. 
 
 Triple. 
 
 Triple. 
 
 Triple. 
 
 Factor 
 Ti-T* 
 Creep, %.... 
 ?\- T 2 
 7 1 , 
 
 1100 
 30 
 0.74 
 2 
 60 
 
 920 
 36 
 0.89 
 2.5 
 60 
 
 830 
 40 
 0.99 
 3 
 60 
 
 630 
 52.5 
 0.74 
 2 
 105 
 
 520 
 63 
 0.89 
 2.5 
 105 
 
 470 
 70 
 0.99 
 3 
 105 
 
 440 
 75 
 0.74 
 2 
 150 
 
 370 
 90 
 0.89 
 2.5 
 150 
 
 330 
 100 
 0.99 
 3 
 150 
 
 These factors are for an arc of contact of 180. For other arcs they 
 are to be multiplied by the figures given below. 
 
 Arc 220 210 200 190 170 160 150 140 130 120 
 
 Multiply by... 0.89 0.92 0.95 0.97 1.04 1.07 1.11 1.16 1.21 1 27 
 
 Taylor's Rules for Belting. F. W. Taylor (Trans. A. S, M. E., 
 xv, 204) describes a nine years' experiment on belting in a machine shop, 
 giving results of tests of 42 belts running night and day. Some of these 
 belts were run on cone pulleys and others on shifting, or fast-and-loose, 
 pulleys. The average net working load on the shifting belts was only 
 0.4 of that of the cone belts. 
 
 The shifting belts varied in dimensions from 39 ft. 7 in. long, 3.5 in. 
 wide, .25 in. thick, to 51 ft. 5 in. long, 6 .5 in. wide, .37 in. thick. The 
 cone belts varied in dimensions from 24 ft. 7 in. long, 2 in. wide, .25 in. 
 thick, to 31 ft. 10 in. long, 4 in. wide, .37 in. thick. 
 
 Belt-clamps were used having spring-balances between the two pairs 
 of clamps, so that the exact tension to which the belt was subjected was 
 accurately weighed when the belt was first put on, and each time it war 
 tightened. The tension under which each belt was spliced was care 
 fully figured so as to place it under an initial strain while the belt 
 was at rest immediately after tightening of 71 Ibs. per inch of width 
 of double belts. This is equivalent, in the case of 
 
 Oak tanned and fulled belts, to 192 Ibs. per sq. in. section; 
 Oak tanned, not fulled belts, to 229 " 
 Semi-raw-hide belts, to 253 ' 
 
 Raw-hide belts to 284 ' 
 
 From the nine years experiment Mr. Taylor draws a number of con. 
 elusions, some of which are given in an abridged form below. 
 
 In using belting so as to obtain the greatest economy and the most 
 satisfactory results, the following rules should be observed: 
 
 
 Oak Tanned 
 and Fulled 
 Leather Belts. 
 
 Other Types 
 of Leather 
 Belts and 
 6- to 7-ply 
 Rubber Belts. 
 
 A double belt, having an arc of contact of 
 180, will give an effective pull on the face 
 of a pulley per inch of widtn of belt of 
 Or, a different form of same rule: 
 The number of sq. ft. of double belt passing 
 around a pulley per minute required to 
 transmit one horse-power is 
 
 35 Ibs. 
 80 sq. ft. 
 
 30 ibs. 
 90 sq. ft. 
 
 Or: The number of lineal feet of double 
 belting 1 in. wide passing around a pulley 
 per minute required to transmit one horse- 
 power is 
 
 950 ft. 
 
 1100ft. 
 
 Or: A double belt 6 in. wide, running 4000 to 
 5000 ft. per min., will transmit 
 
 30 H.P. 
 
 25 H.P. 
 
1144 BELTING. 
 
 The terms "initial tension," "effective pull,'* etc., are thus explained 
 by Mr. Taylor: When pulleys upon which belts are tightened are at rest 
 both strands of the belt (the upper ana lower) are unaer the same stress 
 per in. of width. By "tension," "initial tension," or "tension while at 
 rest," we mean the stress per in. of width, or sq. in. of section, to which 
 one of the strands of the belt is tightened, when at rest. After the belts 
 are in motion and transmitting power, the stress on the slack side, or 
 strand, of the belt becomes less, while that on the tight side or the siae 
 which does the pulling becomes greater than when the belt was at rest. 
 By the term "total load" we mean the total stress per in. of width, or 
 sq. in. of section, on the tight side of belt while in motion. 
 
 The difference between the stress on the tight side of the belt and its 
 slack side, while in motion, represents the effective force or pull which is 
 transmitted from one pulley to another. By the terms "working load," 
 "net working load," or "effective pull," we mean the difference in the 
 tension of the tight and slack sides of the belt per in. of width, or sq. in. 
 section, while in motion, or the net effective force that is transmitted from 
 one pulley to another per in. of width or sq. in. of section. 
 
 The discovery of Messrs. Lewis and Bancroft (Trans. A. S. M. E., 
 vii, 549) that the "sum of the tension on both sides of the belt does not 
 remain constant," upsets all previous theoretical belting formulae. 
 
 The belt speed for maximum economy should be from 4000 to 4500 ft. 
 per minute. 
 
 The best distance from center to center of shafts is from 20 to 25 ft. 
 
 Idler pulleys work most satisfactorily when located on the slack side 
 of the belt about one-quarter way from the driving-pulley. 
 
 Belts are more durable and work more satisfactorily made narrow and 
 thick, rather than wide and thin. 
 
 It is safe and advisable to use: a double belt on a pulley 12 in. diameter 
 or larger; a triple belt on a pulley 20 in. diameter or larger; a quadruple 
 belt on a pulley 30 in. diameter or larger. 
 
 As belts increase in width they should also be made thicker. 
 
 The ends of the belt should be fastened together by splicing and cement- 
 ing, instead of lacing, wiring, or using hooks or clamps of any kind. 
 
 A V-splice should be used on triple and quadruple belts and when 
 idlers are used. Stepped splice, coated with rubber and vulcanized in 
 place, is best for rubber belts. 
 
 For double belting the rule works well of making the splice for all belts 
 up to 10 in. wide, 10 in. long; from 10 in. to 18 in. wide the splice should 
 be the same width as the belt, 18 in. being the greatest length of splice 
 required for double belting. 
 
 Belts should be cleaned and greased every five to six months. 
 
 Double leather belts will last well when repeatedly tightened under 
 a strain (when at rest) of 71 Ibs. per in. of width, or 240 Ibs. per sq. in. 
 section, but they will not maintain this tension for any length of time. 
 
 Belt-clamps having spring-balances between the pairs of clamps should 
 be used for weighing the tension of the belt each time it is tightened. 
 
 The stretch, durability, cost of maintenance, etc., of belts proportioned 
 
 (A) according to the ordinary rules of a total load of 111 Ibs. per inch of 
 width, corresponding to an effective pull of 65 Ibs. per inch of width, and 
 
 (B) according to a more economical rule of a total load of 54 Ibs., corre- 
 sponding to an effective pull of 26 Ibs. per inch of width, are found to be 
 as follows: 
 
 When it is impracticable to accurately weigh the tension of a belt in 
 tightening it, it is safe to shorten a double belt one-half inch for every 
 10 ft. of length for (A) and one inch for every 10 ft. for (B), if it requires 
 tightening. 
 
 Double leather belts, when treated with great care and run night and 
 day at moderate speed, should last for 7 years (A); 18 years (B). 
 
 The cost of all labor and materials used in the maintenance and repairs 
 of double belts, added to the cost of renewals as they give out, through a 
 term of years, will amount on an average per year to 37% of the original 
 cost of the belts (A); 14% or less (B). 
 
 In figuring the total expense of belting, and the manufacturing cost 
 chargeable to this account, by far the largest item is the time lost on the 
 machines while belts are being relaced and repaired. 
 
 The total stretch of leather belting exceeds 6% of the original length. 
 
BELTING. 1145 
 
 The stretch during the first six months of the life of belts is 36% ol 
 their entire stretch (A); 15% (B). 
 
 A doubie belt will stretch 0.47% of its length before requiring to be 
 tightened (A); 0.81% (B). 
 
 The most important consideration in making up tables and rules for the 
 use and care of belting is how to secure the minimum of interruptions to 
 manufacture from this source. 
 
 The average double belt (A), when Tunning night and day in a machine- 
 shop, will cause at least 26 interruptions to manufacture during its life, 
 or 5 interruptions per year, but with (B) interruptions to manufacture 
 will not average oftener for each belt than one in sixteen months. 
 
 The oak-tanned and fulled belts showed themselves to be superior in 
 all respects except the coefficient of friction to either the oak-tanned 
 not fulled, the semi-raw-hide, or raw-hide with tanned face. 
 
 Belts of any width can be successfully shifted backward and forward 
 on tight and loose pulleys. Belts running between 5000 and 6000 ft. 
 per min. and driving 300 H.P. are now being daily shifted on tight and 
 loose pulleys, to throw lines of shafting in and out of use. 
 
 The best form of belt-shifter for wide belts is a pair of rollers twice the 
 width of belt, either of which can be pressed onto the flat surface of the 
 belt on its slack side close to the driven pulley, the axis of the roller 
 making an angle 'of 75 with the center line of the belt. 
 
 Remarks on Mr. Taylor's Rules. (W. Kent, Trans. A. S, M. E., xy, 
 242.) The most notable feature in Mr. Taylor's paper is the great dif- 
 ference between his rules for proper proportioning of belts and those 
 given by earlier writers. A very commonly used rule is, one horse-power 
 may be transmitted by a single belt 1 in. wide running x ft. per min., sub- 
 stituting for x various values, according to the ideas of different engineers, 
 ranging usually from 550 to 1100. 
 
 The practical mechanic of the old school is apt to swear by the figure 
 600 as being thoroughly reliable, while the modern engineer is more apt 
 to use the figure 1000. Mr. Taylor, however, instead of using a figure 
 from 550 to 1100 for a single belt, uses 950 to 1100 for double belts. If 
 we assume that a double belt is twice as strong, or will carry twice as much 
 power, as a single belt, then he uses a figure at least twice as large as that 
 used in modern practice, and would make the cost of belting for a given 
 shop twice as large as if the belting were proportioned according to the 
 most liberal of the customary rules. 
 
 This great difference is to some extent explained by the fact that the 
 
 Eroblem which Mr. Taylor undertakes to solve is quite a different one 
 rom that which is solved by the ordinary rules with their variations. The 
 problem of the latter generally is, "How wide a belt must be used, or how 
 narrow a belt may be used, to transmit a given horse-power?" Mr. 
 Taylor's problem is: " How wide a belt must be used so that a given horse- 
 power may be transmitted with the minimum cost for belt repairs, the 
 longest life to the belt, and the smallest loss and inconvenience from stop- 
 ping the machine while the belt is being tightened or repaired?" 
 
 The difference between the old practical mechanic's rule of a l-in. 
 .wide single belt, 600 ft. per min., transmits one horse-power, and the rule 
 commonly used by engineers, in which 1000 is substituted for 600, is due 
 to the belief of the engineers, not that a horse-power could not be trans- 
 mitted by the belt proportioned by the older rule, but that such a pro- 
 portion involved undue strain from overtightening to prevent slipping e 
 which strain entailed too much journal friction, necessitated frequent 
 tightening, and decreased the length of the life of the belt. 
 
 Mr. Taylor's rule substituting 1100 ft. per min. and doubling the belt. 
 Is a further step, and a long one, in the same direction. Whether it will 
 be taken in any case by engineers will depend upon whether they appre- 
 ciate the extent of the losses dne to slippage of belts slackened by use 
 under overstrain, and the loss of time in tightening and repairing belts, 
 to such a degree as to induce them to allow the first cost of the belts to 
 be doubled in order to avoid these losses. 
 
 It should be noted that Mr. Taylor's experiments were made on rather 
 narrow belts, used for transmitting power from shafting to machinery, 
 and his conclusions may not be applicable to heavy au4 wide belts, 
 %3 engine fly-wheel belts. 
 
1146 BELTING. 
 
 Earth's Studies on Belting. (Trans. A. S. M. E., 1909.) Mr. 
 Carl G. Barth has made an extensive study of the work of earlier writers 
 on the subject of belting, and has derived several new formulae and dia- 
 grams showing the relation of the several variables that enter into the 
 belt problem. He has also devised a slide rule by which calculations of 
 belts may easily be made. He finds that the coefficient of friction de- 
 pends on the velocity of the belt, and may be expressed by the formula 
 
 / = 0.54 - 50Q+ y, in which V is the velocity in feet per minute. 
 
 Taking Mr. Taylor's data as a starting point, Mr Earth has adopted 
 the rule, as a basis for use of belts on belt-driven machines, that for the 
 driving belt of a machine the minimum initial tension must be such 
 that when the belt is doing the maximum amount of work intended, the 
 sum of the tension in the tight side of the belt and one-half the tension in 
 the slack side will equal 240 Ibs. per square inch of cross-section for all 
 belt speeds; and that for a belt driving a countershaft, or any other belt 
 inconvenient to get at for retightening or more readily made of liberal 
 dimensions, this sum will equal 160 Ibs. Further, the maximum initial 
 tension, that is, the initial tensi9n under which a belt is to be put up in 
 the first place, and to which it is to be retightened as often as it drops 
 to the minimum, must be such that the sum defined above is 320 Ibs. 
 for a machine belt, and 240 Ibs. for a counter-shaft belt or a belt simi- 
 larly circumstanced. 
 
 From a set of curves plotted by Mr. Barth from his formula the follow- 
 ing tables are derived. The figures are based upon the conditions named 
 in the above rule, and on an arc of contact = 180. 
 
 Belts on Machines. Tension in tight side -f- 1/2 tension in slack side 
 
 JJOll/O VJ1J. J-TiOr^lilUCO. 
 
 = 240 Ibs. 
 
 J. CHOHJ. 
 
 LJ 111 
 
 ngi 
 
 1U 
 
 IU.C 
 
 T VZ I 
 
 custiuu 
 
 in 
 
 BUbUJ 
 
 v t 
 
 >1UC! 
 
 Velocity, ft. per min. . . 
 
 500 
 
 1000 
 
 2000 
 
 3000 
 
 4000 
 
 5000 
 
 6000 
 
 Initial tension, 
 
 124 
 
 120 
 
 
 121 
 
 
 128 
 
 136 
 
 
 144 
 
 
 152 
 
 Centrifugal tension t c . 
 
 + 
 
 3 
 
 
 13 
 
 
 31 
 
 56 
 
 
 86 
 
 
 124 
 
 Difference, t t c 
 
 123 
 
 117 
 
 
 108 
 
 
 97 
 
 80 
 
 
 58 
 
 
 28 
 
 Tension on tight side, h 
 
 210 
 
 212 
 
 211 
 
 
 207 
 
 198 
 
 
 187 
 
 
 173 
 
 Tension on slack side, tz 
 
 60 
 
 54 
 
 
 57 
 
 
 68 
 
 84 
 
 
 107 
 
 
 134 
 
 ^Effective pull, ti - h. . 
 
 150 
 
 158 
 
 
 154 
 
 
 139 
 
 114 
 
 
 80 
 
 
 39 
 
 Sum of tensions ti 4- tz 
 
 270 
 
 268 
 
 
 269 
 
 
 274 
 
 282 
 
 
 294 
 
 
 307 
 
 H.P. per sq. in. of sec- 
 
 
 
 
 
 
 
 
 
 
 
 
 tion 
 
 2.27 
 
 4.79 
 
 9 
 
 .33 
 
 1 
 
 2.64 
 
 13.82 
 
 12 
 
 .12 
 
 7 
 
 .09 
 
 H.P. per in. width, 5/ 16 
 
 
 
 
 
 
 
 
 
 
 
 
 in. thick 
 
 0.71 
 
 1.50 
 
 2 
 
 .82 
 
 
 3.95 
 
 4.32 
 
 3 
 
 .71 
 
 2 
 
 .22 
 
 Belts driving countershafts, 
 
 1 1 + 1/2 tz = 
 
 = 160 Ibs. 
 
 Velocity of belt, ft. per min 
 
 500 
 
 1000 
 
 2000 
 
 3000 
 
 4000 
 
 5000 
 
 Initial tension, 
 
 
 
 82 
 
 
 81 
 
 83 
 
 89 
 
 
 96 
 
 
 102 
 
 Tension on tight side, t\ 
 
 ...... 
 
 
 140 
 
 
 141 
 
 140 
 
 134 
 
 
 125 
 
 
 114 
 
 Tension on slack side, tz 
 
 
 
 40 
 
 
 38 
 
 41 
 
 53 
 
 
 69 
 
 
 92 
 
 Effective pull, fc - tz 
 
 
 
 100 
 
 
 103 
 
 99 
 
 81 
 
 
 56 
 
 
 22 
 
 Sum of tensions 
 
 
 
 180 
 
 
 179 
 
 181 
 
 187 
 
 
 194 
 
 
 206 
 
 H.P. per sq. in. of section 
 
 1 
 
 .51 
 
 3 
 
 .12 
 
 6.04 
 
 7.36 
 
 6 
 
 .79 
 
 3 
 
 .33. 
 
 H.P. per in. width, s/ 16 in. thick 
 
 .47 
 
 
 
 .97 
 
 1.87 
 
 2.30 
 
 2 
 
 .12 
 
 1 
 
 .04 
 
 MISCELLANEOUS NOTES ON BELTING. 
 
 Formulas are useful for proportioning belts and pulleys, but they fur- 
 nish no means of estimating how much power a particular belt may be 
 transmitting at any given time, any more than the size of the engine is a 
 measure of the load it is actually drawing, or the known strength of a 
 horse is a measure of the load on the wagon. The only reliable means of 
 determining the power actually transmitted is some form of dynamometer. 
 (See Trans. A. S. M. E., vol. xii, p. 707.) 
 
 If we increase the thickness, the power transmitted ought to increase 
 in proportion; and for double belts we should have half the width required 
 for a single belt under the same conditions. With large pulleys and 
 moderate velocities of belt it is probable that this holds good. With 
 l pulleys, however, when a double belt. is used, there is not such per- 
 
MISCELLANEOUS NOTES ON BELTING. 1147 
 
 feet contact between the pulley-face and tlie belt, due to the rigidity of 
 the latter, and more work is necessary to bend the belt-fibers than when a 
 thinner and more pliable belt is used. The centrifugal force tending to 
 throw the belt from the pulley also increases with the thickness, and for 
 these reasons the width of a double belt required to transmit a given, 
 horse-power when used with small pulleys is generally assumed not less 
 than seven-tenths the width of a single belt to transmit the same power, 
 (Flather on "Dynamometers and Measurement of Power.") 
 
 F. W. Taylor, however, finds that great pliability is objectionable, and 
 favors thick belts even for small pulleys. The power consumed in bending 
 the belt around the pulley he considers inappreciable. According to 
 Rankine's formula for centrifugal tension, this tension is proportional to 
 the sectional area of the belt, and hence it does not increase with increase 
 of thickness when the width is decreased in the same proportion, the 
 sectional area remaining constant. 
 
 Scott A. Smith (Trans. A.S.M. E., x, 765) says: The best belts are made 
 from all oak-tanned leather, and curried with the use of cod oil and 
 tallow, all to be of superior quality. Such belts have continued in use 
 thirty to forty years when used as simple driving-belts, driving a proper 
 amount of power, and having had suitable care. The flesh side should 
 not be run to the pulley-face, for the reason that the wear from contact 
 with the pulley should come on the grain side, as that surface of the belt 
 is much weaker in its tensile strength than the flesh side; also as the grain 
 is hard it is more enduring for the wear of attrition; further, if the grain is 
 actually worn off, then the belt may not suffer in its integrity from a 
 ready tendency ef the hard grain side to crack. 
 
 The most intimate contact of a belt with a pulley comes, first, in the 
 smoothness of a pulley-face, including freedom from ridges and hollows 
 left by turning-tools; second, in the smoothness of the surface and even- 
 ness jn the texture or body of a belt ; third, in having the crown of the driv- 
 ing and receiving pulleys exactly alike, as nearly so as is practicable 
 in a commercial sense; fourth, in having the crown of pulleys not over 
 1/8 in. for a 24-in. face, that is to say, that the pulley is not to be over 
 1/4 in. larger in diameter in its center; fifth, in having the crown other 
 than two planes meeting at the center; sixth, the use of any material 
 on or in a belt, in addition to those necessarily used in the currying 
 process, to keep them pliable or increase their tractive quality, should 
 wholly depend upon the exigencies arising in the use of belts; non-use is 
 safer than over-use; seventh, with reference to the lacing of belts, it 
 seems to be a good practice to cut the ends to a convex shape by using a 
 former, so that there may be a nearly uniform stress on the lacing through 
 the center as compared with the edges. For a belt 10 ins. wide, the center 
 of each end should recede 1/10 in, 
 
 Lacing of Belts. In punching a belt for lacing, use an oval punch, 
 the longer diameter of the punch being parallel with the sides of the belt. 
 Punch two rows of holes in each end, placed zigzag. In a 3-in. belt there 
 should be four holes in each end two in each row. In a 6-in. belt, 
 seven holes four in the row nearest the end. A 10-in. belt should have 
 nine holes. The edge of the holes should not come nearer than 3/ 4 in. 
 from the sides, nor 7/g in. from the ends of the belt. The second row 
 should be at least 13/4 ins. from the end. On wide belts these distances 
 should be even a little greater. 
 
 Begin to lace in the center of the belt and take care to keep the ends 
 exactly in line, and to lace both sides with equal tightness. The lacing 
 should not be crossed on the side of the belt that runs next the pulley. 
 In taking up belts, observe the same rules as in putting on new ones. 
 
 Setting a Belt on Quarter-twist. A belt must run squarely on to 
 the pulley. To connect with a belt two horizontal shafts at right angles 
 with each other, say an engine-shaft near the floor with a line attached to 
 the ceiling, will require a quarter-turn. First, ascertain the central point 
 on the face of each pullev at the extremity of the horizontal diameter 
 where the belt will leave the pulley, and then set that point on the driven 
 pulley plumb over the corresponding point on the driver. This will cause 
 the belt to run squarely on to each pulley, and it will leave at an angle 
 greater or less, according to the size of the' pulleys and their distance from 
 each other. 
 
 In quarter-twist belts, in order that the belt may remain on the pulleys* 
 
1148 
 
 BELTING. 
 
 the central plane on each pulley must pass through the point of delivery 
 of the other pulley. This arrangement does not admit of reversed 
 motion. 
 To find the Length of Belt required for two given Pulleys. 
 
 When the length cannot be measured directly by a tape-line, the follow- 
 ing approximate rule may be used: Add the diameter of the two pulleys 
 together, divide the sum by 2, and multiply the quotient by 31/4, and 
 add the product to twice the distance between the centers of the shafts. 
 (See accurate formula below.) 
 
 To find the Angle of the Arc of Contact of a Belt. Divide the 
 difference between the radii of the two pulleys in inches by the distance 
 between their centers, also in inches, and in a table of natural sines find 
 the angle most nearly corresponding with the quotient. Multiply this 
 angle by 2, and add the product to 180 for the angle of contact with the 
 larger pulley, or subtract it from 180 for the smaller pulley. 
 Or, let R = radius of larger pulley, r = radius of smaller; 
 L = distance between centers of the pulleys; 
 a = angle whose sine is (R r) * L. 
 
 Arc of contact with smaller pulley = 180 2 a; 
 Arc of contact with larger pulley = 180 + 2 a. 
 
 To find the Length of Belt in Contact with the Pulley. For the 
 
 larger pulley, multiply the angle a, found as above, by .0349, to the 
 
 Sroduct add 3.1416, and multiply the sum by the radius of the pulley. 
 r length of belt in contact with the pulley 
 
 = radius X (* + .0349 a) = radius X w(l + 3/90). 
 For the smaller pulley, length = radius X OT .0349 a) 
 = radius X *r(l - a) -s-90. 
 
 The above rules refer to Open Belts. The accurate formula for length 
 of an open belt is, 
 
 Length = irR(l + a/90) + wr(l -a/90) -f 2 L cos a. 
 
 = R (IT + 0.0349 a) + r (TT-O .0349 a) + 2 L cos a, 
 
 in which R = radius of larger pulley, r = radius of smaller pulley, 
 
 L ~ distance between centers of pulleys, and a = angle whose 
 sine is 
 
 (R - r) -J- L; cos a = 
 An approximate formula Is 
 Length = 2 L -f- * (R + r) '4- (R - r)V 
 
 For L = 4, R = 2, r = 1, this formula gives length = 17.6748, the 
 accurate formula giving 17.6761 
 For Crossed Belts the formula is 
 
 Length of belt = irR(l +j8/90) -f- irr (1 4- /90) 4- 2 L cos /5 
 = (R + r) X (^ + 0.0349 ) + 2 L cos j8, 
 
 In which /3 = angle whose sine is (R + r) -s- L ; cos = V'z, 2 (R + r) 2 + L. 
 
 To find the Length of Belt when Closely Rolled. The sum of the 
 
 diameter of the roll, and of the eye in inches, X the npmber of turns made 
 by the belt and by 0.1309, = length of the belt in feet. 
 
 To find the Approximate Weight of Belts. Multiply the length 
 of belt, in feet, by the width in inches, and divide the product by 13 for 
 single and 8 for double belt. 
 
 Good oak-tanned leather from the back of the hide weighs almost 
 exactly 1 oz. per sq. ft. per 0.01 in. thickness. The thickness of single 
 belts is 0.16 in. ; of light double belts, 0.24 in. ; of medium weight double 
 belt, 0.28 in.; of standard double belt, 0.33 in.; of 3-ply belts, 0.45 in. 
 (W. O. Webber, in Trans. Natl. Assoc. Cotton Mfrs., 1908, p. 345.) 
 
 Relations of the Size and Speeds of Driving and Driven Pulleys. 
 The driving pulley is called the driver, D, and the driven piillcy the 
 driven, 'd. If the number of teeth in gears is used instead of diameter, 
 in these calculations, number of teeth must be substituted wherever 
 diameter occurs. R = revs, per min. of driver, r = revs, per min. of 
 driven. 
 
 D 
 
MISCELLANEOUS NOTES ON BELTING. 
 
 1149 
 
 Diam. of driver diam. of driven X revs, of driven -r revs, of driver. 
 
 d = DR -r r; 
 Diam. of driven = diam. of driver x revs, of driver + revs, of driven. 
 
 R = dr -s- D\ 
 Revs, of driver = revs, of driven x diam. of driven * diam. of driver. 
 
 r = DR + d\ 
 Revs, of driven = revs, of driver X diam. of driver -s- diam. of driven. 
 
 Evils of Tight Belts. (Jones and Laughlins.) Clamps with power- 
 ful screws are often used to put on belts with extreme tightness, and with 
 most injurious strain upon the leather. They should be very judiciously 
 used for horizontal belts, which should be allowed sufficient slackness 
 to move with a loose undulating vibration on the returning side, as a test 
 that they have no more strain imposed than is necessary simply to trans- 
 mit the power. 
 
 On this subject a New England cotton-mill engineer of large experience 
 says: I believe that three-quarters of the trouble experienced in broken 
 pulleys, hot boxes, etc., can be traced to the fault of tight belts. The 
 enormous and useless pressure thus put upon pulleys must in time break 
 them, if they are made in any reasonable proportions, besides wearing 
 out the whole outfit, and causing heating and consequent destruction of 
 the bearings. Below are figures showing the power taken, in average 
 modern mills with first-class shafting, to drive the shafting alone: 
 
 Mill 
 No. 
 
 Whole 
 Load, 
 H.P. 
 
 Shafting Alone. 
 
 Mill 
 No. 
 
 Whole 
 Load, 
 H.P. 
 
 Shafting Alone. 
 
 Horse- 
 power. 
 
 Per cent 
 of whole. 
 
 Horse- 
 power. 
 
 Per cent 
 of whole. 
 
 4 
 
 199 
 
 472 
 486 
 677 
 
 51 
 111.5 
 134 
 190 
 
 25.6 
 23.6 
 27.5 
 28.1 
 
 5 
 6 
 7 
 8 
 
 759 
 235 
 670 
 677 
 
 172.6 
 84.8 
 262.9 
 182 
 
 22.7 
 36.1 
 39.2 
 26.8 
 
 These may be taken as a fair showing of the power that is required in 
 many of our best mills to drive shafting. It is unreasonable to think that 
 all that power is consumed by a legitimate amount of friction of bearings 
 and belts. I know of no cause for such a loss of power but tight belts. 
 These, when there are hundreds or thousands in a mill, easily multiply 
 the friction on the bearings, and would account for the figures. 
 
 Sag of Belts. Distance between Pulleys. In the location of shafts 
 that are to be connected with each other by belts, care should be taken 
 to secure a proper distance one from the other. This distance should be 
 such as to allow of a gentle sag to the belt when in motion. 
 
 A general rule may be stated thus: Where narrow belts are to be run 
 over small pulleys 15 feet is a good average, the belt having a sag of 
 1 1/2 to 2 inches. 
 
 For larger belts, working on larger pulleys, a distance of 20 to 25 feet 
 does well, with a sag of 21/2 to 4 inches. 
 
 For main belts working on very large pulleys, the distance should be 25 
 to 30 feet, the belts working well with a sag of 4 to 5 inches. 
 
 If too great a distance is attempted, the belt will have an unsteady 
 flapping motion, which will destroy both the belt and machinery. 
 
 Arrangement of Belts and Pulleys. If possible to avoid it, con- 
 nected shafts should never be placed one directly over the other, as in 
 such case the belt must be kept very tight to do the work. For this 
 purp9se belts should be carefully selected of well-stretched leather. 
 
 It is desirable that the angle of the belt with the floor should not exceed 
 45. It is also desirable to locate the shafting and machinery so that 
 belts should run off from each shaft in opposite directions, as this arrange- 
 ment will relieve the bearings from the friction that would result when 
 the belts all pull one way on the shaft. 
 
 In arranging the belts leading from the main line of shafting to the 
 counters, those pulling in an opposite direction should be placed as near 
 each other as practicable, while those pulling in the same direction 
 should be separated. This can often be accomplished by changing the 
 relative positions of the pulleys on the counters. By this procedure 
 much of the friction on the journals may be avoided. 
 
 If possible, machinery should be so placed that the direction of the belt 
 
1150 BELTING. 
 
 motjon shall be from the top of the driving to the top of the driven pulley, 
 when the sag will increase the arc of contact. 
 
 The pulley should be a little wider than the belt required for the work. 
 
 The motion of driving should run with the laps of the belts. 
 
 Tightening or guide pulleys should be applied to the slack side of belts 
 and near the smaller pulley. 
 
 Jones and Laughlins, in their Useful Information, say: The diameter of 
 the pulleys should be as large as can be admitted, provided they will not 
 produce a speed of more than 4750 feet of belt motion per minute. 
 
 They also say: It is better to gear a mill with small pulleys and run 
 them at a high velocity, than with large pulleys and to run them slower. 
 A mill thus geared costs less and has a much neater appearance than with 
 large heavy pulleys. 
 
 M. Arthur Achard (Proc. Inst. M. E., Jan., 1881, p. 62) says: When the 
 belt is wide a partial vacuum is formed between the belt and the pulley 
 at a high velocity. The pressure is then greater than that computed from 
 the tensions in the belt, and the resistance to slipping is greater. This 
 has the advantage of permitting a greater power to be transmitted by a 
 given belt, and of diminishing the strain on the shafting. 
 
 On the other hand, some writers claim that the belt entraps air between 
 itself and the pulley, which tends to diminish the friction, and reduce 
 the tractive force. On this theory some manufacturers perforate the 
 belt with numerous holes to let the air escape. 
 
 Care of Belts. Leather belts should be well protected against water, 
 loose steam, and all other moisture, with which they should not come in 
 contact. But where such conditions prevail fairly good results are 
 obtained by using a special dressing prepared for the purpose of water- 
 proofing leather, though a positive water-proofing material has not yet 
 been discovered. 
 
 Belts made of coarse, loose-fibered leather will do better service in dry 
 and warm places, but if damp or moist conditions exist then the very 
 finest and firmest leather should be used. (Fayerweather & Ladew.) 
 
 Do not allow oil to drip upon the belts. It destroys the life of the leather. 
 
 Leather belting cannot safely stand above 130 of heat. 
 
 "Duxbak" waterproof belt is advertised to withstand any amount 
 of moisture, and temperatures up to 200 degrees. 
 
 Strength of Belting. The ultimate tensile strength of belting does 
 not generally enter as a factor in calculations of power transmission. j 
 
 The strength of the solid leather in belts is from 2000 to 5000 Ibs. per 
 square inch; at the lacings, even if well put together, only about 1000 to 
 1500. If riveted, the joint should have half the strength of the solid 
 belt. The working strain on the driving side is generally taken at not 
 over one-third of the strength of the lacing, or from one-eighth to one- 
 sixteenth of the strength of the solid belt. Dr. Hartig found that the 
 tension in practice varied from 30 to 532 Ibs. per sq. in. , averaging 273 Ibs. 
 
 Effect of Humidity Upon a Leather Belt. (W. W. Bird and F. W. 
 Roys, Trans. A. S. M. E., 1915.) Tests with a 4-in. oak-tanned single 
 belt, with constant horse-power transmitted, and with the center dis- 
 tance and humidity varying, showed increase of the sum of the tensions 
 as the humidity decreased, figures taken from curves of the results 
 being as follows: 
 
 Center distance: 9 ft. 6 in., 9 ft. 61/2 in., 9 ft. 7 in., 9 ft. 71/2 in. 
 Relative Humidity. Sum of the Tensions, pounds. 
 
 90 95 210 325 445 
 
 55 125 260 400 550 
 
 20 150 310 465 620 
 
 Increase of temperature as well as increase of humidity tends to 
 lengthen the belt and decrease the tension. The most important con- 
 clusions are: 
 
 1. If a belt be set up at a medium relative humidity, the tensions will 
 not be excessive at lower relative humidities, nor will there be any 
 great danger of slipping at high relative humidities unless there are 
 excessive temperature changes. 
 
 2. If a belt be set up at any relative humidity with a spring or 
 gravity tightener, a load 50 per cent greater than the standard can 
 be transmitted at either high or low humidity without danger of stretch- 
 ing the belt, slipping, or excessive pressure on the bearings. 
 
MISCELLANEOUS NOTES ON BELTING. 1151 
 
 Adhesion Independent of Diameter. (Schultz Belting Co".) 
 1. The adhesion of the belt to the pulley is the same the arc or number 
 of degrees of contact, aggregate tension or weight being the same 
 without reference to width of belt or diameter of pulley. 
 
 2. A belt will slip just as readily on a pulley four feet in diameter as It 
 will on a pulley two feet in diameter, provided the conditions of the faceg 
 of the pulleys, the arc of contact, the tension, and the number of feet 
 the belt travels per minute are the same in both cases. 
 
 3. To obtain a greater amount of power from belts the pulleys may be 
 covered with leather; this will allow the belts to run very slack and give 
 25% more durability. 
 
 Endless Belts. If the belts are to be endless, they should be put on 
 and drawn together by "belt clamps" made for the purpose. If the belt 
 is made endless at the belt factory, it should never be run on to the pulleys, 
 (est the irregular strain spring the belt. Lift out one shaft, place the 
 belt on the pulleys, and force the shaft back into place. 
 
 Belt Data. A fly-wheel at the Amoskeag Mfg. Co., Manchester, N.H., 
 30 feet diameter, 110 inches face, running 61 revs, per min., carried two 
 heavy double-leather belts 40 inches wide each, and one 24 inches wide. 
 The engine indicated 1950 H.P., of wliich probably 1850 H.P. was trans- 
 mitted by the belts. The belts were heavily loaded, but not overtaxed, 
 the speed being 323 ft. per min. for 1 H.P. per inch of width. 
 
 Samuel Webber (Am. Mach., Feb. 22, 1894) reports a case of a belt 30 
 ins. wide, 3/ 8 in. thick, running for six years at a velocity of 3900 ft. per 
 min., on to a pulley 5 ft. diameter, and transmitting 556 H.P. This gives 
 a velocity of 210 ft. per min. for 1 H.P. per in. of width. By Mr. Nagle's 
 table of riveted belts this belt would be designed for 332 H.P. By Mr. 
 Taylor's rule it would be used to transmit only 123 H.P. 
 
 The above may be taken as examples of what a belt may be made to 
 do, but they should not be used as precedents in designing. It is not 
 stated how much power was lost by the journal friction due to over- 
 tightening of these belts. 
 
 The United States Navy Department Specifications for Leather 
 Belting. Belting to be cut from No. 1 native packer steer hides or 
 their equal. ~A11 hides to be tanned with white or chestnut oak by 
 slow process (six to eight months) and chemical processes imist not be 
 used. The leather is to be thoroughly cured by hand and must not 
 be stuffed or loaded for artificial weight. Leather must not crack 
 open on grain side when doubled strongly by hand with grain side 
 out. Belting is to be cut from central part of the hide no further 
 than 15 in. from backbone or more than 48 in. from tail toward shoulder. 
 
 Belts 8 in. and over must be cut to include backbone. All leather 
 is to be stretched 6 in. in lengthwise direction of the butt and is 
 not to exceed 54 in. after stretching. Centers and sides are to be 
 stretched 6 in. separately. That is, all side leathers from which widths 
 under 8 in. are to be cut, must be stretched after the belting is removed 
 from the backbone center section. Center sections are to be stretched 
 in exactly the same size for which they are to be used. 
 
 For single belts up to 6 in., laps must not exceejd. 6 in. nor be less 
 than 3 1/2 in. long. For single belts over 6 in. laps must not be more 
 than 1 in. wider than belt. 
 
 For double belts, laps must not exceed 5 1/2 in. nor to be less than 
 31/2 in. No filling straps will be permitted. All laps must be held 
 securely at every part with the best quality of belt cement, and when 
 pulled apart shall show no resinous, vitreous, oily or watered condition. 
 Belting is to be stretched again after manufacture. 
 
 Belting is to weigh for all sizes of single belts 16 oz. per sq. ft. and 
 for double belts per sq. ft. as follows: 1 to 2 in., 26 oz.; 21/2 to 4 in., 
 28 oz.; 41/2 to 5 in., 30 oz.; 6 in. and over, 32 oz. 
 
 Only hand cut, green slaughter hides of the best quality are to be 
 used for lacing. Raw hide laces to be cut 1/4. 5 /i6, 3 /8, 7 /i6, V2, 5 /8, 
 and 3/4-in. sizes. They must be cut lengthwise from the hide and 
 have an ultimate tensile strength of not less than 
 
 Width, in 1/4 5/16 3/ 8 7/i 6 l/ 2 5/ 8 8/4 
 
 Tensile strength, Ib 95 125 155 165 180 205 J230 
 
 Belt Dressings. We advise that no belt dressing should be used, 
 except when the belt becomes d.ry and husky, and iu sucb instances wa 
 
1152 BELTING. 
 
 recommend the use of a dressing. Where this is not used beef tallow at 
 blood-warm temperature should be applied and then dried in, either by 
 artificial heat or the sun. The addition of beeswax to the tallow will be 
 of some service if the belts are used in wet or damp places. Resin 
 should never be used on leather belting. (Fayerweather & Ladew.) 
 
 Belts should not be soaked in water before oiling, and penetrating oils 
 should only be used when a belt gets very dry and husky from neglect. 
 It may then be moistened a little, and neatsfoot oil applied. Frequent 
 applications of such oils to a new belt render the leather soft and flabby, 
 thus causing it to stretch, and making it liable to run out of line. A 
 composition of tallow and oil, with a little resin or beeswax, is better to 
 use. Prepared castor-oil dressing is good, and may be applied with a 
 brush or rag while the belt is running. (Alexander Bros.) 
 
 Some forms of belt Dressing, the compositions of which have not been 
 published, appear to have the property of increasing the coefficient of 
 friction between the belt and the pulley, enabling a given power to be 
 transmitted with a lower belt tension than with undressed belts. C. W. 
 Evans (Power, Dec., 1905), gives a diagram, plotted from tests, which 
 shows that three of these compositions gave increased transmission for 
 a given tension, ranging from about 10% for 90 Ibs. tension per inch of 
 width to 100% increase with 20 Ibs. tension. 
 
 Cement for Doth, or Leather. (Moles worth.) 16 parts gutta- 
 percha, 4 india-rubber, 2 pitch, 1 shellac, 2 linseed-oil, cut small, melted 
 together and well mixed. 
 
 Rubber Belting. The advantages claimed for rubber belting are 
 perfect uniformity in width and thickness; it will endure a great degree of 
 heat and cold without injury; it is also specially adapted for use in damp 
 or wet places, or where exposed to the action of steam; it is very durable, 
 and has great tensile strength, and when adjusted for service it has the 
 most perfect hold on the nullevs. hence is less liable to slip than leather. 
 
 Never use animal oil or grease on rubber belts, as it will soon destroy! 
 them. 
 
 Rubber belts will be improved, and their durability increased, by 
 putting on with a painter's brush, and letting it dry, a composition made 
 of equal parts of red lead, black lead, French yellow, and litharge, mixed 
 with boiled linseed-oil and japan enough to make it dry quickly. The 
 effect of this will be to produce a finely polished surface. If, from dust 
 or other cause, the belt should slip, it should be lightly moistened on the 
 pulley side with boiled linseed-oil. (From manufacturers' circulars . ) 
 
 The best conditions are large pulleys and high speeds, low tension and 
 reduced width of belt. 4000 ft. per min. is not an excessive speed on 
 proper sized pulleys. 
 
 H.P. of a 4-plv rubber belt = flength o f arc of contact on smaller pulley 
 in ft. X width of belt in ins. X revs, per min.) -r- 325. For a 5-ply belt 
 multiply by ll/s, for a 6-ply by 12/ 3 , for a 7-ply by 2, for an 8-ply by 21/3. 
 When the proper weight of duck is used a 3- or 4-piy rubber belt is equal 
 to a single leather belt and a 5- or 6-oly rubber to a double leather belt. 
 When the arc of contact is 180, H.P. of a 4-ply belt = width in ins. X 
 velocity in ft. per min. -r- 650. (Boston Belting Co.) 
 
 Steel Belts. The Eloesser-Kraftband-Gesellschaft, of Berlin, has 
 introduced a steel belt for heavy power transmission at high speeds 
 (Am. Mach., Dec. 24, 1908). It is a thin flat band of tempered steel. 
 The ends are soldered and then clamped by a special device consisting of 
 %wo steel plates, tapered to thin edges, which are curved to the radius 
 of the smallest pulley to be used, and joined together by small screws 
 which pass through holes in the ends of the belt. It is stated that the 
 slip of these belts is less than 0.1%; they are about one-fifth the width 
 of a leather belt for the same power, and they are run at a speed of 10,000 
 ft. per minute or upwards. The following figures give a comparison of 
 a rope drive with six ropes 1.9 ins. diam., a leather belt 9.6 ins. wide and 
 a steel belt 4 ins. wide, for transmitting 100 H.P. on pulleys 3 ft. diam. 
 30 ft. apart at 200 r.p.m. 
 
 Rope Leather Steel 
 Drive. Belt. Belt. 
 
 Weight of pulley, Ibs 2200 1120 460 
 
 Weight of rope or belt, Ibs 530 240 30 
 
 Total cost of drive $335 $425 $250 
 
 ?ower lost, percent of 100 H.P,,.. ,..,,,., 13 6 0,5 
 
EOLLER CHAIN AND SPROCKET DRIVES. 1153 
 
 ROLLER CHAIN AND SPROCKET DRIVES. 
 
 The following is abstracted from an article by A. E. Michel, in 
 Mach'y, Feb., 1905. (Revised, March, 1915.) 
 
 Steel chain of accurate pitch, high tensile strength, and good wearing 
 qualities, possesses, when used within proper limitations, advantages 
 enjoyed by no other form of transmission. It is compact, affords a posi- 
 tive speed ratio, and at slow speeds is capable of transmitting heavy 
 strains. On short transmissions it is more efficient than belting and will 
 operate more satisfactorily in damp or oily places. There is no loss of 
 power from stretch, and as it allows of a low tension, journal friction is 
 minimized. 
 
 Roller chain has been known to stand up at a speed of 4,000 ft. per 
 min., and transmit 25 H.P. at 1,250 ft. per min.; but speeds of 1,000 ft. 
 per min. and under give better satisfaction. Block chain is adapted to 
 slower speeds, say 700 ft. per min. and under, and is extensively used on 
 bicycles, small motor cars and machine tools. Where speed and pull are 
 not fixed quantities, it is advisable to keep the speed high, and chain 
 pull low, yet it should be borne in mind that high speeds are more de- 
 structive to chains of large than to those of small pitch. 
 
 The following table of tensile strengths, based on tests of " Diamond" 
 chains taken from stock, may be considered a fair standard: 
 
 ROLLER CHAIN. 
 
 Pitch, in ..... 1/2 5/8 3/4 l 11/4 11/2 13/4 2 ' 
 Tens, strength, 
 
 Jbs ........ 2,500 3,900 5,600 10,000 15,600 18,500 30,500 40,000 
 
 Block chain.. . 1 inch, 1,200 to 2,500; 11/2 inch, 5,000. 
 
 The safe working load of a chain is dependent on the amount of rivet 
 bearing surface, and varies from i/e to 1/30 of the tensile strength, ac- 
 cording to the spead, size of sprockets, and other conditions peculiar to 
 each case. The tendency now is to use the widest possible chain in 
 order to secure maximum rivet bearing surface, thus insuring minimum 
 wear from friction. Manufacturers are making heavier chains than 
 heretofore for the same duty. As short pitch is always desirable, 
 special double and even triple width chains are now made to conform 
 to the requirements when a heavy single width chain of greater pitch 
 is not practical. A double chain has a little more than twice the rivet 
 bearing surface and half again as much tensile strength as the corre- 
 sponding single one. 
 
 The length of chain for a given drive may be found by the following 
 formula: 
 
 All dimensions in inches. D = Distance between centers of shafts. 
 L = Distance between limiting points of contact. R = Pitch radius of 
 large sprocket, r = Pitch radius of small sprocket. N = Number of 
 teeth of large sprocket, n = Number of teeth of small sprocket. P = 
 Pitch of chain and sprockets. (180 + 2 a) == angle of contact on large 
 sprocket. (180 - 2 a) = angle of contact on small sprocket. a = 
 angle whose sine is (R r)/D. A = D cos ct. 
 
 Length of chain required: 
 
 For block chain, the total length specified in ordering should be in 
 multiples of the pitch. For roller chain, the length should be in multi- 
 ples of twice the pitch, as a union of the ends can be effected only with 
 an outside and an inside link. 
 
 Wherever possible, the distance between centers of shafts should per- 
 mit of adjustment in order to regulate the sag of the chain. A chain should 
 be adjusted, in proportion to its length, to show slack when running, care 
 being taken to have it neither too tight nor too loose, as either condition 
 is destructive. If a fixed center distance must be used, and results in 
 too much sag, the .looseness should be taken up by an idler, and when 
 there is any considerable tension on the slack side, this idler must be 
 a sprocket. Where an idler is not practical, another combination of 
 sprockets giving approximately the same speed ratio may be tried, and 
 in this manner a combination giving the proper sag may always be 
 obtained. The Diamond Chain and Mfg. Co. says that the center 
 
1154 BELTING. 
 
 line distance between sprockets should not be less than H/2 times the 
 diameter of the larger sprocket nor more than 10 or 12 ft. 
 
 In automobile drives, too much sag or too great a distance between 
 shafts causes the chain to whip up and down a condition detrimental 
 to smooth running and very destructive to the chain. In this class 
 of work a center distance of over 4 ft. has been used, but greater effi- 
 ciency and longer life are secured from the chain on shorter lengths, 
 say 3 ft. and under. 
 
 Sprocket Wheels. Properly proportioned and machined sprockets are 
 essential to successful chain gearing. The important dimensions of a 
 sprocket are the pitch diameter and the bottom and outside diameters. 
 For block chain these are obtained as follows: 
 
 N = No. of teeth, b = Diameter of round part of chain block. B = 
 Center to center of holes in chain block. A = Center to center of holes 
 in side links, a = 180/JV. Tan Q = sin a 4- (B/A + cos a). 
 
 M Pitch diameter = A /sin Q. 
 
 Bottom diam. = pitch diam. - 6. Outside diam. = pitch diam. -f b. 
 
 For roller chain: N = Number of teeth. P = Pitch of chain. D = 
 Diameter of roller, a = 180 /N. Pitch diameter = P/sin a. 
 
 Bottom diam. = pitch diam. D. 
 
 For sprockets of 17 teeth and over, outside diam. = pitch diam. + D. 
 
 The outside diameters of small sprockets are cut down so that the 
 teeth will clear the roller perfectly at high speeds. 
 
 Outside diam. = pitch diam. -f D E. 
 
 Pitch. 
 
 Values of E. 
 
 8 to 12 
 Teeth. 
 
 13 to 16 
 Teeth. 
 
 1/2 in. to 3/4 in . . 
 
 0.062 in. 
 0.125 in. 
 
 0.031 in. 
 0.062 in. 
 
 1 in. to 2 in 
 
 Sprocket diameters should be very accurate, particularly the base 
 diameter, which should not vary more than 0.002 in. from the calculated 
 values. Sprockets should be gauged to discover thick teeth and inaccur- 
 ate diameters. A poor chain may operate on a good sprocket, but a bad 
 sprocket will ruin a good chain. Sprockets of 12 to 60 teeth give best 
 results. Fewer may oe used, but cause undue elongation In the chain, 
 wear the sprockets and consume too much power. Eight-tooth sprockets 
 ruin almost every roller chain applied to them, and ten and eleven teeth 
 are fitted only for medium and slow speeds with other conditions unusu- 
 ally favorable. 
 
 Sprocket teeth seldom break from insufficient strength, but the tooth 
 must be properly shaped. A chain will not run well unless the sprockets 
 have sidewise clearance and teeth narrowed at the ends by curves begin- 
 ning at the pitch line. 
 
 Calling W the width cf the chain between the links, 
 
 A = 1/2 W = width of tooth at top. B = uniform width below pitch line. 
 B = W 1/64 in. when W = 1/4 in. or less. 
 
 = jp 1/32 in. when W = 5/ ie to 5/g in. inclusive. 
 
 W Vie in. when W = 3/ 4 in. or over. 
 
 If the sprocket is flanged the chain must seat itself properly without the 
 side bars coming into contact with the flange. 
 
 The principal cause of trouble within the chain is elongation. It Is 
 the result of stretch of material or natural wear of rivets and their bearings. 
 To guard against the former, chain makers use special materials of high 
 tensile strength, but a chain subjected to jars and jolts bey9nd the limit ; 
 of elasticity of the material may be put in worse condition in an instant 
 than in months of natural wear. If for any reason a link elongates 
 unduly it should be replaced at once, as one elongated link will eventually 
 ruin the entire chain. Such elongation frequently results from all the 
 load being thrown on at once. 
 
 To minimize natural wear, chains should be well greased inside and , 
 out protected from mud and heavy grit, cleaned often and replaced to , 
 
ROLLER CHAIN AND SPROCKET DRIVES. 1153 
 
 run in the same direction and same side up. A new chain should never 
 be applied to a much-worn sprocket. 
 
 Importance of pitch line clearances: In a sprocket with no clearances 
 a new chain fits perfectly, but after natural wear the pitch of chain and 
 sprocket become unlike. The chain is then elongated and climbs the 
 teeth, which act as wedges, producing enormous strain, and it quickly 
 wrecks itself. With the same chain on a driven sprocket, cut with 
 clearances, all rollers seat against their teeth. After long and useful life, 
 the working roller shifts to the top, and the other rollers still seat with 
 the same ease as when new. Theoretically, all the rollers share the load. 
 This never occurs in practice, for infinitesimal wear within the chain 
 causes one, and only one, roller to bear perfectly seated against the 
 working face of the sprocket tooth at any one time. Clearance alone on 
 the driver will not provide for elongation. To operate properly the 
 pitch of the driver must be lengthened, which is done by increasing the 
 pitch diameter by an amount dependent upon the clearance allowed. 
 For theoretical reasoning on this subject see " Roller Chain Gear," a 
 treatise on English practice, by Hans Renold. 
 
 When the load reverses, each sprocket becomes alternately driver and 
 driven. This happens in a motor car during positive and negative accel- 
 eration, or in ascending or descending a hill. In this event, the above 
 construction is not applicable, for a driven sprocket of longer pitch than 
 the chain will stretch it. No perfect method of equalizing the pitch of a 
 roller chain and its sprockets under reversible load and at all periods of 
 chain elongation has been found. This fault is eliminated in the " silent " 
 type of chain; hence it runs smooth at a very much greater speed than 
 roller chain will stand. 
 
 In practice there are comparatively few roller chain drives with chain 
 pull always in the same direction, so manufacturers generally cut the 
 driver sprockets for these with normal pitch diameter, same as the 
 driven. Recent experiments have proven that the difficulties are greatly 
 lessened by cutting both driver and driven with liberal pitch line clear- 
 rfhce. Accordingly, chain makers now advise the following pitch line 
 clearance for standard rollers: 
 
 Pitch, in., 1/2 3/4 1 11/4 1V 2 i3/ 4 2 
 
 Clearance, In., 1/32 Vie 3 /32 3 /i6 7 /32 Vs 5 /32 
 
 Cutters may be obtained from Brown & Sharpe Mfg. Co. with thia 
 clearance. 
 
 Belting versus Chain Drives. Chains are suitable for positive 
 transmissions of very heavy powers at slow speed. They are properly 
 used for conveying ashes, sand, chemicals and liquids which would cor- 
 rode or destroy belting. Chains of this kind are generaUy made of 
 malleable iron. For conveyers for clean substances, 'flour, wheat ana 
 other grains, belts are preferable, and in the best installations leather is 
 preferred to cotton or rubber, being more durable. Transmission 
 chains have to be carefully made. If the chain is to run smoothly, 
 noiselessly, and without considerable friction, both the links and the 
 sprockets must be mathematically correct. This perfection of design 
 is found only in the highest and best makes of steel chain. 
 
 Deterioration of chains starts in with the beginning of service. Even 
 in such light and flexible duty as bicycle transmission, a chain is sub- 
 jected to sudden severe strains, which either stretch the chain. or distort 
 the bearing surfaces. Either mishap is fatal to smooth, frictionless 
 running. If the transmissi9n is positive, as from motor or shaft to a 
 machine tool, sudden variations in strain become sledge-hammer blows, 
 and the chain must either break or the parts yield. To avoid the evils 
 arising from the stretching of the chain, self-ad justing forms of teeth 
 have been invented, and the Renold and the Morse silent-chain gears 
 are examples. 
 
 Chain drives are recommended for use under the following conditions: 
 (1) Where room is lacking for the proper size pulleys for belts. (2) 
 Where the centers between shafts are too short for belts. (3) Where a 
 positive speed ratio is desired. (4) Where there is moisture, heat or 
 dust that would prevent a belt working properly. (5) Where a maxi- 
 mum power per inch of width is desired. 
 
 The Renold and the Morse chain gears use springs in the sprocket 
 
1156 
 
 BELTING. 
 
 wheel to absorb the shock when a reversal of strain takes place, which 
 is infrequent in ordinary power transmission, but is found in reciprocat- 
 ing air-compressors and pumps, in gas-engine drives where an insufficient 
 balance wheel is supplied, and where a heavy shock load occurs and it is 
 desirable to cushion the effect by mounting the wheel on springs. 
 
 Nickel steel is generally used for the chains. The joint pins are 
 made from 31/2% nickel chrome steel, heat-treated. The ends of the 
 joint pins are softened by an electric arc to facilitate riveting to the 
 chain links. 
 
 Data Used in the Preliminary Design of Morse Silent Chain Drives 
 
 Pitch, in 
 
 1/2 
 
 5/8 
 
 3/4 
 
 9/10 
 
 12/10 
 
 1 1/2 
 
 2 
 
 3 
 
 Minimum no. of teeth: 
 Small sprocket driver.. 
 Small sprocket driven . 
 
 13 
 17 
 
 13 
 17 
 
 13 
 21 
 
 15 
 25 
 
 15 
 29 
 
 17 
 29 
 
 17 
 31 
 
 17 
 35 
 
 19-31 
 
 Desirable no. of teeth 
 in small sprockets 
 
 15-17 
 
 17-21 
 
 17-21 
 
 17-23 
 
 17-23 
 
 17-27 
 
 17-31 
 
 Maximum no. of teeth in 
 large sprockets. (See 
 Note 3.) 
 
 99 
 
 109 
 
 115 
 
 125 
 
 129 
 
 129 
 
 129 
 
 131 
 
 Desirable no. of teeth in 
 large sprockets 
 
 55-75 
 
 55-75 
 
 55-85 
 
 55-95 
 
 55-105 
 
 55-115 
 
 55-115 
 
 55-115 
 
 Pitch diam. of wheel = 
 no. of teeth X 
 
 0.159 
 
 0.199 
 
 0.239 
 
 0.2865 
 
 0.382 
 
 0.477 
 
 0.636 
 
 0.955 
 
 Addendum for outside 
 diam. of sprockets 20 to 
 130T. (See Note 1.), in. 
 
 0.10 
 
 0.12 
 
 0.15 
 
 0.18 
 
 0.24 
 
 0.30 
 
 0.40 
 
 0.60 
 
 Maximum r.p.m 
 
 2400 
 
 1800 
 
 1200 
 
 1100 
 
 850 
 
 600 
 
 400 
 
 250 
 
 Tension per in. width of 
 chain, lb.: 
 Small sprocket driver.. 
 Small sprocket driven . 
 
 80 
 65 
 
 100 
 80 
 
 120 
 95 
 
 150 
 120 
 
 200 
 160 
 
 270 
 210 
 
 450 
 350 
 
 750 
 600 
 
 Radial clearance beyond 
 tooth required for 
 chain, in 
 
 0.50 
 
 0.62 
 
 0.75 
 
 0.90 
 
 1.2 
 
 1.5 
 
 2.0 
 
 3.0 
 
 Approx. weight of chain 
 per in. wide, 1 ft. long, 
 
 1.00 
 
 1.20 
 
 1.50 
 
 1.80 
 
 2.50 
 
 3.00 
 
 4.00 
 
 6.00 
 
 C for solid pinions 
 
 0.0045 
 
 0.0063 
 
 0.009 
 
 0.013 
 
 0.023 
 
 0.035 
 
 0.058 
 
 0.145 
 
 C for armed sprockets . . 
 
 0.16 
 
 0.25 
 
 0.35 
 
 0.45 
 
 0.7 
 
 1.0 
 
 2.0 
 
 4.0 
 
 APPROXIMATE WEIGHTS FOR SOLID AND ARMED SPROCKETS. 
 T = Number of teeth. F = Face in inches. 
 
 C = Constant in lb. per in. in face per tooth as per table. 
 Weight of armed sprocket = T X F X C. 
 Add 25 % for split and 50 % for spring and split sprockets. 
 r Weight of solid pinion = T2 x (F + 1) X C. 
 
 NOTES. 
 1. Number of teeth = T. 
 
 Exact outside diameter = D. 
 For T less than 20 teeth, D = pitch diameter. 
 For T more than 20 teeth, D = pitch diameter -f addendum. 
 2. Use sprockets having an odd number of teeth whenever possible. 
 3. When specially authorized, a larger number of teeth than shown 
 
 may be cut in large sprocket. 
 4. Thickness of sprocket rim, including teeth, should be at least 
 
 1.2 times the chain pitch. 
 
 5. The number of grooves in the sprocket, their width and distance 
 apart, varies according to pitch and width of chain. Leave the 
 designing and turning of grooves to the manufacturer. 
 6. The width of the sprocket should be i/g to 1/4 in. greater on small 
 drives, and 1/4 to 1/2 in. greater on large drives than the nomina 1 
 width of the chain. 
 
GEARING. 1157 
 
 7. An even number of links in the chain and an odd number of teeth 
 
 in the wheels are desirable. 
 
 8. Horizontal drives preferred; tight chain on top necessary for 
 short drives without center adjustment, and desirable for long 
 drives with or without center adjustment. 
 9. Adjustable wheel centers desirable for horizontal drives and 
 
 necessary for vertical drives. 
 10. Avoid vertical drives. 
 11. Allow a side clearance for chain (parallel to axis of sprockets and 
 
 measured from nominal width of chain) equal to the pitch. 
 12. Maximum linear velocity for commercial service, 1200 to 1600 
 ft. per min. 
 
 Comparison of Rope and Chain Drives. Horse-power, 1200; 240 
 to 80 r.p.m. 
 
 Rope. Chain. 
 
 Distance between centers 42 ft. 8 ft. 4 in. 
 
 Diameter driving sheave or sprocket 6 ft. 4 1/2 in. 30.21 in. 
 
 Diameter driven sheave or sprocket 20 ft. 89.42 in. 
 
 The rope drive has 30 ropes, each 1 3/ 4 in. diameter. The chain drive 
 has a Morse silent chain, length, 33.5 ft.; width, 27 in.; pitch, 3 in. 
 
 Data of Some Chain Drives that Have Given Good Service 
 
 
 
 Speed, 
 
 Sprockets, 
 
 Center 
 
 Rev. 
 
 H.P. 
 
 Pitch, 
 
 Width, 
 
 Ft. per 
 
 No of 
 
 Distance, 
 
 per 
 
 Trans- 
 
 In. 
 
 In. 
 
 Min. 
 
 Teeth. 
 
 In. 
 
 Min. 
 
 mitted. 
 
 V8 
 
 21/2 
 
 1550 
 
 17 & 75 
 
 25.5 
 
 1750 & 397 
 
 7.5 
 
 H/2 
 
 12 
 
 1150 
 
 95 & 95 
 
 85 
 
 97 & 97 
 
 200 
 
 H/2 
 
 18 
 
 715 
 
 59 & 95 
 
 169 
 
 97 & 60 
 
 200 
 
 2 
 
 5 
 
 1400 
 
 29 & 57 
 
 68 
 
 418 & 290 
 
 85 
 
 3* 
 
 12 
 
 1450 
 
 61 & 77 
 
 135 
 
 95 & 75 
 
 500 
 
 3 
 
 24 
 
 1450 
 
 61 & 83 
 
 103 
 
 95 & 70 
 
 1000 
 
 3 
 
 27 
 
 1870 
 
 30 & 89 
 
 100 
 
 240 & 80 
 
 1200 
 
 2 
 
 24 
 
 780 
 
 26 & 120 
 
 144 
 
 300 & 65 
 
 350 
 
 A chain transmission gear of 5000 H.P. has been built, with the 
 total width of chain 168 in. The efficiency of the best chain drives 
 when in good condition is claimed to be from 98 to 99%. 
 
 GEARING. 
 
 TOOTHED-WHEEL, GEARING. 
 
 Pitch, Pitch-circle, etc. If two cylinders with parallel axes are 
 pressed together and one of them is rotated on its axis, it will drive the 
 other by means of the friction between the surfaces. The cylinders may 
 be considered as a pair of spur-wheels with an infinite number of very small 
 teeth. If actual teeth are formed upon the cylinders, making alternate 
 elevations and depressions in the cylindrical surfaces, the distance between 
 the axes remaining the same, we have a pair of gear-wheels which will 
 drive one another by pressure upon the faces of the teeth, if the teeth are 
 properly shaped. In making the teeth the cylindrical surface may 
 entirely disappear, but the position it occupied may still be considered as 
 a cylindrical surface, which is called the "pitch-surface," and its trace 
 on the end of the wheel, or on a plane cutting the wheel at right angles to 
 its axis, is called the "pitch-circle" or "pitch-line." The diameter of 
 this circle is called the pitch-diameter, and the distance from the face 
 of one tooth to the corresponding face of the next tooth on the same 
 wheel, measured on an arc of the pitch-circle, is called the "pitch of the 
 tooth," or the circular pitch. 
 
 If two wheels having teeth of the same pitch are geared together so 
 that their pitch-circles touch, it is a property of the pitch-circles that 
 their diameters are proportional to the number of teeth in the wheels, 
 and vice versa; thus, if one wheel is twice the diameter (measured on the 
 pitch-circle) of the other, it has twice as many teeth. If the teeth are 
 properly shaped the linear velocities of the two wheels are equal, and the 
 angular velocities, or speeds of rotation, are inversely proportional to the 
 
1158 
 
 GEARING. 
 
 Thus the wheel that has twice as 
 *,/ 
 " 
 
 number of teeth and to the diameter, 
 many teeth as the other will revolve 
 just half as many times in a minute. 
 
 The "pitch," or distance meas- 
 ured on an arc of the pitch-circle 
 from the face of one tooth to the 
 face of the next, consists of two 
 parts the "thickness" of the 
 tooth and the "space" between it 
 and the next tooth. The space is 
 larger than the thickness by a small 
 amount called the "backlash," 
 which is allowed for imperfections 
 of workmanship. In finely cut 
 gears the backlash may be almost 
 nothing. 
 
 The length of a tooth in the 
 direction of the radius of the wheel 
 is called the "depth," and this is divided into two parts: First, the 
 "addendum," the height of the tooth above the pitch line; second, the 
 "dedendum, " the depth below the pitch-line, which is an amount equal to 
 the addendum of the mating gear. The depth of the space is usually 
 given a little "clearance" to allow for inaccuracies of workmanship, 
 especially in cast gears. 
 
 Referring to Fig. 178 , pi, pi are the pitch-lines, al the addendum-line, 
 rl the root-line or dedendum-line, cl the clearance-line, and b the back- 
 lash. The addendum and dedendum are usually made equal to each 
 Other. (Some writers make the dedendum include the clearance.) 
 No of teeth 3.1416 
 
 Diametral pitch = 
 
 Circular pitch = 
 
 diam. of pitch-circle in inches 
 diam.X 3.1416 3.1416 
 
 circular pitch' 
 
 No. of teeth . diametral pitch 
 
 Some writers use the term diametral pitch to mean 
 circular pitch 
 
 diam. 
 
 No. of teeth 
 but the first definition is the more common and the more 
 
 3.1416 
 
 convenient. A wheel of 12 in. diam. at the pitch-circle, with 48 teeth, is 
 
 48/12 =4 diametral pitch, or simply 4 pitch. The circular pitch of the 
 
 same wheel is 12 X 3.1416 -r- 48 = 0.7854, or 3.1416 -;-_4 = 0.7854 in. 
 
 Relation of Diametral to Circular Pitch.' 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 1 
 
 3. 142 in. 
 
 11 
 
 0.286 in. 
 
 3 
 
 .047 
 
 15/16 
 
 3.351 
 
 1 1/2 
 
 2.094 
 
 12 
 
 .262 
 
 21/2 
 
 .257 
 
 7/8 
 
 3.590 
 
 2 
 
 1.571 
 
 14 
 
 .224 
 
 2 
 
 .571 
 
 13/16 
 
 3.867 
 
 21/4 
 
 1.396 
 
 16 
 
 .196 
 
 7/8 
 
 .676 
 
 3/4 
 
 4.189 
 
 21/2 
 
 1.257 
 
 18 
 
 .175 
 
 3/4 
 
 .795 
 
 H/16 
 
 4.570 
 
 23/ 4 
 
 1.142 
 
 20 
 
 .157 
 
 5/8 
 
 .933 
 
 5/8 
 
 5.027 
 
 3 
 
 1.047 
 
 22 
 
 .143 
 
 1/2 
 
 2.094 
 
 9/16 
 
 5.585 
 
 3l/ 2 
 
 0.898 
 
 24 
 
 .131 
 
 7/16 
 
 2.185 
 
 1/2 
 
 6.283 
 
 4 
 
 .785 
 
 26 
 
 .121 
 
 3/8 
 
 2.285 
 
 7/16 
 
 7.181 
 
 5 
 
 .628 
 
 28 
 
 .112 
 
 5/16 
 
 2.394 
 
 3/8 
 
 8.378 
 
 6 
 
 .524 
 
 30 
 
 .105 
 
 1/4 
 
 2.513 
 
 5/16 
 
 10.053 
 
 7 
 
 .449 
 
 32 
 
 .098 
 
 3 /16 
 
 2.646 
 
 1/4 
 
 12.566 
 
 8 
 
 .393 
 
 36 
 
 .087 
 
 1/8 
 
 2.793 
 
 3/16 
 
 16.755 
 
 9 
 
 .349 
 
 40 
 
 .079 
 
 1/16 
 
 2.957 
 
 1/8 
 
 25.133 
 
 10 
 
 .314 
 
 48 
 
 .065 
 
 
 3.142 
 
 1/16 
 
 50.266 
 
 Since circ. pitch = 
 
 diam. X 3.1416 
 No. of teeth 
 
 diam. 
 
 circ. pitch X No. of teeth 
 3.1416 
 
 which always brings out the diameter as a number with an inconvenient 
 fraction if the pitch is in even inches or simple fractions of an inch. By 
 
TOOTHED-WHEEL GEARING. 
 
 1159 
 
 the diametral-pitch system this inconvenience is avoided. The diameter 
 may be in even inches or convenient fractions, and the number of teeth 
 is usually an even multiple of the number of inches in the diameter. 
 
 Diameter of Pitch-line of Wheels from 10 to 100 Teeth of 1 In. 
 Circular Pitch. 
 
 0*5 
 
 * 
 
 5 
 
 4 
 
 ;> 
 
 I.a 
 5 
 
 0*1 
 
 * 
 
 is 
 
 Q 
 
 4 
 
 1 d 
 
 s. 
 
 6*1 
 
 *& 
 
 is 
 
 Q 
 
 ol 
 
 * 
 
 |.a 
 
 10 
 
 3.183 
 
 26 
 
 8.276 
 
 41 
 
 13.051 
 
 56 
 
 17.825 
 
 71 
 
 22.600 
 
 86 
 
 27.375 
 
 11 
 
 3.501 
 
 27 
 
 8.594 
 
 42 
 
 13.369 
 
 57 
 
 18.144 
 
 72 
 
 22.918 
 
 87 
 
 27.693 
 
 12 
 
 3.820 
 
 28 
 
 8.913 
 
 43 
 
 13.687 
 
 58 
 
 18.462 
 
 73 
 
 23.236 
 
 88 
 
 28.011 
 
 13 
 
 4.138 
 
 29 
 
 9.231 
 
 44 
 
 14.006 
 
 59 
 
 18.781 
 
 74 
 
 23.555 
 
 89 
 
 28.329 
 
 14 
 
 4.456 
 
 30 
 
 9.549 
 
 45 
 
 14.324 
 
 60 
 
 19.099 
 
 75 
 
 23.873 
 
 90 
 
 28.648 
 
 15 
 
 4.775 
 
 31 
 
 9.868 
 
 46 
 
 14.642 
 
 61 
 
 19.417 
 
 76 
 
 24.192 
 
 91 
 
 28.966 
 
 16 
 
 5.093 
 
 32 
 
 10.186 
 
 47 
 
 14.961 
 
 62 
 
 19.735 
 
 77 
 
 24.510 
 
 92 
 
 29.285 
 
 17 
 
 5.411 
 
 33 
 
 10.504 
 
 48 
 
 15.279 
 
 63 
 
 20.054 
 
 78 
 
 24.828 
 
 93 
 
 29.603 
 
 18 
 
 5.730 
 
 34 
 
 10.823 
 
 49 
 
 15.597 
 
 64 
 
 20.372 
 
 79 
 
 25.146 
 
 94 
 
 29.921 
 
 19 
 
 6.048 
 
 35 
 
 11.141 
 
 50 
 
 15.915 
 
 65 
 
 20.690 
 
 80 
 
 25.465 
 
 95 
 
 30.239 
 
 20 
 
 6.366 
 
 36 
 
 11.459 
 
 51 
 
 16.234 
 
 66 
 
 21.008 
 
 81 
 
 25.783 
 
 96 
 
 30.558 
 
 21 
 
 6.685 
 
 37 
 
 11.777 
 
 52 
 
 16.552 
 
 67 
 
 21 .327 
 
 82 
 
 26.101 
 
 97 
 
 30.876 
 
 22 
 
 7.003 
 
 38 
 
 12.096 
 
 53 
 
 16.870 
 
 68 
 
 21 .645 
 
 83 
 
 26.419 
 
 98 
 
 31 194 
 
 23 
 
 7.321 
 
 39 
 
 12.414 
 
 54 
 
 17.189 
 
 69 
 
 21.963 
 
 84 
 
 26.738 
 
 99 
 
 31.512 
 
 24 
 
 7.639 
 
 40 
 
 12.732 
 
 55 
 
 17.507 
 
 70 
 
 22.282 
 
 85 
 
 27.056 
 
 100 
 
 31.831 
 
 25 
 
 7.958 
 
 
 
 
 
 
 
 
 
 
 
 For diameter of wheels of any other pitch than 1 in., multiply the figures 
 in the table by the pitch. Given the diameter and the pitch, to find the 
 number of teeth. Divide the diameter by the pitch, look in the table 
 under diameter for the figure nearest to the quotient, and the number 
 of teeth will be found opposite. 
 
 _ Proportions of Teeth. Circular Pitch = 1. 
 
 ~ 
 
 2. | 3. 
 
 4. 
 
 5. | 6. 
 
 Depth of tooth above pitch-line 
 
 0.35 
 
 30 
 
 37 
 
 0.33 
 
 30 
 
 30 
 
 Depth of tooth below pitch-line 
 Working depth of tooth 
 Total depth of tooth 
 
 .40 
 .70 
 .75 
 
 .40 
 .60 
 .70 
 
 .43 
 .73 
 80 
 
 "]66 
 .75 
 
 .40 
 '76 
 
 .35 
 
 65 
 
 Clearance at root 
 Thickness of tooth 
 
 .05 
 
 45 
 
 .10 
 45 
 
 .07 
 47 
 
 45 
 
 475 
 
 485 
 
 Width of space. . . 
 
 54 
 
 55 
 
 53 
 
 55 
 
 525 
 
 515 
 
 Backlash 
 
 09 
 
 '10 
 
 06 
 
 10 
 
 05 
 
 03 
 
 Thickness of rim 
 
 
 
 47 
 
 45 
 
 70 
 
 65 
 
 Depth oi tooth above pitch- 
 line. . 
 
 25 to 33 
 
 30 
 
 318 
 
 1 ' P 
 
 Depth of tooth below pitch- 
 line. . 
 
 35 to 42 
 
 35+ 08" 
 
 369 
 
 1 157 p 
 
 Working depth of tooth. . . 
 
 
 
 637 
 
 2 + P 
 
 Total depth of tooth 
 Clearance at root 
 
 .6 to .75 
 
 .65 +.08" 
 
 .687 
 .04 to 05 
 
 2.157+P 
 
 157-rP 
 
 Thickness of tooth 
 
 48 to 485 
 
 48 03" 
 
 48 to 5 { 
 
 1.51 + Pto 
 
 Width of space 
 
 .52 to 515 
 
 52+ 03" 
 
 52 to 5 { 
 
 1.57 -v-P 
 1.57 -5-Pto 
 
 Backlash 
 
 .04 to .03 
 
 .04+ .06" 
 
 .0 to .04 
 
 1.63 -T- P 
 .Oto .06-7- P 
 
 * In terms of diametral pitch. 
 
 AUTHORITIES. 1. Sir Wm. Fairbairn. 2, 3. Clark, R. T. D.; "used 
 by engineers in good practice. " 4. Molesworth. 5,6. Coleman Sellers: 
 5 for cast, 6 for cut wheels. 7, 8. Unwin. 9, 10. Leading American 
 manufacturers of cut gears. 
 
 The Chordal Pitch (erroneously called "true pitch" by some authors) 
 is the length of a straight line or chord drawn from center to center of two 
 adiacent teeth. The term is now but little used, except in connection 
 frtth chain and sprocket gearing, 
 
1160 
 
 GEARING. 
 
 Chordal pitch = diam. of pitch-circle X sine of 
 
 Chordal 
 
 180 
 
 No. of teeth 
 
 pitch of a wheel of 10 in. pitch diameter and 10 teeth, 10 X sin 18 
 3.0902 in. Circular pitch of same wheel = 3.1416. Chorda! pitch is 
 used with chain or sprocket wheels, to conform to the pitch of the chain. 
 
 Gears with Short Teeth. There is a tendency in recent years to 
 depart widely from the proportions of teeth given in the above and to 
 use much shorter teeth, especially for heavy machinery. C. W. Hunt 
 gives addendum and dedendum each = 0.25, and the clearance 0.05 of 
 the circular pitch, making the total depth of tooth 0.55 of the circular 
 pitch. The face of the tooth is involute in form, and the angle of action 
 is 141/2, C. H. Logue uses a 20 involute with the following proportions: 
 Addendum 0.25P' = 0.7854 -^P; dedendum 0.30 P' = 0.9424 -* P; 
 clearance, 0.05P' = 0.157P: whole depth 0.55P' = 1.7278 *- P. P' = 
 circular pitch, P = diametral pitch. See papers by R. E. Flanders and 
 Norman Litchfield in Trans. A. S. M. E., 1908. 
 
 John Walker (Am. Mach., Mar. 11, 1897) says: For special purposes of 
 slow-running gearing with great tooth stress I should prefer a length of 
 tooth of 0.4 of the pitch, but for general work a length of 0.6 of the ititch. 
 In 1895 Mr. Walker made two pairs of cut steel gears for the Chicago 
 cable railway with 6-in. circular pitch, length = 0.4 pitch. The pinions 
 had 42 teeth and the gears 62, each 20-in. face. The two pairs were 
 set side by side on their shafts, so as to stagger the teeth, making the 
 total face 40 ins. The gears transmitted 1500 H.P. at 60 r.p.m. replac- 
 ing cast-iron gears of 7V2 in. pitch which had broken in service. 
 Formulae for Determining the Dimensions of Small Gears. 
 (Brown & Sharpe Mfg. Co.) 
 
 P = diametral pitch or the number of teeth to one inch of diameter of 
 pitch-circle; 
 
 
 Larger 
 
 
 
 Wheel. 
 
 * 
 
 
 
 These 
 
 
 
 
 df ~ diameter of pitch-circle 
 
 
 together. 
 
 
 Smaller 
 
 
 
 Wheel. 
 
 
 V = velocity 
 
 
 
 a = distance between the centers of the two wheels; 
 
 b = number of teeth in both wheels; 
 
 t = thickness of tooth or Cutter on pitch-circle; 
 
 s = addendum; 
 D" = working depth of tooth; 
 
 / = amount added to depth of tooth for rounding the corners and for 
 
 clearance; 
 D" + f = whole depth of tooth; 
 
 TT = 3.1416. 
 
 P' = circular pitch, or the distance from the center of one tooth to tha 
 center of the next measured on the pitch-circle. 
 
 Formulae for a single wheel: 
 
 N+2 
 
 D 
 N_ 
 D'' 1 
 
 >' = 
 
 DX^V 
 
 N +2' 
 
 N 
 
 2 
 
 T\rr _ o i 
 
 D - p -2 S , 
 JV = PD-2; 
 
 5 
 
 =1=^=0.3183P'; 
 
 D' 
 
 N 
 
 D 
 
 D = 
 
 fry? 
 
 1.57 
 
 + /=j>(l+f ) -0.3685 P. 
 
 =1/2 P'. 
 
 Formulae for a pair of wheels: 
 
 nv 
 V : 
 
 PD'V 
 
 v ' 
 PD'V 
 
 2a(AT+2) 
 
 6 
 2 a (n+2) 
 
TOOTHED-WHEEL GEARING. 
 
 1161 
 
 
 TV_ 
 
 ~ 
 
 2 
 2aV 
 
 = v + V' 
 
 Width of Teeth. The width of the faces of teeth is generally made 
 from 2 to 3 times the circular pitch, that is from 6.28 to 9.42 divided by 
 the diametral pitch. There is no standard rule for width. 
 
 The following sizes are given in a stock list of cut gears in " Grant's 
 Gears:" 
 
 Diametral pitch. . 346 8 12 16 
 
 Face, inches 3 and 4 21/2 13/ 4 and 2 1 1/4 and 1 1/ 2 3/ 4 and 1 l/ 2 and 5/ 8 
 
 The Walker Company gives: 
 Circular pitch, in. . 1/2 5/g 
 
 3/4 7/8 1 
 
 2 21/2 3 4 5 6 
 
 11/2 
 
 Face, in.* ' li/ 4 li/ 2 13/4 2 21/2 41/2 6 7V2 9121620 
 
 The following proportions of gear-wheels are recommended by Prof. 
 Coleman Sellers^ (Stevens Indicator, April, 1892.) 
 
 Proportions of Gear-wheels. 
 
 
 
 
 Inside of Pitch-line. 
 
 Width of Space. 
 
 Diametral 
 Pitch. 
 
 Circular 
 Pitch. 
 P 
 
 Outside of 
 Pitch-line. 
 P X0.3. 
 
 For Cast 
 or Cut 
 Bevels or 
 for Cast 
 Spurs. 
 
 For Cut 
 Spurs. 
 PX0.35. 
 
 For Cast 
 Spurs or 
 Bevels. 
 PX0.525. 
 
 For Cut 
 Bevels or 
 Spurs. 
 PX0.51. 
 
 
 
 
 PX0.4. 
 
 
 
 
 12 
 
 0.2618 
 
 0.075 
 .079 
 
 0.100 
 .105 
 
 0.088 
 .092 
 
 0.131 
 .137 
 
 0.128 
 .134 
 
 10 
 
 0.31416 
 
 .094 
 
 .126 
 
 .11 
 
 .165 
 
 .16 
 
 
 3/8 
 
 .113 
 
 .150 
 
 .131 
 
 .197 
 
 .191 
 
 8 
 
 0.3927 
 
 .118 
 
 .157 
 
 .137 
 
 .206 
 
 .2 
 
 7 
 
 0.4477 
 
 .134 
 
 .179 
 
 .157 
 
 .235 
 
 .228 
 
 6 
 
 V2 
 0.5236 
 
 .15 
 .157 
 
 .20 
 .209 
 
 .175 
 .183 
 
 .263 
 
 .275 
 
 .255 
 .267 
 
 
 9/16 
 
 .169 
 
 .225 
 
 .197 
 
 .295 
 
 .287 
 
 5 
 
 0.62 8 832 
 
 .188 
 .188 
 
 .25 
 .251 
 
 .219 
 
 .22 
 
 .328 
 .33 
 
 .319 
 .32 
 
 4 
 
 3/4 
 0.7854 
 
 .225 
 .236 
 
 .3 
 
 .314 
 
 .263 
 .275 
 
 .394 
 .412 
 
 .383 
 .401 
 
 
 7/8 
 
 .263 
 
 .35 
 
 .307 
 
 .459 
 
 .446 
 
 
 1 
 
 .3 
 
 .4 
 
 .35 
 
 .525 
 
 .51 
 
 3 
 
 1.0472 
 
 .314 
 
 .419 
 
 .364 
 
 .55 
 
 .534 
 
 
 H/8 
 
 .338 
 
 .45 
 
 .394 
 
 .591 
 
 .574 
 
 2 3/4 
 
 1.1424 
 
 .343 
 
 .457 
 
 .40 
 
 .6 
 
 .583 
 
 21/2 
 
 1.25664 
 
 .375 
 .377 
 
 .5 
 
 .503 
 
 .438 
 .44 
 
 .656 
 .66 
 
 .638 
 .641 
 
 
 13/8 
 
 .413 
 
 .55 
 
 .481 
 
 .722 
 
 .701 
 
 
 U/2 
 
 .45 
 
 .6 
 
 .525 
 
 .788 
 
 .765 
 
 2 
 
 1.5708 
 
 .471 
 
 .628 
 
 .55 
 
 .825 
 
 .801 
 
 
 13/4 
 
 .525 
 
 .7 
 
 .613 
 
 .919 
 
 .893 
 
 
 2 
 
 .6 
 
 .8 
 
 .7 
 
 .05 
 
 .02 
 
 U/2 
 
 2.0944 
 
 \628 
 
 .838 
 
 .733 
 
 .1 
 
 .068 
 
 
 21/4 
 
 .675 
 
 .9 
 
 .788 
 
 .181 
 
 .148 
 
 
 2V2 
 
 .75 
 
 .0 
 
 .875 
 
 .313 
 
 .275 
 
 
 23/4 
 
 .825 
 
 .1 
 
 .963 
 
 .444 
 
 .403 
 
 
 3 
 
 .9 
 
 .2 
 
 1.05 
 
 .575 
 
 .53 
 
 
 3.1416 
 
 .942 
 
 .257 
 
 1.1 
 
 .649 
 
 .602 
 
 
 31/4 
 
 .975 
 
 .3 
 
 1.138 
 
 .706 
 
 .657 
 
 
 31/2 
 
 1.05 
 
 .4 
 
 1 225 
 
 838 
 
 .785 
 
 Thickness of rim below root = depth of toottu 
 
1162 GEARING. 
 
 Rules for Calculating the Speed of Gears and Pulleys, The 
 
 relations of the size and speed of driving and driven gear-wheels are the 
 same as those of belt pulleys. In calculating for gears, multiply or 
 divide by the diameter of the pitch-circle or by the number of teeth, as 
 may be requiied. In calculating for pulleys, multiply or divide by their 
 diameter in inches. 
 
 If D = diam. of driving wheel, d = diam. of driven, R = revolution* 
 per minute of driver, r = revs, per min. of driven, RD = rd; 
 R = rd ~ D; r = RD + d; D = dr -r R; d = DR -r r. 
 
 If N = No. of teeth of driver and n = No. of teeth of driven, NR = nr; 
 N = nr -? R; n = NR -^ r; R = rn * N- r= RN ~ n. 
 
 To find the number of revolutions of the last wheel at the end of a 
 train of spur-wheels, all of which are in a line and mesh into one another, 
 when the revolutions of the first wheel and the number of teeth or the 
 diameter or the first and last are given: Multiply the revolutions of the 
 first wheel by its number of teeth or its diameter, and divide the product 
 by the number of teeth or the diameter of the last wheel. 
 
 To find the number of teeth in each wheel for a train of spur-wheels, 
 each to have a given velocity: Multiply the number of revolutions of 
 , the driving-wheel by its number of teeth, and divide the product by the 
 number of revolutions each wheel is to make. 
 
 To find the number of revolutions of the last wheel in a train of wheels 
 and pinions, when the revolutions of the first or driver, and the diameter, 
 the teeth, or the circumference of all the drivers and pinions are given; 
 Multiply the diameter, the circumference, or the number of teeth of all 
 the driving-wheels together, and this continued product by the number 
 of revolutions of the first wheel, and divide this product by the contin- 
 ued product of the diameter, the circumference, or the number of teeth 
 of all the driven wheels, and the quotient will be the number of revolutions 
 of the last wheel. 
 
 EXAMPLE. 1. A train of wheels consists of four wheels each 12 in. 
 diameter of pitch-circle, and three pinions 4, 4, and 3 in. diameter. The 
 large wheels are the drivers, and the first makes 36 revs, per mill. Re- 
 quired the speed of the last wheel. 
 
 2. What is the speed of the first large wheel if the pinions are the 
 drivers, the 3-in. pinion being the first driver and making 36 revs, per min. ? 
 
 Milling Cutters for Interchangeable Gears. The Pratt & Whit- 
 ney Co. makes a series of cutters for cutting epicycloidal teeth. The 
 number of cutters to cut from a pinion of 12 teeth to a rack is 24 for 
 each pitch coarser than 10. The Brown & Sharpe Mfg. Co. makes a 
 similar series, and also a series for involute teeth, in which eight cutters 
 are made for each pitch, as follows: 
 
 No. 1 2345678 
 
 Will cut from . 135 55 35 26 21 17 14 12 
 
 to Rack 134 54 34 25 20 16 13 
 
 FORMS OF THE TEETH. 
 
 In order that the teeth of wheels and pinions may run together smoothly 
 and with a constant relative velocity, it is necessary that their working 
 faces shall be formed of certain curves called odontoids. The essential 
 property of these curves is that when two teeth are in contact the com- 
 mon normal to the tooth curves at their point of contact must pass through 
 the pitch-point, or point of contact of the two pitch-circles. Two such 
 curves are in common use the cycloid and the involute. 
 
 The Cycloidal Tooth. In Fig. 179 let PL and pi be the pitch- 
 circles of two gear-wheels: GC and gc are two equal generating-cm 
 whose radii should be taken as not greater than one-half of the raaius 
 of the smaller pitch-circle. If the circle gc be rolled to the left on tne 
 larger pitch-circle PL, the point will describe an epicycloid, Qefgri. ir 
 the other srenerating-circle GC be rolled to the right on PL. the point C 
 will describe a bypocycloid a&ccZ. These two curves, which are tangent 
 
FORMS OF THE TEETH. 
 
 1163 
 
 at 0, form the two parts of a tooth curve for a gear whose pitch-circle is 
 PL The upper part Oh is called the face and the lower part Gd is called 
 the'flank. If the same circles be rolled on the other pitch-circle pi, they 
 will describe the curve for a tooth of the gear pi, which will work properly 
 
 The cvcloidal curves may be drawn without actually rolling the gen- 
 erating-circle as follows: On the line PL, from 0, step off and mark equal 
 distances, as 1, 2, 3, 4, etc. From 1, 2, 3, etc., draw radial lines toward 
 the center of PL, and from 6, 7, 8, etc., draw radial lines from .the same 
 center but beyond PL. With the radius of the generating-circle, and 
 w1?h centers successively placed on these radial lines draw arcs of circles 
 tangent to PL at 1, 2, 3, 6, 7. 8, etc. _ With the dividers set jto one ,of the 
 
 and lay them on on me several arcs oe, //, oy, vit,, <*i 
 through the points efgh and abed draw the tooth curves. 
 
 FIG. 179. 
 
 The curves for the mating tooth on the other wheel may be found in 
 like manner by drawing arcs of the generating-circle tangent at equidistant 
 points on the pitch-circle pi. 
 
 The tooth curve of the face Oh is limited by the addendum-line r or r t , 
 and that of the flank OH by the root curve R or R lt R and r represent 
 the root and addendum curves for a large number of small teeth, and Rir 
 the like curves for a small number of large teeth. The form or appearance 
 of the tooth therefore varies according to the number of teeth, while the 
 pitch-circle and the generating-circle may remain the same. 
 
 In the cycloidal system, in order that a set of wheels of different diam- 
 eters but equal pitches shall all correctly work together, it is necessary 
 that the generating-circle used for the teeth of all the wheels shall be 
 the same, and it should have a diameter not greater than half the diam- 
 eter of the pitch-line of the smallest wheel of the set. The customary 
 standard size of the generating-circle of the cycloidal system is one having 
 a diameter equal to the radius of the pitch-circle of a wheel having 12 
 teeth., (gome gear-makers adopt 15 teeth.) This circle gives a radial 
 flank to the teeth of a wheel having 12 teeth. A pinion of 10 or even a 
 smaller number of teeth can be made, but in that case the flanks will be 
 
1164 
 
 GEARING. 
 
 undercut, and the tooth will not be as strong as a tooth with radial 
 flanks. If in any case the describing circle be half the size of the pitch- 
 circle, the flanks will be radial; if it be less, they will spread out toward 
 the root of the tooth, giving a stronger form; but if greater, the flanks 
 will curve in toward each other, whereby the teeth become weaker and 
 difficult to make. 
 
 In some cases cycloidal teeth for a pair of gears are made with the 
 generating-circle of each gear having a radius equal to half the radius 
 of its pitch-circle. In this case each of the gears will have radial flanks. 
 This method makes a smooth working gear, but a disadvantage is that 
 the wheels are not interchangeable with other wheels of the same pitch 
 but different numbers of teeth. 
 
 The rack in the cycloidal system is equivalent to a wheel with an 
 infinite number of teeth. The pitch is equal to the circular pitch of 
 the mating gear. Both faces and flanks are cycloids formed by rolling 
 the generating-circle of the mating gear-wheel on each side of the 
 straight pitch-line of the rack. 
 
 Another method of drawing the cycloidal curves is shown in Fig. 180. 
 It is known as the method of tangent arcs. The generating-circles, as 
 before, are drawn with equal radii, the length of the radius being less 
 than half the radius of pi, the smaller pitch-circle. Equal divisions 1, 2, 
 
 FIG. 180. 
 
 3, 4, etc., are marked off on the pitch-circles and divisions of the same 
 length stepped off on one of the generating-circles, as 0, a, b, c. From the 
 points 1, 2, 3, 4, 5 on the linepO, with radii successively equal to the chord 
 distances a, 06, Oc, Od,Qe, draw the five small arcs F. A line drawn 
 through the outer edges of these small arcs, tangent to them all, will be 
 the hypocycloidal curve for the flank of a tooth below the pitch-line pi. 
 From the points 1, 2, 3, etc., on the line 01, with radii as before, draw the 
 small arcs G. A line tangent to these arcs will be the epicycloid for the 
 face of the same tooth for which the flank curve has already been drawn. 
 In the same way, from centers on the line PO, and OL, with the same 
 radii, the tangent arcs H and K may be drawn,, which will Rive the tooth 
 for the gear whose pitch-circle is PL. 
 
FORMS OF THE TEETH. 
 
 1165 
 
 If the generating-circle had a radius just one-half of the radius of pi, 
 the hypocycloid F would be a straight line, and the flank of the tootb 
 would have been radial. 
 
 The Involute Tooth. In drawing the involute-tooth curve, Fig. 181, 
 the angle of obliquity, or the angle which a common tangent to the teeth, 
 when they are in contact at the pitch-point, makes with a line joining 
 the centers of the wheels, is first arbitrarily determined. It is customary 
 to take it at 15. The pitch-lines pi and PL being drawn in contact at O, 
 the line of obliquity AB is drawn through O normal to a common tangent 
 to the tooth curves, or at the given angle of obliquity to a common tan- 
 gent to the pitch-circles. In the cut the angle is 20. Erom the centers 
 ol the pitch-circles draw circles c and d tangent to the line AB. These 
 circles are called base-lines or base-circles, from which the involutes F 
 and K are drawn. By laying off convenient distances, 0, 1, 2, 3, which 
 should each be less than Vio of the diameter of the base-circle, small arcs 
 can be drawn with successively increasing radii, which will form the 
 involute. The involute extends from the points F and K down to their 
 
 FIG. 181. 
 
 respective base-circles, where a tangent to the involute becomes a radius 
 of the circle, and the remainders of the tooth curves, as G and H, are 
 radial straight lines. 
 
 To draw the teeth of a rack which is to gear with an involute wheel (Fig. 
 182). Let AB be the pitch-line of the rack and AI= IT = the pitch. 
 Through the pitch-point / draw EF at the given angle of obliquity. 
 
 FIG. 182. 
 
 Draw AE and 1'F perpendicular to EF. Through E and F draw lines 
 EGG' and FH parallel to the pitch-line. EGG' will be the addendum- 
 line and HF the flank-line. From / draw IK perpendicular to AB equal 
 to the greatest addendum in the set of wheels of the given pitch and 
 obliquity plus an allowance for clearance equal to 1/8 of the addendum. 
 Through K, parallel to AB, draw the clearance-line. The fronts of the 
 teeth are planes perpendicular to EF, and the backs are planes inclined 
 at the same angle to AB in the contrary direction. The outer half of the 
 working face AE may be slightly curved. Mr. Grant makes it a circular 
 arc drawn from a center on the pitch-line' with a radius = 2.1 Jnches 
 divided by the diametral pitch, or 0.67 in. X circular pitch. 
 
 In the involute system the customary standard form of tooth is one 
 having an angle of obliquity of 15 (Brown and Sharpe use 14 1/2). an 
 
1166 GEARING. 
 
 addendum of about one-third the circular pitch, and a clearance of about 
 
 one-eighth of the addendum. In this system the smallest gear ol a set 
 has 12 teeth, this being the smallest number of teeth that will gear together 
 when made with this angle of obliquity. In gears with less than 30 teeth 
 the points of the teeth must be slightly rounded over to avoid interference 
 (see Grant's Teeth of Gears). All involute teeth of the same pitch and 
 with the same angle of obliquity work smoothly together. The rack to 
 gear with an involute-toothed wheel has straight faces on its teeth, which 
 make an angle with the middle line of the tooth equal to the angle of 
 obliquity, or in the standard form the faces are inclined at an angle ot 
 30 with each other. 
 
 To Draw an Angle of 15 without using a Protractor. From C, on the 
 line A (7, with radius AC, draw an arc AB, and from A, with the same 
 
 radius, cut the arc at B. Bisect 
 the arc BA by drawing small arcs 
 at D from A and B as centers, 
 with the same radius, which must 
 be greater than one-half of AB. 
 Join DC, cutting BA at E. The 
 angle EGA is 30. Bisect the arc 
 AE in like manner, and the angle 
 FCA will be 15. 
 
 A property of involute-toothed 
 wheels is that the distance between 
 the axes of a pair of gears may be 
 altered to a considerable extent 
 without interfering with their ac- 
 tion. The backlash is therefore 
 variable at will, and may be ad- 
 FIG. 183. justed by moving the wheels farther 
 
 from or nearer to each other, and 
 
 may thus be adjusted so as to be no greater than is necessary to prevent 
 jamming of the teeth. 
 
 The relative merits of cycloidal and involute-shaped teeth are a 
 subject of dispute, but there is an increasing tendency to adopt the 
 involute tooth for all purposes. 
 
 Clark (R. T. D., p. 734) says: Involute teeth have the disadvantage of 
 being too much inclined to the radial line, by which an undue pressure is 
 exerted on the bearings. 
 
 Unwin (Elements of Machine Design, 8th ed., p. 265) says: The obliquity 
 of action is ordinarily alleged as a serious objection to involute wheels. 
 Its importance has perhaps been overrated. 
 
 George B. Grant (Am. Mach., Dec. 26, 1885) says: 
 
 1. The work done by the friction of an involute tooth is always less 
 than the same work for any possible epicycloidal tooth. 
 
 2. With respect to work done by friction, a change of the base from a 
 gear of 12 teeth to one of 15 teeth makes an improvement for the epicycloid 
 of less than one-half of one per cent. 
 
 3. For the 12-tooth system the involute has an advantage of 11/5 per 
 cent, and for the 15-tooth system an advantage of 3/ 4 per cent. 
 
 4. That a maximum improvement of about one per cent can be accom- 
 plished by the adoption of any possible non-interchangeable radial flank 
 tooth in preference to the 12-tooth interchangeable system. 
 
 5. That for gears of very few teeth the involute has a decided advan- 
 tage. 
 
 6. That the common opinion among millwrights and the mechanical 
 public in general in favor of the epicycloid is a prejudice that is founded 
 on long-continued custom, and not on an intimate knowledge of the 
 properties of that curve. 
 
 Wilfred Lewis (Proc. Engrs. Club of Phila., vol. x, 1893) says a strong 
 reaction in favor of the involute system is in progress, and he believes 
 that an involute tooth of 22 1/2 obliquity will finally supplant all other 
 forms. 
 
 Approximation by Circular Arcs. Having found the form of the 
 actual" tooth-curve on the drawing-board, circular arcs may be found by 
 trial which will give approximations to the true curves, and these may be 
 used in completing the drawing and the pattern of the gear-wheels. The 
 
FORMS Of THE TEETH. 
 
 1167 
 
 root of the curve is connected to the clearance by a fillet, which should 
 be as large as possible to give increased strength to the tooth, provided 
 it is not large enough to cause interference. 
 
 Molesworth gives a method of construction by.circular arcs as follows : 
 From the radial line at the edge of the tooth on the pitch-line, lay off the 
 line HK at an angle of 75 with the radial line; on this line will be the 
 centers of the root AB and the point EF. The lines struck from these 
 centers are shown hi thick lines. Circles drawn through centers thus 
 found will give the lines in which the remaining centers will be. The 
 radius DA for striking the root AB is the pitch + the thickness of the 
 tooth. The radius CE for striking the point of the tooth EF = the pitch. 
 
 FIG. 184. 
 
 George B. Grant says: It is sometimes attempted to construct the curve 
 by some handy method or empirical rule, but such methods are generally 
 worthless. 
 
 Stub Gear Teeth. The stub gear tooth developed by the Fellows 
 Gear Shaper Co. has been largely adopted for automobile drives. The 
 stub gear tooth has a shorter addendum and dedendum than the 
 ordinary involute tooth. The pressure angle is 20 and the teeth are 
 based on two diametral pitches, one of which is used to obtain the 
 dimensions of the addendum and dedendum, while the other is used 
 for the dimensions of the tooth thickness, the number of teeth and 
 pitch diameter. Stub tooth gears are designated by a fraction as 
 Vs pitch, 10/12 pitch, etc. The numerator designates the pitch deter- 
 mining the thickness of the tooth and number of teeth. The denomi- 
 nator designates the pitch determining depth of the tooth. The 
 clearance is (0.25 -T- diametral pitch). The advantages of this form 
 of tooth compared to the ordinary involute gear tooth are: greater 
 strength; same arc of rolling contact as in 141/2 involute tooth; avoid- 
 ance of extreme sliding contact; more even wearing contact. Dimen- 
 sions of the Fellows system of stub gear teeth are given in the table 
 below: 
 
 Fellows Stub Gear Tooth System (Dimensions in Inches). 
 
 Diametral 
 Pitch. 
 
 Thick- 
 ness of 
 Tooth. 
 
 Adden- 
 dum. 
 
 Working 
 Depth. 
 
 Depth of 
 Space 
 Below 
 Pitch 
 Line. 
 
 Clear- 
 an e. 
 
 Whole 
 Depth of 
 Tooth. 
 
 4/5 
 5/7 
 
 6/8 
 7/9 
 8/10 
 9/11 
 10/12 
 12/ u 
 
 0.3927 
 .3142 
 .2618 
 .2244 
 .1963 
 .1745 
 .1571 
 .1309 
 
 0.2000 
 .1429 
 .1250 
 
 JOOO 
 .0909 
 .0833 
 .0714 
 
 0.4000 
 .2858 
 .2500 
 .2222 
 .2000 
 .1818 
 .1667 
 .1429 
 
 0.2500 
 .1786 
 .1562 
 .1389 
 .1250 
 .1136 
 .1041 
 .0993 
 
 0.0500 
 .0357 
 .0312 
 .0278 
 .0250 
 .0227 
 .0208 
 .0179 
 
 0.4500 
 .3214 
 .2812 
 .2500 
 .2250 
 .2045 
 .1875 
 .1607 
 
 Another system of stub gear teeth is also in use, in which the tooth 
 dimensions are based upon circular pitcL. The addendum is 0.250 X 
 circular pitch, and the dedendum is 0.300 X circular pitch. The former 
 system is the ons in more general use. 
 
1168 
 
 GEARING. 
 
 Stepped Gears. Two gears of the same pitch and diameter mounted 
 side by side on the same shaft will act as a single gear. If one gear is 
 keyed on the shaft so that the teeth of the two wheels are not in line, 
 but the teeth of one wheel slightly in advance of the other, the two gears 
 form a stepped gear. If mated with a similar stepped gear on a parallel 
 shaft the number of teeth in contact will be twice as 
 great as in an ordinary gear, which will increase the 
 strength of the gear and its smoothness of action. 
 
 Twisted Teeth. If a great number of very thin 
 gears were placed together, one slightly in advance of 
 the other, they would still act as a stepped gear. Con- 
 tinuing the subdivision until the thickness of each 
 separate gear is infinitesimal, the faces of the teeth 
 instead of being in steps take the form of a spiral or 
 twisted surface, and we have a twisted gear. The twist 
 may take any shape, and if it is in one direction for half 
 the width of the gear and in the opposite direction for 
 the other half, we have what is known as the herring- 
 bone or double helical tooth. The obliquity of the 
 twisted tooth if twisted in one direction causes an end 
 thrust on the shaft, but if the herring-bone twist is FIG. 185. 
 used, the opposite obliquities neutralize each other. This form of tooth 
 is much used in heavy rolling-mill practice, where great strength and 
 resistance to shocks are necessary. They are frequently made of steel 
 castings (Fig. 185). The angle of the tooth with a line parallel to the 
 axis of the gear is usually 30. 
 
 Spiral or Helical Gears. If a twisted gear has a uniform twist it 
 becomes what is commonly called a spiral gear (properly a helical gear). 
 The line in which the pitch-surface intersects the face of the tooth is part 
 of a helix drawn on the pitch-surface. A spiral wheel may be made with 
 only one helical tooth wrapped around the cylinder several times, in 
 which it becomes a screw or worm. If it has two or three teeth so 
 wrapped, it is a double- or triple-threaded screw or worm. A spiral-gear 
 meshing into a rack is used to drive the table of some forms of planing- 
 machine. For methods of laying out and producing spiral gears see 
 Brown and Sharpe's treatise on Gearing and Halsey's Worm and Spiral 
 Gearing, also Machy., May 1906 and Machifs Reference Series No. 20. 
 
 Worm-gearine. When the axes of two spiral gears are at right 
 angles, and a wheel of one, two, or three threads works with a larger wheel 
 of many threads, it becomes a worm-gear, or endless screw, the smaller 
 wheel or driver being called the worm, and the larger, or driven wheel, 
 the worm-wheel. With this arrangement a high velocity ratio may be 
 obtained with a single pair of wheels. For a one-threaded wheel the veloc- 
 ity ratio is the number of teeth in the worm-wheel. The worm and wheel 
 are commonly so constructed that the worm will drive the wheel, but the 
 wheel wUl not drive the worm. 
 
 To find the diameter of a worm-wheel at the throat, number of teeth and 
 pitch of the worm being given: Add 2 to the number of teeth, multiply 
 
 the sum by 0.3183, and 
 by the pitch of the worm 
 in inches. 
 
 To find the number of 
 teeth, diameter at throat 
 and pitch of worm being 
 given: Divide 3.1416 
 times the diameter by the 
 pitch, and subtract 2 
 from the quotient. 
 
 In Fig. 186 ab is the 
 diam. of the pitch-circle, 
 cd is the diam. at the 
 throat. 
 
 EXAMPLE. Pitch of 
 
 FIG. 186. 
 
 worm 1/4 in., number of teeth 70; required the diam. at the throat. (70 
 + 2) X .3183 X .25 = 5 .73 in. 
 
 For design of worm gearing see Kimball and Barr's Machine Design. 
 For efficiency of worm-gears see page 1171. 
 
FORMS OF THE TEETH. 
 
 1169 
 
 The Hindley Worm. In the Hindley worm-gear the worm, in- 
 stead of being cylindrical in outline, is of an hour-glass shape, the pitch 
 line of the worm being a curved line corresponding to the pitch line of the 
 gear. It is claimed that there is surface contact between the faces of 
 the teeth of the worm and gear, instead of only line contact as in the case 
 of the ordinary worm gear, but this is denied by some writers. For 
 discussion of the Hindiey worm see Am. Mach., April 1, 1897 and 
 Machy., Dec. 1908. The Hindley gear is made by the Albro-Clem 
 Elevator Co., Philadelphia. 
 
 Teeth of Bevel-wheels. (Rankine's Machinery and Millwork.) 
 The teeth of a bevel-wheel have acting surfaces of the conical kind, gen- 
 erated by the motion of a line traversing the apex of the conical pitch- 
 surface, while a point in it is carried round the traces of the teeth upon 
 a spherical surface described about that apex. 
 
 The operations of drawing the traces of the teeth of bevel-wheels exactly, 
 whether by involutes or by rolling curves, are in every respect analogous 
 to those for drawing the traces of the teeth of spur-wheels; except that in 
 the case of bevel-wheels all those operations are to be performed on the 
 surface of a sphere described about the apex, instead of on a plane, sub- 
 stituting poles for centers and great circles for straight lines. 
 
 In consideration of the practical difficulty, especially in the case of 
 large wheels, of obtaining an accurate spherical surface, and of drawing 
 upon it when obtained, the follow- 
 ing approximate method, proposed 
 originally by Tredgold, is generally 
 used: 
 
 Let O, Fig. 187, be the common 
 apex of the pitch-cones, OBI, OB'I, 
 of a pair of bevel-wheels; OC, OC', 
 the axes of those cones; OI their 
 line of contact. Perpendicular to 
 01 draw AIA', cutting the axes in 
 A, A'; make the outer rims of the 
 patterns and of the wheels portions 
 of the cones ABI, A'B'I, of which 
 the narrow zones occupied by the 
 teeth will be sufficiently near for 
 practical purposes to a spherical 
 surface described about O. As the 
 cones ABI, A'B'I cut the pitch- 
 cones at right angles in the outer pitch-circles IB, IB', they may be called 
 the normal cones. To find the traces of the teeth upon the normal cones, 
 draw on a flat surface circular arcs, ID, ID', with the radii AI, A' I; those 
 arcs will be the developments of arcs of the pitch-circles IB, IB' when the 
 conical surfaces ABI, A'B'I are spread out flat. Describe the traces of 
 teeth for the developed arcs as for a pair of spur-wheels, then wrap the 
 developed arcs on the normal cones, so as to make them coincide with 
 the pitch-circles, and trace the teeth on the conical surfaces. 
 
 For formulae and instructions for designing bevel-gears, and for much 
 other valuable information on the subject of gearing, see "Practical 
 Treatise on Gearing," and "Formulas in Gearing," published by Brown 
 & Sharpe Mfg. Co.; and "Teeth of Gears, " by George B. Grant, Lexington, 
 Mass. The student may also consult Rankine's Machinery and Millwork, 
 Reuleaux's Constructor, and Unwin's Elements of Machine Design. See 
 also article on Gearing, by C. W. MacCord in App. Cyc. Mech., vol. ii. 
 
 Annular and Differential Gearing. (S. W. Balch, Am. Mach., 
 Aug. 24, 1893.) In internal gears the sum of the diameters of the describ- 
 ing circles for faces and flanks should not exceed the difference in the 
 pitch diameters of the pinion and its internal gear. The sum may be 
 equal to this difference or it may be less; if it is equal, the faces of the 
 teeth of each wheel will drive the faces as well as the flanks of the teeth of 
 the other wheel. The teeth will therefore make contact with each other 
 at two points at the same time. 
 
 Cycloidal tooth-curves for interchangeable gears are formed with de- 
 scribing circles of about 5/ 8 the pitch diameter of the smallest gear of the 
 series. To admit two such circles between the pitch-circles of the pinion 
 and internal gear the number of teeth in the internal gear should exceed 
 
1170 
 
 GEAEING. 
 
 the number in the pinion by 12 or more, if the teeth are of the customary 
 proportions and curvature used in interchangeable gearing. 
 
 Very often a less difference is desirable, and the teeth may be modified 
 in several ways to make this possible. 
 
 First. The tooth curves resulting from smaller describing circles may 
 be employed. These will give teeth which are more rounding and nar- 
 rower at their tops, and therefore not as desirable as the regular forms. 
 
 Second. The tips of the teeth may be rounded until they clear. This 
 is a cut-and-try method which aims at modifying the teeth to such out- 
 lines as smaller describing circles would give. 
 
 Third. One of the describing circles may be omitted and one only 
 used, which may be equal to the difference between the pitch-circles. 
 This will permit the meshing of gears differing by six teeth. It will usu- 
 ally prove inexpedient to put wheels in inside gears that differ by much 
 less than 12 teeth. 
 
 If a regular diametral pitch and standard tooth forms are determined 
 on, the diameter to which the internal gear-blank is to be bored is calcu- 
 lated by subtracting 2 from the number of teeth, and dividing the re- 
 mainder by the diametral pitch. 
 
 The tooth outlines are the match of a spur-gear of the same number 
 of teeth and diametral pitch, so that the spur-gear will fit the internal 
 gear as a punch fits its die, except that the teeth of each should fail to 
 bottom in the tooth spaces of the other by the customary clearance of one- 
 tenth the thickness of the tooth. 
 
 Internal gearing is particularly valuable when employed in differential 
 action. This is a mechanical movement in which one of the wheels is 
 mounted on a crank so that its center can move in a circle about the center 
 of the other wheel. Means are added which restrain the wheel on the 
 crank from turning over and confine it to the revolution of the crank. 
 
 The ratio of the number of teeth in the revolving wheel compared with 
 the difference between the two will represent the ratio between the revolv- 
 ing wheel and the crank-shaft by which the other is carried. The advan- 
 tage in accomplishing the change of speed with such an arrangement, as 
 compared with ordinary spur-gearing, lies in the almost entire absence of 
 friction and consequent wear of the teeth. 
 
 But for the limitation that the difference between the wheels must not 
 be too small, the possible ratio of speed might be increased* almost indefi- 
 nitely, and one pair of differential gears made to do the service of a whole 
 fcrain of wheels. If the problem is properly worked out with bevel-gears 
 this limitation may be completely set aside, and external and internal 
 bevel-gears, differing by but a single tooth if need be, made to mesh per- 
 fectly with each other. 
 
 EFFICIENCY OF GEARING. 
 
 An extensive series of experiments on the efficiency of gearing, chiefly 
 worm and spiral gearing, is described by Wilfred Lewis in Trans. A. S. 
 M. E., vii, 273. The average results are shown in a diagram, from 
 which the following approximate average figures are taken: 
 
 EFFICIENCY OF SPUR, SPIRAL, AND WORM-GEARING. 
 
 Gearing. 
 
 Pitch. 
 
 Velocity at pitch-line in feet per min. 
 
 3 
 
 10 
 
 40 
 
 100 
 
 200 
 
 Spur pinion 
 
 
 0.90 
 .81 
 .75 
 .67 
 .61 
 .51 
 .43 
 .34 
 
 0.935 
 .87 
 .815 
 .75 
 .70 
 .615 
 .53 
 .43 
 
 0.97 
 .93 
 .89 
 .845 
 .805 
 .74 
 .72 
 .60 
 
 0.98 
 .955 
 .93 
 .90 
 .87 
 .82 
 .765 
 .70 
 
 0.985 
 .965 
 .945 
 .92 
 .90 
 .86 
 .815 
 .765 
 
 
 45 
 30 
 20 
 15 
 '10 
 7 
 5 
 
 
 
 
 Spiral pinion or worm 
 
 The experiments showed the advantage of spur-gearing over all other 
 kinds in both durability and efficiency. The variation from the mean 
 results rarely exceeded 5% in either direction, so long as no cutting 
 occurred, but the variation became much greater and very irregular as 
 soon as cutting began. The loss of power varies with the speed, the 
 
EFFICIENCY OF GEARING. 
 
 1171 
 
 pressure, the temperature, and the condition of the surfaces. The high 
 friction of worm- and spiral-gearing is largely due to end thrust on the 
 collars of the shaft, and may be considerably reduced by roller-bearings 
 for the collars. 
 
 When two worms with opposite spirals run in two spiral worm-gears 
 that also work with each other, and the pressure on one gear is opposite 
 that on the other, there is no thrust on the shaft. Even with light loads 
 a worm will begin to heat and cut if run at too high a speed, the limit for 
 safe working being a velocity of the rubbing surfaces of 200 to 300 ft. 
 per minute, the former being preferable where the gearing has to work 
 continuously. The wheel teeth will keep cool, as they form part of a 
 casting having a large radiating surface; but the worm itself is so small 
 that its heat is dissipated slowly. Whenever the heat generated increases 
 faster than it can be conducted and radiated away, the cutting of the 
 worm may be expected to begin. A low efficiency for a worm-gear means 
 more than the loss of power, since the power which is lost reappears as 
 heat and may cause the rapid destruction of the worm. 
 
 Unwin (Elements of Machine Design, p. 294) says: The efficiency is 
 greater the less the radius of the worm. Generally the radius of the 
 worm = 1 .5 to 3 times the pitch of the thread of the worm or the circular 
 pitch of the worm-wheel. For a one-threaded worm the efficiency is 
 only 2/5 to 1/4: for. a two-threaded worm, 4/ 7 10.2/5; for a three-threaded 
 worm, 2/3 to 1/2 . As so much work is wasted hi friction it is natural that 
 the wear is excessive. The table below gives the calculated efficiencies 
 of worm-wheels of 1,2,3, and 4 threads and ratios of radius of worm to 
 pitch of teeth of from 1 to 6, with a coefficient of friction of 0.15. 
 
 No. of 
 Threads. 
 
 Radius of Worm Pitch. 
 
 1 
 
 H/4 
 
 H/2 
 
 13/4 
 
 2 
 
 21/2 
 
 3 
 
 4 
 
 6 
 
 2 
 3 
 4 
 
 0.50 
 .67 
 .75 
 .80 
 
 0.44 
 .62 
 .70 
 .76 
 
 0.40 
 .57 
 .67 
 .73 
 
 0.36 
 .53 
 .63 
 .70 
 
 0.33 
 .50 
 .60 
 .67 
 
 0.28 
 .44 
 .55 
 .62 
 
 0.25 
 .40 
 .50 
 .57 
 
 0.20 
 .33 
 .43 
 .50 
 
 0.14 
 .25 
 .33 
 .40 
 
 Efficiency of Worm Gearing. Worm gearing as a means of trans- 
 mitting power has generally been looked upon with suspicion, its efficiency 
 being" considered necessarily low and its life short. When properly pro- 
 portioned, however, it is both durable and reasonably efficient. Mr. F. 
 A. Halsey discusses the subject in Am. Machinist, Jan. 13 and 20, 1898. 
 He quotes two formulas for the efficiency of worm gearing: 
 
 In which E = efficiency; a = angle of thread, being angle between thread 
 and a line perpendicular to the axis of the worm:/ = coefficient of friction. 
 
 Eq. (1) applies to the worm thread only, while (2) applies to the worm 
 and step combined, on the assumption that the mean friction radius of the 
 two is equal. "Eq. (1) gives a maximum for E when tan a = VI + /a / 
 . . . (3) and eq. (2) a maximum when tan a: = V2+4/ 2 - 2f .... (4) 
 Using 0.05 for/gives a in (3) = 43 34' and in (4) = 52 49'. 
 
 On plotting equations (1) and (2) the curves show the striking influence 
 of the pitch-angle upon the efficiency, and since the lost work is expended 
 in friction and wear, it is plain why worms of low angle should be short- 
 lived and those of high angle long-lived. The following table is taken 
 from Mr. Halsey 's plotted curves: 
 RELATION OF THREAD-ANGLE, SPEED AND EFFICIENCY OF WORM-GEARS. 
 
 Velocity of 
 Pitch-line, 
 Feet per 
 Minute. 
 
 Angle of Thread. 
 
 5 
 
 -10 
 
 20 
 
 30 
 
 40 
 
 45 
 
 Efficiency. 
 
 3 
 
 10 
 20 
 40 
 100 
 200 
 
 35 
 40 
 47 
 52 
 60 
 70 
 76 
 
 52 
 56 
 62 
 67 
 74 
 82 
 85 
 
 66 
 69 
 74 
 78 
 83 
 88 
 91 
 
 73 
 
 76 
 79 
 83 
 87 
 91 
 92 
 
 76 
 79 
 82 
 83 
 88 
 91 
 92 
 
 77 
 80 
 82 
 86 
 88 
 91 
 92 
 
1172 
 
 GEARING. 
 
 The experiments of Mr. Wilfred Lewis on worms show a very satisfac- 
 tory correspondence with the theory. Mr. Halsey gives a collection of 
 data comprising 16 worms doing heavy duty and having pitch-angles 
 ranging between 4 30' and 45, which show that every worm having an 
 angle above 12 30' was successful in regard to durability, and every worm 
 below 9 was unsuccessful, the overlapping region being occupied by 
 worms some of which were successful and some unsuccessful. In several 
 cases worms of one pitch-angle had been replaced by worms of a different 
 angle, an increase in the angle leading in every case to better results and a 
 decrease to poorer results. He concludes with the following table from 
 experiments by Mr. James Christie, of the Pencoyd Iron Works, and gives 
 data connecting the load upon the teeth with the pitch-line velocity of 
 the worm. 
 
 LIMITING SPEEDS AND PRESSURES OF WORM GEARING. 
 
 
 
 Double- 
 
 Double- 
 
 
 Single-thread 
 
 thread 
 
 thread 
 
 
 Worm \" Pitch, 
 
 Worm 2'- 
 
 Worm 21/o' 
 
 
 27/8 Pitch Diam. 
 
 Pitch. 27/8 
 
 Pitch, 41/2 
 
 
 
 Pitch Diam. 
 
 Pitch Diam. 
 
 Revolutions per minute 
 Velocity at pitch-line, feet per 
 minute 
 
 128 
 96 
 
 201 
 150 
 
 272 
 705 
 
 425 
 37,0 
 
 128 
 96 
 
 201 
 150 
 
 272 
 7.05 
 
 201 
 735 
 
 272 
 319 
 
 425 
 498 
 
 Limiting nressure. oounds. . . 
 
 1700 
 
 1300 
 
 1100 
 
 700 
 
 1100 
 
 1100 
 
 1100 
 
 1100 
 
 700 
 
 400 
 
 Efficiency of Automobile Gears. (G. E. Quick, Horseless Age, Feb. 12, 
 1908.) A set of slide gears was tested by an electric-driven absorption ' 
 dynamometer. The following approximate results are taken from a | 
 series of plotted curves: 
 
 Horse-power input 
 
 
 2 
 
 4 
 
 6 
 
 8 | 10 
 
 14 
 
 18 
 
 
 r.p.m. 
 
 Efficiency, per cent. 
 
 Direct driven, third speed.. . . 
 
 800 
 
 89 
 
 95 
 
 97 
 
 97,5 
 
 97 5 
 
 97 5 
 
 96 
 
 Direct driven, third speed.. . . 
 
 1,500 
 
 80 
 
 89 
 
 93 
 
 95 
 
 96 5 
 
 97 
 
 97 
 
 Second speed, ratio 1 .76 to 1 
 
 800 
 
 87 
 
 97 5 
 
 94 
 
 95 
 
 94 
 
 93 
 
 
 Second speed, ratio 1.76 to 1 
 
 1,500 
 
 79 
 
 88 
 
 9? 5 
 
 94 
 
 95 
 
 95 
 
 94 
 
 First speed, ratio 3.36 to 1 .. . 
 
 800 
 
 75 
 
 87,5 
 
 93 
 
 94 
 
 94 
 
 93 5 
 
 97 * 
 
 First speed, ratio 3.36 to 1... . 
 
 1,500 
 
 70 
 
 84 
 
 89 
 
 97 
 
 93 
 
 92 
 
 
 Reverse speed, ratio 4.32 to 1 . 
 
 800 
 
 75 
 
 84 
 
 87 
 
 87 
 
 86 
 
 87 5 
 
 
 Reverse speed, ratio 4.32 to 1... 
 
 1,500 
 
 
 70 
 
 79 
 
 83 
 
 86 
 
 87 
 
 85 
 
 Worm-gear axle, ratio 6.83 to 1.. 
 Worm-gear axle, ratio 6.83 to 1 .. 
 
 400 
 800 
 
 85 
 
 87 
 87 
 
 86.5 
 88 5 
 
 85.5 
 89 
 
 84 
 89 
 
 80 
 
 88 
 
 75 
 
 87 
 
 Worm-gear axle, ratio 6.83 to 1.. 
 
 1,500 
 
 80 
 
 85 
 
 87.5 
 
 88.5 
 
 89 
 
 89 
 
 89 
 
 Two bevel- wheel axles were tested, one a floating type, ratio 15 to 32. 
 141/2 involute; the other a solid wheel and axle type, ratio 13 to 54, 20 
 involute. Both gave efficiencies of 95 to 96 % at 800 to 1500 r.p.m., 
 and 10 to 26 H.P., with lower efficiencies at lower power and at lower 
 speed. The friction losses include those of the journals and thrust ball 
 bearings. 
 
 The worm was 6-threaded, lead, 4.69 in.; pitch diam., 2.08 in.; the 
 gear had 41 teeth; pitch diam., 10.2 in. The worm was of hardened 
 steel and the gear of phosphor-bronze. A test of a steel gear and steel 
 worm gave somewhat lower efficiencies. In both tests the heating was 
 excessive both in the gears and in the thrust bearings, the balls in which 
 were7/ le in. diam. 
 
 STRENGTH OF GEAR-TEETH. 
 
 The strength of gear-teeth and the horse-power that may be transmitted 
 by them depend upon so many variable and uncertain factors that it is 
 not surprising that the formulas and rules given by different writers 
 show a wide variation. In 1879 John H. Cooper (Jour. Frank. Inst., 
 July, 1879) found that there were then in existence about 48 well-estab- j 
 lished rules for horse-power and working strength, differing from each 
 other in extreme cases about 500%. In 1886 Prof. Wm. Harkness 
 (Proc. A. A. A. S. t 1886), from an examination of the bibliography of the ' 
 subject, beginning in 1796, found that according to tne constants and 
 
STRENGTH OF GEAR-TEETH. 1173 
 
 'formulae used by various authors there were differences of 15 to 1 in the 
 
 power which could be transmitted by a given pair of geared wheels. 
 The various elements which enter into the constitution of a formula to 
 represent the working strength of a toothed wheel are the following: 
 1. The strength of the metal, usually cast iron, which is an extremely 
 variable quantity. 2. The shape of the tooth, and especially the relation 
 of its thickness at the root or point of least strength to the pitch and to 
 the length. 3. The point at which the load is taken to be applied, 
 assumed by some authors to be at the pitch-line, by others at the extreme 
 end, along the whole face, and by still others at a single outer corner. 
 4. The consideration of whether the total load is at any time received 
 by a single tooth or whether it is divided between two teeth. 5. The 
 influence of velocity in causing a tendency to break the teeth by shock. 
 6. The factor of safety assumed to cover all the uncertainties of the 
 other elements of the problem. 
 
 Prof. Harkness, as a result of his investigation, found that all the 
 formulae on the subject might be expressed in one of three forms, viz.; 
 Horse-power = CVpf, or CFp 2 , or CVp*f; 
 
 in which C is a coefficient, V = velocity of pitch-line in feet per second, 
 p = pitch in inches, and / = face of tooth in inches. 
 
 *'rom an examination of precedents he proposed the following formula 
 for cast-iron wheels: 
 
 H.p. = - 910 Vpf 
 
 0.65 V 
 
 He found that the teeth of chronometer and watch movements were 
 subject to stresses four times as great as those which any engineer would 
 dare to use in like proportion upon cast-iron wheels of large size. 
 
 It appears that all of the earlier rules for the strength of teeth neglected 
 the consideration of the variations in their form; the breaking strength, aa 
 said by Mr. Cooper, being based upon the thickness of the teeth at the 
 pitch-line or circle, as if the thickness at the root of the tooth were the 
 same in all cases as it is at the pitch-line. 
 
 Wilfred Lewis (Proc. Eng'rs Club, Phila., Jan., 1893; Am. Mach., 
 June 22, 1893) seems to have been the first to use the form of the tooth 
 in the construction of a working formula and table. He assumes that 
 in well-constructed machinery the load can be more properly taken as 
 well distributed across the tooth than as concentrated in one corner, but 
 that it cannot be safely taken as concentrated at a maximum distance 
 from the root less than the extreme end of the tooth. He assumes that 
 the whole load is taken upon one tooth, and considers the tooth as a 
 beam loaded at one end, and from a series of drawings of teeth of the 
 involute, cycloidal, and radial flank systems, determines the point of 
 weakest cross-section of each, and the ratio of the thickness at that section 
 to the pitch. He thereby obtains the general formula, 
 
 W = spfy; 
 
 In which W is the load transmitted by the teeth, in pounds; s is the safe 
 working stress of the material, taken at 8000 Ibs. for cast iron, when the 
 working speed is 100 ft. or less per minute; p = pitch; / = face, in 
 inches; y = a factor depending on the form of the tooth, whose value for 
 different cases is given in the table on page 1174. 
 
 The values of s in the above table are given by Mr. Lewis tentatively, 
 in the absence of sufficient data upon which to base more definite values, 
 but they have been found to give satisfactory results in practice. 
 
 EXAMPLE. Required to find the working strength of a 12-toothed pin- 
 ion, 1-inch pitch, 2 H-hich face, driving a wheel of 60 teeth at 100 feet or 
 less per minute, and let the teeth be of the 20-degree involute form. In 
 the formula W = spfy we have for a cast-iron pinion s = 8000, pf =2.5, 
 and y = 0.078; and multiplying these values together, we have W = 
 1560 pounds. For the wheel we have y = 0.134 and W = 2680 pounds. 
 
 The cast-iron pinion is, therefore, the measure of strength; but if a 
 steel pinion be substituted we have s = 20,000 and W = 3900 pounds, in 
 which combination the wheel is the weaker, and it therefore becomes the 
 measure of strength. 
 
 For bevel- wheels Mr. Lewis gives the following, referring to Fig. 188: 
 
1174 
 
 GEAKING. 
 
 D = large diameter of bevel; d = small diameter of bevel; p = pitch 
 at large diameter; n = actual number of teeth; / = face of bevel; 
 N formative, number of teeth = n X secant a, or 
 \ the number corresponding to radius R; y = factor de- 
 
 r v T^fj pending upon shape of teeth and formative number N; 
 
 x ^^ /^ \\W = working load on teeth, assumed to be applied at 
 ' the large end of the bevel gear on the pitch line. 
 
 W 
 
 spfy -- ; or . more simply, W 
 
 spfy ; 
 
 FIG. 188. 
 
 which gives almost identical results when d is not less 
 than 2/3 D, as is the case in good practice. 
 
 In Am. Mach., June 22, 1893, Mr. Lewis gives the 
 following formulae for the working strength of the three 
 systems of gearing, which agree very closely with those 
 obtained by use of the table: 
 
 For involute, 20 obliquity, W = spf ( 0. 154 - ^? ) ; 
 
 For involute 15, and cycloidal, W = spf (o.!24 - ^^) : 
 
 For radial flank system, W = spf (o.075 - ^p): 
 
 in which the factor within the parenthesis corresponds to y in the general 
 formula. For the horse-power transmitted, Mr. Lewis's general formula 
 
 W = spfy = 33 ' OOOH - P -, may take the form H.P. = ^rrz> wh ich 
 
 V oo,UUU 
 
 -> = velocity in feet per minute; or since v = dir X r.p.m. * 12 
 :) .2618 d X r.p.m., in which d = diameter in inches, 
 
 It must be borne in mind, however, that in the case of machines which 
 consume power intermittently, such as punching and shearing machines, 
 the gearing should be designed with reference to the maximum load W, 
 which can be brought upon the teeth at any time, and not upon the 
 average horse-power transmitted. 
 
 VALUES OF y IN LEWIS'S FORMULA. 
 
 
 Factor for Strength y. 
 
 
 Factor for Strength, y. 
 
 No. of 
 Teeth. 
 
 Involute 
 20 Ob- 
 liquity. 
 
 Involute 
 15 and 
 Cycloidal 
 
 Radial 
 Flanks. 
 
 No. of 
 Teeth. 
 
 Involute 
 20 Ob- 
 liquity. 
 
 Involute 
 15 and 
 Cycloidal 
 
 Radial 
 Flanks. 
 
 12 
 
 0.078 
 
 0.067 
 
 0.052 
 
 27 
 
 0.111 
 
 0.100 
 
 0.064 
 
 13 
 
 .083 
 
 .070 
 
 .053 
 
 30 
 
 .114 
 
 .102 
 
 .065 
 
 14 
 
 .088 
 
 .072 
 
 .054 
 
 34 
 
 .118 
 
 .104 
 
 .066 
 
 15 
 
 .092 
 
 .075 
 
 .055 
 
 38 
 
 .122 
 
 .107 
 
 .067 
 
 16 
 
 .094 
 
 .077 
 
 .056 
 
 43 
 
 .126 
 
 .110 
 
 .068 
 
 17 
 
 .096 
 
 .080 
 
 .057 
 
 50 
 
 .130 
 
 .112 
 
 .069 
 
 18 
 
 .098 
 
 .083 
 
 .058 
 
 60 
 
 .134 
 
 .114 
 
 .070 
 
 19 
 
 .100 
 
 .087 
 
 .059 
 
 75 
 
 .138 
 
 .116 
 
 .071 
 
 20 
 
 .102 
 
 .090 
 
 .060 
 
 100 
 
 .142 
 
 .118 
 
 .072 
 
 21 
 
 .104 
 
 .092 
 
 .061 
 
 150 
 
 .146 
 
 .120 
 
 .073 
 
 23 
 
 .106 
 
 .094 
 
 .062 
 
 300 
 
 .150 
 
 .122 
 
 .074 
 
 25 
 
 .108 
 
 .097 
 
 .063 
 
 Rack. 
 
 .154 
 
 .124 
 
 .075 
 
 SAFE WORKING STRESS, s, FOR DIFFERENT SPEEDS. 
 
 Speed of Teeth in 
 Ft. per Minute. 
 
 ,<Ko r | 20fl 
 
 300 
 
 600 
 
 900 
 
 1200 
 
 1800 
 
 2400 
 
 Cast iron . . 
 
 8000 6000 
 
 4800 
 
 4000 
 
 3000 
 
 2400 
 
 2000 
 
 1700 
 
 Steel 
 
 20000 115000 
 
 12000 
 
 10000 
 
 7500 
 
 6000 
 
 5000 
 
 4300 
 
 Comparison of the Harkness and Lewis Formulae. Take an 
 average case in which the safe working strength of the material, s = 6000, 
 
STRENGTH OF GEAR-TEETH. 
 
 1175 
 
 D *= 200 ft. per min., and y 0.100, the value in Mr. Lewis's table for an 
 involute tooth of 15 obliquity, or a cycloidal tooth, the number of teetb 
 in the wheel being 27. 
 
 TT -P 
 
 H ' R 
 
 " 33,000 
 if V is taken in feet per second. 
 
 Prof. Harkness gives H.P. = 
 
 6000 p/i?X 0.100 _ pfv __ - nQ1 fv 
 33,000 - 55 - 1-091 P/V. 
 
 0.910 Vpf 
 
 If the V in the denominator 
 
 fl + 0.65 V 
 
 be taken at 200 % 60 = 31/3 ft. per sec., H.P. = 0.571 p/V, or about 
 52% of the result given by Mr. Lewis's formula. This is probably a? 
 close an agreement as can be expected, since Prof. Harkness derived his 
 formula from an investigation of ancient precedents and rule-of-thumb 
 practice, largely with common cast gears, while Mr. Lewis's formula was 
 derived from considerations of modern practice witn machine-molded 
 and cut gears. 
 
 Mr. Lewis takes into consideration the reduction in working strength 
 of a tooth due to increase in velocity by the figures in his table of the 
 values of the safe working stress s for different speeds. Prof. Harkness 
 gives expression to the same reduction by means of the denominator of 
 his formula, Vi 4- 0.65 V. The decrease in strength as computed by 
 this formula is somewhat less than that given in Mr. Lewis's table, and as 
 the figures given in the table are not based on accurate data, a mean 
 between the values given by the formula and the table is probably as 
 near to the true value as may be obtained from our present knowledge. 
 The following table gives the values for different speeds according to Mr. 
 Lewis's table and Prof. Harkness's formula, taking for a basis a working 
 stress a, for cast-iron 8000, and for steel 20,000 Ibs. at speeds of 100 ft. 
 per minute and less: 
 
 V = speed of teeth, ft. per min. . 
 V = speed of teeth, ft. per sec . . 
 
 100 
 
 1 2/3 
 
 200 1 300 
 
 31/sl 5 
 
 600 
 10 
 
 900 
 15 
 
 1200 
 20 
 
 1800 
 30 
 
 2400 
 40 
 
 bafe stress s, cast iron, Lewis . . 
 Relative do., s * 8000 
 
 8000 
 
 .-6930 
 1 
 
 8000 
 8000 
 20000 
 20000 
 
 6000 
 0.75 
 
 .5621 
 0.811 
 6488 
 6200 
 15500 
 15000 
 
 4800 
 0.6 
 .4850 
 0.700 
 5600 
 5200 
 13000 
 12000 
 
 4000 
 0.5 
 
 .3650 
 0.526 
 4208 
 4100 
 10300 
 10000 
 
 3000 
 0.375 
 .3050 
 0.439 
 3512 
 3300 
 8100 
 7500 
 
 2400 
 0.3 
 .2672 
 0.385 
 3080 
 2700 
 6800 
 6000 
 
 2000 
 0.25 
 .2208 
 0.318 
 2544 
 2300 
 5700 
 5000 
 
 1700 
 0.2125 
 .1924 
 0.277 
 2216 
 2000 
 4900 
 4300 
 
 1 j. \/l + 65 V .... 
 
 Relative val c * 693 
 
 , - 8000 x (c -nO. 693) 
 Mean of s and s lt cast-iron = s 2 . 
 Mean of s and si, for steel = 83.. 
 Safe stress for steel, Lewis 
 
 In Am. Mach., Jan. 30, 1902, Mr. Lewis says that 8,000 Ibs. was given 
 as safe for cast-iron teeth, either cut or cast, and that 20,000 Ibs. was 
 intended for any steel suitable f9r gearing whether cast or forged. 
 These were the unit stresses for static loads. 
 
 The iron should be of good quality capable of sustaining about a ton 
 on a test bar 1 in. square between supports 12 in. apart, and the steel 
 should be solid and of good quality. The value given for steel was in- 
 tended to include the lower grades, but when the quality is known to be 
 high, correspondingly higher values may be assigned. 
 
 Comparing the two formulae for the case of s = 8000, corresponding to 
 a speed of 100 ft. per min., we have 
 
 Harkness: H.P. = 
 Lewis: H.P. 
 
 1 
 
 spfyv 
 ~~ 33,000 
 
 o.65 V X .9107p/= 1 .053 pf, 
 spfy V 8000 X 1 2/3 pfy 
 550 550 
 
 24.24p/2/, 
 
 in which y varies according to the shape and number of the teeth. 
 For radial-flank gear with 12 teeth y = 0.052; 24.24 pfy = 1.260p/; 
 
 For 20inv., 19 teeth, or 15inv., 27 teeth y = 0.100; 24.24 pfy = 2.424p/; 
 For 20 involute, 300 teeth y = 0.150; 24.24 pfy = 3.636p/. 
 
 Thus the weakest-shaped tooth, according to Mr. Lewis, will transmit 
 20 per cent more horse-power than is given by Prof. Harkness's formula, 
 in which the shape of the tooth is not considered, and the average-shaped 
 
1176 GEABtNG. 
 
 tooth, according to Mr. Lewis, will transmit more than double the 
 
 horse-power given by Prof. Harkness's formula. 
 
 i Comparison of Other Formulae. Mr, Cooper, in summing up his 
 
 examination, selected an old English rule, which Mr. Lewis considers as 
 a passably correct expression of good general averages, viz.: X = 2000 rf, 
 X = breaking load of tooth in pounds, p = pitch, / = face. If a factor 
 o f safety of 10 be taken, this would give for safe working load W =200 rf- 
 George B. Grant, in his Teeth of Gears, page 33, takes the breaking 
 load at 3500 pf, and, with a factor of safety of 10, gives W = 350 pf. 
 
 Nystrom's Pocket-Book, 20th ed., 1891, says: "The strength and dura- 
 bility of cast-iron teeth require that they shall transmit a force of 80 Ibs. 
 per inch of pitch and per inch breadth of face. " This is equivalent to 
 W = 80 pf, or only 40% of that given by the English rule. 
 
 F. A. Halsey (Clark's Pocket-Book) gives a table calculated from the 
 formula H.P. = pfd X r.p.m. -i- 850. 
 
 Jones & Laughlins give H.P. = pfd X r.p.m. -*- 550. 
 These formulae transformed give W = 128 p/and W 218 pf, respec- 
 tively. 
 
 Unwin, on the assumption that_the load acts on the corners of the 
 teeth, derives a formula p = K ^/W, in which K is a coefficient derived 
 from existing wheels, its values being: for slowly moving gearing not sub- 
 ject to much vibration or shock K = 0.04; in ordinary mill-gearing, 
 running at greater speed and subject to considerable vibration, K = .05; 
 and in wheels subjected to excessive vibration and shock, and in mortise 
 gearing, K = 0.06. Reduced to the form W = Cpf, assuming that/ = 
 2 p, these values of K give W = 262 pf, 200 pf. and 139 pf, respectively. 
 Unwin also give the following, based on the assumption_that the pres- 
 sure is distributed along the edge of the tooth: p = Ki ^p/f^W, where 
 KI = about .0707 for iron wheels and .0848 for mortise wheels when 
 the breadth of face is not less than twice the pitch. For the case of /= 
 2 p and the given values of KI this reduces to W 200 p/and W = 139 pf, 
 respectively. 
 
 Box, in his Treatise on Mill Gearing, gives H.P. = 12 p z f^dn -s- 1000, 
 in which n = number of revolutions per minute. This formula differs 
 /rom the more modern formulae in making the H.P. vary as p 2 /, instead 
 of as pf, and. in this respect it is no doubt incorrect. 
 
 Making the H.P. vary as ^dn or as V-y, instead of directly as v, makes 
 the velocity a factor of the working strength as in the Harkness and 
 Lewis formulas, the relative strength varying as 1/^v, which for different 
 velocities is as follows: 
 
 Speed of teeth in H. per J 10Q 200 300 600 900 120Q 1800 2 400 
 Relative strength = 1 0.707 0.574 0.408 0.333 0.289 0.236 0.20 
 
 showing a somewhat more rapid reduction than is given by Mr. Lewis. 
 
 For the purpose of comparing different formulas they may in general 
 be reduced to either of the following forms: 
 
 H.P. = Cpfv, H.P. = dpfdX r.p.m., W = cpf, 
 
 in which p *= pitch, / = face, d = diameter, all in inches; v = velocity 
 in feet per minute, r.p.m. revolutions per minute, and C, Ci and c coeffi- 
 cients. The formulae for transformation are as follows: 
 
 H.P. = Wv + 33,000 = WX dX r.p.m. -5- 126,050; 
 33,000 H.P. 126,050 H.P. . H.P. H.P. _ W 
 
 T- = dX r.p.m. =33 ' OOOC7p/ ' p/= -ar == C 1 dXr.p.mrT 
 
 Ci 0.2618 C; c = 33,000 C\ C = 3.82 Ci, = 00 ^; c = 126,050 C t . 
 
 oo,UUU 
 
 In the Lewis formula C varies with the form of the tooth and with the 
 speed, and is equal to sy * 33,000, in which y and s are the values taken 
 from the table, and c = sv. 
 
 In the Harkness formula C varies with the speed and is equal to 
 
STRENGTH OF GEAR-TEETH. 117? 
 
 Ql f) 
 
 -(V being in feet per second), = 0.01517 
 
 .vi + 0.65 V 
 
 In the Box formula C varies with the pitch and also with the velocity; 
 
 and equals 12P ^ B r ' P ' m ' - .02345 JL , c = 33,000 C = 774 JL. , 
 
 Vv V v 
 
 For v = 100 ft. per min. C = 77.4 p: for v = 600 ft. per min., c = 31.6 p. 
 
 In the other formulae considered C, C\, and c are constants. Reducing 
 the several formulae to the form W = cpf, we have the following: 
 
 COMPARK3ION OF DIFFERENT FORMULAE FOR STRENGTH OF GEAR-TEETH. 
 
 Safe working pressure per inch pitch and per inch of face, or value ol 
 c in formula W = cpf: 
 
 v = ft. per min. 100 600 
 
 Lewis: Weak form of tooth, radial flank, 12 teeth c = 416 208 
 
 Medium tooth, inv. 15, or cycloid, 27 teeth, c = 800 400 
 
 Strong form of tooth, inv. 20, 300 teeth, .c = 1200 600 
 
 Harkness: Average tooth .c = 347 184 
 
 Box: Tooth of 1 inch pitch c = 77.4 31.6 
 
 Box: Tooth of 3 inches pitch c = 232 95 
 
 The Gleason Works gives for ft. per min. 500 1000 1500 2000 2500 
 
 working stress in pounds = p.f. X 480 400 340 290 240 
 
 These are for cut gears, 18 teeth or more, rigidly supported, for average 
 
 steady loads. Hammering loads, as in rolling mills and saw mills, require 
 
 heavier gears. 
 
 C. W. Hunt, Trans. A.S.M.E., 1908, gives a table of working loads of 
 cut cast gears with a strong short form of tooth, which is practically 
 equivalent to W= 700 pf. 
 
 Various, in which c is independent of form and speed: Old English 
 rule, c = 200; Grant, c 350; Nystrom, c = 80; Halsey, c = 128; Jones 
 & Laughlins, c = 218; Unwin, c = 262, 200, or 139, according to speed, 
 shock, and vibration. 
 
 The value given by Nystrom and those given by Box for teeth of small 
 pitch are so much smaller than those given by the other authorities that 
 they may be rejected as having an entirely unnecessary surplus of strength. 
 The values given by Mr. Lewis seem to rest on the most logical basis, the 
 form of the teeth as well as the velocity being considered; and since they 
 are said to have proven satisfactory in an extended machine practice, 
 they may be considered, reliable for gears that are so well made that 
 the pressure bears along the face of the teeth instead of upon the corners. 
 For rough ordinary work the old English rule W = 200 pf is probably 
 as good as any, except that the figure 200 may be too high for weak forms 
 of tooth and for high speeds. 
 
 The formula W= 200 pfis equivalent to H.P. = p/d X r.p.m. -*-630 pfv 
 -s-165 or, H.P. = 0.0015873 pfd X r.p.m. = .006063 pfv. 
 
 Raw-hide Pinions. Pinions of raw-hide are in common use for 
 gearing shafts driven by electric motors to other shafts which carry 
 machine-cut cast-iron or steel gears, in order to reduce vibration, noise 
 and wear. A formula for the maximum horse-power to be transmitted 
 by such gears, given by the New Process Raw-Hide Co., Syracuse, N. Y., 
 is H.P. = pitch diam. X circ. pitch X face X r.p.m. -*- 850, or pfd X 
 r.p.m. -^ 850. This is about 3/ 4 of the H.P. for cast-iron teeth by the old 
 English rule. The formula is to be used only when the circular pitch 
 does not exceed 1.65 ins. 
 
 Composite gears also are made, consisting of alternate sheets of raw- 
 hide or fibre and steel or bronze, so that a high degree of strength is 
 combined with the smooth-running quality of the fibre. 
 
 Maximum Speed of Gearing. A. Towler, Eng'g, April 19, 1880, 
 p. 388, gives the maximum speeds at which it was possible under favor- 
 able conditions to run toothed gearing safely as follows, in ft. per min.: 
 Ordinary cast-iron wheels, 1800; Helical, 2400; Mortise, 2400; Ordinary 
 cast-steel wheels, 2600; Helical, 3000: special cast-iron machine-cut 
 wheels, 3000. 
 
 Prof. Coleman Sellers (Stevens Indicator, April, 1892) recommends that 
 gearing be not run over 1200 ft. per minute, to avoid great noise, Tke 
 
1178 GEARING. 
 
 Walker Company; Cleveland, Ohio, say that 2200 ft. per min. for iron 
 
 gears and 3000 ft. for wood and iron (mortise gears) are excessive, and 
 should be avoided -if possible. The Corliss engine at the Philadelphia 
 Exhibition (1876) had a fly-wheel 30 ft. in diameter running 35 r.p.m. 
 geared into a pinion 12 ft. diam. The speed of the pitch-line was 3300 ft. 
 
 A Heavy Machine-cut Spur-gear was made in 1891 by the Walker 
 
 Company, Cleveland, Ohio, for a diamond mine in South Africa, with 
 dimensions as follows: Number of teeth, 192; pitch diameter, 30 ft. 
 6.66 ins.; face, 30 ins.; pitch, 6 ins.; bore, 27 ins.; diameter of hub, ft. 
 2 Ins.: weight of hub, 15 tons; and total weight of gear, 663/ 4 tons. The 
 run was made in 12 segments, the joints of the segments being fastened 
 with two bolts each. The spokes were bolted to the middle of the seg- 
 ments and to the hub with four bolts in each end. 
 
 Frictional Gearing. In frictional gearing the wheels are toothless, 
 and one wheel drives the other by means of the friction between the two 
 surfaces which are pressed together. They may be -used where the power 
 to be transmitted is not very great; when the speed is so high that toothed 
 wheels would be noisy; when the shafts require to be frequently put into 
 and out of gear or to have their relative direction of motion reversed; 
 or when it is desired to change the velocity-ratio while the machinery 
 is in motion, as in the case of disk friction-wheels for changing the feed 
 In machine tools. 
 
 Let P = the normal pressure in pounds at the line of contact by which 
 two wheels are pressed together, T = tangential resistance of the driven 
 wheel at the line of contact, / = the coefficient of friction, V the veloc- 
 ity of the pitch-surface in feet per second, and H.P. = horse-power; then 
 T may be equal to or less than/P; H.P. = TV * 550. The value of/ 
 for metal on metal may be taken at 0.15 to 0.20; for wood on metal, 
 0.25 to 0.30; and for wood on compressed paper, 0.20. The tangential 
 driving force T may be as high as 80 Ibs. per inch width of face of the 
 driving surface, but this is accompanied by great pressure and friction on 
 the journal-bearings. 
 
 In frictional grooved gearing circumferential wedge-shaped grooves are 
 cut in the faces of two wheels in contact. If P = the force pressing the 
 wheels together, and N = the normal pressure on all the grooves, P = N 
 (sin a + /cos a), in which 2 a = the inclination of the sides of the grooves, 
 and the maximum tangential available force T = fN. The inclination 
 of the sides of the grooves to a plane at right angles to the axis is usually 
 
 Frictional Grooved Gearing. A set of friction-gears for trans- 
 mitting 150 H.P. is on a steam-dredge described in Proc. Inst. M. E. t 
 July, 1888. Two grooved pinions of 54 in. diam., with 9 grooves of 13/4 in. 
 pitch and angle of 40 cut on their face, are geared into two wheels of 
 1271/2 in. diam. similarly grooved. The wheels can be thrown in and out 
 of gear by levers operating eccentric bushes on the large wheel-shaft. 
 The circumferential speed of the wheels is about 500 ft. per min. Allow- 
 ing for engine friction, if half the power is transmitted through each set 
 of gears the tangential force at the rims is about 3960 Ibs., requiring, if 
 the angle is 40 and the coefficient of friction 0.18, a pressure of 7524 Ibs. 
 between the wheels and pinion to prevent slipping. 
 
 The wear of the wheels proving excessive, the gears were replaced by 
 spur-gear wheels and brake-wheels with steel brake-bands, which arrange- 
 ment has proven more durable than the grooved wheels. Mr. Daniel 
 Adamson states that if the frictional wheels had been run at a higher 
 speed the results would have been better, and says they should run at 
 least 30 ft. per second. 
 
 Power Transmitted by Friction Drives. (W. F. M. Goss, Trans. 
 A. S. M. E., 1907.) A friction drive consists of a fibrous or somewhat 
 yielding driving wheel working in rolling contact with a metallic driven 
 wheel. Such a drive may consist of a pair of plain cylinder wheels 
 mounted upon parallel shafts, or a pair of beveled wheels, or of any 
 other arrangement which will serve in the transmission of motion by 
 rolling contact. 
 
 Driving wheels of each of the materials named in the table below wer* 
 tested in peripheral contact with driving wheels of iron, aluminum and 1 
 type metal, All the wheels were 1 in, diam, ; the face of 
 
FRICTION CLUTCHES. 
 
 1179 
 
 Wheels was 13/4 in., and that of the driven wheels 1/2 in. Records were 
 made of the pressure of contact, of the coefficient of friction developed, 
 
 and of the percentage of slip resulting from the development of the said 
 coefficient of friction. Curves were plotted showing the relation of the 
 coefficient and the slip for pressures of 150 and 400 Ibs. per inch width 
 of face in contact. Another series of tests was made in which the slip 
 was maintained constant at 2% and the pressures were varied. In most 
 of the combinations it was found that with constant slip the coefficient 
 ot friction diminished very slightly as the pressure of contact was in- 
 creased, so that it may be considered practically constant for all pres- 
 sures between 150 and 400 Ibs. per sq. in. 
 
 The crushing strength of each material under the conditions of the 
 test was determined by running each combination with increasing loads 
 until a load was found under which the wheel failed before 15,000 revo- 
 lutions had been made. The results showed the failure of the several 
 fiber wheels under loads per inch of width as follows: Straw fiber 
 750 Ibs.; leather fiber, 1,200 Ibs.; tarred fiber, 1,200 Ibs.; leather, 750 Ibs.; 
 sulphite fiber, 700 Ibs. One-fifth of these pressures is taken as a safe 
 working load. The coefficient of friction approaches its maximum 
 value when the slip between driver and driven wheel is 2%. The safe 
 working horse-power of the drive is calculated on the basis of 60% the 
 coefficient developed at a pressure of 150 Ibs. per inch of width, a re- 
 duction of 40% being made to cover possible decrease of the coefficient 
 in actual service and to cover also loss due to friction of the journals. 
 From these data the following table is constructed showing the H.P. 
 that may be transmitted by driving wheels of the several materials 
 named when in frictionai contact with iron, aluminum and type metal. 
 
 The formula for horse-power is H.P. = X 
 
 = KdWN, in 
 
 ooUUU 
 
 which d = diam. in inches, W = width of face in inches, P = safe work- 
 ing pressure in Ibs. per in. of width, N = revs, per min., / = coefficient 
 of friction, 0.6 a factor for the decrease of the coefficient in service and 
 for the loss in journal friction, K a coefficient including P, / and the 
 numerical constants. 
 COEFFICIENTS OF FRICTION AND HORSE-POWER OF FRICTION DRIVES. 
 
 
 On Iron. 
 
 On Aluminum. 
 
 On Type Metal. 
 
 / 
 
 k 
 
 / 
 
 k 
 
 / 
 
 k 
 
 0.00022 
 0.00035 
 0.00031 
 0.00034 
 0.00029 
 
 Straw fiber 
 
 0.255 
 0.309 
 0.150 
 0.330 
 0.135 
 
 0.00030 
 0.00059 
 0.00029 
 0.00037 
 0.00016 
 
 0.273 
 0.297 
 0.183 
 0.318 
 0.216 
 
 0.00033 
 0.00057 
 0.00035 
 0.00035 
 0.00026 
 
 0.186 
 0.183 
 0.165 
 0.309 
 0.246 
 
 Leather fiber 
 
 Tarred fiber 
 
 Sulphite fiber 
 
 Leather 
 
 Horse-power = K X d WN. 
 
 Friction Clutches. Much valuable information on different forms of 
 friction clutches is given in a paper by Henry Souther in Trans. A. S. M. 
 E., 1908, and in the discussion on the paper. All friction clutches contain 
 two surfaces that rub on each other when the clutch is thrown into gear, 
 and until the friction between them is increased, by the pressure with 
 which they are forced together, to such an extent that the surfaces bind 
 and enable one surface to drive the other. The surfaces may be metal 
 on metal, metal on wood, cork, leather or other substance, leather on 
 leather or other substance, etc. The surfaces may be disks, at right 
 angles to the shaft, blocks sliding on the outer or inner surface, or both, 
 of a pulley rim, or two cones, internal and external, one fitting in the 
 other, or a band or ribbon around a pulley. The driving force which is 
 just sufficient to cause one part of the clutch to drive the other is the 
 product of the total pressure, exerted at right angles to the direction of 
 sliding, and the coefficient of friction. The latter is an axceedingly 
 variable quantity, depending on the nature and condition of the sliding 
 surfaces and on their lubrication. The surfaces must have sufficient 
 area so that the pressure per square inch on that area will not be suffi- 
 cient to cause undue heating and wear. The total pressure on the parts 
 of the mechanism that forces the surfaces together also must not cause 
 undue wear of these parts. 
 
1180 
 
 GEARING. 
 
 For cone clutches, Reuleaux states that the angle of the cone should 
 not be less than 10, hi order that the parts may not become wedged 
 together. He gives the coefficient of cast iron on cast iron, for such 
 clutches, at 0.15. 
 
 For clutches with maple blocks on cast iron Mr. Souther gives a coeffi- 
 cient of 0.37, and for a speed of 100 r.p.m. he gives the following table of 
 capacity of such clutches, made by the Dodge Mfg. Co. 
 
 Horse- 
 power. 
 
 Block 
 
 Area, Ins. 
 
 Diam. at 
 Block, Ins. 
 
 Circumferen- 
 tial Pull at 
 Block Center, 
 Lbs. 
 
 Total 
 Pressure. 
 
 Total Pres- 
 sure per 
 Sq. In. 
 
 25 
 32 
 50 
 98 
 
 120 
 141 
 208 
 280 
 
 16 
 18 
 21.5 
 27.5 
 
 1,960 
 2,240 
 2,900 
 4.500 
 
 5,300 
 6,000 
 7,800 
 12.000 
 
 44 
 44.5 
 37.5 
 43.5 
 
 Prof. I. N. Hollis has found the coefficient of cork on cast iron to be 
 from 0.33 to 0.37, or about double that of cast iron on cast iron or on 
 bronze. A set of cork blocks outlasted a set of maple blocks in the ratio 
 of five to one. Prof. C. M. Allen has found the torque for cork inserts 
 to be nearly double that of a leather-faced clutch for a given dimension. 
 
 Disk clutches for automobiles are made with frictional surfaces of 
 leather, bronze, or copper against iron or steel. The Cadillac Motor Car 
 Co. give the following: Mean radius of leather frictional surface 45/ie ins; 
 area of do., 361/2 sq. ins.; axial pressure, 1000 to 1200 IDS.; H. P. capacity 
 at 400 r.p.m.. 51/2 H.P.: at 1400 r.p.m., 10 H.P. 
 
 C. H. Schlesinger (Horseless Age, Oct. 2, 1907) gives the following 
 formula for the ordinary cone clutch: 
 
 H.P. = PfrR -3- 63,000 sin. 0, 
 
 in which P = assumed pressure of engaging spring in Ibs., / = coeff. of 
 friction, which in ordinary practice is aoout 0.25; r ~ mean radius of 
 the cone, ins.; #=r.p.m. of the motor; = angle of the cone with the 
 axis. Mr. Souther says the value of / = 0.25 is probably near enough 
 for a properly lubricated leather-iron clutch. 
 
 The Hele-Shaw clutch, with V-shaped rings struck up in the surfaces 
 of disks, is described in Proc. Inst. M. E., 1903. A clutch of this form 
 18 ins. diam. between the V's transmitted 1000 H.P. at 700 or 800 r.p.m. 
 
 Coil Friction Clutches. (H. L. Nachman, Am. Mach., April 1, 1909.) 
 Friction clutches are now in use which will transmit 1000, and even 
 more, horse-power. A type of clutch which is satisfactory for the trans- 
 mission of large powers is the coil friction clutch. It consists of a steel 
 coil wound on a chilled cast-iron drum. At each end of the coil a head 
 is formed. The head at one end is attached to the pulley or shaft that is 
 to be set in motion, while that at the other end of the coil serves as a 
 point of application of a force which pulls on the coil to wind it on the 
 drum, thus gripping it firmly. 
 
 The friction of the coil on the drum is the same as that of a rope or 
 belt on a pulley. That is, the relation of the tensions at the two ends of 
 the coil may be found from the equation PlQ=ef ia where P=pull at fixed 
 end of coil; Q=pull at free end of coil; e base of natural logarithms = 
 2.718; fi = coefficient of friction between coils and drum; and a= Angle 
 subtended by coil in radian measure, = 6. 283 for each turn of coil. 
 
 Values of P/Q for different numbers of turns are as follows, assuming 
 N = 0.05 for steel on cast iron, lubricated: 
 No. of turns 1234567 8 
 
 P/Q 
 
 1.37 1.87 2.57 3.51 4.81 6.58 8.60 12.33 
 
 If D = diam. of drum in ins., N = revs., per min., then H.P. *=nDNP*- 
 (12 X 33.000) = 0.00000793 DNP. 
 
HOISTING AND CONVEYING. 
 
 1181 
 
 HOISTING AND CONVEYING. 
 
 Strength of Ropes and Chains. For the weight and strength of rope 
 for hoisting see notes and tables on pages 410 to 416. For strength of 
 chains see page 264. 
 
 Working Strength of Blocks. 
 
 (Boston and Lockport Block Co., 1908.) 
 
 REGULAR BLOCKS WITH LOOSE HOOKS LOADS IN POUNDS 
 
 Size, Inches. 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 Rope diameter, inches .... 
 2 single blocks 
 
 9/16 
 150 
 
 3/ 4 
 250 
 
 V8 
 700 
 
 1 
 
 2000 
 
 11/8 
 4000 
 
 H/4 
 
 7000 
 
 2 double blocks 
 
 250 
 
 400 
 
 1200 
 
 4000 
 
 8000 
 
 12000 
 
 2 triple blocks 
 
 400 
 
 650 
 
 1900 
 
 6000 
 
 12000 
 
 19000 
 
 LOADS IN TONS. 
 
 
 WIDE MORTISE WITH 
 LOOSE HOOKS. 
 
 EXTRA HEAVY WITH 
 SHACKLES. 
 
 Size, inches 
 
 8 
 
 1/2 
 
 2 
 
 10 
 
 I 1/4 
 
 3 
 
 4 
 
 12 
 
 15/16 
 
 6 
 8 
 
 14 
 
 15/8 
 6 
 8 
 10 
 
 16 
 
 13/4 
 10 
 12 
 14 
 
 18 
 2 
 
 20 
 21/4 
 
 22 
 
 21/2 
 
 24 
 3 
 
 Rope, diam., in.. . . 
 2 single blocks 
 2 double blocks. . . . 
 2 triple blocks 
 2 fourfold blocks . . . 
 
 25 
 
 30 
 40 
 
 30 
 35 
 45 
 
 35 
 40 
 55 
 
 40 
 50 
 70 
 
 WORKING LOADS FOR A PAIR OF WIRE-ROPE BLOCKS-TONS 
 
 LOOSE HOOKS. 
 
 SHACKLES. 
 
 Sheave 
 Diam., In. 
 
 Two 
 Singles. 
 
 Two 
 Doubles. 
 
 Two 
 Triples. 
 
 Two 
 
 Singles. 
 
 Two 
 Doubles. 
 
 Two 
 Triples. 
 
 s: 
 
 10 
 
 H 
 
 16 
 18 
 
 3 
 
 4 
 
 6 
 8 
 
 4 
 
 6 
 7 
 
 8 
 10 
 
 5 
 6 
 
 8 
 10 
 12 
 
 4 
 6 
 8 
 10 
 12 
 15 
 
 5 
 8 
 
 to 
 
 12 
 15 
 
 20 
 
 6 
 10 
 12 
 15 
 20 
 25 
 
 Chain Blocks. Referring to the table on the next page, the speed 
 of a chain block is governed by the pull required on the hand chain 
 and the distance the hand chain must travel to lift the load the re- 
 quired distance. The speeds are given for short lifts with men ac- 
 customed to the work; for continuous easy lifting two-thirds of these 
 speeds are attainable. The triplex block lifts rapidly, and the speed 
 increases for light loads because the length of hand chain to be overhauled 
 s small. This fact also enables the operator to lower the load very 
 quickly with the triplex block. The 12- to 20-ton triplex blocks are 
 provided with two separate hand wheels, thus permitting two men to 
 hoist simultaneously, thereby securing double speed. In the triplex 
 block the power is transmitted to the hoisting-chain wheel by means of a 
 train of spur gearing operated by the hand chain. In the duplex block 
 the power is transmitted through a worm wheel and screw. In the dif- 
 ferential block the power is applied by pulling on the slack part of the 
 load chain and the force is multiplied by means of a differential sheave. 
 (See page 539.) The relative efficiency and durability of the three types 
 are as follows: 
 
 
 Differen- 
 tial. 
 
 Duplex. 
 
 Triplex. 
 
 Relative efficiency 
 
 35 
 
 50 
 
 100 
 
 Relative durability 
 
 20 
 
 80 
 
 100 
 
 Relative cost 
 
 40 
 
 80 
 
 100 
 
1182 
 
 HOISTING AND CONVEYING. 
 
 Chain Block Hoisting Speeds. 
 
 (Yale & Towne Mfg. Co., 1908.) 
 
 .9 
 fr* 
 
 F 
 
 Pull 
 in Pounds re- 
 quired on 
 Hand-Chain 
 to Lift 
 Full Loads. 
 
 Feet of Hand- 
 Chain to be 
 Pullea by 
 Operator to 
 Lift Load 
 One Foot 
 High. 
 
 Hoisting Speeds. Feet per Minute 
 Attainable and No. of Men re- 
 quired for Hoisting Full Loads 
 without Pulling over 80 Lb. 
 
 Triplex. 
 
 Duplex. 
 
 Differ- 
 ential. 
 
 H 
 
 9 
 
 5 
 
 H 
 
 X 
 5 
 
 "ft 
 
 Q 
 
 I 1 
 
 1 
 
 "a 
 
 & 
 
 X 
 
 0> 
 
 "ft 
 Q 
 
 L 
 & 
 
 Q 
 
 "3 
 
 
 t-jT3 
 
 & 3 
 
 H.3 
 
 <3-d 
 
 S3 
 
 a 
 
 *8 . 
 6 
 S 
 j 
 
 I 
 
 8 . 
 
 d 
 S 
 
 H 
 
 =3 
 3 
 
 &H 
 
 IM 
 
 fl 
 
 6 
 &* 
 
 V4 
 ,V3 
 
 u/ 2 
 
 3 
 6 
 8 
 10 
 12 
 16 
 20 
 
 
 
 7? 
 
 
 
 18 
 
 
 
 
 
 
 
 6. 
 6. 
 3.70 
 2.50 
 2.30 
 2.30 
 
 1 
 2 
 3 
 3 
 4 
 7 
 
 62 
 82 
 110 
 120 
 114 
 124 
 110 
 130 
 135 
 140 
 130* 
 135* 
 140* 
 
 68 
 87 
 94 
 115 
 132 
 142 
 145 
 145 
 160 
 160 
 
 122 
 216 
 246 
 308 
 557 
 
 21 
 31 
 35 
 42 
 69 
 84 
 126 
 126 
 168 
 210 
 176* 
 
 40 
 59 
 80 
 93 
 126 
 155 
 195 
 252 
 310 
 390 
 
 24 
 30 
 36 
 
 42 
 38 
 
 8. 
 4. 
 4.8 
 3.6 
 2.3 
 1.7 
 1.3 
 1.1 
 0.8 
 0.6 
 1 1 
 
 16. 
 8. 
 9.6 
 7.2 
 4.6 
 3.5 
 2.6 
 2.2 
 1.6 
 1.2 
 ? ? 
 
 24. 
 12. 
 14.4 
 10.8 
 6.9 
 5.2 
 3.9 
 3.3 
 2.4 
 1.8 
 1 1 
 
 1 
 I 
 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 4 
 
 4. 
 2. 
 2.40 
 1.80 
 1.10 
 0.80 
 0.65 
 0.50 
 0.35 
 0.30 
 
 1 
 
 1 
 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 
 
 
 
 
 
 
 
 
 
 
 168* 
 
 
 
 8 
 
 1 6 
 
 ? 4 
 
 4 
 
 
 
 
 
 
 
 710* 
 
 
 
 0.6 
 
 1.2 
 
 1.8 
 
 4 
 
 
 
 
 
 * On each of the two hand-chains. 
 
 t The number of men is based on each man pulling not over 80 Ib 
 One man pulling 160 Ib. or less, as given in the first two columns, can lift 
 the full capacity of any Triplex or Duplex Block. 
 
 Efficiency of Hoisting Tackle. (S. L. Wonson, Eng. News, June 
 11, 1903. 
 
 1 1/4 to 2-in. Manila rope. 
 
 Parts of line. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 
 Ratio of load to pull 
 
 1 91 
 
 ? 64 
 
 '\ 10 
 
 1 84 
 
 4 '-H 
 
 4 7? 
 
 5 OH 
 
 5 M 
 
 
 
 Efficiency, per cent 
 
 96 
 
 88 
 
 ,83 
 
 77 
 
 72 
 
 67 
 
 64 
 
 60 
 
 
 
 3/4-in. Wire rope. 
 
 Parts of line. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 1 12 
 
 13 
 
 Ratio load to pull 
 Efficiency, per cent 
 
 2.73 
 91 
 
 3.47 
 87 
 
 4.11 
 82 
 
 4.70 
 78 
 
 5.20 
 74 
 
 5.68 
 71 
 
 6.08 
 68 
 
 6.46 
 65 
 
 6.787.08 
 62 1 59 
 
 7.34 
 56 
 
 Proportions of Hooks. The following formulae are given by Henry 
 R. Towne, in his Treatise on Cranes, as a result of an extensive experi- 
 mental and mathematical investigation. They apply to hooks of 
 capacities from 250 Ib. to 20,000 Ib. Each size of hook is made from 
 some commercial size of round iron. The basis in each case is. there- 
 fore, the size of iron of which the hook is to be made, indicated by A 
 in the diagram. The dimension D is arbitrarily assumed. The other 
 dimensions, as given by the formulae, are those which, while preserving 
 a proper bearing-face on the interior of the hook for the ropes or chains 
 which may be passed through it, give the greatest resistance to spread- 
 ing and to ultimate rupture, which the amount of material in the original 
 bar admits of. The symbol A is used to indicate the nominal capacity 
 of the hook in tons of 2000 Ib. The formulae which determine the lines 
 
HOOKS. 1183 
 
 of the other parts of the hooks of the several sizes are as follows, the 
 measurements being all expressed in 
 inches : 
 
 D = 0.5 A + 1.25; 
 
 E = 0.64 A+ 1.60; 
 
 F = 0.33 A + 0.85; 
 
 G = 0.75 D; 
 
 H = 1.08 A; 
 
 / = 1.33 A; 
 
 J = 1.20 A; 
 
 K= 1.13 A; 
 
 L = 1.05 A; 
 M= 0.50^4; 
 
 AT =0.85 -0.16; 
 
 O = 0.363 A + 0.66; 
 
 Q = 0.64 A + 1.60; 
 
 U= 0.866 A. 
 
 The dimensions A are necessarily 
 based upon the ordinary merchant sizes 
 of round iron. The sizes which it has 
 been found best to select are the follow- 
 ing: FIG. 189. 
 Capacity of hook: 
 
 1/8 1/41/2 111/22 345 6 8 10 tons 
 Dimension A: 
 
 5/8 H/16 3/4 11/ 16 11/4 13/ 8 1 8/4 2 21/4 21/2 2 7/ 8 31/4 in. 
 
 Experiment has shown that hooks made according to the above formulae 
 will give way first by opening of the jaw, which, however, will not 
 occur except with a load much in excess of the nominal capacity of the 
 hook. This yielding of the hook when overloaded becomes a source of 
 safety, as it constitutes a signal of danger which cannot easily be over- 
 looked, and which must proceed to a considerable length before rupture 
 will occur and the load be dropped. 
 
 Heavy Crane Hooks. A. E. Holcomb, vice-pres. of the Earth Mov- 
 ing Machinery Co., contributes the following (1908). Seven years ago, 
 while engaged in the design of a 100- ton crane, I made a study of the 
 variations in strength with the different sectional forms for hooks in most 
 
 i common use. As a result certain values which gave the best results were 
 
 ! substituted in "Gordon's" formula and a formula was thereby obtained 
 which was good for hooks of any size desired, provided the proper allowable 
 fiber stress per square inch was made use of when designing. From this 
 
 * formula the enclosed table was made up and was published in the American 
 Machinist of Oct. 31, 1901. Since that time hundreds of hooks of cast 
 or hammered steel have been designed and made according to my formula, 
 
 1 and not one of them, so far as I know, has ever failed. 
 
 The Industrial Works, Bay City, Michigan, manufacturers of heavy 
 cranes, in December, 1904, made the following test under actual working 
 
 i conditions: 
 
 A hook was made of hammered steel having an elastic limit or yield 
 point at approximately 36,000 Ibs. per sq. in. fiber stress and having the 
 following important dimensions: d = 75/8 in.; r = 41/2 in.; D = 207/i 6 in. 
 
 When the applied load reached 150,000 Ibs. the hook straightened out 
 until the opening at the mouth of the hook was 21/2 in. larger than 
 formerly, and the distance from center of action line of load to center of 
 gravity of section was found to have decreased 1/2 in., at which point the 
 nook held the load. Upon increasing the load still further, the hook 
 opened still more. From the dimensions of the hook as originally formed, 
 
 i we find from the formula or table that the fiber stress with a load of 
 150,000 Ibs. was 37,900 Ibs. per sq. in., or in excess of the yield point, 
 
 ! whereas making use of the dimensions obtained from the hook when it 
 held we find that the fiber stress per square inch was reduced to 35,940 Ibs., 
 or under the yield point. 
 
 The designer must use his own judgment as to the selection of a proper 
 allowable fik er stress , being governed therein by the nature of the material 
 
1184 
 
 HOISTING AND CONVEYING. 
 
 to be used and the probability of the hookibeing overloaded at some time. 
 Under average conditions I have made use of the following values for (/): 
 
 
 Values of (/) in pounds for a load of 
 
 1,000 to 
 5000 
 Ibs. 
 
 5,000 to 
 15,000 
 Ibs. 
 
 15,000 
 
 to 
 30,000 
 Ibs. 
 
 30,000 
 to 
 60,000 
 
 Ibs. 
 
 60,000 
 to 
 100,000 
 
 Ibs. 
 
 100,000 
 Ibs. 
 and up. 
 
 Cftst iron 
 
 2,000 
 6,000 
 12,000 
 
 2,500 
 8,000 
 16,000 
 
 
 
 
 
 Steel casting 
 
 10,000 
 20,000 
 
 11,250 
 22,500 
 
 12,500 
 25,000 
 
 "27,566' 
 
 Hammered steel 
 
 Mr. Hplcomb's formula is given below, and his table in condensed 
 form is given on page i!85. 
 
 DIRECTIONS. P and /being known, assume r to suit the requirements 
 for which the hook is to be designed. Divide P by /and find the quotient 
 in the column headed by the required r. At the side of the Table, in the 
 same row, will be found the necessary depth of section, d. 
 
 Notation. P = load. S = area of section. R* = square of the radius 
 of gyration. / = allowable fiber stress in Ibs. per sq. in., 20,000 Ibs. for 
 hammered steel. For other letters see Fig. 190. 
 
 ?. = ~__ . General formula. 
 
 n S = - 
 
 - 
 
 <*2(&2+ 4&C + C 2 ). 
 
 (1) 
 
 Vr^X^ (3) 
 
 b + c 3 
 
 :^ + r. . (4) 
 
 0.66d; c = 0.22d, 
 
 Assuming b 
 we have: 
 
 7.44 d+ 12.393 r 
 
 - K. (5) 
 
 D = 2r+ 1.5 d. 
 
 FIG. 190. 
 
 For values of K and r intermediate to those given in the taoie approx- 
 imate values of d may be found by interpolation. Thus, for K = 3.700, 
 r = 2.75. 
 
 r = 2.5 3.0 Int. for 2.75 
 
 K = 3.462 3.213 3.338 
 
 K = 4.128 3.842 3.985 
 
 ((3.700-3.338)) 
 
 Tabular values, 
 
 d = 6.50 
 d = 7.00 
 
 Whence: 
 
 = 6.5-t- 
 
 X (7.0 - 6.5) = 6.78. 
 
 1(3.985-3.338)) 
 
 In like manner, if d and r are given the value of K and the corresponding 
 safe load may be found. 
 
 Strength of Hooks and Shackles. (Boston and Lockport Block Co., 
 1908.) Tests made at the Watertown arsenal on the strength of hooks 
 and shackles showed that they failed at the loads given in the table on 
 page 1 185. In service they should be subjected to only 50 % of the figures 
 in the table. Ordinarily the hook of a block gives way first, and where 
 heavy weights are to be handled shackles are superior to hooks and 
 should be used wherever possible. 
 
 Horse-power Required to Raise a Load at a Given Speed. H.P. = 
 
 Gross weight in Ib. 
 
 X speed in ft. per min. To this add 25 % to 50 % for 
 
 33,000 
 friction, contingencies, etc. The gross weight includes the weight of 
 
HOOKS. 
 
 1185 
 
 Values of K. 
 
 d. 
 
 0.50 | 0.75 | 1.00 | 1.50 [ 2.00 | 2.50 | 3.00 | 3.50 | 4.00 | 5.00 [ 6.00 
 
 2.00 
 2.25 
 2.50 
 2.75 
 3.00 
 3.25 
 3.50 
 3.75 
 4.00 
 4.25 
 4.50 
 4.75 
 5.00 
 5.25 
 5.50 
 5 75 
 
 0.379 
 .496 
 .629 
 .778 
 .944 
 1.143 
 1.342 
 1.558 
 1.790 
 2.038 
 2.304 
 2.586 
 2.884 
 3.214 
 3.532 
 
 0.331 
 
 .437 
 .559 
 .697 
 .852 
 .039 
 .226 
 .429 
 .649 
 .886 
 2.138 
 2.408 
 2.694 
 3.008 
 3.315 
 3.651 
 
 0.292 
 .391 
 .504 
 .632 
 .776 
 .953 
 .129 
 .321 
 .530 
 .754 
 .995 
 2.253 
 2.527 
 2.828 
 3.124 
 3.447 
 3.787 
 4.516 
 5.311 
 6.173 
 7.102 
 8.096 
 9.158 
 
 0.240 
 .329 
 .420 
 .532 
 .659 
 .801 
 .957 
 .148 
 .336 
 .544 
 .760 
 .996 
 2.248 
 2.525 
 2.801 
 3.101 
 3.418 
 4.100 
 4.848 
 5.661 
 6.540 
 7.485 
 8.496 
 9.574 
 10.788 
 12.098 
 13.374 
 14.717 
 16.126 
 17.601 
 
 0.203 
 .275 
 .360 
 .460 
 .572 
 .700 
 .841 
 .998 
 1.187 
 1.373 
 1.575 
 1.793 
 2.072 
 2.281 
 2.538 
 2.818 
 3.115 
 3.754 
 4.459 
 5.227 
 6.061 
 6.960 
 7.924 
 8.954 
 10.220 
 11.381 
 12.608 
 13.901 
 15.261 
 16.686 
 18.178 
 19.735 
 21.359 
 23.050 
 24.807 
 26.630 
 28.520 
 
 0.176 
 .239 
 .316 
 .404 
 .506 
 .621 
 .750 
 .893 
 .067 
 .239 
 .426 
 .627 
 .843 
 2.081 
 2.321 
 2.583 
 2.861 
 3.463 
 4.128 
 4.855 
 5.648 
 6.504 
 7.424 
 8.409 
 9.460 
 10.746 
 11.922 
 13.173 
 14.485 
 15.862 
 17.305 
 18.814 
 20.389 
 22.031 
 23.738 
 25.511 
 27.351 
 
 0.155 
 .212 
 .281 
 .360 
 .454 
 .559 
 .677 
 .808 
 .953 
 .129 
 .321 
 .490 
 .691 
 .913 
 2.140 
 2.385 
 2.646 
 3.213 
 3.842 
 4.533 
 5.287 
 6.104 
 6.984 
 7 928 
 8.932 
 10.008 
 11 316 
 12.518 
 13.785 
 15.117 
 16 514 
 17.976 
 19.504 
 21.098 
 22.758 
 24.483 
 26.274 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "0.411 
 
 .508 
 .617 
 .738 
 .873 
 .038 
 .214 
 .374 
 .563 
 .770 
 .983 
 2.215 
 2.461 
 2.998 
 3.594 
 4.252 
 4.970 
 5.750 
 6.593 
 7.498 
 8.467 
 9.499 
 10.766 
 11.926 
 13.150 
 14.442 
 15.792 
 17.210 
 18.694 
 20.242 
 2 .846 
 23.535 
 25.388 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0.805 
 0.943 
 .124 
 .275 
 .453 
 .647 
 .849 
 2.067 
 2.300 
 2.809 
 3.377 
 4.003 
 4.689 
 5.436 
 6.243 
 7.113 
 8.044 
 9.039 
 10.267 
 11.388 
 12.572 
 13.820 
 15.132 
 16.508 
 17.948 
 19.453 
 2 .023 
 22.658 
 24.358 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1.628 
 1.825 
 2.035 
 2.496 
 3.012 
 3.584 
 4.213 
 4.900 
 5.645 
 6.450 
 7.316 
 8.241 
 9.228 
 10.448 
 11.558 
 12.730 
 13.965 
 15.263 
 16.624 
 18.049 
 19.536 
 21.088 
 22.704 
 
 
 
 6.00 
 6.50 
 7.00 
 7.50 
 8.00 
 8.50 
 9.00 
 9.50 
 10.00 
 10.50 
 11.00 
 11.50 
 12.00 
 12.50 
 13.00 
 13.50 
 14.00 
 14.50 
 15.00 
 15.50 
 16.00 
 
 
 4.003 
 4.757 
 5.578 
 
 
 2.246 
 2.719 
 3.244 
 3.825 
 4.460 
 5.152 
 5.901 
 6.708 
 7.573 
 8.498 
 9.482 
 10.697 
 11.802 
 12.967 
 14.195 
 15.484 
 16.835 
 18.248 
 19.724 
 21.262 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Strength of Hooks and Shackles. 
 
 HOOKS.* | SHACKLES. 
 
 
 4 
 
 g 
 
 
 
 4 
 
 
 
 
 
 M 
 
 c? 
 
 
 
 I 
 
 
 
 Inches. 
 
 Z% 
 1| 
 
 l| 
 
 Description of 
 Fracture. 
 
 tnches. 
 
 -a ^ 
 
 |j 
 
 Description of 
 Fracture. 
 
 ,1" 
 
 H 
 
 1 
 
 
 i 
 
 S 
 
 1 
 
 H 
 
 
 1/2 
 
 1 890 
 
 
 
 isfo 
 
 17310 
 
 103 750 
 
 Eye of shackle 
 
 9/16 
 
 2^560 
 
 
 
 H/o 
 
 20*940 
 
 119800 
 
 Eye of shackle. 
 
 fc 
 
 3,020 
 4,470 
 
 
 
 15/8 
 13/ 4 
 
 23,670 
 27,420 
 
 125,900 
 146,804 
 
 Eye of shackle. 
 Sheared shackle 
 
 20,700 
 
 Eye of shackle. 
 
 7/8 
 
 6,280 
 
 38,100 
 
 Eye of shackle. 
 
 
 
 
 pin. 
 
 1 
 
 12,600 
 13,520 
 
 51,900 
 62,900 
 
 Eye of shackle. 
 Sheared shackle 
 
 17/8 
 
 36,120 
 38,100 
 
 162,700 
 196,600 
 
 Eye of shackle. 
 Shackle at neck 
 
 
 
 
 pin. 
 
 
 
 
 of eye. 
 
 H/4 
 
 16,800 
 
 75,200 
 
 Eye of shackle. 
 
 21/2 
 
 55.380 
 
 210,400 
 
 Eye of shackle. 
 
 * AU the hooks failed by straightening the hook, 
 
1186 HOISTING AND CONVEYING. 
 
 cage, rope, etc. In a shaft with two cages balancing each other use the 
 net load + weight of one rope, instead of the gross weight. 
 
 To find the load which a given pair of engines will start. Let A = area 
 of cylinder in square inches, or total area of both cylinders, if there are 
 two; P = mean effective pressure in cylinder in Ib. per sq. in.; S = stroke 
 of cylinder, inches; C = circumference of hoisting-drum, inches; L 
 load lifted by hoisting-rope, Ib.; F = friction, expressed as a diminution 
 
 of the load. Then L = A x ^ x2 ^ _ Ff 
 
 An example in ColVy Engr., July, 1891, is a pair of hoisting-engines 
 24* X 40", drum 12 ft. diam., average steam-pressure in cylinder = 
 59.5 Ib.; A = 904.8; P = 59.5; S = 40; C = 452.4. Theoretical load, 
 not allowing for friction, A X P X 2 S -*- C * 9589 Ib. The actual load 
 that could just be lifted on trial was 7988 Ib., making friction loss F = 
 1601 Ib., or 20 + per cent of the actual load lifted, or 162/3% of the theo- 
 retical load. 
 
 . The above rule takes no account of the resistance due to inertia of 
 the load, but for all ordinary cases in which the acceleration of speed of 
 the cage is moderate, it is covered by the allowance for friction, etc. The 
 resistance due to inertia is equal to the force required to give the load the 
 velocity acquired in a given time, or, as shown in Mechanics, equal to the 
 
 wv 
 product of the mass by the acceleration, or R = ^ in which R ~ 
 
 resistance in Ib. due to inertia; W = weight of load in Ib.; V = maximum 
 velocity in ft. per second; T = time in seconds taken to acquire the 
 velocity V; g = 32.16. ' 
 
 Safe Loads for Ropes and Chains. The table on p. 1187 was pre- 
 pared by the National Founder's Association and published hi Indust. 
 Eng., Sept., 1914. It shows the safe loads that can be carried by wire 
 rope, crane chain and manila rope of the sizes given when used hi the 
 positions and combinations shown. The loads in the table are lower 
 than those usually specified, in order to insure absolute safety. When 
 handling molten metal, the ropes and chains should be 25 per cent 
 stronger than the figures in the table. 
 
 Effect of Slack Rope upon Strain in Hoisting. A series of tests 
 with a dynamometer are published by the Trenton Iron Co., which show 
 that a dangerous extra strain may be caused by a few inches of slack rope. 
 In one case the cage and full tubs weighed 11,300 Ib.; the strain when the 
 load was lifted gently was 11,525 Ib.; with 3 in. of slack chain it was 
 19,025 Ib.; with 6 in. slack 25,750 Ib., and with 9 in. slack 27,950 Ib. 
 
 Limit of Depth for Hoisting. Taking the weight of a cast-steel 
 hoisting-rope of IVsm. diameter at 2 Ib. per running foot, and its break- 
 Ing strength at 84,000 Ib., it should, theoretically, sustain itself until 
 42 000 feet long before breaking from its own weight. But taking the 
 usual factor of safety 01 7, then the safe working length of such a rope 
 would be only 6000 ft. If a weight of 3 tons is now hung to the rope, 
 which is equivalent to that of a cage of moderate capacity with its loaded 
 cars the maximum length at which such a rope could be used, with the 
 factor of safety of 7, is 3000 ft., or 
 
 2 x + 6000 84,000 ~ 7; /. X = 3000 feet. 
 
 This limit may be greatly increased by using special steel rope of higher 
 strength, by using a smaller factor of safety, and by using taper ropes. 
 (See paper by H. A. Wheeler, Trans. A. I. M. E xix. 107.) 
 
 Large Hoisting Records. At a colliery in North Derbyshire during 
 the first week in June, 1890, 6309 tons were raised from a depth of o09 
 yards, the time of winding being from 7 a.m. to 3.30 p.m. 
 
 At two other Derbyshire pits, 170 and 140 yards in depth, the speed of 
 winding and changing has been brought to such perfection that tubs are 
 drawn and changed three times in one minute. (Proc. Inst. M. E., 1890.) 
 
 At the Nottingham Colliery near Wilkesbarre, Pa., in Oct., 1891, 70,152 
 tons were shipped in 24.15 days, the average hoist per day being 1318 mine 
 cars The depth of hoist was 470 ft., and all coal came from 9ne opening. 
 The'engines were first motion, 22 X48 in., conical drums 4ft. 1 in. long, 7ft. 
 diameter at small end and 9 ft. at large end. (Eng'g News, Nov. 1891 .) 
 Large Engines. Two 34 X 60 in. four-cylinder engines built by 
 Nordberg Mfg. Co. for the Tamarack copper mine at Calumet, Mich., ar 
 
PNEUMATIC HOISTING. 
 
 1187 
 
 Safe Loads for Ropes and Chains. 
 
 
 
 When Used 
 
 When Used 
 
 When Used 
 
 When Used 
 
 NOTE. The safe loads in 
 table are for each SINGLE 
 
 Straight. 
 
 at 60 
 Angle. 
 
 at 45 
 Angle. 
 
 at 30 
 Angle. 
 
 rope or chain. 
 
 When used 
 
 
 
 
 
 double or in other multiples 
 
 
 
 
 
 the loads may b 
 
 e increased 
 
 
 
 yv 
 
 
 proportionately. 
 
 
 
 
 /\ 
 
 ^X 
 
 
 
 
 
 
 
 
 
 Dia. 
 
 
 
 
 
 
 In. 
 
 Lb. 
 
 Lb. 
 
 Lb. 
 
 Lb. 
 
 PLOW STEEL WIRE 
 
 3/8 
 
 . 1,500 
 
 1,275 
 
 1,050 
 
 750 
 
 KROPE. 
 
 
 1/2 
 
 2,400 
 
 2,050 
 
 1,700 
 
 1,200 
 
 
 
 5/8 
 
 4,000 
 
 3,400 
 
 2,800 
 
 2,000 
 
 strands of 
 
 9 or 
 
 3/4 
 
 6,000 
 
 5,100 
 
 4,200 
 
 3,000 
 
 37 wires.] 
 
 
 7/8 
 
 8,000 
 
 6,800 
 
 5,600 
 
 4,000 
 
 
 
 1 
 
 10,000 
 
 8,500 
 
 7,000 
 
 5,000 
 
 If crucible steel rope 
 
 1 1/8 
 
 13,000 
 
 11,000 
 
 9,000 
 
 6,500 
 
 is used reduce 1 
 
 oads 
 
 H/4 
 
 16,000 
 
 13,500 
 
 11,000 
 
 8,000 
 
 one-fifth. 
 
 
 13/8 
 
 19,000 
 
 16,000 
 
 13,000 
 
 9,500 
 
 
 
 1 1/2 
 
 22,000 
 
 19,000 16,000 
 
 11,000 
 
 
 
 3 V* 
 
 600 
 
 500 
 
 425 
 
 300 
 
 CRANE CH/ 
 
 LlN. 
 
 3 3/ 8 
 
 1,200 
 
 1,025 
 
 850 
 
 600 
 
 
 
 
 2,400 
 
 2,050 
 
 1,700 
 
 1,200 
 
 [Best grade of 
 
 O 5/g 
 
 4,000 
 
 3,400 
 
 2,800 
 
 2,000 
 
 wrought iron, h 
 
 and- 
 
 ** 3/4 
 
 5,500 
 
 4,700 
 
 3,900 
 
 2,750 
 
 made, tested, short- 
 link chain.] 
 
 6 H/8 
 
 7,500 
 9,500 
 12,000 
 
 6,400 
 8,000 
 10,200 
 
 5,200 
 6,600 
 8,400 
 
 3,700 
 4,700 
 6,000 
 
 
 
 .2 1 1/4 
 
 15,000 
 
 12,750 
 
 10,500 
 
 7,500 
 
 
 
 ^ 13/8 
 
 22,000 
 
 19,000 
 
 .16,000 
 
 11,000 
 
 
 Dia. 
 
 Cir. 
 
 
 
 
 
 
 In. 
 
 In. 
 
 
 
 
 
 
 3/8 
 
 1 
 
 120 
 
 100 
 
 85 
 
 60 
 
 MANILA ROPE. 
 
 1/2 
 
 U/2 
 
 250 
 
 210 
 
 175 
 
 125 
 
 
 5/8 
 
 2 
 
 360 
 
 300 
 
 250 
 
 180 
 
 
 3/4 
 
 21/4 
 
 520 
 
 440 
 
 360 
 
 260 
 
 [Best long fibre 
 
 7 /8 
 
 23/4 
 
 620 
 
 520 
 
 420 
 
 300 
 
 grade.] 
 
 1 
 
 3 
 
 750 
 
 625 
 
 525 
 
 375 
 
 
 H/8 
 
 31/2 
 
 . 1,000 
 
 850 
 
 700 
 
 500 
 
 
 H/4 
 
 33/4 
 
 1,200 
 
 1,025 
 
 850 
 
 600 
 
 
 H/2 
 
 41/2 
 
 1,600 
 
 1,350 
 
 1,100 
 
 800 
 
 
 13/4 
 
 51/2 
 
 2,100 
 
 1,800 
 
 1,500 
 
 1,050 
 
 
 2 
 
 6 
 
 2,800 
 
 2,400 
 
 2,000 
 
 1,400 
 
 
 21/2 
 
 71/2 
 
 4,000 
 
 3,400 
 
 2,800 
 
 2,000 
 
 
 3 
 
 9 
 
 6,000 
 
 5,100 
 
 4,200 
 
 3,000 
 
 designed to lift a load from a depth of 6,000 ft. at an average hoisting 
 speed of 5,000 ft. per min. The load is made up of ore, 12,000 Ibs. ; cage 
 and cars, 8,500 Ibs.; 6,500 ft. 9f 1^-in. rope, 21,200 Ibs.; total, 41,700 
 Ibs. The center lines of the cylinders are placed 90 apart and the cranks 
 135 apart. By this arrangement three of the four cylinders are al- 
 ways available for starting the hoist. 
 
 Pneumatic Hoisting. (H. A. Wheeler, Trans. A. I. M. E. xix, 107.) 
 A pneumatic hoist was installed in 1876 at Epinac, France, consisting 
 of two continuous air-tight iron cylinders extending from the bottom to 
 the top of the shaft. Within the cylinder moved a piston from which 
 was hung the cage. It was operated by exhausting J/he air from, above 
 the piston, the lower side being open to the atmosphere. Its use was 
 discontinued on account of the failure of the mine. Mr. Wheeler gives 
 a description of the system, but criticizes it as not being equal on the 
 whole to hoisting by steel ropes. 
 
 Pneumatic hoisting-cylinders using compressed air have been used at 
 blast-furnaces, the weighted piston counterbalancing the weight of the 
 
1188 HOISTING AND CONVEYING. 
 
 cage, and the two being connected by a wire rope passing over a pulley- 
 sheave above the top of the cylinder. In the more modern furnaces 
 steam-engine or electric hoists are generally used. 
 
 Electric Mine-Hoists. An important paper on this subject, 'by D. 
 B. Rushfhore and K. A. Pauly, will be found ill Trans. A. I. M. E. t 
 1910. See also Electrical Hoisting, page 1464. 
 
 Counterbalancing of Winding-engines. (H. W. Hughes, Columbia 
 JColl. Qly.) Engines running unbalanced are subject to enormous 
 variations in the load; for let W = weight of cage and empty tubs, say 
 6270 Ib.; c = weight of coal, say 4480 Ib.; r = weight of hoisting rope, 
 eay 6000 Ib.; r' = weight of counterbalance rope hanging down pit, say 
 6000 Ib. The weight to be lifted will be: 
 
 If weight of rope is unbalanced. II weight of rope is balanced. 
 At beginning of lift: 
 
 W + c + r - W or 10,480 Ib. W + c + r - (W + r'), 
 
 At middle of lift: 
 
 
 or 
 
 f-4480 
 Ib. 
 
 2 2 \ 
 
 At end of lift: 
 
 W + c - (W + r) or minus 1520 Ib. W + c + r' - (W + r), , 
 That counterbalancing materially affects the size of winding-engines is 
 shown by a formula given by Mr. Robert Wilson, which is based on the 
 fact that the greatest work a winding-engine has to do is to get a given 
 mass into a certain velocity uniformly accelerated from rest, and to raise 
 a load the distance passed over during the time this velocity is being 
 obtained. 
 
 Let W the weight to be set in motion: one cage, coal, number of. empty 
 tubs on cage, one winding rope from pit head-gear to bottom, 
 and one rope from banking level to bottom. 
 v = greatest velocity attained, uniformly accelerated from rest; 
 g = gravity = 32.2; 
 
 t = time in seconds during which v is obtained; 
 L = unbalanced load on engine; 
 R = ratio of diameter of drum and crank circles; 
 P = average pressure of steam in cylinders; 
 N = number of cylinders; 
 
 S = space passed over by crank-pin during time t : 
 
 (7 = 2/3, constant to reduce angular space passed through by crank to 
 
 the distance passed through by the piston during the time t; 
 
 A = area of one cylinder, without margin f9r friction. To this an 
 
 addition for friction, etc., of engine is to be made, varying 
 
 from 10 to 30% of A. 
 
 1st. Where load is balanced. 
 
 A 
 
 PNSC 
 
 2d. Where load is unbalanced: 
 
 The formula is the same, with the addition of another term to allow for 
 
 the variation in the lengths of the ascending and descending ropes. In 
 
 [this case 
 
 /ii = reduced length of rope in t attached to ascending cage; 
 fe 2 = increased length of rope in t attached to descending cage; 
 w weight of rope per foot in pounds. Then 
 
 \fWv\ , ( /, vt\ hiw 4- hzw i "1 p 
 l(-2^) + {( L 2)- 2 \\ R 
 ~~ 
 
 Applying tne above formula when designing new engines, Mr. Wilson 
 
 found that 30 in. diameter of cylinders would produce equal results, when 
 
 balanced, to those of the 36-in. cylinder in use, the latter being unbalanced. 
 
 Counterbalancing may be employed in the following methods: 
 
 (a) Tapering Rope. At the initial stage the tapering rope enables us 
 
 to wind from greater depths than is possible with ropes of uniform section. 
 
CRANES. 1189 
 
 The thickness of such a rope at any point should only be such as to safely 
 bear the load on it at that point. 
 
 With tapering ropes we obtain a smaller difference between the initial 
 and final load, but the difference is still considerable, and for. perfect 
 equalization of the load we must rely on some other resource. The theory 
 of taper ropes is to obtain a rope of uniform strength, thinner at the cage 
 end where the weight is least, and thicker at the drum end where it is 
 greatest. 
 
 (6) The Counterpoise System C9nsists of a heavy chain working up and 
 down a staple pit, the motion being obtained by means of a special small 
 drum placed on the same axis as the winding drum. It is so arranged 
 that the chain hangs in full length down the staple pit at the commence- 
 ment of the winding; in the center of the run the whole of the chain rests 
 on the bottom of the pit, and, finally, at the end of the winding the counter- 
 poise has been rewound upon the small drum, and is in the same con- 
 dition as it was at the commencement. 
 
 (c) Loaded-wagon System. A plan, formerly much employed, was to 
 have a loaded wagon running on a short incline in place of this heavy 
 chain; the rope actuating this wagon being connected in the same manner 
 as the above to a subsidiary drum. The incline was constructed steep 
 at the commencement, the inclination gradually decreasing to nothing. 
 At the beginning of a wind the wagon was at the top of the incline, and 
 during a portion of the run gradually passed down it till, at the meet of 
 cages, no pull was exerted on the engine the wagon by this time being 
 at the bottom. In the latter part of the wind the resistance was all 
 against the engine, owing to its having to pull the wagon up the incline, 
 and this resistance increased from nothing at the meet of cages to its 
 greatest quantity at the conclusion of the lift. 
 
 (d) The Endless-rope System is preferable to all others, if there is suffi- 
 cient sump room and the shaft is free from tubes, cross timbers, and other 
 impediments. It consists in placing beneath the cages a tail rope, similar 
 in diameter to the winding rope, And, after conveying this down the pit, 
 it is attached beneath the other cage. 
 
 (e) Flat Ropes Coiling on Reels. This means of winding allows of a 
 certain equalization, for the radius of the coil of ascending rope continues to 
 increase, while that of the descending one continues to diminish. Conse- 
 quently, as the resistance decreases in the ascending load the leverage 
 increases, and as the power increases in the other, the leverage diminishes. 
 The variation in the leverage is a constant quantity, and is equal to the 
 thickness of the rope where it is wound on the drum. 
 
 By the above means a remarkable uniformity in the load may be ob- 
 tained, the only objection being the use of flat ropes, which weigh heavier 
 and only last about two-thirds the time of round ones. 
 
 '(/) Conical Drums. Results analogous to the preceding may be 
 obtained by using round ropes coiling on conical drums, which may either 
 be smooth, with the successive coils lying side by side, or they may be 
 provided with a spiral groove. The objection to these forms is, that 
 perfect equalization is not obtained with the conical drums unless the sides 
 are very steep, and consequently there is great risk of the rope slipping; 
 to obviate this, scroll drums were proposed. They are, however, expen- 
 sive, and the lateral displacement of the winding rope from the center 
 line of pulley becomes very great, owing to their necessary large width. 
 (<7) The Koepe System of Winding. An iron pulley with a single cir- 
 cular groove takes the place of the ordinary drum. The winding rope 
 passes from one cage, over its head-gear pulley, round the drum, and, 
 after passing over the other head-gear pulley, is connected with the second 
 cage. The winding rope thus encircles about half the periphery of the 
 drum in the same manner as a driving-belt on an ordinary pulley. There 
 is a balance rope beneath the cages, passing round a pulley in the sump; 
 the arrangement is like an endless rope, with the cages as points of 
 attachment. 
 
 CRANES. 
 
 Classification of Cranes. (Henry R. Towne, Trans. A. S. M. E. iv.; 
 288. Revised in Hoisting, published by The Yale & Towne Mfg. Co.) 
 
 A Hoist is a machine for raising and lowering weights. A Crane is a 
 hoist with the added capacity of moving the load in a horizontal or 
 lateral direction. 
 
1190 HOISTING AND CONVEYING. 
 
 Cranes are divided into two classes, as to their motions, viz. Rotary and 
 Rectilinear, and into four groups, as to their source of motive power, viz. : 
 
 Hand. When operated by manual power. 
 
 Power. When driven by power derived from line shafting. 
 
 Steam, Electric, Hydraulic, or Pneumatic. When driven by an engine 
 or motor attached to the crane, and operated by steam, electricity, water, 
 or air transmitted to the crane from a fixed source of supply. 
 
 Locomotive. When the crane is provided with its own boiler or other 
 generator of power, and is self-propelling; usually being capable of both 
 rotary and rectilinear motions. 
 
 Rotary and Rectilinear Cranes are thus subdivided. 
 
 ROTAEY CRANES. 
 
 (1) Swing-cranes. Having rotation, but no trolley motion. 
 
 (2) Jib-cranes. Having rotation, and a trolley traveling on the jib. 
 
 (3) Column-cranes. Identical with the jib-cranes, but rotating around 
 a fixed column (which usually supports a floor above). 
 
 (4) Pillar-cranes. Having rotation only; the pillar or column being 
 supported entirely from the foundation. 
 
 (5) Pillar Jib-cranes. Identical with the last, except in having a jib 
 and trolley motion. 
 
 (6) Derrick-cranes. Identical with jib-cranes, except that the head of 
 the mast is held in position by guy-rods, instead of by attachment to a 
 roof or ceiling. 
 
 (7) Walking-cranes. Consisting of a pillar or jib-crane mounted on 
 wheels and arranged to travel longitudinally upon one or more rails. 
 
 (8) Locomotive-cranes. Consisting of a pillar-crane mounted on a 
 truck, and provided with a steam-engine capable of propelling and rotat- 
 ing the crane, and of hoisting and lowering the load. 
 
 RECTILINEAR CRANES. 
 
 (9) Bridge-cranes. Having a fixed bridge spanning an opening, and a 
 trolley moving across the bridge. 
 
 (10) Tram-cranes. Consisting of a truck, or short bridge, traveling 
 longitudinally on overhead rails, and without trolley motion. 
 
 (11) Traveling-cranes. Consisting of a bridge moving longitudinally 
 on overhead tracks, and a trolley moving transversely on the bridge. 
 
 (12) Gantries. Consisting of an overhead bridge, carried at each end 
 by a trestle traveling on longitudinal tracks on the ground, and having 
 a trolley moving transversely on the bridge. 
 
 (13) Rotary Bridge-cranes. Combining rotary and rectilinear move- 
 ments and consisting of a bridge pivoted at one end to a central pier or 
 post, and supported at the other end on a circular track; provided with a 
 trolley moving transversely on the bridge. 
 
 For descriptions of these several forms of cranes see Towne's " Treatise 
 on Cranes." 
 
 Stresses in Cranes. See Stresses in Framed Structures, p. 541, ante. 
 
 Position of the Inclined Brace in a Jib-crane. The most econom- 
 ical arrangement is that in which the inclined brace intersects the jib at 
 a distance from the mast equal to four-fifths the effective radius of the 
 crane. (Hoisting.) 
 
 Electric Overhead Traveling Cranes. (From data supplied by 
 Alliance Machine Co., Alliance, O., and Pawling & Harnischfeger, Mil- 
 waukee.) Electric overhead traveling cranes usually have 3 motors, for 
 hoisting, traversing the hoist trolley on the bridge and for moving the 
 bridge, respectively. The usual range of motor sizes is as follows: Hoist, 
 15-50 H.P.; trolley, 3-15 H.P.; bridge, 15-50 H.P. The speeds at which 
 the various motions are made range as follows, the figures being feet per 
 minute: Hoist, 8-60; trolley traverse, 75-200; bridge travel, 200-600. 
 These speeds are varied in the same capacity of crane to suit each par- 
 ticular installation. In general, the speed of the bridge in feet per minute 
 should not exceed (length of runway + 100). If the runway is long and 
 covered by more than one crane, the speed may be made equal to the 
 average distance between cranes + 100. Usually 300 ft. per min. is a 
 good speed. ^For small cranes in special cases, the speeds may be increased, 
 but for cranes of over 50 tons capacity the speed should be below 300 ft. 
 per min. unless the building is made especially strong to stand the strains 
 incident to starting and stopping heavy cranes geared for high speeds. 
 
CRANES. 
 
 1191 
 
 Cranes of over 15 tons capacity usually have an auxiliary hoist of 1/5 the 
 capacity of the main hoist, and usually operated by a separate motor. 
 Wire rope is now almost exclusively used for hoisting: with cranes. The 
 diameter of the drums and sheaves should be not less than 30 times 
 the diameter of the hoisting rope, and should have a factor of safety of 5. 
 Cranes are equipped with automatic load brakes to sustain the load when 
 lifted and to regulate the speed when lowering, it being necessary for the 
 hoist to drive the load down. 
 
 The voltage now standard for crane service is 220 volts at the crane 
 motor, although 110 volts for small cranes is not objectionable. Voltages 
 of 500-600 are inadvisable, especially in foundries and steel works, where 
 dust and metallic oxides cover many parts of the crane and necessitate 
 frequent cleaning to avoid grounds. On account of the danger from the 
 higher voltages, the operators are apt to neglect this part of their work. 
 
 Power Required to Drive Cranes. (Morgan Engineering Co., 
 Alliance, O., 1909.) The power required to drive the different parts of 
 cranes is determined by allowing a certain friction percentage over the 
 power required to move the dead load. On hoist motions 331/3% la 
 allowed for friction of the moving parts, thus giving a motor of 1/3 greater 
 capacity than if friction were neglected. For bridge and trolley motions, 
 a journal friction of the track wheel axles of 10% of the total weight of 
 the crane and load is allowed. There is then added an allowance of 33 1/3% 
 of the horse-power required to drive the crane and load plus the track wheel 
 axle friction, to cover friction of the gearing. In selecting motors, the 
 most important consideration is the maximum starting torque which 
 the motor can exert. With alternating-current motors, this is less than 
 with direct-current motors, requiring a larger motor, particularly on the 
 bridge and trolley motions which require the greatest starting torque. 
 
 Walter G. Stephan says (Iron Trade Rev., Jan. 7, 1909) that the bridge 
 girders should be made of two plates latticed, or box girders, their depth 
 varying from 1/10 to 1/20 of the span. Ihe important feature of crane 
 girder design is ample strength and stiffness, both vertically and laterally. 
 . Especial attention should be given to the transverse strain on the bridge 
 due to sudden stopping or starting of heavy loads. The wheel base on 
 the end trucks should have a ratio to the crane span of 1 to 6, although 
 for long spans this ratio must necessarily be reduced to 1 to 8. Quick- 
 traveling cranes should have as long a wheel base as possible, since the 
 tendency to twist increases with the speed. Where several wheels are 
 necessary at each end to support the crane, equalizing means should be 
 used. 
 
 A recent development in cranes is the four- or six-girder crane for han- 
 dling ladles of molten metal in steel works. The main trolley runs on the 
 outer girders, with the hoist ropes depending between the outer and inner 
 girders. The auxiliary trolley runs on the inner girders, thus being able 
 to pass between the main ropes, and tilt the ladle in either direction. 
 
 Dimensions and Wheel Loads of Electric Traveling Cranes. 
 
 Based on 60-ft. span and 25-ft. lift; wire rope hoist. 
 (Alliance Machine Co., 1908.) 
 
 Capacity, 
 Tons (2000 
 Lb.). 
 
 ~T 
 
 25 
 40 
 50 
 
 Distance Run- 
 way Rail to 
 Highest Point. 
 
 Distance 
 Center of 
 Rail to Ends 
 of Crane. 
 
 Wheel Base of 
 End Truck. 
 
 Maximum 
 Load per 
 Wheel; Trol- 
 ley at End of 
 Bridge. 
 
 Ft. In. 
 6 
 6 6 
 7 4 
 8 
 8 9 
 
 In. 
 9 
 10 
 12 
 12 
 12 
 
 Ft. In. 
 9 
 10 
 11 6 
 12 3 
 12 6 
 
 Pounds. 
 20,000 
 27,000 
 51,000 
 82,000 
 48,000* 
 
 * Has 8 track wheels on bridge. 
 
 Standard cranes are built in intermediate sizes, varying by 5 tons, up 
 (o 40 tons, 
 
1192 
 
 HOISTING AND CONVEYING. 
 
 Standard Hoisting and Traveling Speeds of Electric Cranes. 
 
 (Pawling & Harnischfeger, 1908.) 
 
 Tons (2000 
 Lb.). 
 
 Hoisting 
 Speed, Ft. per 
 Min. 
 
 Bridge Travel 
 Speed, Ft. per 
 Min. 
 
 Capacity 
 Aux. Hoist, 
 Tons. 
 
 Speed Aux. 
 Hoist, Ft. per 
 Min. 
 
 10 
 
 25-100 
 20-75 
 
 300-450 
 300-450 
 
 3 
 
 30-75 
 
 23 
 
 10-40 
 
 25Q-350 
 
 
 d 
 
 50-125) 
 25-60 f 
 
 40 
 
 9-30 
 
 250-350 
 
 
 ,2 
 
 40-100 [ 
 25-60 f 
 
 50 
 
 8-30 
 
 200-300 
 
 
 4 
 
 40-100 \ 
 25-6(1 } 
 
 75 
 
 6-25 
 
 200-250 
 
 15 
 
 20-50 
 
 25 
 
 5-15 
 
 200-250 
 
 25 
 
 20-50 
 
 150 
 
 5-15 
 
 200-250 
 
 25 
 
 20-50 
 
 Trolley travel speed from 100-150 ft. per min. in all cases. 
 Notable Crane Installations. (1909.) 
 
 ^ 
 
 
 
 X 
 
 H.P.of 
 
 ^ 
 
 & 
 
 - 
 
 . 
 
 , 
 
 fl 
 
 
 fl 
 
 
 1 
 
 5 "^ 
 
 Hoist 
 
 
 
 W) 
 
 CJ g 
 
 QJ g 
 
 cs'd' c 
 
 'S3 
 
 
 H 
 
 
 2*"" 
 
 "8J w 
 
 Motor. 
 
 8 
 
 w 
 
 i 
 
 QS 
 
 02"^ 
 
 H |S 
 
 S g 
 
 c: 
 
 . 
 
 
 
 vg 
 
 
 
 *-. ^ 
 
 o| 
 
 Jl 
 
 h 
 acL 
 
 ^1 
 
 *o^ 
 
 M ^ 
 
 I 
 
 a 
 
 " 
 
 I- H 
 
 
 
 Ab 
 
 fej 
 
 
 .H-^ 
 
 ^5 
 
 S 
 
 f 5 
 
 1 
 
 6 
 
 02 
 
 d 
 
 |i 
 
 1 
 
 3.5 
 
 W 
 
 w 
 
 w fe 
 
 S^ 
 
 H* 
 
 1 
 
 il" 
 
 
 Ft. In. 
 
 
 
 
 
 
 
 
 
 
 Ft.In. 
 
 
 150 
 
 65 
 
 1 
 
 25 
 
 75f 
 
 f351 
 \10J 
 
 30 
 
 75 
 
 8-24 
 
 150-200 
 
 100-150 
 
 7 
 
 4 
 
 150 
 
 55 
 
 1 
 
 30 
 
 120 
 
 50 
 
 35 
 
 50 
 
 8 
 
 150-200 
 
 75-100 
 
 
 5 
 
 150 
 
 65 
 
 2 
 
 15 
 
 75f 
 
 30f 
 
 18f 
 
 75 
 
 10-25 
 
 150-200 
 
 100-150 
 
 7"6" 
 
 4 
 
 125* 
 120 
 
 
 2 
 
 
 110 
 
 50f 
 
 rsoi 
 
 \30/ 
 18 
 
 poi 
 
 U5/ 
 10f 
 
 100} 
 
 52J 
 
 10 
 10-25 
 
 200 
 150-300 
 
 f 801 
 \125/ 
 100-150 
 
 5 10 
 5 5 
 
 6 
 7 
 
 56 7 
 
 2 
 
 10 
 
 100 
 
 65 
 
 2 
 
 10 
 
 50f 
 
 18 
 
 10f 
 
 50 
 
 10-25 
 
 200-250 
 
 100-150 
 
 5 5 
 
 8 
 
 80 
 
 74 
 
 2 
 
 10 
 
 40f 
 
 18f 
 
 iot 
 
 40 
 
 10-25 
 
 200-250 
 
 100-150 
 
 5 10l/ 2 
 
 9 
 
 50 
 
 129 111/4 
 
 I 
 
 15 
 
 50 
 
 25 
 
 71/2 
 
 50 
 
 10 
 
 100-150 
 
 80-100 
 
 8 6 
 
 10 
 
 50 
 
 125 10 
 
 ] 
 
 15 
 
 50 
 
 25 
 
 71/2 
 
 50 
 
 10 
 
 100-150 
 
 80-100 
 
 8 6 
 
 11 
 
 50 
 
 121 2 
 
 1 
 
 5 
 
 75 
 
 15 
 
 15 
 
 75 
 
 lH/2 
 
 225 
 
 125 
 
 8 4 
 
 12 
 
 * Four-girder ladle crane, t On each trolley. 
 
 4. Divided equally between 2 motors for series-parallel control. 
 
 1. Pawling & Harnischieger; 2. Alliance Mach. Co.; 3. Morgan Ea- 
 glneering Co.; 4. Midvale Steel Co., Phila.; 5. Homestead Steel Works, 
 Munhall, Pa.; 6. Indiana Steel Co., Gary, Ind.; 7. Oregon Ry. & Nav. 
 Co., Portland, Ore.; 8. El Paso & S. W. Ry., El Paso, Tex.; 9. C. & E. I. 
 Ry., Danville, 111.; 10. 3d Ave. Ry., N. Y. City; 11. United Rys. Co., 
 Baltimore; 12. Carnegie Steel Co., Youngstown, Ohio. 
 
 A 150-ton Pillar-crane was erected in 1893 on Finnieston Quay, 
 Glasgow. The jib is formed of two steel tubes, each 39 in. diam. and 90 
 ft. long. The radius of sweep for heavy lifts is 65 ft. The jib and its load 
 are counterbalanced by a balance-box weighted with 100 tons of iron and 
 steel punchings. In a test a 130-ton load was lifted at the rate of 4 ft. per 
 minute, and a complete revolution made with this load in 5 minutes. 
 Eng'g News, July 20, 1893. 
 
 Compressed-air Traveling-cranes. Compressed-air overhead travel- 
 ing-cranes have been built by the Lane & Bodley Co., of Cincinnati. 
 They are of 20 tons nominal capacity, each about 50 ft. span and 400 ft. 
 length of travel, and are of the triple-motor type, a pair of simple reversing- 
 engines being used for each of the necessary operations, the pair of engines 
 for the bridge and the pair for the trolley travel being each 5-inch bore by 
 7-inch stroke, while the pair for hoisting is 7-inch bore by 9-inch stroke. 
 
LIFTING MAGNETS. 1193 
 
 The air-pressure when required is somewhat over 100 pounds. The air- 
 compressor is allowed to run continuously without a governor, the speed 
 being regulated by the resistance of the air in a receiver. An auxiliary 
 receiver is placed on each traveler, whose object is to provide a supply 
 of air near the engines for immediate demands and independent of the 
 hose connection. Some of the advantages said to be possessed by this 
 type of crane are: simplicity; absence of all moving parts, excepting 
 those required for a particular motion when that motion is in use; no 
 danger from fire, leakage, electric shocks, or freezing; ease of repair: 
 variable speeds and reversal without gearing; almost entire absence of 
 noise; and moderate cost. 
 
 Quay-cranes. An illustrated description of several varieties of sta- 
 tionary and traveling cranes, with results of experiments, is given in a 
 paper on Quay-cranes in the Port of Hamburg by Chas. Nehls, Trans. 
 A. S. C. E., 1893. 
 
 Hydraulic Cranes, Accumulators, etc. See Hydraulic Pressure 
 Transmission, page 812, ante. 
 
 Electric versus Hydraulic Cranes for Docks. A paper by V. L. 
 Raven, in Trans. A. S. M. E., 1904, describes some tests of capacity and 
 efficiency of electric and hydraulic power plants for dock purposes at Mid- 
 dlesbrough, Eng, In loading two cargoes of rails, weighing respectively 
 1210 and 1225 tons, the first was done with a hydraulic crane, in 7 hours, 
 with 3584 Ibs. of coal burned in the power station, and the second with 
 an electric crane in 5V4 hours, with 2912 Ibs. of coal. The total cost in- 
 cluding labor, per 100 tons, was 327 pence with the hydraulic and 245 
 pence for the electric crane, a saving by the latter of 25 %. 
 
 Loading and Unloading and Storage Machinery for coal, ore, etc., 
 is described by G. E. Titcomb in Trans. A. S. M. E., 1908. The paper 
 illustrates automatic ore unloaders for unloading ore from the hold of a 
 vessel and loading it onto cars, and car-dumping machinery, by which 
 a 50-ton car of coal is lifted, turned over and its contents discharged 
 through a chute into a vessel. Methods of storage of coal and of re- 
 loading it on cars are also described. 
 
 Power Required for Traveling-Cranes and Hoists. Ulrich Peters, 
 in Machy, Nov. 1907, develops a series of formulse for the power re- 
 quired to hoist and to move trolleys on cranes. The following is a brief 
 abstract. Resistance to be overcome in moving a trolley or crane- 
 bridge. PI = rolling friction of trolley wheels, Pz = journal friction 
 of wheels or axles, Ps = inertia of trolley and load. P = sum of these 
 
 resistances=P 1 +P 2 4-P 3 = (r+L) (&&& + in which T= weight 
 
 of trolley, L = load, ./i = coeff. of rolling, friction, about 0.002, (0.001 to 
 0.003 for cast iron on steel); / 2 = coeff. of journal friction, = 0.1 for start- 
 ing and 0.01 for running, assuming a load on brasses of 1000 to 3000 Ib. 
 per sq. in.; [fz is more apt to be 0.05 unless the lubrication is perfect. See 
 Friction and Lubrication, W. K.] d = diam. of journal; D = diam. of 
 wheels; v = trolley speed in ft. per min.; t = time in seconds in which 
 the trolley under full load is required to come to the maximum ^speed. 
 Horse-power = sum of the resistances X speed, ft. per min. * 33,000. 
 
 Force required for hoisting and lowering: Fh = actual hoisting force, 
 F = theoretical force or pull, L = load, v = speed in ft. per min. of 
 the rope or chain, c = hoisting speed of the load L, c/v = transmission 
 ratio of the hoist, e = efficiency = FQ/F^. The actual work to raise 
 the load per minute = Fhv = Lc = F v -*- e. The efficiency e is the 
 product of the efficiencies of all the several parts of the hoisting mech- 
 anism, such as sheaves, windlass, gearing, etc. Methods of calculating 
 these efficiencies, with examples, are given at length in the original paper 
 by Mr. Peters. 
 
 Lifting Magnets. (From data furnished by the Electric Controller 
 and Mfg. Co., Cleveland, and the Cutler-Hammer Clutch Co., Milwaukee). 
 Lifting magnets first came into use about 1898. They have had wide 
 application for handling pig iron, scrap, castings, etc. A lifting magnet 
 comprises essentially a maynet winding, a pole-piece, a shoe and a pro- 
 tecting case, which is ribbed to afford ample radiating surface to dissi- 
 pate the heat generated in operation. The winding usually consists of 
 coils, each wound with copper ribbon and insulated with asbestos. The 
 insulation must be designed to withstand a higher voltage than the line 
 
1194 
 
 HOISTING AND CONVEYING. 
 
 voltage, due to the inductive kick when the circuit is opened. The weaf- 
 ing plate, which takes the shocks incident to picking up the load, is usually 
 made of manganese steel. The shape of the pole piece or lifting surface of 
 the magnet must be varied, as the same shape is not usually applicable 
 to all classes of materials. For handling pig iron, scrap, etc., a concave 
 pole surface is usually superior to a flat one, which is adapted to hand- 
 ling plates or flat material of similar character, and which bear equally 
 on the piece to be lifted at both the edge and center. A test of a lift- 
 ing magnet made at the works of the Youngstown Sheet and Tube Co., 
 in 1907, showed the following results: 
 
 Total pig iron unloaded, 109,350 pounds; weight of average lift, 785 
 pounds; time required, 2 hours. 15 minutes; current on magnet, 1 hour 
 15 minutes; current required, 30 amperes. 
 
 The No. 3 and No. 4 magnets are particularly fitted for use on steam- 
 driven locomotive cranes, and when so used are usually supplied with 
 current from a small steam-driven generator set mounted on the crane, 
 steam being drawn from the boiler of the crane. Nos. 5 and 6 are adapted 
 for use with overhead electric traveling cranes in cases where large lifts 
 and high speed of handling are essential. 
 
 SIZES AND CAPACITIES OF THE ELECTEIC CONTROLLER & MFG. Co.'s 
 TYPE S-A LIFTING MAGNETS (1909). 
 
 Size. 
 
 Diam. 
 
 Weight. 
 
 Average 
 Current at 
 220 Volts. 
 
 Lifts in Machine Cast 
 Pig Iron. 
 
 Maximum 
 Lift. 
 
 Average 
 Lift. 
 
 3 
 4 
 5 
 6 
 
 In. 
 36 
 43 
 52 
 61 
 
 Lb. 
 2,100 
 3,200 
 4,800 
 6,600 
 
 Amp. 
 
 27 
 35 
 45 
 
 Lb. 
 1,405 
 
 2,180 
 3,087 
 4,589 
 
 Lb. 
 750 
 1,250 
 1,800 
 2,600 
 
 SIZES AND CAPACITIES OF LIFTING MAGNETS (CUTLER-HAMMER), 1908. 
 
 Size, 
 In. 
 
 Weight 
 Lb. 
 
 Maximum* 
 Lifting 
 Capacity, 
 Lb. 
 
 Average 
 Lifting 
 Capacity, 
 
 Current 
 Required 
 at 220 Volts, 
 Amperes. 
 
 Head-room 
 Required, 
 
 10 
 
 75 
 
 800 
 
 100-300 
 
 1 
 
 
 35 
 
 50 
 
 1,650 
 5,000 
 
 5,000 
 20,000 
 
 500-1,000 
 1,000-2,000 
 
 15-18 
 30-35 
 
 4 
 6 
 
 *This capacity can be obtained only under the most favorable con- 
 ditions, with complete magnetic contact between the magnet and the 
 piece to be lifted. 
 
 The capacity of a lifting magnet in service depends on many other 
 factors than the design of the magnet. Most important is the character 
 of the material handled. Much more can be handled at a single lift 
 with material like billets, ingots, etc., than with scrap, wire, pig iron, 
 etc. The speed of the crane, from which the magnet is suspended, and 
 the distance it must transport the material are also important factors to 
 be considered in calculating the capacity of a given magnet under given 
 conditions. The following results have been selected from a great num- 
 ber of tests of the Electric Controller and Mfg. Co.'s No. 2 Type S magnets 
 in commercial service, and represent what is probably average practice. 
 It should be borne in mind that the average lift is determined from a large 
 number of lifts, including lifts made from a full car of, say, pig iron, 
 where the magnetic conditions are very favorable, and also the " lean " 
 lifts where the car is nearly empty, and magnetic conditions unfavorable; 
 the magnet can reach only a few pigs at one time on the lean lifts, with a 
 consequent heavy decrease in the size of the load. The average lift is 
 therefore less than the maximum lift in handling a given lot 9f material. 
 
 When operated from an ordinary electric overhead traveling crane a 
 magnet of the type used in these trials will handle from 20 to 30 tons 
 per hour of the scrap used by open-hearth furnaces. If operated from 
 a special fast crane, the amount may be somewhat increased. Average 
 lifts in pounds for various materials are as follows: 
 
LIFTING MAGNETS. 
 
 1195 
 
 Skull cracker balls up to 20,000; ingot (or if ground man places 
 
 magnet, two), each, 6,000; billet slabs, 900-6,000. 
 
 The above weights depend on dimensions and whether in pile or 
 stacked evenly. 
 
 Machine cast pig iron, 1,250; sand cast pig iron, 1,150. 
 
 These are values obtained in unloading railway cars, including lean 
 lifts in cleaning up. 
 
 Machine cast pig iron, 1,350; sand cast pig iron, 1,200. 
 
 The above are average lifts from stockpile. 
 
 Heavy melting stock (billets, crop ends of billets, rails or structural 
 shapes, 1,250; boiler plate scrap, 1,100; farmers' scrap (harvesting 
 machinery parts, plow points, etc.), 900; small risers from steel castings, 
 1,600; fine wire scrap, scrap tubing not over 3 ft. long, loose even or 
 lamination scrap, 500; bundled scrap, 1,200; miscellaneous junk deal- 
 ers' scrap, 400-800. 
 
 COMMERCIAL RESULTS WITH A 52-iNCH, 5,000 POUND MAGNET. 
 (Electric Controller & Mfg. Co., 1908.) 
 
 Hoist 
 speed, 
 ft. per 
 
 min. 
 
 Crane. 
 
 Trolley 
 speed, 
 ft. per 
 
 min. 
 
 80 
 80 
 80 
 80 
 200 
 200 
 200 
 200 
 171 
 171 
 171 
 171 
 
 Bridge 
 speed, 
 ft. per 
 
 min. 
 
 315 
 315 
 315 
 315 
 550 
 550 
 550 
 550 
 160 
 160 
 160 
 160 
 
 Distance 
 moved. 
 
 > a 
 
 03 O o 
 
 60 
 35 
 39.3 
 33.9 
 78. 
 78 
 26 
 ' 80 
 25 
 112 
 7 
 5 
 
 8 
 & 
 
 73 
 
 55 
 
 60 
 
 55 
 
 132 
 
 168 
 
 30 
 
 300 
 
 25 
 
 56 
 
 8 
 
 4 
 
 II 
 
 1,650 
 
 1,275 
 
 1,328 
 
 1,234 
 
 1,182 
 
 929 
 
 173 
 
 534 
 
 2,000 
 
 4,000 
 
 1,740 
 
 2,660 
 
 oT . 
 
 II 
 
 75 
 60 
 60 
 55 
 
 135 
 
 190 
 45 
 
 300 
 80 
 
 120 
 15 
 10 
 
 II 
 
 
 
 2 
 3 
 
 5 
 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 
 * 1. Machine cast pig handled from stock pile to charging boxes. 2. 
 Bull heads, ditto. 3. Sand cast pig unloaded from car to stock pile. 
 4. Baled tin and wire untoaded from car to stock pile. 5. Boiler plate 
 scrap handled from stock pile to charging boxes. 6. Farmers' scrap, com- 
 prising knoiiers and butters from threshing and binding machines, sections 
 of cutter bars from mowers, broken steel teeth from hay rakes, plow points, 
 etc. f from stock pile to charging boxes. 7. Small risers from steel castings, 
 handled from stock pile to charging boxes. 8. Laminated plates from 
 armatures and transformers, mixed sizes, from stock pile to charging 
 boxes. 9. Cast iron sewer pipe, 3 feet diameter, weighing 2,000 pounds 
 each, lifted from cars to flat boat. Each pipe had to be blocked and 
 lashed to prevent washing overboard. 10. Pennsylvania Railroad East- 
 River tunnel section castings, convex on one side, concave on other, 
 weighing 4,000 pounds each. Handled from local float to barge for ship- 
 ment. 11. Steel plate i/2-inch X 10 inches X6 feet inches handled 
 from car to float. 12. Steel rails, 40 pounds per yard, 25 feet long. 
 Handled from car to lighter, about 8 rails per lift. 
 
 The above results of tests relate to the Electric Controller & Mfg. 
 Co.'s No. 2 Type " S " magnet, 52 in. diameter and weighing 5200 Ibs. 
 and are the average of a large number of tests made at various plants 
 between the years 1905 and 1908. This type of magnet is being super- 
 seded by the No. 4 Type S-A magnet which is 43 in. diameter, weighs 
 3200 Ibs, and gives substantially the same average lift. 
 
'1196 HOISTING AND CONVEYING. 
 
 TELPHERAGE. 
 
 Telpherage Is a name given to a system of transporting materials !n 
 which the load is suspended from a trolley or small truck running on a 
 cable or overhead rail, and in which the propelling force is obtained 
 from an electric motor carried on the trolley. The trolley, with its 
 motor, is called- a " telpher." A historical and illustrated description 
 of the system is given in a paper by O. M. Clark, in Trans. A. I. E. E., 
 1902. A series of circulars of the Link Belt Co., Philadelphia, show 
 numerous illustrations of the system in operation for handling different 
 classes of materials. Telpherage is especially applicable for moving 
 packages in warehouses, on wharfs, etc. The moving machinery 
 consists of the telpher or the conveying power, with accompanying 
 trailers; the portable electric hoist or the vertical elevating power, and 
 the carriers containing the load. Among the accessories are brakes, 
 switches and controlling devices of many kinds. 
 
 An automatic line is controlled by terminal and intermediate switches 
 which are operated by the men who do the loading and unloading, no 
 additional labor being required. A non-automatic line necessitates a 
 boy to accompany the telpher. The advisability of using the non- 
 automatic rather than the automatic line is usually determined by the 
 distance between stations. 
 
 COAL-HANDLING MACHINERY. 
 
 The following notes and tables are supplied by the Link-Belt Co. 
 
 In large boiler-houses coal is usually delivered from hopper-cars into 
 a track-hopper, about 10 feet wide and 12 to 16 feet long. A feeder set 
 under the track-hopper feeds the coal at a regular rate to a crusher, which 
 reduces it to a size suitable for stokers. 
 
 After crushing, the coal is elevated or conveyed to overhead storage- 
 bins. Overhead storage is preferred for several reasons: 
 
 1. To avoid expensive wheeling of coal in case of a breakdown of the 
 coal-handling machinery. 
 
 2. To avoid running the coal-handling machinery continuously. 
 
 3. Coal kept under cover indoors will not freeze in winter and clog the 
 supply-spouts to the boilers. 
 
 4. It is often cheaper to store overhead than to use valuable ground- 
 space adjacent to the boiler-house. 
 
 5. As distinguished from vault or outside hopper storage, it is cheaper 
 to build steel bins and supports than masonry pits. 
 
 Weight of Overhead Bins. Steel bins of approximately rectangular 
 cross-section, say 10 X 10 feet, will weigh, exclusive of supports, about 
 one-sixth as much as the contained coal. Larger bins, with sloping 
 bottoms, may weigh one-eighth as much as the contained coal. Bag 
 bottom bins of the Berquist type will weigh about one-twelfth as much as 
 the contained coal, not including posts, and about one-ninth as much, 
 including posts. 
 
 Supply-pipes from Bins. The supply-pipes from overhead bins to 
 the boiler-room floor, or to the stoker-hoppers, should not be less than 12 
 inches in diameter. They should be fitted at the top with a flanged cast- 
 ing and a cut-off gate, to permit removal of the pipe when the boilers are 
 to be cleaned or repaired. 
 
 Types of Coal Elevators. Coal elevators consist of buckets of 
 various shapes attached to one or more strands of link-belting or chain, or 
 to rubber belting. The buckets may either be attached continuously or 
 at intervals. The various types are as follows: 
 
 Continuous bucket elevators consist usually of one strand of chain and 
 two sprocket-wheels with buckets attached continuously to the chain. 
 Each bucket after passing the head wheel acts as a chute to direct the 
 flow from the next bucket. This type of elevator will handle the larger 
 sizes of coal. It runs at slow speeds, usually from 90 to 175 feet per min- 
 ute, and has a maximum capacity of about 120 tons per hour. 
 
 Centrifugal discharge elevators consist usually of a single strand of chain, 
 Vvith the buckets attached thereto at intervals. They are used to handle 
 the smaller sizes of coal in small quantities. They run at high speeds, 
 usuallv 34 to 40 revolutions of the head wheel per minute, and have a 
 capacity up to 40 tons per hour. 
 
COAL-HANDLING MACHINERY. 1197 
 
 Perfect discharge elevators consist of two strands of chain, with buckets 
 
 at intervals between them. A pair of idlers set under the head wheels 
 cause the buckets to be completely inverted, and to make a clean delivery 
 into the chutes at the elevator head. This type of elevator is useful in 
 handling material which tends to cling to the buckets. It runs at slow 
 speeds, usually less than 150 feet per minute. The capacity depends on 
 the size of the buckets. 
 
 Combined Elevators and Conveyors are of the following types: 
 
 Gravity discharge elevators, consisting of two strands of chain, with 
 spaced V-shaped buckets fastened between them. After passing the head 
 wheels the buckets act as conveyor-flights and convey the coal in a trough 
 to any desired point. This is the cheapest type of combined elevator and 
 .conveyor, and is economical of power. A machine carrying 100 tons of 
 coal per hour, in buckets 20 inches wide, 10 inches deep, and 24 inches long, 
 spaced 3 feet apart, requires 5 H.P. when loaded and 1 1/2 H.P. when empty 
 for each 100 feet of horizontal run, and 1/9 H.P. for each foot of vertical lift. 
 
 Rigid bucket-carriers consist of two strands of chain with a special 
 bucket rigidly fastened between them. The buckets overlap and are so 
 shaped that they will carry coal around three sides of a rectangle. The 
 coal is carried to any desired point and is discharged by completely 
 inverting the bucket over a turn-wheel. 
 
 Pivoted bucket-carriers consist of two strands of long pitch steel chain to 
 which are attached, in a pivotal manner, large malleable iron or steel 
 buckets so arranged that their adjacent lips are close together' or overlap. 
 Overlapping buckets require special devices for changing the lap at the 
 corner turns. Carriers in which the buckets do not overlap should be 
 fitted with auxiliary pans or buckets, arranged in such a manner as to 
 catch the spill which falls between the lips at the loading point, and so 
 shaped as t9 return the spill to the buckets at the corner turns. Pivoted 
 bucket-carriers will carry coal around four sides of a rectangle, the buckets 
 being dumped on the horizontal run by striking a cam suitably placed. 
 Buckets for these carriers are usually of 2 ft. pitch, and range in width 
 from 18 in. to 48 in. They run at low speeds, usually not over 50 ft. per 
 minute, 40 ft. per minute being most usual. At the latter speed, the 
 capacities when handling coal vary from 40 tons per hour for the 18 in. 
 width to 120 tons for the 48 in. width. On account of the superior con- 
 struction of these carriers and the slow speed at which they run, they are 
 economical of power and durable. The rollers mounted on the chain 
 joints are usually 6 in. diameter, but for severe duty 8-in. rollers are often 
 used. It is usual to make these hollow to carry a quantity of oil for 
 internal lubrication. 
 
 Coal Conveyors. Coal conveyors are of four general types, viz., 
 scraper or flight, bucket, screw, and belt conveyors. 
 
 The flight conveyor consists of a trough of any desired cross-section and 
 a single or double strand of chain carrying scrapers or flights of approxi- 
 mately the same shape as the trough. The flights push the coal ahead of 
 them in the trough to any desired point, where it is discharged through 
 openings in the bottom of the trough. 
 
 For short, low-capacity conveyors, malleable link hook-joint chains 
 are used. For heavier service, malleable pin-joint chains, steel link chains, 
 or monobar, are required. For the heaviest service, two strands of steel 
 link chain, usually with rollers, are used. 
 
 Flight conveyors are of three types: plain scraper, suspended flight, and 
 roller flight. 
 
 In the plain scraper conveyor, the flight is suspended from the chain 
 and drags along the bottom of the trough. It is of low first cost and is 
 useful where noise of operation is not objectionable. It has a maximum 
 capacity of about 30 tons per hour, and requires more power than either 
 of the other two types of flight conveyors. 
 
 Suspended flight conveyors use one or two strands of chain. The flights 
 are attached to cross-bars having wearing-shoes at each end. These wear- 
 ing-shoes slide on angle-iron tracks on each side of the conveyor trough. 
 The flights do not touch the trough at any point. This type of conveyor 
 is used where quietness of operation is a consideration. It is of higner 
 first cost than the plain scraper conveyor,, but requires one-fourth less 
 power for operation. It is economical up to a capacity of about 80 tons 
 per hour. 
 
1198 
 
 HOISTING AND CONVEYING. 
 
 The roller flight conveyor is similar to the suspended flight, except 
 that the wearing-shoes are replaced by rollers. It is highest in first 
 cost of all the flight conveyors, but has the advantages of low power 
 consumption (one-half that of the scraper), low stress in chain, long 
 life of chain, trough, and flights, and noiseless operation. It has an 
 economical maximum capacity of about 120 tons per hour. 
 
 The following formula gives approximately the horse-power at the 
 head wheel required to operate flight conveyors: 
 
 H.P, = (ATL + BWS) -- 1000. 
 
 T = tons of coal per hour; L = length of conveyor in feet, center to 
 center; W = weight of chain, flights, and shoes (both runs) in pounds; 
 iS = speed in feet per minute ; A and B constants depending on angle 
 of incline from horizontal. See example below. 
 
 EXAMPLE. Required the H.P. for a monobar conveyor 200 ft. 
 center to center carrying 100 tons of coal per hour, up a 10 incline at 
 a speed of 100 feet per minute. Conveyor has No. 818 chain and 8 X19 
 suspended flights, spaced 18 inches apart. 
 
 H P 0-5 X 100X200 + 0.008 (400 X 5.7 + 267 X 15.55) X 100 _ 15 15 
 
 1000 
 
 The following table shows the conveying capacities of various sizes 
 of flights at 100 feet per minute in tons, of 2000 lb., per hour. The 
 values are true for continuous feed only. 
 
 Size of 
 Flight. 
 
 Horizontal Conveyors, Tons. 
 
 Inclined Conveyors, Tons. 
 
 Flight 
 Every 
 16". 
 
 Flight 
 Every 
 18". 
 
 Flight 
 Every 
 24". 
 
 Pounds 
 Coal per 
 Flight. 
 
 10 
 Flights 
 Every 
 
 20 
 Flights 
 Every 
 
 30 
 Flights 
 Every 
 24". 
 
 6X14 
 8X19 
 10X24 
 10X30 
 10X36 
 10X42 
 
 69.75 
 
 62 
 130 
 
 46.5 
 97.5 
 172.5 
 220 
 268 
 315 
 
 31 
 65 
 115 
 147 
 179 
 210 
 
 40.5 
 78 
 150 
 
 184 
 225 
 264 
 
 31.5 
 62 
 120 
 146 
 177 
 210 
 
 22.5 
 52 
 90 
 116 
 142 
 167 
 
 
 
 
 
 
 
 
 Bucket Conveyors. Rigid bucket-carriers are used to convey large 
 quantities of coal over a considerable distance when there is no inter- 
 mediate point of discharge. These conveyors are made with two strands 
 of steel roller chain. They are built to carry as much as 10 tons of coal 
 per minute. 
 
 Screw Conveyors. Screw conveyors consist of a helical steel flight, 
 either in one piece or in sections, mounted on a pipe or shaft, and running 
 in a steel or wooden trough. These conveyors are made from 4 to 18 
 inches in diameter, and in sections 8 to 12 feet long. The speed ranges 
 from 20 to 60 revolutions per minute and the capacity from 10 to 30 tons 
 of coal per hour. It is not advisable to use this type of conveyor for coal, 
 as it will only handle the smaller sizes and the nights are very easily dam- 
 aged by any foreign substance of unusual size or shape. 
 
 Belt Conveyors. Rubber and cotton belt conveyors are used for 
 handling coal, ore, sand, gravel etc., in all sizes. They combine a high 
 carrying capacity with low power consumption. 
 
 In some cases the belt is flat, the material being fed to the belt at its 
 center in a narrow stream. In the majority of cases, however, the belt 
 is troughed by means of idler pulleys set at an angle from the horizontal 
 and placed at intervals along the length of the belt. Rubber belts are 
 often made more flexible for deep troughing by removing some of the 
 layers of cotton from the belt and substituting therefor an extra thickness 
 of rubber. 
 
 Belt conveyors may be used for elevating materials up to about 23 
 incline. On greater inclines the material slides back on the belt and spills. 
 With many substances it is important to feed the belt steadily if the con- 
 veyor stands at or near the limiting angle. If the flow is interrupted 
 the material may slide back on the belt. 
 
 Belt conveyprs are run at any speed from 200 to 800 feet per minute, 
 and are made in widths varying from 12 inches to 60 inches. 
 
CONVERGES. 
 
 1199 
 
 Values of A and B. 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 
 2 
 
 6 
 8 
 
 0.343 
 0.378 
 0.40 
 0.44 
 0.47 
 
 0.01 
 0.01 
 0.01 
 0.01 
 0.01 
 
 10 
 14 
 18 
 22 
 26 
 
 0.50 
 0.57 
 0.63 
 0.69 
 0.74 
 
 0.01 
 0.01 
 0.009 
 0.009 
 0.009 
 
 30 
 34 
 38 
 42 
 46 
 
 0.79 
 0.84 
 0.88 
 0.92 
 0.95 
 
 0.009 
 0.008 
 0.008 
 0.007 
 0.007 
 
 For suspended flight conveyors take B as 0.8 and for roller flights as 
 0.6, of the values given in the table. 
 
 Weight of Chain in Pounds per Foot. 
 
 LINK-BELTING. 
 
 MONOBAR. 
 
 Chain 
 No. 
 
 Pitch of Flights, Inches. 
 
 Chain 
 No.* 
 
 Pitch of Flights, Inches. 
 
 12 
 
 18 
 
 24 
 
 36 
 
 12 
 
 18 
 
 24 
 3 6 
 
 36 
 
 48 
 
 54 
 
 72 
 
 78 
 88 
 85 
 103 
 108 
 110 
 114 
 122 
 124 
 
 2.4 
 2.8 
 3.1 
 4.6 
 4.9 
 5.6 
 6.3 
 8.1 
 8.9 
 
 2.3 
 2.7 
 
 2.8 ' 
 4.4 
 4.7 
 5.2 
 6.0 
 7.7 
 8.4 
 
 2.26 
 2.6 
 2.7 
 
 4.3 
 4.4 
 4.9 
 5.9 
 7.4 
 8.2 
 
 2.2 
 2.5 
 2.6 
 4.2 
 4'.1 
 4.7 
 5.7 
 7.2 
 7.9 
 
 612 
 618 
 818 
 824 
 1018 
 1024 
 1224 
 1236 
 1424 
 
 3.9 
 
 
 3 5 
 
 
 
 
 3.0 
 S 7 
 
 
 2.8 
 5 5 
 
 
 
 2.7 
 5.3 
 
 
 
 
 
 4 9 
 
 
 4.7 
 
 
 4.6 
 
 ' '8.8* 
 13.8 
 11.34 
 19.4 
 
 
 11.5 
 
 '9!6 
 14.7 
 
 10.7 
 
 ii*8 
 
 ' 9.07 
 14.04 
 
 10.4 
 
 
 
 ?0 5 
 
 
 19.7 
 
 
 * In monobar the first one or two figures in the number of the chain 
 denote the diameter of the chain in eighths of an inch. The last two 
 figur.es denote the pitch in inches. 
 
 PIN CHAINS. 
 
 ROLLER CHAINS. 
 
 No. 
 
 Pitch of Flights, Inches. 
 
 No. 
 
 Pitch of Flights, Inches. 
 
 12 
 
 18 
 
 24 
 
 36 
 
 12 
 7.7 
 9.5 
 10.5 
 
 18 
 6.9 
 8.8 
 9.5 
 
 24 
 "672 
 8.0 
 9.0 
 
 36 
 T7 
 7.5 
 7.8 
 
 
 
 
 720 
 730 
 825 
 
 5.9 
 6.9 
 9.6 
 
 5.6 
 6.6 
 9.3 
 
 5.4 
 6.4 
 9.1 
 
 5.3 
 6.3 
 8.9 
 
 1112 
 1113 
 1130 
 
 
 
 
 Weight of Flights with Wearing-shoes and Bolts. 
 
 Size, Inches. 
 
 Steel. 
 
 Malleable Iron. 
 
 Suspended Flights. 
 
 Size. 
 
 Weight, Lb. 
 
 4X10 
 
 3.5 
 
 4.3 
 
 6X14 
 
 12.37 
 
 4X12 
 
 3.9 
 
 4.7 
 
 8X19 
 
 15.55 
 
 5X10 
 
 4.1 
 
 5.2 
 
 10X24 
 
 25.57 
 
 5X12 
 
 4.6 
 
 5.7 
 
 10X30 
 
 29.37 
 
 5X15 
 
 5.8 
 
 5.9 
 
 10X36 
 
 33.17 
 
 6X18 
 
 8.1 
 
 9.2 
 
 10X42 
 
 34.97 
 
 8X18 
 
 10.1 
 
 12.7 
 
 
 
 8X20 
 
 11.0 
 
 13.4 
 
 
 
 8X24 
 
 12.6 
 
 14.4 
 
 
 
 10X24 
 
 15.2 
 
 17.4 
 
 
 
 Capacity of Belt Conveyors in Tons of Coal per Hour. 
 
 Width 
 of 
 
 S: 
 
 i 
 
 18 
 
 Velocity, Feet per 
 Minute. 
 
 Width 
 of 
 Belt, 
 Ins. 
 
 Velocity, Feet per Minute. 
 
 300 
 
 34 
 47 
 62 
 78 
 
 350 
 
 400 
 
 300 
 
 350 
 
 400 
 
 450 
 
 500 
 
 72 
 91 
 
 82 
 104 
 
 20 
 
 24 
 30 
 36 
 
 96 
 
 139 
 218 
 315 
 
 112 
 162 
 254 
 368 
 
 128 
 186 
 290 
 420 
 
 210 
 326 
 472 
 
 520 
 
1200 
 
 HOISTING AND CONVEYING. 
 
 For materials other than coal, the figures in the above table should be 
 multiplied by the coefficients given in the table below: 
 
 Material. 
 
 Coefficient. 
 
 Material. 
 
 Coefficient. 
 
 Ashes (damp) 
 
 86 
 
 Earth 
 
 1.4 
 
 Cement 
 
 1.76 
 
 Sand 
 
 1.8 
 
 Clay 
 
 1.26 
 
 Stone (crushed) 
 
 2.0 
 
 Coke 
 
 0.60 
 
 
 
 Belt Conveyor Construction. (C. K. Baldwin, Trans. A. S. M. E.^ 
 1908.) The troughing idlers should be spaced as follows, depending 
 on the weight of the material carried: 
 
 Belt width 12-16 in. 18-22 in. 24-30 in. 32-36 in. 
 Spacing, ft. 4>^-5 4-4 Y 2 3^-4 3-3 Y 2 
 
 The stress in the belt should not exceed 18 to 20 Ib. per inch of width 
 per ply with rubber belts. This may be increased about 20% with 
 belts in which 28 oz. duck is used. Where the power required is small 
 the stiffness of the belt fixes the number of plies. The minimum num- 
 ber of plies is as follows: 
 
 Belt width, in. 12-14 16-20 22-28 30-36 
 
 Minimum plies 3456 
 
 Pulleys of small diameter should be avoided on heavy belts, or the con- 
 stant bending of the belt under heavy stress will cause the friction to 
 lose its hold and destroy the belt. In many cases it is advisable to 
 cover the driving pulley with a rubber lagging to increase the tractive 
 power, particularly in dusty places. The minimum size of driving 
 pulleys to be used is shown in the table below. 
 
 Smallest Diameter of Driving Pulleys for Belt Conveyors. 
 
 Width of 
 Belt. 
 
 Diameter 
 of Pulley. 
 
 Width of 
 Belt. 
 
 Diameter of 
 Pulley. 
 
 Width of 
 Belt. 
 
 Diameter of 
 Pulley. 
 
 In. 
 12 
 14 
 16 
 
 16 
 
 In. 
 16-18 
 16-18 
 20-24 
 20 24 
 
 In. 
 22 
 24 
 26 
 28 
 
 In. 
 20-30 
 24-30 
 24-30 
 24-30 
 
 In. 
 32 
 34 
 36 
 
 In. 
 30-36 
 30-42 
 30-48 
 
 20 
 
 20-24 
 
 30 
 
 30-36 
 
 
 
 Horse-power to Drive Belt Conveyors. (C. K. Baldwin, Trans. 
 A. S. M. E., 1908.) The power required to drive a belt conveyor de- 
 pends on a great variety of conditions, as the spacing of idlers, type of 
 drive, thickness of belt, etc. In figuring the power required, the belt 
 should run no faster than is necessary to carry the desired load.f If it 
 should be necessary to increase the speed, the load should be increased 
 in proportion and the power figured accordingly. 
 
 For level conveyors H.P. = CX TXL + 1000. , 
 
 For inclined conveyors 
 
 H.P. = (C X T XL -J- 1000) + (T XH -5- 1000). 
 
 C ~ power constant from table below; T = load, tons per hour; L = 
 length of conveyor, center to center, ft. ; H = vertical height material is 
 lifted, ft.; S = belt speed, ft, per minute; B = width of belt, in. 
 
 For each movable or fixed tripper add horse-power in column 3 of 
 table. Add 20% to horse-power for each conveyor under 50 ft. long. 
 Add 10% to horse-power for each conveyor between 50 ft. and 100 ft. 
 long. The formulae above do not include gear friction, should the 
 conveyor be gear-driven. 
 
 When horse-power ana speed are known the stress in the belt in pounds 
 per inch of width is 
 
 Stress .H.P.XM.OOO. 
 
 From this the number of plies can be found, using 20 Ib. per ply per 
 inch of width as a maximum for rubber belts. 
 
 Relative Wearing Power of Conveyor Belts. (T. A. Bennett, 
 Trans. A. S. M. E., 1908.) Different materials used in the construction 
 
PNEUMATIC CONVEYING. 
 Constants for Formulae for Belt Conveyors. 
 
 1201 
 
 ; 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 Width of 
 Belt, 
 In. 
 
 C for Mate- 
 rial Weigh- 
 ing from 25 
 Lb. to 75 Lb. 
 per Cu. Ft. 
 
 C for Mate- 
 rial Weigh- 
 ing from 75 
 Lb. to 125Lb. 
 per Cu. Ft. 
 
 H.P. Re- 
 quired for 
 Each Mov- 
 able or 
 Fixed 
 Tripper. 
 
 Minimum 
 Plies of 
 Belt. 
 
 Maximum 
 Plies of 
 Belt. 
 
 12 
 
 0.234 
 
 0.147 
 
 1/2 
 
 3 
 
 4 
 
 14 
 
 0.226 
 
 0.143 
 
 1/2 
 
 3 
 
 4 
 
 16 
 
 0.220 
 
 0.140 
 
 3/4 
 
 4 
 
 5 
 
 18 
 
 0.209 
 
 0.138 
 
 1 
 
 4 
 
 5 
 
 20 
 
 0.205 
 
 0.136 
 
 1 1/4 
 
 4 
 
 6 
 
 22 
 
 0.199 
 
 0.133 
 
 1 1/2 
 
 5 
 
 6 
 
 24 
 
 0.195 
 
 0.131 
 
 13/4 
 
 5 
 
 7 
 
 26 
 
 0.187 
 
 0.127 
 
 2 
 
 5 
 
 7 
 
 28 
 
 0.175 
 
 0.121 
 
 21/4 
 
 5 
 
 8 
 
 30 
 
 0.167 
 
 0.117 
 
 21/2 
 
 6 
 
 8 
 
 32 
 
 0.163 
 
 0.115 
 
 23/4 
 
 6 
 
 9 
 
 34 
 
 0.161 
 
 0.114 
 
 3 
 
 6 
 
 10 
 
 36 
 
 0.157 
 
 0.112 
 
 31/4 
 
 6 
 
 10 
 
 Of conveyors were subjected to the uniform action of a sand blast for 45 
 minutes, and the relative abrasive resisting qualities were found to be as 
 follows, taking the volume of rubber belt worn away as 1.0: 
 
 Rubber belt 1.0 Woven cotton belt, high grade 6 . 5 
 
 Rolled steel bar 1.5 Stitched duck, high grade 8.0 
 
 Cast iron 3.5 Woven cotton belt, low grade, 9.0 to 
 
 Balata belt, including gum cover 5.0 15.0 
 
 A Symposium on Hoisting and Conveying was presented at the Detroit 
 meeting of the A. S. M. E, 1908 (Trans., vol. xxx.), in papers by G. E. 
 Titcomb, S. B. Peck, C. K. Baldwin, C. J. Tomlinson and E. J. Haddock. 
 Among the subjects discussed are the loading and unloading of cargo 
 steamers; car unloaders; storing of ore and coal; continuous conveying of 
 merchandise; conveying in a Portland cement plant, and suspension 
 cable ways. 
 
 PNEUMATIC CONVEYING 
 
 Pneumatic Conveying. A pneumatic conveying system consists of 
 a pipe line, a feeding hopper, a blower or exhauster, and a receiver. It 
 is used for conveying grain, slack coal, sawdust, shavings, and other 
 light material. Grain has been carried over 2,000 ft. Iwrizontally and 
 raised to any desired height. The pressure system is simpler and 
 requires less pipe than the vacuum system, but the latter is more com- 
 mon and is adapted to a greater variety of conditions. The principal 
 advantages of the pneumatic system, as against all types of mechanical 
 conveyors, are simplicity, adaptability to peculiar conditions, the little 
 attention required, few repairs, and shut-downs. (For details of 
 apparatus, etc., see bulletins of the Connersville Blower Co.) 
 
 Pneumatic Postal Transmission. A paper by A. Falkenau (Eng'rs 
 Club of Philadelphia, April, 1894), entitled the "First United States 
 Pneumatic Postal System," gives a description of the system used in 
 London and Paris, and that recently introduced in Philadelphia between 
 the main post-office and a substation. In London the tubes are 2 ]4 and 
 3-inch lead pipes laid in cast-iron pipes for protection. The carriers 
 used in 2 J^-inch tubes are but 1 H inches diameter, the remaining space 
 being taken up by packing. Carriers are despatched singly. First, 
 vacuum alone was used ; later, vacuum and compressed air. The tubes 
 used in the Continental cities in Europe are wrought iron, the Paris tubes 
 being 2 y 2 inches diameter. There the carriers are despatched in trains 
 of six to ten, propelled by a piston. In Philadelphia the size of tube 
 adopted is 6 y% inches, the tubes being of cast iron bored to size. The 
 lengths of the outgoing and return tubes are 2928 feet each. The pressure 
 
1202 HOISTING AND CONVEYING. 
 
 at the main station is 7 lb., at the substation 4 lb., and at the end of the 
 return pipe atmospheric pressure. The compressor has two air-cylinders 
 18 X 24 in. Each carrier holds about 200 letters, but 100 to 150 are 
 taken as an average. Eight carriers may be despatched in a minute, 
 giving a delivery of 48,000 to 72,000 letters per hour.* The time 
 required in transmission is about 57 seconds. 
 
 Pneumatic postal transmission tubes were laid in 1898 by the Batcheller 
 Pneumatic Tube Co. between the general post-offices in New York and 
 Brooklyn, crossing the East River on the Brooklyn bridge. The tubes 
 are cast iron, 12-ft. lengths, bored to 8 1/8 in. diameter. The joints are 
 bells, calked with lead and yarn. There are two tubes, one operating 
 in each direction. Both lines are operated by air-pressure above the 
 atmospheric pressure. One tube is operated by an air-compressor in the 
 New York office and the other by one located in the Brooklyn office. 
 
 The carriers are 24 in. long, in the form of a cylinder 7 in. diameter, 
 and are made of steel, with fibrous bearing-rings which fit the tube. Each 
 carrier will contain about 600 ordinary letters, and they are despatched 
 at intervals of 10 seconds in each direction, the time of transit between 
 the two offices being 31/2 minutes, the carriers travelling at a speed of 
 from 30 to 35 miles per hour. 
 
 One of the air-compressors is of the duplex type and has two steam- 
 cylinders 10 X 20 in. and two air-cylinders 24 X 20 in., delivering 
 1570 cu. ft. of free air per minute, at 75 r.p.m. The power is about 50 H.P. 
 
 Two other duplex air-compressors have steam-cylinders 14 X 18 in. 
 and air-cylinders 261/4X18 in. They are designed for 80 to 90 r.p.m. 
 and to compress to 20 lb. per sq. in. 
 
 Another double line of pneumatic tubes has been laid between the 
 main office and Postal Station H, Lexington Ave. and 44th St., in New 
 York City. This line is about 31/2 miles in length. There are three 
 intermediate stations. The carriers can be so adjusted when they are 
 put into the tube that they will traverse the line and be discharged auto- 
 matically from the tube at the station for which they are intended. The 
 tubes are of the same size as those of the Brooklyn line and are operated 
 in a similar manner. The initial air-pressure is about 12 to 15 lb. On 
 the Brooklyn line it is about 7 lb. 
 
 There is also a tube system between the New York Post-office and the 
 Produce Exchange. For a very complete description of the system and 
 its machinery see "The Pneumatic Despatch Tube System," by B. C. 
 Batcheller, J. B. Lippincott Co., Philadelphia, 1897. 
 
 WIRE-ROPE HAULAGE. 
 
 Methods for transporting coal and other products by means of wire rope, 
 though varying from each other in detail, may be grouped in five classes: 
 I. The Self-acting or Gravity Inclined Plane. 
 II. The Simple Engine-plane. 
 
 III. The Tail-rope System. 
 
 IV. The Endless-rope System. 
 V. The Cable Tramway. 
 
 The following brief description of these systems is abridged from a 
 pamphlet on Wire-rope Haulage, by Wm. Hildenbrand, C.E., published 
 by John A. Roebling's Sons Co., Trenton, N. J. 
 
 I. The Self-acting Inclined Plane. The motive power for the 
 self-acting inclined plane is gravity; consequently this mode of transport- 
 ing coal finds application only in places where the coal is conveyed from a 
 higher to a lower point and where the plane has sufficient grade for the 
 loaded descending cars to raise the empty cars to an upper level. 
 
 At the head of the plane there is a drum, which is generally constructed 
 of wood, having a diameter of seven to ten feet. It is placed high enough 
 to allow men and cars to pass under it. Loaded cars coming from- the pit 
 are either singly or in sets of two or three switched on the traclf of the 
 plane, and their speed in descending is regulated by a brake on the drum. 
 Supporting rollers, to prevent the rope dragging on the ground, are 
 
 * A report of a U. S. Postal Commission states that up to the present 
 time (1910), the sending and receiving apparatus does not permit the 
 successful operation of carrier service with an interval of less than 
 13 to 15 seconds between carriers, for 6- and 8-in, tubes. 
 
WIRE-ROPE HAULAGE. 1203 
 
 generally of wood, 5 to 6 in. in diameter and 18 to 24 in. long, with 
 
 3/4 to 7/ 8 in. iron axles. The distance between the rollers varies from 15 to 
 30 ft., steeper planes requiring less rollers than those with easy grades. 
 Considering only the reduction of friction and what is best for the preserva- 
 tion of rope, a general rule may be given to use rollers of the greatest 
 possible diameter, and to place them as close as economy will permit 
 
 The smallest angle of inclination at which a plane can be made self- 
 acting will be when the motive and resisting forces balance each other. 
 The motive forces are the weights of the loaded car and of the descending 
 rope. The resisting forces consist of the weight of the empty car and 
 ascending rope, of the rolling and axle friction of the cars, and of the axle 
 friction of the supporting rollers. The friction of the drum, stiffness of 
 rope, and resistance of air may be neglected. A general rule cannot be 
 given, because a change in the length of the plane or in the weight of the 
 cars changes the proportion of the forces; also, because the coefficient ot 
 friction, depending on the condition of the road, construction of the cars, 
 etc., is a very uncertain factor. 
 
 For working a plane with a 5/ 8 _in. steel rope and lowering from one to 
 four pit cars weighing empty 1400 Ib. and loaded 4000 lb., the rise in 100 ft. 
 necessary to make the plane self-acting will be from about 5 to 10 ft., 
 decreasing as the number of cars increase, and increasing as the length or 
 plane increases. 
 
 A gravity inclined plane should be slightly concave, steeper at the top 
 than at the bottom. The maximum deflection of the curve should be at 
 an inclination of 45 degrees, and diminish for smaller as well as for steeper 
 inclinations. 
 
 II. The Simple Engine-plane. The name " Engine-plane" is given 
 to a plane on which a load is raised or lowered by means of a single wire 
 rope and stationary steam-engine. It is a cheap and simple method of 
 conveying coal underground, and therefore is applied wherever circum- 
 stances permit it. Under ordinary conditions such as prevail in the 
 Pennsylvania mine region, a train of twenty-five to thirty loaded cars will 
 descend, with reasonable velocity, a straight plane 5000 ft. long on a 
 grade of 1 s/ 4 ft. in 100, while it would appear that 21/4 ft. in 100 is neces- 
 sary for the same number of empty cars. For roads longer than 5000 ft. 
 or containing sharp curves, the grade should be correspondingly larger. 
 
 III. The Tail-rope System. Of all methods for conveying coal 
 underground by wire rope, the tail-rope system has found the most appli- 
 cation. It can be applied under almost any condition. The road may be 
 straight or curved, level or undulating, in one continuous line or with side 
 branches. In general principle a tail-rope plane is the same as an engine- 
 plane worked in both directions with two ropes. One rope, called the 
 *' main rope," serves for drawing the set of full cars outward; the other, 
 called the " tail-rope," is necessary to take back the empty set, which ou 
 a level or undulating road cannot return by gravity. The two drums may 
 be located at the opposite ends of the road, and driven by separate engines, 
 but more frequently they are on the same shaft at one end of the plane, 
 In the first case each rope would require the length of the plane, but in the 
 second case the tail rope must be twice as long, being led from the drum 
 around a sheave at the other end of the plane and back again to its starting- 
 point. When the main rope draws a set of full cars out, the tail-rope drum 
 runs loose on the shaft, and the rope, being attached to the rear car, un- 
 winds itself steadily. Going in, the reverse takes place. Each drum is 
 provided with a brake to check the speed of the train on a down grade and 
 prevent its overrunning the forward rope. As a rule, the tail rope is 
 strained less than the main rope, but in cases of heavy grades dipping out- 
 ward it is possible that the strain in the former may become as large, or 
 even larger, than in the latter, and in the selection of the sizes reference 
 should be had to this circumstance. 
 
 IV. The Endless-rope System. The principal features of this 
 system are as follows: 
 
 1. The rope, as the name indicates, is endless. 2. Motion is given to 
 the rope by a single wheel or drum, and friction is obtained either by a 
 grip-wheel or by passing the rope several times around the wheel. 3. The 
 rope must be kept constantly tight, the tension to be produced by artificial 
 means. It is done in placing either the return-wheel or an extra tension 
 wheel on a carriage and connecting it with a weight hanging over a 
 pulley, or attaching it to a fixed post by a screw which occasionally can be 
 
1204 
 
 HOISTING AND CONVEYING. 
 
 shortened. 4. The cars are attached to the rope by a grip or clutch, 
 which can take hold at any place and let go again, starting and stopping 
 the train at will, without stopping the engine or the motion of the rope 
 5. On a single-track road the rope works forward and backward, but on a 
 double track it is possible to ran it always in the same direction, the full 
 cars going on one track and the empty cars on the other. 
 
 This method of conveying coal, as a rule, has not found as general an in- 
 troduction as the tail-rope system, probably because its efficacy is not so 
 apparent and the opposing difficulties require greater mechanical skill and 
 more complicated appliances. Its advantages are, first, that it requires 
 one-third less rope than the tail-rope system. This advantage, however, 
 is partially counterbalanced by the circumstance that the extra tension in 
 the rope requires a heavier size to move the same load than when a main 
 and tail rope are used. The second and principal advantage is that it is 
 possible to start and stop trains at will without signaling to the engineer. 
 On the other hand, it is more difficult to work curves with the endless sys- 
 tem, and still more so to work different branches, and the constant stretch 
 of the rope under tension or its elongation under changes of temperature 
 frequently causes the. rope to slip on the wheel, in spite of every attention, 
 causing delay in the transportation and injury to the rope. 
 
 Stress in Hoisting-ropes on Inclined Planes. 
 
 (Trenton Iron Co., 1906.) 
 
 
 3 
 
 "3 
 
 18 8 
 
 3d . 
 
 49 
 
 fa*! 
 
 -2 
 
 " C< 
 
 J. 
 
 3 d . 
 
 sl 
 
 J, 
 
 "o 
 
 A i 
 
 s. 
 
 o a 
 
 "1 
 
 .SHJ^ 
 
 feS 
 
 ?! 
 
 Hj3 
 
 IJ 
 
 li 
 
 "H^3 
 
 d 
 
 
 03 O 
 
 ft'C 
 
 . * 
 
 ro o 
 
 X'H 
 
 
 M O 
 
 <D'M 
 
 49 
 
 CU 0>o 
 
 
 
 ^ ^o 
 
 w o 
 
 "5b 
 
 h ^O 
 
 gt 
 
 1 
 
 +3 ^ tfS * 
 
 02 
 
 g 
 
 a 
 
 OQ 
 
 2 
 
 1 
 
 ra 
 
 "Ft! 
 
 
 
 Ft. 
 
 
 
 Ft. 
 
 
 
 
 2 52' 
 
 140 
 
 55 
 
 28 49' 
 
 1003 
 
 110 
 
 47 44' 
 
 1516 
 
 10 
 
 5 43' 
 
 240 
 
 60 
 
 30 58' 
 
 1067 
 
 120 
 
 50 12' 
 
 1573 
 
 15 
 
 8 32' 
 
 336 
 
 63 
 
 33 02' 
 
 1128 
 
 130 
 
 52 26' 
 
 1620 
 
 20 
 
 11 18' 
 
 432 
 
 70 
 
 35 OO 7 
 
 1185 
 
 140 
 
 54 28' 
 
 1663 
 
 25 
 
 14 03' 
 
 527 
 
 75 
 
 36 53' 
 
 1238 
 
 150 
 
 56 W 
 
 1699 
 
 30 
 
 16 42' 
 
 613 
 
 80 
 
 38 40' 
 
 1287 
 
 160 
 
 58 (XK 
 
 1730 
 
 35 
 
 19 18' 
 
 700 
 
 85 
 
 40 22' 
 
 1332 
 
 170 
 
 59 33' 
 
 1758 
 
 40 
 
 21 49' 
 
 782 
 
 90 
 
 42 00' 
 
 1375 
 
 180 
 
 60 57' 
 
 1782 
 
 45 
 
 24 14' 
 
 860 
 
 95 
 
 43 32' 
 
 1415 
 
 190 
 
 62 15' 
 
 1804 
 
 50 
 
 26 34' 
 
 933 
 
 100 
 
 45 OW 
 
 1454 
 
 200 
 
 63 27' 
 
 1822 
 
 The above table is based on an allowance of 40 Ib. per ton for rolling 
 friction, but an additional allowance must be made for stress due to the 
 weight of the rope proportional to the length of the plane. A factor of 
 safety of 5 to 7 should be taken. 
 
 In hoisting the slack-rope should be taken up gently before beginning 
 the lift, otherwise a severe extra strain will be brought on the rope. 
 
 V. Wire-rope Tramways. The methods of conveying products on 
 a suspended rope tramway find especial application in places where a mine 
 is located on one side of a river or deep ravine and the loading station on 
 the other. A wire rope suspended between the two stations forms the 
 track on which material in properly constructed " carriages " or " buggies" 
 is transported. It saves the construction of a bridge or trestlework and is 
 practical for a distance of 2000 feet without an intermediate support. 
 
 There are two distinct classes of rope tramways: 
 
 1. The rope is stationary, forming the track on which a bucket holding 
 the material moves forward and backward, pulled by a smaller endless 
 wire rope. 2. The rope is movable, forming itself an endless line, which 
 serves at the same time as supporting track and as pulling rope. 
 
 Of these two the first method has found more general application, and 
 is especially adapted for long spans, steep inclinations, and heavy loads. 
 
WIRE-ROPE HAULAGE. 1205 
 
 The second method is used for long distances, divided into short spans, 
 and is only applicable for light loads delivered at regular intervals. 
 
 For detailed descriptions of the several systems of wire-rope transporta- 
 tion, see circulars of John A. Roebling's Sons Co., The Trenton Iron Co., 
 A. Leschen & Sons Rope Co. See also paper on Two-rope Haulage Sys- 
 tems, by R. Van A. Norris, Trans. A. S. M. E., xii. 626. 
 
 In the Bleichert System of wire-rope tramways, in which the track rope 
 is stationary, loads up to 2000 Ib. are carried at a speed cf 3 to 4 miles per 
 hour. While the average spans on a level are from 150 to 200 ft., in cross- 
 ing rivers, ravines, etc., spans up to 1500 ft. are frequently adopted. In a 
 tramway on this system at Bingham, Utah, the total length of the line is 
 12,700 ft. with a fall of 1120 ft. The line operates by gravity and carries 
 35 tons per hour. The cost of conveying on this carrier is 73/4 cents per 
 ton of 2000 Ib. for labor and repairs, without any apparent deterioration 
 in the condition of track cables and traction rope. 
 
 The Aerial Wire-rope Tramway of A. Leschen & Sons Co. is of the 
 double-rope type, in which the buckets travel upon stationary track 
 cables and are propelled by an endless traction rope. The buckets are 
 attached to the traction rope by means of clips spaced according to 
 the desired tonnage. The hold on the rope is positive, but the clip is 
 easily removable. The bucket is held in its normal position in the frame 
 by two malleable, iron latches one on each side. A tripping bar 
 engages these latches at the unloading terminal when the bucket dis- 
 charges its material. This operation is automatic and takes place while 
 the carriers are moving. At the loading terminal, the bucket is auto- 
 matically returned to its normal position and latched. Special carriers 
 are provided for the accommodation of any class of material. At each 
 of the terminal stations is a 10-ft. sheave wheel around which the trac- 
 tion rope passes, these wheels being provided with steel grids for the 
 control of the traction rope. When the loaded carriers travel down 
 grade and the difference in elevation is sufficient, this tramway will 
 operate by the force due to gravity, otherwise the power is applied to 
 the sheaves through bevel gearing. Numerous modifications of the 
 system are in use to suit different conditions. 
 
 An Aerial Tramway 21.5 miles long, with an elevation of the loading 
 end above the discharging end of 11,500 ft., built by A. Bleichert & Co. 
 for the government of the Argentine Republic, connecting the mines 9! 
 La Mejicana with the town of Chilecito, is described by Wm. Hewitt in 
 Indust. Eng., Aug. 15, 1909. Some of the inclinations are as much as 
 45 deg., there are some spans nearly 3000 ft. long, and there is a tunnel 
 nearly 500 ft. long. The line is divided into eight sections, each with 
 an independent traction rope. The gravity of the descending loaded 
 carriers is sufficient to make the line self-operating when it is once set 
 in motion, but in order to ensure full control, and to provide for carrying 
 four tons upward while the descending carriers are empty, four steam 
 engines are installed, one for each two sections. The carriers hold 10 cu. 
 ft., or about 1100 Ibs. of ore. The speed is 500 ft. per minute, and the 
 interval between carriers 45 seconds. The stress in the traction rope is 
 as high as 11,000 Ibs. in some sections. 
 
 Suspension Cableways or Cable Hoist-conveyors. 
 
 (Trenton Iron Co.) 
 
 In quarrying, rock-cutting, stripping, piling, dam-building, and many 
 other operations where it is necessary to hoist and convey large individual 
 loads economically, it frequently happens that the application of a system 
 of derricks is impracticable, by reason of the limited area of their effi- 
 ciency and the room which they occupy. To meet such conditions cable 
 hoist-conveyors are adopted, as they can be operated in clear spans up to 
 1500 ft., and in lifting individual loads up to 15 tons. Two types are 
 made one in which the hoisting and conveying are done by separate 
 running ropes, and the other applicable only to inclines in which the 
 carnage descends by gravity, and but one running rope is required. The 
 moving of the carriage in the former is effected by means of an endless 
 rope, and these are commonly known as " endless-rope " hoist-conveyors 
 istinguish them from the latter, which are termed "inclined" hoist- 
 conveyors. 
 
1206 HOISTING AND CONVEYING. 
 
 The general arrangement of the endless-rope hoist-conveyors consists 
 of a main cable passing over towers, A-frames or masts, as may be most 
 convenient, and anchored firmly to the ground at each end, the requisite 
 tension in the cable being maintained by a turnbuckle at one anchorage. 
 
 Upon this cable travels the carriage, which is moved back and forth 
 over the line by means of the endless rope. The hoisting is done by a 
 separate rope, both ropes being operated by an engine specially designed 
 for the purpose, which may be located at either end of the line, and is 
 constructed in such a way that the hoisting-rope is coiled up or paid out 
 automatically as the carriage is moved in and out. Loads may be picked 
 up or discharged at any point along the line. Where sufficient inclination 
 can be obtained in the main cable for the carriage to descend by gravity, 
 and the loading and unloading are done at fixed points, the endless rope can 
 be dispensed with. The carriage, which is similar in construction to the 
 carriage used in the endless-rope cableways, is arrested in its descent by a | 
 stop-block, which may be clamped to the main cable at any desired point, 
 the speed of the descending carriage being under control of a brake on the 
 engine-drum. 
 
 A Double-suspension Cableway, carrying loads of 15 tons, erected near 
 Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury 
 in Trans. A. I. M. E., xx. 766. The span is 733 ft., crossing the Susque- 
 hanna River. Two steel cables, each 2 in. diam., are used. On these 
 cables runs a carriage supported on four wheels and moyed by an endless 
 cable 1 inch in diam. The load consists of a cage carrying a railroad-car 
 loaded with lumber, the latter weighing about 12 tons. The power is 
 furnished by a 50-H.P. engine, and the trip across the river is made in 
 about three minutes. 
 
 A hoisting cableway on the endless-rope system, erected by the Lidger- 
 wood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in 
 length, with main cable 2 1/2 in. diam., and hoisting-rope 13/ 4 in. diam. 
 Loads of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute. 
 
 Another, of still longer span, 1650 ft., was erected by the same company 
 at Holyoke, Mass., for use in the construction of a darn. The main cable 
 is the Elliott or locked-wire cable, having a smooth exterior. In the con- 
 struction of the Chicago Drainage Canal twenty cableways, of 700 ft. span 
 and 8 tons capacity, were used, the towers traveling on rails, 
 
 Tension required to Prevent Slipping of Rope on Drum. (Trenton 
 Iron Co., 1906.) The amount of artificial tension to be applied in an 
 endless rope to prevent slipping on the driving-drum depends on the char- 
 acter of the drum, the condition of the rope and number of laps which it 
 makes. If T and S represent respectively the tensions in the taut and 
 slack lines of the rope; W, the necessary weight to be applied to the tail- 
 sheave; R, the resistance of the cars and rope, allowing for friction; n, the 
 number of half-laps of the rope on the driving-drum; and /, the coefficient 
 of friction, the following relations must exist to prevent slipping: 
 
 T = Sef nir , W = T+ S, and R = T - S] 
 ffnir , i 
 
 from which we obtain W = ; R, 
 
 ef nir - I 
 
 In which e 2.71828, the base of the Naperian system of logarithms. 
 The following are some of the values of/: 
 
 Dry. Wet. Greasy. 
 
 Wire-rope on a grooved iron drum 0.120 0.085 0.070 
 
 Wire-rope on wood-filled sheaves 0. 235 0. 170 0. 140 
 
 Wire-rope on rubber and leather filling . 495 . 400 . 205 
 The importance of keeping the rope dry is evident from these figures. 
 
 afmr i i 
 
 The values of the coefficient -j corresponding to the above values 
 
 of/, for one UD to six half-laps of the rope on the driving-drum or sheaves. 
 are given in the table at the top of p. 1207. 
 
 When the rope is at rest the tension is distributed equally on the two 
 lines of the rope, but when running there will be a difference in the 
 tensions of the taut and slack lines equal to the resistance, and the 
 values of T and S may be readily computed from the foregoing formulae. 
 
WIRE-ROPE HAULAGE. 
 
 1207 
 
 VALUES OF COEFFICIENT (ef nir -f i) 4- 
 
 l) 
 
 / 
 
 n = Number of Half-laps on Driving-wheel. 
 
 1 I 2 | 3 | 4 | 5 
 
 6 
 
 0.070 
 
 9.130 
 
 4.623 
 
 3. 141 
 
 2.418 
 
 .999 
 
 .729 
 
 0.085 
 
 7.536 
 
 3.833 
 
 2.629 
 
 2.047 
 
 .714 
 
 .505 
 
 0.120 
 
 5.345 
 
 2.777 
 
 .953 
 
 .570 
 
 .358 
 
 .232 
 
 0.140 
 
 4.623 
 
 2.418 
 
 .729 
 
 .416 
 
 .249 
 
 .154 
 
 0.170 
 
 3.833 
 
 2.047 
 
 .505 
 
 .268 
 
 .149 
 
 .085 
 
 0.205 
 
 3.212 
 
 1.762 
 
 .338 
 
 .165 
 
 .083 
 
 .043 
 
 0.235 
 
 2.831 
 
 1.592 
 
 .245 
 
 .110 
 
 .051 
 
 .024 
 
 0.400 
 
 1.795 
 
 1.176 
 
 .047 
 
 .013 
 
 .004 
 
 .001 
 
 0.495 
 
 1.538 
 
 1 093 
 
 .019 
 
 .004 
 
 .001 
 
 
 The increase in tension in the endless rope, compared with the main 
 rope. of the tail-rope system, where the stress in the rope is equal to 
 the resistance, is about as follows: 
 
 n = 123456 
 
 Increase in tension in endless rope, 
 
 compared with direct stress %.... 40 9 21/3 2/3 1/5 \/\Q 
 These figures are useful in determining the size of rope. For instance, 
 if the rope makes. two half-laps on the driving drum, the strength of the 
 rope should be 9 % greater than a main rope in the tail-rope system. 
 
 General Formulae for Estimating the Deflection of a Wire Cable 
 Corresponding to a Given Tension. 
 
 (Trenton Iron Co., 1906.) 
 
 Let s = distance between supports or spanrAl?; m and n = arms into 
 which the span is divided by a vertical through the required point of 
 deflection x, m representing the arm corresponding to the loaded side; 
 y horizontal distance from load to point of support corresponding with 
 m;w = wt. of rope per ft.; g = load; t tension; h = required deflection 
 at any point x\ all measures being in feet and pounds. 
 A B 
 
 
 s- n --= 
 
 FIG. 191. 
 
 For deflection due to rope alone, 
 
 , mnw . ws 2 ^ 
 
 h = -r-j- at x, or -7 at center of span. 
 
 iL t o t 
 
 For deflection due to load alone, 
 
 
 h = -T- at x, or ^ at center of span. 
 is A t 
 
 If y = 1/2 $, h = ^ at #, or ^ at center of span, 
 at x, or j-. at center of span. 
 
 If y = m, h = 
 For total deflection, 
 
 wmns + 2 any 
 h = - 
 
 Z IS 
 
 A 
 at x, or 
 
 ws z + 4 gu 
 T\ yy 
 
 o t 
 
 A 
 at center of span. 
 
 rf , wmn -f gn . ws* + 2 gs . 
 
 If 2/ = V2 s, h = y at x, or - at center of span. 
 
 2t of 
 
 wmns + 2 gmn A ws z + 2 gs . 
 
 If y = m, h = - at re, or - . at center of span. 
 
 ^ tS o I 
 
 If the tension is required for a given deflection, transpose t and h in 
 above formulae. 
 
1208 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 Taper Ropes of Uniform Tensile Strength. The true form of rope 
 is not a regular taper but follows a logarithmic curve, the girth rapidly 
 increasing toward the upper end. Mr. Chas. D. West gives the following 
 formula, based on a breaking strain of 80,000 Ib. per sq. in. of the rope, 
 core included, and a factor of safety of 10: log G = F -7-36804- log g, in 
 which F = length in fathoms, and G and g the girth in inches at any two 
 sections F fathoms apart. The girth g is first calculated for a safe strain 
 of 8000 Ib. per sq. in., and then G is obtained by the formula. For a 
 mathematical investigation see The Engineer, April, 1880, p, 267. 
 
 TRANSMISSION OF POWER BY 
 WIRE ROPE. 
 
 The following notes have been furnished to the author by Mr. Wm. 
 Hewitt, Vice-President of the Trenton Iron Co. (See also circulars of the 
 Trenton Iron Co. and of the J9hn A. Roebling's Sons Co., Trenton, N. J.; 
 " Transmission of Power by Wire Ropes," by A. W. Stahl, Van Nostrand's 
 Science Series, No. 28; and Reuleaux's Constructor.) 
 
 The load stress or working tension should not exceed the difference 
 between the safe stress and the bending stress as determined by the tablfe 
 on page 1209. 
 
 The approximate strength of iron-wire rope composed of wires hav- 
 ing a tensile strength of 75,000 to 90,000 Ibs. per sq. in. is half that of 
 cast-steel rope composed of wires of a tensile strength of 150,000 to 
 190,000 Ibs. per sq. in. Extra strong steel wires have a tensile strength 
 of 190,000 to 225,000 and plow-steel wires 225,000 to 275,000 Ibs. per 
 sq. in. 
 
 The 19-wire rope is more flexible than the 7-wire, and for the same 
 load stress may be run around smaller sheaves, but it is not as well 
 adapted to withstand abrasion or surface wear. 
 
 The working tension may be greater, therefore, as the bending stress 
 is less; but since the tension in the slack portion of the rope cannot be 
 less than a certain proportion of the tension in the taut portion, to avoid 
 slipping, a ratio exists between the diameter of sheave and the wires 
 composing the rope corresponding to a maximum safe working tension. 
 This ratio depends upon the number of laps that the rope makes about 
 
 the sheaves, and the kind of filling in 
 the rims or the character of the ma- 
 terial upon which the rope tracks. 
 
 For ordinary purposes the maximum 
 safe stress should be about one-third 
 the ultimate, and for shafts and eleva- 
 tors about one-fourth the ultimate. 
 
 * l^H ofT Hi In estimating the stress due to the load 
 
 T m i\vm W f or shafts and elevators, allowance 
 
 ! should be made for the additional 
 
 stress due to acceleration in starting. 
 For short inclined planes not used for 
 passengers a factor of safety as low as 
 2 1 A is sometimes used, and for derricks, 
 in which large sheaves cannot be used, 
 and long life of the rope is not expected, 
 the factor of safety may be as low as 2. 
 The Seale wire rope is made of six 
 strands of 19 wires, laid 9 around 9 
 around 1, the intermediate layer being smaller than the others. It is 
 intermediate in flexibility between the 7-wire and the ordinary 19-wire 
 rope. (In the Seale cable d = diam. of larger wires.) All ropes 6 
 strands each. Extra flexible rope has 8 strands. 
 
 Section 
 of Rim. 
 
 FIG. 192. 
 
 as 
 
 The sheaves (Fig. 192), are usually of cast iron, and are made as light 
 possible consistent with the requisite strength. Various materials 
 have been used for filling the bottom of the groove, such as tarred oakum, 
 jute yarn, hard wood, India-rubber, and leather. The filling which 
 gives the best satisfaction, however, in ordinary transmissions consists of 
 

 TRANSMISSION OF POWER BY WIRE ROPE. 1209 
 Approximate Breaking Strength of Steel-Wire Ropes. 
 
 6 Strands of 19 Wires Each. 
 
 6 Strands of 7 Wires Each. 
 
 m fi 
 
 Wt. 
 
 Approximate Breaking 
 Stress, Lbs. 
 
 ^ c 
 
 wt. 
 
 Approximate Breaking 
 Stress, Lbs. 
 
 If 
 
 Lbs. 
 
 Cast 
 Steel. 
 
 Extra 
 Strong 
 Steel. 
 
 Plow 
 Steel. 
 
 I| 
 
 Lbs. 
 
 Cast 
 Steel. 
 
 Extra 
 Strong 
 Steel. 
 
 Plow 
 Steel. 
 
 21/4 
 
 8.00 
 
 312,000 
 
 364,000 
 
 416,000 
 
 U/2 
 
 3.55 
 
 136,000 
 
 158,000 
 
 182,000 
 
 13/4 
 
 6.30 
 4.85 
 
 248,000 
 192,000 
 
 288,000 
 224,000 
 
 330,000 
 256,000 
 
 13/8 
 11/4 
 
 3.00 
 2.45 
 
 116,000 
 96,000 
 
 136,000 
 112,000 
 
 156,000 
 128,000 
 
 
 >4 15 
 
 168,000 
 
 194,000 
 
 222,000 
 
 
 2.00 
 
 80,000 
 
 92,000 
 
 106,000 
 
 1 1/2 
 
 3.55 
 
 144,000 
 
 168,000 
 
 192,000 
 
 ] 
 
 1.58 
 
 64,000 
 
 74,000 
 
 84,000 
 
 13/8 
 
 3.00 
 
 124,000 
 
 144,000 
 
 164,000 
 
 7/8 
 
 1.20 
 
 48,000 
 
 56,000 
 
 64,000 
 
 U/4 
 
 2.45 
 
 100,000 
 
 116,000 
 
 134,000 
 
 3/4 
 
 0.89 
 
 37,200 
 
 42,000 
 
 48,000 
 
 U/8 
 
 2.00 
 
 84,000 
 
 98,000 
 
 112,000 
 
 
 0.75 
 
 31,600 
 
 36,800 
 
 42,000 
 
 1 
 
 1 58 
 
 68,000 
 
 78,000 
 
 88,000 
 
 5/8 
 
 0.62 
 
 26,400 
 
 30,200 
 
 34,000 
 
 7/8 
 
 1.20 
 
 52,000 
 
 60,000 
 
 68,000 
 
 9/10 
 
 0.50 
 
 21,200 
 
 24,600 
 
 28,000 
 
 
 0.89 
 
 38,800 
 
 44,000 
 
 50,000 
 
 V2 
 
 0.39 
 
 16,800 
 
 19,400 
 
 22,000 
 
 5/8 
 
 0,62 
 
 27,200 
 
 31,600 
 
 36,000 
 
 7/16 
 
 0.30 
 
 13,200 
 
 15,000 
 
 17,100 
 
 
 0.50 
 
 22,000 
 
 25,400 
 
 29,000 
 
 3/8 
 
 0.22 
 
 9,600 
 
 11,160 
 
 12,700 
 
 
 39 
 
 17 600 
 
 20 200 
 
 22 800 
 
 
 15 
 
 6800 
 
 7 760 
 
 
 7/1A 
 
 30 
 
 13600 
 
 15 600 
 
 17 700 
 
 9/QO 
 
 125 
 
 5*600 
 
 6440 
 
 
 3/Q 
 
 22 
 
 10*000 
 
 if 500 
 
 13 100 
 
 
 
 
 
 
 5/1 fi 
 
 15 
 
 6 800 
 
 8*100 
 
 
 
 
 
 
 
 1/4 
 
 0.10 
 
 4'800 
 
 5,400 
 
 
 
 
 
 
 
 segments of leather and blocks of India-rubber soaked in tar and 
 packed alternately in the groove. Where the working tension is very 
 great, however, the wood filling is to be preferred, as in the case of long- 
 distance transmissions where the rope makes several laps about the 
 sheaves, and is run at a comparatively slow speed. 
 The Bending Stress is determined by the formula 
 
 fc= Ea 
 
 2.06 (R -T- d) + C 
 
 k = bending stress in Ibs.; E = modulus of elasticity = 28,500,000; 
 a = aggregate area of wires, sq. ins.; R = radius of bend; d = diam. of 
 wires, ins. 
 
 For 7-wire rope d = 1/9 diam. of rope; C = 9.27. 
 ' 19-wire " d = 1/15 " " C = 15.45. 
 
 " the Scale cable d =. 1/12 C = 12.36. 
 
 From this formula the tables below and on p. 1210 have been cal- 
 culated. 
 
 Bending Stresses, 7-wire Rope. 
 
 Diam. bend. 24 36 48 
 
 60 
 
 72 
 
 84 [ 96 j 108 | 120 | 132 
 
 Diam. Rope. 
 
 
 
 
 
 
 
 
 
 
 
 V4 
 
 826 
 
 553 
 
 412 
 
 333 
 
 277 
 
 238 
 
 208 
 
 185 
 
 166 
 
 15! 
 
 9 /32 
 
 1,120 
 
 750 
 
 563 
 
 451 
 
 376 
 
 323 
 
 282 
 
 251 
 
 226 
 
 20ft 
 
 5 /16 
 
 1,609 
 
 1,078 
 
 810 
 
 649 
 
 541 
 
 464 
 
 406 
 
 361 
 
 325 
 
 29d 
 
 3/8 
 
 2,774 
 
 1,859 
 
 1,398 
 
 1,120 
 
 934 
 
 801 
 
 702 
 
 624 
 
 562 
 
 511 
 
 7/16 
 
 4,385 
 
 2,982 
 
 2,217 
 
 1,777 
 
 1,482 
 
 1,272 
 
 1,113 
 
 990 
 
 892 
 
 811 
 
 Va 
 
 6,200 
 
 4,161 
 
 3,131 
 
 2,510 
 
 2,095 
 
 1,797 
 
 1,574 
 
 1,400 
 
 1,260 
 
 1,146 
 
 9/16 
 
 9,072 
 
 6,095 
 
 4,589 
 
 3,679 
 
 3,071 
 
 2,635 
 
 2,308 
 
 2,053 
 
 1,848 
 
 1,681 
 
 5/8 
 
 
 8,547 
 
 6,438 
 
 5,164 
 
 4,310 
 
 3,699 
 
 3,240 
 
 2,882 
 
 2,595 
 
 2,360 
 
 Jl/16 
 3/4 
 
 
 
 10,922 
 14,202 
 
 8,230 
 10,706 
 
 6,603 
 8,591 
 
 5,513 
 7,174 
 
 4,731 
 6,158 
 
 4,144 
 5,394 
 
 3,687 
 4,799 
 
 3,320 
 4,322 
 
 3,020 
 3,931 
 
 7 /8 
 
 ...... 
 
 22,592 
 
 17,045 
 
 13,685 
 
 11,431 
 
 9,815 
 
 8,599 
 
 7,651 
 
 6,892 
 
 6,269 
 
 1 
 
 
 
 25 476 
 
 20 464 
 
 17 100 
 
 14686 
 
 12869 
 
 11 452 
 
 10317 
 
 9386 
 
 U/8 
 
 
 
 36289 
 
 29*165 
 
 24,416 
 
 20,942 
 
 18,355 
 
 16,336 
 
 14718 
 
 13,391 
 
 U/4 
 
 
 
 
 40,020 
 
 33,464 
 
 28,754 
 
 25,206 
 
 22,437 
 
 20,216 
 
 18,396 
 
 13/8 
 
 
 
 
 
 44,551 
 
 38.290 
 
 33.571 
 
 29.888 
 
 26.933 
 
 24.510 
 
 n/2 
 
 
 
 
 
 57,835| 49,718[43,599|38,821 134,987| 31,842 
 
1210 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 Bending Stresses, 19-wire Rope. 
 
 Diam.Bend. 
 
 13 
 
 34 
 
 36 
 
 48 
 
 60 
 
 73 
 
 84 
 
 96 
 
 108 
 
 130 
 
 Diam.Rope. 
 
 
 
 
 
 
 
 
 
 
 
 V4 
 
 993 
 
 502 
 
 336 
 
 252 
 
 202 
 
 168 
 
 144 
 
 126 
 
 112 
 
 101 
 
 5/16 
 
 1,863 
 
 944 
 
 632 
 
 475 
 
 380 
 
 317 
 
 272 
 
 238 
 
 212 
 
 191 
 
 3/8 
 
 2,771 
 
 1,406 
 
 942 
 
 708 
 
 567 
 
 473 
 
 406 
 
 355 
 
 316 
 
 285 
 
 7/16 
 
 4,859 
 
 2,473 
 
 1,658 
 
 1,247 
 
 1,000 
 
 834 
 
 716 
 
 627 
 
 557 
 
 502 
 
 V2 
 
 7,125 
 
 3,635 
 
 2,440 
 
 1,836 
 
 1,472 
 
 1,228 
 
 1,054 
 
 923 
 
 821 
 
 739 
 
 o/ie 
 
 
 5,319 
 
 3,573 
 
 2,690 
 
 2,157 
 
 1,800 
 
 1,545 
 
 1,353 
 
 1,203 
 
 1,084 
 
 5/8 
 
 
 7,452 
 
 5,011 
 
 3,774 
 
 3,027 
 
 2,526 
 
 2,169 
 
 1,900 
 
 1,690 
 
 1,522 
 
 U/16 
 
 
 9,767 
 
 6,572 
 
 4,953 
 
 3,973 
 
 3,317 
 
 2,847 
 
 2,494 
 
 2,219 
 
 1,998 
 
 3/4 
 
 
 12,512 
 
 8,427 
 
 6,352 
 
 5,098 
 
 4,257 
 
 3,654 
 
 3,201 
 
 2,848 
 
 2,565 
 
 7/8 
 
 
 19,436 
 
 13,111 
 
 9,891 
 
 7,941 
 
 6,633 
 
 5,696 
 
 4,990 
 
 4,440 
 
 3,999 
 
 1 
 
 
 29,799 
 
 20,136 
 
 15,205 
 
 12,214 
 
 10,206 
 
 8,766 
 
 7,681 
 
 6,836 
 
 6,158 
 
 j;/8 
 
 
 
 28,153 
 
 21,276 
 
 17,099 
 
 14,293 
 
 12,278 
 
 10,761 
 
 9,578 
 
 8,689 
 
 11/4 
 
 
 
 38034 
 
 28,766 
 
 23,130 
 
 19340 
 
 16 618 
 
 14 567 
 
 12 967 
 
 1 1 683 
 
 13/8 
 
 
 
 51*609 
 
 39*,067 
 
 31*430 
 
 26*290 
 
 22*594 
 
 19*811 
 
 17*637 
 
 15*893 
 
 H/2 
 
 
 
 66065 
 
 50*049 
 
 40*284 
 
 33*707 
 
 28*976 
 
 25*410 
 
 22*625 
 
 20*390 
 
 15/8 
 - 13/4 
 
 
 
 
 62', 895 
 79 749 
 
 50*,647 
 64,252 
 
 42*,391 
 53 798 
 
 36*,450 
 46 270 
 
 31*,969 
 40,590 
 
 28*, 470 
 36 152 
 
 25*,661 
 32 589 
 
 
 
 
 17/8 
 
 
 
 
 97018 
 
 78,202 
 
 65*, 500 
 
 56*347 
 
 49*438 
 
 44*039 
 
 39*701 
 
 2 
 
 
 
 
 
 94*016 
 
 78*769 
 
 67778 
 
 59*478 
 
 52*989 
 
 47*777 
 
 21/4 
 
 
 
 
 
 134*319 
 
 112*611 
 
 96*943 
 
 85*103 
 
 75*840 
 
 68 396 
 
 2V2 
 
 
 
 
 
 
 154*, 870 
 
 133 ",386 
 
 117*. 137 
 
 104I.417 
 
 94*189 
 
 
 
 
 
 
 Horse-Power Transmitted* The general formula for the amount 
 of power capable of being transmitted is as follows: 
 
 H.P. = [cd 2 
 
 In which d = diameter of the rope in inches, v = velocity of the rope In 
 feet per second, w = weight of the rope, QI = weight of the terminal 
 sheaves and shafts, 02 weight of the intermediate sheaves and shafts 
 (all in Ibs.), and c = a constant depending on the material of the rope, 
 the filling in the grooves of the sheaves, and the number of laps about 
 the sheaves or drums, a single lap meaning a half-lap at each end. The 
 values of c for one up to six laps for steel rope are given in the following 
 table: 
 
 Number of laps about sheaves or drums 
 
 C lor steei rope on 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Iron 
 
 5.61 
 
 8.81 
 
 10.62 
 
 11.65 
 
 12.16 
 
 12.56 
 
 Wood 
 
 6.70 
 
 9.93 
 
 11.51 
 
 12.26 
 
 12.66 
 
 12.83 
 
 Rubber and leather 
 
 9.29 
 
 11.95 
 
 12.70 
 
 12.91 
 
 12.97 
 
 13.00 
 
 The values of c for iron rope are one half the above. 
 
 When more than three laps are made, the character of the surface in 
 contact is immaterial as far as slippage is concerned. 
 
 From the above formula we have the general rule, that the actual 
 horse-power capable of being transmitted by any wire rope approximately 
 equals c times the square of the diameter of the rope in inches, less six mil' 
 lionths the entire weight of all the moving parts, multiplied by the speed of 
 the rope, in feet per second. 
 
 Instead of grooved drums or a number of sheaves, about which the 
 
 rope makes two or more laps, it is sometimes' found more desirable, 
 especially where space is limited, to use grip-pulleys. The rim is fitted 
 with a continuous se/ies of steel jaws, which bite the rope in contact by 
 
 reason of the pressure of the same against them, but as soon as relieved 
 of this pressure they open readily, offering no resistance to the egress of 
 the rope. 
 
 In the ordinary or " flying " transmission of power, where the rope 
 makes a single lap about sheaves lined with rubber and leather or wood, 
 the ratio between the diameter of the sheaves and the wires of the rope, 
 Corresponding to a maximum safe working tension, is,: For 7-wire rope, 
 
TRANSMISSION OF POWER BY WIRE ROPE. 1211 
 
 steel, 79.6; iron, 160.5. For 12-wire rope, steel, 59.3; iron, 120. For 
 19-wire rope, steel, 47.2; iron, 95.8. 
 
 Diameters of Minimum Sheaves in Inches, Corresponding to a Maxi- 
 mum Safe Working Tension. 
 
 Diameter 
 of Rope, 
 In. 
 
 Steel. 
 
 Iron. 
 
 7-Wire. 
 
 12- Wire. 
 
 19- Wire. 
 
 7-Wire. 
 
 12-Wire. 
 
 19- Wire. 
 
 1/4 
 
 20 
 
 15 
 
 12 
 
 40 
 
 30 
 
 24 
 
 5/16 
 
 25 
 
 19 
 
 15 
 
 50 
 
 38 
 
 30 
 
 3/8 
 
 30 
 
 22 
 
 18 
 
 60 
 
 45 
 
 36 
 
 7/16 
 
 35 
 
 26 
 
 21 
 
 70 
 
 53 
 
 42 
 
 1/2 
 
 40 
 
 30 
 
 24 
 
 80 
 
 60 
 
 48 
 
 9/16 
 
 45 
 
 33 
 
 27 
 
 90 
 
 68 
 
 54 
 
 5/8 
 
 50 
 
 37 
 
 30 
 
 100 
 
 75 
 
 60 
 
 H/16 
 
 55 
 
 41 
 
 32 
 
 110 
 
 83 
 
 66 
 
 8 /4 
 
 60 
 
 44 
 
 35 
 
 120 
 
 90 
 
 72 
 
 7/8 
 
 70 
 
 52 
 
 41 
 
 140 
 
 105 
 
 84 
 
 1 
 
 80 
 
 59 
 
 47 
 
 160 
 
 120 
 
 96 
 
 Assuming the sheaves to be of equal diameter, and of the sizes in the 
 above table, the Horse-power that may be transmitted by a steel rope making 
 a single lap on wood-filled sheaves is given in the table below. 
 
 The transmission of greater horse-powers than 250 is impracticable 
 with filled sheaves, as the tension would be so great that the filling would 
 quickly cut out, and the adhesion on a metallic surface would be insuffi- 
 cient where the rope makes but a single lap. In this case it becomes 
 necessary to use the Reuleaux method, in which the rope is given more 
 than one lap, as referred to below, under the caption " Long-distance 
 Transmissions." 
 Horse-power Transmitted by a Steel Rope on Wood-filled Sheaves. 
 
 Diameter 
 of Rope, 
 In. 
 
 Velocity of Rope in Feet per Second. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 I 90 
 
 100 
 
 & 
 
 % 
 f 
 
 
 
 U/16 
 
 %* 
 7/8 
 
 4 
 
 10 
 13 
 17 
 
 22 
 27 
 32 
 38 
 52 
 68 
 
 8 
 13 
 19 
 26 
 34 
 43 
 53 
 63 
 76 
 104 
 135 
 
 13 
 
 20 
 28 
 38 
 51 
 65 
 79 
 95 
 103 
 156 
 202 
 
 17 
 
 26 
 38 
 51 
 67 
 86 
 104 
 126 
 150 
 206 
 
 21 
 33 
 47 
 63 
 83 
 106 
 130 
 157 
 186 
 
 25 
 40 
 56 
 75 
 99 
 128 
 155 
 186 
 223 
 
 28 
 44 
 64 
 88 
 115 
 147 
 179 
 217 
 
 32 
 51 
 73 
 99 
 130 
 167 
 203 
 245 
 
 37 
 57 
 80 
 109 
 144 
 184 
 225 
 
 40 
 62 
 89 
 121 
 159 
 203 
 24> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The horse-power that may be transmitted by iron ropes is one-half of the 
 above. 
 
 This table gives the amount of horse-power transmitted by wire ropes 
 under maximum safe working tensions. In using wood-lined sheaves, 
 therefore, it is well to make some allowance for the stretching of the 
 rope, and to advocate somewhat heavier equipments than the above table 
 would give; that is, if it is desired to transmit 20 horse-power, for in- 
 stance, to put in a plant that would transmit 25 to 30 horse-power, avoid- 
 ing the necessity of having to take up a comparatively small amount of 
 stretch. On rubber and leather filling, however, the amount of power 
 capable of being transmitted is 40 per cent greater than for wood, so that 
 this filling is generally used, and in this case no allowance need be made 
 for stretch, as such sheaves will likely transmit the power given by the 
 table, under all possible deflections of the rope. 
 
 Under ordinary conditions, ropes of seven wires to the strand, laid 
 about a hemp core, are best adapted to the transmission of power, but 
 conditions often occur where 12- or 19-wire rope is to be preferred, as 
 stated below, under " Limits of Span." 
 
 Deflections of the Rope. The tension of the rope is measured by 
 the amount of sag or deflection at the center at the span, and the deflec- 
 
1212 
 
 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 tion corresponding to the maximum safe working tension is determined 
 by the following formulae, in which S represents the span in feet : 
 
 Steel Rope. Iron Rope. 
 
 Def. of still rope at center, in feet . .h = .00004 S z h = .00008 S z 
 
 driving " ...hi = .000025 S* 7i t = .00005 S 2 
 
 slack " ...fo = .0000875 2 ^ = .00017 5S 2 
 
 Limits of Span. On spans of less than sixty feet, it is impossible to 
 splice the rope to such a degree of nicety as to give exactly the required 
 deflection, and as the rope is further subject to a certain amount of 
 stretch, it becomes necessary in such cases to apply mechanical means 
 for producing the proper tension in order to avoid frequent splicing, 
 which is very objectionable; but care should always be exercised in using 
 such tightening devices that they do not become the means, in unskilled 
 hands, of overstraining the rope. The rope also is more sensitive to 
 every irregularity in the sheaves and the fluctuations in the amount of 
 power transmitted, and is apt to sway to such an extent beyond the 
 narrow limits of the required deflections as to cause a jerking motion, 
 which is very injurious. For this reason on very short spans it is found 
 desirable to use a considerably heavier rope than that actually required 
 to transmit the power; or in other words, instead of a 7-wire rope cor- 
 responding to the conditions of maximum tension, it is better to use a 
 19-wire rope of the same size wires, and to run this under a tension con- 
 siderably below the maximum. In this way are obtained the advantages of 
 increased weight and less stretch, without having to use larger sheaves, 
 while the wear will be greater in proportion to the increased surface. 
 
 In determining the maximum limit of span, the contour of the ground 
 and the available height of the terminal sheaves must be taken into con- 
 sideration. It is customary to transmit the power through the lower 
 portion of the rope, as in this case the greatest deflection in this portion 
 occurs when the rope is at rest. When running, the lower portion rises 
 and the upper portion sinks, thus enabling obstructions to be avoided 
 which otherwise would have to be removed, or make it necessary to erect 
 very high towers. The maximum limit of span in this case is determined 
 by the maximum deflection that may be given to the upper portion of 
 the rope when running, which for sheaves of 10 ft. diameter is about 
 600 feet. 
 
 Much greater spans than this, however, are practicable where the con- 
 tour of the ground is such that the upper portion of the rope may be the 
 driver, and there is nothing to interfere with the proper deflection of the 
 under portion. Some very long transmissions of power have been 
 effected in this way without an intervening support, one at Lockport, 
 N.Y., having a clear span of 1700 feet. 
 
 Long-distance Transmissions. When the distance exceeds the 
 limit for a clear span, intermediate supporting sheaves are used, with 
 plain grooves (not filled), the spacing and size of which will be governed 
 by the contour of the ground and the special conditions involved. The 
 size of these sheaves will depend on the angle of the bend, gauged by the 
 tangents to the curves of the rope at the points of inflection. If the cur- 
 vature due to this angle and the working tension, regardless of the size of 
 the sheaves, as determined by the table on the next page, is less than 
 that of the minimum sheave (see table p. 1211), the intermediate sheaves 
 should not be smaller than such minimum sheave, but if the curvature is 
 greater, smaller intermediate sheaves may be used. 
 
 In very long transmissions of power, requiring numerous intermediate 
 supports, it is found impracticable to run the rope at the high speeds 
 maintained in " flying transmissions." The rope therefore is run under 
 a higher working tension, made practicable by wrapping it several times 
 about grooved terminal drums, with a lap about a sheave on a take-up or 
 counter- weighted carriage, which preserves a constant tension in the slack 
 portion. 
 
 Inclined Transmissions. When the terminal sheaves are not on 
 the same elevation, the tension at the upper sheave will be greater than 
 that at the lower, but this difference is so slight, in most cases, that it 
 may be ignored. The span to be considered is the horizontal distance 
 between the sheaves, and the principles governing the limits of span will 
 
TRANSMISSION OF POWER BY WIRE ROPE. 1213 
 
 hold good in this case, so that for every steep inclinations it becomes 
 necessary to resort to tightening devices for maintaining the requisite 
 tension in the rope. The limiting case of inclined transmissions occurs 
 when one wheel is directly above the other. The rope in this case pro- 
 duces no tension whatever on the lower wheel, while the upper is sub- 
 ject only to the weight of the rope, which is usually so insignificant that 
 it may be neglected altogether, and on vertical transmissions, therefore, 
 mechanical tension is an absolute necessity. 
 
 Bending Curvature of Wire Ropes. The curvature due to any 
 bend in a wire rope is dependent on the tension, and is not always the 
 same as the sheave in contact, but may be greater, which explains how 
 it is that large, ropes are frequently run around comparatively small 
 sheaves without detriment, since it is possible to place these so close that 
 the bending angle on each will be such that the resulting curvature will 
 not overstrain the wires. This curvature may be ascertained from 
 the formula and table below, which give the theoretical radii of 
 curvature in inches for various sizes of ropes and different angles for one 
 pound tension in the rope. Dividing these figures by the square root 
 of the actual tension in pounds, gives the radius of curvature of the rope 
 when this exceeds the curvature of the sheave. The rigidity of the rope 
 or internal friction of the wires and core has not been taken into account 
 in these figures, but the effect of this is insignificant, and it is on the safe 
 side to ignore it. By the "angle of bend' T is meant the angle between 
 the tangents to the curves of the rope at the points of inflection.- When 
 the rope is straight the angle is 180. For angles less than 160 the 
 radius of curvature in most cases will be less than that corresponding to 
 the safe working tension, and the proper size of sheave to use in such 
 cases will be governed by the table headed "Diameters of Minimum 
 Sheaves Corresponding to a Maximum Safe Working Tension" on p. 1211. 
 
 Radius of Curvature of Wire Ropes in Inches for 1-Ib. Ten- 
 sion. Formula: R 2 = Ed*n+ 20 (1 sin ^ 0); in which R = radius of 
 curvature; E = modulus of elasticity = 28,500,000; d = diameter of wires; 
 n = no. of wires in the rope; 6 = angle of bend; t = working stress (Ibs. and 
 ins.). Divide by square root of stress in pounds to obtain radius in inches. 
 
 Diam. of Rope. 
 
 120 
 
 140 
 
 160 
 
 165 
 
 170 
 
 174 
 
 m c 
 
 178 C 
 
 172 ~> 
 
 i 7- Wire Rope. 19- Wire Rope, j 
 
 iA 
 
 38 
 61 
 87 
 116 
 155 
 195 
 238 
 
 66 
 103 
 145 
 198 
 259 
 328 
 406 
 
 56 
 91 
 129 
 174 
 232 
 290 
 355 
 
 98 
 153 
 
 216 
 295 
 386 
 489 
 605 
 
 112 
 
 181 
 257 
 346 
 461 
 578 
 708 
 
 196 
 306 
 430 
 587 
 769 
 975 
 1205 
 
 149 
 242 
 342 
 461 
 615 
 770 
 943 
 
 261 
 
 407 
 572 
 782 
 1024 
 1298 
 1606 
 
 223 
 362 
 513 
 690 
 921 
 1154 
 1414 
 
 391 
 610 
 858 
 1172 
 1535 
 1946 
 2407 
 
 373 
 604 
 856 
 1151 
 1536 
 1925 
 2358 
 
 651 
 
 1018 
 1431 
 1954 
 2559 
 3246 
 4013 
 
 559 
 
 1282 
 1725 
 2302 
 2885 
 3533 
 
 976 
 1525 
 2145 
 2929 
 3835 
 4864 
 6015 
 
 1126 
 1824 
 2586 
 3479 
 4643 
 5818 
 7125 
 
 1969 
 3076 
 4325 
 5907 
 7735 
 9809 
 12129 
 
 2181 
 3533 
 5007 
 6737 
 8991 
 11266 
 13797 
 
 3812 
 5957 
 8375 
 11438 
 14978 
 18994 
 23487 
 
 H 
 
 ?I: ... 
 
 </':: 
 
 i :::::::: 
 
 IH . . 
 
 \y 
 
 
 6/ 
 
 a/ 
 
 7X 
 
 1 8 
 
 \y* . 
 
 \y 
 
 
 The 7-wire rope has 6 strands of 7 wires each, the 19-wlre rope has 
 6 strands of 19 wires each. 
 
1214 ROPE-DRIVING. 
 
 HOPE-DRIVING. 
 
 The transmission of power by cotton or manila ropes is a competitor 
 with gearing and leather belting when the amount of power is large, or 
 the distance between the power and the work is comparatively great. 
 The following is condensed from a paper by C. W. Hunt, Trans. A. S. 
 M. E., xii, 230: 
 
 But few accurate data are available, on account of the long period 
 required in each experiment, a rope lasting from three to six years. 
 Installations which have been successful, as well as those in which the 
 wear of the rope was destructive, indicate that 200 Ibs. on a rope one 
 inch in diameter is a safe and economical working strain. When the 
 strain is materially increased, the wear is rapid. 
 
 In the following equations 
 
 C = circumference of rope, inches; g = gravity; 
 
 D = sag of the rope in feet ; H = horse-power; 
 
 F = centrifugal force in pounds; L = distance between pulleys, ft.; 
 
 P = pounds per foot of rope; w = working strain in pounds; 
 
 R = force in pounds doing useful work; 
 S = strain in pounds on the rppe at the pulley; 
 T = tension in pounds of driving side of the rope; 
 t = tension in pounds on slack side of the rope; 
 v = velocity of the rope in feet per second; 
 W = ultimate breaking strain in pounds. 
 W = 720 C 2 ; P = 0.032 C 2 ; w = 20 C 2 . 
 
 This makes the normal working strain equal to 1/36 of the breaking 
 strength, and about 1/25 of the strength at the splice. The actual strains 
 are ordinarily much greater, owing to the vibrations in running, as well 
 as from imperfectly adjusted tension mechanism. 
 
 For this investigation we assume that the strain on the driving side 
 of a rope is equal to 200 Ibs. on a rope one inch in diameter, and an 
 equivalent strain for other sizes, and that the rope is in motion at vari- 
 ous velocities of from 10 to 140 ft. per second. 
 
 The centrifugal force of the rope in running over the pulley will reduce 
 the amount of force available for the transmission of power. The cen- 
 trifugal force F = Pv 2 - *- g. 
 
 At a speed of about 80 ft. per second, the centrifugal force increases 
 faster than the power from increased velocity of the rope, and at about 
 140 ft. per second equals the assumed allowable tension of the rope. 
 Computing this force at various speeds and then subtracting it from the 
 assumed maximum tension, we have the force available for the trans- 
 mission of power. The whole of this force cannot be used, because a 
 certain amount of tension on the slack side of the rope is needed to give 
 adhesion to the pulley. What tension should be given to the rope for 
 this purpose is uncertain, as there are no experiments which give accurate 
 data. It is known from considerable experience that when the rope runs in 
 a groove whose sides are inclined toward each other at an angle of 45 
 there is sufficient adhesion when the ratio of the tensions T -* t = 2. 
 
 For the present purpose T can be divided into three parts: 1. Tension 
 doing useful work; 2. Tension from centrifugal force; 3. Tension to 
 balance the strain for adhesion. 
 
 The tension t can be divided into two parts: 1. Tension for adhesion; 
 2. Tension from centrifugal force. 
 
 It is evident, however, that the tension required to do a given work 
 should not be materially exceeded during the life of the rope. 
 
 There are two methods of putting ropes on the pulleys; one in which 
 the ropes are single and spliced on, being made very taut at first, and 
 less so as the rope lengthens, stretching until it slips, when it is re- 
 spliced. The other method is to wind a single rope over the pulleys 
 as many turns as needed to obtain the necessary horse-power and put a 
 tension pulley to give the necessary adhesion and also take up the wear. 
 The tension t on one of the ropes required to transmit the normal horse- 
 power for the ordinary speeds and sizes of rope is computed by formula 
 (1), % below. The total tension T on the driving side of the rope is 
 assumed to be the same at all speeds. The centrifugal force, as well as 
 an amount equal to the tension for adhesion on the slack side of the 
 
ROPE-DRIVING. 
 
 1215 
 
 rope, must be taken from the total tension T to ascertain the amount of 
 force available for the transmission of power. 
 
 It is assumed that the tension on the slack side necessary for giving 
 adhesion is equal to one half the force doing useful work on the driving 
 
 .. 80 90 100 110 120 130 14Q 
 
 " Velocity of Driving Hope in feet per second * 
 
 FIG. 193. 
 
 side of the rope: hence the force for useful work is R = 2/3 (T - F); and 
 the tension on the slack side to give the required adhesion is Vs (T F). 
 
 t = (T - F)/3 + F m 
 
 The sum of the tensions T and t is not the same at different speeds, as 
 the equation (1) indicates. As F varies as the square of the velocity, 
 there is, with an increasing speed of the rope, a decreasing useful force, 
 and an increasing total tension, t, on the slack side. 
 With these assumptions of allowable strains the horse-power will be 
 
 H = 2v (!T-F)-K3X550) (2) 
 
 Transmission ropes are usually from 1 to 2 inches in diameter. A 
 computatipn of the horse-power for four sizes at various speeds and 
 under ordinary conditions, based on a maximum strain equivalent to 
 200 Ibs. for a rope one inch in diameter, is given in Fig. 193. The 
 horse-power of other sizes is readily obtained from these. The maxi- 
 mum power is transmitted, under the assumed conditions, at a speed of 
 about 80 feet per second. 
 
 The wear of the rope is both internal and external; the internal is 
 
 caused by the movement of the fibers on each other, under pressure in 
 
 bending over the sheaves, and the external is caused by the slipping and 
 
 the wedging in the grooves of the pulley. Both of these causes of wear 
 
 Horse-power of Transmission Rope at Various Speeds. 
 
 Computed from formula (2) given above. 
 
 it 
 
 Speed of the Rope in feet per minute. 
 
 to*O TO 
 
 IsSis 
 
 1500 
 
 2000 
 
 2500 
 
 3000 
 
 3500 
 
 4000 
 
 4500 
 
 5000 
 
 6000 
 
 7000 
 
 8000 
 
 V2 
 5/8 
 3/4 
 
 | 7/8 
 1 1/4 
 1 1/2 
 ,3 /4 
 
 1.45 
 2.3 
 3.3 
 4.5 
 5.8 
 9.2 
 13.1 
 18 
 23.2 
 
 1.9 
 
 3.2 
 4.3 
 5.9 
 7.7 
 12.1 
 17.4 
 23.7 
 30.8 
 
 2.3 
 3.6 
 5.2 
 7.0 
 9.2 
 14.3 
 20.7 
 28.2 
 36.8 
 
 2.7 
 4.2 
 5.8 
 8.2 
 10.7 
 16.8 
 23.1 
 32.8 
 42.8 
 
 3 
 
 4.6 
 6.7 
 9.1 
 11.9 
 18.6 
 26.8 
 36.4 
 47.6 
 
 3.2 
 5.0 
 7.2 
 9.8 
 12.8 
 20.0 
 28.8 
 39.2 
 51.2 
 
 3.4 
 5.3 
 7.7 
 10.8 
 13.6 
 21.2 
 30.6 
 41.5 
 54.4 
 
 3.4 
 5.3 
 7.7 
 10.8 
 13.7 
 21.4 
 30.8 
 41.8 
 54.8 
 
 3.1 
 4.9 
 7.1 
 9.3 
 12.5 
 19.5 
 28.2 
 37.4 
 50 
 
 2.2 
 3.4 
 4.9 
 6.9 
 8.8 
 13.8 
 19.8 
 27.6 
 35.2 
 
 
 
 
 
 
 
 
 
 
 
 20 
 24 
 30 
 36 
 42 
 54 
 60 
 72 
 84 
 
1216 
 
 ROPE-DRIVING. 
 
 are, within the limits of ordinary practice, assumed to be directly pro- 
 portional to the speed. 
 
 The rope is supposed to have the strain T constant at all speeds on 
 the driving side, and in direct proportion to the area of the cross-section; 
 hence the catenary of the driving side is not affected by the speed or by 
 the diameter of the rope. 
 
 The deflection of the rope between the pulleys on the slack side varies 
 with each change of the load or change of the speed, as the tension equa- 
 tion (1) indicates. 
 
 The deflection of the rope is computed for the assumed value of T and 
 t by the parabolic formula S = j^ + PD, S being the assumed strain 
 
 T on the driving side, and t, calculated by equation (1), on the slack 
 side. The tension t varies with the speed. 
 
 The following notes are from the circular of the C. W. Hunt Co. : 
 For a temporary installation, it might be advisable to increase the work 
 to double that given in the table. 
 
 For convenience in estimating the necessary clearance on the driving 
 and on the slack sides, we insert a table showing the sag of the rope at 
 different speeds when transmitting the horse-power given in the pre- 
 ceding table. When at rest the sag is not the same as when running, 
 being greater on the driving and less on the slack sides of the rope. The 
 sag of the driving side when transmitting the normal horse-power is the 
 same no matter what size of rope is used or what the speed driven at, 
 because the assumption is that the strain on the rope shall be the same 
 at all speeds when transmitting the assumed horse-power, but on the 
 slack side the strains, and consequently the sag, vary with the speed of 
 the rope and also with the horse-power. The table gives the sag for 
 three speeds. If the actual sag is less than given in the table, the rope 
 is strained more than the work requires. 
 
 ; This table is only approximate, and is exact only when the rope is 
 running at its normal speed, transmitting its full load and strained to the 
 assumed amount. All of these conditions are varying in actual work. 
 
 SAG OF THE ROPE BETWEEN PULLEYS. 
 
 Distance 
 between 
 Pulleys 
 in feet. 
 
 Driving Side. 
 
 Slack Side of Rope. 
 
 All Speeds. 
 
 80 ft. per sec. 
 
 60ft. per sec. 
 
 40ft. per sec. 
 
 40 
 60 
 80 
 100 
 120 
 140 
 160 
 
 Ofeet 4 inches 
 " 10 " 
 I " 5 " 
 2 " " 
 2 " 11 " 
 3 " 10 
 5 " 1 " 
 
 feet 7 inches 
 1 5 " 
 2 " 4 " 
 3 " 8 " 
 5 " 3 " 
 7 " 2 " 
 9 " 3 " 
 
 Ofeet 9 inches 
 1 *' 8 " 
 2 " 10 " 
 4 " 5 " 
 6 " 3 " 
 8 " 9 " 
 11 " 3 " 
 
 feet 1 1 inches 
 1 " 11 " 
 3 " 3 " 
 5 " 2 
 7 " 4 " 
 9 " 9 " 
 14 " " 
 
 The size of the pulleys has an important effect on the wear of the rope 
 the larger the sheaves, the less the fibers of the rope slide on each other, 
 and consequently there is less internal wear of the rope. The pulleys 
 should not be less than forty times the diameter of the rope for economical 
 wear, and as much larger as it is possible to make them. This rule apolies 
 also to the idle and tension pulleys as well as to the main driving-pulley. 
 
 TENSION ON THE SLACK PART OF THE ROPE. 
 
 Speed of 
 Rope, in feet 
 per second 
 
 Diameter of the Rope and Pounds Tension on the Slack Rope 
 
 V2 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 n/4 
 
 H/2 
 
 13/4 
 
 2 
 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 
 10 
 14 
 15 
 16 
 18 
 19 
 21 
 24 
 
 27 
 29 
 31 
 33 
 36 
 39 
 43 
 48 
 
 40 
 42 
 45 
 49 
 53 
 59 
 64 
 70 
 
 54 
 56 
 60 
 65 
 71 
 78 
 85 
 93 
 
 71 
 74 
 79 
 85 
 93 
 101 
 111 
 122 
 
 110 
 115 
 123 
 132 
 145 
 158 
 173 
 190 
 
 162 
 170 
 181 
 195 
 214 
 236 
 255 
 279 
 
 216 
 226 
 240 
 259 
 285 
 310 
 340 
 372 
 
 283 
 296 
 315 
 339 
 373 
 406 
 445 
 487 
 
ROPE-DEIVING. 
 
 1217 
 
 The angle of the sides of the grooves in which the rope runs varies, 
 with different engineers, from 45 to 60 U . It is very important that the 
 sides of these grooves should be carefully polished, as the fibers of the 
 rope rubbing on the metal as it comes from the lathe tools will gradually 
 break fiber by fiber, and so give the rope a short life. It is also neces- 
 sary to carefully avoid all sand or blow holes, as they will cut the rope 
 out with surprising rapidity. 
 
 Much depends also upon the arrangement of the rope on the pulleys. 
 especially where a tension weight is used. Experience shows that the 
 increased wear on the rope from bending the rope first in one direction 
 and then in the other is similar to that of wire rope. At mines where 
 two cages are used, one being hoisted and one lowered by the same 
 engine doing the same work, the wire ropes, cut from the same coil, are 
 usually arranged so that one rope is bent continuously in one direction 
 and the other rope is bent first in one direction and then in the other, in 
 winding on the drum of the engine. The rope having the opposite bends 
 wears much more rapidly than the other, lasting about three quarters 
 as long as its mate. This difference in wear shows in manila rope, both 
 in transmission of power and in coal-hoisting. The pulleys should be 
 arranged, as far as possible, to bend the rope in one direction. 
 DIAMETER OF PULLEYS AND WEIGHT OF ROPE. 
 
 Diameter of 
 
 i ^ 
 In inches. 
 
 Smallest Diameter 
 of Pulleys, in 
 inches. 
 
 Length of Rope to 
 allow for Splicing, 
 in feet. 
 
 Approximate 
 Weight, in Ibs. per 
 foot of rope. 
 
 Va 
 
 20 
 
 6 
 
 0.12 
 
 5/8 
 
 24 
 
 6 
 
 0.18 
 
 3/4 
 
 30 
 
 7 
 
 0.24 
 
 7/8 
 
 36 
 
 8 
 
 0.32 
 
 1 
 
 42 
 
 9 
 
 0.49 
 
 H/4 
 
 54 
 
 10 
 
 0.60 
 
 n/2 
 
 60 
 
 12 
 
 0.83 
 
 13/4 
 
 72 
 
 13 
 
 1.10 
 
 2 
 
 84 
 
 14 
 
 1.40 
 
 For large amounts of power it is common to use a number of ropes 
 lying side by side in grooves, each spliced separately. For lighter drives 
 some engineers use one rope wrapped as many times around the pulleys 
 as is necessary to get the horse-power required, with a tension pulley to 
 take up the slack as the rope wears when first put in use. The weight 
 put upon this tension pulley should be carefully adjusted, as the over- 
 straining 9f the rope from this cause is one of the most common errors 
 in rope-driving. We therefore give a table showing the proper strain on 
 the rope for the various sizes, from which the tension weight to transmit 
 the horse-power in the tables is easily deduced. This strain can be still 
 further reduced if the horse-power transmitted is usually less than the 
 nominal work which the rope was proportioned to do, or if the angle of 
 groove in the pulleys is acute. 
 
 With a given velocity of the driving-rope, the weight of rope required 
 for transmitting a given horse-power is the same, no matter what size 
 rope is adopted. The smaller rope will require more parts, but the 
 weight will be the same. 
 
 Miscellaneous Notes on Rope-Driving. Reuleaux gives formulae 
 for calculating sources of loss in hemp-rope transmission due to (1) journal 
 friction, (2) stiffness of ropes, and (3) creep of ropes. The constants in 
 these formluse are, however, uncertain from lack of experimental data. 
 He calculates an average case giving loss of power due to journal friction 
 = 4%, to stiffness 7.8%, and to creep 5%, or 16.8% in all, and says this 
 is not to be considered higher than the actual loss. 
 
 Spencer Miller, in a paper entitled "A Problem in Continuous Rope- 
 driving " (Trans. A. S. C. E., 1897), reviews the difficulties which occur in 
 rope-driving, with a continuous rope from a large to a small pulley. He 
 adopts the angle of 45 as a minimum angle to use on the smaller pulley, 
 and recommends that the larger pulley be grooved with a wider angle to* a 
 degree such that the resistance to slipping is equal in both wheels. 
 
 Mr. Miller refers to a 250-H.P. drive which has been running ten years, 1 
 large pulley being grooved 60 and the smaller 45. This drive was 
 
 esigned to use a 1 M-in. manila rope, but the grooves were made deep 
 
1218 
 
 ROPE-DRIVING. 
 
 Prom the 
 
 Data of Manila Transmission Rope. 
 
 1 Blue Book " of The American Mfg. Co., New York. 
 
 
 
 
 
 
 Length of 
 
 w 
 
 
 i 
 
 s 
 
 
 
 JS 
 
 
 Splice, Ft. 
 
 E 1 ^ 
 
 
 1 
 
 Q 
 
 Is 
 
 H 
 
 
 
 % m 
 
 
 
 
 
 8 
 
 "o 
 
 is 
 
 Wrg 
 
 III 
 
 1 
 
 
 
 
 
 ^> 
 
 | . 
 
 
 s 
 
 2 * 
 
 ' S 
 
 
 I 
 
 a 
 
 1 
 
 || 
 
 12 
 
 S 
 
 1 
 
 4* 
 
 I* 
 
 |^EH 
 
 43 
 
 w 
 
 vO 
 
 i" 8 
 
 | 
 
 3/4 
 
 0.5625 
 
 0.20 
 
 3,950 
 
 112 
 
 6 
 
 8 
 
 
 28 
 
 760 
 
 7 /8 
 
 7656 
 
 0.26 
 
 5,400 
 
 153 
 
 6 
 
 8 
 
 4 
 
 32 
 
 650 
 
 -I 
 
 1. 
 
 0.34 
 
 7,000 
 
 200 
 
 7 
 
 10 
 
 14 
 
 36 
 
 570 
 
 H/8 
 
 1.2656 
 
 0.43 
 
 8,900 
 
 253 
 
 7 
 
 10 
 
 16 
 
 40 
 
 510 
 
 I V4 
 
 1.5625 
 
 0.53 
 
 10,900 
 
 312 
 
 7 
 
 10 
 
 16 
 
 46 
 
 460 
 
 13/8 
 
 1.8906 
 
 0.65 
 
 13,200 
 
 378 
 
 8 
 
 12 
 
 16 
 
 50 
 
 415 
 
 U/2 
 15/8 
 13/4 
 
 2.25 
 2.6406 
 3.0625 
 
 0.77 
 0.90 
 1.04 
 
 15,700 
 18,500 
 21,400 
 
 450 
 528 
 612 
 
 8 
 8 
 8 
 
 12 
 12 
 12 
 
 18 
 18 
 18 
 
 54 
 60 
 64 
 
 380 
 344 
 330 
 
 2 
 
 4 
 
 1.36 
 
 28,000 
 
 800 
 
 9 
 
 14 
 
 20 
 
 72 
 
 290 
 
 2V4 
 21/2 
 
 5.0625 
 6.25 
 
 1.73 
 2.13 
 
 35,400 
 43,700 
 
 1,012 
 1,250 
 
 9 
 10 
 
 14 
 16 
 
 20 
 22 
 
 82 
 90 
 
 255 
 230 
 
 Weight of transmission rope 
 Breaking strength 
 Maximum allowable tension 
 Diam. smallest practicable 
 
 sheave, 
 Velocity of rope (assumed) 
 
 =- 0.34 X diam.* 
 = 7,000 X diam. 2 
 = 200 X diam. 2 
 
 36 X diam. 
 = 5.400 ft. per min. 
 enough so that a 7/ 8 -in. rope would not bottom. In order to determine the 
 value of the drive a common 7/ 8 -in. rope was put in at first, and lasted six 
 years, working under a factor of safety of only 1'4. He recommends, how- 
 ever, for continuous rope-driving a factor of safety .of not less than 20. 
 
 A heavy rope-drive on the separate, or English, rope system is described 
 and illustrated in Power, April, 1892, It is in use at the India Mill at Dar- 
 wen, England, and is driven by a 2000-H.P. engine at 54 revs, per min. 
 The fly-wheel is 30 ft. diameter, weighs 65 tons, and is arranged with 30 
 grooves for 1 3/4-in. ropes. These ropes lead off to receiving-pulleys upon 
 the several floors, so that each floor receives its power direct from the fly- 
 wheel. The speed of the ropes is 5089 ft. per min., and five 7-ft. receivers 
 are used. Lambeth cotton ropes are used. (For much other information 
 on this subject see " Rope-Driving," by J. J. Flather, John Wiley & Sons.) 
 
 Cotton Ropes are advantageously used as bands or cords on the 
 smaller machine appliances; the fiber, being softer and more flexible 
 than manila hemo, gives good results for small sheaves; but for large 
 drives, where power transmitted is in considerable amounts, cotton rope, 
 as compared with manila, is hardly to be considered, on account of 
 the following disadvantages: It is less durable; it is injuriously affected 
 by the weather, so that for exposed drives, paper-mill work, or use in 
 water-wheel pits, it is absolutely unsatisfactory; it is difficult, if not 
 impossible, to splice uniformly; even the best quality cotton rope is 
 much inferior to manila in strength, the breaking strain of the highest 
 grade being but 4000 X diam. 2 as against 7000 X diam. 2 for manila; while, 
 for the transmission of equal powers, the cost of a cotton rope varies 
 from one-third to one-half more than manila. (" Blue Book " of the 
 Amer. Mfg. Co.) 
 
 A different opinion is found in a paper by E. Kenyon in Proc. lust. 
 Engrs. and Shipbuilders of Scotland, 1904. He says: Evidences of the 
 progress of cotton in the manufacture of driving-ropes are so far-reaching 
 that its superiority may be considered as much an accepted principle in 
 rope transmission as the law of gravitation is in science. As to the longevity 
 of cotton ropes, 24 cotton ropes 13/4-in. diam. are transmitting 820 H.P. at a 
 peripheral speed of 4396 ft. per min., from a driving pulley 28 ft. diam. 
 All the card-room ropes in this drive have been running since 1878, a 
 period of 26 years, without any attention whatever. 
 
FKICTION AND LUBRICATION, 
 
 1219 
 
 FRICTION AND LUBRICATION. 
 
 , Friction is defined by Rankine as that force which acts between two 
 bodies at their surface of contact so as to resist their sliding on each 
 other, and which depends on the force with which the bodies are pressed 
 together. 
 
 Coefficient of Friction. The ratio of the force required to slide a 
 body along a horizontal plane surface to the weight of the body is called 
 the coefficient of friction. It is equivalent to the tangent of the angle of 
 repose, which is the angle of inclination to the horizontal of an inclined 
 plane on which the body will just overcome its tendency to slide. The 
 angle is usually denoted by 0, and the coefficient by /. / = tan 6. 
 
 Friction of Eest and of Motion. The force required to start a 
 body sliding is called the friction of rest, and the force required to con- 
 tinue its sliding after having started is called the friction of motion. 
 
 Rolling Friction is the force required to roll a cylindrical or spheri- 
 cal body on a plane or on a curved surface. It depends on the nature of 
 the surfaces and on the force with which they are pressed together, but 
 is essentially different from ordinary, or sliding, friction. 
 
 Friction of Solids. Rennie's experiments (1829) on friction of solids, 
 usually unlubricated and dry* led to the following conclusions: 
 
 1. The laws of sliding friction differ with the character of the bodies 
 rubbing together. 
 
 2. The friction of fibrous material is increased by increased extent of 
 surface and by time of contact, and is diminished by pressure and speed. 
 
 3. With wood, metal, and stones, within the limit of abrasion, friction 
 varies only with the pressure, and is independent of the extent of surface, 
 time of contact, and velocity. 
 
 4. The limit of abrasion is determined by the hardness of the softer of 
 the two rubbing parts. 
 
 5. Friction is greatest with soft and least with hard materials. 
 
 6. The friction of lubricated surfaces is determined by the nature of 
 the lubricant rather than by that of the solids themselves. 
 
 Friction of Rest. (Rennie.) 
 
 Pressure, 
 Lbs. 
 per Square 
 Inch. 
 
 Values of /. 
 
 Wrought Iron on 
 Wrought Iron. 
 
 Wrought on 
 Cast Iron. 
 
 Steel on 
 Cast Iron. 
 
 Brass on 
 Cast Iron. 
 
 187 
 224 
 336 
 448 
 560 
 672 
 784 
 
 0.25 
 .27 
 .31 
 .38 
 .41 
 Abraded 
 
 0.28 
 .29 
 .33 
 .37 
 .37 
 .38 
 Abraded 
 
 0.30 
 .33 
 .35 
 .35 
 .36 
 .40 
 Abraded 
 
 0.23 
 .22 
 .21 
 .21 
 .23 
 .23 
 .23 
 
 Law of Unlubricated Friction. A. M. Wellington, Eng'g News, 
 April 7, 1888, states that the most important and the best determined of 
 all the laws of unlubricated friction may be thus expressed: 
 
 The coefficient of unlubricated friction decreases materially with 
 velocity, is very much greater at minute velocities of 0+, falls very 
 rapidly with minute increases of such velocities, and continues to fall 
 much less rapidly with higher velocities up to a certain varying point, 
 following closely the laws which obtain with lubricated friction. 
 
 Friction of Steel Tires Sliding on Steel Rails. (Westinghouse & 
 Galton.) 
 
 Speed, miles per hour 10 15 25 . 38 45 50 
 
 Coefficient of friction 0.110 .087 ,08O .051 .047 .040 
 
 Adhesion, Ibs. per gross ton 246 195 179 128 114 90 
 
 Rolling Friction is a consequence of the irregularities of form and 
 the roughness of surface of bodies rolling one over the other. Its laws 
 are not yet definitely established in consequence of the uncertainty 
 which exists in experiment as to how much of the resistance is due to 
 roughness of surface, how much to original and permanent irregularity 
 of form, and how much to distortion under the load. (Thurston.) 
 
1220 
 
 FRICTION AND LUBRICATION. 
 
 Coefficients of Rolling Friction. If R = resistance applied at the 
 circumference of the wheel, W = total weight, r = radius of the wheel, 
 and / = a coefficient, R = fW -f- r. /is very variable. Coulomb gives 
 0.06 for wood, 0.005 for metal, where W is in pounds and r in feet. Tred- 
 gold made the value of / for iron on iron 0.002. For wagons on soft soil 
 Morin found / = 0.065, and on hard smooth roads 0.002. 
 
 A Committee of the Society of Arts (Clark, R. T. D.) reported a 
 loaded omnibus to exhibit a resistance on various loads as below: 
 Pavement. Speed per hour. Coefficient. Resistance. 
 
 Granite 2.87 miles. 0.007 17. 41 per ton. 
 
 Asphalt 3.56 " 0.0121 27.14 
 
 Wood 3.34 0.0185 41.60 
 
 Macadam, graveled 3.45 0.0199 44.48 
 
 Macadam, granite, new.. .. 3.51 0.0451 101.09 
 
 Thurston gives the value of/ for ordinary railroads, 0.003; welf-laiQ 
 railroad track, 0.002; best possible railroad track, 0.001. 
 
 The few experiments that have been made upon the coefficients ol 
 rolling friction, apart from axle friction, are too incomplete to serve as a 
 basis for practical rules. (Trautwine.) 
 
 Laws of Fluid Friction. For all fluids, whether liquid or gaseous, 
 the resistance is (1) independent of the pressure between the masses in 
 contact; (2) directly proportional to the area of rubbing-surface; (3) pro- 
 portional to the square of the relative velocity at moderate and high 
 speeds, and to the velocity nearly at low speeds; (4) independent of the 
 nature of the surfaces of the solid against which the stream may flow, but 
 dependent to some extent upon their degree of roughness; (5) proportional 
 to the density of the fluid, and related in some way to its viscosity. 
 (Thurston.) 
 
 The Friction of Lubricated Surfaces approximates that of solid friction 
 as the journal is run dry, and that of fluid friction as it is flooded with oil. 
 Angles of Repose and Coefficients of Friction of Building Materials. 
 (From Rankine's Applied Mechanics.) 
 
 
 e. 
 
 / = tan 9. 
 
 1 -r- tan 
 
 Dry masonry and brickwork. . . 
 Masonry and brickwork with 
 damp mortar. 
 
 31 to 35 
 
 361/2 
 22 
 35 to 162/3 
 26 1/2 to 11 1/3 
 31 to 111/3 
 14 to 81/2 
 27 
 181/4 
 14 to 45 
 
 21 to 37 
 45 
 17 
 
 39 to 48 
 
 0.6 to 0.7 
 
 0.74 
 about 0.4 
 0.7 to 0.3 
 0.5 to 0.2 
 0.6 to 0.2 
 0.25 to 0.15 
 0.51 
 0.33 
 0.25 to 1.0 
 
 0.38 to 0.75 
 1.0 
 0.31 
 
 0.81 
 
 1.67 to 1.4 
 
 1.35 
 2.5 
 1.43 to 3. 3 
 2 to 5 
 1.67 to 5 
 4 to 6.67 
 1.96 
 3. 
 4 to 1 
 
 2.63 to 1.33 
 3.23 
 1.23 to 0.9 
 
 
 Iron on stone 
 
 Timber on timber 
 
 Timber on metals 
 
 Metals on metals 
 
 Masonry on dry clay . . . 
 
 Masonry on moist clay 
 
 Earth on earth 
 
 Earth on earth, dry sand, clay, 
 and mixed earth 
 
 Earth pn earth, damp clay 
 Earth on earth wet clay 
 
 Earth on earth, shingle, and 
 gravel 
 
 Coefficients of Friction of Journals. (Morin.) 
 
 Material. 
 
 Unguent. 
 
 Lubrication. 
 
 Intermittent . 
 
 Continuous. 
 
 Cast iron on cast iron | 
 
 Oil, lard, tallow. 
 Unctuous and wet 
 Oil, lard, tallow. 
 Unctuous and wet 
 Oil, lard. 
 
 Oil, lard, tallow. 
 
 Oil, lard. 
 Unctuous. 
 Olive oil. 
 Lard. 
 
 0.07 to 0.08 
 0.14 
 0.07 to 0.08 
 0.16 
 
 0.03 to 0.054 
 0.03 to 0.054 
 
 0.09 
 0.03 to 0.054 
 
 Cast iron on lignum vitae . . . 
 Wrought iron on cast iron . ) 
 Wrought iron on bronze. . j 
 
 Iron on lignum vitas | 
 Bronze on bronze | 
 
 0.07 to 0.08 
 
 0.11 
 0.19 
 0.10 
 09 
 
 
FRICTION AND LTJBEICATION. 
 
 1221 
 
 Prof. Thurston says concerning the foreg9ing figures that much better 
 results are probably obtained in good practice with ordinary machinery. 
 Those here given are so modified by variations of speed, pressure, and 
 temperature, that they cannot be taken as correct for general purposes. 
 
 Friction of Motion.- The following is a table of the angle of repose 
 0, the coefficient of friction / = tan 0, and its reciprocal, 1 + f, for the 
 materials of mechanism condensed from the tables of General Morin 
 (1831) and other sources, as given by Rankine: 
 
 No. 
 
 Surfaces. 
 
 I 
 
 I 
 
 f. 
 
 1 
 
 Wood on wood, dry 
 
 14 to 26 1/2 
 
 0.25 to 0.5 
 
 4 to 2 
 
 7 
 
 " " " soaped 
 
 1 1 1/2 to 2 
 
 02 to 04 
 
 5 to 25 
 
 1 
 
 Metals on oak dry 
 
 261/2 to 31 
 
 05 to 6 
 
 2 to 1 .67 
 
 4 
 
 " wet 
 
 131/2 to 14 
 
 0.24 to 0.26 
 
 4.17 to 3. 85 
 
 *> 
 
 ** " soapy . . . 
 
 1 1 1/2 
 
 2 
 
 
 ft 
 
 " elm dry 
 
 111/2 to 14 
 
 0.2 to 0.25 
 
 5 to 4 
 
 
 
 28 
 
 0.53 
 
 1.89 
 
 8 
 
 
 18l/ 2 
 
 0.33 
 
 3 
 
 9 
 
 Leather on oak 
 
 15 to 191/2 
 
 0.27 to 0.38 
 
 3. 7 to 2. 86 
 
 10 
 
 
 29l/ 2 
 
 0.56 
 
 1.79 
 
 11 
 
 12 
 13 
 14 
 
 ** metals, wet 
 greasy . . 
 oily 
 Metals on metals dry 
 
 20 
 13 
 81/2 
 81/2 to 11 
 
 0.36 
 0.23 
 0.15 
 0.15 to 0.2 
 
 2.78 
 4.35 
 6.67 
 6.67 to 5 
 
 |5 
 
 *' " " wet 
 
 161/2 
 
 0.3 
 
 3.33 
 
 16 
 
 Smooth surfaces, occasion- 
 ally greased 
 
 4 to 41/2 
 
 0.07 to 0.08 
 
 14.3 to 12.5 
 
 17 
 
 Smooth surfaces, continu- 
 ously greased 
 
 3 
 
 0.05 
 
 20 
 
 18 
 
 Smooth surfaces, best results 
 
 1 3/ 4 to 2 
 
 0.03 to 0.036 
 
 
 19 
 
 Bronze on lignum vitse, con- 
 stantly wet 
 
 3? 
 
 0.05? 
 
 
 Average Coefficients of Friction. Journal of cast iron in bronze 
 bearing; velocity 720 feet per minute; temperature 70 F.; intermittent 
 feed through an oil-hole. (Thurston on Friction and Lost Work.) 
 
 Pressures, Pounds per Square Inch. 
 
 
 
 8 
 
 
 16 
 
 
 
 32 
 
 
 
 48 
 
 
 Sperm, lard, neatsfoot, etc. . 
 Olive, cotton-seed, rape, etc. 
 Cod and menhaden 
 
 .159 
 .160 
 
 ?48 
 
 to 
 to 
 to 
 
 .250 
 .283 
 778 
 
 .138 to 
 .107 to 
 124 to 
 
 .192 
 .245 
 167 
 
 .086 
 .101 
 097 
 
 to 
 to 
 to 
 
 .141 
 .168 
 10? 
 
 .077 
 .079 
 081 
 
 to 
 to 
 
 to 
 
 .144 
 .131 
 1?? 
 
 Mineral lubricating-oils .... 
 
 .154 
 
 to 
 
 .261 
 
 .145 to 
 
 .233 
 
 .086 
 
 to 
 
 .178 
 
 .094 
 
 to 
 
 .222 
 
 With fine steel journals running in bronze bearings and continuous 
 lubrication, coefficients far below those above given are obtained. 
 Thus with sperm-oil the coefficient with 50 Ibs. per square inch pres- 
 sure was 0.0034; with 200 Ibs., 0.0051; with 300 Ibs., 0.0057. 
 
 For very low pressures, as in spindles, the coefficients are much 
 higher. Thus Mr. Woodbury found, at a temperature of 100 and a 
 velocity of 600 feet per minute, 
 
 Pressures, Ibs. per sq. in. . . 1 23 4 5 
 
 Coefficient 0.38 0.27 0.22 0.18 0.17 
 
 These high coefficients, however, and the great decrease in the co- 
 efficient at increased pressures are limited as a practical matter only to 
 the smaller pressures which exist especially in spinning machinery, 
 where the pressure is so light and the film of oil so thick that the viscos- 
 ity of the oil is an important part of the total frictional resistance. 
 
 Experiments on Friction of a Journal Lubricated by an Oil- 
 bath (reported by the Committee on Friction, Proc. Inst. M. E., 
 Nov., 1883) show that the absolute friction, that is, the absolute tan- 
 gential force per square inch of bearing, required to resist the tendency 
 of the brass to go round with the journal, is nearly a constant under all 
 loads, within ordinary working limits. Most certainly it does not in- 
 
1222 FBICTION AND LUBRICATION 
 
 crease in direct proportion to the load, as it should do according to thd 
 ordinary theory of solid friction. The results of these experiments 
 seem to show that the friction of a perfectly lubricated journal follows 
 the laws of liquid friction much more closely than those of solid friction. 
 They show that under these circumstances the friction is nearly inde- 
 pendent of the pressure per square inch, and that it increases with the 
 velocity, though at a rate not nearly so rapid as the square of the velocity. 
 
 The experiments on friction at different temperatures indicate a great 
 diminution in the friction as the temperature rises. Thus in the case of 
 lard-oil, taking a speed of 450 r.p.m., the coefficient of friction at a tem- 
 perature of 120 is only one-third of what it was at a temperature of 60. 
 
 The journal was of steel, 4 ins. diameter and 6 ins. long, and a gun- 
 metal brass, embracing somewhat less than half the circumference of the 
 journal, rested on its upper side, on which the load was applied. When 
 the bottom of the journal was immersed in oil, and the oil therefore carried 
 under the brass by rotation of the journal, the greatest load carried with 
 rape-oil was 573 Ibs. per sq. in., and with mineral oil 625 Ibs. 
 
 In experiments with ordinary lubrication, the oil being fed in at the 
 center of the top of the brass, and a distributing groove being cut in the 
 brass parallel to the axis of the journal, the bearing would not run cool 
 with only 100 Ibs. per sq. in., the oil being pressed out from the bearing- 
 surface and through the oil-hole, instead of being carried in by it. On 
 introducing the oil at the sides through two parallel grooves, the lubrica- 
 tion appeared to be satisfactory, but the bearing seized with 380 Ibs. 
 per sq. in. 
 
 When the oil was introduced through two oil-holes, one near each end 
 of the brass, and each connected with a curved groove, the brass refused 
 to take its oil or run cool, and seized with a load of only 200 Ibs. per sq. in. 
 
 With an oil-pad under the journal feeding rape-oil, the bearing fairly 
 carried 551 Ibs. Mr. Tower's conclusion from these experiments is that 
 the friction depends on the quantity and uniformity of distribution of the 
 oil, and may be anything between the oil-bath results and seizing, accord- 
 ing to the perfection or imperfection of the lubrication. The lubrication 
 may be very small, giving a coefficient of Vioo; but it appeared as though 
 it could not be diminished and the friction increased much beyond this 
 point without imminent risk of heating and seizing. The oil-bath prob- 
 ably represents the most perfect lubrication possible, and the limit 
 beyond which friction cannot be reduced by lubrication; and the experi- 
 ments show that with speeds of from 100 to 200 feet per minute, by 
 properly proportioning the bearing-surface to the load, it is possible to 
 reduce the coefficient of friction to as low as Viooo. A coefficient of Visoo 
 is easily attainable, and probably is frequently attained, in ordinary 
 engine-bearings in which the direction of the force is rapidly alternating 
 and the oil given an opportunity to get between the surfaces, while the 
 duration of the force in one direction is not sufficient to allow time for 
 the oil film to be squeezed out. 
 
 Observations on the behavior of the apparatus gave reason to believe 
 that with perfect lubrication the speed of minimum friction was from 
 100 to 150 feet per minute, and that this speed of minimum friction tends 
 to be higher with an increase of load, and also with less perfect lubrica- i 
 tion. By the speed of minimum friction is meant that speed in approach- 
 ing which from rest the friction diminishes, and above which the friction 
 increases. 
 
 Coefficients of Friction of Motion and of Rest of a Journal. 
 A cast-iron journal in steel boxes, tested by Prof. Thurston at a sneed of 
 rubbing of 150 feet per minute, with lard "and with sperm oil, gave the | 
 following : 
 
 Press, per sq. in., Ibs . 50 100 250 500 750 1000 
 
 Coeff., with sperm. .. 0.013 0.008 0.005 0.004 0.0043 0.009 ! 
 Coeff., with lard 0.02 0.01370.0085 0.00530.0066 0.125: 
 
 The coefficients at starting were: 
 
 Withsperm 0.07 0.135 0.14 0.15 0.185 0.18 
 
 Withlard 0.07 0.11 0.11 0.10 0.12 
 
 The coefficient at a speed of 150 feet per minute decreases with in- i 
 crease of pressure until 500 Ibs. per sq. in. is reached; above this it 
 creases. The coefficient at rest or at starting increases with the pressure 
 throughout the range of the tests. 
 
FRICTION AND LUBRICATION. 
 
 1223 
 
 Coefficients of Friction of Journal with Oil-bath. Abstract of 
 results of Tower's experiments on friction (Proc. Inst. M. E., Nov., 
 1883). Journal, 4 in. diam., 6 in. long; temperature, 90 F. 
 
 Lubricant in Bath. 
 
 Nominal Load, in Lbs. per Sq. In. 
 
 625 
 
 520 
 
 415 
 
 310 
 
 205 
 
 153 
 
 100 
 
 Coefficient of Friction. 
 
 Lard, oil' 157 ft per rnin 
 
 
 .0009 
 .0017 
 .0014 
 .0022 
 seized 
 
 .0012 
 .0021 
 .0016 
 .0027 
 .0015 
 .0021 
 
 .0009 
 .0016 
 .0012 
 .002 
 
 0014 
 .0029 
 .0022 
 .004 
 .0011 
 .0019 
 
 .0008 
 .0016 
 .0014 
 .0024 
 
 0056 
 
 .0020 
 .0042 
 .0034 
 .0066 
 .0016 
 .0027 
 
 .0014 
 .0024 
 .0021 
 .0035 
 
 0098 
 
 .0027 
 .0052 
 .0038 
 .0083 
 .0019 
 .0037 
 
 .002 
 .004 
 
 .0042 
 .009 
 .0076 
 .0151 
 .003 
 .0064 
 
 .004 
 .007 
 .004 
 .007 
 
 .0125 
 .0152 
 
 .0099 
 .0133 
 
 " 471 " " 
 
 
 Mineral grease: 157 ft. per min 
 471 " " .... 
 
 .001 
 .002 
 
 "471 " 
 
 
 Rape-oil* 157ft per min 
 
 (573 lb. 
 .001 
 
 .001 
 .0015 
 .0012 
 .0018 
 
 "471 " " 
 
 Mineral-oil: 157 ft. per min 
 "471 " " 
 Rape-oil fed by ' 
 siphon lubricator:{]57ft, t per min. 
 
 Rape-oil, pad 
 under journal: j]^^. per min. 
 
 .0013 
 
 
 
 
 ..... 
 
 .0068 
 0099 
 
 .0077 
 0105 
 
 
 
 
 
 
 0099 
 
 0078 
 
 
 Comparative friction of different lubricants under same circumstances, 
 temperature 90, oil-bath: sperm-oil, 100; rape-oil, 106; mineral oil, 129; 
 lard, 135; olive oil, 135; mineral grease, 217. 
 
 Value of Anti-friction Metals. (Denton.) The various white 
 metals available for lining brasses do not afford coefficients of friction 
 lower than can be obtained with bare brass, but they are less liable to 
 "overheating," because of the superiority of such material over bronze 
 in ability to permit of abrasion or crushing, without excessive increase of 
 friction. 
 
 Thurston (Friction and Lost Work) says that gun-bronze, Babbitt, 
 and other soft white alloys have substantially the same friction; in other 
 words, the friction is determined by the nature of the unguent and not 
 by that of the rubbing-surfaces, when the latter are in good order. The 
 soft metals run at higher temperatures than the bronze. This, however, 
 does not necessarily indicate a serious defect, but simply deficient con- 
 ductivity. The value of the white alloys for bearings lies mainly in their 
 ready reduction to a smooth surface after any local or general injury by 
 alteration of either surface or form. 
 
 Cast Iron for Bearings. (Joshua Rose.) Cast iron appears to be an 
 exception to the general rule, that the harder the metal the greater the 
 resistance to 'vear, because cast iron is softer in its texture and easier to 
 cut with steel tools than steel or wrought iron, but in some situations it 
 is far more durable than hardened steel; thus when surrounded by steam 
 it will wear better than will any other metal. Thus, for instance, ex- 
 perience has demonstrated that piston-rings of cast iron will wear smoother, 
 better, and equally as long as those of steel, and longer than those of 
 either wrought iron or brass, whether the cylinder in which it works be 
 composed of brass, steel, wrought iron, or cast iron; the latter being the 
 more noteworthy, since two surfaces of the same metal do not, as a rule, 
 wear or work well together. So also slide-valves of brass are not found 
 to wear so long or so smoothly as those of cast iron, let the metal of which 
 the seating is composed be whatever it may; while, on the other hand, a 
 cast-iron slide-valve will wear longer of itself and cause less wear tc 
 its seat, if the latter is of cast iron, than if of steel, wrought iron, or 
 brass. 
 
 Friction of Metals under Steam-pressure. The friction of brass 
 upon iron under steam-pressure is double that of iron upon iron. (G. H. 
 Babcock, Trans. A. S. M. E. t i, 151.) 
 
 Morin's "Laws of Friction." 1. The friction between two bodies 
 is directly proportioned to the pressure-, i.e., the coefficient is constant 
 *or all pressures. 
 
1224 FRICTION AND LUBRICATION. 
 
 
 2. The coefficient and amount of friction, pressure being the same, are 
 independent of the areas in contact. 
 
 3. The coefficient of friction is independent of velocity, although static 
 friction (friction of rest) is greater than the friction of motion. 
 
 Eng'g News, April 7, 1888, comments on these "laws" as follows: 
 From 1831 till about 1876 there was no attempt worth speaking of to 
 enlarge our knowledge of the laws of friction, which during all that period 
 was assumed to be complete, although it was really worse than nothing, 
 since it was for the most part wholly false. In the year first mentioned 
 Morin began a series of experiments which extended over two or three 
 years, and which resulted in the enunciation of these three "funda- 
 mental laws of friction," no one of which is even approximately true. 
 
 For fifty years these laws were accepted as axiomatic, and were quoted 
 as such without question in every scientific work published during that 
 whole period. Now that they are so thoroughly discredited it has been 
 attempted to explain away their defects on the ground that they cover 
 only a very limited range of pressures, areas, velocities, etc., and that 
 Morin himself only announced them as true within the range of his con- 
 ditions. It is now clearly established that there are no limits or con- 
 ditions within which any one of them even approximates to exactitude, 
 and that there are many conditions under which they lead to the wildest 
 kind of error, while many of the constants were as inaccurate as the laws. 
 For example, in Morin's "Table of Coefficients of Moving Friction of 
 Smooth Plane Surfaces, perfectly lubricated," which may be found in 
 hundreds of text-books now in use, the coefficient of wrought iron on 
 brass is given as 0.075 to 0.103, which would make the rolling friction of 
 railway trains 15 to 20 Ibs. per ton instead of the 3 to 6 Ibs. which it 
 actually is. 
 
 General Morin, in a letter to the Secretary of the Institution of Mechan- 
 ical Engineers, dated March 15, 1879, writes as follows concerning his 
 experiments on friction made more than forty years before: "The results 
 furnished by my experiments as to the relations between pressure, surface, 
 and speed on the one hand, and sliding friction on the other, have always 
 been regarded by myself, not as mathematical laws, but as close approxi- 
 mations to the truth, within the limits of the data of the experiments 
 themselves. The same holds, in my opinion, for many other laws of 
 practical mechanics, such as those of rolling resistance, fluid resistance, 
 etc. " 
 
 Prof. J. E. Denton (Stevens Indicator, July, 1890) says: It has been 
 generally assumed that friction between lubricated surfaces follows the 
 simple law that the amount of the friction is some fixed fraction of 
 the pressure between the surfaces, such fraction being independent of the 
 intensity of the pressure per square inch and the velocity of rubbing, 
 between certain limits of practice, and that the fixed fraction referred to 
 is represented by the coefficients of friction given by the experiments of 
 Morin or obtained from experimental data which represent conditions of 
 practical lubrication, such as those given in Webber's Manual of Power. 
 
 By the experiments of Thurston, Woodbury, Tower, etc., however, it 
 appears that the friction between lubricated metallic surfaces, such as 
 machine bearings, is not directly proportional to the pressure,is not 
 independent of the speed, and that the coefficients of Morin and Webber 
 are about tenfold too great for modern journals. 
 
 Prof. Denton offers an explanation of this apparent contradiction of 
 authorities by showing, with laboratory testing-machine data, that 
 Morin's laws hold for bearings lubricated by a restricted feed of lubricant, 
 such as is afforded by the oil-cups common to machinery; whereas the 
 modern experiments have been made with a surplus feed or superabun- 
 flance or lubricant, sucn as is provided only in railroad-car journals, and 
 a few special cases of practice. 
 
 That the low coefficients of friction obtained under the latter conditions 
 are realized in the case of car-journals, is proved by the fact that the 
 temperature of car-boxes remains at 100 at high velocities; and experi- 
 ment shows that this temperature is consistent only with a coefficient of 
 friction of a fraction of one per cent. Deductions from experiments on 
 train resistance also indicate the same low degree of friction. But these 
 low coefficients do not account for the internal friction of steam-engines 
 as well as do the coefficients of Morin and Webber, 
 
AND LUfi&ICATlON. 1225 
 
 In American Machinist, Oct. 23, 1890, Prof, Benton says: Morin's 
 
 measurements of friction of lubricated journals did not extend to light 
 pressures. They apply only to the conditions of general shafting and 
 engine work. 
 
 He clearly understood that there was a frictional resistance, due solely 
 to the viscosity of the oil, and that therefore, for very light pressures, 
 the laws which he enunciated did not prevail. 
 
 He applied his dynamometers to ordinary shaft-journals without 
 special preparation of the rubbing-surfaces, and without resorting to 
 artificial methods of supplying the oil. 
 
 Later experimenters have with few exceptions devoted themselves 
 exclusively to the measurement of resistance practically due to viscosity 
 alone. They have eliminated the resistance to which Morin confined his 
 measurements, namely, the friction due to such contacts of the rubbing- 
 surfaces as prevail with a very thin film of lubricant between compara- 
 tively rough surfaces. 
 
 Prof. Denton also says (Trans. A. S. M. E., x, 518): "I do not believe 
 there is a particle of proof in any investigation of friction ever made, 
 that Morin's laws do not hold for ordinary practical oil-cups or restricted 
 rates of feed." 
 
 Laws of Friction of Well-lubricated Journals. John Goodman 
 (Trans. Inst. C. E., 1886, Eng'g News, April 7 and 14, 1888), reviewing 
 the results obtained from the testing-machines of Thurston, Tower, and 
 Stroudley, arrives at the following laws: 
 
 LAWS OF FRICTION: WELL-LUBRICATED SURFACES. 
 (Oil-bath.) 
 
 1. The coefficient of friction with the surfaces efficiently lubricated in 
 from Ve to Vio that for dry or scantily lubricated surfaces. 
 
 2. The coefficient of friction for moderate pressures and speeds varies 
 approximately inversely as the normal pressure; the frictional resistance 
 varies as the area in contact, the normal pressure remaining constant. 
 
 3. At very low journal speeds the coefficient of friction is abnormally 
 high; but as the speed of sliding increases from about 10 to 100 ft. per 
 min., the friction diminishes, and again rises when that speed is exceeded, 
 varying approximately as the square root of the speed. 
 
 4. The coefficient of friction varies approximately inversely as the 
 temperature, within certain limits, namely, just before abrasion takes 
 place. 
 
 The evidence upon which these laws are based is taken from various 
 modern experiments. That relating to Law 1 is derived from the " First 
 Report on Friction Experiments," by Mr. Beauchamp Tower. 
 
 Method of Lubrication. 
 
 Coefficient of 
 Friction. 
 
 Comparative 
 Friction. 
 
 Oil-bath 
 
 00139 
 
 1 00 
 
 Siphon lubricator 
 
 0.0098 
 
 7 06 
 
 Pad under journal 
 
 0.0090 
 
 6.48 
 
 With a load of 293 Ibs. per sq. in. and a journal speed of 314 ft. per 
 min. Mr. Tower found the coefficient of friction to be .0016 with an oil- 
 bath, and 0.0097, or six times as much, with a pad. The very low co- 
 efficients obtained by Mr. Tower will be accounted for by Law 2, as he 
 found that the frictional resistance per square inch under varying loads 
 is nearly constant, as below: 
 
 Load in Ibs. per sq. in. 529 468 415 363 310 258 205 153 100 
 Frictional resist, per J Q 416 0>5U Q 498 . 4 72 0.464 0.438 0.43 0.458 0.45 
 
 The frictional resistance per square inch is the product of the coefficient 
 of friction into the load per square inch on horizontal sections of the brass. 
 Hence, if this product be a constant, the one factor must vary inversely 
 as the other, or a high load will give a low coefficient, and vice versa. 
 
 For ordinary lubrication, the coefficient is more constant under varying 
 loads- the frictionai resistance then varies directly as the load, as shown 
 by Mr, Tower in Table VIII of bis report (Proc. Inst. M. E.\ 1883), 
 
1226 
 
 FRICTION AND LUBRICATION* 
 
 With respect to Law 3, A. M. Wellington (Trans. A. S. C. E., 1884), 
 in experiments on journals revolving at very low velocities, found that 
 the friction was then very great, and nearly constant under varying 
 conditions of the lubrication, load, and temperature. But as the speed 
 increased the friction fell slowly and regularly, and again returned to 
 the original amount when the velocity was reduced to the same rate. 
 This is shown in the following table: 
 Speed, feet per minute: 
 
 0+ 2.16 ' 3.33 4.86 8.82 21.42 35.37 53.01 89.28 106.02 
 Coefficient of friction : 
 0.118 0.094 0.070 0.069 0.055 0.047 0.040 0.035 0.030 0.026 
 
 It was also found by Prof. Kimball that when the journal velocity 
 was increased from 6 to 110 ft. per min., the friction was reduced 
 70%; in another case the friction was reduced 67% when the velocity 
 was increased from 1 to 100 ft. per min. ; but after that point was reached 
 the coefficient varied approximately with the square root of the velocity. 
 
 The following 'results were obtained by Mr. Tower: 
 
 Feet per minute 
 
 209 
 
 262 
 
 314 
 
 366 
 
 419 
 
 471 
 
 Nominal Load 
 per Sq. In. 
 
 Coeff . of friction 
 ( u 
 
 0.0010 
 .0013 
 .0014 
 
 0.0012 
 .0014 
 .0015 
 
 0.0013 
 .0015 
 .0017 
 
 0.0014 
 .0017 
 .0019 
 
 0.0015 
 .0018 
 .0021 
 
 0.0017 
 .002 
 .0024 
 
 520 Ibs. 
 468 Ibs. 
 415 Ibs. 
 
 The variation of friction with temperature is approximately in the 
 inverse ratio, Law 4. Take, for example, Mr. Tower's results, at 
 262 ft. per minute: 
 
 Temp. F. 
 
 110 
 
 100 
 
 90 
 
 80 
 
 70 
 
 60 
 
 Observed. 
 
 0044 
 
 0.0051 
 
 0.006 
 
 0.0073 
 
 0.0092 
 
 0.0119 
 
 Calculated 
 
 0.00451 
 
 0.00518 
 
 0.00608 
 
 0.00733 
 
 0.00964 
 
 0.01252 
 
 This law does not hold good for pad or siphon lubrication, as then the 
 coefficient of friction diminishes more rapidly for given increments of 
 temperature, but on a gradually decreasing scale, until the normal 
 temperature has been reached; this normal temperature increases 
 directly as the load per sq. in. This is shown in the following table 
 taken from Mr. Stroudley's experiments with a pad of rape-oil: 
 
 Temp. F 
 
 105 
 
 110 
 
 115 
 
 120 
 0.0140 
 0.0020 
 
 125 
 
 130 
 
 135 
 
 140 
 
 145? 
 
 Coefficient 
 Decrease of coeff . . 
 
 0.022 
 
 0.0180 
 0.0040 
 
 0.0160 
 0.0020 
 
 0.0125 
 0.0015 
 
 0.0115 
 0.0010 
 
 0.0110 
 0.0005 
 
 0.0106 
 0.0004 
 
 0.0102 
 0.0002 
 
 In the Galton-Westinghouse experiments it was found that with 
 velocities below 100 ft. per min., and with low pressures, the frictional 
 resistance varied directly as the normal pressure ; but when a velocity of 
 100 ft.per min. was exceeded, the coefficient of friction greatly diminished ; 
 from the same experiments Prof. Kennedy found that the coefficient of 
 friction for high pressures was sensibly less than for low. 
 
 Allowable Pressures on Bearing-surfaces. (Proc. InsL M. E. t 
 May, 1888.) The Committee on Friction experimented with a steel 
 ring of rectangular section, pressed between two cast-iron disks, the 
 annular bearing-surfaces of which were covered with gun-metal, and were 
 12 in. inside diameter and 14 in. outside. The two disks were rotated 
 together, and the steel ring was prevented from rotating by means of a 
 lever, the Iwlding force of which was measured. When oiled through 
 grooves cut in each face of the ring and tested at from 50 to 130 revs. 
 per min., it was found that a pressure of 75 Ibs. per sq. in. of bearing- 
 surface was as much as it would bear safely at the highest speed without 
 seizing, although it carried 90 Ibs. per sq. in. at the lowest speed. The 
 coefficient of friction is also much higher than for a cylindrical bearing, 
 and the friction follows the law of the friction of solids much more nearly 
 than that of liquids. This is doubtless due to the much less perfect 
 lubrication applicable to this form of bearing compared with a cylindrical 
 one. The coefficient of friction appears to be about the same with the 
 same load at all speeds, or, in other words, to be independent of the 
 speed; but it seems to diminish somewhat as the load is increased, and 
 may be stated approximately as 1/20 at 15 Ibs. per sq. in., diminishing to 
 1/30 at 75 Ibs. per sq. in. 
 
 The high .coefficients of friction are explained by the difficulty of lubri- 
 cating a collar-bearing. It" is similar to the slide-block of an engine; 
 
FRICTION AND LUBRICATION. 1227 
 
 which can carry only about one-tenth the load per sq. in. that can be> 
 carried by the crank-pins. 
 
 * In experiments on cylindrical journals it has been shown that when a 
 cylindrical journal was lubricated from the side on which the pressure 
 bore, 100 Ibs. per sq. in. was the limit of pressure that it would carry; 
 but when it came to be lubricated on the lower side and was allowed to 
 drag the oil in with it, 600 Ibs. per sq. in. was reached with impunity; 
 and if the 600 Ibs. per sq. in., which was reckoned upon the full diameter 
 of the bearing, came to be reckoned on the sixth part of the circle that was 
 taking the greater proportion of the load, it followed that the pressure 
 upon that part of the circle amounted to about 1200 Ibs. per sq. in. 
 
 In connection with these experiments Mr. Wicksteed states that in 
 drilling-machines the pressure on the collars is frequently as high as 336 
 Ibs. per sq. in., but the speed of rubbing in this case is lower than it was 
 in any of the experiments of the Research Committee. In machines 
 working very slowly and intermittently, as in testing-machines, very 
 much higher pressures are admissible. Prof. Thurston (Friction and 
 Lost Work, p. 240) says 7000 to 9000 Ibs. pressure per square inch 
 is reached on the slow working and rarely moved pivots of swing 
 bridges. 
 
 Mr. Adamson mentions the case of a heavy upright shaft carried upon 
 a small footstep-bearing, where a weight of at least 20 tons was carried 
 on a shaft of 5 in. diameter, or, say, 20 sq. in. area, giying a pressure of 
 1 ton per sq. in. The speed was 190 to 200 revs, per min. It was neces- 
 sary to force the oil under the bearing by means of a pump. For heavy 
 horizontal shafts, such as a fly-wheel shaft, carrying 100 tons on two jour- 
 nals, his practice for getting oil into the bearings was to flatten the journal 
 along one side throughout its whole length to the extent of about an 
 eighth of an inch in width for each inch in diameter up to 8 in. diameter; 
 above that size rather less flat in proportion to the diameter. At first 
 sight it appeared alarming to get a continuous flat place coming round 
 in every revolution of a heavily loaded shaft; yet it carried th a oil effec- 
 tually into the bearing, which ran much better in consequence than a 
 truly cylindrical journal without a flat side. 
 
 In thrust-bearings on torpedo-boats Mr. Thornycroft allows a pressure 
 of never more than 50 Ibs. per sq. in. 
 
 Mr. Tower says (Proc. Inst. M. E., Jan., 1884) : In eccentric-pins of punch- 
 ing and shearing machines very high pressures are sometimes used with- 
 out seizing. In addition to the alternation in the direction, the pressure 
 is applied for only a very short space of time in these machines, so that 
 the oil has no time to be squeezed out. 
 
 In the discussion on Mr. Tower's paper (Proc. Inst. M. E.. 1885) it was 
 stated that it is well known from practical experience that with a con- 
 stant load on an ordinary journal it is difficult and almost impossible 
 to have more than 200 Ibs. per square inch, otherwise the bearing would 
 get hot and the oil go out of it ; but when the motion was reciprocating, 
 so that the load was alternately relieved from the journal, as with crank- 
 pins and similar journals, much higher loads might be applied than even 
 700 or 800 Ibs. per square inch. 
 
 Mr. Goodman (Proc. Inst. C. E., 1886) found that the total frictional 
 resistance is materially reduced by diminishing the width of the brass. 
 
 The lubrication is most efficient in reducing the friction when the brass 
 subtends an angle of from 120 to 60. The film is probably at its best 
 between the angles 80 and 110. 
 
 In the case of a brass of a railway axle-bearing where an oil-groove is 
 cut along its crown and an oil-hole is drilled through the top of the brass 
 into it, the wear is invariably on the off side, which is probably due to 
 the oil escaping as soon as it reaches the crown of the brass, and so leaving 
 the off side almost dry, where the wear consequently ensues. 
 
 In railway axles the brass wears always on the forward side. The 
 same observation has been made in marine-engine journals, which always 
 wear in exactly the reverse way to what might be expected. Mr. Stroud- 
 ley thinks this peculiarity is due to a film of lubricant being drawn in 
 from the under side of the journal to the aft part of the brass, which 
 effectually lubricates and prevents wear on that side; and that when the 
 lubricant reaches the forward side of the brass it is so attenuated down 
 to a wedge shape that there is insufficient lubrication, and greater wear 
 consequently follows. 
 
1228 FRICTION AND LUBRICATION. 
 
 C. J. Field (Power, Feb., 1893) says: One of the most vital points of an 
 engine for electrical service is that of main bearings. They should have 
 a surface velocity of not exceeding 350 feet per minute, with a mean 
 bearing-pressure per square inch of projected area of journal of not more 
 than 80 Ibs. This is considerably within the safe limit of cool perform- 
 ance and easy operation. If the bearings are designed in this way, it 
 would admit the use of grease on all the main wearing-surface, which in 
 a large type of engines for this class of work we think advisable. 
 
 Oil-pressure in a Bearing. Mr. Beauchamp Tower (Proc. Inst. 
 M. E., Jan., 1885) made experiments with a brass bearing 4 ins. diameter 
 by 6 ins. long, to determine the pressure of the oil between the brass and 
 the journal. The bearing was half immersed in oil, and had a total 
 load of 8008 Ibs. upon it. The journal rotated 150 r.p.m. The pressure 
 of the oil was determined by drilling small holes in the bearing at different 
 points and connecting them by tubes to a Bourdon gauge. It was found 
 that the pressure varied from 310 to 625 Ibs. per sq. in., the greatest 
 pressure being a little to the "off" side of the center line of the top of the 
 bearing, in the direction of motion of the journal. The sum of the up- 
 ward force exerted by these pressures for the whole lubricated area was 
 nearly equal to the total pressure on the bearing. The speed was re- 
 duced from 150 to 20 r.p.m., but the oil-pressure remained the same, 
 showing that the brass was as completely oil-borne at the lower speed as 
 at the higher. The following was the observed friction at the lower speed: 
 
 Nominal load, Ibs. per sq. in.. .. 443 333 211 89 
 
 Coefficient of friction .00132 .00168 .00247 .0044 | 
 
 The nominal load per square inch is the total load divided by the 
 product of the diameter and length of the journal. At the low speed 
 of 20 r.p.m. it was increased to 676 Ibs. per sq. in. without any signs of 
 heating or seizing. 
 
 Friction of Car-lournal Brasses. (J. E. Denton, Trans. A. 5. M. E., 
 xii, 405.) A new brass dressed with an emery-wheel, loaded with 5000 
 ibs., may have an actual bearing-surface on the journal, as shown by the 
 polish or a portion of the surface, of only 1 square inch. With this pressure 
 of 5000 Ibs. per sq. in., the coefficient of friction may be 6%, and the 
 brass may be overheated, scarred and cut, but, on the contrary, it may 
 wear down evenly to a smooth bearing, giving a highly polished area of 
 contact of 3 sq. ins., or more, inside of two hours of running, gradually 
 decreasing the pressure per square inch of contact, and a coefficient of 
 friction of less than 0.5%. A reciprocating motion in the direction of the 
 axis is of importance in reducing the friction. With such polished sur- 
 faces any oil will lubricate, and the coefficient of friction then depends 
 on the viscosity of the oil. With a pressure of 1000 Ibs. per sq. in., revo- 
 lutions from 170 to 320 per min., and temperatures of 75 to 113 F., with 
 both sperm and paramne oils, a coefficient of as low as 0.11% has been 
 obtained, the oil being fed continuously by a pad. 
 
 Experiments on O verheating of Bearings. Hot Boxes. (Denton.) 
 Tests with car brasses loaded from 1100 to 4500 Ibs. per sq. in. gave 
 7 cases of overheating out of 32 trials. The tests show how purely a 
 matter of chance is the overheating, as a brass which ran hot at 5000 Ibs. 
 load on one day would run cool on a later date at the same or higher 
 pressure. The explanation of this apparently arbitrary difference of 
 behavior is that tne accidental variations of the smoothness of the sur- 
 faces, almost infinitesimal in their magnitude, cause variations of friction 
 which are always tending to produce overheating, and it is solely a matter 
 of chance when these tendencies preponderate over the lubricating 
 influence of the oil. There is no appreciable advantage shown by sperm- 
 oil, when there is no tendency to overheat that is, paraffine can lubri- 
 cate under the highest pressures which occur, as well as sperm, when the 
 surfaces are within the conditions affording the minimum coefficients of 
 
 Sperm and other oils of high heat-resisting qualities, like vegetable oil 
 and petroleum cylinder stocks, differ from the more volatile lubricants, 
 like paraffine, only in their ability to reduce the chances of the continual 
 accidental infinitesimal abrasion producing overheating. 
 
 The effect of emery or other gritty substance in reducing overheating 
 of a bearing is thus explained: 
 
FRICTION AND LUBRICATION* 1229 
 
 The effect of the emery upon the surfaces of the bearings is to cover the 
 latter with a series of parallel grooves, and apparently after such grooves 
 are made the presence of the emery does not practically increase the 
 friction over its amount when pure oil only is between the surfaces. 
 
 The infinite number of grooves constitute a very perfect means of insuring 
 a uniform oil supply at every point of the bearings. As long as grooves 
 in the journal match with those in the brasses the friction appears to 
 amount to only about 10% to 15% of the pressure. But if a smooth 
 journal is placed between a set of brasses which are grooved, and pres- 
 sure be applied, the journal crushes the grooves and becomes brazed 
 or coated with brass, and then the coefficient of friction becomes upward 
 of 40%. If then emery is applied, the friction is made very much less by 
 its presence, because the grooves are made to match each other, and a 
 uniform oil supply prevails at every point of the bearings, whereas before 
 the application of the emery many spots of the bearing receive no oil 
 between them. 
 
 Moment of Friction and Work of Friction of Sliding-surfaces, etc. 
 
 Moment of Friction, Energy lost b'y Fric- 
 inch-lbs. tion in ft.-lbs. 
 
 per min. 
 Flat surfaces ............................ fWS 
 
 Shafts and journals ......... 1/2 fWd 0.2QlSfWdn 
 
 Flat pivots ---- ' ............ 2/3/fPr 0.349 /PFm 
 
 Collar-bearing .............. 
 
 Conical pivot ............... 2/sfWr cosec a 0.349/TFrn cosec a 
 
 Conical journal ............. 2/sfWr sec a 0.349 fWrn sec a 
 
 Truncated-cone pivot ........ 2 /^ r ^f O'^^f^ 
 
 Hemispherical pivot ........ fWr 0.5236 fWrn 
 
 Tractiix, or Schiele's "anti- 
 
 friction" pivot ........... fWr 0.5236 fWrn 
 
 In the above / = coefficient of friction; 
 
 W = weight on journal or pivot in pounds; 
 r = radius, d = diameter, in inches; 
 S = space in feet through which sliding takes place; 
 TZ = outer radius, r t = inner radius; 
 n = number of revolutions per minute; 
 a * the half-angle of the cone, i.e., the angle of the slope 
 
 with the axis. 
 To obtain the horse-power, divide the quantities in the last column 
 
 by 33,000. Horse-power absorbed by friction of a shaft = / og r.^ 
 
 t 
 
 The formula for energy lost by shafts and journals is approximately 
 true for loosely fitted bearings. Prof. Thurston shows that the correct 
 formula varies according to the character of fit of the bearing; thus for 
 loosely fitted journals, if U = the energy lost, 
 
 wn inch-pounds - - 26 / 18/Wn foot-lbs. 
 
 For perfectly fitted journals U = 2.54 fvrWn inch-lbs.= 0.3325 fWdn 
 ft.-lbs. 
 
 For a bearing in which the journal is so grasped as to give a uniform 
 pressure throughout, U = f^rWn inch-lbs. = 0.4112 fWdn ft.-lbs. 
 
 Resistance of railway trains and wagons due to friction of trains: 
 
 Pull on draw-bar = /X 2240 & R pounds per gross ton, 
 in which R is the ratio of the radius of the wheel to the radius .of journal. 
 
 A cylindrical journal, perfectly fitted into a bearing, and carrying a 
 total load, distributes the pressure due to this load unequally on the 
 bearing, the maximum pressure being at the extremity of the vertical 
 radius, while at the extremities of the horizontal diameter the pressure 
 is zero. At any point of the bearing-surface at the extremity of a radius 
 which makes an angle 6 with the vertical radius the normal pressure is 
 proportional to cos 0. If p = normal pressure on a unit of surface, 
 
1230 FRICTION AND LUBRICATION. 
 
 w = total load on a unit of length of the journal, and r = radius of journal, 
 
 w cos = 1.57 rp, p = w cos tt *- 1.57 r. 
 
 Tests of Large Shaft Bearings are reported by Albert Kingsbury 
 in Trans. A. S. M. E., 1905. A horizontal shaft was supported in two 
 bearings 9 X 30 ins., and a third bearing 15 X 40 ins., midway between the 
 other two, was pressed upwards against the shaft by a weighed lever, so 
 that it was subjected to a pressure of 25 to 50 tons. The journals were 
 flooded with oil from a supply tank. The shaft was driven by an electric 
 motor, and the friction H.P. was determined by measuring the current 
 supplied. Following are the principal results: 
 
 Load, tons* 
 
 25 25 25 25 25 33.6 42.3 47 47 50.5 
 Load per sq. in.* 
 
 83 83 83 83 83 112 141 157 157 168 
 Speed, r.p.m. 
 
 309 506 180 179 301 454 480 946 1243 1286 
 Speed, ft. per min.* 
 
 1215 1990 708 704 1180 1785 1890 3720 4900 5050 
 Friction H.P.f 
 
 12.6 21.7 6.43 5.12 10.1 16 17.9 41.9 47.8 52.3 
 Coeff. of frictionf 
 
 .0045 .0048 .0040 .0037 .0037 .0029 .0024 .0025 .0022 .0022 
 * On the large bearing. t Three bearings. 
 
 The last three tests were with paraffin oil; the others with heavy machine 
 oil. 
 
 Clearance between Journal and Bearing. John W. Upp, in 
 Trans. A. S. M. E., 1905 gives a table showing the diameter of bore 
 of horizontal and vertical bearings according to the practice of one of the 
 leading builders of electrical machinery. The maximum diameter of the 
 journal is the same as its nominal diameter, with an allowable variation 
 below maximum of 0.0005 in. up to 3 in. diam., 0.001 in. from 31/2 to 9 in., 
 and 0.0015 in. from 10 to 24 in. The maximum bore of a horizontal bear- 
 ing is larger than the diam. of the journal by from 0.002 in. for a i/2-in. 
 journal to 0.009 'for 6 in., f9r journals 7 to 15 in. it is 0.004 + 0.001 X 
 diam., and for 16 to 24 in. it is uniformly 0.02 in. For vertical journals the 
 clearance is less by from 0.001 to 0.004 in. according to the diameter. The 
 allowable variation above the minimum bore is from 0.001 to 0.005. 
 
 Allowable Pressures on Bearings. J. T. Nicholson, in a pap._ 
 read before the Manchester Assoc. of Engrs. (Am. Mach., Jan. 16, 1908, 
 Eng. Digest, Feb., 1908), as a result of a theoretical study of the lubrication 
 of bearings and of their emission of heat, obtains the formula p = P/ld 
 40 (dN) /*, in which p = allowable pressure per sq. in. of projected area, 
 P = total pressure, I = length and d = diam. of journal, N = revs, per 
 min. It appears from this formula that the greater the speed the greater 
 the allowable pressure per sq. in., so that for a 1-in. journal the allowable 
 pressure per sq. in. is 126 Ibs. at 100 r.p.m. and 189 Ibs. at 500 r.p.m., and 
 for a 5-in. journal 189 Ibs. at 100 and 283 Ibs. at 500 r.p.m. W. H. Scott 
 (Eng. Digest, Feb., 1908) says this is contrary to the teaching of practical 
 experience, and therefore the formula is inaccurate. Mr. Scott, from a 
 study of the experiments of Tower, Lasche, and Stribeck, derives the 
 following formulae for the several conditions named: 
 
 For main bearings of double-acting vertical engines, p = 750 
 44 horizontal 4t . p = 660 
 44 single-acting four-cycle gas en- 
 gines ....................................... p = 1350 D1 /i2/N l /4 
 
 For crank pins of vert, and hor. double-acting engines . p = 1560 
 " " " " single-acting four-cycle gas engines, p = 3000 
 For dead loads with ordinary lubrication .......... p = 400 N 
 
 11 forced " ........ p = 1600 N' 
 
 p allowable pressure in Ibs. per sq. in. of projected area; D = diam,. 
 in ins. ; N = revs. per. min. 
 
FKICTION AND LUBRICATION. 1231 
 
 F. W. Taylor (Trans. A. S. M. E., 1905), as the result of an investigation 
 of line shaft and mill "bearings that were running near the limit of dura- 
 bility and heating yet not dangerously heating, gives the formula PV =* 
 400. P = pressure in Ibs. per sq. in. of projected area, V = velocity of 
 circumference of bearing in ft. per sec. 
 
 The formula is applicable to bearings in ordinary shop or mill use on 
 shafting which is intended to run with the care and attention which such 
 bearings usually receive, and gives the maximum or most severe duty to 
 which it is safe to subject ordinary chain or oiled ball and socket bearings 
 which are babbitted. It is not safe for ordinary shafting to use cast-iron 
 boxes, with either sight feed, wick feed, or grease-cup oiling, under as severe 
 conditions as P X V = 200. 
 
 Arcbbutt and Deeley's "Lubrication and Lubricants " gives the follow- 
 ing allowable pressures in Ibs. per sq. in. of projected area of bearings. 
 Crank-pin of shearing and punching machine, hard steel, inter- 
 mittent load bearing 300C 
 
 Bronze crosshead neck journals 1200 
 
 Crank pins, large slow engine 80 X S 
 
 Crank pins, marine engines 400-500 
 
 Main crankshaft bearing, fast marine 40C 
 
 Same, slow marine 600 
 
 Railway coach journals 300-400 
 
 Flywheel shaft journals 150-200 
 
 Small engine crank pin 150-200 
 
 Small slide block, marine engine 100 
 
 Stationary engine slide blocks 25-125 
 
 Same, usual case 30- 60 
 
 Propeller thrust bearings 50- 70 
 
 Shafts in cast-iron steps, high speed 15 . 
 
 Bearing Pressures for Heavy Intermittent Loads. (Oberlm Smith, 
 Trans. A. S. M. E., 1905.) In a punching press of about 84 tons capa- 
 city, the pressure upon the front journal of the main shaft is about 
 2400 Ibs. per sq. in. of projected area. Upon the eccentric the pressure 
 against the pitman driving the ram is some 7000 Ibs. per sq. in. both 
 surfaces being of cast iron, and sometimes running at a surface speed of 
 140 feet per minute. Such machines run year in and year out with but 
 little trouble in the way of heating or " cutting." An instance of excessive 
 pressure may be cited in the case of a Ferracute toggle press, where the 
 whole ram pressure of 400 tons is brought to bear upon hardened steel 
 toggle-pins, running in cast iron or bronze bearings, 3 in. in diam. by nearly 
 ^4 in. long. These run habitually, for maximum work, under a load of 
 20,000 Ibs. per sq. in. 
 
 Bearings for Very High Rotative Speeds. (Proc. Inst. M. E., 
 Oct., 1888, p. 482.) In the Parsons steam-turbine, which has a speed as 
 high as 18,000 rev. per min., as it is impossible to secure absolute accuracy 
 of balance, the bearings are of special construction so as to allow of a 
 certain very small amount of lateral freedom. For this purpose the 
 bearing is surrounded by two sets of steel washers Vi6 in. thick and of 
 different diameters, the larger fitting close in the casing and about 1/32 in. 
 clear of the bearing, and the smaller fitting close on the bearing and about 
 V32 in. clear of the casing. These are arranged alternately, and are 
 pressed together by a spiral spring. Consequently any lateral movement 
 of the bearing causes them to slide mutually against one another, and by 
 their friction to check or damp any vibrations that may be set up in the 
 spindle. The tendency of the spindle is then to rotate about its axis of 
 mass, and the bearings are thereby relieved from excessive pressure, and 
 the machine from undue vibration. The allowing of the turbine itself 
 to find its own center of gyration is a well-known device in other branches 
 of mechanics: as in the instance of the centrifugal hydro-extractor, where 
 a mass very much out of balance is allowed to find its own center of 
 gyration; the faster it runs the more steadily does it revolve and the less 
 is the vibration Another illustration is to be found in the spindles of 
 spinning machinery which run at about 10,000 or 11,000 revs, per min.: 
 although of very small dimensions, the outside diameter of Mie largest 
 portion or driving whorl being perhaps n9t more than 11/4 in., it is found 
 impracticable to run them at that speed in what might be called a hard- 
 and-fast bearing. They are therefore run with some elastic substance 
 
1232 FRICTION AND LUBRICATION. 
 
 surrounding the bearing, such as steel springs, hemp, or cork. Any 
 elastic substance is sufficient to absorb the vibration, and permit of 
 absolutely steady running. 
 
 Bearing Pressures in Shafts of Parsons Turbines. The product of 
 the bearing pressure in Ib. per sq. in. and the peripheral velocity in ft. 
 per sec. is generally about 2500 (Proc., Inst. Elect. Engrs., June, 1905). 
 
 Thrust Bearings in Marine Practice. (G. W. Dickie, Trans. A. S. 
 M. E., 1905.) The approximate pressure on a thrust bearing of a propeller 
 shaft assuming two thirds of the indicated horse-power to be effective 
 
 on the propeller is P = I.H.P. X ^^ * ^080 = ^nF' X 2l7 ' 1 ' in 
 which S = speed of ship in knots per hour, P = total thrust in Ibs. The 
 following are data of water-cooled bearings which have given satisfactory 
 service: 
 
 Speed in knots 22 221/2 28 21 
 
 Thrust-ring surface, horse-shoe type, 
 
 sq. ins 1188 891 581 2268 
 
 Horse-power, one engine, I.H.P 11,500 6,800 4,200 15,000 
 
 Indicated pressure on bearing, Ibs,. .. 112,700 89,000 33,600 154,000 
 
 Pressure per sq. in. of surface, Ibs 95 100 58 68. 1 
 
 Mean speed of bearing surfaces, ft. per 
 
 min , 642 610 827 504 
 
 Bearings for Locomotives. (G. M. Basford, Trans., A. S. J\f. E., 
 1905.) Bearing areas for Ioc9motive journals are determined chiefly 
 by the possibilities of lubrication. On driving journals the following 
 figures of pressure in Ibs. per sq. in. of projected area give good service: 
 passenger, 190; freight, 200; switching, 220 Ibs. Crank pins may be 
 loaded from 1500 to 1700 Ibs.; wrist pins to 4000 Ibs. per sq. in. Car and 
 tender bearings are usually loaded from 300 to 325 Ibs. per sq. in. 
 
 Bearings of Corliss Engines. (P. H. Been, Trans, A. S. M. E., 
 1905.) In the practice of one of the largest builders the greatest pressure 
 allowed per sq. m. of projected area for all shafts is 140 Ibs. On most 
 engines the pressure per sq. in. multiplied by the velocity of the bearing 
 surface in ft. per sec. lies between 1000 and 1300. 
 
 Edwin Reynolds says that a main engine bearing to be safe against 
 undue heating should be of such a size that the product of the square root 
 of the speed of rubbing-surface in feet per second multiplied by the pounds 
 per square inch of projected area, should not exceed 375 for a horizontal 
 engine, or 500 for a vertical engine when the shaft is lifted at every revo- 
 lution. Locomotive driving boxes in some cases give the product as high 
 as 585, but this is accounted for by the cooling action of the air. (Am. 
 Mach., Sept. 17, 1903.) 
 
 Temperature of Engine Bearings. (A. M. Mattice, Trans. A. S. M. 
 E., 1905.) An examination of the temperature of bearings of a large num- 
 ber of engines of various makes showed more above 135 F. than below 
 that figure. Many bearings were running with a temperature over 150, 
 and in one case at 180, and in all of these cases the bearings were giving 
 no trouble. 
 
 PIVOT-BEARINGS. 
 
 The Schiele Curve. W. H. Harrison (Am. Mack., 1891) says the 
 Schiele curve is not as good a form for a bearing as the segment of a 
 sphere. He says: A mill-stone weighing a ton frequently bears its whole 
 weight upon the flat end of a hard-steel pivot 1 Vs in. diam., or 1 sq. in. 
 area of bearing; but to carry a weight of 3000 Ibs. he advises an end 
 bearing about 4 ins. diam., made in the form of a segment of a sphere 
 about 1/2 in. in height. The die or fixed bearing should be dished to fit 
 the pivot. This form gives a chance for the bearing to adjust itself, 
 which it does not have when made flat, or when made with the Schiele 
 curve. If a side bearing is necessary it can be arranged farther up the 
 shaft. The pivot and die should be of steel, hardened; cross-gutters 
 should be in the die to allow oil to flow, and a central oil-hole should be 
 made in the shaft. 
 
 The advantage claimed for the Schiele bearing is that the pressure is 
 uniformly distributed over its surface, and that it therefore wears uni- 
 formly. Wilfred Lewis (Am. Mach., April 19, 1894) says that its merits 
 
BALL-BEARINGS, BOLLER-BEAHINGS, ETC. 1233 
 
 as a thrust-bearing have been vastly overestimated; that the term 
 "anti-friction" applied to it is a misnomer, since its friction is greater 
 than that of a flat step or collar of the same diameter. He advises that 
 flat thrust-bearings should always be annular in form, having an inside 
 diameter one-half of the external diameter. 
 
 Friction of a Flat Pivot-bearing. The Research Committee on 
 Friction (Proc. Inst. M. E., 1891) experimented on a step-bearing, flat- 
 tended, 3 in. diam., the oil being forced into the bearing through a hole 
 in its center and distributed through two radial grooves, insuring thorough 
 lubrication. The step was of steel and the bearing of manganese-bronze. 
 At revolutions per min. 50 128 194 290 353 
 
 The coefficient of friction \ 0.0181 0.0053 0.0051 0.0044 0.0053 
 
 varied between / and 0.0221 0.0113 0.0102 0.0178 0.0167 
 
 With a white-metal bearing at 128 revs, the coefficient of friction was 
 a little larger than with the manganese-bronze. At the higher speeds 
 the coefficient of friction was less, owing to the more perfect lubrication, 
 as shown by the more rapid circulation of the oil. At 128 revs, the 
 bronze-bearing heated and seized on one occasion with a load of 260 Ibs., 
 and on another occasion with 300 Ibs. per sq. in. The white-metal bear- 
 ing under similar conditions heated and seized with a load of 240 Ibs. 
 per sq. in. The steel footstep on manganese-bronze was afterwards 
 tried, lubricating, with three and with four radial grooves; but the friction 
 was from one and a half times to twice as great as with only the two 
 grooves. 
 
 Mercury-bath Pivot. A nearly frictionless step-bearing may be 
 obtained by floating the bearing with its superincumbent weight upon 
 mercury. Such an apparatus is used in the lighthouses of La Heve, 
 Havre. It is thus described in Eng'g, July 14, 1893, p. 41: 
 
 The optical apparatus, weighing about 1 ton, rests on a circular cast- 
 iron table, which is supported by a vertical shaft of wrought iron 2.36 in. 
 diameter. This is kept in position at the top by a bronze ring and outer 
 iron support, and at the bottom in the same way, while it rotates on a 
 removable steel pivot resting in a steel socket, which is fitted to the base 
 of the support. To the vertical shaft there is rigidly fixed a floating cast- 
 iron ring 17.1 in. diameter and 11.8 in. in depth, which is plunged into 
 and rotates in a mercury bath contained in a fixed outer drum or tank, 
 the clearance between the vertical surfaces of the drum and ring being 
 only 0.2 in., so as to reduce as much as possible the volume of mercury 
 (about 220 Ibs.), while the horizontal clearance at the bottom is 0.4 in. 
 BALL-BEARINGS, BOIXEB-BEABINGS, ETC. 
 
 Friction-rollers. If a journal instead of revolving on ordinary 
 bearings be supported on friction-rollers the force required to make the 
 journal revolve will be reduced in nearly the same proportion that the 
 diameter of the axles of the rollers is less than the diameter of the rollers 
 themselves. In experiments by A. M. Wellington with a journal 31/2 in. 
 diam. supported on rollers 8 in. diam., whose axles were 13/4 in. diam., the 
 friction in starting from rest was 1/4 the friction of an ordinary 3V2-in 
 bearing, but at a car speed of 10 miles per hour it was V.2 that of the ordi- 
 nary bearing. The ratio of the diam. of the axle to diam. of roller was 
 13/4: 8, or as 1 to 4.6. 
 
 Coefficients of Friction of Boiler Bearings. C. H. Benjamin, Machy. 
 Oct., 1905. Comparative tests of plain babbitted, McKeel plain roller, 
 and Hyatt roller bearings gave the following values of the coefficient of 
 friction at a speed of 560 r.p.m.: 
 
 Diameter 
 of Journal. 
 
 Hyatt Bearing. 
 
 McKeel Bearing. 
 
 Babbitt Bearing. 
 
 Max. 
 
 Min. 
 
 Ave. 
 
 Max. 
 
 Min. 
 
 Ave. 
 .022 
 
 Max. 
 
 Min. 
 
 Ave. 
 
 1 15/15 
 
 23/ 16 
 27/J6 
 
 2 15/1 6 
 
 .032 
 .019 
 .042 
 .029 
 
 .012 
 .011 
 .025 
 .022 
 
 .018 
 .014 
 .032 
 .025 
 
 .033 
 
 .017 
 
 .074 
 .088 
 .114 
 .125 
 
 .029 
 .078 
 .083 
 .089 
 
 .043 
 .082 
 .096 
 .107 
 
 .028 
 .039 
 
 .015 
 .019 
 
 .021 
 .027 
 
 The friction of the roller-bearing is from one-fifth to one-third that ol 
 a plain bearing at moderate loads and speeds. It is noticeable that as. 
 the load on a roller-bearing increases the coefficient of friction decreases. 
 
 A slight change in the pressure due to the adjusting nuts was sufficient 
 to increase the friction considerably. In the McKeel bearing the rolls 
 
1234 
 
 FRICTION AND LUBRICATION. 
 
 t>ore on a cast-iron sleeve and in the Hyatt on a soft-steel one. If rollcH 
 bearings are properly adjusted and not overloaded a saving of from 2-3 
 to 3-4 of the friction may be reasonably expected. 
 
 McKeel bearings contained rolls turned from solid steel and guided by 
 spherical ends fitting recesses in cage rings at each end. The cage rings 
 were joined to each other by steel rods parallel to the rolls 
 
 Lubrication is absolutely necessary with ball and roller bearings, 
 although the contrary claim is often advanced. Under favorable con- 
 ditions an almost imperceptible, film is sufficient; a sufficient quantity 
 to immerse half the lowest ball should always be provided as a rust 
 preventive. Rust and grit must be kept out of ball and roller bearings. 
 Acid or rancid lubricants are as destructive as rust. (Henry Hess.) 
 
 Both ball and roller bearings, to give the best satisfaction, should be 
 made of steel, hardened and ground; accurately fitted, and in proper 
 alignment with the shaft and load; cleaned and oiled regularly, and fitted 
 with as large-size balls or rollers as possible, depending upon the revolutions 
 per minute and load to be carried. Oil is absolutely necessary on both 
 ball and roller bearings, to prevent rust. (S. S. Eveland.) 
 
 Roller Bearings. The Mossberg roller bearings for journals are made 
 in the sizes given in the table below. D = diam. of journal; d = diam. of 
 roll; N = number of rolls; P = safe load on journals, in Ibs. The rolls 
 are enclosed in a bronze supporting cage. (Trans. A. S. M. E., 1905.) 
 
 i ^ 
 
 d 
 
 N 
 
 P 
 
 D 
 
 d 
 
 N 
 
 P 
 
 D 
 
 d 
 
 N 
 
 P 
 
 2 
 
 V4 
 
 20 
 
 3,500 
 
 6 
 
 U/16 
 
 24 
 
 50,000 
 
 15 
 
 13/8 
 
 28 
 
 255,000 
 
 21/2 
 
 5/16 
 3/8 
 
 22 
 22 
 
 7,000 
 13,000 
 
 7 
 8 
 
 is/16 
 
 7/8 
 
 22 
 
 22 
 
 70.COO 
 90,000 
 
 18 
 20 
 
 13/8 
 11/2 
 
 32 
 34 
 
 325,000 
 400,000 
 
 4 
 
 7/lfl 
 
 24 
 
 24,000 
 
 9 
 
 1 
 
 24 
 
 115,000 
 
 24 
 
 U/o 
 
 38 
 
 576,000 
 
 5 
 
 tt/te 
 
 24 
 
 37,000 
 
 12 
 
 H/4 
 
 26 
 
 175,000 
 
 
 
 
 
 Surface speed of journal to 50 ft. per min. Length of journal li/2 
 diameters. The rolls are made of tool steel not too high in carbon, and of 
 spring temper. The journal or shaft should be made not above a medium 
 spring temper. The box should be made of high carbon steel and tem- 
 pered as hard as possible. 
 
 Conical Roller Thrust Bearings. The Mossberg thrust bearing is 
 made of conical rollers contained in a cage, and two collars, one being 
 stationary and the other fixed to the shaft and revolving with it. One 
 side of each collar is made conical to correspond with the rollers which 
 bear on it. The apex of the cones is at the center of the shaft. The 
 angle of the cones is 6 to 7 degrees. Larger angles are objectionable, 
 giving excessive end thrust. The following sizes are made: 
 
 Diameter 
 of Shaft. 
 Ins. 
 
 Outside 
 Diameter 
 of Ring. 
 Ins. 
 
 No. of 
 Rolls. 
 
 Safe Pressure on Bearing. 
 
 Area of 
 Pressure 
 Plate. 
 Sq. ins. 
 
 Speed 
 75 Rev. 
 Lbs. 
 
 Speed 
 150 Rev. 
 Lbs. 
 
 21/16-21/4 
 31/16-31/4 
 41/16-41/4 
 51/16-51/4 
 61/16-61/2 
 81/16-81/2 
 91/16-91/2 
 
 59/16 
 105/ 16 
 
 $ 
 
 lo 8 ^ 
 
 30 
 30 
 30 
 30 
 30 
 32 
 32 
 
 10 
 20 
 35 
 54 
 78 
 132 
 162 
 
 19,000 
 40,000 
 70,000 
 108,000 
 125,000 
 200,000 
 300,000 
 
 9500 
 20,000 
 35,000 
 56,000 
 62,000 
 100,000 
 150,000 
 
 Plain Roller Thrust Bearings. S. S. Eveland, of the Standard 
 Roller Bearing Co., contributes the following data of plain roller thrust 
 bearings in use in 1903. The bearing consists of a large number of short 
 cylindrical rollers enclosed in openings in a disk placed between two 
 hardened steel plates. He says "our plain roller bearing is theoretically 
 wrong, but in practice it works perfectly, and has replaced many thou* 
 sand ball-bearings which have proven unsatisfactory." 
 
BALL-BEARINGS, ROLLER-BEARINGS, ETC. 1235 
 
 Size of 
 Bearing, 
 Ins. 
 
 Number and 
 Size of Rollers, 
 Ins. 
 
 R.p.m. 
 
 Wt. on 
 Bearings, 
 Lbs. 
 
 Lineal 
 Inches. 
 
 Weight 
 per lin. 
 in., Lbs. 
 
 Weight 
 on each 
 Roll,Lb. 
 
 43/ 4 X 6H/16 
 43/4X 71/4 
 
 5 1/2 X 8 1/2 
 7 Xl03/ 8 
 
 71/2X11 5/16 
 8 X151/2 
 
 36 5/ 8 X5/16 
 32 3/4 X5/8 
 54 3/4X5/ 8 
 48 1 XV2 
 54 I Xl/2 
 70 1 1/4 X5/8 
 
 500 
 470 
 . 420 
 370 
 325 
 300 
 
 6.000 
 10,000 
 15,000 
 20,000 
 25,000 
 60,000 
 
 11 V4 
 12 
 201/4 
 24 
 27 
 45 
 
 546 
 833 
 750 
 833 
 988 
 1334 
 
 167 
 312 
 279 
 417 
 463 
 833 
 
 The Hyatt Roller Bearing. (A. L. Williston, Trans. A. S. M. E., 
 1 1905.) The distinctive feature of the Hyatt roller bearing is a flexible 
 roller, made of a strip of steel wound into a coil or spring of uniform diam- 
 eter. A roller of this construction insures a uniform distribution of the 
 : load along the line of contact of the roller and the surfaces on which it 
 ! operates. It also permits any slight irregularities in either journal or box 
 without causing excessive pressure. The roller is hollow and serves as 
 ; an oil reservoir. For a heavy load, a roller of heavy stock can be made- 
 while for a high-speed bearing under light pressure a roller of light weight, 
 ; made from thin stock, can be used. Following are the results of some tests 
 i of the Hyatt bearing in comparison with other bearings: 
 
 A shaft 152 ft. long, 215/ 16 in. diam. supported by 20 bearings, belt- 
 : driven from one end, gave a friction load of 2.28 H.P. with babbitted 
 i bearings, and 0.80' H.P. with Hyatt bearings. With 88 countershafts 
 j running in babbitted bearings, the H.P. required was 8.85 when the main 
 shaft was in babbitted bearings and 6.36 H.P. when it was in Hyatt bearings. 
 Comparative tests of solid rollers and of Hyatt rollers were made in 
 ! 1898 at the Franklin Institute by placing two sets of rollers between three 
 fiat plates, putting the plates under load in a testing machine and measur- 
 ing the force required to move the middle plate. All the rollers were 
 8/4 in. diam., 10 ins. long. The Hyatt rollers were made of 1/2 X Vs in. 
 . Bteel strip. With 2000 Ibs. load and plain rollers it took 26 Ibs. to move 
 : the plate, and with the Hyatt rollers 9 Ibs. With 3000 Ibs. load and 
 plain rollers the resistance was 34 Ibs., with Hyatt rollers 17 Ibs. 
 
 In teats with a pendulum friction testing machine at the Case Scientific 
 School, with a bearing 115/ 16 in. diam. the coefficient of friction with the 
 Hyatt bearing was from 0.0362 down to 0.0196, the loads increasing from 
 64 to 264 Ibs.; with cast-iron bearings and the same loads the coefficient 
 was from 0.165 to 0.098. 
 
 In tests at Purdue University with bearings 4 X 1V2 ins. and loads 
 from 1900 to 8300 Ibs., the average coefficients with different bearings and 
 : different speeds were as follows: 
 
 Hyatt bearing 130 r.p.m. 0.0114 302 r.p.m. 0.0099 585 r.p.m. 0.0147 
 Cast-iron bearing 128 " 0.0548 302 " 0.0592 410 " 0.0683 
 Bronze bearing 130 " 0.0576 320 " 0.0661 582 " 0.140 
 
 The cast-iron bearing at 128 r.p.m. seized with 8300 Ibs., and at 410 
 r.p.m. with 5900 Ibs. The bronze bearing seized at 130 r.p.m. with 3500 Ibs., 
 at 320 r.p.m. with 5100 Ibs., and at 582 r.p.m. with 2700 Ibs. - 
 
 The makers have found that the advantages of roller bearings of the 
 type described are especially great with either high speeds or heavy loads. 
 i Generally, the best results are obtained for line-shaft work up to speeds of 
 600 rev. per min., when a load of 30 Ibs. per square inch of projected area 
 is allowed. For heavy load at slow speed, such as in crane and truck 
 wheels, a load of 500 Ibs. gives the best results. 
 
 The Friction Coefficient of a well-made annular ball-bearing is 0.001 
 and 0.002 of the load referred to the shaft diameter and is independent 
 of the speed and load. The friction coefficient of a good roller bearing 
 is from 0.0035 to 0.014; it rises very much if the load is light. It in- 
 creases also when the speeds are very low, though not so much as with 
 plain bearings. (Henry Hess.) 
 
 Notes on Ball Bearings. The following notes are contributed by 
 Mr. Henry Hess, 1910. Ball bearings in modern use date from the bi- 
 cycle. That brought in the adjustable cup and cone and three-point 
 contact type. Under the demands for greater load resistance and relia- 
 bility the two-point contact type, without adjustability, was evolved; 
 that is now used under loads from a few pounds to many tons. Such a 
 
1236 FKICTION AND 'LUBRICATION. 
 
 bearing consists of an inner race, an outer race and the series of balls 
 that roll in tracks of curved cross section. Various designs are used, 
 differing chiefly in the devices for separating the balls and in the arrange- 
 ment for introducing the balls between the races. The most widely 
 used type has races that are of the same cross section throughout, un- 
 broken by any openings for the introduction of balls. To introduce 
 the balls the two races are first eccentrically placed; the balls will fill 
 slightly more than a half circumference; elastic separators or solid cages 
 are used to space the balls. 
 
 Another type has a filling opening of sufficient depth cut into one race; 
 the race continuity is restored by a small piece that is let in. This type 
 is usually filled with balls, without cages or separators. The filling 
 opening is always placed at the unloaded side of the bearing, where the 
 weakening of the race is not important. This type has been almost en- 
 tirely discarded in favor of the one above described. 
 
 A third type has a filling opening cut into each race not quite deep 
 enough to tangent the bottom of the ball track. As this weakened 
 section necessarily comes under the load during each revolution, the 
 carrying capacity is reduced. After slight wear there develops an inter- 
 ference of the balls with the edges of these openings, which seriously 
 reduces the speeds and load capacity. This interference precludes the 
 use of this type to take end thrust. 
 
 The carrying capacity of a ball-bearing is directly proportional to the 
 number of balls and to the square of the ball diameter. 
 
 It may be written as: 
 
 L = Knd 2 , in which L = load capacity in pounds; n = number of 
 balls; d^ball diameter in eighths of an inch. K varies with the condition 
 and type of bearing, as also with the material and speed. 
 
 For a certain special steel that hardens throughout and is also unusu- 
 ally tough, employed by " DWF" or " HB" (the originators of the modern 
 two-point type), the following values apply. For other steels lesser values 
 must be used. 
 
 I. For Radial Bearings : 
 
 K =* 9 for uninterrupted race track, cross-section curvature = 0.52 
 
 and 9/ 16 in. ball diameter respectively for inner and outer races, 
 
 separated balls, uniform load, and steady speed up to 3000 
 
 revs, per min. 
 K = 5 for full ball type, filling opening in one race at the unloaded 
 
 side, otherwise as above. 
 K = 2.5 for both ball tracks interrupted by filling openings, inelastic 
 
 cage separators f9r balls, or full ball, speeds not above 2000 
 
 revs, per min., uniform load. 
 K = 0.9 for thrust on a radial bearing of the first type, as above. The 
 
 larger the balls the smaller K. The type with filling openings 
 
 in each race is not suitable for end thrust. 
 
 The radial load bearing is, up to high speeds, practically unaffected 
 by speed, as to carrying capacity. 
 
 II. Thrust Bearings: 
 
 With the thrust type, consisting of one flat plate and one seat plate 
 with grooved ball races, the load capacity decreases with speed or 
 
 KI= constant for material and race cross-section, etc., R = revolu- 
 tions per minute. R ranges from about 3000 revs, per min. down to 1 rev. 
 per min. as for crane hooks and similar elements. 
 
 KI= 25 to 40 for material used by the DWF or HB, and race cross- 
 section radius = approx. 1.66 ball radius. 
 
 KI= 0.5 for unhardened steel, occasionally used for very large races; 
 a steel that is fairly hard without tempering must be used, and then only 
 when there is no hammering or sharp load variation. 
 
 Balls must be carefully selected to make sure that all that are used 
 in the same bearing do not vary among one another by more than O.OOOi 
 inch. A ball that is more than that larger than its fellows will sustain 
 more than its proportion of the load, and may therefore be overloaded 
 and will in turn overload the races. 
 
BALL-BEARINGS, ROLLER-BEARINGS, ETC. 1237 
 
 The usual test of ball quality, which consists in compressing a ball 
 between flat plates and noting the load at rupture, gives the quality of 
 the plates, but not of the balls. It is the ability of the ball to resist 
 permanent deformation that is of importance. As the deformations 
 involved are very small the test is a difficult one to carry out. Of even 
 greater importance than a small deformation under load is uniformity of 
 such deformation between the balls employed; a hard ball will deform 
 less than its softer mate and so will carry more than its share of the 
 load, and will therefore be overloaded and in turn overload the races. 
 
 Coned bearings for balls are objectionable. The defect in all these 
 forms of bearings is their adjustable feature. A bearing properly propor- 
 tioned with reference to a certain load may be enormously overloaded by 
 a little extra effort applied to the wrench, or on the other hand the bear- 
 ing may be adjusted with too little pressure, so that the balls will rattle, 
 and the results consequently be unsatisfactory. The prevalent idea that 
 coned ball-bearings can be adjusted to compensate for wear is erroneous. 
 
 Mr. Hess's paper, in Trans. A. S. M. E., 1907, contains a great deal of 
 useful information on the practical design of ball-bearings, including 
 different forms of raceways. He prefers a two-point bearing, in which 
 the ball races have a curved section, with sustaining surfaces at right 
 angles with the direction of the load. 
 
 Formulae for Number of Balls in a Bearing. (H. Rolfe, Am. Mach., 
 Dec. 3, 1896.) Let D = diam. 9f ball circle (the circle passing through 
 the centers of the balls); d diam. of balls; n = number of balls; s = 
 average clearance space between the balls. Then D = (d + s) -r- sin 
 (180/n); d = D sin (180/n) - s; s = D sin (180 /n) - d; n =180 4- 
 angle whose sine is (d + s) -=->. The clearance s should be about 0.003 in. 
 VALUES OF 180/n AND OF SIN 180/n. 
 
 
 
 
 
 
 
 8 
 \ 
 
 
 
 
 
 
 
 
 
 n. 
 
 
 
 1 
 
 n. 
 
 s 
 
 1 
 
 . 
 
 
 
 
 n. 
 
 
 
 i 
 
 
 1 
 
 .S 
 
 *w 
 
 
 1 
 
 a 
 '53 
 
 
 
 
 .& 
 '53 
 
 
 i 
 
 a 
 
 z 
 
 3 
 
 60 
 
 0.86603 
 
 15 
 
 12 
 
 0.20791 
 
 27 
 
 '6.667 
 
 0.11609 
 
 39 
 
 4.615 
 
 0.08047 
 
 A 
 
 45 
 
 .70711 
 
 16 
 
 11.250 
 
 .19509 
 
 28 
 
 6.429 
 
 .11197 
 
 40 
 
 4.500 
 
 .07846 
 
 5 
 
 36 
 
 .58799 
 
 17 
 
 10.588 
 
 .18375 
 
 29 
 
 6.207 
 
 .10812 
 
 41 
 
 4.390 
 
 .07655 
 
 6 
 
 30 
 
 .50000 
 
 18 
 
 10 
 
 .17365 
 
 30 
 
 6 
 
 .10453 
 
 42 
 
 4.286 
 
 .07473 
 
 7 
 
 25.714 
 
 .43388 
 
 19 
 
 9.474 
 
 .16454 
 
 31 
 
 5.806 
 
 .10117 
 
 43 
 
 4.186 
 
 .07300 
 
 8 
 
 22.500 
 
 .38268 
 
 20 
 
 9. 
 
 . 15643 
 
 32 
 
 5.625 
 
 .09801 
 
 44 
 
 4.091 
 
 .07134 
 
 9 
 
 20 
 
 .34202 
 
 21 
 
 8.571 
 
 .14904 
 
 33 
 
 5.455 
 
 .09506 
 
 45 
 
 4 
 
 .06976 
 
 10 
 
 18 
 
 .30902 
 
 22 
 
 8.182 
 
 .14233 
 
 34 
 
 5.294 
 
 .09227 
 
 46 
 
 3.913 
 
 .06825 
 
 11 
 
 16.364 
 
 .28173 
 
 23 
 
 7.826 
 
 .13616 
 
 35 
 
 5.143 
 
 .08963 
 
 47 
 
 3.830 
 
 .06679 
 
 12 
 
 15 
 
 .25882 
 
 24 
 
 7.500 
 
 . 13053 
 
 36 
 
 5 
 
 .08716 
 
 48 
 
 3.750 
 
 .06540 
 
 13 
 
 13.846 
 
 .23931 
 
 25 
 
 7.200 
 
 . 12533 
 
 37 
 
 4.865 
 
 .08510 
 
 49 
 
 3.673 
 
 .06407 
 
 14 
 
 12.857 
 
 .22252 
 
 26 
 
 6.923 
 
 .12055 
 
 38 
 
 4.737 
 
 .08258 
 
 50 
 
 3.600 
 
 .06279 
 
 Grades of Balls for Bearings. (S. S. Eyeland, Trans. A. S. M. E. t 
 1905.) "A" grade balls vary about 0.0025 in. in diameter; "B" grade, 
 0.001 to 0.002 in.; while " high-duty" or special balls are furnished varying 
 not over 0.0001 in. The crushing strength of balls is of little importance 
 as to the load a bearing will carry, the revolutions per minute being quite 
 as important as the load. 
 
 Saving of Power by Use of Bali-Bearings. Henry Hess (Trans. 
 A. S. M. E., 1909) describes a series of tests made by Dodge and Day pn a 
 2 15 /16 in. line shaft 72 ft. long, alternately equipped with plain ring-oiling 
 babbitted boxes and with H ess-Bright ball-bearings. Eight countershafts 
 were driven from pulleys on the line shaft. The countershaft pulleys had 
 plain bearings. The conclusions from the tests made under normal belt 
 conditions of 44 and 57 Ibs. per inch width of angle of single belt are as 
 follows: 
 
 a. Savings due to the substitution of ball-bearings for plain bearings on 
 line shafts may be safely calculated by using 0.0015 as the coefficient of 
 ball-bearing friction, 0.03 as the coefficient of line shaft friction, and 0.08 
 as the coefficient of countershaft friction. 
 
 b. When the belts from line shaft to countershaft pull all in one direc- 
 tion and nearly horizontally the saving due to the substitution of ball- 
 
1238 FRICTION AND LUBRICATION. 
 
 bearings for plain bearings on the line shaft may be safely taken as 35% 
 of the bearing friction. 
 
 c. When ball-bearings are used also on the countershafts the savings 
 will be correspondingly greater and may amount to 70% or more of the 
 bearing friction. 
 
 d. These percentages of savings are percentages of the friction work 
 lost in the plain bearings; they are not percentages of the total power 
 transmitted. The latter will depend upon the ratio of the total power 
 transmitted to that absorbed in the line and countershafts. 
 
 e. The power consumed in the plain line and countershafts varies, as 
 is well known, from 10 to 60% in different industries and shops. The- 
 substitution of ball-bearings for plain bearings on the line shaft only, under 
 conditions of paragraph "a," will thus result in saving of total power of 
 35 X 0.10 = 3.5% to 35 X 0.60 = 21%. By using ball-bearings on the 
 countershafts also, the saving of total power will be from 70 X 0.10 = 7% 
 to 70 X 0.60 = 42%. 
 
 KNIFE-EDGE BEARINGS. 
 
 Allowable loads on knife-edges vary with the manner in which the 
 pivots or knife-edges are held in the lever and the pivot supports or 
 seats secured to the base of weighing machines. The extension of the 
 pivot beyond the solid support is practically worthless. A high-grade 
 uniform tool steel with carbon 0.90% to 1.00% should be used. The 
 temper of the seats should be drawn to a very light straw color; that of 
 the pivots should be slightly darker. The angle of 90 for the knife-edge 
 has given good results for heavy loads. For ordinary weighing ma- 
 cliinery and most testing machinery 5000 Ib. per in. of length is ample. 
 Loads of 10,000 Ib. per inch of length are permissible, but the pivot 
 must be flat at its upper portion, normal to the load and supported its 
 whole length, with a minimum deflection of parts to secure reasonable 
 accuracy. The edge may be made perfectly sharp, for loads up to 
 1000 Ib. per inch of length. For greater loads the sharp edge is rubbed 
 with an oilstone, so that a smoothness is just visible. A pronounced 
 radius of knife-edge will decrease the sensibility of the apparatus. 
 (Jos. W. Bramwell, Eng. News, June 14, 1906.) 
 
 FRICTION OF STEAM-ENGINES. 
 
 Distribution of the Friction of Engines. Prof. Thurston, in his 
 "Friction and Lost Work," gives the following: 
 
 3. 
 
 35.0 
 21.0 
 
 Main bearings 
 
 1. 
 . . . . 47 
 
 2. 
 35 4 
 
 Piston and rod 
 
 . ... 32.9 
 
 25 
 
 Crank-pin 
 
 6 8 
 
 5 1 
 
 
 54 
 
 4 1 
 
 Valve and rod 
 
 25 
 
 26 4 
 
 Eccentric strap 
 
 53 
 
 4 
 
 Link and eccentric. . . 
 
 
 
 13.0 
 
 22.0 
 9.0 
 Total 100.0 100.0 100.0 
 
 No. 1, Straight-line, 6 x 12 in., balanced valve; No. 2, Straight-line, 
 6 x 12 in., unbalanced valve; No. 3, 7 x 10 in., Lansing traction, locomo- 
 tive valve-gear. 
 
 Prof. Thurston's tests on a number of different styles of engines indicate 
 that the friction of any engine is practically constant under all loads. 
 (Trans. A. S. M. E., viii, 86; ix, 74.) 
 
 In a straight-line engine, 8 x 14 in., I.H.P. from 7.41 to 57.54, the 
 friction H.P. varied irregularly between 1.97 and 4.02, the variation 
 being independent of the load. With 50 H.P. on the brake the I.H.P. 
 was only 52.6, the friction being only 2.6 H.P., or about 5%. 
 
 A compound condensing-engine, tested from to 102.6 brake H.P., gave 
 I.H.P. from 14.92 to 117.8 H.P., the friction H.P. varying only from 
 14.92 to 17.42. At the maximum load the friction was 15.2 H.P., or 
 12.9%. 
 
 The friction increases with increase of the boiler-pressure from 30 to 70 
 IDS., and then becomes constant. The friction generally increases with 
 Increase of speed, but there are exceptions to this rule. 
 
 Prof. Den ton (Stevens Indicator, July, 1890), comparing the calculated 
 friction on a number of engines with the friction as determined by measure- 
 
FHICTION BRAKES AND FHICTION CLUTCHES. 1239 
 
 ment, finds that in one case, a 75-ton ammonia ice-machine, the friction of 
 the compressor, 171/2 H.P., is accounted for by a coefficient of friction, 
 of 71/2% on all the external bearings, allowing 6% of the entire friction 
 of the machine for the friction of pistons, stuffing-boxes, and valves. In 
 the case of the Pawtucket pumping-engine, estimating the friction of the 
 external bearings with a coefficient of friction of 6% and that of the 
 pistons, valves, and stuffing-boxes as in the case of the ice-machine, we 
 have the total friction distributed as follows: 
 
 Horse- Percent 
 
 Crank-pins and effect of piston-thrust on main shaft .71* ^11 4* 
 
 Weight of fly-wheel and main shaft 1 .95 33 4 
 
 Steam-valves 23 37 
 
 Eccentric '07 1 '2 
 
 Pistons .43 7 '2 
 
 Stuffing-boxes, six altogether 72 113 
 
 Air-pump 2.10 32 '.& 
 
 Total friction of engine with load 6 .21 100 
 
 Total friction per cent of indicated power. 4.27 
 
 The friction of this engine, though very low in proportion to the indi- 
 cated power, is satisfactorily accounted for by Morin's law used with a 
 coefficient of friction of 5%. In both cases the main items of friction are 
 those due to the weight of the fly-wheel and main shaft and to the piston- 
 thrust on crank-pins and main-shaft bearings. In the ice-machine the 
 latter items are the larger owing to the extra crank-pin to work the pumps, 
 while in the Pawtucket engine the former preponderates, as the crank- 
 thrusts are partly absorbed by the piump-pistons, and only the surplus 
 effect acts on the crank-shaft. 
 
 Prof. Denton describes in Trans. A. S. M. E., x. 392, an apparatus by 
 which he measured the friction of the piston packing-ring. When the 
 parts of the piston were thoroughty devoid of lubricant, the coefficient 
 of friction was found to be about 7 1/2%; with an oil-feed of one drop in 
 two minutes the coefficient was about 5%; with one drop per minute it 
 was about 3%. These rates of feed gave unsatisfactory lubrication, the 
 piston groaning at the ends of the stroke when run slowly, and the flow of 
 oil left upon the surfaces was found by analysis to contain about 50% of 
 iron. A feed of two drops per minute reduced the coefficient of friction 
 to about 1%, and gave practically perfect lubrication, the oil retaining its 
 natural color and purity. 
 
 FRICTION BRAKES AND FRICTION CLUTCHES. 
 
 Friction Brakes are used for slowing down or stopping a moving 
 machine by converting its energy of motion into heat, or for controlling 
 the speed of a descending load. The simplest form is the block brake, 
 commonly used for railway car wheels, which resists the motion of the 
 wheel not only with the force due to ordinary sliding friction, but with 
 that due to cutting or grinding away the surface of the metals in contact. 
 If P = total pressure acting normal to the sliding surface, / = coefficient 
 of friction, and v velocity in feet per minute, then the energy absorbed, 
 in foot-pounds per minute, is Pfv. If the surface is lubricated and the 
 pressure per square inch not great enough to squeeze out the lubricant, 
 then the value of / for different materials may be taken from Morin's 
 tables for friction of motion, page 1221, but if the pressure is great enough 
 to force out the lubricant, then the coefficient becomes much greater 
 and the surfaces will cut and wear, with a rapid' rise of temperature. 
 
 Other forms of brakes are disk brakes and cone brakes, in which a 
 disk or cone is carried by the rotating shaft and a mating disk or cone 
 is pressed against it by a lever or other means; and band brakes, also 
 called strap or ribbon brakes, in which a flexible band encircles the 
 cylindrical surface of a rotating drum or wheel, and tension applied 
 to one end of the band brings it in contact with that surface. For band 
 brakes the theory of friction of belts applies. See page 1138. For much 
 information on the theory and practice of friction brakes see articles by 
 C. F. Blake in Mach'y, Jan., 1901, Mar., 1905, and Aug., 1906, and by 
 3. R. Douglas, Am. Mach., Dec. 26, 1901, and R. B. Brown, Mach'y. 
 April, 1909. For friction brake dynamometers see Dynamometers. 
 
1240 FRICTION AND LUBRICATION. 
 
 Friction Clutches are used for putting shafts in motion gradually, 
 without shock. If two shafts, in line with each other, one in motion and 
 the other at rest, each having a disk keyed to the end, and the disks 
 almost touching, are moved toward each other so that the disks are 
 brought in contact with some pressure, the shaft at rest will be put in 
 motion gradually, while the disks rub on each other, until it acquires the 
 velocity of the driving shaft, when the friction ceases and the disks may 
 then be locked together. This is an elementary form of friction clutch. 
 A great variety of styles are made in which the sliding surfaces may be 
 disks, cones, and gripping btocks of various forms. The work done by a 
 clutch while the surfaces are in sliding contact, and before they are locked 
 together is the overcoming of the inertia of the driven shaft and of all 
 the mechanism driven by it, and giving it the velocity of the driving 
 shaft. The principles of friction brakes apply to friction clutches. The 
 sliding surfaces must be of sufficient area to keep the normal pressure 
 below tha,t at which they will overheat, cut and wear, and to dissipate 
 the heat generated by friction. The following values of the coefficient 
 of friction to be used in designing clutches are given by C. W. Hunt: 
 cork on iron, 0.35; leather on iron, 0.3; wood on iron, 0.2; iron on iron, 
 0.25 to 0.3. Lower values than these should be assumed for velocities 
 exceeding 400 ft. per minute. The pressure per square inch in disk 
 clutches should not exceed 25 or 30 Ibs., and wooden surfaces should 
 not be loaded beyond 20 to 25 Ibs. per sq. in. See Kimball and Barr on 
 Machine Design, also Trans. A. S. M. E., 1903 and 1908. 
 
 Electrically Operated Brakes are discussed by H. A Steen in a 
 paper read before the Engrs. Socy. of W. Penna., reprinted in Iron Trade 
 Rev., Dec. 24, 1908. Formulae are given for the time required for stop- 
 ping, for the heat generated and the temperature rise, for different types 
 of brakes. 
 
 Magnetic and Electric Brakes. For braking the load on electric 
 cranes a band brake is used which is held off the drum by the action of 
 a magnet or solenoid, and is put on by the action of a spring or weight. 
 The solenoid usually consists of a coil of wire connected in series with the 
 motor, and a plunger working inside of the coil. It should be so pro- 
 portioned that its action is not delayed by residual magnetism when the 
 current is cut off. Too rapid action is prevented by making the end of 
 the solenoid an air dash-pot. 
 
 For electric-driven machinery an electric motor makes a most efficient 
 brake by reversing the directi9n of the electric current, causing the motor 
 to become a generator supplying current to a rheostat in which it is con- 
 verted into heat and dissipated. In some cases the electric current 
 generated, instead of being absorbed in a rheostat, is fed into the main 
 electric circuit. In this case the energy of the rotating mass, instead 9f 
 being wasted in friction or in electrical heating, is converted into electric 
 energy and thus conserved for further use. 
 
 Design of Band Brakes. (R. A. Greene, Am. Mach. t Oct. 8, 1908.) 
 In the practice of the Browning Engineering Co., Cleveland, O., in 
 regard to the design of band brakes the equations are: 
 
 2 T 
 
 T= PX, t = T -P, S = * J , #= S X DX 0.262 X revolutions per 
 
 L) X r 
 
 minute, in which T = the greater tension on the band, t = the lesser 
 tension on the band, P = equivalent load on the brake drum, X = factor 
 
 from the accompanying table, X = \r _ -, i n which N = 10 27288 / C 
 
 where / = the coefficient of friction and c the length of arc of contact in 
 degrees divided by 360. D = diam. of brake drum, F = width of face 
 of brake drum, S = a checking factor which has a maximum limit of 65, 
 1? = a checking factor which has a limit of 54,000 (Yale & Towne practice) 
 or 60,000 (Brown hoist practice). 
 
 EXAMPLE. A band brake is to be designed having an arc of contact 
 of 260, coefficient of friction = 0.2, drum diameter 30 ins., face 4 ins , 
 speed 100 r.p.m., and a load of 3000 Ibs. acting on a diameter of 20 ins. 
 
 Then 
 
 P= 3000 X 20-4- 30=2000 pounds, X = 1.68 (from table), T = 2000 X 
 1.68 = 3360 pounds, t = 3360 - 2000 = 1360 pounds, S = 2 X3360-*- 
 (30X4)=56 (within the limit), * = 56X30 X 0.262 X 100=44,000 (within 
 the limit). 
 
FRICTION OF HYDRAULIC PLUNGER PACKING. 1241 
 
 Degrees. 
 
 Values of X. 
 
 Degrees. 
 
 Values of X. 
 
 f =0.2. 
 
 / =0.3. 
 
 / =0.4. 
 
 f =0.2. 
 
 / =0.3. 
 
 / =0.4. 
 
 180 
 195 
 210 
 240 
 250 
 
 2.14 
 2.03 
 1.93 
 1.76 
 1.72 
 
 .64 
 ' .56 
 .50 
 .40 
 .37 
 
 .40 
 .35 
 .30 
 .23 
 .21 
 
 260 
 270 
 280 
 290 
 300 
 
 .68 
 .64 
 .60 
 .57 
 .54 
 
 .35 
 
 .32 
 .30 
 .28 
 .26 
 
 .19 
 .18 
 .17 
 .15 
 .14 
 
 FRICTION OF HYDRAULIC PLUNGER PACKING. 
 
 The "Taschenbuch der Hutte" (15th edition, vol. 1, p. 202) says: "For 
 stuffing-boxes with hemp, cotton or leather packing, with water pressures 
 between 1 and 50 atmospheres, the frictional loss is dependent upon the 
 water pressure, the circumference of the packed surface, and a coefficient 
 n, which is constant lor this range of pressure. The loss is independent 
 of the depth of stuffing-box or leather ring, and is given by the formula 
 F = Kpd, in which F = total frictional loss in pounds, p pressure in pounds 
 per sq. in., d diameter of plunger in inches. 
 
 K is a coefficient, which depends on the kind and condition of the pack- 
 ing, and is given as follows for various cases. 
 
 For cotton or hemp, loose or braided, dipped in hot tallow; plungers 
 smooth, glands not pulled down too tight, packing therefore retaining 
 its elasticity; dimensions such as usually occur, K = 0.072. 
 
 Same conditions, after packing is some months old, K = 0.132. 
 
 Materials the same, but with hard packing, unfavorable conditions, 
 etc., /C = as much as 0.299. 
 
 Leather packing; soft leather, well made, etc., K = 0.036 to 0.084. 
 
 Hard, stiffly tanned leather, K = 0.12 to 0.156. 
 
 Unfavorable conditions; rough plungers, gritty water, etc., K=&s much 
 as 0.239. 
 
 Weisbach-Hermann, " Mechanics of Hoisting Machinery," gives a 
 formula which when translated into the same notation as the one in 
 " Hutte " is 
 
 F = 0.0312 pd to 0.0767 pd. 
 
 Since the total pressure on a plunger is l /4nd?p, the ratio of the loss of 
 pressure to the total pressure is Kpd-- l /47td 2 p, or, using the extreme values 
 of K, 0.0312 and 0.299. the ratio ranges from 0.04 -s-d to Q.38 + d, or from 
 4 to 38 per cent divided by the diameter in inches. 
 
 Walter Ferris (Am. Mack., Feb. 3, 1898) derives from the formula 
 given above the following formula for the pressure produced by a hemp- 
 packed hydraulic intensitier made with two plungers of different diameters: 
 
 A-KD 
 
 in which ^2 = pressure per sq. in. produced by the intensifier, pi= initial 
 
 Sressure, A=area and D = diam. of the larger plunger, o = area and d = 
 iam. of the smaller plunger, and K an experimental coefficient. He gives 
 the following results of tests of an intensifier with a small plunger 8 ins. 
 diam. and two large plungers, 14V4 and 173/4 ins., either one of which could 
 be used as desired. 
 
 Diam. of large plunger, in. 141/4 141/4 173/4 173/4 
 
 Initial pressure, Ibs. per sq. in. 285 475 335 350 
 
 Intensified pressure, ibs. per sq. in. 750 1450 1450 1510 
 
 Intensified if there were no friction 905 1505 1650 1725 
 
 Intensified calculated by formula* 806 1433 1572 1643 
 
 Efficiency of machine 0.83 0.965 0.88 0.875 
 
 LUBRICATION. 
 
 Measurement of the Durability of Lubricants. (J. E. Denton, 
 Trans. A. S. M. E., xi, 1013.) Practical differences of durability of 
 lubricants depend not on any differences of inherent ability to resist 
 being "worn out" by rubbing, but upon the rate at which they flow 
 through and away from the bearing-surfaces. The conditions which 
 
 * Assuming K = 0.2. 
 each case was 0,953, 
 
 The efficiency calculated by the formula in 
 
1242 FRICTION AND LUBRICATION. 
 
 control this flow are so delicate in their influence that all attempts thus 
 far made to measure durability of lubricants may be said to have failed 
 to make distinctions of lubricating value having any practical significance. 
 In some kinds of service the limit to the consumption of oil depends upon 
 the extent to which dust or other refuse becomes mixed with it, as in 
 railroad-car lubrication and in the case of agricultural machinery. The 
 economy of one oil over another, so far as the quality used is concerned 
 that is, so far as durability is concerned is simply proportional to the 
 rate at which it can insinuate itself into and flow out of minute orifices or 
 cracks. Oils will differ in their ability to do this, first, in proportion to 
 their viscosity, and, second, in proportion to the capillary properties which 
 they may possess by virtue of the particular ingredients used in their 
 composition. Where the thickness of film between rubbing-surfaces 
 must be so great that large amounts of oil pass through bearings in a given 
 time, and the surroundings are such as to permit oil to be fed at high 
 temperatures or applied by a method not requiring a perfect fluidity, it is 
 probable that the least amount of oil will be used when the viscosity is as 
 great as in the petroleum cylinder stocks. When, however, the oil must 
 flow freely at ordinary temperatures and the feed of oil is restricted, as in 
 the case of crank-pin bearings, it is not practicable to feed such heavy 
 oils in a satisfactory manner. Oils of less viscosity or of a fluidity 
 approximating to lard-oil must then be used. 
 
 Relatiw Value of Lubricants. (J. E. Denton, Am. Mach., Oct 30 
 1890.) The three elements which determine the value of a lubricant 
 are the cost due to consumption of lubricants, the cost spent for coal to 
 overcome the frictional resistance caused by use of the lubricant, and the 
 cost due to the metallic wear on the journal and the brasses. 
 
 The Qualifications of a Good Lubricant, as laid down by W. H. 
 Bailey, in Proc. Inst. C. E., vol. xlv, p. 372, are: 1. Sufficient body to 
 keep the surfaces free from contact under maximum pressure. 2. The 
 greatest possible fluidity consistent with the foregoing condition. 3. The 
 lowest possible coefficient of friction, which in bath lubrication would be 
 for fluid friction approximately. 4. The greatest capacity for storing 
 and carrying away heat. 5. A high temperature of decomposition. 
 6. Power to resist oxidation or the action of the atmosphere. 7. Freedom 
 from corrosive action on the metals upon which the lubricant is used. 
 
 The Examination of Lubricating Oils. (Prof. Thos. B. Stillman, 
 Stevens Indicator, July, 1890.) The generally accepted conditions of 
 a good lubricant are as follows: 
 
 1. "Body" enough to prevent the surfaces to which it is applied from 
 coming in contact with each other. (Viscosity.) 
 
 2. Freedom from corrosive acid, of either mineral or animal origin. 
 
 3. As fluid as possible consistent with "body." 
 
 4. A minimum coefficient of friction. 
 
 5. High "flash" and burning points. 
 
 6. Freedom from materials liable to produce oxidation or "gumming." 
 The examinations to be made to verify the above are both chemical and 
 
 mechanical, and are usually arranged in the following order: 
 
 1. Identification of the oil, whether a simple mineral oil, or animal oil, 
 or a mixture. 2. Density. 3. Viscosity. 4. Flash-point. 5. Burning- 
 point. 6. Acidity. 7. Coefficient of friction. 8. Cold test. 
 
 Detailed directions for making all of the above tests are given in Prof, 
 Stillman's article. See also Stillman's Engineering Chemistry, p. 366. 
 
 Notes on Specifications for Petroleum Lubricants. (C. M. Everest, 
 Vice-Pres. Vacuum Oil Co., Proc. Engineering Congress, Chicago World's 
 Fair, 1893.) The specific gravity was the first standard established for 
 determining quality of lubricating oils, but it has long since been dis- 
 carded as a conclusive test of lubricating quality. However, as the 
 specific gravity of a particular petroleum oil increases the viscosity also 
 increases. 
 
 The object of the fire test of a lubricant, as well as its flash test, is the 
 prevention of danger from fire through the use of an oil that will evolve 
 inflammable vapors. The lowest fire test permissible is 300, which gives 
 a liberal factor of safety under ordinary conditions. 
 
 The cold test of an oil, i.e., the temperature at which the oil will congeal, 
 should be well below the temperature at which it is used; otherwise the 
 coefficient of friction would be correspondingly increased," 
 
IMBRICATION. 1243 
 
 Viscosity, or fluidity, of an oil is usually expressed in seconds of time in 
 which a given quantity of oil will flow through a certain orifice at the tem- 
 perature stated, comparison sometimes being ma.de with water, sometimes 
 with sperm-oil, and again with rape-seed oil. It seems evident that 
 within limits the lower the viscosity of an oil (without a too near approach 
 to metallic contact of the rubbing surfaces) the lower will be the coefficient 
 of friction. But we consider that each bearing in a mill or factory would 
 probably require an oil of different viscosity from any other bearingin the 
 mill, in order to give its lowest coefficient of friction, and that slight 
 variations in the condition of a particular bearing would change the re- 
 quirements of that bearing; and further, that when nearing the "danger 
 point" the question of viscosity alone probably does not govern. 
 
 The requirement of the New England Manufacturers' Association, that 
 an oil shall not lose over 5% of its volume when heated to 140 Fahr. for 
 12 hours, is to prevent losses by evaporation, with the resultant effects. 
 
 The precipitation test gives no indication of the quality of the oil itself, 
 as the free carbon in improperly manufactured oils can be easily removed. 
 
 It is doubtful whether oil buyers who require certain given standards 
 of laboratory tests are better served than those who do not. Some of 
 the standards are so faulty that to pass them an oil manufacturer must 
 supply oil he knows to be faulty; and the requirements of the best stand- 
 ards can generally be met by products that will give inferior results in 
 actual serivce. 
 
 Penna. B. B. Specifications for Petroleum Products, 1900. 
 Five different grades of petroleum products will be used. 
 
 The materials desired under this specification are the products of the 
 distillation and refining of petroleum unmixed with any other substances. 
 
 150 Fire-test Oil. This grade of oil will not be accepted if sample 
 (1) is not "water-white" in color; (2) flashes below 130 Fahrenheit; 
 (3) burns below 151 Fahrenheit; (4) is cloudy or shipment has cloudy 
 barrels when received, from the presence of glue or suspended matter; 
 (5) becomes opaque or shows cloud when the sample has been 10 minutes 
 at a temperature of Fahrenheit. 
 
 300 Fire-test Oil. This grade of oil will not be accepted if sample 
 (1) is not "water-white" in color; (2) flashes below 249 Fahrenheit; 
 (3) burns below 298 Fahrenheit; (4) is cloudy or shipment has cloudy 
 barrels when received, from the presence of glue or suspended matter; 
 (5) becomes opaque or shows cloud when the sample has been 10 minutes 
 at a temperature of 32 Fahrenheit; (6) shows precipitation when some 
 of the sample is heated to 450 F. The precipitation test is made by 
 having about two fluid ounces of the oil in a six-ounce beaker, with a 
 thermometer suspended in the oil, and then heating slowly until the 
 thermometer shows the required temperature. The oil changes color, 
 but must show no precipitation. 
 
 Parafflne and Neutral Oils. These grades of oil will not be accepted 
 if the sample from shipment (1) is so dark in color that printing with 
 long-primer type cannot be read with ordinary daylight through a layer of 
 the oil 1/2 inch thick; (2) flashes below 298 F.: (3) has a gravity at 
 60 F., below 24 or above 35 Baume"; (4) from October 1st to May 1st 
 has a cold test above 10 F., and from May 1st to October 1st has a cold- 
 test above 32 F. 
 
 The color test is made by having a layer of the oil of the prescribed 
 thickness in a proper glass vessel, and then putting the printing on one 
 side of the vessel and reading it through the layer of oil with the back 
 of the observer toward the source of light. x 
 
 Well Oil. This grade of oil will not be accepted if the sample from 
 shipment (1) flashes, from May 1st to October 1st, below 298 F., or 
 from October 1st to May 1st, below 249 F.; (2) has a gravity at 60 F., 
 below 28 or above 31 Baume; (3) from October 1st to May 1st has 
 a cold test above 10 F., and from May 1st to October 1st has a cold test 
 above 32 F.; (4) shows any precipitation when 5 cubic centimeters are 
 mixed with 95 c.c. of gasoline. The precipitation test is to exclude tarry 
 and suspended matter. It is made by putting 95 c.c. of 88 B. gasoline, 
 which must not be above 80 F. in temperature, into a 100 c.c. graduate, 
 then adding the prescribed amount of oil and shaking thoroughly. Allow 
 to stand ten minutes. With satisfactory oil no separated or precipitated 
 material can foe seen. 
 
1244 
 
 FRICTION AND LUBBICATION. 
 
 500 Fire-test Oil This grade of oil will not be accepted if sample 
 from shipment (1) flashes below 494 F.; (2) shows precipitation with 
 gasoline when tested as described for well oil. 
 
 Printed directions for determining flashing and burning tests and for 
 making cold tests and taking gravity are furnished by the railroad company. 
 
 Penna. R. K. Specifications for Lubricating Oils (1894). (In 
 force in 1902.) 
 
 Constituent Oils. 
 
 Parts by volume. 
 
 Extra lard-oil 
 
 
 
 
 
 
 
 
 
 1 
 
 "4" 
 
 Extra, No 1 lard-oil 
 
 
 
 1 
 
 1 
 4 
 
 1 
 2 
 
 1 
 2 
 
 1 
 "4 
 
 1 
 1 
 
 "t 
 
 1 
 2 
 .... 
 
 >3 
 
 500 fire-test oil 
 
 
 1 
 
 Paraffine oil 
 
 
 Well oil 
 
 1 
 
 
 
 A 
 
 
 
 
 
 Used for 
 
 B 
 
 c t 
 
 C 2 
 
 C 3 
 
 Di 
 
 D 2 
 
 E 
 
 A, freight dars; engine oil on shifting-engines; miscellaneous greasing 
 
 in foundries, etc. B, cylinder lubricant on marine equipment and on 
 stationary engines. C, engine oil; all engine machinery; engine and 
 tender truck boxes; shafting and machine tools; bolt cutting; general 
 lubrication except cars. D, passenger-car lubrication. E, cylinder 
 lubricant for locomotives. Ci, Di, for use in Dec., Jan., and Feb.; Ct, 
 Dz, in March, April, May, Sept., Oct., and Nov.; Cs, Ds, in June, July, 
 and August. Weights per gallon, A, 7.4 Ibs.; B, C, D, E, 7.5 Ibs. 
 
 Grease Lubricants. Tests made on an Olsen lubricant testing machine 
 at Cornell University are reported in Power, Nov. 9, 1909. It was found 
 that some of the commercial greases stood much higher pressures than 
 the oils tested, and that the coefficients of friction at moderate loads were 
 often as low as those of the oils. The journal of the testing machine 
 was 33/4 in. diam., 3 1/2 in. long, and the babbitt bearing shoe had a projected 
 area of 5.8 sq. in. The speed was 240 r.p.m. and each test lasted one 
 hour, except when the bearing showed overheating. The following are 
 the coefficients of friction obtained in the tests: 
 
 Lbs. 
 per 
 sq.in. 
 
 Min- 
 eral 
 Grease, 
 
 Ani- 
 mal 
 Grease. 
 
 Graph- 
 ite 
 Grease. 
 
 Min- 
 eral 
 Grease. 
 
 Engine 
 Oil. 
 
 Engine 
 Oil. 
 
 Grease. 
 
 Grease. 
 
 86.2 
 172.4 
 258.6 
 344.8 
 431.0 
 
 0.024 
 0.021 
 0.021 
 0.025 
 0.050 
 
 0.023 
 0.023 
 0.023 
 0.025 
 0.035 
 
 0.04 
 0.05 
 
 0.023 
 0.018 
 0.018 
 0.019 
 0.028 
 
 0.019 
 0.04 
 0.06 
 
 0.015 
 0.022 
 0.037 
 
 0.020 
 0.015 
 0.014 
 0.017 
 0.026 
 
 0.025 
 0.022 
 0.020 
 0.020 
 0.019 
 
 
 Testing Oil for Steam Turbines. (Robert Job, Trans. Am. Soc. for 
 Testing Mails., 1909.) 
 
 In some types of steam-turbines, the bearings are very closely adjusted 
 and, if the oil is not clear and free from waxy substances, clogging and 
 heating quickly results. A number of red engine and turbine oils some 
 of which had given good service and others bad service were tested and 
 it was found that clearness and freedom from turbidity were of importance, 
 but mere color, or lack of color, seemed to have little influence, and good 
 service results were obtained with oils which were of a red color, as well 
 as with those which were filtered to an amber color. 
 
 Heating Test. It was found that on heating the oils to 450 F. all 
 which had given bad service showed a marked darkening of color, while 
 those which had proved satisfactory showed little change. With oils 
 that had been filtered or else had been chemically treated in such manner 
 that the so-called " amorphous waxes " had been completely removed, 
 on applying the heating test only a slight darkening of color resulted. 
 It is of advantage in addition to other requirements to specify that an 
 oil for steam turbines on being heated to 450 F. for five minutes shall 
 show not more than a slight darkening of color. The test is that com- 
 monly used in test of 300 oil for burning purposes. 
 
 Separating Test. It is known that elimination of the waxes causes an 
 increase in the ease with which the oil separates from hot water when 
 thoroughly shaken with it. This condition can be taken advantage 9f 
 py prescribing that when one ounce of the oil is place'd in a 4-oz. bottle 
 
LUBRICATION. .' 1245 
 
 " with twd ounces of boiling water, the bottle corked and shaken narcr tor 
 one minute and let stand, the oil must separate from the water within a 
 specified time, depending upon the nature of the oil, and that there must 
 be no appearance of waxy substances at the line of demarcation between 
 the oil and the water. 
 
 Quantity of Oil needed to Run an Engine. The Vacuum Oil Co. in 
 1892, in response to an inquiry as to cost of oil to run a 1000-H.P. Corliss 
 engine, wrote: The cost of running two engines of equal size of the same 
 make is not always the same. Therefore, while we could furnish figures 
 showing what it is costing some of our customers having Corliss engines 
 of 1000 H.P., we could only give a general idea, which in itself might be 
 considerably out of the way as to the probable cost of cylinder- and 
 engine-oils per year for a particular engine. Such an engine ought to 
 run readily on less than 8 drops of 600 W oil per minute. If 3000 drops 
 are figured to the quart, and 8 drops used per minute, it would take about 
 two and one half barrels (52.5 gallons) of 600 W cylinder-oil, at 65 cents 
 per gallon, or about $85 for cylinder-oil per year, running 6 days a week 
 and 10 hours a day. Engine-oil would be even more difficult to guess at 
 what the cost would be, because it would depend upon the number of 
 cups required on the engine, which varies somewhat according to the 
 style of the engine. It would doubtless be safe, however, to calculate 
 at the outside that not more than twice as much engine-oil would be 
 required as of cylinder-oil. 
 
 The Vacuum Oil Co. in 1892 published the following results of practice 
 with "600 W" cylinder-oil: 
 rnrii^ pnmnrmnri Anmnp I 2 ^ and 33 x 48; 83 revs, per min.; 1 drop of 
 
 ine ' 1 oil per min. to 1 drop in two minutes, 
 triple exp. ' 20, 33, and 46 x 48; 1 drop every 2 minutes. 
 
 (20 and 36 x 36; 143 revs, per min.; 2 dro^s 
 Porter- Allen of oil per min., reduced afterwards to . drcp 
 
 ( per min. 
 
 (15 and 25 x 16; 240 revs, per min.; 1 drop 
 ( every 4 minutes. 
 
 Results of tests on ocean-steamers communicated to the author by 
 Prof. Denton in 1892 gave: for 1200-H.P. marine engine, 5 to 6 English 
 gallons (6 to 7.2 U. S. gals.) of engine-oil per 24 hours for external lubri- 
 cation; and for a 1500-H.P. marine engine, triple expansion, running 
 75 revs, per min., 6 to 7 English gals, per 24 hours. The cylinder-oil 
 consumption is exceedingly variable, from 1 to 4 gals, per day on 
 different engines, including cylinder-oil used to swab the piston-rods. 
 
 Cylinder Lubrication. J. H. Spoor, in Power, Jan. 4, 1910, has made 
 a study of a great number of records of the amount of oil used for lubri- 
 cating icylinders of different engines, and has reduced them to a sys- 
 tematic basis of the equivalent number of pints of oil used in a 10-hour 
 day for different areas of surface lubricated. The surface is determined 
 in square inches by multiplying the circumference of the cylinder by the 
 length of stroke. The results are plotted in a series of curves for different 
 types of engines, and approximate average figures taken from these curves 
 are given below: 
 
 Compound Engines. 
 
 Sq. ins. lubricated 2,000 4,000 6,000 8,000 10,000 12,000 18,000 
 
 Pints of oil used in 10 hrs. 2 3.5 4.3 5 5.5 6 6.5 
 
 Corliss Engines. 
 
 Sq. ins. lubricated 1,000 2,000 3,000 4,000 
 
 Pints of oil in 10 hrs. Avge 0.9 1.65 2.25 3.75 
 
 Max 1.2 2.25 
 
 Min 1.00 
 
 Automatic high-speed engines, about 2 pints per 1,000 sq. in. 
 
 Simple slide-valve engines, about 0.5 pint per 1,000 sq. in. 
 
 As shown in the figures under 2,000 Corliss, a certain engine may take 
 21/4 times as much oil as another engine of the same size. The difference 
 maybe due to smoothness of cylinder surf ace, kind and pressure of piston 
 rings, quality of oil, method of introdiicing the lubricant, etc. Variations 
 in speed of a given type of engine and in steam pressure do not appear to 
 make much difference, but the small automatic high-speed engine takes 
 more oil than any other type. Vertical marine engines are commonly run 
 
1246 FKICTION AND LUBRICATION. 
 
 without any cylinder oil, except that used occasionally to swab the piston 
 rods. 
 
 Quantity of Oil used on a Locomotive Crank-pin. Prof. Denton. 
 Trans. A. S. M. E. % xi, 1020, says: A very economical case of practical 
 oil-consumption is when a locomotive main crank-pin consumes about 
 six cubic inches of oil in a thousand miles of service. This is equivalent 
 to a consumption of one milligram to seventy square inches of surface 
 rubbed over. 
 
 Soda Mixture for Machine Tools* (Penna. R. R. 1894.) Dissolve 
 6 Ibs. of common sal-soda in 40 gallons of water and stir thoroughly. 
 When needed for use mix a gallon of this solution with about a pint of 
 engine oil. Used for the cutting parts of machine tools instead of oil. 
 
 Water as a Lubricant. (C. W. Naylor, Trans. A. S. M. E. t 1905.) 
 Two steel jack-shafts 18 ft. long with bearings 5 X 14 ins. each receiving 
 175 H.P. from engines and driving 5 electric generators, with six belts all 
 pulling horizontally on the same side of the shaft, gave trouble by heating 
 when lubricated with oil or grease. Water was substituted, and the shafts 
 ran for 11 years, 10 hours a day, without serious interruption. Oil was fed 
 to the shaft before closing down for the night, to prevent rusting. The 
 wear of the babbitted bearings in 11 years was about 1/4 in., and of the shaft 
 nil. 
 
 Acheson's " Deflocculated " Graphite. (Trans. A.I.E.E., 1907; 
 Eng. News, Aug. 1, 1907.) In 1906, Mr. E. G. Acheson discovered a 
 process of producing a fine, pure, unctuous graphite in the electric fur- 
 nace. He calls it deflocculated graphite. By treating this graphite 
 in the disintegrated form with a water solution of tannin, the amount 
 of tannin being from 3% to 6% of the weight of the graphite treated, 
 he found that it would be retained in suspension in water, and that it 
 was in such a fine state of subdivision that a large part of it would run 
 through the finest filter paper, the filtrate being an intensely black liquid 
 in which the graphite would remain suspended for months. The addition 
 of a minute quantity of hydrochloric acid causes the graphite to floccu- 
 late and group together so that it will no longer flow through filter paper. 
 The same effect has been obtained with alumina, clay, lampblack and 
 siloxicon, by treatment with tannin. The graphite thus suspended in 
 water, known as "aquedag" has been successfully used as a lubricant 
 for journals with sight-feed and with chain-feed oilers. It also prevents 
 rust in iron and steel. The deflocculated graphite has also been sus- 
 pended in oil, in a dehydrated condition, making an excellent lubricant 
 known as "mtdag." Tests by Prof. C. H. Benjamin of oil with 0.5% 
 of graphite showed that it had a lower coefficient of friction than the oil 
 alone. 
 
 SOLID LUBRICANTS. 
 
 Graphite in a condition of powder and used as a solid lubricant, so 
 called, to distinguish it from a liquid lubricant, has been found to do well 
 where the latter has failed. 
 
 Rennie, in 1829, says: "Graphite lessened friction in all cases where it 
 was used." General Morin, at a later date, concluded from experiments 
 that it could be used with advantage under heavy pressures; and Prof. 
 Thurston found it well adapted for use under both light and heavy pres- 
 sures when mixed with certain oils. It is especially valuable to prevent 
 abrasion and cutting under heavy loads and at low velocities. 
 
 For comparative tests of various oils with and without graphite, see 
 paper on lubrication and lubricants, by C. F. Mabery, Jour. A.S.M.E., 
 Feb., 1910. 
 
 Soapstone, also called talc and steatite, in the form of powder and 
 mixed with oil or fat, is sometimes used as a lubricant. Graphite or 
 soapst9ne, mixed with soap, is used on surfaces of wood working against 
 either iron or wood. 
 
 Metaline is a solid compound, usually containing graphite, made in the 
 form of small cylinders which are fitted permanently into holes drilled 
 in the surface of the bearing. The bearing thus fitted runs without any 
 other lubrication. 
 
 Bushings fitted with graphite packed into grooves are made by the 
 Graphite Lubricating Co., Bound Brook, N. J. 
 
THE FOUNDRY. 
 
 1247 
 
 THE FOUNDRY. 
 
 (See also Cast-iron, pp. 437 to 445, and Fans and Blowers, pp. 653 to 673.) 
 
 Cupola Practice. 
 
 The following table and the notes accompanying it are condensed from 
 an article by Simpson Bolland in Am. Mach., June 30, 1892: 
 
 Diam. of lining in 
 
 36 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 84 
 
 Height to char'g door, ft. .. 
 Fuel used in bed, Ibs 
 
 12 
 840 
 
 13 
 1380 
 
 14 
 
 1650 
 
 15 
 
 1920 
 
 15 
 2190 
 
 16 
 
 2460 
 
 16 
 3000 
 
 First charge of iron, Ibs.. . . 
 Other fuel charges, Ibs 
 
 2520 
 302 
 
 4140 
 554 
 
 4950 
 680 
 
 5760 
 806 
 
 6570 
 932 
 
 7380 
 1058 
 
 9000 
 1310 
 
 Other iron charges, Ibs 
 Diam. blast pipe, in 
 
 2718 
 14 
 
 4986 
 18 
 
 6120 
 20 
 
 7254 
 22 
 
 8388 
 22 
 
 9522 
 24 
 
 11,790 
 26 
 
 No. of 6-in. round tuyeres. . 
 Equiv. No. flat tuyeres 
 Width of flat tuyeres, in 
 Height of flat tuyeres, in. . . 
 Blast pressure oz 
 
 3.7 
 4 
 
 2 
 13.5 
 8 
 
 6.8 
 6 
 2.5 
 13.5 
 12 
 
 10.7 
 8 
 2.5 
 15.5 
 14 
 
 13.7 
 8 
 
 16.5 
 14 
 
 15.4 
 8 
 
 18.5 
 14 
 
 19 
 10 
 3 
 
 18.5 
 16 
 
 31 
 16 
 3.5 
 16 
 16 
 
 Size of Root blower, No 
 Revs, per min 
 
 2 
 241 
 
 4 
 212 
 
 4 
 277 
 
 5 
 
 192 
 
 240 
 
 6 
 163 
 
 160 
 
 Engine for blower, H.P 
 Sturtevant blower, No 
 Engine for blower, H.P 
 Melting cap., Ibs. per hr. . . . 
 
 2.5 
 4 
 3 
 4820 
 
 10 
 6 
 
 93/ 4 
 
 10,760 
 
 14 
 
 7 
 16 
 13,850 
 
 ,8V, 
 
 22 
 16,940 
 
 23 
 8 
 22 
 21,200 
 
 33 
 9 
 35 
 26,070 
 
 47 
 10 
 48 
 37,530 
 
 Mr. Bolland says that the melting capacities in the table are not sup-; 
 posed to be all that can be melted in the hour by some of the best cupolas, 
 but are simply the amounts which a common cupola under ordinary 
 circumstances may be expected to melt in the time specified. 
 
 By height of cupola is meant the distance from the base to the bottom 
 side of the charging door. The distance from the sand-bed, after it has 
 been formed at the bottom of the cupola, up to the under side of the 
 tuyeres is taken at 10 ins. in all cases. 
 
 All the amounts for fuel are based upon a bottom of 10 ins. deep. The 
 quantity of fuel used on the bed is more in proportion as the depth is 
 increased, and less when it is made shallower. 
 
 The amount of fuel required on the bed is based on the supposition that 
 the cupola is a straight one all through, and that the bottom is 10 ins. 
 deep. If the bottom be more, as in those of the Colliau type, then addi- 
 tional fuel will be needed. 
 
 First Charge of Iron. The amounts given are safe figures to work upon 
 in every instance, yet it will always be in order, after proving the ability 
 of the bed to carry the load quoted, to make a slow and gradual increase 
 of the load until it is fully demonstrated just how much burden the bed 
 will carry. 
 
 Succeeding Charges of Fuel and Iron. The highest proportions are 
 not favored, for the simple reason that successful melting with any greater 
 proportion of iron to fuel is not the rule, but, rather, the except^n. 
 
 Diameter of Main Blast-pipe. The sizes given are of sufficient area 
 for all lengths up to 100 feet. 
 
 Tuyeres. Any arrangement or disposition of tuyeres may be made, 
 which shall answer in their totality to the areas given in the table. On no 
 consideration must the tuyere area be reduced; thus, an 84-inch cupola 
 must have tuyere area equal to 31 pipes 6 ins. diam., or 16 flat tuyeres 
 16 X 31/2 ins. The tuyeres should be arranged in such a manner as will 
 concentrate the fire at the melting-point into the smallest possible com- 
 pass, so that the metal in fusion will have less- space to traverse while 
 exposed to the oxidizing influence of the blast. 
 
 To accomplish this, recourse has been had to the placing of additional 
 rows of tuyeres in some instances the "Stewart rapid cupola" having 
 three rows, and the "Colliau cupola, furnace" having two rows, of tuyeres* 
 
1248 THE FOUNDRY. 
 
 [Cupolas as large as 84 inches in diameter are now (1906) built without 
 boshes. The most recent development with this size" cupola is to place a 
 center tuyere in the bottom discharging air vertically upwards.] 
 
 Blast-pressure. About 30,000 cu. ft. of air are consumed in melting a 
 ton of iron, which would weigh about 2400 pounds, or more than both 
 iron and fuel. When the proper quantity of air is supplied, the com- 
 bustion of the fuel is perfect, and carbonic-acid gas is the result. When 
 the supply of air is insufficient, the combustion is imperfect, and car- 
 bonic-oxide gas is the result. The amount of heat evolved in these two 
 cases is as 15 to 4V2, showing a loss of over two-thirds of the heat by 
 imperfect combustion. fCombustion is never perfect in the cupola except 
 near the tuyeres. The CO2 formed by complete combustion is largely 
 reduced to CO in passing through the hot coke above the fusion zone.] 
 
 It is not always true that we obtain the most rapid melting when we are 
 forcing into the cupola the largest quantity of air. Too much air absorbs 
 heat, reduces the temperature, and retards combustion, and the fire in the 
 cupola may be extinguished with too much blast. 
 
 Slag in Cupolas. A certain amount of slag is necessary to protect the 
 molten iron which has fallen to the bottom from the action of the blast ; if 
 it was not there, the iron would suffer from decarbonization. 
 
 When slag from any cause forms in too great abundance, it should be 
 led away by inserting a hole a little below the tuyeres, through which it 
 will find its way as the iron rises in the bottom. 
 
 With clean iron and fuel, slag seldom forms to any appreciable extent 
 in small heats; but when the cupola is to be taxed to its utmost capacity 
 it is then incumbent on the melter to flux the charges all through the heat, 
 carrying it away in the manner directed. 
 
 The best flux for this purp9se is the chips from a white-marble yard. 
 About 6 pounds to the ton of iron will give good results when all is clean. 
 [Fluor-spar is now largely used as a flux.] 
 
 When fuel is bad, or iron is dirty, or both together, it becomes imperative 
 that the slag be kept running all the time. 
 
 Fuel for Cupolas. The best fuel for melting iron is coke, because it 
 requires less blast, makes hotter iron, and melts faster than coal. When 
 coal must be used, care should be exercised in its selection. All anthra- 
 cites which are bright, black, hard, and free from slate, will melt iron 
 admirably. For the best results, small cupolas should be charged with 
 the size called "egg," a still larger grade for medium-sized cupolas, and 
 what is called "lump" will answer for all large cupolas, when care is taken 
 to pack it carefully on the charges. 
 
 Melting Capacity of Different Cupolas. The following figures 
 are given by W. B. Snow, in The Foundry, Aug., 1908, showing the 
 records of capacity and the blast pressure of several cupolas: 
 Diam. of lining, 
 
 ins 44 44 47 49 54 54 54 60 60 60 74 
 
 Tons per hour .. 6.7 7.3 8.4 9.1 7.7 8.8 10.212.414.813.813.0 
 Pressure, oz. per 
 
 sq. in 12.9 16.4 17.5 11.8 13.6 11.0 20.8 15.5 16.8 12.6 8.7 
 
 From plotted diagrams of records of 46 tests of different cupolas the 
 following figures are obtained: 
 
 Diam. of lining, ins 30 36 42 48 54 60 66 72 
 
 Max. tons per hour 3 5 7.3 9.512 15 18 21 
 
 Avge. " " " 2.5 4 5.5 7.5 9 11 13 16 
 
 Max. pressure, oz 11 12 13.5 14 14.6 15.2 15.7 16 
 
 For a given cupola and blower the melting rate increases as the square 
 root of the pressure. A cupola melting 9 tons per hour with 10 ounces 
 pressure will melt about 10 tons with 12.5 ounces, and 11 t9ns with 15 
 ounces. The power required varies as the cube of the melting rate, so 
 that it would require (11/9) 3 = 1.82 times as much power for 11 tons as 
 for 9 tons. Hence the advantage of large cupolas and blowers with light 
 pressures. 
 
 Charging a Cupola. Chas. A. Smith (Am. Mach., Feb. 12, 1891) 
 gives the following: A 28-in. cupola should have from 300 to 400 Ibs. of 
 coke on bottom bed; a 36-in. cupola, 700 to 800 Ibs.; a 48-in. cupola, 
 1500 Ibs.; and a 60-in, cupola should have one ton of fuel ou bottom bed, 
 
THE FOUNDRY. 
 
 1249 
 
 To every pound of fuel on the bed, three, and sometimes four pounds of 
 metal can be added with safety, if the cupola has proper blast ; in after- 
 charges, to every pound of fuel add 8 to 10 pounds of metal; any well- 
 constructed cupola will stand ten. 
 
 F. P. Wolcott (Am. Mach., Mar. 5, 1891) gives the following as the 
 practice of the Colwell Iron-works, Carteret, N. J.: "We melt daily from 
 twenty to forty tons of iron, with an average of 11.2 pounds of iron to 
 one of fuel. In a 36-in. cupola seven to nine pounds is good melting, 
 but in a cupola that lines up 48 to 60 inches, anything less than nine 
 pounds shows a defect in arrangement of tuyeres or strength of blast, 
 or in charging up." 
 
 "The Holder's Text-book," by Thos. D. West, gives forty-six reports 
 in tabular form of cupola practice in thirty States, reaching from Maine 
 to Oregon. 
 
 Improvement of Cupola Practice. The following records are given 
 by J. R. Fortune and H. S. Wells (Proc. A. S. M. E. t Mar., 1908) showing 
 how ordinary cupola practice may be improved by making a few changes. 
 The cupola is 13 ft. 4 in. in height from the top of the sand bottom to 
 the charging door, and of three diameters, 50 in. for the first 3 ft. 6 in., 
 then 54 in. for the next 2 ft. 4 in., then 60 in. to the top. When driven 
 with a No. 8 Stuftevant blower, the maximum melting rate, from iron 
 down to blast otf, was 8.5 tons per hour. A No. 11 high-pressure blower 
 was then installed. Test No. 1 in the table below gives the result with 
 cupola charges as follows in pounds: Bed, 590 coke, followed by 826 coke, 
 2000 iron; 400 co&e, 2000 iron; 300 coke, 2000 iron; and thereafter all 
 charges were 200 eoke, 2000 iron. The time between starting fire and start- 
 ing blast was 2 hr. 30 min., and the time from blast on to iron down, 
 11 min. The melting rate, tons per hour, is figured for the time from 
 iron down to blast off. The tuyeres were eight rectangular openings 
 Hi/4 in. high and of a total area of 1/9.02 of the area of the 54-in. circle. 
 
 No. of Test. 
 
 1 
 
 2 
 
 
 
 
 
 
 8 
 
 9 
 
 10 
 
 22.35 
 11 17 
 
 
 
 
 
 
 Total tons... 
 Tons per hr 
 
 22.7 
 9 45 
 
 24. 
 8 88 
 
 22.15 
 8 86 
 
 24.25 
 9 15 
 
 24.25 
 9 66 
 
 22.65 
 10 24 
 
 24. 
 10 43 
 
 20.30 
 10 91 
 
 23.85 
 11 35 
 
 Lbs. per min* 
 Iron -T- cokef 
 Blast, oz 
 
 19.81 
 7.54 
 11.60 
 
 18.61 
 7.40 
 10.63 
 
 18.55 
 7.28 
 10.00 
 
 19.17 
 8.58 
 9.47 
 
 20.25 
 8.94 
 9.80 
 
 21.44 
 8.71 
 9.86 
 
 21.82 
 9.02 
 10.00 
 
 22.95 
 9.02 
 10.13 
 
 23.77 
 10.02 
 10.55 
 
 23.39 
 9.49 
 10.55 
 
 * Per sq. ft. cupola area at 54 in. diam. from iron down to blast off. 
 t Including bed. 
 
 The tuyeres were then enlarged, making their area 1/5.98 of the cupola 
 (54 in.) area, and the results are shown in tests No. 2 and 3 of the table. 
 The iron was too hot, and the coke charge was decreased to a ratio of 
 1/13.33 instead of 1/10, the bed of coke being increased. The result, 
 test No. 4, was an increased rate of melting, a decrease in the amount of 
 coke, and a decrease in the blast pressure. Tests 5, 6, 7, 8 and 9 were 
 then made, the coke being decreased, while the blast pressure was in- 
 creased, resulting in a decided increase in the melting speed. In tests 
 5, 6 and 7 the iron layer was 13.33 times the weight of the coke layer; 
 in test 8, 14.28 times; and in test 9, 15.38 times. In test 9 it was noticed 
 that the iron was not at the proper temperature, and in test 10 the coke 
 layer was increased to a ratio of 1 to 14.28 without altering the blast 
 pressure; this resulted in a decreased melt per hour. It has been found 
 that a coke charge of 150 Ibs. to 2000 Ibs. of iron, with a blast pressure 
 of 10.5 ounces, results in a melt of 11.5 tons per hour, the iron coming 
 down at the proper temperature. 
 
 An excess of coke decreases the melting rate. Iron in the cupola is 
 melted in a fixed zone, the first charge 9f iron above the bed being melted 
 by burning coke in the bed. As this iron is melted, the charge of coke 
 above it descends and restores to the bed the amount which has been 
 burned away. If there is too much coke in the charge, the iron is held 
 above the melting zone, and the excess coke must be burned away before 
 it can be melted, and this of course decreases the economy and the melting 
 speed. 
 
1250 
 
 THE FOUNDRY. 
 
 Cupola Charges in Stove-foundries. (Iron Age, April 14, 1892.) 
 No two cupolas are charged exactly the same. The amount of fuel on 
 the bed or between the charges differs, while varying amounts of iron are 
 used in the charges. Below will be found charging-lists from some of the 
 prominent stove-foundries in the country: 
 
 Ibs. 
 
 A Bed of f uel, coke 1,500 
 
 First charge of iron 5,000 
 
 All other charges of iron 1,000 
 
 First and second charges of 
 coke, each 200 
 
 Ibs. 
 Four next charges of coke, 
 
 each 150 
 
 Six next charges of coke, each 120 
 Nineteen next charges of coke, 
 
 each 100 
 
 Thus for a melt of 18 tons there would be 5120 Ibs. of coke used, giving 
 a ratio of 7 to 1. Increase the amount of iron melted to 24 tons, and a 
 ratio of 8 pounds of iron to 1 of coal is obtained. 
 
 Ibs. 
 
 Ibs 
 
 Second and third charges of 
 fuel 130 
 
 All other charges of fuel, 
 each 100 
 
 B Bed of fuel, coke 1,600 
 
 First charge of iron 1 ,800 
 
 First charge of fuel ......... 1 50 
 
 All other charges of iron, 
 
 each 1,000 
 
 For an 18-ton melt 5060 Ibs. of coke would be necessary, giving a ratio 
 of 7.1 Ibs. of iron to 1 pound of coke. 
 Ibs. 
 
 C Bed of fuel, coke 1,600 
 
 First charge of iron 4,000 
 
 First and second charges of 
 
 coke 200 
 
 In a melt of 18 tons 4100 Ibs. of coke would be used, or a ratio of 8.5 to 1. 
 
 All other charges of iron . . . 
 All other charges of coke. . . 
 
 Ibs. 
 
 2,000 
 
 150 
 
 Ibs. 
 
 D Bed of fuel, coke 1 ,800 
 
 First charge of iron 5,600 
 
 Ibs. 
 
 All charges of coke, each 200 
 
 All other charges of iron 2,900 
 
 In a melt of 18 tons, 3900 ibs. of fuel would be used, giving a ratio of 
 9.4 pounds of iron to 1 of coke. Very high, indeed, for stove-plate. 
 
 Ibs. 
 
 All other charges of iron, each 2,000 
 All other charges of coal, each 175 
 
 Ibs. 
 
 E-Bed of fuel, coal 1,900 
 
 First charge of iron 5,000 
 
 First charge of coal 200 
 
 In a melt of 18 tons 4700 Ibs. of coal would be used, giving a ratio of 
 7.7 Ibs. of iron to 1 Ib. of coal. 
 
 These are sufficient to demonstrate the varying practices existing 
 among different stove-foundries. In all these places the iron was proper 
 for stove-plate purposes, and apparently there was little or no difference 
 in the kind of work in the sand at the different foundries. 
 
 Foundry Blower Practice. (W. B. Snow, Trans. A. S. M. E. t 
 1907.) The velocity of air produced by a blower is expressed by the 
 formula V = ^2 gp/d. If p, the pressure, is taken in ounces per sq. in., 
 and d, the density, in pounds per cu. ft. of dry air at 50 and atmospheric 
 pressure of 14.69 Ibs. or 235 ounces. = 0.77884 Ib., the formula reduces 
 to'F = v^.746, 700 p/(235 4- p), no allowance being made for change of 
 temperature during discharge. From this formula the following figures 
 are obtained. Q = volume discharged per min. through an orifice of 
 1 sq. ft. effective area, H.P. = horse-power required to move the given 
 volume under the given conditions, p = pressure in ounces per sq. in. 
 
 P 
 I 
 
 2 
 3 
 
 4 
 5 
 
 Q 
 
 H.P. 
 
 P 
 6 
 7 
 8 
 9 
 10 
 
 Q 
 
 H.P. 
 
 P 
 
 Q 
 
 H.P. 
 
 P 
 
 
 
 H .P. 
 
 35.85 
 50.59 
 61.83 
 71.24 
 79.48 
 
 0.00978 
 0.02759 
 0.05058 
 0.07771 
 0.1084 
 
 86.89 
 93.66 
 99.92 
 105.76 
 111.25 
 
 0.1422 
 0.1788 
 0.2180 
 0.2596 
 0.3034 
 
 11 
 12 
 13 
 14 
 15 
 
 116.45 
 121.38 
 126.06 
 130.57 
 134.89 
 
 0.3493 
 0.3972 
 0.447C 
 0.4986 
 0.5518 
 
 16 
 17 
 18 
 19 
 20 
 
 139.03 
 143.03 
 146.88 
 150.61 
 154.22 
 
 0.6067 
 0.6631 
 0.7211 
 0.7804 
 0.8412 
 
 The greatest effective area over which a fan will maintain the maximum 
 velocity of discharge is known as the "capacity area" or "square inches 
 of blast." As originally established by Sturtevant it is represented by 
 = diam, of wheel in ins., W = width of wheel at circumference, 
 
THE FOUNDRY. 
 
 1251 
 
 In inches. For the ordinary type of fan at constant speed maximum 
 efficiency and power are secured at or near the capacity area; the powei 
 per unit of volume and the pressure decrease as the discharge area and 
 volume increase; with closed outlet the power is approximately one-third 
 of that at capacity area. 
 
 The following table is calculated on these bases: Capacity area per inch 
 of width at periphery of wheel = 1/3 of diam. Air, 50 F. Velocity 
 of discharge = circumferential speed of the wheel. Power = double the 
 theoretical. In rotary positive blowers, as well as in fans, the velocity 
 and the volume vary as the number of revolutions, the pressure varies 
 as the square, and the power as the cube of the number of revolutions. 
 In the fan, however, increase of pressure can be had only by increasing 
 the revolutions, while in the rotary blower a great range of pressure is 
 obtainable with constant speed by merely varying the resistance. With a 
 rotary blower at constant speed, theoretically, and disregarding the effect 
 of changes in temperature arid density, the volume is constant: the velocity 
 varies inversely as the effective outlet area; the pressure varies inversely 
 as the square of the outlet area, hence as the square of the velocity; 
 and the power varies directly as the pressure. The maximum power is 
 required when a fan discharges against the least, and when a rotary 
 blower discharges against the greatest resistance. 
 
 PERFORMANCE OF CUPOLA FAN BLOWERS AT CAPACITY AREA PER INCH 
 OF PERIPHERAL WIDTH. 
 
 B 
 
 o'S 
 
 P 
 
 .2-3 
 
 Q 
 
 Item. 
 
 Total Pressure in Ounces per Square Inch. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 ! 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 2660.0 
 520.0 
 1.7 
 
 2860.0 
 560.0 
 2.1 
 
 3050.0 
 600.0 
 2.6 
 
 3230.0 
 640.0 
 3.1 
 
 3400.0 
 670.0 
 3.6 
 
 3560.0 
 700.0 
 4.2 
 
 3710.0 
 730.0 
 4.8 
 
 3850.0 
 760.0 
 5.4 
 
 3990.0 
 780.0 
 6.0 
 
 4120.0 
 810.0 
 6.6 
 
 4250.0 
 830.0 
 7.3 
 
 -1 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 2000.0 
 700.0 
 2.3 
 
 2150.0 
 750.0 
 2.9 
 
 2290.0 
 800.0 
 3.5 
 
 2420.0 
 850.0 
 4.2 
 
 2550.0 
 890.0 
 4.9 
 
 2670.0 
 930.0 
 5.6 
 
 2780.0 
 970.0 
 6.4 
 
 2890.0 
 1010.0 
 7.1 
 
 2990.0 
 1040.0 
 8.0 
 
 3090.0 
 1080.0 
 8.8 
 
 3190.0 
 1110.0 
 9.7 
 
 -1 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 1590.0 
 870.0 
 2.8 
 
 1720.0 
 940.0 
 3.6 
 
 1830.0 
 1000.0 
 4.4 
 
 1940.0 
 1060.0 
 5.2 
 
 2040.0 
 1110.0 
 6.1 
 
 2140.0 
 1160.0 
 7.0 
 
 2230.0 
 1210.0 
 7.9 
 
 2310.0 
 1260.0 
 8.9 
 
 2390.0 
 1310.0 
 10.0 
 
 2470.0 
 1350.0 
 11.0 
 
 2550.0 
 1390.0 
 12.1 
 
 -1 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 1330.0 
 1040.0 
 
 1430.0 
 1120.0 
 
 1530.0 
 1200.0 
 
 1620.0 
 1270.0 
 
 1700.0 
 1340.0 
 
 1780.0 
 1400.0 
 
 1850.0 
 1460.0 
 
 1930.0 
 15100 
 
 2000.0 
 1570 
 
 2060.0 
 16200 
 
 2120.0 
 16700 
 
 3.4 
 
 4.3 
 
 5.2 
 
 6.2 
 
 7.3 
 
 8.4 
 
 9.5 
 
 10.7 
 
 11.9 
 
 13.2 
 
 14.5 
 
 -! 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 1140.0 
 1220.0 
 3.9 
 
 1230.0 
 1310.0 
 5.0 
 
 1310.0 
 1400.0 
 6.1 
 
 1380.0 
 1480.0 
 7.3 
 
 1460.0 
 1560.0 
 8.5 
 
 1530.0 
 1630.0 
 9.8 
 
 1590.0 
 1700.0 
 11.1 
 
 1650.0 
 1770.0 
 12.5 
 
 1710.0 
 1830.0 
 13.9 
 
 1770.0 
 1890.0 
 15.4 
 
 1820.0 
 1950.0 
 17.0 
 
 1 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 1000.0 
 1390.0 
 4.5 
 
 1070.0 
 1500.0 
 5.7 
 
 1150.0 
 1600.0 
 7.0 
 
 1210.0 
 1690.0 
 8.3 
 
 1270.0 
 1780.0 
 9.7 
 
 1330.0 
 1860.0 
 11.2 
 
 1390.0 
 1940.0 
 12.7 
 
 1450.0 
 2020.0 
 14.3 
 
 1500.0 
 2090.0 
 15.9 
 
 1550.0 
 2160.0 
 17.7 
 
 1590.0 
 2230.0 
 21.0 
 
 The air supply required by a cupola varies with the melting ratio, the 
 density of the charges, and the incidental leakage. Average practice is 
 represented by the following: 
 
 Lbs. iron per Ib. coke 6 7 8 9 10 
 
 Cu. ft. air per ton of iron 33,000 31,00029,000 27,00025,000 
 
 It is customary to provide blower capacity on a basis of 30,000 cu. ft., 
 which corresp9nds to 75 to 80% of the chemical requirements for complete 
 combustion with average coke, and a melting ratio of 7.5 to 1. 
 
 In comparative tests with a 54-inch lining cupola under identical con- 
 ditions as to contents, alternately run with a No. 10 Sturtevant fan and 
 a 33 cu. ft. Connersville rotary, with the fan the pressure varied between 
 12V2 and 141/8 ounces in the wind box, the net power from 25 to 38.5 H.P., 
 while with the rotary blower the pressure varied between 10 1/2 and 25 
 ounces, and the power between 19 and 45 H,P. With the fan 28.84 tons 
 
1252 
 
 THE FOUNDRY. 
 
 were melted m 3.77 hours, or 7.65 tons per hour, while with the rotary 
 Dlower 2.82 hours were required to melt 31.5 tons, an hourly rate of 10 6 
 tons, an increase of nearly 40 per cent in output. This reduces to a net 
 input of 4.09 H.P. per ton melted per hour with the fan, and 2.98 H.P. 
 with the rotary blower; an apparent advantage of 27% in favor of the 
 rotary. Had the rotary been of smaller capacity such excessive pressures 
 would not have been necessary, the power would have been decreased, 
 and the duration of the heat prolonged, with probable decrease in the 
 H.P. hours per ton. Had the fan been run at higher speed the H.P. 
 would have increased, the time decreased and the power per ton per hour 
 would have more closely approached that required by the rotary blower. 
 Theoretically, for otherwise constant conditions, the following relations 
 hold for cupolas and melting rates within the range of practical operation: 
 
 For a givenjcupolaj For a given melting rate: For a given volume; 
 
 M oc F.v/P.or^/HJP. V oc 1 -r- Z>* M*D 
 
 V^M P oc d For a given cupola 
 
 P oo F 2 H.P. oc P or 1 * D E OG M 2 , or P 
 
 H.P. oc Af 3 or VP* E oc M, P, or 1 * D 4 Duration of heat 
 
 oc 1 -f- Vp 
 
 M = melting rate; V = volume; P = pressure; H.P. = horse-power; 
 D = diam. of lining; E = operating efficiency = power per ton per hour; 
 d = depth of the charge; oc, varies as. 
 
 These relations might be the source of formulae for practical use were 
 it possible to establish accurate coefficients. But the variety in cupolas, 
 tuyere proportions, character of fuel and iron, and difference in charging 
 practice are bewildering and discouraging. Maximum efficiency in a 
 given case can only be assured after direct experiment. Something short 
 of the maximum is usually accepted in ignorance of the ultimate possi- 
 bilities. 
 
 The actual melting range of a cupola is ordinarily between 0.6 and 
 0.75 ton per hour per sq. ft. of cross section. The limits of air supply 
 per minute per sq. ft. are roughly 2500 and 4000 cu. ft. The possible 
 power required varies even more widely, ranging from 1.5 to 3.75 H.P. 
 per sq. ft., corresponding to 2.5 and 5 H.P. per ton per hour for the melting 
 rates specified. The power may be roughly calculated, from the theoreti- 
 cal requirement of 0.27 H.P. to deliver 1000 cu. ft. per minute against 
 1 oz. pressure. The rjower increases directly with the pressure, and de- 
 pends also on the efficiency of. the blower. Current practice can only be 
 expressed between limits as in the following table. 
 
 RANGE OF PERFORMANCE OF CUPOLA BLOWERS. 
 
 Diameter inside 
 Lining, in. 
 
 Capacity per 
 Hour, tons. 
 
 Pressure 
 per sq. 
 m., oz. 
 
 Volume of Air 
 permin., cu. ft. 
 
 Horse- 
 power. 
 
 18 
 
 25- 0.5 
 
 5- 7 
 
 150^ 300 
 
 05-15 
 
 24 .. 
 
 1.00- 1.5 
 
 7- 9 
 
 600- 900 
 
 20-60 
 
 30 
 
 2 00- 3 5 
 
 8-11 
 
 1 200- 2 000 
 
 5 0- 15 
 
 36 . 
 
 4.00- 5.0 
 
 8-12 
 
 2 200- 2 800 
 
 10 0- 23 
 
 42... 
 
 5.00- 7.0 
 
 8-13 
 
 2,700- 3,700 
 
 12.0- 32.0 
 
 48 
 
 8 00-10 
 
 8-13 
 
 4 000- 5 000 
 
 18 0- 45 
 
 54... 
 
 9.00-12.0 
 
 9-14 
 
 4,500- 6,000 
 
 22.0- 60.0 
 
 60 
 
 12 00-15 
 
 9-14 
 
 6 000- 7 500 
 
 30 0- 75 
 
 66... 
 
 14.00-18.0 
 
 9-15 
 
 7,000- 9 000 
 
 35.0- 90 
 
 72 
 
 17 00-21 
 
 10-15 
 
 8 500- 10' 500 
 
 45 0-110 
 
 78 
 
 19 00-24.0 
 
 10-16 
 
 9,500-12,000 
 
 52.0-130 
 
 84 
 
 21.00-27.0 
 
 10-16 
 
 10,500-13,500 
 
 60.0-150.0 
 
 Results of Increased Driving. (Erie City Iron-works, 1891.) 
 May-Dec., 1890: 60-in. cupola, 100 tons clean castings a week, melting 
 8 tons per hour; iron per pound of fuel, 7V2 Iks.; per cent weight of good 
 castings to iron charged, 753/4. Jan.-May, 1891: Increased rate of melt- 
 ing to 111/2 tons per hour: iron per Ib. fuel, 91/2; per cent weight of good 
 castings, 75; one week, 131/4 tons per hour, 10.3 Ibs. iron per Ib. fuel; 
 per cent weight of good castings, 75.3. The increase was made by putting 
 m an additional row of tuyeres and using stronger blast, 14 ounces. Coke 
 was used as fuel. (W. O. Webber, Trans. A. S. M . E., xii, 1045.) 
 
THE FOUNDRY. 1253 
 
 Power Required for a Cupola Fan. (Thos. D. West, The Foundry, 
 April, 1904.) The power required when a fan is connected with a cupola 
 depends on the length and diameter of the piping, the number of bends, 
 valves, etc., and on the resistance to the passage of blast through the 
 cupola. The approximate power required in everyday practice is the 
 difference between the power required to run the fan with the outlet open 
 and with it closed. Another rule is to take 75% of the maximum power 
 or that with the outlet open. A fan driving a cupola 66 ins. diam., 
 1800 r.p.m., driven by an electric motor required horse-power and gave 
 pressures as follows : Outlet open, 146.6; outlet closed, 37.2, pressure 
 15 oz.; attached to cupola, with no fuel in it, 120.5, 5 oz.; after kindling 
 and coke had been fired, 101.0, 10 oz.; during the run 70.8 to 76.7, 11 to 
 13 oz., the variations being due to changes in the resistances to the passage 
 of the blast. 
 
 Utilization of Cupola Gases. Jules De Clercy, in a paper read 
 before the Amer. Foundrymen's Assn., advises the return of a portion of 
 the gases from the upper part of the charge to the tuyeres, and thus 
 utilizing the carbon monoxide they contain. He says that A. Baillot 
 has thereby succeeded in melting 15 Ibs. of iron per Ib. of coke, and at the 
 same time obtained a greater melting speed and a superior quality of 
 castings. 
 
 Loss in Melting Iron in Cupolas. G. O. Vair, Am. Mack., March 
 5, 1891, gives a record of a 45-in. Colliau cupola as follows: 
 
 Ratio of fuel to iron, 1 to 7.42. 
 Good castings 21,314 Ibs. 
 
 K New scrap 3,005 " 
 Millings 200 " 
 Loss of metal 1,481 ' 
 Amount melted 26,000 Ibs. 
 Loss of metal, 5.69%. Ratio of loss, 1 to 17.55. 
 se of Softeners in Foundry Practice. (W. Graham, Iron Age, 
 June 27, 1889.) In the foundry the problem is to have the right pro- 
 portions of combined and graphitic carbon in the resulting casting; this 
 is done by getting the proper proportion of silicon. The variations in 
 the proportions of silicon afford a reliable and inexpensive means of 
 producing a cast iron of any required mechanical charae-ter which is 
 possible with the material employed. In this way, by mixing suitable 
 irons in the right proportions, a required grade of casting can be made 
 more cheaply than by using irons in which the necessary proportions are 
 already found. 
 
 Hard irons, mottled and white irons, and even steel scrap, all containing 
 low percentages of silicon and high percentages of combined carbon, 
 could be employed if an iron having a large amount of silicon were mixed 
 with them in sufficient amount. This would bring the silicon to the 
 proper proportion and would cause the combined carbon to be forced into 
 the graphitic state, and the resulting casting would be soft. High-silicon 
 irons used in this way are called "softeners." 
 
 Mr. Keep found that more silicon is lost during the remelting of pig of 
 over 10% silicon than in remelting pig iron of lower percentages of silicon. 
 He also points out the possible disadvantage of using ferro-silicons con- 
 taining as high a percentage of combined carbon as 0.70% to overcome 
 the bad effects of combined carbon in other irons. 
 
 The Scotch irons generally contain much more phosphorus than is 
 desired in irons to be employed in making the strongest castings. It is a 
 mistake to mix with strong low-phosphorus irons an iron that would 
 increase the amount of phosphorus for the sake of adding softening 
 qualities, when softness can be produced by mixing irons of the same low 
 phosphorus. 
 
 (For further discussion of the influence of silicon, see pages 438 and 447.) 
 
 Weakness of Large Castings. (W. A. Bole, Trans. A. S. M. E., 
 1907.) Thin castings, by virtue of their more rapid cooling, are almost 
 certain to be stronger per unit section than would be the case if the same 
 metal were poured into larger and heavier shapes. Many large iron castings 
 are of questionable strength, because of internal strains and lack of har- 
 mony between their elements, even though the casting is poured out of iron 
 of the best quality. This may be due to lack of experience on the part of 
 
1254: THE FOUNDRY. 
 
 the designer, especially in the cooling and shrinking of the various parts 
 of a large casting after being poured. 
 
 Castings are often designed with a .useless multiplicity 9f ribs, walls, 
 gussets, brackets, etc., which, by their asynchronous cooling and their 
 inharmonious shrinkage and contraction, may entirely defeat the intention 
 of the designer. 
 
 There are some castings which, by virtue of their shapes, can be specially 
 treated by the foundryman, and artificial cooling of certain critical parts 
 may be effected in order to compel such parts to cool more rapidly than 
 they would naturally do, and the strength of the casting may by such 
 means be beneficially affected. As for instance in the case of a fly-wheel 
 with heavy rim but comparatively light arms and hub; it may be bene- 
 ficial to remove the flask and expose the rim to the air so as to hasten its 
 natural rate of cooling, while the arms and hub are still kept muffled up 
 in the sand of the mold and their cooling retarded as much as possible. 
 
 Large fillets are often highly detrimental to good results. Where two 
 walls meet and intersect, as in the shape of a T, if a large fillet is swept 
 at the juncture, there will be a pool of liquid metal at this point which will 
 remain liquid for a longer time than either wall, the result being a void, 
 or "draw," at the juncture point. 
 
 Risers and sink heads should often be employed on iron castings. In 
 large iron-foundry work interior cavities may exist without detection, 
 and some of these may be avoided by the use of suitable feeding devices, 
 risers and sink heads. 
 
 Specimens from a casting having at one point a tensile strength as high 
 as 30,250 Ibs. per sq. in. have shown as low as 20,500 in another and 
 heavier section. Large sections cannot be cast to yield the high strength 
 of specimen test pieces cast in smaller sections. 
 
 The paper describes a successful method of artificial cooling, by means of 
 a coil of pipe with flowing water, of portions of molds containing cylinder 
 heads with ports cast in them. Before adopting this method the internal 
 ribs in these castings always cracked by contraction. 
 
 Shrinkage of Castings. The allowance necessary for shrinkage 
 varies for different kinds of metal, and the different conditions under 
 which they are cast. For castings where the thickness runs about one 
 inch, cast under ordinary conditions, the following allowance can be made: 
 
 For cast iron, Vs inch per foot. For zinc, 5/ 16 inch per foot. 
 
 ' brass, 3/ 16 ' tin, 1/12 ' 
 
 " steel, V4 * aluminum, 3/ 16 ' 
 
 ' mal. iron, 1/8 ' britannia, V32 ' 
 
 Thicker castings, under the same conditions, will shrink less, and thinner 
 ones more, than this standard. The quality of the material and the man- 
 ner of molding and cooling will also make a difference. (See also 
 Shrinkage of Cast Iron, page 447.) 
 
 Mr. Keep (Trans. A. S. M. E., vol. xvi) gives the following "approxi- 
 mate key for regulating foundry mixtures" so as to produce a shrinkage 
 of Vs in. per ft. in castings of different sections: 
 
 Size of casting 1/2 1 2 3 4 in. sq. 
 
 Silicon required, per cent 3.25 2.75 2.25 1.75 1.25 per cent. 
 
 Shrinkage of a i/2-in. test-bar.. 0.125 .135 .145 .155 .165 in per. ft. 
 
 Growth of Cast Iron by Heating. (Proc. I. and S. Inst., 1909.) 
 Investigations by Profs. Rugan and Carpenter confirm Mr. Outerbridge's 
 experiments. (See- page 449 ) They found: 1. Heating white iron causes 
 it to become gray, and it expands more than sufficient to overcome the 
 original shrinkage. 2. Iron when heated increases in weight, probably 
 due to absorption of oxygen. 3. The change in size due to heating is 
 not only a molecular change, but also a chemical one. 4. The growth of 
 one bar was shown to be due to penetration of gases. When heated in 
 vacuo it contracted. 
 
 Hard Iron due to Excessive Silicon. W. J. Keep in Jour. Am. 
 Foundry men's Assn., Feb., 1898, reports a case of hard iron containing 
 graphite, 3.04; combined C, 0.10; Si, 3.97; P, 0.61; S, 0.05; Mn, 0.56. He 
 says: For stove plate and light hardware castings it is an advantage to 
 have Si as high as 3.50. When it is much above that the surface of the 
 castings often become very hard, though the center will be very soft. 
 
THE FOUNDRY. 
 
 1255 
 
 The surface of heavier parts of a casting having 3.97 Si will be harder than 
 the surface of thinner parts. Ordinarily if a casting is hard an increase 
 of silicon softens it, but after reaching 3.00 or 3.50 per cent, silicon hardens 
 
 Ferro-Alloys for Foundry Use. E. Houghton (Iron Tr. Rev., 
 Oct. 24, 1907.) The objects of the use of ferro-alloys in the foundry are: 
 1, to act as deoxidizers and desulphurizers, the added element remaining 
 only in small quantities in the finished casting; 2, to alter the composition 
 of the casting and so to control its mechanical properties. Some of these 
 alloys are made in the blast furnace, but the purest grades are made in 
 the electric furnace. The following table shows the range of composition 
 of blast furnace alloys made by the Darwen & Mostyn Iron Co. All of 
 these alloys may be made of purer quality in the electric furnace. 
 
 
 Ferro 
 Mn. 
 
 Spiegel- 
 eisen. 
 
 Silicon 
 Spiegel. 
 
 Ferro- 
 sil. 
 
 Ferro- 
 phos. 
 
 Ferro* 
 Chrome. 
 
 Mn... 
 
 41.5- 87.9 
 0.10- 0.63 
 0.09- 0.20 
 5.62- 7.00 
 nil 
 
 9.25-29.75 
 0.42- 0.95 
 0.06- 0.09 
 3.94- 5.20 
 nil-trace 
 
 17.50-20.87 
 9.45-14.23 
 0.07- 0.10 
 1.05- 1.89 
 nil 
 
 1.17- 2.20 
 8.10-17.00 
 0.06- 0.08 
 0.90- 1.75 
 0.02- 0.05 
 
 3.00- 5.90 
 0.50- 0.84 
 15.71-20.50 
 0.27- 0.30 
 0.16- 0.33 
 
 1.55-2.30 
 0.13-0.36 
 0.04- 0.07 
 5.34- 7.12 
 Cr, 13.50-41.39 
 
 Si 
 p 
 
 C ... 
 
 s 
 
 
 The following are typical analyses of other alloys made in the electric 
 furnace: 
 
 
 Si 
 
 Fe 
 
 Mn 
 
 Al 
 
 Ca 
 
 Mg 
 
 C 
 
 S 
 
 P 
 
 TI 
 
 Ferro-tftanium ... 
 
 1.21 
 
 
 
 30 
 
 
 
 3.28 
 0.55 
 1.14 
 
 0.03 
 0.01 
 0.01 
 
 0.02 
 0.03 
 0.04 
 
 53.0 
 
 Ferro-aluminum-silicide 
 Fei ro-calcium-silicide 
 
 45.65 
 69.80 
 
 44.15 
 11.15 
 
 tr. 
 0.22 
 
 9.45 
 2.55 
 
 nil 
 15.05 
 
 nil 
 
 0.26 
 
 Ferro-aluminum, Al, 5, 10 and 20%. Metallic manganese. Mn, 95 to 
 98; Fe, 2 to 4; C, under 5. Do. refined. Mn, 99; Fe, 1 ; C, 0. 
 
 Dangerous Ferro-silicon. Phosphoretted and arseniuretted hydro- 
 gen, highly poisonous gases, are said to be disengaged in a humid atmos- 
 phere from ferro-silicon containing between 30 and 40% and between 47 
 and 65% of Si, and there is therefore danger in transporting it in passenger 
 steamships. A French commission has recommended the abandonment 
 of the manufacture of FeSi of these critical percentages. (La Lumiere 
 Electrique, Dec. 11, 1909. Elep. Rev., Feb. 26, 1910.) 
 
 Quality of Foundry Coke. (R. Moldenke, Trans. A. S. M. E., 
 1907.) Usually the sulphur, ash and fixed carbon are sufficient to give 
 a fair idea of the value of coke, apart from its physical structure, specific 
 gravity, etc. The advent of by-product coke will necessitate closer 
 attention to moisture Beehive coke, when shipped in open cars, may, 
 through inattention, cause the purchase of from 6 to 10 per cent of water 
 at coke prices. 
 
 Concerning sulphur, very hot running of the cupola results in less sulphur 
 in the iron. In good coke, the amount of S should not exceed 1.2 per 
 cent; but, unfortunately, the percentage often runs as high as 2.00. If 
 the coke has a good structure, an average specific gravity, not over 11 per 
 cent of ash and over 86 per cent of fixed carbon, it does not matter much 
 whether it be of the "72 hour" or "24 hour" variety. Departure from 
 the normal composition of a coke of any particular region should place the 
 foundryman on his guard at once, and sometimes the plentiful use of 
 limestone at the right moment may save many castings. 
 
 Castings made in Permanent Cast-iron Molds. E. A. Custer, in 
 a paper before the Am. Foundrymen's Assn. (Eng. News, May 27, 1909), 
 describes the method of making castings in iron molds, and the quality 
 of these castings. Very heavy m9lds are used, no provision is made 
 against shrinkage, and the casting is removed from the mold as soon as 
 1 it has set, giving it no time to chill or to shrink by cooling. Over 6000 
 pieces have been cast in a single mold without its showing any signs of 
 
1256 
 
 THE FOUNDRY. 
 
 failure. The mold should be so heavy that it will not become highly 
 heated in use. Casting a 4-in. pipe weighing 65 Ibs. every seven min- 
 utes in a mold weighing 6500 Ibs. did not raise the temperature above 
 300 F. In using permanent molds the iron as it comes from the cupola 
 should be very hot. The best results in casting pipe are had with iron 
 containing over 3% carbon and about 2% silicon. Iron when cast in 
 an iron mold and removed as soon as it sets, possesses some unusual prop- 
 erties. It will take a temper, and when tempered will retain magnetism. 
 If the casting be taken from the mold at a bright heat and suddenly 
 quenched in cold water, it has the cutting power of a good high-carbon 
 steel, whether the iron be high or low in silicon, phosphorus, sulphur or 
 manganese. There is no evidence of "chill"; no white crystals are shown. 
 
 Chilling molten iron swiftly to the point of setting, and then allowing 
 it to cool gradually, produces a metal that is entirely new to the art. It 
 has the chemical characteristics of cast iron, with the exception of com- 
 bined carbon, and it als9 possesses some of the properties of high-carbon 
 steel. A piece o-f cast iron that has 0.44% combined, and over 2% free 
 carbon, has been tempered repeatedly and will do better service in a lathe 
 than a good non-alloy steel. Once this peculiar property is imparted to 
 the casting, it is impossible to eliminate it except by remelting. A bar of 
 iron so treated can be held in a flame until the metal drips from the end, 
 and yet quenching will restore it to its original hardness. 
 
 The character of the iron before being quenched is very fine, close- 
 grained, and yet it is easily machined. If permanent molds can be used 
 with success in the foundry, and a system of continuous pouring be 
 inaugurated which in duplicate work would obviate the necessity of having 
 molders, why is it necessary to melt pig iron in the cupola? What could 
 be more ideal than a series of permanent molds supplied with molten iron 
 practically direct from the blast furnace? The interposition of a reheating 
 ladle such as is used by the steel makers makes possible the treatment of 
 the molten iron. 
 
 The molten iron from the blast furnace is much hotter than that ob- 
 tained from the cupola, so that there is every reason to believe that the 
 castings obtained from a blast fur'nace would be of a better quality than 
 when the pig is remelted in the cupola. 
 
 It is immaterial whether an iron contains 1.75 or 3% silicon, so long as 
 the molten mass is at the proper temperature, so that the high tempera- 
 tures obtained from .he blast furnace would go far toward offsetting the 
 variations in the impurities. 
 
 R. H. Probert (Castings, July, 1909) gives the following analysis of 
 molds which gave the best results: Si, 2.02; S, 0.07; P, 0.89; Mn, 0.29: 
 C.C., 0.84: G.C., 2.76. Molds made from iron with the following analysis 
 were worthless: Si, 3.30; S, 0.06; P, 0.67; Mn, 0.12; C.C., 0.19; G.C., 2.98. 
 
 Weight of Castings determined from Weight of Pattern. 
 
 (Rose's Pattern-makers' Assistant.) 
 
 A Pattern weighing One 
 Pound, made of 
 
 Will weigh when cast in 
 
 Cast 
 Iron. 
 
 Zinc. 
 
 Copper. 
 
 Yellow 
 Brass. 
 
 Gun 
 metal. 
 
 Mahogany Nassau 
 
 Ibs. 
 10.7 
 12.9 
 8.5 
 12.5 
 16.7 
 14.1 
 
 Ibs. 
 10.4 
 12.7 
 8.2 
 12.1 
 16.1 
 13.6 
 
 Ibs. 
 12.8 
 15.3 
 10.1 
 14.9 
 19.8 
 16.7 
 
 Ibs. 
 12.2 
 14.6 
 9.7 
 14.2 
 19.0 
 16.0 
 
 Ibs. 
 12.5 
 15. 
 9.9 
 14.6 
 19.5 
 16.5 
 
 Honduras 
 
 Spanish 
 
 Pine r^d 
 
 1 white 
 
 
 
 MoWing Sand. (Walter Bagshaw, Proc. Tnst. M. E., 1891.) The 
 chemical composition of sand will affect the nature of the casting, no 
 matter what treatment it undergoes. Stated generally, good sand is 
 composed of 94 parts silica, 5 parts alumina, and traces of magnesia and 
 *xide of iron. Sand containing much of the metallic oxides, and especially 
 
THE FOUNDRY. 
 
 1257 
 
 lime, is to be avoided. Geographical position is the chief factor governing 
 the selection of sand ; and whether weak or strong, its deficiencies are made 
 up for by the skill of the inolder. For this reason the same sand is often 
 used f9r both heavy and light castings, the proportion of coal varying 
 according to the nature of the casting. A common mixture of facing- 
 sand consists of six parts by weight of old sand, four of new sand, and one 
 of coal-dust. Floor-sand requires only half the above proportions of new 
 sand and coal-dust to renew it. German founders adopt one part by 
 measure of new sand to two of old sand; to which is added coal-dust in 
 the proportion of one-tenth of the bulk for large castings, and one-twen- 
 tieth for small castings. A few founders mix street-sweepings with the 
 coal in order to get porosity when the metal in the mold is likely to be 
 a long time in setting. Plumbago is effective in preventing destruction 
 of the sand; but owing to its refractory nature, it must not be dusted 
 on in such quantities as to close the pores and prevent free exit of the 
 gases. Powdered French chalk, soapstone, and other substances are 
 sometimes used for facing the mold; but next to plumbago, oak charcoal 
 takes the best place, notwithstanding its liability to float occasionally and 
 give a rough casting. 
 
 For the treatment of sand in the molding-shop the most primitive 
 method is that .of hand-riddling and treading. Here the materials are 
 roughly proportioned by volume, and riddled over an iron plate in a flat 
 heap, where the mixture is trodden into a cake by stamping with the feet; 
 it is turned over with the shovel, and the process repeated. Tough 
 sand can be obtained in this manner, its toughness being usually tested 
 by squeezing a handful into a ball and then breaking it; but the process 
 is slow and tedious. Other things being equal, the chief characteristics 
 of a good molding-sand are toughness and porosity, qualities that depend 
 on the manner of mixing as well as on uniform ramming. 
 
 Toughness of Sand. In order to. test the relative toughness, sand 
 mixed in various ways was pressed under a uniform load into bars 1 in. sq. 
 and about 12 in. long, and each bar was made to project further and 
 further over the edge of a table until its end broke off by its own weight. 
 Old sand from the shop floor had very irregular cohesion, breaking at all 
 lengths of projections from 1/2 in. to 1 1/2 in. New sand in its natural state 
 held together until an overhang of 23/4 in. was reached. A mixture of old 
 sand, new sand, and coal-dust 
 
 Mixed under rollers broke at 2 to 2 1/4 in. of overhang. 
 
 in the centrifugal machine ... '* 2 " 2Vi " 
 
 through a riddle " 1 3/ 4 " 2Vs " 
 
 showing as a mean of the tests only slight differences between the last 
 three methods, but in favor of machine-work. In many instances the 
 fractures were so uneven that minute measurements were not taken. 
 
 Heinrich Ries (Castings, July, 19QS) says that chemical analysis gives 
 little or no information regarding the bonding power, texture, permea- 
 bility or use of sand, the only case in which it is of value being in the 
 selection of a highly silicious sand for certain work such as steel casting. 
 
 Dimensions of Foundry Ladles. The following table gives the 
 dimensions, inside the lining, of ladles from 25 Ibs. to 16 tons capacity. 
 All the ladles are supposed to have straight sides. (Am. Mach., Aug. 4, 
 1892.) 
 
 Cap'y. 
 
 Diam. 
 
 Depth. 
 
 Cap'y. 
 
 Diam. 
 
 Depth. 
 
 Cap'y. 
 
 Diam. 
 
 Depth. 
 
 16 tons 
 14 
 12 
 10 
 8 
 6 
 4 
 
 m. 
 54 
 52 
 49 
 46 
 43 
 39 
 34 
 
 in. 
 56 
 53 
 50 
 48 
 44 
 40 
 35 
 
 3 tons 
 2 " 
 
 U/2" 
 1 ton 
 
 3/4" 
 1/2" 
 1/4" 
 
 in. 
 31 
 27 
 
 !f /2 
 
 20 
 17 
 13V 2 
 
 in. 
 32 
 28 
 25 
 22 
 20 
 17 
 131/2 
 
 300 Ibs. 
 250 " 
 200 " 
 150 " 
 100 " 
 75 " 
 50 " 
 
 in. 
 
 1U/2 
 ,03 /4 
 
 9 
 
 8 
 7 
 
 61/2 
 
 j|i /2 
 '88 
 
 81/2 
 7V2 
 61/2 
 
1258 
 
 THE MACHINE-SHOP. 
 
 THE MACHINE-SHOP. 
 
 SPEED OF CUTTING-TOOLS IN LATHES, MILLING 
 MACHINES, ETC. 
 
 Relation of diameter of rotating tool or piece, number of revolution 
 and cutting-speed: 
 
 Let d = diam. of rotating piece in inches, n = No. of revs, per min.; 
 = speed of circumference in feet per minute; 
 *dn ,,_ S ' 3.82 J 3.825 
 
 S = 
 S - 
 
 T2~ 
 
 d = 
 
 Approximate rule: Number of revolutions per minute = 4 X speed Ln 
 feet per minute * diameter in inches. 
 
 Table of Cutting-speeds. 
 
 Feet per minute. 
 
 {J 
 
 1J 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 75 
 
 too 
 
 150 
 
 200 
 
 250 
 
 300 
 
 Revolutions per minute. 
 
 */4 
 
 152.8 
 
 305.6 
 
 458.4 
 
 611.2 
 
 764.0 
 
 1145.9 
 
 1527.9 
 
 2291.83055.8)3819.74583.7 
 
 3/8 
 
 1/2 
 
 101.9 
 76.4 
 
 203.7 
 152.8 
 
 305.6 
 229.2 
 
 407.4 
 305.6 
 
 509.3 
 382.0 
 
 763.7 
 572.9 
 
 1018.6 
 763.9 
 
 1 527.51 2036. 7i 2545. 8 3055.0 
 1145.9 1527.9 1909.92291.8 
 
 5/8 
 
 61.1 
 
 122.2 
 
 183.4 
 
 244.5 
 
 305.6 
 
 458.4 
 
 611.2 
 
 916.7 
 
 1222.3 1527.9 
 
 1833.5 
 
 3/4 
 
 50.9 
 
 101.8 
 
 152.8 
 
 203.7 
 
 254.6 
 
 382,0 
 
 509.3 
 
 763.9 
 
 1018.611273.2 
 
 1527.9 
 
 7/ 8 
 
 43.7 
 
 87.3 
 
 130.9 
 
 174.6 
 
 218.3 
 
 327.4 
 
 436.6 
 
 654.9 
 
 873. 3! 1091. 5 
 
 1309.8 
 
 1 
 
 38.2 
 
 76.4 
 
 114.6 
 
 152.8 
 
 191.0 
 
 286.5 
 
 382.0 
 
 573.0 
 
 763.9 954.9 
 
 1145.9 
 
 1 1/8 
 
 34.0 
 
 67.9 
 
 101.8 
 
 135.8 
 
 169.7 
 
 254.4 
 
 339.5 
 
 508.8 
 
 678.4 848.0 
 
 1017.6 
 
 1 1/4 
 
 30.6 
 
 61.1 
 
 91.7 
 
 122.2 
 
 152.8 
 
 229.2 
 
 305.6 
 
 458.4 
 
 611.2 763.9 
 
 916.7 
 
 1 3 /8 
 
 27.8 
 
 55.6 
 
 83.3 
 
 111.1 
 
 138.9 
 
 208.3 
 
 277.7 
 
 416.5 
 
 555.4 694.2 
 
 833.1 
 
 H/2 
 
 25.5 
 
 50.9 
 
 76.4 
 
 101.8 
 
 127.2 
 
 190.8 
 
 254.4 
 
 381.6 
 
 508.8! 636.0 
 
 763.2 
 
 13/4 
 
 21.8 
 
 43.7 
 
 65.5 
 
 87.3 
 
 109.2 
 
 163.6 
 
 218.1 
 
 327.2 
 
 436.2| 545.3 
 
 654.3 
 
 2 
 
 19.1 
 
 38.2 
 
 57.3 
 
 76.4 
 
 95.5 
 
 143.2 
 
 191.0 
 
 286.5 
 
 382 
 
 477.5 
 
 573.0 
 
 21/4 
 
 17.0 
 
 34.0 
 
 50.9 
 
 67.9 
 
 84.9 
 
 127.2 
 
 169.6 
 
 254.4 
 
 339.2 
 
 424.0 
 
 508.8 
 
 21/2 
 
 15.3 
 
 30.6 
 
 45.3 
 
 61.1 
 
 76.4 
 
 114.6 
 
 152.8 
 
 229.2 
 
 305.6 
 
 382 Oi 458.4 
 
 23/4 
 
 13.9 
 
 27.8 
 
 41.7 
 
 55.6 
 
 69.5 
 
 104.0 
 
 138.7 
 
 208.3 
 
 277.3 
 
 346.6 
 
 416.0 
 
 
 12.7 
 
 25.5 
 
 38.2 
 
 50.9 
 
 63.7 
 
 95.4 
 
 127.2 
 
 190.8 
 
 254.4 
 
 318.0 
 
 381.6 
 
 31/2 
 
 109 
 
 21 .8 
 
 32.7 
 
 43.7 
 
 54.6 
 
 81.6 
 
 108.9 
 
 163.3 
 
 217.7 
 
 272.2 
 
 326.6 
 
 4 
 
 9.6 
 
 19.1 
 
 28.7 
 
 38.2 
 
 47.8 
 
 71.6 
 
 95.5 
 
 143.2 
 
 191.0 
 
 238.7 
 
 286.5 
 
 41/2 
 
 8.5 
 
 17.0 
 
 25.5 
 
 34.0 
 
 42.5 
 
 63.6 
 
 84.8 
 
 127.2 
 
 169.6 
 
 212.0 
 
 254.4 
 
 
 7.6 
 
 15.3 
 
 22.9 
 
 30.6 
 
 33.1 
 
 57.3 
 
 76.4 
 
 114.6 
 
 152.8 
 
 191.0 
 
 229.2 
 
 51/2 
 
 6.9 
 
 13.9 
 
 20.8 
 
 27.8 
 
 34.7 
 
 52.1 
 
 69.4 
 
 104.2 
 
 138.9 
 
 173.6 
 
 208.3 
 
 6 
 
 6.4 
 
 12.7 
 
 19.1 
 
 25.5 
 
 31.8 
 
 47.6 
 
 63.4 
 
 95.1 
 
 126.8 
 
 158 5 
 
 190.2 
 
 7 
 
 5.5 
 
 10.9 
 
 16.4 
 
 21.8 
 
 27.3 
 
 41.0 
 
 54.6 
 
 81.9 
 
 109.2 
 
 136. 6^ 163.9 
 
 8 
 
 4.8 
 
 9.6 
 
 14.3 
 
 19.1 
 
 23.9 
 
 35.8 
 
 47.7 
 
 71.6 
 
 95.5 
 
 119.4 
 
 143.2 
 
 9 
 
 4.2 
 
 8.5 
 
 12.7 
 
 17.0 
 
 21.2 
 
 31.8 
 
 42.4 
 
 63.6 
 
 84.8 
 
 106.0 
 
 127.2 
 
 10 
 
 3.8 
 
 7.6 
 
 11.5 
 
 15.3 
 
 19.1 
 
 28.6 
 
 38.2 
 
 57.3 
 
 76.4 
 
 95.5 
 
 114.6 
 
 11 
 
 3.5 
 
 6.9 
 
 10.4 
 
 13.9 
 
 17.4 
 
 26.0 
 
 34.7 
 
 52.1 
 
 69.4 
 
 86.8 
 
 104.2 
 
 12 
 
 3.2 
 
 6.4 
 
 9.5 
 
 12.7 
 
 15.9 
 
 23.8 
 
 31.7 
 
 47.6 
 
 63.4 
 
 79.3 
 
 95.1 
 
 13 
 
 2.9 
 
 5.9 
 
 8.8 
 
 11.8 
 
 14.7 
 
 22.1 
 
 29.4 
 
 44.1 
 
 58 8 
 
 73.5 
 
 88.2 
 
 14 
 
 2.7 
 
 5.5 
 
 8.2 
 
 10.9 
 
 13.6 
 
 20.5 
 
 27.3 
 
 40.9 
 
 54.6 
 
 68.3 
 
 81.9 
 
 15 
 
 2.5 
 
 5.1 
 
 7.6 
 
 10.2 
 
 12.7 
 
 19.1 
 
 25.4 
 
 38 2 
 
 50.9 
 
 63. 6| 763 
 
 16 
 
 2.4 
 
 4.8 
 
 7.2 
 
 9.5 
 
 11.9 
 
 17.9 
 
 23.9 
 
 35.8 
 
 47.8 
 
 59 7 
 
 71 6 
 
 18 
 
 2.1 
 
 4.2 
 
 6.4 
 
 8.5 
 
 10.6 
 
 15.9 
 
 21.2 
 
 31.8 
 
 42.4 
 
 530 
 
 63.6 
 
 20 
 
 .9 
 
 3.8 
 
 57 
 
 7.6 
 
 9.6 
 
 14 3 
 
 19.1 
 
 28.6 
 
 38.2 
 
 47.8 
 
 57 3 
 
 22 
 
 .7 
 
 3.5 
 
 5.2 
 
 6.9 
 
 8.7 
 
 12.9 
 
 17.2 
 
 25.8 
 
 34.4 
 
 43.0 
 
 51 6 
 
 24 
 
 .6 
 
 3.2 
 
 4.8 
 
 6.4 
 
 8.0 
 
 11.9 
 
 15.9 
 
 23.8 
 
 31.7 
 
 40.1 
 
 47.6 
 
 26 
 
 .5 
 
 2.9 
 
 4.4 
 
 5.9 
 
 7.3 
 
 10.9 
 
 14.5 
 
 21.8 
 
 29.0 
 
 36.3 
 
 43.5 
 
 28 
 
 .4 
 
 2.7 
 
 4.1 
 
 5.5 
 
 6.8 
 
 10.3 
 
 13.7 
 
 20.5 
 
 27.3 
 
 34.2 
 
 41.0 
 
 30 
 
 .3 
 
 2.5' 
 
 3.8 
 
 5.1 
 
 6.4 
 
 9.5 
 
 12.7 
 
 19.1 
 
 25.4 
 
 31.8 
 
 38.2 
 
 36 
 
 
 2.1 
 
 3.2 
 
 4.2 
 
 5.3 
 
 7.9 
 
 10.6 
 
 15.9 
 
 21.2 
 
 26.5 
 
 31.8 
 
 42 
 
 0^9 
 
 1.8 
 
 2.7 
 
 3.6 
 
 4.5 
 
 6.8 
 
 9.1 
 
 13.6 
 
 18.2 
 
 22.8 
 
 27.3 
 
 48 
 
 0.8 
 
 1.6 
 
 2.4 
 
 3.2 
 
 4.0 
 
 6.0 
 
 7.9 
 
 12.0 
 
 15.9 
 
 19.9 
 
 23.9 
 
 54 
 
 0.7 
 
 1.4 
 
 2.1 
 
 2.8 
 
 3.5 
 
 5.3 
 
 7.0 
 
 10.6 
 
 14.1 
 
 17.6 
 
 21.1 
 
 60 
 
 0.6 1.3 1.9 2.5 3.2 4.8 6.3 9.5 
 
 12.7 15.8 
 
 19.0 
 
GEARING OF LATHES. 1259 
 
 The Speed of Counter-shaft of the lathe is determined by an 
 assumption of a slow speed with the back gear, say 6 feet per minute, 
 on the largest diameter that the lathe will swing. 
 
 EXAMPLE. A 30-inch lathe will swing 30 inches =, say, 90 inches 
 circumference = 7 feet 6 inches; the lowest triple gear should give a 
 speed of 5 or 6 feet per minute. 
 
 Spindle Speeds of Lathes. The spindle speeds of lathes are usu- 
 ally in geometric progression, being obtained either by a combination of 
 cone-pulley and back gears, or by a single pulley in connection with a 
 gear train. Either of these systems may be used with a variable speed 
 motor, giving a wide range of available speeds. 
 
 It is desirable to keep work rotating at a rate that will give the most 
 economical cutting speed, necessitating, sometimes, frequent changes in 
 spindle speed. A variable speed motor arranged for 20 speeds in geometric 
 progression, any one of which can be used with any speed due to the 
 mechanical combination of belts and back gears, gives a fine gradation of 
 cutting speeds. The spindle speeds obtained with the higher speeds of 
 the motor in connection with a certain mechanical arrangement of belt 
 and back gears may overlap those obtained with the lower speeds avail- 
 able in the motor in connection with the next higher speed arrangement 
 of belt and gears, -but about 200 useful speeds are possible. E. R. Douglas 
 (Elec. Rev., Feb. 10, 1906) presents an arrangement of variable speed 
 motor and geared head lathe, with 22 speed variations in the motor and 3 in 
 the head. The speed range of the spindle is from 4.1 to 500 r.p.m. By 
 the use of this arrangement, and taking advantage of the speed changes 
 possible for different diameters of the work, a saving of 35.4 per cent was 
 obtained in the time of turning a piece ordinarily requiring 289 minutes. 
 
 Rule for Gearing Lathes for Screw-cutting. (Garvin Machine 
 Co.) Read from the lathe index the number of threads per inch cut 
 by equal gears, and multiply it by any number that will give for a pro- 
 duct a gear on the index; put this gear upon the stud, then multiply the 
 number of threads per inch to be cut by the same number, and put the 
 resulting gear upon the screw. 
 
 EXAMPLE. To cut 
 
 . 
 
 . threads per inch. We find on the index 
 
 that 48 into 48 cuts 6 threads per inch, then 6 X 4 = 24, gear on stud, 
 and \\ 1 A X 4 = 46, gear on screw. Any multiplier may be used so long 
 as the products include gears that belong with the lathe. For instance, 
 instead of 4 as a multiplier we may use 6. Thus, 6 X 6 = 36, gear upon 
 stud, and 11 ^ X 6 = 69, gear upon screw. 
 
 Rules for Calculating Simple and Compound Gearing where 
 there is no Index. (Am. Mach.) If the lathe is simple-geared, 
 and the stud runs at the same speed as the spindle, select some 
 gear for the screw, and multiply its number of teeth by the number 
 of threads per inch in the lead-screw, and divide this result by the num- 
 ber of threads per inch to be cut. This will give the number of teeth in 
 the gear for the stud. If this result is a fractional number, or a number 
 which is not among the gears on hand, then try some other gear for the 
 screw. Or, select the gear for the stud first, then multiply its number of 
 teeth by the number of threads per inch to be cut, and divide by the 
 number of threads per inch on the lead-screw. This will give the num- 
 ber of teeth for the gear on the screw. If the lathe is compound, select 
 at random all the driving-gears, multiply the numbers of their teeth 
 together, and this product by the number of threads to be cut. Then 
 select at random all the driven gears except 'one; multiply the numbers 
 of their teeth together, and this product by the number of threads per 
 inch in the lead-screw. Now divide the first result by the second, to 
 obtain the number of teeth in the remaining driven gear. Or, select 
 at random all the driven gears. Multiply the numbers of their teeth 
 ' together, and this product by the number of threads per inch in the 
 lead-screw. Then select at random all the driving-gears except one. 
 Multiply the numbers of their teeth together, and this result by the num- 
 ber of threads per inch of the screw to be cut. Divide the first result by 
 the last, to obtain the number of teeth in the remaining driver. When 
 the gears on the compounding stud are fast together, and cannot be 
 changed, then the driven one has usually twice as many teeth as the 
 other, or driver, in which case in the calculations consider the lead-screw 
 to fcave twice as many threads per inch as it actually has, and then ignore 
 
1260 
 
 THE MACHINE-SHOP. 
 
 the compounding entirely. Some lathes are so constructed that the stud 
 on which the first driver is placed revolves only half as last as the spindle. 
 This can be ignored in the calculations by doubling the number of threads 
 of the lead-screw. If both the last conditions are present ignore them 
 in the calculations by multiplying the number of threads per inch in the 
 lead-screw by four. If the thread to be cut is a fractional one, or if the 
 pitch of the lead-screw is fractional, or if both are fractional, then reduce 
 the fractions to a common denominator, and use the numerators of these 
 fractions as if they equaled the pitch of the screw to be cut, and of the 
 lead-screw, respectively. Then use that part of the rule given above 
 which applies to the lathe in question. For instance, suppose it is desired 
 to cut a thread of 25/ 32 -inch pitch, and the lead-screw has 4 threads per 
 inch. Then the pitch of the lead-screw will be 1/4 inch, which is equal to 
 8/32 inch. We now have two fractions, 25/ 32 and 8/ 32 , and the two screws 
 will be in the proportion of 25 to 8, and the gears can be figured by the 
 above rule, assuming the number of threads to be cut to be 8 per inch, 
 and those on the lead-screw to be 25 per inch. But this latter number 
 may be further modified by conditions named above, such as a reduced 
 speed of the stud, or fixed compound gears. In the instance given, if 
 the lead-screw had been 2 1/2 threads per inch, then its pitch being Vio 
 inch, we have the fractions 4/io and 25/ 32 , which, reduced to a common 
 denominator, are 64/ 160 and 125/ 160 , and the gears will be the same as if the 
 lead -screw had 125 threads per inch, and the screw to be cut 64 threads 
 per inch. 
 
 On this subject consult also "Formulas in Gearing," published by 
 Brown & Sharpe Mfg. Co., and Jamieson's Applied Mechanics. 
 
 Change-gears for Screw-cutting Lathes. There is a lack of 
 uniformity among lathe-builders as to the change-gears provided for 
 screw-cutting. W. R. Macdonald, in Am. Mach., April 7, 1892, pro- 
 posed the following series, by which 33 whole threads (not fractional) 
 may be cut by changes of only nine gears: 
 
 
 Spindle. 
 
 
 fc 
 
 
 Whole Threads. 
 
 I 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 110 
 
 120 
 
 130 
 
 
 20 
 
 
 8 
 
 6 
 
 44/5 
 
 4 
 
 33/7 
 
 22/n 
 
 2 
 
 1 H/13 
 
 2 
 
 11 
 
 22 
 
 44 
 
 30 
 
 18 
 
 
 9 
 
 7V* 
 
 6 
 
 51/7 
 
 33/n 
 
 3 
 
 2 10/13 
 
 3 
 
 12 
 
 24 
 
 48 
 
 40 
 
 24 
 
 16 
 
 12 
 
 93/5 
 
 8 
 
 66/ 7 
 
 44/u 
 
 4 
 
 39/13 
 
 4 
 
 13 
 
 26 
 
 52 
 
 50 
 
 30 
 
 20 
 
 15 
 
 
 10 
 
 84/7 
 
 55/u 
 
 5 
 
 48/13 
 
 5 
 
 14 
 
 28 
 
 66 
 
 60 
 
 36 
 
 24 
 
 18 
 
 H2/5. 
 
 
 102/ 7 
 
 66/11 
 
 6 
 
 57/ 13 
 
 6 
 
 15 
 
 30 
 
 72 
 
 70 
 
 42 
 
 28 
 
 21 
 
 164/ 5 
 
 14 
 
 
 77/n 
 
 7 
 
 68/ 13 
 
 7 
 
 16 
 
 33 
 
 78 
 
 110 
 
 66 
 
 44 
 
 33 
 
 262/5 
 
 22 
 
 186/ 7 
 
 
 11 
 
 102/ 13 
 
 8 
 
 18 
 
 36 
 
 
 120 
 
 72 
 
 48 
 
 36 
 
 284/5 
 
 24 
 
 204/ 7 
 
 131/n 
 
 
 1 1 Vl3 
 
 9 
 
 20 
 
 39 
 
 
 130 
 
 78 
 
 52 
 
 39 
 
 31 Vs 
 
 26 
 
 223/7 
 
 142/n 
 
 13 
 
 
 10 
 
 21 
 
 42 
 
 
 Ten gears are sufficient to cut all the usual threads, with the exception 
 of perhaps 111/2, the standard pipe-thread; in ordinary practice any 
 fractional thread between 11 and 12 will be near enough for the custom- 
 ary short pipe-thread; if not, the addition of a single gear will give it. 
 
 In this table the pitch of the lead-screw is 12, and it may be objected 
 to as too fine for the purpose. This may be rectified by making the real 
 pitch 6 or any other desirable pitch, and establishing the proper ratio 
 between the lathe spindle and the gear-stud. 
 
 "Quick Change Gears." About 1905, lathe manufacturers began 
 building "quick change" lathes in which gear changing for screw- 
 cutting is eliminated. The lead-screw carries a cone of gears, one of which 
 is in mesh with a movable gear in a nest of gears driven from the spindle. 
 By changing the position of this movable gear, in relation to the cone 9f 
 gears, the proper ratio of speeds between the spindle and lead-screws is 
 obtained for cutting any desired thread usual in the range of the machine. 
 About 16 different numbers of threads per inch can usually be cut by 
 means of the "quick change" gear train. Different threads from those 
 usually available can be cut by means of change gears between the spindle 
 
TAYLOR'S EXPERIMENTS. 
 
 1261 
 
 and " quick change " gear train. The threads per inch usually available 
 range from 2 to 46 in a 12-in. lathe to 1 to 24 in a 30-in. lathe. Catalogs 
 of lathe manufacturers should be consulted for constructional details. 
 
 Shapes of Tools. For illustrations and descriptions of various forms 
 of cutting- tools, see Taylor's Experiments, below; also see Standard 
 Planer Tools, p. 1271, and articles on Lathe Tools in Appleton's Cyc. 
 Mech., vol. ii, and in Modern Mechanism. 
 
 Cold Chisels. Angle of cutting-faces (Joshua Rose): For cast steel, 
 about 65 degrees; for gun-metal or brass, about 50 degrees; for copper 
 and soft metals, about 30 to 35 degrees. 
 
 Metric Screw-threads may be cut on lathes with inch-divided lead- 
 ing-screws, by the use of change- wheels with 50 and 127 teeth; since 127 
 centimeters = 50 inches (127 X 0.3937 = 49.9999 in.). 
 
 Rule for Setting the Taper in a Lathe. (Am. Mach.) IjTo rule 
 can be given which will produce exact results, owing to the fapt that 
 the centers enter the work an indefinite distance. If it were not for 
 this circumstance the following would be an exact rule, and it is an approx- 
 imation as it is. To find the distance to set the center over: Divide the 
 difference in the diameters of the large and small ends of the taper by 2, 
 and multiply this quotient by the ratio which the total length of the shaft 
 bears to the length of the tapered portion. EXAMPLE: Suppose a shaft 
 three feet long is -to have a taper turned on the end one foot long, the large 
 end of the taper being two inches and the small end one inch diameter, 
 
 inches. 
 
 F Lubricants for Lathe Centers. Machinery recommends as lubri- 
 cants for lathe centers to prevent cutting or abrasion: 1. Dry or 
 powdered red lead mixed with a good mineral oil to the consistency of 
 cream. 2. White lead mixed with sperm oil, together withi enough 
 graphite to give the mixture a dark red color. 3. One part graphite, 
 four parts tallow, thoroughly mixed. 
 
 TAYLOR'S EXPERIMENTS. 
 
 Fred W. Taylor directed a series of experiments, extending over 26 
 years, on feeds, speeds, shape of tool, composition of tool steel, and 
 heat treatment. His results are given in Trans. A. S. M. E., xxviii, 
 "The Art of Cutting Metals." The notes below apply mainly to tools 
 r of high speed steel and to heavy work requiring tools not less than 
 V2 by 3/4 inch in cross-section. 
 
 Proper Shape of Lathe Tool. Mr. Taylor discovered the best 
 shape for lathe tools to be as shown in Fig. 194 with the angles given 
 in the following table, when used on materials of the class shown. 
 The exact outline of the nose of the tool is shown in Fig. 195. The 
 actual dimensions of a 1-inch roughing tool are shown in Fig. 196. 
 Let R = radius of point of tool, A = width of tool, L length of shank, 
 and // = height of shank, all in inches. Then L = I4A -f 4; H = 1.5A; 
 R = 0.5 A 0.3125 for cutting hard steel and cast iron; R =? 0.5A 
 0.1875 for soft steel. The meaning of the terms back slope, etc., is 
 shown in Fig. 194. 
 
 Angles for Tools. 
 
 * Material cut. 
 
 a = clearance. 
 
 b = back slope. 
 
 c = side slope. 
 
 Cast iron; Hard steel. 
 
 6 degrees. 
 
 8 degrees. 
 
 14 degrees. 
 
 Medium or Soft steel. 
 
 6 degrees. 
 
 8 degrees. 
 
 22 degrees. 
 
 Tire steel. 
 
 6 degrees. 
 
 5 degrees. 
 
 9 degrees. 
 
 * As far as the shape of the tool is concerned, Taylor divided metals 
 to be cut into general classes: (a) cast iron and hard steel, steel of 
 0.45-0.50 per cent carbon, 100,000 pounds tensile strength, and 18 per 
 cent stretch, being a low limit of hardness; (6) soft steel, softer than 
 above; (c) chilled iron; (d) tire steel; (e) extremely soft steel of carbon, 
 say, 0.10-0.15 per cent. 
 
 The table presupposes the use of an automatic tool grinder. If tools 
 are ground by hand the clearance angle should be 9 degrees. The lip 
 angles for tools cutting hard steel and cast iron should be 68 degrees; 
 
Clearance- 
 Flank- 
 
 Section Through Line A-B Showing 
 Greatest, or True Slope of Lip Surface. 
 
 FIQ. 194. 
 
 FIG. 195. 
 
TAYLOR S EXPERIMENTS. 
 
 1263 
 
 for soft steel, 61 degrees; for chilled iron, 86 to 90 degrees; for tire steel, 
 74 degrees; for extremely soft steel, keener than 61 degrees. A tool 
 should be given more side than back slope; it can then be ground more 
 times without weakening, the chip does not strike the tool post or clamps, 
 
 r 
 
 FIG. 196. 
 
 and it is also easier to feed. The nose of the tool should be set to one 
 side, as in Fig. 196 above, to avoid any tendency to upset. To use 
 a tool of this shape, lathe tool posts should be set lower below the 
 center of the work than is now (1907) customary. 
 
 Forging and Grinding Tools. The best method of dressing a tool 
 is to turn one end up nearly at right angles to the shank, so that the 
 nose will be high above the top of the body of the tool. Dressing can 
 be thus done in two heats. Tools should leave the smith shop with 
 a clearance angle of 20 degrees. Detailed directions for dressing a tool 
 are given in Mr. Taylor's paper. To avoid overheating the tool in grind 
 ing, a stream of water, of at least five gallons a minute, should be thrown 
 at low velocity on the nose of the tool where it is in contact with the 
 emery wheel. In hand grinding, tools should not be held firmly against 
 the wheel, but should be moved over its surface. It is of the utmost 
 importance that high speed steel tools should not be heated above 1200 F. 
 in grinding. Automatic tool grinders are economical, even in a small 
 shop. Grinding machines should have some means for automatically 
 adjusting the pressure of the tool against the grinding wheel. Each size 
 of tool should have adapted to it a pressure, automatically adjusted, and 
 which is just sufficient to grind rapidly without overheating the tool. 
 Standard shapes should be adopted, to which all tools should be ground, 
 there being no economy in automatic grinding without standard shapes, 
 
 Best Grinding Wheel. The best grinding wheel was found to be 
 a corundum wheel, of a mixture of 24 and 30 grit. 
 
1264 THE MACHINE-SHOP. 
 
 Pressure of Tool, etc. Mr. Taylor found that there is no definite 
 relation between the cutting speed of tools and the pressure with which 
 the chip bears on the lip surface of the tool. He found, however, that 
 the pressure per square inch of sectional area of the chip increases 
 slightly as the thickness of the chip decreases. The feeding pressure of 
 the tool is sometimes equal to the entire driving pressure of the chip against 
 the lip surface of the tool, and the feed gears should be designed to deliver 
 a pressure of this magnitude at the nose of the tool. 
 
 Chatter. Chatter is caused by: too small lathe dogs; imperfect 
 bearing at the points where the face plate drives the dogs; badly made or 
 badly fitted gears; shafts in the machine of too small diameter, or of too 
 great length; loose fits in bearings. A tool which chatters must be run 
 at a cutting speed about 15 per cent slower than can be used if the tool 
 does not chatter, irrespective of the use or non-use of water on the tool. 
 A higher cutting speed can be used with an intermittent cut, as occurs 
 on a planer, or shaper, or in turning, say, the periphery of a gear, than 
 with a steady cut. To avoid chatter, tools should have curved cutting 
 edges, or two or more tools should be used at the same time in the same 
 machine. The body of the tool should be greater in height than width, 
 and should have a true, solid bearing on the tool support, which latter 
 should extend to almost beneath the cutting edge of the tool. Machines 
 should be made massive beyond the metal needed for strength alone, 
 and steady rests should be used on long work. It is advisable to use a 
 steady rest, when turning any cylindrical piece of diameter D, when the 
 length exceeds 12 Z), 
 
 Use of Water on Tool. With the best high speed steel tools, a 
 gain of 14 per cent in cutting speed can be made in cutting cast-iron 
 and hard steel to 35 per cent on very soft steel by throwing a heavy 
 stream of water directly on the chip at the point where it is being re- 
 moved from the forging by the tool. Not less than three gallons a 
 minute should be used for a 2 X 2i/2-in. tool. The gain is practically 
 the same for all qualities of steel, regardless of hardness and whether 
 thick or thin chips are being cut. 
 
 Interval between Grindings. Mr. Taylor derived a table showing 
 how long various sizes of tools should run without regrinding to give the 
 maximum work for the lowest all-around cost. Time a tool should run 
 continuously without regrinding equals 7 X (time to change tool + 
 proper portion of time for redressing -f time for grinding + time equi- 
 valent to cost of the tool steel ground off). 
 
 INTERVAL BETWEEN GRINDINGS, AT MAXIMUM ECONOMICAL 
 CUTTING SPEEDS. 
 
 Size of tool. 
 Inches. 
 Hours. 
 
 1/2 X3/4 S/g 
 
 &' *&' 
 
 78 7/ 8 X 1 3/8 
 
 1X.V, 
 
 Size of toot. 
 Inches. 
 Hours. 
 
 1 V4X 1 7/8 
 
 U/2X2 1/4 
 
 13/ 4 X2 3/ 4 
 
 2 X 3 
 2.75 
 
 If the proper cutting speed (A) is known for a cut of given duration, 
 the speed for a cut (B) of different duration can be obtained by multiply- 
 ing (A) by the factor given in the following table: 
 
 Duration of cut in minutes: 
 
 At known speed (A) 20 40 20 40 80 80 
 
 At derived speed (B) 40 80 80 20 40 20 
 
 Factor 0.92 0.92 0.84 1.09 1.09 1.19 
 
 For cutting speeds of high-speed lathe tools to last 11/2 hours, see 
 tables on pages 1266 and 1267. 
 
 Effect of Feed and Depth of Cut on Cutting Speed. With a given 
 depth of cut, metal can be removed faster with a coarse feed and slow 
 speed, than with fine feed and high speed. 'With a given depth of cut. 
 a cutting speed of S, and a feed of F, 5 varies approximately as 1[\/F. 
 With tools of the best high speed steel, varying the feed and depth of 
 cut varies the cutting speed in the same ratio when cutting hard steel 
 as when cutting soft steel. 
 
TAYLOR'S EXPERIMENTS. 1265 
 
 Best High Speed Tool Steel Composition Heat Treatment. 
 
 Mr. Taylor and Maunsel White developed a number of high speed 
 steels, the one showing the best all-around qualities having the following 
 chemical composition: Vanadium, 0.29; tungsten, 18.19; chromium, 
 5.47; carbon, 0.674; manganese, 0.11; silicon, 0.043. The use of 
 vanadium materially improves high speed steel. The following method 
 of treatment is described as the best for this or any other composition of 
 high speed steel. The tool should be forged at a light yellow heat, and, 
 after forging slowly and uniformly heated to a bright cherry red, allowing 
 plenty of time for the heat to penetrate to the center of the tool, in order 
 to avoid danger of cracking due to too rapid heating. The tool should 
 then be heated from a bright cherry red to practically its melting-point as 
 rapidly as possible in an intensely hot fire; if the extreme nose of the tool 
 is slightly fused no harm is done. Time should be allowed for the tool 
 to become uniformly hot from the heel to the lip surface. 
 
 After the high heat has been given the tools, as above described, they 
 should be cooled rapidly until they are below the "breaking-down point, 
 or. say, down to or below 1550 F. The quality of the tool will be but 
 little affected whether it is cooled rapidly or slowly from this point down 
 to the temperature of the air. Therefore, after all parts of a tool from 
 the outside to the center have reached a uniform temperature below the 
 breaking-down point, it is the practice sometimes to lay it down in any 
 part of the room or shop which is free from moisture, and let it cool in 
 the air, and sometimes to cool it in an air blast to the temperature of the 
 air. 
 
 The best method of cooling from the high heat to below the breaking- 
 down point is to plunge the tools into a bath of red-hot molten lead below 
 the temperature of 1550 F. They should then be plunged into a lead 
 bath maintained at a uniform temperature of 1150 F., because the same 
 bath is afterward used for reheating the tools to give them their second 
 treatment. This bath should contain a sufficiently large body of the lead 
 so that its temperature can be maintained uniform; and for this purpose 
 should be used preferably a lead bath containing about 3600 Ib. of lead. 
 
 Too much stress cannot be laid upon the importance of never allowing 
 the tool to have its temperature even slightly raised for a very short 
 time during the process of cooling down. The temperature must either 
 remain absolutely stationary or continue to fall after the operation of 
 cooling has once started, or the tool will be injured. Any temporary rise 
 of temperature during cooling, however small, will injure the tool. This, 
 however, applies only to cooling the tool to the temperature of about 
 1240 F. Between the limits of 1240 degrees and the temperature of 
 the air, the tool can be raised or lowered in temperature time after time 
 and for any length of time without injury. And it should also be noted 
 that during the first operation of heating the tool from its cold state to 
 the melting-point, no injury results from allowing it to cool slightly and 
 then reheating. It is from reheating during the operation of cooling 
 from the high heat to 1240 F. that the tool is injured. 
 
 The above-described operation is commonly known as the first or high- 
 heat treatment. 
 
 To briefly recapitulate, the first or high-heat treatment consists of 
 heating the tool 
 
 (a) slowly to 1500 F.; 
 
 (b) rapidly from that temperature to just below the melting-point. 
 
 (c) coqiing fast to below the breaking-down point, i.e., 1550F. 
 
 (d) cooling either fast or slowly from 1550 F. to temperature of the air. 
 
 Second Treatment, Reheating the Cooled Tool. After air- 
 temperature has been reached the tool should be reheated to a temperature 
 of from 700 to 1240 F., preferably by plunging it in the before-mentioned 
 lead bath at 1150 F. and kept at that temperature at least five minutes. 
 To avoid danger of fire cracks, the tool should be heated slowly before 
 immersing in the bath. The above tool heated in this fashion possesses 
 a high degree of "red hardness" (ability to cut steel with the nose of the 
 tool at red heat), while it is not extraordinarily hard at ordinary tem- 
 peratures. It is difficult to injure it by overheating on the grindstone or 
 in the lathe. It will operate at 90 per cent of its maximum cutting speed, 
 even without the second or low-heat treatment. A coke fire is prefer- 
 able for giving the first heat, and it should be made as deep as possible. 
 
1266 
 
 THE MACHINE-SHOP. 
 
 
 
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TAYLOR'S EXPERIMENTS. 
 
 1267 
 
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1268 THE MACHINE-SHOP. 
 
 Cooling the tool by plunging it in oil or water, renders it liable to fire 
 cracks and to brittleness in the body. Next to the lead bath an air blast 
 is preferable for cooling. 
 
 Best Method of Treating Tools in Small Shops. For small 
 shops, in treating high-speed tools, Mr. Taylor considers the best method 
 to be as follows for the blacksmith who is equipped only with the 
 apparatus ordinarily found in a smith-shop. 
 
 After the tools have been forged and before starting to give them their 
 heat, fuel should be added to the smith's fire so as to give a good deep 
 bed either of coke about the size of a walnut or of first-class blacksmiths' 
 soft coal. A number of tools should then be laid with their noses at a 
 slight distance from the hotter portion of the fire, so that they may all 
 be pre-heating while the fire is being blown up to its proper intensity. 
 After reaching its proper intensity, the tools should be heated one at a time 
 over the hottest part of the fire as rapidly as practicable up to just below 
 their melting-point. During this operation they should be repeatedly 
 turned over and over so as to insure a uniform high heat throughout the 
 whole end of the t9ol. As soon as each tool reaches its high heat, it 
 should be placed with its nose under a heavy air blast and allowed to 
 cool to the temperature of the air before being removed from the blast. 
 
 Unfortunately, however, the blacksmith's fire is so shallow that it is 
 incapable of maintaining its most intense heat for more than a com- 
 paratively few minutes, and, therefore, it is only through these few min- 
 utes that first-class high-speed tools can be properly heated in the smith's 
 fire. Great numbers of high-speed tools are daily turned out from 
 smiths' fires which are not sufficiently intense in their heat, and they are 
 therefore inferior in red hardness and produce irregular cutting tools. 
 
 On the whole, a blacksmith's fire made from coke may be regarded as 
 better for giving the high heat to tools than a soft-coal fire, merely 
 because a coke fire can be more easily made by the smith which will 
 remain capable for a longer period of heating the tools quickly to their 
 melting-points. 
 
 Quality of Different Tool Steels. Mr. Taylor in a letter to the 
 author, Dec. 30, 1907, says : 
 
 First. Any of a half dozen makes of high speed tools now on the market 
 are amply good, and but little attention need be paid to the special direc- 
 tions for heating and cooling high speed tools given by the makers of the 
 tool steel. The most important matter is that an intensely hot fire should 
 be used for giving the tools their high heat, and that they should not be 
 allowed to soak a long time in this fire. They should be heated as fast 
 as possible and then cooled in an air blast. 
 
 Second. The greatest number of tools are ruined on the emery wheel 
 through overheating, either because a wheel whose surface is glazed is 
 used, or because too small a stream of water is run upon the nose of the 
 tool. The emery wheel should be kept sharp through frequent dress- 
 ings with a diamond tool. 
 
 Third. Uniformity is the most important quality in high speed tools. 
 For this reason, only one make of high speed tool steel should be used 
 in each shop. 
 
 Economical Cutting Speeds. Tools shaped as in Fig. 196, and 
 of the chemical composition and heat treatment given in the preced- 
 ing paragraphs, should be run at the cutting speeds given in the tables 
 on pages 1266 and 1267 in order to last one hour and 30 minutes with- 
 out re-grinding. 
 
 Cutting Speed of Parting and Thread Tools. To find the economical 
 cutting speed of a parting tool of the best high-speed steel, first ascer- 
 tain the thickness of chip which is to be cut by the tool. Then from 
 the tables on pages 1266 and 1267, under the standard 7/ 8 -in. tool and 
 3/16 in. depth of cut, and opposite the feed which most nearly corre- 
 sponds to the thickness of chip to be taken by the parting tool, find 
 the speed. Divide the figure so found by 2.7 to ascertain the speed for 
 the parting tool. For thread tools, the process is the same, except 
 that the divisor is 4. The thickness of chip in the latter case is the ad- 
 vance in inches per revolution of the tool toward the center of the work. 
 
 Durability of Cutting Tools. E. G. Herbert (Am. Mach., June 24, 
 1909) shows that the durability of a tool depends mainly on the tem- 
 perature to which its extreme edge is raised, and that the rate of evolu- 
 tion of heat and consequently the durability is proportional to the thick- 
 
STELLITE. 
 
 1269 
 
 ness and to the area of the chip and to the cube of the cutting speed. 
 Or if ti = thickness or feed, Ci = depth of cut, a\ = area of the cut and 
 s\ = cutting speed, for any given set of working conditions, and fcc 2 a 2 and 
 s-2 values for another set of conditions, then the durability of the tool 
 will be the same when fcaiSi 3 = 2 2 a 2 S2 3 , or for constant durability s 2 = 
 
 Sl^tfl'Ci) -h(* 2 2C2). 
 
 Other High-Speed Steels. Am. Mach. April 8, May 20 and 27, 
 1909, describes the operations of some new varieties of high-speed steel 
 made by Sheffield manufacturers, which show results superior to those 
 of the earlier high-speed steels in endurance of tool, ability to cut very 
 hard metals, and higher speeds. The following are the results of some 
 of the tests in lathe-work: 
 
 Tool 
 size, 
 in. 
 
 Material Cut. 
 
 Diam. 
 in. 
 
 Depth, 
 cut in. 
 
 Feed 
 in. 
 
 Speed 
 ft. per 
 min. 
 
 Length of 
 Cut. 
 
 1 I/ A 
 
 Steel 2 00 
 
 
 3 /8 
 
 Vl6 
 
 36 
 
 43/4 in.* 
 
 \1/A 
 
 Steel' 70 C 
 
 
 l/ 4 
 
 Vl6 
 
 48 
 
 13 in t 
 
 1 I/A 
 
 Steel' 70 C 
 
 
 3 /16 
 
 VlO 
 
 65 
 
 8 7/8 in. 
 
 7/0 
 
 Steel 40 C 
 
 4 
 
 1/8 
 
 Vl6 
 
 65 
 
 28 ins., t 
 
 7/g 
 
 Steel, 0.40.C 
 
 
 Vs 
 
 V32 
 
 120 
 
 28 ins., 
 
 7/8 
 
 
 5ft. 
 
 1/8 to 3/ie 
 
 VlO 
 
 56 
 
 4 1/2 ins. 
 
 1/1 
 
 
 5ft. 
 
 5 /16 
 
 V32 
 
 107 
 
 6 ins. 
 
 1/2 
 
 Cast iron 
 
 5ft. 
 
 Vs 
 
 va 
 
 55 
 
 Sins. 
 
 11/4 
 
 Steel 0.40C 
 
 5 3/ 8 in. 
 
 Va 
 
 Vio 
 
 90 
 
 54 ins. 
 
 1x2 
 
 Steel 
 
 9 3/ 4 in. 
 
 3/8 
 
 Vs 
 
 64 
 
 72 ins. 
 
 1x2 
 
 Nickel steel 
 
 3 1/2 in. 
 
 V2 
 
 0072 
 
 52 
 
 124 ins. 
 
 li/4 
 
 U/4 
 
 Steel casting, 0.45C.. 
 Steel, 0.60C 
 
 20 in. 
 7 1/2 in. 
 
 3/8 
 9/64 
 
 Vs 
 
 V26 
 
 50 
 115 
 
 15 to 20 min. U 
 18 in. 
 
 * Then 1 3/4 in. at 50 ft. per min. t Then 1 Vs in. at 65 ft. per min. 
 Then 28 ins. at 98 ft. Then 22 ins. at 160 ft. || Required 28 H.P. 
 Chilled rolls, too hard for ordinary high-speed steel, were cut at a speed 
 of 80 ft. per min., with 5/ 16 in. depth of cut and 1/8 in. feed. 
 The following results were obtained in drilling: 
 
 Drill 
 size. 
 
 Material. 
 
 Rev. 
 
 per 
 min. 
 
 Feed 
 per 
 rev. 
 
 Speed 
 per 
 mm. 
 
 Drilled without Re- 
 grinding. 
 
 3/4 in 
 
 Close cast iron 
 
 466 
 
 0.018 
 
 8 1/2 in. 
 
 70 holes, 3 ins. deep. 
 
 3/4 
 
 Steel 25 C 
 
 247 
 
 0.011 
 
 
 60 holes, 23/4 ins. deep. 
 
 3/4 
 
 is/ie 
 
 Hard steel 
 Steel 
 
 526 
 400 
 
 
 6 in. 
 
 3V2 
 
 12 holes, 21/2 ins. deep. 
 14 in. at one operation. 
 
 A milling cutter 5 in. diam., with 54 teeth, milling teeth in saw-blanks, 
 at a cutting speed of 56 ft. per min. and a feed of 1 in. per min., cuts 
 80 blanks (three or more together), each 32 in. diam., 3/ 8 in. thick, 240 
 teeth, before re-grinding. 
 
 Stellite. An alloy of 25% chromium, 65% cobalt and 10% molyb- 
 denum, to which the name "stellite" has been given, is described in 
 Ir. Tr. Review, Mar. 5, 1914. This alloy is extremely hard, and retains 
 its hardness even when red hot, thus making it useful as a substitute 
 for tool steel. Tests made with stellite as a cutting tool on various 
 materials showed the following cutting speeds, the speed attained by 
 high-speed steel in the same tests being given for comparison : 
 
 
 Cutting Speed, 
 Ft. per Min. 
 
 
 Cutting Speed, 
 Ft. per Min. 
 
 Phosphor-bronze. . 
 Tool steel.. 
 
 Stellite. Steel. 
 . 900 125 
 133 80 
 
 Seamless tubing. 
 Cast iron . . 
 
 Stellite. Steel. 
 . . 400 100 
 200 100 
 
 A circular issued by the Midvale Steel Co. gives the following direc- 
 tions for the use of stellite, with a i/2-in. square lathe tool: For cutting 
 steel of 0.30 carbon or under, the limits will be: Depth of cut, i/g in.; 
 feed, Vie in. per revolution; speed, 100 to 300 ft. per min., depending 
 on the other conditions. For steel of 0.35 to 1.00 carbon, with the 
 same depth of cut and feed as above the speed should be from 50 to 
 
1270 THE MACHINE-SHOP. 
 
 150 ft. per min. In cutting cast iron it is recommended that light 
 cuts, and heavy feeds, say up to 1/4 in., be used. The depth of cut 
 can run to 1/4 or 3/g in. under moderate feeds. Stellite cannot be 
 forged, but is cast and ground to shape. It is extremely brittle, and 
 its use is restricted to such tools as can be supported close to the cutting 
 edge. ' It should not be used when the cut is one that will subject the 
 tool to heavy shocks. The fields for which it is recommended are: 
 For turning steel, where turning represents a large proportion of the 
 work to be done, and where the capacity of the lathe has not been 
 reached with the steel tool; for turning cast iron that is not so hard 
 that a slow speed with a steel tool is necessary, and where the capacity 
 of the machine has not been reached with a steel tool ; for inserted teeth 
 in milling cutters and reamers in. a limited field where speed is important. 
 For other data on the heat treatment, forging, etc., of tool steels, see 
 also pages 491 to 497. 
 
 PLANER WORK. 
 
 Work that Should be Planed. The planer is adapted for finishing 
 flat surfaces where great accuracy is required. The Cincinnati Planer 
 Co. gives (1912) in "A* Treatise on Planing" the following list of work 
 which should be planed: Locomotive frames, cylinders, shoes, wedges, 
 and driving-boxes; printing-press tables, frames, bearings, bases; 
 laundry frames, mangle chests; engine steam chests, valves, frames, 
 pillow blocks, connecting-rods; rolling-mill guides, frames, bearings, 
 key ways, tables; woodworking saw tables, frames, knife arbors, knives, 
 bases; textile machinery frames, guides, bearing stands, legs; electric 
 motor and generator bases and frame segments; forging machinery 
 dies, guides, arches, header frames, bases; machine tool beds, tables, 
 carriages, rails, slides, knees, columns. 
 
 , , , , . 
 
 Cutting and Return Speeds. A cutting speed of about 55 ft. 
 inute is about as high as it is practical to use on the planer, and 
 should be decreased for most materials. The table below shows the 
 
 per 
 this 
 
 . 
 
 speeds recommended by the Cincinnati Planer Co. The lower cutting 
 speed of the planer tool, as compared with the lathe, is probably due to 
 the absence of a cooling lubricant on long cuts. If the cut is inter- 
 mittent, as in planing a series of castings with gaps in between, the 
 cutting speed can be higher than with a continuous cut of equal total 
 length, probably due to the partial cooling of the tool during the inter- 
 vals of cutting. Return speeds of 75 to 100 ft. per minute are as high 
 as are recommended, although the author has seen planers operating 
 at a return speed as high as 135 ft. per minute. An increase in the 
 cutting speed is much more effective in increasing the capacity of the 
 machine than an increase in the return speed, and it is better to increase 
 the cutting speed by 25 % than to double the return speed. 
 
 PLANER CUTTING SPEEDS, FEET PER MINUTE. 
 
 Iron, cast, roughing 40 to 50 
 
 Iron, cast, finishing 20 to 25 
 
 Iron, wrought, roughing. . 30 to 45 
 Iron wrought, finishing . . 20 
 
 Steel, cast, roughing .... 30 to 35 
 
 Steel, cast, finishing 20 
 
 Steel machinery 30 to 35 
 
 Bronze and Brass 50 to 60 
 
 Planer Feeds. For rough -planing cast-iron feeds range from i/s 
 to 3/i6 in.; for steel i/ie to i/g in. For finishing cast iron with a broad 
 nose tool the feed may range from 1/2 to 3/ 4 in. per stroke. The feed 
 should be as heavy as possible, in order to decrease the time required, 
 although when planing to a finished edge, a feed of as low as i/ie in. 
 must be used to avoid breaking the edge at the end of the stroke. 
 
 Power Requirements for Planing. The principal power requirement 
 in planing is that required for reversing at the end of the stroke. The 
 largest portion is used in reversing the planer pulleys, which, running 
 at high speeds, store up considerable energy. The substitution of 
 aluminum alloy pulleys by some planer builders for the cast-iron ones 
 usually employed has reduced the power requirements for reversal and 
 has increased the capacity of the machine by increasing the number of 
 strokes which can be made per hour. The Cincinnati Planer Co. (1912) 
 reports that with a 35-ft. cutting speed and an 85-ft. return speed, on a 
 4-ft, cut, 165 strokes were made in 30 minutes with cast-iron pulleys 
 
PLANER WORK. 
 
 1271 
 
 and 189 in the same time with aluminum pulleys. In another test, 
 cast-iron pulleys required 39 horse-power at the reverse while aluminum 
 pulleys required 30 horse-power. For other data on power required, 
 see pages 1296, 1302 and 1303. 
 
 Time Required for Planing. The Cincinnati Planer Co. has devised 
 a slide rule, shown in Fig. 197, for determining the time required to 
 machine work in a variable speed planer. It is adapted for use with 
 cutting speeds of 20 to 60 ft. per min., return speeds of 50 to 130 ft. 
 per min. and a feed range of from i/ie to 1 in. per stroke. The feed 
 which is to be used (scale B) is set opposite the intersection of the 
 
 FIG. 197. PLANER TIME SLIDE .RULE. 
 
 cutting-speed curve with the return speed line (Scale A). The time 
 is read on scale D underneath the figure representing the area in square 
 inches to be planed (width X length) on scale C. To the time so deter- 
 mined must be added the time required for setting up the work in the 
 machine. 
 
 The following tables have also been prepared by the Cincinnati 
 Planer Co. for determining times for planer operation. 
 
 Planer Table Travel, Feet per Hour. 
 
 (Divide by length of stroke in feet for number of strokes per hour.) 
 
 Speed 
 of Cut, 
 Ft. per 
 Min. 
 
 Return Speed, Feet per Minute. 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 120 " 
 
 150 
 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 
 857.1 
 1000.0 
 1125.0 
 1235.3 
 1333.3 
 1421.0 
 1500.0 
 
 900.0 
 1058.8 
 1200.0 
 1321.3 
 1440.0 
 1542.8 
 1636.4 
 
 933.3 
 1105.3 
 1260.0 
 1400.0 
 1527.3 
 1643.5 
 1750.0 
 
 960.0 
 1142.9 
 1309.1 
 1460.9 
 1600.0 
 1728.0 
 1846.2 
 
 981.8 
 1173.9 
 1350.0 
 1512.0 
 1661.5 
 1800.0 
 1928.6 
 
 1000.0 
 1200.0 
 1384.6 
 1555.6 
 1714.3 
 1862.1 
 2000.0 
 
 1028.6 
 1241.4 
 1440.0 
 1625.8 
 1800.0 
 1863.6 
 2117.6 
 
 1058.8 
 1285.7 
 1500.0 
 1702.7 
 1894.7 
 2076.9 
 2250.0 
 
 Time of Planer Travel per Foot. 
 
 * 
 
 p* 
 
 n 
 
 'c ** 
 
 Jll 
 
 1** 
 
 Je 
 
 m 
 
 | j| 
 
 J&g 
 
 * 0) 
 
 3 c 
 
 ji 
 
 'O ^J 
 
 1*1 
 
 afe 
 
 OQ 
 
 h 
 
 - 0) 
 
 f a d 
 
 | 
 
 OT 
 
 \A 
 
 J&8 
 
 f*d 
 
 Jtfj 
 
 8 ^ 
 
 III 
 
 10 
 15 
 20 
 25 
 30 
 35 
 40 
 
 6.0 
 4.0 
 3.0 
 2.4 
 2.0 
 1.72 
 1.5 
 
 45 
 50 
 55 
 60 
 65 
 70 
 75 
 
 1.33 
 1.2 
 1.09 
 1.0 
 0.923 
 . .857 
 .80 
 
 80 
 85 
 90 
 95 
 100 
 105 
 110 
 
 0.75 
 .705 
 .666 
 .631 
 .60 
 .571 
 .545 
 
 120 
 130 
 140 
 150 
 160 
 170 
 180 
 
 0.5 
 .461 
 .428 
 .40 
 .375 
 .353 
 .333 
 
 190 
 200 
 220 
 240 
 260 
 280 
 300 
 
 0.316 
 .30 
 .273 
 .25 - 
 .23 
 .214 
 .20 
 
 Standard Planer Tools. Carl G. Earth designed for the use of 
 the Watertown Arsenal a full line of planer tools, as shown in the 
 drawings, Figs. 198 to 213, and in the tables below. These tools were 
 developed according to the principles discovered by Taylor and Barth 
 in the investigation into the "Art of Cutting Metals" (see p. 1261), 
 
1272 
 
 THE MACHINE-SHOP. 
 
 and may be regarded as forming a standard line of tools of the best- 
 shape for their respective purposes. They are described in Am. Mach.. 
 Jan. 21 and 28, 1915. 
 
 Round Nose Roughing Tools (Dimensions in Inches). 
 
 FIG. 198. FIG. 199. 
 
 RIGHT OR LEFT HAND (Figs. 198 and 199). 
 
 E R (rad.) 
 
 C 
 
 17/8 
 23/ 8 
 21/2 
 27/ 8 
 21/2 
 31/4 
 33/ 4 
 
 Parting Tools* (Dimensions in Inches). 
 
 FIG. 200. 
 FLUSH NOSE, CENTRAL 
 
 FIG. 201. 
 HIGH NOSE, RIGHT HAND, 
 
 A 
 
 5/8 
 
 H/4 
 
 (Fig. 200) 
 B C 
 
 1 1 1/4 
 
 1 1/8 1 1/2 
 H/2 2 
 1 7/8 2 1/2 
 
 D 
 
 13/4 
 2 
 
 21/4 
 2 
 
 E 
 
 1/4 
 3/8 
 1/2 
 5/8 
 
 
 1 
 
 l 
 
 AL 
 D 
 
 1/4 
 1/2 
 1/2 
 
 V2 
 7/8 
 1/4 
 
 STRAIGHT (Fig. 201). 
 A B C D 
 
 1/2 3/4 11/8 H/2 
 5/8 1 13/8 15/ 8 
 3/4 H/8 H/2 1 3 A 
 1 1/2 2 2 
 
 1/4 17/8 21/8 21/2 
 
 STRAIGHT (Fig. 202). 
 E F 
 
 1/4 3 
 5/16 3 1/2 
 1/4 3 
 3/8 4 3/4 
 1/2 6 
 
 A 
 
 5/8 
 8/4 
 
 IJ/4 
 
 H/4 
 
 H/2 
 
 SET BACK NOSE, 
 B C 
 
 1 13/4 
 H/8 2 
 1 1 3/4 
 11/2 23/4 
 
 1 7/8 3 1/2 
 1 1/4 2 1/8 
 1 V2 2 S/g 
 
 CENTE 
 
 1 
 1 
 1 
 2 
 2 
 1 
 2 
 
 * See note at foot of page 1273. 
 
 E 
 
 1/4 
 5/16 
 5/16 
 3/8 
 1/2 
 
 H 
 H/8 
 
 H/2 
 
 17/8 
 H/4 
 H/3 
 
STANDARD PLANER TOOLS. 
 
 1273 
 
 FIG. 203. 
 
 
 ___ L 
 
 < I 
 
 ~a f. 
 
 1 
 
 i r 
 
 FIG. 204. FIG. 205. 
 
 Finishing Tools (Dimensions in Inches). 
 
 SHEARING CUT (Fig. 203). 
 B C D E 
 
 3/4 3/4 3/4 7/8 
 
 111 13/i 6 
 
 H/8 H/8 H/8 H/2 
 
 H/2 H/2 H/2 2 
 
 SQUARE, HIGH NOSE, BENT 45 DEG. (Fig. 204). 
 A B C D E F 
 
 1 H/2 21/8 2 13/8 3/4 
 
 H/4 17/8 27/8 21/ 2 13/8 7/ 8 
 
 A 
 
 1/2 
 5/8 
 3/4 
 
 F 
 
 7/ 16 
 9/ 16 
 
 5/8 
 7/ 8 
 
 External Keyway Tools (Dimensions in In.) C 
 SET BACK NOSE (Fig. 205). *~ 
 
 A B C D 
 
 1/2 3/4 1 1/4 
 
 5/8 1 H/4 5/ 16 
 
 3/4 H/8 H/2 3/8 
 
 i <3 
 
 F F K 
 
 1 1/2 i/ 2 Width 
 
 13/4 5/8 of 
 
 2 1/4 3/4 Keyway 
 
 SET BACK NOSE* (Fig. 206). 
 
 A 
 
 3/4 
 
 H/4 
 H/2 
 
 B C 
 
 H/8 1 
 
 H/2 H/4 
 
 17/8 15/8 
 
 2 1/4 2 
 
 D 
 
 1 
 
 13/8 
 13/4 
 2 
 
 E 
 
 H/4 
 H/2 
 2 
 
 21/2 
 
 F 
 
 25/ 8 
 31/2 
 
 41/ 2 
 51/2 
 
 Fig. 206. 
 
 * The sides of the nose of parting tools and external keyway tools 
 with set back nose (Fig. 206) have a taper back from the ciitting edge of 
 1 deg. That is, in the plan each upper edge of the nose tapers inward 
 1 deg. from a plane parallel to the side of the tool. Each side also 
 tapers downwards from the upper edge 2 degs. from a plane parallel 
 to the side of the tool. 
 
1274 
 
 THE MACHINE-SHOP. 
 
 i ! ' 
 
 1 
 
 FIG. 207. 
 
 FIG. 208. 
 
 ' u 
 
 s^ r 
 
 ^_j 
 
 
 --JV 
 
 FIG. 209. 
 
 I ill 
 
 FIG. 211. 
 
 3T 
 
 FIG. 212. 
 
 FIG. 213. 
 
MILLING MACHINE PRACTICE. 
 
 1275 
 
 Fillet Forming Tools (Dimensions in Inches). 
 
 ISO-DEGREE (Fig. 
 
 207). 
 
 
 
 ISO-DEGREE (Fig. 
 
 208). 
 
 A 
 
 B 
 
 C 
 
 
 D 
 
 
 E 
 
 
 R 
 
 A B C D 
 
 R 
 
 5/8 
 
 1 
 
 1 
 
 
 1/4 
 
 
 0.04 
 
 0.02 
 
 5/8 1 1 0. 
 
 2 
 
 0.1 
 
 5/8 
 
 1 
 
 1 
 
 
 3/8 
 
 
 0.10 
 
 0.05 
 
 5/8 110. 
 
 4 
 
 0.2 
 
 3/i 
 
 ll/o 
 
 1 1/4 
 
 
 1 
 
 
 n so 
 
 n 
 
 40 
 
 
 
 
 u /4 
 
 J. Vo 
 
 
 VARIOUS RADII (Fig 
 
 209). 
 
 
 
 Rad. 
 
 A 
 
 B 
 
 
 C 
 
 
 D 
 
 E F G H J 
 
 K 
 
 L 
 
 5/8 
 
 . 3/4 
 
 U/8 
 
 
 U/4 
 
 
 5/16 
 
 3/16 7/ 8 5/8 1/4 1/4 
 
 3/8 
 
 V2 
 
 0.8 
 
 3/4 
 
 U/8 
 
 
 1.6 
 
 
 3/8 
 
 I/ 
 
 t 
 
 /8 5/8 1/4 1/4 
 
 3/8 
 
 1/2 
 
 U/4 
 
 U/2 
 
 21/4 
 
 
 21/2 
 
 
 7/16 
 
 5/16 1 1/8 1 1/4 S/g 
 
 1/2 
 
 5/8 
 
 13/4 
 
 ^ U/2 
 
 21/4 
 
 
 31/2 
 
 
 1/2 
 
 3/8 U/8 1 V4 3/ 8 
 
 1/2 
 
 5/8 
 
 Radius Forming Tools 
 
 (Dimensions in Inches). 
 
 ISO-DEGREE 
 
 90-DEGREE, RIGHT AND 
 
 LEFT 
 
 
 
 (Fig. 
 
 210). 
 
 
 HAND (Fig. 211). 
 
 
 
 R(rad.) A 
 
 B 
 
 
 C 
 
 
 D 
 
 
 K(rad.) ABC 
 
 D 
 
 1/16 
 
 5/8 
 
 1 
 
 
 3/ 
 
 S 
 
 1 
 
 
 1/32 
 
 5/8 1 1 
 
 
 5/16 
 
 1/8 
 
 5/8 
 
 1 
 
 
 I/ 
 
 2 
 
 1 
 
 
 1/16 
 
 5/8 1 1 
 
 
 3/8 
 
 1/4 
 
 5/8 
 
 1 
 
 
 
 
 1 
 
 
 1/8 
 
 5/8 1 1 
 
 
 1/2 
 
 i/a 
 
 5/8 
 
 1 
 
 U/4 
 
 1 
 
 
 1/4 
 
 5/8 1 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1/2 
 
 5/s 1 1 
 
 1 
 
 1/4 
 
 90-DEGREE, RIGHT HAND OR 
 
 LEFT HAND (Figs. 212 and 213). 
 
 
 R 
 
 (rad.) 
 
 
 A 
 
 
 B 
 
 C 
 
 D E F 
 
 
 
 
 
 3/4 
 
 
 3/4 
 
 1 
 
 1/8 
 
 5/16 1 
 
 1/8 11/8 U/8 
 
 
 
 
 1 
 
 
 
 3/4 
 
 1 
 
 1/8 
 
 3/ 
 
 8 1 
 
 1/4 1 3/8 1 1/4 
 
 
 
 
 1 
 
 1/2 
 
 1 
 
 
 1 
 
 1/2 
 
 5/ 
 
 8 2 
 
 21/4 2 
 
 
 
 
 2 
 
 
 1 
 
 1/2 
 
 21/4 
 
 3/4 21/2 3 25/ 8 
 
 MILLING MACHINE PRACTICE. 
 
 Forms of Milling Cutters. Milling cutters are made from either 
 high speed or carbon steel. The former can be subjected to the more 
 severe service and are especially adapted to the removal of large 
 amounts of metal, thus dictating their use as roughing cutters. The 
 varieties of cutters in common use and the work to which they are 
 adapted are as follows: 
 
 The Plain Milling Cutter is a cylinder with teeth on the periphery 
 only, and is used for producing a flat surface parallel to the axis of the 
 cutter. Plain milling cutters are made in a wide variety of diameters 
 and widths for the various requirements of slab milling, key way cut- 
 ting, sawing, etc. Cutters less than 3/ 4 in. wide are usually made with 
 straight teeth, while wider cutters have teeth that are a portion of a 
 spiral. The spiral form enables each tooth to take a shearing cut, 
 reduces the stress on the teeth, and prevents shock as each tooth 
 engages the work, thus producing smoother surfaces on wide work. 
 The spiral cutter requires less power to operate, and as it is under 
 less strain, the tendency to chatter is reduced. Cutters for milling 
 wide surfaces, whether of the spiral or straight type sometimes have 
 nicks cut in the teeth, the nicks being staggered in the consecutive 
 teeth. It is claimed that such cutters can be run with coarser feeds 
 than plain cutters, as the nicks break up the chips and prevent jamming 
 of the teeth. Nicked cutters are condemned by many authorities, 
 however, for the reason that that portion of a following tooth opposite 
 a nick is required to do double the usual amount of work With a re- 
 sulting tendency to breakage. 
 
 . The Side Milling Cutter is a plain milling cutter with the addition 
 of teeth on both sides. Side milling cutters are used in a large variety 
 of work. Two or more are often placed on the same arbor with a space 
 between them, in which case they are known as straddle mills. Straddle 
 mills are advantageously used where the work has to be milled on 
 two parallel sides, *as in bolt heads, tongues, etc. Side milling cutters 
 are often made with interlocking side teeth for milling slots to a stand- 
 ard width, the width of the slot being maintained by means of packing 
 washers between the two parts of the cutter. 
 
1276 THE MACHINE-SHOP. 
 
 Face Milling Cutters have teeth cut on the periphery and on one face 
 of a disk. The face mill is fastened to the end of the machine spindle 
 and the teeth on the face come in full contact with the work, only a 
 small portion of the peripheral teeth being in action. Some face 
 mills have no teeth at all on the periphery. 
 
 The End Mill, like the face mill, has teeth on the periphery and 
 on one end. It is used for light milling operations, such as the milling 
 of slots, facing narrow surfaces, and for making cuts on the periphery 
 of pieces. End mills are of four general types: The solid end mill, the 
 end mill with center cut, the slotting end mill with two lips, and the 
 shell end mill. The first and the last have either straight or spiral 
 teeth. In the solid end mill the teeth are cut in the same piece that 
 forms the shank. The shell end mill has a hole through its center so 
 that it can be mounted on an arbor, and it should be used in preference 
 to the solid mill whenever possible, as it is cheaper to replace when 
 worn out or broken. Tire teeth of end mills with center cut are de- 
 signed to cut at the inner end, whereas the teeth of solid mills have 
 no cutting edge at this point. Center cut end mills are used for mill- 
 ing shallow recesses in surfaces where there has been no hole bored 
 previously for starting the cut, for milling^squares on the ends of shafts 
 and for similar work. They have fewer teeth and can take heavier 
 cuts than solid . end mills or shell end mills. Slotting end mills are 
 adapted to the rapid milling of deep slots from the solid where there 
 has been no hole bored for starting the cut. A depth of cut equal 
 to one-half the diameter of the mill can usually be taken from solid 
 stock. 
 
 The T-Slot cutter has teeth on its periphery and alternating teeth 
 on its sides, the teeth being cut on the same piece that forms the shank. 
 In making a T-slot, a groove is first cut with an ordinary side milling 
 cutter or a two-lipped end mill, after which the wide groove at the 
 bottom is cut with the T-slot cutter. 
 
 Angular Cutters have teeth that are at some oblique angle to the 
 axis. The cutter may have more than one angle. They are used for 
 milling the edge of a piece to a required angle, or for cutting teeth in 
 cutters or reamers. In work such as dovetailing where the cutter 
 cannot be fastened to the arbor with a nut, it is made with a threaded 
 hole or with the cutter in one piece with the shank. 
 
 Form Cutters are of irregular outline for exactly duplicating pieces. 
 In one style of form cutter the teeth are sharpened by grinding on the 
 tops of the teeth, which necessarily changes the contour of the teeth 
 and therefore the outline produced. The usual style is so made that 
 it may be sharpened by grinding the face of the tooth, without alter- 
 ing the contour. This permits the cutter to be used for duplicate 
 interchangeable work until it has been ground to a point where the 
 teeth are too slender to stand the strain of the work. 
 
 Fly Cutters consist of a single cutter similar in shape to a planer 
 tool, held in and rotated by an arbor. As they have but a single 
 cutting edge, they are used but rarely outside of the experiment room 
 or tool-room. The fly cutter can be formed exactly to any desired 
 shape and will reproduce this shape exactly. Its field is those opera- 
 tions that would not bear the expense of special shaped commercial 
 cutters, as where but one or two teeth are to be made of a special form. 
 
 Inserted Tooth Cutters. When it is required to use plain milling cutters 
 of a greater diameter than about 8 in., or side milling cutters of greater 
 than 6 in. diameter, it is preferable to insert the teeth in a disk or head, 
 so as to avoid the expense of making solid cutters and the difficulty 
 of hardening them, not merely because of the risk of breakage in hard- 
 ening them, but also on account of the difficulty in obtaining a uni- 
 form degree of hardness or temper. The face of the inserted tooth 
 should be undercut a few degrees from the radial line, thereby giving 
 a smoother cut and consuming less power than would be the case were 
 the face of the tooth flush with the radial line. Drawings of inserted 
 tooth cutters furnished the author by the Cincinnati Milling Machine 
 Co., show a rake of the teeth of from 10 to 15 degrees. 
 
 Number of Teeth. There is no standard rule for the number of 
 teeth in milling cutters. The sizes offered commercially by cutter 
 manufacturers have been found as a rule satisfactory for most purposes, 
 
MILLING MACHINE PRACTICE. 
 
 1277 
 
 but in roughing out work where as much metal is to be removed as 
 possible in a given time, cutters with a smaller number of teeth than 
 the standard mills are advisable. Furthermore, a short lead spiral 
 on coarse tooth cutters adapts them to a large range of work that is 
 not in the heavier class. Such cutters show a considerable saving of 
 power over cutters with a larger number of teeth. The number of teeth 
 in cutters of various types is given in Machinery, April, 190, as follows: 
 Plain milling cutters are usually manufactured in sizes from 2 to 5 
 in. diameter, and up to 6-in. face. The use of solid plain milling 
 cutters of over 5-in. face is not advised, and cutters over 5-in. face 
 should be made in two or more interlocking sections. 
 
 NUMBER OF TEETH AND AMOUNT OF SPIRAL OF PLAIN MILLING CUTTERS 
 dia -_I 
 
 No. of teeth = 
 
 
 ; Length of Spiral = 9 X diam. 4- 4. 
 
 Diameter of cutter, 
 
 2 21/4 21/2 23/4 3 31/2 4 41/2 5 51/2 6 61/2 7 7 1/2 8 
 Number of teeth, 
 
 16 18 18 18 20 20 22 24 24 26 26 28 30 30 32 
 Length of one turn of spiral, inches, 
 22 241/4 261/2 283/ 4 31 35 1/2 40 441/2 49 531/2 58 621/2 67 71 1/2 76 
 
 A cutter with ah included angle of 60 (12 on one side and 48 on the 
 other) is recommended for fluting plain milling cutters, although cutters 
 of 52 (12 and 40) are commonly furnished by manufacturers. The 
 angle of relief of milling cutters should be between 5 and 7. 
 
 The teeth of side milling cutters should have the same general form 
 as those of plain milling cutters, excepting that the cutter used to 
 form them should have an included angle of about 75. 
 
 NUMBER OF TEETH IN SIDE MILLING CUTTERS. 
 
 Number of teeth = 3.1 diam. + 11. 
 Diameter of cutter, 
 
 221/4 2 1/2 23/4 33 1/ 2 4 41/2 5 51/2 6 6 1/2 7 71/2 8 9 
 Number of teeth, 
 
 18 18 18 20 20 22 24 24 26 28 30 32 32 34 36 38 
 Keyways in Milling Cutters. A number of manufacturers have 
 adopted the keyways shown below, as standards. The dimensions in 
 inches are given in the tables, 
 
 FIG. 214. SQUARE KEYWAY. r FIG. 215. HALF-RQUND KEYWAY. 
 
 SQUARE KEYWAYS. 
 
 Diam. 
 Hole, 
 
 3/8-8/16 
 
 5/8-7/8 
 
 15/16-H/8 
 
 13/10-13/8 
 
 17/16-13/4 
 
 1 13/16-2 
 
 21/16-21/2 
 
 29/W-3 
 
 Width 
 W 
 
 3 /32 
 
 VS 
 
 5/32 
 
 3/16 
 
 V4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 Depth. 
 D 
 
 3/64 
 
 Vl6 
 
 5/64 
 
 3/32 
 
 VS 
 
 5/32 
 
 3/16 
 
 3/16 
 
 Radius, 
 R 
 
 0.020 
 
 0.030 
 
 0.035 
 
 0.040 
 
 0.050 
 
 0.060 
 
 0.060 
 
 0.060 
 
 HALF-ROUND KEYWAYS. 
 
 Diam. 
 Hole, H 
 
 8/8-5/8 
 
 H/16-13/16 
 
 7/8-1 3/16 
 
 1 1/4-1 7/16 
 
 H/2-2 
 
 2 V16-2 7/ 16 
 
 2 1/2-3 
 
 Width 
 W 
 
 1/8 
 
 3/16 
 
 1/4 
 
 5/10 
 
 3/8 
 
 7/16 
 
 1/2 
 
 Depth, 
 D 
 
 Vl6 
 
 3/32 
 
 1/8 
 
 5/32 
 
 3/16 
 
 7/32 
 
 1/4 
 
1278 
 
 THE MACHINE-SHOP. 
 
 Diameter of Cutters. It is advisable to use cutters of as small a 
 diameter as the strength will admit. The smaller the cutter, the 
 shorter the distance it will have to travel in milling a given length. 
 With small mills also there is less liability to chatter than with large 
 ones. In addition they require less power and are not as expensive 
 as large ones. The Brown & Sharpe Mfg. Co. states that a difference 
 of 1/2 in. in he diameter of the mills made a difference of 10% in the 
 cost of their work. In surface milling the cutter should, if possible, be 
 wider than the work. 
 
 .Clearance and Rake of Cutters. The clearance of milling cutters, 
 or the amount of material removed from the top of the teeth back of 
 the cutting edge to permit it to clear the surface of the work instead of 
 scraping over it, depends on the diameter of the cutters. It must be 
 greater for small cutters than for large ones. For plain cutters over 
 3 in. diameter, the clearance angle should be 4 degrees, and for cutters 
 of less than 3 in. it should be 6 degrees. For end mills it should be about 
 2 degrees. It is considered advisable to have the teeth of end mills from 
 0.001 to 0.002 in. lower at the center than at the outside. The Cin- 
 cinnati Milling Machine Co. has furnished the author with drawings 
 of cutters of various types. In these the teeth have a front rake of 
 10 degrees.. 
 
 Power Required for Milling. (Mech. Engr., Oct. 26, 1907.) 
 Mr. S. Strieff made a series of experiments to determine the power 
 required to drive milling cutters of high-speed steel. The results are 
 shown in the table below. A proportionately higher amount of power 
 is required for light than heavy milling, as the power to drive the machine 
 is the same at all loads. The table also shows that the depth of cut does 
 not increase the power required in the same proportion as the width, and 
 that work with a quick feed and a deep but comparatively narrow cut 
 requires less power than a wide cut of moderate depth with slow feed, 
 the amount of metal removed being the same in both cases. 
 
 Power Required for Milling. 
 
 
 
 
 
 
 
 " 
 
 
 i'fc 
 
 Feed. 
 
 1^ 
 
 fl 
 
 n 
 
 3 
 O 
 
 a; 
 
 o 
 
 S*- 
 
 fclg 
 
 Number o 
 Revoluti< 
 of Cuttei 
 Minute. 
 
 Per Min- 
 ute, In- 
 ches. 
 
 Per Rev- 
 olution, 
 Inches. 
 
 Cutting S] 
 of Cuttei 
 per Mini 
 
 Depth of < 
 Inches. 
 
 Width of i 
 Inches. 
 
 Horse-Po\ 
 Required 
 
 3rf 
 
 *!! 
 
 Horse-Po\ 
 Required 
 Pound-H 
 
 24 
 
 2.46 
 
 0.10 
 
 37 
 
 0.26 
 
 23.6 
 
 25 
 
 245 
 
 0.102 
 
 24 
 
 3.50 
 
 0.15 
 
 37 
 
 0.26 
 
 10.2 
 
 17 
 
 150 
 
 0.113 
 
 24 
 
 4.35 
 
 0.18 
 
 37 
 
 0.14 
 
 9.8 
 
 17 
 
 97 
 
 0.175 
 
 24 
 
 3.50 
 
 0.15 
 
 37 
 
 0.49 
 
 9.8 
 
 27 
 
 490 
 
 0.055 
 
 19 
 
 4.33. 
 
 0.23 
 
 29.5 
 
 0.28 
 
 9.3 
 
 17 
 
 331 
 
 0.051 
 
 23 
 
 4.17 
 
 0.18 
 
 36 
 
 0.28 
 
 20.5 
 
 27 
 
 386 
 
 0.070 
 
 23 
 
 4.17 
 
 0.18 
 
 36 
 
 0.28 
 
 9.8 
 
 20 
 
 183 
 
 0.109 
 
 40 
 
 1.89 
 
 0.05 
 
 64 
 
 0.24 
 
 10.2 
 
 17 
 
 74 
 
 0.230 
 
 40 
 
 3.94 
 
 0.10 
 
 64 
 
 0.37 
 
 13.8 
 
 21 
 
 331 
 
 0.063 
 
 40 
 
 5.79 
 
 0.14 
 
 64 
 
 0.16 
 
 16.5 
 
 17 
 
 123 
 
 0.138 
 
 P. V. Vernon reports (En'gr, Mar. 9, 1909) some milling machine 
 tests made by Alfred Herbert, Ltd., showing the horse-power required 
 to slab mild steel and cast iron. The tests reported include 44 on 
 steel and 38 on cast iron. The horse-power was determined from the 
 current readings and includes the motor losses and also a constant 
 loss of 1.8 H.P. in the jack shaft and countershaft of the machine. 
 
 HORSE-POWER PER Cu. IN. PER MINUTE REQUIRED FOR SLABBING. 
 Maximum. Minimum. Average. 
 
 Steel 3.02 1.95 2.52 
 
 Cast iron 1.25 0.89 1.10 
 
 Later tests reported to the Manchester Assoc. of Engrs., Nov. 23, 
 1912, by Mr. Vernon, embodied the following conclusions: (1) A 5-in. 
 double belt, driving a 16-in. pulley at 400 r.p.m. (100,531 sq. in. of 
 
MILLING MACHINE PRACTICE. 
 
 1279 
 
 belt per min.) geared to drive 4i/2-in. high-speed cutter at 70 ft. per 
 min. is able to remove as much as 48.1 cu. in. of cast iron or 24.31 cu. 
 in- of mild steel per minute. (2) 2090 sq. in. of double belt passing 
 over a pulley per minute will remove 1 cu. in. of cast iron in a milling 
 machine. To remove 1 cu. in. of steel the belt surface passing should 
 be 4135 sq. in. (3) A 4 i/2-in. high-speed cutter on a 2-in. arbor, run- 
 ning at 70 ft. per min. is capable of removing at least 3.63 cu. in. of 
 cast iron, and possibly as much as 6.01 cu. in., and at least 2.125 cu. 
 in. of mild steel, and possibly as much as 3.03 cu. in. per min. for each 
 inch of width of belt, up to 8 in. From the earlier tests noted above 
 the conclusion was reached that 1 H.P. would remove as much as 1.84 
 cu. in. of cast iron per min., and 0.74 cu. in. of mild steel. In these 
 tests the feed in cast iron ranged between 1 27/ 32 and 109/ig in. per min., 
 the depth of cut from 0.14 to 1.10 in., while in steel the feeds ranged 
 from 5/ 8 to 103/8 in. per min. and the depth of cut from 0.10 to 1.10 
 in. per min. 
 
 A. L. De Leeuw gives in Am. Mach., Aug. 8, 1912, the results of a 
 large number of tests to determine the horse-power consumed in cutting 
 machinery steel in the milling machine. From the tests there reported 
 the following table has been compiled, the figures given showing the 
 test in each class in which the maximum amount of metal per horse- 
 power per minute was removed. The figures for horse-power are net, 
 the motor losses having been deducted. 
 
 Power Required for Milling Machinery Steel (A. L. De Leeuw). 
 
 
 
 
 
 
 3fc 
 
 ^ 
 
 
 
 
 
 
 3fe 
 
 ^ 
 
 
 *f 
 
 3 
 
 
 fe 
 
 fe 
 
 la 
 
 9 
 
 
 d 
 
 
 8 
 
 y 
 
 s 
 
 S 
 
 
 U 
 
 
 ^ 
 
 1 
 
 oli 
 
 o 
 fc 
 
 CJ 
 
 O 
 
 *0 
 
 a . 
 
 ^ 
 
 o 
 
 oli 
 
 o 
 
 .J 
 
 
 fe 
 
 
 AH 
 
 . o i 
 
 
 
 
 ._ 
 
 
 
 
 . o t 
 
 
 ". 
 
 ex 
 
 S !H 
 
 11 S 
 
 I 
 
 "Iw 
 
 1 
 
 ll 
 
 5 g 
 
 g +* 
 
 ^1 
 
 1 
 
 5l^ 
 
 1 
 
 || 
 
 0) 
 
 Q 
 
 tf 
 
 & 
 
 
 
 w 
 
 O 
 
 5 
 
 s~ 
 
 1^ 
 
 
 
 t 
 
 I 
 
 
 
 U 
 
 S~ 
 
 1/8 
 
 20.5 
 
 12.31 
 
 10.96 
 
 0.702 
 
 
 B 
 
 5/16 
 
 20.0 
 
 4.57 
 
 11.959 
 
 0.712 
 
 
 A 
 
 
 25.0 
 
 15.4 
 
 13.473 
 
 0.714 
 
 
 A 
 
 
 20.0 
 
 4.56 
 
 7.34 
 
 0.972 
 
 
 A 
 
 
 20.0 
 
 11.81 
 
 7.555 
 
 0.977 
 
 
 A 
 
 
 21.5 
 
 4.89 
 
 7.14 
 
 1.07 
 
 
 C 
 
 
 20.0 
 
 11.83 
 
 7.34 
 
 1.007 
 
 
 A 
 
 
 16.0 
 
 7.70 
 
 11.0 
 
 1.092 
 
 2 
 
 D 
 
 
 22.0 
 
 12.96 
 
 6.85 
 
 1.183 
 
 
 C 
 
 3/8 
 
 20.0 
 
 3.48 
 
 10.96 
 
 0.596 
 
 
 B 
 
 /16 
 
 20.0 
 
 7.34 
 
 10.70 
 
 0.643 
 
 
 B 
 
 
 20.0 
 
 3.49 
 
 7.07 
 
 0.925 
 
 
 A 
 
 
 20.0 
 
 7.29 
 
 9.749 
 
 0.701 
 
 
 A 
 
 
 40.5 
 
 6.22 
 
 12.35 
 
 0.944 
 
 3 
 
 D 
 
 
 20.0 
 
 7.29 
 
 7.07 
 
 0.967 
 
 
 A 
 
 
 40. 
 
 7.8 
 
 14.55 
 
 1.001 
 
 3 
 
 D 
 
 
 21.5 
 
 7.96 
 
 6.85 
 
 1.09 
 
 
 C 
 
 
 22. 
 
 3.86 
 
 6.85 
 
 1.056 
 
 1 
 
 C 
 
 /4 
 
 20.0 
 
 5.9 
 
 12.62 
 
 0.584 
 
 
 B 
 
 
 15.75 
 
 7.66 
 
 12.64 
 
 1.137 
 
 2 
 
 D 
 
 
 20.0 
 
 5.84 
 
 11.41 
 
 0.64 
 
 
 A 
 
 1/2 
 
 15.5 
 
 4.61 
 
 12.64 
 
 0.912 
 
 2 
 
 D 
 
 
 19.0 
 
 5.58 
 
 7.62 
 
 0.915 
 
 
 A 
 
 
 40.0 
 
 6.09 
 
 15.93 
 
 0.955 
 
 3 
 
 D 
 
 
 21.5 
 
 6.26 
 
 7.14 
 
 1.096 
 
 
 C 
 
 5/8 
 
 40.0 
 
 4.71 
 
 17.07 
 
 0.863 
 
 3 
 
 D 
 
 5/16 
 
 20.5 
 
 4.68 
 
 13.20 
 
 0.554 
 
 
 B 
 
 3/4 
 
 39.5 
 
 3.63 
 
 17.38 
 
 0.782 
 
 3 
 
 D 
 
 NOTE 1. Cutter No. 1 is an 8-in., 12-blade face mill; No. 2 is a 
 10-in., 16-blade high-power face mill; No. 3 is a 41/2 in., 10-tooth 
 spiral nicked cutter. 
 
 NOTE 2. Material A, Elastic Limit 36,400 Ib. per sq. in., elongation 
 36%, reduction of area 66%; material B, E. L. 36,200 Ib. per sq. in., 
 elong. 36.5%, red. of area 59. 6%; material C, E. L. 37,400 Ib. per sq. in., 
 elong. 36.5%, red. of area 60%; material D, E. L. 55,000 Ib. per sq. in., 
 elong. and red. of area not given; 0.26 carbon, 0.5% manganese. 
 
 Modern Milling Practice (1914).^ The limit of milling operations is 
 determined by the strength and durability of the cutter. A rigid 
 frame on the machine and powerful feed mechanism increase these. 
 The chief causes of low output are: Improperly constructed cutters; 
 insufficient rigidity in the machine; and timidity, due to lack of ex- 
 perience, of both builders and operators. The principal cause of 
 cutter failures is insufficient space for chips between the cutter teeth. 
 Fixed rules cannot be laid down for proper feeds and speeds of milling 
 cutters, these depending on the character and hardness of the metal 
 
1280 THE MACHINE-SHOP. 
 
 being cut. On roughing cuts it is desirable to run the cutter at a speed 
 well within its limit, and use as heavy a feed as the machine can pull. 
 The size of chip taken by each tooth of the cutter with the heaviest 
 feeds is comparatively light, and with properly sharpened cutters 
 there is little danger of breaking the cutter by giving too great a feed. 
 It is considered better practice, however, to break an occasional cutter 
 than to run machines at a low rate. It is not considered desirable to 
 run even high speed steel cutters at excessive speeds. The great value 
 of these cutters is their long life and ability to hold a cutting edge as 
 compared with carbon steel cutters. It is important to keep the 
 cutters sharp, as accurate or fast work is impossible with dulled teeth, 
 and a dull cutter will wear away faster than a sharp one. Cutter 
 grinders should always be used for sharpening cutters. 
 
 The following speeds in feet per minute are a good basis for roughing 
 the materials indicated: 
 Carbon steel cutters, 
 
 Cast Iron. Machinery Steel. Tool Steel. Brass and Bronze. 
 
 40 to 60 30 to 40 20 to 30 80 to 100 
 
 High speed steel cutters, 
 
 80 to 100 80 to 100 60 to 80 150 to 200 
 
 On cast-iron work a jet of air delivered to the cutter with sufficient 
 force to blow the chips away as fast as made permits faster feeds and 
 prolongs the cutter's life. A stream of oil fed under heavy pressure to 
 wash the chips away has the same effect when cutting steel. On finish- 
 ing cuts the rate of feed used determines the grade of the finish. If a 
 spiral mill is used the feed should range from 0.036 in. to 0.05 in. per 
 revolution of a 3-in. diameter cutter. As such cuts are light the speed 
 of cutting can be much higher than that used for roughing cuts. The 
 nature of the cut is a factor in determining speeds ; a saw can run twice 
 as fast as a surface mill. (Seepara?rar)h,p. 1282, on high-speed milling:.) 
 Keyseating and similar work can be best done with a plain cutter 
 rather than a side mill. 
 
 Castings should be pickled in a solution of sulphuric acid, diluted 
 with water to a specific gravity of 25 deg. (Baume), before milling, to 
 rempve the hard skin and sand which are destructive to cutters. If the 
 castings are later to be painted, they should not be immersed in the 
 pickling bath. It is better to pour the solution over them, allowing 
 it to dry before making another application. This should be repeated 
 4 or 5 times. Forgings should be pickled in a solution of sulphuric acid 
 and water of a specific gravity of 30 deg. (Baume), for from 3 to 12 
 hours. After pickling, forgings and castings should be washed with 
 hot water to remove the sand and acid. 
 
 Milling "with" or "against" the Feed. Tests made with the 
 Brown & Sharpe No. 5 milling-machine (described by H. L. Arnold, 
 in Am. Mack., Oct. 18, 1884) to determine the relative advantage of 
 running the milling cutter with or against the feed "with the feed" 
 meaning that the teeth of the cutter strike on the top surface or 
 " scale " of cast-iron work in process of being milled, and "against the 
 feed " meaning that the teeth begin to cut in the clean, newly cut surface 
 of the work and cut upwards toward the scale showed a decided advan- 
 tage in favor of running the cutter against the feed. The result is 
 directly opposite to that obtained in tests of a Pratt & Whitney machine 
 by experts of the Pratt & Whitney Co. 
 
 In the tests with the Brown & Sharpe machine the cutters used were 6 
 inches face by 4 1/2 and 3 inches diameter, respectively, 15 teeth in each 
 mill, 42 revolutions per minute in each case, or nearly 50 feet per minute 
 surface speed for the 4l/2 : inch and 33 feet per minute for the 3-inch mill. 
 The revolution marks were 6 to the inch, giving: a feed of 7 inches per 
 minute, and a cut per tooth of 0.011 inch. When the machine was 
 forced to the limit of its driving the depth of cut was 11/32 inch when the 
 cutter ran in the "old" way, or against the feed, and only 1/4 inch when 
 it ran in the "new" way, or with the feed. The endurance of the mill- 
 ing cutters was much greater when they were run in the "old" way. 
 The Brown & Sharpe Mfg. Co. says that it is sometimes advisable to 
 mill with the feed, as in surfacing two sides of a piece with straddle 
 mills, the cutters will then tend to hold the work down. In milling 
 deep slots or cutting off stock with thin cutters or saws, milling with the 
 feed is less likely to crowd the cutter sidewfce and make a crooked slot. 
 
MILLING MACHINE PRACTICE. 1281 
 
 Lubricant for Milling Cutters. (Brown & Sharpe Mfg. Co., 1907.) 
 An excellent lubricant, to use with a pump, for milling cutters is made 
 by mixing together and boiling for one-half hour, 1/4 Ib. sal soda, tfz 
 pint lard oil, 1/2 pint soft soap and water enough to make 10 quarts. 
 Oil is also frequently used in milling steel, wrought iron, malleable iron 
 or tough bronze. 
 
 Typical Milling Jobs Speeds Feeds. The notes below compiled 
 from data furnished by the Brown & Sharpe Mfg. Co. and the Cin- 
 cinnati Milling Machine Co. (1915) show examples of what is con- 
 sidered good commercial milling practice. 
 
 Bars of 0.60 Carbon steel, 5/ 8 in. thick, 21/2 in. wide, 113/ 4 in. long, 
 had 22 rack teeth, 7/ 16 in. pitch arid Vs in. deep milled in the edge. 
 The bars were locked four at a time in a vise. A gang of four cutters 
 was used, at 41 r.p.m. and a feed of 0.023 in. per revolution, equivalent 
 to WIG in. per minute. Two vises were used, the operator loading one 
 while the bars in the other were being machined. The time required 
 per piece including chucking and removing, was 0.71 minute. For 
 milling two recesses in the upper edges of these same bars, after the rack 
 teeth were cut, they were mounted two in a vise with distance pieces 
 between, and a gang of foiir 3i/2-in. side mills was used, milling all four 
 recesses at once. The mills rotated at 50 r.p.m., and the feed was 
 0.068 per revolution, equivalent to 3.4 in. per minute. Two vises were 
 used as before, and the total time per rack was 2.2 minutes. The final 
 operation was the milling of a slot in the bar, for which purpose it was 
 held at the ends in two vises. Two holes were first drilled in the piece 
 through one of which the cutter was threaded. The slot was 1-in. 
 wide and 9 in. long. A is/ig-in. helical cutter was used at 160 r.p.m. 
 A roughing cut was first taken at a feed of 0.015 per revolution, equiv- 
 alent to 2.4 in. per min., after which the piece was removed and 
 allowed to cool before the finishing cut was taken at a feed of 0.068 in. 
 per revolution, or 10.8 in. per minute. The roughing cut removed 
 11/2 cu. in. of steel per minute. The total time, including chucking, 
 removing, etc., was 7.5 minutes. 
 
 Gray iron castings 8 1/4 in. long, 8 1/2 in. wide, 4 1/4 in. thick, with 
 two flanges 7/ 8 in. high and 7/g in. thick projecting above the upper 
 face, were milled on the entire upper surface and the two sides, includ- 
 ing top and sides of flanges at one operation by a gang of straddle mills, 
 the largest cutter being 101/2 in. diameter and running at 21 r.p.m., 
 with 6.3 in. feed per minute. Metal was removed at the rate of 19 cu. in. 
 per minute, the maximum depth of cut being 3/ 16 in. The pieces were 
 held in a string jig, removed as fast as they were traversed by the gang 
 of cutters, and others were chucked in their places. They were milled 
 in lots of 125 without resharpening of the cutters. Time per piece, 
 2 minutes. 
 
 A gray iron casting 22 in. wide and 9 in. long was milled on its upper 
 surface by a gang of three 6-in. spiral mills with a total face width of 
 24 in., mounted on a 2-in. arbor. The depth of cut was 3/ 8 in. and the 
 table feed was 73/ 4 in. per minute. 
 
 A surface about 1 in. wide all around an aluminum transmission 
 case 12 x 14 in. was milled by means of a 10i/2-in. inserted tooth face 
 mill at 236 r.p.m. Depth of cut, i/g in., table feed, 0.068 in. per revolu- 
 tion or 20 in. per minute. A double fixture was used, one piece being 
 inserted while the other was being, milled. Time, including chucking 
 and removal, 21/2 minutes per piec5. 
 
 Gray iron castings, 10 1/4 in. wide, 14 in. long X 1 3 /4 in. thick, finished 
 all over, and a slot -Vs X 1 in. cut from the solid. A gang of five cutters 
 was used, two of 8 in., two of 3 1/2 in. and one of 53/4 in. diameter, re- 
 spectively. These took a cut 3/ 16 in. deep across the top, and two 
 edges, and milled the slot in one operation. The table travel was 
 .2 in. per minute. Tho average time, including chucking, was 15.6 
 minutes. 
 
 Gray iron castings, 3 in. and 61/2 in. wide X 251/4 in. long, 1 1/4 in. 
 thick, were surfaced by a face mill 8 in. diameter at a surface speed of 
 80 feet per minute. The cut was 3/ 16 in., and the table travel 11.4 in. 
 per minute in the 3-in. part and 8 in. per minute in the 6 i/2-in. part. 
 The total time for finishing, including chucking, was seven minutes. 
 The planer required 23 minutes for the same operation. In finishing 
 
1282 
 
 THE MACHINE-SHOP. 
 
 the opposite side of these castings, two castings were milled at one setting, 
 3/i6 in. of stock being removed all over and two slots s/g X Vs in. 
 milled from the solid. A gang of seven cutters, 3 of 3 in., 2 of 4 1/4 in., 
 and 1 of 8 1/4 in. diameter was used at 38 r.p.m. and a feed of 0.1 in., 
 giving a table travel of 3.8 in. per minute. These two castings were 
 finished in 18 minutes, including chucking, the actual nulling time being 
 eight minutes on each piece. A planer working at 55 ft. cutting speed 
 finished the same job in 36 minutes. 
 
 An inserted- tooth face mill 12 in. diameter took a 9-in. cut, i/g in. 
 deep across the entire face of a gray iron casting at a table travel of 
 5 in. per minute. The length of cut was 18 in. and the time required 
 6 1/2 minutes. 
 
 The following table summarizes a number of typical jobs of milling : 
 
 Typical Milling Jobs. 
 
 
 
 Cut, In. 
 
 Cutter. 
 
 If 
 
 
 i-s 
 
 1 
 
 o 
 
 Nature of 
 
 Material 
 
 
 
 
 
 M<^5 
 
 jj 
 
 2 
 
 S c . 
 
 Work. 
 
 Cut. 
 
 
 
 r 
 
 J 
 
 sfc 
 
 I" 
 
 H a 
 
 S5 
 
 
 
 d 
 
 
 g 
 
 
 rt 
 
 
 
 tf . 
 
 
 
 $ 
 
 !S 
 
 eu g 
 
 PH 
 
 "C-M 
 
 o> w 
 
 3j9 
 
 tb <i5 3 
 
 
 
 & 
 
 P 
 
 Q~ 
 
 tf 
 
 w fo 
 
 & 
 
 H M 
 
 S a 
 
 Face Milling 
 
 Cast Iron 
 
 1/8 
 
 6 
 
 8 
 
 26 
 
 54 
 
 0.168 
 
 4.36 
 
 3.27 
 
 
 " 
 
 
 8 
 
 9.5 1 
 
 26 
 
 64 
 
 0.58 
 
 15.0 
 
 15.0 
 
 
 " 
 
 0.150 
 
 8 
 
 9 5 1 
 
 24 
 
 60 
 
 0.625 
 
 15. 
 
 18.0 
 
 
 Mall. Iron 
 
 1/16-3/32 
 
 6 2 
 
 7.5 
 
 56 
 
 110 
 
 0.223 
 
 12.5 
 
 
 
 SteeP 
 
 
 5 
 
 6 1 
 
 32 
 
 50 
 
 0.148 
 
 4.75 
 
 '92 ' ' 
 
 
 " 6 
 
 1/8 6 
 
 6 
 
 9.5i 
 
 24 
 
 60 
 
 0.52 
 
 12.5 
 
 9.375 
 
 Surfacing 
 
 Cast Iron 
 
 1/32 
 
 3 
 
 4 
 
 68 
 
 71 
 
 0.18 
 
 12.75 
 
 1.75 
 
 
 " 
 
 0.1 . 
 
 12 
 
 4.54 
 
 45 
 
 52 
 
 0.266 
 
 12.0 
 
 14.4 
 
 
 < 
 
 0.1 
 
 4 
 
 3* 
 
 104 
 
 81 
 
 0.144 
 
 15.0 
 
 6.0 
 
 
 " 
 
 i/a 
 
 4 
 
 35 
 
 104 
 
 81 
 
 0.078 
 
 8.125 
 
 4.06 
 
 
 " 
 
 1/8 
 
 8 
 
 3.55 
 
 90 
 
 83 
 
 0.167 
 
 15.0 
 
 15.00 
 
 
 " 
 
 1/8 
 
 12 
 
 3.5i 
 
 53 
 
 55 
 
 0.226 
 
 12.0 
 
 14.4 
 
 
 " 
 
 0.225 
 
 8 
 
 3.55 
 
 85 
 
 77 
 
 0.118 
 
 10.0 
 
 18.0 
 
 
 " 
 
 1/4 
 
 8 
 
 3.55 
 
 81 
 
 75 
 
 0.154 
 
 12.5 
 
 25.0 
 
 
 " 
 
 1/4 
 
 8 
 
 3.55 
 
 94 
 
 86 
 
 0.159 
 
 15.0 
 
 30.0 
 
 
 Tool Steel 
 
 1/16 
 
 21/2 
 
 37 
 
 37 
 
 29 
 
 0.05 
 
 1.85 
 
 0.289 
 
 
 Steel 
 
 0.1 
 
 6 
 
 35 
 
 104 
 
 81 
 
 0.037 
 
 3.875 
 
 2.32 
 
 
 " 
 
 0.15 
 
 6 
 
 35 
 
 104 
 
 81 
 
 0.037 
 
 3.875 
 
 3.48 
 
 
 " 
 
 0.166 
 
 6 
 
 3.55 
 
 90 
 
 83 
 
 0.083 
 
 7.5 
 
 7.5 
 
 
 " 
 
 0.222 
 
 6 
 
 3.55 
 
 105 
 
 96 
 
 0.071 
 
 7.5 
 
 10.0 
 
 
 " 
 
 0.240 
 
 6 
 
 3.55 
 
 94 
 
 86 
 
 0.133 
 
 12.5 
 
 18.0 
 
 
 " 
 
 0.311 
 
 6 
 
 3.55 
 
 100 
 
 92 
 
 0.075 
 
 7.5 
 
 14.0 
 
 
 Brass 
 
 0.01 
 
 21/2 
 
 37 
 
 100 
 
 78 
 
 0.25 
 
 25.0 
 
 0.675 
 
 
 Bronze 
 
 1/64 
 
 3 
 
 33 
 
 166 
 
 130 
 
 0.05 
 
 8.3 
 
 0.389 
 
 T-Slotting 
 
 Cast Iron 
 
 See No 
 
 te 
 
 1 1/16 
 
 252 
 
 75 
 
 0.05 
 
 12.6 
 
 6.693 
 
 Slotting! 
 
 Steel 
 
 
 1 3/16 
 
 1.5H 
 
 163 
 
 65 
 
 0.007 
 
 1.25 
 
 2.2 
 
 Sawing 
 
 
 
 / 
 
 3/64 
 
 5 
 
 70 
 
 91 
 
 0.05 
 
 3.5 
 
 
 1 Inserted teeth, high-speed steel. - Maximum. 3 Chrome nickel 
 steel. 4 Carbon steel, nicked spiral cutter. 6 High-speed steel, spiral 
 nicked cutter. Machinery steel, tensile strength, 65,000 Ib. 7 End 
 mill. 8 End mill with spiral teeth; work done by peripheral teeth. 
 9 Both sides of cutter engaged, making slot width equal to cutter 
 diameter; slot IVie X 1/2 in. 10 Milling slots from solid plate 13/i 6 in. 
 thick. 11 Helical end mill, front of which is formed as a regular twist 
 drill. Operator first drills through the^plate with it, and then uses it 
 as a milling cutter. 
 
 High Speed Milling. L. P. Alford describes (Am. Mach., April 16, 
 1914) a system of high-speed milling developed by the Cincinnati 
 Milling Machine Co., which permits of cutter speeds and feeds from 
 8 to 12 times as great as are ordinarily used. The fundamental con- 
 dition for this practice is the provision of ample lubrication of the 
 
MILLING MACHINE PBACTICE. 
 
 1283 
 
 cutter and work. The cutter is deluged with about 12 gal. per minute 
 of lubricant, which is delivered through a hood which complete!}' sur- 
 rounds the cutter. The lubricant is delivered under pressure, and 
 in addition to cooling the cutter and work, washes away the chips 
 from the teeth of the cutter, preventing them from being carried back 
 into the cut, clogging it, dulling the cutter and marring the finished 
 surface. - Other requisites for high-speed milling are powerful, heavy 
 and rigid machines, and cutters with wide spaced teeth which will 
 permit the use of heavy feeds and 'high speeds. The following tests 
 were cited to show what is possible with this system of milling. The 
 material cut was machinery steel, 0.2 carbon, 0.5 manganese, with a 
 tensile strength of 55,000 to 65,000 Ib. per sq. in. The cutters were 
 of high speed steel. 
 
 Data and Results of High Speed Milling Tests. 
 
 
 Cutter. 
 
 d 
 
 M 
 
 Cut. 
 
 Cutter 
 Speed. 
 
 
 
 1 
 
 J 
 
 . 
 
 i 
 
 > 
 
 s f 
 
 
 
 A 
 
 
 fe 
 
 
 
 1 
 
 jK 
 
 J2 So 
 
 rt h-t 
 
 5 ' 
 
 p 
 
 Jl 
 
 M . 
 
 I* 
 
 tx 
 
 a 
 
 S 
 
 i 
 
 bo 
 
 3 
 
 I 
 
 a.S 
 
 T3 CB 
 
 r 
 
 1 
 
 S 
 
 25 
 
 31/2 
 
 9 
 
 10 
 
 6 
 
 1 1/2 
 
 1/8 
 
 5 
 
 18 
 
 500 
 
 458 
 
 30 1/2 
 
 2 
 
 S 
 
 25 
 
 31/2 
 
 9 
 
 to 
 
 6 
 
 
 0.02 
 
 5 
 
 18 
 
 500 
 
 458 
 
 7.23 
 
 3 
 
 H 
 
 69 
 
 31/2 
 
 ^ 
 
 15 
 
 6 
 
 1 1/2 
 
 (1/16 I 
 
 
 
 510 
 
 470 
 
 301/2 
 
 4 
 
 L 
 
 
 
 16 
 
 15 
 
 1 
 
 U/2 
 
 j 3/16 
 M/4 f 
 
 
 
 510 
 
 835 
 
 301/2 
 
 
 
 
 
 
 
 
 
 1 7-Tooth 1 
 
 
 
 
 
 5 
 
 G 
 
 7' 
 
 M/2 
 
 12 
 
 10 
 
 
 H/4 
 
 -<30-PitchV.. 
 
 181/4 
 
 218 
 
 200 
 
 112 
 
 
 
 
 
 
 
 
 
 ( Gear. | 
 
 
 
 
 
 62 
 
 S 
 
 25 
 
 31/2 
 
 9 
 
 to 
 
 6 
 
 H/2 
 
 .Vi 
 
 5 
 
 21/2 
 
 87 
 
 80 
 
 20 
 
 1 Diametral Pitch. 2 Same cutter and block as in Test No. 1, but 
 run without lubricant. Test stopped when cutter showed signs of 
 distress after cutting 2*/2 in. Edges of teeth blued. 
 
 NOTE. S, spiral mill; H, helical mill; L, slotting cutter; G, gear 
 cutter. 
 
 As a criterion of the life of cutters under the above conditions, a cutter 
 of the type used in test No. 5, was run to destruction. It milled 6700 
 in., not including cutter approach, the equivalent of cutting 223 gears 
 of 1-in. face, 7 pitch, 30 teeth. 
 
 Limiting Factors of Milling Practice. Discussing the above tests 
 Mr. Alford gives the following as the limiting factors of milling ma- 
 chine practice: (1) Power of the machine. Increased speed requires 
 greater power per cubic inch of metal removed; according to the 
 Cincinnati Milling Machine Co., doubling the speed necessitates a 10% 
 increase of power per cubic inch of metal removed. (2) Ability of the 
 cutter to remove metal. Increased speed, with the same feed increases 
 the ability of the cutter to cut, due to the smaller chip removed by 
 each tooth. This means a decrease of strain, wear and heating effect. 
 The total or final heating effect is increased, but this may be counter- 
 acted by copious lubrication. (3) Size and spring of arbor. The size 
 of the arbor is limited by the size of commercial cutters. The strain 
 on the arbor depends on the feed per minute. An increase of speed, 
 lessening the pressure per tooth, reduces the arbor strain, and tends 
 to do away with the limitation imposed by the arbor. (4) Heating of 
 the cutter, often the most important limitation. This can be over- 
 come by sufficient lubricant to remove all heat as fast as it is generated. 
 (5) Wear of the cutter. This is dependent on the number of lineal 
 inches milled, depth of cut and feed per revolution being constant. 
 Increased speed increases the wear per unit of time. Wear may be 
 somewhat reduced with high speed by copious lubrication which washes 
 away the chips, thus preventing the grinding action due to cutting 
 up chips. (6) Breakage of cutters. Frail cutters limit production, 
 as only a certain maximum feed per revolution, dependent on their 
 
1284 
 
 THE MACHINE-SHOP. 
 
 strength, can be taken. Increased speed, with constant feed, will 
 increase production without increasing the cutter strain or danger of 
 breakage. (7) Heating of work. Uneven local heating when milling 
 will produce uneven surfaces, for the swelled portions will be cut away. 
 This action is progressive as the total heat increases as the cut advances. 
 The absence or prevention of heating by copious lubrication does 
 away with this limitation. (8) Spring of work. This limitation is 
 minimized for the same reasons given in (6). (9) Spring of fixture. 
 The same analysis applies as in (6). If the pressure per tooth is re- 
 duced, the pressure for holding may be reduced, and clamping fixtures 
 may be made to operate more quickly. An increase in cutting speed 
 therefore will tend to increase the speed of operation of the clamping 
 devices and fixtures. (10) Spring of the machine. The same argu- 
 ments apply as in (9). (11) Distance of revolution marks on the work. 
 This is the limiting feature in perhaps 90% of milling work, which is 
 governed by polishing or some subsequent operation. If the marks 
 are far apart, polishing cannot be satisfactorily done. Increased 
 speed, with constant feed will bring these marks closer together. (12) 
 Smoothness of cuC. High speed milling, both by the action of centrif- 
 ugal force and by copious flooding removes the chips completely from 
 the cutter and eliminates the grinding effect on the finished surface. 
 With a given distance between revolution marks, high speed will give 
 a smoother surface. 
 
 Speeds and Feeds for Gear Cutting. The speeds and feeds which 
 can be used in gear cutting are affected by many variables, among 
 which may be noted: The material and shape of the cutter, the latter 
 condition involving both the strength and the ability of the teeth to 
 clear themselves of chips; the material and shape of the gear, shape 
 influencing the speed and feed in that a heavy rugged gear will permit 
 , higher speeds and heavier feeds, even in hard material than will a light 
 springy one; accuracy of finish required; quality of lubricant used; 
 rigidity of machine. The following table shows tentative speeds 
 recommended by Gould and Eberhardt, which may serve as a pre- 
 liminary guide, pending the determination of the best combination 
 for each particular case. They represent average practice in medium 
 grades of cast iron and steel. 
 
 
 High-Speed Steel Cutters. 
 
 Carbon Steel Cutters. 
 
 Min. 
 
 Average. 
 
 Max. 
 
 Min. 
 
 Average . 
 
 Max. 
 
 Cast iron, ft. per min.. 
 Steel, ft. per min 
 
 60 
 45 
 
 70 
 50 
 
 80 
 55 
 
 35 
 
 25 
 
 60 
 40 
 
 45 
 30 
 
 The feeds in inches per minute recommended by the same company, 
 depend on the capacity of the machine and on the size of the teeth. 
 Thus, in a machine whose maximum capacity is for gears with teeth 
 of one diametral pitch in cast iron and of 1 1/4 diametral pitch in steel, 
 the feeds range from 2.3 ,in. per minute in cast iron for gears of 1 
 diametral pitch to 6.9 in. for gears of 6 diametral pitch, carbon steel 
 cutters being used. For high-speed steel cutters, the corresponding fig- 
 ures are 3.5 and 11.0 in. In steel, the feeds under the same conditions 
 are 1.9 in. and 4.5 in. per minute with carbon steel cutters and 2.8 in. 
 and 6.9 in. per minute with high-speed steel cutters. Likewise in a 
 machine whose maximum capacity is teeth of 4 diametral pitch for 
 cast-iron gears and 5 diametral pitch for steel gears, the feed given for 
 carbon steel cutters for gears of 4 diametral pitch is 2.6 in. per minute 
 in cast iron and 1.5 in. per minute in steel. For gears of 24 diametral 
 pitch the figures are for cast iron 7.6 in. per minute, and for steel 5.8 in. 
 per minute. Using high-speed steel cutters, the corresponding figures 
 are: 4 diametral pitch, cast iron 4.5 in. per minute; steel, 3.5 in. per 
 minute; 24 diametral pitch, cast iron 10 in. per minute; steel, 7.6 in. per 
 minute. These figures merely show the range of feeds that are possible 
 in gear cutting, and the tables furnished by the manufacturers of gear- 
 cutting machines should be consulted for the proper feeds for particular 
 cases. 
 
DRILLS AND DRILLING. 
 
 1285 
 
 DRILLS AND DRILLING. 
 
 r Constant for Finding Speeds of Drills. For finding the speed in 
 feet when the number of revolutions is given ; or the number of revolu- 
 tions, when the speed in feet is given. 
 
 Constant = 12 -=- (size of drill X 3.1416). 
 
 Number of revolutions = Constant X speed in feet. 
 
 Speed in feet = Number of revolutions -r- constant. 
 
 Size 
 Drill, 
 In. 
 
 Con- 
 stant. 
 
 Size 
 Drill, 
 In. 
 
 Con- 
 stant. 
 
 Size 
 Drill, 
 In. 
 
 Con- 
 stant. 
 
 Size 
 Drill. 
 In. 
 
 Con- 
 stant. 
 
 Size 
 Drill, 
 In. 
 
 Con- 
 stant. 
 
 1/8 
 
 30.55 
 
 3/4 
 
 5.09 
 
 3/8 
 
 2.78 
 
 2 
 
 .91 
 
 25/ g 
 
 .45 
 
 3/16 
 
 20.38 
 
 13/16 
 
 4.70 
 
 7/16 
 
 2.66 
 
 21/16 
 
 .85 
 
 2 H/16 
 
 .42 
 
 1/4 
 
 15.28 
 
 7/8 
 
 4.36 
 
 1/2 
 
 2.55 
 
 21/8 
 
 .80 
 
 23/4 
 
 .39 
 
 5/16 
 
 12.22 
 
 15/16 
 
 4.07 
 
 9/16 
 
 2.44 
 
 23/i 6 
 
 .75 
 
 2 13/16 
 
 .36 
 
 3/8 
 
 10.19 
 
 
 3.82 
 
 5/8 
 
 2.35 
 
 21/4 
 
 .70 
 
 27/ 8 
 
 .33 
 
 7/16 
 
 8.73 
 
 1/16 
 
 3.59 
 
 H/16 
 
 2.26 
 
 25/16 
 
 .65 
 
 2 15/16 
 
 .30 
 
 1/2 
 
 7.64 
 
 1/8 
 
 3.39 
 
 3/4 
 
 2.18 
 
 23/8 
 
 .61 
 
 3 
 
 .27 
 
 9/16 
 
 6.79 
 
 3/16 
 
 3.22 
 
 13/16 
 
 2.11 
 
 27/16 
 
 .57 
 
 31/16 
 
 .25 
 
 i 5/8 
 
 6.11 
 
 
 3.06 
 
 7/8 
 
 2.04 
 
 21/2 
 
 .53 
 
 31/8 
 
 .22 
 
 H/16 
 
 5.56 
 
 5/16 
 
 2.91 
 
 15/16 
 
 1.97 
 
 29/16 
 
 .49 
 
 31/4 
 
 .18 
 
 The Cleveland Twist Drill Co., Cleveland, states (1915) that it is 
 
 safe to start carbon steel drills with a peripheral speed of 30 ft. per 
 minute in soft tool and machinery steel, 35 ft. per min. in cast iron, and 
 
 60 ft. per min. in brass. In all cases a feed of from 0.004 to 0.007 in. 
 per revolution should be used for drills 1/2 in. diam. and smaller, and of 
 from 0.005 to 0.015 in. per revolution for drills larger than J^ in. In 
 the case of high speed steel drills these fee\Js should not be changed, but 
 the peripheral speed may be increased from 2 to 2 1/2 times. The table 
 below is calculated on the basis of the speeds given above for carbon 
 steel drills, and on the basis of speeds 2 1/3 times higher for high-speed 
 drills. The running speed may be higher or lower than the starting 
 speed, and must be determined by good individual judgment for each 
 case. 
 
 Starting Speeds for Carbon and High-Speed Steel Drills in 
 Steel, Cast Iron and Brass, R. P. M. 
 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Brass. 
 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Brass. 
 
 Drill 
 
 
 
 
 
 
 
 Drill 
 
 
 > 
 
 
 
 
 
 Diam., 
 
 
 T3 
 
 d 
 
 d 
 
 H 
 
 
 Diam., 
 
 J* 
 
 'd 
 
 J* 
 
 "8 
 
 c 
 
 
 In. 
 
 
 
 -si 
 
 | 
 
 .d! 
 
 | 
 
 
 In. 
 
 
 A 0, 
 
 
 .di, 
 
 | 
 
 
 
 8 
 
 Jwo 
 
 
 
 tfS 
 
 rt 
 
 .MM 
 
 
 8 
 
 bcc/2 
 
 Sf 
 
 Sfw 
 
 
 SPoa 
 
 
 
 
 W 
 
 O 
 
 w 
 
 u 
 
 a 
 
 
 o 
 
 W 
 
 u 
 
 w 
 
 5 
 
 a 
 
 1/16 
 
 1833 
 
 4278 
 
 2139 
 
 4991 
 
 3667 
 
 
 H/8 
 
 102 
 
 238 
 
 119 
 
 278 
 
 204 
 
 475 
 
 1/8 
 
 917 
 
 2139 
 
 1070 
 
 2496 
 
 1833 
 
 4278 
 
 H/4 
 
 92 
 
 214 
 
 107 
 
 249 
 
 183 
 
 428 
 
 3/16 
 
 611 
 
 1426 
 
 713 
 
 1664 
 
 1222 
 
 2852 
 
 13/8 
 
 83 
 
 194 
 
 97 
 
 227 
 
 167 
 
 389 
 
 1/4 
 
 458 
 
 1070 
 
 535 
 
 1248 
 
 917 
 
 2139 
 
 H/2 
 
 76 
 
 178 
 
 89 
 
 208 
 
 153 
 
 357 
 
 5/16 
 
 367 
 
 856 
 
 428 
 
 998 
 
 733 
 
 1711 
 
 15/8 
 
 70 
 
 165 
 
 82 
 
 192 
 
 141 
 
 329 
 
 3/8 
 
 306 
 
 713 
 
 357 
 
 832 
 
 611 
 
 1426 
 
 13/4 
 
 65 
 
 153 
 
 76 
 
 178 
 
 131 
 
 306 
 
 7/16 
 
 262 
 
 611 
 
 306 
 
 714 
 
 524 
 
 1222 
 
 17/8 
 
 61 
 
 143 
 
 71 
 
 166 
 
 122 
 
 285 
 
 1/2 
 
 229 
 
 535 
 
 263 
 
 614 
 
 458 
 
 1070 
 
 2 
 
 57 
 
 134 
 
 67 
 
 156 
 
 115 
 
 267 
 
 5/8 
 
 183 
 
 428 
 
 215 
 
 500 
 
 367 
 
 856 
 
 2V4 
 
 51 
 
 119 
 
 60 
 
 139 
 
 102 
 
 238 
 
 3/4 
 
 153 
 
 357 
 
 178 
 
 415 
 
 306 
 
 713 
 
 21/2 
 
 46 
 
 107 
 
 54 
 
 125 
 
 92 
 
 214 
 
 7/8 
 
 131 
 
 306 
 
 153 
 
 357 
 
 262 
 
 611 
 
 23/4 
 
 42 
 
 97 
 
 49 
 
 114 
 
 83 
 
 194 
 
 1 
 
 115 
 
 267 
 
 134 
 
 312 
 
 229 
 
 535 
 
 3 
 
 38 
 
 89 
 
 45 
 
 104 
 
 76 
 
 178 
 
 A drill with a tendency to wear away on the outside is running too fast; 
 if it breaks or chips on the cutting edges it has too much feed. 
 
 Forms of Drills. The common form of twist drill is a cylinder with 
 two spiral flutes milled in it. Another type, for heavy duty, consists 
 of a twisted bar of flat steel. The angle that the cutting edges makes 
 with the axis of the drill has been fixed at about 59. A decrease 
 in this angle decreases the pressure required for feeding the drill, but 
 increases the power required to turn it. The cutting edge of a spotting 
 
1286 
 
 THE MACHINE-SHOP. 
 
 drill should make an angle of about 50 with the axis of the drill. 
 The clearance angle, that is, the angle between the surface back of the 
 cutting edge and a plane perpendicular to the axis of the drill, ranges 
 from 12 to 15, the angle increasing slightly toward the center. In 
 general, the small clearance is best for hard metals and the large 
 clearance for soft metals. 
 
 Drilling Compounds. The following drilling compounds or lubri- 
 cants are recommended when drilling the materials given below : 
 
 Steel (hard) kerosene, turpentine, 
 
 soda water. 
 
 Steel (soft) soda water, lard oil. 
 Iron (wrought) soda water, lard 
 
 oil. 
 
 Iron (malleable) soda water. 
 Iron (cast) none or air blast. 
 Brass paraffine oil. 
 Aluminum soda water, kerosene. 
 
 Warming the lubricant before applying it to high-speed drills is 
 recommended, and precautions should be taken against suddenly chilling 
 high-speed drills by the lubricant after they have become heated. 
 
 Twist Drill and Steel Wire Gages. Three standards of gages for 
 twist drills and steel wire are in use the Manufacturers' Standard, 
 used by the Morse Twist Drill Co., Brown & Sharpe, and other manu- 
 facturers, the Stubs gage, and that of the Standard Tool Co. The 
 Stubs and Manufacturers' gages are given in the table on page 30. 
 The Standard Tool Co. gage agrees with the Manufacturers' gage for 
 sizes from Nos. 1 to 60, inclusive, and with the Stubs gage for sizes 
 from Nos. 61 to 80. In addition it has additional H sizes interpolated 
 at Nos. 601/2, 681/2, 69 1/2, 71 1/2. 731/2, 741/2, 781/2, and 791/2. 
 
 Power Required to Drive High-Speed Drills. H. M. Norris, me- 
 chanical engineer of the Cincinnnti-Bickford Tool Co., found (1914) 
 that the power absorbed by a 6-foot, high-speed, high-power, plain 
 radial drill fitted with a variable speed motor, in driving drills in 
 machine steel under a stream of water, varied in accordance with the 
 formula: 
 
 H.P. = 0.152 (R + 2.1) di.s/o.74 [ r - / + 6.8 
 
 L \ d 
 
 R = ratio between speed of the intake shaft and speed of the spindle; 
 d = diameter of drill, in.; /= feed in thousandths of an inch per revolu- 
 tion; r = rev. per min. 
 
 The values deduced from this formula are given in the table, p. 1287; 
 the figures 1, 2, and 4 in the column "Ratio R" represent the ratios of 
 1 to 1, 1 to 2, and 1 to 4 respectively. The table also gives the results 
 obtained in drilling medium cast-iron, but these, at this writing, have 
 not been reduced to a formula. 
 
 The American Tool Works Co., Cincinnati, has furnished the 
 author with the tests given in the table below, made in 1912, showing 
 the power required to drive drills in a 6-foot plain triple-geared radial 
 drill made by that company. This table shows the results obtained 
 with speeds and feeds higher than those given by Mr. Norris. 
 
 Power Required to Drive Drills. (Amer. Tool Works Co., 1912.) 
 
 Size 
 of 
 Drill, 
 In. 
 
 Cast Iron. 
 
 Steel. 
 
 Speed. 
 
 Feed. 
 
 Horse- 
 power 
 
 Speed. 
 
 Feed. 
 
 Horse- 
 power. 
 
 Rev. 
 per 
 Min. 
 
 Ft. 
 Min. 
 
 Per 
 Rev., 
 In. 
 
 In. 
 per 
 Min. 
 
 Rev. 
 per 
 Min. 
 
 Ft. 
 per 
 Min. 
 
 Per 
 
 Rev., 
 In. 
 
 In. 
 per 
 Min. 
 
 U/4 
 
 H/2 
 
 yA 
 
 f, 
 
 430 
 430 
 430 
 430 
 297 
 202 
 178 
 143 
 
 111.25 
 140 
 157 
 197 
 156 
 119 
 116.5 
 112 
 
 0.049 
 .049 
 .049 
 .049 
 .049 
 .036 
 .036 
 .036 
 
 21.07 
 21.07 
 21.07 
 21.07 
 14.56 
 7.27 
 6.40 
 5.14 
 
 8.26 
 11.65 
 18.65 
 19.75 
 19.79 
 14.82 
 11.24 
 14.31 
 
 335 
 258 
 229 
 178 
 143 
 143 
 143 
 47.5 
 
 88 
 84.5 
 90 
 81.5 
 75 
 84.2 
 93.6 
 37.2 
 
 0.036 
 .026 
 .018 
 .018 
 .018 
 .018 
 .013 
 .026 
 
 12.06 
 6.70 
 4.12 
 3.20 
 2.57 
 2.57 
 1.86 
 1.21 
 
 13.50 
 10.43 
 14.86 
 9.91 
 12.32 
 15.06 
 13.51 
 12.46 
 
DRILLS AND DRILLING. 
 
 1287 
 
 Power Required for Drilling Cast Iron and Steel. (H. M. N orris, 1915.) 
 
 
 
 
 
 Cast Iron. 
 
 Machinery Steel. 
 
 c 
 
 .S 
 
 
 
 0.020 in. 
 
 0.030 in. 
 
 0.040 in. 
 
 0.012 in. 
 
 0.016 in. 
 
 0.020 in. 
 
 i9 
 
 r 
 
 Ifc 
 
 c 
 
 
 Feed. 
 
 Feed. 
 
 Feed. 
 
 Feed. 
 
 Feed. 
 
 Feed. 
 
 .2 
 
 If 
 
 ' 
 & 
 
 &5 
 
 M 
 
 0) 
 
 
 M. 
 
 si 
 
 M 
 
 
 
 ft-S 
 
 fc 
 
 Jd 
 
 ft-~ 
 
 | 
 
 ** . 
 
 fe 
 
 fc 
 
 .5 
 
 ft 
 
 
 
 g g 
 
 w ft 
 
 "5 G 
 
 < ft 
 
 5 G 
 
 w p, 
 
 "5 c 
 
 03 ft 
 
 3 c 
 
 M ft 
 
 5 c 
 
 tl 
 
 3 
 
 -p 
 
 i 
 
 '-P 
 
 ft'3 
 
 g 
 
 ft'3 
 
 O 
 
 8*1 
 
 o 
 
 1 
 
 i 
 
 fa 
 
 
 
 8*1 
 
 
 
 Q 
 
 O 
 
 & 
 
 tf 
 
 Q 
 
 w 
 
 Q 
 
 w 
 
 Q 
 
 W 
 
 Q 
 
 w 
 
 Q 
 
 W 
 
 Q 
 
 W 
 
 3/4 
 
 60 
 
 306 
 
 
 6.12 
 
 2.76 
 
 9.18 
 
 3.52 
 
 12.24 
 
 4.20 
 
 3.67 
 
 2.84 
 
 4.90 
 
 3.53 
 
 6.12 
 
 4.15 
 
 3/4 
 
 70 
 
 357 
 
 
 7.14 
 
 3.36 
 
 10.71 
 
 4.29 
 
 14.28 
 
 5.10 
 
 4.28 
 
 3.49 
 
 5.72 
 
 4.32 
 
 7.14 
 
 5.09 
 
 3/4 
 
 80 
 
 408 
 
 
 8.16 
 
 3.98 
 
 12.24 
 
 5.08 
 
 16.32 
 
 6.04 
 
 4.90 
 
 4.12 
 
 6.53 
 
 5.10 
 
 8.16 
 
 6.02 
 
 3/4 
 
 90 
 
 459 
 
 
 9.18 
 
 4.60 
 
 13.77 
 
 5.86 
 
 18.35 
 
 6.96 
 
 5.51 
 
 4.76 
 
 7.34 
 
 5.89 
 
 9.18 
 
 6.95 
 
 3/4 
 
 100 
 
 509 
 
 
 10.18 
 
 5.21 
 
 15.27 
 
 6.64 
 
 20.36 
 
 7.89 
 
 6.11 
 
 5.40 
 
 8.14 
 
 6.68 
 
 10.18 
 
 7.88 
 
 
 60 
 
 229 
 
 2 
 
 4.58 
 
 2.88 
 
 6.87 
 
 3.67 
 
 9.16 
 
 4.36 
 
 2.75 
 
 4.01 
 
 3.66 
 
 4.96 
 
 4.58 
 
 5.85 
 
 
 70 
 
 267 
 
 
 5.34 
 
 3.09 
 
 8.00 
 
 3.94 
 
 10.67 
 
 4.68 
 
 3.21 
 
 3.72 
 
 4.27 
 
 4.60 
 
 5.34 
 
 5.43 
 
 
 80 
 
 306 
 
 
 6.12 
 
 3.66 
 
 9.18 
 
 4.66 12.2-4 
 
 5.54 
 
 3.67 
 
 4.394.89 
 
 5.44 
 
 6.12 
 
 6.42 
 
 
 90 
 
 344 
 
 6.88 
 
 4.22 
 
 10.32 
 
 5.38 13.76 
 
 6.39 
 
 4.13 
 
 5.165.50 
 
 6.39 
 
 6.88 
 
 7.54 
 
 
 100 
 
 382' 
 
 7.64 
 
 4.79 
 
 11.46 
 
 6.11 
 
 15.27 
 
 7.26 
 
 4.59 
 
 5.79 
 
 6.11 
 
 7.17 
 
 7.64 
 
 8.46 
 
 U/4 
 
 60 
 
 183 1 2 
 
 3.66 
 
 3.10 
 
 5.49 
 
 3.95 
 
 7.32 
 
 4.70 
 
 2.19 
 
 4.21 
 
 2.93 
 
 5.21 
 
 3.66 
 
 6.15 
 
 11/4 
 
 70 214 2 4.28 
 
 3.80 
 
 6.42 
 
 4.84 
 
 8.56 5.75|2.57 
 
 5.173.42 
 
 6.40 
 
 4.28 
 
 7.55 
 
 11/4 
 
 80 245 2 4.90 
 
 4.50 
 
 7.36 
 
 5.74 
 
 9.80 6.822.94 
 
 5.96j3.92 
 
 7.57 
 
 4.90 
 
 8.93 
 
 11/4 
 
 90 
 
 275 
 
 5.48 
 
 3.95 
 
 8.22 
 
 5.04 11.00 5.993.29 
 
 5.3514.38 
 
 6.62 
 
 5.48 
 
 7.81 
 
 U/4 
 
 100 
 
 306 
 
 
 6.12 
 
 4.49 
 
 9.18 
 
 5.73 
 
 12.24 
 
 6.81 
 
 3.67 
 
 6.08 
 
 4.89 
 
 7.52 
 
 6.12 
 
 8.87 
 
 U/2 
 
 60 
 
 153 
 
 2 
 
 3.12 
 
 3.27 
 
 4.59 
 
 4.17 
 
 6.12 
 
 4.96 
 
 1.84 
 
 4.36 
 
 2.45 
 
 5.39 
 
 3.12 
 
 6.36 
 
 U/2 
 
 70 178 
 
 2 
 
 3.561 4.02 
 
 5.34 
 
 5.12 7.02 
 
 6.0812.14 
 
 5.352.85 
 
 6.62 
 
 3.56 
 
 7.81 
 
 U/2 
 
 80 204 2 4.08 4.77 6.06 
 
 6.08 8.16 
 
 7.232.45 
 
 6.35 3. 26| 7.86 
 
 4.08 
 
 9.27 
 
 11/2 
 
 90 230 2 4.60 5.51 
 
 6.90 
 
 7.03 9.20 
 
 8.362.76 
 
 7.353.68J 9.10 
 
 4.60 
 
 10.73 
 
 U/2 100 
 
 254 
 
 2 
 
 5.04 6.27 
 
 7.62 
 
 7.99 
 
 10.16 
 
 9.50 
 
 3.05 
 
 8.34 
 
 4.07 
 
 10.32 
 
 5.04 
 
 12.17 
 
 13/4 
 
 60 
 
 131 
 
 2 
 
 2.62 3.42 
 
 3.93 
 
 4.36 
 
 5.24 
 
 5.18 
 
 .57 
 
 4.48 
 
 2.10 
 
 5.55 
 
 2.62 
 
 6.55 
 
 13/4 
 
 70 
 
 153 
 
 2 
 
 3.06 4.2li 4.59 
 
 5.37 
 
 6.12 
 
 6.38 
 
 .84 
 
 5.532.45 
 
 6.84 
 
 3.06 
 
 8.07 
 
 13/4 80 175 2 
 
 3.50 5.00! 5.25 
 
 6.38 
 
 7.00 
 
 7.58i2.10 
 
 6.562.80 
 
 8.12 
 
 3.50 
 
 9.58 
 
 13/4 ! 90 196 2 2.921 5.80 5.88 
 
 7.39 
 
 7.84 8.78 : 2.35 
 
 7.602.14 
 
 9.41 
 
 3.92 11.10 
 
 13/4 
 
 100 
 
 218 
 
 2 
 
 4.36 
 
 6.59 
 
 6.52 
 
 8.40 9.12 
 
 9.98 
 
 2.62 
 
 8.633.49 
 
 10.68 
 
 4.36 
 
 12.60 
 
 2 
 
 60 
 
 115 
 
 4 
 
 2.30 
 
 4.87 
 
 3.45 
 
 6.22 4.60 
 
 7.39 
 
 .38 
 
 6.82 1.84 
 
 8.44 
 
 2.30 
 
 9.96 
 
 2 
 
 70 
 
 134 
 
 
 2.68 
 
 4.38 
 
 4.04 
 
 5.59 5.36 
 
 6.64 .61 
 
 5.662.14 
 
 7.00 
 
 2.68 
 
 8.26 
 
 2 
 
 80 
 
 153 
 
 2 
 
 3.06 
 
 5.21 
 
 4.59 
 
 6.65 6.12 
 
 7.90 
 
 .84 
 
 6.73 
 
 2.45 
 
 8.33 
 
 3.06 
 
 9.83 
 
 2 
 
 90 
 
 172 
 
 2 3.44 
 
 6.04 
 
 5.16 
 
 7.71 6.88 
 
 9.16 
 
 2.06 
 
 7.81 
 
 2.75 
 
 9.66 
 
 3.44 
 
 11.40 
 
 2 
 
 100 
 
 191 
 
 2 
 
 3.82 
 
 6.87 
 
 5.73 
 
 8.77 
 
 7.64 
 
 10.32 
 
 2.29 
 
 8.87 
 
 3.06 
 
 10.98 
 
 3.82 
 
 12.95 
 
 21/4 
 
 60 
 
 102 
 
 4 
 
 2.04 
 
 5.18 
 
 3.06 
 
 6.60 
 
 4.08 
 
 7.84 
 
 .22 
 
 6.95 
 
 1.63 
 
 8.60 
 
 2.04 
 
 10.14 
 
 21/4 
 
 70 
 
 119 
 
 4 
 
 2.38 
 
 6.40 
 
 3.57 
 
 8.16 4.76 
 
 9.70 
 
 .43 
 
 8.60 
 
 1.90 
 
 10.64 
 
 2.38 
 
 12.55 
 
 21/4 
 
 80 
 
 136 
 
 2 
 
 2.68 
 
 5.40 
 
 4.08 
 
 6.88 5.44 
 
 8.18 
 
 .63 
 
 6.88 
 
 2.18 
 
 8.52 
 
 2.68 
 
 10.05 
 
 21/4 
 
 90 
 
 153 
 
 2 
 
 3.06 
 
 6.27 
 
 4.59 
 
 7.99 6.12 
 
 9.50 
 
 .84 
 
 7.98 
 
 2.45 
 
 9.88 
 
 3.06 
 
 11.65 
 
 21/4 
 
 100 
 
 170 
 
 
 3.40 
 
 7.13 
 
 5.10 
 
 9.09 
 
 6.80 
 
 10.80 
 
 2.04 
 
 90.9 
 
 2.72 
 
 11.25 
 
 3.40 
 
 13.27 
 
 21/2 
 
 60 
 
 92 
 
 4 
 
 1.83 
 
 5.46 
 
 2.75 
 
 6.96 
 
 3.67 
 
 8.27 
 
 .10 
 
 7.06 
 
 1.47 
 
 8.74 
 
 1.83 
 
 10.31 
 
 21/2 
 
 70 
 
 107 4 
 
 2.14 6.76 
 
 3.21 
 
 8.63 4.28 
 
 10.26 
 
 .28 
 
 8.75 
 
 1.71 
 
 10.83 
 
 2.14 
 
 12.77 
 
 2V >' 80 
 
 122 4 
 
 2.44 8.06 
 
 3.66 
 
 10.29 
 
 4.88 
 
 12.23 
 
 .46 
 
 10.43 
 
 1.95 
 
 12.91 
 
 2.44 
 
 15.23 
 
 21/2 90 
 
 138 2 2.76 
 
 6.46 
 
 4.14 
 
 8.24 
 
 5.52 
 
 9.79 .66 
 
 8.14 
 
 2.21 
 
 10.08 
 
 2.76 
 
 11.89 
 
 21/2 100 
 
 153 
 
 2 3.06 
 
 7.36 
 
 4.59 
 
 9.39 
 
 6.12 
 
 11.16 
 
 .84 
 
 9.28 
 
 2.45 
 
 11.49 
 
 3.06 
 
 13.55 
 
 23/ 4 60 
 
 83 
 
 4 1.67 
 
 5.73 
 
 2.50 
 
 7.30 
 
 3.34 
 
 8.68 
 
 .00 
 
 7.15 
 
 1.33 
 
 8.85 
 
 1.67 
 
 10.44 
 
 23/4 70 97 4 1.94 7.11 2.92 9.06 
 
 3.89 
 
 10.77 .17 
 
 8.87 
 
 1.55 
 
 10.98 
 
 1.94 
 
 12.95 
 
 23/4 
 
 80 111 4 2.22 
 
 8.49 3.3310.83 
 
 4.44 
 
 12.87 
 
 .33 
 
 10.62 
 
 1.78 
 
 13.14 
 
 2.22 
 
 15.50 
 
 23/4 
 
 90 125 4 2.50 9.90 3.75 
 
 12.62 
 
 5.00 
 
 15.00 
 
 .50 
 
 12.34 
 
 2.00 
 
 15.27 
 
 2.50 
 
 18.00 
 
 23/4 100 
 
 139 
 
 2 
 
 2.78 
 
 7.59 
 
 4.17 
 
 9:68 
 
 5.56 
 
 11.50 
 
 .67 
 
 9.46 
 
 2.23 
 
 11.71 
 
 2.78 
 
 13.81 
 
 3 
 
 60 
 
 76 
 
 4 
 
 1.53 
 
 5.96 
 
 2.29 
 
 7.60 
 
 3.06 9.03 
 
 0.92 
 
 7.22 
 
 1.22 
 
 8.94 
 
 1.53 
 
 10.55 
 
 3 
 
 70 
 
 89 
 
 4 1.78 7.42 
 
 2.67 
 
 9.46 
 
 3.56 
 
 11.25 
 
 .07 
 
 8.98)1.43 
 
 11.12 
 
 1.78 
 
 13.12 
 
 3 
 
 80 
 
 102 
 
 4 2.04 
 
 8.88 
 
 3.06 
 
 11.32 
 
 4.08 
 
 13.45 
 
 .27 
 
 10.75 1.63 
 
 13.31 
 
 2.04 
 
 15.71 
 
 3 
 
 90 
 
 115 
 
 4 
 
 2.30 
 
 10.33 
 
 3.45 
 
 13.17 
 
 4.60 
 
 15. 6511.38 
 
 12.52 
 
 1.84 
 
 15.48 
 
 2.30 
 
 18.26 
 
 3 
 
 100 
 
 127 
 
 4 
 
 2.54il1.75 
 
 3.81 
 
 15.00 
 
 5.08 
 
 17.82'l.52 
 
 14.26 
 
 2.03 
 
 17.65 
 
 2.54 
 
 20.82 
 
1288 
 
 THE MACHINE-SHOP. 
 
 Feeds for Drills. According to Mr. Norris, the rate at which a drill 
 may be advanced per revolution depends upon the toughness of the 
 material to be drilled, the ability of the machine to resist thrust without 
 forfeiture of alignment and upon the knowledge that is exercised in the 
 grinding of the drill the size of its included angle, the width of its 
 chisel point, and the keenness and evenness of its cutting edges, all being 
 deciding factors. Were it not for the weakening effect on the drill it 
 could be said that the stiff er the machine, the less the included angle; 
 the narrower the chisel point, the smaller the degree of the spiral; the 
 greater the uniformity of the cutting lips and the more efficacious the 
 lubricant in minimizing the frictionai resistance of the chips, the coarser 
 becomes the feed it is permissible to use. But, inasmuch as the 
 durability of the drill must not be impaired, the advantage obtainable 
 through the application of these axioms has its limitations. The 
 keenness of edges needed to attain maximum efficiency in cutting cast- 
 iron disqualifies for work in steel a drill suitable for use in cast-iron. 
 The highest rate of feed at which drills of from 3/ 8 to 3 in. diam. may 
 be operated in steel appears to be about 0.060 in. per revolution, but 
 the employment of such feeds increases, rather than decreases the cost of 
 work. The feeds provided in the product of the Cincinnati-Bickford 
 Tool Co. range from 0.006 in. to 0.040 in. per revolution, which, under 
 favorable conditions, may be utilized as follows: 
 
 CAST IRON 
 
 STEEL 
 
 Hard . 006 to . 010 in. 
 
 Medium 0.0X2 to 0.018 in. 
 
 Soft 0. 020 to . 028 in. 
 
 Hard. 
 
 0.015 to 0.020 in. 
 
 Medium 0.020 to 0.030 in. 
 
 Soft 0.030 to 0.040 in. 
 
 Speed of Drills. Mr. Norris says further that while an occasional 
 drill is found that will withstand for days a cutting speed of 150 ft. 
 per minute, in either cast-iron or steel (the latter under a lubricant), 
 it is rarely expedient to drive any but very small ones faster than 100 
 ft. per mih. Operating drills at an excessive speed is an expensive fad. 
 It is more economical to err in the other direction. The most satis- 
 factory results have been obtained at a cutting speed of 80 ft. per min. 
 
 in cast-iron and ^ + 76 ft. in steel. This formula will decrease 
 
 the cutting speed from 100 ft. per min. for a V^in. drill to 80 ft. for a 
 3-in. drill. The reason for this reduction is that a stream of liquid 
 sufficient to keep a small drill cool is insufficient to prevent overheating 
 in a large one. 
 
 In order to facilitate the use of the formulae for horse-power there 
 
 KO O 
 
 is given in the following table the deduced values for /- 74 , d 1 - 25 , - 
 
 + 6.8 and ^ + 76. 
 
 Values of f*-, 
 
 co 9 19 
 
 1.25, 2. + 6.8 and of = + 76. 
 
 * 
 
 
 I. 
 
 
 oo 
 
 
 A 
 
 
 L 
 
 
 00 
 
 J! 
 
 3 
 
 
 
 fl^C3 
 
 
 
 
 * 
 
 
 c w 
 
 
 
 
 
 I 
 
 ^ 
 
 J| 
 
 % 
 
 N 1 
 
 2 Its 
 
 I 
 
 2 
 
 I" 
 
 3 
 
 "13 
 
 *\. 
 
 
 - 
 
 0.008 
 
 0.02807 
 
 1/2 
 
 0.421 
 
 111.2 
 
 100.0 
 
 0.022 
 
 0.05934 
 
 17/8 
 
 2.194 
 
 34.6 
 
 82 
 
 .4 
 
 .009 
 
 .03063 
 
 5/8 
 
 .556 
 
 90.3 
 
 95.2 
 
 .024 
 
 .06329 
 
 2 
 
 2.378 
 
 32.9 
 
 82 
 
 .0 
 
 .010 
 
 .03312 
 
 3/4 
 
 .698 
 
 76.4 
 
 92.0 
 
 .026 
 
 .06715 
 
 21/8 
 
 2.566 
 
 31.4 
 
 81 
 
 .6 
 
 .011 
 
 .03553 
 
 7/8 
 
 .846 
 
 66.6 
 
 89.7 
 
 .028 
 
 .07094 
 
 21/4 
 
 2.756 
 
 30.0 
 
 81 
 
 .3 
 
 .012 
 
 .03789 
 
 
 1.000 
 
 59.0 
 
 88.0 
 
 .030 
 
 .07466 
 
 23/8 
 
 2.948 
 
 28.8 
 
 81 
 
 .0 
 
 .013 
 
 .04021 
 
 11/8 
 
 .158 
 
 53.2 
 
 86.9 
 
 .032 
 
 .07831 
 
 21/2 
 
 3.144 
 
 27.7 
 
 80 
 
 .0 
 
 .014 
 
 .04248 
 
 H/4 
 
 .322 
 
 48.5 
 
 85.6 
 
 .034 
 
 .08190 
 
 25/8 
 
 3.342 
 
 26.7 
 
 80 
 
 .6 
 
 .015 
 
 .04470 
 
 13/8 
 
 .489 
 
 44.8 
 
 84.7 
 
 .036 
 
 .08544 
 
 23/4 
 
 3.541 
 
 25.8 
 
 80 
 
 .4 
 
 .016 
 
 .04689 
 
 11/2 
 
 .660 
 
 41.6 
 
 84.0 
 
 .038 
 
 .08894 
 
 27/8 
 
 3.741 
 
 25.0 
 
 80 
 
 .2 
 
 .018 
 
 .05115 
 
 15/8 
 
 .833 
 
 38.9 
 
 83.4 
 
 .040 
 
 .09237 
 
 3 
 
 3.948 
 
 24.2 
 
 80 
 
 .0 
 
 .020 
 
 .05530 
 
 13/4 
 
 2.013 
 
 36.6 
 
 82.9 
 
 
 
 
 
 
 
 ^. 
 
DRILLS AND DRILLING. 
 
 1289 
 
 Extreme Results with Drills. The Cleveland Twist Drill Co. 
 furnishes the following table of results of drilling tests made at the 
 convention of Railway Master Mechanics' Association at Atlantic City, 
 N. J., June, 1911. The object of the tests was to demonstrate good 
 shop practice, drilling being done at speeds and feeds considered 
 economical under average shop conditions, and also to show what were 
 the ultimate possibilities of drills and machines. The drills used were 
 flat twisted drills, and the ordinary milled drill. The record per- 
 formance for high-speed drilling is test No. 4, in which a 1 1/4 in. drill re- 
 peatedly drilled through a casting at 57 1/2 in. per minute. In the tests 
 to demonstrate good shop conditions, the drill in test No. 17 drilled 68 
 holes, removing 1418 cu. in. of metal without being reground, and was 
 in good condition at the close of the test. The Cleveland Twist Drill 
 Co. does not recommend the high speeds and heavy feeds attained as 
 economical shop practice, but points out that the results can be duplicat- 
 ed by carefully established ideal conditions of absolute rigidity in the 
 machine, solid clamping of the work, perfect grinding of the drill and 
 expert handling. 
 
 Record Performances of High-Speed Drills. 
 
 No. 
 
 Sizes of 
 Drill, 
 In. 
 
 Material 
 
 R.P.M. 
 
 Feed 
 Rev. 
 
 Inches 
 Drilled 
 per Min. 
 
 Rev., 
 Speed in 
 Feet 
 per Min. 
 
 Cu. In. 
 Metal 
 Removed 
 per Min. 
 
 j 
 
 H/4 
 
 
 500 
 
 0.050 
 
 25 
 
 163.6 
 
 30.68 
 
 2 
 
 HA 
 
 o 
 
 325 
 
 0.100 
 
 321/2 
 
 106 
 
 39.88 
 
 3 
 
 H/4 
 
 jgj 
 
 475 
 
 0.100 
 
 471/2 
 
 155 
 
 58.29 
 
 4 
 
 H/4 
 
 H 
 
 575 
 
 0.100 
 
 571/2 
 
 188 
 
 70.56 
 
 5 
 
 U/2 
 
 ^ 
 
 300 
 
 0.030 
 
 9 
 
 117 
 
 15.90 
 
 6 
 
 U/2 
 
 rt 
 
 325 
 
 0.100 
 
 321/2 
 
 127.6 
 
 . 57.43 
 
 7 
 
 11/2 
 
 
 335 
 
 0.100 
 
 331/2 
 
 131.5 
 
 59.19 
 
 8 
 
 U/2 
 
 
 
 355 
 
 0.100 
 
 351/2 
 
 139.4 
 
 62.73 
 
 9 
 
 13/4 
 
 I I 
 
 235 
 
 0.100 
 
 231/2 
 
 107.6 
 
 56.52 
 
 10 
 
 13/4 
 
 M 
 
 350 
 
 0.100 
 
 35 
 
 160 
 
 84.19 
 
 11 
 
 25/16 
 
 a 
 
 190 
 
 0.050 
 
 91/2 
 
 115 
 
 39.90 
 
 12 
 
 3 
 
 o 
 
 120 
 
 0.100 
 
 12 
 
 94 
 
 84.82 
 
 13 
 
 H/4 
 
 
 350 
 
 0.030 
 
 101/2 
 
 113.7 
 
 12.88 
 
 14 
 
 15/8 
 
 
 
 225 
 
 0.040 
 
 9 
 
 94.8 
 
 18.66 
 
 15 
 
 25/16 
 
 41 
 
 165 
 
 0.020 
 
 31/4 
 
 100 
 
 13.86 
 
 16 
 
 25/16 
 
 C/2 O 
 
 200 
 
 0.020 
 
 4 
 
 121 
 
 16.80 
 
 17 
 
 21/2* 
 
 bl 
 
 150 
 
 0.015 
 
 21/4 
 
 98 
 
 11.04 
 
 18 
 
 21/2* 
 
 5^ 
 
 150 
 
 0.040 
 
 6 
 
 98 
 
 29.45 
 
 19 
 
 21/2* 
 
 
 175 
 
 0.040 
 
 7 
 
 114.5 
 
 34.36 
 
 20 
 
 13/4 
 
 o^. 
 
 275 
 
 0.030 
 
 81/4 
 
 125 
 
 19.84 
 
 21 
 
 3 
 
 M| 
 
 150 
 
 0.030 
 
 41/2 
 
 117.8 
 
 31.81 
 
 22 
 
 31/4 
 
 
 150 
 
 O.C30 
 
 41/2 
 
 127 
 
 37.33 
 
 * Milled drills; all other drills are flat twisted drills. 
 
 Experiments on Twist Drills. An extensive series of experiments 
 on the forces acting on twist drills of high-speed steel when operating 
 on cast-iron and steel is reported by Dempster Smith and A. Poliakoff, 
 in Proc. Inst. M. &., 1909. Abstracted in Am. Mach., May, 1909, and 
 Indust. Eng., May, 1909. Approximate equations derived from the 
 first set of experiments are as follows: 
 
 Torque in pounds-feet, 1= (1800 t+ 9) d\ for medium cast-iron; 
 T = (3200 t + 20)d 2 , for medium steel. End thrust, lb., P = 115,000 
 t - 200, for medium cast-iron; P = 160,000(d - 0.5)- 1000, for 
 medium steel; d = diam., t = feed per revolution of drill, both in inches. 
 The steel was of medium hardness, 0.29 C, 0.625 Mn. 
 
 The end thrust in enlarging holes in medium steel from one size to 
 a larger was as follows: 3/ 4 in. to 1 in., P = 15,200 t + 60; 1 in. to 1 1/2 in., 
 P = 25,500 t + ; 3/4 in. to 1 1/2 in., P = 30,000 t + 200. 
 
 A second series of experiments with soft cast-iron of C.C., 0.2; G.C., 
 29; Si, 1,41; Mn, 0.68; S, 0.035; P, 1.48, and medium steel of C, 0.31; 
 
1290 
 
 THE MACHINE-SHOPo 
 
 Si, 0.07; Mn, 0.50; S, 0.018; P, 0.033; tensile strength, 72,600 Ib. per 
 sq. in., gave results from which were derived the following approximate 
 equations : 
 Torque, lb.-ft., T = 740 di.8#.7, or 10 d2 + 100 (14 d2 + 3) for cast iron, 
 
 T = 1640 di-8^o.7, or 28 d2(i + 100 t) for medium steel, 
 End thrust, Ib. P = 35,500 do.? #.75, O r 200 d + 10,000 1 for cast iron, 
 
 P = 35,500 do.7 0.3, or 750 d + 1000 t (75 d + 50) for 
 
 medium steel, 
 and for different sizes of drill the following equations: 
 
 Drill. 
 
 3 /4 
 
 1 
 
 IVa 
 
 Cast iron T = 
 
 5 + 1.1001 
 
 10 + 1,750 t 
 
 25 +3,700 t 
 
 Cast iron P = . 
 
 1 25 +82, 000 t 
 
 200 +89 000 t 
 
 350 + 103 000 t 
 
 Steel T = 
 
 7 5 +3,350 
 
 17 5 -f 4,400 
 
 40 -f-9,000 t 
 
 Steel P = 
 
 550 + 109 ,000 t 
 
 750 + 131, 000 t 
 
 1.250 + 1 62,000 t 
 
 
 
 
 
 Drill. 
 
 2 
 
 2V2 
 
 3 
 
 Cast iron T = 
 Cast iron P =* 
 
 40 +5, 900 t 
 500 + 1 10,000 / 
 
 60 +8,800 t 
 600 + 1 26,000 t 
 
 90 + 1 2,900 / 
 850 + 140,000 t 
 
 Steel T = 
 
 75 +1 2,500 / 
 
 112 5 + 19,050 t 
 
 175 +26,250 t 
 
 Steel P = 
 
 1. 500 + 181, 250 t 
 
 1, 725 +224.375* 
 
 2,350 +280,000 t 
 
 The tests above referred to were made'without lubricants. When 
 lubricants were used in drilling steel the average torque varied from 
 72% with 1/400 in. feed to 92% with 1/35 in. feed of that obtained when 
 operating dry. The thrust for soft, medium and hard steel is 26%, 
 37%, and 12% respectively less than when operating dry, no marked 
 difference being found, as in the torque, with different feeds. The horse- 
 power varies as 2-07 and as do.8 for a given drill and speed. The torque 
 and horse-power when drilling medium steel is about 2.1 times that 
 required for cast iron with the same drill speed and feed. The horse- 
 power per cu. in. of metal removed is inversely proportional to dO-2 jo.3, 
 and is independent of the revolutions. 
 
 While the chisel point of the drill scarcely affects the torque it is ac- 
 countable for about 20 % of the thrust. Tests made with a preliminary 
 hole drilled before the main drill was used to enlarge the hole showed 
 that the work required to drill a hole where only one drill is used is 
 greater than that required to drill the hole in two operations, with drills 
 of different diameter. 
 
 For economy of power a drill with a larger point angle than 120 is to 
 be preferred, but the increased end thrust strains the machine in propor- 
 tion, and there is more danger of breaking the drill. 
 
 Cutting Speeds for Tapping and Threading. (Am. Mach., Aug. 3, 
 1911.) The National Machine Co., for tapping and threading, uses 
 speeds of 233 r.p.m. for sizes and holes up to 1/4 in. diameter, and 140 
 r.p.m. for sizes from 1/4 in. to 1/2 in. diameter, with a lubricant of 
 screw-cutting oil. Both the Bignall & Keeler Co. and the Standard 
 Engineering Co. recommend a cutting speed of 15 ft. per minute. 
 The former recommends lard oil as a lubricant. The practice of the 
 F. E. Wells Co. in tapping and the Landis Machine Co. in threading 
 in machines of the bolt cutter type is as follows: 
 
 Speeds for Tapping and Threading r. p. m. 
 
 Mate- 
 rial. 
 
 F. E. Wells. 
 
 Landis. 
 
 Mate- 
 rial. 
 
 F. E. Wells. 
 
 Landis. 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Steel. 
 
 Cast 
 Iron. 
 
 Lubri- 
 cant. 
 
 Oil. 
 
 Oil or 
 Soda 
 Comp. 
 
 Oil. 
 
 Petro- 
 leum. 
 
 Lubri- 
 cant. 
 
 Oil. 
 
 Oil or 
 Soda 
 Comp. 
 
 Oil. 
 
 Petro- 
 leum. 
 
 1/4 in. 
 
 3/8 " 
 1/2 " 
 /8 " 
 
 299 
 153 
 115 
 91 
 
 382 
 255 
 191 
 153 
 
 280 
 220 
 175 
 
 200 
 150 
 125 
 
 3/ 4 in. 
 
 !/*;; 
 
 76 
 
 127 
 
 140 
 115 
 75 
 6 
 
 100 
 85 
 55 
 45 
 
 
 
 
 
CASE-HARDENING. 1291 
 
 SAWING METALS. 
 
 Speeds and Feeds for Cold Sawing Metals. (Mach'y, Jan., 1914). 
 For sawing 0.30 carbon, open-hearth machine steel bars in a cold 
 sawing machine, a feed of 1 in. per minute and a peripheral speed of 
 approximately 45 ft. per minute was used. The bars were 5 in. diam- 
 eter, and an average of 145 were sawed with one sharpening of the 
 saw. For some classes of work a feed of 2 in. per minute can be used, 
 but 3/4 in. per minute is advisable for 0.30 carbon steel with the saw 
 in good condition. For tool steel and ajloy steel the best economy 
 will be obtained with a feed of 1/2 in. per minute and a surface speed 
 of 30 ft. per minute, with a grinding every 100 pieces. 
 
 Hack Sawing Machines. Charles Wicksteed (Proc. Inst. Mech. 
 Engrs., 1912) says that the important considerations to be observed in 
 using hack sawing machines are: For ordinary work, a coarse pitch 
 tooth, not less than 10 to the inch is best; extra strength of the saw is 
 to be obtained by extra depth, not extra thickness, of blade; the greatest 
 weight that a blade will take without injury is 7 Ib. per tooth or 70 Ib. 
 per in. ; a 6-in. machine thus will use the full capacity of the blade on 
 4-in. bars with a weight of 210 Ib. on the blade. As the size of the 
 machine increases, the weight increases proportionately, a 15-in. ma- 
 chine employing 700 Ib. and using the full capacity of the blade when 
 sawing a 10-in. surface. A hack sawing machine will cut true to 0.01 
 in. in a mild steel bar at a speed roughly of 1 to 2 sq. in. per minute. 
 
 Saws for Copper. A special saw for cutting copper has teeth with 
 a front rake of 10. The metal is ground away at the sides of the 
 teeth to provide clearance. The number of teeth should be com- 
 paratively small. A pitch of about 1 in. giving 10 teeth in 3-in. saw 
 renders good service. 
 
 CASE-HAEDENING, ETC. 
 
 Case-hardening of Iron and Steel, Cementation, Harveyizing. 
 When iron or soft steel is heated to redness or above in contact with 
 charcoal or other carbonaceous material, the carbon gradually penetrates 
 the metal, converting it into high carbon steel. The depth of penetra- 
 tion and the percentage of carbon absorbed increase with the tempera- 
 ture and with the length of time allowed for the process. In the ( old 
 cementation process for converting wrought iron into "blister steel" for 
 re-melting in crucibles flat bars were packed with charcoal in an oven 
 which was kept at a red heat for several days. In the Harvey process of 
 hardening the surface of armor plate, the plate is covered with charcoal 
 and heated in a furnace, and then rapidly cooled by a spray of water. 
 
 In case-hardening, a very hard surface is given to articles of iron or 
 soft steel by covering them or packing them in a box or oven with a ma- 
 terial containing carbon, heating them to redness while so covered, and 
 then chilling them. Many different substances have been used for the 
 purpose, such as wood or bone charcoal, charred leather, sugar, cyanide 
 of patassium, bichromate of potash, etc. Hydrocarbons, such as illu- 
 minating gas, gasolene or naphtha, are also used. Amer. Machinist, 
 Feb. 20, 1908, describes a furnace made by the American Gas Furnace 
 Company of Elizabeth, N. J., for case-hardening by gas. The best results 
 are obtained with soft steel, 0.12 to 0.15 carbon, and not over 0.35 man- 
 ganese, but steel of 0.20 to 0.22 carbon may be used. The carbon begins 
 to penetrate the steel at about 1300 F., and 1700 F. should never be 
 exceeded with ordinary steels. A depth of carbonizing of 1/64 in. is 
 obtained with gas in one hour, and 1/4 in. in 12 hours. After carbonizing 
 the steel should be annealed at about 1625 F. and cpoled slowly, then 
 re-heated to about 1400 F. and quenched in water. Nickel-chrome steels 
 may be carbonized at 2000 F. and tungsten steels at 2200 F. 
 
 Change of Shape due to Hardening and Tempering. J. E. Storey. 
 Am. Mack., Feb. 20, 1908, describes some experiments on the change of 
 dimensions of steel bars 4 in. long, 7/s in. diam. in hardening and temper- 
 ing. On hardening the length increased in different pieces .0001 to 
 .0014 in., but in two pieces a slight shrinkage, maximum .00017, was found. 
 The diameters increased .0003 to .0036 in. On tempering the length 
 decreased .0017 to .0108 in. as compared with the original 4 ins. length, 
 while the diameter was increased .0003 to .0029; a few samples showing 
 a decrease, max. 0009 in. The general effect of hardening is a slight 
 Increase in bulk, which increase is reduced by tempering. 
 
1292 
 
 THE MACHINE-SHOP. 
 
 POWER REQUIRED FOR MACHINE TOOLS. 
 
 Resistance Overcome in Cutting Metal. (Trans. S. M. E. t 
 viii, 308.) Some experiments made at the works of William Sellers 
 & Co. showed that the resistance in cutting steel in a lathe would vary 
 from 180,000 to 700,000 pounds per square inch of section removed, 
 while for cast iron the resistance is about one-third as much. The 
 power required to remove a given amount of metal depends on the 
 shape of the cut and on the shape and sharpness of the tool used. If 
 the cut is nearly square in section, the power required is a minimum; 
 if wide and thin, a maximum. The dullness of a tool affects but little 
 the power required for a heavy cut. 
 
 F. W. Taylor, in the Art of Cutting Metals (Trans. A. S. M. E., 
 xviii) gives the tangential pressure of the chip on the tool as ranging 
 from 70,000 Ib. per sq. in. when cutting soft cast iron with a coarse 
 feed, to 198,000 Ib. per sq. in. when cutting hard cast iron with a fine 
 feed. In cutting steel, the pressure of the chip on the tool per sq. in. 
 ranged from 184,000 Ib. to 376,000 Ib. The pressure, he found, is 
 independent of the speed, and in the case of steel is independent of 
 the hardness of the steel. It increases as the quality of the steel grows 
 finer; that is, high grade steel, whether hard or soft, will give higher 
 pressures than low grade steel. He also found that an increase in 
 the tensile strength and ductility of the steel increases the pressure, 
 the former having the greater effect. 
 
 Horse-power Required to Run Lathes. The power required to 
 do useful work varies with the depth and breadth of chip, with the 
 shape of tool and with the nature and density of metal operated upon ; 
 and the power required to run a machine empty is often a variable 
 quantity. For instance, when the machine is new, and the working 
 parts have not become worn or fitted to each other as they will be after 
 running a few months, the power required will be greater than will be 
 the case after the running parts have become better fitted. 
 
 Another cause of variation of the power absorbed is the driving-belt; 
 A tight belt will increase the friction. 
 
 A third cause is the variation of journal-friction, due to slacking up 
 or tightening the cap-screws, and also the end-thrust bearing screw. 
 
 Owing to the demand imposed by high speed tool steels stouter 
 machines are more necessary than formerly; these possess more rigid 
 frames and powerful driving gears. The most modern (1915) forms 
 of lathes obtain all speed changes by means of geared head-stocks, 
 power being delivered at a single speed by a belt, or by a motor. If a 
 motor drive is used, a speed variation may be obtained in addition to 
 those available in the head, by using a variable speed motor, whose 
 range usually is about 3:1. The tables on p. 1293 show the results of 
 tests made by the Lodge & Shipley Co. in 1906 to determine the power 
 required to remove metal in a 20-in. lathe with a cone pulley drive, and 
 also in a similar lathe with a geared head. 
 
 Power Required to Drive Machine Tools. The power required 
 to drive a machine tool varies with the material to be cut. There is 
 considerable lack of agreement among authorities on the power re- 
 quired. Prof. C. H. Benjamin (Mach'y, Sept., 1902) gives a formula 
 H.P. = cW, c being a constant and W the pounds of metal removed 
 per hour, c varies both with the quality of metal and the type of 
 machine. 
 
 Values of c. 
 
 
 Lathe. 
 
 Planer. 
 
 Shaper. 
 
 Milling 
 Machine. 
 
 Cast iron 
 
 0.035 
 
 0.032 
 
 0.030 
 
 0.14 
 
 
 067 
 
 
 
 
 Tool steel 
 
 
 
 
 0.30 
 
 Bronze 
 
 
 
 
 0.10 
 
 In each case the power to drive the machine without load should be 
 added. G. M. Campbell (Proc. Engr. Soc. W., Pa., 1906) gives, ex- 
 clusive of friction losses, H.P. = Kw, K being a constant and w the 
 pounds of metal removed per minute. For hard steel K = 2.5; for soft 
 
POWER REQUIRED FOR MACHINE TOOLS. 1293 
 
 Horse-power Kequired to Remove Metal in Lathes. 
 
 (Lodge & Shipley Mach. Tool Co., 1906.) 
 20-lNCH CONE-HEAD LATHE. 
 
 
 Cutting 
 
 Cut, In. 
 
 Diam. 
 
 Cu. in. 
 
 Lb. 
 
 H.P. used 
 by Lathe. 
 
 Cu.in. 
 
 Material 
 
 Speed, 
 
 
 of 
 
 remov- 
 
 remov- 
 
 
 remov- 
 
 Cut. 
 
 ft. per 
 min. 
 
 Depth. 
 
 Feed. 
 
 work, 
 in. 
 
 ed per 
 min. 
 
 ed per 
 hour. 
 
 Idle. 
 
 With 
 Cut. 
 
 ed per 
 HJP. 
 
 Crucible 
 
 f 35 
 
 0.109 
 
 1/8 
 
 227/32 
 
 5.74 
 
 96 
 
 0.48 
 
 3.90 
 
 1.471 
 
 Steel 
 
 S 65 
 
 0.055 
 
 V8 
 
 35/ 8 
 
 5.33 
 
 90 
 
 0.74 
 
 4.60 
 
 1.158 
 
 0.60 
 
 ) 62.5 
 
 0.109 
 
 Vl6 
 
 35/16 
 
 5.125 
 
 86 
 
 0.49 
 
 4.65 
 
 1.102 
 
 Carbon 
 
 ( 32.5 
 
 0.094 
 
 VlO 
 
 
 3.656 
 
 62 
 
 0.49 
 
 2.64 
 
 1.384 
 
 
 f 62.5 
 
 0.273 
 
 1/1? 
 
 35/32 
 
 17.09 
 
 266 
 
 0.66 
 
 5.44 
 
 3.141 
 
 Cast 
 
 ) 60 
 
 0.430 
 
 Vl9 
 
 221/64 
 
 16.27 
 
 253 
 
 0.59 
 
 4.77 
 
 3.410 
 
 Iron 
 
 ) 37.5 
 
 0.334 
 
 1/16 
 
 221/32 
 
 10.76 
 
 167 
 
 0.45 
 
 3.91 
 
 2.751 
 
 
 ( 115 
 
 0.086 
 
 Vl2 
 
 155/64 
 
 9.88 
 
 153 
 
 0.21 
 
 2.54 
 
 3.889 
 
 Open- 
 hearth 
 Steel 
 0.30 
 Carbon 
 
 % 50 
 
 ) 45 
 ) 45 
 ( 32.5 
 
 0.109 
 0.117 
 0.217 
 0.109 
 
 1/8 
 1/8 
 Vl9 
 1/8 
 
 2V 2 32 
 
 217/64 
 223/64 
 
 8.2 
 7.91 
 6.439 
 5.33 
 
 138 
 134 
 109 
 90 
 
 0.69 
 0.53 
 0.69 
 0.36 
 
 5.34 
 5.11 
 4.10 
 4.04 
 
 1.535 
 1.547 
 1.570 
 1.319 
 
 Average H.P. running idle 0.53; average H.P. with cut 4.25. 
 20-lNCH GEARED-HEAD LATHE, 
 
 
 
 
 
 
 
 H.P. used 
 
 
 
 Cutting 
 
 Cut, in. 
 
 Diam. 
 
 Cu. in. 
 
 Lb. 
 
 by Lathe. 
 
 Cu. in. 
 
 Material. 
 
 Speed, 
 
 
 of 
 
 remov- 
 
 remov- 
 
 
 remov- 
 
 Cut. 
 
 ft. per 
 min. 
 
 Depth. 
 
 Feed. 
 
 work 
 in. 
 
 ed per 
 
 miii. 
 
 ed per 
 hour. 
 
 Idle. 
 
 With 
 Cut. 
 
 ed per 
 H.P. 
 
 0.50 
 
 ( 40 
 
 0.266 
 
 VlO 
 
 227/32 
 
 12.75 
 
 215 
 
 2.11 
 
 11.1 
 
 1.142 
 
 Carbon 
 
 )50 
 
 0.281 
 
 Vl5 
 
 
 11.25 
 
 190 
 
 .58 
 
 8.35 
 
 1.347 
 
 Crucible 
 
 )75 
 
 0.281 
 
 1/15 
 
 227/32 
 
 16.87 
 
 285 
 
 .58 
 
 12.69 
 
 1.329 
 
 Steel. 
 
 (85 
 
 0.109 
 
 1/15 
 
 2V4 
 
 7.43 
 
 126 
 
 .28 
 
 8.98 
 
 0.827 
 
 
 f 45 
 
 0.609 
 
 1/16 
 
 721/32 
 
 2057 
 
 320 
 
 .34 
 
 694 
 
 2.963 
 
 Cast 
 
 )62.5 
 
 0.609 
 
 Vl6 
 
 721/32 
 
 28.56 
 
 445 
 
 .35 
 
 9.50 
 
 3.006 
 
 Iron 
 
 )85 
 
 0.641 
 
 Vl6 
 
 721/32 
 
 40.82 
 
 636 
 
 .64 
 
 12.69 
 
 3.216 
 
 
 (80 
 
 0.281 
 
 1/8 
 
 3 3/32 
 
 33.75 
 
 526 
 
 .18 
 
 10.49 
 
 3.217 
 
 Open- 
 hearth 
 
 Qfool 
 
 f 125 
 ) 105 
 
 0.250 
 0.188 
 
 V28 
 
 1/12 
 
 4 21/32 
 4 5/32 
 
 13.4 
 19.68 
 
 226 
 332 
 
 1.62 
 0.94 
 
 10.60 
 11.56 
 
 1.265 
 1.702 
 
 oteei 
 15 
 
 ) 40 
 
 0.172 
 
 1/6 
 
 
 13.75 
 
 232 
 
 1.75 
 
 12.49 
 
 1.100 
 
 Carbon 
 
 ( 180 
 
 0.094 
 
 1/16 
 
 3 Vl6 
 
 12.65 
 
 213 
 
 2.15 
 
 11.20 
 
 1.129 
 
 Carbo 
 TV! 
 
 Average H.P. running idle 1.543; average H.P. with cut 10.55. 
 
 This 
 
 steel K = 1.8; for wrought iron, K = 2.0; for cast iron, K = 1.4. 
 formula gives results aBout 50% lower than Prof. Benjamin's. 
 
 L. L. Pomeroy (Gen. Elec. Rev., 1908) gives: H.P. required to drive = 
 12 FDSNC, in which F = feed and D = depth of cut, in inches, S = 
 speed in ft. per min., N = number of tools cutting, C = a constant, 
 whose values with ordinary carbon steel tools are: for cast iron, 0.35 to 
 0.5; soft steel or wrought iron, 0.45 to 0.7; locomotive driving-wheel 
 tires, 0.7 to 1.0; very hard steel, 1.0 to 1.1. This formula is based on 
 Prof. Flather's dynamometer tests. An analysis of experiments by 
 Dr. Nicholson of Manchester, which confirm the formula, showed the 
 average H.P. required at the motor per pound of metal removed per 
 minute to be as follows : Medium or soft steel, or wrought iron, 2.4 H.P. ; 
 hard steel, 2.65 H.P.; cast iron, soft or medium, 1.00 H.P.; cast iron, 
 hard, 1.36 H.P. 
 
1294 
 
 THE MACHINE-SHOP. 
 
 Actual tests (1906) of a number of machine tools in the shops of the 
 Pittsburg and Lake Erie R.R. showed the horse-power absorbed hi 
 driving under the conditions given in the table on p. 1295. The 
 results obtained are compared with those computed by Campbell's 
 formula on p. 1292. It will be observed that the sizes of motors actu- 
 ally used on the various machines in the table agree quite closely with 
 the sizes recommend od in the tables, pp. 1294 to 1298. 
 
 Sizes of Motors for Machine Tools. The size of motor applied to 
 machine tools which are driven by an individual motor is usually deter- 
 mined by the experience of the manufacturer, rather than by any 
 formula. The same lathe, for instance, will be fitted with a larger 
 motor if it is required to take heavy roughing cuts continuously in 
 tough steel, than if it is to have a more general run of lighter work in 
 cast iron. Even if it does, under the latter conditions of service, 
 occasionally receive a job up to the limit of its capacity, the motor will 
 be able to stand the temporary overload, whereas a continuous overload 
 would soon ruin it. The conditions under which the machine will 
 operate should therefore be stated when it or the motor to drive it 
 is purchased. The tables given on pages 1294 to 1298 show the 
 sizes of motors for machine tools as recommended by the Westinghouse 
 Elect. & Mfg. Co. The sizes given embody average practice. The 
 type of motor to be used varies with the conditions of servic*, and the 
 type suitable for the different classes of machinery are indicated by 
 the following symbols: 
 
 A. Adjustable speed, shunt wound, direct current motor; used where 
 a number of speeds are essential. 
 
 B. Constant speed, shunt wound, direct current motor; used when 
 the desired speeds are obtainable by. a cone pulley or gear box, or where 
 only a single speed is required. 
 
 C. Squirrel cage induction motor; used where direct current is not 
 available. A cone pulley or gear box is necessary if more than one 
 speed is desired. 
 
 D. Constant speed, compound wound, direct-current motor, used 
 when different speeds are obtainable by means of a cone pulley or 
 gear box, or where but one speed is necessary. 
 
 E. Wound secondary or squirrel cage induction motor with about 
 10% slip; used where direct current is not available, or where one 
 speed is required. 
 
 F. Adjustable speed, compound wound, direct current motor; used 
 where a number of speeds are necessary. 
 
 G. Standard bending roll motor. 
 
 H. Standard machine tool traverse motor. 
 
 Turning and Boring Machines* 
 
 ENGINE LATHES Motor A, B or C. 
 
 Swing, in 12 14 16 
 
 18 
 
 Horse-power, average 1/2 8/4-1 1-2 2-3 
 
 20-22 24-27 
 
 3 5 
 
 7.5-10 7.5-10 
 
 48-54 60-84 
 15-20 
 20-25 
 
 20-25 
 25-30 
 
 Horse-power, heavy 2 2-3 2-3 3-5 
 
 Swing, in 30 32-36 38-42 
 
 Horse-power, average 5-7.5 7.5-10 10-15 
 
 Horse-power, heavy 7.5-10 10-15 15-20 
 
 WHEEL LATHES Motor A, B or C. 
 
 Size, in 48 51-60 79-84 90 100 
 
 Horse-power 15-20 15-20 25-30 30-40 40-50 
 
 H.P. of tail stock motor (jff) 555 5-7.5 5-7.5 
 
 AXLE LATHES Motor A, B or C. 
 
 Single 5, 7.5, 10 Horse-power 
 
 Double 10, 15, 20 
 
 BUFFING LATHES Motor B or C. 
 
 Number of wheels 2 2 2 2 
 
 Diameter of wheels, in 6 10 12 14 
 
 Horse-power 1/4-1/2 1-2 2-3 3-5 
 
 For brass tubing and other special work use about double the 
 above H.P. 
 
POWER REQUIRED FOR MACHINE TOOLS. 1295 
 
 Horse-power to Drive Machine Tools. 
 
 J_ 
 
 72-in. wheel 
 lathe ' 
 
 Material. 
 
 Cut, Inches. 
 
 Speed, 
 Ft. per Min. 
 
 Wt. Removed, 
 Lb. per Min. 
 
 H.P.Re 
 quired. 
 
 1 
 
 3 
 
 o 
 
 
 
 I 
 
 ,d 
 a 
 
 & 
 
 13 
 
 3 
 
 1 
 
 J3 
 ~B 
 
 K 
 
 O 
 
 fa 
 
 Hard steel 
 
 Via 
 
 1/8 
 3/16 
 3 /16 
 
 3/16 & V4 
 3/16&V4 
 5 /16&3/8 
 3/8 &3/ 8 
 
 13.7 
 11.6 
 13.2 
 13.2 
 
 1.69 
 2.15 
 5.55 
 6.3 
 
 4.5 
 6.4 
 8.4 
 12.0 
 
 4.2 
 5.4 
 13.9 
 15.7 
 
 25 H.P. shunt 
 wound vari- 
 able speed. 
 
 90-in. wheel 
 lathe 
 
 Hard steel 
 
 3/16 
 3/16 
 
 1/5 
 
 3/16&3/16 
 5 /16& 5 /16 
 1/4 &V4 
 
 13.0 
 8.8 
 15.5 
 
 3.1 
 3.5 
 5.3 
 
 12.0 
 8.1 
 9.0 
 
 7.7 
 8.7 
 13.2 
 
 25 H.P. shunt 
 wound vari- 
 able speed. 
 
 42-in. lathe 
 
 Soft steel 
 Cast iron 
 
 Vl6 
 Vl6 
 Vl6 
 1/16 
 Vl6 
 Vl6 
 
 1/4 
 1/8 
 >/8 
 1/8 
 3/16 
 3/16 
 
 44 
 44 
 44 
 108 
 46 
 58 
 
 2.33 
 1.17 
 1.17 
 2.63 
 1.74 
 2.12 
 
 3.8 
 1.7 
 2.6 
 5.8 
 2.9 
 2.2 
 
 4.2 
 1.9 
 1.9 
 3.7 
 2.5 
 3.0 
 
 15 H.P. shunt 
 wound vari- 
 able speed. 
 
 30-in. lathe 
 
 Wro't iron 
 Cast iron 
 
 1/8 
 1/8 
 3/32 
 3/32 
 1/64 
 
 3/16 
 3/16 
 5 /32 
 1/16 
 
 V4 
 
 54 
 42 
 42 
 61 
 47 
 
 4.2 
 3.2 
 1.92 
 1.12 
 2.30 
 
 6.6 
 4.0 
 3.0 
 1.5 
 2.0 
 
 T9 
 5.0 
 
 T9 
 2.6 
 9.6 
 7.2 
 2.6 
 2.7 
 
 8.4 
 6.4 
 2.7 
 1.6 
 3.2 
 
 10 H.P. shunt 
 wound vari- 
 able speed. 
 
 Axle lathe 
 
 Soft steel 
 
 3/16 
 Vl6 
 
 1/4 
 V4 
 
 27 
 51 
 
 4.3 
 2.7 
 
 7.7 
 4.9 
 
 35H.P.sh.w'd 
 var. speed.^ 
 
 72-in. boring 
 mill . . 
 
 Soft steel 
 Cast iron 
 
 1/8 
 3/16 
 1/8 
 1/8 
 1/16 
 Vl6 
 
 1/16&V32 
 
 1/32&V16 
 1/8 &V8 
 3/16 
 3/8 
 V4 
 
 44 
 40 
 51 
 47 
 28 
 39 
 
 1.76 
 2.38 
 5.41 
 3.75 
 2.05 
 1.90 
 
 3.2 
 4.3 
 9.7 
 6.8 
 2.9 
 2.7 
 
 25 H.P. shunt 
 wound vari- 
 able speed. 
 
 24-in. drill 
 press . 
 
 Wro't iron 
 
 1/64 
 1/64 
 1/64 
 
 1/64 
 1/64 
 
 11/4to3* 
 11/ 4 to3* 
 1l/4to3* 
 1 1/4 drill 
 11/4 drill 
 
 25.1 
 29.7 
 25.9 
 74.5 
 20.9 
 
 0.81 
 0.96 
 0.83 
 0.52 
 0.54 
 
 2.3 
 2.7 
 1.3 
 3.5 
 1.2 
 
 5.9 
 6.5 
 21.0 
 2.7 
 6.5 
 9.3 
 7.6 
 23.2 
 
 1.6 
 1.9 
 1.7 
 1.0 
 1.1 
 
 
 60-in. planer 
 
 Soft steel 
 Wro't iron 
 Cast iron 
 
 1/6 
 1/6 
 
 * 
 
 1/8 
 1/8&V16 
 1/7 
 1/4 
 
 % 
 5 /16& 5 /16 
 1/32&V32 
 1/8 &Vl6 
 1/4 & 5 /16 
 V4 &V4 
 7/16&3/8 
 
 25.5 
 25.7 
 23 
 17.5 
 22.2 
 30 
 22.6 
 28.9 
 
 3.62 
 3.65 
 8.95 
 1.82 
 1.72 
 4.74 
 5.03 
 18.3 
 
 6.5 
 6.6 
 17.9 
 3.6 
 3.4 
 6.6 
 7.1 
 25.6 
 
 20 H.P. com- 
 pound 
 wound vari- 
 able speed. 
 
 42-in. planer 
 
 Soft steel 
 Cast iron 
 
 5/32 
 
 1/8 
 3/16 
 3/16 
 
 3/8 
 3/8 
 
 
 
 24.3 
 36 
 37 
 37 
 
 4.73 
 3.7 
 4.06 
 2.71 
 
 2.1 
 7.8 
 4.7 
 4.1 
 
 9.5 
 
 1.4 
 5.7 
 3.8 
 
 5 H.P. com- 
 pound 
 wound vari- 
 able speed. 
 
 19-in.slotter 
 
 rlard steel 
 Soft steel 
 
 V32 
 1/32 
 
 1/4 
 3 /8 
 
 30.0 
 23.3 
 
 0.8 
 0.93 
 
 2.0 
 1.3 
 
 2.0 
 1.7 
 
 3 H.P. comp. 
 w'd var. speed. 
 
 Enlarging hole from smaller dimensions to larger. 
 
1296 
 
 THE MACHINE-SHOP. 
 
 BOEING AND TURNING MILLS Motor A, B or C. 
 
 In. In. In. Ft. Ft. Ft. Ft. 
 
 37-42 50 60-84 7-9 10-12 14-16 16-25 
 
 H. P., average.. 5-7.5 7.5 7.5-10 10-15 10-15 15-20 20-25 
 
 H.P., heavy... 7.5-10 7.5-10 10-15 30-40 ..... ..... 
 
 CYLINDER BORING MACHINES Motor A, B or C. 
 
 Diameter of spindle, in 4 6 8 
 
 Maximum boring diameter, in 10 30 40 
 
 Horse-power 7.5 10 35 
 
 HORIZONTAL BORING, DRILLING AND MILLING MACHINES 
 Motors A, B or C. 
 
 Size of spindle, in 3.5-4.5 4.5-5.5 5.5-6.5 
 
 Horse-power per spindle ... 5-7.5 7.5-10 10-15 
 
 Drilling Machines. 
 
 Sensitive Drills up to 1/2 in i/ 4 -3/ 4 H.P. Motor A, B or C. 
 
 UPRIGHT DRILLS Motor A, B or C. 
 
 Size, in 12-20 24-28 30-32 36-40 50-60 
 
 Horse-power 1235 5-7.5 
 
 RADIAL DRILLS Motor A, B or C. 
 
 Length of arm, ft 3 4 5-7 8-10 
 
 Horse-power, average 1-2 2-3 3-5 5-7.5 
 
 Horse-power, heavy 3 5-7.5 5-7.5 7.5-30 
 
 MULTIPLE SPINDLE DRILLS Motor A, B or C. 
 
 Size of drill, in. l/ 32 -i/4 1/16-3/8 3/ 16 -l/ 2 i/ 4 -3/ 4 s/g-1 222 
 No. of spindles, 
 
 up to 6-10 10 10 10 10 4 6 8 
 
 Horse-power.. 3 5 7.5 10 10-15 7.5 10 15 
 
 Planing Machinery. 
 
 PLANERS Motor C, D or F. 
 
 Width, in 22 24 27 30 36 42 
 
 Distance under rail, in. 22 24 27 30 36 42 
 
 Horse-power 3 3-5 3-5 5-7.5 10-15 15-20 
 
 Width, in 48 54 60 72 84 100 
 
 Distance under rail, in.. 48 54 60 72 84 100 
 
 Horse-power 15-20 20-25 20-25 25-30 30 40 
 
 SHAPERS Motor A, B or C. 
 
 Traverse Head. 
 
 Stroke, in 12-16 18 20-24 30 20 ~24 
 
 H. P., single head 2 2-3 3-5 5-7.5 7.5 10 
 
 SLOTTERS KEYSEATERS Motor A, B or C. 
 
 Stroke, in 6 8 10 12 14 
 
 Horse-power 3 3-5 5 5 5-7 1/2 
 
 Stroke, in 16 18 20 24 30 
 
 Horse-power 7.5 7.5-10 10-15 10-15 10-15 
 
 Milling Machinery. 
 
 PLAIN MILLING MACHINES Motor A, B or C. 
 
 Table feed, in 34 42 50 
 
 Cross feed, in 10 12 12 
 
 Vertical feed, in 20 20 21 
 
 Horse-power 7.5 10 15 
 
 r UNIVERSAL MILLING MACHINES Motor 4^ B or C. 
 
 Machine number 1 H/2 2 3 4 "5 
 
 Horse-power 1-2 1-2 3-5 5-7.5 7.5-10 10-15 
 
POWER REQUIRED FOR MACHINE TOOLS. 1297 
 
 VERTICAL MILLING MACHINES Motor .4, 73 or C. 
 
 Height under Spindle, in 12 14 18 20 24 
 
 Horse-power 5 7.5 10 15 20 
 
 VERTICAL SLABBING MACHINES Motor A, B or C. 
 
 Width of work, in 24 32-36 42 
 
 Horse-power 7.5 10 15 
 
 HORIZONTAL SLABBING MACHINES Motor A, B or C. 
 
 Width between housings, in . . 24 30 36 60 72 
 
 Horse-power, average 7.5-10 7.5-10 10-15 25 25 
 
 Horse-power, heavy 10-15 10-15 20-25 50-60 75 
 
 GEAR CUTTERS Motor A, B or C. 
 
 Size, in 36X9 48X10 30X12 60X12 72X14 64X20 
 
 Horse-power.. 2-3 3-5 5-7.5 5-7.5 7.5-10 10-15 
 
 ROTARY PLANERS Motor A, B or C. 
 
 Diam. of cutter, in.... 24 30 36-42 48-54 60 72 84 96-100 
 
 Horse-power. 5 7.5 10 15 20 25 30 40 
 
 SAWS, COLD AND CUT-OFF Motor A, B or C. 
 
 Size of saw, in 20 26 32 36 42 48 
 
 Horse-power 3 5 7.5 10-15 20 25 
 
 Bolt and Nut Machinery. 
 
 BOLT CUTTERS Motor A, B or C. 
 
 Single. Double. Triple. 
 
 Size, in. . . 1, .1 1/4; 1 1/2 
 
 H.P 1-2 
 
 1 3/4, 212 1/4, 3 l/ 2 I 4, 6 II, 1 1/2 1 2, 2 1/ 2 | 1, 1 1/2, 2 
 
 2! 1, 
 
 2-3 | 3-5 " 1 5-7.5 | 2-3" | 3-5 I 3-7.5 
 
 BOLT POINTERS Motor B or C. 
 
 Size, in 1 1/2, 2 1/2 Horse-power 1-2 
 
 NUT TAPPERS Motor A, B or C. 
 
 4 Spindle. 6 Spindle. 10 Spindle. 
 
 Size, in 1,2 2 2 
 
 Horse-power 3 3 5 
 
 NUT FACING MACHINE Motor B or C. 
 
 Size, in 1,2 Horse-power 2-3 
 
 BOLT HEADING, UPSETTING AND FORGING Motor D, E or F. 
 
 Size, in 3/ 4 -l l/ 2 H/2-2 2 1/2-3 4-6 
 
 Horse-power 5-7.5 10-15 20-25 30-40 
 
 Bending or Forming Machinery Hammers. 
 
 BULLDOZERS Motor D or E. 
 
 Width, in 29 34 39 45 63 
 
 Head movement, in 14 16 16 18 20 
 
 Horse-power 5 7.5 10 15 20 
 
 BENDING AND STRAIGHTENING ROLLS Motor E or G. 
 
 Width, ft 4 6 6 6 8 10 10 24 
 
 Thickness, in 3/ 8 s/ 16 7/ 16 3/4 7/ 8 ii/ 8 u/ 2 1 
 
 Horse-power 5 5 7.5 15 25 35 50 50 
 
 HAMMERS Motor D or E. 
 
 Size, Ib 15 to 75 100 to 200 
 
 Horse-power 1/2 to 5 5 to 7 . 5 
 
 Bliss drop hammers require approximately 1 H.P. for every 100 Ib. 
 weight of hammer head. 
 
 Pipe Threading and Cutting-off Machinery. 
 
 i Motor A, B or C. 
 
 Pipe size, in. . 1/4-2 1/2-3 1-4 H/4-6 2-8 3-10 4-12 8-18 24 
 Horse-power. 2 3 33-5 3-5 5 5 7.5 10 
 
1298 THE MACHINE-SHOP. 
 
 Punching and Shearing Machinery. 
 
 Presses for^notching sheet-iron Motor A L B or C 1/2 to 3 H.P. 
 
 PUNCHES Motor D or E. 
 
 Diameter, in.. 3/ 8 i/ 2 5/ 8 s/ 4 7/ 8 i i n/ 4 is/ 4 2 2l/ 2 
 Thickness, in.. 1/4 1/2 Vs 3 /4 3/4 1/2 1. 1 1 1 H/2 
 
 Horse-power. . 1 2-3 2-3 3-5 5 5 7.5 7.5-10 10-15 10-15 15-25 
 
 SHEARS Motor D or E. 
 
 Width, in 30-42 50-60 72-96 
 
 Horse-power to cut i/s-in. iron. 345 
 Horse-power to cut l/4-in. iron.. 5 7.5 10 
 
 Bolt shears 71/2 H.P. Double angle shears 10 H.P. 
 
 LEVER SHEARS Motor D or E. 
 
 Size, in 1X1 1 1/2 X 1 1/2 2X2 6X1 21/2X21/2 
 
 Horse-power 5 7.5 15 15 
 
 Size, in 1X7 2,3/4 X 23/ 4 H/ 2 X 8 31/2 X 31/2 41/2 round 
 
 Horse-power 15 20 25 30 30 
 
 PLATE SHEARS Motor D or E. 
 Size of plate, in., 
 
 3/8 X 24 1 X 24 2 X 14 1 X 42 1 1/2 X 42 1 1/4 X 54 1 1/2 X 72 1 1/4 X 100 
 Cuts per min., 
 
 35 20 15 20 15 18 20 10-12 
 
 Stroke, in., 
 
 3 3 41/4 4 41/2 6 151/2 71/2 
 
 Horse-power, 
 
 10 15 30 20 60 75 10 75 
 
 Hydrostatic Wheel Presses Motor B or C. 
 
 Size, tons . 100 200 300 400 600 
 
 Horse-power 5 7.5 7.5 10 
 
 Grinding Machinery. 
 
 GRINDING MACHINES (FOR SHAFTS, ETC.) Motor A, B or C. 
 Wheels diameter, in. ... 10 10 10 10 14 18 18 18 
 
 Length of work, in 50 72 96 120 72 120 144 168 
 
 H.P., average work.... 555 5 10 10 10 10 
 
 ' heavy work 7.5 7.5 7.5 7.5 15 15 15 15 
 
 EMERY WHEEL GRINDERS, ETC. Motor B or C. 
 
 K umber of wheels 2 2 2 2 2 2 
 
 Size of wheels, in 6 10 12 18 24 26 
 
 Horse-power 1/2-1 2 3 5-7.5 7.5-10 7.5-10 
 
 MISCELLANEOUS GRINDERS Motor B or C. 
 
 Wet tool grinder, 2 to 3 H.P.; flexible swinging grinding and polish- 
 ing machine, 3 H.P.; angle cock grinder, 3 H. P.; piston rod grinder, 
 3 H.P.; twist drill grinder, 2 H.P.; automatic tool grinder, 3 to 5 H.P. 
 
 In selecting a motor for a machine tool, advantage should be taken 
 of the fact that motors will stand considerable overloads for short 
 periods. This will lead to the selection of smaller nu>tors than are 
 usual. The tendency is to select a motor to fit the maximum capacity 
 of the machine, rather than one whose capacity is more nearly that of 
 the average capacity of the tool. 
 
 A. G. Popcke (Am. Mach., Sept. 26 and Oct. 3, 1912) outlines more 
 accurate methods of determining the sizes of motors required for 
 driving machine tools, based upon an analysis of the working condi- 
 tions, and also the considerations other than those of power which 
 govern the selection of the motor. To determine motor capacity, 
 the following data are necessary: Horse-power, speed and voltage; and 
 in addition for alternating current, frequency and phase. To estimate 
 the horse-power the following must be known: Type of tool; depth of 
 cut (all tools being considered), inches; feed, in. per revolution; speed, 
 ft. per minute; duration of both average and maximum cuts; duration 
 of peak of maximum load ; number of peaks per hour. From the area 
 of the cut (depth X feed) and the cutting speed, the cubic inches of 
 
POWER REQUIRED FOR MACHINE TOOLS. 1299 
 
 metal removed per minute can be calculated for both average and 
 maximum cuts, and these figures, multiplied by the constants below 
 give the horse-power required, to which the friction load of the machine 
 must be added. 
 
 HORSE-POWER CONSTANTS FOR CUTTING METAL. 
 
 H.P. per Cu. 
 
 In. per Min. 
 
 Steel, 50 carbon or more. . 1.0 to 1.25 
 Brass and similar alloys. . 0.2 to 0.25 
 
 H.P. per Cu. 
 
 In. per Min. 
 
 Cast iron 0.3 to 0.5 
 
 Wrought iron 0.6 
 
 Machinery steel 0.6 
 
 These constants apply to round nose tools used in accordance with 
 the conditions recommended by F. W. Taylor (see p. 1261). For 
 twist drills the power requirements per cubic inch are about double 
 the figures given above. 
 
 The size of the motor selected will depend on the heating of the 
 motor while under load, and as the load is usually intermittent, the 
 heating will depend upon the square root of the mean square value of 
 the power required. In a given cycle in which the several power values 
 are Pi, Pi, Ps, utilized durmg periods of ti, h, t3, respectively, the square 
 root of the mean square will be 
 
 'Pi 2 tl + P 2 2 fe + P 3 2 u \ 
 
 ti + h + t 3 
 
 The heating of the motor will be the same as if it were run constantly 
 at a load equal to the square root of the mean square load. In making 
 the motor selection, however, it should be observed whether or not the 
 duration of the maximum load will be greater than the motor can suc- 
 cessfully withstand. Thus a 100% overload for a period of 10 seconds 
 can easily be carried by a properly designed motor, while if prolonged 
 such a load may burn it out. When selecting motors for widely fluctu- 
 ating intermittent loads, the limits above rated load which must be 
 taken into consideration are for alternating current, pull at starting 
 torque, and speed regulation; and for direct current motors, commuta- 
 tion, speed regulation and stability. The pull at the starting torque 
 of an induction motor is from 2.5 to 3.5 times the full-load torque, and 
 the speed regulation, or percentage drop in speed between no load and 
 full load, known as the slip, is, at full load, from 5 to 7%. At other 
 loads it is approximately proportional to the load. Commutating pole, 
 direct current motors will stand 100% to 125% overload without 
 sparking. The speed regulation at full load is 10 to 15 %, depending 
 on the speed of the motor. With non-commutating pole motors the 
 speed decreases with overloads in proportion to the loads, while on 
 commutating pole motors it increases up to 100% overload, thus giving 
 approximately the same speed at double load as at full load. A com- 
 mutating pole motor can be made stable at overloads, which will in- 
 crease the drop in speed. The better the speed regulation, however, 
 the less certain is the stability and the motor for driving machine tools 
 must be a compromise between these two factors. Motors, however, 
 are available which can be safely operated on intermittent loads where 
 the maximum load is 200% of the rated load. In machine tool work, 
 a large speed reduction, giving a stable motor is advisable when varia- 
 tions occur in the work done by the cutting tool on long jobs, thus 
 protecting the cutting tools, the machines and the work. An adjust- 
 able speed motor with a speed reduction of 25 % is of advantage under 
 such circumstances. 
 
 In applying the principles outlined above to the selection of a machine 
 tool motor, the average and maximum conditions of service of the 
 machine should be determined by laying out typical jobs in which 
 these conditions are present. The power cycles are determined from 
 the amount of metal removed on each cut as previously explained and 
 the duration of each cut is ascertained from the length of the cut, the 
 spindle speed and the feed per revolution. The square root of the 
 mean square value of the power required is next determined, the time 
 while the machine is idle during the periods of adjustment being added 
 in the denominator of the formula for this value, A motor whose 
 
1300 THE MACHINE-SHOP. 
 
 capacity is in the neighborhood of the value ascertained is then selected, 
 and the relation of the maximum load to the rated motor capacity is 
 observed to ascertain whether or not the motor, in addition to carry- 
 ing the average load, is capable of carrying the maximum load without 
 injury. For instance, if the square root of the mean square value is 
 5.5 II. P. a 5-H.P. motor would be under an overload of 10%, which 
 is well within the capacity of a well designed machine. If the maxi- 
 mum load requires 8.3 H.P. for a period of three minutes the motor 
 will be overloaded 66% for this period which is also within the limits 
 set by good motor design. 
 
 According to Mr. Popcke, other questions than horse-power govern 
 the selection of a motor for a machine tool. The speed of the^motor 
 depends upon the speed of the machine shaft, which ranges from 50 to 
 60 r.p.m. on forging machines to 200. to 300 r.p.m. on machine tools, 
 and as high as 1000 to 2000 r.p.m. on grinding and wood-working ma- 
 chinery. The speeds usually obtainable with 60-cycle alternating 
 current motors are 1700-1800, 1100-1200, 850-900, 650-720 and 
 550-600 r.p.m. The speeds available on standard direct current 
 motors are approximately the same. On 25-cycle alternating current 
 motors the usual speeds are 700-750, 550^600, and 350-375 r.p.m. 
 The following factors are considered in selecting motors for belt drives: 
 Speed .reductions, pulley sizes, belt speeds, motor speeds, distance 
 between pulley centers, arc of contact, use of idler pulleys, mounting 
 of motor. Involved in the speed reductions are the sizes of the motor 
 and machine pulleys and the belt speed. The standard sizes of motor 
 pulleys which have been adopted in connection with standard speed 
 ratings of the various sizes of motors have standardized the belt speeds. 
 The maximum and minimum standard speed ratings of the motors, 
 together with the maximum and minimum pulley diameters are given 
 in the following table: 
 HORSE-POWER OF MOTOR. 
 
 1 2 3 5 71/2 10 15 20 25 30 35 40 50 
 R.P.M , MAXIMUM. 
 
 1700 1700 18CO 1800 1700 1700 1700 1700 1400 1700 1700 1700 1700 
 Pulley Diameter, standard. 
 
 31/231/24 4 5 6 7 8 9 9 10 11 11 
 Pulley Diameter, minimum. 
 
 3 3 33l/ 2 441/ 2 5 6 6 1/ 2 61/2 7 7 1/2 8 
 
 R.P.M., MINIMUM. 
 
 850 850 850 650 600 600 650 600 600 675 600 565 
 
 Pulley Diameter, standard. 
 
 4 5 6 8 9 11 11 12 13 13 14 16 
 
 Pulley Diameter, minimum. 
 
 31/2 4 41/2 6 61/271/2 8 9 10 10 12 13 1/2 
 
 The minimum size of pulley is specified on account of the reduction 
 of pulley size increasing the strains on the motor bearings and shaft. 
 The arc of contact has great effect on the success of a belt-driven motor 
 installation. The arc of contact depends on the distance between the 
 pulley centers and on the speed reduction. Where it is necessary to 
 increase the arc of contact, idler pulleys are of service. In machine 
 work the size of the motor pulley is sometimes fixed by the necessity 
 of belting the motor to the machine flywheel, in which case care must 
 be taken that the diameter of the motor pulley is not less than the 
 minimum size specified. The arc of contact must also be considered, 
 as in a large speed reduction this will be decreased and will seriously 
 affect the amount of power transmitted. The effect of decreasing the 
 arc of contact is shown below, the power transmitted by a 180 deg. arc 
 of contact being taken as 100. 
 
 Arc of contact, deg 180 170 160 150 140 130 120 
 
 Power transmitted, % . . 100 94 89 83 78 72 67 
 The cost of a motor per horse-power increases as the speed decreases. 
 Therefore, for maximum economy in first cost as high a speed as 
 possible should be selected without, however, going below the minimum 
 pulley diameter. Back geared motors are useful where extremely low 
 speeds are required. A speed ratio of 6:1 between the armature and 
 the motor countershaft is usually satisfactory, any further speed 
 reduction to the machine pulley being obtained by means of the pulley 
 
POWER REQUIRED FOR MACHINE TOOLS. 1301 
 Data for Standard Geared Connections for Constant Speed Motors. 
 
 
 Maximum Speed Rating. 
 
 Minimum Speed Rating. 
 
 
 
 
 No. of Teeth. 
 
 
 .s 
 
 
 
 No. of Teeth. 
 
 
 .S 
 
 1 
 
 
 1 
 
 
 ^ S 
 
 _ 
 
 xlj 
 
 g 
 
 
 1 
 
 
 S 
 
 ^ 
 
 t* 
 
 
 o 
 PH 
 
 i 
 
 id 
 
 
 lg 
 
 *l 
 
 Id 
 
 
 
 5 
 
 g 
 
 S 
 
 S" 
 
 T3 o 
 
 & 'S 
 
 OJ 
 
 w c 
 
 PH" 
 
 1 
 
 i 
 
 2 
 
 
 i| 
 
 S-n 
 
 .S'S 
 
 . o 
 
 d 
 
 PH 
 
 o> 
 
 5.2 
 
 .s^ 
 
 -S'S 
 
 TiS 
 
 jjj 
 
 w 
 
 
 
 Q 
 
 
 SS 
 
 
 3 
 
 S 
 
 
 
 b 
 
 
 
 Ss 
 
 S 
 
 
 s 
 
 j 
 
 1700 
 
 8 
 
 17 
 
 15 
 
 13 
 
 940 
 
 1.63 
 
 1200 
 
 8 
 
 17 
 
 15 
 
 13 
 
 665 
 
 1.63 
 
 2 
 
 1700 
 
 8 
 
 17 
 
 15 
 
 13 
 
 940 
 
 1.63 
 
 850 
 
 6 
 
 18 
 
 21 
 
 19 
 
 615 
 
 2.38 
 
 3 
 
 1800 
 
 8 
 
 22 
 
 20 
 
 19 
 
 1300 
 
 2.38 
 
 850 
 
 6 
 
 18 
 
 18 
 
 18 
 
 670 
 
 3.0 
 
 5 
 
 1800 
 
 8 
 
 22 
 
 21 
 
 19 
 
 1300 
 
 2.38 
 
 850 
 
 6 
 
 21 
 
 19 
 
 18 
 
 990 
 
 3.0 
 
 7.5 
 
 1700 
 
 6 
 
 18 
 
 18 
 
 18 
 
 1400 
 
 3.0 
 
 650 
 
 5 
 
 20 
 
 18 
 
 18 
 
 685 
 
 3.6 
 
 10 
 
 1700 
 
 6 
 
 21 
 
 19 
 
 18 
 
 1420 
 
 3.0 
 
 600 
 
 5 
 
 21 
 
 19 
 
 19 
 
 665 
 
 3.8 
 
 15 
 
 1700 
 
 5 
 
 19 
 
 18 
 
 18 
 
 1700 
 
 3.6 
 
 600 
 
 41/9 
 
 22 
 
 19 
 
 19 
 
 770 
 
 4.22 
 
 20 
 
 1700 
 
 5 
 
 20 
 
 18 
 
 18 
 
 1780 
 
 3.6 
 
 650 
 
 4 
 
 21 
 
 18 
 
 18 
 
 890 
 
 4.5 
 
 25 
 
 1400 
 
 5 
 
 21 
 
 19 
 
 19 
 
 1550 
 
 3.8 
 
 600 
 
 4 
 
 22 
 
 19 
 
 18 
 
 864 
 
 4.5 
 
 30 
 
 1700 
 
 5 
 
 21 
 
 19 
 
 19 
 
 1880 
 
 3.8 
 
 600 
 
 31/4 
 
 20 
 
 
 18 
 
 970 
 
 5.53 
 
 35 
 
 1700 
 
 4V? 
 
 22 
 
 18 
 
 18 
 
 2180 
 
 4.0 
 
 675 
 
 31/4 
 
 20 
 
 .... 
 
 18 
 
 1080 
 
 5.53 
 
 40 
 
 1700 
 
 4 1/9 
 
 22 
 
 19 
 
 19 
 
 2180 
 
 4.22 
 
 600 
 
 3 
 
 18 
 
 
 15 
 
 940 
 
 5.0 
 
 50 
 
 1700 
 
 4 
 
 21 
 
 18 
 
 18 
 
 2340 
 
 4.5 
 
 565 
 
 3 
 
 20 
 
 
 18 
 
 990 
 
 6.0 
 
 Data for Standard Geared Connections for Adjustable Speed Motors. 
 
 
 Maximum Speed Rating. 
 
 Horse- 
 
 
 
 Min. 
 
 Gear Data. 
 
 Pitch Line 
 
 Power . 
 
 Min. 
 R.P.M. 
 of 
 Motor. 
 
 Speed 
 Ratio. 
 
 Diam. 
 of 
 Pulley, 
 in. 
 
 
 Speed at 
 Min. Diam. 
 
 Min. 
 No. of 
 Teeth. 
 
 Min. 
 Diam., 
 in. 
 
 Diam. 
 Pitch. 
 
 Min. 
 
 Max. 
 
 j 
 
 740 
 
 3 
 
 3 
 
 19 
 
 2.38 
 
 8 
 
 460 
 
 1380 
 
 2 
 
 1100 
 
 2 
 
 3 
 
 19 
 
 2.38 
 
 8 
 
 690 
 
 1380 
 
 3 
 
 1000 
 
 2 
 
 3 
 
 19 
 
 2.38 
 
 8 
 
 625 
 
 1250 
 
 5 
 
 1000 
 
 2 
 
 4 
 
 18 
 
 3.0 
 
 6 
 
 790 
 
 1580 
 
 7V2 
 
 900 
 
 2 
 
 5 
 
 18 
 
 3.0 
 
 6 
 
 705 
 
 1410 
 
 10 
 
 850 
 
 2 
 
 6 
 
 18 
 
 3.6 
 
 5 
 
 800 
 
 1600 
 
 15 
 
 780 
 
 2 
 
 6l/ 2 
 
 19 
 
 3.8 
 
 5 
 
 780 
 
 1560 
 
 20 
 
 650 
 
 2 
 
 71/2 
 
 19 
 
 4.22 
 
 41/2 
 
 720 
 
 1440 
 
 25 
 
 550 
 
 2 
 
 9 
 
 18 
 
 4.5 
 
 4 
 
 645 
 
 1290 
 
 30 
 
 550 
 
 2 
 
 10 
 
 18 
 
 5.53 
 
 3l/ 4 
 
 800 
 
 1600 
 
 40 
 
 550 
 
 2 
 
 12 
 
 15 
 
 5.0 
 
 31/2 
 
 720 
 
 1440 
 
 50 
 
 500 
 
 2 
 
 121/2 
 
 18 
 
 6.0 
 
 3 
 
 790 
 
 1580 
 
 
 Minimum Speed Rating. 
 
 1 
 
 450 
 
 4 
 
 3 
 
 19 
 
 2.38 
 
 8 
 
 280 
 
 1120 
 
 2 
 
 450 
 
 4 
 
 4 
 
 18 
 
 3.0 
 
 6 
 
 355 
 
 1420 
 
 3 
 
 375 
 
 4 
 
 5 
 
 18 
 
 3.0 
 
 6 
 
 294 
 
 1176 
 
 5 
 
 375 
 
 4 
 
 6 
 
 18 
 
 3.6 
 
 5 
 
 355 
 
 1420 
 
 71/2 
 
 350 
 
 4 
 
 61/2 
 
 19 
 
 3.8 
 
 5 
 
 350 
 
 1400 
 
 10 
 
 375 
 
 4 
 
 7 
 
 18 
 
 4.0 
 
 41/2 
 
 390 
 
 1560 
 
 15 
 
 375 
 
 4 
 
 9 
 
 18 
 
 4.5 
 
 
 440 
 
 1760 
 
 20 
 
 300 
 
 4 
 
 12 
 
 15 
 
 5.0 
 
 3 
 
 390 
 
 1560 
 
 25 
 
 300 
 
 4 
 
 121/2 
 
 18 
 
 6.0 
 
 3 
 
 470 
 
 1880 
 
 30 
 
 250 
 
 4 
 
 14 
 
 18 
 
 6.0 
 
 3 
 
 390 
 
 1560 
 
 40 
 
 250 
 
 4 
 
 16 
 
 19 
 
 6.33 
 
 3 
 
 415 
 
 1660 
 
 50 
 
 325 
 
 3 
 
 16 
 
 19 
 
 6.33 
 
 3 
 
 540 
 
 1620 
 
1302 
 
 THE MACHINE-SHOP. 
 
 on the motor countershaft. Back geared motors are used where che 
 machine speed is below 150 to 100 r.p.m. The initial speed of the 
 back geared motor should not exceed 1200 r.p.m. when the horse-power 
 is from 10 to 20 and should not exceed 900 or even 720 r.p.m. when 
 the horse-power is greater than this figure. 
 
 For equipment where the motor is geared to the machine, the follow- 
 ing are the governing considerations: Speed reduction, pitch line 
 speed, number of teeth on gears, width of face of gears, center distances, 
 use of idler gears, motor mounting. Noise limits the pitch line speed 
 to about 1000 feet per minute with steel gears. For speeds of 1000 
 to 2000 feet per minute, cloth or rawhide pinions should be used and 
 speeds in excess of 2000 feet per minute should be avoided if possible. 
 Stresses in bearings and motor shafts limit the minimum size of motor 
 pinions just as they limit the size of pulleys. The maximum and 
 minimum speed ratings and the corresponding standard and minimum 
 sizes of pinions for constant speed and adjustable speed motors are 
 given in the tables on the preceding page. The second table also gives 
 the minimum pulley diameters for adjustable speed motors. 
 
 For additional data on machine tool motors see Electrical Engineer- 
 ing, p. 1466. 
 
 Motor Requirements for Milling Machines. See p. 1278. 
 
 Power Required for Drilling. See p. 1286. 
 
 Motor Requirements of Planers. (A. G. Popcke, Am. Mach., Sept. 
 26, 1912.) Manufacturers usually specify motors for planers that are 
 larger than necessary, due to the heavy peak load imposed at the instant 
 of reversal. Before the advent of interpole, commutating motors, this 
 peak load caused sparking unless a large motor was used. The com- 
 mutating motor eliminates this trouble and permits the use of a smaller 
 motor. A flywheel on the countershaft, from which the forward and 
 reverse belts are driven, will assist in the carrying of the peak loads, 
 and will allow the use of a smaller driving motor than otherwise. The 
 table below shows the results of tests of planers with a graphic record- 
 ing ammeter, and gives the power required at different portions of the 
 planer cycle. It also shows the motors recommended and installed, 
 which are handling the work satisfactorily, and also the size of motors 
 specified by the makers of the tools. 
 
 Power Requirements of Planers. 
 
 
 
 Observed Power 
 
 
 
 
 
 Motor 
 
 Re quirements. 
 
 
 Motor 
 In- 
 
 
 Size of 
 
 Used 
 
 
 
 _ 
 
 'cS 
 
 
 stalled, 
 
 Motor 
 
 Planer. 
 
 for 
 
 & 
 
 M 
 
 <n t* 
 
 I 
 
 Remarks. 
 
 Based 
 
 Speci- 
 
 
 Test. 
 
 3 o 
 
 
 o>o 
 
 0> o 3 
 
 
 on 
 
 fied. 
 
 
 
 ra 
 
 Is 
 
 S5 
 
 eftf 
 
 
 Test. 
 
 
 In. Ft. 
 
 H.P. 
 
 K.W. 
 
 K.W. 
 
 K.W. 
 
 K.W. 
 
 
 H.P. 
 
 H.P. 
 
 56 X 15 
 
 3 
 
 1.3 
 
 3.5 
 
 4.0 
 
 5.3 
 
 Average work 
 
 ) 
 
 
 
 5 
 
 1.8 
 
 2.8 
 
 3.5 
 
 5.3 
 
 5 Tons on table 
 
 [ 5 
 
 15 
 
 ** 
 
 5 
 
 2.5 
 
 
 6 
 
 6 
 
 Short stroke 
 
 f 
 
 
 54 X 16 
 
 30 
 
 4 
 
 "6 " 
 
 8 
 
 10.5 
 
 Average stroke 
 
 
 
 
 30 
 
 4 
 
 7 
 
 10 
 
 12 
 
 Short stroke 
 
 i 5 
 
 15 
 
 
 
 5 
 
 1.8 
 
 2.3 
 
 3.5 
 
 5.5 
 
 Average stroke 
 
 
 
 48 X 12 
 
 5 
 
 2 
 
 7 
 
 8 
 
 9 
 
 Average work 
 
 71/2 
 
 15 
 
 24 X 10 
 
 71/2 
 
 2 
 
 4.5 
 
 4.3 
 
 5.5 { 
 
 Motor geared 
 balance wheel 
 
 } * 
 
 71/2 
 
 42 X 12* 
 
 5 
 
 1.5 
 
 2.5 
 
 5 
 
 7 
 
 Average work 
 
 71/2 
 
 15 
 
 48 X 12 
 
 30 
 
 5 
 
 10 
 
 14 
 
 19 
 
 No. bal. wheel 
 
 71/2 
 
 15 
 
 37 X 8 
 36 X 8 
 
 5 
 
 5 
 
 1.8 
 1.5 
 
 3 
 
 2 
 
 4 
 2.5 
 
 6 
 4 
 
 Average work 
 
 5 
 3 
 
 10 
 5 
 
 36 X 8 
 
 5 
 
 1.8 
 
 2 
 
 3 
 
 5 
 
 " 
 
 3 
 
 5 
 
 * Open side. 
 
 The Cincinnati Planer Co. has furnished the author with the results 
 of a test of 72 in. X 24 ft. planer, fitted with a reversible motor drive, 
 cutting cast iron, To run the table in the direction^ the cut required 
 
POWER REQUIRED FOR WOOD-WORKING MACHINES. 1303 
 
 2.06 H.P. ; reversing from cutting to return stroke, 13 H.P.; reversing 
 from return to cutting stroke, 14.4 H.P. 
 
 Test on 72 X 24-in. Reversible Motor-Driven Planer. 
 
 -Depth 
 of Cut, 
 In. 
 
 Feed, 
 In. 
 
 Number 
 of Tools 
 Cutting. 
 
 Cutting 
 Speed, 
 Ft. per 
 Min. 
 
 H.P. 
 Required, 
 Including 
 Friction. 
 
 Pressure 
 per Sq. In. 
 in 
 Cast Iron. 
 
 1/2 
 
 3/16 
 
 2 
 
 30 
 
 23 
 
 123,200 
 
 1/2 
 
 3/16 
 
 2 
 
 40 
 
 26.7 
 
 108,680 
 
 1/2 
 
 3/16 
 
 2 
 
 60 
 
 37.5 
 
 104,133 
 
 1/2 
 
 3/32 
 
 2 
 
 30 
 
 11.5 
 
 111.419 
 
 1/2 
 
 3/32 
 
 2 
 
 60 
 
 23 
 
 123,200 
 
 1/4 
 
 3/16 
 
 2 
 
 30 
 
 10.1 
 
 95,090 
 
 1/4 
 
 3/16 
 
 2 
 
 60 
 
 20.2 
 
 106,830 
 
 V4 . 
 
 3/32 
 
 2 
 
 30 
 
 7.3 
 
 124,572 
 
 1/4 
 
 3/32 
 
 2 
 
 60 
 
 14.4 
 
 145.726 
 
 Power Required for Wood-Working Machinery. (E. G. Fox, EL 
 Rev., June 13, 1914.). The factors influencing the power required 
 for wood- working machines are: Design, speed of working, including 
 feed and depth of cut, condition of machine and cutters, nature of 
 material. Machines handling one kind of material may be motored 
 for their ordinary load, while those having diverse work must be 
 motored for their heaviest service. The data below are based upon 
 tests as well as on figures furnished by manufacturers. 
 
 Band Saws. The motors should have good starting torque, and 
 with resaws should be .capable of developing 1.5 full load torque 
 at starting, and should have good overload characteristics. Belted 
 motors are recommended for most installations. 
 
 BAND-SAWS. 
 
 Wheel diameter, in ............ 42 38 36 36 34 30 
 
 R.P.M ....................... 400-500 450 500 400 500 500 
 
 Maximum depth of timber, in .. 20 16 16 14 12 12 
 
 H.P. of motor ................. 5 553 
 
 3 
 
 BAND-RESAWS. 
 
 Wheel diameter, in .......... 60 54 48 44 42 40 38 
 
 R.P.M ...................... 550 600 650 650 650 700 450 
 
 Width saw blade, in .......... 8 6 5 4 4 3 2 
 
 Maximum depth of timber, in .. 36 30 26 24 24 20 12 
 
 H.P. of motor ................ 50 40 30 20 15 15 7.5 
 
 R.P.M. of motor ............. 600 600 720 720 720 720 514 
 
 Add for jointing attachment on 48-in. saw, 7.5 H.P. 
 
 BAND RIP SAWS POWER FEED. 
 
 Wheel Diam., Max. Timber Motor Motor 
 
 in. R.P.M. Depth, in. H.P. R.P.M. 
 
 42 650 12 15 720 
 
 40 600 15 10 600 
 
 Add 2 H.P. for return rolls, if used. Speeds given are for direct 
 connection. 
 
 Circular Saws. Circular saws are not as widely used as band-saws 
 for resawing, as they require more power, run at lower speeds and waste 
 more stock. Splitting with circular saws requires from 15 to 20% 
 more power than cross-cutting. Band-saws require about the same 
 power for both. 
 
 CIRCULAR SAWS. 
 Maximum diameter of saw, in ....... 42 36 
 
 R.P.M. of saw .................... 900 1000 
 
 Maximum capacity, in., horizontal. .. 17 14 
 4 vertical ............ 
 
 Horse-power ...................... 25 25 
 
 32 30 24 
 
 1225 1200 1225 
 
 11 10 8 
 
 8 6 6 
 
 20 20 20 
 
1304 
 
 THE MACHINE-SHOP. 
 
 CIRCULAR RIP-SAWS. 
 
 Maximum diameter of saw, in 20 16 12 
 
 Maximum R.P.M. of saw 2100 2600 2400 
 
 Maximum thickness of stock, in 6 5 2 
 
 Feed, ft. per min 60-180 64-194 50-100 
 
 Horse-power 15 15 7.5 
 
 HAND-FEED CIRCULAR RIP-SAWS. 
 Maximum diameter of saw, in. 14 16 20 24 30 36 
 
 R.P.M. of saw 2700 2400 2000 1600 1250 1000 
 
 Horse-power 7.5 10 15 15 20 20 
 
 POWER-FEED GANG RIPPING-MACHINE. 
 
 Number of saws 2 3 4 8 
 
 Maximum R.P.M 3400 2300 2500 2500 
 
 Diameter of saws, in 10 15 14 14 
 
 Feed, ft. per min 180 200 100-180 90-200 
 
 Horse-power 15 30 25 35 
 
 CIRCULAR CUT-OFF SAWS. 
 
 . Maximum saw diameter, in 14 16 
 
 R.P.M. of saws 2700 2600 
 
 Hcrse-power 5 7.5 
 
 INSIDE MOLDERS. 
 
 Maximum capacity, in 8X4 10 X 4 12 X 6 14X6 
 
 Horse-power 25 25 35 35 
 
 OUTSIDE MOLDERS. 
 Maximum capacity, in. 4X4 6X4 8X4 10X4 12X5 14X6 
 
 Horse-power 10 15 20 25 30 35 
 
 STICKERS. 
 Maximum size of timber, in... 16X4- 18X4 20 X 4 
 
 Horse-power ". 5 7.5 10 
 
 JOINTERS. 
 
 Maximum width of. timber, in 8 12 16 20 24 36 
 
 Horse-power 2 2 3 5 7.5 7.5 
 
 The recommendations for molders, stickers and jointers are based 
 on a maximum depth of cut of 3/ 32 in. If the cut is greater, the size of 
 motor should be correspondingly increased. 
 
 Surfacers. The motor sizes given below are for medium work with 
 maximum depths of cut of i/g in. For planing mill work, on heavy 
 stock with, deep cuts the sizes should be increased about 5 H.P. 
 
 SINGLE SURFACERS. 
 Maximum width of timber, in. 16 20 24 30 36 
 
 Horse-power 7.5 10 10 15 15 
 
 DOUBLE SURFACERS. 
 
 Maximum width of timber, in 26 30 36 
 
 Horse-power, heavy work 35 35 
 
 Horse-power, medium work 20 25 30 
 
 Timber Sizers. The following figures apply to heavy service in 
 dressing timber to size, surfacing four sides simultaneously. 
 Max. size of timber, in. . 20 X 16 20 X 18 20 X 20 30 X 18 30 X 20 
 
 Horse-power 60 60-75 60-75 75 75 
 
 DRUM SANDERS. 
 
 Number of drums 1 1 1 2 2 2 2 
 
 Max. Width of Stock, in 30 36 42 30 36 42 48 
 
 Horse-power 10 15 15 20 20 20 25 
 
 Number of drums 3 3 3 3 3 3 3 
 
 Maximum width of stock, in ... 30 36 42-48 54-66 72 78 84 
 
 Horse-power 20 25 30 35 40 40 50 
 
 When material is sanded to size and full width of sander is used with 
 panels fed continuously, add 5 H.P. to above motor sizes. 
 TENONERS HAND-FEED. 
 
 Length of tenon, in 7 single 7 double 
 
 Horse-power 7.5 10 
 
POWER REQUIRED FOR MACHINES IN GROUPS. 1305 
 
 Shapers.- For ordinary service on reversible single- or two-spindle 
 machines, use a 5 H.P. motor. For extra heavy work, as in carriage 
 factories, railroad shops, etc., use a 7.5 H.P. motor. 
 
 SCRAPING MACHINES. 
 Maximum width of stock, in. . . 12 26 30 42 
 
 Horse-power 2 3 3 5 
 
 AUTOMATIC LATHES. 
 Maximum diameter and length of stock, in. 2.75 X 72 3 X 50 5 X 50 
 
 Horse-power 10 15-20 20 
 
 BORERS. 
 
 Number of bits 112 348 
 
 Maximum diameter of bits, in 1 2 0.75 0.75 0.5 0.5 
 
 Horse-power 3 5 3 5 5 10 
 
 CHISEL MORTISING-MACHINES. 
 
 Maximum number of chisels 1 1 1 1 2 
 
 Maximum size of chisel square, in 0.5 0.75 0.75 1.25 1 
 
 Horse-power 2 2 3 5 3 
 
 Maximum number of chisels 3 4 5 6 7 
 
 Maximum size of chisel square, in 1 1 13/ie is/ig 13/ig 
 
 Horse-power 5 5 5 7.5 7.5 
 
 PLANERS AND MATCHERS. 
 
 For planing and matching timber at one operation. 
 Maximum size of timber, in. . 9X6 15 X 6 20 X 6 24 X 6 26 X 8 
 Horse-power 35 40 45 45 45 
 
 Box board matchers are similar to planers and matchers, but the 
 work is much lighter. Hand-fed machines usually require a 7.5 H.P. 
 motor, while power-fed machines require 10 H.P. 
 
 Horse-power Required to Drive Shafting. Samuel Webber in his 
 "Manual of Power" gives, among numerous tables of power required 
 to drive textile machinery, a table of results of tests of shafting. A line 
 of 21/8-in. shafting, 342 ft. long, weighing 4098 lb., with pulleys weigh- 
 ing 5331 lb., or a total of 9429 lb., supported on 47 bearings, 216 rev- 
 olutions per minute, required 1.858 H.P. to drive it. This gives a 
 coefficient of friction of 5.52 %. In seventeen tests the coefficient ranged 
 from 3.34% to 11.4%, averaging 5.73%. J. T. Henthorn states (Trans. 
 A. S. M. E., vi, 462) that in print-mills which he examined the friction 
 of the shafting and engine was in 7 cases below 20% and in 35 cases 
 between 20% and 30%, in 11 cases from 30% to 35% and in 2 cases 
 above 35%, the average being 25.9%. Mr. Barrus in eight cotton- 
 mills found the range to be between 18% and 25.7%, the average being 
 22%. Mr. Flather (Dynamometers) believes that for shops using 
 heavy machinery the percentage of power required to drive the shafting 
 will average from 40% to 50% of the total power expended. Under 
 the head of shafting are included elevators, fans and blowers. 
 
 Power Required to Drive Machines In Groups. L. P. Alford 
 (Am. Mac/2., Oct. 31, 1907) gives the results of an investigation to 
 determine the power required to drive machinery in groups. The 
 method employed comprised disconnecting parts of the shafting in a 
 belt-driven plant, and driving the disconnected porti9n with its ma- 
 chines by an electric motor, readings of the power required being taken 
 every 5 minutes. The average power required for the entire factory 
 was considerably less than the sum of the power required for the in- 
 dividual machines, due to tools being stopped at some portion of the 
 day for adjustment, replacement of work, etc. The conditions of 
 group driving are such that fixed rules cannot be laid down, but a study 
 must be made of each individual case. The results of the several thou- 
 sand observations made in the investigation are given in the accom- 
 panying table. The observations were made before the introduction 
 of high speed steel, and the figures probably should be modified some- 
 what for more modern practice. The sum of the individual horsepower 
 values as given in the table is about 20% higher than the power actual jy 
 used in the factory, due to a lessening of the average horse-power in 
 each department. The reason for this is the working conditions exist- 
 ing, in that all tools were not used to their maximum or even average 
 
1306 
 
 THE MACHINE-SHOP: 
 
 capacity at the same time. In determining the size of motor for each 
 department, the total horse-power required by the tools in that depart- 
 ment, as given in the table, was diminished by 20%, and the friction 
 load of line and countershafts was added. 
 
 Power Required by Machine Tools in Groups. 
 
 Size. 
 
 Maxi- 
 mum 
 H.P. 
 
 Aver- 
 age 
 H.P. 
 
 Size. 
 
 Maxi- 
 mum 
 H.P. 
 
 Aver- 
 age 
 H.P. 
 
 Size, 
 
 Maxi- 
 mum 
 H.P. 
 
 Aver- 
 age 
 H.P. 
 
 Boring 
 36 in.i 
 42 2 
 
 Cam 
 No. 2 
 " 4 
 " 5 
 Note 3 
 " 4 
 Cutting- 
 1 15/16 in. 
 2 in. 
 3 in. 
 Drilling 
 Note 5 
 " 6 
 " 7 
 " 8 
 " 9 
 " 10 
 " 11 
 16 in. 
 18 " 
 20 " 
 22 " 
 24 " 
 26 " 
 28 " 
 30 " 
 34 " 
 36 " 
 46 " 
 50 " 
 Gear 
 No. 4 1/2 
 3 
 3 
 
 Gr 
 
 No. 312 
 " 4 
 
 " 111 3 
 
 2" 
 
 314 
 115 
 21 5 
 
 Mach 
 0.78 
 1.72 
 
 Cutte 
 
 mes. 
 0.52 
 1.08 
 rs. 
 0.67 
 0.32 
 0.32 
 0.32 
 0.32 
 chine. 
 0.12 
 0.14-0.18 
 0.20-0.22 
 ines. 
 0.72 
 1.12 
 0.31 
 0.32 
 0.35 
 0.48 
 0.71 
 0.25 
 0.35 
 0.42 
 0.59 
 0.47 
 0.22 
 0.25 
 0.30 
 0.45 
 0.53 
 0.63 
 0.83 
 rs. 
 0.15-0.32 
 0.20 
 0.20 
 
 0.32 
 0.53 
 0.80 
 0.40 
 0.50 
 0.60 
 0.76 
 
 Grind 
 Note 16 
 " 17 
 Drop 
 40 Ib. 
 250 
 400' 
 600 
 800 
 1000 
 1500 
 Power 
 lOOlb. 
 150 " 
 Ke 
 No. 4 
 L 
 20 in.i* 
 30 " is 
 12 " 
 14 " 
 16 " 
 16 " 
 18 " 
 20 " 
 22 " 
 24 " 
 24 " 
 28 " 
 38 " 
 10 " 19 
 
 14 " 19 
 
 15 20 
 
 #21 
 
 No. I 22 
 2X24 in. 23 
 14 in. 24 
 
 16 " 24 
 36 " 25 
 
 Milling 
 No. 1 
 " 3 
 " 4 
 
 " 41/2 
 
 " 6 
 
 ers (C< 
 3.29 
 
 Hamm 
 
 mi.} 
 0.97 
 0.41-0.82 
 ers. * 
 0.10 
 2.00 
 2.50 
 3.00 
 3.50 
 4.00 
 5.00 
 lers. 
 1.50 
 1.75 
 
 0.28-0.32 
 
 0.35 
 0.41 
 0.24 
 0.26 
 0.34 
 0.36 
 0.39 
 0.44 
 0.32 
 0.25 
 0.31 
 0.31 
 0.58 
 0.10 
 0.12 
 0.25 
 0.70 
 0.33-0.63 
 1.20-1.80 
 0.31 
 0.36 
 1.30 
 ines. 
 0.30 
 0.26 
 0.19-0.29 
 0.13-0.19 
 0.26 
 
 Milling M 
 No. 7 
 14 
 15 
 
 326 
 
 5 26 
 
 3 
 1 
 2 
 5 
 
 7 
 
 u/2 27 
 PI 
 
 17 in. 
 22 X 60 in. 
 22 X 60 
 24 X 72 
 26 X 60 
 30 X 72 
 30 X 96 
 36X120 
 50X108 
 34 in.28 
 24 29 
 
 Polishi 
 No. 3 
 
 Fund- 
 No. 3 
 Profilin 
 No. T 
 
 Ban 
 36 in. 
 Circ 
 9 in. 
 13 " 
 13 " 
 Ha 
 12-14 in. 
 Screw 
 No. 1 
 " 2 
 " 2 
 
 achine 
 
 aners. 
 2.01 
 2.34 
 1.44 
 
 'l'.59' 
 4.91 
 5.46 
 4.00 
 2.94 
 7.75 
 3.40 
 ngSta 
 
 i Press 
 2.59 
 y ]Mac 
 
 s (Cow/.) 
 0.83 
 0.25 
 0.25 
 0.26 
 0.55 
 0.17-0.25 
 0.15 
 0.25 
 0.30 
 0.83 
 0.20 
 
 1.0 -0.43 
 1.16-0.53 
 0.70 
 0.84 
 0.81 
 1.31 
 1.56 
 1.60 
 1.14 
 3.70 
 2.00 
 nds. 
 1.00 
 1.09 
 es. 
 1.26 
 lines. 
 0.50 
 0.40 
 
 30 
 
 0.87 
 iw. 
 1.05 
 1.04 
 1.21 
 
 7. 
 
 0.06 
 nes. 
 0.60 
 0.37 
 0.72 
 
 0.48 
 0.48 
 
 
 
 
 
 
 off Ma 
 
 
 
 0.28 
 0.34 
 r Mach 
 
 '3.*18' 
 
 Hamn 
 
 
 yseater 
 0.64 
 athes. 
 
 
 
 0.48 
 '6.48' 
 
 
 
 
 
 0.37 
 
 Cutte 
 
 inders 
 '1.42' 
 
 'j.63' 
 1.97 
 
 'i.5b' 
 
 Mach 
 0.47 
 0.64 
 
 d-Saw 
 3.00 
 ular 82 
 3.77 
 3.75 
 5.82 
 ck Sav 
 
 Machi 
 
 NOTES. i Single head. 2 Double head. 3 Lathe type, single head. 4 Lathe 
 type, double head. 5 No. radial. 6 No. 1 radial. 7 Single spindle, 
 sensitive. 8 2-spindle. 3-spindle, sensitive. 1 4-spindle. n 6-spindle. 
 12 Cutter and reamer, i 3 Plain. "Surface. ^Universal. i fi Wet tool, 
 carrying 20-in. wheel. l7 Wet grinder with two 24-in. wheels. 18 Boring 
 lathe, is Speed lathe. 20 Squaring-up lathe. 21 Gisholt turret lathe. 
 22 Potter & Johnson semi-automatic. 23 Jones & Lamson flat turret. 21 Wood 
 turning. 25 p u tnam gap lathe, used for wood turning. 26 Vertical. 2 ? Hand. 
 88 Wood panel planer. 29 Wood surfacer. 30 Used for pattern work. 
 
MACHINE TOOL DRIVES, SPEEDS AND FEEDS. 1307 
 
 A similar investigation, reported by H. C. Spillman (Mach'y, June, 
 1913), showed that but 20% of the total power supplied to the motor 
 is applied in useful work in the machines, 72% being absorbed in friction 
 losses in machines and shafting, and 8% disappearing as electrical 
 losses. 
 
 MACHINE TOOL DRIVES, SPEEDS AND FEEDS. 
 
 Geometrical Progression of Speeds and Feeds. It has become 
 generally accepted that the speeds available on a given machine tool 
 should be in a geometric progression. There is, however, by no means 
 a uniformity in the ratio of the various geometric series adopted by 
 the different makers. This ratio will be found to range from 1.3 to 1.7 
 on the usual types of cone-driven machines, and the speeds available 
 under different conditions of open belt and back gear operation present 
 many duplications and are often far from a true geometric progression 
 when considered over the entire range of speeds. Carl G. Barth (Am. 
 Mach., Jan. 11, 1912) suggests a ratio of ^2~"= 1.189. With this ratio, 
 the revolutions per minute of the spindle are doubled every fourth 
 speed. An editorial (Am. Mach., Dec. 3, 1914) discussing the advan- 
 tage of adopting this ratio for a speed series shows that it will fulfill 
 all the ordinary requirements of machine tool work, and that practically 
 any desired speed in either lathe or drill press can be obtained when 
 the machine is speeded according to a geometric progression based 
 on the ratio 1.189. At the present writing (1915) this ratio has been 
 adopted by several machine tool builders. 
 
 The necessity for the adoption of a standard ratio for speeds and 
 feeds on machine tools is discussed in Am. Mach., Dec. 3 and 10, 1914, 
 in describing the respeeding of machines at the Watertown arsenal and 
 elsewhere. The speeds originally available on many of the machines 
 presented many duplications of open belt speeds when back-geared, and 
 the speeds on any one machine considered as a whole were not in any 
 regular series. Thus a lathe with supposedly 20 speeds had practically, 
 due to duplication of speeds in the open belt and back-gear series, only 
 12 speeds. The rearrangement of the gearing and the pulleys made 
 all 20 speeds available, and in practical accord with a geometric series 
 with a ratio of 1.189. In the same article there are tabulated the 
 speeds of nine 16-in. lathes offered in response to a' request for bids. 
 In no case did the speeds available on one lathe correspond with those 
 on any other, nor did any set of speeds even approximate the ideal 
 speeds. Even three machines offered by one maker had wide variations 
 in their speeds. Such a condition precludes the possibility of using 
 machines interchangeably for the same service, and, as stated by Mr. 
 Barth, is the basis of much of the trouble regarding piece rates in machine 
 shop work. See also article by Robert T. Kent, Iron Age, July 3, 1913. 
 
 A geometrical progression of the fe^ds available on machine tools is 
 also desirable, and Mr. Barth has recommended the same ratio for 
 the feed series as for the speed series, *\/2~= 1.189. The reasons for 
 adopting this ratio are given in the article above cited, Am. Mach., 
 Jan. 11, 1912. 
 
 Methods of Driving Machine Tools. P. A. Halsey in a lecture at 
 Columbia University (Indust. Eng., Sept., 1914) compares the relative 
 advantages of the ordinary 5-step cone pulley, the 3-step cone pulley, 
 the constant speed pulley and the individual motor as a drive for 
 machine tools. In the 5-step cone pulley drive the large intervals 
 between the speeds available on the different cone steps decrease the 
 output of the machine, due to the fact that except in those few cases 
 where the cone speed is nearly equal to the cutting speed the next 
 lower cone speed must be used. Also on account of the proportions 
 of the cone, the belt speed is unnecessarily low, and as the belt is moved 
 to the largest cone step its speed is still further decreased. On the 
 larger steps the belt is frequently incapable of delivering the power 
 required by the heavier cuts which go with large work. This defect 
 is remedied in the 3-step cone pulley, in which the difference in the 
 diameters of the steps is not so pronounced, the additional number of 
 speed changes being obtained by double back gears. 
 
 Mr. Halsey compares two specific cases: (1) A 5-step cone with 
 single back gears, the cone step diameters being respectively 4, 6, 8, 30, 
 
1308 THE MACHINE-SHOP. 
 
 and 12 in. (2) A 3-step cone with double back gears, the cone step 
 diameters being respectively 11 17/32, 129/32, and 13 in. In case 1 a 2 1/2- 
 in. belt, and in case 2 a 4-in. belt, is used. The change from 3 to 5 steps 
 reduces the ratio of the highest to the lowest speed on the cone, and ife 
 increases the 'belt speed and therefore the power on all steps, but 
 particularly on the large ones where it is most needed. The effect of 
 these changes can be shown by calculating the respective powers with 
 the belts on the largest steps of the two cones. Assume (case 1) that 
 the speed with the belt on the 4-in. step is 100. Then the speed with 
 the belt on the largest step will be 100 X 4 /i2 = 331/3. To maintain 
 the same cone speed in case 2, the highest belt speed will be 
 100 (11 17/32 -=- 4) = 288 +; the lowest will be 288 (11 !7/ 32 + 13) = 255 +. 
 The smallest step in case 1 is too small for a double belt, while in case 2 
 a double belt can be used on the smallest step. In order to compare 
 the power capacities of the two machines the belt speed must be 
 multiplied by a factor reprasenting the greater pulling power of the 
 double belt, say 1.43, and also by the ratio of the belt widths, 1.6. If 
 LI and Z/2 represent respectively the power capacities of the large steps 
 of cases 1 and 2, and Si and 82 the power capacities of the small steps, 
 then 
 
 fs-fljx 1.43x1.6-6.5 
 
 - 
 
 803 . . 
 
 That is, the power capacity of the 3-step cone is 6.5 times as great 
 as that of the 5-step cone with the belt on the small step, and 17.5 times 
 as great with the belt on the large step. The defect of the arrange- 
 ment given in case 2 is that it provides a smaller number of speeds 
 and a smaller range of speeds than does case 1. The remedy is the 
 provision of additional back gears if the additional speeds or greater 
 range is necessary. Mr. Halsey further points out that direct connec- 
 tion between the cone pulley and the work spindle has been retained 
 in many cases where it should have been discarded, since with large 
 work the belt speed will become too low to transmit adequate power, 
 and it is better practice to interpose gearing between the pulley and the 
 spindle, and thus speed up the belt and pulley. In changing machines 
 in accordance with the above suggestions, it is advisable to so design 
 the gearing as to obtain speeds which will be in geometric progression 
 as explained in a previous paragraph. For methods of laying out cone 
 pulleys, see p. 1 136. For methods of laying out the driving gears of 
 machine tools see "Halsey's Handbook for Machine Designers and 
 Draftsmen," p. 77. 
 
 In the Constant Speed Pulley dwve, the belt pulley of the machine is 
 driven at a constant speed and the power is transmitted to the machine 
 from the pulley through a train of gears arranged in a gear box. By 
 the shifting of appropriate levers any particular set of gears can be put 
 in engagement, thus making instantly available any speed in the range 
 of the machine. This arrangement makes the obtaining of a geometric 
 series of speeds a particularly easy matter. The constant speed pulley 
 drive possesses the advantage of giving a self-contained machine, 
 particularly adapted to the individual motor drive. It has found 
 wide application in the milling machine and in certain types of lathes. 
 
 The Individual Motor Drive has, according to Mr. Halsey, a field in 
 the driving of portable floor plate tools, for machines in isolated posi- 
 tions, or for tools so located that line shafts cannot be conveniently 
 laid out for them, and for large machines where the cost of the motor 
 Is a relatively small part of the total cost of the tool. The disadvantage 
 of the individual motor for the small or medium size tool is that the 
 power capacity of the motor must be equal to the maximum power 
 requirement of the machine and that no advantage can be taken of 
 the average power requirements of several machines as is possible in 
 the group drive where one motor drives several machines. This in- 
 creases the first cost of the motors, and they are also usually worked 
 at low efficiency, due to the fact that they are most of the time 
 underloaded. 
 
ABRASIVE PROCESSES 1309 
 
 ABRASIVE PROCESSES. 
 
 Abrasive cutting is performed by means of stones, sand, emery, glass, 
 corundum, carborundum, crocus, rouge, chilled globules of iron, and in 
 some cases by soft, friable iron alone. (See paper by John Richards, 
 read before the Technical Society of the Pacific Coast, Am. Mach. t Aug. 
 20, 1891, and Eng. & M. Jour., July 25 and Aug. 15, 1891.) 
 
 The " Cold Saw." For sawing any section of iron while cold 
 the cold saw is sometimes used. This consists simply of a plain soft 
 steel or iron disk without teeth, about 42 inches diameter and 3/ 1( 5 inch 
 thick. The velocity of the circumference is about 15,000 feet per minute. 
 One of these saws will saw through an ordinary steel rail cold in about 
 one minute. In this saw the steel or iron is ground off by the friction 
 of the disk, and is not cut as with the teeth of an ordinary saw. It has 
 generally been found more profitable, however, to saw iron with disks or 
 band-saws fitted with cutting-teeth, which run at moderate speeds and 
 cut the metal as do the teeth of a milling-cutter. 
 
 Reese's Fusing-disk. Reese's fusing-disk is an application of the 
 cold saw to cutting iron or steel in the form of bars, tubes, cylinders, 
 etc., in which the piece to be cut is made to revolve at a slower rate or 
 speed than the saw. By this means only a small surface of the bar to 
 be cut is presented at a time to the circumference of the saw. The 
 saw is about the same size as the cold saw above described, and is rotated 
 at a velocity of about 25,000 feet per minute. The heat generated by 
 the friction of this saw against the small surface of the bar rotated against 
 it is so great that the particles of iron or steel in the bar are actually fused, 
 and the "sawdust" welds as it falls into a solid mass. This disk will cut 
 either cast iron, wrought iron, or steel. It will cut a bar of steel 13/g 
 inch diameter in one minute, including the time of setting it in the machine, 
 the bar being rotated about 200 turns per minute. 
 
 Cutting Stone with Wire. A plan of cutting stone by means 
 of a wire cord has been tried in Europe. While retaining sand as the 
 cutting agent, M. Paulin Gay, of Marseilles, has succeeded in applying 
 it by mechanical means, and as continuously as formerly the sand-blast 
 and band-saw, with both of which appliances his system that of the 
 "helicoidal wire cord" has considerable analogy. An engine puts in 
 motion a continuous wire cord (varying from five to seven thirty-seconds 
 of an inch in diameter, according to the work), composed of three mild- 
 steel wires twisted at a certain pitch, that is found to give the best results 
 in practice, at a speed of from 15 to 17 feet per second. 
 
 The Sand-blast. In the sand-blast, invented by B. F. Tilghman, 
 of Philadelphia, and first exhibited at the American Institute Fair, 
 New York, in 1871, common sand, powdered quartz, emery, or any sharp 
 cutting material is blown by a jet of air or steam on glass, metal, or other 
 comparatively brittle substance, by which means the latter is cut, drilled, 
 or engraved. To protect those portions of the surface which it is desired 
 shall not be abraded it is only necessary to cover them with a soft or 
 tough material, such as lead, rubber, leather, paper, wax, or rubber- 
 paint. (See description in App. Cyc. Mech.; also U. fc>. report of Vienna 
 Exhibition, 1873, vol. iii. 316.) 
 
 A "jet of sand" impelled by steam of moderate pressure, or even by 
 the blast of an ordinary fan, depolishes glass in a few seconds; wood is 
 cut quite rapidly; and metals are given the so-called "frosted" surface 
 with, great rapidity. With a jet issuing from under 300 pounds pressure, 
 a hole was cut through a piece of corundum 1 1/2 inches thick in 25 minutes. 
 
 The sand-blast has been a'pplied to the cleaning of metal castings and 
 sheet metal, the graining of zinc plates for lithographic purposes, the 
 frosting of silverware, the cutting of figures on stone and glass, and the 
 cutting of devices on monuments or tombstones, the recutting of files, 
 etc. The time required to sharpen a worn-out 14-inch bastard file is 
 about four minutes. About one pint of sand, passed through a No. 
 120 sieve, and 4 H.P. of 60-lb. steam are required for the operation. 
 For cleaning castings, compressed air at from 8 to 10 pounds pressure 
 per square inch is employed. Chilled-iron globules instead of quartz 
 or flint-sand are used with good results, both as to speed of working and 
 cost of material, when the operation can be carried on under proper 
 conditions. With the expenditure of 2 H.P. in compressing air, 2 square 
 feet of ordinary scale on the surface of steel and iron plates can be 
 
1310 THE MACHINE-SHOP. 
 
 removed per minute. The surface thus prepared is ready for tinning, 
 galvanizing, plating, bronzing, painting, etc. By continuing the opera- 
 tion the hard skin on the surface of castings, which is so destructive to 
 the cutting edges of milling and other tools, can be removed. Small 
 castings are placed in a sort of slowly rotating barrel, open at one or 
 both ends, through which the blast is directed downward against them 
 as they tumble over and over. No portion of the surface escapes the 
 action of the sand. Plain cored work, such as valve-bodies, can be 
 cleaned perfectly both inside and out. One hundred Ibs. of castings 
 can be cleaned in from 10 to 15 minutes with a blast created by 2 H.P. 
 The same weight of small forgings can be scaled in from 20 to 30 minutes. 
 Iron Age, March 8, 1894. 
 
 Polishing and Buffing. The type of polishing wheel to be used de- 
 pends on the class of work. For rough polishing on flat surfaces or 
 where the corners are to be square, a paper or a wooden wheel, faced 
 with leather to which emery or some other abrasive is glued is used. 
 For large flat work, or curved surfaces, bull neck, solid canvas, solid 
 sheepskin, paper or wooden wheels are used. These wheels are also 
 used for such work as stove trimmings, agricultural implements, tools, 
 cast iron and brass parts, etc. Loose or stitched sheepskin, loose or 
 stitched canvas and solid or stitched laminated felt wneels are used 
 for roughing irregular shapes requiring a soft faced wheel which will 
 come in contact with every crevice of the work. Bull neck or wooden 
 wheels are used whenever coloring or finishing is to be done on cast 
 or sheet metal. For work requiring a high polish, as guns, cutlery, 
 etc., sea horse is often employed. The hardness of the wheel depends 
 on the service in which it is to be used, and in the case of linen, canvas, 
 leather, or other built-up wheels on steel centers, is governed by the 
 depth of the flanges clamping the wheel on the arbor; the larger the 
 flanges the harder is the wheel. For most polishing operations, a 
 peripheral speed of the wheel of from 3000 to 6000 ft. per minute is 
 sufficient, and 4000 ft. will serve for most purposes. These are the 
 speeds recommended for muslin, felt or sea horse wheels, although 
 some claims are advanced for speeds as high as 7500 ft., it being stated 
 that lower speeds will scratch the work. 
 
 Buffing is the process of obtaining a grainless finish of high luster 
 on plated surfaces. The degree of luster depends on the finish of the 
 surface prior to plating. The work is done on a soft wheel to which 
 a polishing composition has been applied. The polishing composition 
 comprises a heavy grease containing polishing material, as flour-emery, 
 rouge, tripoli, crocus, etc. According to the Chicago Wheel and Mfg. 
 Co. the following compositions are adapted to the different varieties 
 of work. For cutting down and polishing brass, bronze and Britannia 
 metal preparatory to plating, tripoli composition; for smooth surfaces 
 on nickel and brass, crocus composition; for coloring brass, copper, 
 nickel, bronze, German silver, etc., either in solid or plated metal, 
 White Diamond XXX composition; for chased or embossed parts, or 
 for cutting down silver-plated pieces which are afterward to be colored 
 with rouge and alcohol, White Diamond XXXX composition is used; 
 for nickel-plated pieces with a high luster, White Coloring composition, 
 made of Vienna lime is used. Where rapid, sharp, even cutting is 
 desired, emery cake is used. Chandelier rouge is used to produce a 
 deep color on brass and bronze parts. 
 
 Laps and Lapping. A series of tests was made by W. -A. Knight 
 and A. A. Case (Jour. A. S. M. E., Aug., 1915) to determine the effect 
 on the rate of cutting with different combinations of abrasive lubricant 
 and lap material. The tests were made with hardened steel speci- 
 mens, and comparative results were obtained with emery, alunduin and 
 carborundum used in connection with lard oil, machine oil, gasoline, 
 kerosene, turpentine, alcohol and soda water. The lap materials were 
 cast iron, soft steel and copper. The following conclusions were 
 derived from the invesigation : The initial rate of cutting is not 
 greatly different for the different abrasives; carborundum maintains 
 its rate better than either of the others, alundum next, and emery the 
 least; carborundum wears the lap about twice as fast, and alundum 
 11/4 times as fast as emery; there is no advantage in using an abrasive 
 coarser than No. 150; the rate of cutting is practically proportional to 
 
EMERY WHEELS AND GRINDSTONES. 1311 
 
 the pressure; the wear of the laps is in the proportions of cast iron 
 1.00, steel 1.27, copper 2.62, and this wear is inversely proportional to 
 the hardness by the Brinell test; in general, copper and steel cut faster 
 than cast iron, but where permanence of form is a consideration, cast 
 iron is the superior metal ; gasoline and kerosene are the best lubricants 
 to use with cast-iron lap, kerosene, on account of its non-evaporative 
 qualities, being first choice; machine and lard oil are the best lubri- 
 cants to use with copper or steel lap, but they are least effective on the 
 cast lap; for all laps and all abrasives (of those tested) the cutting is 
 faster with lard oil than with machine oil; alcohol shows no particular 
 merit for the work ; turpentine does fairly good work with carborundum, 
 but in general, is not as good as kerosene or gasoline; soda water com- 
 pares favorably with other lubricants, and on the whole it is slightly 
 better than alcohol or turpentine; wet lapping is from 1.2 to 6 times 
 as fast as dry lapping, depending on the material of the lap and the 
 method of charging. 
 
 EMERY WHEELS AND GRINDSTONES. 
 
 References. "American Machinist Grinding Book"; "Grits and 
 Grinds," Norton Company; "Points about Grinding Wheels and their 
 Selection," Brown & Sharpe Mfg. Co.; "Table of Causes of Grinding 
 Wheel Accidents," Independence Inspection Bureau; "Safeguarding 
 Grinding Wheels," Report of Committee of National Machine Tool 
 Builders' Association; Bulletin, "Safeguarding High Speed Grinding 
 Wheels, "National Founders' Association; "Operation of Grinding Wheels 
 in Machine Grinding," Geo. I. Alden, Journal A.S.M.E., Jan., 1915. 
 
 Selection of Abrasive Wheels. (Contributed by the Norton Com- 
 pany, 1915.) The user of a modern grinding wheel should thoroughly 
 understand these essential features; the definition of grain and grade, 
 the particular conditions of grinding which cause them to vary; the 
 methods of balancing and mounting; truing and dressing; the effect of 
 machine vibration and arc of contact upon grain and grade; the rela- 
 tion of work speed and wheel speed for production and finish; safe- 
 guards and dust removal systems. 
 
 Grain. Abrasive grains are numbered according to the meshes per 
 lineal inch of the screen through which they have been graded. The 
 numbers used in wheels are 8, 10, 12, 14, 16, 20, 24, 30, 36, 46, 54, 60, 
 70, 80, 90, 120, 150, 180, 200; when finer than 200, the grains are termed 
 flours, being designated as F, 2F, 3F, 4F, XF, 65C, 65F, F being the 
 coarsest and 65F, the finest. Grits from 12 to 30 are generally used 
 on all heavy work such as snagging; 36 to 80 cover nearly all tool grind- 
 ing, saw gumming, and other operations where precision in measurement 
 is sought; 90 and finer are used for special work such as grinding steel 
 balls and fine edge work; the flour sizes are used mostly for sharpening 
 and rubbing stones. The number representing the grades of abrasive 
 leave a degree of smoothness of surface which may be compared to that 
 left by files as follows: 8 and 10 represent the cut of a wood rasp; 
 16, 20, coarse-rough file; 24, 30, ordinary rough file; 36, 40, bastard file; 
 46, 60, second-cut file; 70, 80, smooth file; 90, 100, superfine file; 
 120F, 2F, dead-smooth file. 
 
 Grade. When the retentive properties of the bond are great, the 
 wheel is called hard ; when the grains are easily broken out, it is called 
 soft. A wheel is of the proper grade when its cutting grains are auto- 
 matically replaced when dulled. Wheels that are too hard glaze. Dress- 
 ing re-sharpens them, the points of the dresser breaking out and break- 
 ing off the cutting grains by percussion. 
 
 Soft wheels are used on hard materials, like hardened steel. Here the 
 cutting particles are quickly dulled and must be renewed. On softer 
 materials, like mild steel and wrought iron, harder grades can be used, 
 the grains not dulling so quickly. 
 
 The area of surface to be ground in contact with the wheel is of the 
 utmost importance in determining the grade. If it is a point contact 
 like grinding a ball or if an extremely narrow fin is to be removed, we 
 must use a very strongly bonded wheel, on account of the leverage ex- 
 erted oil its grain, which tends to tear out the cutting particles before 
 
1312 
 
 THE MACHINE-SHOP. 
 
 Revolutions per Minute Required for Specified Rates of 
 
 Periphery Speed. Also Stress per Square Inch on 
 
 Norton Wheels at the Specified Rates. 
 
 
 Surface Speeds, Feet per Minute. 
 
 a* 
 
 M 
 
 1000 
 
 2000 
 
 3000 
 
 4000 
 
 5000 
 
 6000 
 
 7000 
 
 8000 
 
 9000 
 
 1000C 
 
 
 Stress per Square Inch, Pounds. 
 
 1 
 
 3 
 
 12 
 
 27 
 
 48 
 
 75 
 
 108 
 
 147 
 
 192 
 
 243 
 
 300 
 
 15 
 
 Revolutions per Minute. 
 
 i 
 
 3820 
 
 7639 
 
 11459 
 
 15279 
 
 19099 
 
 22918 
 
 26738 
 
 30558 
 
 34377 
 
 38197 
 
 2 
 
 1910 
 
 3820 
 
 5730 
 
 7639 
 
 9549 
 
 11459 
 
 13369 
 
 15279 
 
 17189 
 
 19098 
 
 3 
 
 1273 
 
 2546 
 
 3820 
 
 5093 
 
 6366 
 
 7639 
 
 8913 
 
 10186 
 
 11459 
 
 12732 
 
 4 
 
 955 
 
 1910 
 
 2865 
 
 3820 
 
 4775 
 
 5729 
 
 6684 
 
 7639 
 
 8594 
 
 9549 
 
 5 
 
 764 
 
 1528 
 
 2292 
 
 3056 
 
 3820 
 
 4584 
 
 5347 
 
 6111 
 
 6875 
 
 7639 
 
 6 
 
 637 
 
 1273 
 
 1910 
 
 2546 
 
 3183 
 
 3820 
 
 4456 
 
 5093 
 
 5729 
 
 6366 
 
 7 
 
 546 
 
 1091 
 
 1637 
 
 2183 
 
 2728 
 
 3274 
 
 3820 
 
 4365 
 
 4911 
 
 5457 
 
 8 
 
 477 
 
 955 
 
 1432 
 
 1910 
 
 2387 
 
 2865 
 
 3342 
 
 3820 
 
 4297 
 
 4775 
 
 10 
 
 382 
 
 764 
 
 1146 
 
 1528 
 
 1910 
 
 2292 
 
 2674 
 
 3056 
 
 3438 
 
 3820 
 
 12 
 
 318 
 
 637 
 
 955 
 
 1273 
 
 1591 
 
 1910 
 
 2228 
 
 2546 
 
 2865 
 
 3183 
 
 14 
 
 273 
 
 546 
 
 818 
 
 1091 
 
 1364 
 
 1637 
 
 1910 
 
 2183 
 
 2455 
 
 2728 
 
 16 
 
 239 
 
 477 
 
 716 
 
 955 
 
 1194 
 
 1432 
 
 1671 
 
 1910 
 
 2148 
 
 2387 
 
 18 
 
 212 
 
 424 
 
 637 
 
 849 
 
 1061 
 
 1273 
 
 1485 
 
 1698 
 
 1910 
 
 2122 
 
 20 
 
 191 
 
 382 
 
 573 
 
 764 
 
 955 
 
 1146 
 
 1337 
 
 1528 
 
 1719 
 
 1910 
 
 22 
 
 174 
 
 347 
 
 521 
 
 694 
 
 868 
 
 1042 
 
 1215 
 
 1389 
 
 1563 
 
 1736 
 
 24 
 
 159 
 
 318 
 
 477 
 
 637 
 
 796 
 
 955 
 
 1114 
 
 1273 
 
 1432 
 
 1591 
 
 30 
 
 127 
 
 255 
 
 382 
 
 509 
 
 637 
 
 764 
 
 891 
 
 1018 
 
 1146 
 
 1273 
 
 36 
 
 106 
 
 212 
 
 318 
 
 424 
 
 530 
 
 637 
 
 743 
 
 849 
 
 955 
 
 1061 
 
 Table to Figure Surface Speeds of Wheels. 
 (Circumferences in Feet , Diameters in Inches. ) 
 
 
 
 
 
 
 
 IN 
 
 
 
 
 
 -M 
 P=4 
 
 
 +a 
 
 P4 
 
 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 
 1 
 
 
 1 
 
 
 1 
 
 
 1 
 
 
 1 
 
 
 1 
 
 
 
 g 
 
 
 
 B 
 
 
 
 g 
 
 
 
 
 
 
 g 
 
 1 
 
 | 
 
 5 
 
 8 
 
 q 
 
 q 
 
 Q 
 
 6 
 
 a 
 
 
 
 '& 
 
 8 
 
 8 
 
 5 
 
 i 
 
 .262 
 
 13 
 
 3.403 
 
 25 
 
 6.546 
 
 37 
 
 9.687 
 
 49 
 
 12.828 
 
 61 
 
 15.970 
 
 2 
 
 .524 
 
 14 
 
 3.665 
 
 26 
 
 6.807 
 
 38 
 
 9.948 
 
 50 
 
 13.090 
 
 62 
 
 16.232 
 
 3 
 
 .785 
 
 15 
 
 3.927 
 
 27 
 
 7.069 
 
 39 
 
 10.210 
 
 51 
 
 13.352 
 
 63 
 
 16.493 
 
 4 
 
 1.047 
 
 16 
 
 4.189 
 
 28 
 
 7.330 
 
 40 
 
 10.472 
 
 52 
 
 13.613 
 
 64 
 
 16.755 
 
 5 
 
 1.309 
 
 17 
 
 4.451 
 
 29 
 
 7.592 
 
 41 
 
 10.734 
 
 53 
 
 13.875 
 
 65 
 
 17.017 
 
 6 
 
 1.571 
 
 18 
 
 4.712 
 
 30 
 
 7.854 
 
 42 
 
 10.996 
 
 54 
 
 14.137 
 
 66 
 
 17.279 
 
 7 
 
 1.833 
 
 19 
 
 4.974 
 
 31 
 
 8.116 
 
 43 
 
 11.257 
 
 55 
 
 14.499 
 
 67 
 
 17.541 
 
 8 
 
 2.094 
 
 20 
 
 5.236 
 
 32 
 
 8.377 
 
 44 
 
 11.519 
 
 56 
 
 14.661 
 
 68 
 
 17.802 
 
 9 
 
 2.356 
 
 21 
 
 5.498 
 
 33 
 
 8.639 
 
 45 
 
 11.781 
 
 57 
 
 14.923 
 
 69 
 
 18.064 
 
 10 
 
 2.618 
 
 22 
 
 5.760 
 
 34 
 
 8.901 
 
 46 
 
 12.043 
 
 58 
 
 15.184 
 
 70 
 
 18.326 
 
 11 
 
 2.880 
 
 23 
 
 6.021 
 
 35 
 
 9.163 
 
 47 
 
 12.305 
 
 59 
 
 15.446 
 
 71 
 
 18.588 
 
 12 
 
 3.142 
 
 24 
 
 6.283 
 
 36 
 
 9.425 
 
 48 
 
 12.566 
 
 60 
 
 15.708 
 
 72 
 
 18.850 
 
 To find surface speed, in feet, per minute, of a wheel. 
 
 RULE.- Multiply the circumference (see above table) by its revolu- 
 tions per minute. 
 
 Surface speed and diam. of wheel being given, to find number of revo- 
 lutions of wheel spindle. 
 
 RULE. Multiply surface speed, in feet, per min., by 12 arid divide the 
 product by 3.14 times the diam, of the wheel in inches. 
 
ABRASIVES. 1313 
 
 they have done their work. If the contact is a broad one, as in grind- 
 ing a hole, or where the work brings a large part pf the surface of 
 the wheel into operation, softer grades must be used, because the depth 
 of cut. is so infinitely small that the cutting points in work become 
 dulled quickly and must be renewed, or the wheel glazes and loses its 
 efficiency. 
 
 Vibrations in grinding machines cause percussion on the cutting 
 grains, necessitating harder wheels. Wheels mounted on rigid machines 
 can be softer in grade and are much more efficient. 
 
 Speeds of Grinding Wheels. The factor of safety in vitrified wheels 
 is proportional to the grade of hardness. Bursting limits are from 12,000 
 to 25,000 feet per minute, surface speed. Wheels are tested by standard 
 makers at speeds in excess of 9000 feet surface speed per minute. 
 Running speeds in practice are from 4000 to 6000 feet, depending on 
 work, condition of machine, and mounting. 
 
 Generally speaking, grinding of tools, reamers, cutters, and surface 
 grinding is done at about 4000 feet, snagging and rough forms of hand 
 grinding at 5000 to 5500 feet, cylindrical grinding, or where the work is 
 rigidly held and where the wheel feed is under control, from 5500 to 6500 
 feet, and in some instances as high as 7500 feet. 
 
 These speeds are all for vitrified wheels. The same speeds will apply 
 to wheels made by the elastic and silicate processes. 
 
 Grain Depth of Cut. An analysis of the action of the wheel when 
 in operation shows how theoretical considerations bear out the truth of 
 the empirical rules for the use of grinding wheels in machine grinding. 
 A paper by Geo. I. Alden (Jour. Am. Soc. M. E., Jan., 1915) gives the 
 essential distinction between the radial or real depth at which the 
 wheel cuts and the depth which the abrasive grain in the wheel cuts 
 into the material being ground. The latter depth is termed the "grain 
 depth of cut." This grain depth of cut is the controlling factor in se- 
 curing the correct working of the wheel. A formula is deduced for com- 
 puting the grain depth of cut, the application of the analysis is explained 
 and these conclusions reached by Prof. Alden: 1 Other factors remain- 
 ing consta.nt, increase of work speed increases grain depth of cut, and 
 makes a wheel appear softer. 2 A decrease of wheel speed increases 
 grain depth of cut. 3 Diminishing the diameter of the wheel increases 
 the grain depth of cut; increasing the diameter of the wheel decreases 
 the grain depth of cut. 4 Decreasing the diameter of work increases 
 the grain depth of cut; conversely, increasing the diameter of work de- 
 creases the grain depth of cut. 
 
 A table pf arcs of contact of wheel and work for a limited range of 
 diameters is given, also a table of values of one of the factors in the 
 formula for grain depth of cut. 
 
 Artificial Abrasives. Since 1900 artificial abrasives, made in 
 various types of electric furnaces, have been displacing natural abra- 
 sives, and they are to-day almost exclusively used. This has been due 
 largely to the ability to control the purity of the raw material and to 
 insure uniformity of cutting action of the finished products. Artificial 
 abrasives are divided into the aluminous group (examples, Alundum, 
 Aloxite and Boro-Carbone), and the silicon carbide group (examples, 
 Crystolon, Carborundum, Carbolite). The abrasive action of the 
 aluminous group is due to the amount of oxide of aluminum, which in 
 these artificial abrasives is in excess of 90%, slightly more than the best 
 corundum and considerably in excess of the alumina content of emery, 
 which rarely exceeds 70%. The aluminous abrasives are characterized 
 by a high degree of toughness and are particularly adapted for grinding 
 materials of high tensile strength such as steel and its alloys. The sili- 
 cate carbide group is not duplicated by Nature and is somewhat harder 
 and more brittle than the aluminous group. The silicon carbide abra- 
 sives are now recognized as standard for grinding materials of low 
 tensile strength such as cast iron, brass pearl, marble, granite and 
 leather. 
 
 Selection of Emery Wheels. The Norton Co. (1915) publishes the 
 accompanying table showing the proper grain and grade of wheel for 
 different services. The column headed grain indicates the coarseness of 
 the material composing the wheel, being designated by the number of 
 
1314 
 
 THE MACHINE-SHOP. 
 
 meshes per inch of a sieve through which the grains pass. A No. 20 
 grain will pass through a 20-mesh sieve, but not through a 30-mesh, etc. 
 
 EXPLANATION OF GRADE LETTERS. 
 
 Extremely 
 Soft. 
 A 
 B 
 C 
 D 
 
 Soft. 
 
 E 
 F 
 G 
 H 
 
 Medium 
 Soft. 
 I 
 J 
 K 
 L 
 
 Medium. 
 
 M 
 N 
 
 P 
 
 Medium 
 Hard. 
 Q 
 R 
 S 
 T 
 
 Hard. 
 
 U 
 W 
 
 Extremely 
 Hard. 
 Y 
 Z 
 
 FOP Grinding High-speed Tool Steel, The American Emery Wheel 
 Co. recommends a wheel one number coarser and one grade softer than 
 a wheel for grinding carbon steel for the same service. 
 
 Balancing. The standard makers of grinding wheels send out 
 wheels balanced within narrow limits, accomplished by inserting lead 
 near the hole. As the wheels wear down it frequently becomes necessary 
 for the user to balance them by removing some of the lead. 
 
 Mounting Grinding Wheels Safety Devices. A code for the mount- 
 ing of grinding wheels was adopted by 23 manufacturers of grinding 
 wheels in the U. S. and Canada in 1914, and approved by the Na- 
 tional Machine Tool Builders' Association. An abstract of the code is 
 given in Indust. Eng., Jan., 1915. The code recognizes as safety devices 
 protection flanges, protection hoods, and protection chucks. 
 
 Protection flanges of the double or single concave type, used in con- 
 junction with wheels having double or single convex tapered sides or 
 side are recommended. For double tapered wheels they shall have a 
 oaper of not less than 3/4 in. per foot for each flange. For single tapered 
 wheels they shall have a taper of not less than 3/4 in. per foot. Each 
 flange, whether straight or tapered, shall be recessed at the center at 
 least 1/16 in. on the side next to the wheel. All tapered flanges over 10 in. 
 diameter shall be of steel or material of equal strength. Both flanges in 
 contact with the wheels shall be of the same diameter. Wheels should 
 never be run without flanges. 
 
 The following table gives the dimensions of flanges to be used where 
 no hoods are provided: A = Maximum flat spot at center of flange. 
 B = Flat spot at center of wheel. C = Minimum diameter of flange. 
 D = thickness of flange at bore. E - minimum diameter of recess. 
 F = Minimum thickness of each flange at bore; all dimensions are 
 in inches. 
 
 Dia. of 
 Wheel. 6 8 
 AGO 
 
 B 
 C 
 D 
 E 
 
 10 12 14 16 18 20 22 
 044 4444 
 11 2 41/2 41/2 6666 
 35 6 6 8 10 12 14 16 
 
 3/8 3/8 1/2 5/ 8 
 2 31/2 4 4 
 
 5/8 5/ 8 
 51/2 7 
 
 3/4 3/4 3/4 
 
 24 
 4 
 6 
 
 18 
 
 3/4 
 
 26 
 4 
 6 
 
 20 
 
 3/4 
 
 28 
 4 
 6 
 
 22 
 
 7/8 
 
 30 
 4 
 6 
 
 24 
 
 8 9 101/2 12 131/2 141/2 16 
 
 F 3/ 8 3/ 8 l/ 2 5/ 8 8/4 7/ 8 1 1 1 l/ 8 1 1/ 8 1 1/ 8 1 1/4 1 1/4 
 
 Where protection hoods are provided, straight flanges and straight 
 wheels may be used, the dimensions being as follows, and the reference 
 letters having the same meaning as above: 
 
 Dia. of 
 
 Wheel. 6 8 10 12 14 16 18 20 22 24 26 28 30 
 
 C 2 3 31/24 41/251/26 7 71/28 8 1/2 10 10 
 
 2 21/4 23/4 3 31/2 4 41/2! 5 51/26 77 
 
 E 
 F 
 
 3/8 3/ 8 3/ 8 1/2 
 
 1/2 5/8 V8 5/ 8 5/ 8 5/ 8 8/4 3/ 4 
 
 Protection hoods shall be used where practical with wheels not 
 provided with protection flanges, and shall be sufficiently strong to 
 retain all pieces of a broken grinding wheel. They shall conform as 
 nearly as possible to the periphery of the wheel, and leave exposed the 
 
EMERV WHEELS AND GRINDSTONES. 
 
 1315 
 
 Table for Selection of Grades. 
 
 Class of Work. 
 
 Alundum. 
 
 Crystolon. 
 
 Grain. 
 
 Grade. 
 
 Grain. 
 
 Grade. 
 
 Aluminum castings 
 
 36 to 46 
 
 3 to 4 Elas 
 
 20 to 24 
 20 " 24 
 24 " 36 
 30 " 46 
 16 " 30 
 20 " 30 
 16 " 24 
 20 " 30 
 20 " 30 
 
 36 "60 
 
 16 " 20 
 20 " 30 
 
 30 "36 
 24 " 30 
 
 24 " 46 
 j 70 " 80 
 
 1 80 
 30 to 46 
 30 " 50 
 
 P to R 
 Q " R 
 P " R 
 I " L 
 I " L 
 Q " S 
 Q " S 
 Q " R 
 Q 
 
 I " L 
 
 R " S 
 Q " S 
 
 K " L 
 
 R " S 
 
 J " M 
 
 \ 1 A to 2 
 Elas 
 J 
 12 to 5 
 ) Elas. 
 KtoM 
 
 Brass or bronze castings (large) . 
 Brass or bronze castings (small) . 
 Cast iron, cylindrical 
 
 
 
 24 comb 
 16 to 46 
 24 " 30 
 16 " 20 
 20 " 30 
 
 J to K 
 H " K 
 P " R 
 Q " R 
 
 P " U 
 
 Cast iron, surfacing . 
 
 Cast iron (small) castings. . . . 
 Cast iron (large) castings .... 
 Chilled iron castings 
 
 Dies chilled iron 
 
 Dies, steel 
 
 36 to 60 
 20 " 30 
 30 
 
 J to L 
 P " R 
 
 P " Q 
 
 
 Hammers, cast steel 
 
 Interior of Automobile Cylinders, 
 (cast iron) 
 
 Internal grinding, hardened steel 
 Knives (paper), automatic grinding 
 Knives (planer) , automatic grinding 
 Knives (planing mill), hand grind- 
 ing 
 
 46 to 60 
 36 " 46 
 30 " 46 
 
 46 " 60 
 
 30 " 60 
 46 "120 
 j 20 '24 
 | 20 '36 
 20 36 
 14 ' 20 
 20 '30 
 
 46 " 60 
 46 " 60 
 16 " 24 
 
 J to M 
 J " K 
 J " K 
 
 J to M 
 J " M 
 J " M 
 PSil. 
 toP 
 " Q 
 P " U 
 P " R 
 
 I " M 
 J " M 
 Q " S 
 
 Knives, shear and shear blades . 
 Lathe centers 
 
 Lathe and planer tools 
 
 Machine-shop use, general . . . 
 Malleable iron castings (large) 
 Malleable iron castings (small) 
 Milling cutters, automatic or semi- 
 automatic grinding 
 
 Milling cutters, hand grinding . . 
 Plows (steel), surfacing 
 
 Pulleys (C.I.), surfacing faces of . 
 Radiators (cast iron), edges of . . 
 Reamers, taps, milling cutters, 
 etc., hand grinding 
 Reamers, taps, milling cutters, 
 
 46 to 120 
 46 " 60 
 
 46 " 60 
 24 " 36 
 
 ;o| 
 
 
 K " 
 
 J " M 
 J " M 
 
 \y* " 2 
 
 Elas. 
 
 Rolls, (cast iron) wet 
 
 Rolls (chilled iron), finishing . . 
 
 Rolls (chilled iron), roughing. . . 
 Rubber . . . 
 
 30 to 50 
 36 " 50 
 60 
 ( 24 comb. 
 130 to 60 
 16 " 36 
 j 24 comb. 
 1 46 to 60 
 16 " 46 
 10 " 20 
 20 " 30 
 16 " 46 
 
 14 " 16 
 16 " 24 
 46 " 60 
 36 "60 
 12 " 30 
 46 " 60 
 
 J to K. 
 M " N 
 " Q 
 L " P 
 L " 
 H " K 
 K 
 J to L 
 H " K 
 Q " W 
 P " R 
 L " P 
 
 Q " U 
 P " R 
 
 M 
 K to M 
 
 P " U 
 K " M 
 
 Saws, gumming and sharpening . 
 Saws, cold cutting-off . . . : . 
 
 Steel (soft), cylindrical grinding . 
 
 Steel (soft), surface grinding . . 
 Steel (hardened), cylindrical grind- 
 ing 
 
 Steel (hardened) , surface grinding 
 Steel, large castings 
 
 Steel, small castings 
 
 Steel (manganese), safe work . . 
 Steel (manganese), frogs and 
 switches 
 
 Structural steel 
 
 Twist drills, hand grinding . . . 
 Twist drills, special machines . . 
 Wrought iron 
 
 Woodworking tools 
 
1316 THE MACHINE-SHOP. 
 
 least portion of the wheel compatible with the work. A sliding tongue 
 to close the opening in the hood as the wheel is reduced in diameter 
 should be provided. Protruding ends of the wheel arbors and their 
 nuts shall be guarded. 
 
 Cups, cylinders and sectional ring wheels shall be either protected with 
 hoods, enclosed in protection chucks, or surrounded with protection 
 bands. Not more than one-quarter of the height of such grinding 
 wheels shall protrude beyond the provided protection. 
 
 Grinding wheels shall fit freely on the spindles. Wheel arbor holes 
 shall be made 0.005 in. larger than the machine arbor. The soft metal 
 bushing shall not extend beyond the sides of the wheel at the center. 
 Ends of spindles shall be threaded left and right so that the nuts on 
 both ends will tend to tighten as the spindles revolve. Care should 
 be taken that the spindles are arranged to revolve in the proper 
 direction. 
 
 Wheel washers of compressible material, such as blotting paper, 
 rubber or leather, not thicker than 0.025 in., shall be fitted between the 
 wheel and its flanges. It is recommended that the wheel washers be 
 slightly larger than the diameter of the flanges used. 
 
 When tightening clamping nuts, care shall be taken to tighten them 
 only enough to hold the wheel flrmly. Flanges must be frequently in- 
 spected to guard against the use of those which have become bent or 
 out of balance. If a tapered wheel has broken, the flanges must be 
 carefully inspected for truth before using with a new wheel. Clamping 
 nuts shall also be inspected. 
 
 Minimum Sizes of Machine Spindles in Inches for Various 
 Diameters and Thickness of Grinding Wheels. 
 
 - Thickness of Wheel in Inches 
 
 2 2X 2 1 A 3 
 
 222 
 
 2K 2M 2^ 
 
 2X 3 2 3 
 
 Safe Speeds. A peripheral speed of 5,000 "ft. per min. is recom- 
 mended as the standard operating spee.d for vitrified and silicate 
 straight wheels, tapered wheels and shapes other than those known as 
 cup and cylinder wheels, which are used on bench, floor, swing frame 
 and other machines for rough grinding. In no case shall a peripheral 
 speed of 6500 ft. be exceeded. 
 
 A peripheral speed of 4500 ft. per min. is recommended as the 
 standard operating speed for vitrified and silicate wheels of the cup and 
 cylinder shape, used on bench, floor, swing frame, and other machines 
 for rough grinding. In no case shall 5500 ft. be exceeded. 
 
 For elastic, vulcanite and wheels of other organic bonds, the recom- 
 mendations of individual wheel manufacturers shall be followed. 
 
 For precision grinding an operating peripheral speed of 6500 ft. per 
 min. may be recommended. 
 
 If a wheel spindle is driven by a variable-speed motor some device 
 shall be used which will prevent the motor from being run at too high 
 speeds. Cone pulleys determining the speed of a wheel should never 
 be used unless belt-locking devices are provided. Machines should 
 
EMERY WHEELS AND GRINDSTONES. 1317 
 
 V 
 
 be provided with a stop or some method of fixing the maximum size 
 of wheel which may be used, at the speed at which the wheel spindle 
 is running. 
 
 If wheels become out of balance through wear and cannot be balanced 
 by truing or dressing, they should be removed from the machine. 
 
 A wheel used in wet grinding shall not be allowed to stand partly 
 immersed in the water. The water-soaked portion may throw the 
 wheel dangerously out of balance. 
 
 Wheel dressers shall be equipped with rigid guards over the tops of 
 the cutters, to protect operator from flying pieces of broken cutters. 
 
 Goggles shall be provided for use of grinding wheel operators where 
 there is danger of eye injury. 
 
 Work shall not be forced against a cold wheel, but applied gradually, 
 giving the wheel an opportunity to warm and thereby eliminate possible 
 breakage. This applies to starting work in the morning in grinding 
 rooms which are not heated in winter and new wheels which have been 
 stored in a cold place. 
 
 Grinding as a Substitute for Finish Turning in the Lathe. 
 C. H. Norton (Trans. Am. Soc. M. E. 1912) recommends the use 
 of the grinding machine as a substitute for the lathe for many forms 
 of cylindrical work. He advocates the elimination of the finishing 
 cut in the lathe, claiming it is more economical to grind to size immedi- 
 ately after the roughing cut than to finish turn and then grind. For 
 this practice, work should not be turned closer than 1/32 in. of finish 
 diameter, and coarse feeds, often as coarse as four to the inch, should 
 be used. He cites instances where this method produced pieces in 18 
 minutes, where the former method of rough and finish turning and then 
 grinding to size required 28 % minutes. In 1913, the Norton Grinding 
 Co. was using the grinding machine to the exclusion of the lathe for 
 automobile crank-shafts and similar pieces, grinding to size from the 
 rough forging. Instances and methods are shown in Indust. Eng. t 
 April, 1913. 
 
 Truing and Dressing. (Norton Co., 1915). A wheel is trued to 
 make it concentric and to give it an accurate surface.. Dressing is to 
 sharpen or renew the surface of the wheel when glazed or loaded. 
 Truing on precision grinding machines is performed by a diamond held 
 rigidly in a fixed tool post never in the hand. There should always 
 be a liberal supply of lubricant or water flowing on the diamond while 
 the truing is being done. In modern practice, truing is for two other 
 purposes, as well as to make the wheel perfectly true: one for sharpening 
 the wheel to obtain production and the other for dulling the wheel to 
 obtain finish. Truing in rough grinding operations is performed by 
 using a dresser, usually an instrument containing steel-cutting wheels, 
 and in practice the rest is adjusted to form a rigid support for the lugs 
 on the dresser, care being taken to see that the dresser is not caught 
 between the wheel and the rest. In using the dresser to sharpen up 
 the surface of the wheel, the rest is left in its usual close adjustment to 
 the wheel. Truing and dressing are two of the most neglected and 
 least understood features in the proper use of grinding wheels. 
 
 Special Wheels. Rim wheels and iron-center wheels are specialties 
 that require the maker's guarantee and assignment of speed. 
 
 Safe Speeds for Grindstones and Emery Wheels. G. D. Hiscox 
 (Iron Age, April 7, 1892), by an application of the formula for centri- 
 fugal force in fly-wheels (see Fly-wheels), obtains the figures for strains 
 in grindstones and emery wheels which are given in the tables below. 
 His formulae are: 
 
 Stress per sq. in. of section of a grindstone = (0.7071Z>xA r ) 2 X0.0000795 
 Stress per sq.in. of section of an emery wheel= (0.7071Z>XA0 2 X0.00010226 
 
 D = diameter in feet, N = revolutions per minute. 
 
 He takes the weight of sandstone at 0.078 Ib. per cubic inch, and that 
 of an emery wheel at 0.1 Ib. per cubic inch; Ohio stone weighs about 
 0.081 Ib. and Huron stone about 0.089 Ib. per cubic inch. The Ohio 
 stone will bear a speed at the periphery of 2500 to 3000 ft. per min., 
 which latter should never be exceeded. The Huron stone can be 
 trusted up to 4000 ft., when properly clamped between flanges and 
 not excessively wedged in setting. Apart from the speed of grindstones 
 
1318 
 
 THE MACHINE-SHOP. 
 
 as a cause of bursting, probably the majority of accidents have really 
 been caused by wedging them on the shaft and over-wedging to true 
 them. The holes being square, the excessive driving of wedges to true 
 the stones starts cracks in the corners that eventually run out until 
 the centrifugal strain becomes greater than the tenacity of the remain- 
 ing solid stone. Hence the necessity of great caution in the use of 
 wedges, as well as the holding of large quick-running stones between 
 large flanges and leather washers. 
 
 The Iron Age says the strength of grindstones when wet is reduced 
 40 to 50%. A section of a stone soaked all night in water broke at a 
 stress of 80 Ib. per sq. in. A section of the same stone dry broke at 
 146 Ib. per sq. in. A better quality stone broke at stresses of 186 and 
 116 Ib. per sq. in. when dry and wet respectively. 
 
 Strains in Grindstones. 
 
 LIMIT OF VELOCITY AND APPROXIMATE ACTUAL STRAIN PER SQUARE 
 
 INCH OF SECTIONAL AREA FOR GRINDSTONES OF 
 
 MEDIUM TENSILE STRENGTH. 
 
 Diam- ' 
 eter. 
 
 Revolutions per Minute. 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 350 
 
 400 
 
 feet. 
 
 fy, 
 
 31/2 
 4V 2 
 
 6 
 
 7 
 
 Ibs. 
 1 .58 
 2.47 
 3.57 
 4.86 
 6.35 
 8.04 
 9.93 
 14.30 
 19.44 
 
 Ibs. 
 3.57 
 5.57 
 8.04 
 10.93 
 14.30 
 18.08 
 22.34 
 32.17 
 
 Ibs. 
 6.35 
 9.88 
 14.28 
 19.44 
 27.37 
 32.16 
 
 Ibs. 
 9.93 
 15.49 
 22.34 
 30.38 
 
 Ibs. 
 14.30 
 22.29 
 32.16 
 
 Ibs. 
 18.36 
 28.64 
 
 Ibs. 
 25.42 
 39.75 
 
 
 
 
 
 
 Approximate breaking strain ten 
 times the strain for size opposite the 
 bottom figure in each column. 
 
 
 
 The figures at the bottom of columns designate the limit of velocity 
 (in revolutions per minute at the head of the columns) for stones of the 
 diameter in the first column opposite the designating figure. 
 
 A general rule of safety for any size grindstone that has a compact and 
 strong grain is to limit the peripheral velocity to 47 feet per second. 
 
 Joshua Rose (Modern Machine-shop Practice) says: The average cir- 
 cumferential speed of grindstones in workshops may be given as follows: 
 
 For grinding machinists' tools, about 900 feet per minute. 
 
 carpenters' 600 " 
 
 The speeds of stones for file-grinding and other similar rapid grinding 
 is thus given in the "Grinders' List." 
 
 Diam. ft 8 71/2 7 61/2 6 51/2 5 41/2 4 31/2 3 
 
 Revs, per min. . : . . . 135 144 154 166 180 196 216 240 270 308 360 
 
 TAPER BOLTS, PINS, REAMERS, ETC. 
 
 Standard Steel Mandrels. (The Pratt & Whitney Co.) These 
 mandrels are made of tool-steel, hardened, and ground true on their 
 centers. Centers are also ground to true 60 degree cones. The ends are 
 of a form best adapted to resist injury likely to be caused by driving. 
 They are slightly taper. Sizes, -1/4 inch diameter by 33/4 inches long to 
 4 inches diameter by 17 inches long, diameters advancing by 16ths. 
 
 Taper Bolts for Locomotives. Bolt-threads, U. S. Standard, ex- 
 cept stay-bolts and boiler-studs, V- threads, 12 per inch; valves, cocks, 
 and plugs, V-threads, 14 per inch, and i/g-inch taper per 1 inch. 
 Standard bolt taper 1/15 inch per foot. 
 
 Taper Reamers. The Pratt & Whitney Co. makes standard taper 
 reamers for locomotive work taper i/ie inch per foot from 1/4 inch diam- 
 eter; 4-inch length of flute to 2-inch diameter, 18-inch length of flute, 
 diameters advancing by 16ths and 32ds. P. & W. Co.'s standard taper 
 pin reamers taper 1/4 inch per foot, are made in 15 sizes of diameters, 
 0.135 to 1.250 inches; length of flute, 1 7/ 16 inches to 14 inches. 
 
TAPER PINS, BOLTS, REAMERS, ETC. 
 
 1319 
 
 Morse Tapers. 
 
 Number of J 
 Taper. 
 
 Diam of Plug 
 at Small End. 
 
 Diam. at End 
 of Socket. 
 
 Standard Plug 
 Depth. 
 
 Whole Length 
 of Shank. 
 
 Depth of Hole. 
 
 End of Socket 
 to Key- way. 
 
 Length of Key- 
 way, ' 
 
 Width of Key- 
 way. 
 
 4 
 
 "5 o 
 
 MH 
 1 
 
 Diameter of 
 Tongue. 
 
 Thickness of 
 Tongue. 
 
 Had. of Mill 
 for Tongue. 1 
 
 Radius of 
 Tongue. 
 
 Shank Depth. 
 
 Taper per Foot. 
 
 
 D 
 
 A 
 
 P 
 
 B 
 
 // 
 
 K 
 
 L 
 
 TF 
 
 T 
 
 d 
 
 t 
 
 R 
 
 a 
 
 S 
 
 
 
 
 252 
 
 356 
 
 2 
 
 211/32 
 
 21/32 
 
 115/1G 
 
 9/16 
 
 .160 
 
 1/4 
 
 .235 
 
 5/32 
 
 5/32 
 
 .04 
 
 27/32 
 
 .625 
 
 1 
 
 .369 
 
 .475 
 
 21/8 
 
 29/16 
 
 23/16 
 
 21/16 
 
 3/4 
 
 .213 
 
 3/8 
 
 .343 
 
 13/64 
 
 3/16 
 
 .05 
 
 27/ie 
 
 .600 
 
 2 
 
 .572 
 
 .700 
 
 29/16 
 
 3l/ 8 
 
 25/8 
 
 21/2 
 
 7/8 
 
 26 
 
 7/16 
 
 l7 /32 
 
 1/4 
 
 1/4 
 
 .06 
 
 215/16 
 
 .602 
 
 3 
 
 .778 
 
 .938 
 
 33/16 
 
 37/8 
 
 31/4 
 
 31/16 
 
 1Vl6 
 
 322 
 
 Vl6 
 
 23/32 
 
 5/16 
 
 9/32 
 
 .08 
 
 3U/16 
 
 .602 
 
 4 
 
 1.020 
 
 1.231 
 
 41/16 
 
 47/ 8 
 
 41/8 
 
 37/8 
 
 U/4 
 
 .478 
 
 5/8 
 
 31/32 
 
 15/32 
 
 5/16 
 
 .10 
 
 45/ 8 
 
 .623 
 
 5 
 
 1.475 
 
 1.748 
 
 53/16 
 
 61/8 
 
 51/4 
 
 415/ie 
 
 U/2 
 
 .635 
 
 3 /4 
 
 U3/32 
 
 5/8 
 
 3/8 
 
 .12 
 
 57/ 8 
 
 .630 
 
 6 
 
 2.116 
 
 2.494 
 
 7V4 
 
 89/16 
 
 73/8 
 
 7 
 
 13/ 4 
 
 .76 
 
 11/8 
 
 2 
 
 3/4 
 
 V2 
 
 .15 
 
 81/4 
 
 .626 
 
 7 
 
 2.75 
 
 3.27 
 
 10 
 
 115/8 
 
 101/8 
 
 91/2 
 
 25/8 
 
 1.135 
 
 l3/ 8 
 
 25/8 
 
 11/8 
 
 3/4 
 
 .18 
 
 1U/4 
 
 .625 
 
 Brown & Sharpe Mfg. Co. publishes (Machy's Data Sheets) a list of 
 18 sizes of tapers ranging from 0.20 in. to 3 in. diam. at the small end; 
 taper 0.5 in. to 1 ft., except No. 10, which is 0.5161 in. per ft. 
 
 
 
 c 
 
 
 
 
 J>~ 
 
 i 
 
 *- 
 
 FIG. 216. Morse Tapers. See table above. 
 
 The Jar no Taper is 0.05 inch per inch = 0.6 inch per foot. The 
 number of the taper is its diameter in tenths of an inch at the small end, 
 in eighths of an inch at the large end, and the length in halves of an inch. 
 Thus, No. 3 Jarno taper is 11/2 inches long, 0.3 inch diameter at the small 
 end ami % inch diameter at the large end, 
 
1320 
 
 THE MACHINE-SHOP. 
 
 ..?::::::::::: ^ 
 
 i 
 
 2 -s . . .3 J3 -ds 
 
 - -- -^ : s 3.c 
 
 3-* ^<^^ .* ** -^ ^^^^ * ^. ^ -So 
 
 1| 
 
 oooooooo tnunirnA -u-nnmin t* >> 
 
 JQ5 
 
 ft 
 
 ^^j ^^^^-HO^^CO^t-^^^O.^OCC,, 
 
 ^-1 
 
 _5 cp 
 
 Jl 
 
 !P !?5 . . .- . . .co- . _ _ ^!r; 
 
 03" 
 
 fi - - - ^ ^ 
 
 Q e<i <*, I'M s .1 ? ._ri 
 
 "So ^ 
 
 '_tO J-H 
 
 *e5""s" * *^Teo~ ' * O -' 
 
 -:- we<:> '""* -oc;. 
 
 ^ <P D 
 
 q<MooSSooco*"oS* \ " "3 p< b." 
 
 2 
 S 
 
 5 
 
 ^^ : : : :2:2: : :22 : :22 :::::::::: Q? 
 
 OOCOOOQOvO^OsOsOr^f^^;^ Cj<N -OO 
 
 soo c 
 
 * 
 
 ( tn 
 
 M 
 
 05 < 
 
 ^tl 
 
PUNCHES AND DIES, PRESSES, ETC 
 
 1321 
 
 Standard Steel Taper-pins. The following sizes are made by The 
 
 Pratt & Whitney Co.: Taper 1/4 inch to the foot. 
 Number: 
 
 0123 456789 10 
 Diameter large end: 
 
 0.156 0.172 0.193 0.219 0.250 0.289 0.341 0.409 0.492 0.591 0.706 
 Approximate fractional sizes: 
 
 19 /64 u /32 13 /32 V2 1 
 
 5 /32 n /64 
 
 Lengths from 
 
 3/4 3/ 4 
 
 To* 
 
 1 H/4 
 
 3 /l6 
 3/ 4 
 
 7/32 
 3/4 
 
 H/2 l 3 /4 
 
 8/4 8/4 8/4 
 2 21/4 31/4 
 
 ll/ 4 1 1/ 2 
 41/2 5V 4 
 
 23 /32 
 
 H/ 2 
 
 6 
 
 Diameter small end of standard taper-pin reamerrf 
 0.135 0.146 0.162 0.183 0.208 0.240 0.279 0.331 0.398 0.482 0.581 
 
 Dimensions of T-Slots, T-Bolts and T-Nuts. 
 (Pratt & Whitney Standard Dimensions in Inches). 
 
 Slot. 
 
 Bolt and Nut. 
 
 Width 
 8 
 
 W 
 
 BJ 
 
 Min. 
 
 c 
 
 Diam. 
 of 
 Bolt. 
 
 D 
 
 Diam. 
 of 
 Head 
 or 
 
 Nut. 
 H 
 
 Thick- 
 ness of 
 Head 
 or 
 Nut. 
 T 
 
 Width 
 of 
 Stem. 
 
 J 
 
 Height 
 of 
 Stem. 
 
 N 
 
 Diam. 
 of 
 Hole. 
 
 K 
 
 5/16 
 3/8 
 7/16 
 
 1/2 
 5/8 
 3/4 
 
 7/8 
 
 1/2 
 5/8 
 "/16 
 13/16 
 15/16 
 13/16 
 1 5/18 
 15/8 
 1 7/8 
 
 3/16 
 
 3/16 
 1/4 
 9/32 
 5/16 
 3/8 
 1/2 
 9/16 
 5/8 
 
 5/32 
 5/32 
 */M 
 
 7/32 
 9/32 
 13/32 
 17/32 
 
 H/15 
 13/18 
 
 3/16 
 V4 ' 
 5/16 
 
 3/8 
 
 l 
 
 9/n 
 /il 
 
 3/4 
 7/8 
 
 7/16 
 9/16 
 5/8 
 3/4 
 7/8 
 11/8 
 1 V4 
 1 1/2 
 13/ 4 
 
 1/8 
 1/8 
 3/16 
 ' 3/16 
 1/4 
 H/32 
 15/32 
 9/16 
 H/16 
 
 3/16 
 1/4 
 5/16 
 3/8 
 7/16 
 9/16 
 H/16 
 3/4 
 7/8 
 
 3/32 
 
 1/8 
 1/8 
 5/32 
 3/16 
 3/16 
 1/4 
 5/16 
 5/16 
 
 1/8 
 1/8 3/ 16 
 3/16 V4 
 1/4 5/iQ 
 5/16 3/ 8 
 7/16 ' V2 
 9/16 5/ 8 
 5/8 3/4 
 3/4 7/ 8 
 
 t Maximum thicknesses: Up to 5/g-in. bolts, 5 +1/16 in.; H/ie-in. bolt, 
 1 in.; 3/4-in. bolt, 1 1/ie in.; 7/ 8 -in. bolt, 1 3/ 16 in. 
 
 PUNCHES AND DIES, PRESSES, ETC. 
 
 Clearance between Punch and Die. For computing the amount 
 of clearance that a die should have, or, in other words, the difference 
 in size between die and punch, the general rule is to make the diam- 
 eter of die-hole equal to the diameter of the punch, plus 2/ 10 the thickness 
 of the plate. Or, D = d + Q.2t, in which D = diameter of die-hole, 
 d = diameter of punch, and t = thickness of plate. For very thick 
 plates some mechanics prefer to make the die-hole a little smaller than 
 called for by the above rule. For ordinary boiler-work the die is made 
 from 1/10 to 3/ 10 of the thickness of the plate larger than the diameter 
 of the punch; and some boiler-makers advocate making the punch fit 
 
 * Lengths vary by 1/4 inch each size, 
 t Taken 1/2 inch from extreme end . 
 about 1/2 inch. 
 
 Each size overlaps smaller one 
 
1322 
 
 THE MACHINE-SHOP. 
 
 the die accurately. For punching nuts, the punch fits in the die. 
 (Am. Mach.) 
 
 The clearance between the punch and die when blanking, perforating 
 and forming flat thin stock of different materials in the power press 
 for light machine parts such as typewriters, adding machines, etc., 
 are shown in the following table compiled by E. Dean (Am. Mach., 
 May 4, 1905). In using the table, the class of work to be done must 
 be considered. For perforating work, the punch is made to the de- 
 sired size, and the clearance is made on the die. For blanking, the 
 die is of the desired size and the clearance is obtained by making the 
 punch smaller. 
 
 Punch and Die Clearances for Different Materials and Thicknesses. 
 
 Thick- 
 ness 
 of 
 Stock, 
 In. 
 
 Clearance 
 for 
 Brass 
 and Soft 
 Steel, In. 
 
 Clearance 
 for 
 Medium 
 Rolled 
 Steel, In. 
 
 Clearance 
 for 
 Hard 
 Rolled 
 Steel, In. 
 
 Thick- 
 ness 
 of 
 Stock, 
 In: 
 
 Clearance 
 for 
 Brass 
 and Soft 
 Steel, In. 
 
 Clearance 
 for 
 Medium 
 Rolled 
 Steel, In. 
 
 Clear- 
 ance for 
 Hard 
 Rolled 
 Steel, In. 
 
 0.01 
 .02 
 .03 
 .04 
 .05 
 .06 
 .07 
 .08 
 .09 
 .10 
 
 0.0005 
 .001 
 .0015 
 .002 
 .0025 
 .003 
 .0035 
 .004 
 .0045 
 .005 
 
 0.0006 
 .0012 
 .0018 
 .0024 
 .003 
 .0036 
 .0042 
 .0048 
 .0054 
 .006 
 
 0.0007 
 .0014 
 .0021 
 .0028 
 .0035 
 .0042 
 .0049 
 .0056 
 .0063 
 .007 
 
 0.11 
 .12 
 .13 
 .14 
 .15 
 .16 
 .17 
 .18 
 .19 
 .20 
 
 0.0055 
 .006 
 .0065 
 .007 
 .0075 
 .008 
 .0085 
 .009 
 .0095 
 .010 
 
 0.0066 
 .0072 
 .0078 
 .0084 
 .009 
 .0096 
 .0102 
 .0108 
 .0114 
 .0120 
 
 0.0077 
 .0084 
 .0091 
 .0098 
 .0105 
 .0112 
 .0119 
 .0126 
 .0133 
 .0140 
 
 Kennedy's Spiral Punch. (The Pratt & Whitney Co.) B. Mar- 
 tell, Chief Surveyor of Lloyd's Register, reported tests of Kennedy's 
 spiral punches in which a 7/ 8 -inch spiral punch penetrated a 5/g-inch 
 plate at a pressure of 22 to 25 tons, while a flat punch required 33 to 35 
 tons. Steel boiler-plates punched with a flat punch gave an average 
 tensile strength of 58,579 pounds per square inch, and an elongation in 
 two inches across the hole of 5.2 per cent, while plates punched with a 
 spiral punch gave 63,929 pounds, and 10.6 per cent elongation. 
 
 The spiral shear form is not recommended for punches for use in metal 
 of a thickness greater than the diameter of the punch. This form is of 
 greatest benefit when the thickness of metal v/orked is less than two 
 thirds the diameter of punch. 
 
 Size of Blanks used in the Drawing-press. Oberlin Smith 
 (Jour. Frank. Inst., Nov. 1886) gives three methods of finding the 
 size of blanks. The first is a tentative method, and consists simply in a 
 series of experiments with various blanks, until the proper one is found. 
 This is for use mainly in complicated cases, and when the cutting por- 
 tions of the die and punch can be finally sized after the other work is 
 done. The second method is by weighing the sample piece, and then, 
 knowing the weight of the sheet metal per square inch, computing the 
 diameter of a piece having the required area to equal the sample in 
 weight. The third method is by computation, and the formula is x*= 
 >/rf2 _j_ 4^ f or a sharp-cornered cup, where x = diameter of blank, 
 d = diameter of cup, h = height of cup. For a round-corner ed cup 
 where the corner is small, say radius of corner less than 1/4 height of cup, 
 the formula is x = (^(d* + 4d/0 r, about ;T being the radius of the 
 corner. This is based upon the assumption that the thickness of the 
 metal is not to be altered by the drawing operation. 
 
 Pressure attainable by the Use of the Drop-press. (R. H. 
 Thurston, Trans. A. S. M. E., v, 53.) A set of copper cylinders 
 was prepared, of pure Lake Superior copper; they were subjected to the 
 action of presses of different weights and of different heights of fall. 
 Companion specimens of copper were compressed to exactly the same 
 amount, and measures were obtained of the loads producing compression, 
 and of the amount of work done in producing the compression by the 
 drop. Comparing one with the other it was found that the work done 
 with the hammer was 90 per cent, of the work which should have been 
 
FLY-WHEELS FOR PUNCHES, PRESSES, ETC. 1323 
 
 done witJi perfect efficiency. That is to say, the work done in the test- 
 ing-machine was equal to 90 per cent of that due the weight of the drop 
 falling the given distance. 
 
 Formula: Mean pressure in pounds 
 
 For pressures per square inch, divide by the mean area opposed to 
 crushing action during the operation. 
 
 Similar experiments on Bessemer steel plugs by A. W. Moseley and 
 J. L. Bacon (Trans. A, S. M. E., xxvii. 605) indicated an efficiency for the 
 drop hammer of about 70 per cent. 
 
 An extensive series of experiments is reported in Am. Mach., Mar. 
 10, 1910. These were made by W. T. Sears, and consisted of the 
 compression of lead plugs under a falling weight, ranging from 20 to 
 200 lb., dropped from heights ranging up to 360 in. The tests showed 
 that after a certain velocity of the falling weight had been attained, 
 the speed had little effect on the compression of the plug. This speed 
 was fixed at 10 ft. per second, but its exact value is uncertain. 
 
 Flow of Metals. (David Townsend, Jour. Frank. Inst., March, 
 1878.) In punching holes 7/ 16 -inch diameter through iron blocks 13/4 
 inches thick, it was found that the core punched out was only !Vi6 
 inches thick, and its volume was only about 32 per cent of the volume 
 of the hole. Therefore, 68 per cent of the metal displaced by punching 
 the hole flowed into the block itself, increasing its dimensions. 
 
 Fly-wheels for Presses, Punches, Shears, etc. The function of the 
 fly-wheel on punching and other machinery in which action is inter- 
 mittent is to store up energy during that portion of the stroke when 
 no work is being done and to give it out during the period of actual 
 working. The giving up of energy is accompanied by a reduction in 
 the velocity of the fly-wheel. 
 Notation: 
 
 E = total energy in the wheel at maximum velocity, ft.-lb. 
 
 E\ = energy given out by the wheel during speed reduction, 
 
 ft.-lb. 
 vi = initial velocity of the center of gravity of fly-wheel rim, 
 
 ft. per sec. 
 V2 = velocity of center of gravijby of fly-wheel rim at end of period 
 
 in which energy is given out. 
 H.P. = horse-power required. 
 
 N = strokes of press or shear per min. 
 . T = time required per stroke, sees. 
 
 t = time required for actual cutting of metal per stroke, sees, 
 w = weight of fly-wheel rim, lb. 
 d = diameter of rim at center of gravity. 
 R = r.p.m. of fly-wheel at initial velocity. 
 c and ci = constants. 
 
 a = width of fly-wheel rim, in. 
 b = depth of fly-wheel rim, in. 
 y = ratio of depth to width of rim. 
 g = acceleration due to gravity = 32.2 
 Formulae: 
 
 p _ w vi z _ wvi z 
 ~ 2 g ~ 64.4 
 
 _ 27r RN 
 
 60 
 
 A simplified method for calculating fly-wheels for punches and shears 
 is given in Machinery's Handbook, p. 289. Using the notation as above, 
 
 EN = E . _ / t __L\. 
 ' 33,000 TX550V 
 
1324 
 
 THE MACHINE-SHOP. 
 
 For cast-iron fly-wheels with maximum stresses of 1000 Ib. per so; . in.i 
 =aEii R= 1940 -i-D. 
 
 VALUES OF c AND c\. 
 
 Per Cent 
 Reduction. 
 
 21/2 
 
 5 
 
 71/2 
 
 10 
 
 15 
 
 20 
 
 c 
 
 0.00000213 
 0.1250 
 
 0.00000426 
 0.0625 
 
 0.00000617 
 0.0432 
 
 0.00000810 
 0.0328 
 
 0.00001180 
 0.0225 
 
 0.00001535 
 0.0173 
 
 Ci. . 
 
 For belt-driven machines, the limiting low velocity vz is the speed 
 at which the belt will run off the pulley. Wilfred Lewis, Trans. A. S. 
 M. E., vol. vii, shows that this takes place when the slip exceeds 20 
 per cent of the belt speed. This gives a limiting condition for belt 
 
 drives of punches and shears of W = 180 ( j 
 
 FORCING, SHRINKING AND RUNNING FITS. 
 
 Forcing Fits of Pins and Axles by Hydraulic Pressure. A 
 
 4-inch axle is turned 0.015 inch diameter larger than the hole into which 
 it is to be fitted. They are pressed on by a pressure of 30 to 35 tons. 
 (Lecture by Coleman Sellers, 1872.) 
 
 For forcing the crank-pin into a locomotive driving-wheel, when the 
 pinhole is perfectly true and smooth, the pin should be pressed in with a 
 pressure of 6 tons for every inch of diameter of the wheel fit. When the 
 hole is not perfectly true, which may be the result of shrinking the tire on 
 the wheel center after the hole for the crank-pin has been bored, or if the 
 hole is not perfectly smooth, the pressure may have to be increased to 9 
 tons for every inch of diameter of the wheel-fit. (Am. Machinist.) 
 
 Pressure Table for Mounting Wheels and Crank Pins. 
 
 (Santa Fe R.R. System, 1915.) 
 
 Driving Axles. 
 
 Eng. Truck Axles 
 
 Crank Pins. 
 
 Car Truck Axles. 
 
 Diam. of Wheel 
 Fit, In. 
 
 Pressure, Tons. 
 Wheel 
 Centers. 
 
 Ic 
 i i 
 
 O 3 
 
 s s 
 5 
 
 Pressure, Tons 
 Wheel 
 Centers. 
 
 I 
 
 iSo 
 
 Pressure, Tons. 
 Wheel 
 Centers. 
 
 Diam. of Wheel 
 Fit, In. 
 
 Pressure, 
 Tons. 
 Wheels. 
 
 Cast 
 Iron. 
 
 Steel 
 
 Cast 
 Iron. 
 
 Steel 
 
 Q + 
 
 g 
 
 3 
 
 3 
 4 
 5 
 i 
 7 
 
 71/2 
 8 V2 
 9V2 
 
 Cast 
 Iron. 
 
 Steel 
 
 Cast 
 Iron. 
 
 Steel 
 or 
 Steel 
 Tired* 
 
 4v, 
 
 6 
 
 8 
 9 
 10 
 11 
 12 
 
 45- 50 
 50- 55 
 60- 65 
 70- 75 
 80- 85 
 90- 95 
 100-105 
 110-115 
 120-125 
 
 72- 80 
 80- 88 
 96-104 
 112-120 
 128-136 
 144-152 
 160-168 
 176-184 
 192-200 
 
 3V 2 
 
 [1/2 
 
 fVi 
 
 6Vi 
 
 rl /2 
 
 20-25 
 25-30 
 30-35 
 35-40 
 40-45 
 45-50 
 50-55 
 55-60 
 60-65 
 65-70 
 
 35- 42 
 42- 50 
 50- 57 
 57- 65 
 65- 72 
 72- 80 
 80- 87 
 87- 95 
 95-102 
 102-110 
 
 30 
 40 
 50 
 60 
 70 
 75 
 80 
 85 
 90 
 95 
 
 36- 45 
 53- 60 
 68- 75 
 83- 90 
 98-105 
 105-113 
 
 4 
 
 h 
 
 6V 2 
 
 25-35 
 35-45 
 40-50 
 45-55 
 50-60 
 55-65 
 
 30-40 
 45-55 
 50-60- 
 50-65 
 55-70 
 60-75 
 
 113-120 
 120-128 
 128-135 
 135-143 
 
 CRANK AXLES. 
 All crank discs, 
 110-150 tons. 
 All center webs 
 150-200 tons. 
 
 * Tires on. 
 
 NOTE. In mounting wheels and crank pins, care should be taken to 
 see that for at least two-thirds of the wheel fit the pressure required 
 shall be between the maximum and minimum limits given in the table, 
 or if only one pressure is shown in the table, the actual pressure re- 
 quired should be as near as possible to that pressure. 
 
 In mounting driving wheels with tires on, the maximum pressures 
 given in the tables or even 10 per cent higher pressure than the maxi- 
 mum pressure may be used. 
 
 Shrinkage of Tires. Allow i/64 inch for each 12 in. in diameter. 
 
FORCE AND SHRINK FITS. 
 
 1325 
 
 Ground Fits for Machine Parts. The practice of the Brown & 
 Sharpe Mfg. Co. in tolerances and allowances for ground fits is given hi 
 a paper by W. A. Viall (Trans. A. S. M. E., xxxii) from which the 
 table below has been prepared. The limfbs given can be recommended 
 for satisfactory commercial work in the production of machine parts 
 and may be followed under ordinary conditions. In special cases it 
 may be necessary to vary slightly from the tables. 
 
 Allowances and Tolerances for Fits Practice of the Brown & 
 Sharpe Mfg. Co. ^ 
 
 Kind of Fit. 
 
 Diameter, Up to and Including 
 
 1/2 In. 
 
 1 In. 
 
 2 In. 
 
 RUNNING FITS 
 Ordinary speed 
 
 -.00025 to -.00075 
 
 -.0005 to -.001 
 -.00025 to -.0005 
 Oto -.00025 
 
 Oto +.00025 
 +.0005 to +.001 
 +.00075 to +.0015 
 
 +.00025 to +.0005 
 
 +.0005 to +.001 
 to +.0005 
 
 -.00075 to -.0015 
 
 -.001 to -.002 
 -.0005 to -.001 
 Oto -.0005 
 
 +.00025 to .0005 
 +.001 to +.002 
 +.0015 to +.0025 
 
 +.0005 to +.001 
 
 +.001 to +.0025 
 Oto +.00075 
 
 -.0015 to -.0025 
 
 -.002 to -.003 
 -.001 to -.002 
 Oto -.001 
 
 + 0005 to +.00075 
 +.002 to +.003 
 +.0025 to +.OC4 
 
 +.001 to +.0015 
 
 +.0025 to +.0035 
 to +.001 
 
 High speed, heavy 
 pressure, rocker 
 shafts 
 
 SLIDING FITS 
 
 STANDARD FITS. . 
 
 DRIVING FITS 
 For pieces to be 
 taken apart 
 
 Ordinary 
 
 FORCING FITS .... 
 
 SHRINKING FITS 
 For pieces to take 
 hardened shells 3/g 
 in. thick or less. . . . 
 For pieces to take 
 shells more than 
 3/8 in. thick 
 GRINDING LIMITS FOR 
 HOLES 
 
 Kind of Fit. 
 
 Diameter Up to and Including 
 
 3 1/2 In. 
 
 6 In. 
 
 12 In. 
 
 RUNNING FITS 
 Ordinary speed.' 
 
 - .0025 to - .0035 
 
 - .003 to - .0045 
 - .002 to - .0035 
 Oto -.0015 
 
 +.00075 to +.001 
 +.003 to +.004 
 +.004 to +.006 
 
 +.0015 to +.002 
 
 +.0035 to +.005 
 Oto +.0015 
 
 - .0035 to - .005 
 
 -.0045 to -.0065 
 - .003 to - .005 
 to - .002 
 
 +.001 to +.0015 
 +.004 to +.005 
 +.006 to +.009 
 
 +.002 to +.003 
 
 +.005 to +.007 
 to +.002 
 
 
 High speed, heavy 
 pressure, rocker 
 shafts 
 
 
 SLIDING FITS 
 
 
 STANDARD FITS 
 
 
 DRIVING FITS 
 For pieces to be 
 taken apart 
 Ordinary 
 
 
 
 FORCING FITS 
 
 
 SHRINKING FITS 
 For pieces to take 
 hardened shells 3/g 
 in. thick or less. . . . 
 For pieces to take 
 shells more than 
 % in. thick 
 GRINDING LIMITS FOR 
 HOLES 
 
 
 
 to +.0025 
 
 Running Fits. Wm. Sangster (Am. Mach., July 8, 1909) gives the 
 practice of different manufacturers as follows : 
 
 An electric manufacturing Co. allows a clearance of 0.003 to 0.004 in. for 
 shafts 1 1/2 to 2 1/4 in. diam, ; 0.003 to 0.006 for 21/2 in. ; 0.004 to 0.006 for 
 
1326 
 
 THE MACHINE-SHOP. 
 
 23/4 to 31/2 ins.; 0.005 to 0.007 in. for 4 and 41/2 ins.; 0.006 to 008 in 
 for 5 ins.; 0.009 to 0.011 in. for 6 ins. Dodge Mfg. Co. allows from I/R! 
 for 1-in. ordinary bearings to a little over 1/32 in. for 6-in. Clutch sleeves 
 0.008 to 0.015 in.; loose pulleys as close as 0.003 in. in the smaller sizes! 
 and about 1/64 in. on a 2i/2-in. hole. 
 
 Watt Mining Car Wheel Co. allows Vi6 in. for all sizes of wheels, and 
 Vie in. end play. A large fan-blower concern allows 0.005 to 0.01 in. 
 on fan journals from 9/ 16 to 27/i 6 ins. 
 
 Limits of Diameters for Fits. C. W. Hunt Co. (Am. Mack July 16 
 1903.) For parallel shafts and bushings (shafts changing): d = diam. 
 in ins. 
 
 Shafts: Press fit, + 0.001 d + (0 to 0.001 in.). Drive fit, + 0.0005 d + 
 
 (0. to 0.001 in.). 
 Shafts: Hand fit, + 0.001 to 0.002 in. for shafts 1 to 3 in.; 0.002 to 003 
 
 in. for 4 to 6 in.; 0.003 to 0.004 in. for 7 to 10 in. 
 
 Holes: all fits to 0.002 in. for 1 to 3 in.; to 0.003 in. for 4 to 6 in 
 to 0.004 in. for 7 to 10 in. 
 
 Parallel journals and bearings (journals changing): 
 
 Close fit - 0.001 d + (0.002 to 0.004 in.); Free fit - 0.001 d + (0 007 
 to 0.01 in.); Loose fit, - 0.003 d + (0.02 to 0.025). Limits of diameters 
 for taper shaft and bushings (holes changing). Shaft turned to standard 
 taper 3/ 16 in. per ft., large end to nominal size 0.001 in. Holes are 
 reamed until the large end is small by from 0.001 d + 0.004 to 005 in 
 for press fit, from 0.0005 d + 0.001 in. f9r drive fit, and from to 0.001 in. 
 for hand fit. In press fits the shaft is pressed into the hole until the 
 true sizes match, or Vi6 in. for each Viooo in. that the hole is small. 
 The above formulae apply to steel shafts and cast-iron wheels or other 
 members. 
 
 Shaft Allowances for Electrical Machinery. The General Electric 
 Co. (1915) gives the following table of allowances for sliding and press 
 fits. 
 
 
 
 
 Press Fit 
 
 Press Fit 
 
 
 
 Nominal 
 Diam., 
 In. 
 
 ' Sliding 
 Fit. 
 
 Com- 
 mutator 
 and Split 
 Hub. 
 
 for 
 Armature 
 Spider 
 Solid 
 
 for 
 Armature 
 Spider 
 Solid 
 
 Press 
 Fit for 
 Coupling. 
 
 Shrink 
 Fit. 
 
 
 
 
 Steel. 
 
 Cast Iron. 
 
 
 
 2 
 
 -0.0015 
 
 +0.0005 
 
 4-0.00075 
 
 4-0.0015 
 
 4-0.00175 
 
 +0.0025 
 
 4 
 
 - .002 
 
 -I- .0005 
 
 + .0015 
 
 4- .0025 
 
 4- .003 
 
 + .004 
 
 8 
 
 - .004 
 
 + .001 
 
 4- .002 
 
 4- .0035 
 
 4- .0045 
 
 + .006 
 
 12 
 
 - .005 
 
 + .001 
 
 4- .0025 
 
 4- .0045 
 
 4- .0055 
 
 + .0075 
 
 16 
 
 - .0055 
 
 + .001 
 
 + .003 
 
 + .005 
 
 4- .006 
 
 + .009 
 
 20 
 
 - .006 
 
 + .0015 
 
 + .0035 
 
 4- .0055 
 
 4- .007 
 
 + .010 
 
 24 
 
 - .007 
 
 + .0015 
 
 4- .0035 
 
 4- .006 
 
 4- .0075 
 
 + .011 
 
 28 
 
 - .0075 
 
 + .0015 
 
 4- .004 
 
 4- -0065 
 
 4- .0085 
 
 + .012 
 
 32 
 
 - .008 
 
 + .0015 
 
 4- .0045 
 
 4- .007 
 
 4- .009 . 
 
 + .0125 
 
 36 
 
 - .0085 
 
 + .002 
 
 4- .0045 
 
 4- .0075 
 
 4- .0095 
 
 + .0135 
 
 40 
 
 - .009 
 
 + .002 
 
 4- .005 
 
 4- .008 
 
 4- .010 
 
 + .014 
 
 44 
 
 - .0095 
 
 + .002 
 
 + .005 
 
 4- .0085 
 
 4- .0105 
 
 + .0145 
 
 48 
 
 - .010 
 
 4- .002 
 
 4- .0055 
 
 4- .009 
 
 4- .011 
 
 + .015 
 
 Pressure Required for Press Fits. (Am. Mach., March 7, 1907.) 
 
 Crank fits up to D =10. P = 9.9 D - 14. 
 
 Crank fits D = 12 to 24. P 5 D + 40. 
 
 Straight crank-pins. P = 13 D. 
 
 Taper crank-pins. P =* 14 D 7. 
 
 The allowance for cranks and straight pins is 0.0025 inch per inch of 
 diameter Taper cranks, taper Vie inch per inch, are fitted on the 
 lathe to within i/s inch of shoulder and then forced home. 
 
 Stresses due to Force and Shrink Fits. S. H. .Moore, Trans. 
 A. S. M. ?., vol. xxiv, gives the following allowances for different fits: 
 
FORCE AND SHRINK FITS. 
 
 1327 
 
 For shrinkage fits, d =(17/ 16 u+ 0.5) * 1000. For forced fits, 'd = 
 (2 D + 0.5) -s- 1000, For driven fits, d = (i/ 2 D + 0.5) * 1000. d = 
 allowance or the amount the diameter of the shaft exceeds the diameter 
 of the hole in the ring and D = nominal diameter of the shaft. A. L. 
 Jenkins, Eng. News, Mar. 17, 1910, says the values obtained from the 
 formula for forced fits are about twice as large as those frequently used 
 in practice, and in many, cases they lead to excessive stresses in the ring. 
 He calculates from Lamp's formula for hoop stress in a ring subjected to 
 internal pressure the relation between the stress and the allowance for 
 fit, and deduces the following formulae. 
 
 Sfo = 15,000,000 d * (k + 0.6); S h , = 15,000,000 d -s- (1 + 0.6/fc) ; for a 
 
 cast-iron ring on a steel shaft. 
 S hl = 30,000,000 d -4- (1 + fc); S h2 = 30,000,000, d * (1 + 1/K); for a 
 
 steel ring on a steel shaft. 
 8^= radial unit pressure between the surfaces; 8^=. unit tensile or 
 
 hoop stress in the ring; 
 
 d = allowance per inch of diameter, K a constant whose value depends 
 on t, the thickness, and r, the radius of the ring, as follows. 
 Values of t *- r, 
 
 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.25 1.5 1.75 2.0 3.0 
 Values of K, 
 3.083 2.600 2.282 2.058 1.892 1.766 1.666 1.492 1.380 1.300 1.250 1.133. 
 
 The allowances for forced and shrinkage fits should be based on the 
 stresses they produce, as determined by the above formula, and not on 
 the diameter of the shaft. 
 
 Force Required to Start Force and Shrink Fits. (Am. Mach., 
 Mar. 7, 1907.) A series of experiments was made at the Alabama Poly- 
 technic Institute on spindles 1 in. diam. pressed or shrunk into cast-iron 
 disks 6 in. diam., 11/4. in. thick. The disks were bored and finished with 
 a reamer to 1 in. diam. with an error believed not to exceed 0.00025 in. 
 The shafts were ground to sizes 0.001 to 0.003 in. over 1 in. Some of the 
 spindles were forced into the disks by a testing machine, the others had 
 the disks shrunk on. Some of each sort were tested by pulling the 
 spindle from the disk in the testing machine, others by twisting the disk 
 on the spindle,. The force required to start 'the spindle in the twisting 
 tests was reduced to equivalent force at the circumference of the spindle, 
 for comparison with the tension tests. The results were as follows: 
 D = diam. of spindle; F = force in Ibs.: 
 
 Force Fits, 
 Tension. 
 
 Force Fits, 
 Torsion. 
 
 Shrink Fits, 
 Tension. 
 
 Shrink Fits, 
 Torsion. 
 
 D 
 
 1.001 
 1.0015 
 1.002 
 1 .0025 
 
 F.lbs. 
 
 Per 
 
 sq. in. 
 
 D 
 
 F.lbs. 
 
 Per 
 
 sq.in. 
 
 D 
 
 F.lbs. 
 
 Per 
 sq.in. 
 
 D 
 
 F.lbs. 
 
 Per 
 
 sq.in. 
 
 700 
 2290 
 3118 
 4395 
 5410 
 
 1000 
 2150 
 2570 
 4000 
 
 318 
 685 
 818 
 1272 
 
 1.0015 
 1.0015 
 1.002 
 1.0025 
 
 2200 
 2800 
 4200 
 4600 
 
 700 
 892 
 1335 
 1465 
 
 .001 
 .001 
 .002 
 .002 
 .0025 
 .0025 
 
 5320 
 5820 
 7500 
 8100 
 9340 
 9710 
 
 1695 
 1853 
 2385 
 2580 
 2974 
 3090 
 
 1.001 
 1.0015 
 1.0015 
 1.0025 
 1.003 
 
 2200 
 7200 
 9800 
 13800 
 17000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1328 THE MACHINE-SHOP. 
 
 KEYS. 
 
 Formulae for Flat and Square Keys. Great divergence exists in 
 the dimensions of square and flat keys as given by various authorities. 
 The following are the formulae in common use: 
 
 Notation. D = diameter of shaft; w = width of key; t= thickness 
 of key ; I = length of key, all dimensions being in inches. 
 E. G. Parkhurst's rule: w = i/s D; t = i/g>; taper 1 /sin. per ft. 
 
 Michigan saw-mill practice: w = 1/4 D; t = w. 
 J. T. Hawkins's rule: w = 1/3 Z>; t = 1/4 D. 
 
 Machinery's Handbook, rule 1: w = 1/4 D; t = i/e D\ I = 1.5 Z). 
 Machinery's Handbook, rule 2: w = 3/ 16 D + i/ie; t = i/s D -f- l/s; 
 
 I = 0.3 Z>2 -=- t. 
 
 For splines or feather keys interchange w and t. 
 
 F. W. Halsey (" Handbook for Machine Designers and Draftsmen") 
 says: The common driven key for securing a crank or gear to a shaft 
 is commonly made with a width of 1/4 -D up to about a 4-in. shaft, 
 about 13/8 in. for a 6-in., 1 3/ 4 in. for an 8-in., and 21/4 in. for a 10-in. 
 shaft. The depth should be from s/8 w to 3/ 4 w. If the work is at 
 all severe the length should be at least 1.5 D. The taper is commonly 
 1/8 in. per ft. 
 
 Unwin ("Elements of Machine Design ") gives: Width = 1/4 D+ i/s in. 
 Thickness = i/s D -f i/s in. When wheels or pulleys transmitting only 
 a small amount of power are keyed on large shafts, he says, these 
 dimensions are excessive. In that case, if H.P. = horse-power trans- 
 mitted by the wheel or pulley, JV = r.p.m., P = force acting at the cir- 
 cumference, in pounds, and R = radius of pulley in inches, take 
 
 8 /100H.P. \~PR '. 
 D = yN r V^30 
 
 John Richards, in an article in Gassier' s Magazine, writes as follows: 
 There are two kinds or systems of keys, both proper and necessary, but 
 widely different in nature. 1. The C9mmon fastening key, usually made 
 in width one fourth of the shaft's diameter, and the depth five eighths 
 to one-third the width. These keys are tapered and fit on all sides, or, 
 as it is commonly described, "bear all over." They perform the double 
 function in most cases of driving or transmitting and fastening the 
 keyed-on member against movement endwise on the shaft. Such keys, 
 when properly made, drive as a strut, diagonally from corner to corner. 
 
 2. The other kind or class of keys are not tapered and fit on their 
 sides only, a slight clearance being left on the back to insure against 
 wedge action or radial strain. These keys drive by shearing strain. 
 
 For fixed work where there is no sliding movement such keys are com- 
 monly made of square section, the sides only being planed, so the depth 
 is more than the width by so much as is cut away in finishing or fitting. 
 
 For sliding bearings, as in the case of drilling-machine spindles, the 
 depth should be increased, and in cases where there is heavy strain 
 there should be two keys or feathers instead of one. 
 
 The following tables are from proportions adopted in practical use. 
 
 Flat keys, as in the first table, are employed for fixed work when the 
 parts are to be held not only against torsional strain, but also against 
 movement endwise; and in case of heavy strain the strut principle being 
 the strongest and most secure against movement when there is strain 
 each way, as in the case of engine cranks and first movers generally. 
 The objections to the system for general use are, straining the work out 
 of truth, the care and expense required in fitting, and destroying the 
 evidence of good or bad fitting of the keyed joint. When a wheel or 
 other part is fastened with a tapering key of this kind there is no means 
 of knowing whether the work is well fitted or not. For this reason such 
 keys are not employed by machine-tool-makers, and in the case of 
 accurate work of any kind, indeed, cannot be, because of the wedging 
 strain, and also the difficulty of inspecting completed work. 
 
 I. DIMENSIONS OF FLAT KEYS, IN INCHES. 
 
 Diam. of shaft 
 
 1 
 
 1 V4 
 
 1 I/? 
 
 13/ 4 
 
 2 
 
 2 if?, 
 
 3 
 
 31/2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 Breadth of keys. . . 
 
 1/4 
 
 5/1fi 
 
 3/8 
 
 7/1R 
 
 l/? 
 
 5/8 
 
 3/ 4 
 
 7/8 
 
 ] 
 
 H/8 
 
 13/8 
 
 M/2 
 
 13/4 
 
 Depth of keys.. . . 
 
 5/32 
 
 3/16 
 
 1/4 
 
 9/32 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 5/8 
 
 H/16 
 
 13/16 
 
 7/8 
 
 1 
 
KEYS. 
 
 1329 
 
 II. DIMENSIONS OF SQUARE KEYS, IN INCHES. 
 
 Diameter of shaft . . 
 Breadth of keys . . . 
 Depth of keys 
 
 1 
 
 5/32 
 3/16 
 
 1 V4 
 7/32 
 
 1/4 
 
 1 V2 
 9/32 
 5/16 
 
 1 3/4 
 H/32 
 
 3/8 
 
 2 
 
 13/32 
 
 7/16 
 
 21/2 
 15/32 
 1/2 
 
 3 
 
 17/32 
 9/16 
 
 31/2 
 9/32 
 
 5/8 
 
 H/16 
 
 3/4 
 
 III. DIMENSIONS OF SLIDING FEATHER KEYS, IN INCHES. 
 
 Diameter of shaft . . 
 
 1 V4 
 
 1 1/7! 
 
 1 3/4 
 
 2 
 
 21/4 
 
 21/2 
 
 3 
 
 3V* 
 
 4 
 
 4 ^/?, 
 
 Breadth of keys . . . 
 
 1/4 
 
 1/4 
 
 5/1fi 
 
 5/16 
 
 3/8 
 
 3/8 
 
 l/?, 
 
 9/16 
 
 9/16 
 
 5/8 
 
 Depth of keys 
 
 3/8 
 
 3/8 
 
 7/16 
 
 7/16 
 
 1/2 
 
 1/2 
 
 5/8 
 
 ' 3/4 
 
 3/4 
 
 7/8 
 
 Depth of Key Seats. The depth of- a flat or square key is equally 
 divided between the shaft and the hub. The depth to which a milling 
 cutter is sunk into the shaft in milling a key way is equal to one-half 
 the depth of the key plus the height of the arc projecting above the 
 intersection of the side of the key way with the circumference of the 
 shaft. This height can be calculated from the formula 
 
 h = r- Vr2 - (1/2 w)2 
 
 in which r is the radius of the shaft, h the height of the arc, and w the 
 width of the key. 
 
 The Lewis Key. The disadvantage of the ordinary flat key is that 
 it must be carefully fitted. A key fitting tight on top and bottom of 
 the keyway drives partly by friction. If fitted only on the sides of 
 the keyway it exerts a prying action on the hub and shaft, and is sub- 
 jected to severe bending and shearing stresses. Square or flat keys 
 should fit tight on all four sides, but in practice this is prohibitive on 
 account of the expense. To avoid the difficulty inherent in ordinary 
 flat keys, the Lewis key shown in Fig. 217 was devised by Wilfred 
 Lewis. It is subject to compression only, but is expensive to fit. 
 
 FIG. 217. 
 
 FIG. 218. 
 
 The Earth Key. (Fred. Oyen, Am. Mach., Nov. 14, 1907, and Feb. 
 20, 1908.) The key shown in Fig. 218 was devised by Carl G. Earth 
 to combine the advantages of the Lewis key with those of the ordinary 
 rectangular key. The Barth key is rectangular with one-half of both 
 sides bevelled at 45. The key does not need to fit tightly, as pressure 
 tends to drive it into its seat. There is no tendency to turn it, and 
 the only stress to which it is subject is compression. This key has 
 been used in many cases as a feather to replace rectangular feather 
 keys which have given trouble. It has found wide application as a 
 feather key in drill sockets and drill shanks, reamers, etc., which are 
 commonly driven with a tang. 
 
 Reducing sockets for drill presses are fitted with a Barth key dove- 
 tailed inside and a similar keyway on the outside. No. 1 Morse taper 
 shank has a keyway for No. 1 Barth key and fits into a No. 1 reducing 
 socket. No. 2 shank has No. 2 Morse taper and a keyway for No. 2 
 Barth key, etc. Dimensions of the various sizes of the Barth key are 
 shown in the following table: 
 
1330 
 
 THE MACHINE-SHOP. 
 
 Dimensions of Dovetailed Bar th Keys. 
 
 No. of 
 Earth Key. 
 
 No. of Morse 
 Taper in 
 Which Used. 
 
 w, 
 In. 
 
 W, 
 In. 
 
 D, 
 In. 
 
 1 
 2 
 3 
 
 4 
 
 5 
 
 2 
 3 
 4 
 5 
 
 1/8 
 5/32 
 3/16 
 
 V4 
 5/16 
 
 0.132 
 0.165 
 0.199 
 0.264 
 0.329 
 
 5/128 
 3/64 
 Vl6 
 5/64 
 3/23 
 
 The Earth key has been adapted to a complete line of standard taper 
 sockets, shanks, driving keys, holdback 
 keys, drifts, adapters, and reducers at the 
 Watertown Arsenal. The standards, which 
 cover both Brown & Sharpe and Morse 
 tapers are given in Am. Mach., Dec. 24, 
 1914. 
 
 Do trick & Harvey Keys. (Am. Mach., 
 Feb. 11, 1915.) The Detrick & Harvey 
 Machine Co., Baltimore, uses square keys 
 of dimensions shown in Pig. 219 and the 
 following table. Although these are smaller 
 than the square key generally used, there 
 is no case known in which one of them has 
 sheared off. The dimension C is for setting 
 the key, and the dimension B gives the 
 diameter across the corners of the key. All 
 dimensions are in inches. 
 
 FIG. 219. 
 
 Dimensions of Detrick & Harvey Keys. 
 
 D 
 
 A 
 
 B 
 
 C 
 
 D 
 
 A 
 
 B 
 
 C 
 
 D 
 
 A 
 
 B 
 
 C 
 
 1/2 
 
 1/8 
 
 0.623 
 
 0.555 
 
 3/8 
 
 9/32 
 
 1.652 
 
 1.501 
 
 31/2 
 
 H/16 
 
 4.177 
 
 3.808 
 
 9/16 
 
 1/8 
 
 .685 
 
 .618 
 
 1/2 
 
 5/16 
 
 1.806 
 
 1.640 
 
 33/4 
 
 3/4 
 
 4.487 
 
 4.087 
 
 5/8 
 
 5/32 
 
 .778 
 
 .693 
 
 5/8 
 
 5/16 
 
 1.931 
 
 1.766 
 
 4 
 
 13/16 
 
 4.797 
 
 4.364 
 
 H/16 
 
 5/32 
 
 .841 
 
 .756 
 
 3/4 
 
 7/16 
 
 2.176 
 
 1.941 
 
 41/4 
 
 13/16 
 
 5.049 
 
 4.616 
 
 3/4 
 
 3/16 
 
 .933 
 
 .832 
 
 7/8 
 
 7/16 
 
 2.302 
 
 2.067 
 
 41/2 
 
 13/16 
 
 5.303 
 
 4.868 
 
 13/16 
 
 3/16 
 
 .996 
 
 .895 
 
 2 
 
 7/16 
 
 2.428 
 
 2.194 
 
 43/4 
 
 7/8 
 
 5.619 
 
 5.147 
 
 7/8 
 
 3/16 
 
 .058 
 
 .958 
 
 2 1/4 
 
 9/16 
 
 2.796 
 
 2.496 
 
 5 
 
 7/8 
 
 5.864 
 
 5.399 
 
 15/16 
 
 3/16 
 
 .122 
 
 1.022 
 
 21/2 
 
 9/16 
 
 3.050 
 
 2.749 
 
 51/4 
 
 7/8 
 
 6.115 
 
 5.650 
 
 
 1/4 
 
 .242 
 
 1.109 
 
 23/4 
 
 5/8 
 
 3.361 
 
 3.027 
 
 51/2 
 
 15/16 
 
 6.422 
 
 5.928 
 
 1 1/8 
 
 1/4 
 
 .368 
 
 1.236 
 
 
 5/8 
 
 3.616 
 
 3.280 
 
 53/4 
 
 15/16 
 
 6.676 
 
 6.180 
 
 H/4 
 
 9/32 
 
 .524 
 
 1.375 
 
 31/4 
 
 H/16 
 
 3.925 
 
 3.556 
 
 6 
 
 15/16 
 
 6.927 
 
 6.432 
 
 FIG. 220. 
 
 The Kennedy Key. The Kennedy 
 key, largely used in rolling mill work, is 
 shown in Fig. 220. In these keys w = 
 I = 1/4 D. They are tapered i/g in. per 
 ft. on top, while the sides are a neat fit. 
 The keys are so set in the shaft that 
 diagonals through them intersect at the 
 axis of the shaft. The hub is bored for 
 a press fit and then is rebored eccen- 
 trically about 1/64 D off center. The 
 keyways are cut in the eccentric side. 
 General practice is to use single keys 
 for diameters up to and including 6 in. 
 where the torque is constant and the 
 power transmitted always in one direc- 
 tion. For shafts above 6 in. diameter 
 double keys should be used, and if the 
 torque is intermittent and in alternate 
 directions, double keys should be used 
 down to shaft diameters of 4 in. 
 
KEYS. 
 
 1331 
 
 The Nordberg Key. The Nordberg 
 Mfg. Co. has adopted for the ends of 
 shafts round keys shown in Fig. 223. 
 The advantages of this key are: No 
 tendency toward deformation ; they are 
 a driven fit in the direction of the 
 shear; they are always in true shear and 
 are cheaper than the square key. In 
 manufacturing a hole A is drilled in the 
 joint and next a hole B as large as the 
 size of the keyway will admit is drilled 
 in the shaft in order to avoid the ten- 
 dency of the drill used for drilling the 
 keyway to size to crowd into the soft 
 cast iron. In the table the reamer 
 diameters given are of the small end. 
 The taper is i/ie in. per ft., measured 
 on the diameter. 
 
 FIG. 221. 
 
 Dimensions of Nordberg Standard Round Keys. 
 
 Diam. 
 of 
 Shaft, 
 In. 
 
 Diam. 
 of 
 Reamer 
 In. 
 
 Cutting 
 Length 
 of 
 Reamer 
 In. 
 
 Diam. 
 of 
 Shaft, 
 In. 
 
 Diam. 
 of 
 Reamer 
 In. 
 
 Cutting 
 Length 
 of 
 Reamer 
 In. 
 
 Diam. 
 of 
 Shaft, 
 In. 
 
 Diam. 
 of 
 Reamer 
 In. 
 
 Cutting 
 Length 
 of 
 Reamer 
 In. 
 
 2 15/16-3 
 3 7/ 16 -3 1/2 
 3 7/ 8 -4 
 
 4 3/ 8 -4 1/2 
 51/2 
 
 6 
 
 3/4 
 
 7/8 
 
 1/8 
 1/4 
 3/8 
 1/2 
 
 41/4 
 4V2 
 47/8 
 
 45/8 
 47/8 
 61/8 
 
 8> 
 
 o ( 
 
 91 
 10 J 
 11 V 
 12) 
 
 13) 
 14V 
 
 15/8 
 2 
 29/16 
 
 6 7/ 8 & 8 
 101/4 
 12 
 
 16) 
 17V 
 18) 
 19) 
 20V 
 21 f 
 22) 
 23V 
 
 31/8 
 3 H/16 
 4 1/4 
 
 12 
 13 
 
 14 1/4 
 
 
 
 
 15\ 
 
 
 
 24 f 
 
 
 
 The Woodruff Key. The Woodruff key shown in Fig. 222 is exten- 
 sively used in machine construction. Dimensions are given in the 
 following table. The key should project above the shaft a distance 
 equal to one-half the thickness. For ordinary practice medium-sized 
 keys should be used: 
 
 .&. I 
 
 STANDARD. FIG. 222. SPECIAL. 
 
 Dimensions of Woodruff Standard Keys Inches. 
 
 
 
 
 
 o, 
 
 
 
 
 
 a 
 
 
 
 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 " 
 
 - 
 
 
 
 
 ** 
 
 H 
 
 
 
 
 
 -H^ 
 
 No. 
 
 o . 
 
 . s 
 
 
 >> 
 
 _, rt 
 
 ^ 
 
 No. 
 
 . 
 
 . ^ 
 
 
 o >> 
 
 _, cU 
 
 y o^ 
 
 * >> 
 
 No. 
 
 , 
 
 i ^ 
 
 >> 
 
 2s* 
 
 
 Is 
 
 QW 
 
 .i* 
 
 o K - 
 
 2 g 
 
 H c 
 
 is 
 
 a > 
 
 OJ 0) 
 
 QW 
 
 ll* 
 
 Of/2 O 
 
 
 
 
 5t2 
 
 M* 
 
 .2 OB 
 
 3 $ 
 He 
 
 i3 
 
 II 
 
 m 
 
 Otfi o 
 
 
 Is 
 
 QW 
 
 
 
 II 
 
 in! 
 
 Ssz 
 
 Utt^ 
 
 1 
 
 1/2 
 
 1/16 
 
 1/3? 
 
 3/64 
 
 12 
 
 7/8 
 
 7/3? 
 
 7/64 
 
 1/16 
 
 20 
 
 1/4 
 
 7/3? 
 
 7/64 
 
 5/64 
 
 2 
 
 1/2 
 
 3/3? 
 
 3/64 
 
 3/64 
 
 A 
 
 7/8 
 
 1/4 
 
 1/8 
 
 1/16 
 
 21 
 
 1/4 
 
 1/4 
 
 1/8 
 
 5/64 
 
 3 
 
 I/? 
 
 1/8 
 
 Vlfi 
 
 3/64 
 
 13 
 
 
 3/16 
 
 3/3? 
 
 1/16 
 
 D 
 
 1/4 
 
 5/16 
 
 5/3? 
 
 5/64 
 
 4 
 
 5/8 
 
 3/32 
 
 3/64 
 
 1/16 
 
 14 
 
 
 7/3? 
 
 7/64 
 
 1/16 
 
 E 
 
 1/4 
 
 3/8 
 
 3/16 
 
 5/64 
 
 5 
 
 5/8 
 
 1/8 
 
 1/16 
 
 Vl6 
 
 15 
 
 
 1/4 
 
 1/8 
 
 1/16 
 
 22 
 
 3/8 
 
 1/4 
 
 1/8 
 
 3/32 
 
 6 
 
 5/8 
 
 5/3? 
 
 5/64 
 
 1/16 
 
 B 
 
 
 5/16 
 
 5/30 
 
 1/16 
 
 23 
 
 3/8 
 
 5/16 
 
 5/3? 
 
 3/32 
 
 7 
 
 3/4 
 
 1/8 
 
 1/16 
 
 1/16 
 
 16 
 
 1/8 
 
 3/16 
 
 3/3? 
 
 5/64 
 
 F 
 
 3/8 
 
 3/8 
 
 3/16 
 
 3/32 
 
 8 
 
 3/4 
 
 5/3? 
 
 5/64 
 
 1/16 
 
 17 
 
 1/8 
 
 7/3? 
 
 7/64 
 
 5/64 
 
 24 
 
 1/2 
 
 1/4 
 
 1/8 
 
 7/64 
 
 9 
 
 3/ 4 
 
 3/1fi 
 
 3/3? 
 
 1/16 
 
 18 
 
 1/8 
 
 1/4 
 
 1/8 
 
 5/64 
 
 25 
 
 I/? 
 
 5/16 
 
 5/3? 
 
 7/64 
 
 10 
 
 7/8 
 
 5/3? 
 
 5/64 
 
 1/16 
 
 C 
 
 1/8 
 
 6/16 
 
 5/3? 
 
 5/64 
 
 G 
 
 1/2 
 
 3/8 
 
 3/16 
 
 7/fi4 
 
 11 
 
 7/8 
 
 3/16 
 
 3/32 
 
 1/16 
 
 19 
 
 1/4 
 
 3/16 
 
 3/32 
 
 5/64 
 
 
 
 
 
 
1332 THE MACHINE-SHOP. 
 
 Dimensions of Woodruff Special Keys Inches. 
 
 No. 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 Dimension 
 a 
 6 
 
 d 
 
 e 
 
 21/8 
 3/16 
 3/32 
 17/32 
 3/32 
 
 21/8 
 1/4 
 1/8 
 17/32 
 3/32 
 
 21/8 
 5/16 
 5/32 
 17/32 
 3/32 
 
 21/8 
 3/8 
 3/16 
 17/32 
 3/32 
 
 31/2 
 3/8 
 3/16 
 13/16 
 3/16 
 
 31/2 
 7/16 
 7/32 
 13/16 
 3/16 
 
 3l/ 2 
 
 1/2 
 1/4 
 13/16 ^ 
 3/16 
 
 3l/ 2 
 
 9/16 
 9/32 
 13/16 
 3/16 
 
 31/2 
 
 5/8 
 5/16 
 
 ^ I6 
 3 /16 
 
 Woodruff Keys Suitable for Different Shaft Diameters'. 
 
 Shaft 
 Diam. 
 
 Key 
 Nos. 
 
 Shaft 
 Diam. 
 
 Key 
 Nos. 
 
 Shaft 
 Diam. 
 
 Key 
 
 Nos. 
 
 Shaft 
 Diam. 
 
 Key 
 Nos. 
 
 5/16-3/8 
 7/16-1/2 
 9/16-5/8 
 H/16-3/4 
 
 1 
 2,4 
 3,5 
 3, 5.7 
 
 13/16 
 7/8-1-ViG 
 
 I 1/16-1 1/8 
 
 6,8 
 6, 8, 10 
 9, 11, 13 
 9,11,13,16 
 
 1 3/16 
 1 1/4-1 5/i 6 
 1 3/8-1 7/i 6 
 1 1/2-1 5/8 
 
 11, 13, 16 
 12,14,17,20 
 14, 17.20 
 15, 18,21.24 
 
 1 H/16-1 3/4 
 1 13/16-2 
 2 1/16-21/2 
 
 18,21.24 
 23.25 
 25 
 
 Cw3 K 
 
 Gib Keys. ''Machinery's Handbook " gives the following formulae for 
 dimensions of gib keys. (See Pig. 223). All dimensions are in inches. 
 
 D = diameter of shaft; w = width 
 of key; T = thickness of key, large 
 end; S = safe shearing strength of 
 material in key; G = length of gib; 
 h = projection of gib above top oi' 
 key. 
 
 w = 1/4 D up to 6 in.; over 6 in. 
 w = 0.211 D. 
 
 T = i/e D up to 6 in. ; over 6 in. T = l/s D. 
 
 G = w. 
 
 Length = length of hub + 1/2 in. Taper 1/s in. per ft. 
 
 Safe twisting moment per in. of length of key = 1/2 D X W X S. 
 
 Keyways for Milling Cutters. For keyways for milling cutters 
 see p. 1277. 
 
 Length 
 
 FIG. 223. 
 Minimum value 3/i 6 in. 
 
 HOLDING-POWER OF KEYS AND SET-SCREWS. 
 
 Tests of the Holding-power of Set-screws in Pulleys. (G. Lanza, 
 Trans. A. S. M. E.,x, 230.) These tests were made by using a pulley 
 fastened -to the shaft by two set-screws with the shaft keyed to the 
 holders; then the load required at the rim of the pulley to cause it to 
 slip was determined, and this being multiplied by the number 6,037 
 (obtained by adding to the radius of the pulley one-half the diameter 
 of the wire rope, and dividing the sum by twice the radius of the shaft, 
 since there were two set-screws in action at a time) gives the holding- 
 power of the set-screws. The set-screws used were of wrought iron, 
 5/8 of an inch in diameter, and ten threads to the inch; the shaft used 
 was of steel and rather hard, the set-screws making but little impression 
 upon it. They were set up with a force of 75 pounds at the end of a 
 ten-inch monkey-wrench. The set-screws used were of four kinds, 
 marked respectively A, B, C, and D. The results were as follows: 
 
 A, ends perfectly flat, 9/i6-in. diam. 1412 to 2294 Ibs. 
 
 B, radius of rounded ends about l/2-m. 2747 to 3079 Ibs. 
 
 C, radius of rounded ends about l/4-in. 1902 to 3079 Ibs. 
 
 D, ends cup-shaped and case-hardened 1962 to 2958 Ibs. 
 
 average 2064. 
 
 average 2912. 
 
 average 2573. 
 
 average 2470. 
 
 REMARKS. A. The set-screws were not entirely normal to the shaft; 
 hence they bore less in the earlier trials, before they had become flattened 
 by wear. > 
 
 B. The ends of these set-screws, after the first two trials, were found 
 to be flattened, the flattened area having a diameter of about 1/4 inch. 
 
InB. 
 
 DYNAMOMETERS. 1333 
 
 The ends were found, after the first two trials, to be flattened, aa 
 
 D. The first test held well because the edges were sharp, then the 
 holding-power fell off till they had become flattened in a manner similar 
 to B, when the holding-power increased again. 
 
 Tests of the Holding-power of Keys. (Lanza.) The load was 
 applied as in the tests of set-screws, the shaft being firmly keyed to the 
 holders. The load required at the rim of the pulley to shear the keys 
 was determined, and this, multiplied by a suitable constant, determined 
 in a similar v/ay to that used in the case of set-screws, gives us the shear- 
 ing strength per square inch of the keys. 
 
 The keys tested were of eight kinds, denoted, respectively, by the 
 letters A, B, C, D, E, F, G and H, arid the results were as follows: A, B, D, 
 and F, each 4 tests; E, 3 tests; C, G, and H, each 2 tests. 
 
 A, Norway iron, 2" X W X W32", 40,184 to 47,760 Ibs. ; average, 42,726 
 
 B, refined iron, 2" X 1/4" X is/32", 36,482 to 39,254 Ibs. ; average, 38,059 
 
 C, tool steel, 1" X 1/4" X 15/32", 91,344 & 100,056 Ibs. ; 
 
 D, mach'y steel, 2" X 1/4" X 15/32" 64,630 to 70,186 Ibs.; average, 66,875 
 
 E, Norway iron, 1 1/3" X W X 7/io" 36,850 to 37,222 Ibs. ; average, 37,036 
 
 F, cast-iron, 2" X 1/4" X 15/32", 30,278 to 36,944 Ibs.; average, 33,034 
 
 G, cast-iron, 1 1/3" X 3/ 8 " X 7/ie", 37,222 & 38,700. 
 H, cast-iron, V X 1/2" X 7/i 6 ", 29,814 & 38,978. 
 
 The first dimension is the length, the second the width and the third 
 the height. 
 
 In A ana B some crushing took place before shearing. In E, the 
 keys, being only 7/iQ inch deep, tipped slightly in the key-way. In H, in 
 the first test, there was a defect in the key-way of the pulley. 
 
 DYNAMOMETERS. 
 
 Dynamometers are instruments used for measuring power. They are 
 of several classes, as: 1. Traction dynamometers, used for determining 
 the power required to pull a car or other vehicle, or a plow or harrow. 
 2. Brake or absorption dynamometers, in which the power of a rotating 
 shaft or wheel is absorbed or converted into heat by the friction of a 
 brake; and 3. Transmission dynamometers, in which the power in a 
 rotating shaft is measured during its transmission through a belt or other 
 connection to another shaft, without being absorbed. 
 
 Traction Dynamometers generally contain two principal parts: (1) A 
 spring or series of springs, through which the pull is exerted, the exten- 
 sion of the spring measuring the 
 amount of the pulling force; and 
 (2) a paper-covered drum, rota- 
 ted either at a uniform speed by 
 clockwork, or at a speed propor- 
 tional to the speed of the trac- 
 tion, through gearing, on which 
 the extension of the spring is reg- 
 istered by a pencil. From the 
 average height of the diagram 
 drawn by the pencil above the 
 FIG. 224. zero-line the average pulling 
 
 force in pounds is obtained, and 
 
 this multiplied by the distance traversed, in feet, gives the work done, in 
 foot-pounds. The product divided by the time in minutes and by 33,000 
 gives the horse-power. 
 
 The Prony brake is the typical form of absorption dynamometer. 
 (See Fig. 224. from Flather on Dynamometers.) 
 
 Primarily this consists of a lever connected to a revolving shaft or pul- 
 ley in such a manner that the friction induced between the surfaces in 
 contact will tend to rotate the arm in the direction in which the shaft 
 revolves. This rotation is counterbalanced by weights P, hung in the 
 scale-pan at the end of the lever. In order to measure the power for a 
 given number of revolutions of pulley, we add weights to the scale-pan 
 
1334 DYNAMOMETERS. 
 
 and screw up on bolts &,&, until the friction induced balances the weights 
 and the lever is maintained in its horizontal position while the revolu- 
 tions of the shaft per minute remain constant. 
 
 For small powers the beam is generally omitted the friction being 
 measured by weighting a band or strap thrown over the pulley. Ropes 
 or cords are often used for the same purpose. 
 
 Instead of hanging weights in a scale-pan, as in Fig. 224, the friction 
 may be weighed on a plat form-scale; in this case, the direction of rotation 
 being the same, the lever-arm will be on the opposite side of the shaft. 
 
 In a modification of this brake, the brake-wheel is keyed to the shaft, 
 and its rim is provided with inner flanges which form an annular trough 
 for the retention of water to keep the pulley from heating. A small 
 stream of water constantly discharges into the trough and revolves with 
 the pulley the centrifugal force of the particles of water overcoming the 
 action of gravity ; a waste-pipe with its end flattened is so placed in the 
 trough that it acts as a scoop, and removes all surplus water. The brake 
 consists of a flexible strap to which are fitted blocks of wood forming the 
 rubbing-surface; the ends of the strap are connected by an adjustable 
 bolt-clamp, by means of which any desired tension may be obtained. 
 
 The horse-power or work of the shaft is determined from the following : 
 
 Let W = work of shaft, equals power absorbed, per minute; 
 
 P = unbalanced pressure or weight in pounds, acting on lever- 
 arm at distance L ; 
 
 L = length of lever-arm in feet from center of shaft; 
 V a= velocity of a point in feet per minute at distance L, if arm 
 
 were allowed to rotate at the speed of the shaft; 
 N = number of revolutions per minute; 
 H.P. = horse-power. 
 
 Then will W - PV =2 nLNP. 
 
 Since H.P. = PV -*- 33,000, we have H.P. = 2 nLNP * 33,000. 
 
 If L = 33 -* 2 it, we obtain H.P. = NP * 1000. 33 -J- 2 n is practically 
 5 ft. 3 in., a value often used in practice for the length of arm. 
 
 If the rubbing-surface be too small, the resulting friction will show 
 great irregularity probably on account of insufficient lubrication 
 the jaws being allowed to seize the pulley, thus producing shocks and 
 sudden vibrations of the lever-arm. 
 
 Soft woods, such as bass, plane-tree, beech, poplar, or maple, are all 
 to be preferred to* the harder woods for brake-blocks. The rubbing-sur- 
 face should be well lubricated with a heavy grease. 
 
 The Alden Absorption-dynamometer. (G. I. Alden, Trans. A. S. 
 M. E., vol. xi, 958; also xii, 700 and xiii, 429.) This dynamometer is a 
 friction-brake, which is capable in quite moderate sizes of absorbing 
 large powers with unusual steadiness and complete regulation. A 
 smooth cast-iron disk is keyed on the rotating shaft. This is inclosed 
 in a cast-iron shell, formed of two disks and a ring at their circumference, 
 which is free to revolve on the shaft. To the interior of each of the sides 
 of the shell is fitted a copper plate, inclosing between itself and the side a 
 water-tight space. Water under pressure from the city pipes is admitted 
 into each of these spaces, forcing the copper plate against' the central disk. 
 The chamber inclosing the disk is filled with oil. To the outer shell is 
 fixed a weighted arm, which resists the tendency of the shell to rotate 
 with the shaft, caused by the friction of the plates against the central 
 disk. Four brakes of this type, 56 in. diam., were used in testing the 
 experimental locomotive at Purdue University (Trans. A. S. M. E., 
 xiii, 429). Each was designed for a maximum moment of 10,500 foot- 
 pounds with a water-pressure of 40 Ibs. per sq. in. The area in effective 
 contact with the copper plates on either side is represented by an annular 
 surface having its outer radius equal to 28 ins. and its inner radius equal 
 to 10 ins. The apparent coefficient of friction between the plates and the 
 disk was 3V2%. 
 
 Capacity of Friction-brakes. W. W. Beaumont (Proc. Inst. C. E.. 
 1889) has deduced a formula by means of which the relative capacity of 
 brakes can be compared, judging from the amount of horse-power ascer- 
 tained by their use. 
 
 If W width of rubbing-surface on brake- wheel in inches; V vel. 
 of point on Circqm, of wheel in feet per minute; K coefficient; then 
 K~ WV -*-H.P. 
 
DYNAMOMETERS. 
 
 1335 
 
 Prof. Flather obtains the values of K given in the last column of the 
 subjoined table: 
 
 % 
 Horse-power. 
 
 R.P.M. Brake- 
 pulley. 
 
 Brake- 
 pulley. 
 
 g 
 
 *. 
 
 
 o*S 
 J.S 
 
 Design of Brake. 
 
 Value of K. 
 
 Sj 
 
 43 
 
 8 o 
 
 a d 
 b-t'~ 
 
 Diameter, 
 in feet . 
 
 21 
 19 
 
 20 
 40 
 33 
 130 
 24 
 180 
 475 
 125\ 
 250| 
 401 
 125 f 
 
 150 
 148.5 
 146 
 180 
 150 
 150 
 142 
 100 
 76.2 
 290\ 
 250 f 
 322) 
 290 f 
 
 7 
 7 
 7 
 10.5 
 10.5 
 10 
 12 
 24 
 24 
 
 24 
 13 
 
 5 
 
 5 
 5 
 5 
 5 
 9 
 6 
 5 
 7 
 
 4 
 4 
 
 33 
 
 33.38 
 32.19 
 32 
 32 
 
 '38.31 
 126.1 
 191 
 
 63 
 273/4 
 
 Royal Ag Soc compensating 
 
 785 
 858 
 802 
 741 
 749 
 282 
 1385 
 209 
 847 
 
 465 
 847 
 
 McLaren compensating 
 
 
 Garrett water-cooled and comp 
 
 
 
 Balk 
 
 Gatelv & Kletsch water-cooled 
 
 
 
 
 k ' 
 
 The above calculations for eleven brakes give values of K varying from 
 84.7 to 1385 for actual horse-powers tested, the average being K = 655. 
 
 Instead of assuming an average coefficient, Prof. Fiather proposes thq 
 following: 
 
 Water-cooled brake, non-compensating, K = 400; W = 400 H.P. -*- V. 
 
 Water-cooled brake, compensating, K = 750; F" = 750 H.P. -* V. 
 
 Non-cooling brake, with or without compensating device, / = 900: W = 
 900 H.P. +V. 
 
 A brake described in Am. Mach., July 27, 1905, had an iron water- 
 cooled drum, 30 in. diam., 20 in. face, with brake blocks of maple attached 
 to an iron strap nearly surrounding the drum. At 250 r.p.m., or a cir- 
 cumferental speed of 1963 ft. per min., the limit of its capacity was about 
 140 H.P.; above that power the blocks took fire. At 140 H.P. the total 
 surface passing under the brake blocks per minute was 3272 sq. ft., or 
 23.37 per H.P. This corresponds to a value of K = 285. 
 
 Several forms of Prony brake, including rope and strap brakes, are 
 described by G. E. Quick in Am. Mach., Nov. 17, 1908. Some other 
 forms are shown in Am. Electrician, Feb., 1903. 
 
 A 6000 H.P. Hydraulic Absorption Dynamometer, built by the W T est- 
 Inghouse Machine Co., is described by E. H. Longwell in Eng. News, 
 Dec. 30, 1909. It was designed for testing the efficiency of the Melville 
 and Me Alpine turbine reduction gear (see page 1095). This dynamometer 
 consists of a rotor mounted on a shaft coupled to the reduction gear and 
 rotating within a closed casing which is prevented from turning by a 
 6 ft. lever arm, the end of which transmits pressure through an I-beam 
 lever to a platform scale. The rotor carries several rows of steam turbine 
 vanes and the casing carries corresponding rows of stationary vanes, so 
 arranged as to baffle and agitate the water passing through the brake, 
 which is heated to boiling temperature by the friction. The dynamom- 
 eter was run for 40 hours continuously, and proved to be a highly 
 accurate instrument. 
 
 Transmission Dynamometers are of various forms, as the Batchelder 
 dynamometer, in which the power is transmitted through a "train-arm" 
 of bevel gearing, with its modifications, as the one described by the author 
 in Trans. A. I. M. E., viii, 177, and the one described by Samuel Webber 
 in Trans. A. S. M. E., x, 514; belt dynamometers, as the Tatham; the 
 Van Winkle dynamometer, in which the power is transmitted from a 
 revolving shaft to another in line with it, the two almost touching, 
 through the medium of coiled springs fastened to arms or disk keyed to 
 the shafts; the Brackett and the Webb cradle dynamometers, used for 
 measuring the power required to run dynamo-electric machines. De- 
 scriptions of the four last named are given in Flather on Dynamometers, 
 
 The Kenerson transmission dynamometer is described in Trans. A. S. 
 M. E.. 1909. It has the form of a shaft coupling, one part of which con- 
 
1336 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 tains a cavity filled with oil and covered by a flexible copper diaphragm. 
 
 The other part, by means of bent levers and a thrust ball-bearing, brings 
 an axial pressure on the diaphragm and on the oil, and the pressure of the 
 oil is measured by a gauge. 
 
 Much information on various fprms of dynamometers will be found in 
 Trans. A. S. M. E., vols. vii to xv, inclusive, indexed under Dynamometers. 
 
 ICE-MAKING- OR REFRIGERATING 
 MACHINES. 
 
 References. An elab9rate discussion of the thermodynamic theory 
 of the action of the various fluids used in the production of cold was 
 published by M. Ledoiix in the Annales des Mines, and translated in Van 
 Nostrand's Magazine in 1879. This work, revised and additions made 
 in the light of recent experience by Professors Den ton, Jacobus, and 
 Riesenberger, was reprinted in 1892. (Van Nostrand's Science Series, 
 No. 46.) The work is largely mathematical, but it also contains much 
 information of immediate practical value, from which some of the mat- 
 ter given below is taken. Other references are Wood's Thermody- 
 namics, Chap. V. and numerous papers by Professors Wood, Denton, 
 Jacobus, and Linde in Trans. A. S. M. E., vols. x to xiv; Johnson's 
 Cyclopaedia, article on Refrigerating-machines; and the following books: 
 Siebel's Compend of Mechanical Refrigeration; Modern Refrigerating 
 Machinery, by Lorenz, translated by Pope; Refrigerating Machines, by 
 Gardner T. Voorhees; Refrigeration, by J. Wemyss Anderson, and Re- 
 frigeration, Cold Storage and Ice-making, by A. J. Wallis-Taylor. For 
 properties of Ammonia and Sulphur Dioxide, see papers by Professors 
 Wood and Jacobus, Trans. A. S. M. E., vols. x and xii. 
 
 For illustrated descriptions of refrigerating-machines, see catalogues of 
 builders, as Frick & Co., Waynesboro, Pa.; De La Vergne Refrigerating- 
 machine Co., New York; Vilter Mfg. Co., Milwaukee; York Mfg., York, Co., 
 Pa.; Henry Vogt Machine Co., Louisville, Ky.; Carbondale Machine Co., 
 Carbondale, Pa.; and others. See also articles in Ice and Refrigeration. 
 
 Operations of a Refrigerating-machine. Apparatus designed for 
 refrigerating is based upon the following series of operations: 
 
 Compress a gas or vapor by means of some external force, then relieve 
 it of its heat so as to diminish its volume; next, cause this compressed gas 
 or vapor to expand so as to produce mechanical work, and thus lower 
 its temperature. The absorption of heat at this stage by the gas, in 
 resuming its original condition, constitutes the refrigerating effect of the 
 apparatus. 
 
 A refrigerating-machine is a heat-engine reversed. 
 
 From this similarity between heat-motors and freezing-machines it 
 results that all the equations deduced from the mechanical theory of heat 
 to determine the performance of the first, apply equally to the second. 
 
 The efficiency depends upon the difference between the extremes of 
 temperature. 
 
 The useful effect of a refrigerating-machine depends upon the ratio 
 between the heat-units eliminated and the work expended in compressing 
 and expanding. 
 
 This result is independent of the nature of the body employed. 
 
 Unlike the heat-motors, the freezing-machine possesses the greatest 
 efficiency when the range of temperature is small, and when the final 
 temperature is elevated. 
 
 If the temperatures are the same, there is no theoretical advantage in 
 employing a gas rather than a vapor in order to produce cold. 
 
 The choice of the intermediate body would be determined by practical 
 considerations based on the physical characteristics of the body, such as 
 the greater or less facility for manipulating it, the extreme pressures 
 required for the best effects, etc. 
 
 Air offers the double advantage that it is everywhere obtainable, and 
 that we can vary at will the higher pressures, independent of the tempera- 
 ture of the refrigerant. But to produce a given useful effect the apparatus 
 must be of larger dimensions than that required by liquefiable vanors. 
 
 The maximum pressure is determined by the temperature of the con- 
 denser and the nature of the volatile liquid ; this pressure is often high. 
 
BOILING POINTS OF REFRIGERATING LIQUIDS. 1337 
 
 When a change of volume of a saturated vapor is made under constant 
 pressure, the temperature remains constant. The addition or subtraction 
 of heat, which produces the change of volume, is represented by an 
 increase or a diminution of the quantity of liquid mixed with the vapor. 
 
 On the other hand, when vapors, even if saturated, are no longer in 
 contact with their liquids, and receive an addition of heat either through 
 compression by a mechanical force, or from some external source of heat, 
 they comport themselves nearly in the same way as permanent gases, 
 and become superheated. 
 
 It results from this property, that refrigerating-machmes using a 
 liquefiable gas will afford results differing according to the method of 
 working, and depending upon the state of the gas, whether it remains 
 constantly saturated, or is supejrheated during a part of the cycle of 
 working. 
 
 The temperature of the condenser is determined by local conditions. 
 The interior will exceed by 9 to 18 the temperature of the water fur- 
 nished to the exterior. This latter will vary from about 52 F., the 
 temperatiye of water from considerable depth below the surface, to 
 about 95 F., the temperature of surface-water in hot climates. The 
 volatile liquid employed in the machine ought not at this temperature to 
 have a tension above that which can be readily managed by the apparatus. 
 
 On the other hand, if the tension of the gas at the minimum temperature 
 is too low, it becomes necessary to give to the compression-cylinder 
 large dimensions, in order that the weight of vapor compressed by a 
 single stroke of the piston shall be sufficient t<j produce a notably useful 
 effect. 
 
 These two conditions, to which may be added others, such as those 
 depending upon the greater or less facility of obtaining the liquid, upon 
 the dangers incurred in its use, either from its inflammability or unhealth- 
 fulness, and finally upon its action upon the metals, limit the choice to a 
 small number of substances. 
 
 The gases or vapors generally available are: sulphuric ether, sulphurous 
 oxide, ammonia, methylic ether, and carbonic acid. 
 
 The following table, derived, from Regnault, shows the tensions of the 
 vapors of these substances at temperatures between 22 and 4- 104. 
 
 Pressures and Boiling-points of Liquids available for Use 
 in Refrigerating-machines. 
 
 Temp. 
 
 
 of 
 Ebulli- 
 
 Tension of Vapor, in Ibs. per sq. in., above Zero. 
 
 tion. 
 
 
 Deg. 
 
 Fahr. 
 
 Sul- 
 phuric 
 Ether. 
 
 Sulphur 
 Dioxide. 
 
 Ammonia. 
 
 ro.)y 
 
 Methylic 
 Ether. 
 
 Carbonic 
 Acid. 
 
 Pictet 
 Fluid. 
 
 Ethyl 
 Chlonde 
 
 -31 
 
 
 
 13.23 
 
 
 
 
 
 -22 
 
 
 5.56 
 
 16.95 
 
 11 15 
 
 
 
 2 13 
 
 13 
 
 
 7 23 
 
 21 51 
 
 13 85 
 
 251 6 
 
 
 20ft 
 
 - 4 
 
 1.30 
 
 9.27 
 
 27.04 
 
 17.06 
 
 292.9 
 
 ""\3.5" 
 
 3.63 
 
 5 
 
 1.70 
 
 11.76 
 
 33.67 
 
 20.84 
 
 340.1 
 
 16.2 
 
 4.63 
 
 14 
 
 2.19 
 
 14.75 
 
 41.58 
 
 25.27 
 
 393.4 
 
 19.3 
 
 5.84 
 
 23 
 
 2.79 
 
 18.31 
 
 50.91 
 
 30.41 
 
 453.4 
 
 22.9 
 
 7 28 
 
 32 
 
 3.55 
 
 22.53 
 
 61.85 
 
 36.34 
 
 520.4 
 
 26.9 
 
 9 00 
 
 41 
 
 4.45 
 
 27.48 
 
 74.55. 
 
 43.13 
 
 594.8 
 
 31.2 
 
 11 01 
 
 50 
 
 5.54 
 
 33.26 
 
 89.21 
 
 50.84 
 
 676.9 
 
 36.2 
 
 13 36 
 
 59 
 
 6.84 
 
 39.93 
 
 105.99 
 
 59.56 
 
 766.9 
 
 41.7 
 
 16 10 
 
 68 
 
 8.38 
 
 47.62 
 
 125.08 
 
 69.35 
 
 864.9 
 
 48.1 
 
 19 26 
 
 77 
 
 10.19 
 
 56.39 
 
 146.64 
 
 80.28 
 
 971.1 
 
 55.6 
 
 22 90 
 
 86 
 
 12.31 
 
 66.37 
 
 170.83 
 
 92.41 
 
 1085.6 
 
 64.1 
 
 27 05 
 
 95 
 
 14.76 
 
 77.64 
 
 197.83 
 
 
 1207.9 
 
 73 2 
 
 31 78 
 
 104 
 
 17.59 
 
 90.32 
 
 227 76 
 
 
 1338.2 
 
 82 9 
 
 37 12 
 
 The table shows that the use of ether does not readily lead to the 
 production of low temperatures, because its pressure becomes then very 
 feeble. Ammonia, on the contrary, is well adapted to the production 
 of low temperatures. 
 
1338 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 i Methylic ether yields low temperatures without attaining too great 
 pressures at the temperature of the condenser. Sulphur dioxide readily 
 affords temperatures of 14 to 5, while its pressure is only 3 to 4 
 atmospheres at the ordinary temperature of the condenser. These latter 
 substances then lend themselves conveniently for the production of cold 
 by means of mechanical force. 
 
 The " Pictet fluid " is a mixture of 97% sulphur dioxide and 3% carbonic 
 acid. At atmospheric pressure it affords a temperature 14 low'er than 
 sulphur dioxide. (It is not now used 1910.) 
 
 Carbonic acid is in use to a limited extent, but the relatively greater 
 compactness of compressor that it requires, and its inoffensive character, 
 are leading to its recommendation for service on shipboard. 
 
 Certain ammonia plants are operated with a surplus of liquid present 
 during compression, so that superheating is prevented. This practice is 
 known as the "cold " or " wet " system of compression. 
 
 Ethyl chloride, CoHsCl, is a colorless gas which at atmospheric pressure 
 condenses to a liquid at 54.5 F. The latent heat at 23 F. is given at 174 
 B.T.U. Density of the gas (air = l) = 2.227. Specific heat at constant 
 pressure. 0.274; at constant volume, 0.243. 
 
 Nothing definite is known regarding the application of methylic ether or 
 of the petroleum product chymogene in practical refrigerating service. 
 The inflammability of the latter and the cumbrousness of the compressor 
 required are objections to its use. 
 
 PROPERTIED OF SULPHUR DIOXIDE AND 
 AMMONIA GAS. 
 
 Ledoux's Table for Saturated Sulphur-dioxide Gas. 
 
 Heat-units expressed in B.T.U. per pound of sulphur dioxide. 
 
 .1 
 
 2-- 
 
 OJ3 bi)"* 
 |. 
 
 ffU 
 
 Absolute Pres- 
 sure in Ibs. per 
 sq. in. 
 
 P *- 144 
 
 Total Heat 
 reckoned from 
 32 F. 
 A. 
 
 Heat of Liquid 
 reckoned from 
 32 F. 
 Q 
 
 Latent Heat of 
 Evaporation. 
 r 
 
 Heat Equivalent 
 of External 
 Work. 
 APu 
 
 Internal La- 
 tent Heat. 
 P 
 
 Increase of 
 Volume dur- 
 ing Evapo- ; 
 ration. 
 U 
 
 Density of Va- 
 por or Weight 
 of 1 cu. ft. 
 
 1 -5- V 
 
 Des. F. 
 
 Lb. 
 
 B.T.U, 
 
 B.T.U. 
 
 B.T.U. 
 
 B.T.U. 
 
 B.T.U. 
 
 Cu.ft. 
 
 Lb. 
 
 -22 
 
 5.56 
 
 157.43 
 
 -19.56 
 
 176.99 
 
 13.59 
 
 163.39 
 
 13.17 
 
 0.076 
 
 -13 
 
 7.23 
 
 158.64 
 
 - 16.30 
 
 174.95 
 
 13.83 
 
 161.12 
 
 10.27 
 
 .097 
 
 - 4 
 
 9.27 
 
 159.84 
 
 - 13.05 
 
 172.89 
 
 14.05 
 
 158.84 
 
 8.12 
 
 .123 
 
 5 
 
 11.76 
 
 161.03 
 
 - 9,79 
 
 170.82 
 
 14.26 
 
 156.56 
 
 6.50 
 
 .153 
 
 14 
 
 14.74 
 
 162.20 
 
 - 6.53 
 
 168.73 
 
 14.46 
 
 154.27 
 
 5.25 
 
 .190 
 
 23 
 
 18.31 
 
 163.36 
 
 - 3.27 
 
 166.63 
 
 14.66 
 
 151.97 
 
 4.29 
 
 .232 
 
 32 
 
 22.53 
 
 164.51 
 
 0.00 
 
 164.51 
 
 14.84 
 
 149.68 
 
 3.54 
 
 .282 
 
 41 
 
 27.48 
 
 165.65 
 
 3.27 
 
 162.38 
 
 15.01 
 
 147.37 
 
 2.93 
 
 .340 
 
 50 
 
 33.25 
 
 166.78 
 
 6.55 
 
 160.23 
 
 15.17 
 
 145.06 
 
 2.45 
 
 .407 
 
 59 
 
 39.93 
 
 167.90 
 
 9.83 
 
 158.07 
 
 15.32 
 
 142.75 
 
 2.07 
 
 .483 
 
 68 
 
 47.61 
 
 168.99 
 
 13.11 
 
 155.89 
 
 15.46 
 
 140.43 
 
 1.75 
 
 .570 
 
 77 
 
 56.39 
 
 170.09 
 
 16.39 
 
 153.70 
 
 15.59 
 
 138.11 
 
 1.49 
 
 .669 
 
 86 
 
 66.36 
 
 171.17 
 
 19.69 
 
 151.49 
 
 15.71 
 
 135.78 
 
 1.27 
 
 .780 
 
 95 
 
 77.64 
 
 172.24 
 
 22.98 
 
 149.26 
 
 . 15.82 
 
 133.45 
 
 1.09 
 
 .906 
 
 104 
 
 90.31 
 
 173.30 
 
 26.28 
 
 147.02 
 
 15.91 
 
 131.11 
 
 0.91 
 
 1.046 
 
 E. F. Miller (Trans. A. S. M. E., 1903) reports a series of tests on the 
 pressure of SO 2 at various temperatures, the results agreeing closely with 
 those of Regnault up to the highest figure of the latter, 149 F., 178 Ibs. 
 absolute. He gives a table of pressures and temperatures for every 
 degree between 40 and 217. The results obtained at temperatures 
 between 113 and 212 are as below: 
 Temp. F. 
 
 113 122 131 140 149 158 167 176 194 203 212 
 Pres. Ibs. per sq. in. 
 
 104,4 120,1 137,5 150.7 179.5 203.8 230.7 260.5 331.1 371.8 418, 
 
PROPERTIES OP AMMONIA. 
 
 1339 
 
 Properties of Ammonia. For a discussion of the properties of am- 
 monia and a bibliography of investigations of ammonia, see Bulletin 66 
 of the University of Illinois Experiment Station. See also "Properties 
 of Steam and Ammonia," by G. A. Goodenough (John Wiley & Sons, 
 1915). Prof. Goodenough says that experiments on the properties of 
 ammonia are by no means as complete or as concordant as the experi- 
 ments on water vapor; hence any formulation for ammonia must be 
 regarded as tentative and subject to revision as further experimental 
 evidence becomes available. 
 
 Properties of Saturated Ammonia. 
 
 (From Goodenough 's Tables.) 
 
 Absolute 
 Pressure, Lb. 
 per Sq. In. 
 
 Temperature, 
 Deg. F. 
 
 3,a 
 OH} 
 fe 
 
 gft 
 ^ 
 >* 
 
 & 
 
 JJ 3 
 
 u 
 
 M ^ 
 
 V 
 
 a 
 
 Total Heat 
 B.T.tf. 
 
 Latent Heat 
 B.T.U. 
 
 Entropy. 
 
 T3 
 
 s; 
 
 J 
 
 * 
 
 l 
 
 O o/+3 
 a oj 
 >.S 
 
 Si 
 * 
 
 -a 
 
 8| 
 a 
 
 s ti 
 
 1 
 
 -103.7 
 
 225.0 
 
 0.0044 
 
 
 
 644.6 
 
 603.0 
 
 
 .8107 
 
 5 
 
 - 62.0 
 
 49.3 
 
 0.0203 
 
 -98.1 
 
 519.1 
 
 617.2 
 
 571.5 
 
 -0.2207 
 
 .5523 
 
 10 
 
 - 40.4 
 
 25.75 
 
 0.0388 
 
 -75.7 
 
 526.4 
 
 602.2 
 
 554.6 
 
 -0.1661 
 
 .4363 
 
 15 
 
 -26.4 
 
 17.60 
 
 0.0568 
 
 -61.2 
 
 530.9 
 
 592.1 
 
 543.3 
 
 -0.1324 
 
 .3669 
 
 20 
 
 - 15.9 
 
 13.45 
 
 0.0744 
 
 -50.3 
 
 534.0 
 
 584.3 
 
 534.7 
 
 -0.1075 
 
 .3168 
 
 25 
 
 - 7.2 
 
 10.88 
 
 0.0919 
 
 -41.3 
 
 536.5 
 
 577.8 
 
 527.4 
 
 -0.0876 
 
 .2771 
 
 30 
 
 + 0.1 
 
 9.17 
 
 0.1090 
 
 -33.6 
 
 538.5 
 
 572.1 
 
 521.3 
 
 -0.0708 
 
 .2447 
 
 35 
 
 6.5 
 
 7.93 
 
 0. 1 260 
 
 -26.9 
 
 540.3 
 
 567.1 
 
 515.8 
 
 -0.0561 
 
 .2167 
 
 40 
 
 12.2 
 
 6.99 
 
 0.1430 
 
 -20.8 
 
 541.8 
 
 562.6 
 
 511.0 
 
 -0.0433 
 
 .1924 
 
 45 
 
 17.4 
 
 6.25 
 
 0.1598 
 
 -15.3 
 
 543.! 
 
 558.4 
 
 506.4 
 
 -0.0319 
 
 .1707 
 
 50 
 
 22.1 
 
 5.66 
 
 0.1765 
 
 -10.3 
 
 544.3 
 
 554.6 
 
 502.3 
 
 -0.0216 
 
 .1512 
 
 55 
 
 26.4 
 
 5.18 
 
 0.1931 
 
 - 5.7 
 
 545.3 
 
 551.1 
 
 498.6 
 
 -0.0122 
 
 .1338 
 
 60 
 
 30.5 
 
 4.77 
 
 0.2096 
 
 1 3 
 
 546.3 
 
 547.7 
 
 495.0 
 
 -0.0033 
 
 .1175 
 
 65 
 
 34.3 
 
 4.42 
 
 0.2261 
 
 + 2.7 
 
 547.2 
 
 544.5 
 
 491.6 
 
 +0.0051 
 
 .1023 
 
 70 
 
 37.9 
 
 4.12 
 
 0.2425 
 
 6.6 
 
 548.1 
 
 541.4 
 
 488.4 
 
 0.0128 
 
 .0883 
 
 75 
 
 41.3 
 
 3.86 
 
 0.2589 
 
 10.3 
 
 548.8 
 
 538.5 
 
 485.3 
 
 0.0201 
 
 .0751 
 
 80 
 
 44.5 
 
 3.63 
 
 0.2753 
 
 13.8 
 
 549.5 
 
 535.8 
 
 482.3 
 
 0.0271 
 
 .0627 
 
 85 
 
 47.6 
 
 3.43 
 
 0.2917 
 
 17.2 
 
 550.2 
 
 533.1 
 
 479.5 
 
 0.0336 
 
 .0511 
 
 90 
 
 50.5 
 
 3.25 
 
 0.3081 
 
 20.4 
 
 550.9 
 
 530.5 
 
 476.8 
 
 0.0398 
 
 .0400 
 
 95 
 
 53.3 
 
 3.08 
 
 0.3246 
 
 23.5 
 
 551.5 
 
 528.0 
 
 474.3 
 
 0.0458 
 
 .0295 
 
 100 
 
 56.0 
 
 2.93 
 
 0.3409 
 
 26.5 
 
 552.1 
 
 525.6 
 
 471.8 
 
 0.0516 
 
 .0195 
 
 110 
 
 61.1 
 
 2.678 
 
 0.3735 
 
 32.1 
 
 553.1 
 
 521.0 
 
 467.0 
 
 0.0625 
 
 .0006 
 
 120 
 
 65.8 
 
 2.466 
 
 0.4056 
 
 37.4 
 
 554.1 
 
 516.7 
 
 462.5 
 
 0.0725 
 
 0.9834 
 
 130 
 
 70.4 
 
 2.283 
 
 0.4381 
 
 42.5 
 
 555.0 
 
 512.5 
 
 458.2 
 
 0.0820 
 
 0.9672 
 
 140 
 
 74.5 
 
 2.124 
 
 0.4707 
 
 47.3 
 
 555.9 
 
 508.6 
 
 454.2 
 
 0.0910 
 
 0.9521 
 
 150 
 
 78.5 
 
 .989 
 
 0.5028 
 
 51.8 
 
 556.7 
 
 504.8 
 
 450.3 
 
 0.0993 
 
 0.9382 
 
 160 
 
 82.3 
 
 .868 
 
 0.5353 
 
 56.2 
 
 557.4 
 
 501.1 
 
 446.6 
 
 0.1074 
 
 0.9249 
 
 170 
 
 85.9 
 
 .763 
 
 0.5673 
 
 60.5 
 
 558.1 
 
 497.6 
 
 443.0 
 
 0.1152 
 
 0.9121 
 
 180 
 
 89.4 
 
 .666 
 
 0.6000 
 
 64.6 
 
 558.8 
 
 494.1 
 
 439.5 
 
 0.1226 
 
 0.9001 
 
 190 
 
 92.7 
 
 .580 
 
 0.6330 
 
 68.6 
 
 559.4 
 
 490.9 
 
 436.2 
 
 0.1296 
 
 0.8887 
 
 200 
 
 95.9 
 
 .504 
 
 0.665 
 
 72.3 
 
 560.0 
 
 487.6 
 
 433.0 
 
 0.1363 
 
 0.8779 
 
 220 
 
 101.8 
 
 .370 
 
 0.730 
 
 79.5 
 
 561.0 
 
 481.5 
 
 426.8 
 
 0.1488 
 
 0.8578 
 
 240 
 
 107.4 
 
 .258 
 
 0.795 
 
 86.4 
 
 562.0 
 
 475.6 
 
 421.0 
 
 0.1609 
 
 0.8389 
 
 260 
 
 112.7 
 
 .161 
 
 0.861 
 
 93.0 
 
 562.9 
 
 470.0 
 
 415.4 
 
 0.1722 
 
 0.8213 
 
 280 
 
 117.6 
 
 .079 
 
 0.927 
 
 99.2 
 
 563.8 
 
 464.6 
 
 410.2 
 
 0.1829 
 
 0.8048 
 
 300 
 
 122.4 
 
 .007 
 
 0.993 
 
 105.3 
 
 564.6 
 
 459.3 
 
 405.0 
 
 0.1932 
 
 0.7893 
 
 350 
 
 133.2 
 
 0.863 
 
 .159 
 
 119.6 
 
 566.4 
 
 446.8 
 
 392.8 
 
 0.2171 
 
 0.7538 
 
 400 
 
 142.9 
 
 0.752 
 
 .330 
 
 132.9 
 
 567.9 
 
 435.0 
 
 381.5 
 
 0.2390 
 
 0.7220 
 
 450 
 
 151.8 
 
 0.665 
 
 .504 
 
 145.6 
 
 569.3 
 
 423.8 
 
 370.8 
 
 0.2593 
 
 0.6931 
 
 500 
 
 160.0 
 
 0.597 
 
 .675 
 
 157.5 
 
 570.5 
 
 413.0 
 
 360.5 
 
 0.2786 
 
 0.6664 
 
 550 
 
 167.6 
 
 0.539 
 
 .855 
 
 169.2 
 
 571.7 
 
 402.5 
 
 350.8 
 
 0.2965 
 
 0.6419 
 
 600 
 
 174.7 
 
 0.491 
 
 2.038 
 
 180.4 
 
 572.7 
 
 392.3 
 
 341.3 
 
 0.3138 
 
 0.6186 
 
 650 
 
 181.4 
 
 0.449 
 
 2.227 
 
 191.4 
 
 573.6 
 
 382.2 
 
 332.0 
 
 0.3307 
 
 0.5963 
 
 700 
 
 187.7 
 
 0.414 
 
 2.416 
 
 202.1 
 
 574.4 
 
 372.2 
 
 322.8 
 
 0.3469 
 
 0.5758 
 
 761.4 
 
 195.0 
 
 0.376 
 
 2.660 
 
 215.2 
 
 575.4 
 
 360.2 
 
 311.8 
 
 0.3664 
 
 0.5503 
 
1340 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 f = volume, 
 Pressure in 
 
 Properties of Superheated Ammonia. 
 
 (From Goodenough's Tables.) 
 
 cu. ft. per lb., n = entropy, h = total heat, B.T.U. per Ib. 
 lb. per sq. in. ; temperatures in deg. F. 
 
 Pressure, 15 
 Temp. (-26.4 P.) 
 
 20 
 (-15.9) 
 
 25 
 
 (-7.2) 
 
 30 
 
 (+0.1) 
 
 Sat. 
 25 
 50 
 100 
 150 
 200 
 240 
 
 V 
 
 17.6 
 18.9 
 21.1 
 23.3 
 25.5 
 27.7 
 29.3 
 
 n 
 .234 
 .267 
 .320 
 .367 
 .410 
 .449 
 .479 
 
 h 
 530.9 
 545.2 
 571.1 
 596.4 
 621.4 
 646.5 
 666.9 
 
 V 
 
 13.4 
 14.0 
 15.8 
 17.5 
 19.1 
 21.4 
 22.0 
 
 n 
 1.209 
 1.229 
 1.284 
 1.332 
 1.376 
 1.431 
 1.446 
 
 h 
 534.0 
 542.9 
 569.8 
 595.5 
 620.8 
 656.2 
 666.4 
 
 V 
 
 10.9 
 11.1 
 12.6 
 13.9 
 15.2 
 16.5 
 17.6 
 
 n 
 1.190 
 1.199 
 1.256 
 1.305 
 1.349 
 1.389 
 1.419 
 
 h 
 
 536.5 
 540.8 
 568.4 
 594.5 
 620.1 
 645.6 
 666.0 
 
 V 
 
 9.17 
 
 id.4i 
 
 11.55 
 12.65 
 13.74 
 14.59 
 
 n 
 1.174 
 
 Y.233 
 1.283 
 1.327 
 1.367 
 1.398 
 
 h 
 538.5 
 
 56 7. i 
 593.7 
 619.5 
 645.2 
 665.7 
 
 Pressure, 40 
 Temp. ( 2.2) 
 
 50' 
 
 (22.1) 
 
 60 
 
 (30.5) 
 
 70 
 
 (37.9) 
 
 Sat. 
 50 
 100 
 150 
 200 
 300 
 
 6.99 
 7.72 
 8.59 
 9.44 
 10.26 
 
 .149 
 .195 
 .247 
 .292 
 .333 
 
 541.8 
 564.3 
 591.8 
 618.2 
 644.3 
 
 5.67 
 6.11 
 
 6.83 
 7.51 
 8.17 
 9.47 
 
 1.130 
 1.165 
 1.218 
 1.264 
 1.306 
 1.380 
 
 544.3 
 561.5 
 590.0 
 617.0 
 643.3 
 695.7 
 
 4.77 
 5.03 
 5.65 
 6.22 
 6.79 
 7.87 
 
 1.114 
 1.139 
 1.194 
 1.242 
 1.283 
 1.358 
 
 546.3 
 558.8 
 588.2 
 615.8 
 642.4 
 695.1 
 
 4.12 
 4.27 
 4.81 
 5.31 
 5.80 
 6.73 
 
 1.101 
 1.117 
 1.174 
 1.222 
 1.265 
 1.339 
 
 548.1 
 556.0 
 586.5 
 614.6 
 641.5 
 694.6 
 
 Pressure, 80 
 Temp. (44.5) 
 
 90 
 
 (50.5) 
 
 100 
 (56.0) 
 
 120 
 
 (65.8) 
 
 Sat. 
 100 
 150 
 200 
 300 
 340 
 
 3.63 
 4.18 
 4.62 
 5.04 
 5.87 
 
 .090 
 .156 
 .205 
 .248 
 .323 
 
 549.5 
 584.7 
 613.4 
 640.6 
 694.1 
 
 3.25 
 3.69 
 4.09 
 4.47 
 5.21 
 5.50 
 
 1.080 
 1.140 
 1.190 
 1.233 
 .1.309 
 1.337 
 
 550.9 
 582.9 
 612.1 
 639.8 
 693.5 
 714.9 
 
 2.94 
 3.29 
 3.66 
 4.01 
 4.67 
 4.93 
 
 1.071 
 1.125 
 1.176 
 1.220 
 1.297 
 1.324 
 
 552.1 
 581.1 
 610.8 
 638.9 
 693.0 
 714.6 
 
 2.47 
 2.71 
 3.02 
 3.31 
 3.87 
 4.09 
 
 1.056 
 1.099 
 1.152 
 1.197 
 1.275 
 1.302 
 
 554.1 
 577.5 
 608.4 
 637.1 
 692.1 
 713.9 
 
 Pressure, 140 
 Temp. (74.5) 
 
 160 
 
 (82.3) 
 
 200 
 (95.9) 
 
 240 
 (107.4) 
 
 Sat. 
 100 
 150 
 200 
 300 
 360 
 
 2.12 
 2.29 
 2.56 
 2.82 
 3.30 
 3.58 
 
 1.043 
 .076 
 .131 
 .177 
 .256 
 .297 
 
 555.9 
 573.9 
 605.9 
 635.3 
 691.1 
 723.9 
 
 1.87 
 1.97 
 2.22 
 2.44 
 2.66 
 3.12 
 
 1.032 
 1.056 
 1.112 
 1.160 
 1.202 
 1.281 
 
 557.4 
 570.3 
 603.5 
 633.6 
 662.1 
 722.9 
 
 1.50 
 1.52 
 1.73 
 1.92 
 2.27 
 2.47 
 
 1.014 
 1.020 
 1.080 
 1.130 
 1.212 
 1.254 
 
 560-0 
 563.1 
 598.4 
 630.0 
 687.7 
 721.0 
 
 1.26 
 
 1.42 
 1.57 
 1.87 
 2.04 
 
 1.000 
 
 Y.053 
 1.105 
 1.189 
 1.232 
 
 562.0 
 
 593.5 
 626.4 
 685.6 
 719.3 
 
 Thermal Properties of Liquid Ammonia. 
 
 (From Goodenough's Tables.) 
 
 
 Satu- 
 
 
 
 
 
 Satu- 
 
 
 
 
 
 ration 
 
 Vol. 
 
 Weight 
 
 
 
 ration 
 
 Vol. 
 
 Weight 
 
 
 Temp. 
 
 Pres- 
 
 of 
 
 of 
 
 144 X 
 
 Temp. 
 
 Pres- 
 
 of 
 
 of 
 
 144 X 
 
 Deg.F. 
 
 sure, 
 
 1 Lb., 
 
 1 Cu. 
 
 Apv. 
 
 F. 
 
 sure, 
 
 1 Lb., 
 
 1 Cu. 
 
 Apv. 
 
 
 Lb.per 
 
 Cu. Ft. 
 
 Ft., Lb. 
 
 
 
 Lb.per 
 
 Cu. Ft. 
 
 Ft., Lb. 
 
 
 
 Sq. In. 
 
 
 
 
 
 Sq. In. 
 
 
 
 
 -110 
 
 0.758 
 
 0.02202 
 
 45.42 
 
 0.003 
 
 60 
 
 107.7 
 
 0.02609 
 
 38.33 
 
 0.520 
 
 -100 
 
 1.176 
 
 .02220 
 
 45.04 
 
 .005 
 
 70 
 
 129.2 
 
 .02643 
 
 37.85 
 
 .632 
 
 - 80 
 
 2.626 
 
 .02258 
 
 44.28 
 
 .011 
 
 80 
 
 153.9 
 
 .02678 
 
 37.35 
 
 .76 
 
 - 60 
 
 5.358 
 
 .02299 
 
 43.51 
 
 .023 
 
 90 
 
 181.8 
 
 .02714 
 
 36.84 
 
 .92 
 
 - 40 
 
 10.12 
 
 .02342 
 
 42.71 
 
 .044 
 
 100 
 
 213.8 
 
 .02754 
 
 36.32 
 
 1.09 
 
 - 20 
 
 17.91 
 
 .02388 
 
 41.88 
 
 .079 
 
 120 
 
 289.9 
 
 .02839 
 
 35.23 
 
 1.52 
 
 
 
 29.95 
 
 .02437 
 
 41.04 
 
 .135 
 
 140 
 
 384.4 
 
 .02936 
 
 34.06 
 
 2.09 
 
 10 
 
 38.02 
 
 .02463 
 
 40.61 
 
 .173 
 
 160 
 
 500.1 
 
 .0305 
 
 32.80 
 
 2.82 
 
 20 
 
 47.75 
 
 .02490 
 
 40.17 
 
 .220 
 
 180 
 
 639.5 
 
 .0318 
 
 31.5 
 
 3.77 
 
 30 
 
 59.35 
 
 .02518 
 
 39.72 
 
 .247 
 
 200 
 
 805.6 
 
 .0335 
 
 29.9 
 
 4.99 
 
 40 
 
 73.03 
 
 .02547 
 
 39.27 
 
 .344 
 
 250 
 
 1357.4 
 
 .0404 
 
 24.8 
 
 10.2 
 
 50 
 
 89.1 
 
 .02577 
 
 38.81 
 
 .425 
 
 273.2 
 
 1690.0 
 
 .0678 
 
 14.75 
 
 21.2 
 
 A = reciprocal of Joule's equivalent = 
 sq. in.; v vol. of 1 lb., cu ft. 
 
 1/777.6; p = pressure, lb. per 
 
PROPERTIES OF AMMONIA. 
 
 1341 
 
 Solubility of Ammonia. (Siebel.) One pound of water will dis- 
 solve the following weights of ammonia at the pressures and tempera- 
 tures F stated. 4 
 
 Abs. 
 Press, 
 per 
 sq.m. 
 
 32 
 
 68 
 
 104 
 
 Abs. 
 Press, 
 per 
 sq.m. 
 
 32 
 
 68 
 
 104 
 
 Abs. 
 Press, 
 per 
 sq. in. 
 
 32 
 
 68 
 
 104 
 
 0.486 
 0.493 
 0.511 
 0.530 
 0.547 
 0.565 
 0.579 
 
 Ib. 
 14.67 
 15.44 
 16.41 
 17.37 
 18.34 
 19.30 
 20.27 
 
 Ib. 
 0.899 
 0.937 
 0.980 
 1.029 
 1.077 
 1.126 
 1.177 
 
 Ib. 
 0.518 
 0.535 
 0.556 
 0.574 
 0.594 
 0.613 
 0.632 
 
 Ib. 
 0.338 
 0.349 
 0.363 
 0.378 
 0.391 
 0.404 
 0.414 
 
 Ib. 
 21.23 
 22.19 
 23.16 
 24.13 
 25.09 
 26.06 
 27.02 
 
 Ib. 
 .236 
 .283 
 .330 
 .385 
 .442 
 .496 
 .549 
 
 Ib. 
 0.651 
 0.669 
 0.685 
 0.704 
 0.722 
 0.741 
 0.761 
 
 Ib. 
 0.425 
 0.434 
 0.445 
 0.454 
 0.463 
 0.472 
 0.479 
 
 Ib. 
 27.99 
 28.95 
 30.88 
 32.81 
 34.74 
 36.67 
 38.60 
 
 Ib. 
 .603 
 .656 
 .758 
 .861 
 .966 
 2.070 
 
 Ib. 
 0.780 
 0.801 
 0.842 
 0.881 
 0.919 
 0.955 
 0.992 
 
 Strength of Aqua Ammonia at 60 F. 
 
 %NHabywt. 24 6 8 10 12 14 16 18 
 Sp. gr. 0.986 .979 .972 .966 .960 .953 .945 .938 .931 
 % NHs 20 22 24 26 28 30 32 34 36 
 Sp. gr. 0.925 .919 .913 .907 .902 .897 .892 .888 .884 
 Properties of Saturated Vapors. The figures in the following table 
 are given by Lorenz, on the authority of M oilier and of Zeuner. 
 
 ., 
 
 Heat of 
 Vaporization, 
 B.T.U. per Ib. 
 
 Heat of Liquid, 
 B.T.U. per Ib. 
 
 Absolute 
 Pressure, 
 Ibs. per sq. in. 
 
 Volume of 
 lib., 
 cubic feet. 
 
 NH 3 
 
 C0 2 
 
 SO 2 
 
 NH 3 
 
 CO 2 
 
 S0 2 
 
 NH 3 
 
 CO 2 SO 2 
 
 NH 3 
 
 CO 2 
 
 S0 2 
 8 06 
 
 - 4 
 + 14 
 32 
 50 
 68 
 86 
 104 
 
 589 
 
 117 6 
 
 171.0 
 
 -31.21 
 
 -17.19 
 
 -11.16 
 
 27.1 
 
 288.7 9.27 
 
 10 33 
 
 31? 
 
 580 
 
 110 7 
 
 168 2 
 
 -15 89 
 
 - 9 00 
 
 - 5.69 
 
 41.5 
 
 385 4 14 75 
 
 6 92 
 
 229 
 
 5 ?7 
 
 569.0 
 555 5 
 
 99.8 
 86 
 
 164.2 
 158 9 
 
 
 16 51 
 
 
 
 10 28 
 
 
 5 90 
 
 61.9 
 89 1 
 
 503.5 22.53 
 650 1 33 26 
 
 4.77 
 3 38 
 
 0.167 
 120 
 
 3.59 
 
 ? 44 
 
 539.9 
 521.4 
 500.4 
 
 66.5 
 27.1 
 
 152.5 
 144.8 
 135.9 
 
 33.58 
 51.28 
 69.58 
 
 23.08 
 45.45 
 
 12.03 
 18.34 
 
 24.88 
 
 125.0 
 170.8 
 227.7 
 
 826.447.61 
 040. 66.36 
 90.30 
 
 2.47 
 1.83 
 1.39 
 
 0.083 
 0.048 
 
 1.71 
 1.22 
 88 
 
 The figures for CO2 in the above table differ widely from those of 
 Regnault,.and are no doubt more reliable. 
 
 Heat Generated by Absorption of Ammonia. (Berthelot, from 
 Siebel.) Heat developed when a solution of 1 Ib. NH 3 in n Ibs. watei 
 is diluted with a great amount of water = Q = 142/n B.T.U. Assuming 
 925 B.T.U. to be developed when 1 Ib. NH 3 is absorbed by a great deal 
 (say 200 Ibs.) of water, the heat developed in making solutions of different 
 strengths (1 Ib. NH 3 to n Ibs. water) = Q t = 925 142/n B.T U Heat 
 developed when b Ibs. NH 3 is added to a solution of 1 Ib. NH 3 + n Ibs 
 water = Q 3 = 925&- 142 (26+ W)/n B.T.U. 
 
 Let the weak liquor enter the absorber with a strength of 10 % = 1 Ib 
 NH 3 + 9 Ibs. water, and the strong liquor leave the absorber with a 
 strength of 25%, = 3 Ibs. NH 3 + 9 Ibs. water, b = 2, n = 9- Q 3 = 925 X 
 2 - 142 (4 + 4)/9 = 1724 B.T.U. Hence by dissolving 2 Ibs. of ammonia 
 gas or vapor in a solution of 1 Ib. ammonia in 9 Ibs. water we obtain 
 12 Ibs. of a 25% solution, and the heat generated is 1724 B.T.U. 
 
 Cooling Effect, Compressor Volume, and Power Required. The 
 following table gives the theoretical results computed on the basis of 
 a temperature in the evaporator of 14 F. and in the condenser of 68 F 
 in the first three columns of figures the cooling agent is supposed to flow 
 through the regulating valve with this latter temperature; in the last 
 three it is previously cooled to 50 F. 
 
 From the stroke-volume per 100,000 B.T.U. the minimum theoretical 
 horse-power is obtained as follows: Adiabatic compression is assumed 
 for the ratio of the absolute condenser pressure to that of the vaporizer 
 and the mean pressure through the stroke thus found, in Ibs per sq ft 
 multiplying this by the stroke volume per hour and dividing by 1 980 000 
 gives the net horse-power. The ratio of the mean effective pressure 
 M.P., to the vaporizer pressure, V.P., for different ratios of condenser 
 pressure, C.P., to vaporizer pressure is given on the next page. 
 
1342 ICE-MAKING OK REFRIGERATING-MACHINES. 
 
 Cooling Effect, Compressor Volume, and Power Required, with 
 _ Different Cooling Agents. (Lorenz.) ___ 
 
 Cooling Agent. 
 
 NH 3 
 
 CO 2 
 
 S0 2 
 
 NH 3 
 
 C0 2 
 
 SO 2 
 
 1. Temp, in front of regulating 
 valve . 
 
 68 
 
 68 
 
 68 
 
 50 
 
 50 
 
 50 
 
 2. Vaporizer pressure, Ibs. per 
 sq. in 
 
 41 5 
 
 385 4 
 
 14 75 
 
 41 5 
 
 385 4 
 
 14 75 
 
 3. Condenser pressure, Ibs. per 
 sq. in 
 
 125 
 
 826 4 
 
 47 61 
 
 125 
 
 826 4 
 
 47 61 
 
 4. Heat of evaporation, B.T.U. 
 per Ib 
 
 580 2 
 
 110 7 
 
 168 2 
 
 580 2 
 
 110 7 
 
 168 2 
 
 5. Heat imparted to the liquid 
 6. Cold produced per Ib. B.T.U 
 7. Cooling agent circulated for 
 yield of 100,000 B.T.U. per 
 hour, Ibs .... 
 
 49.47 
 530.73 
 
 188 4 
 
 32.08 
 78.62 
 
 1272 
 
 17.72 
 150.48 
 
 664 3 
 
 32^4 
 547.8- 
 
 182 5 
 
 19.28 
 91.42 
 
 1094 
 
 11.59 
 156.61 
 
 638 5 
 
 8. Stroke volume for 100,666 
 B.T.U. per hour, cu. ft 
 9. Minimum H.P. per 100,000 
 B.T.U. per hour 
 
 1,300 
 4 98 
 
 292 
 4 98 
 
 3,507 
 4 98 
 
 1,264 
 4 98 
 
 242 
 4 98 
 
 3,365 
 4 98 
 
 10. Ratio Heat of evap. -* .cold 
 produced . . 
 
 1 093 
 
 1 408 
 
 1 118 
 
 1 059 
 
 1 211 
 
 1 074 
 
 1 1 . Ratio total work to minimum 
 12. Total I.H.P. per 100,000 
 B.T.U. per hour 
 
 1.175 
 5 85 
 
 1.513 
 7 53 
 
 1.202 
 5 99 
 
 1.133 
 5 67 
 
 1.302 
 6 48 
 
 1.155 
 5 75 
 
 13. Cooling effect per I.H.P. hr.. 
 
 17,100 
 
 13,300 
 
 16.700 
 
 17,600 
 
 15,400 
 
 17.400 
 
 RATIOS OP CONDENSER PRESSURE, C. P., AND ME AN ^EFFECTIVE 
 SURE, M. P., TO VAPORIZER PRESSURE, V. P. 
 
 PRES- 
 
 PH 
 
 fc 
 
 PH 
 
 PH 
 
 PH 
 
 PH 
 
 PH 
 
 & 
 
 PH 
 
 PH 
 
 PH 
 > 
 
 PH 
 
 1- 
 
 f 
 
 1- 
 
 * 
 
 1- 
 
 ! 
 
 * 
 
 * 
 
 1- 
 
 4 
 
 1- 
 
 1- 
 
 6 
 
 PH 
 
 a 
 
 g 
 
 PH 
 
 a 
 
 | 
 
 PH 
 
 a 
 
 PH 
 O 
 
 PH 
 % 
 
 PH 
 O 
 
 PH 
 S 
 
 S 
 
 PH 
 % 
 
 1.0 
 
 0. 
 
 2.0 
 
 0.752 
 
 3.0 
 
 .249 
 
 4.0 
 
 .684 
 
 5.0 
 
 1.947 
 
 6.0 
 
 2.216 
 
 1.2 
 
 0.186 
 
 2.2 
 
 0.865 
 
 3.2 
 
 .344 
 
 4.2 
 
 .711 
 
 5.2 
 
 2.006 
 
 7.0 
 
 2.454 
 
 1.4 
 
 0.350 
 
 2,4 
 
 0.970 
 
 3,4 
 
 .414 
 
 4,4 
 
 .766 
 
 5.4 
 
 2.062 
 
 8.0 
 
 2.666 
 
 1 6 
 
 0.487 
 
 2 6 
 
 1 070 
 
 3 6 
 
 491 
 
 4 6 
 
 829 
 
 5 6 
 
 2.116 
 
 9 
 
 2 858 
 
 1.8 
 
 0.630 
 
 2.8 
 
 1.163 
 
 3.8 
 
 .564 
 
 4.8 
 
 .891 
 
 5.8 
 
 2.168 
 
 10 
 
 3.036 
 
 The minimum theoretical horse-power thus obtained is increased by 
 the ratio of the heat of evaporation to the available cooling action (line 
 4 -*- line 6, = line 10 of the table) and by an allowance for the resistance 
 of the valves taken at 7.5% to obtain the total H.P. given in the table. 
 
 To the theoretical horse-power given in line 12 Lorenz makes numerous 
 additions, viz.: friction of the compression and driving machine 0.90, 
 1.10, 0.90, 0.85, 0.95, 0.85 respectively for the six columns in the table; 
 also H.P. for stirring 0.3; for cooling- water pumps, 0.45; for brine pumps, 
 2.2; for transmission of power, 0.6, making the total H.P. for the six cases 
 10.30, 12.18, 10.44, 10.07, 10.98, 10.15. He also makes deductions from 
 the theoretical generation of cold of 100,000 B.T.U. per hour, for a brewery 
 cooling installation, for irregularities of valves, etc., for NHs and SO2 
 machines 10% and for CO* machines 5%; for cooling loss through stirring 
 765 B.T.U., through brine pumps 5610 B.T.U., and through radiation 
 4500 B.T.U., making the net cooling for NH 3 and SOs machines 79,125 
 B.T.U. and for COs machines 84,125 B.T.U., and the cold generated per 
 effective H.P. in the six cases, 7682, 6908, 7578, 7848, 7662, and 7796 
 B.T.U. 
 
 The figures given in the tables are not to be considered as holding 
 generally or extended t9 other condenser and evaporator temperatures. 
 Each change of condition requires a separate calculation. The final 
 results indicate that for the various cooling systems no appreciable 
 difference exists in the work required for the same amount of cold 
 delivered at the place where it is to be applied. 
 
PROPERTIES OF DIFFERENT COOLING AGENTS. 1343 
 
 Properties of Brine Used to Absorb Refrigerating Effect of 
 Ammonia. (J. E. Den ton, Trans. A. S. M. E., x, 799). A solution of 
 Liverpool salt in well-water having a specific gravity of 1.17, or a weight 
 per cubic foot of 73 Ibs., will not sensibly thicken or congeal at.0 F. 
 
 The mean specific heat between 39 and 16 Fahr. was found by 
 Denton to be 0.805. Brine of the same specific gravity has a specific 
 heat of 0.805 at 65 Fahr., according to Naumann. 
 
 Naumann's values (Lehr-und Handbuch der Thermochemie, 1882) are: 
 
 Specific heat 0.791 0.805*0.863 0.895 0.941 0.962 0.978 
 
 Specific gravity 1.187 1.170 1.103 1.072 1.044 1.023 1.012 
 
 Properties of Salt Brine (Carbondale Calcium Co.) 
 
 Deg. Baume" 60 F 1 5 10 15 19 
 
 Deg. Salinometer 60 F 4 20 40 60 80 
 
 Sp. gravity 60 F 1.007 1.037 1.073 1.115 1.150 
 
 Per cent of salt, by wt.. .. 1 5 10 15 20 
 
 Wt. of 1 gallon, Ibs 8.40 8,65 8.95 9.30 9.60 
 
 Wt. of 1 cu. ft., Ibs 62.8 64.7 66.95 69.57 71.76 
 
 Freezing point F 31.8 25.4 18.6 12.2 6.86 
 
 Specific heat 0.992 0.960 0.892 0.855 0.829 
 
 23 
 
 100 
 
 1.191 
 25 
 
 9.94 
 74.26 
 
 1.00 
 
 0.783 
 brine. 
 
 Chloride of Calcium solution is commonly used instead of 
 
 According to Naumann, a solution of 1.0255 sp. gr. has a specific heat of 
 0.957. A solution of 1.163 sp. gr. in the test reported in Eng'g, July 22, 
 1887, gave a specific heat of 0.827. 
 
 H. C. Dickinson (Science, April 23, 1909) gives the following values of the 
 specific heat of solutions of chemically pure calcium chloride. 
 
 Density Specific Heat Temperature, C. 
 
 1.07... 0.869 + 0.00057 t (- 5 to + 15) 
 
 1.14 0.773 + 0.00064 t (- 10 to + 20) 
 
 1.20 0.710 + 0.00064* (- 20 to + 20) 
 
 1.26 0.662 + 0.00064 t (- 25 to + 20) 
 
 The advantages of chloride of calcium solution are its lower freezing point 
 and that it has little or no corrosive action on iron and brass. Calcium 
 chloride is sold in the fused or granulated state, in steel drums, contain- 
 ing about 75% anhydrous chloride and 25% water, or in solution contain- 
 ing 40 to 50% anhydrous chloride, in tank cars. The following data 
 are taken from the catalogue of the Carbondale Calcium Co. 
 
 PROPERTIES OF " SOLVAY " CALCIUM CHLORIDE SOLUTION. 
 
 &" 
 
 m 
 
 02 
 
 I 
 
 fflfa 
 
 I. 
 
 5.5 
 11 
 17 
 20 
 
 1.007 
 1.041 
 1.085 
 1.131 
 1.159 
 
 +31.10 
 
 27.68 
 22.38 
 12.20 
 4.64 
 
 1.169 
 1.179 
 1.189 
 1.219 
 1.250 
 
 + 1.76 
 
 - 1.48 
 
 - 4.90 
 -17.14 
 -32.62 
 
 32 
 
 35 
 
 35.5 
 
 36.5 
 
 37.5 
 
 -54.40 
 -25.24 
 - 9.76 
 + 2.84 
 14.36 
 
 Quantity of 75% calcium chloride required to make solutions of different 
 
 specific gravities and freezing points. 
 
 Sp. gravity] 1.250 1.225 1.200 1.175 1.150 1.125 1.100 
 
 Lbs. per cu ft. solu- 
 tion 28.06 25.06 22.05 19.15 16.26 13.47 10.70 
 
 Lbs. per gallon 3.76 3.36 2.95. 2.56 2.18 1.80 1.43 
 
 Freezing point F. .-32.6 -19.5 -8.7 Zero +7.5 +13.3 +18.5 
 
 Boiling points of calcium chloride solutions: 
 
 Sp. Gr. at 59 F.. . . 1.104 1.185 1.238 1.341 1.383 solid at 59, 
 Boiling point F... 215.6 221.0 230.0 240.8 248.0 266.0 282.2 306.5 
 Sp.gr.atboilingpoint 1.085 1.119 1.209 1.308 1.365 1.452 1.526 1.619 
 
 * Interpolated. 
 
1344 ICE-MAKING OR REFRIGERATING-MACHINES 
 
 "Ice-melting Effect." It is agreed that the term "ice-melting 
 effect" means the cold produced in an insulated bath of brine, on the 
 assumption that each 144 B.T.U. represents one pound of ice, this 
 being the latent heat of fusion of ice, or the heat required to melt a pound 
 of ice at 32 to water at the same temperature. The performance of a 
 machine, expressed in pounds or tons of "ice-melting capacity," does 
 not mean that the refrigerating-machine would make the same amount 
 of actual ice, but that the cold produced is equivalent to the effect of the 
 melting of ice at 32 to water of that temperature. 
 
 in maKing artilicial ice tne water frozen is generally about 70 F. when 
 submitted to the refrigerating effect of a machine; second, the ice is 
 chilled from 12 to 20 below its freezing-point; third, there is a dissipa- 
 tion of cold, from the exposure of the brine tank and the manipulation of 
 the ice-cans: therefore the weight of actual ice made, multiplied by its 
 latent heat of fusion, 144 thermal units, represents only about three- 
 fourths of the cold produced in the brine by the refrigerating fluid per 
 I.H.P. of the engine driving the compressing-pumps. Again, there is 
 considerable fuel consumed to operate the brine-circulating pump, the 
 condensing-water and feed-pumps, and to reboil, or purify, the condensed 
 steam from which the ice fe frozen. This fuel, together with that wasted 
 in leakage and drip water, amounts to about one-half that required to 
 drive the main steam-engine. Hence the pounds of actual ice manu- 
 factured from distilled water is just about half the equivalent of the 
 refrigerating effect produced in the brine per indicated horse-power of the 
 steam-cylinders. 
 
 When ice is made directly from natural water by means of the "plate 
 system," about half of the fuel, used with distilled water, is saved by 
 avoiding the rebelling, and using steam expansively in a compound 
 engine. 
 
 Ether-machines, used in India, are said to have produced about 6 Ibs. 
 of actual ice per pound of fuel consumed. 
 
 The ether machine is obsolete, because the density of the vapor of ether, 
 at the necessary working-pressure, requires that the compressing-cylinder 
 shall be about 6 times larger than for sulphur dioxide, and 17 times 
 larger than for ammonia. 
 
 Air-machines require about 1.2 times greater capacity of compressing 
 cylinder, and are, as a whole, more cumbersome than ether machines, 
 but they remain in use on shipboard. In using air the expansion must 
 take place in a cylinder doing work, instead of through a simple expansion- 
 cock which is used with vapor machines. The work done in the expansion- 
 cylinder is utilized in assisting the compressor. 
 
 The Allen Dense Air Machine takes for compression air of considerable 
 pressure which is contained in the machine and in a system of pipes. The 
 air at 60 or 70 Ibs. pressure is compressed to 210 or 240 Ibs. It is then 
 passed through a coil immersed in circulating water and cooled to nearly 
 the temperature of the water. It then passes into an expander, which is, 
 in construction, a common form of steam-engine with a cut-off valve. 
 This engine takes out of the air a quantity of heat equivalent to the 
 work done by the air while expanding, to the original pressure of 60 or 
 70 Ibs., and reduces its temperature to about 90 to 120 F. below the 
 temperature of the cooling water supply. The return stroke of the piston 
 pushes the air out through insulated pipes to the places that are to be 
 refrigerated, from which it is returned to the compressor. 
 
 The air pushed out by the expander is commonly about 35 to 55 below 
 zero F. In arrangements where not all the cold is taken out of the air 
 by the refrigerating apparatus, the highly compressed air after cooling 
 in the coil is further Cooled by being brought in surface contact with the 
 returning and still cold air, before entering the expander. By this means 
 temperatures of 70 to 90 below zero may be obtained. 
 
 The refrigerating: effect in B.T.U. per minute is: Lbs. of air handled per 
 min. X 0.2375 X difference of temperature of air passing out of ex- 
 pander and of that returning to the machine. 
 
 Carbon-dioxide Machines are in extensive use on shipboard. S. H. 
 Bunnell (Eng. News, April 9, 1903) says there are over 1500 CO 2 plants 
 on shipboard. He describes a large duplex CO 2 compressor built by the 
 Brown-Oochrane Co., Lorain, O. Tests of CO 2 machines by a committee 
 of the Danish Agricultural Society were reported in 1899, in "Ice and 
 
MACHINES USING DIFFERENT COOLING AGENTS. 1345 
 
 Cold Storage," of London. Carbon-dioxide machines are built also by 
 Kroeschel Bros., Chicago. 
 
 Methyl-Chloride machines are made by Railway and Stationary Re- 
 frigerating Co., New York City. The compressor is a rotary pump. 
 When driven by an electric motor the complete apparatus is very com- 
 pact, and is therefore suitable for refrigerator cars or other places where 
 space is restricted 
 
 Sulphur-Dioxide Machines. Results of theoretical calculations 
 are given in a table by Ledoux showing an ice-melting capacity per hour 
 per horse-power ranging from 134 to 63 Ibs., and per pound of coal rang- 
 ing from 44.7 to 21.1 Ibs., as the temperature corresponding to the pres- 
 sure of the vapor in the condenser rises from 59 to 104 F. The theoret- 
 ical results do not represent the actual. 
 
 Prof. Denton says concerning Ledoux's theoretical results: The 
 figures given are higher than those obtained in practice, because the 
 effect of superheating of the gas during admission to the cylinder is not 
 considered. This superheating may cause an increase of work of about 
 
 25%. - 
 
 tank, 
 
 that i ^ - , _ 
 
 conditions of an absolute pressure in the condenser 9f 56 Ibs. per sq. in. 
 and the corresponding temperature of 77 F., will give about 22 Ibs. of 
 ice-melting capacity per pound of coal, which is about 60% of the theor* 
 etir-al amount neglecting friction, or 70^ including friction. 
 
 Sulphur-dioxide machines are not (1910) used in the United States. 
 
 Refrigera ting-Machines using Vapor of Water. (Ledoux.) In 
 these machines, sometimes called vacuum machines, water, at ordinary 
 temperatures, is injected into, or placed in connection with, a chamber 
 in which a strong vacuum is maintained. A portion of the water vapor- 
 izes, the heat to cause the vaporization being supplied from the water not 
 vaporized, so that the latter is chilled or frozen to ice. If brine is used 
 instead of pure water, its temperature may be reduced below the freez- 
 ing-point of water. The water vapor is compressed from, say, a pressure 
 of 0.1 Ib. per sq. in. to 1 Yi Ibs. and discharged into a condenser. It is 
 then condensed and removed by means of an ordinary air-pump. The 
 principle of action of such a machine is the same as that of volatile- 
 vapor machines. 
 
 A theoretical calculation for ice-making, assuming a lower temperature 
 of 32 F., a pressure in the condenser of 1 Y^ Ibs. per sq. in. and a coal 
 consumption of 3 Ibs. per I.H.P. per hour, gives an ice-melting effect of 
 34.5 Ibs. per pound of coal, neglecting friction. Ammonia for ice-making 
 conditions gives 40.9 Ibs. The volume of the compressing cylinder is 
 about 150 times the theoretical volume for an ammonia machine for 
 these conditions. 
 
 [The Patten Vacuum Ice Co., Of Baltimore, has a large plant on this 
 system in operation (1910).] 
 
 Ammonia Compression-machines. "Cold" vs. "Dry" Systems of 
 Compression. In the "cold" system or "humid" system some of the 
 ammonia entering the compression cylinder is liquid, so that the heat 
 developed in the cylinder is absorbed by the liquid and the temperature 
 of the ammonia thereby confined to the boiling-point due to the con- 
 denser-pressure. No jacket is therefore required about the cylinder. 
 
 In the " dry " or " hot " system all ammonia entering the compressor is 
 gaseous, and the temperature becomes by compression several hundred 
 degrees greater than the boiling-point due to the condenser-pressure. A 
 water-jacket is therefore necessary to permit the cylinder to be properly 
 lubricated. 
 
 Dry, Wet and Flooded Systems. (York Mfg. Co.) An expansion 
 system, or one where the ammonia leaves the coil slightly superheated, 
 requires about 33 jf % more pipe surface than a wet compression system, 
 in which the ammonia leaves the coils containing sufficient entrained 
 liquid to maintain a wet compression condition in the compressor. 
 
 The flooded system is ono where the ammonia is allowed to flow through 
 the coils and into a trap, where the gas is separated from the liquid, the 
 gas passing on to the compressor, while the liquid goes around through 
 the coils again, together with the fresh liquid, which is fed into the trap. 
 Such a system requires only about one-half the evaporating surface that 
 
1346 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 an expansion system does to do the same work. The relative proportions 
 of the three systems may be expressed as follows: 
 
 A Dry Compression plant will need, with an Expansion Evaporating 
 System, a medium size compressor, a large size evaporating system, a 
 small amount of ammonia. 
 
 A Dry Compression plant will need, with a Flooded Evaporating Sys- 
 tem, a small size compressor, a small size evaporating system, a large 
 am; unt of ammonia. 
 
 A Wet Compression plant will need, with a Wet Compression Evapo- 
 rating System, a large size compressor, a medium size evaporating sys- 
 tem, a medium amount of ammonia. 
 
 The Ammonia Absorption-machine comprises a generator which 
 contains a concentrated solution of ammonia in water; this generator 
 is heated either directly by a fire, or indirectly by pipes leading from a 
 steam-boiler. The vapor passes first into an " analyzer," a chamber con- 
 nected with the upper part of the generator which separates some of the 
 water from the vapor, then into a rectifier, where the vapor is partly 
 cooled, precipitating more water, which returns to the generator, and 
 then to the condenser. The upper part of the cooler or brine-tank is in 
 communication with the lower part of the condenser. 
 
 An absorption-chamber is filled with a weak solution of ammonia ; a 
 tube puts this chamber in communication with the cooling-tank. 
 
 The absorption-chamber communicates witfi the boiler by two tubes: 
 one leads from the bottom of the generator to the top of the chamber, the 
 other leads from the bottom of the chamber to the top of the generator. 
 Upon the latter is mounted a pump, to force the liquid from the absorp- 
 tion-chamber, where the pressure is maintained at about one atmosphere 
 into the generator, where the pressure is from 8 to 12 atmospheres. 
 
 To work the apparatus the ammonia solution in the generator is first 
 heated. This releases the gas from the solution, and the pressure rises. 
 When it reaches the tension of the saturated gas at the temperature of 
 the condenser there is a liquefaction of the gas, and also of a small 
 amount of steam. By means of a cock the flow of the liquefied gas into 
 the refrigerating coils contained in the cooler is regulated. It is here 
 vaporized by absorbing the heat from the substance placed there to be 
 cooled. As fast as it is vaporized.it is absorbed by the weak solution in 
 the absorbing-chamber. 
 
 Under the influence of the heat in the boiler the solution is unequally 
 saturated, the stronger solution being uppermost. The weaker portion 
 is conveyed by the pipe entering the "top of the absorbing-chamber, the 
 flow being regulated by a cock, while the pump sends an equal quantity 
 of strong solution from the chamber back to the boiler. 
 
 The working of the apparatus depends upon the adjustment and regu- 
 lation of the flow of the gas and liquid ; by these means the pressure is 
 varied, and consequently the temperature in the cooler may be controlled. 
 
 The working is similar to that of compression-machines. The absorp- 
 tion-chamber fills the office of aspirator, and the generator plays the part 
 of compressor. The mechanical force producing exhaustion is here re- 
 placed by the affinity of water for ammonia gas, and the mechanical force 
 required for compression is replaced by the heat which severs this affinity 
 and sets the gas at liberty. 
 
 Reece's absorption apparatus (1870) is thus described by Wallis-Taylor. 
 The charge of liquid ammonia (26 Baume) is vaporized by the application 
 of heat, and the mixed vapor passed to the analyzer and rectifier, wherein 
 the bulk of the water is condensed at a comparatively elevated temperature 
 and returned to the generator. The ammoniacal vapor or gas is then 
 passed to the condenser, where it is liquefied under the combined action 
 of the cooling-water and of the pressure maintained in the generator. The 
 liquid ammonia, practically anhydrous, is then used in the refrigerator, 
 and tb^ vapor therefrom, still under considerable pressure, is admitted to 
 the cylinder of an engine used to drive a pump for returning the strong 
 solution to the generator, after which it is passed to the absorber, where 
 it meets and is absorbed by the weak liquor from the generator, and the 
 strong liquor so formed is forced back into the generator by means of the 
 pump. The temperature exchanger, introduced in 1875, provides for 
 the hot liquor on its way from the generator to the absorber giving up 
 its heat to the cooler liquid from the absorber on its way to the generator. 
 
 Wallis-Taylor describes also marine refrigerating, ice-making cold 
 
AMMONIA MACHINES. 
 
 1347 
 
 storage, the application of refrigeration in breweries, dairies, etc.; and the 
 management and testing of apparatus. 
 
 For the best results the following conditions are necessary (Voorhees): 
 1. The generator should have ample liquid evaporating surface to make 
 dry gas. 2., The temperature of the gas to the rectifier should be as low 
 as possible. 3. The drip Iiqu9r returned to the generator from the recti- 
 fier should be as hot as possible. 4. The gas from the rectifier to the 
 condenser should not be over 10 to 50 hotter than the condensing tem- 
 perature of the gas. 5. The exchanger should exchange upwards of 
 90% of the heat ot the hot weak liquor to the cold strong liquor. The 
 weight of strong liquor pumped should be from 7 to 8 times that of the 
 anhydrous ammonia circulated in the refrigerator. 
 
 To produce one ton of refrigeration at 8.5 Ibs. suction and 170 Ibs. gauge 
 condenser pressure, about 3.5 times as many heat units are actually used 
 by an absorption machine as by a compression machine (compound con- 
 densing engine driven), but, 9wing to the low efficiency of the steam 
 engine, due to the heat wasted in the exhaust and in cylinder condensation, 
 the actual weight of steam used per hour per ton of refrigeration is the 
 same for both the absorption machine and the compressor. 
 
 Relative Performance of Ammonia Compression- and Absorp- 
 tion- machines, assuming no Water to be Entrained with the 
 Ammonia-gas in the Condenser. (Denton and Jacobus, Trans. A. S. 
 M. E., xiii.) It is assumed in the calculation for both machines that 
 1 Ib. of coal imparts 10,000 B.T.U. to the boiler. The condensed steam 
 from the generator of the absorption-machine is assumed to be returned 
 
 Condenser. 
 
 61.2 
 59.0 
 59.0 
 59.0 
 86.0 
 86.0 
 86.0 
 85.0 
 104.0 
 104.0 
 
 969 
 967 
 931 
 1000 
 988 
 966 
 1025 
 1002 
 1002 
 1041 
 
 *5% of water entrained in the ammonia will lower the economy of 
 the absorption-machine about 15 % to 20 % below the figures given in 
 the table. 
 
 to the boiler at the temperature of the steam entering 1 the generator. 
 The engine of the compression-machine is assumed to exhaust through a 
 feed- water heater that heats the feed-water to 212 F. The engine is 
 assumed to consume 261/4 Ibs. of water per hour per horse-power. The 
 figures for the compression-machine include the effect of friction, which 
 is taken at 15% of the net work of compression. 
 
 (For discussion of the efficiency of the ab^rption system, see Ledoux's 
 work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus, 
 Trans. A. S. M. E. t xiv. 1416, 1436; and papers by Denton and Jacobus. 
 Trans. A. S. M. E., x, 792, xiii, 507. 
 
1348 ICE-MAKING OR REFRIGERATING-MACHlNES. 
 
 Relative Efficiency of a Refrigerating-Machine. The efficiency 
 of a refrigerating-machine is sometimes expressed as the quotient of 
 the quantity of heat received by the ammonia from the brine, that is, the 
 quantity of useful work done, divided by the heat equivalent of the 
 mechanical work done in the compressor. Thus in column 1 of the table 
 of performance of the 75-ton machine (page!363) the heat given by the 
 brine to the ammonia per minute is 14,776 B.T.U. The horse-power of 
 the ammonia cylinder is 65.7, and its heat equivalent = 65.7 x 33,000 * 
 778 = 2786 B.T.U. Then 14,776 * 2786 = 5.304, efficiency. The ap- 
 parent paradox that the efficiency is greater than unity, which is im- 
 possible in any machine, is thus explained. The working fluid, as 
 ammonia, receives heat from the brine and rejects heat into the condenser. 
 (If the compressor is jacketed, a portion is rejected into the jacket-water.) 
 The heat rejected into the condenser is greater than that received from the 
 brine; the difference (plus or minus a small difference radiated to or from 
 the atmosphere) is heat received by the ammonia from the compressor. 
 The work to be done by the compressor is not the mechanical equivalent 
 of the refrigeration of the brine, but only that necessary to supply the dif- 
 ference between the heat rejected by the ammonia into the condenser and 
 that received from the brine. If cooling water colder than the brine were 
 available, the brine might transfer its heat directly into the cooling water, 
 and there would be no need of ammonia or of a compressor; but since such 
 cold water is not available, the brine rejects its heat into the cplder 
 ammonia, and then the compressor is required to heat the ammonia to 
 such a temperature that it may reject heat into the cooling water. 
 
 The maximum theoretical efficiency of a refrigerating machine is ex- 
 pressed by the quotient T -*- (T t T ), in which T t is the highest and T 
 the lowest temperature of the ammonia or other refrigerating agent. 
 
 The efficiency of a refrigerating plant referred to the amount of fuel 
 consumed is 
 
 /-Pounds circulated per hour^ ( 
 1 x specific heat x range > 
 Ice-melting capacity ) = I of temperature 
 
 per pound of fuel j 
 
 Cold Watet 
 
 144 X pounds of fuel used per hour 
 
 1 I 
 
 _____ Compressor * ^ 
 
 Condenser 
 
 309 339* '10 3 
 
 82 . i y 61 
 
 Brine Tank 
 
 Ammonia 
 Coils 
 
 
 
 | { 85 * Heat received U^~~ 
 Warm Water from compression. Heat received 
 
 9 o Brine Outlet 
 
 Cold Rooa 
 
 Heat rejected from brine 
 
 DIAGRAM OF AMMONIA COMPRESSION MACHINE. 
 
 II 
 
 Condenser 
 
 Torce Pump 
 DIAGRAM OF AMMONIA ABSORPTION MACHINE. 
 
EFFICIENCY OF REFRIGERATING SYSTEMS. " 1349 
 
 The Ice-melting capacity is expressed as follows: 
 
 Tons (of 2000 Ibs.) , { '" * MS heat } of brine drculated per 
 
 Ice-melting ca- i = l x ra "ge of temp. ) nour 
 
 pacity per 24 hours J 144 x 2000 
 
 The analogy between a heat-engine and a refrigerating-machine is as 
 follows: A steam-engine receives heat from the boiler, converts a part 
 of it into mechanical work in the cylinder, and throws away the differ- 
 ence into the condenser. The ammonia in a compression refrigerating- 
 machine receives heat from the brine- tank or cold room, receives an 
 additional amount of heat from the mechanical work done in the com- 
 pression-cylinder, and throws away the sum into the condenser. The 
 efficiency of the steam-engine = work done -i- heat received from boiler. 
 The efficiency of the refrigerating-machine = heat received from the 
 brine-tank or cold-room -j- heat required to produce the work in the 
 compression-cylinder. In the ammonia absorption-apparatus, the 
 ammonia receives heat from the brine-tank and additional heat from 
 the boiler or generator, and rejects the sum into the condenser and into 
 the cooling water supplied to the absorber. The efficiency = heat 
 received from the brine -5- heat received from the boiler. 
 
 The Efficiency of Refrigerating Systems depends on the tempera- 
 ture of the condenser water, whether there is sufficient condenser 
 surface for the compressor and whether or not the condenser pipes are 
 free from uncondensable foreign gases. With these things right, con- 
 denser pressure for different temperatures of cooling water should be 
 approximately as follows: 
 
 1 gallon per minute per ton per 24 hours 
 
 Cooling water, F 60 65 70 75 80 85 90 
 
 Condenser pressure, gage, Ib 183 200 220 235 255 280 300 
 
 Condensed liquid ammonia, F 95 100 105 110 115 120 125 
 
 2 gallons per minute per ton per 24 
 
 hours Condenser pressure, gage, Ib . 130 153 168 183 200 220 235 
 Condensed liquid ammonia, F 77 85 90 93 100 105 110 
 
 3 gallons per minute per ton per 24 
 
 hours Condenser pressure, gage, Ib. 125 140 155 170 185 200 215 
 
 Condensed liquid ammonia, F 75 85 90 93 95 100 105 
 
 The evaporating or back pressure within the expansion coils of a re- 
 frigerating system depends upon the temperatures on the outside of such 
 coils, i.e., the air or brine to be copied. For average practice back pres- 
 sures for the production of required temperatures should be approxi- 
 mately as follows: 
 Tempera ture of room, P. ... 10 15 20 28 32 36 40 50 60 
 
 Back pressure, gage, Ib 10 12 15 22 25 27 30 35 40 
 
 Temperature of ammonia, F. 10 5 8 12 14 17 22 26 
 The condenser pressure should be kept as low as possible and the back 
 pressure as high as possible, narrow limits between such pressures being 
 as important to the efficiency of a refrigerating system as wide ones are 
 to that of a steam engine in which the economy increases with the range 
 between boiler pressure and condenser pressure. (F. E. Matthews, 
 Power, Jan. 26, 1909.) 
 
 Cylinder-heating. In compression-machines employing volatile 
 vapors the principal cause of the difference between the theoretical and 
 the practical result is the heating of the ammonia, by the warm cylinder 
 walls, during its entrance into the compressor, thereby expanding it, so 
 that to compress a pound of ammonia a greater number of revolutions 
 must be made by the compressing-pumps than corresponds to the density 
 of the ammonia-gas as it issues from the brine-tank. t 
 
 Volumetric Efficiency. The volumetric efficiency of a compressor 
 is the ratio of the actual weight of ammonia pumped to the amount 
 calculated from the piston displacement. Mr. Voorhees deduces from 
 Denton's experiments the formula: Volumetric efficiency = E 1 
 (ti fo)/1330, in which t\ = the theoretical temperature of gas after 
 compression and h = temperature of gas delivered to the compressor. 
 The temperature ti, = Ti 460, is calculated from the formula for adia- 
 batic compression, Ti = To (Pi/Po) ' 24 . in which T\ and To are absolute 
 temperatures and Pi and Po absolute pressures. In eight tests by Prof. 
 Denton the volumetric efficiency ranged from 73.5% to 84%, and they 
 
1350 ICE-MAKING OB REFRIGERATING-MACHINES. 
 
 vary less than 1% from the efficiencies calculated by the formula. The 
 temperature of the gas discharged from the compressor averaged 57 less 
 than the theoretical. 
 
 The volumetric efficiency of a dry compressor is greatest when the va- 
 por comes to the compressor with little or no superheat; 30 superheat of 
 the suction gas reduces the capacity of the compressor 4%, and 100 9%. 
 
 The following table (from Voorhees) gives the theoretical discharge, 
 temperatures (h) and volumetric efficiencies (E) by the formula, and the 
 actual cubic feet of displacement of compressor (F) per ton of refrigera- 
 tion per minute for the given gage. pressures of suction and condenser. 
 
 Suction Pressures. 
 
 
 
 15 
 
 30 
 
 Cond. press., 140. . 
 Cond. press., 1 70 . . 
 Cond. press., 200. . 
 
 ti 
 323 
 221 
 167 
 
 E 
 0.76 
 0.83 
 0.87 
 
 F 
 10.35 
 
 4.57 
 2.96 
 
 ti 
 
 358 
 254 
 192 
 
 E 
 0.73 
 0.81 
 0.86 
 
 F 
 11.02 
 4.78 
 3.07 
 
 ti 
 
 388 
 280 
 216 
 
 E 
 0.71 
 0.79 
 0.84 
 
 F 
 11.57 
 5.03 
 3.21 
 
 Pounds of Ammonia per Minute to Produce 1 Ton of Refrigeration, 
 and Percentage of Liquid Evaporated at the Expansion Valve. 
 
 Condenser Pressure and 
 Temperature. 
 
 1401bs.,80. 
 
 1701bs.,90. 
 
 200 Ibs., 100. 
 
 Refrigerator, pressure and 
 temperature lbs.,-29... 
 Refrigerator pressure and 
 temperature 15 lbs.,-0... 
 Refrigerator pressure and 
 temperature, 30 lbs.,-17 .. 
 
 0.431 lb., 19% 
 0. 420 lb., 14.4% 
 0.4151b.,11.6% 
 
 0.441 lb., 20.8% 
 0. 430 lb., 16.2% 
 0. 425 lb., 13.4% 
 
 0. 451 lb.\ 22.5% 
 0.440 lb., 18.0% 
 0. 434 lb., 15.2% 
 
 Mean Effective Pressure, and Horse-power. Voorhees deduces 
 the following (Ice and Refrig., 1902) : M.E.P. = 4.333 p [(PI/PO) o- 231 1], 
 po = suction and p\ condenser pressure, abs*. Ibs. per sq. in. The maxi- 
 mum M.E.P. occurs when po = pi -r- 3.113. The percentage of stroke 
 during which the gas is discharged from the compressor is Vi = (po/pi) ' 769 . 
 
 The compressor horse-power, C.H.P., is 0.00437 F X M.E.P. 
 
 The friction of the compressor and its engine combined is given by 
 Voorhees as 33Va% of the compressor H.P. or 25% of the engine H.P. 
 Values of the mean effective pressure per ton of refrigeration (M), the 
 compressor horse-power (C) and the engine horse-power (E) are given 
 below for the conditions named. 
 
 Suction Pressure. 
 
 
 
 
 
 
 15 
 
 
 
 30 
 
 
 Cond. press., 140... 
 Cond. press., 1 70 ... 
 
 (M) 
 46.5 
 50.5 
 
 (C) 
 2.10 
 2.42 
 
 (E) 
 2.80 
 3.23 
 
 (M) 
 59.5 
 67.0 
 
 (C) 
 1.19 
 1.40 
 
 (E) 
 1.59 
 1.87 
 
 (M) 
 64.5 
 75.0 
 
 (C) 
 0.83 
 1.00 
 
 ffl 
 
 1.33 
 
 Cond. press., 200... 
 
 55.0 
 
 2.78 
 
 3.71 
 
 74.5 
 
 1.64 
 
 2.19 
 
 85.0 
 
 1.19 
 
 1.59 
 
 By cooling the liquid between the condenser and the expansion valve 
 the capacity will be increased and the horse-power per ton reduced. With 
 compression from 15 to 170 Ibs., if the liquid at the expansion valve is 
 cooled to 76 instead of 90 the H.P. per ton will be reduced 3%. 
 
 Prof. Lucke deduces a formula for the I. H.P. per ton of refrigerating 
 capacity, as follows: 
 
 p = mean effective pressure, Ibs. per sq. in. ; L = length of stroke in 
 ft.; a = area of piston in sq. ins. ; n = no. of compressions per minute; 
 EC = apparent volumetric efficiency, the ratio of the volume of ammonia 
 apparently taken in per stroke to the full displacement of the piston; 
 We = weight of 1 cu.ft. of ammonia vapor at the back pressure, as it- 
 exists in the cylinder when compression begins; Lc = latent heat of 
 vaporization available for refrigeration; 288,000 = B.T.U. equivalent 
 to 1 ton of refrigeration ; T = tons refrigeration per 24 hours. 
 I.H.P. = pLan + 33,000 0.87 x j^ 
 
 T LaEc nwc X Lc X 60 X 24 ~ W C L C EC 
 144 X 288,000 
 
 The Voorhees Multiple Effect Compressor is based upon the fact 
 that both the economy and the capacity of a compression machine vary 
 with the back pressure. In the past it has always been necessary to run a 
 compressor at a gas suction pressure corresponding to the lowest required 
 
QUANTITY OF AMMONIA KEQUIBED. 
 
 1351 
 
 temperature. The multiple effect compressor takes in gas from two or 
 more refrigerators at two or more different suction pressures and tem- 
 peratures on the same suction stroke of the compressor. The suction gas 
 of the higher pressure helps to compress the lower suction pressure gas. 
 There are two sets of suction valves in the compressor cylinder ; the low 
 temperature and corresponding low back pressure being connected to 
 one suction port, usually in the cylinder head, and the high back pres- 
 sure connected to the other. At the beginning of the stroke the cylinder 
 is filled with the low pressure gas and as the piston reaches the end of its 
 suction stroke, the second or high back pressure port is uncovered, the 
 low pressure suction valve closing automatically, and the cylinder is 
 completely filled with gas at the high pressure. By this means the 
 compressor operates with an economy and capacity corresponding to the 
 higher back pressure, making a gain in capacity of often 50% or more. 
 (Trans. Am. Soc. Refrig. Engrs., 1906.) 
 
 Quantity of Ammonia Required per Ton of Refrigeration. 
 The following table is condensed from one given by F. E. Matthews in 
 Trans. A. S. M. E., 1905. The weight in Ibs. per minute is calculated 
 from the formula P = (144 X 2000) -* [1440 1 - (fti - ho)] in which 
 I is the latent heat of evaporation at the back pressure in the cooler, and 
 hi and /?<> the heat of the liquid at the temperatures of the condenser and 
 the cooler respectively. The specific heat of the liquid has been taken 
 at unity. The ton of refrigeration is 2000 Ibs. in 24 hours = 288,000 
 B.T.U. 
 
 B = Pounds of ammonia evaporated per minute. 
 
 C = Cubic feet of gas to be handled per minute by the compressor. | 
 
 
 
 Head or Condenser Gauge Pressure and Corresponding 
 
 I. 
 
 
 Temperature. 
 
 w. 
 B.P. 
 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 
 
 190 
 
 200 
 
 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 Ib. 
 
 
 
 63.5 
 
 68 
 
 72.6 
 
 77.4 
 
 80.3 
 
 83.8 
 
 87.4 
 
 90.8 
 
 93.8 
 
 96.9 
 
 100 
 
 572.78 ) 
 
 B 
 
 .4159 
 
 .4199 
 
 .4240 
 
 .4284 
 
 .4310 
 
 .4343 
 
 .4376 
 
 .4408 
 
 .4440 
 
 .4470 
 
 .4501 
 
 .0556 > 
 ) 
 
 C 
 
 7.482 
 
 7.551 
 
 7.626 
 
 7.703 
 
 7.761 
 
 7.812 
 
 7.870 
 
 7.929 
 
 7.986 
 
 8.041 
 
 8.095 
 
 566.14) 
 
 B 
 
 .4122 
 
 .4160 
 
 .4202 
 
 .4243 
 
 .4271 
 
 .4308 
 
 .4335 
 
 .4366 
 
 .4397 
 
 .4437 
 
 .4458 
 
 .0133 j 
 
 C 
 
 5.636 
 
 5.675 
 
 5.732 
 
 5 .790 
 
 5.826 
 
 5.878 
 
 5.914 
 
 5.970 
 
 5.999 
 
 6.039 
 
 6.081 
 
 560.69 } 
 
 B 
 
 .4093 
 
 .4130 
 
 .4171 
 
 .4204 
 
 .4237 
 
 .4271 
 
 .4302 
 
 .4332 
 
 .4363 
 
 .4392 
 
 .4423 
 
 .0910 > 
 10 
 
 C 
 
 4.502 
 
 4.543 
 
 4.587 
 
 4.625 
 
 4.662 
 
 4.698 
 
 4.733 
 
 4.766 
 
 4.799 
 
 4.833 
 
 4.865 
 
 556.11 
 
 B 
 
 .4068 
 
 .4106 
 
 .4145 
 
 .4186 
 
 .4211 
 
 .4244 
 
 .4276 
 
 .4288 
 
 .4336 
 
 .4365 
 
 .4394 
 
 .1083 > 
 15 
 
 C 
 
 3.756 
 
 3.791 
 
 3.827 
 
 3.866 
 
 3.889 
 
 3.918 
 
 3.948 
 
 3.975 
 
 4.003 
 
 4.030 
 
 4.058 
 
 552,83 
 
 B 
 
 .4040 
 
 .4077 
 
 .4116 
 
 .4158 
 
 .4182 
 
 .4214 
 
 .4245 
 
 .4275 
 
 .4304 
 
 .4333 
 
 .4362 
 
 '20 
 
 C 
 
 3.211 
 
 3.241 
 
 3.272 
 
 3.305 
 
 3,324 
 
 3.350 
 
 3.375 
 
 3.398 
 
 3.422 
 
 3.444 
 
 3.467 
 
 548.40 J 
 
 B 
 
 .4025 
 
 .4062 
 
 .4102 
 
 .4140 
 
 .4167 
 
 .4198 
 
 .4229 
 
 .4258 
 
 .4287 
 
 .4316 
 
 .4345 
 
 if 
 
 C 
 
 2.819 
 
 2.843 
 
 2.870 
 
 2.898 
 
 2.916 
 
 2.938 
 
 2.959 
 
 2.980 
 
 3.000 
 
 3.020 
 
 3.040 
 
 545.13 
 
 B 
 
 .4013 
 
 .4049 
 
 .4088 
 
 .4128 
 
 .4152 
 
 .4184 
 
 .4213 
 
 .4243 
 
 .4273 
 
 .4300 
 
 .4329 
 
 .1600 > 
 30 ) 
 
 C 
 
 2.507 
 
 2.530 
 
 2.555 
 
 2.580 
 
 2.600 
 
 2.615 
 
 2.633 
 
 2.653 
 
 2.671 
 
 2.687 
 
 2.706 
 
 542.80 
 
 B 
 
 .3991 
 
 .4028 
 
 .4066 
 
 .4105 
 
 .4130 
 
 .4161 
 
 .4188 
 
 .4220 
 
 .4249 
 
 .4277 
 
 .4305 
 
 .1766 
 
 C 
 
 2.260 
 
 2.280 
 
 2.302 
 
 2.925 
 
 2.338 
 
 2.356 
 
 2.373 
 
 2.390 
 
 2.406 
 
 2.422 
 
 2.443 
 
 539.35 ) 
 
 1041 ( 
 
 B 
 
 .3984 
 
 .4020 
 
 .4058 
 
 .4098 
 
 .4122 
 
 .4153 
 
 .4183 
 
 .4211 
 
 .4240 
 
 .4269 
 
 .4296 
 
 . 1 V4 1 > 
 
 40 \ 
 
 C 
 
 2.052 
 
 2.071 
 
 2.090 
 
 2.111 
 
 2.123 
 
 2.139 
 
 2.155 
 
 2.175 
 
 2.185 
 
 2.200 
 
 2.214 
 
 I, Latent heat of volatilization, w, weight of vapor per cubic foot. 
 B.P. back pressure or suction gauge pressure. 
 
 Back pressures 5 10 15 20 25 30 35 40 
 
 Temperatures. -28.5 -17.5 -8.5 -15.66 11.5 16.8 21.7 26.1 
 
 Mr. Matthews defines a standard ton of refrigeration as the equiva- 
 lent of 27 Ibs. of anhydrous ammonia evaporated per hour from liquid 
 
1352 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 at 90 F. into saturated vapor at 15.67 Ibs. gauge pressure (0 F.). 
 which requires 12,000 B.T.U.; or 20,950 units of evaporation, each of 
 which is equal to 572.78 B.T.U., the heat required to evaporate 1 Ib. 
 of ammonia from a temperature of 28.5 F. into saturated vapor at 
 atmospheric pressure. 
 
 Size and Capacities of Ammonia Refrigerating - Machines. 
 York Mfg. Co. Based on 15.67 Ibs. back pressure, 185 Ibs. condensing 
 pressure, and condensing water at 60 F. 
 
 SINGLE-ACTING COMPRESSORS. 
 
 DOUBLE-ACTING COMPRESSOBS. 
 
 Compressors . 
 
 Engine. 
 
 Capacity 
 
 Compressors. 
 
 Engine. 
 
 Capacity 
 
 
 
 
 
 Tons 
 
 
 
 
 
 Tons 
 
 Bore. 
 
 Stroke. 
 
 Bore. 
 
 Stroke. 
 
 Refrig- 
 
 Bore. 
 
 Stroke. 
 
 Bore. 
 
 Stroke. 
 
 Refrig- 
 
 
 
 
 
 eration. 
 
 
 
 
 
 eration. 
 
 71/2 
 
 10 
 
 11 1/2 
 
 10 
 
 10 
 
 9 
 
 15 
 
 13 I/? 
 
 12 
 
 20 
 
 9 
 
 12 
 
 131/2 
 
 12 
 
 20 
 
 11 
 
 18 
 
 16 
 
 15 
 
 30 
 
 11 
 
 15 
 
 16 
 
 15 
 
 30 
 
 121/0 
 
 21 
 
 18 
 
 18 
 
 40 
 
 121/2 
 
 18 
 
 18 
 
 18 
 
 40 
 
 14 
 
 24 
 
 20 
 
 21 
 
 65 
 
 14 
 
 21 
 
 20 
 
 21 
 
 65 
 
 16 
 
 28 
 
 24 
 
 24 
 
 90 
 
 16 
 
 24 
 
 24 
 
 24 
 
 90 
 
 18 
 
 32 
 
 26 
 
 28 
 
 125 
 
 18 
 
 28 
 
 26 
 
 28 
 
 125 
 
 21 
 
 36 
 
 28 l/o 
 
 32 
 
 175 
 
 21 
 
 32 
 
 281/2 
 
 32 
 
 175 
 
 24 
 
 40 
 
 34 
 
 36 
 
 250 
 
 24 
 
 36 
 
 34 
 
 36 
 
 250 
 
 26 
 
 60 
 
 38 
 
 54 
 
 350 
 
 27 . 
 
 42 
 
 36 
 
 42 
 
 350 
 
 
 
 
 
 
 30 
 
 48 
 
 44 
 
 48 
 
 500 
 
 
 
 
 
 
 For larger capacities the machines are built with duplex compressors, 
 driven by simple, tandem or cross dbmpound engines. 
 
 DISPLACEMENT AND HORSE-POWER PER TON OF REFRIGERATION 
 Dry Compression. S.A., Single-acting; D.A., Double-acting. 
 
 Condenser Gauge 
 Pressure and 
 Corresp. Temp. 
 of Liquid at 
 Expansion Valve. 
 
 Suction Gauge Pressure and Corresponding Temp. 
 
 51b.= 
 - 17.5F. 
 
 101b.= 
 - 8.5 F. 
 
 15.671b. 
 = 0F. 
 
 20 Ib. = 
 5.7 F. 
 
 25 Ib. = 
 1I.5F. 
 
 & 
 
 v? 
 
 55 
 
 j 
 ^ 
 
 d j 
 
 5 a 
 
 g 
 
 ^ 
 
 *& 
 
 ^ 
 
 5 s 
 
 7829 
 8901 
 8092 
 9224 
 8362 
 9555 
 8630 
 9890 
 
 I.H.P. 
 per Ton. 
 
 *| 
 
 a 5 
 
 J 
 $1. 
 
 & 
 3 5 
 
 I.H.P. 
 per Ton. 
 
 1451b. 82 F., S.A... 
 145 Ib. 82 F., D.A.. 
 165 Ib. 89 F., S.A.. 
 165 Ib. 89 F., D.A. 
 1851b. 95.5 F., S.A. 
 185 Ib. 95.5 F.,D.A. 
 2051b.101.4F.,S.A. 
 2051b.l01.4F.,D.A. 
 
 12,608 
 14,645 
 13,045 
 15,203 
 13,491 
 15,774 
 13,947 
 16,362 
 
 1.654 
 1.921 
 1.834 
 2.137 
 2.013 
 2.354 
 2.192 
 2.571 
 
 9,811 
 11,300 
 10,148 
 11,720 
 10,487 
 12,150 
 10,834 
 12,590 
 
 .4 
 .612 
 .56 
 .802 
 .72 
 .993 
 .879 
 2.184 
 
 .195 
 .358 
 .341 
 .529 
 .4865 
 .7 
 .631 
 .87 
 
 6765 
 7625 
 6990 
 7898 
 7219 
 8176 
 7450 
 8459 
 
 .065 
 .2 
 .201 
 .357 
 .336 
 .513 
 .47 
 .67 
 
 5836 
 6522 
 6027 
 6751 
 6223 
 6985 
 6420 
 7222 
 
 0.943 
 .054 
 .071 
 .2 
 .197 
 .344 
 .323 
 .488 
 
 * Cu. in. Displacement per Min. per Ton of Refrigeration. 
 
 The volumetric efficiency ranges from 63.5 to 76.5% for double-acting 
 and from 74.5 to 85.5 % for single-acting compressors, increasing with the 
 decrease of condenser pressure and with the increase of suction pressure. 
 
 Where the liquid is cooled lower than the temperature corresponding 
 to the condensing pressure, there will be a reduction in horse-power and 
 displacement proportional to the increase of work done by each pound 
 of liquid handled. The I.H.P. is that of the compressor. For Engine 
 Horse-power add 17 % up to 20 tons capacity and 15 % for larger machines. 
 
 SMALL SIZES OF REFRIGERATING-MACHINES. 
 
 
 Single-acting, 
 Vertical. 
 
 Double-acting, 
 Horizontal. 
 
 Capacity, tons 
 
 1 1/4 
 
 3 
 
 6 
 
 21/2 
 
 6 
 
 10 
 
 Compressor, diam., in 
 
 4 1/2 
 5 
 
 6 
 6 
 6 
 6 
 
 2-6 
 6 
 8 
 6 
 
 4 
 6 
 6 
 8 
 
 51/2 
 8 
 8 
 8 
 
 7 
 10 
 10 
 10 
 
 Compressor, stroke, in . . . ... 
 
 Engine diam , in 
 
 Engine, stroke, in 
 
CONDENSERS FOR REFRIGERATING-MACHINES. 1353 
 
 Rated Capacity of Refrigerating -Machines. It is customary to 
 rate refrigerating machines in tons of refrigerating capacity in 24 hours, 
 on the basis of a suction pressure of 15.67 Ibs. gauge, corresponding to 
 F. temperature of saturated ammonia vapor, and a condensing pressure 
 of 185 Ibs. gauge, corresponding to 95.5 F. The actual capacity increases 
 with the increase of the suction pressure, and decreases with the increase 
 of the condensing pressure. The following table shows the calculated 
 capacities and horse-power of a machine rated at 40 H.P., when run at 
 different pressures. (York Mfg. Co.) The horse-power required increases 
 with the increase of both the suction and the condensing pressure. 
 
 Condenser Press. 
 Temp. 
 
 Suction Gauge Pressure and Corresponding Temp. 
 
 51b.= 
 -17.5F 
 
 10 Ib. = 
 -8.5 F. 
 
 15.67 Ib. 
 
 = 0F. 
 
 20 Ib. = 
 5.7 F. 
 
 25 Ib. = 
 11.5 F. 
 
 30 Ib. = 
 16.8F. 
 
 H 
 
 OH 
 
 w 
 
 1 
 
 Pk 
 W 
 
 
 
 1 
 
 Pu 
 W 
 
 
 
 1 
 
 Pk 
 W 
 
 1 
 
 CM 
 
 w 
 
 1 
 
 fC 
 
 a 
 
 63.4 
 70.1 
 76.5 
 86.2 
 
 145 Ib. = 82 F.. 
 165 Ib. = 89 F 
 185 Ib. = 95.5 F...... 
 205 Ib. = 101.4 F 
 
 26.6 
 25.7 
 
 24.8 
 24 
 
 50.6 
 54.2 
 57.4 
 60.5 
 
 34.2 
 33.1 
 32 
 31 
 
 55.1 
 59.4 
 63.3 
 67 
 
 42.8 
 41.4 
 40 
 38.9 
 
 58.8 
 63.8 
 68.6 
 72.9 
 
 49.6 
 48 
 46.5 
 45 
 
 60.7 
 66.3 
 71.4 
 76.1 
 
 57.5 
 55.7 
 53.9 
 52.3 
 
 62.3 
 68.6 
 74.2 
 79.6 
 
 65.3 
 63.2 
 61.3 
 59.4 
 
 Piston Speeds and Revolutions per Minute. There is a great diver- 
 sity in the practice of different builders as to the size of compressor, the 
 piston speed and the number of revolutions per minute for a given 
 rated capacity. F. E. Matthews, Trans. A. S. M. E., 1905, has plotted 
 a diagram of the various speeds and revolutions adopted by four promi- 
 nent builders, and from average curves the following figures are obtained: 
 
 R.P.M 
 Piston speeds. 
 
 90 
 200 
 
 78 
 215 
 
 73 68 
 228|240 
 
 64 
 250 
 
 60 
 270 
 
 581/2 
 280 
 
 57 
 286 
 
 56 
 290 
 
 55 
 
 293 
 
 54 
 296 
 
 53 
 300 
 
 52 
 315 
 
 51 
 340 
 
 481/2 
 378 
 
 46 
 425 
 
 Mr. Matthews recommends a standard rating of machines based on 
 these revolutions and speeds and on an apparent compressor displace- 
 ment of 4.4 cu. ft. per minute per ton rating. 
 
 Condensers for Refrigerating^ Machines are of two kinds: sub- 
 merged, and open-air evaporative. The submerged condenser requires 
 a large volume of cooling water for maximum efficiency. According 
 to Siebel the amount of condensing surface, the water entering at 70 
 and leaving at 80, is 40 sq ft. for each ton of refrigerating capacity, or 
 64 lineal feet of 2-in. pipe. Frequently only 20 sq. ft., or 90 ft. of li/4-in. 
 pipe, is used, but this necessitates higher condenser pressures. If F. = 
 sq. ft. of cooling surface, h = heat of evaporation of 1 Ib. ammonia at 
 the condenser temperature, K . = Ibs. of ammonia circulated per minute, 
 m = B.T.IT, transferred per minute per sq. ft. of condenser surface, 
 t = temperature of the ammonia in the coils and t\ the temperature of 
 the water outside, F = hK -* m(t - k). For t = 80 and t\ = 70, m 
 may be taken at 0.5. Practically the amount of water required will 
 vary from 3 to 7 gallons per minute per ton of refrigeration. When 
 cooling water is scarce, cooling towers are commonly used. 
 
 E. T. Shinkle gives the average surface of several submerged con- 
 densers as equal to 167 lineal feet of 1-in. pipe per ton of refrigeration. 
 
 Open air or evaporation surface condensers are usually made of a stack 
 of parallel tubes with return bends, and means for distributing the water 
 so that it will flow uniformly over the pipe surface. Shinkle gives as the 
 average surface of open-air coolers 142 ft. of 1-in. pipe, or 99 ft. of 1 1/4 in. 
 pipe per ton of refrigerating capacity. 
 
 CAPACITY OF CONDENSERS. (York Mfg. Co.) The following table 
 shows the capacities and horse-power per ton refrigeration of one section 
 counter-current double-pipe condenser, li/4-in. and 2-in. pipe, 12 pipes 
 high, 19 feet in length outside of water bends, for water velocities 100 ft. 
 to 400 ft. per minute: initial temperature of condensing water 70. 
 
 The horse-power per ton is for single-acting compressor with 15.67 
 Ibs. suction pressure. 
 
 The friction in water pump and connections should be added to 
 water horse-power and to total horse-power. 
 
1354 ICE-MAKING OR REFR1GERATING-MACHINES. 
 
 Capacity of Condensers 
 
 High Pressure Constant. 
 
 Condensing Water. 
 
 Cap'y 
 Tons 
 Refrig. 
 per 24 
 hours. 
 
 Con- 
 densing 
 Pressure 
 Lbs. per 
 sq. in. 
 
 Horse-power per Ton 
 Refrigeration. 
 
 Veloc- 
 ity 
 thr'gh 
 11/4-in. 
 pipe. 
 Ft. per 
 min. 
 
 Total 
 gallons 
 used 
 per 
 mm. 
 
 Gallons 
 per min 
 per ton 
 Refrig. 
 
 Fric- 
 tion 
 thr'gh 
 Coil. 
 Lbs. 
 per 
 sq. in. 
 
 Engine 
 driving 
 Com- 
 pressor 
 
 Circu- 
 lating 
 Water 
 thr'gh 
 Con- 
 denser. 
 
 Total 
 Engine 
 and 
 Water 
 Circu- 
 lation. 
 
 100 
 150 
 200 
 250 
 300 
 400 
 
 7.77 
 11.65 
 15.54 
 19.42 
 23.31 
 31.08 
 
 .16 
 .165 
 .165 
 .18 
 .24 
 .30 
 
 2.28 
 5.75 
 9.98 
 15. 
 21.6 
 37.8 
 
 6.7 
 10. 
 13.4 
 16.4 
 18.8 
 24. 
 
 185 
 185 
 185 
 185 
 185 
 185 
 
 .71 
 .71 
 .71 
 .71 
 .71 
 .71 
 
 0.0016 
 0.004 
 0.007 
 0.011 
 0.016 
 0.030 
 
 .7116 
 .714 
 .717 
 .721 
 .726 
 .74 
 
 Capacity Constant. 
 
 100 
 150 
 200 
 250 
 300 
 400 
 
 7.77 
 11.65 
 15.54 
 19.42 
 23.31 
 31.08 
 
 0.777 
 1.165 
 1.554 
 1.942 
 2.331- 
 3.108 
 
 2.28 
 5.75 
 9.98 
 15. 
 21.6 
 37.8 
 
 10. 
 10. 
 10. 
 10. 
 10. 
 10. 
 
 225 
 185 
 165 
 155 
 148 
 140 
 
 2.04 
 .71 
 .54 
 .46 
 .40 
 .33 
 
 0.001 
 0.004 
 0.009 
 0.018 
 0.030 
 0.071 
 
 2.041 
 .714 
 .549 
 .478 
 .43 
 .401 
 
 Cooling-Tower Practice in Refrigerating - Plants. (B. F. Hart, 
 Jr., Southern Engr., Mar., 1909.) The efficiency of a cooling-tower de- 
 pends on exposing the greatest quantity of water surface to the cooling 
 air-currents. In a tower designed to handle 100 gallons per minute the 
 ranges of temperature found when handling different quantities of 
 water were as follows: 
 
 Gallons of water per minute 148 
 
 Temperature of the atmosphere 78- 
 
 Relative humidity, % 47 
 
 Initial temperature 85.5 
 
 Final temperature 78 
 
 Range 7.5 
 
 109 
 78.5 
 49 
 85 
 76 
 9 
 
 58 
 
 78 
 
 47 
 
 86 
 
 75 
 
 11 
 
 The final temperatures which may be obtained when the initial 
 temperature does not exceed 100 are as follows: 
 
 Atmosphere Temp. 
 
 95 
 
 90 
 
 85 
 
 80 
 
 75 
 
 70 
 
 
 Final temperature of water leaving tower. 
 
 (90 
 80 
 60 
 50 
 40 
 
 100 
 98 
 95 
 92 
 89 
 85 
 
 95 
 92 
 90 
 88 
 84 
 80 
 
 90 
 88 
 86 
 83 
 79 
 76 
 
 85 
 83 
 80 
 78 
 75 
 71 
 
 80 
 78 
 76 
 74 
 70 
 67 
 
 75 
 73 
 71 
 69 
 66 
 63 
 
 For ammonia condensers we figure on supplying 3 gallons per minute of 
 circulating water per ton of refrigeration, or 6 gallons per minute per ton of 
 ice made per 24 hours, and guarantee a reduction range from 150 to 160 
 down to about 100 when the temperature of the atmosphere does not 
 exceed 80 nor the relative humidity 60%. When the temperature of the 
 atmosphere and the humidity are both above 90 the speed of the pumps 
 and the ammonia pressure must be increased. 
 
 The Kefrigeratlng-Coils of a Pictet ice-machine described by Ledoux 
 had 79 sq. ft. of surface for each 100,000 theoretic negative heat-units 
 produced per hour. The temperature corresponding to the pressure of 
 the dioxide in the coils is 10.4 F., and that of the bath (calcium chloride 
 solution) in which they were immersed is 19.4. 
 
TEST-TRIALS OF REFRIGERATING-MACHINES. 1355 
 
 Comparison of Actual and Theoretical Ice-melting Capacity. 
 
 The following is a comparison of the theoretical ice-melting capacity of 
 an ammonia compression machine with that obtained in some of Prof. 
 Schroter's tests on a Linde machine having a compression-cy Under 
 9.9-in. bore and 16.5 in. stroke, and also in tests by Prof. Den ton on a 
 machine having two single-acting compression-cylinders, 12 in. X 30 in.: 
 
 No of 
 
 Temp, in Degrees F. 
 Corresponding to 
 Pressure of Vapor. 
 
 Ice-melting Capacity per Ib. of Coal, 
 assuming 3 Ibs. per hour per 
 Horse-power. 
 
 Test. 
 
 Condenser. 
 
 Suction. 
 
 Theoretical 
 Friction* 
 Included. 
 
 Actual. 
 
 Per cent of 
 Loss Due to 
 Cylinder 
 Superheating. 
 
 & f 1 
 
 72.3 
 
 26.6 
 
 50.4 
 
 40.6 
 
 19.4 
 
 SI 2 
 
 70.5 
 
 14.3 
 
 37.6 
 
 30.0 
 
 20.2 
 
 1 3 
 
 69.2 
 
 0.5 
 
 29.4 
 
 22.0 
 
 25.2 
 
 &( 4 
 
 68.5 
 
 -11.8 
 
 22.8 
 
 16.1 
 
 29.4 
 
 | (24 
 
 84.2 
 
 15.0 
 
 27.4 
 
 24.2 
 
 11.7 
 
 c i 26 
 
 82.7 
 
 - 3.2 
 
 21.6 
 
 17.5 
 
 19.0 
 
 125 
 
 84.6 
 
 -10.8 
 
 18.8 
 
 14.5 
 
 22.9 
 
 * Friction taken at figures observed in the tests, which range from 
 14 % to 20 % of the work of the steam-cylinder. 
 
 TEST-TRIALS OF REFRIGERATING-MACHINES. 
 
 (G. Linde, Trans. A. S. M. E., xiv, 1414.) 
 
 The purpose of the test is to determine the ratio of consumption and 
 production, so that there will have to be measured both the refrigera- 
 tive effect and the heat (or mechanical work) consumed, also the cool- 
 ing water. The refrigerative effect is the product of the number of 
 heat-units (Q) abstracted from the body to be cooled, and the quotient 
 (T c - T) -5- T: in which T c = absolute temperature at which heat is 
 transmitted to the cooling water, and T = absolute temperature at 
 which heat is taken from the body to be cooled. 
 
 The determination of the quantity of cold will be possible with the 
 proper exactness only when the machine is employed during the test to 
 refrigerate a liquid ; and if the cold be found from the quantity of liquid 
 circulated per unit of time, from its range of refrigeration, and from its 
 specific heat. Sufficient exactness cannot be obtained by the refrigera- 
 tion of a current of circulating air, nor from the manufacture of a certain 
 quantity of ice, nor from a calculation of the fluid circulating within the 
 machine (for instance, the quantity of ammonia circulated by the com- 
 pressor). Thus the refrigeration of brine will generally form the basis 
 for tests making any pretension to accuracy. The degree of refrigeration 
 should not be greater than necessary for allowing the range of temperature 
 to be measured with the necessary exactness; a range of temperature of 
 from 5 to 6 Fahr. will suffice. 
 
 The condenser measurements for cooling water and its temperatures 
 will be possible with sufficient accuracy only with submerged condensers. 
 The measurement of the quantity of brine circulated, and of the cool- 
 ing water, is usually effected by water-meters inserted into the conduits. 
 If the necessary precautions are observed, this method is admissible. 
 For quite precise tests, however, the use of two accurately gauged 
 tanks which are alternately filled and emptied must be advised. 
 
 To measure the temperatures of brine and cooling water at the entrance 
 and exit of refrigerator and condenser respectively, the employment of 
 specially constructed and frequently standardized thermometers is in- 
 dispensable ; no less important is the precaution of using at each spot si- 
 multaneously two thermometers, and of changing the position of one such 
 thermometer series from inlet to outlet (and vice versa) after the expiration 
 of one-half of the test, in order that possible errors may be compensated. 
 It is important to determine the specific heat of the brine used in 
 each instance for its corresponding temperature range, as small differ- 
 ences in the composition and the concentration may cause considerable 
 variations. (Continued on page 1358.) 
 
f 1 P 1 ? on i* ^oppression-machines. Ammonia gas possesses the advantage of affording about three times the useful effect ]rt 
 of sulphur dioxide for the same volume described by the piston. 
 Ihe perfection of ammonia apparatus now renders it so convenient and reliable that no practical advantage results from 
 tne lower pressures afforded by sulphur dioxide. 
 The results of the calculations for ammonia are given in the table below: '-' 
 
 PERFORMANCE OF AMMONIA COMPRESSION-MACHINES. 
 ir? 44"bs rh ers ed 'n^"??, ^ ompression as in ordinar y practice. Temperature of condenser, 64.4 Fahr. Pressure in condenser, g 
 
 KING OR REFRIGERATING 
 
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 ;; 
 
 irlP in thl T f for . ammonia are higher than the actual, for the same reasons that have been stated for suit 
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 JSSSSS * C 3 rc , ulat ? d . m 4 , a 7 - ton refrigerating machine was measured directly by means of a special meter s 
 addition to determining the effect of superheating, the latent heats can be calculated at the suction and condenser p 
 
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 Work of Com- 
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 siioo-3ui;Bja3uja^; ui 
 jod^'jo ajnssajj o; 3ui 
 -puodsajjoQ ajn^jaduiaj^ 
 
 i 
 
 i 
 
TEST-TRIALS OF REFRIGERATING- MACHINES. 1357 
 
 MPLE COCK 
 SSURE AND 
 
 S 
 
 ROUGH A 
 AT THIS PR 
 
 ZPfc 
 
 2s 
 S | 
 
 ail 
 
 iP(8 
 
 igs 
 
 |S| 
 
 sSg* 
 
 h S 
 3^K 
 
 o o 
 
 S5 fc 
 
 6 
 
 OR 0.1 2 
 SQ. IN., 
 CORR 
 
 
 
 I 
 
 4SB 
 
 a 
 c 
 
 
 
 o 
 
 F 
 
 1 
 URE 
 
 ATING E 
 ABSOL 
 
 sjnoq ^g ui 
 
 jo 
 
 -aoj jo uoj, 
 
 -sij jo -; 
 
 s !d: 
 
 n>^ 
 
 Per Hour 
 per H.P. 
 
 uoi? 
 * 
 
 uoi; 
 
 jad anojj 
 
 -pnpui 'papuadx^j 
 ' 
 
 uopou^ ^no 
 iM 'papuadxg 
 - 
 
 -tpUJ JO 'uOI^OIJtjJ q^IA 
 
 'iioissajduiOQ jo 3(j6 
 
 'uoissaaduioQ jo 
 
 
 00 T t> o O > 
 
 ts i>. U-N ON >o NO rx 
 
 r<^ ON 00 tx, NO 
 
 
 papuad 
 ?oa#g[ 
 P oi 
 
 jasuapuoQ 
 raoij A'-BMra paia 
 
 uoissaidraoo 
 jo pug ;t3 aimuiaduiax 
 
 jasuapuoQ 
 m ainssajj a'jnjosqv 
 
 jasuapuoQ ui 
 jo -SS8JJ o^ anQ[ ' 
 
 [Flip 
 
 go 
 i 
 
 9 
 
 OUGH A SIMPLE 
 ESSURE AND THE 
 
 *& 
 
 AND 
 
 AT T 
 
 F. 
 
 386 B. O MMONIA 
 KEN INTO THE COMPRE 
 TEMPERATURE OF 
 
 U. FT. OR 
 Q. IN., AND 
 
 
 OO -^ 1^ \O 
 
 C'ON oo r>Ti>TNo"rr 
 
 
 O /*! OO ON T\ 
 
 INtNWMNO 
 
 O NO OO OO 
 
1358 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 As regards the measurement of consumption, the programme will not 
 have any special rules in cases where only the measurement of steam and 
 cooling water is undertaken, as will be mainly the case for trials of absorp- 
 tion-machines. For compression-machines the steam consumption 
 depends both on the quality of the steam-engine and on that of the 
 remgerating-machine, while it is evidently desirable to know the con- 
 sumption of the former separately from that of the latter. As a rule 
 steam-engine and compressor are coupled directly together, thus render- 
 ing a direct measurement of the power absorbed by the refrigerating- 
 machine impossible, and it will have to suffice to ascertain the indicated 
 work both of steam-engine and compressor. By further measuring 
 the work for the engine running empty, and by comparing the differences 
 in power between steam-engine and compressor resulting for wide varia- 
 tions of condenser-pressures, the effective consumption of work L e for 
 the refrigerating-machine can be found very closely. In general, it will 
 suffice to use the indicated work found in the steam-cylinder, especially 
 as from this observation the expenditure of heat can be directly deter- 
 mined. Ordinarily the use of the indicated work in the compressor- 
 cylinder, for purposes of comparison, should be avoided; firstly, because 
 there are usually certain accessory apparatus to be driven (agitators, etc.), 
 belonging to the refrigerating-machine proper; and secondly, because 
 the external friction would be excluded. 
 
 Report of Test. Reports intended to be used for comparison with 
 the figures found for other machines will have to embrace at least the 
 following observations: 
 Refrigerator: 
 
 Quantity of brine circulated per hour r ........................ .... 
 
 Brine temperature at inlet to refrigerator .......................... 
 
 Brine temperature at outlet of refrigerator ....................... T 
 
 Specific gravity of brine (at 64 Fahr.) ...... . ...................... 
 
 Specific heat of brine ............................................ 
 
 Heat abstracted (cold produced) . . .............................. Q e 
 
 Absolute pressure in the refrigerator .............................. 
 
 Condenser: 
 
 Quantity of cooling water per hour ................................. 
 
 Temperature at inlet to condenser ................................ 
 
 Temperature at outlet of condenser ............................ T c 
 
 Heat abstracted .............................................. Qi 
 
 Absolute pressure in the condenser ..... ........................... 
 
 Temperature of gases entering the condenser ............ ............ 
 
 ABSORPTION-MACHINE . 
 
 Still: 
 
 Steam consumed per hour 
 
 Abs. pressure of heating steam 
 
 Temperature of condensed steam at 
 outlet 
 
 Heat imparted to still Q' e 
 
 Absorber: 
 
 Quantity of cooling water per hour . . 
 
 Temperature at inlet 
 
 Temperature at outlet 
 
 Heat removed Qz 
 
 Pump for Ammonia Liquor: 
 
 Indicated work of steam-engine .... 
 
 Steam-consumption for pump 
 
 Thermal equivalent for work of 
 
 pump ALp 
 
 Total sum of losses by radiation and 
 
 convection Qz 
 
 Heat Balance: 
 
 Qe + Q'e = Q I + Q Z ^ Q 3 - 
 For the calculation of efficiency and for comparison of various tests, 
 the actual efficiencies must be compared with the theoretical maximum 
 of efficiency Q -T- GAL) max. = T + (T c - T} corresponding to the 
 temperature range, 
 
 COMPRESSION-MACHINE . 
 Compressor: 
 
 Indicated work .......... LI 
 
 Temperature of gases at inlet 
 Temperature of gases at exit 
 Steam-engine: 
 
 Feed-water per hour. 
 
 Temperature of feed-water . . 
 Absolute steam-pressure be- 
 
 fore steam-engine 
 
 Indicated work of steam-en- 
 gine L e 
 
 Condensing water per hour.. . 
 
 Temperature of do 
 
 Total sum of losses by radia- 
 tion and convection. . Q$ 
 Heat Balance: 
 
 Q e + AL C = Qi Qs. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1359 
 
 Heat Balance. We possess an important aid for checking the cor- 
 rectness of the results found in each trial by forming the balance in each 
 case for the heat received and rejected. Only those tests should be re- 
 garded as correct beyond doubt which show a sufficient conformity in 
 the heat balance. It is true that in certain instances it may not be easy 
 to account fully for the transmission of heat between the several parts of 
 the machine and its environment by radiation and convection, but gener- 
 ally (particularly for compression-machines) it will be possible to obtain 
 for the heat received and rejected a balance exhibiting small discrepancies 
 only. 
 
 Temperature Range. For the temperatures (T and TC) at which the 
 heat is abstracted in the refrigerator and imparted to the condenser, it is 
 correct to select the temperature of the brine leaving the refrigerator and 
 'that of the cooling water leaving the condenser, because it is in principle 
 impossible to keep the refrigerator pressure higher than would correspond 
 to the lowest brine temperature, or to reduce the condenser pressure 
 below that corresponding to the outlet temperature of the cooling water. 
 Prof. Linde shows that the maximum theoretical efficiency of a com- 
 pression-machine may be expressed by the formula 
 Q -H (AL) = T + (T C - T 7 ), 
 in which Q = quantity of heat abstracted (cold produced); 
 
 AL = thermal equivalent of the mechanical work expended; 
 L = the mechanical work, and A = I -*- 778: 
 T = absolute temperature of heat abstraction (refrigerator); 
 T c = absolute temperature of heat rejection (condenser). 
 If u = ratio between the heat equivalent of the mechanical work AL 
 and the quantity of heat Q' which must be imparted to the motor to 
 produce the work L, then 
 
 AL -J- Q' = u, and Q'/Q - (T c - 70 * (uT). 
 
 It follows that the expenditure of heat Q' necessary for the production 
 of the quantity of cold Q in a compression-machine will be the smaller, 
 the smaller the difference of temperature T c T. 
 
 Metering the Ammonia. For a complete test of an ammonia 
 refrigerating-machine it is advisable to measure the quantity of ammonia 
 circulated, as was done in the test of the 75-ton machine described by 
 Prof. Den ton. (Trans. A. S. M. E., xii, 326.) 
 
 ACTUAL PERFORMANCES OF ICE-MAKING MACHINES. 
 
 The table given on page 1360 is abridged from Denton, Jacobus, and 
 Riesenberger's translation of Ledoux on Ice-making Machines. The 
 following shows the class and size of the machines tested, referred to by 
 letters in the table, with the names of the authorities: 
 
 Class of Machines. 
 
 Authority. 
 
 Dimensions of Com- 
 pression-cylinder in 
 inches. 
 
 Bore. 
 
 Stroke. 
 
 A. Ammonia cold-compression 
 
 Schroter. 
 
 ( Renwick & 
 \ Jacobus. 
 Denton. 
 
 9.9 
 11.3 
 28.0 
 
 10.0 
 12.0 
 
 16.5 
 
 24.4 
 23.8 
 
 18.0 
 30.0 
 
 B. Pictet fluid dry-compression 
 
 C. Bell-Coleman air 
 
 D. Closed cycle air 
 
 E. Ammonia dry-compression 
 
 F. Ammonia absorption 
 
 In class A, a German double-acting machine with compression cylinder 
 9.9 in. bore, 16 in. stroke, tested by Prof. Schroter, the ice-melting capac- 
 ity ranges from 46.29 t9 16.14 Ibs. of ice per pound of coal, according as 
 the suction pressure varies from about 45 to 8 Ibs. above the atmosphere, 
 this pressure being the condition which mainly controls the economy of 
 compression machines. These results are equivalent to realizing from 
 72% to 57% of theoretically perfect performances. The higher per cents 
 appear to occur with the higher suction-pressures, indicating a greater 
 loss from cylinder-heating (a phenomenon the reverse of cylinder conden- 
 
1360 ICE-MAKING OK REFKIGERATING-MACHINES. 
 
 sation in steam-engines), as the range of the temperature of the gas in 
 the compression-cylinder is greater. 
 
 In E, an American single-acting compression-machine, two compression 
 cylinders each 12 X 30 in., operating on the "dry system," tested by 
 Prof. Denton, the percentage of theoretical effect realized ranges from 
 69.5 % to 62.6 % . The friction losses are higher for the American machine. 
 The latter's higher efficiency may be attributed, therefore, to more perfect 
 displacement. 
 
 The largest ' 'ice-melting capacity " in the American machine is 24. IGlbs. 
 
 Actual .Performance of Ice-making Machines. 
 
 
 
 & 
 
 M.S . 
 
 fit G - b 
 
 8 
 
 
 
 
 
 
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 8:3 o>-d 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
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 X a*^ 
 
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 g 
 
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 w 
 
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 tf 
 
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 Q"" 
 
 w 
 
 I * 
 
 A 
 
 i 
 
 135 
 
 55 
 
 72 
 
 27 
 
 43 
 
 37 
 
 44.9 
 
 17.9 
 
 14.4 
 
 26.2 
 
 40.63 
 
 30.8 
 
 19.1 
 
 54.8 
 
 
 2 
 
 131 
 
 42 
 
 70 
 
 14 
 
 28 
 
 23 
 
 45.1 
 
 18.0 
 
 16.7 
 
 19.5 
 
 30.01 
 
 33.5 
 
 20.2 
 
 53.4 
 
 it 
 
 3 
 
 128 
 
 30 
 
 69 
 
 
 14 
 
 9 
 
 45.1 
 
 16.8 
 
 16.0 
 
 13.3 
 
 22.03 
 
 37.1 
 
 25.2 
 
 50.3 
 
 i 
 
 4 
 
 126 
 
 22 
 
 68 
 
 -12 
 
 30 
 
 - 5 
 
 44.8 
 
 15.5 
 
 19.5 
 
 9.0 
 
 16.14 
 
 42.9 
 
 29.1 
 
 44.7 
 
 t 
 
 5 
 
 200 
 
 42 
 
 95 
 
 14 
 
 28 
 
 23 
 
 45.0 
 
 24.1 
 
 10.5 
 
 16.5 
 
 19.07 
 
 36.0 
 
 28.5 
 
 77.0 
 
 
 
 6 
 
 136 
 
 60 
 
 72 
 
 30 
 
 44 
 
 37 
 
 45.2 
 
 17.9 
 
 10.7 
 
 29.8 
 
 46.29 
 
 28.5 
 
 19.9 
 
 56.8 
 
 i 
 
 7 
 
 131 
 
 45 
 
 71 
 
 18 
 
 28 
 
 23 
 
 45.1 
 
 18.0 
 
 12.1 
 
 21.6 
 
 33.23 
 
 31.3 
 
 21.9 
 
 56.4 
 
 * 
 
 8 
 
 126 
 
 24 
 
 68 
 
 - 9 
 
 
 
 - 6 
 
 44.7 
 
 15.6 
 
 18.0 
 
 9.9 
 
 17.55 
 
 41.1 
 
 28.3 
 
 46. J 
 
 < 
 
 9 
 
 117 
 
 41 
 
 64 
 
 13 
 
 28 
 
 23 
 
 45.0 
 
 16.4 
 
 13.5 
 
 20.0 
 
 33.77 
 
 33.1 
 
 22.9 
 
 50.6 
 
 t 
 
 10 
 
 130 
 
 60 
 
 70 
 
 31 
 
 43 
 
 37 
 
 31.7 
 
 12.0 
 
 14.8 
 
 19.5 
 
 45.01 
 
 35.2 
 
 23.8 
 
 52.0 
 
 B 
 
 11 
 
 57 
 
 21 
 
 77 
 
 28 
 
 43 
 
 37 
 
 57.0 
 
 21.5 
 
 22.9 
 
 25.6 
 
 33.07 
 
 39.9 
 
 22.2 
 
 24.1 
 
 
 12 
 
 56 
 
 15 
 
 76 
 
 14 
 
 28 
 
 23 
 
 56.8 
 
 20.6 
 
 22.9 
 
 17.9 
 
 24.11 
 
 41.3 
 
 24.0 
 
 23.1 
 
 ii 
 
 13 
 
 55 
 
 10 
 
 75 
 
 - 2 
 
 14 
 
 9 
 
 57.1 
 
 18.5 
 
 24.0 
 
 11.6 
 
 17.47 
 
 42.2 
 
 25.2 
 
 20.4 
 
 1C 
 
 14 
 
 60 
 
 7 
 
 81 
 
 -16 
 
 
 
 - 6 
 
 57.6 
 
 15.7 
 
 25.7 
 
 5.7 
 
 10.14 
 
 54.5 
 
 38.5 
 
 16.8 
 
 M 
 
 15 
 
 91 
 
 15 
 
 104 
 
 14 
 
 28 
 
 23 
 
 59.3 
 
 27.2 
 
 16.9 
 
 15.7 
 
 16.05 
 
 36.2 
 
 23.1 
 
 31.5 
 
 1C 
 
 16 
 
 61 
 
 22 
 
 81 
 
 31 
 
 44 
 
 37 
 
 57.3 
 
 21.6 
 
 14.0 
 
 28.1 
 
 36.19 
 
 33.4 
 
 22.5 
 
 26.8 
 
 M 
 
 17 
 
 59 
 
 16 
 
 80 
 
 16 
 
 28 
 
 23 
 
 57.5 
 
 20.5 
 
 12.8 
 
 19.3 
 
 26.24 
 
 34.6 
 
 25.0 
 
 25.6 
 
 i 
 
 18 
 
 59 
 
 7 
 
 79 
 
 -16 
 
 
 
 - 6 
 
 57.8 
 
 15.9 
 
 21.1 
 
 6.8 
 
 11.93 
 
 47.5 
 
 33.4 
 
 18.0 
 
 M 
 
 19 
 
 54 
 
 22 
 
 75 
 
 31 
 
 43 
 
 37 
 
 35.3 
 
 12.4 
 
 22.3 
 
 17.0 
 
 38.04 
 
 39.5 
 
 22.6 
 
 22.6 
 
 
 
 20 
 
 89 
 
 16 
 
 103 
 
 16 
 
 28 
 
 23 
 
 42.9 
 
 19.9 
 
 14.7 
 
 11.9 
 
 16.68 
 
 37.7 
 
 27.0 
 
 32.7 
 
 
 
 21 
 
 62 
 
 6 
 
 82 
 
 -17 
 
 
 
 - 5 
 
 34.8 
 
 9.9 
 
 24.3 
 
 3.5 
 
 9.86 
 
 54.2 
 
 39.5 
 
 17.7 
 
 c 
 
 22 
 
 59 
 
 15 
 
 65* 
 
 -53* 
 
 
 
 63.2 
 
 83.2 
 
 21.9 
 
 10.3 
 
 3.42 
 
 71.7 
 
 56.9 
 
 26.6 
 
 D 
 
 23 
 
 175 
 
 54 
 
 81* 
 
 -40* 
 
 
 
 93.4 
 
 38.1 
 
 32.1 
 
 4.9 
 
 3.0 
 
 80.0 
 
 63.0 
 
 89.2 
 
 E 
 
 24 
 
 166 
 
 43 
 
 84 
 
 15 
 
 37' 
 
 "28 
 
 58.1 
 
 85.0 
 
 22.7 
 
 73.9 
 
 24.16 
 
 32.8 
 
 11.7 
 
 65.9 
 
 
 25 
 
 167 
 
 23 
 
 85 
 
 -11 
 
 6 
 
 2 
 
 57.7 
 
 72.6 
 
 18.6 
 
 37.9 
 
 14.52 
 
 37.4 
 
 22.7 
 
 57.6 
 
 
 
 26 
 
 162 
 
 28 
 
 83 
 
 - 3 
 
 14 
 
 2 
 
 57.9 
 
 73.6 
 
 19.3 
 
 46.5 
 
 17,55 
 
 34.9 
 
 18.6 
 
 59.9 
 
 ii 
 
 27 
 
 176 
 
 42 
 
 88 
 
 14 
 
 36 
 
 28 
 
 58.9 
 
 88.6 
 
 19.7 
 
 74.4 
 
 23.31 
 
 30.5 
 
 13.5 
 
 70.5 
 
 F 
 
 28 
 
 152 
 
 40 
 
 79 
 
 13 
 
 21 
 
 16 
 
 
 
 
 4? ?. 
 
 70 1 
 
 47.8 
 
 
 
 * Temperature of air at entrance and exit of expansion-cylinder. 
 
 f On a basis of 3 Ibs. of coal per hour per H.P. of steam-cylinder of 
 compression-machine and an evaporation of 11.1 Ibs. of water per pound 
 of combustible from and at 212 F. in the absorption-machine. 
 
 J Per cent of theoretical with no friction. 
 
 Loss due to heating during aspiration of gas in the compression- 
 cylinder and to radiation and superheating at brine-tank. 
 
 U Actual, including resistance due to inlet and exit valves. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1361 
 
 This corresponds to the highest suction-pressures used in American 
 practice for such refrigeration as is required in beer-storage cellars using 
 the direct-expansion system. The conditions most nearly corresponding 
 to American brewery practice in the German tests are those in line 5, 
 which give an "ice-melting capacity" of 19.07 Ibs. 
 
 For the manufacture of artificial ice, the conditions of practice are those 
 of lines 3 and 4, and lines 25 and 26. In the former the condensing pres- 
 sure used requires more expense for cooling water than is common in 
 American practice. The ice-melting capacity is therefore greater in the 
 German machine, being 22.03 and 16.14 Ibs. against 17.55 and 14.52 for 
 the American apparatus. 
 
 CLASS B. Sulphur Dioxide or Pictet Machines. No records are 
 available for determination of the "ice-melting capacity" of machines 
 using pure sulphur dioxide. In the " Pictet fluid, " a mixture of about 97 % 
 of sulphur dioxide and 3% of carbonic acid, the presence of the carbonic 
 acid affords a temperature about 14 Fahr. degrees lower than is obtained 
 with pure sulphur dioxide at atmospheric pressure. The latent heat of 
 this mixture has never been determined, but is assumed to be equal to 
 that of pure sulphur dioxide. 
 
 For brewery refrigerating conditions, line 17, we have 26.24 Ibs. "ice- 
 melting capacity," and for ice-making conditions, line 13, the "ice- 
 melting capacity" is 17.47 Ibs. These figures are practically as econom- 
 ical as those for ammonia, the per cent of theoretical effect realized 
 ranging from 65.4 to 57.8. At extremely low temperatures, 15 
 Fahr., lines 14 and 18, the per cent realized is as low as 42.5. 
 
 Performance of a 75-ton Ammonia Compression-machine. (J. E. 
 Denton, Trans. A. S. M. E., xii, 326.) The machine had two single- 
 acting compression cylinders 12 X 30 in., and one Corliss steam- 
 cylinder, double-acting, 18 X 36 in. It was rated by the manufac- 
 turers as a 50-ton machine, but it showed 75 tons of ice-refrigerating 
 effect per 24 hours during the test. 
 
 The most probable figures of performance hi eight trials are as follows: 
 
 No. of Trials. 
 
 Ammonia 
 Pressures, 
 Ibs. above 
 Atmosphere. 
 
 Brine 
 Tempera- 
 tures, 
 Degrees F. 
 
 w 
 
 gg.3 
 
 ;p 
 
 '8-c o 
 
 tf V 3 
 
 ft <!>* O 
 
 5^H- 
 
 CM CM U| 
 
 l^ 
 
 . i f*N 
 
 t>> ** 
 fy u, ^> CQ, 
 
 IG33 
 
 O j ^ Cj (_, 
 
 oo 8. 
 qt-i<j>j a 
 
 Water-consump- 
 tion, gals, of 
 Water per min. 
 per ton of Ca- 
 pacity. 
 
 Ratio of Actual 
 Weights of Am- 
 monia circu- 
 lated. 
 
 | 
 
 1 
 
 3 
 
 oS 
 
 & 
 
 Con- 
 densing 
 
 Suc- 
 tion. 
 
 Inlet. 
 
 Outlet. 
 
 8 
 7 
 4 
 6 
 2 
 
 151 
 161 
 147 
 152 
 105 
 135 
 
 28 
 27.5 
 13.0 
 8.2 
 7.6 
 15.7 
 
 36.76 
 36.36 
 14.29 
 6.27 
 
 6.40 
 4.62 
 
 28.86 
 28.45 
 2.29 
 2.03 
 -2.22 
 3.22 
 
 70.3 
 70.1 
 42.0 
 36.43 
 37.20 
 27.2 
 
 22.60 
 22.27 
 16.27 
 14.10 
 17.00 
 13.20 
 
 0.80 
 1.09 
 0.83 
 1.1 
 2.00 
 1.25 
 
 .0 
 .0 
 .70 
 .93 
 .91- 
 2.59 
 
 .C 
 
 .c 
 
 .60 
 .92 
 .88 
 2.57 
 
 The principal results in four tests are given in the table on page 
 1363. The fuel economy under different conditions of operation is 
 shown in the following table: 
 
 Condensing Pres- 
 sure, Ibs. 
 
 Suction-pressure, 
 Ibs. 
 
 Pounds of Ice-melting Effect with 
 Engines 
 
 B.T.U. per Ib. of Steam 
 with Engines 
 
 Non-con- 
 densing. 
 
 Non-com- 
 pound Con- 
 densing. 
 
 Compound 
 Con- 
 densing. 
 
 Non-condens- 
 ing. 
 
 Condensing. 
 
 ll 
 
 65 
 
 fi * 
 
 P-iU 
 
 S 
 g S 
 
 fioQ 
 
 . 
 
 OJ O 
 PnO 
 
 S 
 
 |! 
 
 f^cc 
 
 6j 
 
 JSJQ 
 
 Perlb. 
 Steam. 
 
 150 
 150 
 105 
 105 
 
 28 
 7 
 28 
 
 24 
 14 
 34.5 
 22 
 
 2.90 
 1.69 
 4.16 
 2.65" 
 
 30 
 17.5 
 43 
 27.5 
 
 3.61 
 2.11 
 5.18 
 3.31 
 
 37.5 
 21.5 
 54 
 34.5 
 
 4.51 
 2.58 
 6.50 
 4.16 
 
 393 
 240 
 591 
 376 
 
 513 
 300 
 725 
 470 
 
 640 
 366 
 923 
 591 
 
1362 ICE-MAKING OK KEFR1GERATING-MACHINES. 
 
 The non-condensing engine is assumed to require 25 Ibs. of steam 
 per I.H.P. per hour, the non-compound condensing 20 Ibs., and the 
 compound condensing 16 Ibs., and the boiler efficiency is assumed at 
 8.3 Ibs. of water per Ib. coal under working conditions. The following 
 conclusions were derived from the investigation: 
 
 1. The capacity of the machine is proportional, almost entirely, to the 
 weight of ammonia circulated. This weight depends on the suction- 
 pressure and the displacement of the compressor-pumps. The practical 
 suction-pressures range from 7 Ibs. above the atmosphere, with which a 
 temperature of F. can be produced, to 28 Ibs. above the atmosphere, 
 with which the temperatures of refrigeration are confined to about 28 F. 
 At the lower pressure only about one-half as much weight of ammonia 
 can be circulated as at the upper pressure, the proportion being about in 
 accordance with the ratios of the absolute pressures, 22 and 42 Ibs. 
 respectively. For each cubic foot of piston-displacement per minute a 
 capacity of about one-sixth of a ton of refrigerating effect per 24 hours 
 can be produced at the lower pressure, and of about one-third of a ton at 
 the upper pressure. No other elements practically affect the capacity 
 of a machine, provided the cooling-surface in the brine-tank or other space 
 to be cooled is equal to about 36 sq. ft. per ton of capacity at 28 Ibs. back 
 pressure. For example, a difference of 100% in the rate of circulation of 
 brine, while producing a proportional difference in the range of tempera- 
 ture of the latter, made no practical difference in capacity. 
 
 The brine-tank was 101/2 X 13 X 10 2/3 ft., and contained 8000 lineal 
 feet of 1-in. pipe as cooling-surface. The cqndensing-tank was 12 X10 
 X 10 ft., and contained 5000 lineal feet of 1-in. pipe as cooling-surface. 
 
 2. The economy in coal-consumption depends mainly upon both the 
 suction-pressures and condensing-pressures. Maximum economy with a 
 given type of engine, where water must be bought at average city prices, 
 is obtained at 28 Ibs. suction-pressure and about 150 Ibs. condensiiig- 
 pressure. Under these conditions, for a non-condensing steam-engine 
 consuming coal at the rate of 3 Ibs. per hour per I.H.P. of steam-cylinders, 
 24 Ibs. of ice-refrigerating effect are obtained per Ib. of coal consumed. 
 For the same condensing-pressure, and with 7 Ibs. suction-pressure, which 
 affords temperatures of F., the possible economy falls to about 14 Ibs. of 
 refrigerating effect per Ib. of coal consumed. The condensing-pressure is 
 determined by the amount of condensing-water supplied to liquefy the 
 ammonia in the condenser. If the latter is about 1 gallon per minute 
 per ton of refrigerating effect per 24 hours, a condensing-pressure .of 
 150 Ibs. results, if the initial temperature of the water is about 56 F. 
 Twenty-five per cent less water causes the condensing-pressure to in- 
 crease to 190 Ibs. The work of compression is thereby increased about 
 20%, and the resulting "economy" is reduced to about 18 Ibs. of "ice 
 effect" per Ib. of coal at 28 Ibs. suction-pressure and 11.5 at 7 Ibs. If, on 
 the other hand, the supply of water is made 3 gallons per minute, the 
 condensing-pressure may be confined to about 105 Ibs. The work of 
 compression is thereby reduced about 25%, and a proportional increase 
 of economy results. Minor alterations of economy depend on the initial 
 temperature of the condensing-water and variations of latent heat, but 
 these are confined within about 5% of the gross result, the main element 
 of control being the work of compression, as affected by the back pressure 
 and condensing-pressure, or both. If the steam-engine supplying the 
 motive power may use a condenser to secure a vacuum, an increase of 
 economy of 25% is available over the above figures, making the Ibs. of 
 "ice effect" per Ib. of coal for 150 Ibs. condensing-pressure and 28 Ibs. 
 suction-pressure 30.0, and for 7 Ibs. suction-pressure, 17.5. It is, however, 
 impracticable to use a condenser in cities where water is bought. The 
 latter must be practically free of cost to be available for this purpose. 
 In this case it may be assumed that water will also be available for con- 
 densing the ammonia to obtain as low a condensing-pressure as about 
 100 Ibs., and the economy of the refrigerating-machine becomes, for 
 28 Ibs. back pressure, 43.0 IDS. of " ice-effect " per Ib. of coal, or for 7 Ibs. 
 back pressure 27.5 Ibs. of ice effect per Ib. of coal. If a compound con- 
 densing-engine can be used with a steam-consumption per hour per 
 horse-power of 16 Ibs. of water, the economy of the refrigerating-machine 
 may be 25% higher than the figures last named, making for 28 Ibs. back 
 pressure a refrigerating-effect of 54.0 Ibs. per Ib. of coal, and for 7 Ibs. 
 back pressure a refrigerating effect of 34.0 Ibs. per Ib. of coal. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1363 
 
 Performance of a 75-ton Refrigerating-machine. (Denton.) 
 
 * 
 
 Maximum Capacity and 
 Economy at 28 Ibs. 
 Back Pressure. 
 
 Maximum Capacity and 
 Economy at Zero, 
 Brine, and 8 Ibs. Back 
 Pressure. 
 
 Maximum Capacity and 
 Economy for Zero, 
 Brine, 13 Ibs. Back 
 Pressure. 
 
 Maximum Capacity and 
 Economy at 27.5 Ibs. 
 Back Pressure. 
 
 Av high ammonia press above atmos 
 
 151 Ibs. 
 28 " 
 36.76 
 28.86 
 7.9 
 2281 
 44.65 
 83.66 
 39.01 
 442 
 25 
 24.0 
 *28.17 
 
 *71.3 
 + 14 
 34.2 
 *39 
 213 
 200 
 84.5 
 
 14776 
 2786 
 140 
 17702 
 
 17242 
 6C3 
 182 
 18032 
 330 
 22% 
 58.09 
 32.5 
 65.9 
 85.0 
 65.7 
 23.0 
 
 0.75 
 
 74.8 
 
 24.1 
 $0.166 
 
 $0.128 
 $0.294 
 
 152 Ibs. 
 8.2 " 
 6.27 
 2.03 
 4.24 
 2173 
 56.65 
 85.4 
 28.75 
 315 
 44 
 16.2 
 14.68 
 
 *68 
 -8 
 14.7 
 25 
 263 
 218 
 84.0 
 
 7186 
 2320 
 147 
 9653 
 
 9056 
 712 
 338 
 10106 
 453 
 31% 
 57.7 
 27.17 
 53.3 
 71.7 
 54.7 
 24.0 
 
 1.185 
 36.43 
 
 14.1 
 
 $0.283 
 
 $0.200 
 $0.483 
 
 147 Ibs. 
 13 " 
 14.29 
 2.29 
 12.00 
 943 
 46.9 
 85.46 
 38.56 
 257 
 40 
 16.4 
 16.67 
 
 *63.7 
 -5 
 3.0 
 10.13 
 239 
 209 
 82.5 
 
 8824 
 2518 
 167 
 11409 
 
 9910 
 656 
 250 
 10816 
 407 
 26% 
 57.88 
 27. S3 
 59.86 
 73.6 
 59.37 
 20.0 
 
 0.797 
 
 44 64 
 
 17.27 
 
 $0.231 
 
 $0.136 
 $0.467 
 
 161 Ibs. 
 27.5 " 
 
 "28 '.45 
 7.91 
 2374 
 54.00 
 82.86* 
 28.80 
 601.5 
 14 
 29.1 
 28.32 
 
 76.7 
 14 
 29.2 
 34 
 221 
 168 
 88.0 
 
 14647 
 3020 
 141 
 17708 
 
 17359 
 406 
 252 
 18017 
 309 
 13% 
 58.89 
 32.97 
 70.54 
 88.63 
 71.20 
 19.67 
 
 0.990 
 74.56 
 
 23.37 
 $0.170 
 
 $0.169 
 $0.339 
 
 Av. back ammonia press, above atmos 
 Av. temperature brine inlet 
 Av temperature brine outlet 
 
 Av range of temperature 
 
 Lbs. of brine. circulated per minute 
 AV temp condensing-water at inlet 
 
 Av temp conderising-water at outlet .... 
 
 Av range of temperature . 
 
 Lbs. water circulated p. min. thro' cond'ser 
 ijbs water per min through jackets 
 
 
 Lbs ammonia circulated per min 
 
 Probable temperature of liquid ammonia, 
 entrance to brine-tank 
 
 Temp, of amm. corresp. to av. back press. 
 Av. temperature of gas leaving brine- tanks 
 Temperature of gas entering compressor 
 Av. temperature of gas leaving compressor 
 
 Temperature due to condensing pressure. . . 
 Heat given ammonia: 
 
 By compressor B T U per minute 
 
 By atmosphere B T U per minute .... 
 
 Total heat rec. by amm., B.T.U. per min.... 
 Heat taken from ammonia: 
 
 By jackets, B.T.U. per min 
 
 By atmosphere B.TU. per min 
 
 Total heat rej. by amm., B.T.U. per min 
 Dif . of heat rec'd and rej., B.T.U. per min.. . 
 % work of compression removed by jackets 
 Av. revolutions per min. .. 
 
 Mean eff. press, steam-cyl., Ibs. per sq. in.. . 
 Mean eff. press, amm.-cyl., Ibs. per sq. in. . . 
 Av. H.P. steam-cylinder 
 
 Av. H.P. ammonia-cylinder 
 
 Friction in per cent of steam H.P 
 
 Total cooling water, gallons per min. per 
 ton per 24 hours 
 
 Tons ice-melting capacity per 24 hours 
 Lbs. ice-refrigerating eff. per Ib. coal at 3 
 Ibs. per H.P. per hour. . . . 
 
 Cost coal per ton of ice-refrigerating effect 
 at $4 per ton 
 
 Cost water per ton of ice- refrigerating effect 
 atSlperlOOOcu.ft 
 
 Total cost of 1 ton of ice-refrigerating eff. . . 
 
 Figures marked thus (*) are obtained by calculation; all other figures 
 Obtained from experimental data; temperatures in Fahrenheit are degree* 
 
1364 ICE-MAKING OR REFRIGERATING-MACHINES. 
 
 Ammonia Compression-machine. 
 
 ACTUAL RESULTS OBTAINED AT THE MUNICH TESTS. 
 (Prof. Linde, Trans. A. S. M. E., xiv, 1419.) 
 
 No. of Test 
 
 1 1 2 | 3 
 
 4 
 
 5 
 
 Temp, of refrig- ) Inlet, deg. F ... . 
 crated brine J Outlet, deg. F... 
 Specific heat of brine 
 
 43.194 
 37.054 
 0.861 
 1,039.38 
 .342,909 
 * 338. 76 
 15.80 
 24,813 
 21,703 
 1,100.8 
 
 28.344 
 22.885 
 0.851 
 908.84 
 263,950 
 260.83 
 16.47 
 18,471 
 16,026 
 785.6 
 
 13.952 
 
 8.771 
 0.843 
 633.89 
 172,776 
 187.506 
 15.28 
 12,770 
 11,307 
 564.9 
 
 -0.279 
 -5.879 
 0.837 
 414.98 
 121,474 
 139.99 
 14.24 
 10,140 
 8,530 
 435.82 
 
 28.251 
 23.072 
 0.851 
 800.93 
 220,284 
 97.76 
 21.61 
 11,151 
 10,194 
 512.12 
 
 Brine circ per hour cu ft 
 
 Cold produced, B.T.U. per hour. . ^ 
 Cooling water per hour, cu. ft . 
 I.H.P. in steam-engine cylinder. . . 
 Cold pro- ) Per I.H.P. in comp.-cyl 
 duced per > Per I.H.P. in steam-cyl 
 h.,B.T.U. ) Per Ib. of steam. . . 
 
 
 A test of a 35-ton absorption-machine in New Haven, Conn., by Prof. 
 Denton (Trans. A. S. M. E., x, 792), gave an ice-melting effect of 20.1 
 Ibs. per Ib. of coal on a basis of boiler economy equivalent to 3 Ibs. of 
 
 steam per I.H.P. in a good non-condensing steam-engine. The ammonia 
 was worked between 138 and 23 Ibs. pressure above the atmosphere. 
 
 Performance of a Single-acting Ammonia Compressor. Tests 
 were made at the works of the Eastman Kodak Co., Rochester, N.Y., of 
 a machine fitted with two York Mfg. Co.'s single-acting compressors, 
 15 in. diam., 22 in. stroke, to determine the horse-power per ton of 
 refrigeration. Following are. the principal average results (Bulletin 
 of York Mfg. Co.): 
 
 Date of Test, 1908 
 
 Mar. CJMar. 7 
 
 Mar. 8 
 
 Mar. 9 
 
 Mar. 
 10. 
 
 Mar. 
 11. 
 
 Mar. 
 14. 
 
 
 Temp, dischg. gas, av 
 Temp, suction gas, av . . . . 
 Temp, suction at cooler. . 
 Temp, liquid at exp. valve 
 Temp, brine inlet 
 
 216.2 
 15.2 
 9.33 
 74.85 
 22.89 
 13.58 
 45.1 
 20.76 
 20.11 
 183.96 
 69.35 
 49.08 
 1.418 
 
 217.8 
 14.3 
 9.36 
 74.16 
 23.19 
 13.96 
 45.0 
 20.43 
 19.90 
 184.41 
 69.80 
 48.79 
 1.427 
 
 250.6 
 16.8 
 10.37 
 71.98 
 25.26 
 14.44 
 45.1 
 21.04 
 19.97 
 186.99 
 70.05 
 50.38 
 1.389 
 
 245.8 
 14.8 
 9.29 
 77.91 
 22.73 
 13.02 
 34.3 
 15.59 
 20.04 
 187.27 
 52.57 
 37.01 
 1.422 
 
 253.0 
 13.5 
 9.90 
 76.61 
 27.35 
 15.53 
 56.0 
 25.99 
 20.18 
 187.90 
 89.48 
 61.39 
 1.425 
 
 242.9 
 18.2 
 13.20 
 82.88 
 28.41 
 16.06 
 67.8 
 
 255.5 
 17.9 
 9.13 
 
 76.98 
 23.43 
 12.87 
 44.8 
 20.40 
 20.38 
 183.81 
 68.61 
 49.31 
 1.375 
 
 Temp, brine, outlet 
 Revs per min 
 
 Lbs. liquid NHs per min. . 
 Sue. press, at mach. Ib. . . 
 Condenser pressure 
 
 18.13 
 186.8 
 105.11 
 66.65 
 1,439 
 
 Indicated H.P 
 
 Tons Refrig. Capy, 24 hrs. 
 I.H.P. per ton capacity . . 
 
 Full details of these tests were reported to the Am. Socy. of Refrig. 
 Engrs. and published in Ice and Refrigeration, 1908. 
 
 Performance of Absorption Machines. From an elaborate review 
 by Mr. Voorhees of the action of an absorption machine under certain 
 stated conditions, showing the quantity of ammonia circulated per hour 
 per ton of refrigeration, its temperature, etc., at the several stages of 
 the operation, and its course through the several parts of the apparatus, 
 the following condensed statement is obtained: 
 
 Generator. 30.9 Ibs. dry steam, 38 Ibs. gauge pressure condensed, 
 evaporates 32.2% strong liquor to 22.3% weak liquor. 
 
 Exchanger. 3.01 Ibs. weak liquor at 264 cools to 111. 
 
 Absorber. Adds 0.43 Ibs. vapor from the brine cooler, making 3.44 
 Ibs. strong liquor at 111 to go to the rnnn>. 
 
 Exchanger. 3.44 Ibs. heated to 224, some of it is now gas, and the 
 rest liquor of a little less than 32% NH 3 . 
 
 Analyzer. (A series of shelves in a tank above the generator) delivers 
 strong liquor to the generator, while the vapor, 91 % NH 3 , 0.4982 Ib., goes 
 to the rectifier. 
 
 Rectifier. Cools the gas to 110 separating water vapor as 0.0682 Ib. 
 drip liquor which returns through a trap to the. generator. 
 
 Condenser. 0.43 Ib. NHs gas at 110 cooled and condensed to liquid 
 at 90 by 2 gals, of water per min. heated from 73 to 86. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1365 
 
 Expansion Valve and Cooler. Reduces liquid to and boils it at 0, 
 cooling 3 gals, of brine per min. from 12 to 3. Gas passes to absorber 
 and the cycle is repeated. 
 
 Of the 2 gals, per min. of cooling water flowing from the condenser, 
 0.2 gal. goes to the rectifier, where it is heated to 142, and 1.8 gal. through 
 the absorber, where it is heated to 110. 
 
 Heat Balance. Absorbed in the generator 496; in the brine cooler, 
 200, Total 696 B.T.U. Rejected; condenser, 220; absorber, 383; rectifier, 
 93; Total 696 B.T.U. 
 
 The following table shows the strength of the liquors and the quantity 
 of steam required per hour per ton of refrigeration under the conditions 
 stated: v 
 
 Condenser Pressures. 
 
 
 140 
 
 170 
 
 200 
 
 Suction Pressures. 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 SI per cent . . . 
 
 24 
 13.13 
 30.1 
 1.7 
 
 35 
 25.75 
 27.9 
 1.6 
 
 42 
 33.70 
 22.9 
 1.4 
 
 22 
 10.85 
 41.3 
 2.1 
 
 32 
 22.3 
 30.9 
 1.9 
 
 38 
 29.15 
 26.2 
 1.8 
 
 18 
 6.28 
 48.7 
 2.4 
 
 28 
 17.7 
 34.1 
 2.3 
 
 36 
 26.9 
 27.9 
 2.2 
 
 Wl per cent 
 SG, pounds 
 
 SL, pounds 
 
 SI, strong liquor; Wl, weak liquor; SG, Ibs. of steam per hour per ton 
 of refrigeration for the generator, SL, do. for the liquor pump. Pressures 
 are in Ibs. per sq. in., gauge. 
 
 The following table gives the steam consumption in Ibs. per hour per 
 ton of refrigeration, for engine-driven compressors and for absorption 
 machines with liquor pump not exhausting into the generator at the suc- 
 tion and condenser pressures (gauge) given: SC, simple non-condensing 
 engine, CC. compound condensing engine, A, absorption machine. 
 
 Condenser Pressures. 
 
 140 
 
 170 
 
 200 
 
 
 Suction Pressures. 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 sc 
 
 78.3 
 42.0 
 31.8 
 
 44.5 
 23.8 
 29.5 
 
 31.1 
 16.6 
 24.3 
 
 90.5 
 48.4 
 43.4 
 
 52.5 
 
 28.0 
 32.8 
 
 37.2 
 19.0 
 28.0 
 
 104.0 
 55.6 
 51.1 
 
 61.4 
 32.7 
 36.4 
 
 44.5 
 23.9 
 30.1 
 
 cc 
 
 A 
 
 The economy of the absorption machine is much better for all condi- 
 tions than that of a simple non-condensing engine-driven compressor. 
 At suction gauge pressures above 8 to 10 Ibs. the economy of the com- 
 pound condensing engine-driven compressor exceeds that of the absorp- 
 tion machine, the absorption machine giving the superior economy at 
 suction pressures below 8 to 10 Ibs. 
 
 Means for Applying the Cold. (M. C. Bannister, Liverpool Eng'g 
 Soc'y, 1890.) The most useful means for applying the cold to vari9us 
 uses is a saturated solution of brine or chloride of magnesium, which 
 remains liquid at 5 Fahr. The brine is first cooled by being circulated 
 in contact with the refrigerator-tubes, and then distributed through 
 coils of pipes, arranged either in the substances requiring a reduction of 
 temperature, or in the cold stores or rooms prepared for them; the air 
 coming in contact with the cold tubes is immediately chilled, and the 
 moisture in the air deposited on the pipes. It then falls, making room 
 for warmer air, and so circulates until the whole room is at the tempera- 
 ture of the brine in the pipes. 
 
 The Direct Expansion Method consists in cpnveying the compressed 
 cooled ammonia (or other refrigerating agent) directly to the room to be 
 cooled, and then expanding it through an expansion cock into pipes in the 
 room. Advantages of this system are its simplicity and its rapidity of 
 
1366 ICE-MAKING OR REFBIGERATING-MACHINES. 
 
 action in cooling a room; disadvantages are the danger of leakage of the 
 gas and the fact that the machine cannot be stopped without a rapid rise 
 in the temperature of the room. With the brine system, with a large 
 amount of cold brine in the tank, the machine may be stopped for a con- 
 siderable time without serious cooling of the. room. 
 
 Air has also been used as the circulating medium. The ammonia-pipes 
 refrigerate the air in a cooling-chamber, and large conduits are used to 
 convey it to and return it from the rooms to be cooled. An advantage of 
 this system is that by it a room may be refrigerated more quickly than by 
 brine-coils. The returning air deposits its moisture on the ammonia- 
 pipes, in the form of snow, which is removed by mechanical brushes. 
 
 ' ARTIFICIAL-ICE MANUFACTURE. 
 
 Under summer conditions, with condensing water at 70, artificial-ice 
 machines use ammonia at a condenser pressure, about 190 Ibs. above the 
 atmosphere and 15 Ibs. suction-pressure. 
 
 In a compression type of machine the useful circulation of ammonia, 
 allowing for the effect of cylinder-heating, is about 13 Ibs. per hour per 
 indicated horse-power of the steam-cylinder. This weight of ammonia 
 produces about 32 Ibs. of ice at 15 from water at 70. If the ice is made 
 from distilled water, as in the "can system," the amount of the latter 
 supplied by the boilers is about 33% greater than the weight of ice 
 obtained. This excess represents steam escaping to the atmosphere 
 from the re-boiler and steam-condenser, to purify the distilled water, or 
 free it from air; also, the loss through leaks and drips, and loss by melting 
 of the ice in extracting it from the cans. The total steam consumed per 
 horse-power is, therefore, about 32 x 1.33 = 43.0 Ibs. About 7.0 Ibs. 
 of this covers the steam-consumption of the steam-engines driving the 
 
 the required amount of distilled water. There is, therefore, nothing to be 
 gained by using steam at high rates of expansion in the steam-engines, in 
 making artificial ice from distilled water. If the cooling water for the 
 ammonia-coils and steam-condenser is not too hard for use in the boilers, 
 it may enter the latter at about 175 F., by restricting the quantity to 
 11/2 gallons per minute per ton of ice. With good coal 8V2 Ibs. of feed- 
 water may then be evaporated, on the average, per Ib. of coal. 
 
 The ice made per pound of coal will then be 32 ~ (43.0 ~- 8.5) = 6.0 
 Ibs. This corresponds with the results of average practice. 
 
 If ice is manufactured by the "plate system," no distilled water is 
 used for freezing. Hence the water evaporated by the boiler may be 
 reduced to the amount which will drive the steam-motors, and the latter 
 may use steam expansively to any extent consistent with the powei 
 required to compress the ammonia, operate the feed and filter pumps, 
 and the hoisting machinery. The latter may require about 15% of the 
 power needed for compressing the ammonia. 
 
 If a compound condensing steam-engine is used for driving the com- 
 pressors, the steam per indicated steam horse-power, or per 32 Ibs. of 
 net ice, may be 14 IDS. per hour. The other motors at 50 Ibs. of steam 
 per horse-power will use 7.5 Ibs. per hour, marking the total consumption 
 per steam horse-power of the compressor 21.5 Ibs. Taking the evapora- 
 tion at 8 Ibs., the feed-water temperature being limited to about 110, the 
 coal per horse-power is 2.7 Ibs. per hour. The net ice per Ib. of coal is 
 then about 32 -i- 2.7 =11.8 Ibs. The best results with "plate-system" 
 plants, using a compound steam-engine, have thus far afforded about 10V2 
 Ibs. of ice per Ib. of coal. 
 
 In the "plate system" the ice gradually forms, in from 8 to 10 days, to 
 a thickness of about 14 inches, on the hollow plates, 10 x 14 feet in area, in 
 which the cooling fluid circulates. 
 
 In the "can system" the water is frozen in blocks weighing about 
 300 Ibs. each, and the freezing is completed in from 40 to 48 hours. The 
 freezing-tank area occupied by the "plate system" is, therefore, about 
 twelve times, and the cubic contents about four times, as much as required 
 in the "can system." 
 
 The investment for the "plate" is about one-third greater than for the 
 "can' ! system. In the latter system ice is being drawn throughout the 
 
ARTIFICIAL-ICE MANUFACTURE. 1367 
 
 24 hours, and the hoisting is done by hand tackle. Some "can" plants 
 are equipped with pneumatic hoists and on large hoists electric cranes are 
 used to advantage. In the "plate system" the entire daily product is 
 drawn, cut, and stored in a few hours, the hoisting being performed 
 by power. The distribution of cost is as follows for the two systems, tak- 
 ing the cost for the "can" or distilled-water system as 100, which repre- 
 sents an actual cost of about $1.25 per net ton: 
 
 Can System. Plate System. 
 
 Hoisting and storing ice 14.2 2.8 
 
 Engineers, firemen, and coal-passer 15.0 13.9 
 
 Coal at $3.50 per gross ton 42 .2 20 .0 
 
 Water pumped directly from a natural source 
 
 at 5 cts. per 1000 cubic feet 1.3 2.6 
 
 Interest and depreciation at 10% 24 .6 32 .7 
 
 Repairs 2.7 3.4 
 
 100.00 75.4 
 
 A compound condensing engine is assumed to be used by the "plate 
 system." 
 
 Test of the New York Hygeia Ice-making Plant. (By Messrs. 
 Hupfel, Griswold, and Mackenzie; Stevens Indicator, Jan., 1894.) 
 
 The final results of the tests were as follows: 
 
 Net ice made per pound of coal, in pounds 7.12 
 
 Pounds of net ice per hour per horse-power 37 .8 
 
 Net ice manufactured per day (12 hours) in tons 07 
 
 Av. pressure of ammonia-gas at condenser, Ibs. per sq. in. above 
 
 atmos 135 .2 
 
 Average back pressure of amm.-gas, Ibs. per sq. in. above atmos. 15.8 
 
 Average temperature of brine in freezing-tanks, degrees F 19 .7 
 
 Total number of cans filled per week 4389 
 
 Ratio of cooling-surface of coils in brine-tank to can-surface 7 to 10 
 
 An Absorption Evaporator Ice-making System, built by the Carbon- 
 dale Machine Co. is in operation at the ice plant of the Richmond Ice Co., 
 Clifton, Staten Island, N. Y., which produces the extra distilled water by 
 an evaporator at practically no fuel cost, and thus about 10 tons of dis- 
 tilled water ice per ton of coal is obtained. Steam from the boiler at 
 100 Ibs. pressure enters an evaporator, distilling off steam at 70 Ibs., 
 which operates the pumps and auxiliary machinery. These exhaust 
 into the ice machine generator under 10 Ibs. pressure, where the exhaust 
 is condensed. In a 100-ton plant the evaporator will condense 43 tons 
 of live steam, distilling off 40 tons of steam to operate the auxiliaries, 
 which exhaust into the generator; 20 tons of live steam has to be added 
 to this exhaust, making 60 tons in all, which is the amount required to 
 operate the generator. The 60 tons of condensation from the generator 
 and 43 tons from the evaporator go to the re-boiler, making 103 tons ol 
 distilled water to be frozen into ice. The total steam consumption is the 
 60 tons condensed in the generator plus 3 tons for radiation, or 63 tons 
 in all. Hence if the boiler evaporates 6.6 Ibs. water per pound of coal 
 the economy of the plant will be 10 1/2 Ibs. ice per pound of coal, a result 
 which cannot be obtained even with compound condensing engines and 
 compression machines. 
 
 Heat-excnangmg coils, on the order of a closed feed-water heater, are 
 used to heat the feed-water going to the boiler. The condensation leav- 
 ing the generator and evaporator at a high temperature is utilized for 
 this purpose; by this means securing a feed-water temperature con- 
 siderably in excess of 212. 
 
 Ice-Making with Exhaust Steam. The exhaust steam from electric 
 light plants is oeing utilized to manufacture ice on the absorption system. 
 A 10-ton plant at the Holdredge Lighting Co., Holdredge, Neb., built by 
 the Carbondale Machine Co., is described in Elec. World, April 7, 1910. 
 Here 11 tons of ice were made per day with exhaust steam from the 
 electric engines at 21/2 Ibs. pressure, using 6V3 K.W., or 8V2 H.P., for 
 driving the circulating pumps. 
 
 Tons of Ice per Ton of Coal. From a long table by Mr. Voorhees, 
 showing the net tons of plate ice that may be made in. well-designed 
 plants under a variety of conditions as to type of engine, the following 
 figures are taken: 
 
1368 
 
 MARINE ENGINEERING. 
 
 Compression, Simple Corliss engine, non-condensing 6.1 tons 
 
 Absorption liquor pump and auxiliaries not exhausting into 
 
 generator, simple, non-condensing engine 10.0 
 
 Compression, C9mpound condensing engine 11.2 
 
 Compression triple-expansion condensing engine 12.8 
 
 Absorption, pump and auxiliaries exhausting into generator, 
 
 Corliss non-condensing engine 13.3 
 
 Compression and absorption, compound engine, non-condensing 16.0 
 
 Compression, triple-expansion condensing engine, multiple effect 16.5 
 Compression and absorption, triple-expansion non-condensing 
 
 engine, multiple effect 19.5 
 
 Standard Ice Cans or Moulds. 
 
 (Buffalo Refrigerating Machine Co.) 
 
 Weight of 
 Block. 
 
 Size of Can. 
 
 Time of 
 Freezing. 
 
 Weight of 
 Block. 
 
 Size of Can. 
 
 Time of 
 Freezing. 
 
 pounds 
 
 50 
 100 
 150 
 150 
 200 
 
 4x10x24 
 6x12x26 
 8x15x32 
 8x15x44 
 10x15x36 
 10x20x36 
 
 hours 
 12 
 20 
 36 
 36 
 48 
 48 
 
 pounds 
 100 
 200 
 300 
 400 
 200 
 
 11x11x32 
 11x22x32 
 11x22x44 
 11x22x56 
 14X14X40 
 
 hours 
 48 
 54 
 54 
 54 
 66 
 
 The above given time of freezing is with a brine temperature of 15 F. 
 
 Cubic Feet of Well-insulated Space per Ton of Refrigeration. 
 
 (F. W. Niebling Co., Cincinnati, *O.) 
 
 Room Temperature. 
 
 0F. 
 
 10 
 
 20 
 
 32 
 
 36 
 
 Size of Room. 
 
 Cubic Feet per Ton. 
 
 Up to 1,000 cu. ft 
 
 200 
 600 
 1000 
 
 400 
 1200 
 2000 
 
 800 
 2500 
 4000 
 
 1400 
 4500 
 6000 
 
 2000 
 6000 
 8000 
 
 2500 
 8000 
 10.000 
 
 1,000 to 10,000 cu. ft 
 Over 10,000 cu. ft 
 
 MARINE ENGINEERING-. 
 
 Rules for Measuring Dimensions and Obtaining Tonnage t>f 
 Vessels. (Record of American and Foreign Shipping. American Bureau 
 of Shipping, N. Y., 1890.) The dimensions to be measured as follows; 
 
 I. Length, L. From the fore-side of stem to the after-side of stern- 
 post measured at middle line, on the upper deck of all vessels, except 
 those having a continuous hurricane-deck extending right fore and aft, 
 in which the length is to be measured on the range of deck immediately 
 below the hurricane-deck. 
 
 Vessels having clipper heads, raking forward, or receding stems, or 
 raking stern-posts, the length to be the distance of the fore-side of stem 
 from aft-side of stern-post at the deep-load water-line measured at middle 
 line. (The inner or propeller-post to be taken as stern-post in screw- 
 steamers.) 
 
 II. Breadth, B. To be measured over the widest frame at its widest 
 part; in other words, the molded breadth. 
 
 III. Depth, D. To be measured at the dead-flat frame and at middle 
 line of yessel. It shall be the distance from the top of floor-plate to the 
 upper side of upper deck-beam in all vessels except those having a con- 
 tinuous hurricane-deck, extending right fore and aft, and not intended 
 for the American coasting trade, in which the depth is to be the distance 
 from top of floor-plate to ^midway between top of hurricane deck-beam 
 and the top of deck-beam of the deck immediately below hurricane-deck. 
 
 In vessels fitted with a continuous hurricane-deck, extending right 
 fore and aft, and intended for the American coasting trade, the depth is 
 
MAKINE ENGINEERING. 1369 
 
 to be the distance from top of floor-plate to top of deck-beam of deck 
 immediately below hurricane-deck. 
 
 Rule for Obtaining Tonnage. Multiply together the length, breadth, 
 and depth, and their product by 0.75; divide the last product by 100; 
 the quotient will be the tonnage. L X B X D X 0.75-7-100 = tonnage. 
 
 The U. S. Custom-house Tonnage Law, May 6, 1864, provides that 
 " the register tonnage of a vessel shall be her entire internal cubic capacity 
 in tons of 100 cubic feet each." This measurement includes all the space 
 between upper decks, however many there may be. Explicit directions 
 for making the measurements are given in the law. 
 
 The Displacement of a Vessel (measured in tons of 2240 Ibs.) is 
 the weight of the volume of water which it displaces. For sea-water it is 
 equal to the volume of the vessel beneath the water-line, in cubic feet, 
 divided by 35, which figure is the number of cubic feet of sea-water at 
 60 F. in a ton of 2240 Ibs. For fresh water the divisor is 35.93. The 
 U. S. register tonnage will equal the displacement when the entire internal 
 cubic capacity bears to the displacement the ratio of 100 to 35. 
 
 The displacement or gross tonnage is sometimes approximately esti- 
 mated as follows: Let L denote the length in feet of the boat, B its extreme 
 breadth in feet, and D the mean draught in feet; the product of these 
 three dimensions will give the volume of a parallelopipedon in cubic feet. 
 Putting V for this volume, we have V = L X B X D. 
 
 The volume of displacement may then be expressed as a percentage 
 of the volume V, known as the " block coefficient. " This percentage varies 
 far different classes of ships. In racing yachts with very deep keels it 
 varies from 22 to 33: in modern merchantmen from 55 to 90; for ordinary 
 small boats probably 50 will give a fair estimate. The volume of dis- 
 placement in cubic feet divided by 35 gives the displacement in tons. 
 
 Coefficient of Fineness. A term used to express the relation between 
 the displacement of a Ship and the volume of a rectangular prism or box. 
 whose lineal dimensions are the length, breadth, 'and draught. 
 
 Coefficient of fineness = D X 35-J-(L X B X T7); D being the displace- 
 ment in tons of 35 cubic feet of sea-water to the ton, L the length between 
 perpendiculars, B the extreme breadth and W the mean draught, all in feet. 
 
 Coefficient of Water-lines. An expression of the relation of the dis- 
 placement to the volume of the prism whose section equals the midship 
 section of the ship, and length equal to the length of the ship. 
 
 Coefficient of water-lines = D X 35 * (area of immersed water sectionX-L). 
 Seaton gives the following values: 
 
 Coefficient Coefficient of 
 of Fineness. Water-lines 
 
 Finely-shaped ships .55 .63 
 
 Fairly-shaped ships 0.61 0.67 
 
 Ordinary merchant steamers 10 to 11 knots. . . .65 . 72 
 
 Cargo steamers, 9 to 10 knots % .70 .76 
 
 Modern cargo steamers of large size .78 .83 
 
 Resistance of Ships. The resistance of a ship passing through watei 
 mav vary from a number of causes, as speed, form of body, displacement, 
 midship dimensions, character of wetted surface, fineness of lines, etc. 
 The resistance of the water is twofold; 1st. That due to the displacement 
 of the water at the bow and -its replacement at the stern, with the con- 
 sequent formation of waves. 2d. The friction between the wetted sur- 
 face of the ship and the water, known as skin resistance. A common 
 approximate formula for resistance of vessels is 
 Resistance = speech x x/displacementsxa constant, or R = S*D 2 h X C. 
 
 \f D l = displacement in pounds, Si = speed in feet per minute, R re- 
 sistance in pounds, R = cS^Di 2 /3. The work done in overcoming the re- 
 sistance through a distance equal to Si is R X Si = cS^Di 2 ^; and if E is 
 the efficiency of the propeller and machinery combined, the indicated 
 horse-power I.H.P. = cS^D^h ~ (E X 33,000). 
 
 If S = speed in knots, D = displacement in tons, and C a constant 
 which includes all the constants for form of vessel, efficiency of mechan- 
 ism, etc., I.H.P. = SW 2 /3 + C. 
 
 The wetted surface varies as the cube root of the square of the displace- 
 ment: thus, let L be the length of edge of a cube just immersed, whose 
 
1370 
 
 MARINE ENGINEERING. 
 
 displacement is D and wetted surface W. Then D = L 3 or L =^D t 
 and TF = 5X L* = 5 X (-\/D) 2 . That is, TF varies as Z) 2 ' 3 . 
 
 Another approximate formula is 
 
 I.H.P. = area of immersed midship section X 3 -~ K. 
 
 The usefulness of these two formulae depends upon the accuracy of the 
 so-called "constants" C and K, which vary with the size and form of the 
 ship, and probably also with the speed. Seaton gives the following, 
 which may be taken roughly as the values of C and K under the condi- 
 tions expressed: 
 
 General Description of Ship. 
 
 Speed, 
 knots. 
 
 Value 
 of C. 
 
 Value 
 of K. 
 
 Ship"} over 400 feet long finely shaped 
 
 15 to 
 15 " 
 13 " 
 11 
 11 
 9 
 13 
 11 
 9 
 11 
 9 
 11 
 9 
 9 
 11 
 10 
 9 
 9 
 
 17 
 17 
 15 
 13 
 13 
 11 
 15 
 13 
 11 
 13 
 11 
 12 
 11 
 11 
 12 
 11 
 10 
 10 
 
 240 
 190 
 240 
 260 
 240 
 260 
 200 
 240 
 260 
 220 
 250 
 220 
 240 
 220 
 200 
 210 
 230 
 200 
 
 620 
 500 
 650 
 700 
 650 
 700 
 580 
 660 
 700 
 620 
 680 
 600 
 640 
 620 
 550 
 580 
 620 
 600 
 
 " 300 " .... 
 
 
 14 4 It 
 
 Snips over 300 feet long fairly shaped 
 
 
 Ships over 250 feet long finely shaped 
 
 
 4< 41 II 
 
 Ships over 250 feet long fairly shaped 
 
 
 Ships over 200 feet long, finely shaped . . 
 
 
 Ships over 200 feet long, fairly shaped 
 
 Ships under 200 feet long, finely shaped 
 
 
 41 ' II 
 
 Ships under 200 feet long, fairly shaped 
 
 Coefficient of Performance of Vessels. The quotient 
 
 ^(displacement) 2 X (speed in knots)^- tons of coal in 24 hours 
 
 gives a coefficient of performance which represents the comparative cost 
 of propulsion in coal expended. Sixteen vessels with three-stage expan- 
 sion-engines in 1890 gave an average coefficient of 14,810, the range being 
 from 12,150 to 16,700. 
 
 In 1881 seventeen vessels with two-stage expansion-engines gave an 
 average coefficient of 11,710. In 1881 the length of the vessels tested 
 ranged from 260 to 320, and in 1890 from 295 to 400. The speed in knots 
 divided by the square root of the length in feet in 1881 averaged 0.539; 
 and in 1890, 0.579; ranging from 0.520 to 0.641. (Proc. Inst. M. E. t 
 July, 1891, p. 329.) 
 
 Defects of the Common Formula for Resistance. Modern 
 experiments throw doubt upon the truth of the statement that the resist- 
 ance varies as the square of the speed. (See Robt. Hansel's letters in 
 Engineering, 1891; also his paper on The Mechanical Theory of Steam- 
 ship Propulsion, read before Section G of the Engineering Congress, 
 Chicago, 1893.) 
 
 Seaton says: In small steamers the chief resistance is the skin resistance. 
 In very fine steamers at high speeds the amount of power required seems 
 excessive when compared with that of ordinary steam&s at ordinary 
 speeds. 
 
 In torpedo-launches at certain high speeds the resistance increases at a 
 lower rate than the square of the speed. 
 
 In ordinary sea-going and river steamers the reverse seems to be the 
 case. 
 
 Rankine's Formula for total resistance of vessels of the "wave-lino" 
 type is: 
 
 R = ALBV* (1 + 4 sin2 9 + sin4 0), 
 
 in which equation 9 is the mean angle of greatest obliquity of the stream- 
 lines, A is a constant multiplier, B the mean wetted girth of the surface 
 exposed to friction, L the length in feet, and V the speed in knots. The 
 
MARINE ENGINEERING. 1371 
 
 power demanded to impel a ship is thus the product of a constant to be 
 determined by experiment, the area of the wetted surface, the cube ol 
 the speed, and the quantity in the parenthesis, which is known as the 
 " coefficient of augmentation. " In calculating the resistance of ships the 
 last term of the coefficient may be neglected as too small to be practically 
 \mportant. In applying the formula, the mean of the squares of the 
 sines of the angles of maximum obliquity of the water-lines is to be taken 
 for sin 2 8, and the rule will then read thus: 
 
 To obtain the resistance of a ship of good form, in pounds, multiply the 
 length in feet by the mean immersed girth and by the coefficient of aug- 
 mentation, and then take the product of this "augmented surface," as 
 Rankine termed it, by the square of the speed in knots, and by the proper 
 constant coefficient selected from the following: 
 
 For clean painted vessels, iron hulls A = 0.01 
 
 For clean coppered vessels A = 0.009 to 0.008 
 
 For moderately rough iron vessels A = 0.011 + 
 
 The net, or effective, horse-power demanded will be quite closely 
 obtained by multiplying the resistance calculated, as above, by the speed 
 in knots and dividing by 326. The gross, or indicated, power is obtained 
 by multiplying the last quantity by the reciprocal of the efficiency of the 
 machinery and propeller, which usually should be about 0.6. Rankine 
 uses as a divisor in this case 200 to 260. 
 
 The form of the vessel, even when designed by skillful and experienced 
 naval architects, will of ten vary to such an extent as to cause the above 
 constant coefficients to vary somewhat: and the range of variation with 
 good forms is found to be from 0.8 to 1.5 the figures given. 
 
 For well-shaped iron vessels, an approximate formula for the horse- 
 power required is H. P. = F 3 ~- 20,000, in which S is the "augmented 
 surface." The expression SV 3 -f- H.P. has been called by Rankine the 
 coefficient of propulsion. In the Hudson River steamer "Mary Powell," 
 according to Thurston, this coefficient was as high as 23,500. 
 
 The expression DF* *- H.P. has been called the locomotive performance. 
 (See Rankine's Treatise on Shipbuilding, 1864; Thurston's Manual of the 
 Steam-engine, part H, p. 16; also paper by F. T. Bowles, U. S. N., Proc. 
 IT. S. Naval Institute, 1883.) 
 
 Rankine's metnod for calculating the resistance is said by Seaton to 
 give more accurate and reliable results than those obtained by the older 
 rules, but it is criticised as being difficult and inconvenient of application 
 
 Empirical Equations for Wetted Surface. (Peabody, Naval Archi- 
 tecture, page 411). L = length, feet; B = beam; H = mean draught; 
 D = displacement in tons; K= block coefficient. 
 
 Taylor Surface = C\/T>L. Values of C for different ratios B -i- H are: 
 
 B -f- H = 2 2.2 2.4 2.6 2.8 3.0 3.2 3.4 
 
 C =15.63 15.54 15.50 15.51 15.55 15.62 15.71 15.83 
 
 Normand Surface = 1.52 LH + (3.74 + 0.85 K*) LB. 
 Mumford Surface = L (1.74 + KB). 
 
 Errors of these approximate equations as applied to several types of 
 vessels are shown by Professors Durand and McDermott (Trans. 
 Soc. Nav. Archts. & Mar. Engrs., Vol. 2), as follows: Taylor - 2.69 to 
 + 2.52%; Normand, - 1.55 to + 2.57%; Mumford, to - 0.95%, 
 except one lake freight vessel, L = 299, B = 40.9, D = 15.9, K = 0.825, 
 on which Mumford's formula was 12.55 % in error. 
 
 E. R. Mumford's Method of Calculating Wetted Surfaces is given 
 in a paper by Archibald Denny, Eng'g, Sept. 21, 1894. The following 
 is his formula, which gives closely accurate results for medium draughts, 
 beams, and finenesses; 
 
 S = (L X D X 1.7) + (L X B X C), 
 
 in which S = wetted surface in square feet; L -= length between perpen- 
 diculars in feet; D = middle draught in feet; B = beam in feet; C 
 block coefficient. 
 
 The formula may also be expressed in the form S = L(1.7 D + BC). 
 
 In the case of twin-screw ships having projecting shaft-casings, or in 
 
1372 
 
 MARINE ENGINEERING. 
 
 the case of a ship having a deep keel or bilge keels, an addition must be 
 made for such projections. The formula gives results which are in 
 general much more accurate than those obtained by Kirk's method. It 
 underestimates the surface when the beam, draught, or block coefficients 
 are excessive; but the error is small except in the case of abnormal forms, 
 such as stern-wheel steamers having very excessive beams (nearly one- 
 fourth the length), and also very full block coefficients. The formula 
 gives a surface about 6% too small for such forms. 
 
 The wetted surface of the block is nearly equal to that of the ship of 
 the same length, beam and draught; usually 2% to 5% greater. In 
 exceedingly fine hollow-line ships it may be 8% greater. 
 
 Area of bottom of block = (F + M) X B; 
 
 Area of sides = 2 M X H. 
 
 Area of sides of ends = 4 X 
 
 . 
 
 X//; 
 
 Tangent of half angle of entrance = i/zB/F = B/(2 F). 
 From this, by a table of natural tangents, the angle of entrance may be 
 obtained: 
 
 Angle of Entrance Fore-body in 
 of the Block Model, parts of length. 
 Ocean-going steamers, 14 knots and upw'd 18 to 15 .3 to .36 
 
 12 to 14 knots ..... 21 to 18 .26 to 0.3 
 cargo steamers, 10 to 12 knots.. 30 to 22 .22 to .26 
 Dr. Kirk's Method. This method is generally used on the Clyde. 
 The general idea proposed by Dr. Kirk is to reduce all ships to so 
 definite and simple a form that they may be easily compared; and the 
 magnitude of certain features of this form shall determine the suitability 
 of the ship for speed, etc. 
 
 The form consists of a middle body, which is a rectangular parallele- 
 piped, and fore-body and after-body, prisms having isosceles triangles for 
 Inses, as shown in Fig. 225. 
 
 FIG. 225. 
 
 This is called a block model, and is such that its length is equal to that 
 of the ship, the depth is equal to the mean draught, the capacity equal 
 to the displacement volume, and its area of section equal to the area of 
 immersed midship section. The dimensions of the block model may be 
 obtained as follows: Let AG = HB = length of fore- or after-body = F; 
 GH = length of middle body = M; KL = mean draught = H; EK = 
 area of immersed midship section * KL =B. Volume of block =(F+M) X 
 BX H; midship section = BX H-, displacement in tons = volume in 
 cubic ft. * 35. 
 
 AH = AG -h GH = F + M = displacement X 35 - (B X #). 
 
 To find the Indicated Horse-power from the Wetted Surface. 
 (Seaton.) In ordinary cases the horse-power per 100 feet of wetted 
 surface may be found by assuming that the rate for a speed of 1 
 is 5, and that the quantity varies as the cube of the speed. For example: 
 To find the number of I.'H.P. necessary to drive a ship at a speed of 15 
 knots, having a wetted skin of block model of 16,200 square feet: 
 
 The rate per 100 feet = (1 5/10)3 X 5 = 16.875. 
 Then I.H.P. reauired = 16.875 X 162 *= 2734. 
 When the ship is exeptionally well-proportioned, the bottom quite 
 
TVTA.RINL &NGINEEKING. 
 
 1373 
 
 clean, and the etticiency of the machinery high, as low a rate as 4 LH.P. 
 per 100 feet of wetted skin of block model may be allowed. 
 
 The gross indicated horse-power includes the power necessary to over- 
 come the friction and other resistance of the engine itself and the shafting, 
 and also the power lost in the propeller. In other words, I.H.P. is no 
 meas'ire of the resistance of the ship, and can only be relied on as a means 
 of deciding the size of engines far speed, so long as the efficiency of the 
 engine and propeller is known definitely, or so long as similar engines and 
 propellers are employed in ships to be compared. The former is difficult 
 to obtain, and it is nearly impossible in practice to know how much of 
 the power shown in the cylinders is employed usefully in overcoming the 
 resistance of the ship. The following example is given to show the vari- 
 ation in the efficiency of propellers: 
 
 Knots. I.H.P. 
 
 H.M.S. "Amazon," with a 4-bladed screw, gave 12.064 with 1940 
 
 H.M.S. "Amazon," with a 2-bladed screw, increased 
 
 pitch, and fewer revolutions per minute 12.396 ' 1663 
 
 H.M.S. " Iris," with a 4-bladerf screw 16.577 " 7503 
 
 H.M.S. "Iris." with 2-bladed screw, increased pitch, 
 
 fewer revolutions per knot 18.587 7556 
 
 Relative Horse-power Required for Different Speeds of Vessels. 
 (Horse-power for 10 knots = 1.) The horsVpower is taken usually to 
 vary as the cube of the speed, but in different vessels and at different 
 speeds it may vary from the 2.8 power to the 3.5 power, depending upon 
 the lines of the vessel and upon the efficiency of the engines, the pro- 
 peller, etc. (The power may vary at a much higher rate than the 3.5 
 power of the speed when the speed is much less than normal, and the 
 machinery is therefore working at less than its normal efficiency ) 
 
 13 03 
 
 Oj 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 HPoc 
 
 g2-S 
 
 .0769 
 
 .239 
 
 .535 
 
 
 .666 
 
 2.565 
 
 3.729 
 
 5.185 
 
 6.964 
 
 9.095 
 
 11.60 
 
 14.52 
 
 17 87 
 
 71 67 
 
 g2-9 
 
 .0701 
 
 .227 
 
 .524 
 
 
 .697 
 
 2,653 
 
 3 908 
 
 5 499 
 
 7 464 
 
 9 841 
 
 12 67 
 
 15 97 
 
 19 80 
 
 74 19 
 
 S3 
 
 .0640 
 
 .216 
 
 .512 
 
 
 .728 
 
 2.744 
 
 4 096 
 
 5.832 
 
 8 
 
 10,65 
 
 13,82 
 
 17,58 
 
 71 95 
 
 77 
 
 g3-l 
 
 .0584 
 
 .205 
 
 .501 
 
 
 .760 
 
 2.838 
 
 4.293 
 
 6.185 
 
 8,574 
 
 11.52 
 
 15.09 
 
 19.34 
 
 74 33 
 
 30 14 
 
 g3-2 
 
 .0533 
 
 .195 
 
 .490 
 
 
 .792 
 
 2.935 
 
 4.500 
 
 6.559 
 
 9.189 
 
 12.47 
 
 16.47 
 
 21.28 
 
 26,97 
 
 33 63 
 
 g3-3 
 
 .0486 
 
 .185 
 
 .479 
 
 
 .825 
 
 3,0^6 
 
 4 716 
 
 6 957 
 
 9 849 
 
 13 49 
 
 17 98 
 
 73 41 
 
 79 90 
 
 37 54 
 
 g3-4 
 
 .0444 
 
 .176 
 
 .468 
 
 
 .859 
 
 3.139 
 
 4.943 
 
 7,378 
 
 10 56 
 
 14.60 
 
 19 62 
 
 25 76 
 
 33 14 
 
 41 00 
 
 gS-5 
 
 0405 
 
 167 
 
 458 
 
 
 893 
 
 3 747 
 
 5 181 
 
 7 874 
 
 11 31 
 
 15 79 
 
 71 47, 
 
 28.34 
 
 36.73 
 
 46.77 
 
 EXAMPLE IN USE OF THE TABLE. A certain vessel makes 14 knots 
 speed with 587 I.H.P. and 16 knots with 900 I.H.P. What I.H.P. will 
 be required at 18 knots, the rate of increase of horse-power wjth increase 
 of speed remaining constant? The first step is to find the rate of 
 increase, thus: 14* : 16* :: 587 : 9QO. 
 
 x log 16 - x log 14 = log 900 - log 587; 
 X (0.204120 - 0.146128) = 2.954243 - 2.768638, 
 whence x (the exponent of S in formula H.P.oc S*) = 3.2. 
 
 From the table, for S 3 - 2 and 16 knots, the I.H.P. is 4.5 times the 
 I.H.P. at 10 knots; .-. H.P. at 10 knots = 900 -=- 4.5 = 200. 
 
 From the table for ,S 3 - 2 and 18 knots, the I.H.P. is 6.559 times the 
 I.H.P. at 10 knots; .-. H.P. at 18 knots = 200 X 6.559 = 1312 H.P. 
 
 Resistance per Horse-power for Different Speeds. (One horse- 
 power = 33.000 Ibs. resistance overcome through 1 ft. in 1 min.) The 
 resistances per horse-power for various speeds are as follows: For a 
 speed of 1 knot, or 6080 feet per hour = 10H/3 ft. per min., 33,000 * 
 1011/3 = 325.658 Ibs. per horse-power; and for any other speed 325.658 
 Ibs. divided by the speed in knots; or for 
 
 1 knot 325.66 Ibs. 
 
 2 knots 162.83 
 
 108.55 
 81.41 
 65.13 
 54.28 
 46.52 
 
 8 knots 40.71 Ibs. 
 
 9 
 
 10 
 11 
 12 
 13 
 
 14 
 
 36.18 
 32.57 
 29.61 
 27.14 
 25.05 
 23.26 
 
 15 knots 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21.71 IDS. 
 
 20.35 
 
 19.16 
 
 18.09 
 
 17.14 
 
 16.28 
 
1374 
 
 MARINE ENGINEERING. 
 
 More accurate methods than those above given for estimating the horse- 
 power required for any prop9sed ship are: 1. Estimations calculated 
 from the results of trials of "similar" vessels driven at "corresponding" 
 speeds; "similar", vessels being those that have the same ratio 01 length 
 to breadth and to draught, and the same coefficient of fineness, and 
 "corresponding" speeds ttwse which are proportional to the square roots 
 of the lengths of the respective vessels, iroude found that the resistances 
 of such vessels varied almost exactly as wetted surface X (speed) 2 
 
 2. The method employed by the British Admiralty and by some Clyde 
 shipbuilders, viz., ascertaining the resistance of a model of the vessel, 
 12 to 20 ft. long, in a tank, and calculating the power from the results 
 obtained. 
 
 Estimated Displacement, Horse-power, etc. The table on the 
 next page, calculated by the author, will be found convenient for making 
 approximate estimates. 
 
 The figures in 7th column are calculated by the formula H. P. S Z D$+ c 
 in which c = 200 for vessels under 200 ft. long when C = 0.65, and 210 
 when C = 0.55; c = 200 for vessels 200 to 400 ft. long when C =0.75, 
 220 when C = 0.65, 240 when C = 0.55; c = 230 for vessels over 400 ft. 
 long when C = 0.75, 250 when C = 0.65, 260 when C = 0.55. 
 
 The figures in the 8th column -are based on 5 H.P. per 100 sq. ft. of 
 wetted surface. 
 
 The diameters of screw in the 9th column are from formula D = 3.31 
 -5/I.H.P., and in the 10th column from formula D = 2.71 ^/I.H.P. 
 
 To find the diameter of screw for any other speed than 10 knots, revolu- 
 tions being 100 per minute, multiply the diameter given in the table by 
 the 5th root of the cube of the given speed * 10. For any other revolu- 
 tions per minute than 100, divide by the revolutions and multiply by 100. 
 
 To find the approximate horse-power for any other speed than 10 knots, 
 multiply the horse-power given in the table by the cube of the ratio of the 
 given speed to 10, or by the relative figure from table on p. 1373. 
 
 F. E. Cardullo, Mach'y, April, 1907, gives the following formula as 
 closely approximating the speed 6 f A modern types of hulls: S = 6.35 
 
 /T TT "P 
 
 ', , in which S = speed in knots, D = displacement in tons. 
 D '3 
 
 we take S = 10 knots, then I.H.P. -~ D 2 /3 = 3.906. Let D = 10,000, and. 
 S = 10, then H.P. = 1813. The table on page 1375 gives for a displace- 
 ment of 10,400 tons and a coefficient of fineness 0.65, 1966 and 1760 H.P., 
 averaging 1863 H.P. 
 
 Internal Combustion Marine Engines. Linton Hope (Eng'g, 
 April 8, 1910), in a paper on the application of internal combustion engines 
 to fishing boats and fine-lined commercial vessels, gives a table showing 
 the brake H.P. required to propel such vessels at various speeds. The 
 following table is an abridgment. L=load water line; D= displacement 
 in tons. 
 
 Block Coefficient. 
 
 0.25 
 
 0.3 
 
 0.35 
 
 0.4 
 
 4 
 
 5 1 6 
 
 7 
 
 8 | 9 
 
 10 
 
 L 
 
 78 
 71 
 65 
 59 
 54 
 50 
 46 
 41 
 38 
 35 
 32 
 30 
 28 
 
 D 
 
 L | D 
 
 L | D 
 
 L 
 
 D 
 
 Brake Horse-power. 
 
 105 
 81 
 
 62 
 47 
 36 
 28 
 22 
 17 
 13 
 9 
 61/2 
 41/2 
 3V4 
 
 75 
 69 
 63 
 57 
 52 
 48 
 44 
 40 
 37 
 34 
 31 
 29 
 27 
 
 100 
 77 
 60 
 45 
 35 
 27 
 21 
 16 
 12 
 81/2 
 6 
 41/4 
 
 72 
 66 
 60 
 54 
 50 
 46 
 42 
 38 
 35 
 32 
 30 
 28 
 26 
 
 95 
 73 
 58 
 44 
 34 
 26 
 20 
 15 
 
 ,u/ 2 
 
 58 
 
 23/4 
 
 69 
 63 
 
 57 
 52 
 48 
 44 
 40 
 37 
 34 
 31 
 29 
 27 
 25 
 
 90 
 70 
 55 
 
 42 
 32 
 25 
 19 
 14 
 11 
 71/2 
 
 31/2 
 21/2 
 
 20 
 17 
 15 
 13 
 11 
 9 
 8 
 7 
 6 
 5 
 4 
 3 
 2V2 
 
 30 
 25 
 22 
 19 
 16 
 13 
 12 
 11 
 9 
 
 h 
 
 41/2 
 
 43 
 37 
 32 
 27 
 24 
 20 
 17 
 15 
 13 
 11 
 9 
 7 
 6V2 
 
 60 
 51 
 44 
 39 
 34 
 29 
 25 
 22 
 19 
 16 
 14 
 12 
 11 
 
 81 
 69 
 60 
 53 
 48 
 44 
 40 
 37 
 34 
 
 110 
 93 
 82 
 76 
 71 
 
 150 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Speed in Knots. 
 
MARINE ENGINEERING. 
 
 1375 
 
 Estimated Displacement, Horse-power, etc., of Steam-vessels of 
 Various Sizes. 
 
 jl" 
 
 S*J 
 
 If 
 
 m <M 
 
 1^ 
 
 II 
 
 Is 
 
 8BS jf 
 |-o I 
 
 Displacement. 
 LDX C 
 
 Wetted Surface 
 L (1.7 D+ JiC) 
 
 Sq. ft. 
 
 Estimated Horse- 
 power at 10 knots. 
 
 Diam. of Sorew for 10 
 knots speed and 100 ' 
 revs, per minute. 
 
 85 
 
 tons. 
 
 Calc. 
 from Dis- 
 placem't. 
 
 \jaic. irom 
 Wetted 
 Surface. 
 
 If Pitch = 
 Diam. 
 
 If Pitch =1 
 1.4 Diam. 
 
 12 
 
 3 
 
 1.5 
 
 0.55 
 
 0.85 
 
 48 
 
 4.3 
 
 2.4 
 
 4.4 
 
 3.6 
 
 16 I 
 
 3 
 
 1.5 
 
 .55 
 
 1.13 
 
 64 
 
 * 5.2 
 
 3.2 
 
 4.6 
 
 3.8 
 
 16 1 
 
 4 
 
 2 
 
 .65 
 
 2.38 
 
 96 
 
 8.9 
 
 4.8 
 
 5.1 
 
 4.2 
 
 ?nl 
 
 3 
 
 1.5 
 
 .55 
 
 1.41 
 
 80 
 
 6.0 
 
 4.0 
 
 4.7 
 
 3.9 
 
 20 i 
 
 4 
 
 2 
 
 .65 
 
 2.97 
 
 120 
 
 10.3 
 
 6.0 
 
 5.3 
 
 4.3 
 
 74] 
 
 3.5 
 
 1.5 
 
 .55 
 
 1.98 
 
 104 
 
 7.5 
 
 5.2 
 
 5 
 
 4.1 
 
 24 { 
 
 4.5 
 
 2 
 
 .65 
 
 4.01 
 
 152 
 
 12.6 
 
 7.6 
 
 5.5 
 
 4.5 
 
 30 i 
 
 4 
 
 2 
 
 .55 
 
 3.77 
 
 168 
 
 11.5 
 
 8.4 
 
 5.4 
 
 4.4 
 
 30 { 
 
 5 
 
 2.5 
 
 .65 
 
 6.96 
 
 224 
 
 18.2 
 
 11.2 
 
 5.9 
 
 4.8 
 
 40 J 
 
 4.5 
 
 2 
 
 .55 
 
 5.66 
 
 235 
 
 15.1 
 
 11.8 
 
 5.7 
 
 4.7 
 
 40{ 
 
 6 
 
 2.5 
 
 .65 
 
 11.1 
 
 326 
 
 24.9 
 
 16.3 
 
 6.3 
 
 5.2 
 
 50 1 
 
 6 
 
 3 
 
 .55 
 
 14.1 
 
 420 
 
 27.8 
 
 21.0 
 
 6.4 
 
 5.4 
 
 50 | 
 
 8 
 
 3.5 
 
 .65 
 
 26 
 
 558 
 
 43.9 
 
 27.9 
 
 7.1 
 
 5.8 
 
 60 1 
 
 8 
 
 3.5 
 
 .55 
 
 26.4 
 
 621 
 
 42.2 
 
 31.1 
 
 7.0 
 
 5.7 
 
 60 \ 
 
 10 
 
 4 
 
 .65 
 
 44.6 
 
 798 
 
 62.9 
 
 39.9 
 
 7.6 
 
 6.2 
 
 70 
 
 10 
 
 4 
 
 .55 
 
 44 
 
 861 
 
 59.4 
 
 43.1 
 
 7.5 
 
 6.1 
 
 70 i 
 
 12 
 
 4.5 
 
 .65 
 
 70.2 
 
 1082 
 
 85.1 
 
 54.1 
 
 8.1 
 
 6.6 
 
 8oi 
 
 12 
 
 4.5 
 
 .55 
 
 67.9 
 
 1140 
 
 79.2 
 
 57.0 
 
 7.9 
 
 6.5 
 
 WM 
 
 14 
 
 5 
 
 .65 
 
 104.0 
 
 1408 
 
 111 
 
 70.4 
 
 8.5 
 
 7.0 
 
 on { 
 
 13 
 
 5 
 
 .55 
 
 91.9 
 
 1408 
 
 97 
 
 70.4 
 
 8.3 
 
 6.8 
 
 yj I 
 
 16 
 
 6 
 
 .65 
 
 160 
 
 1854 
 
 147 
 
 92.7 
 
 9 
 
 7.3 
 
 ( 
 
 13 
 
 5 
 
 .55 
 
 102 
 
 1565 
 
 104 
 
 78.3 
 
 8.4 
 
 6.9 
 
 100 { 
 
 15 
 
 5.5 
 
 .65 
 
 153 
 
 1910 
 
 143 
 
 95.5 
 
 8.9 
 
 7.3 
 
 ( 
 
 17 
 
 6 
 
 .75 
 
 219 
 
 2295 
 
 202 
 
 115 
 
 9.6 
 
 7.8 
 
 
 14 
 
 5.5 
 
 .55 
 
 145 
 
 2046 
 
 131 
 
 102 
 
 8.8 
 
 7.2 
 
 1205 
 
 16 
 
 6 
 
 .65 
 
 214 
 
 2472 
 
 179 
 
 124 
 
 9.4 
 
 7.6 
 
 ( 
 
 18 
 
 6.5 
 
 .75 
 
 301 
 
 2946 
 
 250 
 
 147 
 
 10 
 
 8.2 
 
 
 16 
 
 6 
 
 ; 55 
 
 211 
 
 2660 
 
 169 
 
 133 
 
 9.2 
 
 7.4 
 
 140 
 
 18 
 
 6.5 
 
 .65 
 
 306 
 
 3185 
 
 227 
 
 159 
 
 9.8 
 
 8.0 
 
 f 
 
 20 
 
 7 
 
 .75 
 
 420 
 
 3766 
 
 312 
 
 188 
 
 10.5 
 
 8.5 
 
 < 
 
 17 
 
 6.5 
 
 .55 
 
 278 
 
 3264 
 
 203 
 
 163 
 
 9.6 
 
 7.8 
 
 160 J 
 
 19 
 
 7 
 
 .65 
 
 395 
 
 3880 
 
 269 
 
 194 
 
 10.1 
 
 8.3 
 
 ( 
 
 21 
 
 7.5 
 
 .75 
 
 540 
 
 4560 
 
 368 
 
 228 
 
 10.8 
 
 8.8 
 
 ( 
 
 20 
 
 7 
 
 .55 
 
 396 
 
 4122 
 
 257 
 
 206 
 
 10.1 
 
 8.2 
 
 180) 
 
 22 
 
 7.5 
 
 .65 
 
 552 
 
 4869 
 
 337 
 
 243 
 
 10.6 
 
 8.7 
 
 ( 
 
 24 
 
 8 
 
 .75 
 
 741 
 
 5688 
 
 455 
 
 284 
 
 11.3 
 
 9.2 
 
 
 22 
 
 7 
 
 .55 
 
 484 
 
 4800 
 
 257 
 
 240 
 
 10.1 
 
 8.2 
 
 200 | 
 
 25 
 
 8 
 
 .65 
 
 743 
 
 5970 
 
 373 
 
 299 
 
 10.8 
 
 8.8 
 
 1 
 
 28 
 
 9 
 
 .75 
 
 1080 
 
 7260 
 
 526 
 
 363 
 
 11.6 
 
 9.5 
 
 ( 
 
 28 
 
 8 
 
 .55 
 
 880 
 
 7250 
 
 383 
 
 363 
 
 10.9 
 
 8.9 
 
 250 { 
 
 32 
 
 10 
 
 .65 
 
 1486 
 
 9450 
 
 592 
 
 473 
 
 11.9 
 
 9.7 
 
 ( 
 
 36 
 
 12 
 
 .75 
 
 2314 
 
 11850 
 
 875 
 
 593 
 
 12.8 
 
 10.5 
 
 
 32 
 
 10 
 
 .55 
 
 1509 
 
 10380 
 
 548 
 
 519 
 
 11.7 
 
 9.6 
 
 300 J 
 
 36 
 
 12 
 
 .65 
 
 2407 
 
 13140 
 
 806 
 
 657 
 
 12.6 
 
 10.4 
 
 ( 
 
 40 
 
 14 
 
 .75 
 
 3600 
 
 17140 
 
 1175 
 
 857 
 
 13.6 
 
 11.1 
 
 
 38 
 
 12 
 
 .55 
 
 2508 
 
 14455 
 
 769 
 
 723 
 
 12.5 
 
 10.2 
 
 350] 
 
 42 
 
 14 
 
 .65 
 
 3822 
 
 17885 
 
 1111 
 
 894 
 
 13.5 
 
 11.0 
 
 I 
 
 46 
 
 16 
 
 .75 
 
 5520 
 
 21595 
 
 1562 
 
 1080 
 
 14.4 
 
 11.8 
 
 ( 
 
 44 
 
 14 
 
 .55 
 
 3872 
 
 19200 
 
 1028 
 
 960 
 
 13.3 
 
 10.8 
 
 400 ] 
 
 48 
 
 16 
 
 .65 
 
 5705 
 
 23360 
 
 1451 
 
 1168 
 
 14.2 
 
 11.6 
 
 ( 
 
 52 
 
 18 
 
 .75 
 
 8023 
 
 27840 
 
 2006 
 
 1392 
 
 15.2 
 
 12.4 
 
 ( 
 
 50 
 
 16 
 
 .55 
 
 5657 
 
 24515 
 
 1221 
 
 1226 
 
 13.7 
 
 11.2 
 
 450 ] 
 
 54 
 
 18 
 
 .65 
 
 8123 
 
 29565 
 
 1616 
 
 1478 
 
 14.5 
 
 11.9 
 
 ( 
 
 58 
 
 20 
 
 .75 
 
 11157 
 
 34875 
 
 2171 
 
 1744 
 
 15.4 
 
 12.6 
 
 CAA ( 
 
 52 
 
 18 
 
 .55 
 
 7354 
 
 29600 
 
 1454 
 
 1480 
 
 14.2 
 
 11.6 
 
 500 
 
 56 
 
 20 
 
 .65 
 
 10400 
 
 35200 
 
 1966 
 
 1760 
 
 15.1 
 
 12.4 
 
 ( 
 
 60 
 
 22 
 
 .75 
 
 14143 
 
 41200 
 
 2543 
 
 2060 
 
 15.9 
 
 13.0 
 
 ( 
 
 56 
 
 20 
 
 .55 
 
 9680 
 
 36245 
 
 1747 
 
 1812 
 
 14.7 
 
 12.0 
 
 550 
 
 60 
 
 22 
 
 .65 
 
 13483 
 
 42735 
 
 2266 
 
 2137 
 
 15.5 
 
 12.7 
 
 ( 
 
 64 
 
 24 
 
 .75 
 
 18103 
 
 49665 
 
 2998 
 
 2483 
 
 16.4 
 
 13.4 
 
 
 60 
 
 22 
 
 .55 
 
 12446 
 
 42900 
 
 2065 
 
 2145 
 
 15.2 
 
 12.5 
 
 600 1 
 
 64 
 
 24 
 
 .65 
 
 17115 
 
 50220 
 
 2656 
 
 2511 
 
 15.4 
 
 13.1 
 
 ( 
 
 68 
 
 26 
 
 .75 
 
 22731 
 
 58020 
 
 3489 
 
 2901 
 
 16.9 
 
 13.8 
 
1376 
 
 MARINE ENGINEERING. 
 
 
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 TU, 
 
 UO 'SUOJ, 
 
 IBIJX uo 
 
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 4, ^ ?> 5 i~ 2 -3 -g g Jg 
 
 ^ 
 
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 ft 
 
THE SCREW-PROPELLER. 1377 
 
 THE SCREW-PROPELLER. 
 
 The "pitch" of a propeller is the distance which any point in a blade 
 describing a helix will travel in the direction of the axis during one revolu- 
 tion, the point being assumed to move around the axis. The pitch of a 
 propeller with a uniform pitch is equal to the distance a propeller will 
 advance during one revolution, provided there is no slip. In a case of 
 this kind, the term " pitch" is analogous to the term "pitch of the thread" 
 of an ordinary single-threaded screw. 
 
 Let P pitch of screw in feet, R = number of revolutions per second, 
 V = velocity of stream from the propeller = P X R, v = velocity of the 
 ship in feet per second, V v = slip, A = area in square feet of section 
 of stream from the screw, approximately the area of a circle of the same 
 diameter, A X V = volume of water projected astern from the ship in 
 cubic feet per second. Taking the weight of a cubic foot of sea-water 
 at 64 Ibs., and the force of gravity at 32, we have from the common for- 
 mula for force of acceleration, viz.: F= M j = ~, or F vi, when 
 t =1 second. 
 
 Thrust of screw in pounds = ^ (V v) 2 AV (V v). 
 
 O4 
 
 Rankine (Rules, Tables, and Data, p. 275) gives the following: To 
 calculate the thrust of a propelling instrument (jet, paddle, or screw) in 
 pounds, multiply together the transverse sectional area, in square feet, 
 of the stream driven astern by the propeller; the speed of the stream 
 relatively to the ship in knots? the real slip, or part of that speed which is 
 impressed on the stream by the propeller, also in knots; and the constant 
 5.66 for sea-water, or 5.5 for fresh water. If S = speed of the screw in 
 knots, s = speed of ship in knots, A area of the stream in square feet 
 (of sea-water), 
 
 Thrust in pounds = A X S (S - s) X 5.66. 
 
 The real slip is the velocity (relative to water at rest) of the water pro- 
 jected sternward ; the apparent slip is the difference between the speed of 
 the ship and the speed of the screw; i.e., the product of the pitch of the 
 screw by the number of revolutions. 
 
 This apparent slip is sometimes negative, due to the working of the 
 screw in disturbed water which has a forward velocity, following the ship. 
 Negative apparent slip is an indication that the propeller is not suited 
 to the ship. The apparent slip should generally be about 8% to 10% at 
 full speed in well-formed vessels with moderately fine lines; in bluff cargo 
 boats it rarely exceeds 5%. 
 
 The effective area of a screw is the sectional area of the stream of water 
 laid hold of by the propeller, and is generally, if not always, greater than 
 the actual area, in a ratio which in good ordinary examples is 1.2 or there- 
 abouts, and is sometimes as high as 1.4: a fact probably due to the stiffness 
 of the water, which communicates motion laterally amongst its particles. 
 (Rankine's Shipbuilding, p. 89.) 
 
 Prof. D. S. Jacobus, Trans. A. S. M. E., xi, 1028, found the ratio of the 
 effective to the actual disk area of the screws of different vessels to be as 
 follows : 
 
 Tug-boat, with ordinary true-pitch screw 1 .42 
 
 Tug-boat, with screw having blades projecting backward ... 57 
 
 Ferryboat " Bergen, " with or- ( at speed of 12.09 stat. miles per hr .' 1 '53 
 
 dinary true-pitch screw \ at speed of 13.4 stat. miles per hr. . 1 !48 
 
 Steamer "Homer Ramsdell," with ordinary true-pitch screw 1 .20 
 
 Size of Screw. Seaton says: The size of a screw depends on so 
 many things that it is very difficult to lay down any rule for guidance, 
 and much must always be left to the experience of the designer, to allow 
 for all the circumstances of each particular case. The following rules are 
 given for ordinary cases (Seaton and Rounthwaite's Pocket-book): 
 
 P *= pitch of propeller in feet = jgQoo^e) ' in which s ~ s P eed in 
 knots, R = revolutions per minute, and x = percentage Of apparent 
 slip. For a slip of 10%, pitcn = U3,G S -r #, 
 
1378 
 
 MARINE ENGINEERING. 
 
 D =diameter of propeller = 
 
 r~ , K being a coefficient given 
 
 100 / 
 
 in the table below. If K = 20, D = 20,000 "^I.H.P. 
 
 Total developed area of blades = C ^/I.H.P +R 
 
 cient to be taken from the table 
 
 r- (P x R) 3 . 
 in which C is a coeffi- 
 
 Another formula for pitch, given in'Seaton's Marine Engineering, is 
 -, in which C= 737 for ordinary vessels, and 660 for slow- 
 speed cargo vessels with full lines. 
 
 Thickness of blade at root = \ ^ X &, in which d 
 
 = diameter of tail 
 
 shaft in inches, n = number of "blades, b = breadth of blade in inches 
 where it joins the boss, measured parallel to the shaft axis; k = 4 for cast 
 iron, 1.5 for cast steel, 2 for gun-metal, 1.5 for high-class bronze 
 
 Thickness of blade at tip: Cast iron 0.04 D + 0.4 in.; cast steel 03 D 4- 
 0.4m.; gun-metal 0.03 D + 0.2 in.; high-class bronze 0.02 D +03 in 
 where D = diameter of propeller in feet. 
 
 Propeller Coefficients. 
 
 Description of Vessel. 
 
 III 
 
 <o| 
 $ 
 
 No. of 
 Blades 
 per Screw 
 
 |&i 
 
 
 
 SjO 
 
 
 
 ^ <a 
 
 ai^l 
 
 2 05-73 d 
 j-C 
 
 Bluff cargo boats 
 
 8-10 
 10-13 
 13-17 
 13-17 
 17-22 
 17-22 
 16-22 
 16-22 
 20-26 
 
 One 
 
 Twin 
 One 
 Twin 
 
 One 
 
 4 
 4 
 4 
 4 
 4 
 3 
 4 
 3 
 3 
 
 17 -17.5 
 18 -19 
 19.5-20.5 
 20.5-21.5 
 21 -22 
 22 -23 
 21 -22.5 
 22 -23.5 
 25 
 
 19 -17.5 
 17 -15.5 
 15 -13 
 14.5-12.5 
 12.5-11 
 10.5- 9 
 11.5-10.5 
 8.5-7 
 7-6 
 
 Cast iron 
 C.I. or S, 
 G.M.orB 
 
 B.orF.S. 
 
 Cargo, moderate lines 
 Pass, and mail, fine lines. 
 
 " ve *y fr*? 
 
 Naval vessels, ** 
 Torpedo-boats, " " 
 
 C. I., cast iron; G. M., gun-metal; B., bronze; S., steel; F.S., forged steel. 
 
 From the formulae D = 20,000 k ' ** H '^' 
 P = D and R = 100, we obtain D = ^400 X I.H.P. = 3.31 -y/I.H.P. 
 
 If P = 1.4 D and R = 100, then D = ^145.8 X I.H.P. = 2.71 ^/I.H.P. 
 
 From these two formulae the figures for diameter of screw in the table 
 on page 1375 have been calculated. They may be used as rough approx- 
 imations to the correct diameter of screw for any given horse-power, for 
 a speed of 10 knots and 100 revolutions per minute. 
 
 For any other number of revolutions per minute multiply the figures 
 in the table by 100 and divide by the given number of revolutions. For 
 any other speed than 10 knots, since the I.H.P. varies appntximately as 
 the cube of the speed, and the diameter of the screw as the 5th root of the 
 I.H.P., multiply the diameter given for 10 knots by the 5th root of the 
 cube of one-tenth of the given speed. Or, multiply by the following 
 factors: 
 
 For speed of knots: 
 45 6 7 8 9 11 12 13 14 15 16 
 
 $(8 *- 10)8 
 
 = 0.577 0.660 0.736 0.807 0.875 0.939 1.059 1.116 1.170 1.224 1.275 1.327 
 
 Speed: 
 
 17 18 19 20 21 22 23 24 25 26 27 28 
 ^ (S ~- 10)3 
 = 1.375 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855 
 
 For more accurate determinations of diameter and pitch of screw, the 
 formulae and coefficients given bv Seaton, quoted above, should 1 
 
THE SCREW-PROPELLER. 
 
 1379 
 
 Efficiency of the Propeller. According to Rankine, if the slip of 
 the water be s, its weight W, the resistance R, and the speed of the ship v. 
 # = Ws + g- Rv = Wsv + g. 
 
 This impelling action must, to secure maximum efnciencjr of propeller, 
 be effected by an instrument which takes hold of the fluid without shock 
 or disturbance of the surrounding mass, and, by a steady acceleration, 
 gives it the required final velocity of discharge. The velocity of the 
 propeller overcoming the resistance R would then be 
 
 [v+ (v+s)] + 2 =v + s/2; 
 and the work performed would be 
 
 R(v+ s/2) = Wvs -- g + Ws 2 * 2 g, 
 
 the first of the last two terms being useful, the second the minimum lost 
 work; the latter being the wasted energy of the water thrown backward. 
 The efficiency is E = v -* (v + s/2); and this is the limit attainable with 
 a perfect propelling instrument, which limit is approached the more nearly 
 as the conditions above prescribed are the more nearly fulfilled. The 
 efficiency of the propelling instrument is probably rarely much above 
 0.60, and never above 0.80. 
 
 In designing the screw-propeller, as was shown by Dr. Froude, the 
 best angle for the surface is that of 45 with the plane of the disk; but as 
 all parts of the blade cannot be given the same angle, it should, where 
 practicable, be so proportioned that the "pitch-angle at the center of 
 effort" should be made 45. The maximum possible efficiency is then, 
 according to Froude, 77%. In order that the water should be taken on 
 without shock and discharged with maximum backward velocity, the 
 screw must have an axially increasing pitch. 
 
 The true screw is the usual form of propeller in all steamers; both mer- 
 chant andnaval. (Thurston, Manual of the Steam-engine, partii, p. 176.) 
 
 The combined efficiency of screw, shaft, engine, etc., is generally taken 
 at 50%. In some cases it may reach 60% or 65%. Rankine takes the 
 effective H.P. to equal the I.H.P. -f- 1.63. 
 
 .Results of Researches on the efficiency of screw-propellers are sum- 
 marized by S. W. Barnaby, in a paper read before section G of the Engi* 
 neering Congress, Chicago, 1893. He states that the following general 
 principles have been established: 
 
 (a) There is a definite amount of real slip at which, and at which only, 
 maximum efficiency can be obtained with a screw of any given type, 
 and this amount varies with the pitch-ratio. The slip-ratio proper to a 
 given ratio of pitch to diameter has been discovered and tabulated for a 
 screw of a standard type, as below : 
 
 Pitch-ratio and Slip for Screws of Standard Form. 
 
 Pitch-ratio. 
 
 Real Slip of 
 Screw. 
 
 Pitch-ratio . 
 
 Real Slip of 
 Screw. 
 
 Pitch-ratio . 
 
 Real Slip of 
 Screw. 
 
 0.8 
 0.9 
 1.0 
 I.I 
 1.2 
 1.3 
 
 15.55 
 16.22 
 16.88 
 17.55 
 18.2 
 18.8 
 
 .4 
 .5 
 .6 
 
 '.8 
 .9 
 
 19.5 
 20.1 
 20.7 
 21.3 
 21.8 
 22.4 
 
 2.0 
 
 2!2 
 2.3 
 2.4 
 25 
 
 22.9 
 23.5 
 24.0 
 24.5 
 25.0 
 25.4 
 
 (5) Screws of large pitch-ratio, besides being less efficient in them- 
 selves, add to the resistance of the hull by an amount bearing some pro- 
 portion to their distance from it, and to the amount of rotation left in 
 the race. 
 
 (c) The best pitch-ratio lies probably between 1.1 and 1.5. 
 
 (d) The fuller the lines of the vessel, the less the pitch-ratio should be. 
 
 (e) Coarse-pitched screws should be placed further from the stern 
 than fine-pitched ones. 
 
 (/) Apparent negative slip is a natural result of abnormal proportions 
 of propellers. 
 
 . (0) Three blades are to be preferred for high-speed vessels, but when 
 the diameter is unduly restricted, four or even more may be advantageously 
 employed. 
 
 (fi) An efficient form of blade is an ellipse having a minor axis equal 
 to four-tenths the major axis. 
 
 (i) The pitch of wide-bladed screws should increase from forward to 
 aft, but a uniform pitch gives satisfactory results when the blades are 
 
1380 
 
 MAKINE ENGINEERING. 
 
 narrow, and the amount of the pitch variation should be a function of the 
 width of the blade. 
 
 0') A considerable inclination of screw-shaft produces violation, and 
 with right-handed twin-screws turning outwards, if the shafts are inclined 
 at all, it should be upwards and outwards from the propellers. 
 
 For results of experiments with screw-propellers, see F. C. Marshall, 
 Proc. Inst. M. E., 1881; R. E. Froude, Trans. Inst. Nav. Archs., 1886; 
 G. A. Calvert, Trans. Inst. Nav. Archs., 1887; S. W. Barnaby, Proc. Inst. 
 
 in propellers* with pitch ratios from 1.0 to 1.5 ratio of width of blade to 
 diameter of Vg to Vs. and ratio of developed area of blade to disk area of 
 0.201 to 0.322. 
 
 One of the most important results deduced from experiments on model 
 screws is that they appear to have practically equal efficiencies through- 
 out a wide range both in pitch-ratio and in surface-ratio; so that great 
 latitude is left to the designer in regard to the form of the propeller. 
 Although these experiments are not a direct guide to the selection of the 
 most efficient propeller for a particular ship, they supply the means of 
 analyzing the performances of screws fitted to vessels, and of thus in- 
 directly determining what are likely to be the best dimensions of screw 
 for a vessel of a class whose results are known. (Proc.Jnst. M. E., July, 
 1891.) 
 
 Mr. Barnaby in Proc. Inst. C. E., 1890, gives a table to be used in cal- 
 culations for determining the best dimensions of screws for any given 
 speed and H.P. from which the following table is abridged. It is deduced 
 from Froude's experiments at Torquay. (Trans. Inst. Nav. Archs., 1886.) 
 
 CA = disk area in S Q- ft. X FVH.P. CR = revs, per min. X D/V. 
 V = speed in knots, D = diam. of screw in ft. H.P. = effective H.P. 
 on the screw shaft. Disk area = 0.7854 Z) 2 = CA X I. H.P./ F 3 . Revs, 
 per min. = CR X V/D. The constants CA an d CR assume a standard 
 value of the speed of the wake, equal to 10% of the speed of the ship. 
 In a very full ship it may amount to 30%, therefore V should be reduced 
 when using .the constants by amounts varying from 20% to as the 
 form varies from "very full" to "fairly fine." 
 
 Effy. of 
 Screw, %. 
 
 6 
 
 S 
 
 6 
 
 7 
 
 6 
 
 S 
 
 6 
 
 9 
 
 6 
 
 S 
 
 6 
 
 1 
 
 6 
 
 1 
 
 Pitch ratio. 
 
 CA 
 
 C B 
 
 CA 
 
 C R 
 
 CA 
 
 CR 
 
 CA 
 
 CR 
 
 CA 
 
 CR 
 
 CA 
 
 CR 
 
 CA 
 
 CR 
 
 0.80 
 .00 
 .20 
 .40 
 .60 
 .80 
 
 468 
 546 
 625 
 704 
 780 
 
 122 
 99 
 83 
 72 
 63 
 
 304 
 355 
 405 
 456 
 507 
 558 
 
 128 
 104 
 87 
 76 
 67 
 60 
 
 215 
 251 
 
 288 
 325 
 360 
 3Q6 
 
 134 
 109 
 92 
 80 
 71 
 64 
 
 157 
 
 184 
 210 
 236 
 263 
 ?QO 
 
 142 
 115 
 97 
 85 
 75 
 68 
 
 115 
 135 
 154 
 173 
 193 
 71? 
 
 150 
 
 123 
 104 
 90 
 80 
 73 
 
 86 
 100 
 115 
 129 
 144 
 15Q 
 
 160 
 131 
 111 
 97 
 
 87 
 78 
 
 65 
 76 
 87 
 98 
 109 
 170 
 
 171 
 
 140 
 119 
 104 
 93 
 84 
 
 200 
 
 
 
 60Q 
 
 55 
 
 43? 
 
 58 
 
 315 
 
 6? 
 
 ?3i 
 
 67 
 
 173 
 
 7? 
 
 131 
 
 77 
 
 2 20 
 
 
 
 660 
 
 50 
 
 46Q 
 
 54 
 
 34? 
 
 57 
 
 ?50 
 
 6? 
 
 187 
 
 67 
 
 147 
 
 7? 
 
 2.40 
 
 
 
 710 
 
 47 
 
 505 
 
 50 
 
 369 
 
 53 
 
 270 
 
 57 
 
 202 
 
 62 
 
 153 
 
 67 
 
 Comparison of Marine Engines for the Years 1872, 1881, 1891, 1901. 
 
 (Jas. McKechnie. Proc. Inst. M. E. 1901.) 
 
 Average Results. 
 
 
 1872. 
 
 1881. 
 
 1891. 
 
 1901. 
 
 
 5274 
 
 77.4 
 
 158.5 
 
 197 
 
 Heating surface per sq. ft. grate 
 
 
 30 4 
 
 31.0 
 
 38 & 43* 
 
 Heat'g surf., per I.H.P., sq. ft 
 Coal per sq ft. of grate Ibs perhr. ... 
 
 4.41 
 
 3.917 
 13 8 
 
 3.275 
 15.0 
 
 3.0 
 
 18&28* 
 
 
 55.67 
 
 59.76 
 
 63.75 
 
 87 
 
 
 376 
 
 467 
 
 529 
 
 654 
 
 Coal per I.H.P. per hr., Ibs 
 
 2 11 
 
 1.83 
 
 1.52 
 
 1.48 
 
 Av. consumption, long voyage 
 
 
 2.0 
 
 1.75 
 
 1.55 
 
 * Natural and forced draft respectively. 
 Summary of Results. (1891 to 1901). Steam pressures have been 
 increased in the merchant marine from 158 Ibs. to 197 Ibs. per sq. in 
 
MARINE PRACTICE. 
 
 1381 
 
 the maximum attained being 267 Ibs. per sq. in., and 300 Ibs. in the 
 naval service. The piston speed of mercantile machinery has gone up 
 from 529 to 654 ft. per minute, the maximum in merchant practice 
 being about 900 ft., and in naval practice 960 ft. for large engines, and 
 1300 ft. in torpedo-boat destroyers. Boilers also yield a greater power 
 for a given surface, and thus the average power per ton of machinery 
 has gone up from an average of 6 to about 7 I.H.P., while ten years ago 
 the highest sustained ocean speed was 20.7 knots, it is now 23.38 knots; 
 the highest speed for large warships was 22 knots and is now 23 knots 
 on a trial of double the duration; the maximum speed attained by any 
 craft was 25 knots, as compared with 36.581 knots now, while tho 
 number of ships of over 20 knots was 8 in 1891, and is 58 now (1901). 
 Turbines and Boilers of the "Lusitania." (Thomas Bell, Proc. 
 Inst. Nav. Archts., 1908.) Some of the principal dimensions of the 
 turbines and boilers of the "Lusitania" are as follows: 
 
 Turbines. 
 
 Diameter 
 of Rotor, 
 Ins. 
 
 Length of Blades, Ins. 
 
 In First 
 Expansion. 
 
 In Last 
 Expansion. 
 
 H.P... 
 
 96 
 140 
 104 
 
 23/4 
 81/4 
 21/4 
 
 V2V. 
 
 - 8 
 
 L.P 
 
 
 Total cooling surface, main condensers, 82,800 sq. ft; area of exhaust 
 jnlet, 158 sq. ft; bore of circulating discharge pipes, 32 ins. 
 
 BOILERS. Working pressure, 195 Ibs. per sq. in.; 23 double-ended 
 boilers, 17 ft. 6 in. mean diameter by 22 ft. long; 2 single-ended boilers, 
 17 ft. 6 in. mean diameter by 11 ft. 4 in. long; total number of furnaces, 
 192; total grate surface, 4048 sq. ft.; total heating surface, 158,35.2 sq. ft.; 
 total length of boiler-rooms, 336 ft.; total length of main and auxiliary 
 engine rooms, 149 ft. 8 in. 
 
 The following are the weights of the various revolving parts, and the 
 size of bearings and the pressure: Weight of one H.P. turbine rotor 
 complete, 86 tons; one L.P. rotor, 120 tons; one astern rotor, 62 tons. 
 
 
 Main Bearing 
 Journals. 
 
 Pressure 
 per Sq. In. 
 of Bearing 
 Surface. 
 
 At. 190 Revs. 
 Surface Speed 
 of Journal. 
 
 Diameter. 
 
 Effective 
 Length. 
 
 H P. rotor 
 
 27 1/8 in. 
 33 l/s in. 
 24 1/8 in. 
 
 44 3/ 4 in. 
 56 1/2 in. 
 34 3/4 in. 
 
 80 Ibs. 
 72 Ibs. 
 83 Ibs. 
 
 1350 ft. per min. 
 1 650 ft. per min. 
 1200ft. per min. 
 
 L.P. rotor 
 
 Astern rotor 
 
 Performance of the "Lusitania." (Thos. Bell, Proc. Inst. Nav. 
 Archts., 1908; Power, May 12, 1908.) The following records were ob- 
 tained in the official trials: 
 
 Speed in knots 15 .77 
 
 Shaft horse-power 13,400 
 
 Steam cons, per shaft, H.P. hr. 
 
 of turbines, Ibs 21 . 23 
 
 of auxiliaries, Ibs 5.3 
 
 total Ibs.. *** 26.53 
 
 Temp, of feed- water, * F 200 
 
 Coal cons. Ibs. per shaft 
 H.P. hr 
 
 18 
 
 20,500 
 
 17.24 
 3.72 
 
 2 260 96 
 
 21 
 33,000 
 
 14.91 
 
 2.6 
 
 17.51 
 
 199 
 
 23 
 
 48,000 
 
 13.92 
 2.01 
 
 2.52 2.01 1.68 1.56 
 
 25.4 
 68,850 
 
 12.77 
 
 1.69 
 
 14.46 
 
 165 
 
 1.43 
 
 Estimated steam and coal consumption under service conditions, at 
 
 same speeds: 
 Steam cons, of auxiliaries, 
 
 pershaft H.P. hr., Ibs.. 6.97 4.92 3,41 2.65 2.17 
 Steam cons, of total per 
 
 shaft H.P. hr., Ibs 28.20 22.16 18.32 16.57 14.94 
 
 Coal cons., Ibs. per shaft 
 
 H.P.hr.,lbs 2.76 2.17 1.8 1.62 1.46 
 
 Est. coal cons., on a voyage 
 
 of 3100 nautical miles, 
 
 gross tons 3,270 3,440 3,930 4, 700 5,490 
 
 The following figures are taken from the records of a voyage from 
 
1382 
 
 MARINE ENGINEERING. 
 
 jj-bs 'a 
 
 *- 
 
 o-- ir> PO >- >> oo CM -< 
 
 O tS vC5 vC5 O^ 
 
 ICMCM-? 
 
 O CS O 
 
 T O c^i 
 
 no pa'adg 
 
 
 3 SO -rr m . 
 
 -~S S? 5 i ?? r~ 
 
 mmr^oo c 
 
 %Oir\ 
 
 
 OOOO 
 
 
 .*n3 
 
 :fl 
 
 
 I JL.fi > O GO 0> 
 
 Iiflsisgi 
 
 2"P-2-S bc^^ooo 
 ^.23^ ftd o_io 
 S-adO'ScjCoh. 
 
 rsP^Jn^ri 
 
 &o C j_-^ nVr>l> c 
 
 f-5^0-2 Soo-g-d 
 
 |oi^|<g 
 
 ^^^dS^OceO 
 
 itilsl^iS 
 Si?8ii^ 
 
 385*8 511 
 |g25n.&|| 
 
 t^s^>eo dio^o'tHC) 
 
 ^ .lla^s^ 
 
 S'S-So^. 0) <D(N 
 
 ||^ c ^.S5^5o 
 
 a^.S 5 *ll^ 
 
 n ^ . bjoO ^ ( ? 
 Q o;^ P'S 
 
 f to 
 
 arso 
 mea 
 59 i 
 pling 
 angle 
 as 
 ing r 
 take 
 .0%; 
 
 of 
 
 P 
 n. 
 d 
 ip 
 
 Sllol'l 
 
 
 3 .2 3 w 3 oT; w * 
 
 |i|lll-|I 
 
 S,^ 8 .gifl 8 8. 
 g Syge^gSS 
 
 cu _, o ce 3 Jfi^ S? 1 " 1 
 
 S ?i&8 1*3^3 
 a 8^s2^ : i'S 
 
 nd 
 
 &-< '"-> <J 
 
 S <PO"*^ 
 
 'M^iO-nO 
 
 5 S * 2 a.i***t'fl) 
 
 *eaSi!!s3K 
 
 *ttO fe"S . ^^T3 ^ C 
 
 *t|sa|2lsg 
 &82.-*l|3a| 
 
 L : l|tf!pi 
 
 fllllll 
 
 jS & iiM|i 
 
 o > S'^H^o- 14 .^ 
 eS>^c3&J) goio-g 
 "St ^'^ = S -Sfe^ 
 
THE PADDLE-WHEEL. 1383 
 
 Queenstown to Sandy Hook, 2781 nautical miles, Nov. 3-8, 1908, 4 days, 
 18 hrs., 40m.: Averages: Steam pressure at bo>lers, 168 IDS.; temperature 
 hot-well, 74.5; feed-water, 197; vacuum, 28.1 in.; speed, 24.25 knots; 
 speed, best day, 24.8 knots; revolutions, 181.1; slip, 15.9%. Total coal, 
 4976 tons. Steam consumption: main turbines, 851,500 Ibs., = 13.1 Ibs. 
 per shaft H.P. hr. (on a basis of 65,000 shaft H.P.); auxiliary machinery, 
 114,000 Ibs., = 1.75 per H.P. hr.; evaporating plant and heating, 32,500 Ibs., 
 = 0.5.1b. per H.P. hr. Total, 998,000 Ibs., = 15.35 Ibs. per shaft H.P. 
 hour. Average coal burned, 43 1/2 tons per hour. Water evaporated 
 per lb., coal 10.2 Ibs. from feed at 196, = 10.9 Ibs. from and at 212. 
 Coal for all purposes per shaft H.P. hour, 1.5 Ibs. Coal per sq. ft. of 
 grate per hour, 24.1 Ibs. The coal was half Yorkshire, half South Wales. 
 
 In September, 1909, the "Lusitania" made the westward passage, 2784 
 miles from Daunt's Rock near Queenstown to Ambrose Channel Lightship, 
 off Sandy Hook, in 4 days 11 h. 42 m., averaging 25.85 knots for the entire 
 passage. Four successive days runs, from noon to noon, were 650, 652. 
 651 and 674 miles. 
 
 Reciprocating Engines with a Low-Pressure Turbine. The 
 " Laurentic, " built for the Canadian trade of the White Star Line, 
 14,000 tons gross register, is a triple-screw steamer, with the two outer 
 screws driven by' four-cylinder triple-expansion engines, and the central 
 screw by a Parsons turbine. The steam, of 200 Ibs. boiler pressure, first 
 passes to the reciprocating engines, where it expands to from 14 to 17 Ibs. 
 absolute, and then passes to the turbine. For maneuvering the ship 
 into and out of port the turbine is not used, and the steam passes directly 
 from the engines to the condensers. During the trial trip the combined 
 engine-turbine outfit developed 12,000 H.P., with a speed of 171/2 knots, 
 and showed a coal consumption of 1.1 Ibs. and a water consumption of 
 11 Ibs. per indicated horse-power hour. (Power, May 18, 1909.) 
 
 The " Kronprinzessin Cecilie" of the North German Lloyd Co., is 
 probably the last high-speed transatlantic steamer of very great power 
 that will be built with reciprocating engines. Its dimensions are: length, 
 706 ft.; beam, 72 ft.; depth, 44 ft. 2 in.; displacement, 26,000 tons. Four 
 12,000 H.P. engines, two on each shaft, in tandem. Cylinders, 373/8, 
 491/4, 74V8 and 1121/4 ins., by 6 ft. stroke. Steam, 230 Ibs., delivered 
 from 19 cylindrical boilers, through four 17-in. steampipes. Coal used 
 in 24 hours, 764 tons, in 124 furnaces; 1.4 Ibs. per H.P. hour, including 
 auxiliaries. Speed on trial trip on a 60-mile course, 24.02 knots. (Set. 
 Am., Aug. 24, 1907.) 
 
 THE PADDLE-WHEEL. 
 
 Paddle-wheels with Radial Floats. (Seaton's Marine Engineering.) 
 The effective diameter of a radial wheel is usually taken from the centers 
 of opposite floats; but it is difficult to say what is absolutely that diameter, 
 as much depends on the form of float, the amount of dip, and the waves 
 set in motion by the wheel. The slip of a radial wheel is from 15 to 30 
 per cent, depending on the size of float. 
 
 Area of one float = C X I.H.P. *- D. 
 
 D {3 the effective diameter in feet, and C is a multiplier, varying from 0.25 
 in tugs to 0.175 in fast-running light steamers. 
 
 The breadth of the float is usually about 1/4 its length, and its thickness 
 about i/g its breadth. The number of floats varies directly with the diam- 
 eter, and there should be one float for every foot of diameter. 
 
 (For a discussion of the action of the radial wheel, see Thurston, 
 Manual of the Steam-engine, part ii, p. 182.) 
 
 Feathering Paddle-wheels. (Seaton.) The diameter of a feather- 
 ing-wheel is found as follows: The amount of slip varies from 12 to 20 
 per cent, although when the floats are small or the resistance great it 
 is as high as 25 per cent; a well-designed wheel on a well-formed ship 
 should not exceed 15 per cent under ordinary circumstances, 
 
 If K is the speed of the ship in knots, S the percentage of slip, and R 
 the revolutions per minute, 
 
 Diameter of wheel at centers = K (100 + S) + (3.14 X R). 
 
 The diameter, however, must be such as will suit the structure of the 
 ship, so that a modification may be necessary on this account, and the 
 revolutions altered to suit it. The diameter will also depend on the 
 amount of "dip" or immersion of float. 
 
1384- MARINE ENGINEERING. 
 
 When a ship is working always in smooth water the immersion of the 
 top edge should not exceed 1/8 the breadth of the float; and for general 
 service at sea an immersion of 1/2 the breadth of the float is sufficient. 
 If the ship is intended to carry cargo, the immersion when light need not 
 be more than 2 or 3 inches, and should not be more than the breadth of 
 float when at the deepest draught; indeed, the efficiency of the wheel falls 
 off rapidly with the immersion of the wheel. 
 
 Area of one float = C X I.H.P. * D. 
 
 C is a multiplier, varying from 0.3 to 0.35; D is the diameter of the 
 wheel to the float centers, in feet. 
 
 The number of floats = 1/2 (7) +2). 
 The breadth of the float = 0.35 X the length. 
 The thickness of floats = 1/12 the breadth. 
 Diameter of gudgeons = thickness of float. 
 Seatonand Rounthwaite's Pocket-book gives: 
 
 Number of floats = 60 -* V^5 
 where R is number of revolutions per minute. 
 
 Area of one float (in square feet) = ^ 
 
 where N number of floats in one wheel. 
 
 For vessels plying always in smooth water K = 1200. For sea-going 
 steamers K = 1400. For tugs and such craft as require to stop and 
 start frequently in a tide-way K = 1600. 
 
 It will be quite accurate enough if the last four figures of the cube 
 (D X R) 3 be taken as ciphers. 
 
 For illustrated description of the feathering paddle-wheel see Seaton's 
 Marine Engineering, or Seaton and Rounthwaite's Pocket-book. The 
 diameter of a feathering-wheel is about one-half that of a radial wheel 
 for equal efficiency. (Thurston.) 
 
 Efficiency of Paddle-wheels. Computations by Prof. Thurston of 
 the efficiency of propulsion by paddle-wheels give for light river steamers 
 with ratio of velocity of the vessel, v, to velocity of the paddle-float at 
 center of pressure, V, or v/V, = 3/4, with a dip = 3/ 2 o radius of the wheel 
 and a slip of 25 per cent, an efficiency of 0.714; and for ocean steamers 
 with the same slip and ratio of v/V. and a dip =1/3 radius, an efficiency of 
 0.685. 
 
 JET-PROPULSION. 
 
 Numerous experiments have been made in driving a vessel by the 
 reaction of a jet of water pumped through an orifice in the stern, but 
 they have all resulted in commercial failure. Two-jet propulsion steamers, 
 the " Waterwitch, " 1100 tons, and the "Squirt," a small torpedo-boat, 
 were built by the British Government. The former was tried in 1867, 
 and gave an efficiency of apparatus of only 18 per cent. The latter gave 
 a speed of 12 knots, as against 17 knots attained by a sister-ship having a 
 screw and equal steam-power. The mathematical theory of the efficiency 
 of the jet was discussed by Rankine in The Engineer, Jan. 11, 1867, and 
 he showed that the greater the quantity of water operated on by a jet- 
 propeller, the greater is the efficiency. In defiance both of the theory 
 and of the results of earlier experiments, and also of the opinions of many 
 naval engineers, more than $200,000 were spent in 1888-90 in New York 
 upon two experimental boats, the "Prima Vista" and the "Evolution," 
 in which the jet was made of very small size, in the latter case only 5/g-inch 
 diameter, and with a pressure of 2500 Ibs. per square inch. As had been 
 predicted, the vessel was a total failure. (See article by the author in 
 Mechanics, March, 1891.) 
 
 The theory of the jet-propeller is similar to that of the screw-propeller. 
 If A = the area of the jet in square feet, V its velocity with reference to 
 the orifice, in feet per second, v = the velocity of the ship in reference to 
 the <earth, then the thrust of the jet (see Screw-propeller, ante) is 2 A V 
 (V v). The work done on the vessel is 2 AV(V - v) v, and the work 
 wasted on the rearward projection of the jet is 1/2 X 2 AV(V v) a . 
 
 The efficiency is 2 ^ y (/^/J^V _, )2 -#; This expression 
 equals unity when V = v, that is, when the velocity of the jet with refer- 
 ence to the earth, or V v, =0; but then the thrust of the propeller is 
 also Q. The greater the value of V as compared with v, the J^ the 
 
CONSTRUCTION OF BUILDINGS. 
 
 1385 
 
 efficiency. For V = 20 v, as was proposed in the "Evolution," the 
 efficiency of the jet would be less than 10 per cent, and this would be 
 further reduced by the friction of the pumping mechanism and of the 
 water in pipes. 
 
 It is practically impossible to devise any system of hydraulic or jet 
 propulsion which can compare favorably, under these conditions, with 
 the screw or the paddle-wheel. 
 
 Reaction of a Jet. If a jet of water issues horizontally from a vessel, 
 the reaction on the side of the vessel opposite the orifice is equal to the 
 weight of a column of water the section of which is the area of the orifice, 
 and the height is twice the head. 
 
 The propelling force in jet-propulsion is the reaction of the stream 
 issuing from the orifice, and it is the same whether the jet is discharged 
 under water, in the open air, or against a solid wall. For proof, see 
 account of trials by C. J. Everett, Jr., given by Prof. J. Burkitt Webb, 
 Trans. A. S. M. E., xii, 904. 
 
 CONSTRUCTION OF BUILDINGS.* 
 
 FOUNDATIONS. 
 
 Bearing Power of Soils. Ira O. Baker, ! Treatise on Masonry 
 Construction.'! 
 
 Kind of Material. 
 
 Bearing Power in 
 Tons per Square Foot. 
 
 Minimum. 
 
 Maximum. 
 
 Rock the hardest in thick layers, in native bed. 
 
 200 
 25 
 15 
 5 
 4 
 2 
 
 8 
 
 4 
 
 0.5 
 
 
 30 
 20 
 10 
 6 
 
 10 
 6 
 
 1 
 
 Rock equal to best brick masonry 
 
 
 Clay on thick beds always dry.. 
 
 
 Clay soft . . . 
 
 
 Sand compact and. well cemented .. 
 
 Sand clean drv 
 
 Quicksand, alluvial soils, etc 
 
 The building code of Greater New York specifies the following as the 
 maximum permissible loads for different soUs: 
 
 " Soft clay, one ton per square foot; 
 
 " Ordinary clay and sand together, in layers, wet and springy, two 
 tons per square foot ; 
 
 "Loam, clay or fine sand, firm and dry, three tons per square foot; 
 
 " Very firm coarse sand, stiff gravel or hard clay, four tons per square 
 foot, or as otherwise determined by the Commissioner of Build- 
 ings having jurisdiction." 
 
 Pocket-book." The latter in its preface mentions the following works of 
 reference: "Notes on Building Construction," 3 vols., Rivingtons, pub- 
 lishers, London; "Building Superintendence," by T. M. Clark (J. R. 
 Osgood &Co., Boston); " The American House Carpenter," and " The Theory 
 of Transverse Strains," both by R. G. Hatfield; "Graphical Analysis of 
 Roof-trusses," by Prof. C. E. Greene; "The Fire Protection of Mills," by 
 C. J. H. Woodbury; "House Drainage and Water Service," by James C. 
 Bayles; "The Builder's Guide and Estimator's Price-book," and "Plaster- 
 ing Mortars and Cements, by Fred.T. Hodgson; "Foundations and Con- 
 crete Works," and "Art of Building," by E. Dobson, Weale's Series, 
 London. 
 
1386 
 
 CONSTRUCTION OF BUILDINGS. 
 
 Bearing: rower of Piles. Engineering News Formula: Safe load in 
 tons = 2 Wh -* (S + 1). W = weight of hammer in tons, h = height of fall 
 of hammer in feet, S penetration under last blow, or the average under 
 last five blows, in inches. 
 
 Safe Strength of Brick Piers, exceeding six diameters in height. 
 < Kidder.) 
 
 Piers laid with rich lime mortar, Ibs. per sq. in., 110 5 H/D. 
 Piers laid with 1 to 2 natural cement mortar, 140 - 51/2 H/D. 
 Piers laid with 1 to 3 Portland cement mortar, 200 6 H/D. 
 H = height; D = least horizontal dimension, in feet. 
 
 Thickness of Foundation Walls. (Kidder.) 
 
 Height of Building. 
 
 Dwellings, 
 Hotels, etc. 
 
 Warehouses. 
 
 Brick. 
 
 Stone. 
 
 Brick. 
 
 Stone. 
 
 Two stories . 
 
 Inches. 
 12 or 16 
 16 
 20 
 
 24 
 28 
 
 Inches. 
 20 
 20 
 24 
 28 
 32 
 
 Inches. 
 16 
 20 
 24 
 24 
 28 
 
 Inches. 
 20 
 
 24 
 28 
 28 
 
 32 
 
 
 Four stories . v ... 
 
 
 
 
 MASONRY. 
 
 Allowable Pressures on Masonry in Tons per Square Foot. (Kidder.) 
 
 Different Cities.* 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 Granite, cut 
 
 60 
 
 
 72-172 
 
 
 
 
 40 
 
 
 40 
 
 
 50-165 
 
 
 
 
 
 Sandstone hard cut 
 
 30 
 
 
 28-115 
 
 
 
 
 12 
 
 Hard-burned brick in Portland cement. . . 
 
 
 
 18 
 
 121/2 
 
 15 
 
 
 
 Hard-burned brick in natural cement 
 Hard-burned brick in cement and lime . . . 
 Hard-burned brick in lime mortar 
 
 15 
 12 
 8 
 
 9 
 6 
 
 15 
 
 m/, 
 
 61/9 
 
 iii/i 
 
 15 
 
 12 
 8 
 
 9 
 
 *8* 
 
 Pressed brick in Portland cement 
 
 
 1? 
 
 
 
 
 
 
 Pressed brick in natural cement 
 
 
 9 
 
 
 
 
 
 ii 
 
 Rubble stone in natural cement 
 
 
 
 8 
 
 
 
 10 
 
 12 
 
 In foundations: 
 Dimension stone 
 
 
 6 
 
 
 5-7 
 
 
 
 V' 
 
 Portland cement concrete! 
 
 
 4 
 
 15 
 
 
 
 15 
 
 10 
 
 Natural cement concrete 
 
 
 
 8 
 
 4 
 
 
 
 4 
 
 *From building laws, (1) Boston, 1897; (2) Buffalo, 1897; (3) New 
 York, 1899; (4) Chicago, 1893; (5) St. Louis, 1897; (6) Philadelphia, 
 1899; (7) Denver, 1898. 
 
 Crushing Strength of 12-in. Cubes of Concrete. (Kidder.) 
 Pounds per square foot. The concrete was made of 1 part Portland 
 cement, 2 parts sand, with average concrete stone and gravel, as below. 
 
 
 10 days. 
 
 45 days. 
 
 3 mos. 
 
 6 mos. 
 
 1 year. 
 
 6 parts stone . . . 
 
 130,750 
 
 172,325 
 
 324,875 
 
 361,600 
 
 440,040 
 
 3 parts stone, 3 gravel 
 4 parts stone, 2 gravel 
 
 136,750 
 
 266,962 
 
 
 298,037 
 
 396,200 
 408,300 
 
 6 parts (3/4 stone, 1/4 grano- 
 lithic) 
 
 
 
 
 
 388,700 
 
 6 parts average gravel 
 6 parts coarse stone, no fine. 
 
 99,900 
 
 234,475 
 
 385,612 
 134,475 
 
 265,550 
 220,350 
 
 406,700 
 266,300 
 
 Reinforced Concrete. The building laws of New York, St. Louis, 
 Cleveland and Buffalo, and the National Board of Fire Underwriters agree 
 in prescribing the following as the maximum allowable working stresses: 
 
BEAMS AND GIKDERS. 1387 
 
 Extreme fiber stress in compression in con- 
 crete 500 lbs. <4 per sq. In. 
 
 Shearing stress in concrete 50 
 
 Direct compression in concrete 350 
 
 Adhesion of steel to concrete 50 
 
 Tensile stress in steel 16,000 
 
 Shearing stress in steel 10,000 
 
 BEAMS AND GIRDERS. 
 Safe Loads on Beams. Uniformly distributed load: 
 
 2 X breadth X square of depth X A 
 span in feet 
 
 Breadth in inches - Pan in feet X toad . 
 2 X square of depth X A 
 
 Safe load in Ibs. = 
 
 The depth is taken in inches. The coefficient A, is 1/18 the maximum 
 fiber stress for safe loads, and is the safe Ipad for a beam 1 in. square, 1 ft. 
 span. The foltowing values of A are given by Kidder as one-third of 
 the breaking weight of timber of the quality used in first-class buildings. 
 The values for stones are based on a factor of safety of six. 
 VALUES FOR A. - COEFFICIENT FOR BEAMS. 
 
 Cast iron. .' 308 
 
 Wrought iron 666 
 
 Steel. 888 
 
 American Woods: 
 
 Chestnut 60 
 
 Hemlock 55 
 
 Oak, white... 75 
 
 Pine, Georgia yellow 100 
 
 Pine, Oregon 90 
 
 Pine, red or Norway 70 
 
 Pine, white, Eastern 60 
 
 Pine, white. Western 65 
 
 Pine, Texas yellow 90 
 
 Spruce 70 
 
 Whitewood (poplar) 65 
 
 Redwood (California) 60 
 
 Bluestone flagging (Hudson 
 
 River) 25 
 
 Granite, average 17 
 
 Limestone 14 
 
 Marble 17 
 
 Sandstone 8 to 1 1 
 
 Slate 50 
 
 Safe Loads in Tons, Uniformly Distributed, for White-oak Beams. 
 
 (In accordance with the Building Laws of Boston.) 
 
 W safe load in pounds; P, extreme fiber- 
 4 PBD 2 stress = 1000 Ibs. per square inch, for white 
 oak; B, breadth in inches; D, depth in inches; 
 L, distance between supports in inches. 
 
 Formula: W = 
 
 3L 
 
 Distance between Supports in Feet. 
 
 *! 
 
 &- 
 
 6 | 8 
 
 10 
 
 11 
 
 12 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 21 
 
 23 
 
 25 
 
 26 
 
 & 
 
 Safe Load in Tons of 2000 Pounds. 
 
 2x6 
 
 67 
 
 50 
 
 40 
 
 36 
 
 33 
 
 29 
 
 27 
 
 25 
 
 24 
 
 22 
 
 
 
 
 
 
 2x8 
 
 1.19 
 
 0!89 
 
 OJI 
 
 0!65 
 
 0.59 
 
 0.51 
 
 0.47 
 
 0.44 
 
 0.42 
 
 0.40 
 
 0.37 
 
 0.34 
 
 0.31 
 
 0.28 
 
 
 2x10 
 
 1.85 
 
 1.39 
 
 1.11 
 
 1.01 
 
 0.93 
 
 0.79 
 
 0.74 
 
 0.69 
 
 0.65 
 
 0.62 
 
 0.58 
 
 0.53 
 
 0.48 
 
 0.43 
 
 0.43 
 
 2x12 
 
 2.67 
 
 2.00 
 
 1.60 
 
 1.45 
 
 1.33 
 
 1.14 
 
 1.07 
 
 1.00 
 
 0.94 
 
 0.89 
 
 0.84 
 
 0.76 
 
 0.70 
 
 0.64 
 
 0.62 
 
 3x6 
 
 1.00 
 
 0.75 
 
 0.60 
 
 0.55 
 
 0.50 
 
 0.43 
 
 0.40 
 
 0.37 
 
 0.35 
 
 0.33 
 
 0.32 
 
 0.29 
 
 0.26 
 
 
 
 3x8 
 
 1.78 
 
 1.33 
 
 1.07 
 
 0.97 
 
 0.89 
 
 0.76 
 
 0.71 
 
 0.67 
 
 0.63 
 
 0.59 
 
 0.56 
 
 0.51 
 
 0.46 
 
 6!43 
 
 6.'4J 
 
 3x10 
 
 2.78 
 
 2.08 
 
 1.67 
 
 1.52 
 
 .39 
 
 .19 
 
 1.11 
 
 1.04 
 
 0.98 
 
 0.93 
 
 0.88 
 
 0.79 
 
 0.72 
 
 0.67 
 
 0.64 
 
 3x12 
 
 4.00 
 
 3.00 
 
 2.40 
 
 2.18 
 
 2.00 
 
 1.71 
 
 1.60 
 
 1.50 
 
 .41 
 
 .33 
 
 1.26 
 
 1.14 
 
 1.04 
 
 0.96 
 
 0.92 
 
 3x14 
 
 5.45 
 
 4.08 
 
 3.27 
 
 2.97 
 
 2 72 
 
 2.37 
 
 2.18 
 
 2.04 
 
 .92 
 
 .82 
 
 .72 
 
 1.56 
 
 1.42 
 
 1.31 
 
 1.25 
 
 3x16 
 
 7.11 
 
 5.33 
 
 4.27 
 
 3.88 
 
 3.56 
 
 3.05 
 
 2.84 
 
 2.67 
 
 2.51 
 
 2.37 
 
 2.25 
 
 2.03 
 
 1.86 
 
 1.71 
 
 1.64 
 
 4x10 
 
 3.70 
 
 2.78 
 
 2.22 
 
 2.02 
 
 1.85 
 
 1.59 
 
 1.48 
 
 1.39 
 
 1.31 
 
 1.23 
 
 1.17 
 
 1.06 
 
 0.97 
 
 0.89 
 
 0.85 
 
 4x12 
 
 5.33 
 
 4.00 
 
 3.20 
 
 2.91 
 
 2.67 
 
 2.29 
 
 2.13 
 
 2.00 
 
 1.88 
 
 1.78 
 
 1.68 
 
 1.52 
 
 1.39 
 
 1.28 
 
 1.23 
 
 4x14 
 
 7 76 
 
 5 44 
 
 4 36 
 
 * 96 
 
 3 63 
 
 3 11 
 
 7 90 
 
 7, 7? 
 
 ?, 56 
 
 7, 47, 
 
 7. 29 
 
 2.07 
 
 1.90 
 
 1.74 
 
 1.68 
 
 4X16 
 
 9.48 
 
 7.11 
 
 5.69 
 
 5.17 
 
 4.74 
 
 4.06 
 
 3.79 
 
 3.56 
 
 3.35 
 
 3.16 
 
 3.00 
 
 2.71 
 
 2.47 
 
 2.28 
 
 2.19 
 
 4x18 
 
 12.00 
 
 9.00 
 
 7.20 
 
 6.55 
 
 6.00 
 
 5.14 
 
 4.80 
 
 4.50 
 
 4.24 
 
 4.00 
 
 3.79 
 
 3.43 
 
 3.13 
 
 2.88 
 
 2.77 
 
 For other kinds of wood than white oak multiply the figures in the 
 table by a figure selected from those given below (which represent the 
 
1388 
 
 CONSTRUCTION OF BUILDINGS- 
 
 safe stress per square inch on beams of different kinds of wood accord- 
 ing to the building laws of the cities named) and divide by 1000. 
 
 
 Hem- 
 lock. 
 
 Spruce. 
 
 White 
 Pine. 
 
 Oak. 
 
 Yellow 
 Pine. 
 
 New York . 
 
 800 
 
 900 
 
 900 
 
 1100 
 
 1 100* 
 
 Boston 
 
 
 750 
 
 750 
 
 lOOOf 
 
 1250 
 
 Chicago 
 
 
 
 900 
 
 1080 
 
 1440 
 
 * Georgia pine. t White oak. 
 
 Maximum Permissible Stresses in Structural Materials used in 
 Buildings. (Building Ordinances of the City of Chicago, 1893.) Cast 
 iron, crushing stress: For plates, 15,000 Ibs. per square inch; for lintels, 
 brackets, or corbels, compression 13,500 Ibs. per square inch, and tension 
 3000 Ibs. per square inch. For girders, beams, corbels, brackets, and 
 trusses, 16,000 Ibs. per square inch for steel and 12,000 Ibs. for iron. 
 
 For plate girders: 
 
 Flange area = maximum bending moment in ft .-Ibs. *- (CD). 
 
 D = distance between center of gravity of flanges in feet. 
 
 C = 13,500 for steel, 10,000 for iron. 
 
 Web area = maximum shear *- C. 
 
 C = lOiOOQ for steel; 6,000 for iron. 
 
 For rivets in single shear per square inch of rivet area: 
 
 If shop-driven, steel, 9000 Ibs., iron, 7500 Ibs.; if field-driven steel 
 7500 Ibs., iron, 6000 Ibs. 
 For timber girders: S = cbd~ -f- I. 
 
 b = breadth of beam in inches, d = depth of beam in inches, I length 
 of beam in feet, c = 160 for long-leaf yellow pine, 120 for oak, 100 for 
 white or Norway pine. 
 
 WALLS. 
 
 Thickness of Walls of Buildings. Kidder gives the following gen- 
 eral rule for mercantile buildings over four stories in height : 
 
 For brick equal to those used in Boston or Chicago, make the thickness 
 of the three upper stories 16 ins., of the next three below 20 ins., the next 
 three 24 ins., and the next three 28 ins. For a poorer quality of material 
 make only the two upper stories 16 ins. thick, the next three 20 ins. and 
 so on down. 
 
 In buildings less than five stories in height the top story may be 12 
 ins. in thickness. 
 
 THICKNESS OF WALLS IN INCHES, FOR MERCANTILE BUILDINGS AND FOR 
 ALL BUILDINGS OVER FIVE STORIES IN HEIGHT . (The figures show the 
 range of the thicknesses required by the ordinances of eight different 
 cities. Condensed from Kidder.) 
 
 Stories 
 
 Stories. 
 
 High. 
 
 1st. 
 
 2d. 
 
 3d. 
 
 4th. 
 
 5th. 
 
 6th. 
 
 7th. 
 
 8th. 
 
 9th. 
 
 10th 
 
 llth 
 
 12th 
 
 2 
 
 12-18 
 
 12-13 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 13-20 
 
 12-18 
 
 12-16 
 
 
 
 
 
 
 
 
 
 
 4 
 
 16-22 
 
 16-18 
 
 12-18 
 
 12-16 
 
 
 
 
 
 
 
 
 
 5 
 
 18-22 
 
 16-22 
 
 16-20 
 
 12-20 
 
 12-16 
 
 
 
 
 
 
 
 
 6 
 
 20-26 
 
 18-22 
 
 16-22 
 
 16-20 
 
 13-20 
 
 12-16 
 
 
 
 
 
 
 
 7 
 
 20-28 
 
 20-26 
 
 18-24 
 
 16-22 
 
 16-20 
 
 13-20 
 
 12-17 
 
 
 
 
 
 
 8 
 
 22-32 
 
 20-28 
 
 20-26 
 
 18-24 
 
 16-22 
 
 16-20 
 
 13-20 
 
 12-17 
 
 
 
 
 
 9 
 
 24-32 
 
 24-32 
 
 20-28 
 
 20-26 
 
 20-24 
 
 16-22 
 
 16-20 
 
 16-20 
 
 12-17 
 
 
 
 
 10 
 
 24-36 
 
 24-32 
 
 24-32 
 
 20-28 
 
 20-26 
 
 20-24 
 
 16-22 
 
 16-20 
 
 16-20 
 
 12-17 
 
 
 
 11 
 
 28-36 
 
 28-36 
 
 24-32 
 
 24-30 
 
 24-28 
 
 20-26 
 
 20-24 
 
 20-22 
 
 16-20 
 
 16-20 
 
 13-17 
 
 
 12 
 
 28-40 
 
 28-36 
 
 28-36 
 
 24-32 
 
 24-32 
 
 24-28 
 
 20-26 
 
 20-24 
 
 20-22 
 
 16-20 
 
 16-20 
 
 13-17 
 
 (Extract from the Building Laws of the City of New York, 1893.) 
 Walls of Warehouses, Stores, Factories, and Stables. 25 feet 
 or less in width between walls, not less than 12 in. to height of 40 ft. 
 If 40 to 60 ft. in height, not less than 16 in. to 40 ft., and 12 in. thence 
 to top; 
 
COLUMNS AND POSTS. 1389 
 
 60 to 80 ft. in height, not less than 20 in. to 25 ft., and 16 in. thence to 
 
 top; 
 75 to 85 ft. in height, not less than 24 in. to 20 ft.; 20 in. to 60 ft., and 
 
 16 in. to top; 
 85 to 100 ft. in height, not less than 28 in. to 25 ft.; 24 in; to 50 ft.; 
 
 20 in. to 75 ft., and 16 in. to top; 
 
 Over 100 ft. in height, each additional 25 ft. in height, or part thereof, 
 next above the curb, shall be increased 4 inches in thickness, the 
 upper 100 feet remaining the same as specified for a wall of that 
 height. 
 
 If walls are over 25 feet apart, the bearing- walls shall, be 4 inches 
 thicker than above specified for every 121/2 feet or fraction thereof that 
 said walls are more than 25 feet apart. 
 
 Strength of Floors, Roofs, and Supports. 
 
 Floors calculated to 
 bear safely per sq. ft., in 
 addition to their own wt. 
 Floors of dwelling, tenement, apartment-house or hotel, not 
 
 less than 70 Ibs. 
 
 Floors of office-building, not less than 100 " 
 
 Floors of public-assembly building, not less than 120 " 
 
 Floors of store, factory, warehouse, etc., not less than 150 " 
 
 Roofs of all buildings, not less than 50 " 
 
 Hivery ttoor shall be of sufficient strength to bear safely the weight to be 
 imposed thereon, in addition to the weight of the materials of which the 
 floor is composed. 
 
 Columns and Posts. The strength of all columns and posts shall 
 be computed according to Gordon's formulae, and the crushing weights in 
 pounds, to the square ~inch of section, for the following-named materials, 
 shall be taken as the coefficients in said formulae, namely: Cast iron, 80,000; 
 wrought or rolled iron, 40,000: rolled steel, 48,000: white pine and spruce, 
 3500: pitch or Georgia pine y 5000; American oak, 6000. The breaking 
 strength of wooden beams and girders shall be computed according to 
 the formulae in which the constants for transverse strains for central load 
 shall be as follows, namely: Hemlock, 400; white pine, 450; spruce, 450; 
 pitch or Georgia pine, 550 ; American oak, 550 ; and for wooden beams and 
 girders carrying a uniformly distributed load the constants will be doubled. 
 The factors of safety shall be as. one to four for all beams, girders, and 
 other pieces subject to a transverse strain; as one to four for all posts, 
 columns, and other vertical supports when of wrought iron or rolled steel; 
 as one to five for other materials, subject to a compfessive strain; as one 
 to six for tie-rods, tie-beams, and other pieces subject to a tensile strain. 
 Good, solid, natural earth shall be deemed to sustain safely a load of four 
 tons to the superficial foot, or as otherwise determined by the super- 
 intendent of buildings, and the width of footing-courses shall be at least 
 sufficient to meet this requirement. In computing the width of walls, 
 a cubic foot of brickwork shall be deemed to weigh 115 Ibs. Sandstone, 
 white marble, granite, and other kinds of building-stone shall be deemed 
 to weigh 160 Ibs. per cubic foot. The safe-bearing load to apply to 
 good brickwork shall be taken at 8 tons per superficial foot when good 
 lime mortar is used, 111/2 tons per superficial foot when good lime and 
 cement mortar mixed is used, and 15 tons per superficial foot when good 
 cement mortar is used. 
 
 Fire-proof Buildings Iron and Steel Columns. All cast-iron, 
 wrought-iron, or rolled-steel columns shall be made true and snwoth at 
 both ends, and shall rest on iron ofe steel bed-plates, and have iron or 
 steel cap-plates, which shall also be made true. All iron or steel trimmer- 
 beams, headers, and tail-beams shall be suitably framed and connected 
 together, and the iron girders, columns, beams, trusses, and all other iron- 
 work of all floors and roofs shall be strapped, bolted, anchored, and con- 
 nected together, and to the walls, in a strong and substantial manner. 
 Where beams are framed into headers, the angle-irons, which are bolted 
 to the tail-beams, shall have at least two bolts for all beams over 7 inches 
 in depth, and three bolts for all beams 12 inches and over in depth, and 
 these bolts shall not be less than 3/ 4 inch in diameter. Each one of such 
 
1390 CONSTRUCTION OF BUILDINGS. 
 
 * \ 
 
 angles or knees, when bolted to girders, shall have the same number~of 
 bolts as stated for the other leg. The angle-iron in no case shall be less 
 in thickness than the header or trimmer to which it is bolted, and the 
 width of angle in no case shall be less than one third the depth of beam, 
 excepting that no angle-knee shall be less than 2 1/2 inches wide, nor 
 required to be more than 6 inches wide. All wrought-iron or rolled-steel 
 beams 8 inches deep and under shall have bearings equal to their depth, 
 if resting on a wall; 9 to 12 inch beams shall have a bearing of 10 inches, 
 and all beams more than 12 inches in depth shall ha.ve bearings of not 
 less than 12 inches if resting on a wall. Where beams rest on iron sup- 
 ports, and are properly tied to the same, no greater bearings shall be 
 required than one third of the depth of the beams. Iron or steel floor- 
 beams shall be so arranged as to spacing and length of beams that the 
 load to be supported by them, together with the weights of the materials 
 used in the construction of the said floors, shall n9t cause a deflection of 
 the said beams of more than 1/30 of an inch per linear foot of span; and 
 they shall be tied together at intervals of not more than eight times the 
 depth of the beam. 
 
 Under the ends of all iron or steel beams, where they rest on the walls, a 
 stone or cast-iron template shall be built into the walls. Said template 
 shall be 8 inches wide in 12-inch walls, and in all walls of greater thickness 
 said template shall be 12 inches wide; and such templates, if of stone, 
 shall not be in any case less than 21/2 inches in thickness, and no template 
 shall be less than 12 inches long. 
 
 No cast-iron post or columns shall be used in any building of a less 
 average thickness of shaft than three quarters of an inch, nor shall it 
 have an unsupported length of more than twenty times its least lateral 
 dimensions or diameter. No wrought-iron or rolled-steel column shall 
 have an unsupported length of more than thirty times its least lateral 
 dimensions or diameter, nor shall its metal be less than one fourth of an 
 inch in thickness. 
 
 Lintels, Bearings and Supports. All iron or steel lintels shall 
 have bearings proportionate to the weight to be imposed thereon, but no 
 lintel used to span any opening more than 10 feet in width shall have a 
 bearing less than 12 inches at each end, if resting on a wall; but if resting 
 on an iron post, such lintel shall have a bearing of at least 6 inches at each 
 end, by the thickness of the wall to be supported. 
 
 Strains on Girders and Rivets. Rolled iron or steel beam girders, 
 or riveted iron or steel plate girders used as lintels or as girders, carrying 
 a wall or floor or both, shall be so prop9rtioned that the loads which may 
 come upon them shall not produce strains in tension or compression upon 
 the flanges of more than 12,000 Ibs. for iron, nor more than 15,000 Ibs. 
 for steel per square inch of the gross section of each of such flanges, nor 
 a shearing strain upon the web-plate of more than 6000 Ibs. per square 
 inch of section of such web-plate, if of iron, nor more than 7000 pounds 
 if of steel; but no web-plate shall be less than 1/4 inch in thickness. Rivets 
 in plate girders shall not be less than 5/s inch in diameter, and shall not be 
 spaced more than 6 inches apart in any case. They shall be so spaced 
 that their shearing strains shall not exceed 9000 Ibs. per square inch, on 
 their diameter, multiplied by the thickness of the plates through which 
 they pass. The riveted plate girders shall be proportioned upon the 
 supposition that the bending or chord strains are resisted entirely by the 
 upper and lower flanges, and that tne shearing strains are resisted en- 
 tirely by the web-plate. No part of the web shall be estimated as flange 
 area, nor more than one half of that portion 01 the angle-iron which lies 
 against the web. The distance between the centers of gravity of the 
 flange areas will be considered as the effective depth of the girder. 
 
 The building laws of the city of New York contain a great amount of 
 detail in addition to the extracts above, and penalties are provided for 
 violation. See An Act creating a Department of Buildings, etc., Chapter 
 275, Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., 
 New York. 
 
 FLOORS. 
 
 Maximum Load on Floors. (Eng'g, Nov. 18, 1892, p. 644.) Maxi- 
 mum load per square foot of floor surface due to the weight of a dense 
 crowd. Considerable variation is apparent in the figures given by many 
 authorities, as the following table shows: 
 
STRENGTH OF FLOCKS, 1391 
 
 Authorities. Weight of Crowd. 
 
 Ibs. per sq. ft. 
 
 French practice, quoted by Trautwine and Stoney 41 
 
 Hatfield ("Transverse Strains, " p. 80) 70 
 
 Mr. Page, London, quoted by Trautwine 84 
 
 Maximum load on American highway bridges according to 
 
 Waddell's general specifications ' 100 
 
 Mr. Nash, architect of Buckingham Palace 120 
 
 Experiments by Prof. W. N. Kernot, at Melbourne j j||j 2 
 
 Experiments by Mr. B. B. Stoney ("On Stresses," p. 617) 147^4 
 
 Experiments by Prof. L. J. Johnson, Eng. News, April 14, f 134.2 
 
 1904 -. . (to 156.9 
 
 The highest results were obtained by crowding a number of persons 
 previously weighed into a small room, the men being tightly packed so as 
 to resemble such a crowd as frequently occurs on the stairways and plat- 
 forms of a theatre or other public building. 
 
 Safe Allowances for Floor Loads. (Kidder.) Lbs. per square foot 
 
 For dwellings, sleeping and lodging rooms 40 Ibs. 
 
 For schoolrooms 50 
 
 For offices, Upper stories 60 
 
 For offices, first story 80 
 
 For stables and carriage houses 65. 
 
 For banking rooms, churches and theaters 80 
 
 For assembly halls, dancing halls, and the corridors of all 
 
 public buildings, including hotels 120 ' 
 
 For drill rooms 150 ' 
 
 For ordinary stores, lighc storage, and light manufactur- 
 ing 120* M 
 
 * Also to sustain a concentrated load at any point of 4000 Ibs. 
 
 STRENGTH OF FLOORS. 
 
 (From circular of the Boston Manufacturers' Mutual Insurance Co.) * 
 
 The tables on p. 1393 were prepared by C. J. H. Woodbury, for deter- 
 mining safe loads on floors. Care should be observed to select the 
 figure giving the greatest possible amount and concentration of load as 
 the one which may be put upon any beam or set of floor-beams; and 
 in no case should beams be subjected to greater loads than those speci- 
 fied, unless a l9wer factor of safety is warranted under the advice of a 
 competent engineer. These tables are computed for beams one inch in 
 width, because the strength of beams increases directly as the width 
 when the beams are broad enough not to cripple. 
 
 Beams or heavy timbers used in the construction of a factory or ware- 
 house should not be painted, varnished or oiled, filled or encased in 
 impervious concrete, air-proof plastering, or metal for at least three years, 
 lest fermentation should destroy them by what is called "dry rot." 
 
 It is, on the whole, safer to make floor-beams in two parts with a 
 small open space between, so that proper ventilation may be secured. 
 
 These tables apply to distributed loads, but the first can be used in 
 respect to floors which may carry concentrated loads by using half the 
 figure given in the table, since a beam will bear twice as much load 
 when evenly distributed over its length as it would if the load was 
 concentrated in the centsr of the span. 
 
 The weight of the floor should be deducted from the figure given in 
 the table, in order to ascertain the net load which may be placed upon 
 any floor. The weight of spruce may be taken at 36 Ibs. per cubic 
 foot, and that of Southern pine at 48 Ibs. per cubic foot. 
 
 Table I was computed upon a working modulus of rupture of South- 
 ern pine of 2160 Ibs., using a factor of safety of six. It can also be 
 applied to ascertaining the strength of spruce beams if the figures 
 given in the table arc multiplied by 0.78; or in designing a floor to be 
 sustained by spruce beams, multiply the required load by 1.28, and 
 use the dimensions as given by the table. 
 
 EXAMPLE. Required the safe load per square foot of floor, which 
 may be safely sustained by a floor on Southern pine 10 X 14 in. beams, 
 8 ft, on centers, and 20 ft. span. In Table I a 1 X 14 in. beam, 20 ft. 
 
1392 CONSTRUCTION OF BUILDINGS, 
 
 span, will sustain 118 Ibs. per foot of span; and for a beam 10 ins. wide 
 the load would be 1180 Ibs. per foot of span, or 1471/2 Ibs. per sq. ft. of 
 floor for Southern-pine beams. From this should be deducted the 
 weight of the floor, 171/2 Ibs. per sq. ft., leaving 130 Ibs. per sq. ft. as a 
 safe load. If the beams are of spruce, multiply 1471/2 by 0.78, reduc- 
 ing the load to 115 Ibs. Deducting the weight of the floor, 16 Ibs., 
 leaves the safe net load as 90 Ibs. per sq. ft. for spruce beams. 
 
 Table II applies to floors whose strength must be in excess of that 
 necessary to sustain the weight, in order to meet the conditions of deli- 
 cate or rapidly moving machinery, to the end that the vibration or 
 distortion of the floor may be reduced to the least practicable limit. 
 
 In the table the limit is that of a load which would cause a bending 
 of the beams to a curve, of which the average radius would be 1250 ft. 
 
 This table is based upon a modulus of elasticity obtained from obser- 
 vations upon the deflection of loaded storehouse floors, and is taken at 
 2,000,000 Ibs. for Southern pine; the same table can be applied to spruce, 
 whose modulus of x elasticity is taken as 1,200,000 Ibs., if six tenths 91 
 the load for Southern pine is taken as the proper load for spruce; or, in 
 the matter of designing, the load should be increased one and two thirds 
 times, and the dimension of timbers for this increased load as found in 
 the table should be used for spruce. 
 
 It can also be applied to beams and floor-timbers supported at each 
 end and in the middle, remembering that the deflection of a beam sup- 
 ported in that manner is only 0.4 that of a beam of equal span which 
 rests at each end ; that is to say, the floor-planks are 2 V2 times as stiff, 
 cut two bays in length, as they would be if cut only one bay in length. 
 When a floor-plank two bays in length is evenly loaded, 3/ 16 of the load 
 on the plank is sustained by the beam at each end of the plank, and io/ifj 
 by the beam under the middle of the plank; so that for a completed floor 
 3/8 of the load would be sustained by the beams under the joints of the 
 plank, and 5/g of the load by the beams under the middle of the plank: 
 this is the reason of the importance of breaking joints in a floor-plank 
 every 3 ft. in order that each beam shall receive an identical load. If 
 - it were not so, 3/g of the whole load upon the floor would be sustained 
 by every other beam, and 5/8 of the load by the alternate beams. 
 
 Repeating the former example for the load on a mill floor on Southern- 
 pine beams 10 X 14 ins., and 20 ft. span, 8 ft. centers: In Table II a 
 1 X 14 in. beam should receive 61 Ibs. per foot of span, or 75 Ibs. per 
 sq. ft. of floor, for Southern-pine beams. Deducting the weight of the 
 floor, 171/2 Ibs. per sq. ft., 57 Ibs. per sq. ft. is the advisable load. 
 
 If the beams are of spruce, the result of 75 Ibs. should be multiplied 
 by 0.6, reducing the load to 45 Ibs. The weight of the floor, in this 
 instance amounting to 16 Ibs., would leave the net load as 29 Ibs. for 
 spruce beams. 
 
 If the beams were two spans in length, they could, under these con- 
 ditions, support two and a half times as much load with an equal amount 
 of deflection., unless such load should exceed tlie limit of safe load as found 
 by Table I, as would be the case under the conditions of this problem. 
 
 Maximum Spans for 1, 3 and 3 Inch Plank. (Am. Macli., Feb. 11, 
 1904.) Let w = load per sq. ft.; I = length in in*; ; W = wl/12; S = 
 safe fiber stress, using a factor of safety of 10; 6 = wic?*h of plank; d = 
 thickness; p = deflection, E = coefficient of elasticity, sT = moment of 
 inertia = Vl2 bd*. 
 
 Then Wl/S = Sbd*/Q; s = 5 Wl* ^ 384 EL Taking S at 1200 Ibs., E 
 at 850,000 and s = L -* 360 for long-leaf yellow pine, the following figures 
 for maximum span, in inches, are obtained: 
 
 Uniform load, Ibs. per sq.ft.. 40 60 80 100 150 200 250 300 
 
 i to -niankJ Forstren g tn - 7 5 61 53 48 39 33 
 
 1K t For deflection .37 33 30 28 24 22 
 
 9 in n i nn i,f For strength.. 151 123 107 96 78 67 60 55 
 lk \ For deflection . 75 66 60 55 48 44 41 38 
 
 sir T^ioni, | For strength.. 227 185 161 144 117 101 91 83 
 1K 1 For deflection. 113 99 90 83 73 66 61 58 
 For white oak S may be taken at 1000 and E at 550,000; for Canadian 
 spruce, S = 800, E = 600,000; for hemlock, S = 600, E = 450,000. 
 
BTREiSfGTll OF FL001W, 
 
 1393 
 
 I. Safe Distributed Loads upon Southern-pine Beams One Inch 
 in Width. 
 
 (C. J. H, Woodbury.) 
 
 (If the load is concentrated at the center of the span, the beams 
 will sustain half the amount given in the table.) 
 
 1 
 
 i 
 
 a 
 m 
 
 Depth of Beam in inches. 
 
 2 
 
 3 
 
 4 | 5 
 
 6 | 7 
 
 8 
 
 9 
 
 10 | 11 
 
 12|l3 
 
 14 
 
 15 
 
 16 
 
 Load in pounds per foot of Span. 
 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 
 38 
 27 
 20 
 15 
 
 86 
 60 
 
 44 
 34 
 27 
 22 
 
 154 
 107 
 
 78 
 60 
 47 
 33 
 32 
 27 
 
 240 
 167 
 122 
 94 
 74 
 60 
 50 
 42 
 35 
 31 
 27 
 
 346 
 240 
 176 
 135 
 107 
 86 
 71 
 60 
 51 
 44 
 38 
 34 
 30 
 
 470 
 327 
 240 
 184 
 145 
 118 
 97 
 82 
 70 
 60 
 52 
 46 
 41 
 36 
 
 614 
 427 
 314 
 240 
 190 
 154 
 127 
 107 
 90 
 78 
 68 
 60 
 53 
 47 
 43 
 38 
 
 778 
 540 
 397 
 304 
 240 
 194 
 161 
 135 
 115 
 9Q 
 86 
 76 
 67 
 60 
 54 
 49 
 44 
 
 960 
 667 
 490 
 375 
 296 
 240 
 198 
 167 
 142 
 123 
 107 
 94 
 83 
 74 
 66 
 60 
 54 
 50 
 45 
 
 807 
 593 
 454 
 359 
 290 
 240 
 202 
 172 
 148 
 129 
 113 
 101 
 90 
 80 
 73 
 66 
 60 
 55 
 50 
 46 
 
 705 
 540 
 427 
 346 
 286 
 240 
 205 
 176 
 154 
 135 
 120 
 107 
 96 
 86 
 78 
 71 
 65 
 60 
 55 
 
 828 
 634 
 501 
 406 
 335 
 282 
 240 
 207 
 180 
 158 
 140 
 125 
 112 
 101 
 92 
 84 
 77 
 70 
 65 
 
 735 
 581 
 470 
 389 
 327 
 278 
 240 
 209 
 184 
 163 
 145 
 130 
 118 
 107 
 97 
 89 
 82 
 75 
 
 667 
 540 
 446 
 375 
 320 
 276 
 240 
 211 
 187 
 167 
 150 
 135 
 122 
 112 
 102 
 94 
 86 
 
 759 
 614 
 508 
 474 
 364 
 314 
 273 
 240 
 217 
 190 
 170 
 154 
 139 
 127 
 116 
 107 
 98 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 II. Distributed Loads upon Southern-pine Beams Sufficient to 
 Produce Standard Limit of Deflection. 
 
 1 
 
 ef 
 
 a 
 
 VI 
 
 ~T 
 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 
 Depth of Beam in inches. 
 
 Deflection, 
 inches. I 
 
 2 
 
 3 
 
 4 
 
 5 | 6 | 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 Load in pounds per foot of Span. 
 
 3 
 
 2 
 
 10 
 
 7 
 5 
 4 
 
 23 
 16 
 12 
 9 
 7 
 6 
 
 44 
 31 
 23 
 17 
 14 
 11 
 9 
 
 77 
 53 
 39 
 30 
 24 
 19 
 16 
 13 
 11 
 
 122 
 85 
 62 
 48 
 38 
 30 
 25 
 21 
 18 
 16 
 14 
 
 182 
 126 
 93 
 71 
 56 
 46 
 38 
 32 
 27 
 23 
 20 
 18 
 16 
 
 259 
 180 
 132 
 101 
 80 
 65 
 54 
 45 
 38 
 33 
 29 
 25 
 22 
 20 
 18 
 
 247 
 181 
 139 
 110 
 89 
 73 
 62 
 53 
 45 
 40 
 35 
 31 
 27 
 25 
 22 
 20 
 
 241 
 185 
 146 
 118 
 98 
 82 
 70 
 60 
 53 
 46 
 41 
 37 
 33 
 30 
 27 
 24 
 22 
 
 240 
 190 
 154 
 127 
 107 
 91 
 78 
 68 
 60 
 53 
 47 
 43 
 38 
 35 
 32 
 29 
 27 
 25 
 
 305 
 241 
 195 
 161 
 136 
 116 
 100 
 87 
 76 
 68 
 60 
 54 
 49 
 44 
 40 
 37 
 34 
 31 
 
 301 
 244 
 202 
 169 
 144 
 124 
 108 
 95 
 84 
 75 
 68 
 61 
 55 
 50 
 46 
 42 
 39 
 
 300 
 248 
 208 
 178 
 153 
 133 
 117 
 104 
 93 
 83 
 75 
 68 
 62 
 57 
 52 
 48 
 
 301 
 253 
 215 
 186 
 162 
 147 
 126 
 112 
 101 
 91 
 83 
 75 
 69 
 63 
 58 
 
 .0300 
 .0432 
 .0588 
 .0768 
 .0972 
 .1200 
 .1452 
 .1728 
 .2028 
 .2352 
 .2700 
 .3072 
 .3468 
 .3888 
 .4332 
 .4800 
 .5292 
 .5808 
 .6348 
 .6912 
 .7500 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Mill Columns. Timber posts offer more resistance to fire than iron 
 pillars, and have generally displaced them in millwork. Experiments 
 
1394 
 
 CONSTRUCTION OF BUlLblNGS. 
 
 at the U. S. Arsenal at Watertown, Mass., show that sound timber posts 
 of the proportions customarily used in millwork yield by direct crush- 
 ing, the strength being directly as the area at the smallest part. The 
 columns yielded at about 4500 Ibs. per sq. in., confirming the general 
 practice of allowing 600 Ibs. per sq. in. as a safe load. Square columns 
 are one fourth stronger than round ones of the same diameter. 
 
 COST OF BUILDINGS. 
 
 Approximate Cost of Mill. Buildings. Chas. T. Main (Eng. News, 
 Jan. 27, 1910) gives a series of diagrams of the cost in New England 
 Jan., 1910, per sq. ft. of floor space of different sizes of brick mill build- 
 ings, one to six stories high, of the type known as "slow-burning," cal- 
 culated for total floor loads of about 75 Ibs. per sq. ft. Figures taken 
 from the diagrams are given in the table below. The costs include 
 ordinary foundations and plumbing, but no heating, sprinklers or lighting. 
 COST OF BRICK MILL BUILDINGS PER SQ. FT. OF FLOOR AREA. 
 
 Length, feet. 50 100 150 200 250 300 350 400 500 
 
 One Story. 
 
 Width 25 ft. 
 50 
 75 
 125 
 
 $1.90 
 1.52 
 1.41 
 1.32 
 
 $1.66 
 1.29 
 1.21 
 1.09 
 
 $1.58 
 1.21 
 1.12 
 1.02 
 
 $1.54 
 1.18 
 1.08 
 0.98 
 
 $1.51 
 1.16 
 1.06 
 0.96 
 
 $1.49 
 1.15 
 1.04 
 0.94 
 
 $1.48 
 1.14 
 1.03 
 0.94 
 
 $1.47 
 1.13 
 1.02 
 0.93 
 
 $1.46 
 1.13 
 1.02 
 0.92 
 
 Two Stories. 
 
 25 
 50 
 75 
 125 
 
 2.00 
 1.50 
 1.34 
 1.22 
 
 1.62 
 1.21 
 1.08 
 0.97 
 
 1.52 
 1.13 
 1.01 
 0.90 
 
 1.47 
 1.09 
 0.97 
 0.86 
 
 1.44 
 1.06 
 0.94 
 0.84 
 
 1.41 
 1.05 
 0.92 
 0.82 
 
 1.39 
 1.04 
 0.92 
 0.81 
 
 1.38 
 1.03 
 0.91 
 0.80 
 
 1.36 
 1.02 
 0.90 
 0.8J 
 
 Three Stories. 
 
 25 
 50 
 75 
 125 
 
 1.$8 
 1.47 
 1.30 
 1.18 
 
 1.57 
 1.17 
 1.05 
 0.93 
 
 1 47 
 1.07 
 0.98 
 0.86 
 
 1.42 
 1.03 
 0.94 
 0.82 
 
 1.39 
 1.01 
 0.91 
 0.80 
 
 1.38 
 1.00 
 0.89 
 0.78 
 
 1.36 
 0.98 
 0.88 
 0.77 
 
 1.35 
 0.98 
 0.87 
 0.76 
 
 1.34 
 0.98 
 0.86 
 0.76 
 
 Four Stories. 
 
 25 
 50 
 75 
 125 
 
 2.00 
 1.38 
 1.32 
 1.20 
 
 1.61 
 1.17 
 1.08 
 0.93 
 
 1.50 
 1.10 
 97 
 0.85 
 
 1.45 
 1.05 
 0.93 
 0.81 
 
 1.42 
 1.02 
 0.90 
 0.78 
 
 1.40 
 1.00 
 0.88 
 0.77 
 
 1.38 
 1.00 
 0.88 
 0.76 
 
 1.37 
 0.99 
 0.87 
 0.75 
 
 1.36 
 0.98 
 0.87 
 0.74 
 
 Six Stories. 
 
 25 
 50 
 75 
 
 125 
 
 2.10 
 1.53 
 1.35 
 1.22 
 
 1.72 
 1.21 
 1.08 
 0.96 
 
 1.57 
 1.12 
 0.98 
 0.86 
 
 1.51 
 1.08 
 0.94 
 0.82 
 
 1.48 
 1.05 
 0.92 
 0.79 
 
 1.46 
 1.04 
 0.90 
 0.78 
 
 1.44 
 1.03 
 0.89 
 0.77 
 
 1.43 
 1.02 
 0.88 
 0.76 
 
 1.42 
 1.02 
 0.86 
 0.76 
 
 
 The cost per sq. ft. of a building 100 ft. wide will be about midway 
 between that of one 75 ft. wide and one 125 ft. wide, and the cost of a 
 five-story building about midway between the costs of a four- and a six- 
 story. The data for estimating the above costs are as follows: 
 
 
 Stories High. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Foundations, includ- ) Outside walls 
 
 $2.00 
 1.75 
 
 $2.90 
 2.25 
 
 $3.80 
 2.80 
 
 $4.70 
 3.40 
 
 $5.60 
 3.90 
 
 $6.50 
 4.50 
 
 Brick walls, cost per ) Outside walls. . 
 sq. ft. of surface. . . ) Inside walls 
 
 0.40 
 0.40 
 
 0.44 
 0.40 
 
 0.47 
 0.40 
 
 0.50 
 0.43 
 
 0.53 
 0.45 
 
 0.57 
 0.47 
 
 Columns, including piers and castings, cost each $15. 
 Assumed Height of Stories. From ground to first floor, 3 ft. Buildings 
 
COST OF BUILDINGS. 1395 
 
 25 ft. wide, stories 13 ft. high; 50 ft. wide, 14 ft. high; 75 ft. wide, 15 ft 
 high; 100 ft. and 125 ft. wide, 16 ft. high. 
 
 Floors, 32 cts. per sq. ft. of gross floor space not including columns. 
 Columns included, 38 cts. 
 
 Roof, 25 cts. per sq. ft., not including columns. Columns included, 
 30 cts. Roof to project 18 ins. all around buildings. 
 
 Stairways, including partitions, $100" each flight. Two stairways and 
 one elevator tower for buildings up to 150 ft. long; two stairways and two 
 elevator towers for buildings up to 300 ft. long. In buildings over two 
 stories, three stairways and three elevator towers for buildings over 300 ft 
 long. 
 
 in buildings over two stories, plumbing $75 for each fixture including 
 piping and partitions. Two fixtures on each floor up to 5000 sq. ft. oi 
 floor space and one fixture for each additional 5000 sq. ft. of floor or 
 fraction thereof. 
 Modifications of the above Costs: 
 
 1. If the soil is poor or the conditions of the site are such as to require 
 more than ordinary foundations, the cost will be increased. 
 
 2. If the building is to be used for ordinary storage purposes with low 
 stories and no top floors, the cost will be decreased from about 10% for 
 large low buildings to 25% for small high ones, about 20% usually being 
 a fair allowance. 
 
 3. If the building is to be used for manufacturing and is substantially 
 built of wood, the cost will be decreased from about 6% for large one- 
 story buildings to 33% for high small buildings; 15% would usually be a 
 lair allowance. 
 
 4. If the building is to be used for storage with low stories and built 
 substantially of wood, the cost will be decreased from 13% -for large 
 one-story buildings to 50% for small high buildings; 30% would usually 
 be a fair allowance. 
 
 5. If the total floor loads are more than 75 Ibs. per sq. ft. the cost is 
 increased. 
 
 6. For office buildings, the cost must be increased to cover architectural 
 features on the outside and interior finish. 
 
 Reinforced-concrete buildings designed to carry floor loads of 100 Ibs. 
 per so. ft. or less will cost about 25% more than the slow-burning type 
 of mill construction. 
 
1396 ELECTRICAL ENGINEERING. 
 
 ELECTRICAL ENGINEERING.* 
 
 STANDARDS OF MEASUREMENT. 
 
 C.G.S. (Centimeter, Gramme, Second) or "Absolute" System 
 of Physical Measurements: 
 
 Unit of space or distance 1 centimeter, cm.; 
 
 Unit of mass = 1 gramme, gm.; 
 
 Unit of time = 1 second, sec.; 
 
 Unit of velocity = space -f- time = 1 centimeter in 1 second; 
 Unit of acceleration = change of 1 unit of velocity in 1 second ; 
 Acceleration due to gravity, = 980.665 centimeters per sec. per sec. 
 
 Unit of force = 1 dyne= ^ gm. = f- 2 U>.= 0.000002248! Ib. 
 
 A dyne is that force which, acting on a mass of one gramme during one 
 second, will give it a velocity of one centimeter per second. The weight 
 of one gramme in latitude 40 to 45 is about 980 dynes, at the equator 
 973 dynes, and at the poles nearly 984 dynes. Taking the value of g, 
 the acceleration due to gravity, in British measures at 32.1740 feet per 
 second at lat. 45 at the sea level, and the meter = 39.37 inches, we have 
 
 1 gramme = 32.174 X 12 -s- 0.3937 = 980.665 dynes. 
 Unit of work = 1 erg =1 dyne-centimeter = 0.000000073756 ft.-lb.; 
 Unit of power = 1 watt = 10 million ergs per second, 
 
 = 0.73756 foot-pound per second. 
 
 = 55Q 56 = 7^7 horse-power = 0.0013410 H.P. 
 
 C.G.S. unit magnetic pole is one which reacts on an equal pole at a 
 centimeter's distance with the force of 1 dyne. 
 
 C.G.S. unit of magnetic field strength, the gauss, is the intensity of 
 field which surrounding unit pole acts on it with a force of 1 dyne. 
 
 C.G.S. unit of electro-motive force = the force produced by the cuttingr 
 of a field of 1 gauss intensity at a velocity of 1 centimeter per second (in 
 a direction normal to the field and to the cpnductor) by 1 centimeter ol 
 conductor. The volt is 100,000,000 times this unit. 
 
 C.G.S. unit of electrical current == the current in a conductor (located 
 in a plane normal to the field) when each centimeter is urged across a 
 magnetic field of 1 gauss intensity with a force of 1 dyne. One-tenth of 
 this is the ampere. 
 
 The C.G.S. unit 9f quantity of electricity is that represented by the 
 flow of 1 C.G.S. unit of current for 1 second. One-tenth of this is the 
 coulomb. 
 
 The Practical Units used in Electrical Calculations are: 
 
 Ampere, the unit of current strength, or rate of flow, represented by /. 
 
 Volt, the unit of electro-motive force, electrical pressure, or difference 
 of potential, represented by E. 
 
 Ohm, the unit of resistance, represented by R. 
 
 Coulomb (or ampere-second), the unit of quantity, Q. 
 
 Ampere-hour = 3600 coulombs, Q f . 
 
 Watt (volt-ampere), the unit of power, P. 
 
 Joule (or watt-second), the unit of energy or work, W. 
 
 Farad, the unit of electrostatic capacity, represented by C. 
 
 Henry, the unit of inductance, represented by L. 
 
 Using letters to represent the units, the relations between them may 
 be expressed by the following formulae, in which t represents one second 
 and T one hour: 
 
 /=|, Q = It, Q' = IT, C7 = |, W=QE, P = IE. 
 
 As these relations contain no coefficient other than unity, the letters 
 may represent any quantities given in terms of those units. For exam- 
 ple, if E represents the number of volts electro-motive force, and R the 
 number of ohms resistance in a circuit, then their ratio E -T- R will give 
 the number of amperes current strength in that circuit. 
 
 The above six formulae can be combined by substitution or elimination, 
 
 * In the revision of this chapter the author has had the assistance 
 of Mr. David B. Rushmore. 
 
STANDARDS OF MEASUREMENTS, 1397 
 
 so as to give the relations between any of the quantities. The most 
 important of these are the following: 
 
 The definitions of these units as adopted at the International Electrical 
 Congress at Chicago in 1893. and as established by Act of Congress of 
 the United States, July 12, 1894, are as follows: 
 
 The ohm is substantially equal to 10 9 (or 1,000,000,000) units of resist- 
 ance of the C.G.S. system, and is represented by the resistance offered 
 to an unvarying electric current by a column of mercury at 32 F., 14.4521 
 grammes in mass, of a constant cross-sectional area, and of the length of 
 106.3 centimeters. 
 
 The ampere is Vio of the unit of current of the C.G.S. system, and is 
 the practical equivalent of the unvarying current which when passed 
 through a solution of nitrate of silver in water in accordance with standard 
 specifications deposits silver at the rate of 0.001118 gramme per second. 
 
 The volt is the electro-motive force that, steadily applied to a con- 
 ductor whose resistance is one ohm, will produce a current of one ampere, 
 and is practically equivalent to 1000/1434 (or 0.6974) of the electro- 
 motive force between the Doles or electrodes of a Clark's cell at a tem- 
 perature of 15C., and prepared in the manner described in the standard 
 specifications. [The e.m.f. of a Weston normal cell is 1.0183 volts at 20 C.] 
 
 The coulomb is the quantity of electricity transferred by a current of one 
 ampere in one second. 
 
 The farad is the capacity of a condenser charged to a potential of one 
 volt by one coulomb of electricity. 
 
 The joule is equal to 10,000,000 units of work in the C.G.S. system, and 
 is practically equivalent to the energy expended in one second by an 
 ampere in an ohm. 
 
 The watt is equal to 10,000,000 units of power in the C.G.S. system, and 
 is practically equivalent to the work done at the rate of one joule per 
 second. 
 
 The henry is the induction jn a circuit when the electro-motive force 
 induced in this circuit is one volt, while the inducing current varies at the 
 rate of one ampere per second. 
 
 The ohm, volt, etc., as above defined, are called the "international" 
 ohm, volt, etc., to distinguish them from the "legal" ohm, B.A. unit, etc. 
 
 The value of the ohm, determined by a committee of the British Asso- 
 ciation in 1863, called the B.A. unit, was the resistance of a certain piece 
 of copper wire. The so-called "legal" ohm, as adopted at the Inter- 
 national Congress" of Electricians in Paris in 1884, was a correction of the 
 B.A. unit, and was defined as the resistance of a column of mercury 
 1 square millimeter in section and 106 centimeters long, at a temperature 
 of 32 F. 1 legal ohm =1.0112 B.A. units; 1 international ohm =1.0023 
 legal ohm; 1 legal ohm =0.9977 int. ohm. 
 
 DERIVED UNITS. 
 1 megohm = 1 million ohms; 
 1 microhm = 1 millionth of an ohm; 
 1 milliampere = 1/1000 of an ampere; 
 1 micro-farad = 1 millionth of a farad. 
 
 RELATIONS OF VARIOUS UNITS. 
 1 ampere .................. =1 coulomb per second; 
 
 1 volt-ampere (direct current) = 1 watt = 1 volt-coulomb per sec. ; 
 
 ( = 0.73756 foot-pound per second, 
 1 watt .................... { = 0.00094859 heat-unit per sec. (Fahr.), 
 
 = 1 /745-7 of one horse-power; 
 = 0.73756 foot-pound, 
 
 1 joule = 10 7 ergs . 
 
 1 British thermal unit . 
 
 : work done by one watt in one sec., 
 = 0.00094859 heat-unit; 
 = 0.23904 gram calories; 
 = 1054.2 joules; 
 = 777.54 foot-pounds; 
 = 25.200 gram calories; 
 
1398 ELECTRICAL ENGINEERING. 
 
 1 mean gram calorie { I fc"***, 1 * * ; 
 
 1 kilowatt, or 1000 watts = 1000/745.7 or 1.3410 horse-powers; 
 
 1 kilowatt-hour 
 
 1000 volt-ampere hours ..... 
 
 1 British Board of Trade unit 
 
 1 horse-power 
 
 1.3410 horse-power hours, 
 = 2,655,220 foot-pounds, 
 = 3415 heat-units; 
 = 745.7 watts = 745.7 volt-amperes, 
 
 = 33,000 foot-pounds per minute. 
 The ohm, ampere, and volt are denned in terms of one another as 
 follows: Ohm, the resistance of a conductor through which a current of 
 one ampere will pass when the electro-motive force is one volt. Ampere, 
 the quantity of current which will flow through a resistance of one ohm 
 when the electro-motive force is one volt. Volt, the electro-motive force 
 required to cause one ampere to flow through a resistance of one ohm. 
 
 For Methods of Making Electrical Measurements, Testing, etc., 
 see "American Handbook for Electrical Engineers"; Karapetoff's 
 "Experimental Electrical Engineering": Bedell's "Direct and Alter- 
 nating Current Manual"; 1914 Standardization Rules of A. I. E. E. 
 
 Equivalent Electrical and Mechanical Units. H. Ward Leonard 
 published in The Electrical Engineer, Feb. 25, 1895, a table of useful 
 equivalents of electrical and mechanical units, from which the table on 
 page 1399 is taken, with some modifications. 
 L Units of the Magnetic Circuit. 
 
 Unit magnetic pole is a pole of such strength that when placed at a dis- 
 tance of one centimeter from a similar pole of equal strength it repels it 
 with a force of one dyne. 
 
 Magnetic Moment is the product of the strength 'of either pole into the 
 distance between the two poles. 
 
 Intensity of Magnetization is the magnetic moment of a magnet divided 
 by its volume. 
 
 Intensity of Magnetic Field is the force exerted by the field upon a unit 
 magnetic pole. The unit is the gauss. 
 
 Gauss = unit of field strength, or density, symbol H is that intensity 
 of field which acts on a unit pole with a force of one dyne, = one line of 
 force per square centimeter. One gauss produces 1 dyne of force per 
 centimeter length of conductor upon a 'current of 10 amperes, or an 
 electro-motive force of 1/100,000,000 volt in a centimeter length of con- 
 ductor when its velocity across the field is 1 centimeter per second. A field of 
 H units is one which acts with H dynes on unit pole, or H lines per 
 square centimeter. A unit magnetic pole has 4?r lines of. force proceeding 
 from it. 
 
 Maxwell = unit of magnetic flux, is the amount of magnetism passing 
 through a square centimeter of a field of unit density. Symbol, $. 
 
 In non-magnetic materials a unit of intensity of flux is the same as 
 unit intensity of field. The name maxwell is given to a unit quantity 
 of flux, and one maxwell per square centimeter in non-magnetic materials 
 is the same as the gauss. In magnetic materials the flux produced by 
 the molecular magnets is added to the field (Norris). 
 
 Magnetic Flux, <, is equal to the average field intensity multiplied by 
 the cross-sectional area. The unit is the maxwell. Maxwells per square 
 inch= gausses X 6.45. 
 
 Magnetic Induction, symbol B, is the flux or the number of magnetic 
 lines per unit of area of cross-section of magnetized material, the area 
 being at every point perpendicular to the direction of the flux. It is 
 equal to the product of the field intensity, H, and the permeability, .. 
 
 Gilbert = unit of magnetomotive force, is the amount of M.M.F. that 
 would be produced by a coil of 10 -* 4rc or 0.7958 ampere-turns. Symbol F. 
 
 The M.M.F. of a coil is equal to 1.2566 times the ampere-turns. 
 
 If a solenoid is wound with 100 turns of insulated wire carrying a current 
 of 5 amperes, the M.M.F. exerted will be 500 ampere-turns X 1.2566 = 
 628.3 gilberts. 
 
 Oersted = unit of magnetic reluctance; a magnetic circuit has a re- 
 luctance of 1 oersted when unit m.m.f. produces unit flux. Symbol, R. 
 
 Reluctance is that quantity in a magnetic circuit which limits the flux 
 
 *Mean of the values of Reynolds and Moorby and of Barnes- 
 Marks & Davis, Steam Tables, 1909* 
 
EQUIVALENT ELECTRICAL AND MECHANICAL UNITS. 1399 
 
 cod 
 
 Ill 
 
 83 a 
 
 > O TO S fl) HH 
 
 .*! ffJ lg 
 
 
 
 I*P! 
 
 
 
 T3 2 
 
 il: 
 
 I I 
 *: ii 
 
 d 1 ' ii 
 
 n 
 
 pj 
 
 w 
 
 j^il^lilS 
 
 g gc5 en rj 
 
 in'o'cK'rx' 
 
 si $ 
 
 CNCH 
 
 .1 
 
 -Pj! 
 Wj 
 
1400 
 
 ELECTRICAL. ENGINEERING. 
 
 under a given M.M.F. It corresponds to the resistance in the electric cir- 
 cuit. 
 
 Permeance is the reciprocal of reluctance. 
 
 The reluctivity of any medium is its specific reluctance, and in the C.G.S. 
 system is the reluctance offered by a cubic centimeter of the body between 
 opposed parallel faces. The reluctivity of nearly all substances, other 
 than the magnetic metals, is sensibly that of vacuum, is equal to unity, 
 and is independent of the flux density. 
 
 Permeability is the reciprocal of magnetic reluctivity. It is a number 
 and the symb9l is ft. 
 
 Materials differ in regard to the resistance they offer to the passage 
 of lines of force; thus iron is more permeable than air. The permeability 
 of a substance is expressed by a coefficient, //, which denotes its relation 
 to the permeability of air, which is taken as 1. If H = number of mag- 
 netic lines per square centimeter which will pass through an air-space 
 between the poles of a magnet, and B the number of lines which will 
 pass through a certain piece of iron in that space, then n B -T- H. The 
 permeability varies with the quality of the iron, and the degree of satura- 
 tion, reaching a practical limit for soft wrought iron when B= about 
 18,000 and for cast iron when B = about 10,000 C.G.S. lines per square 
 centimeter. 
 
 The permeability of a number of materials may be determined by means 
 of the table on page. 1431. 
 
 ANALOGIES BETWEEN THE FLOW OF WATER AND 
 ELECTRICITY. 
 
 ELECTRICITY. 
 
 Volts; electro-motive force; differ- 
 ence of potential; E. or E.M.P. 
 
 Ohms, resistance, R. Increases di- 
 rectly as the length of the conduc- 
 tor or wire and inversely as its sec- 
 tional area, R c I -f- s. It varies 
 with the nature of the conductor. 
 
 Amperes; current; current strength; 
 intensity of current; rate of flow; 
 1 ampere = 1 coulomb per second-. 
 
 WATER. 
 
 Head, difference of level, in feet. 
 
 Difference of pressure, Ibs. per sq. in. 
 
 Resistance of pipes, apertures, etc., 
 increases with length of pipe, with 
 contractions, roughness, etc.; de- 
 creases with increase of sectional 
 area. % 
 
 Rate of flow, as cubic ft. per second, 
 gallons per min., etc., or volume 
 divided by the time. In the min- 
 ing regions sometimes expressed 
 in "miners' inches." 
 
 Quantity, usually measured in cubic ) Coulomb, unit of quantity, Q, 
 ft. or gallons, but is also equiva- I rate of flow X time, as ampere- 
 lent to rate of flow X time, as cu. f seconds. 1 ampere-hour = 3600 
 ft. per second for so many hours. J coulombs. 
 
 Joule, volt-coulomb, TF, the unit of 
 
 Work, or energy, measured in foot- 
 pounds; product of weight of fall- 
 ing water into height of fall; in 
 pumping, product of quantity in 
 cubic feet into the pressure in Ibs. 
 per square foot against which the 
 water is pumped. 
 
 Power, rate of work. Horse-power = 
 ft.-lbs. of work in 1 min. -7- 33,000. 
 In water flowing in pipes, rate of 
 flow in cu. ft. per second X resist- 
 ance to the flow in Ibs. per sq. ft. 
 ^550. 
 
 work, = product of quantity by 
 the electro-motive force = volt- 
 ampere-second. 1 joule = 0.7373 
 foot-pound. 
 
 If / (amperes) = rate of flow, and 
 E (volts) = difference of pressure 
 between two points in a circuit, 
 energy expended = IEt, = I 2 Rt. 
 
 Watt, unit of power, P, = volts X 
 amperes, current or rate of 
 flow X difference of potential. 
 
 1 watt = 0.7373 foot-pound per sec. 
 = 1/746 of a horse-power. 
 
 ELECTRICAL RESISTANCE. 
 
 Laws of Electrical Resistance. The resistance, R, of any con- 
 ductor varies directly as its length, I, and inversely as its sectional area, s, 
 or R QC I -T- s. 
 
 If r = the resistance of a conductor 1 unit in length and 1 square unit 
 in sectional area, R = rl-i- $. The common unit of length for electrical 
 
ELECTRICAL RESISTANCE. 
 
 1401 
 
 calculations in English measure is the foot, and the unit of area of wires 
 is the circular mil = the area of a circle 0.001 in. diameter. 1 mil-foot = 
 1 foot long 1 circ.-mil area. 
 
 Resistance of 1 mil-foot of soft copper wire at 51 F. = 10 international 
 ohms. 
 
 EXAMPLE. What is the resistance of a wire 1000 ft. long, 0.1 in. diam ' 
 0.1 in. diam. = 10,000 circ. mils. 
 
 R = rl -f- s = 10 X 1000 -f- 10,000 = 1 ohm. 
 
 Specific resistance, also called resistivity, is the resistance of a material 
 of unit length and section as compared with the resistance of soft copper 
 
 Conductivity is the reciprocal of specific resistance, or the relative 
 conducting power compared with copper taken at 100. 
 
 Conductance is the reciprocal of resistance. 
 
 Relative Conductivities of Different Metals at and 100 C. 
 
 (Matthiessen.) 
 
 Metals. 
 
 Conductivities. 
 
 Metals. 
 
 Conductivities. 
 
 At 0C. 
 At 32 F. 
 
 At 100C. 
 At 21 2 F. 
 
 At 0C. 
 At 32 F. 
 
 At 100C. 
 At 212 F. 
 
 Silver, .hard 
 
 100 
 99.95 
 77.96 
 29.02 
 23.72 
 18.00 
 16.80 
 
 71.56 
 70.27 
 55.90 
 20.67 
 16.77 
 
 Tin 
 
 12.36 
 8.32 
 4.76 
 4.62 
 1 60 
 
 8.67 
 5.86 
 3.33 
 3.26 
 
 Copper, hard. . . . 
 Gold, hard 
 
 Lead 
 
 Arsenic 
 Antimony 
 Mercury, pure 
 
 Zinc, pressed .... 
 Cadmium 
 Platinum, soft. . . 
 Iron, soft 
 
 Bismuth 
 
 1.245 
 
 0.878 
 
 
 
 Resistance of Various Metals and Alloys. Condensed from a 
 table compiled by H. F. Parshall and H. M. Hobart from different 
 
 authorities. R =~resistance in ohms per mil foot = resistance per centi- 
 meter cube X 6.015. C = per cent increase of resistance per degree C. 
 
 
 R 
 
 C 
 
 
 R | C 
 
 Aluminum, 99% pure 
 Aluminum, 94; copper, 6.. 
 Al. bronze, Al 10; Cu, 90 . . 
 Antimony, compressed. . . 
 Bismuth, compressed 
 Cadmium pure 
 
 15.4 
 17.4 
 75.5 
 211 
 780 
 60 
 9.35 
 9.54 
 17.7 
 37.8 
 31.7 
 53.0 
 89 5 
 
 0.423 
 .381 
 .105 
 .389 
 .354 
 .419 
 .428 
 .388 
 
 .158 
 
 .090 
 065 
 
 White cast iron 
 
 340 
 684 
 82.8 
 63 
 401 
 177 
 123 
 
 287 
 294 
 393 
 566 
 73.7 
 61.1 
 539 
 145 
 33.6 
 8.82 
 78.5 
 34.5 
 
 .127 
 .201 
 .411 
 
 .000 
 .000 
 .000 
 .072 
 .435 
 .354 
 .247 
 .133 
 .394 
 .400 
 .440 
 .406 
 
 Gray cast iron 
 
 Wrought iron 
 Soft steel, C, 0.045 . . . 
 
 Manganese steel, Mn, 12. . 
 Nickel steel, Ni, 4.35 
 Lead pure ... 
 
 Copper annealed, (D). . . . 
 Copper annealed, (M) ... 
 Copper 88; silicon, 12 
 Copper 65.8; zinc, 34.2. . . . 
 Copper 90; lead, 10 
 Copper, 97; aluminum, 3. . 
 Cu, 87; Ni 6 5- Al 65 
 
 Manganin, 
 Cu, 84; Mn, 12;Ni, 4 
 Cu, 80.5; Mn, 3;Ni, 16.5 
 Cu, 79.5;Mn, 19.7; Fe, 0.8 
 Mercury 
 
 Nickel 
 
 Copper, 65; nickel, 25 
 Cu, 70; manganese, 30 
 German silver 
 Cu, 60; Zn, 25; Ni, 15.... 
 Gold, 99.9% pure 
 Gold 67- silver 33 
 
 205 
 605 
 
 180 
 13.2 
 61.8 
 54.5 
 
 .019 
 .004 
 
 .036 
 .377 
 .065 
 .625 
 
 Palladium pure 
 
 Platinum, annealed 
 Platinum, 67; silver, 33 ... 
 Phosphor bronze 
 
 Silver, pure 
 Tin pure 
 
 Iron, very pure 
 
 Zinc, pure 
 
 (D) Dewarand Fleming; (M) Matthiessen. 
 
 Conductivity of Aluminum. J. W. Richards (Jour. Frank.. Inst. 9 
 Mar., 1897) gives for hard-drawn aluminum of purity 98.5, 99.0, 99.5, 
 and 99.75% respectively a conductivity of 55, 59, 61, and 63 to 64%, 
 copper being 100%. The Pittsburg Reduction Co. claims that its purest 
 aluminum has a conductivity of over 64.5%. (Eng'g News, Dec. 17, 
 1896.) 
 
 German Silver. The resistance of German silver depends on its 
 composition. Matthiessen gives it as nearly 13 times that of copper, 
 with a temperature coefficient of 0,0004433 per degree 0, Weston, how- 
 
1402 ELECTRICAL ENGINEERING. 
 
 ever (Proc. Electrical Congress, 1893, p. 179), has found copper-nickel- 
 zinc alloys (German silver) which had a resistance of nearly 28 times 
 
 nearly 
 
 M^__. _, temperature coefficient or aho 
 _ . atthiessen. 
 
 Conductors and Insulators in Order of Their Value. 
 
 that of copper, and a temperature coefficient of about one-half that 
 Ma " 
 
 CONDUCTORS. 
 
 All metals 
 
 Well-burned charcoal 
 
 Plumbago 
 
 Acid solutions 
 
 Saline solutions 
 
 Metallic ores 
 
 Animal fluids 
 
 Living vegetable substances 
 
 Moist earth 
 
 Water 
 
 INSULATORS (NON-CONDUCTORS). 
 
 Dry air Ebonite 
 
 Shellac Gutta-percha 
 
 Paraffin India-rubber 
 
 Amber Silk 
 
 Resins Dry paper 
 
 Sulphur Parchment 
 
 Wax Dry leather 
 
 Jet Porcelain 
 
 Glass Oils 
 Mica 
 
 According to Culley, the resistance of distilled water is 6754 million 
 times as great as that of copper. Impurities in water decrease its 
 resistance. 
 
 Resistance Varies with Temperature. For every degree Centi- 
 grade the resistance of copper increases about 0.4%, or for every degree 
 F., 0.2222%. Thus a piece 9f copper wire having a resistance of 10 
 ohms at 32 would have a resistance of 11.11 ohms at 82 F. 
 
 The following table shows the amount of resistance of a few sub- 
 stances used for various electrical purposes by which 1 ohm is increased 
 by a rise of temperature of 1 C. 
 
 Platinoid 0.00021 
 
 Platinum silver 0.00031 
 
 German silver (see above) . . 0.00044 
 
 Gold, silver . 00065 
 
 Cast iron 0.00080 
 
 Copper . 00400 
 
 Annealing. Resistance is lessened by annealing. Matthiessen gives 
 the following relative conductivities for copper and silver, the comparison 
 being made with pure silver at 100 C. : 
 
 Metal. Temp. C. Hard. Annealed. Ratio, 
 
 Copper 11 95.31 97.83 1 to 1.027 
 
 Silver 14.6 95.36 103.33 1 to 1.084 
 
 Dr. Siemens compared the conductivities of copper, silver, and brass 
 with the following results. Ratio of hard to annealed: 
 
 Copper 1 to 1.058 Silver 1 to 1.145 Brass 1 to 1.180 
 
 STANDARD VALUES FOR RESISTIVITY AND TEMPERATURE 
 COEFFICIENT OF COPPER. 
 
 Bureau of Standards, 1914. 
 
 The Bureau of Standards made measurements of a large number of 
 representative samples of copper and established standard values of 
 resistivity and temperature coefficients, which have been adopted by 
 the International Electrochemical Commission. 
 
 Conductivity of Copper. 
 
 The following rules of the International Electrical Commission have 
 been adopted by the American Institute of Electrical Engineers. 
 
 The following shall be taken as normal values for standard annealed 
 copper: 
 
 (1) At a temperature of 20 C. the resistance of a wire of standard 
 annealed copper one meter in length and of a uniform section of 1 square 
 millimeter is 1/58 ohm = 0.017241. . . .ohm. 
 
 (2) At a temperature of 20 C. the density of standard annealed 
 copper is 8.89 grams per cubic centimeter. 
 
 (3) At a temperature of 20 C. the "constant mass" temperature 
 coefficient of resistance of standard annealed copper, measured between 
 two potential points rigidly fixed to the wire, is 0.00393 = 1/254.45 
 , , , . per degree centigrade, 
 
RESISTANCE OF COPPER. 1403 * 
 
 (4) As a consequence it follows from (1) and (2) that, at a temper- 
 ature of 20 C. the resistance of a wire of standard annealed copper of 
 uniform section, one meter in length and weighing one gram, is (1/58) 
 
 X 8.89 = 0.15328 ohm. 
 
 Paragraphs (1) and (4) define what are sometimes called "volume 
 resistivity" and "mass resistivity" respectively. This may be ex- 
 pressed in other units as follows: Volume resistivity = 1.7241 
 microhm-cm, (or microhms in a cm. cube) at 20 C. = 0.67879 microhm 
 inch at 20 C. and mass resistivity = 875.20 ohms (mile, pound) at 
 20 C. 
 
 The new value is known as the International Annealed Copper 
 Standard, and is equivalent to 
 
 0.'017241 ohm (meter, mm2) at 20 C. 
 
 The units of mass resistivity and volume resistivity are interrelated 
 through the density; this was taken as 8.89 grams per cm 3 at 20 C. by 
 the International Electrochemical Commission. The International 
 Annealed Copper Standard, in various units of mass resistivity and 
 volume resistivity, is: 
 
 0.15328 ohm (meter, gram) at 20 C. 
 875.20 ohms (mile, pound) at 20 C. 
 
 0.017241 ohm (meter, mm2) at 20 C. 
 1.7241 microhm-cm, at 20 C. 
 0.67879 microhm-inch at 20 C. 
 10.371 ohms (mil, foot) at 20 C. 
 
 The Temperature Coefficient of Resistance of Copper. The Bureau of 
 Standards' investigation of the temperature coefficient showed that 
 the coefficient varies with different samples, but that the relation of 
 conductivity to temperature coefficient is substantially a simple pro- 
 portionality. 
 
 The general law may be expressed by the following practical rule: 
 The 20 C. temperature coefficient of a sample of copper is the product 
 of the per cent, conductivity by 0.00393. There are sometimes cases 
 when the temperature coefficient is more easily measured than the 
 conductivity, and the conductivity can be computed from the relation: 
 per cent, conductivity = 254.5 X temperature coefficient. 
 
 When a temperature coefficient of resistance must be assumed the 
 best value to assume for good commercial annealed copper wire is that 
 corresponding to 100 per cent, conductivity, viz.: 
 
 Co = 0.00427, ais = 0.00401, 2 o = 0.00393, a 2 & = 0.00385 
 / Rt - #20 
 
 This value was adopted as standard by the International Electro- 
 chemical Commission in 1913. It would usually apply to instruments 
 and machines, since they are generally wound with annealed wire. 
 Experiment has shown that distortions such as those caused by winding 
 and ordinary handling do not affect the temperature coefficient. 
 
 Similarly, when assumption is unavoidable, the temperature coeffi- 
 cient of* good commercial hard-drawn copper wire may be taken as 
 that corresponding to a conductivity of 97.3 per cent., viz.: 
 
 GO = 0.00414, aw = 0.00390, a w = 0.00382, an = 0.00375 
 
 Rule for reducing resistivity from one temperature to another: 
 The change of resistivity of copper per degree C. is a constant, inde- 
 pendent of the temperature of reference and of the sample of copper. 
 This "resistivity-temperature constant" may be taken, for general 
 purposes, as 0.00060 ohm (meter, gram), or 0.0068 microhm-cm. 
 More exactly, it is: 
 
 0.000.597 ohm (meter, gram) 
 or, 0.000.0681 ohm (meter, mm 2 ) 
 or, 0.006.81 microhm-cm, 
 or, 3.41 ohms (mile, pound) 
 
 or, 0.002.68 microhm-inch, 
 or, 0.040-9 ohm (mil, foot). 
 
 Continued on p. 1406. 
 
1404 
 
 ELECTRICAL ENGINEERING. 
 
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 1405 
 
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 Square 
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 5<NiA OiAfS Oh 
 
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 OO^vO 
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 OOOhs 
 
1406 ELECTRICAL ENGINEERING. 
 
 Resistivity of Hard-Drawn Copper Wires. In general the resistivity 
 ot hard-drawn wires varies with the size of the wire, while the resistivity 
 of annealed wires does not. The difference between the resistivity of 
 annealed and hard-drawn wires increases as the diameter of the wire 
 decreases. This general conclusion is, however, complicated in any 
 particular case by the number of drawings between annealings, amount 
 of reduction to each drawing, etc. For No. 12 A.W.G. (B. & S ), the 
 conductivity of hard-drawn wires was found to be less than the con- 
 ductivity of annealed wires by 2.7 per cent, 
 
 f Co PP er - The international standard density for copper, 
 at 20 C., is 8.89 grams per cubic centimeter. This is the value which 
 has been used by the A.I.E.E., and most other authorities in the past. 
 Recent measurements have indicated this value as a mean. This den- 
 sity, 8.89, at 20 C., corresponds to a density of 8.90 at C. In 
 English units, the density at 20 C. = 0.32117 pounds per cubic inch. 
 For a complete treatise on this subject, see Bulletin No. 31, Bureau 
 of Standards. 
 
 Approximate Rules for the Resistance of Copper Wire. The re- 
 
 sistance of any copper wire at 20 C. or 68 F., according to Matthies- 
 
 sen's standard, is R = ' -, in which R is the resistance in inter- 
 
 national ohms, I the length of the wire in feet, and d its diameter in 
 mils, (1 mil = Viooo inch.) 
 
 A No. 10 wire, A.W.G. , 0.1019 in. diam (practically 0.1 in.), 1000 
 ft. in length, has a resistance of 1 ohm at 68 F. and weighs 31.4 Ibs. 
 
 If a wire of a given length and size by the American or Brown & 
 Sharpe gauge has a certain resistance, a wire of the same length and 
 three numbers higher has twice the resistance, six numbers higher 
 four times the resistance, etc. 
 
 Wire gauge, A.W.G. No ..... 000 1 4 7 10 13 16 19 22 
 
 Relative resistance .......... 16 8 4 2 1 1/2 1/4 Vs Vie 
 
 section or weight ... i/ie Vs 1/4 V2 1 2 4 8 16 
 
 DIRECT ELECTRIC CURRENTS. 
 
 Ohm's Law. This law expresses the relation between the three 
 fundamental units of resistance, electrical pressure, and current. It is: 
 
 Current = ^Metrical pressure B _ Rm E 
 
 resistance R I 
 
 In terms of the units of the three quantities, 
 
 volts volts 
 
 Amperes = ; volts = amperes X ohms; 
 
 EXAMPLES: Simple Circuits. 1. If the source has an effective electrical 
 pressure of 100 volts, and the resistance is two onrns, what is the current? 
 
 7=f = M = 50 amperes. 
 
 Li Ji 
 
 2. What pressure will give a current of 50 amperes through a resistance 
 of 2 ohms? E = IR = 50 X 2 = 100 volts. 
 
 3. What resistance is required to obtain a current of 50 amperes when 
 the pressure is 100 volts? R = E -~ I = 100 -=- 50 = 2 ohms. 
 
 Ohm's law applies equally to a complete electrical circuit and to any 
 part thereof. 
 
 Series Circuits. If conductors are arranged one after the other they 
 are said to be in series, and the total resistance of the circuit is the sum of 
 the resistances of its several parts. Let A, Fig. 226, be a source of current, 
 such as a battery or generator, producing a aiflerence of potential or 
 
DIRECT ELECTRIC CURRENTS. 1407 
 
 E.M.F. of 120 volts, measured across ab, and let the circuit contain four 
 conductors whose resistances, n, rz, n, r <t are 1 ohm each, and three 
 other resistances, Ri, Rz, Rz, each 2 ohms. The 
 total resistance is 10 ohms, and by Ohm's law 
 
 ^ . the current / = E + R = 120 * 10 = 12 am- 
 
 s- A r s peres. This current is constant throughout the 
 
 T_ <O_ circuit, and a series circuit is therefore one of 
 
 constant current. The drop of potential in the 
 whole circuit from a around to b is 120 volts, 
 or E - RI. The drop in any portion depends 
 on the resistance of that portion; thus from a to 
 Ri the resistance is 1 ohm, the constant current 12 amperes, and the drop 
 1 X 12 = 12 volts. The drop in passing through each of the resistance 
 Ri, Rz, Rs is 2 X 12 = 24 volts. 
 
 Parallel, Divided, or Multiple Circuits. Let B, Fig. 227, be a 
 generator producing an E.M.F. of 220 volts across the terminals ab. 
 The current is divided, so that part 
 flows through the main wires ac and 
 part through the "shunt" s, having a 
 resistance of 0.5 ohm. Also the current 
 has three paths between c and d, viz., 
 through the three resistances in parallel 
 Ri, Rz, Rs, of 2 ohms each. Consider 
 
 that the resistance of the wires is so small , . 
 
 that it may be neglected. Let Mie con- b d 9 h 
 
 ductances of the four paths be repre- 
 sented by C s . Ci, Cz, Ca. The total FIG. 227. 
 conductance is C s 4- Ci+ Cz + Cz = C and the total resistance R = 
 1 -s- C. The conductance of each path is the reciprocal of its resistance, 
 the total conductance is the sum of the separate conductances, and the 
 resistance of the combined or "parallel" paths is the reciprocal of the 
 total conductance. 
 
 K = l- (o|5 + | + l+|)= 1-3.5 -0.286 ohm. 
 
 The current 7 = E * R = 770 amperes. 
 
 Conductors in Series and Parallel. Let the resistances in parallel 
 be the same as in Fig. 227, with the additional resistance of 0.1 ohm 
 in each of the six sections of the main wires, ac, bd, etc., in series. The 
 voltage across ab being 220 volts, determine the drop in voltage at the 
 several points, the total current, and the current through each path. 
 The problem is somewhat complicated. It may be solved as follows: 
 Consider first the points eg: here there are two paths for the current, 
 efqfi and eg. Find the resistance and the conductance of each and the 
 total resistance (the reciprocal of the joint conductance) of the parallel 
 paths. Next consider the points cd; here there are two paths one 
 through e and the other through cd. Find the total resistance as before. 
 Finally consider the points ab; here there are two paths one through 
 c, the other through s. Find the conductances of each and their sum. 
 The product of this sum and the voltage at ab will be the total amperes 
 of current, and the current through any path will be proportional to the 
 conductance of that path. The resistances, R, and conductances, C, 
 of the several paths are as follows: 
 
 R C 
 
 R a of efRzhg = 0.1 4- 2 H- 0.1 = 2.2 0.4545 
 
 Rb of eRzg = 2 0.5 
 
 Joint R c = 1.048 0.9545 
 
 Rd of ce + dg + R c = 1.248 0.8013 
 
 R e of cRid = 2 0.5 
 
 Joint Rf- 0.7687 1,3013 , 
 
1408 ELECTRICAL ENGINEERING. 
 
 R g of ac + Id + Rf = 0.9687 1.0332 
 
 = 0.5 2 
 
 Joint R a + Rfr = 0.330 3.0332 
 
 Total current = 220 X 3.0332 = 667.3 amperes. 
 Current through s = 220 X 2 = 440 amp.; through c = 227.3 amp. 
 "cRid = 227.3 X 0.5 4- 1.3013 = 87.34 amp. 
 
 e = 227.3 X 0.8013 -f- 1.3013 = 139.96 " 
 41 eRtg = 139.96 X 0.5 -*- 0.9545 = 73.31 " 
 44 /# 3 = 139.96 X 0.4545 ~ 0.9545 = 66.65 " 
 The drop in voltage in any section of the line is found by the formula 
 E = RI, R being the resistance of that section and / the current in it. 
 As the R of each section is 0.1 ohm we find E for ac and bd each = 22.7 
 volts, for ce and dg each 14.0 volts, and for ef and gh each 6.67 volts. 
 The voltage across cd is 220 - 2 X 22.7 = 174.6 volts; across eg,174.6- 2 
 X 14.0 = 146.6, and across fh 146.6 - 2X 667 = 133.3 volts. Taking 
 these voltages and the resistances Ri, Rz, Rs, each 2 ohms, we find from 
 / = E -r R the current through each of these resistances 87.3, 73.3, and 
 66.65 amperes as before. 
 
 Internal Resistance. In a simple circuit we have two resistances, 
 that of the circuit 72 and that of the internal parts of the source of electro- 
 motive force, called internal resistance, r. The formula of Ohm's law 
 when the internal resistance is considered is 7 = E * (R + r). 
 
 Power of the Circuit. The power, or rate of work, in watts = 
 current in amperes X electro-motive force in volts = / X E. Since 
 7 = E *- R, watts = E 2 -f- R = electro-motive force 2 -~ resistance. 
 
 EXAMPLE. What H.P. is required to supply 100 lamps of 40 ohms 
 resistance each, requiring an electro-motive force of 60 volts? 
 
 The number of volt-amperes for each lamp is =?- = j , 1 volt-ampere 
 
 Af)2 
 
 = 0.00134 H.P.; therefore gp X 100 X 0.00134 - 12 H.P. (electrical) 
 very nearly. 
 
 Electrical, Brake, and Indicated Horse-power. The power given 
 by a dynamo = volts X amperes -f- 1000 = kilowatts, kw. Volts X out 
 amperes - 746 electrical horse-power, E.H.P. The power put into a 
 dynamo shaft by a direct-connected engine or other prime mover is 
 called the shaft or brake horse-power, B.H.P. If e\ is the efficiency of the 
 dynamo, B.H.P. = E.H.P. -~ e\. If ei is the mechanical efficiency of the 
 engine, the indicated horse-power, I.H.P. = brake H.P. -f- 62 = E.H.P. ~- 
 (1X62). 
 
 If ei and e 2 each = 91.5%, I.H.P. = E.H.P. X 1.194 = kw. X 1.60. In 
 direct-connected units of 250 kw. or less the rated H.P. of the engine is 
 commonly taken as 1.6 X the rated kw. of the generator. 
 
 Electric motors are rated at the H.P. given out at the pulley or belt. 
 H.P. of motor = E.H.P. supplied X efficiency of motor. 
 
 Heat Generated by a Current. Joule's law shows that the heat 
 developed in a conductor is directly proportional, 1st, to its resistance; 
 2d, to the square of the current strength; and 3d, to the time during 
 which the current flows, or H = PRL Since / = E * R, 
 
 Or, heat = current 2 X resistance X time 
 
 = electro-motive force X current X time. 
 = electro-motive force 2 X time resistance. 
 Q = quantity of electricity flowing = It = (Et -- R). 
 H = EQ\ or heat = electro-motive force X quantity. 
 
 The electro-motive force here is that causing the flow, or the differ- 
 ence in potential between the ends of the conductor. 
 
 The electrical unit of heat, or "joule" = 10 7 ergs = heat generated in 
 ?ne second by a current of 1 ampere flowing through a resistance of one 
 
DIRECT ELECTRIC CURRENTS. 1409 
 
 ohm = 0.239" gramme of water raised 1 C. H = PRt X 0.239 gramme 
 calories = I*Rt X 0.0009478 British thermal units. 
 
 In electric lighting the energy of the current is converted into heat in 
 the lamps. The resistance of the lamp is made great so that the required 
 quantity of heat may be developed, wnile in the wire leading to and from 
 the lamp the resistance is made as small as is commercially practicable, 
 so that as little energy as possible may be wasted in heating the wire. 
 
 Heating of Conductors. (From Kapp's Electrical Transmission of 
 Energy.) It becomes a matter of great importance to determine before- 
 hand what rise in temperature' is to be expected in each given case, and 
 if that rise should be found o be greater than appears safe, provision must 
 be made to increase the rate at which heat is carried off. This can gen- 
 erally be done by increasing the superficial area of the conductor. Say 
 we have one circular conductor of 1 square inch area, and find that with 
 1000 amperes flowing it would become too hot. Now by splitting up this 
 conductor into 10 separate wires each one-tenth of a square inch cross- 
 sectional area, we have not altered the total amount of energy trans- 
 formed into heat, but we have increased the surface exposed to the cooling 
 action of the surrounding air in the ratio of 1 : v^lO, and therefore the ten 
 thin wires can dissipate more than three times the heat, as compared with 
 the single thick wire. 
 
 Prof. Forbes states that an insulated wire carries a greater current with- 
 out overheating than a bare wire if the diameter be not too great, Assum- 
 ing the diameter of the cable to be twice the diam. of the conductor, a 
 greater current can be carried in insulated wires than in bare wires up to 
 1.9 inch diam. of conductor. If diam. of cable = 4 times diam. of con- 
 ductor, this is the case up to 1.1 inch diam. of conductor. 
 
 Heating of Bare Wires. The following formulae are given by 
 Keimelly: 
 
 72 . 7 72 
 
 x 90,000 + t; d=44.8 ' 
 
 J. " -7j /S J7U f uuw T ,, u. l-*.o ^ ~ . ' 
 
 T = temperature of the wire and t that of the air, in Fahrenheit degrees; 
 7 - current in amperes, d = diameter of the wire in mils. 
 
 If we take T - t = 90 F., ^/90 = 4.48, then 
 
 d = 10 $1* and 7 = V^3 .4. 1000. 
 
 This latter formula gives for the carrying capacity in amperes of bare 
 wires almost exactly the figures given for weather-proof wires in the 
 Fire Underwriters' table, except in the case of Nos. 18 and 16, B. & S. 
 gauge, for which the formula gives 8 and 11 amperes, respectively, instead 
 of 5 and 8 amperes, given in the table. 
 
 Heating of Coils. The rise of temperature in magnet coils due to 
 the passage of current through the wire is approximately proportional to 
 the watts lost in the coil per unit of effective radiating surface, thus: 
 . PR . PR 
 toe or - 
 
 t being the temperature rise in degrees Fahr.; S t the effective radiating 
 surface; and k a coefficient which varies widely, according to condition. 
 In electromagnet coils of small size and power, k may be as large as 0.015. 
 Ordinarily it ranges from 0.012 down to 0.005; a fair average is 0.007. 
 The more exposed the coil is to air circulation, the larger is the value of k\ 
 the larger the proportion of iron to copper, by weight, in the core and 
 winding, the thinner the winding with relation to its dimension parallel 
 with the magnet core, and the larger the "space factor" of the winding, 
 the larger will be the value of k.- The space factor is the ratio of the 
 actual C9pper cross-section of the whole coil to the gross cross-section of 
 copper, insulation, and interstices. 
 
 Fusion of Wires. W. H. Preece gives a formula for the current 
 required to fuse wires of different metals, viz., I = ad*h in which d is the 
 diameter in inches and a a coefficient whose value for different metals 
 is as follows: Copper, 10,244; aluminum, 7585; platinum, 5172; German 
 silver, 5230; platinoid, 4750; iron, 3148; tin, 1462; lead, 1379; alloy of 2 
 lead and 1 tin, 1318. 
 
1410 
 
 ELECTRICAL ENGINEERING. 
 
 Allowable Carrying Capacity of Copper Wires. 
 
 (For inside wiring, National Board of Fire Underwriters' Rules.) 
 
 B.&S. 
 
 Gauge. 
 
 Circular 
 Mils. 
 
 Amperes. 
 
 Circular 
 Mils. 
 
 Amperes. 
 
 Rubber 
 Covered. 
 
 Other In- 
 sulation. 
 
 Rubber 
 Covered. 
 
 Other In- 
 sulation. 
 
 18 
 
 1,624 
 
 3 
 
 5 
 
 200,000 
 
 200 
 
 300 
 
 16 
 
 2,583 
 
 6 
 
 8 
 
 300,000 
 
 270 
 
 400 
 
 14 
 
 4,107 
 
 12 
 
 16 
 
 400,000 
 
 330 
 
 500 
 
 12 
 
 6,530 
 
 17 
 
 23 
 
 500,000 
 
 390 
 
 590 
 
 10 
 
 10,380 
 
 24 
 
 32 
 
 600,000 
 
 450 
 
 680 
 
 8 
 
 16,510 
 
 33 
 
 46 
 
 700,000 
 
 500 
 
 760 
 
 6 
 
 26,250 
 
 46 
 
 65 
 
 800,000 
 
 550 
 
 840 
 
 5 
 
 33,100 
 
 54 
 
 77 
 
 900,000 
 
 600 
 
 920 
 
 4 
 
 41,740 
 
 65 
 
 92 
 
 ,000,000 
 
 650 
 
 ,000 
 
 3 
 
 52,630 
 
 76 
 
 110 
 
 ,100,000 
 
 690 
 
 ,080 
 
 2 
 
 66,370 
 
 90 
 
 131 
 
 ,200,000 
 
 730 
 
 ,150 
 
 
 83,690 
 
 107 
 
 156 
 
 ,300,000 
 
 770 
 
 ,220 
 
 
 
 105,500 
 
 127 
 
 185 
 
 ,400,000 
 
 810 
 
 ,290 
 
 00 
 
 133,100 
 
 150 
 
 220 
 
 ,600,000 
 
 890 
 
 ,430 
 
 000 
 
 167,800 
 
 177 
 
 262 
 
 ,800,000 
 
 970 
 
 ,550 
 
 0000 
 
 211,600 
 
 210 
 
 312 
 
 2,000,000 
 
 1,050 
 
 ,670 
 
 Wires smaller than No. 14 B. & S. gauge must not be used except in fix- 
 tures and pendant cords. 
 
 The lower limit is specified for rubber-covered wires to prevent deteriora- 
 tion of the insulation by the heat of the wires. 
 
 For insulated aluminum wire the safe-carrying capacity is 84 per cent of 
 that of copper wire with the same insulation. 
 
 See pamphlets published by the National Board of Fire Underwriters, 
 New York, for complete specifications and rules for wiring. 
 
 Underwriters' Insulation. The thickness of insulation required 
 by the rules of the National Board of Fire Underwriters varies with the size 
 of the wire, the character of the insulatipn, and the voltage. The thick- 
 ness of insulation on rubber-covered wires carrying voltages up to 600 
 varies from 1/32 inch for a No. 18 B. & S. gauge wire to 1/8 inch for a wire of 
 1.000,000 circular mils. Weather-proof insulation is required to be slightly 
 thicker. For voltages of over 600 the insulation varies from i/ie inch 
 for No. 14 B. & S. gage to 9/64 inch for 1,000,000 C. JM. and over. 
 
 ELECTRIC TRANSMISSION, DIRECT CURRENTS. 
 
 Cross-section of Wire Required fof a Given Current. 
 
 Let R = resistance of a given line of copper wire, in ohms; 
 r = " "1 mil-foot of copper; 
 
 L = length of wire, in feet; 
 e = drop in voltage between the two ends; 
 I = current, in amperes; 
 A = sectional area of wire, in circular mils; 
 
 then I = ; R = y ; R = r ^; whence A = r -^. 
 
 The value of r for soft copper wire at 68 F. is 10.371 international 
 ohms. For ordinary drawn copper wire the value of 10.8 is commonly 
 taken, corresponding to a conductivity of 97.2 per cent. 
 
 For a circuit, going and return, the total length is 2 L, and the formula 
 becomes A = 21.67L H- e, L here being the distance from the point of 
 supply to the point of deh'very. 
 
 If E is the voltage at the generator and a the per cent of drop in the 
 line, then e = Ea -r- 100, and A = 2160 IL -=- aE. 
 
 jp 21 An P7" 
 
 If P = the power in watts, = El, then I = =?, and A = =^ . 
 
 Cj CLEj* 
 
 If Pj. = the power in kilowatts, A = 2,160,000 P^L + aE 2 . 
 
 If L m = the distance in miles and A^, the area in circular inches, then 
 
ELECTRIC TRANSMISSION, DIRECT CURRENT. 1411 
 
 A c = 6405 PkL m + aE 2 . If A s = area in square inches, A s = 5030 
 PkL m H- aE 2 . When the area in circular mils has been determined by 
 either of these formulae reference should be made to the table of Allow- 
 able Capacity of Wires, to see if the calculated size is sufficient to avoid 
 overheating. For all interior wiring the rules of the National Board of 
 Fire Underwriters should be followed. 
 
 Weight o'f Copper for a Given Power. Taking the weight of 
 a mil-foot of copper at 0.000003027 lb., the weight of copper in a circuit of 
 length 2 Land cross-section A, in circ. mils, is 0.000006054 LA Ibs., = W. 
 Substituting for A its value 2 160 PL * aE 2 we have 
 
 W = 0.0 130766 PL 2 ' -* aE 2 ; P in watts, L in ft. 
 
 W = 13.0766 P k L 2 -* aE 2 ; P& in kilowatts, L in ft. 
 
 W = 364,556,000 P k L 2 m + aE 2 ; P k in kilowatts, L m in miles. 
 
 The weight of copper required varies directly as the power transmitted ; 
 inversely as the percentage of drop or loss; directly as the square of the 
 distance; and inversely as the square of the voltage. 
 
 From the last formula the following table has been calculated: 
 
 WEIGHT OF COPPER WIRE TO CARRY 1000 KILOWATTS WITH 10% Loss. 
 
 Distance 
 in Miles. 
 
 1 
 
 5 
 
 10 
 
 20 
 
 50 
 
 100 
 
 Volts. 
 
 Weight in Lbs. 
 
 500 
 1,000 
 2,000 
 5,000 
 10,000 
 20,000 
 40,000 
 60.000 
 
 145,822 
 36,456 
 9,114 
 1,458 
 365 
 91 
 
 3,645,560 
 911,390 
 227,848 
 36,456 
 9,114 
 2,278 
 570 
 
 
 
 
 
 3,645,560 
 911,390 
 145,822 
 36,456 
 9,114 
 2.278 
 1,013 
 
 
 
 
 3,645,560 
 593,290 
 145,822 
 36,456 
 9,114 
 4,051 
 
 
 
 3,645,560 
 911,390 
 227,848 
 * 56,962 
 25,316 
 
 
 3,645.560 
 911,390 
 227,848 
 101,266 
 
 
 In calculating the distance, an addition of about 5 per cent should 
 be made for sag of the wires. 
 
 Short-circuiting. From the law I = E/R it is seen that with any 
 pressure E, the current I will become very great if R is made very 
 small. In short-circuiting the resistance becomes small and the current 
 therefore great. Hence the dangers of short-circuiting a current. 
 
 ECONOMY OF ELECTRIC TRANSMISSION. 
 
 The loss of power in a transmission line is ordinarily given in per 
 cent of the total power consumed in the conductors at maximum load. 
 Whatever the line pressure may be, the size of the conductors varies 
 inversely with the percentage of loss. Consequently the maximum line 
 loss which can be allowed is dependent on the most economical size of 
 the line conductors. 
 
 In 1881 Lord Kelvin gave out a statement in regard to the most 
 economical size of conductors. This statement, which is known as 
 "Kelvin's law," was as follows: 
 
 "The most economical area of conductor will be that for which the 
 annual interest on the capital outlay equals the annual cost of energy 
 wasted." 
 
 According to this rule, the cheaper the cost of power, the less should 
 be the capital outlay for the conductors, thus allowing a smaller size 
 to be used. George Forbes states that the most economical section of 
 the conductor is independent of the voltage and the distance, and is 
 proportional to the current. 
 
 It is generally assumed that the cost of the pole line and the insula- 
 tors is constant and not affected by the variation in the size of the line 
 conductors. 
 
 If A = interest cost per year of conductors erected, in dollars, 
 B = value of the line loss per year, in dollars; then for the most 
 economical cross-section of the conductors 
 A =J3. 
 
1412 ELECTRICAL ENGINEERING. 
 
 If K = Cost per kilowatt-year of lost power, in dollars, 
 
 KI = Cost per pound of wires erected, in dollars, 
 
 L = Length of line in 1000 ft., 
 
 >a s= Cross-section of conductor in circular mils, 
 
 I = Line current in amperes, 
 
 p = per cent interest, 
 
 then A = ^ X KI x 0.003 XLXD*. 
 
 L 
 B = K X I z X 10.5 X j=c 2 
 
 ^ x KI x 0.003 XLXD* = KXI*X lo.s'x ^, 
 
 Z>2 = 592 I 
 
 D* is the cross-section, in circular mils, that will give the most eco- 
 nomical line loss. 
 
 In the following, the above equation is worked out for three different 
 rates of interest: 
 
 For 4%, Z> 2 = 296 I \| ; For 5%, DZ = 265 I \l ; 
 II KI i KI ' 
 
 For 6%, D* = 242 I \l 
 KI 
 
 In determining the value of I, care must be taken that the annual 
 mean value of the current is used. The value of K must also be the 
 one for which the power, representing the line loss, can be produced, 
 and not that for which it can be sold. 
 
 Wire Tables. The tables on the following page show the relation 
 between load, distance, and "drop" or loss by voltage in a two- wire 
 direct-current circuit of any standard size of wire. The tables are based 
 on the formula 
 
 (21.6 IL) -7- A - Drop in volts. 
 
 I = current in amperes, L = distance in feet from point of supply to 
 point of delivery, A = sectional area of wire in circular mils. The 
 factors I and L are combined in the table, in the compound factor 
 "ampere feet." 
 
 EXAMPLES IN THE USE OF THE WIRE TABLES. 1. Required the max- 
 imum load in amperes at 220 volts that can be carried 95 feet by No. 6 
 wire without exceeding 11/2% drop. 
 
 Find No. 6 in the 220-volt column of Table I; opposite this in the 
 1V2% column is the number 4005, which is the ampere-feet. Dividing 
 this by the required distance (95 feet) gives the load, 42.15 amperes. 
 
 Example 2. A 500- volt line is to carry 100 amperes 600 feet with a 
 drop not exceeding 5 % ; what size of wire will be required? 
 
 The ampere-feet will be 100 X 600 = 60,000. Referring to the 5% 
 column of Table II, the nearest number of ampere-feet is 60,750, which 
 is opposite No. 3 wire in the 500- volt column. 
 
 These tables also show the percentage of the power delivered to a line 
 that is lost in non-inductive alternating-current circuits. Such circuits 
 are obtained when the load consists of incandescent lamps and the cir- 
 cuit wires lie only an inch or two apart, as in conduit wiring. 
 
 Efficiency of Electric Systems. The efficiency of a system is the 
 ratio of the power delivered by the electric motors at the distant end of 
 the line to the power delivered to the dynamo-electric machines at the 
 other end. The efficiency of a generator or motor varies with its load 
 and with the size of the machine, ranging about as follows: 
 
 Average Full-load Efficiency of Generators: 
 
 K.W 25 50 100 200 500 1000 2000 3000 
 
 Eff. % 88 90 91 92 93 94 94.5 95 
 
 Average Full-load Efficiency of Motors: 
 
 H.P 1 2 5 10 25 50 100 200 500 
 
 Eff. % .... 80 82 85 87 88 90 * 91 92 93 
 
 The efficiency of both generators and motors decreases, at first very 
 
ELECTRIC TRANSMISSION, DIRECT CURRENT. 1413 
 
 WIRE TABLE RELATION BETWEEN LOAD, DISTANCE, Loss, AND 
 
 SIZE OF CONDUCTOR. 
 
 NOTE. The numbers in the body of the tables are Ampere-Feet, i.e., 
 Amperes X Distance (length of one wire). See examples below. 
 
 Table I. 110-volt and 220-volt Two-wire Circuits. 
 
 Wire Sizes; 
 B. & S. Gauge. 
 
 Line Loss in Percentage of the Rated Voltage; and Power 
 Loss in Percentage of the Delivered Power. 
 
 110V. 
 
 220V. 
 
 1 
 
 H/2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 0000 
 000 
 
 0000 
 000 
 00 
 
 
 1 
 
 21,550 
 17,080 
 13,550 
 10,750 
 8,520 
 
 32,325 
 25,620 
 20,325 
 16,125 
 12,780 
 
 43,100 
 34,160 
 27,100 
 21,500 
 17,040 
 
 64,650 
 51,240 
 40,650 
 32,250 
 25,560 
 
 86,200 
 68,320 
 54,200 
 43,000 
 34,080 
 
 107,750 
 85,400 
 67,750 
 53,750 
 42,600 
 
 129,300 
 102,480 
 81,300 
 64,500 
 51,120 
 
 172,400 
 136,640 
 108,400 
 86,000 
 68,160 
 
 215,500 
 170,800 
 135,500 
 107,500 
 85,200 
 
 00 
 
 
 1 
 2 
 3 
 
 2 
 3 
 4 
 
 6 
 
 6,750 
 5,360 
 4,250 
 3,370 
 2,670 
 
 10,140 
 8,040 
 6,375 
 5,055 
 4,005 
 
 13,520 
 10,720 
 8,500 
 6,740 
 5,340 
 
 20,280 
 16,080 
 12,750 
 10,110 
 8,010 
 
 27,040 
 21,4^0 
 17,000 
 13,480 
 10,680 
 
 33,800 
 26,800 
 21,250 
 16,850 
 13,350 
 
 40,560 
 32,160 
 25,500 
 20,220 
 16,020 
 
 54,080 
 42,880 
 34,000 
 26,960 
 21,360 
 
 67,600 
 53,600 
 42,500 
 33,700 
 26,700 
 
 4 
 
 6 
 
 7 
 8 
 
 7 
 8 
 9 
 10 
 11 
 
 2,120 
 1,680 
 1,330 
 1,055 
 838 
 
 3,180 
 2,520 
 1,995 
 1,582 
 1,257 
 
 4,240 
 3,360 
 2,660 
 2,110 
 1,675 
 
 6,360 
 5,040 
 3,990 
 3,165 
 2,514 
 
 8,480 
 6,720 
 5,320 
 4,220 
 3,350 
 
 10,600 
 8,400 
 6,650 
 5,275 
 4,190 
 
 12,720 
 10,800 
 7,980 
 6,330 
 5,028 
 
 16,960 
 13,440 
 10,640 
 8,440 
 6,700 
 
 21,200 
 16,800 
 13,300 
 10,550 
 8,380 
 
 9 
 
 10 
 11 
 12 
 14 
 
 12 
 13 
 14 
 
 665 
 527 
 418 
 332 
 209 
 
 997 
 790 
 627 
 498 
 313 
 
 1,330 
 1,054 
 836 
 665 
 418 
 
 1,995 
 1,580 
 1,254 
 997 
 627 
 
 2,660 
 2,108 
 1,672 
 1,330 
 836 
 
 3,320 
 2,635 
 2,090 
 1,660 
 1.045 
 
 3,990 
 3,160 
 2,508 
 1,995 
 1,354 
 
 5,320 
 4,215 
 3,344 
 2,660 
 1,672 
 
 . 6.650 
 5J270 
 4,180 
 3,325 
 2,090 
 
 Table II. 500, 1000, and 2000 Volt Circuits. 
 
 Wire Sizes; 
 B. & S. Gauge. 
 
 Line Loss in Percentage of the Rated Voltage ; and 
 Power Loss in Percentage of the Delivered Power. 
 
 500V. 
 
 1000V. 
 
 2000V. 
 
 1 
 
 H/2 
 
 2 
 
 2V2 
 
 3 
 
 4 
 
 5 
 
 0000 
 000 
 
 00 
 
 1 
 2 
 3 
 
 4 
 5 
 6 
 7 
 
 8 
 
 9 
 
 10 
 
 n 
 
 12 
 14 
 
 0000 
 000 
 00 
 
 
 1 
 
 2 
 3 
 
 4 
 
 6 
 
 7 
 8 
 9 
 10 
 11 
 
 12 
 13 
 14 
 
 
 1 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 97,960 
 77,690 
 61,620 
 48,880 
 38,750 
 
 30,760 
 24,370 
 19,320 
 15,320 
 12,150 
 
 9,640 
 7,640 
 6,060 
 4,805 
 3,810 
 
 3,020 
 2,395 
 1,900 
 1,510 
 950 
 
 146,940 
 116,535 
 92,430 
 73,320 
 58,125 
 
 46,140 
 36,555 
 28,980 
 22,980 
 18,225 
 
 14,460 
 11,460 
 9,090 
 7,207 
 5,715 
 
 4,530 
 3,592 
 2,850 
 2,265 
 1,425 
 
 195,920 
 155,380 
 123,240 
 97,760 
 77,500 
 
 61,520 
 48,740 
 38,640 
 30,640 
 24,300 
 
 19,280 
 15,280 
 12,120 
 9,610 
 7,620 
 
 6,040 
 4,790 
 3,800 
 3,020 
 1,900 
 
 244,900 
 194,225 
 154,050 
 122,200 
 96,875 
 
 76,900 
 60,925 
 48,300 
 38,300 
 30,375 
 
 24,100 
 19,100 
 15,150 
 12,010 
 9,525 
 
 7,550 
 5,985 
 4,750 
 3,775 
 2.375 
 
 293,880 
 233,970 
 184,860 
 146,640 
 116,250 
 
 92,280 
 73,110 
 57,960 
 45,960 
 36,450 
 
 28,920 
 22,920 
 18,180 
 14,415 
 11,430 
 
 9,060 
 7,185 
 5,700 
 4,530 
 2,850 
 
 391,840 
 310,760 
 246,480 
 195,420 
 155,000 
 
 123,040 
 97,480 
 77,280 
 61,280 
 48,300 
 
 38,560 
 30,560 
 24,240 
 19,220 
 15,220 
 
 12,080 
 9,580 
 7,600 
 6,040 
 3,800 
 
 489,800 
 388,450 
 308,100 
 244,400 
 193,750 
 
 153,800 
 121,850 
 96,600 
 76,600 
 60,750 
 
 48,200 
 38,200 
 30,300 
 24,025 
 19,050 
 
 15,100 
 11,975 
 9,500 
 7,550 
 4,750 
 
 
 
 
 
 
1414 
 
 ELECTRICAL ENGINEERING. 
 
 slowly and then more rapidly, as the load decreases. Each machine 
 has its "characteristic" curve of efficiency, showing the ratio of output 
 to input at different loads. Roughly the decrease in efficiency for direct- 
 current machines at half-load varies from 3% to 10% for the smallest 
 sizes. The loss in transmission, due to fall in electrical pressure or 
 "dop" in the line, is governed by the size of the wires, the other 
 conditions remaining the same. For a long-distance transmission 
 plant this will vary from 5 % upwards. 
 
 With generator efficiency and motor efficiency each 90%, and trans- 
 mission loss 5 %, the combined efficiency is 0.90 X 0.90 X 0.95 = 76.95 %. 
 
 Resistances of Pure Aluminum Wire.* 
 
 Conductivity 62 in the Matthiesen Standard Scale. Pure aluminum 
 weighs 167.111 pounds per cubic foot. 
 
 II 
 
 OM 
 
 gog 
 
 <A 
 
 Resistances at 70 F. 
 
 oT o 
 
 a* 
 
 Ow 
 
 S* 
 
 <ffi 
 
 Resistances at 70 F. 
 
 Ohms 
 perlOOO 
 Feet. 
 
 Ohms 
 Mile. 
 
 Feet 
 Ohm. 
 
 Ohms per 
 Pound. 
 
 Ohms 
 perlOOO 
 Feet. 
 
 Ohms 
 per 
 Mile. 
 
 Feet 
 per 
 Ohm. 
 
 Ohms per 
 Pound. 
 
 0000 
 
 0.07904 
 
 0.41730 
 
 12652. 
 
 0.00040985 
 
 19 
 
 12.985 
 
 68.564 
 
 77.05 
 
 11.070 
 
 000 
 
 .09966 
 
 .52623 
 
 10034. 
 
 .00065102 
 
 20 
 
 16.381 
 
 86.500 
 
 61.06 
 
 17.595 
 
 00 
 
 .12569 
 
 .66362 
 
 7956. 
 
 .0010364 
 
 21 
 
 20.649 
 
 109.02 
 
 48.43 
 
 27.971 
 
 
 
 .15849 
 
 .83684 
 
 6310. 
 
 .0016479 
 
 22 
 
 26.025 
 
 137.42 
 
 38.44 
 
 44.450 
 
 1 
 
 .19982 
 
 1.0552 
 
 5005. 
 
 .0026194 
 
 23 
 
 32.830 
 
 173.35 
 
 30.45 
 
 70.700 
 
 2 
 
 .25200 
 
 1.3305 
 
 3968. 
 
 .0041656 
 
 24 
 
 41.400 
 
 218.60 
 
 24.16 
 
 112.43 
 
 3 
 
 .31778 
 
 1.6779 
 
 3147. 
 
 .0066250 
 
 25 
 
 52.200 
 
 275.61 
 
 19.16 
 
 178.78 
 
 4 
 
 .40067 
 
 2.1156 
 
 2496. 
 
 .010531 
 
 26 
 
 65.856 
 
 347.70 
 
 15.19 
 
 284.36 
 
 5 
 
 .50526 
 
 2.6679 
 
 1975. 
 
 .016749 
 
 27 
 
 83.010 
 
 438.32 
 
 12.05 
 
 452.62 
 
 6 
 
 .63720 
 
 3.3687 
 
 1569. 
 
 .026628 
 
 28 
 
 104.67 
 
 552.64 
 
 9.55 
 
 718.95 
 
 7 
 
 .80350 
 
 4.2425 
 
 1245. 
 
 .042335 
 
 29 
 
 132.00 
 
 697.01 
 
 7.58 
 
 1142.9 
 
 8 
 
 1.0131 
 
 5.3498 
 
 987.0 
 
 .067318 
 
 30 
 
 166.43 
 
 878.80 
 
 6.01 
 
 1817.2 
 
 9 
 
 1.2773 
 
 6.7442 
 
 783.0 
 
 .10710 
 
 31 
 
 209.85 
 
 1108.0 
 
 4.77 
 
 2888.0 
 
 10 
 
 1.6111 
 
 8.5065 
 
 620.8 
 
 .17028 
 
 32 
 
 264.68 
 
 1397.6 
 
 3.78 
 
 4595.5 
 
 11 
 
 2.0312 
 
 10.723 
 
 492.4 
 
 .27061 
 
 33 
 
 333.68 
 
 1760.2 
 
 3.00 
 
 7302.0 
 
 12 
 
 2.5615 
 
 13.525 
 
 390.5 
 
 .43040 
 
 34 
 
 420.87 
 
 2222.2 
 
 2.38 
 
 11627. 
 
 13 
 
 3.2300 
 
 17.055 
 
 309.6 
 
 .68437 
 
 35 
 
 530.60 
 
 2801.8 
 
 1.88 
 
 18440. 
 
 14 
 
 4.0724 
 
 21.502 
 
 245.6 
 
 1.0877 
 
 36 
 
 669.00 
 
 3532.5 
 
 1.50 
 
 29352. 
 
 15 
 
 5.1354 
 
 27.114 
 
 194.8 
 
 1.7308 
 
 37 
 
 843.46 
 
 4453.0 
 
 1.19 
 
 46600. 
 
 16 
 
 6.4755 
 
 34.190 
 
 154.4 
 
 2.7505 
 
 38 
 
 1064.0 
 
 5618.0 
 
 0.95 
 
 74240. 
 
 17 
 
 8.1670 
 
 43.124 
 
 122.5 
 
 4.3746 
 
 39 
 
 1341.2 
 
 7082.0 
 
 0.75 
 
 118070. 
 
 18 
 
 10.300 
 
 54.388 
 
 97.10 
 
 6.9590 
 
 40 
 
 1691.1 
 
 8930.0 
 
 0.59 
 
 187700. 
 
 * Calculated on the basis of Dr. Matthiessen's standard, viz.: The 
 resistance of a pure soft copper wire 1 meter long, having a weight of 
 1 gram = 0.141729 International Ohm at C. 
 (From Aluminum for Electrical Conductors; Pittsburgh Reduction Co.) 
 
 ELECTRIC RAILWAYS. 
 
 While 600 volts is still maintained as a standard for street railway 
 systems, experience has shown that the most economical operation of 
 high-speed suburban and interurban railroads can be obtained with 
 1200 to 1500 volts on the trolley. Steam railroad electrifications will, 
 however, be accomplished most satisfactorily with 2400 or 3000 volts 
 direct current. 
 
 Schedule Speeds, Miles per Hour. 
 CITY SERVICE. 
 
 Max. 
 
 Stops per Mile. 
 
 Speed. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 15... 
 
 10.8 
 
 9.9 
 
 9.3 
 
 8.7 
 
 8.3 
 
 7.9 
 
 7.5 
 
 7.2 
 
 20... 
 
 13.7 
 
 12.1 
 
 11 .1 
 
 10.3 
 
 9.6 
 
 9.0 
 
 8.6 
 
 8.1 
 
 25 
 
 16 3 
 
 14.2 
 
 12.7 
 
 11 .5 
 
 10.6 
 
 9.9 
 
 9.3 
 
 8.7 
 
 30 
 
 18.5 
 
 15.6 
 
 13.8 
 
 12.4 
 
 11.3 
 
 10.5 
 
 9.8 
 
 9.2 
 
ELECTRIC RAILWAYS. 
 
 1415 
 
 INTERURBAN SERVICE. 
 
 Max. 
 
 
 
 
 Miles I 
 
 >etween 
 
 Stops. 
 
 
 
 
 Speed. 
 
 1/1 
 
 3/4 
 
 1 
 
 1.5 
 
 2 
 
 3 
 
 4 
 
 5 
 
 10 
 
 30. 
 
 14 
 
 15 5 
 
 16 7 
 
 18 5 
 
 19.7 
 
 21 
 
 22 
 
 22 5 
 
 23 9 
 
 40. . 
 
 15.4 
 
 18.1 
 
 20.0 
 
 22.7 
 
 24.5 
 
 26.7 
 
 28.0 
 
 28.9 
 
 30 8 
 
 50 
 
 16 2 
 
 19 5 
 
 21 9 
 
 25 6 
 
 27 9 
 
 31 
 
 32 9 
 
 34 2 
 
 37 2 
 
 60 
 
 17.0 
 
 20.8 
 
 23.6 
 
 27.9 
 
 30.9 
 
 34.8 
 
 37.5 
 
 39.3 
 
 43.6 
 
 The figures in the above tables include stops of 5 seconds each for the 
 city service and of 15 seconds for the interurban service, besides a 15 % 
 margin for line drop and traffic delays. The ratio of acceleration is 
 approximately 1.5 miles per hour per second for the city service and 
 1.2 miles per hour per second for the interurban service, the braking 
 being 1.5 miles per hour per second and the coasting approximately 
 10% of the running time exclusive of stop. 
 
 Train Resistance. (General Electric Co.) The horse-power output 
 at the rim of the wheels is equal to, 
 
 H P = T XF.X Feet T X F X V 
 
 33,000 X Minutes 375 
 
 When reduced to Kilowatts, 
 
 _ TXFX V X 746 _ 2 X TXFX V 
 
 
 
 375 X 1000 
 
 The kilowatt input to train is equal to, 
 
 1000 
 
 appro*. 
 
 T , 2XTXFXV 
 
 KW. = : 
 
 1000 X Eff. 
 Where T = Total weight of train in tons. 
 
 F = Train resistance, including that due to grades and curves, 
 
 in Ibs. per ton. 
 V = Speed in miles per hour. 
 Eff = Efficiency of motors at speed V. 
 The train resistance may be found from the following formula: 
 
 Where F = Train resistance in Ibs., per ton. 
 T = Total weight of train in tons. 
 V = Speed in miles per hour. 
 A = End cross-section in sq. ft. 
 N = Number of cars in train. 
 
 is limited to a value of 3.5. 
 
 VT 
 
 Tractive Resistance of a 28-ton Electric Car (Harold H. Dunn, 
 Bull. 74, Univ'y of 111. Expt. Station, April, 1914). Mean of all tests: 
 Miles per hr. .5 10 15 -20 25 30 35 40 45 
 Lb. per ton.. 5.25 6.80 8.62 10.75 13.03 15.75 18.75 22.13 26.12 
 Two formulae have been derived from the results: 
 R = 4 + 0.222 S + 0.00582 S*. 
 R = 4 + 0.222 3 + 0.00181 ~ S 2 . 
 
 A = cross-sectional area of the car in sq. ft. W = weight of the car 
 in tons. 
 
 The formulae should not be used beyond the limit of 45 miles per hour. 
 
 Rates of Acceleration. Electric Locomotive Passenger Service, 0.3 to 
 0.6 mile per hour per second. 
 
 Electric Motor Cars, Interurban Service, 0.8 to 1.3 miles per hour 
 per second. 
 
 Electric Motor Cars, City Service, 1.5 miles per hour per second. 
 
 Electric Motor Cars, Rapid Transit Service, 1.5 to 2.0 miles per hour 
 per second. 
 
 Highest Practical Bate, 2.0 to 2,5 miles per Jiour per second, 
 
1416 
 
 ELECTRICAL ENGINEERING. 
 
 Safe Maximum Speed on Curves. 
 
 Radius of Curve, Ft. 10,000 5000 2000 1000 500 200 100 50 
 Speed, miles per hr., 100 75 50 35 25 15 10 6 
 The above values apply only when full elevation is given the outer 
 rail. For city service such elevation is not possible and the maxi- 
 mum speed will, therefore, be less under such cpnditions. The same 
 restriction applies with steel wheel flanges of 3/ 4 inch or less. 
 
 Coefficient of Adhesion. The following are the average values of 
 the coefficient of adhesion between wheels and rails, based on a uniform 
 torque: 
 
 Clean, dry rail, 30%. 
 
 Wet rail, 18%; 
 
 Rail covered with sleet, 15? 
 Rail covered with dry snow, 10 , , 
 
 Electrical Resistance of Steel Bails. The resistance of steel rails 
 varies considerably, due to the difference in chemical composition. 
 Ordinary traction rails have a specific resistance averaging 12 times 
 that of copper, while for contact rails (third rails) the average is only 
 8 times. The values given in the following table are in ohms at 75 F. 
 and with no joints. 
 
 with sand, 22%. 
 
 with sand, 20%. 
 
 o', with sand, 15%. 
 
 Weight of Rails, 
 Lbs. per Yard. 
 
 Actual 
 Area, 
 Sq. In. 
 
 Actual Area 
 in 
 Circular Mils. 
 
 Resistance 
 per Mile, 
 8 to 1 Ratio. 
 
 Resistance 
 per Mile, 
 1 2 to 1 Ratio. 
 
 40. 
 
 3 92 
 
 4 918300 
 
 09 1 1 8 
 
 13395 
 
 45.. 
 
 4 42 
 
 5,627 700 
 
 07915 
 
 1 1 905 
 
 50... 
 
 4.90 
 
 6,238,800 
 
 07135 
 
 10710 
 
 60. 
 
 5 88 
 
 7 486 600 
 
 05955 
 
 08920 
 
 70... 
 
 6 86 
 
 8,734400 
 
 05105 
 
 07660 
 
 75.. 
 
 7.35 
 
 9,230,900 
 
 04780 
 
 07185 
 
 80. 
 
 7 84 
 
 9 982 1 00 
 
 04465 
 
 06695 
 
 90. . 
 
 8 82 
 
 1 1 ,229,900 
 
 03975 
 
 05955 
 
 100 
 
 9.80 
 
 12,477,700 
 
 0.03750 
 
 0.05365 
 
 Resistance of Rail Bonds. The resistance of bonded rails will 
 vary, depending on the amount of contact made by the splice bars and 
 rail ends, but in selecting bonds this element of the return circuit 
 should be disregarded, as it is quite unreliable and frequently negligible. 
 
 Size of Conductor. 
 
 Diameter of 
 Terminal, 
 in Inches. 
 
 Resistance per In. 
 of Conductor. 
 75 Fahr. 
 
 Carrying 
 Capacity, 
 Amp. 
 
 0. . , 
 
 1/2 
 
 00000829 
 
 210 
 
 00.. . 
 
 5/8 
 
 00000657 
 
 265 
 
 000. . 
 
 3/4 
 
 00000521 
 
 335 
 
 0000. . 
 
 7/8 
 
 000004 1 4 
 
 425 
 
 250,000 C. M . . 
 
 7/ 8 
 
 00000350 
 
 500 
 
 300,000 C. M. . 
 
 
 00000275 
 
 600 
 
 350,000 C. M. . . 
 
 
 00000250 
 
 700 
 
 400,000 C. M. . . 
 
 
 00000219 
 
 800 
 
 450,000 C. M. . 
 
 
 00000196 
 
 900 
 
 500,000 C. M 
 
 
 .00000175 
 
 1000 
 
 Electric Locomotives. In selecting an electric locomotive the prin- 
 cipal points to be determined are the weight of the locomotive, the 
 type and capacity of the equipment, and the mechanical features. 
 The weight upon the drivers must be enough to pull the heaviest 
 trains under the most adverse conditions. Therefore the weight of the 
 heaviest train, the maximum grade and curvature must be ascertained. 
 It must be known whether the locomotive is expected to start the train 
 under these conditions, or whether it will start upon the level and only 
 meet maximum grade conditions when running. 
 
 In order to determine the motor equipment all the data of the service 
 conditions are required, such as the speed required under various condi- 
 tions of load and grade. The maximum free-running speed will be ap- 
 proximately 50 to 75 per cent greater than the rated full load speed. 
 Mechanical limitations must also be considered, such as track clear- 
 ajices, limiting weight on drivers, type of couplings, etc, 
 
RAILWAYS. 
 
 1417 
 
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1418 
 
 ELECTRICAL ENGINEERING. 
 
 
 
 
 
 
 
 
 
 
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 ie of Road and Section Electrified. 
 
 altimore & Ohio, Baltimore, Md. 
 Baltimore Tunnels 
 
 ew York Central R.R., New York 
 to Harmon 
 
 1 
 
 ew York, New Haven & Hartford j 
 R.R., New York to New Haven ! 
 
 rand Trunk Ry. Co., 
 St. Clair Tunnel Co., Pt. Huron, 
 Mich., St. Clair Tunnel 
 
 reat Northern R.R., Cascade Tun- 
 nel, Washington 
 
 .ichigan Central R.R., Detroit 
 River Tunnel, Detroit, Mich. 
 
 Dston & Maine R.R., North Adams, 
 Mass., Hoosac Tunnel 
 
 snn. Tunnel & Terminal R.R. 
 Pennsylvania R.R. into New 
 York City 
 
 utte, Anaconda & Pacific R.R., j 
 Butte to Anaconda, Montana 
 
 orf oik & Western R.R., Bluefield to 
 Elkhorn, W. Va. 
 
 anadian Northern, Montreal, Can. 
 
 Continuous Rating," which means 
 Pounds Tractive Effort," in which 1 
 
 
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ELECTRIC WELDING. 
 
 1419 
 
 Relative Efficiencies of Electric Railway Distributing Systems. The 
 
 table on p. 1417 shows the approximate all-day combined efficiencies 
 from prime mover to train wheels for various methods of trunk line 
 electrifications. The trains are supposed to be handled by electric 
 locomotives, and in each instance a considerable length of line is con- 
 templated, making it necessary to have a 100,000-volt high-tension 
 primary distribution or a multiplicity of power sources. 
 
 Space will not permit a complete treatment 9f the subject of Electric 
 Railways in this work. For further information consult: "American 
 Handbook for Electrical Engineers"; Standard Handbook for Electrical 
 Engineers"; "Foster's Electrical Engineer's Pocket Book"; Burch, 
 "Electric Traction for Railway Trains"; Harding, "Electric Railway 
 Engineering." 
 
 ELECTRIC WELDING. 
 
 Electric welding is divided into two general classes, arc heating 
 and resistance heating. 
 
 Arc Welding. In this process the heat of the arc is utilized to 
 bring the metals to be welded to the melting temperature, when the- 
 joint is filled with molten metal, usually introduced in the form of a 
 rod. This system is usually operated by direct current, and as the 
 positive side of a direct current arc generates heat at a rate approxi- 
 mately three times that of the negative side, the positive side is used for 
 performing the welding operation. 
 
 Two kinds of arcs may be used for this class of welding, the carbon 
 arc and the metallic arc. The former requires an e. m. f. varying from 
 50 to 100 volts and the value of the current is varied over a range of 
 100 to 750 amperes, 300 being the average. The metallic arc, how- 
 ever, requires an e. m. f. of only from 15 to 30 volts, the length of the 
 arc being very short as compared with the carbon arc. 
 
 The arc should be as stable as possible, and the current should, 
 therefore, be of a constant value. The regulation may be accomplished 
 by inserting resistance in series in the circuit, but this system is nat- 
 urally very wasteful and greater economy may be obtained by pro- 
 viding motor-generator sets, with the generator of the variable voltage 
 
 The following costs, Table I (from Electrical World) were compiled 
 from the records of an electric railway repair shop: 
 
 TABLE I. 
 
 Data on Electric Welding Repairs in Railway Shops. 
 
 
 Time in 
 Minutes. 
 
 Kw. 
 
 Average 
 Costs. 
 
 Gear-case lugs .... 
 
 10 
 
 6 
 
 $0.07 
 
 Armature shaft (broken) 2-in 
 
 60 
 
 20-30 
 
 0.80 
 
 Dowel-pin holes .' 
 
 5-12 
 
 4-8 
 
 0.07 
 
 Broken motor cases 
 
 150-200 
 
 75-90 
 
 4.98 
 
 Broken lugs on a compressor cover, doors 
 and grease-cup hinges . . .... 
 
 2-5 
 
 1-3 
 
 0.03 
 
 Broken truck frames 
 
 30-60 
 
 20-35 
 
 0.63 
 
 Worn bolt holes in motors and trucks ..... 
 Enlarged and elongated holes in brake levers 
 Armature shafts, 2-in., worn in journals . . . 
 Armature shafts worn in keyways . ... 
 
 5-10 
 2-4 
 120-180 
 10-15 
 
 3-5 
 
 1 V 2 -3 
 60-90 
 7-12 
 
 0.05 
 0.03 
 3.75 
 0.10 
 
 Armature shaft, worn thread 
 
 20-30 
 
 10-15 
 
 0.24 
 
 Air-brake armature shafts (broken) . . 
 
 20-30 
 
 10-20 
 
 0.27 
 
 Leaking axle boxes 
 
 5-15 
 
 3-7 
 
 0.08 
 
 Resistance Welding. Resistance welding is done by the heat 
 developed by a large amperage carrying through the joining metals by 
 means of a low voltage. Single-phase alternating current is generally 
 used for the operation, which may be broadly divided into two classes 
 butt-welding and spot-welding. The former covers all work on which 
 the ends or the sides of the material are welded together, while spot- 
 welding is used for joining metal sheets together at any point by a 
 spot the size of a rivet, without punching holes or using rivets. 
 
 For resistance welding a very low voltage is used, varying from 2 
 to 8 volts, the line voltage being stepped down by special transformers. 
 
1420 
 
 ELECTRICAL ENGINEERING. 
 
 The current consumption, in amperes, varies with the work and the 
 time taken to make the weld. 
 
 The following tables (from Iron Trade Review) give the cost of 
 resistance welding. Table II gives the results obtained by butt- 
 welding round stock ranging from 1/4 to 1 inch diameter, in the short- 
 est and longest time possible. The difference in current consumption 
 is very great and in most cases the shorter time in seconds was the most 
 economical of the two, although neither is the most economical rate 
 at which the material can be welded. 
 
 TABLE II. Shortest and Longest Butt-welding Periods. 
 
 Size, In. 
 
 Time, 
 Seconds. 
 
 Current 
 Amperes. 
 
 Volts per 
 Square 
 Inch. 
 
 Size, In. 
 
 Time, 
 Seconds. 
 
 Current 
 Amperes. 
 
 Volts per 
 Square 
 Inch. 
 
 1/4 
 
 i 
 
 3/8 
 
 $ 
 
 9/16 
 
 9/16 
 
 2.7 
 5 
 4 
 5.27 
 4 
 15.8 
 3.6 
 21.5 
 
 1960 
 1645 
 4330 
 2190 
 6600 
 1800 
 8400 
 3400 
 
 39.5 
 35.5 
 45.5 
 19.7 
 36.6 
 13 
 8 
 12.25 
 
 5/8 
 V8 
 3/4 
 3/4 
 V8 
 
 1 V8 
 1 
 
 3.5 
 10.85 
 4 
 22.2 
 
 17 
 33 
 114 
 
 9400 
 5510 
 10000 
 9400 
 11900 
 10550 
 7740 
 4450 
 
 33.7 
 18.85 
 16.26 
 19.7 
 27.7 
 19.6 
 10.35 
 16.1 
 
 Table III contains the results of tests made to determine the cost of 
 power for making electric butt welds on material ranging from 1/4 to 
 2 inches in diameter. 
 
 TABLE HI. Cost of Power. 
 
 Area, 
 Sq. In. 
 
 Kw. 
 
 Welding 
 Time, 
 Seconds. 
 
 Cost per 
 1000 
 Welds* 
 
 Area, 
 Sq. In. 
 
 Kw. 
 
 Welding 
 Time, 
 Seconds. 
 
 Cost per 
 1000 
 Welds* 
 
 0.05 
 0.11 
 0.20 
 0.31 
 0.44 
 0.60 
 
 h 
 
 10 
 12 
 15 
 
 5 
 6 
 10 
 12 
 15 
 20 
 
 $0.07 
 0.13 
 0.22 
 0.33 
 0.50 
 0.83 
 
 0.79 
 0.99 
 1.23 
 1.77 
 2.41 
 3.14 
 
 18 
 20 
 26 
 40 
 45 
 56 
 
 30 
 30 
 40 
 60 
 70 
 80 
 
 $1.50 
 1.66 , 
 2.89 
 6.67 
 8.75 ' 
 12.44 
 
 Table IV gives the time, power and! cost per 100 spot-welds, with 
 current at 1/4 cent per Kw.-hr., for welding Nos. 10 to 28 gage sheets. 
 
 TABLE IV. Cost of Welding. 
 
 Gage. 
 
 Kw. 
 
 Time in 
 Seconds. 
 
 Cost per 
 1000 Welds, 
 Cents.* 
 
 Gage. 
 
 Kw. 
 
 Time in 
 Seconds. 
 
 Cost per 
 1000 Welds, 
 
 Cents. 
 
 10 
 12 
 14 
 16 
 
 18 
 
 18 
 16 
 14 
 12 
 10 
 
 1.5 
 
 tlo 
 
 0.9 
 0.8 
 
 3.5 
 
 2.75 
 2.5 
 2.25 
 
 20 
 22 
 24 
 26 
 28 
 
 9 
 
 8 
 
 6 
 5 
 
 0.7 
 0.6 
 0.5 
 0.4 
 0.3 
 
 1.75 
 1.5 
 1.25 
 
 * Current at 1 cent per Kw.-hr. 
 
 ELECTRIC HEATERS. 
 
 Wherever a comparatively small amount of heat is desired to be auto- 
 matically and uniformly maintained, and started or stopped on the 
 instant without waste, there is the province of the electric heater. 
 
 The elementary form of heater is some form of resistance, such as 
 coils of thin wire introduced into an electric circuit and surrounded with 
 a substance which will permit the conduction and radiafion of heat, and 
 at the same time serve to electrically insulate the resistance. 
 
 This resistance should be proportional to the electro-motive force of 
 the current used and to the equation of Joule's law: 
 H = imt X 0.24, 
 
ELECTRIC HEATING. 1421 
 
 where I is the current in amperes! R, the resistance in ohms; t, the time 
 in seconds; and H, the heat in gram-centigrade units. 
 
 Since the resistance of metals increases as their temperature increases, 
 a thin wire heated by current passing through it will resist more, and 
 grow hotter and hotter until its rate of loss of heat by conduction and 
 radiation equals the rate at which heat is supplied by the current. In a 
 short wire, before heat enough can be dispelled for commercial purposes, 
 fusion will begin ; and in electric heaters it is necessary to use either long 
 lengths of thin wire, or carbon, which alone of all conductors resists 
 fusion. In the majority of heaters, coils of thin wire are used, separately 
 embedded in some substance of poor electrical but good thermal 
 conductivity. 
 
 Relative Efficiency of Electric and of Steam Heating. Suppose 
 that by the use of good coal, careful firing, well-designed boilers and 
 triple-expansion engines we are able in daily practice to generate 1 H.P. 
 at the fly-wheel with an expenditure of 2 1/2 Ib. of coal per hour. 
 
 We have then to convert this energy into electricity, transmit it by 
 wire to the heater, and convert it into heat by passing it through a 
 resistance-coil. We may set the combined efficiency of the dynamo and 
 line circuit at 85.%, and will suppose that all the electricity is converted 
 into heat in the resistance-coils of the radiator. Then 1 brake H.P. at 
 the engine =0.85 electrical H.P. at the resistance coil = 1,683,000 
 ft.-lb. energy per hour = 2180 heat-units. But since it required 2 1/2 
 Ibs. of coal to develop 1 brake H.P., it follows that the heat given out 
 at the radiator per pound of coal burned in the boiler furnace will be 
 2180-^21/2 = 872 H.U. An ordinary steam-heating system utilizes 
 9652 H.U. per Ib. of coal for heating; hence the efficiency of the electric 
 system is to the efficiency of the steam-heating system as 872 is to 9652, 
 or about 1 to 11. (Eng'g News, Aug. 9, '90; Mar. 30, '92; May 15, '93.) 
 
 Heat Required to Warm and Ventilate a Room. The heat re- 
 quired to raise the temperature of a given space or room to a certain 
 value depends upon the ventilation, the character of the walls, the di- 
 mensions, proportions of the room, etc. One watt-hour of electrical 
 energy will raise the temperature of one cubic foot of air (measured at 
 70) 191 F., or 1 watt will raise the temperature of a cubic foot of air 
 at the rate of 0.0531 F. per second, or approximately 3.2 per minute. 
 In addition to raising the temperature of the air to the desired value, 
 the loss of heat through conduction and ventilation must be supplied. 
 (See Heating and Ventilation.) 
 
 EXAMPLE. Assume a room of a capacity of 3000 cu. ft., in which 
 the air is changed every 20 minutes, the temperature to be main- 
 tained 30 above the outside air. 
 
 3000 -T- 20 = 150 cu. ft. per minute. 
 
 (150 X 30) -s- 3.2 = 1406 watts necessary to supply the ventilation 
 loss. To begin with, to raise the air in the room 30 will require 
 
 (3000 X 30) -T- 191 =471 watt-hours 
 
 and therefore the total energy used during the first hour will be 
 1406 + 471 = 1877 watt-hours or 1.88 Kw.-hours. 
 
 Domestic Heating. Electric heating is extensively used for house- 
 hold cooking apparatus. The time taken to heat water in any quantity 
 to any definite temperature not exceeding boiling point can be deter- 
 mined by the formula: 
 
 V (T* - Ti) 1831 
 PX Eff. 
 
 Where t = time in minutes, V = number of pints, T\ = initial tem- 
 perature, F., Tz = final temperature, F., P = energy consumption 
 in watts, Eff. = Efficiency of cooking utensil, per cent. 
 
 EXAMPLE. To heat 1 pint of water 100 F. with a 220- watt heater 
 with 50% efficiency, time = (1 X 100 X 1831) -~ (220 X 50) = 16.6 min. 
 
 The following table (compiled by the National Electric Light Asso- 
 ciation) gives the watts consumed and cost of operation of different 
 domestic heating devices, the cost of current being at the rate of 5 cents 
 per Kw.-hr. 
 
1422 ELECTRICAL ENGINEERING. 
 
 Cost of Operation of Domestic Heating Appliances. 
 
 Apparatus. Watts. Cents per hr. 
 
 Broilers, 3 heat* 300 to 1200 1.5 to 6 
 
 Chafing dishes, 3 heat 200 to 500 1 to 2.5 
 
 Coffee percolators for 6-in. stove 100 to 440 0.5 to 2.2 
 
 Curling-iron heaters 60 0.3 
 
 Double boilers for 6-in., 3-heat stove 100 to 440 0.5 to 2.2 
 
 Flatiron (domestic size) , 3 Ib 275 1 
 
 Flatiron (domestic size), 4 Ib 350 1.4 
 
 Flatiron (domestic size) , 5 Ib 400 2 
 
 Flatiron (domestic size), 6 Ib 475 2.4 
 
 Flatiron (domestic size), 7.5 Ib 540 2.7 
 
 Flatiron (domestic size), 9 Ib 610 3.05 
 
 Frying kettles, 8 in. diameter 825 4.125 
 
 Griddle-cake cookers, 9 in. by 12 in., 3-heat 330 to 880 1.7 to 4.4 
 
 Griddle-cake cookers, 12 in. by 18 in., 3-heat 500 to 1500 2.5 to 7.5 
 
 Ornamental stoves 250 to 500 1.25 to 2.5 
 
 Ovens 1200 to 1500 6 to 7.5 
 
 Plate warmers 300 J .5 
 
 Radiators . 700 to 6000 3.5 to 30 
 
 Ranges: 3-heat, 4 to 6 people 1000 to 4515 5 to 22 
 
 Ranges: 3-heat, 6 to 12 people 1100 to 5250 5.5 to 26 
 
 Ranges: 3-heat, 12 to 20 people 2000 to 7200 10 to 36 
 
 Toasters, 9 in. by 12 in., 3-heat 330 to 880 1.6 to 4.4 
 
 Urns, 1-gal., 3-heat 110 to 440 0.5 to 2.2 
 
 Urns, 2-gal., 3-heat 220 to 660 1.1 to 3.3 
 
 Experience has shown that 300 watt-hours per meal per person is a 
 
 liberal allowance for electric cooking; or in a family of five, four kilo- 
 watt hours per day is an average. 
 
 ELECTBIC FURNACES. 
 
 In the combustion furnace, no matter what form of fuel is used, the 
 temperature cannot exceed 2000 C. (3632 F.), and for higher temper- 
 atures the electric furnace must be used. The intensity of the heat 
 in this type of furnace depends .on the amount of current that passes, 
 and as most substances are conductors when hot, the degree of intensity 
 possible is theoretically unlimited. In practice, however, the conduct- 
 ing substance begins to fuse when heated to its melting point, and one 
 is then confronted with the physical difficulty of keeping the con- 
 ducting medium in place, or, if this be accomplished, the conducting 
 medium ultimately vaporizes,, the gaseous materials escape, and heat 
 is thus carried away from the furnace as rapidly as it is supplied. The 
 temperature of the electric arc, which is somewhere between 3600 
 and 4000 C. (6512 - 7232 F.), is perhaps the highest temperature 
 attainable at present. 
 
 Electric furnaces may be divided in two broad classes, arc furnaces 
 and resistance furnaces. In the former the heat is generated by passing 
 an electric current through the space between the ends of two elec- 
 trodes, forming the so-called arc. In the resistance furnace the heat 
 is generated in the interior of a body due to its electrical resistance. 
 
 There are three typical forms of arc furnaces, their common feature 
 being that most and sometimes all of the heat is transmitted to the 
 material by radiation, which extends in all directions. In all the fur- 
 naces the arc must be started by a quick movement of the electrodes and 
 afterwards these must be continuously fed together as they are 
 consumed. 
 
 The chief characteristics of the three main types of arc furnaces are: 
 
 1. The direct-heating type, in which two or more electrodes are 
 used and the heating is accomplished by conduction and radiation. 
 The current passes from one electrode down through the slag, across 
 through the bath and up through the slag to the other electrode. The 
 - Heroult furnace belongs to this type. 
 
 The Girod furnace is also T>f the direct-heating type, the current 
 arcing from the electrodes, which are connected to one side of the cir- 
 cuit. to a fixed electrode in the bottom. 
 
 * The apparatus can be set at three different heats or temperatures, 
 
ELECTRIC FURNACES. 1423 
 
 2. The indirect-heating type. To this type belongs the Stassano 
 furnace, in which the arc extends between two or more carbon elec- 
 trodes above the charge, and therefore passes over but does not come 
 in contact with the charge, the heating being accomplished by radiation. 
 
 3. The smothered type, in which the arc extends from the end of the 
 upper electrode, which extends beneath the surface of the charge, to 
 the lower fixed electrode in the bottom of the furnace. 
 
 The direct and indirect heating arc furnaces are extensively used 
 for melting and refining metals, while examples of the smothered type 
 are the ferro-silicon and calcium carbide furnaces. 
 
 Resistance furnaces may also be divided in two distinct types, those 
 of direct and indirect heating. 
 
 1. Direct heating. In these the heat is produced in the material by 
 its own resistance, and enters the material at the highest efficiency. 
 
 The material may be placed in a channel between two electrodes at 
 the ends which lead the current to and from it, the charge being sur- 
 rounded with insulating material to reduce the loss of heat. The 
 Acheson graphite furnaces are of this type. 
 
 Under this classification also come the induction furnaces in which 
 the terminal electrodes are eliminated and the heat generated solely 
 by induction. .The furnace consists essentially of an iron core, around 
 one leg of which is wound a primary winding enclosed in a refractory 
 case and usually cooled by means of forced draft. The annular hearth 
 surrounds this primary coil and is separated from it by means of 
 refractory material. This hearth contains the metal and acts as a 
 secondary winding of one turn. The voltage induced in this turn is 
 quite small so that the energy transformed from the primary coil 
 results in a very large current in the secondary, which heats the metal 
 and thus nearly all the electrical energy is converted into heat in the 
 metal to be melted. The Kjellin and the Rochling-Rodenhauser fur- 
 naces belong to this type. They are extensively used for steel refining. 
 
 2. Indirect heating furnaces have the heat generated in an internal 
 or external resistor and it is transferred to the charge by conduction 
 and radiation. Such furnaces are used for small moderate temperature 
 work. 
 
 Uses of Electric Furnaces. 
 
 Pig Iron. When the electric furnace is used for smelting of iron 
 ore it is only necessary to supply enough carbon for the reduction, this 
 amount being approximately one-third of what is required in the 
 ordinary blast furnace for both the heating and reduction. From re- 
 peated trial runs with electric smelting furnaces in Norway and Sweden 
 it has been found that coke as a reducing agent does not give "satisfac- 
 tory results, and charcoal is therefore used exclusively. 
 
 The table on p. 1424 gives a summary of the most important figures 
 relating to the economical results which were obtained with the electric 
 iron ore furnaces in Sweden. 
 
 Steel Refining. Electric furnaces are used in the manufacture of 
 crucible quality steel, and the number is constantly increasing, both 
 arc and induction furnaces being in general use. 
 
 The following data as to the cost of electric steel refining are taken 
 from an article in Stahl und Eisen, April 10, 1913. This article gives 
 the results which have been obtained in Germany by the Heroult 
 furnace and it contains a discussion of electric steel production from a 
 large-industry point of view. 
 
 The total refining cost must include many items as well as the cost 
 of current; for example, the cost of fluxes (ore, lime, sand, etc.), the 
 additions of ferro-alloys, relining, maintenance, and repairs, electrode 
 consumption, wages, and, finally, interest and depreciation. The totals 
 of these items and the cost of current, which is the largest item, are 
 given below: 
 
 Total Refining Costs (Per Ton). 
 
 5- ton 10- ton 15-ton 20- ton 
 
 Basic. Acid. Basic. Acid. Basic. Acid. Basic. Acid. 
 Total costs .... $2.79 $1.79 $2.45 $1.45 $2.28 $1.34 $2.15 $1.25 
 Cost of current 1.19 0.77 1.07 0.59 1.01 0.54 0.95 0.48 
 The figures are based on prevailing market prices. Current is taken 
 
1424 
 
 ELECTRICAL ENGINEERING. 
 
 Data on Electric Smelting of Pig Iron in Sweden. 
 
 
 Nov. 15, 1910, 
 May 29, 1911. 
 
 Aug. 4, 1911, 
 to 
 June21,1912. 
 
 Aug. 12, 1912, 
 Sept. 30, 191 2. 
 
 October to 
 December, 
 1912. 
 
 Ore, concentrates 
 and briquettes, kg. 
 Limestone kg. 
 
 4,336,338 
 345,405 
 
 7,917,214 
 647,479 
 
 1,406,530 
 1 08, 1 50 
 
 2,914,830 
 169,944 
 
 Charcoal hi.* 
 
 65,474 
 
 107,282 
 
 21,859 
 
 44,934 
 
 Coke kg. 
 
 
 70854 
 
 
 
 Elec. energy, kw. hrs. 
 Iron in ore, per cent. 
 Iron produced . . kg. 
 Slag per ton of 
 iron .... kg. 
 
 6,339,131 
 60.79 
 2,636,098 
 
 350 
 
 10,845,180 
 60.75 
 4,809,670 
 
 324 
 
 1,939,073 
 68.67 
 965,915 
 
 192 
 
 3,957,565 
 65.38 
 1,905,865 
 
 Electrodes per ton 
 of iron, gross .kg. 
 Electrodes per ton 
 of iron, net. .kg. 
 Charcoal per ton 
 of iron. hi 
 
 10.00 
 4.95 
 24 84 
 
 6.08 
 5.17 
 22 31 
 
 3.02 
 3.02 
 22 63 
 
 2.78 
 2.78 
 23 58 
 
 
 
 
 
 
 Working time 
 
 Hr. Min. 
 4,441 20 
 
 Hr. Min. 
 7,218 23 
 
 Hr. Min. 
 1 , 1 73 08 
 
 Hr. Min. 
 2,158 30 
 
 Repairs 
 
 236 53 
 
 506 07 
 
 13 47 
 
 49 30 
 
 Repairs in per cent, 
 of total time .... 
 Average load, kw . . 
 Kw.-hrs. per ton of 
 iron 
 
 5.05 
 1,427 
 
 2,405 
 
 6.55 
 1,502 
 
 2,255 
 
 1 .16 
 1,653 
 
 2,007 
 
 2.24 
 1,833 
 
 2,076 
 
 Iron per kw. year, 
 tons .... 
 
 3.64 
 
 3.88 
 
 4.36 
 
 4.22 
 
 Iron per h.p. year, 
 tons . . 
 
 2.68 
 
 2.86 
 
 3.20 
 
 3.10 
 
 * 1 hectoliter = 3.53 cu. ft. = 2.84 U. S. bushels. 
 
 at 0.595c. per Kw.-hr., which is a figure that should be easy of attain- 
 ment for most steel plants. The time per heat is taken as 2 1/4 to 2 1/2 
 hours. Three-phase furnaces are considered, and in the installation 
 cost of the plant must be included transformers, cables, and switch- 
 boards. The amount of current required is as follows: 
 Size of Furnace, Tons 1 2 5 10 25 
 
 Kilowatts 300-350 400-450 750-800 1000-1200 3000-3500 
 
 Ferro- Alloys. The electric furnace has clearly demonstrated its 
 advantages in the manufacture of ferro-alloys. The production of a 
 ferro-alloy low in carbon or with a high percentage of the alloying 
 element is limited in the blast furnace by three difficulties first, the 
 temperature is too low for the reduction of some of the oxides of the 
 alloying metals; second, it is difficult to obtain an alloy containing 
 a high percentage of the special metal; and third, it is impossible to 
 produce a ferro-alloy low in carbon, because of the great excess of 
 carbon in the charge. With the crucible, owing to the small scale of 
 operation necessary, the process is expensive. Owing to the temper- 
 ature limitation, certain oxides can not be reduced and metals of high 
 melting point can not be melted ; it is difficult to obtain an alloy with a 
 high percentage of the special metal ; and if a graphite crucible is used, 
 the percentage of carbon tends to be high in the ferro-alloy. 
 
 Non-ferrous Metals. In the metallurgy of non-ferrous metals the 
 electric furnace has had a greater application for the treatment of zinc 
 ores than in the metallurgy of any of the other non-ferrous metals 
 except aluminum. Since 1885, when an electric furnace for the treat- 
 ment of zinc ores was patented by the Cowles brothers, experimental 
 work has been done on a very large scale. However, the process has 
 not been applied to any great extent because of the difficulty of con- 
 densing the zinc vapor produced in smelting in the electric furnace, and 
 
ELECTRIC ACCUMULATORS. 
 
 1425 
 
 eo it may be said that the electric smelting of zinc ores is yet in the 
 experimental stage. 
 
 Silundum, or silicified carbon, is a product obtained when carbon is 
 heated in the vapor of silicon in an electric furnace. It is a form of car- 
 borundum, and has similar properties; it is very hard, resists high 
 temperatures, and is acid-proof. It is a conductor of electricity, its 
 resistance being about three times that of carbon. It can be heated in 
 the air up to 1600 C. without showing any sign of oxidation. At about 
 3700, however, the silicon leaves the carbon and combines with the 
 oxygen of the air. Silundum can not be melted. The first use to which 
 the material was applied was for electric cooking and heating. For 
 heating purposes the silundum rods can be used single, in lengths up to 
 32 in., depending on the diameter, as solid, round, flat, or square rods or 
 tubes, or in the form of a grid mounted in a frame and provided with 
 contact wires. (EL Review, London. Eng. Digest, Feb., 1909.) 
 
 PRIMARY BATTERIES. 
 
 Following is a partial list of some of the best known primary cells or 
 batteries. 
 
 Name. 
 
 Elem< 
 
 mts. 
 
 + . 
 
 Electrolyte. 
 
 Depolarizer. 
 
 E.M.F. 
 volts. 
 
 Daniell 
 Gravity 
 
 Cu 
 Cu 
 Pt 
 C 
 Cu 
 C 
 Pt 
 Pt 
 C 
 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Cd 
 Zn 
 
 Dilute H 2 SO 4 
 ZnSO 4 
 Dilute H 2 SO 4 
 Dilute H 2 SO 4 
 Cone. NaOH 
 NH 4 C1 
 ZnS0 4 
 CdS0 4 
 Various electro 
 
 Concent. CuSO 4 
 Concent. CaSO 4 
 HN0 3 
 K ? Cr 2 O 7 
 CuO 
 MnO 2 
 Hg 2 S0 4 
 Hg 2 S0 4 
 yte pastes. 
 
 1.07 
 
 i!f 
 
 2.1 
 0.7-0.9 
 1.4 
 1.44 
 1.02 
 1-1.8 
 
 Grove 
 
 Fuller 
 
 Edison- Lalande 
 Leclanche 
 
 Clark 
 
 \Veston 
 
 Dry battery 
 
 The gravity cell is used for telegraph work. It is suitable for closed 
 circuits, and should not be used where it is to stand for a long time on 
 open circuit. 
 
 The Fuller cell is adapted to telephones or any intermittent work. It 
 can stand on open circuit for months without deterioration. 
 
 The Edison-Lalande cell is suitable for either closed or open circuits. 
 
 The Leclanche cell is adapted for open circuit intermittent work, such 
 as bells, telephones, etc. 
 
 The Clark and Weston cells are used for electrical standards. The 
 Weston cell has largely superseded the Clark. 
 
 Dry cells are in common use for house service, igniters for gas engines, 
 etc. 
 
 Batteries are coupled in series of two or more to obtain an e.m.f. 
 .greater than that of one cell, and in multiple to obtain more amperes 
 without change of e.m.f. 
 
 Spark coils, or induction coils, with interrupters, are used to obtain 
 ignition sparks for gas engines, etc. 
 
 ELECTRIC ACCUMULATORS OR STORAGE BATTERIES. 
 
 Secondary or storage batteries may be divided in two general 
 classes: viz., the lead battery and the Edison alkaline battery. They 
 are composed of a number of cells connected in series or multiple. The 
 voltage is independent of the size of the cell and is a function of the 
 electro -chemical properties used for the electrodes and electrolytes, 
 being approximately two volts per cell. The current, however, is ap- 
 proximately proportional to the surface of the electrodes that are sub- 
 merged in the electrolyte. 
 
 Lead Batteries. The lead battery consists of two electrodes, the 
 positive and negative, immersed in the electrolyte. The two electrodes 
 are sponge lead (Pb) for the negative, and peroxide of lead (Pbp2) for 
 the positive, these forming the active couple, the electrolyte being di- 
 lute sulphuric acid. The two sets of electrodes are called an element 
 and they can be readily distinguished by their colors, the positive pe 
 
1426 ELECTRICAL ENGINEERING. 
 
 oxide plate being of a velvety brown chocolate color and the negative 
 lead sponge plate of a light gray. 
 
 Inside of the cell the current starts from the negative electrode to- 
 ward the positive, and the positive electrode, therefore, is that por- 
 tion of the battery from which the electric current passes out into the 
 load circuit, this being termed "discharge," as compared to the storing 
 of energy, which is termed "charge." When the cell gives out current, 
 the elements gradually change in composition, becoming mixtures or 
 compounds of lead and lead sulphate at the negative electrode, and lead 
 peroxide and lead sulphate at the positive electrode, the chemical 
 change caused by the giving out of electrical energy being a gradual 
 formation of lead sulphate. 
 
 Lead batteries are made with two different types of plates, the 
 "formed" or Plante plate, and the "pasted" or Faure plate. In the 
 former, the active material is formed electro-chemically on the surface of 
 the plate body, while in the latter it is first applied mechanically in the 
 form of lead oxide and afterward! subjected to the forming process. As 
 a rule the negative plates are always of the Faure type. Positive Plante 
 plates have a long life, while the life of positive Faure plates is limited 
 to a considerable extent by the number of charges. The latter, how- 
 ever, give a greater capacity for the same weight than the formed plate, 
 and are, therefore, used where light weight is required, such as for elec- 
 tric vehicles. Positive plates have ordinarily a shorter life than 
 negative. 
 
 The capacity of a storage battery is measured in ampere-hours, and 
 varies with the discharge rate. An arbitrary standard of the 8-hour 
 rate is now universally adopted, but if the rate is increased, the capacity 
 is diminished. So, for example, at a one-hour discharge rate only about 
 half the number of ampere-hours can be obtained from a cell that it can 
 supply at the 8-hour rate. An 80-ampere-hour battery thus means one 
 which will discharge 10 amperes continuously for eight hours without 
 falling below the minimum allowable voltage. 
 
 When a battery is being discharged, the voltage sinks gradually and 
 it should never be discharged below some fixed limit, because an ex- 
 cessive quantity cf sulphate will then form, which may injure the plates 
 both electrically and mechanically, tending to crack and loosen the 
 active material. This condition is indicated by the deposit of white 
 sulphate on the surfaces of the plates. The voltage at which a lead 
 battery is assumed to be completely discharged depends on the dis- 
 charge rate and may be computed from the formula 
 
 E = 1.66+ 0.0175* 
 where t = time of discharge in hours. 
 
 Thus for an 8-hour rate the discharge should be stopped when the 
 voltage has dropped to 180, while for an 1-hour rate, it should be 
 stopped when it has dropped to 168. 
 
 The voltage rises gradually during the charging from about 2.15 per 
 cell at the beginning to about 2.55 at the end. The rate of charging is 
 usually specified by the manufacturer. In certain instances it is equal 
 to the 8-hour discharge rate, while in others the instructions may be to 
 start the charge between the 3- and 5-hour rate, reducing the current 
 to the 8-hour rate as soon as the plates gas freely. The time required 
 for a charge will, of course, depend upon the amount of the previous 
 discharge. If this has been two-thirds of the rated capacity of the bat- 
 tery, about three hours at the starting rate and an hour and a half or two 
 hours afc the finishing rate will be necessary; i.e., from 10 to 15 per cent 
 more charge than the amount taken out on the discharge is ordinarily 
 required. 
 
 At regularly weekly or bi-weekly intervals the battery should be 
 given an overcharge f9r the purpose of equalizing all cells, reducing 
 all sulphate, and keeping the plates in good general condition. Such 
 overcharge is a regular charge continued until the voltage does not 
 show any rise for four or five consecutive readings 15 minutes apart, 
 all cells then gasing freely. A charging voltage of 2.7 volts should be 
 provided for such overcharges. 
 
 The specific gravity of the electrolyte, will reach a maximum in 
 
 e same manner as the voltage, and readings of this in the various 
 
 Is of the battery should be taken toward the end of the charge 
 
 \ 
 
ELECTRIC ACCUMULATORS. 1427 
 
 with a hydrometer. These readings will act as a check on those taken 
 on the voltage, and while it may not be found practicable to do this 
 every time the battery is charged, it is very important and should be 
 done at least once a week. If batteries are used intermittently and 
 allowed to stand some time without charge or discharge, the electrolyte 
 should be of low density, not over 1.210. 
 
 Several different methods may be adopted for controlling the dis- 
 charge voltage and maintaining a uniform pressure at the lights, viz.: 
 (1) by connecting in additional or "end" cells one at a time, as the 
 voltage drops, by means of an end cell switch; (2) by a rheostat, whose 
 resistance is cut out step by step; (3) by counter electro-motive force 
 cells, which, like a rheostat, cut down the battery voltage at the be- 
 ginning of discharge, and are cut out of circuit one by one by means 
 of an end cell switch. 
 
 Also, several methods may be employed for obtaining the necessary 
 increase of voltage for charging, viz.; (1) by dividing the battery into 
 two equal parts and charging these in parallel through a suitable re- 
 sistance, the generator running at normal (lamp) voltage; (2) by 
 raising the voltage of the generator sufficiently to charge all the cells in 
 one series; (3) by means of a booster, whose voltage is added to that 
 of the generator, and is varied to give the total required. 
 
 In a lead storage-cell, if the surface and quantity of active material 
 be accurately proportioned, and if the discharge be commenced imme- 
 diately after the termination of the charge, then a current efficiency of 
 as much as 98 % may be obtained, provided the rate of discharge is low 
 and well regulated. Since the current efficiency decreases as the dis- 
 charge rate increases, and since very low discharge rates are seldom used 
 in practice, efficiencies as high as this are never obtained practically, the 
 average being about 90%. 
 
 After a battery has been erected and all connections made and the 
 current ready, the electrolyte may be poured into the jars, and as soon 
 thereafter as possible the initial charging should commence. Never 
 allow a battery to stand longer than two hours after the acid is put in, 
 before starting the charge. This should be as continuous as possible, 
 until all cells gas freely and the specific gravity and voltage show no 
 rise over a period of 10 hours. The duration of such a charge may vary 
 from 30 to 100 hours, and is always given by the manufacturer. The 
 temperature in any one cell should not be permitted to go above 100 F. ; 
 if this occurs, the charging rate must be reduced or the charge tem- 
 porarily stopped. 
 
 The level of the electrolyte should be kept above the top of the plates 
 by adding pure fresh water. Addition of new electrolyte is seldom 
 necessary and should be done only on advice from the manufacturer. 
 
 The sediment which collects in the bottom of the cells should always 
 be removed before it touches the plates. 
 
 The battery room should be well ventilated, especially when charging, 
 and great care taken not to bring an exposed flame near the cells when 
 charging or shortly after. 
 
 Metals or impurities of any kind must not be allowed to get into 
 the cells. If this should happen, the impurity should be removed at once, 
 and if badly contaminated, the electrolyte replaced with new. If in 
 doubt as to the purity of electrolyte or water, the manufacturers should 
 be consulted. 
 
 To take cells out of commission, the electrolyte should be drawn off; 
 the cells filled with water and allowed to stand for 12 or 15 hours. The 
 water can then be drawn off and the plates allowed to dry. When 
 putting into service again, the same procedure should be followed as 
 with the initial charge. 
 
 Lead storage batteries are extensively used for the following appli- 
 cations: 
 
 Stand-by service in central stations. 
 
 Voltage regulation on D. C. distribution lines. 
 
 To carry peak loads of central stations. 
 
 Voltage regulation in isolated building plants. 
 
 To carry load of isolated plant, when the plant is shut down for 
 the night. 
 
 To furnish country places with power where such places are off the 
 line of central stations, 
 
1428 ELECTRICAL ENGINEERING. 
 
 To furnish current for talking circuits in telephone service. 
 
 To furnish current for signal work. 
 
 To light trains in connection with a generator system. 
 
 To operate submarine torpedo boats. 
 
 For ignition, starting and lighting on gas cars. 
 
 To propel electric pleasure and commercial vehicles. 
 
 To regulate long distance transmission lines. 
 
 For a complete treatise on lead storage batteries see Lyndon, " Storage 
 Battery Engineering." 
 
 Edison Alkaline Battery. The Edison storage battery is considerably 
 lighter, although not as efficient as the lead battery, and for that 
 reason it is extensively used for vehicle service. Its weight varies from 
 14 to 18 watt-hours per pound. 
 
 The active materials of this battery are oxides of nickel and iron in 
 the positive and negative grids respectively, the electrolyte being a 
 solution of caustic potash in water with a small amount of lithium 
 hydrate. The first charging of a cell reduces the iron oxide to metallic 
 iron while converting the nickel hydrate to a very high oxide of nickel, 
 black in color. On discharge, the metallic iron goes back to iron 
 oxide and the high nickel oxide goes to a lower oxide, but not to its orig- 
 inal form of green nickel hydrate, and every cycle thereafter during 
 charging the positive changes to a high nickel oxide. Current passing 
 in either direction (charge or discharge) decomposes the potassium 
 hydrate of the electrolyte and the oxidation and the reduction at the 
 electrodes are brought about by the action of its elements. An amount 
 of potassium hydrate equal to that decomposed is always reformed at 
 one of the electrodes by a secondary chemical reaction, and con- 
 sequently there is none of it lost and its density remains constant. The 
 eventual results of charging, therefore, are a transference of oxygen from 
 the iron to the nickel electrode and that of discharging is a transference 
 back again. 
 
 The density of the electrolyte does not change during charge or dis- 
 charge and consequently hydrometer readings are unnecessary. 
 
 To give the best output and efficiency, the manufacturer gives the 
 normal rate of charge as 7 hours and discharge as 5 hours. The rates 
 are, however, optional, and may with certain restrictions be based on 
 the operating conditions. The discharge starts at 1.44 volts per cell, 
 falls rapidly for the first hour, and slowly for 4 l /2 hours. The voltage at 
 the end of 5 hours, the normal discharge period, is 1.11 per cell. 
 
 The charge starts at 1.54 volts per cell, rises rapidly for three- 
 quarters of an hour, and then slowly until it becomes practically con- 
 Btant at the end of 7 hours. The voltage is then 1.81 per cell. 
 
 ELECTROLYSIS. 
 
 Electrolysis is the separation of a chemical compound into its con- 
 stituents by an electric current. Faraday gave the nomenclature of 
 electrolysis. The compound to be decomposed is the electrolyte, and 
 the process electrolysis. The plates or poles of the battery are elec- 
 trodes. The plate where the greatest pressure exists is the anode, and 
 the other pole is the cathode. The products of decomposition are ions. 
 
 Lord Rayleigh found that a current of one ampere will deposit 
 0.017253 grain, or 0.001118 gram of silver per second on one of the 
 plates of a silver voltameter, the liquid employed being a solution of 
 silver nitrate containing from ] 5 % to 20 % of the salt. The weight of 
 hydrogen similarly set free by a current of one ampere is 0.00001038 
 gram per second. 
 
 Knowing the amount of hydrogen thus set free, and the chemical 
 equivalents of the constituents of other substances, we can calculate 
 what weight of their elements will be set free or deposited in a given 
 time by a given current. Thus, the current that liberates 1 gram of 
 hydrogen will liberate 8 grams of oxygen, or 107.7 grams of silver, the 
 numbers 8 and 107.7 being the chemical equivalents for oxygen and 
 silver respectively. 
 
 To find the weight of metal deposited by a given current in a given 
 time, find the weight of hydrogen liberated by the given current in the 
 given time, and multiply by the chemical equivalent of the metal. 
 
ELECTROLYSIS. 
 
 1429 
 
 The table below (from "Practical Electrical Engineering") is calcu- 
 lated upon Lord Rayleigh's determination of the electro-chemical 
 equivalents and Roscoe's atomic weights. 
 
 ELECTRO-CHEMICAL EQUIVALENTS. 
 
 Clements. 
 
 Valency.* 
 
 Atomic Weight.f 
 
 Chemical Equiv- 
 alent. 
 
 Electro-chemical 
 Equivalent (mil- 
 ligrams per 
 coulomb). 
 
 Coulombs per 
 gram. 
 
 Grams per 
 ampere hour. 
 
 ELECTRO-POSITIVE. 
 
 Hi 
 
 1 00 
 
 1 00 
 
 010384 
 
 96293.00 
 
 0.03738 
 
 Potassium 
 
 K{ 
 
 39 04 
 
 39 04 
 
 40539 
 
 2467 50 
 
 1.45950 
 
 
 Nai 
 
 22 99 
 
 22 99 
 
 23873 
 
 4188.90 
 
 0.85942 
 
 Aluminum 
 
 A1 3 
 
 27 1 
 
 9 1 
 
 09449 
 
 1058 30 
 
 0.34018 
 
 
 Mo- 2 
 
 23 94 
 
 11 97 
 
 12430 
 
 804.03 
 
 0.44747 
 
 Gold 
 
 
 196 2 
 
 65 4 
 
 67911 
 
 1473 50 
 
 2.44480 
 
 Silver 
 
 A 0-1 
 
 107 66 
 
 107 66 
 
 1 11800 
 
 894 41 
 
 4.02500 
 
 Copper (cupric) 
 (cuprous) . . . 
 
 Cu 2 
 Cut 
 
 63.00 
 63 00 
 
 31.5 
 63 00 
 
 0.32709 
 65419 
 
 3058.60 
 1525 30 
 
 1.17700 
 2.35500 
 
 Mercury (mercuric) .... 
 (mercurous). . 
 Tin (stannic) 
 
 Hg 2 
 H gl 
 
 Sn4 
 
 199.8 
 199.8 
 117 8 
 
 99.9 
 199.8 
 29 45 
 
 1 .03740 
 2.07470 
 30581 
 
 963.99 
 481.99 
 3270 00 
 
 3.73450 
 7.46900 
 1 10090 
 
 ' (stannous) 
 
 Sn 2 
 
 117 8 
 
 58 9 
 
 61162 
 
 1635.00 
 
 2.20180 
 
 
 Fe 4 
 
 55 9 
 
 18 641 
 
 19356 
 
 5166.4 
 
 0.69681 
 
 " (ferrous) . . 
 
 Fe 2 
 
 55 9 
 
 27 95 
 
 29035 
 
 3445.50 
 
 1 .04480 
 
 Nickel .. 
 
 Ni 2 
 
 58 6 
 
 29 3 
 
 30425 
 
 3286 80 
 
 1 .09530 
 
 Zinc 
 
 Zn<> 
 
 64*9 
 
 32 45 
 
 33696 
 
 2967.10 
 
 1.21330 
 
 Lead 
 
 Pb2 
 
 206.4 
 
 103.2 
 
 1.07160 
 
 933.26 
 
 3.85780 
 
 ELECTRO-NEGATIVE. 
 Oxygen 
 
 On 
 
 15 96 
 
 7 98 
 
 08286 
 
 
 
 Chlorine 
 
 cii 
 
 35 37 
 
 35 37 
 
 36728 
 
 
 
 Iodine 
 
 I, 
 
 126 53 
 
 126 53 
 
 1 31300 
 
 
 
 Bromine 
 
 Br, 
 
 79 75 
 
 79 7*> 
 
 82812 
 
 
 
 Nitrogen 
 
 N 3 J 
 
 14]01 
 
 4.67 
 
 0.04849 
 
 
 
 * Valency is the atom-fixing or atom-replacing power of an element com- 
 pared with hydrogen, whose valency is unity. 
 
 fAtomic weight is the weight of one atom of each element compared 
 with hydrogen, whose atomic weight is unity. 
 
 tBecquerel's extension of Faraday's law showed that the electro-chemical 
 equivalent of an element is proportional to its chemical equivalent. The 
 latter is equal to its combining weight, and not to atomic weight *- valency, 
 as denned by Thompson, Hospitalier, and others who have copied their 
 tables. For example, the ferric salt is an exception to Thompson's rule, 
 as are sesqui-salts in general. 
 
 Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes 
 = weight of hvdrogen liberated per second X number of seconds X current 
 strength X 107.7 = 0.00001038X10X10X107.7 = 0.1 1178 gram. 
 
 Weight of copper deposited in 1 hour by a current of 10 amperes = 
 
 0.00001038 X 3600 X10X 31.5 = 11.77 grams. 
 
 Since 1 ampere per second liberates 0.00001038 gram of hydrogen, 
 strength of current in amperes 
 
 = weight In grams of H liberated per second * 0.00001038 
 
 weight of element liberated per second 
 ~~ 0.00001038 Xchemical equivalent of element 
 
1430 ELECTRICAL ENGINEERING. 
 
 THE MAGNETIC CIRCUIT. 
 
 For units of the magnetic circuit, see page 1398. 
 
 Lines and Loops of Force. It is conventionally assumed that the 
 attractions and repulsions shown by the action of a magnet or a con- 
 ductor upon iron filings are due to " lines of force " surrounding the 
 magnet or conductor. The " number of lines " indicates the magnitude 
 of the forces acting. As the iron filings arrange themselves in concentric. 
 circles, we may assume that the forces may be represented by closed 
 curves or *' loops of force." The following assumptions are made con- 
 cerning the loops of force in a conductive circuit: 
 
 1. That the lines or loops of force in the conductor are parallel to the 
 axis of the conductor. 
 
 2. That the loops of force external to the conductor are proportonal in 
 number to the current in the conductor, that is, a definite current gener- 
 ates a definite number of loops of force. These may be stated as the 
 strength of field in proportion to the current. 
 
 3. That the radii of the loops of force are at right angles to the axis oi 
 the conductor. 
 
 The magnetic force proceeding from a point is equal at all points on the 
 surface of an imaginary sphere described by a given radius about that 
 point. A sphere of radius 1 cm. has a surface of 4 it square centimeters 
 If <= total flux, expressed as the number of lines of force emanating from 
 a magnetic pole having a strength M, 
 
 . 
 
 Magnetic moment of a magnet = product of strength of pole M and its 
 length, or distance between its poles L. Magnetic moment =<L-*- 4?r. 
 
 If B = number of lines flowing through each square centimeter of cross- 
 section of a bar-magnet, or the " specific induction," and A = cross-section 
 Magnetic Moment = LAB-^47t. 
 
 If the bar-magnet be suspended in a magnetic field of density H and so 
 placed that the lines of the field are all horizontal and at right angles to the 
 axis of the bar, the north pole will be pulled forward, that is, in the direc- 
 tion in which the lines flow, and the south pole will be pulled in the 
 opposite direction,- the two forces producing a torsional moment or torque, 
 Torque = JfLH =Z/ABH -5- 4rc, in dyne-centimeters. 
 
 Magnetic attraction or repulsion emanating from a point varies inversely 
 as the square of the distance from that point. The law of inverse squares, 
 however, is not true when the magnetism proceeds from a surface of appre- 
 ciable extent, and the distances are small, as in dynamo-electric machines 
 and ordinary electromagnets. 
 
 The Magnetic Circuit. In the electric circuit 
 
 Current = P K]V ;- F - . or 7-f ; Amperes = ^ 
 Resistance ' R ' ohms 
 
 Similarly, in the magnetic circuit 
 
 Magnetomotive Force F Gilberts 
 
 Flux= - Reluctance -- OT *~ R ' Maxwells- ^^^- 
 Reluctance is the reciprocal of permeance, and permeance is equal to 
 permeability X path area -5- path length (metric measure); hence 
 
 <b= Ffj.a-r- I. 
 
 One ampere-turn produces 1.257 gilberts of magnetomotive force and 
 one inch equals 2.54 centimeters; hence, in inch measure, 
 
 <= (1.257^) / 6.45 a -f- 2.541= 3.192tiaA t + I. 
 
 The ampere-turns required to produce a given magnetic flux in a given 
 path will be 
 
 A t =* #-5- 3.192 /to = 0.3133 #-5-/ta. 
 
 Since magnetic flux-?- area of path = magnetic density, the ampere-turn 
 required to produce a density B, in lines of force per square inch of area 
 of path, will be 
 
 A t = 0.3133 Bl -i- v. 
 
 This formular is used in practical work, as the magnetic density must 
 be predetermined in order to ascertain the permeability of the material 
 under its working conditions. When a magnetic circuit includes several 
 qualities of material, such as wrought iron, cast iron, and air, it is most 
 direct to work in terms of ampere-turns per unit length of path. The 
 
THE MAGNETIC CIRCUIT. 
 
 1431 
 
 ampere-turns for each material are determined separately, and the wind- 
 ing is designed to produce the sum of all the ampere-turns. The following 
 table gives the average results from a number of tests made by Dr. Samuel 
 Sheldon: 
 
 VALUES OP B AND H 
 
 
 05 Q 
 
 e 
 
 Cast Iron. 
 
 Cast Steel. 
 
 Wrought Iron. 
 
 Sheet Metal. 
 
 H 
 
 ! Ai 
 
 l-Sj 
 
 
 
 S&. 
 
 03 
 
 0) 
 
 g.l c . 
 
 i 
 
 x o, . 
 
 | 
 
 IN 
 
 1 0> 
 
 x a . 
 
 
 
 ||| 
 
 00 6 1 
 
 jtJ 
 
 m ll 
 
 
 it 
 
 
 "4* 
 
 & a; g 
 
 10 
 20 
 
 7.95 
 15.90 
 
 20.2 
 40.4 
 
 4.3 
 
 5.7 
 
 27.7 
 36.8 
 
 11.5 
 13.8 
 
 74.2 
 89.0 
 
 13.0 
 14.7 
 
 83.8 
 94.8 
 
 14.3 
 15.6 
 
 92.2 
 100.7 
 
 30 
 
 23.85 
 
 60.6 
 
 6.5 
 
 41.9 
 
 14.9 
 
 96.1 
 
 15.3 
 
 98.6 
 
 16.2 
 
 104.5 
 
 40 
 
 31.80 
 
 80.8 
 
 7.1 
 
 45.8 
 
 15.5 
 
 100.0 
 
 15.7 
 
 101.2 
 
 16.6 
 
 107.1 
 
 50 
 
 39.75 
 
 101.0 
 
 7.6 
 
 49.0 
 
 16.0 
 
 103.2 
 
 16.0 
 
 103.2 
 
 16.9 
 
 109.0 
 
 60 
 
 47.70 
 
 121.2 
 
 8.0 
 
 51.6 
 
 16.5 
 
 106.5 
 
 16.3 
 
 105.2 
 
 17.3 
 
 111.6 
 
 70 
 
 55,65 
 
 141.4 
 
 8.4 
 
 59.2 
 
 16.9 
 
 109.0 
 
 16.5 
 
 106.5 
 
 17.5 
 
 112.9 
 
 80 
 
 63.65 
 
 161.6 
 
 8.7 
 
 56.1 
 
 17.2 
 
 111.0 
 
 16.7 
 
 107.8 
 
 17.7 
 
 114.1 
 
 90 
 
 71.60 
 
 181.8 
 
 9.0 
 
 58.0 
 
 17.4 
 
 112.2 
 
 16.9 
 
 109.0 
 
 18.0 
 
 116.1 
 
 100 
 
 79.50 
 
 202.0 
 
 9.4 
 
 60.6 
 
 17.7 
 
 114.1 
 
 17.2 
 
 110.9 
 
 18.2 
 
 117.3 
 
 150 
 
 119.25 
 
 303.0 
 
 10.6 
 
 68.3 
 
 18.5 
 
 119.2 
 
 18.0 
 
 116.1 
 
 19.0 
 
 122.7 
 
 200 
 
 159.0 
 
 404.0 
 
 11.7 
 
 75.5 
 
 19.2 
 
 123.9 
 
 18.7 
 
 120.8 
 
 1.96 
 
 126.5 
 
 250 
 
 198.8 
 
 505.0 
 
 12.4 
 
 80.0 
 
 19.7 
 
 127.1 
 
 19.2 
 
 123.9 
 
 20.2 
 
 130.2 
 
 300 
 
 238.5 
 
 606.0 
 
 13.2 
 
 85.1 
 
 20.1 
 
 129.6 
 
 19.7 
 
 127.1 
 
 20.7 
 
 133.5 
 
 H = 1.257 ampere-turns per cm. = 0.495 ampere-turns per inch. 
 
 EXAMPLE. A magnetic circuit consists of 12 ins. of cast steel of 8sq. 
 ins. cross-section; 4 ins. of cast iron of 22 sq. ins. cross-section; 3 ins. of 
 sheet iron of 8 sq. ins. cross-section; and two air-g?pseach Vie in. long and 
 of 12 sq. ins. area. Required, the ampere-turns to produce a flux of 
 768,000 maxwells, which is to be uniform throughout the magnetic circuit. - 
 
 The flux density in the steel is 768,000-^8 = 96,000 maxwells; the am- 
 pere-turns per inch of length, according to Sheldon's table, are 60.6, so 
 that the 12 in. of steel will require 727.2 ampere-turns. 
 
 The density in the cast iron is 768,000-^-22 = 34,900; the ampere-turn, 
 = 4X 40=160. 
 
 The density in the sheet iron = 768,000 *- 8 = 96,000; ampere-turns per 
 inch = 30; total ampere-turns for sheet iron = 90. 
 
 The air-gap density is 768,000 -* 12 = 64,000; ampere-turns per in. = 
 0.3133B; ampere-turns required for air-gap = 0.3133 X 64,000-^-8=2506.4. 
 
 The entire circuit will require 727.2+ 160+ 90 + 2506.4 = 3483.6 am- 
 pere-turns, assuming uniform flux throughout. 
 
 In practice there is considerable "leakage" of magnetic lines of force; 
 that is, many of the lines stray away from the useful path, there being no 
 material opaque to magnetism and therefore no means of restricting it to 
 a given path. The amount of leakage is proportional to the permeance 
 of the leakage paths available between two points in a magnetic circuit 
 which are at different magnetic potentials, such as opposite ends of a 
 magnet coil. It is seldom practicable to predetermine with any approach 
 to accuracy the magnetic leakage that will occur under given conditions 
 unless one has profuse data obtained experimentally under similar con- 
 ditions. In dynamo-electric machines the leakage coefficient varies from 
 1 .3 to 2. 
 
 Tractive or Lifting Force of a Magnet. The lifting power or 
 " pull " exerted by an electro-magnet upon an armature in actual contact 
 with its pole-faces is given by the formula 
 
 Lbs.= B2<z-r- 72, 134,000, 
 
 a being the area of contact in square inches and B the magnetic density 
 over this area. If the armature is very close to the pole-faces this for- 
 mula also applies with sufficient accuracy for all practical puposes, but 
 a considerable air-gap renders it inapplicable. 
 
 The design of solenoids for the coif-and-plunger type of electro-magnets 
 
1432 
 
 ELECTRICAL ENGINEERING. 
 
 is described by C. R. Underbill in his book, " Solenoids, Electro-Magnets; 
 and Electro-Magnetic Windings." 
 
 Various forms of magnetic chucks are illustrated and described by 
 O. S. Walker, hi Am. Mach., Feb. 11, 1909. 
 
 For magnets used in hoisting, see page 1193. 
 
 Determining the Polarity of Electro - Magnets. If a wire ifi 
 wound around a magnet in a right-handed helix, the end at which the 
 current flows into the helix is the south pole. If a wire is wound around 
 an ordinary wood-screw, and the current flows around the helix in the 
 direction from the head of the screw to the point, the head of the screw 
 is the south pole. If a magnet is held so that the south pole is opposite 
 the eye of the observer, the wire being wound a a right-handed helix 
 around it, the current flows in a right-handed direction, with the hands 
 of a clock. 
 
 Determining the Direction of a Current. Place a wire carrying 
 a current above and parallel to a pivoted magnetic needle. If the cur- 
 rent be flowing along the wire from N. to S., it will cause the N.-seeking 
 pole to turn to the eastward; if it be flowing from S. to N., the pole will 
 turn to the westward. If the wire be below the needle, these motions 
 will be reversed. 
 
 Maxwell's rule. The direction of the current and that of the resisting 
 magnetic force are related to each other as are the rotation and the for- 
 ward travel of an ordinary (right-handed) corkscrew. 
 
 DYNAMO-ELECTRIC MACHINES. 
 
 A dynamo-electric machine is a machine for converting mechanical 
 energy into electrical energy, or vice versa. It may be either a direct 
 current or an alternating current machine. 
 
 Rating. The A. I.E. E. Standardization Rules (1914) recommend 
 that in the case of Direct Current Generators, the rating shall be ex- 
 pressed in Kilowatts (Kw.) available at the terminals. 
 
 In the case of Alternators and Transformers, the rating shall be 
 expressed in kilovolt-amperes (Kv.-a.) available at the terminals, at a 
 specified power factor. The corresponding kilowatts should also 
 preferably be stated. 
 
 In the case of Motors, it is recommended that the rating shall be 
 expressed in kilowatts (Kw.) available at the shaft. Since the input of 
 machinery of this class is measured in electrical units and since the out- 
 put has a definite relation to the input, it is logical to measure the 
 delivered power in the same units as are employed for the receiving 
 power. However, on account of the prevailing practice of expressing 
 mechanical output in horse-power, it is recommended that for machin- 
 ery of this class the rating should, for the present, be expressed both in 
 kilowatts and in horse-power; as follows: 
 
 approx. equiv. h.p.- 
 
 The horse-power rating of a motor may, for practical purposes, be 
 taken as 4/3 of the kilowatt rating. 
 
 There are various kinds of ratings, such as: 
 
 Continuous Rating. A machine rated for continuous service shall be 
 able to operate continuously at its rated output, without exceeding any 
 of the limitations specified. 
 
 Short-Time Rating. A machine rated for short-time service (i.e., 
 service including runs alternating with stoppages of sufficient duration 
 to ensure substantial cooling) shall be able to operate at its rated out- 
 put during a limited period, to be specified in each case, without exceed- 
 ing any of the limitations specified. 
 
 Nominal Ratings. For railway motors and railway sub-station 
 machinery, certain nominal ratings are employed. 
 
 Duty-Cycle Operation. Many machines are operated on a cycle of 
 duty which repeats itself with more or less regularity. For purposes of 
 rating, either a continuous or a "short-time" " equivalent load " may be 
 selected which shall simulate as nearly as possible the thermal condi- 
 tions of the actual duty cycle. 
 
 Standard durations of equivalent tests shall be for machines oper- 
 ating under specified duty-cycles: 5 min., 10 min., 30 min., 60 min.. 
 
DYNAMO-ELECTRIC MACHINES. 1433 
 
 120 min., and continuous. Of these the first 5 are short-time ratings 
 selected as being thermally equivalent to the specified duty cycle. 
 When, for example, a short-time rating of 10 minutes' duration is 
 adopted, and the thermally equivalent load is 25 kw. for that period, 
 then such a machine shall be stated to have a 10-minute rating of 
 25 kw. In every case the equivalent short-time test shall commence 
 only when the windings and other parts of the machine are within 5 C. 
 of the ambient temperature at the time of starting the test. In the 
 absence of any specification as to the kind of rating, the continu- 
 ous rating shall be understood. 
 
 Temperature Limitations of the Capacity of Electrical Machinery. 
 The capacity, so far as relates to temperature, is usually hmi ted by the 
 maximum temperature at which the materials in the machine, espe- 
 cially those employed for insulation, may be operated for long periods 
 without deterioration. When the safe limits are exceeded, deterioration 
 is rapid. The insulating material becomes permanently damaged by 
 excessive temperature, the damage increasing with the length of time 
 that the excessive temperature is maintained, and with the amount of 
 excess temperature, until finally the insulation breaks down. 
 
 Ambient Temperature of Reference for Air. The standard ambient 
 temperature of reference, when the cooling medium is air, shall be 40 C. 
 (104 P.). 
 
 The permissible rises in temperature given in column 2 of the table 
 on p. 1434 have been calculated on the basis of the standard ambient 
 temperature of reference, by substracting 40 C. from the highest tem- 
 peratures permissible, which are given in column 1 of the same table. 
 
 Altitude. Increased altitude has the effect of increasing the temper- 
 ature rise of some types of machinery. In the absence of information in 
 regard to the height above sea level at winch the machine is intended to 
 work in ordinary service, this height is assumed not to exceed 1000 
 meters (3300 feet). For machinery operating at an altitude of 1000 
 meters or less, a test at any altitude less than 1000 meters is satisfactory, 
 and no correction shall be apDlied to the observed temperatures. 
 Machines intended for operation at higher altitudes shall be regarded as 
 special. When a machine is intended for service at altitudes above 
 1000 meters (3300 feet) the permissible temperature rise at sea level, 
 until more nearly accurate information is available, shall be reduced by 
 1 per cent for each 100 meters (130 ft.) by which the altitude exceeds 
 1000 meters. Water-cooled oil transformers are exempt from this 
 reduction. 
 
 Ambient Temperature of Reference for Water-Cooled Machinery. For 
 water-cooled machinery, the standard temperature of reference for in- 
 coming cooling water shall be 25 C. (77 F.), measured at the intake of 
 the machine. 
 
 Corrections for the Deviation of the Ambient Temperature, at the time 
 of test, from the reference value of 40 C. The effect on the temperature 
 rise of the precise value of the ambient temperature at the time of test 
 is small, obscure, and of doubtful direction. No correction shall be 
 made for ambient temperature deviations from the standard value of 
 40 C. It is desirable, however, that tests should be conducted at 
 ambient temperatures not lower than 25 C. Exception to this rule is 
 made in the case of air-blast transformers, in which, if the ingoing air 
 temperature during the test differs from 40 C., a correction on account 
 of difference in resistance and difference in convection shall be made by 
 changing the "observable" temperature rise of the windings by 0.5 per 
 cent for each degree centigrade. Thus with a room temperature of 
 30 C. the "observable" rise of temperature shall be increased by 5 
 per cent, and with a room temperature of 15 C. the "observable" rise 
 of temperature shall be increased by 12.5 per cent. 
 
 The actual temperatures attained in the different parts of a machine, 
 and not the rises in temperature, affect the life of the insulation of the 
 machine. The temperatures in the different parts of a machine which it 
 is desired to ascertain, are the maximum temperatures reached in those 
 parts. 
 
 As it is usually impossible to. determine the maximum temperature 
 attained in insulated windings, it is convenient to apply a correction to 
 the observable temperature, to approximate the difference between 
 the actual maximum temperature and the observable temperature by 
 
1434 ELECTRICAL ENGINEERING. 
 
 the method used. This correction or margin of security is provided to 
 cover the errors due to fallibility in the location of the measuring 
 devices, as well as inherent inaccuracies in measurement and methods. 
 
 Methods of Determining the Temperature of Different Parts of a 
 Machine. Three methods will be considered. One or other of these 
 methods will usually be appropriate for commercial measurements on 
 any particular type of machine. 
 
 No. 1. Thermometer Method. This method consists in the deter- 
 mination of the temperature by mercury or alcohol thermometers, by 
 resistance thermometers, or by thermo-couples, applied to the hottest 
 accessible part of the completed machine, as distinguished from the 
 thermo-couples or resistance coils imbedded in the machine as described 
 under Method No. 3. When Method No. 1 is used, the hottest-spot 
 temperature for windings shall be estimated by adding a hottest-spot 
 correction of 15 C. to the highest temperature observed, in order to 
 allow for the impossibility of locating any of the thermometers at the 
 hottest spot. 
 
 Exception. In cases where the thermometer is applied directly to 
 the surfaces of a bare winding, such as an edgewise strip conductor, or a 
 cast copper winding, a hottest-spot correction of 5 C. instead of 15 C. 
 shall be made. For bare metallic surfaces not forming part of a winding, 
 no correction is to be applied. 
 
 No. 2. Resistance Method. This method consists in the measurement 
 of the temperature of windings by their increase in resistance, corrected 
 to the instant of shut-down when necessary. In the application of 
 this method thermometer measurements must also be made whenever 
 practicable without disassembling the machine, in order to increase 
 the probability of revealing the highest observable temperature. 
 Whichever method yields the higher temperature, that temperature 
 shall be taken as the "highest observable" temperature and a hottest- 
 spot correction of 10 C. added thereto. 
 
 In the case of resistance measurements, the temperature coefficient 
 of copper shall be deduced from the formula I/ (234. 5 -f t). Thus, at 
 an initial temperature t = 40 C., the temperature coefficient or in- 
 crease in resistance per degree centigrade rise is I/ (274. 5) = 0.00364. 
 
 No, 3. Imbedded Temperature-Detector Method. Thermo-couples or 
 resistance coils, located as nearly as possible at the estimated hottest 
 spot. This method is only to be used with coils placed in slots. 
 
 Temperature Limits. In the following table column 1 gives the per- 
 missible limits for the hottest-spot temperatures of insulations, and 
 column 2 the highest permissible temperature rise of the hottest spot 
 above 40 0. permitted under rated-load conditions, for the purpose of 
 fixing the Institute rating. The rise of temperature observed must never 
 exceed the limits in column 2 of the table. The highest temperatures 
 attained in any machine corresponding to the output for which it is 
 rated must not exceed the values indicated in column 1 of the table 
 and the clauses following: 
 
 Hottest-Spot Temperatures and Corresponding Permissible Tem- 
 perature Rises. 
 
 Class. 
 
 Insulation. 
 
 Col. 1. 
 
 Col. 2. 
 
 A 1 
 A2 
 B 
 
 C 
 
 Cotton, silk, paper, and other fibrous materials, not so 
 treated as to increase the thermal limit 
 
 95 C. 
 105 C. 
 
 125 C. 
 Nolim 
 fie 
 
 55 C. 
 65 C. 
 
 85 C. 
 t speci- 
 d. 
 
 Similar to A 1, but treated or impregnated and in- 
 cluding enameled wire . 
 
 Mica, asbestos, or other material capable r y f resisting 
 high temperatures, in which any Class A material 
 or binder, if used, is for structural purposes only, 
 and may be destroyed without impairing the insu- 
 lating or mechanical qualities 
 
 Fireproof and refractory materials 
 
 
DYNAMO-ELECTRIC MACHINES. 
 
 1435 
 
 Summary of (he Temperature Conditions under the Three Methods 
 of Measurement for Insulations of Classes A 19 A 2 , and B. 
 
 & 
 
 5 
 
 AI 
 
 Hottest 
 Spot 
 Temp. 
 
 Thermometer 
 only. 
 
 Resistance.* 
 
 Imbedded Thermo-couples or Resistance Coils. 
 
 Double-layer 
 Windings. 
 All voltages. 
 
 Single-layer 
 Windings. 
 5000 volts or 
 less. 
 
 Single-layer Windings above 5000 
 volts. 
 
 a b 
 
 a 6 
 
 a b 
 
 a b 
 
 Hottest 
 Spot 
 Correction. 
 
 Limiting 
 Observable 
 Temperat'r 
 
 Limiting 
 Observable 
 Temp. Rise 
 above 40. 
 
 95 
 
 15 80 
 
 10 85 
 
 5 90 
 
 10 85 
 
 10+(E-5)f 
 
 85 - (E-5) 
 
 45 - (E-5) 
 
 A 2 
 
 105 
 
 15 90 
 
 10 95 
 
 5 100 
 
 10 95 
 
 10-KE-5) 
 
 95 - (E-5) 
 
 55 - (E-5) 
 
 B 
 
 125 
 
 15 110 
 
 10 115 
 
 5 120 
 
 10 115 
 
 10+(E-5) 
 
 115- (E-5) 
 
 75 - (E-5) 
 
 * With thermometer check when practicable. 
 
 a Hottest-spot correction. b Limiting observable temperature. 
 The limit of the observable temperature rise above 40 always = (b 40). 
 
 t In this formula E represents the rated pressure between terminals 
 in kilo volts. Thus for a three-phase machine with single-layer winding 
 of 11 kilo volts between terminals, the hottest spot correction to be added 
 to the maximum observable temperature will be 16 C. 
 
 Special Cases of Temperature Limits. Tem.perature of Oil. 
 The oil in which apparatus is immersed shall in no part have an observ- 
 able temperature in excess of 90 C. 
 
 Water-cooled Transformers. The hottest-spot temperature shall not 
 exceed 85 C. 
 
 Commutators. The observable temperature shall in no case be per- 
 mitted to exceed the values given in the table for the insulation em- 
 ployed, either in the commutator or in any insulation whose temper- 
 ature would be affected by the heat of the commutator. 
 
 For commutators so constructed that no difficulties from expansion 
 can occur, the following temperature limits are suggested: 
 
 Current per Brush Arm. Maximum Permissible Temp. 
 
 200 amperes or less. 130 C. 
 
 200 to 900 amperes. 130 C. less 5 deg. for each 100 
 
 amperes increase above 200. 
 900 amperes and over. 95 C. 
 
 Moving Force of a Dynamo-electric Machine. A wire through 
 which a current passes has, when placed in a magnetic field, a tendency 
 to move perpendicular t9 itself and at right angles to the lines of the 
 field. The force producing this tendency is P = IBI dynes, in which 
 1= length of the wire, / = the current in C.G.S. units, and = the induc- 
 tion, or flux density, in the field in gausses or lines per square centimeter. 
 
 If the current / is taken in amperes, P = lBI-irlQ = lBfX 10~*. 
 
 If Pfr is taken in kilograms, 
 
 P k = ZB/ -5-9,810,000 = 10.1937 IBI X 1CT 8 kilograms. 
 
 EXAMPLE. The mean strength of field, B, of a dynamo is 5000 C.G.S. 
 lines- a current of 100 amperes flows through a wire; the force acts upon 
 lOcentimetersof the wire = 10.1937 X 10 X 100 X5000 X 10~ 8 = 0.5097 kilo- 
 grams. 
 
 Torque of an Armature. The torque of an armature is the moment 
 tending to turn it. In a generator it is the moment which must be 
 applied to the armature to turn it in order to produce current. In a motor 
 it is the turning moment; which the armature gives to the pulley. 
 
1436 ELECTRICAL ENGINEERING. 
 
 Let / == current in the armature in amperes, E the electromotive fores 
 in volts, T = the torque in pound-feet, <= the flux through the armature 
 in maxwells, N = the number of conductors around the armature, and n = 
 the number of revolutions per second. Then 
 
 Watts IE = 2nnTX 1.356.* 
 
 In any machine if the flux be constant, E is directly proportional to the 
 speed and = <j>Nn * 10 8 ; whence 
 
 ^/-MO 8 = 
 AN1 
 = = 
 
 10 8 X2*X1.356 8.52 X 10* 
 
 Let I length of armature in inches, d = diameter of armature in inches, 
 B = flux density in maxwells per square inch, and let m = the ratio of the 
 conductors under the influence of the pole-pieces to the whole number of 
 conductors on the armature. Then 
 
 < = iwe/X IX BXm. 
 
 These formulae apply to both generators and motors. They show that 
 torque is independent of the speed and varies directly with the current and 
 the flux. The total peripheral force is obtained by dividing the torque by 
 the radius (in feet) of the armature, and the drag on each conductor is 
 obtained by dividing the total peripheral force by the number of conductors 
 under the influence of the pole-pieces at one time. 
 
 EXAMPLE. Given an armature of length I = 20 inches, diameter d = 12 
 inches, number of conductors N = 120, of which 80 are under the influence 
 of the pole-pieces at one time; let the flux density B = 30,000 maxwells 
 per sq. in. and the current / = 400 amperes. 
 
 = i| X 20 X 30,000 X ~~ = 7,540,000. 
 
 7,540,000 X 120 X 400 
 T = 8.52X100,000,000 = 42 
 Total peripheral force = 424.8 -J- 0.5 = 849.6 Ibs. 
 Drag per conductor = 849.6 *- 120 = 7.08 Ibs. 
 
 The work done in one revolution = torque X circumference of a circle 
 of 1 foot radius = 424.8 X 6.28 = 2670 foot-pounds. 
 
 Let the revolutions per minute equal 500, then the horse-power 
 _2670X500 
 
 33000 
 
 Torque, Horse-pow0* and Revolutions. T torque in pound-feet, 
 H.P. = T X Rpm. >fe72832 t 33,000 = IE -=- 745.7. Whence Torque 
 = 7. 0432 El -r- Rpm.xmJ?. times the watts 4- the revs, per min. nearly. 
 
 Electromotive Force of the Armature Circuit. From the horse- 
 power, calculated as above, together with the amperes, we can obtain 
 theE.M.F., IE= H.P. X 745.7, whence E M F.or= H.P. X 745. 7^- 7. 
 
 If H.P., as above, = 40.5, and 1= 400, E = 40 ' 5 ^ 45 ' 7 = 75.5 volts. 
 
 The E.M.F. may also be calculated by the following formulae: 
 /= Total current through armature; 
 e a = E.M.F. in armature in volts; 
 
 Af= Number of active conductors counted all around armature; 
 p = Number of pairs of poles (p = 1 in a two-pole machine); 
 n= Speed in revolutions per minute; 
 tf= Total flux in maxwells. 
 
 \ e f ,=4>N ~ 10~ 8 for two-pole machines. 
 Electromotive 1 
 
 force: | _ p$N n^ for multipolar machines with series- 
 
 [ e a~ 10 8 60 wound armature 
 
 Strength of the Magnetic Field. Let / = current in amperes. N =* 
 number of turns in the coil. A area of the cross-section of the core in 
 
 * 1 ft.-lb. per second = 1.356 watts. 
 
DIRECT-CURRENT GENERATORS. 1437 
 
 square centimeters, 1= length of core In centimeters, p the permeability of 
 the core, and #= flux in maxwells. Then 
 
 Magnetomotive Force ^ 1.257 N 1 t 
 * )a * Reluctance * ' 
 
 In a dynamo-electric machine the reluctance will be made up of three 
 separate quantities, viz.: that of the field magnet cores, that of the air 
 spaces between the field magnet pole-pieces and the armature, and that 
 of the armature. The total reluctance is the sum of the three. Let Li, 
 L 2 , L 2 be the length of the path of magnetic lines in the field magnet 
 cores,* in the air-gaps, and in the armature respectively; and let AI, 
 A 2 , Az be the areas of the cross-sections perpendicular to the path of the 
 magnetic lines in the field magnet cores, the air-gaps, and the armature 
 respectively. Let the permeability of the field magnet cores be /n, and of 
 the armature jus. The permeability of the air-gaps is taken as unity. Then 
 the total reluctance of the machine will be 
 
 .Li t L 2 + Lz 9 
 AIHI AZ ASUS 
 
 1.257 NT 
 UX '^~ 
 
 The ampere-turns necessary to create a given flux in a machine may be 
 found by the formula, 
 
 [(Li -? A t f*i) + (L 2 -^ 2 ) + (3 -s- Aw*)] 
 1.257 
 
 But the total flux generated by the field coils is not available to produce 
 current in the armature. There is a leakage between the field magnets, 
 and this must be allowed for in calculations. The leakage coefficient 
 varies from 1.3 to 2 in different machines. The meaning of the coefficient 
 is that if a flux of say 100 maxwells per square cm. are desired in the field 
 coils, it will be necessary to provide ampere turns for 1.3 X 100 = 130 
 maxwells, if the leakage coefficient be 1.3. 
 
 Another method of calculating the ampere-turns necessary to produce a 
 given flux is to calculate the magnetomotive force required in each portion 
 of the machine, separately, introducing the leakage coefficient in the calcu- 
 lation for the field magnets, and dividing the sum of the magnetomotive 
 forces by 1.257. 
 
 In the ordinary type of multipolar machine there are as many magnetic 
 circuits as there are poles. Each winding energizes part of two circuits. 
 The calculation is made in the same manner as for a single magnetic circuit. 
 
 DIRECT-CURRENT GENERATORS. 
 
 Direct-current generators may be separately excited, in which case 
 the field magnets are excited or magnetized from some external source, 
 as, for instance, a storage battery or another continuous-current dynamo. 
 Such generators are used to some extent in connection with regulating 
 sets, but as a rule almost all direct-current generators are self-excited, 
 in which case the magnetizing current for the field-coils is furnished by 
 the dynamo Itself. 
 
 Direct-current generators (as well as motors) may be classified accord- 
 ing to the manner of the field- winding into : 
 
 1. Series-wound Dynamo. The field- winding and the external circuit 
 are connected in series with the armature- winding, so that the entire 
 armature current must pass through the field-coils. 
 
 Since in a series-wound dynamo the armature-coils, the field, and the 
 external circuit are in series, any increase in the resistance of the exter- 
 nal circuit will decrease the electro-motive force from the decrease in the 
 magnetizing currents. A decrease in the resistance of the external cir- 
 
 * The length of the path in the field-magnet cores LI includes that 
 portion of the path which lies in the piece joining the cores of the 
 various field-magnets. 
 
1438 ELECTRICAL ENGINEERING. 
 
 cuit will, in a like manner, increase the electro-motive force from the 
 increase in the magnetizing current. The use of a regulator avoids 
 these changes in the electro-motive force. 
 
 2. Shunt-wound Dynamo. The field-magnet coils are placed in a 
 shunt to the armature circuit, so that only a portion of the current 
 generated passes through the field-magnet coils, but all the difference 
 of potential of the armature acts at the terminals of the field-circuit. 
 
 In a shunt- wound dynamo an increase in the resistance of the external 
 circuit increases the electro-motive force, and a decrease in the resistance 
 of the external circuit decreases the electro- motive force. This is just 
 the reverse of the series-wound dynamo. 
 
 In a shunt-wound dynamo a continuous balancing of the current 
 occurs, the current dividing at the brushes between the field and the 
 external circuit in the inverse proportion to the resistance of these 
 circuits. If the resistance of the external circuit becomes greater, a 
 proportionately greater current passes through the field magnets, and 
 so causes the electro-motive force to become greater. If, on the con- 
 trary, the resistance of the external circuit decreases, less current passes 
 through the field, and the electro-motive force is proportionately 
 decreased. 
 
 3. Compound-wound Dynamo. The field magnets are wound with 
 two separate sets of C9ils, one of which is in series with the armature 
 and the external circuit, and the other in shunt with the armature or 
 the external circuit. 
 
 A compound generator is made for the purpose of delivering current 
 at constant potential either at the terminals of the machine or at some 
 distant receiving point on the line. In the former case the machine is 
 flat-compounded, the ideal being the same terminal voltage at full load 
 as at no load, giving a practically horizontal voltage characteristic. 
 In the latter case the machine is over-compounded, giving a terminal 
 voltage which rises from no load to full load to compensate for line 
 drop, so that at the receiving end of the line the voltage will be constant 
 at all loads. 
 
 The standard voltages for ordinary light and power service are 125 
 and 250 volts, while for railway service they have been built for voltages 
 as high as 1200, and in one particular installation two such machines 
 are connected in series furnishing a supply voltage of 2400 volts. 
 
 Many direct-current generators are provided with commutatinp? 
 poles, and such machines may be operated over an extremely wide range 
 of load and voltage with fixed brush positions and sparkless commu- 
 tation. The commutating winding produces a magnetic field which is 
 in a direction to assist the reversal of current in the coil undergoing 
 commutation and also directly opposed to the field generated by arma- 
 ture reaction which tends to retard the reversal of current in this coil. 
 The commutating field thus completely nullifies the distortive effect of 
 armature reaction on the main field flux in the commutating zone, and 
 generates an e.m.f. which helps the brush to commutate the current 
 without sparking, and with a consequent increased life of the commu- 
 tator and brushes. 
 
 Commutating poles are placed between the main poles of direct- 
 current generators and motors. They are used for the purpose of 
 nullifying the effect of the armature reaction upon the magnetic field 
 adjacent to the neutral point. The armature reaction tends to move the 
 neutral point from its proper mechanical position, and it is obvious that 
 a number of ampere turns setting up magnetic lines of force equal to 
 and opposing the directions of those set up by the armature ampere 
 turns will nullify that effect on the neutral occasioned by the armature 
 reaction. 
 
 The commutating pole winding is connected in series with the arma- 
 ture and has a number of turns per pole sufficient to give a magnetic 
 strength that will not only counteract the armature reaction above 
 referred to, but will actually reverse the current in the coil when it is 
 in the commutating zone. 
 
 The commutating zone is the region over which the brushes may have 
 to be moved in order to obtain good commutation between no load and 
 full load. With commutating pole machines no such movement is 
 necessary and the reversal takes place in the coils short circuited under 
 the brushes. 
 
ALTERNATING CURRENTS. 1439 
 
 Inasmuch as the commutating windings are directly in series with 
 the armature, their strength varies directly with the armature current 
 and provides the correct rectifying effect for proper reversal of current 
 in the coils at all loads. Hence it is unnecessary to shift the brushes as 
 the load changes. 
 
 Parallel Operation. The first requisite for satisfactory parallel 
 operation of direct current generators is that they have the same char- 
 acteristics. They must have the same degree of compounding for any 
 percentage of their rated load. The resistance of series fields with their 
 shunt resistances and cable connections to the bus-bar should further- 
 more be inversely proportional to the capacities of the machines; i.e., no 
 matter what size cables are used, the resistances of the two connections 
 must be so proportioned that the drop will be the same for both ma- 
 chines between the equalizer junction and the main bus-bar when each 
 machine is delivering its full-load current. 
 
 Three-Wire System. The chief advantage of the Edison three- 
 wire system over the ordinary two-wire installation is that of econ- 
 omy in distribution. In a two-wire system with a given load and a 
 given percentage of voltage drop, the distribution at 250 volts requires 
 only one-quarter the weight of copper required for a distribution at 125 
 volts. A neutral, wire in the three-wire system will, however, modify 
 this proportion of copper, the final saving depending on the size of the 
 neutral. In well-designed systems, the maximum unbalanced current 
 carried by the neutral will be about 25 per cent of the full load. There- 
 fore the size of the neutral need not be larger than 25 per cent of the 
 capacity of the outside mains, and the weight of the copper in this case 
 would be 9/32 of that used in distributing the same power by a two- 
 wire system. 
 
 The practical methods available for operating direct-current three- 
 wire systems are: 1. Two generators. 2. One generator with balancer 
 set. 3. One generator with storage battery. 4. One generator with 
 balancing coil. 5. Three-wire generator. 
 
 ALTERNATING CURRENTS.* 
 
 The advantages of alternating over direct currents are: 1. Greater 
 simplicity of dynamos and motors, no commutators being required; 2. 
 The feasibility of obtaining high voltages, by means of static trans- 
 formers, for cheapening the cost of transmission; 3. The facility of 
 transforming from one voltage to another, either higher or lower, for 
 different purposes. 
 
 A direct current is uniform in strength and direction, while an alter- 
 nating current rapidly rises from zero to a maximum, falls to zero, re- 
 verses its direction, attains a maximum in the new direction, and again 
 returns to zero. This series of changes can best be represented by a 
 curve the abscissas of which represent time and the ordinates either 
 current or electro-motive force (e.m.f.). The curve usually chosen for 
 this purpose is the sine curve, Fig. 228 ; the best forms of alternators give a 
 curve that is a very close approximation to the sine curve, and all calcu- 
 lations and deductions of formulae are based on it. The equation of the 
 sine curve is y = sin x, in which y is any ordinate, and x is the angle 
 passed over by a moving radius vector. 
 
 After the flow of a direct current has been once established, the only 
 opposition to the flow is the resistance offered by the conductor to the 
 passage of current through it. This resistance of the conductor, in 
 treating of alternating currents, is sometimes spoken of as ohmic resist- 
 ance. The word resistance, used alone, always means the ohmic 
 resistance. In alternating currents, in addition to the resistance, sev- 
 
 * Only a very brief treatment of the subject of alternating currents can 
 be given in this book. The following works are recommended as val- 
 uable for reference: Steinmetz, "Theoretical Elements of Electrical 
 Engineering. Alternating Current Phenomena"; Cohen, "Formulae 
 and Tables for the Calculation of Alternating Current Problems ' ' ; Jack- 
 son, "Alternating Currents and Alternating Current Machinery"; 
 Bedell, "Direct and Alternating Current Manual"; Timbie, "Alter- 
 nating Currents," 
 
1440 ELECTRICAL ENGINEERING. 
 
 eral other quantities, which affect the flow of current, must be taken 
 into consideratioa These quantities are inductance, capacity, and skin 
 effect. They are discussed under separate headings. 
 The current and the e.m.f. may be in phase with each other, that is 
 they may attain their maximum strength at the same instant, or they 
 may not, depending on the character of the circuit. In a circuit .con- 
 taining only resistance, the current and e.m.f. are in phase; in a current 
 containing inductance the e.m.f. attains its maximum value before the 
 current, or leads the current. In a circuit containing capacity the cur- 
 rent leads the e.m.f. If both capacity and inductance are present in a 
 circuit, they will tend to neutralize each other. 
 
 Maximum, Average, and Effective Values. The strength and the 
 e.m.f. of an alternating current being constantly varied, the maximum 
 value of either is attained only for an instant in each period. The maxi- 
 mum values are little used in calculations, except in deducing formulae 
 and for proportioning insulation, which must stand the maximum 
 pressure. The average value is obtained by averaging the ordinates of 
 the sine curve representing the current, and is 2 -j- IT or 0.637 of the 
 maximum value. 
 
 The value of greatest imp9rtance is the effective, or "square root of 
 the mean square," value. It is obtained by taking the square root of the 
 mean of the squares of the ordinates of the sine curve. The effective 
 value is the value shown on alternating-current measuring instruments. 
 The product of the square of the effective value of the current and the 
 resistance of the circuit is the heat lost in the circuit. 
 
 The relation of the maximum, average, and effective values is: } 
 ^Effec. = %ax. X 0.707 ; # Aver . = Max . X 0.637 ; % ax . = 1.41 X %fec. 
 
 Frequency. The time required for an alternating current to pass 
 through one complete cycle, as from one maximum point to the next (a 
 and b, Fig. 228) , is termed the period. The number of periods in a second 
 is termed the frequency of the current. Since the current changes its 
 direction twice in each period, the number of reversals or alternations is 
 doable the frequency. A current of 120 alternations per second has a 
 period of 1/60 and a frequency of 60. The frequency of a current is equal 
 to one-half the number of poles on the generator, multiplied by the number 
 of revolutions per second. Frequency is denoted by the letter/. 
 
 The frequencies most generally used in the United States are 25, 40, 60, 
 125, and 133 cycles per second. The Standardization Report of the 
 A I.E.E. recommends the adpptionof three frequencies, viz. 25, 60 and 120. 
 
 With the higher frequencies both transformers and conductors will be 
 less costly in a circuit of a given resistance but the capacity and inductance 
 effects in each will be increased, and these tend to increase the cost. With 
 high frequencies it also becomes difficult to operate alternators in parallel. 
 
 A l9w frequency current cannot be used on lighting circuits, as the lights 
 will nicker when the frequency drops below a certain figure. For arc lights 
 the frequency should not be less than 40. For incandescent lamps it should 
 not be less than 25. If the circuit is to supply both power and light a 
 frequency of 60 is usually desirable. For power transmission to long dis- 
 tances a l9w frequency, say 25, is considered desirable, in order to lessen 
 the capacity effects. If the alternating current is to be converted into 
 direct current for lighting purposes a low frequency may be used, as the 
 frequency will then have no effect on the lights. 
 
 Inductance. Inductance is that property of an electrical circuit by 
 which it resists a change in the current. A current flowing through a 
 conductor produces a magnetic flux 
 around tne conductor, n tne current 
 be changed in strength or directipn, 
 the flux is also changed, producing 
 in the conductor an e.m.f. whose direc- 
 tion is opposed to that of the current 
 in the conductor. This counter e.m.f. 
 is the counter e.m.f. of inductance. 
 It is proportional to the rate of change 
 of current, provided that the perme- 
 ability of the medium around the con- 
 duet or remains constant, The unit of FJG. 228, 
 
ALTERNATING CURRENTS. 1441 
 
 Inductance is the henry, symbol L. A circuit has an inductance of one 
 henry if a uniform variation of current at the rate of one ampere per 
 second produces a counter e.m.f. of one volt. 
 
 The effect of inductance on the circuit is to cause the current to lag 
 behind the e.m.f. as shown in Fig. 228, in which abscissas represents time, 
 and ordinates represent e.m.f. and current strengths respectively. 
 
 Capacity. Any insulated conductor "has the power of holding a quan- 
 tity of static electricity. This power is termed the capacity of the body. 
 The capacity of a circuit 'is measured by the quantity of electricity in it 
 when at unit potential. It may be increased by means of a condenser. 
 A condenser consists of two parallel conductors, insulated from each other 
 by a non-conductor. The conductors are usually in sheet form. 
 
 The unit of capacity is a farad, symbol C. A condenser has a capacity 
 of one farad when one coulomb of electricity contained in it produces a dif- 
 ference of potential of one volt, or when a rate of change of pressure of 
 one volt per second produces a current of one ampere. The farad is too 
 large a unit to be conveniently used in practice, and the micro-farad or 
 one-millionth of a farad is used instead. The effect of capacity on a 
 circuit is to cause the e.m.f. to lag behind the current. Both inductance 
 and capacity may be measured with a Wheatstone bridge by sub- 
 stituting for a standard resistance a standard of inductance or a stand- 
 ard of capacity. 
 
 Power Factor. In direct-current work the power, measured in watts, 
 is the product of the volts and amperes in the circuit. In alternating-cur- 
 rent work this is only true when the current and e.m.f. are in phase. If 
 the current either lags or leads, the values shown on the vole and ammeters 
 will not be true simultaneous values. Referring to Fig. 228, it will be 
 seen that the product of the ordinates of current and e.m.f. at any partic- 
 ular instant will not be equal to the product of the effective values which 
 are shown on the instruments. The power in the circuit at any instant is 
 the product of the simultaneous values of current and e.m.f.. and the volts 
 and amperes shown on the recording instruments must be multiplied 
 together and their product multiplied by a power factor before the true 
 watts are obtained. This power factor, which is the ratio of the volt- 
 amperes to the watts, is also the cosine of the angle of lag or lead of 
 the current. Thus 
 
 P = I X E X power factor = I X E X cos 0, 
 where is the angle of lag or lead of the current. 
 
 A watt-meter, however, gives the true power in a circuit directly. 
 The method of obtaining the angle of lag is shown on p. 1442. 
 
 Reactance, Impedance, Admittance. In addition to the ohmic re- 
 sistance of a circuit there are also resistances due to inductance, capacity, 
 and skin effect. The virtual resistance due to inductance and capacity 
 is termed the reactance of the circuit. If inductance only be present in 
 circuit, the reactance will vary directly as the inductance. If capacity 
 only be present, the reactance will vary inversely as the capacity. 
 
 Inductive reactance =2 TT/L; Condensive reactance = * . 
 
 2 7T J O 
 
 The total apparent resistance of the circuit, due to both the ohmic resist- 
 ance and the total reactance, is termed the impedance, and is equal to the 
 square root of the sum of the squares of the resistance and the reactance. 
 Impedance =Z = ^/II 2 + (2 Tr/D 2 when inductance is present in the circuit. 
 
 Impedance =Z=-y # 2 + (^fc] when ca P aci ty is present in the circuit. 
 
 Admittance is the reciprocal of impedance, = 1 * Z. 
 . If both inductance and capacity are present in the circuit, the reactance 
 of one tends to balance that of the other; the total reactance is the alge- 
 braic sum of the two reactances; thus, _ 
 
 Total reactance = X = 2 TT/L - -^Jc ; Z = \ R * + ( 2 ** L ~ J^fC )*' 
 
 In all cases the tangent of the angle of lag or lead is the reactance divided 
 by the resistance, In the last case 
 
1442 
 
 ELECTRICAL ENGINEERING. 
 
 Skin Effect. Alternating currents tend to have a greater density at 
 the surface than at the axis of a conductor. The effect of this is to make 
 the virtual resistance of a wire greater than its true ohmic resistance. 
 "With low frequencies and small wires the skin effect is small, but it be- 
 comes quite important with high frequencies and large wires. With 
 magnetic material it is much higher than with non-magnetic. 
 
 The skin effect factor, by which the ohmic resistance is to be multi- 
 plied to obtain the virtual resistance is given by Berg in the following 
 approximate formula: 
 
 1+X |777W 
 
 2 
 For Copper Cable: lj \ =0.0105 d z f; for Aluminum Cable: ( ^\ =0.0063 
 
 d 2 /, where d = diameter of cable, and / = frequency. 
 
 For the same per cent increase, due to skin effect, a cable can have 
 13% larger diameter than a solid wire; in other words, the skin effect is 
 the same as long as the ohmic resistance is the same, whether a solid 
 wire or a cable is used. 
 
 Ohm's Law applied to Alternating- Current Circuits. To apply 
 Ohm's law to alternating-current circuits a slight change is necessary 
 in the expression of the law. Impedance is substituted for resistance. 
 The law should read 
 
 E E 
 
 1 = 
 
 Impedance Polygons. 1 . Series Circuits. The impedance of a circuit 
 can be determined graphically as follows : Suppose a circuit to contain 
 a resistance R and an inductance L, and to carry a current I of frequency 
 /. In Fig. 229 draw the line ab proportional to R, and representing the 
 direction of current. At b erect be perpendicular to ab and propor- 
 tional to 2 irfL. Join a and c. The line, ac represents the impedance of 
 the circuit. The angle 9 between ab and ac is the angle of lag of the cur- 
 rent behind the e.m.f., and the power factor of the circuit is cosine 0. 
 The e.m.f. of the circuit is E = IZ. 
 
 FIG. 229. 
 
 27T/L 
 
 R 61 
 
 FIG. 230. 
 
 1 
 
 27T/K 
 
 FIG. 231. 
 
 FlG. 232. 
 
 If the above circuit contained, instead of the inductance I/, a capacity 
 C, then would the polygon be drawn as in Fig. 230. The line be would 
 
 be proportional to ^ ^ and would be drawn in a direction opposite to 
 
 " 7TJ O 
 
 that of be in Fig. 229. The impedance would again be Z, the e.m.f. 
 would be Z X /, but the current would lead the e.m.f. by the angle 0. 
 
 Suppose the circuit to contain resistance, inductance, and capacity, 
 the lines of the impedance polygon would then be laid off as in Fig. 231. 
 The impedance of ttye circuit would be represented by afl, ami the angle 
 
ALTERNATING CURRENTS. 
 
 1443 
 
 of lag by 0. If the capacity of the circuit had been such that cd was 
 less than be, then would the e.m.f. have led the current. 
 
 If between the inductance and capacity In the circuit in the previous ex- 
 amples there be interposed another resistance, the impedance polygon will 
 take the form of Fig. 232. The lines representing either resistances, in- \ 
 ductances, or capacities in the circuit follow each other in all cases as do 
 the resistances, inductances, and capacities in the circuit, each line having 
 its appropriate direction and magnitude. 
 
 EXAMPLE. A circuit (Fig. 233) contains a resistance, R it of 15 ohms, a 
 capacity. C^ t of 100 microfarads (0.000100 farad), a resistance, R& of 12 
 
 FIG. 233. 
 
 ohms, and inductance of Z/i, of 0.05 henry, and a resistance 72a, of 20 ohms. 
 Find the impedance and electromotive force when a current of 2 amperes 
 is sent through the circuit, and the current when e.m.f. of 120 volts is 
 impressed on the circuit, frequency being taken as 60. Also find the angle 
 of lag, the power factor, and the power in the circuit when 120 volts are 
 impressed. 
 
 The resistance is represented in Fig. 234 by the horizontal line 06, 15 
 units long. The capacity is represented by the line be, drawn downwards 
 from b and whose length is 
 
 a -".55 
 
 S 1 
 ii -j 
 
 S * 
 
 t? C CM 
 
 e R 3 =20 . 
 
 d 
 4. 
 
 CJ R 2 =12 
 FIG. 23 
 
 2X3.1416X60X0.0001 
 From the point c a horizontal line cd, 12 units long, is drawn to represent 
 R 2 . From the point d the line de is drawn vertically upwards to represent 
 the inductance LI. Its length is 
 
 27T/Z,! =2X3.1416X60X0.05 = 18.85. 
 From the point e a horizontal line ef, 20 
 units long, is drawn to represent Rs. The 
 line adjoining a and / will represent the 
 impedance of the circuit in ohms. The 
 angle d, between ab and a/, is the angle of 
 lag of the e.m.f. behind the current. The 
 impedance in this case is 47.5 ohms, and 
 the angle of lag is 9 15'. 
 
 The e.m.f. when a current of 2 amperes 
 is sent through is 
 
 IZ = E = 2 X 47.5 = 95 volts. 
 If an e.m.f. of 120 volts be impressed on the circuit, the current flowing 
 through will be 
 
 , 120 120 
 
 /= -5T- = T^T 2.53 amperes. 
 
 46 47. o 
 
 The power factor == cos 6 = cos 9 15' = 0.987. 
 
 The power in the circuit at 120 volts is 
 
 I X E X cos e = 2.53 X 120 X 0.987 = 299.6 watts. 
 
 2. Parallel Circuits. If two circuits be ar- 
 ranged in parallel, the current flowing in each 
 circuit will be inversely proportional to the 
 impedance of that circuit. The e.m.f. of each 
 circuit is the e.m.f. across the terminals at 
 either end of the main circuit, where the vari- 
 ous branches separate. Consider a circuit, 
 Fig. 235, consisting of two branches. The 
 first branch contains a resistance R, and an 
 inductance Lj. hi series with it. The second FIG. 235. 
 
1444 
 
 ELECTRICAL ENGINEERING. 
 
 branch contains a resistance # 2 in series with, an inductance L 2 . The 
 impedance of the circuit may be determined by treating each of the 
 two branches as a separate series circuit, and drawing the impedance 
 polygon for each branch on that assumption. Having found the im- 
 pedance the current flowing in either branch will be the reciprocal of 
 the impedance multiplied by the e.m.f. across the terminals. The 
 current in the entire circuit is the geometrical sum of the current in 
 the two branches. 
 
 The admittance of the equivalent simple circuit may be obtained by 
 drawing a parallelogram, two of whose adjoining sides are made parallel to 
 the impedance lines of each branch and equal to the two admittances 
 respectively. 
 
 The diagonal of the parallelogram will represent the admittance of the 
 equivalent simple circuit. The admittance multiplied by the e.m.f. gives 
 the total current in the circuit. 
 
 EXAMPLE. Given the circuit in Fig. 236, consisting of two branches. 
 Branch 1 consists of a resistance RI = 12 ohms, an inductance LI = 0.05 
 henry, a resistance R 2 = 4 ohms, and a capacity Ci = 120 microfarads 
 (0.00012 farad). Branch 2 consists of an inductance L 2 = 0.015 henry, a 
 resistance Rz =10 ohms, and an inductance La = 0.03 henry. An e.m.f. 
 of 100 volts is impressed on the circuit at a frequency of 60. Find the ad- 
 mittance of the entire circuit, the current, the power factor, and the power 
 
 R 1 =12 U=.05 
 
 =.0619 
 FlG. 237. 
 
AWERNAT1NG CURRENTS. 
 
 1445 
 
 In the circuit. Construct the impedance polygons for the two branches 
 separately as shown in Fig. 237, a and &. The impedance in branch 
 1 is 16.4 ohms, and the current is (1/16.4) X 100 = 6.19 amperes. The 
 angle of lead of the current is 1 45'. The impedance in branch 2 is 
 19.5 ohms and the current is (1/19.5) X 100 = 5.13 amperes. The 
 angle of lag of the current is 61. 
 
 The current in the entire circuit is found by taking the admittances of 
 the two branches, and drawing them from the point o, in Fig. 237 c, parallel 
 to the impedance lines in their respective polygons. The diagonal from o 
 is the admittance of the entire circuit, and in this case is equal to 0.092. 
 The current in the circuit is 0.092 X 100 = 9.2 amperes. The power factor 
 is 0.944 and the power in the circuit is 100 X 0.944 X 9.2 = 868.48 watts. 
 
 Self-Inductance of Lines and Circuits. The following formulae 
 and table, taken from Crocker's " Electric Lighting," give a method of cal- 
 culating the self-inductance of two parallel aerial wires forming part of the 
 same circuit and composed of copper, or other non-magnetic material: 
 
 L per foot = (l5.24 + 140.3 log ~\ lO" 9 . 
 
 (2 A\ 
 80.5 -f 740 log ~j-\ 10-. 
 
 in which L is the inductance in henrys of each wire, A is the Interaxial dis- 
 tance between the two wires, and d is the diameter of each, both in inches. 
 If the circuit is of iron wire, the formulae become 
 
 L per foot = (2286 + 140.3 log ^) 10-*. 
 L per mile = (l2070 + 740 log ^-\ lO" 6 . 
 
 INDUCTANCE, IN MILLIHENRYS PER MILE, FOR EACH OF Two 
 PARALLEL COPPER WIRES. 
 
 Interaxial 
 Distance, 
 
 Ins. 
 
 American Wire Gauge Number. 
 
 0000 
 
 000 
 
 00 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 
 10 
 
 1.615 
 1.838 
 2.061 
 2.192 
 2.356 
 2.507 
 
 12 
 
 6 
 12 
 24 
 36 
 60 
 % 
 
 .130 
 .353 
 .576 
 .707 
 .871 
 2.023 
 
 1.168 
 1.391 
 1.614 
 1.745 
 1.909 
 2.059 
 
 1.205 
 1.428 
 1.651 
 1.784 
 1.946 
 2.097 
 
 1.242 
 1.465 
 1.688 
 1.818 
 1.982 
 2J34 
 
 1.280 
 1.502 
 1.725 
 1.856 
 2.023 
 2.172 
 
 1.317 
 1.540 
 1.764 
 1.893 
 2.058 
 2.210 
 
 !:$ 
 
 1.800 
 1.931 
 2.095 
 2.246 
 
 1.392 
 1.614 
 1.838 
 1.968 
 2.132 
 2.283 
 
 1.466 
 1.689 
 1.912 
 2.043 
 2.208 
 2.358 
 
 1.540 
 1.764 
 1.986 
 2.117 
 2.282 
 2.433 
 
 1.690 
 1.913 
 2.135 
 2.266 
 2.432 
 2.582 
 
 Capacity of Conductors. AH conductors are included in three 
 classes, viz.: 1. Insulated conductors with metallic protecti9n; 2. Single 
 aerial conductor with earth return; 3. Metallic circuit consisting of two 
 parallel aerial wires. The capacity of the lines may be calculated by 
 means of the following formulae taken from Crocker's " Electric Lighting. 
 
 Class 1. C per foot = ^^^,' C per mile- 38 ' 83 " ^ 
 
 ' log(D + dy 
 Class 2. C per foot = fj 3 , 1 * " , C per mile - 
 
 log (D H- d) ' 
 38.83 X 10- 9 
 = log (4/1 -T- d) 
 
 feperfootofeachwire^jfl^. 
 
 OlaSS O. "^ i Q . n \f -I r\ t) 
 
 C per mile of each wire - iy ' 4J 
 
 ~log(2A+d) 
 
 In which C is the capacity in farads, D the internal diameter of the metallic 
 covering, d the diameter of the conductor, h the height of the conductor 
 above the ground, and A the interaxial distance between two parallel wires 
 all in inches; A: is a dielectric constant which for air is equal to 1 and for 
 pure rubber is equal to 2.5. The formulae in classes 2 and 3 assume the wires 
 to be bare. If they are insulated, k must be introduced in the numerator 
 and given a value slightly greater than 1. 
 
 Single-phase and Polyphase Currents. A single-phase current 
 is a simple alternating current carried on a single pair of wires and is 
 
1446 
 
 ELECTRICAL ENGINEERING. 
 
 generated on a machine having a single armature winding. It is repre- 
 sented by a single sine curve. 
 
 Polyphase currents are known as two-phase, three-phase, six-phase, or 
 any other number, and are represented by a corresponding number of sine 
 curves. The most commonly used systems are the two-phase and three- 
 phase. 
 
 1. Two-phase Currents. In a two-phase system there are two single- 
 phase alternating currents bearing a definite time relation to each other 
 and represented by two sine curves (Fig. 238). 
 The two separate currents may be generated by 
 the same or by separate machines. If by sepa- 
 rate machines, the armatures of the two should 
 be positively coupled together. Two-phase cur- 
 rents are usually generated by a machine with 
 two armature windings, each winding termi- 
 nating in two collector rings. The two windings 
 are so related that the two currents will be 90 
 
 vxy 
 
 FIG. 238. 
 
 apart. For this reason two phase-currents are also called " quarter- 
 phase " currents. 
 
 Two-phase currents may be distributed on either three or four wires. 
 The three-wire system of distribution is shovyn in Fig. 239- One of the 
 return wires is dispensed with, connection being made across to the other 
 as shown. The common return wire should be made 1.41 times the area 
 of either of the other two wires, these two being equal in size. 
 
 The four-wire system of distribution is shown in Fig. 240. The two 
 phases are entirely independent, and for lighting purposes may be operated 
 as two single-phase circuits. 
 
 FIG. 239. 
 
 FIG. 240. 
 
 2. Three-phase Currents. Three-phase currents consist of three alter- 
 nating currents, differing in phase by 120, and represented by three sine 
 curves, as in Fig. 241. They may be distributed by three or six wires. If 
 distributed by the six-wire system, it is analogous to the four-wire, two- 
 phase system, and is equivalent to three single-phase circuits. In the 
 three-wire system of distribution the circuits may be connected in two 
 different ways, known respectively as the Y or star connection, and the A 
 (delta) or mesh connection. 
 
 XXX 
 
 FIG. 241. 
 
 FIG. 242. 
 
 The Y connection is shown in Fig. 242. The three circuits are joined 
 at the point o, known as the neutral point, and the three wires carrying the 
 current are connected at the points a, b, and c, respectively. If the three 
 circuits ao, bo, and co are compo3ed of lights, they must be equally loaded 
 or the lights will fluctuate. If the three circuits are perfectly balanced, 
 fche lights will remain steady. In this form of connection each wire may 
 
ALTERNATING CURRENTS. 
 
 1M7 
 
 be considered as the return wire for the other 
 two. If the three circuits are unbalanced, a 
 return wire may be run from the neutral ppint 
 o to the neutral point of the armature wind- 
 ing on the generator. The system will then 
 be four-wire, and will work properly with un- 
 balanced circuits. 
 
 The A connection is shown in Fig. 243. 
 Each of the three circuits ab, ac, be, receives 
 the current due to a separate coil in the arma- 
 ture winding. This form of connection will 
 work properly even if the circuits are unbal- 
 anced; and if the circuit contains lamps, they 
 will not fluctuate when the circuit changes 
 from a balanced to an unbalanced condition, 
 or vice versa. 
 
 Measurement of Power in Polyphase Circuits. 1. Two-phase 
 Circuits. The power of two-phase currents distributed by four wires 
 may be measured by two wattmeters introduced into the circuit as shown 
 in Fig. 240. The sum of the readings of the two instruments is the total 
 power. If but one wattmeter is available, it should be introduced first in 
 one circuit, and then in the other. If the current or e.m.f. does not vary 
 during the operati9n, the result will be correct. If the circuits are per- 
 fectly balanced, twice the reading of one wattmeter will be the total power,, 
 Wi 
 
 FIG. 243. 
 
 FIG. 244. 
 
 FIG. 245. 
 
 The power of two-phase currents distributed by three wires may be 
 measured by two wattmeters as shown in Fig. 239. The sum of the two 
 readings is the total power. If but one wattmeter is available, the coarse- 
 wire coil should be connected in series with the wire ef and one extremity 
 of the pressure-coil should be connected to some point on ef. The other 
 end should be connected first to the wire a and then to the wire d, a read- 
 ing being taken in each position of the wire. The sum of the readings 
 gives the power in the circuits. 
 
 2. Three-phase Circuits. The power in a three-phase circuit may be 
 measured by three wattmeters, connected as in Fig. 244 if the system is 
 Y-connected, and as in Fig. 245 if the system is A-connected. The sum 
 of the wattmeter readings gives the power in the system. If the circuits 
 are perfectly balanced, three times the reading of one wattmeter is the 
 total power. 
 
 The power in a A-connected system 
 may be measured by two watt-meters, as 
 shown in Fig. 246. If the power factor of 
 the system is greater than 0.50, the arith- 
 metical sum of the readings is the power 
 in the circuit. If the power factor is less 
 than 0.50, the arithmetical difference of 
 the readings is the power. Whether the 
 power factor is greater or less than 0.50 
 may be discovered by interchanging the 
 wattmeters without disturbing the rela- 
 tive connection of their coarse- and fine- 
 wire coils. If the deflections of the needles 
 are reversed, the difference of the readings 
 
 FIG. 246. 
 
 is the power. If the needles are deflected in the same direction as at 
 first, the sum of the readings is the power. 
 
1448 ELECTRICAL ENGINEERING. 
 
 ALTERNATING-CURRENT GENERATORS. 
 
 Synchronous Generators. The function of the alternating-current 
 synchronous generator is to transform mechanical energy into electrical 
 energy, either single-phase or polyphase. It comprises a comparatively 
 constant magnetic field and an armature generating electro-motive forces 
 and delivering currents in synchronism with the motion of the machine. 
 
 Alternating-current generators are generally designed to operate at 
 normal load and 80% power factor without exceeding a specified tem- 
 perature rise, and should such a machine have to be operated with a load 
 of lower power factor, its rating will be reduced, when based on the same 
 temperature guarantee. 
 
 Synchronous generators are almost always of the revolving field type, 
 and may be either of a horizontal or vertical design. 
 
 Rating. The normal full-load rating is usually based on continu- 
 ous operation with a certain rated voltage, current, power factor, fre- 
 quency and speed. The overload guarantees should refer to the normal 
 conditions of operation, and an overload capacity of 25% for two hours 
 has generally been accepted as standard, although in several instances 
 a 50% two-hour overload is required. Of late (1915), however, gen- 
 erators are often given a maximum continuous rating with a temper- 
 ature rise not exceeding 50 C. (122 P.). 
 
 The rated full-load current is that current which, with rated terminal 
 voltage, gives the rated kilowatts or rated kilovolt-amperes. In ma- 
 chines in which the rated voltage differs from the no-load voltage, the 
 rated current should refer to the former. The rated output may be 
 determined as follows: 
 
 If E = full-load terminal voltage and I = rated current, then for a 
 
 El 
 
 single-phase generator, K.V.A. = 77^-. 
 
 lOUO 
 
 For a two-phase generator the total output is equal to the output of 
 the two single-phase circuits, and if I, in this case, is the rated current 
 
 O 77 1 7 
 
 per circuit, the output for a two-phase generator is, K.V.A. = ^-. 
 
 100O 
 
 For a three-phase generator there are three circuits to be considered, 
 whether the machine is star or delta connected. If E is the terminal 
 voltage and I the line current, then for a three-phase generator, 
 
 KVA - V3X EI 
 1000 
 
 The capacity of a polyphase generator, whether operating two- or 
 three-phase, is always the same, while, if operating under the same 
 conditions single-phase, in which case one phase is ineffective, the 
 rating is only about 71% of what it would be if operated as a poly- 
 phase generator. This relation, however, does not hold true for a ma- 
 chine which is initially built for single-phase service, and in such a case 
 the distribution of the winding can be made such as to increase the 
 capacity somewhat. The inherent regulation is generally made poorer 
 thereby, but by the use of massive damping devices it can be materially 
 improved. 
 
 Efficiency. The efficiency of a generator is the ratio of the power 
 output to the power input, the difference between these two quantities 
 being equal to the losses. The method commonly and most readily 
 used for obtaining the efficiency is to determine these losses and then 
 compute the efficiency by dividing the power output by the sum of the 
 power output plus the losses. 
 
 The guaranteed efficiency should always refer to the energy load 
 (the energy load is the load doing useful work, and is equal to the total 
 K.V.A. X the power factor of the load), and if is most important that 
 the power factor of the load is also given. In certain cases the guaran- 
 teed efficiency is based on a K.V.A. output, but the inconsistency of 
 such a method is apparent, as the following example will illustrate: 
 
 Assume a generator rated 100 K.V.A. (ICO Kw. at unity power- 
 factor) or 100 K.V.A. (80 Kw. 0.8 P.F.), and that the losses at unity and 
 80% power factors are 10 and 11 Kw. respectively, the efficiency is then; 
 
ALTERNATING-CURRENT GENERATORS. 1449 
 > 
 
 Based on 100 Kw. 1.0 P.F., 
 inn 
 
 Based on 80 Kw. 0.8 P.F., 
 
 Based on 100 K.V.A. 0.8 P.F., 
 
 From the last two values it is seen that for 80% power-factor if based 
 on ths K.V.A., a 2 % greater efficiency guarantee can be made, although 
 this value has no meaning, as it is based on apparent power. 
 
 The losses in the generator consist of: The copper losses in the 
 armature and field, proportional to the square of the armature and field 
 currents respectively; the core loss, slightly increasing from no-load to 
 full-load; the load loss, having a value approximately one-third of the 
 short-circuiting core loss; and finally, the friction and windage losses, 
 which are practically constant. 
 
 Regulation. Such a close inherent voltage- regulation as was for- 
 merly required is not any longer desirable, since a good voltage regula- 
 tion may readily be accomplished by means of automatic voltage regu- 
 lators, which perform their function whether the fluctuations are due to 
 a change of load, speed, or power factor. 
 
 A close inherent regulation would require a low reactance generator, 
 which means an expensive machine. A low reactance machine also, in 
 case of short circuits, would allow a very large current to flow through 
 the machine and through any other apparatus that may be within the 
 circuit enclosed by the short-circuit. These short-circuit currents reach 
 enormous values in large central stations, and in order to reduce the 
 currents to safe values large reactances are necessary. It is, however, 
 not possible to design high-speed turbo-generators for the necessary 
 reactance, and external reactances must usually be inserted in the gen- 
 erator leads or between the bus-sections. By so limiting the abnormal 
 flow of current the generating system is relieved from the disastrous 
 effects of such short circuits. 
 
 Rating of a Generating Unit. In determining the proper rating 
 and capacity of the generators for a power station, the generator and the 
 prime mover must of necessity be treated together as a combination so 
 as to secure the highest operating efficiency. With steam-engines the 
 ratings are usually such that the engine is working under its most eco- 
 nomical load at the rating of the electrical generator. With gas engines, 
 however, the efficiency increases with the load beyond the capacity of 
 the engine, and for this reason the rating of such an engine is generally 
 made as nearly as possible to its maximum capacity with only a small 
 margin for regulating purposes. With steam turbines the efficiency 
 curve is very flat so that it is the desirable overload capacity which 
 limits the rating of the turbine. In the water-wheel unit, the efficiency 
 usually falls off rapidly above and below the maximum point, so that 
 the rating of the generator should correspond to the point of maximum 
 efficiency of the wheel. 
 
 The effect of the power factor should also be considered when deter- 
 mining the prime mover as well as the generator capacity, and many 
 mistakes have been made in this respect. The generator may, for ex- 
 ample, have been designed and rated on the basis of unity power factor 
 operation with a, prime mover having a corresponding capacity. After 
 installation it is, however, found that the actual operating power factor 
 is 0.80, with the result that only 80 per cent of the prime mover capacity 
 can be utilized without overloading the generator. 
 
 Windings. The greatest number of all alternating-current gener- 
 ators are wound three-phase with the armature windings connected in 
 star. This is preferable to delta connection, as a smaller number of 
 conductors is required for a given voltage, while on the other hand the 
 danger of the circulation of triple-frequency currents in the closed 
 armature winding is avoided. 
 
1450 ELECTRICAL ENGINEERING. 
 
 Voltages. Standard generator voltages for all frequencies are 240, 
 480, 600, 1150, 2300, 4000, 6600, with the corresponding motor voltages 
 220, 440, 550, 1040, 2090, 6000. There is no nwtor voltage corresponding 
 to 4000 volts, since this is only used on lighting three-phase, four-wire 
 distributing systems. In addition 11,000 volts is also standard for 60 
 cycles, and 13,200 volts for 25 cycles. 
 
 Parallel Operation. In order that an alternating-current generator 
 shall be able to carry a load, a current must flow corresponding to this 
 load. The e.m.f. required to generate this current is the resultant of the 
 terminal and the induced e.m.f. 's of the generator, the displacement be- 
 tween these e.m.f. 's being due to the impulse of the prime mover. In 
 the same manner when two or more generators are operating in parallel 
 the division in load between the different units is entirely dependent on 
 the turning efforts of the prime movers, and a change in the field excita- 
 tion, as with direct-current generators, will have no effect whatsoever. 
 
 For a satisfactory parallel operation it is important that the e.m.f. 's 
 and frequencies of the generators be the same, as. if this is not the 
 case, cross currents will flow between the units. These cross currents 
 may be either wattless or they may represent a transfer of energy, de- 
 pending on whether they are caused by a difference in the e.m.f. or in 
 the frequency of the machines. 
 
 Exciters (E. A. Lof, in Coal Age). Synchronous generators as well as 
 synchronous motors are dependent on a direct-current excitation for 
 their operation, and the energy for the excitation is generally obtained 
 from direct-current generators, termed "exciters." These should have 
 a capacity sufficient to excite all of the synchronous apparatus in the 
 station when these machines are operating at their maximum load and 
 true operating power factor. It is not enough to provide for the 
 excitation when operating at unity power factor, because the exci- 
 tation which is required at lower power factors is considerably higher 
 than at unity power factor. 
 
 For small and medium size plants a 125- volt exciter pressure is gen- 
 erally chosen, while for larger installations a 250- volt excitation will 
 prove more economical. 
 
 There are many different ways of driving exciters. They may be 
 direct-connected to the main units if these are of moderate speed. Such 
 an arrangement may prove satisfactory for two or three units, but 
 when the number of units is higher the system becomes rather compli- 
 cated. Another objection is that in case of trouble with an exciter, the 
 whole generating unit will have to be shut down. When two direct- 
 connected units are used, they should each have a capacity sufficiently 
 large to excite both the generators, and with three units the capacity of 
 either exciter should preferably be such that it can excite two of the 
 generators. For four or more units it should only be necessary to give 
 each exciter a capacity sufficient for one generator, and if necessary a 
 motor-driven exciter unit can be installed as a reserve. 
 
 The system, however, which seems to be the most widely used and 
 which offers the greatest reliability, is that in which the excitation is 
 obtained from a common source, consisting of as few exciters as possible. 
 One or two units are then generally provided for normal excitation, de- 
 pending on the size of the station, a third unit being installed as a re- 
 serve. It is also common practice to have the regular units driven by 
 prime movers, such as steam-engines or water-wheels, while the reserve 
 unit is motor-driven. 
 
 Still another system which is becoming common is to install low- 
 voltage generators, driven either by a non-condensing steam turbine in 
 case of a steam-plant or a water-wheel in a hydro-electric plant. The 
 exciters are then motor-driven, current for driving them being obtained 
 from the low voltage generator. The steam from the turbines would 
 then, of course, be taken to the feed-water heaters, and in addition to 
 the exciters, all the other auxiliaries, such as the circulating pumps, 
 etc., would also be motor-driven. 
 
 In order to insure a close voltage regulation of the system, automatic 
 regulators are commonly installed in connection with the exciters, their 
 principle being to automatically increase or decrease the excitation by 
 rapidly opening or closing a shunt circuit across the exciter-field rheo- 
 stat, and thus keep a constant bus-bar voltage regardless of the load. 
 
TRANSFORMERS. 1451 
 
 TRANSFORMERS. 
 
 A transformer consists essentially of two coils of wire, one coarse and 
 one fine, wound upon an iron core. Its function is to transform elec- 
 trical energy from one potential to another, although it may also be 
 used for phase transformation. If the transformer causes a change from 
 high to low voltage, it is known as a "step-down" transformer; if from 
 low to high voltage, it is known as a "step-up" transformer. 
 
 Primary and Secondary. In regard to the use of the terms high- 
 voltage, low- voltage, primary and secondary, the A.I.E.E. Standardiza- 
 tion Rules read as follows: 
 
 "The terms ' high- voltage ' and ' low- voltage ' are used to distinguish 
 the winding having the greater from that having the lesser number of 
 turns. The terms 'primary' and 'secondary' serve to distinguish the 
 windings in regard to energy flow, the primary being that which receives 
 the energy from the supply circuit, and the secondary that which re- 
 ceives the energy by induction from the primary." 
 
 The terms primary and secondary are, however, often confused, and 
 in order to avoid any misunderstanding, it is preferable that the terms 
 high- voltage and low- voltage be used instead of primary and secondary. 
 
 Voltage Ratio. The A.I.E.E. Standardization Rules also state that 
 " The voltage ratio of a transformer is the ratio of the r.m.s. (square root 
 of mean square) primary terminal voltage to the r.m.s. secondary ter- 
 minal voltage under specified conditions of load." It also defines 
 "The ratio of a transformer, unless otherwise specified, as the ratio of 
 the number of turns in the high-voltage winding to that in the low- 
 voltage winding: i.e., the turn-ratio.' 11 
 
 The two ratios are equal when one of the windings is open and the 
 transformer does not carry any load. When loaded, the resistance 
 and inductance of the windings cause a drop in the voltage, thus modi- 
 fying the ratio of transformation slightly. 
 
 Rating. A transformer should be rated by its kilovolt - ampere 
 (K.V.A.) output. It is equal to the product of the voltage and current, 
 and is, therefore, the same whether the different coils are connected in 
 series or parallel. If the load is of unity power factor, the kilowatt out- 
 put is the same as the kilo volt-ampere output, but if the power factor 
 is less, the kilowatt output will be correspondingly less. For example, a 
 100 K.V.A. transformer will have a full-load rating of 100 K.W. at 100% 
 power factor, 90 K.W. at 90% power factor, etc. 
 
 Efficiency. There are two sources of loss in the transformer, viz., 
 the copper loss and the iron loss. The copper loss is proportional to the 
 square of the current, being the 12 R loss due to heat. If Ii, Ri, be the 
 current and resistance respectively of the primary, and Ii, Ri, the cur- 
 rent and resistance respectively of the secondary, then the total copper 
 loss is W c = /i2 .R! -f 7 2 2 #2 and the percentage of copper loss is 
 
 * 2 ' , where W p is the energy delivered to the primary. The iron 
 
 loss is constant at all loads, and is due to hysteresis and eddy currents. 
 
 The efficiency of a transformer is the ratio of the output in watts at 
 the secondary terminals to the input at the primary terminals. At full 
 load the output is equal to the input less the iron and copper losses. 
 The full-load efficiency of a transformer is usually very high, being from 
 92 per cent to 98 per cent. As the copper loss varies as the square of 
 the load, the efficiency of a transformer varies considerably at different 
 loads. Transformers on lighting circuits usually operate at full load 
 but a very small part of the day, though they use some current all the 
 time to supply the iron losses. For transformers operated only a part of 
 the time, the "all-day" efficiency is more important than the full-load 
 efficiency. It is computed by comparing the watt-hours output to the 
 watt-hours input. 
 
 The all-day efficiency of a 10-Kw. transformer, whose copper and 
 iron losses at full load are each 1.5 per cent, and which operates 3 hours 
 at full load, 2 hours at half load, and 19 hours at no load, is computed as 
 follows: 
 
 Iron loss, all loads = 10 X 0.015 = 0.15 K.W. 
 Copper loss, full load = 10 X 0.015 = 0.15 K.W. 
 
1452 
 
 ELECTRICAL ENGINEERING. 
 
 Copper less, 1/2 load = 0.15 X (1/2) 2 = 0.0375 K.W. 
 Iron loss, K.W. hours = 0.15 X 24 = 3.6. 
 Copper loss, full load, K.W. hours = 0.15 X 3 = 0.45. 
 Copper loss, 1/2 load, K.W. hours = 0.0375 X 2 = 0.075. 
 
 Output, K.W. hours = j (10 X 3) + (5 X 2) } =40. 
 
 Input, K.W. hours = 40 + 3.6 + 0.45 + 0.075 = 44.125. 
 All-day efficiency = 40 -r 44.125 = 0.907. 
 
 Connections. Among the great variety of transformer manipula- 
 tions in power and general distribution work, either for straight voltage 
 transformation or for phase transformation, the following are the most 
 generally used: 
 
 Voltage Transformation: 
 Single-phase. 
 Two-phase. 
 
 Three-phase, delta-delta. 
 Three-phase, delta-star, and vice versa. 
 Three-phase, star-star. 
 Three-phase, open-delta. 
 Three-phase, Tee. 
 Phase Transformation: 
 
 Two- or three-phase to single-phase. 
 Two-phase to six-phase. 
 Three-phase to two-phase. 
 Three-phase to six-phase. 
 
 The transformer connections mostly used are delta-delta or delta-star 
 with neutral grounded. 
 
 For moderate voltage systems, the isolated delta connection is to 
 be preferred, although for high-tension systems with very high voltages 
 
 FIG. 247. 
 
 FIG. 249. 
 
 practice has proved that the high-tension winding star connected and 
 the neutral grounded will give a more satisfactory operation. 
 
 Tee -Connection. (Fig. 247.) T- connection requires only two single 
 transformers of which one is provided with a 50 per cent tap to which 
 the other is connected. The latter may be designed for only 86.6% of 
 the line or main transformer voltage, but generally it is made identical 
 with the main transformer and operated at reduced flux density. 
 
 Delta-Connection. (Fig. 248.) The e.m.f. between the mains is the 
 same as that in any one transformer measured between terminals, and 
 each transformer must, therefore, be wound for the full line voltage, but 
 
 only for or 57.7 per cent of the line current. 
 
 \/~3 
 
 Star-Connection. (Fig. 249.) In the star-connection each trans- 
 former has one terminal connected to a common junction, or neutral 
 point. Each transformer is wound for only 57.7 per cent of the line 
 voltage, but for the full line current. 
 
 Reactance. In order to obtain a good voltage regulation, it has been 
 the custom to design the transformers with a reactance as low as H/2 to 
 2 per cent. Recent experience has, however, shown that in high power 
 systems such transformers are unsafe, owing to the enormous mechan- 
 ical strain produced on the transformer and system by the excessive 
 short-circuit currents permitted by such low impedance transformers. 
 
SYNCHRONOUS CONVERTERS. 1453 
 
 A 2 per cent reactance means that at full load current, 2 per cent or 1/50 
 of the supply voltage is consumed by the reactance. At short circuit 
 the total voltage would have to be consumed by the transformer re- 
 actance, and the short-circuit current at full voltage is then fifty times 
 full load current. Safety thus requires that in high power systems the 
 transformers should be designed for a much higher reactance and the 
 present practice (1915) is, therefore, to design such transformers for 
 6 to 8 per cent reactance, and sometimes even for as high as 10 per cent. 
 
 Cooling. According to the method used in diss.'pating the heat 
 generated by the losses, transformers may be classified as: 1. Oil 
 cooled. 2. Water cooled. 3. Air blast. 
 
 Parallel Operation. In order that two or more transformers or groups 
 of transformers shall operate successfully in parallel, it is necessary that 
 their polarity be the same, that their voltages and voltage ratios be 
 identical, and that their impedances be inversely proportional to the 
 ratings. 
 
 Auto Transformers. -Auto transformers may be used where the 
 required voltage change is small. Their action is similar to that of 
 ordinary transformers, the essential difference between the two being 
 that in the transformer the high- voltage and low-voltage windings are 
 separate and insulated from each other while in the auto-transformer a 
 portion of the winding is common to both the high and low voltage 
 circuits. 
 
 The high- and low- voltage currents in both types of transformers 
 are in opposite direction to each other, and thus in an auto-transformer 
 a portion of the winding carries only the difference between the two 
 currents. 
 
 Auto transformers are extensively used for alternating current motor 
 starters, and also to some extent in moderate voltage generating stations. 
 
 Constant-Current Transformers. The transformers heretofore dis- 
 cussed are constant-potential transformers and operate at a constant 
 voltage with a variable current. For the operation of lamps in series a 
 constant-current transformer is required. There are a number of types 
 of this transformer. That manufactured by the General Electric Co. 
 operates by causing the primary and secondary coils to approach or to 
 separate on any change in the current. 
 
 SYNCHRONOUS CONVERTERS. 
 
 A synchronous converter is essentially a continuous-current gener- 
 ator, which, in addition to its commutator, is supplied with two or more 
 collector rings connected to suitable points in the armature winding. If 
 such a machine be driven by mechanical power, it will evidently deliver 
 either alternating or direct current, and, conversely, if supplied with 
 electric power, it will operate either as a synchronous motor, as a direct- 
 current motor, or as a synchronous converter. When operated as a 
 converter, the alternating current enters the armature winding through 
 the collector rings, and aftei* being rectified by the commutator, is de- 
 livered as direct current, or vice versa. 
 
 The alternating and direct current e.m.f. stand hi a certain relation 
 or ratio to each other, and this depends upon the number of phases and 
 frequency of the system used, and also upon the ratio of maximum to 
 the square root of the mean square value of the impressed e.m.f. (that 
 is, the e.m.f. of the supply circuit). It also depends upon the load of 
 the machine, the ohmic armature losses, the position of the direct- 
 current brushes on the commutator, the excitation, the ratio of pole arc 
 to pole pitch, and upon the operating conditions, that is, whether the 
 machine is used to convert from alternating to direct current or vice 
 versa. Synchronous converters for 60 cycles, which usually have a 
 lower ratio of pole arc to pole pitch than 25 cycle converters, have, as a 
 rule, a higher voltage ratio and, when used as inverted converters, a 
 lower voltage ratio than corresponding 25 cycle machines. 
 
 In the two-ring or single-phase converter, the two collector rings are 
 connected to armature conductors with the same angular distance apart 
 as commutator bars under adjacent sets of brushes. At this instant 
 the e.m.f. between the collector rings is at its maximum value and 
 equal to the e.m.f. between the direct-current brushes. Therefore, 
 tne direct-current e.m.f. (JS) of a two-ring single-phase synchronous 
 
1454 ELECTRICAL ENGINEERING. 
 
 converter is equal to the maximum value (\/2~X E 2 ) of the sine wave 
 e.m.f. between the two collector rings. Therefore, 
 
 E 
 
 E 2 = 
 V^2 
 
 in which E% is the effective value of the single-phase alternating e.m.f. 
 
 The effective e.m.f. between the two collector rings, which are con- 
 nected to the armature winding at points 120 electrical degrees apart, 
 that is, between any two rings of a three-ring three-phase converter, is 
 represented by that chord of a polygon which subtends an angle of 
 120 degrees. Likewise, the e.m.f. between two rings which are con- 
 nected to the armature winding at points 90 electrical degrees apart, as 
 between two adjacent rings in a four-ring quarter-phase converter, is 
 represented by the chord which subtends an 'angle of 90 electrical de- 
 grees; and the chord which subtends an angle of 60 electrical degrees 
 represents the e.m.f. between two adjacent rings of a six-ring six- 
 phase synchronous converter. 
 
 In general, the effective e.m.f., E\, between adjacent rings of an 
 n-ring converter, is represented by that chord of a polygon which sub- 
 
 n 
 
 tends an angle of ^ or . Therefore, 
 
 This gives the following theoretical values of the effective alternating 
 e.m.f. between adjacent collector rings of a two-ring, three-ring, four- 
 ring and six-ring synchronous converter, expressed in terms of the 
 e.m.f., E, between the direct-current brushes: 
 
 7^ 
 
 For single-phase Ei = -= = 0.707 E, 
 
 For three-phase Ei = = 0.612 E, 
 
 2 \^2 
 
 77" 
 
 For quarter-phase Ei = = 0.500 E, 
 
 For six-phase Ei = E f __ = 0.354 E. 
 
 2 V2 
 
 The above ratios represent, as before stated, the effective alternating 
 e.m.f. between two adjacent collector rings. For quarter- and six-phase 
 converters the different phases of the supply circuit, however, are not 
 connected as a rule to adjacent rings and the ratios given above are not 
 the ones to be used for determining the alternating supply voltage for 
 these types of synchronous converters. 
 
 For the four-ring quarter-phase converter, each phase of the supply 
 circuit is generally connected to diametrically opposite points of the 
 armature winding and the ratio will, under such conditions, be equal 
 to the ratio for the two-ring single-phase converters, that is, for quarter- 
 
 phase Ei = -^L = 0.707 E. 
 
 V/2 
 
 For six-phase synchronous converters two different arrangements of 
 the connections are generally used. One is called the "double delta" 
 connection and the other the "diametrical" connection. In the first 
 case, the voltage ratio is the same as for the three-phase synchronous 
 converter and simpfy consists of two "delta" systems. The trans- 
 formers can also be connected in "double-star," and in such a case the 
 ratio between the three-phase voltage between the terminals of each 
 star and the direct voltage will be the same as for "double-delta," 
 
 while the voltage of each transformer coil, or voltage to neutral, is = 
 
 V^ 
 times as much. With the diametrical connection the ratio is the same 
 
SYNCHRONOUS CONVEHTEKb. 1455 
 
 as for the two-ring single-phase converter, it being analogous to three 
 such systems. Therefore 
 
 Six-phase double-delta, JEj. = ?^ = 0.612 E. 
 2\/2 
 
 Six-phase diametrical, EI = -^L = 0.707 E. 
 
 Vz 
 
 The ratio of the effective e.m.f., E , between any collector ring and 
 the neutral point is always 
 
 E Q = -= = 0.354 E. 
 2 \/2 
 
 The given voltage ratios are, as stated, only theoretical , as the losses 
 in the winding have been neglected and the assumption has been made 
 that both the impressed and the counter generated converter e.m.f. 
 has a sine wave shape. The ratio between the alternating and direct 
 terminal voltages is somewhat different from the theoretical ratio due 
 to the voltage drop in the armature and to the wave shapes of the 
 e.m.f. 's. The exact ratios are always furnished by the manufacturer. 
 
 Synchronous converters may be either of the shunt- or compound- 
 wound type, the choice depending on the character of the service for 
 which they are to be used. In the majority of installations, especially 
 for power purposes, compound- wound converters are generally used 
 because they automatically regulate for a comparatively constant 
 direct-current voltage. 
 
 In order to change the direct voltage in the ordinary type of syn- 
 chronous converter with constant voltage ratio, it is necessary to 
 provide means for changing the applied alternating voltage correspond- 
 ingly. This can be done in several ways, one of which is to provide taps 
 on the step-down transformers and adjust the ratio of transformation 
 by means of a dial switch. A much better method, however, is the use 
 of an induction regulator between the transformer secondary terminals 
 and the synchronous converter. This regulator consists of a stationary 
 series winding and a movable potential winding, which can be turned 
 through a certain angle, and at each angular position will raise or lower 
 the voltage at the collector rings a certain amount, through the mutual 
 action of the current and potential windings. This method of control 
 is generally used with shunt- wound synchronous converters in order to 
 keep the voltage constant, when the line drop is excessive. The induc- 
 tion regulator is either hand-operated by means of chain or motor 
 drive, or the control can be made automatic by using a contact-making 
 voltmeter and relay, which will automatically control the regulator 
 motor. 
 
 The voltage regulation can also be accomplished by taking ad van tag/" 
 of the fact that an alternating current passing over an inductive circuit 
 will decrease in potential if lagging, and increase if leading. By pro- 
 viding the synchronous converter with a series field winding in addition 
 to the shunt field, the excitation can be automatically regulated as the 
 load comes on. The inductance of the supply circuit and step-down 
 transformers is, however, frequently not sufficient to cause the required 
 boost in the voltage, and in such a case it becomes necessary to insert 
 extra reactance coils in the line or provide the step-down transformers 
 with extra high reactance. 
 
 There are three feasible methods of starting synchronous converters: 
 First, the application of alternating current at reduced voltage to the 
 collection rings; second, the application of direct current to the commu- 
 tator and starting the machine as a direct-current motor; third, the use 
 of an auxiliary starting motor mechanically connected. 
 
 The alternating current starting method has many advantages over 
 the other methods. It is self-synchronizing, and, therefore, entirely 
 eliminates the difficulty of accurately adjusting the speed. When the 
 speed of the prime movers is liable to be variable, the ability to start a 
 machine quickly and get it on the line in the shortest possible time is a 
 great advantage inherent to .this method of starting. It is possible for 
 the Converter to drop into step with its direct-current voltage reversed 
 from that of the bus to which the machine is to be connected, but the 
 
1456 ELECTRICAL ENGINEERING. 
 
 machine can easily be made to drop back a pole by a self-exciting field 
 reversing switch on the machine frame. This method of starting makes 
 the operation of the machine so simple that the liability of confusion 
 and mistakes by operators Is greatly reduced. 
 
 If several synchronous converters are to supply the same direct- 
 current system, they can be connected in parallel in the same manner 
 as shunt- or compound -wound generators, and they are even frequently 
 operated in parallel with such generators and storage batteries. The 
 different converters will divide the load according to their direct-current 
 
 r s voltage regulation from no-load to 1 
 
 load, and if a battery is also operated in parallel the voltage drop should 
 be sufficiently large so as to cause the battery to take the excessive 
 loads. Synchronous converters operated in parallel should not be con- 
 nected to the same transformer secondaries. Such a connection would 
 form a closed local circuit in which heavy cross-currents would flow 
 when any difference in the operating conditions of the machine occurs, 
 as, for example, if the brushes of one of the machines were slightly 
 displaced relative to the other. 
 
 Compound-wound converters for parallel operation should be pro- 
 vided with equalizer switches. For connecting a compound- wound con- 
 verter in parallel with one already running, the equalizer switch is 
 closed first, so as to energize the series field from the running machine. 
 Next, the shunt field circuit is closed and the field adjusted so that the 
 voltage will correspond to that of the first machine, and finally the 
 main switch is closed. The load can then be transferred from the first 
 to the second converter by weakening the shunt field of the former and 
 strengthening that of the latter. 
 
 MOTOR-GENERATORS. 
 
 Motor-generator sets may be divided into three general classes: 
 
 1. Direct current to direct current sets, including balancing sets for 
 three-wire lighting systems, and for variable speed motor work, boosters 
 for storage battery charging and railway or lighting feeders. 
 
 2. Alternating current to direct current sets or vice versa. These are 
 used for excitation purposes and for supply of lighting, railway or 
 power systems. The sets may be driven either with synchronous or 
 induction motors, the former being equipped with an auxiliary squirrel 
 cage winding on the fields so as to be self-starting at reduced voltage. 
 
 3. Alternating current to alternating current sets between the two 
 periodicities; commonly called "frequency changers." 
 
 Balancers. The balancer set, a form of direct-current compensator, 
 is a variation of the regular motor-generator set, in that the units of 
 which it is composed may be, alternately, motor or generator, and the 
 secondary circuit is interconnected with the primary. On account of 
 the latter feature, the efficiency of transformation is higher and a 
 larger output is obtainable from a given amount of material than in the 
 straight motor-generator set. 
 
 Balancer sets are widely used to provide the neutral of Edison 
 three-wire lighting systems. They are also installed for power service 
 in connection with the use of 250-volt motors on a 500-volt service 
 or 125- volt motors on a 250-volt service. 
 
 The potential of the system being given, the capacity of a three- wire 
 balancer set is fixed by the maximum current the neutral wire is required 
 to carry. This figure is a more definite specification of capacity than a 
 statement in per cent of unbalanced load. 
 
 As designed for power work and generally for lighting service, the 
 brushes of each machine are set at the neutral point in order to get the 
 best results for operating alternately either as a generator or motor. 
 Where the changes of balance are so gradual as to permit of hand ad- 
 justment, if desired, a considerable increase in output is obtainable. 
 
 Boosters. Boosters are extensively used in railway stations to raise 
 the potential of the feeders extending to distant points of the system; 
 for storage-battery charging and regulation; and in connection with the 
 Edison three-wire lighting system. The design of the various sets is 
 closely dependent upon their application. 
 
ALTERNATING-CURRENT CIRCUITS. 1457 
 
 Booster sets are constructed in either "series- or shunt-wound types, 
 and they may be arranged for either automatic or hand regulation, 
 depending on the nature of the service required. 
 
 Where there are a number of lighting feeders connected and run at 
 full load for only a short time each day it will generally be economical 
 to install boosters rather than to invest in additional feeder copper. 
 It is important, however, to consider each case where the question of 
 installing a booster arises, as a separate problem, and to determine if 
 the value of the power lost represents an amount lower than the interest 
 charge on the extra copper necessary to deliver the same potential 
 without the use of a booster. 
 
 Dynamotors. A dynamotor is a machine for reducing a direct- 
 current voltage, and it is extensively used in connection with high voltage 
 railway equipments for obtaining a moderate voltage for the control. It 
 has two armature windings and commutators on one drum, with the field 
 between them. The control current is taken midway between the arma- 
 tures and is returned to the ground side of the dynamotor. This insures 
 that the maximum potential on the control circuit, under normal condi- 
 tions, will be approximately one-half of the line voltage, and the potential 
 to grounded parts no greater than when operated directly on a line voltage 
 of one-half the amount. 
 
 Frequency Changers. A periodicity of 25 cycles has been quite gen- 
 erally selected for railway service. Also in certain large cities, current of 
 the same frequency is generated in central stations and distributed: to 
 substations in which are installed rotary converters supplying an Edison 
 three-wire network. 
 
 Inasmuch as the periodicity of 60 cycles is more favorable than 25 
 cycles for alternating current lighting, frequency changers, similar to that 
 shown above, are installed to furnish high tension 60-cycle current for 
 distribution to outlying districts beyond the reach of the three-wire 
 system. 
 
 In the design of frequency changers speeds must be selected that are 
 common to the two periodicities of the system upon which they are tc . 
 be used; since 300 r.p.m. is the highest speed common to 25 and 60 cycles, 
 at which speed small sets are expensive per kilowatt, a line of sets with ' 
 4 or 8 pole motors and 10 or 20 pole generators has been developed, giving 
 62 1/2 cycles from 25 cycles or 60 cycles from 24 cycles. 
 
 Where parallel operation is required between synchronous motor- 
 driven frequency changers, a mechanical adjustment is necessary between 
 the fields or armatures of the generator and motor to obtain equal division 
 of the load. The adjustment is best obtained by the cradle construction. 
 The stator of one machine is bolted to a cradle fastened to the base, and 
 by taking out the bolts the frame can be turned around through a small 
 angle relatively to the cradle, and therefore to the stator field of the other 
 machine, where the bolts can be replaced. 
 
 The Mercury Arc Rectifier consists of a mercury vapor arc enclosed 
 In an exhausted glass vessel into which are sealed two terminal anodes 
 connected to the two wires of an alternating-current circuit. A third 
 terminal, at the bottom of the vessel, is a mercury cathode. When an 
 arc is operating, it is a good conductor from either anode to the cathode, 
 but practically an insulator in the other direction. The two anodes 
 connected across the terminals of the alternating-current line become 
 alternately positive and negative. While either anode is positive, there 
 is an arc carrying the current between it and the cathode. When the 
 polarity of the alternating-current reverses, the arc passes from the other 
 anode to the mercury cathode, which is always negative. The current 
 leading out from the mercury cathode is uni-directional. By means of 
 reactances, the pulsations are smoothed out and the current at the cathode 
 becomes a true direct current with pulsations of small amplitude. 
 
 ALTERNATING-CURRENT CIRCUITS. 
 
 Calculation of Alternating-current Circuits. The following formulae 
 and tables are issued by the General Electric Co. They afford a con- 
 venient method of calculating the sizes of conductors for, and determining 
 the losses in, alternating-current circuits. They apply only to circuits 
 in which the conductors are spaced 18 inches apart, but a slight increase 
 or decrease in this distance does not alter the figures appreciably. If 
 
1458 
 
 KLECTH1CAL ENGINEERING. 
 
 the conductors arc less than 18 inches apart, the loss of voltage is de- 
 
 creased, and vice versa. 
 
 Let W == total power delivered In watts: 
 
 D = distance of transmission (one way) in feet; 
 
 P* per cent loss of delivered power ( W) ; 
 
 E = voltage between main conductors at consumers end of circuit-, 
 
 K a constant; for continuous current = 2160; 
 
 T = a variable depending on the system and nature of the load; for 
 continuous current = 1; 
 
 M = a variable, depending on the size of wire and frequency; for con- 
 tinuous current = 1 ; 
 
 A = a factor; for continuous current = 6.04. 
 
 D X W X K 
 Area of conductor, circular mills = 
 
 p x E* 
 
 Current in main conductors = Wx T + E; 
 Volts lost in lines = P X E X M -r 100; 
 
 ^ z>2 x WXKXA 
 
 Pounds copper = - 
 
 The value of M is found from the formula: M -- 
 
 X = 0.000882 / flogio (} + 0.109J 
 
 X = Reactance. 
 
 R = Resistance, ohms per 1000 ft., at 60 F. 
 sen's standard.) 
 
 d = inches between wires. 
 
 r = radius of wire, inches. 
 
 / = cycles per second. 
 
 (Wire 100% Matthics- 
 
 
 VALUES OF M WIRES 18 IN. APART, f 
 
 WIRES 36 IN. APART. $ 
 
 25 Cycles. 
 
 60 Cycles. 
 
 25 Cycles. 
 
 Power 
 
 Factors. 
 
 0.95 0.90 0.85 0.80 
 
 0.95 0.90 0.85 0.80 
 
 0.95 0.90 0.85 0.80 
 
 Wire Sizes. 
 0000 
 000 
 00 
 
 1 
 2 
 
 4 
 
 6 
 7 
 
 8 
 9 
 10 
 
 .17 1.16 1.12 1.06 
 .12 1.09 1.05 0.99 
 .08 1.04 0.99 .92 
 .05 1.00 .94 .87 
 .02 0.96 .90 .83 
 .00 .93 .86 .79 
 0.98 .91 .84 .76 
 .96 .89 .81 .74 
 .95 .88 .80 .72 
 .94 .86 .78 .70 
 .94 .85 .77 .69 
 .93 .85 .76 .68 
 .92 .84 .76 .67 
 .92 .83 .75 .67 
 
 ( 
 
 .53 
 .41 
 .32 
 .24 
 .18 
 .12 
 .08 
 .05 
 .02 ( 
 .00 
 ).98 
 .97 
 .95 
 .94 
 
 .64 .67 .66 
 .49 .50 .47 
 .36 .35 .31 
 .26 .24 .19 
 .17 .14 .08 
 .10 .06 .00 
 .05 0.99 0.93 
 .00 .94 .87 
 ).97 .90 .83 
 .94 .87 .79 
 .91 .84 .76 
 .89 .82 .74 
 .88 .80 .72 
 .86 .79 .71 
 
 .22 1.23 1.20 1.15 
 .16 1.15 1.11 1.05 
 .11 1.08 1.04 0.97 
 .07 1.03 0.98 .91 
 .04 0.99 .93 .86 
 .02 .95 .89 .82 
 
 JFor higher volt- 
 ages, 10,000 to 200,- 
 000. 
 
 Per cent of 
 Power Factor. 
 
 Value of K. 
 
 Value of T. 
 
 sL 
 
 a 4 ** 
 >*o 
 
 100 
 
 95 
 
 85 
 
 J0_ 
 
 3380 
 1690 
 1690 
 
 100 95 
 
 85 
 
 80 
 
 System: 
 Single-phase 
 
 2160 
 1080 
 1080 
 
 2400,3000 
 1200 1500 
 1200 1500 
 
 1.00 1.05 1.17 
 0.500.530.59 
 0.58 0.61 0.68 
 
 1.25 
 0.62 
 0.72 
 
 6.04 
 12.08 
 9.06 
 
 Two-phase, 4- wire 
 
 Three-phase, 3-wire 
 
 * P should be expressed as a whole number, not as a decimal; thus 
 a 5 per cent loss should be written 5, not .05. 
 
 t As corrected by Harold Pender, see Elect. World, July 1, 1905. The 
 formula for M is approximate, and gives values correct within 2 % for 
 any case likely to arise in practice. 
 
ALTERNATING-CURRENT CIRCUITS. 
 
 1459 
 
 . Relative Weight of Copper Required in Different Systems for 
 Equal Effective Voltages. 
 
 Direct current, ordinary two- wire system 1 . 000 
 
 three-wire system, all wires same size 0. 375 
 
 neutral one-half size 0.313 
 
 Alternating current, single-phase two-wire, and two-phase four- wirel. 000 
 Two-phase three-wire, voltage between outer and middle wire 
 
 same as in single-phase two-wire . 729 
 
 voltage between two outer wires same ... 1 . 457 
 
 Three-phase three- wire . 750 
 
 " four-wire 0.333 
 
 The weight of copper is inversely proportional to the squares of the 
 voltages, other things being equal. The maximum value of an alter- 
 nating e.m.f. is 1.41 times its effective rating. For derivation of the 
 above figures see Crocker's "Electric Lighting," vol. ii. 
 
 Approximate Rule for Size of Wires for Three-Phase Transmission 
 Lines. (General Electric Co.) 
 
 The table given below is for use in making rough estimates for the 
 sizes of wires for three-phase transmission, as in the following example. 
 
 Required. The size of wires to deliver 500 Kw. at 6000 volts, at the 
 end of a three-phase line 12 miles long, allowing an energy loss of 10% 
 and a power factor of 85%. If the example called for the transmission 
 of 100 Kw. (on which the table is based), we should look in the 6000- 
 volt column for the nearest figure to the given distance, and take the 
 size of wire corresponding. But the example calls for the transmission 
 of five times this amount of power, and the size of wire varies directly 
 as the distance, which in this case is 12 miles. Therefore we look for 
 the product 5 X 12 = 60 in the 6000- volt column of the table. The 
 nearest value is 60.44 and the size of wire corresponding is No. 00, which 
 is, therefore, the size capable of transmitting 100 Kw. over a line 60.44 
 miles long, or 500 Kw. over a line 12 miles long, as required by the example. 
 
 If it is desired to ascertain the size of wire which will given an energy 
 loss of 5%, or one-half the loss for which the table is computed, it is 
 only necessary to multiply the value, obtained by 2, since the area 
 varies inversely as the per cent energy loss. 
 
 DISTANCES TO WHICH 100 Kw. THREE-PHASE CURRENT CAN BE TRANS- 
 MITTED OVER DIFFERENT SIZES OF WIRES AT DIFFERENT POTEN- 
 TIALS, ASSUMING AN ENERGY Loss OF 10% AND A POWER FACTOR 
 OF 85%. 
 
 Num- 
 
 Area in 
 
 Distance of Transmission for Various Potentials at 
 
 ber 
 
 Circular 
 
 Receiving End, in Miles. 
 
 B. & S. 
 
 Mils. 
 
 2,000 
 
 4,000 
 
 6.000 
 
 8,000 
 
 10,000 
 
 15,000 
 
 20.000 
 
 25,000 
 
 30,000 
 
 6 
 
 26,250 
 
 1.32 
 
 5.28 
 
 11.92 
 
 21.12 
 
 33.1 
 
 74.50 
 
 132.4 
 
 206.75 
 
 298 
 
 5 
 
 33,100 
 
 1.66 
 
 6.64 
 
 15.00 
 
 26.56 
 
 41.6 
 
 93.75 
 
 166.4 
 
 260.00 
 
 375 
 
 4 
 
 41,740 
 
 2.10 
 
 8.40 
 
 18.96 
 
 33.60 
 
 52.6 
 
 118.50 
 
 210.4 
 
 328.75 
 
 474 
 
 3 
 
 52,630 
 
 2.54 
 
 10.16 
 
 23.84 
 
 40.64 
 
 66.2 
 
 149.00 
 
 254.8 
 
 413.75 
 
 596 
 
 2 
 
 66.370 
 
 3.33 
 
 13.32 
 
 30.04 
 
 53.28 
 
 83.4 
 
 187.75 
 
 333.6 
 
 521.25 
 
 751 
 
 
 83,690 
 
 4.21 
 
 16.84 
 
 37.92 
 
 67.36 
 
 105.3 
 
 212.00 
 
 421.2 
 
 658.00 
 
 948 
 
 
 
 105,500 
 
 5.29 
 
 21.16 
 
 47.68 
 
 84.64 
 
 132.4 
 
 298.00 
 
 529.6 
 
 827.50 
 
 1192 
 
 00 
 
 133,100 
 
 6.71 
 
 26.84 
 
 60.44 
 
 107.36 
 
 167.9 
 
 377.75 
 
 671.6 
 
 1049.25 
 
 1511 
 
 000 
 
 167,800 
 
 8.45 
 
 33.80 
 
 76.16 
 
 135.20 
 
 211.4 
 
 476.00 
 
 845.6 
 
 1321.25 
 
 1904 
 
 0000 
 
 211,600 
 
 10.62 
 
 42.48 
 
 95.68 
 
 169.92 
 
 265.7 
 
 598.00 
 
 1062.8 
 
 1660.50 
 
 2392 
 
 
 250,000 
 
 12.58 
 
 50.32 
 
 113.32 
 
 201.28 
 
 3147 
 
 708.25 
 
 1258.8 
 
 1966.75 
 
 2833 
 
 
 500,000 
 
 25.17 
 
 100.68 
 
 226.64 
 
 402.72 
 
 629.4 
 
 1416.50 
 
 2517.6 
 
 3933.75 
 
 5666 
 
 Notes on High-tension Transmission. The cross-sectional area and, 
 consequently, weight of conductors vary inversely as the square of the 
 voltage for a given power transmission. The cost of conductors is there- 
 fore reduced 75% every time the voltage is doubled. The cost of other 
 apparatus and appliances increases with increasing voltage. For long- 
 distance lines the saving in copper with the 'highest practicable voltages 
 is so great that the other expenses are rendered practically negligible. In 
 the shorter lines, however, the" most suitable voltage must be determined 
 
1460 
 
 ELECTRICAL ENGINEERING. 
 
 in each individual case. The voltages in the following table will serve ad 
 a guide. 
 
 VOLTAGES ADVISABLE FOR VARIOUS LINE LENGTHS. 
 
 Miles. 
 
 Volts. 
 
 Miles. 
 
 Volts. 
 
 Miles. 
 
 Volts. 
 
 1-2 
 2-3 
 
 500-1000 
 1000-2300 
 2300-6600 
 
 3-10 
 10-15 
 15-20 
 
 6600-13,200 
 13,200-22,000 
 22,000-44,000 
 
 20-40 
 40-60 
 60-100 
 
 44,000- 66,000 
 66,000- 88,000 
 88,000-110,000 
 
 Standard machinery is made for 2300, 6600, 13,200, 22,000, 33,000, 
 44,000, 66,000, 88,000 and 110,000 volts, and standard generators are 
 made for the above voltages up to and including 13,200 volts. When 
 the line voltage is higjier than 13,200, step-up transformers must be 
 employed. In a given case the saving in cost of conductor by using the 
 higher voltage may be more than offset by the cost of transformers, and 
 the question of voltage must be determined for each case. 
 
 Line Spacing. Line conductors should be so spaced as to lessen the 
 tendency to leakage and to prevent the wires from swinging together 
 or against the towers. With suspended disk insulators the radius of free 
 movement is increased, and special account should be taken of spacing 
 when these insulators are used. The spacing should be only sufficient 
 for safety, since increased spacing increases the self-induction of the line, 
 and while it lessens the capacity, it does so only in a slight degree. The 
 following spacing is in accordance with average practice. 
 
 CONDUCTOR SPACING ADVISABLE FOR VARIOUS VOLTAGES. 
 Volts. Spacing. Volts. Spacing. 
 
 33,000 3 feet. 88,000 8 feet. 
 
 44,000 4 feet. 110,000 10 feet. 
 
 66,000 6 feet. 140,000 12 feet. 
 
 Aluminum Conductors. The conductivity of aluminum is generally 
 taken at 63.3%, that of hard-drawn copper of the same cross-sectional 
 area. The weight of Al is 30.2 % that of C9pper, and therefore an Al 
 conductor of the same length and conductivity as a given copper con- 
 ductor weighs 47.7% as much. The cost of Al must therefore be 2.097 
 times that of hard-drawn copper to give equal cost for the same length 
 and conductivity. Owing to the mechanical unreliability of solid Al 
 conductors, stranded conductors are used in all sizes, including even the 
 smallest. 
 
 The Size of the Line Conductors depends on both economical and 
 electrical considerations, except where the length of the span is the gov- 
 erning feature. With expensive steel towers it becomes necessary to 
 string the conductors for higher stresses so as to reduce the sags and 
 consequently the height of the towers as much as possible. It has, there- 
 fore, become a general practice to erect the conductors so that the stress 
 at the worst load conditions equals one-half the ultimate strength of the 
 conductor material, which gives a factor of safety of two. The load to 
 which a line conductor is subjected, besides its own weight and ice, is 
 acting in a vertical direction, the pressure imposed by the wind acting in 
 a horizontal direction. It is also evident that the stress will be greater 
 in extremely cold weather because of the contraction of the wires, and 
 it is generally agreed that the worst load condition would occur at F. 
 with an actual wind velocity of 56 miles per hour (8 pounds pressure 
 per square foot projected area) and with an ice covering one-half inch 
 thick. The maximum temperature is considered to be 130 F., and the 
 cables should be so supported that at this temperature the sag does not 
 become excessive, but allows a clearance between the lowest conductor 
 and ground of from 25 to 30 feet. 
 
 Line conductors may be either of copper or aluminum. It is advisable for 
 mechanical reasons in spans of 200 to 300 feet never to use smaller cable 
 than No. 5 B. & S. copper, or No. 1. B. & S. aluminum (equivalent of 
 No. 3 copper). For spans greater than 300 feet, the minimum sizes of 
 cable allowable are those which will give a reasonable sag at the most 
 severe^ climatic conditions assumed. Frequently the size of conductors, 
 
ELECTRIC MOTORS. 1461 
 
 determined by electrical considerations, limits the length of spans to a 
 smaller value than is economical. This may occur even with moderately 
 long spans 500 to 600 feet when the character of the country is such as 
 to make transportation costly or when expensive foundations must be 
 used. In such cases it will often be found that a saving can be made by 
 increasing the size of conductor, thereby allowing an increase in the length 
 of span and the use of fewer towers of approximately the same height and 
 not greatly increased weight. 
 
 The sag or deflection at the center of a span can be figured by the 
 formula: 
 
 ~ 8T 
 
 where D = deflection in feet; S = length of span in feet; W = resultant of 
 weight and wind in Ibs. per foot of cable; T = tension on cable in Ibs. 
 
 A 135,000- Volt Three-phase Transmission System from Cook Falls, 
 Mich., to Flint, Mich., 125 miles distant, is described in Power, Aug. 
 9, 1910. The generating equipment comprises three 3000-K.W. 
 GCFcycle alternators, mounted on horizontal shafts driven by water- 
 wheels. The available head of water is 40 ft., and the flow averages 
 1 100 cu. ft. per second. The transmission line consists of three No. 
 copper wires carried on suspension-type insulators hung from the cross- 
 arms of 55-ft. tripod steel towers. The wires are at the angles of an 
 isosceles triangle with a 12-ft. base and 17-ft. sides, the lowest wire 
 40 ft. above the ground. The insulators have eight disks linked in 
 series, each disk having been tested to withstand continuously 75,000 
 volts, and subjected to 100,000 volts for a brief period. 
 
 ELECTRIC MOTORS. 
 
 Classification. Motors maybe classified according to type, speed, and 
 mechanical features. The first cover: 
 
 Direct Current 1. Series. 2. Shunt. 3. Compound. 
 
 Alternating Current (single-phase and polyphase) 1. Synchronous. 
 2. Synchronous Induction. 3. Induction. 3a. Phase- wound. 3 b. Squirrel- 
 Cage. 4. Commutator. 
 According to their speed, they are classified as 
 
 Constant Speed: covering cases where the speed is constant or varies 
 slightly. 
 
 Adjustable Speed: covering cases where the speed may be varied over a 
 considerable range, but when once fixed remains at this value independent 
 of the load changes. 
 
 Varying Speed: covering cases where the speed changes with the 
 load, usually decreasing as the load increases. 
 
 Multi-Speed: covering cases where several -distinct speeds may be 
 obtained by changing the connections of the windings or by other means. 
 
 According to their mechanical features motors may be classified as: 
 (1) Open. (2) Mechanically Protected. (3) Semi-Enclosed. (4) Totally 
 Enclosed. (5) Enclosed, Externally Ventilated. (6) Enclosed, Self- Venti- 
 lated. (7) Moisture Proof. (8) Splash and Water Proof. (9) Submergible. 
 (10) Acid Proof. (11) Explosion Proof. 
 
 Limitations. The principal limitations in the ratings of motors are: 
 (1) Mechanical Strength. (2) Heating. (3) Commutation. (4) Reg- 
 ulation. (5) Efficiency. 
 
 CHARACTERISTICS OF MOTORS AFFECTING THEIR 
 APPLICATIONS. 
 
 (D. B. Rushmore, "American Handbook for Electrical Engineers.") 
 
 Series Motor. This motor is used when a powerful starting torque and 
 rapid acceleration are required, without an excessive instantaneous de- 
 mand of energy. The torque is practically independent of the voltage and 
 at low-flux densities varies directly as the square of the current, but as 
 the magnetization approaches saturation it becomes more nearly p:*opor- 
 tional to the first power of the current. The maximum torque exists at 
 
1462 ELECTRICAL ENGINEERING. 
 
 low speed, this being the most valuable feature of the series motor. 
 Dangerously high speeds may be attained by the armature with very 
 light loads, and series motors should for this reason be either geared or 
 direct connected to the load. 
 
 Speed Control of Series Motor. The speed of a series motor on 
 constant potential varies automatically with the load, increasing as the 
 load decreases. The speed may, however, be adjusted if some means of 
 varying the impressed voltage is provided. As the work required of a 
 series motor is very often intermittent in character, the insertion of re- 
 sistance in the armature circuit to reduce the speed is permissible from an 
 economic standpoint in such cases. In others, such as railway work, where 
 two or four motors are used, reduced voltage is most readily and economi- 
 cally obtained by connecting the motors in series or in series parallel. 
 
 Shunt Motor. This motor has good starting characteristics and a prac- 
 tically constant speed, varying only slightly with load changes. The speed 
 can, however, be adjusted, either by changing the e.m.f. impressed on the 
 armature or by changing the field flux. 
 
 Speed Adjustment by Armature-voltage Control, i.e., by changing 
 the e.m.f. impressed on the armature, does not change the full-load torque 
 which the motor is capable of exerting, since the rated torque depends only 
 upon field flux and rated armature current. These methods are therefore 
 constant-torque methods and are properly adapted to loads in which the 
 torque remains constant regardless of speed. The method most generally 
 used for varying the impressed e.m.f. with a single-voltage system is by 
 means of inserting resistance in series with the armature. The efficiency 
 with this method is, of course, very low at slow speeds. The speed regu- 
 lation with varying loads may also be very poor. 
 
 There are several systems of controlling the motor speeds by applying 
 different voltages, such as by the use of three-wire generators or two-wire 
 generators with balancer sets or by the Ward Leonard system. This latter 
 system, which is the most practical, consists of a constant-speed motor 
 driving a generator which supplies current to the motor whose speed is to 
 be adjusted. This arrangement is very satisfactory, but on account of the 
 expense of providing three full-sized machines instead of one to perform 
 the work, the cost may be prohibitive except with very large motors, such 
 iis for hoists, etc. 
 
 Speed Adjustment by Shunt-field Control, i.e., by inserting resistance 
 in the shunt-field circuit, is the simplest of all methods of speed variation, 
 but with ordinary shunt motors the range of speed variation by this means 
 is small. Where a variation of more than from 20 to 30 per cent is desired, 
 a motor of modified design and of a certain increased size is generally re- 
 quired, because the field must be more powerful with respect to the arma- 
 ture than in the case of standard single-speed motors. Variable-speed 
 motors of the field-weakening type are not constant torque, but constant- 
 output motors, i.e., the torque falls proportionally as the speed increases. 
 
 A speed variation up to 3 to 1 meets, as a rule, afl requirements, and such 
 motors can readily be obtained in commercial sizes. Should a greater 
 speed variation be desired, say 4 to 1 or 5 to 1, it is possible to accomplish 
 this by the commutating-pole shunt motor with field control only. A 
 combined field and armature control would, however, be a better method. 
 
 Compound Motor. This motor is provided with both a series and a 
 shunt field. The two fields are usually connected so that they act in the 
 same direction, in which case the motor is called a "cumulative" com- 
 pound motor. "Differential" compound motors, with the two fields 
 opposing, are sometimes employed for special services. The cumulative, 
 or ordinary, compound motor combines the characteristics of the shunt 
 and series motors, having a speed not extremely variable under load 
 changes, but developing a powerful starting torque and an increasing 
 torque with increasing load. Motors having a comparatively weak series 
 field are employed extensively in shop practice where the motor may be 
 required to start under heavy load, but must maintain an approximately 
 constant speed after starting, or when the load is removed. The heavily 
 compounded motor is used where powerful starting torque and rapid accel- 
 eration are necessary, with a speed not varying too widely under load 
 changes, such as for rolling mills, etc. 
 
 The speed control employed with compound motors may be any of the 
 various methods explained in connection witn the shunt motor. For 
 
CHAHACTEtttSTtCS OF MOTORS. 1463 
 
 certain service the control may be entirely rheostatic, the series winding 
 being cut out after the motor has come up to speed. 
 
 Induction Mo toy. The induction motor is essentially a constant-speed 
 machine, although the speed may be varied either by varying the applied 
 stator frequency or by introducing resistance in the rotor circuit. It is 
 built in two distinct types, namely, the squirrel-cage and the phase-wound. 
 
 Squirrel-cage Motor. The squirrel-cage type is used for constant- 
 speed service with infrequent starting. It has a relatively small starting 
 torque per ampere and draws a large starting current from the line. By 
 increasing the resistance of the rotor, it may, however, also be built in the 
 smaller sizes for a high starting torque, rapid acceleration and frequent 
 starting, for such applications as sugar and laundry centrifugals, etc., 
 where simplicity of control is desirable. They are also used for operat- 
 ing punches, shears, etc., where a fly-wheel is provided for storing the 
 ' energy. 
 
 Induction Motor with Wound Rotor. For service requiring high 
 starting torque combined with moderate starting current a motor with 
 the wound type of rotor is best adapted. A motor with the resistance 
 mounted inside the rotor should not be used to operate machinery having 
 large inertia or excessive static friction, since full starting current may be 
 required for a long period before the apparatus attains full speed, and, as 
 the capacity of the internal resistance is small, excessive temperatures may 
 result. This type of motor is, as a rule, not built above 200 horse-power, 
 due to mechanical difficulties involved in connection with the internal 
 resistance. 
 
 A motor with external resistance should be used for moderate and large 
 sizes. The rotor must then be provided with collector rings and brushes. 
 The contact resistance of these as well as the leads and the controller 
 fingers, which are in the circuit all the time, may impair the efficiency and 
 regulation of the motor, especially if the controller and the resistance are 
 located some distance from the motor. The phase-wound induction motor 
 with an external variable-rotor resistance is best adapted for a variable- 
 speed service, as the losses necessary to obtain reduced speeds are external 
 to the motor itself. 
 
 Multi-speed Induction Motors. It often happens that the service 
 is such that two or three speeds will be satisfactory for the operation of 
 the machinery and that these speeds must be independent of the load. 
 Under such conditions multi-speed motors can frequently be used. In 
 these motors the different synchronous speeds are produced by changing 
 the number of poles in the magnetic circuit. Each of these speeds is fixed, 
 if no resistance is used in the secondary circuit. With multi-speed motors, 
 as with single-speed motors, however, resistance may be used in the sec- 
 ondary circuit for varying the speed. 
 
 A change of the number of poles jnay be made hi any of the following 
 ways: 
 
 1. By the use of single magnetic and electric circuits, changing the 
 number of poles by re-grouping the coils. 2. By the use of single mag- 
 netic circuits and independent electric circuits. 3. By means of separate 
 magnetic and electric circuits, the so-called Cascade connection. 
 
 Synchronous Motor. The speed of a synchronous motor is constant, 
 being fixed by the number of poles and the frequency of the applied volt- 
 age. The single-phase type is not self-starting and the polyphase type has 
 in itself a very poor starting torque. They may, however, be made self- 
 starting in the same manner as squirrel-cage induction motors, by the use- 
 of an amortisseur or cage- winding, similar^in construction to that used 
 for induction motors. 
 
 The speed-torque curve of a synchronous motor is similar to that of an 
 induction motor except that the torque values are lower for a given resis- 
 tance of rotor winding on account of the construction of the machine. The 
 starting winding must be designed with both the load at start and the load 
 at synchronous speed in mind, because too great a slip may cause the 
 ' motor to shut down when the field is put on. It is, however, seldom that 
 the same motor will be called upon to start a heavy load and at the same 
 time synchronize a heavy load, as the load usually consists principally of 
 either static friction, as in the use of motor-generator sets, line shafting, 
 etc., or it comes up with the speed as in the case of a fan blower or centrif- 
 ugal pump. The former case would be met by a high-resistance squint 
 cage winding and the latter would require a low resistance. 
 
1464 ELECTRICAL ENGINEERING. 
 
 Single-phase Series Motor. This type of commutator 1 motor has a very 
 powerful starting torque, high power factor, and relatively high efficiency. 
 It is most generally used for traction work, the speed being controlled by 
 varying the applied voltage which can most readily be done by means of 
 an auto-transformer with a number of taps. 
 
 Repulsion Induction Motor. This type of commutator motor has a 
 limited speed and an increase of torque with decrease in speed. The action 
 of the compensating field insures a power factor approximately unity at 
 full load and closely approaching unity over a wide range in load. In ad- 
 dition, it serves to restrict the maximum no-load speed and also permits, 
 where varying speed service is involved, an increase over the synchronous 
 speed. 
 
 Starting of Repulsion Motors. A repulsion motor, if started by 
 directly closing the line switch, will develop about 21/2 times full-load 
 torque. The starting current corresponding to full-load starting torque is 
 from 2 to 21/4 times full-load running current. 'As a general rule, starting 
 boxes are not required up to and including 2-horse-power rating. From 
 2 to 5 horse-power the use of a rheostat is optional, dependent upon the 
 degree and care to be exercised in maintaining voltage regulation. Start- 
 ing boxes should, however, preferably be used on sizes above 5 horse- 
 power, especially where light and power circuits are combined. 
 
 Reversible Repulsion Motors. The repulsion motor may be designed 
 for reversible service. This is accomplished by adding an auxiliary revers- 
 ing winding spaced 90 from the main field winding and connected in 
 series with it. By reversing the relative polarity of the two wincttngs, 
 the direction of rotation is changed in a simpler manner than by mechani- 
 cal shifting of the brush holder yoke. Instant reversal may be effected 
 from full speed in one direction to full speed in the other, about 200 per 
 cent of normal running torque being developed at the moment of speed 
 reversal in either direction. 
 
 Variable-speed Repulsion Motors. In addition to the constant-speed 
 lepulsion motor, two other types are also available, one for constant- 
 torque and variable-speed service, the other for adjustable speed inde- 
 pendent of torque. In general, variable^speed repulsion motors are not 
 applicable to lathes, boring mills, or similar machines where the service 
 requires adjustable speed and constant horse-power at all speeds below 
 and above normal. When a certain amount of variable speed is required 
 lit approximately constant torque, such as in driving fans, blowers, print- 
 ing presses, etc., the repulsion motor successfully meets a wide field of 
 application. 
 
 MOTOR APPLICATIONS. 
 
 Pumps (E. A. Lof, in Coal Age), Pumps are either of the reciprocating 
 or centrifugal type. In the former the volume of water can be varied 
 either by changing the speed or by the use of a by-pass valve. The latter 
 method is, of course, less economical, and speed variation is, therefore, 
 preferable. In starting large pumps the water may, however, be delivered 
 through a by-pass until the motor is up to speed, when this passage is 
 gradually closed and the water delivered into the pipe system. The load 
 at starting, therefore, only consists of the friction losses, and usually does 
 not exceed 25 per cent of the full-load torque. 
 
 Either direct- or alternating-current motors may be used for driving 
 reciprocating pumps. When of the former class, the compound-wound 
 type is generally selected for single-acting pumps on account of their 
 rather pulsating load, while for duplex and triplex pumps, having steadier 
 characteristics of power demand, the shunt- wound motor is used to ad- 
 vantage. Both squirrel-cage and phase-wound induction motors are 
 suitable, the latter as a rule being selected where it is desirable to reduce 
 the starting current to a minimum or where a somewhat variable speed 
 is required. 
 
 Synchronous motors may also be used for driving large pumps of mod- 
 erate speed, and are admirably adapted for such service, while their 
 characteristics are such that by over-exciting their fields they may be 
 made to considerably improve the power factor of the system. By-pass 
 valves should preferably be provided on the pumps, when this type of 
 motor is employed, so as to reduce the starting current as much as possible. 
 
 In selecting the motor equipment for a centrifugal pump, its character- 
 istics as affected by the service conditions must be carefully predetermined, 
 
MOTOR APPLICATIONS. 1465 
 
 and in some respects the operating features of this type of water lift are 
 entirely opposite to those of reciprocating pumps. 
 
 With constant speed an increase of the resistance against which the 
 reciprocating pump operates increases the water pressure and, therefore, 
 the load on the motor, while with the centrifugal pump an increase of the 
 resistance reduces the load. The volume of water delivered by a recip- 
 rocating pump is not affected by the reduction of the head, but the 
 required power is lessened. A reduction of the head with a centrifugal 
 pump, however, increases the volume of water, and as the efficiency at the 
 same time goes down rapidly, the load increases. It is, therefore, of im- 
 portance to know what this overload, caused by a reduction of the head, 
 amounts to, and the duration of the overload; and the capacity of the 
 motor should, as a rule, be governed by the low- and not the high-head 
 conditions. 
 
 The starting condition must be given careful consideration in selecting 
 the motors. In starting a centrifugal pump the discharge valve may be 
 entirely closed until the motor comes up to speed, so that the latter may 
 start as nearly light as possible. As 'the machine accelerates, the water is 
 churned around in the casing, causing the motor to load up as it ap- 
 proaches full speed, when, with pumps of the usual design, it takes from 
 40 to 50 per cent of full-load torque to drive it even though pumping 
 no water. 
 
 Shunt-wound, direct-current motors and either squirrel-cage or phase- 
 wound induction motors are well adapted for this type of pump and will 
 readily meet the above conditions. A synchronous motor may lead to 
 difficulties unless precautions are taken in designing the squirrel-cage 
 starting winding with a sufficiently low resistance so that it will develop 
 enough torque to pull the motor into synchronism. When this is done, 
 however, the starting current is increased and a compromise must usually 
 be made. 
 
 Fans. Either direct- or alternating-current motors can be used for 
 driving fans. Where the air-supply must be regulated, such as in mines, 
 the motors must be of the adjustable-speed type. Direct-current motors 
 may be either of the shunt- or compound- wound type, the speed regulation 
 being accompanied by field control. Shunt-wound motors are generally 
 used, but compound-wound motors are preferable for very large fans 
 requiring a great starting torque. 
 
 With an alternating-current system, the phase-wound induction motor 
 should be used, the speed regulation being accomplished by inserting 
 resistance in the secondary rotor circuit. 
 
 Air Compressors. Air compressors may be divided in two classes, 
 centrifugal and reciprocating. The former require a high speed for their 
 operation, while the speed of the latter is comparatively low. 
 
 Shunt-wound, direct-current motors and both squirrel-cage and phase- 
 wound induction motors are used for driving them, the phase-wound type 
 being preferable for larger units, where a low starting current is desirable. 
 
 With direct-current systems, shunt-wound motors are usually used for 
 centrifugal compressors and compound-wound for the reciprocating type. 
 
 Hoists (E. A. Lof, in Coal Age}. The two principal classes of electric 
 mine-hoist equipments are: The direct-current motor operated from its 
 own motor-generator set by generator field control, and the induction 
 motor. The direct-current motor lends itself well to direct connection, as 
 the characteristics of slow-speed motors of this type are excellent. The 
 cost of a direct-connected motor will, in practically all cases, be higher 
 than that of a geared motor, but in. some instances this is largely offset by 
 the saving in gearing, etc. Where, however, a considerable saving can be 
 made by using a geared motor, and where the mechanical advantages of a 
 direct-connected hoist are not an important consideration, a geared direct- 
 current motor should be employed. Such a motor should be separately 
 excited and shunt-wound, and the current should be obtained from a 
 separately excited generator of similar type, both machines being driven 
 by a direct-coupled induction motor where the source of supply is alter- 
 nating current, as is almost invariably the case. 
 
 The control of the hoist motor is effected by regulating and reversing 
 the exciting current of the direct-current generator, thus varying the 
 voltage impressed upon the motor terminals. The current for the motor 
 and dynamo fields is supplied from the direct-connected exciter, and in, 
 
1466 ELECTRICAL ENGINEERING. 
 
 the case of the motor it is maintained constant. As the rapidity of hoist- 
 ing is practically proportional to the voltage impressed upon the motor 
 armature, the controlling gear is arranged so that the speed will be directly 
 proportional to the distance by which the controlling lever is moved away 
 from the neutral position. This system of hoisting has the great advan- 
 tage that the rheostatic losses are reduced to a minimum and that the 
 operator has perfect control over the motor. 
 
 In many cases it is highly desirable to reduce the instantaneous peak 
 loads and equalize the current input to the hoist. This is especially true 
 where the power charge is based wholly or partly on the maximum de- 
 mand, and any practicable method, therefore, by which energy may be 
 taken from the line and stored during periods of light load and discharged 
 when the hoist load is heavy, makes it possible to greatly reduce the 
 maximum input and consequently the charge for power. 
 
 The simplest method of effecting this is by adding a fly-wheel to the 
 motor-generator set, previously described. In order to permit the fly- 
 wheel to take care of the peaks, and equalize the load, the speed of the 
 set must be varied according to the demand for power. This is accom- 
 plished by an automatic slip regulator connected in i,he secondary circuit 
 of the induction motor, which, in this case, must be of the phase-wound 
 
 The second important class of electric hoisting systems is, as previously 
 stated, driven by induction motors. Excessive low-speed motors of this 
 type and of moderate capacities do not show particularly good electrical 
 characteristics. For large-capacity hoists at high-rope speeds, using as 
 small a drum diameter as is consistent with good practice, a direct- 
 connected induction motor is, in some instances, entirely feasible, and a 
 number of such equipments are in actual operation abroad. However, 
 the great majority of induction- motor-driven hoists now in use and which 
 will be installed in the future are and will continue to be of the geared type. 
 
 The induction motor must be of the phase-wound type, and the speed 
 control is accomplished by cutting in or out resistance in the secondary 
 circuit. Drum controllers with grid rasistances are used up to about 200 
 lorse-power, while between this and 400 horse-power it is customary to 
 provide a complete magnetic-contactor control. Above 400 horse-power 
 the liquid rheostat is usually employed as a secondary resistance and 
 control. 
 
 For equalizing the load taken by an induction-motor-driven hoist, a 
 fly-wheel motor balancer may be used. This consists of a shunt-wound or 
 compound-wound direct-current motor, connected to a heavy fly-wheel 
 and carrying a direct^connected exciter. The motor balancer is floated 
 indirectly across the incoming line circuit, being tied in by means of a 
 rotary converter or motor-generator set. A regulator actuated by the 
 line current controls the direct-current motor field, so that when the 
 power taken by the hoist drops below the average, the field is automati- 
 cally reduced, causing the fly-wheel set to speed up and absorb power 
 from the supply system and store it in the fly-wheel. When the load on 
 the hoist motor exceeds the average, the operation is reversed, the fly- 
 wheel set slows down, and power is returned to the system through the 
 rotary converter. 
 
 Machine Tools (Abstracted from C. Fair, General Electric Review, 1914). 
 In general, the most satisfactory electrical equipment for machine shops, 
 using a large number of motors, would be one having available both A.C. 
 and D.C. distribution; A.C. for all constant speed machines and D.C. for 
 adjustable speed machines. 
 
 In the smaller shops, with rare exceptions, the cilice of motors would 
 depend upon the current available, which in the majority of cases would 
 be alternating current. The size and product of the small factory make 
 a proper layout a comparatively simple matter, while in larger factories 
 skill and ingenuity are essential to obtain the most advantageous equip- 
 ment. The standard motor of to-day will answer for the majority of the 
 machine tools, although special motors are in some cases necessary. 
 
 When equipping tools with individual drives, the controlling apparatus 
 as well as the motor should be attached directly to the tool whenever 
 possible. In the case of portable tools this, of course, is a necessity. 
 
 A graphic recording wattmeter in circuit with a tool is of value in 
 efficient management, as it not only tells the actual power consumed t 
 
MOTOR APPLICATIONS. 
 
 1467 
 
 the machine, showing whether or not the tool is properly motored, but it 
 also shows whether the tool is operating at its maximum rate, by register- 
 ing the time of unproductive cycles or the length of time the tool is idle. 
 By analysis, the cause of the lost time may be discovered and a change of 
 operating conditions can be made with a corresponding increase in 
 production. 
 
 Motors for Machine Tools. 
 
 Tool 
 
 ] 
 
 D. C. 
 
 A. 
 
 C. 
 
 
 Shunt. 
 
 Comp. 
 
 * 
 
 t 
 
 Bolt cutter 
 
 y 
 
 
 * 
 
 
 Bolt and rivet header . 
 
 
 120% 
 
 # 
 
 t 
 
 Bulldozers 
 
 
 / 40% 
 {20% 
 
 
 T 
 
 Boring machines .... 
 
 y 
 
 (40% 
 
 ' * ' 
 
 
 Boring mills 
 
 v 
 
 
 * 
 
 
 Raising and lowering cross rails on bor- 
 ing mills and planers 
 
 ** 
 
 20% 
 
 
 f 
 
 
 v 
 
 
 * 
 
 
 Bending machines 
 
 
 {20% 
 
 * 
 
 t 
 
 
 *# 
 
 140% 
 {20% 
 
 
 
 
 
 I 50% 
 J 20% 
 
 ' # 
 
 jj 
 
 Centering machines 
 
 v 
 
 I 50% 
 
 ' * 
 
 
 Chucking machines 
 
 v 
 
 
 * 
 
 
 Boring, milling and drilling machines. . 
 Drill, radial 
 
 V 
 
 
 * 
 * 
 
 
 Drill press . 
 
 V 
 
 
 * 
 
 
 Grinder tool, etc 
 
 v 
 
 
 * 
 
 
 Grinder castings ... 
 
 v 
 
 20% 
 
 * 
 
 
 Gear cutters 
 
 v . 
 
 20% 
 
 * 
 
 
 
 
 {20% 
 
 
 t 
 
 Keyseater milling broach 
 
 v 
 
 (40% 
 
 ' * ' 
 
 
 Keyseater reciprocating . 
 
 
 20% 
 
 * - 
 
 
 Lathes 
 
 v 
 
 
 * 
 
 
 Lathe carriages 
 
 ** 
 
 50% 
 
 
 t 
 
 Milling machines 
 
 v 
 
 
 * 
 
 
 Heavy slab milling . . 
 
 V 
 
 20% 
 
 * 
 
 
 Pipe cutters 
 
 v 
 
 
 * 
 
 
 Punch presses 
 
 
 \m 
 
 * 
 
 t 
 
 Planers 
 
 
 I 40% 
 20% 
 
 ' * 
 
 t 
 
 Planers rotary . 
 
 v 
 
 io%? 
 
 * 
 
 
 Saw small circular 
 
 v 
 
 
 * 
 
 
 Saw cold bar and I-beam 
 
 
 20% 
 
 * 
 
 
 Saw hot 
 
 
 20% 
 
 * 
 
 
 Screw machine ... .... . . 
 
 v 
 
 
 * 
 
 
 Shapers 
 
 v 
 
 10% 
 
 * 
 
 
 Shears . *- 
 
 
 {20% 
 
 * 
 
 t 
 
 Blotters 
 
 v 
 
 ( 40% 
 20% 
 
 ' * ' 
 
 
 Swaging 
 
 
 *20% 
 
 * 
 
 t 
 
 Tappers 
 
 v 
 
 *40% 
 
 ' * ' 
 
 
 Tumbling barrels or mills 
 
 
 20% 
 
 * 
 
 
 * Squirrel cage rotor. 
 
 t Squirrel cage rotor high starting torque. 
 
 j Slip ring induction motor with external rotor resistance. 
 
 Does not apply to reversing motors. 
 
 ** D. C. series mo tor. 
 
1468 
 
 ELECTRICAL ENGINEERING. 
 
 The table on p. 1467 will, in a general way, aid in the choice of motors. 
 The great variety and size of tools of the same name make it necessary 
 in a general list, such as this, to double-check a number of tools. It 
 must be kept in mind, however, that various circumstances, such as size 
 and roughness of work, and fly-wheel capacity, etc., may call for radical 
 departures in the choice of motors, this list being compiled to meet average 
 conditions. 
 
 Shunt motors, for instance, are used in the following cases: When work 
 is of a fairly steady nature, when considerable range of adjustment of 
 speed is required, as on lathes and boring mills, and on group and line- 
 shaft drives, etc. 
 
 Compound-wound motors are used where there are sudden calls for 
 excessive power of short duration, as on planers without reversing 
 motor drives, punch presses, bending rolls, etc. 
 
 Series motors should be used where speed regulation is not essential, 
 and where excessive starting torque is required, as, for instance, in moving 
 carriages of large lathes, in raising and lowering the cross rails of planers 
 and boring mills, and for operating cranes, etc., but not where the motor 
 can be run without load, through the opening of a clutch, or by a belt 
 leaving ics pulley, as the motor would run away if the operator failed to 
 shut off the power. 
 
 When in doubt as to the choice of compound or series motors of small 
 horse-power, the choice might be determined by the simplicity of control 
 in favor of the series motor. 
 
 The alternating-current motor of the squirrel-cage rotor type corre- 
 sponds to the constant-speed, shunt, direct-current motor; but with a 
 high-resistance rotor it approaches more closely the characteristics of a 
 compound, direct-current motor. It is understood that the variable- 
 speed machines checked in the table above under the alternating-current 
 squirrel-cage rotor column have the necessary mechanical speed changes. 
 
 The slip-ring induction motor with external rotor resistance would be 
 used for variable speed, but this must not be construed to mean that it 
 corresponds to a direct-current, adjustable-speed motor, as it has the 
 characteristics of a direct- current shunt motor with armature control. 
 
 The self-contained, rotor resistance type could be used for lineshaft 
 drives, and for groups when of sufficient size. 
 
 Multi-speed, alternating-current motors are those giving a number of 
 definite speeds, usually 600 and 1200, or 600, 900, 1200, and 1800 r.p.m., 
 and are made for both constant power and constant torque. These motors 
 would be used where alternating current only was available, and where 
 the speed ranges of the motor, together with one or two change gears, 
 would give the required speeds. These motors should, however, be used 
 with discretion, especially on sizes above six horse-power. 
 
 The adjustable speed, A.C., commutator brush-shifting type of motor 
 wifch shunt characteristics would, on account of high cost, be used mostly 
 where an adjustable speed motor w^as highly desirable and where A.C. 
 only was available and where there were not enough machines calling for 
 adjustable speed drive to warrant putting in a motor-generator set. 
 
 ILLUMINATION ELECTRIC AND GAS LIGHTING.* 
 
 Illumination. Some writers distinguish "lighting" and "illumina- 
 tion." Lighting refers to the character of the lights themselves, as 
 dazzling, brilliant, or soft and pleasing, and illumination to the quantity 
 of light reflected from objects, by which they are rendered visible. If 
 the objects in a room are clearly seen, then the room is well illuminated. 
 
 The quantity of light is estimated in candle-power per square foot of 
 area or per cubic foot of space. The amount of illumination given by 
 one candle at a distance of 1 ft. is known as a foot-candle. Since the 
 illumination varies inversely as the square of the distance, one foot- 
 candle is given by a 16-candle-power lamp at a distance of 4 ft., or by a 
 25-c.-p. lamp at a distance of 5 ft. 
 
 Terms, Units, Definitions. Quantity of light proceeding from a 
 source of light, measured in units of luminous flux, or lumens. 
 
 Intensity with which the flux is emitted from a radiant in a single 
 direction, called candle-power. 
 
 Illumination, density of the light flux incident upon an area. 
 
 * Contributed by Prof. W. H. Timbie. 
 
ILLUMINATION. 1469 
 
 Luminosity, brightness of surface; flux emitted per unit area of 
 surface. 
 
 Candle-power, the unit of luminous intensity. A spermaceti candlo- 
 burning at the rate of 120 grains per hour is the old standard used in 
 the gas industry. It is very unsatisfactory as a standard and is being 
 displaced by others. 
 
 The hefner lamp, burning amyl acetate, is the legal standard in Ger- 
 many. The unit of luminous intensity produced by this lamp when 
 constructed and operated as prescribed is called a hefner. The standard 
 laboratories of Great Britain, France, and America have agreed upon 
 the following relative values of the units used in the several countries: 
 1 International Candle = 1 Pentane Candle = 1 Bougie Decimale = J 
 American Candle =1.11 Hefners = 0.104 Carcel unit. 1 Hefner = 
 0.90 International Candle. 
 
 Intrinsic Brilliancy of a source of light = candle-power per square 
 inch of surface exposed in a given direction. 
 
 Lumen, the unit of luminous flux, is the quantity of light included in 
 a unit solid angle and radiated from a source of unit intensity. A unit 
 solid angle is the angular space subtended at the surface of a sphere by 
 an area equal to the square of the radius, or by 1 -r-4n, or 1/12.5664 of 
 the surface of the sphere. The light of a source whose average intensity 
 in all directions is 1 candle-power, or one mean spherical candle-power, 
 has a total flux of 12.5664 lumens. 
 
 Foot-candle, the unit of illumination, = 1 lumen per square foot; the 
 illumination received by a surface every point of which is distant one 
 foot from a source of one candle-power. 
 
 Lux, or meter-candle, 1 lumen per square meter; 1 foot-candle = 10.76 
 meter-candles. 
 
 Law of Inverse Squares. The illumination of any surface is inversely 
 proportional to the square of its distance from the source of light. This 
 is strictly true when the source of light is a point, and is very nearly 
 true in all cases when the distance is more than ten times the greatest 
 dimension of the light-giving surface. 
 
 Law of Cosines. When a surface is illuminated by a beam of light 
 striking it at an angle other than a right angle, the illumination is pro- 
 portional to the cosine of the angle the beam makes with a normal to 
 the surface. 
 
 If E = the illumination at any point in a surface, I the intensity of 
 light coming from a source, Q the angle of deviation of the direction of 
 the beam from a normal to the surface, and I the distance from the 
 source, then E = I cos 6 ~ I*. 
 
 Relative Color Values of Various Illuminants. The light pro- 
 ceeding from any source may be analyzed in terms of the elementary 
 color elements, red, green and blue, by means of the spectroscope, or by 
 a colorimeter. The following relative values have been obtained by 
 the Ives colorimeter (Trans. III., Eng. Soc., iii, 631). In all cases the 
 red rays in the light are taken as 100, and the two figures given are 
 respectively the proportions of green and blue relative to 100 red. 
 
 Average daylight, 100,100. Blue sky, 106,120. Overcast sky, 92, 85. 
 Afternoon sunlight, 91, 56. Direct-current carbon arc, 64, 39. Mercury 
 arc (red 100), 130, 190. Moore carbon dioxide tube, 120, 520. Wels- 
 bach mantle, 3/4% cerium, 81, 28. Do., 11/4% cerium, 69, 14.5. Do., 
 13/4% cerium, 63, 12.3. Tungsten lamp, 1.25 watts per mean horizon- 
 tal candle-power, 55, 12.1. Nernst glower, bare, 51.5, 11.3. Tantalum 
 lamp, 2 watts per m. h. c.-p., 49, 8.3. Gem lamp, 2.5 watts per m. h. 
 c.-p., 48, 8.3. Carbon incandescent lamp, 3.1 watts per m. h. c.-p., 45, 
 7.4. Flaming arc, 36.5, 9. Gas flame, open fish-tail burner, 40, 5.8. 
 Moore nitrogen tube, 28, 6.6. Hefner lamp, 35, 3.8. 
 
 Relation of Illumination to Vision. Wickenden gives the following 
 summary of the principles of effective vision: 
 
 1. The eye works with approximately normal efficiency, upon sur- 
 faces possessing an effective luminosity of one foot-candle or more. 
 
 2. Excessive illumination and inadequate illumination strain and 
 fatigue the eye in an effort* to secure sharp perception. 
 
 3. Intrinsic brilliancy of more than 5 c.-p. per sq. in. should be re- 
 duced by a diffusing medium when the rays enter the eye at an angle 
 below 60 with the horizontal. 
 
1470 ELECTRICAL ENGINEERING. 
 
 4. Flickering, unsteady, and streaky illumination strains the retina 
 in the effort to maintain uniform vision. 
 
 5. True color values are obtained only from light possessing all the 
 elements of diffused daylight in approximately equivalent proportions. 
 
 6. An excess of ultra-violet rays is to be avoided for hygienic reasons. 
 
 7. Esthetic considerations commend light of a faint reddish tint- as 
 warm and cheerful in comparison with the cold effects of the green tints, 
 although the latter are more effective in revealing fine detail. 
 
 Types of Electric Lamps. The carbon arc lamp is now rapidly dis- 
 appearing on account of the cost of maintenance of the open type and 
 the low efficiency of the enclosed type. Gas-filled tungsten lamps now 
 operate at less cost on the same circuits on which these arcs formerly 
 burned. 
 
 The Flaming Arc. The carbons are impregnated with calcium fluor- 
 ide or other luminescent salts. The current is usually 8 to 12 amperes 
 and the voltage per lamp 35 to 60. The regenerative flame arc is a 
 highly efficient variety of the flame arc. 
 
 The Magnetite Arc has for a cathode a thin iron tube packed with- a 
 mixture of magnetite, FesCU, and titanium and chromium oxides. The 
 anode consists of copper or brass. It is well adapted to series opera- 
 tion with low currents. The 4-ampere lamp, using 80 volts per lamp, 
 is highly successful for street illumination. 
 
 The Tungsten Incandescent (vacuum) depends upon the heating of 
 a drawn tungsten filament to incandescence in a vacuum. They are 
 made in sizes for 25, 40, 60, 100, 150, 250, 400, 500, 750, and 1000 watts 
 and average about 1 candle-power for each watt, with a life of 1000 
 hours, before the candle-power falls below 80% at rated voltage. 
 
 The Tungsten Incandescent (gas-filled) has the advantage of having 
 longer life and being smaller than the vacuum lamp of the same watt- 
 age. They are filled with an inert gas, generally nitrogen or argon, 
 and have an efficiency of 2 candle-power per watt in the larger 'sizes 
 (the average being about 1.7 candle-power per watt), with a life of 
 1300 hours. 
 
 The Mercury Vapor Lamp is an arc of luminous mercury vapor con- 
 tained in a glass tube from which the air has been exhausted. A small 
 quantity of mercury is contained in the tube, and platinum wires are 
 inserted in each end. When the tube is placed in a horizontal position 
 so that a thin thread of mercury lies along it, making electrical con- 
 nection with the wires, and a current is passed through it, part of the 
 mercury is vaporized, and on the tube being inclined so that the liquid 
 mercury remains at one end, an electric arc is formed in the vapor 
 throughout the tube. The tubes are made about one inch in diameter 
 and of different lengths, as below. The mercury vapor lamp is very 
 efficient, ranging from 1.9 c.-p. per watt for the 900 c.-p. size to 1.55 
 c.-p. per watt for the 300 c.-p. size. The color of the light is unsatis- 
 factory, being deficient in red rays, but it possesses a very penetrating 
 quality which makes it valuable in drafting rooms and wherever a 
 light is needed to bring small details out sharply. The spectrum con- 
 sists of three bands, of yellow, green, and violet, respectively. The 
 intrinsic brilliancy of the lamp is very moderate, about 17 c.-p. per sq. 
 in. Commercial lamps are made of the sizes given below. The lamp 
 is essentially a direct-current lamp, but it may be adapted to alternat- 
 ing-current by use of the principle of the mercury-arc rectifier. The 
 tubes have a life ordinarily of about 1000 hours. 
 
 The Quartz-Tube Mercury-Arc Lamp operates at a higher voyage 
 and gives much nearer a white light. Owing to the injurious ultra- 
 violet rays given out by this form, it must always be enclosed in a 
 globe of clear glass. The efficiency ranges from 2.4 to 3.3 c.-p. per 
 watt and the life averages 3000 hours. It is made in sizes from 1000 
 to 3500 c.-p. 
 
 Street Lighting. Street lighting may be divided into three classes: 
 
 (a) "White-Way" or display illumination. 
 
 (b) Main road illumination. 
 
 (c) Residence district lighting. 
 
 The object of " White- Way" illumination is generally advertising and 
 many more lights are used than are necessary for proper road illumina- 
 tion. The lamps generally used are the titanium arc, the magnetite 
 
ILLUMINATION. 
 
 1471 
 
 arc, the yellow flaming arc, and the white flaming arc of over 1000 c.-p. 
 See last column of Table VI. 
 
 In "Main-road" illumination the purpose is to illuminate the road 
 appreciably for night automobile travel. The lamps generally used 
 are some type of the 300-watt flaming arc, the magnetite arc, or the 
 titanium arc of Table IV. These are usually placed from 200 to 300 
 ft. apart at heights varying from 15 to 18 ft. 
 
 For Residential-district Lighting, where vehicle travel is infrequent 
 and slow, the smaller sizes (40 to 100 c.-p.) of tungsten lamps are used 
 spaced from 100 to 200 ft. at height varying from 15 to 18 ft. according 
 to shading of the road by the foliage. Tungsten lamps of the higher 
 candle-powers of 200 to 450 are also used with spacings of 200 ft. and 
 over, with reflectors designed to give the best distribution of the light. 
 
 I Hum illation by Arc Lamps at Different Distances. Several dia- 
 grams and curves showing the light distribution in a vertical plane 
 and the illumination at different distances of different types of lamps 
 are given by Wickenden. From the latter are taken the approximate 
 figures in the table below. The carbon and the magnetite lamps were 
 25 ft. high, the flame arcs 21 ft. 
 
 TABLE I. Illumination by Arc Lamps. 
 
 Horizontal Distance from Lamp, Feet. 
 
 20 
 
 30 
 
 40 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 Kind of Lamp. 
 
 Foot-candles, normal illumination. 
 
 A. Open carbon arc, D.C., 6.6 amp. 
 B. Enclosed carbon arc, A.C. 6.6 
 C. Flame arc, 10 
 D. Regenerative arc, 7 
 E. Magnetite arc, 6.6 
 F. Magnetite arc, 4 
 
 6!io 
 
 0.40 
 0.19 
 
 0.29 
 .135 
 
 0.20 
 0.10 
 1.10 
 0.65 
 0.51 
 0.21 
 
 .032 
 .027 
 .31 
 .15 
 .15 
 .07 
 
 .OH 
 .013 
 .14 
 .055 
 .075 
 .035 
 
 .006 
 .006 
 .08 
 .03 
 .045 
 .022 
 
 .002 
 .002 
 .05 
 .02 
 .025 
 .018 
 
 
 
 0.85 
 0.69 
 0.30 
 
 6'.47 
 
 1.00 
 0.40 
 
 A. 6.6 amp., D.C., open arc, clear globe. 
 
 B. 6.6 amp., A.C., enclosed arc, opal inner and clear outer globe, 
 small reflector. 
 
 C. 10 amp., flame arc, vertical electrodes; 50 volts, 1520 M.H. C.-P.*; 
 0.33 watt per M.L.H.C.-P.*; 10 hours per trim. 
 
 D. 7 amp., regenerative flame arc, 70 volts, 2440 M.L.H.C.-P., 0.2 
 watt per M.L.H.C.-P., 70 hours per trim. 
 
 E. 6.6 amp., B.C. series magnetite arc, 79 volts, 510 watts, 1450 
 M.L.H.C.-P. 75 to 100 hours per trim. 
 
 F. 4 amp., B.C. series magnetite arc, 80 volts, 320 watts, 575 M.L.H. 
 C.-P., 150 to 200 hours per trim. 
 
 TABLE II. Data of Some Arc Lamps. 
 
 Type of Lamp. 
 
 Hours 
 Trim. 
 
 Am- 
 peres. 
 
 Ter- 
 minal 
 Volts. 
 
 Ter- 
 minal 
 Watts. 
 
 Watts 
 per 
 M.L.H. 
 C.-P. 
 
 D.C. series carbon, open 
 
 9 to 12 
 
 9 6 
 
 50 
 
 480 
 
 6 
 
 D.C. series carbon, enclosed 
 A.C. series carbon, enclosed 
 D.C. multiple carbon, enclosed. . 
 A.C. multiple carbon, enclosed. . . 
 D.C. flame arcs, open 
 
 100 to 150 
 70 to 1 00 
 100 to 150 
 70 to 100 
 10 to 16 
 
 6.6 
 7.5 
 5.0 
 6.0 
 10 
 
 72 
 75 
 110 
 110 
 55 
 
 475 
 480 
 550 
 430 
 440 
 
 0.9 
 1.25 
 2.25 
 2.40 
 0.45 
 
 Regenerative, semi-enclosed 
 A.C. flame arcs, open 
 
 70 
 10 to 16 
 
 5 
 10 
 
 70 
 55 
 
 350 
 467 
 
 0.26 
 0.55 
 
 Magnetite, open 
 
 70 to 100 
 
 6.6 
 
 80 
 
 528 
 
 0.45 
 
 Values of watts per M.L.H. C.- P. approximate for open carbon arcs and 
 magnetite arcs with clear globes, enclosed arcs with opalescent inner and 
 clear outer globes, and for flame and regenerative arcs with opal globes. 
 
 * M.H. C.-P. =mean horizontal candle-power; 
 
 ,-P, =mean lower hemispherical candle-power, 
 
1472 
 
 ELECTRICAL ENGINEERING. 
 
 Relative Efficiency of Dluminants. The advent of the gas-filled 
 tungsten incandescent lamp of high efficiency and high candle-power 
 has driven the less efficient arc lamps from the field. At present (1915) 
 the incandescent lamp of the 200- or 300-watt size is more efficient than 
 the arc lamp of the same candle-power. On the other hand, the 1000- 
 c.-p. arcs are more efficient than the incandescent lamps of the same 
 size. The field for the arc lamp seems to be in the higher candle-power 
 sizes. Dr. Steinmetz in The General Electric Review for March, 1914, 
 gives the following tables. 
 
 r TABLE III. Relative Efficiency of Dluminants. 
 
 (Irrespective of Size, in Available Mean Spherical C.-P. per Watt). 
 
 
 Available 
 Mean 
 Spherical 
 C.-P. per 
 Watt. 
 
 (Street 
 Lighting) 
 10 C.-P.* 
 per Watt 
 
 Available 
 Mean 
 Spherical 
 C.-P. 
 
 3.1 watt per h. c.-p. carbon filament. . . . 
 2.5 watt per h. c.-p. gem filament 
 450 watt 6.6 amp. series enclosed a.c. 
 carbon arc . 
 
 0.21 
 0.26 
 
 0.39 
 
 0.4 
 0.5 
 
 0.5 
 
 Any 
 Any 
 
 175 
 
 Nitrogen M^oore tube 
 
 45 
 
 
 
 480 watt 6.6 amp. series enclosed d.c. 
 carbon arc 
 
 (D.62 
 
 1.0 
 
 300 
 
 1 watt per h. c.-p. mazda lamp 
 500 watt d.c. "intensified" carbon arc . 
 
 0.64 
 0.78 
 
 1.25 
 
 Any 
 
 4 amp. 300 watt d.c. special magnetite arc 
 Neon M^oore tube 
 
 .0 
 
 2.2 ' 
 
 300 
 
 0.5 watt per h. c.-p. gas-filled mazda lamp 
 4 amp. 300 watt d.c. special magnetite arc 
 6.6 amp. 500 watt d.c. standard magnetite 
 arc 
 
 .28 
 .4 
 
 .5 
 
 2.5 
 3.0 
 
 3.2 
 
 Above 350 
 
 (420) 
 
 750 
 
 Mercury lamp in glass tube, best values 
 
 55 
 
 
 
 6.6 amp. 500 watt d.c. special magnetite 
 arc . . . 
 
 .7 
 
 3.6 
 
 850 
 
 220 watt a.c. titanium arc 
 300 watt yellow flame arc, best value. . . . 
 500 watt white flame arc, best values. . . . 
 Mercury lamp in quartz tube, best values 
 
 .9 
 .95 
 .95 
 2 
 
 4.0 
 4.0 
 4.0 
 
 420 
 
 (585) 
 (975) 
 
 Exper. 350 watt a.c. titanium arc 
 Melting tungsten in vacuum 
 
 2.7 
 2 88 
 
 5.4 
 
 (950) 
 
 500 watt yellow flame arc, best value. . . . 
 Exper. 500 watt a.c. titanium arc ....... 
 Titanium arc, best values (high power) . . 
 
 3.1 
 
 3.6 
 5.2 
 
 6.2 
 7.0 
 
 (1550) 
 (1800) 
 
 *The expression 10 c.-p. per watt means the candle-power per watt 
 on a circle 10 below the horizontal plane of the filament. 
 
 TABLE IV. Efficiency of 300-Watt llluminants. 
 
 
 Available 
 Mean 
 Spherical 
 C.-P. per 
 Watt. 
 
 Available 
 Mean 
 Spherical 
 C.-P. 
 
 Mazda lamp (1 watt per h. c.-p).. . . ... 
 
 0.64 
 
 190 
 
 Standard 4 amp. d.c. magnetite arc 
 
 .0 
 
 300 
 
 White flame carbon arc, best 
 
 .2 
 
 360 
 
 Gas-filled mazda lamp (0.5 watt per h. c.-p.) 
 
 .28 
 
 384 
 
 Special 4 amp. d.c. magnetite arc 
 
 4 
 
 420 
 
 Yellow flame carbon arc, best 
 
 .95 
 
 585 
 
 A.C. titanium arc 
 
 2.4 
 
 720 
 
ILLUMINATION. 
 
 1473 
 
 TABLE V. Efficiency of 500-Watt Illuminants. 
 
 
 Available 
 Mean 
 Spherical 
 C.-P. per 
 Watt. 
 
 Available 
 Mean 
 Spherical 
 C.-P. 
 
 A.C. series enclosed carbon arc 
 
 0.42 
 
 210 
 
 Mazda lamp (1 watt per h. c.-p.) 
 
 64 
 
 320 
 
 D.C. series enclosed carbon arc 
 
 0.65 
 
 325 
 
 Gas-filled mazda lamp (0.5 watt per h. c.-p.) 
 
 1.28 
 
 640 
 
 Standard 6.6 amp. d.c. magnetite arc 
 
 1.5 
 
 750 
 
 Special 6.6 amp. d.c. magnetite arc 
 
 1 7 
 
 850 
 
 White flame carbon arc, best 
 
 1 95 
 
 975 
 
 Quartz mercury lamp 
 
 2 
 
 1000 
 
 Yellow flame carbon arc, best 
 
 3 ] 
 
 1550 
 
 A.C. titanium arc 
 
 3.6 
 
 1800 
 
 Characteristics of Tungsten Lamps. Vacuum Type. The accom- 
 panying Table VII refers to tungsten lamps of the 25, 60, and 100 watt 
 size. They show the changes which take place in the candle-power, 
 watts, watts per candle-power and life when used at the various voltages. 
 It is to be noted that a 4% increase in voltage above the normal (100%) 
 increases the candle-power 15%, the efficiency 6%, but decreases the 
 life 38%. 
 
 TABLE VI. Relative Efficiency of Various C-P. of Illiiminaiits. 
 
 200 Mean 
 Spherical 
 C.-P. 
 
 300 Mean 
 Spherical 
 C.-P. 
 
 400 Mean 
 Spherical 
 C.-P. 
 
 500 Mean 
 Spherical 
 C.-P. 
 
 1000 Mean 
 Spherical 
 C.-P. 
 
 Type. 
 
 S 
 
 
 
 Type. 
 
 1 
 
 Type. 
 
 4^ 
 
 1 
 
 Type. 
 
 
 
 
 
 Type. 
 
 1 
 
 A.C. 
 
 carbon 
 D.C. 
 carbon 
 Mazda 
 
 490 
 
 380 
 310 
 
 A.C. 
 
 carbon 
 D.C. 
 carbon 
 Mazda 
 
 Standard 
 magnetite 
 Special 
 magnetite. . 
 
 620 
 
 480 
 470 
 
 300 
 250 
 
 Mazda . . . 
 
 6?n 
 
 Standard 
 magnetite 
 
 400 
 
 Gas-filled 
 mazda 
 
 780 
 700 
 55C 
 520 
 
 400 
 360 
 
 Standard 
 magnetite. 
 Gas-filled 
 mazda 
 Special 
 magnetite. . 
 
 Titanium. . 
 
 350 
 310 
 290 
 210 
 
 Gas-filled 
 mazda 
 Special 
 magnetite . . 
 White 
 Flame 
 Yellow 
 Flame 
 Titanium. . 
 
 390 
 350 
 350 
 
 280 
 250 
 
 Standard 
 magnetite. . 
 Special 
 magnetite. . 
 White 
 Flame 
 Yellow 
 Flame 
 Titanium . . 
 
 
 
 
 
 Interior Illumination. There are three systems for artificially light- 
 ing interiors. All three are easily adapted for the use of either gas or 
 electricity or both: (1) Direct lighting; (2) indirect lighting; (3) semi- 
 indirect lighting. 
 
 (1) Direct Lighting. When the room is illuminated almost entirely 
 by the light which comes directly from the lamps without reflection 
 from walls and ceilings, it is said to be illuminated by direct lighting. 
 This is the usual form of lighting. 
 
 (2) Indirect Lighting. When a room is illuminated by the light of 
 concealed lamps which is reflected from the walls and ceiling, ,the 
 system of illumination is said to be indirect. The ceiling and walls 
 must be light-colored. There is an entire lack of shadows in a room 
 thus lighted. 
 
 (3) Semi-indirect Lighting. When a room is illuminated mostly by 
 light reflected from the walls and ceiling but still receives 15 or 20% 
 directly from the lamps, the system of illumination is said to be semi- 
 indirect. This system produces particularly pleasing effects. 
 
 The Quantity of Electricity and Gas Necessary to Illuminate Various 
 Rooms. Practically all modern illumination is done either by tungsten 
 incandescent electric lamps or gas lamps with incandescent mantles. 
 
1474 
 
 ELECTRICAL ENGINEERING. 
 
 TABLE VII. Characteristics of Mazda (Vacuum) Lamps. 
 
 Per Cent of 
 Rated Voltage. 
 
 o '. 
 
 jjj 
 
 s^ 
 
 Per Cent of 
 Rated Watts. 
 
 Efficiency in 
 C.-P. per Watt. 
 
 Life in Per Cent 
 of Rated Life. 
 
 Per Cent of 
 Rated Amperes. 
 
 Per Cent of 
 Rated Ohms. 
 
 Per Cent of 
 Rated Voltage. 
 
 Per Cent of 
 Rated C.-P. 
 
 Per Cent of 
 Rated Watts. 
 
 Efficiency in 
 C.-P. per Watt. 
 
 Life in Per Cent 
 of Rated Life. 
 
 Per Cent of 
 Rated Amperes . 
 
 Per Cent of 
 Rated Ohms. 
 
 50 
 
 8 
 
 33 
 
 
 
 67 
 
 77 
 
 10? 
 
 108 
 
 103 
 
 934 
 
 80 
 
 
 
 60 
 70 
 75 
 
 15 
 
 27 
 36 
 
 44 
 57 
 63 
 
 0.231 
 0.429 
 0.500 
 
 
 72 
 82 
 84 
 
 80 
 
 87 
 88 
 
 104 
 106 
 108 
 
 115 
 123 
 130 
 
 106 
 110 
 113 
 
 0.971 
 .01 
 .03 
 
 62 
 48 
 35 
 
 "103" 
 
 "l6i' 
 
 80 
 
 45 
 
 71 
 
 578 
 
 
 88 
 
 92 
 
 110 
 
 139 
 
 117 
 
 08 
 
 25 
 
 106 
 
 104 
 
 85 
 
 57 
 
 77 
 
 0.658 
 
 
 91 
 
 94 
 
 115 
 
 161 
 
 
 .16 
 
 
 108 
 
 106 
 
 90 
 92 
 94 
 96 
 Q8 
 
 69 
 75 
 81 
 87 
 93 
 
 85 
 88 
 91 
 94 
 97 
 
 0.736 
 0.769 
 0.799 
 0.833 
 880 
 
 230 
 180 
 135 
 
 94 
 96 ' 
 
 96 
 ' '98 ' 
 
 120 
 125 
 130 
 140 
 150 
 
 187 
 213 
 242 
 
 133 
 142 
 
 .27 
 .35 
 .47 
 .67 
 85 
 
 
 112 
 114 
 117 
 122 
 127 
 
 108 
 110 
 112 
 115 
 118 
 
 100 
 
 100 
 
 100 
 
 0.909 
 
 100 
 
 100 
 
 100 
 
 
 
 
 
 
 
 
 The following table of electricity and gas necessary to light rooms 
 used for given purposes is based on the fact that in the modern mazda 
 lamps 1.1 watt produces 1 c.-p., and in the best gas lamps with incan- 
 descent mantles, 0.04 cu. ft. per hour of gas produces 1 c.-p. Inasmuch 
 as there are no bright spots in the room to fatigue the eye, when in- 
 direct and semi-indirect systems are used, a lower degree of illumina- 
 tion is sufficient to enable objects to be clearly seen. Hence, although 
 the indirect and semi-indirect systems are less efficient, the following 
 table applies to. all these methods : 
 
 TABLE VIII. Electricity or Gas Necessary to Sufficiently 
 Illuminate Booms. 
 
 Use of Rooms. 
 
 Watts 
 
 S?2?- 
 
 Work- 
 ing 
 Plane. 
 
 Cu. Ft. 
 per Hour 
 per Sq. 
 Ft. of 
 Working 
 Plane. 
 
 Use of Rooms. 
 
 Watts 
 per Sq. 
 Ft. of 
 Work- 
 ing 
 Plane. 
 
 Cu. Ft. 
 per Hour 
 per Sq. 
 Ft. of 
 Working 
 Plane. 
 
 Assembly hall .... 
 Ball room . 
 
 0.8-0.1 
 1.2-1.3 
 
 0.032-0.04 
 0.05 -0.052 
 
 Library (book 
 stacks) 
 
 0.3-0.6 
 
 0.012-0.24 
 
 Barber shop 
 Bed room (resi- 
 dence) 
 Church 
 Class room 
 (school) 
 Corridor 
 Dining room 
 (residence) 
 Drafting room . . . 
 Drill hall . . 
 
 1.5-1.7 
 
 0.3-0.35 
 1.0-1.3 
 
 1.2-1.3 
 0.4-0.5 
 
 0.9-1.0 
 2.5-2.8 
 0.5-0.6 
 
 0.06 -0.07 
 
 0.012-0.014 
 0.04 -0.05 
 
 0.048-0.052 
 0.016-0.02 
 
 0.036-0.04 
 0.10 -0.112 
 0.02 -0.025 
 
 Library (resi- 
 dence) 
 Lobby (hotel) 
 Machine shop. . . . 
 Music room (resi- 
 dence) 
 Office (banking 
 and accounting) . 
 Office (general).. . 
 Operating room 
 (hospital) 
 
 1.0-1.1 
 1.5-1.6 
 2.0-2.2 
 
 0.5-0.6 
 
 1.5-1.6 
 1.3-1.5 
 
 3.5-3.9 
 
 0.04 -0.044 
 0.06 -0.065 
 0.08 -O.OCC 
 
 0.02- 0.025 
 
 0.06 -0.065 
 0.052-0.06 
 
 0.14 -0.15 
 
 Foundry 
 Kitchen 
 Library (public 
 reading room).. . 
 
 3.0-4.0 
 1.2-1.3 
 
 1.4-1.5 
 
 0.12 -0.16 
 0.05 -0.052 
 
 0.055-0.06 
 
 Restaurant 
 Store 
 Warerooms 
 Wood-working 
 shop 
 
 1.5-1.7 
 1.4-1.7 
 0.3-0.9 
 
 1.5-1.8 
 
 0.06 -0.07 
 0.055-0.07 
 0.012-0.030 
 
 0.06 -0.072 
 
 For gas-filled tungsten and Welsbach "Kinetic" use 0.6 of above 
 values. Data on gas furnished by F. R. Pierce, Welsbach Co. 
 
ILLUMINATION. 
 
 1473 
 
 Example of Use of Table Tin. 
 
 Specify the proper lighting arrangements for a banking office 25 ft. X 
 40 ft. with a 13-ft. ceiling. 
 
 The four-lamp fixture is an efficient and pleasing arrangement of 
 lamps. It does not give quite as uniform distribution of light as 
 individual lamps uniformly spaced, but the effect is much more pleasing 
 and the distribution is very satisfactory. 
 Using Electricity. 
 
 Watts per sq. ft. needed =1.5-1.6 (Table VIII). 
 Total watts needed = 1.5 X 40 X 25. 
 
 = 1500 watts. 
 
 Using four-lamp fixtures, we shall need six fixtures, as in Fig. 250, in 
 two rows of 3 each. 
 
 Watts per fixture = ^p = 250. 
 250 
 
 Watts per lamp 
 
 4 
 
 = 62.5. 
 
 On consulting Table IX we find we can use 60-watt lamps as the 
 standard lamp nearest the size computed. If at any place more light 
 
 is needed, 100-watt lamps may be 
 substituted in the nearest fixture. 
 
 Using Gas. To use gas with the 
 same number of similar fixtures, we 
 would have to use lamps which 
 correspond to the 60-watt mazda. 
 Allowing 25 watts to the cu. ft. per 
 hour of gas, we would need a lamp 
 
 which would burn or 2 1/2 cu. ft. 
 
 
 
 c: 
 
 \ 
 
 /" ? % 
 
 /^ V 
 
 * 
 
 / 
 
 E' <-o ttT> 
 jj 
 
 V| ^ 
 
 < [14 ft > 
 
 ^ / 
 
 = 14- ft: > 
 
 u*. 
 
 1 V 
 
 / f \ 
 
 / V 
 
 ^ 
 
 ' 
 
 ^ 
 
 S 7 
 
 ^ 
 
 FIG. 250. 
 
 per hour of gas. By Table IX, we 
 see that this is a standard size. 
 
 The foregoing rules are merely 
 intended to serve as a guide for 
 planning correct illumination. They 
 are not intended to take the place of judgment and intelligence. The 
 details of each lighting project differ slightly from the details of every 
 other lighting project and due weight should be given to ways in which 
 these details affect the application of general rules. 
 
 TABLE IX. Standard Units; Mazda and Welsbach. 
 
 Watts 
 (105- 
 125 
 Volts). 
 
 C.-P. 
 per 
 Watt. 
 
 Welsbach 
 Inverted. 
 
 Watts 
 (105- 
 125 
 Volts). 
 
 C.-P. 
 
 per 
 
 Watt. 
 
 Welsbach 
 Inverted. 
 
 Wei 
 Up 
 
 sbach 
 right. 
 
 Cu. 
 Ft. 
 
 Equiv. 
 Watts 
 per 
 Hour. 
 
 Cu. 
 Ft. 
 
 Equiv. 
 Watts 
 per 
 Hour. 
 
 Cu. 
 Ft. 
 
 Equiv. 
 
 Watts 
 
 H^r. 
 
 10 
 15 
 20 
 25 
 40 
 60 
 100 
 
 0.77 
 0.80 
 0.855 
 0.88 
 0.91 
 0.935 
 0.98 
 
 
 
 
 
 
 
 
 
 
 
 150 
 250 
 400 
 500 
 750 
 1000 
 
 .11 
 .11 
 .33 
 .43 
 .67 
 .82 
 
 
 
 
 
 
 
 10 
 
 250 
 
 
 
 
 
 
 
 1.6 
 2.5 
 4.0 
 4.5 
 
 40 
 62.5 
 100 
 112.5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5.5 
 
 135.5 
 
 Cost of Electric Lighting. (A. A. Wohlauer, El World, May 16, 
 1908, corrected, July, 1915.) The following table shows the relative 
 cost of 1000 candle-hours of illumination by lamps of different kinds, 
 based on costs of 2, 4 and 10 cents per Kw.-hour for electric energy. 
 The life, K, is that of the lamp for incandescent lamps, of the electrode 
 " : arc lamps, and of the vapor tube for vapor lamps. 
 
1476 ELECTRICAL ENGINEERING. 
 
 L s mean spherical candle-power. 
 S s = watts per mean spherical candle. 
 P = renewal cost per trim or life, cents. 
 K = life in hours. 
 C r = 1000P/(KL S ). 
 
 GI = (S s X R) + C r = cost'per 1000 candle-hours. 
 R = rate in cts. per K.W. hour. 
 
 Illuminant. I Amp. I Volts. | L s \ S s I P I K I C r \ Rating. 
 
 Incandescent Lamps. 
 
 R=2 4 10 
 
 Carbon ... . 
 
 0.31 
 
 110 
 
 13 2 
 
 3 8 
 
 16 
 
 450 
 
 2 7 
 
 16 c.-p. 
 
 10 3 
 
 17 9 
 
 40 7 
 
 Gem 
 
 0.45 
 
 110 
 
 16 5 
 
 3 OS 
 
 ?0 
 
 450 
 
 2.7 
 
 20 c.-p. 
 
 8 8 
 
 14 9 
 
 33 ? 
 
 Tungsten 
 
 0.91 
 
 110 
 
 72 
 
 1.4 
 
 70 
 
 1000 
 
 0.97 
 
 100 Watt 
 
 3.8 
 
 6.6 
 
 15.0 
 
 Direct-Current Arc Lamps. 
 
 TT 
 
 8.6 
 
 9 
 
 9.2 
 
 7.11 
 
 5.4 
 
 3.6 
 1.76 
 
 Open arc 
 
 Enclosed 
 
 Carbon 
 
 Miniature 
 
 Magnetite. . . . 
 
 Flaming 
 
 Inclined flam- 
 ing 
 
 Inclined en- 
 closed flaming 
 
 10 
 5.0 
 
 10 
 2.5 
 3.5 
 
 10 
 
 10 
 5.5 
 
 55 
 110 
 HO 
 110 
 110 
 
 55 
 
 55 
 100 
 
 400 
 
 1.3 
 
 260 2.1 
 
 5502.0 
 
 150 
 
 225 
 
 600 
 
 1100 
 
 1.8 
 1.7 
 0.75 
 
 0.5 
 
 1500 0.365 
 
 2 
 0.2 
 
 2 
 
 0.31 
 
 2.4 
 
 1.6 
 0.1 
 
 10 amp. 
 
 10 
 2.5 
 3.5 
 10 
 
 10 
 5.5 
 
 4.6 
 4.4 
 
 5.6 
 3.71 
 3.9 
 
 2.6 
 
 1.03 
 
 21.2 
 21 
 20 
 17.3 
 9.9 
 
 6.6 
 
 Mercury-Vapor Lamps. 
 
 Cooper Hewittl 3.5 
 Quartz | 3.5 
 
 110 I 7701 0.5 
 220 113001 0.6 
 
 1200140000.4 I 
 70030000.135 
 
 3.5amp.| 
 
 .4 12.4 15.4 
 .3412.5416.14 
 
 Recent Street Lighting Installations. 
 
 (Preston S. Millar, Proc. A. I. E. E., July, 1915). 
 
 & 
 
 o 
 
 Width, 
 Roadway, 
 Ft. 
 
 No. of 
 Lighting 
 Units. 
 
 Linear 
 Spacing, 
 Ft. 4 
 
 Height in 
 Feet. 
 
 Kind of 
 Buildings. 5 
 
 Location of 
 Lamps. 6 
 
 Kind of 
 Mount. 9 
 
 Lamps. 10 
 
 Globesll. 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 
 6 
 7 
 8 
 
 36 
 47 
 42 
 80 
 
 901 j 
 
 109 
 60 
 
 50 
 90 
 102 
 222 
 82 
 (twin) 
 123 
 2003 
 
 80 
 69 
 94 
 100 
 
 }i 
 
 100 
 100 
 100 
 
 18 
 24 
 25 
 14.5 
 
 14 
 
 15 
 19 
 13.5 
 
 B 
 
 "B' 
 
 B 
 B 
 
 A 
 B 
 B 
 
 
 
 S 
 
 s 
 
 
 
 s 
 
 s 
 s 
 o 
 
 K 
 P 
 P 
 P 
 
 P 
 P 
 P 
 P 
 
 D.C., 6.6 amp. LA. 
 A.C., SF. 
 A.C., SF. 
 6.6 amp. Mag. 
 
 600 c.-p. Mazda C. 
 
 6.6 amp. Mag. 
 120v., 400w M.C. 
 400 c.-p., 15 amp. M.C. 
 
 A 
 B 
 B 
 A 
 
 N 
 
 A 
 C 
 K 
 
 9 
 10 
 
 50 
 92 
 
 56 
 
 400 
 92 
 
 17.5 
 19.8 
 
 R 
 B 
 
 s 
 o 
 
 P 
 
 K 
 
 1000 c.-p. M.C. 
 4.0 amp. D.C. LA. 
 
 A 
 
 A 
 
 11 
 
 1? 
 
 80 
 36 
 
 79 
 
 105 
 220 
 
 22 
 22 
 
 Ap. 
 
 note 7 
 note 8 
 
 P 
 p 
 
 120v., 400w., M.C. 
 600 c.-p. M.C. 
 
 C 
 
 B 
 
 13 
 
 502 
 
 246 
 
 120 
 
 10.25 
 
 R 
 
 S 
 
 P 
 
 5.5 amp. series M.C. 
 
 B 
 
 (NOTES.) * Between building lines. 2 160 ft. between building lines. 
 8 Two per post. 4 Along one curb. 5 Kind of buildings: B, business 
 structures; A, all kinds; Ap., apartments; R, residences. 6 O, both 
 curbs, opposite; S, staggered. 7 In center of block (on center isle) . On 
 curb of intersecting streets at house line of cross-street intersection, 
 s East curb only. K, brackets on trolley poles; P, ornamental posts. 
 
ELECTRICAL SYMBOLS. 
 
 1477 
 
 10 LA, luminous arc; SF, series flame arc; Mag., inverted magnetite; 
 M.C., Mazda C. "A, alabaster; B, alba; N, novulux; C, Carrara; 
 R, C.R.I., globe and translucent glass reflectors. 
 
 Cities. 1. 5th Ave., Pittsburgh; 2. Federal St., Pittsburgh; 3. 
 Dearborn St., Chicago; 4. Main St., Rochester, N. Y.; 5. Main St., 
 Hartford, Conn.; 6. Penna. Ave., Washington, D. C.; 7. 5th Ave., 
 New York; 8. Market St., Corning, N. Y.; 9. Lake Ave., Rochester; 
 10. Grand Ave., Milwaukee; 11. 7th Ave., New York; 12. Troy St., 
 Chicago; 13. 16th St., Washington. 
 
 SYMBOLS USED IN ELECTRICAL DIAGRAMS. 
 
 a- SPST 
 cb ED- SPOT 
 
 a H~ DPST 
 - 
 
 Galvanometer. Ammeter. Voltmeter. Wattmeter* 
 
 Switches; 5, single; wvyv\A_ 
 D, double; P, pole; Non-inductive 
 1 , throw. Resistance. 
 
 <> <> <>$ 
 Lamps. 
 
 Inductive 
 Resistance. 
 
 Capacity 
 or Condense*. 
 
 Motor Shunt-wound Motor Series-wound 
 or Generator. or Generator. Motor or Generator. 
 
 luuJ 
 
 n 
 
 Two-phase Three-phase Battery. Trans- Compound- Separately 
 Generator. Generator. former, wound Motor excited Motor 
 
 or Generator, or Generator. 
 
INDEX. 
 
 A BBREVIATIONS, 1 
 
 /A Abrasion, resistance to, of 
 * * manganese steel, 495 
 Abrasive processes, 1309-1318 
 Abrasives, artificial, 1313 
 Abscissas, 70 
 Absolute temperature, 567 
 
 zero, 567 
 
 Absorption of gases, 605 
 of water by brick, 370 
 refrigerating machines, 1346, 
 
 1364 
 
 Accelerated motion, 526 
 Acceleration, definition of, 521, 
 
 526 
 
 force of, 526 
 
 ratesof , on electric railways, 1415 
 work of, 529 
 
 Accumulators, electric, 1425 
 Acetylene and calcium carbide, 
 
 855 
 
 blowpipe, 857 
 flame welding, 488 
 generators and burners, 857 
 heating value of, 856 
 Acheson's deflocculated graphite, 
 
 1246 
 
 Acme screw thread, 234 
 Adhesion between wheels and 
 
 rails, 1416 
 
 Adiabatic compression of air, 633 
 curve, 959 
 expansion, 601 
 
 expansion in compressed air- 
 engines, 638 
 
 expansion of air, 635, 638 
 expansion of steam, 959 
 Admiralty metal, composition of, 
 
 390 
 
 Admittance of alternating cur- 
 rents, 1441 
 Aerial tramways, track cable for, 
 
 260 
 
 Air (see also Atmosphere), 606-681 
 and vapor mixture, weight of, 
 
 610-613 
 
 -bound pipas, 748 
 carbonic acid allowable in, 681, 
 
 685 
 
 compressed, 623, 632-653 
 (see Compressed air) 
 Air Compressors, centrifugal, 648 
 effect of intake temperatures, 
 
 647 
 electric motors for, 1465 
 
 Air compressors, high altitude, 
 
 table of, 639 
 hydraulic, 650 
 intercoolers for, 648 
 steam consumption of, 644 
 tables of, 641-643 
 tests of, 643 
 
 Air, contamination of, 687 
 cooling of, 594, 710 
 density and pressure, 607, 613 
 Air, flow of, in pipes, 617-624 
 in long pipes, 618-624 
 in ventilating ducts, 683 
 through orifices, 615-617, 670 
 Air, friction of, in underground 
 
 passages, 714 
 head of, due to temperature 
 
 differences, 716 
 heating of (see also Heating) 
 heating, heat-units absorbed in, 
 
 691 
 
 heating of, by compression, 632 
 horse-power required to com- 
 press, 637 
 
 in feed-pump discharges, 1074 
 inhaled by a man, 687 
 leaks in steam boilers, 891 
 -lift pump, 808 
 -lift pump for oil wells, 809 
 liquid, 605 
 loss of pressure of, in pipes, 
 
 617-624 
 
 manometer, 607 
 pipes in house heating, capacity 
 
 of, 691 
 pressures, conversion table for, 
 
 607 
 
 properties of, 606 
 -pump, 1071-1073 
 -pump for condenser, 1071, 
 
 -pump, maximum work of, 1074 
 
 pyrometer, 555 
 
 saturated, temperatures, pres- 
 sures and volume, table, 1072 
 
 saturated, volume at different 
 vacuums, 1072 
 
 specific heat of, 564 
 
 thermometer, 557 
 
 velocity of, in pipes, by ane- 
 mometer, 624 
 
 volume at different tempera- 
 tures, 692 
 
 volume transmitted in pipes, 
 table, 623, 624 
 
 1479 
 
1480 
 
 air-alt 
 
 INDEX. 
 
 alt-ana 
 
 Air, volumes, densities, and pres- 
 sures, 607, 613 
 
 washing, 687 
 
 water vapor in 1 pound of, 1081 
 
 weight and volume of, 27 
 
 weight of, 176 
 
 weight of (table), 609, 613 
 Alcohol as fuel, 843 
 
 denatured, 843 
 
 engines, 1102 
 
 vapor tension of, 844 
 Alden absorption dynamometer, 
 
 1334 
 
 Algebra, 33-37 
 Algebraic symbols, 1 
 Alligation, 9 
 
 Alloy steels, 470-480 (see Steel) 
 Alloys, 384-410 
 
 aluminum, 396-399 
 
 aluminum-antimony, 399 
 
 aluminum-copper, 396 
 
 aluminum-silicon-iron, 398 
 
 aluminum, tests of, 398 
 
 aluminum- tungsten, 399 
 
 aluminum-zinc, 399 
 
 antimony, 405, 407 
 
 bearing metal, 405 
 
 bismuth, 404 
 
 caution as to strength of, 398 
 
 composition by mixture and by 
 analysis, 388 
 
 composition of, in brass foun- 
 dries, 390 
 
 copper-manganese, 401 
 
 copper-tin, 384 
 
 copper-tin-lead, 394 
 
 copper-tin-zinc, 387-390 
 
 copper-zinc, 386 
 
 copper-zinc-iron, 393 
 
 ferro-, 1255 
 
 ferro-, manufacture of, 1424 
 
 for casting under pressure, 395 
 
 fusible, 404 
 
 Japanese, 393 
 
 liquation of metals in, 388 
 
 magnetic, of non-magnetic 
 metals, 402 
 
 miscellaneous, analyses and 
 properties, 392 
 
 nickel, 402 
 
 the strongest bronze, 389 
 
 vanadium and copper, 395 
 
 white metal, 407 
 Alternating currents, 1440-1460 
 
 admittance, 1441 
 
 average, maximum, and effec- 
 tive values, 1440 
 
 calculation of circuits, 1457 
 
 capacity, 1440 
 
 capacity of conductors, 1446 
 
 converters, 1453 
 
 delta connection, 1446 
 
 frequency, 1440 
 
 generators, for, 1448 
 
 impedance, 1441 
 
 impedance polygons, 1442 
 
 inductance, 1440 
 
 induction motor, 1463 
 
 Alternating currents, measure- 
 ment of power in polyphase 
 circuits, 1447 
 
 motors, variable speed, 1463 
 
 Ohm's law applied to, 1442 
 
 power factor, 1440 
 
 reactance, 1441 
 
 single and polyphase, 1445 
 
 skin effect, 1442 
 
 standard voltages of, 1460 
 
 synchronous motors, 1463 
 
 transformers, 1451 
 
 Y-connection, 1446 
 Altitude by barometer, 608 
 Aluminum, 177, 380 
 
 alloys (see a Iso Alloys), 396-399 
 
 alloys, tests of, 398 
 
 alloys used in automobile con- 
 struction, 400 
 
 brass, 397 
 
 bronze, 396 
 
 bronze wire, 248 
 
 coating on iron, 473 
 
 conductors, cost compared with 
 copper, 1459 
 
 effect of, on cast iron, 439 
 
 electrical conductivity of, 1401 
 
 plates, sheets, and bars, weight 
 of, tables, 230 
 
 properties and uses, 380 
 
 sheets and bars, table, 230 
 
 solder, 382-383 
 
 steel, 496 
 
 strength of, 381, 383 
 
 thermit process, 400 
 
 tubing, 226 
 
 wire, 248, 381, 383 
 
 wire, electrical resistance of, 
 
 table, 1414 
 Ammonia, aqua, strength of, 1341 
 
 -absorption refrigerating ma- 
 chine, 1346, 1364 
 
 -absorption refrigerating ma- 
 chine, test of, 1364 
 
 carbon dioxide and sulphur 
 dioxide, cooling effect, and 
 compressor volume, 1341 
 
 -compression machines, tests of, 
 1359-1364 
 
 -compression refrigerating ma- 
 chines, 1345, 1356 
 
 gas, properties of, 1338 
 
 heat generated by absorption 
 of, 1341 
 
 liquid, properties of, 1340 
 
 solubility of, 1341 
 
 superheated, properties of, 1340 
 Ampere, definition of, 1397 
 Analyses, asbestos, 270 
 
 boiler scale, 722 
 
 boiler water, 722 
 
 cast iron, 439-450 
 
 coals, 821-830 
 
 crucible steel, 490, 494 
 
 fire-clay, 269 
 
 gas, 854 
 
 gases of combustion. 817 
 
 magnesite, 270 
 
ana-arm 
 
 INDEX. 
 
 art-baz 
 
 1481 
 
 Analyses of rubber goods, 378 
 Analytical geometry, 7O-73 
 Anchor bolts for chimneys, 957 
 
 forgings, strength of, 353 
 Anemometer, 624 
 Angle, economical, of framed 
 
 structures, 548 
 of repose of building material, 
 
 1220 
 Angles, Carnegie steel, properties 
 
 of, table, 317-321 
 plotting, without protractor, 53 
 problems in, 38 
 steel, gage lines for, 321 
 steel, tests of, 362 
 steel, used as beams, table of 
 
 safe loads, 321 
 trigonometrical properties of, 
 
 66 
 
 Angular velocity, 522 
 Animal power, 532-534 
 Annealing, effect on conductivity, 
 
 1402 
 
 effect of, on steel, 479 
 influence of, on magnetic capac- 
 ity of steel, 483 
 . malleable castings, 455 
 of steel, 484, 492 (see Steel) 
 of steel forgings, 482 
 of structural steel, 484 
 Annuities, 15-17 
 Annular gearing, 1169 
 Anthracite, classification of, 819, 
 
 828 
 
 composition of, 819, 820, 828 
 gas, 845 
 sizes of, 823 
 space occupied by, 823 
 Anti-friction curve, 50, 1232 
 
 metals, 1223 
 Anti-logarithm, 136 
 Antimony, in alloys, 405, 407 
 
 properties of, 177 
 Apothecaries' measure and weight, 
 
 18, 19 
 Arbitration bar, for cast iron, 
 
 441 
 
 Arc, circular, length of, 58 
 circular, relations of, 58 
 lamps (see Electric lighting) 
 lights, electric, 1469 
 Arcs, circular, table, 122-124 
 Arches, corrugated, 195 
 Area of circles, square feet, di- 
 ameters in feet and inches, 
 131. 132 
 
 of circles, table, 111-119 
 of geometric .alplane figures, 
 
 54-61 
 
 of irregular figures, 56, 57 
 of sphere, 62 
 Arithmetic, 2-32 
 Arithmetical progression, 10 
 Armature circuit, e.m.f. of, 1436 
 
 torque of, 1435 
 "Armco ingot iron," 477 
 Armor-plates, heat treatment of, 
 482 
 
 Artesian well pumping by com- 
 pressed air, 810 
 Asbestos, 270 
 
 Asphaltum coating for iron, 471 
 Asses, work of, 534 
 Asymptotes of hyperbola, 73 
 Atmosphere (see also Air) 
 
 equivalent pressures of, 27 
 
 moisture in, 609-613 
 
 pressure of, 607, 608 
 Atomic weights (table), 173 
 Austenite, 480 
 Autogenous welding, 488 
 Automatic cut-off engines, water 
 
 consumption of, 967 
 Automobile engines, rated capac- 
 ity of, 1101 
 
 gears, efficiency of, 1172 
 
 screws and nuts, table, 232 
 Automobiles, steel used in, 510 
 Avogadro's law of gases, 604 
 Avoirdupois weight, 19 
 Axles, forcing fits of, by hydraulic 
 pressure, 1324 
 
 railroad, effect of cold on, 465 
 
 steel, specifications for, 507, 509 
 
 steel, strength of, 354 
 
 BABBITT metal, 407, 408 
 Bagasse as fuel, 839 
 Balances, to weigh on in- 
 correct, 20 
 
 Balls and rollers, carrying capac- 
 ity of, 340 
 
 for bearings, grades of, 1237 
 hollow copper, resistance to 
 
 collapse, 345 
 Ball-bearings, 1233, 1235 
 
 saving of power by, 1237 
 Band brakes, design of, 1240 
 Bands and belts for carrying coal, 
 
 etc., 1198 
 
 and belts, theory of, 1138 
 Bank discount, 13 
 Bar iron (see Wrought iron) 
 Bars, eye, tests of, 360 
 
 iron and steel, commercial sizes 
 
 of, 182 
 
 Lowmoor iron, strength of, 352 
 of various materials, weights of, 
 
 181 
 
 steel (see Steel) 
 
 twisted, tensile strength of, 280 
 wrought-iron, compression tests 
 
 of, 359 
 Barometer, leveling with, 607 
 
 to find altitude by, 608 
 Barometric readings for various 
 
 altitudes, 608 
 Barrels, to find volume of, 65 
 
 number of, in tanks, 134 
 Barth key, 1329 
 Basic Bessemer steel, strength of, 
 
 476 
 Batteries, primary electric, 1425 
 
 storage, 1425-1428 
 Baume's hydrometer, 175 
 Bazin's experiments on weirs, 763 
 
1482 
 
 bea-bel 
 
 INDEX. 
 
 bcl-hlo 
 
 Beams and girders, safe loads on, 
 1387 
 
 formula for flexure of, 299 
 
 formulae for transverse strength 
 of, 299 
 
 of uniform strength, 301 
 
 special, coefficients for loads on, 
 300 
 
 steel, formulae for safe loads on, 
 298 
 
 wooden, safe loads, by building 
 laws, 1387 
 
 yellow pine, safe loads on, 1387, 
 
 1393 
 Beardslee's tests on elevation of 
 
 elastic limit, 275 
 Bearing-metal alloys, 405 
 
 practice, 407 
 Bearing-metals, anti-friction, 1223 
 
 composition of, 390 
 Bearing pressure on rivets, 426 
 
 pressure with intermittent 
 
 loads, 1231 
 
 Bearings, allowable pressure on, 
 1226, 1230 
 
 and journals clearance in, 1230 
 
 ball, 1233, 1235 
 
 cast-iron, 1223 
 
 conical roller, 1234 
 
 engine, calculating dimensions 
 of, 1042-1044 
 
 engine, temperature of, 1232 
 
 for high rotative speeds, 1231 
 
 for steam turbines, 1232 
 
 knife-edge, 1238 
 
 mercury pivot, 1233 
 
 of Corliss engines, 1232 
 
 of locomotives, 1232 
 
 oil pivot, in Curtis steam tur- 
 bine, 1083 
 
 oil pressure in, 1228 
 
 overheating of, 1228 
 
 pivot, 1229, 1232 
 
 roller, 1233 
 
 shaft, length of, 1034 
 
 steam-engine, 1232, 1238 
 
 thrust, 1232 
 
 Bed-plates of steam-engine, 1044 
 Bell-metal, composition of, 390 
 Belt conveyors, 1198-1201 
 
 dressings, 1151 
 
 factors, 1142 
 
 Belts and pulleys, arrangement 
 of, 1149 
 
 care of, 1150 
 
 cement for leather or cloth, 1 152 
 
 centrifugal tension of, 1139 
 
 effect of humidityon, 1150 
 
 endless, 1151 
 
 evil of tight, 1149 
 
 lacing of, 1147 
 
 length of, 1148 
 
 open and crossed, 1136 
 
 quarter twist, 1147 
 
 sag of, 1149 
 
 steel, 1152 
 Belting, 1138-1152 
 
 Earth's studies on, 1146 
 
 Belting, formulae, 1139 
 
 friction of, 1138 
 
 horse-power of, 1139-1142 
 
 notes on, 1146 
 
 practice, 1139 
 
 rubber, 1152 
 
 strength of, 357, 1150 
 
 Taylor's rules for, 1143 
 
 theory of, 1138 
 
 vs, chain drives, 1155 
 
 width for given horse-power, 
 
 1140 
 
 Bends, effects of, on flow of water 
 in pipes, 747, 748 
 
 in pipes, 624 
 
 in pipes, table, 221, 222 
 
 pipe, flexibility of, 221 
 
 valves, etc., resistance to flow 
 
 in, 879 
 Bending curvature of wire rope, 
 
 1213 
 
 Bent lever, 514, 536 
 Bernouilli's theorem, 617, 765 
 Bessemer converter, temperature 
 in, 555 
 
 steel, 475 (see Steel, Bessemer) 
 Bessemerized cast iron, 453 
 Bethlehem girder beams, proper- 
 ties of, table, 331 
 
 I-beams, table, 332 
 
 steel H-columns, 333 
 Bevel wheels, 1169 
 Billets, steel, specifications for, 507 
 Binomial, any power of, 33 
 
 theorem, 37 
 
 Bins, coal-storage, 1196 
 Birmingham gage, 28 
 Bismuth alloys, 404 
 
 properties of, 178 
 Bituminous coal (see Coal) 
 
 coating for pipe, 206 
 Black body radiation, 579 
 Blast area of fans, 655 
 
 pipes (see Pipes) 
 
 Blast - furnace, consumption of 
 charcoal in, 837 
 
 gas, 855 
 
 steam-boilers for, 899 
 
 temperatures in, 555 
 Blechynden's tests of heat trans- 
 mission, 593 
 Blocks or pulleys, 538, 539, 1181 
 
 or pulleys, strength of, 1181 
 Blooms, steel weight of, table, 190 
 Blow, force of, 529 
 Blowers (see also Fans), 663-681 
 
 and fans, comparative efficiency, 
 656 
 
 blast-pipe diameters for, 671 
 
 in foundries, 1250 
 
 rotary, 677 
 
 rotary, for cupolas, 678 
 
 steam-jet, 679 
 
 Blowing-engines, dimensions of, 
 680 
 
 horse-power of, 680 
 Blowing-machines, centrifugal, 
 648, 649 
 
bio-bra 
 
 INDEX. 
 
 bra-bul 
 
 1483 
 
 Blowpipe, acetylene, 857 
 
 Blue heat, effect on steel, 482 
 
 Board measure, 20 
 
 Boats (see Ships) 
 
 Boats, motor, power required for, 
 
 1101 
 
 Bodies, falling, laws- of, 521 
 Boiler compounds, 930 
 
 explosions, 932 
 
 feed-pumps, 792 
 
 feeders, gravity, 938 
 
 furnaces, height of, 889 
 
 furnaces, use of steam in, 854 
 
 heads, 914 
 
 heads, strength of, 337, 338 
 
 heating-surface for steam heat- 
 ing, 693-697 
 
 plate, strength of, at high 
 temperatures, 463 
 
 scale, analyses of, 722 
 
 tube joints, rolled, slipping 
 point of, 364 
 
 tubes, dimensions of, table, 204 
 
 tubes, expanded, holding power 
 
 of, 364 
 Boilers for house heating, 693 
 
 for steam-heating, 694-697 
 
 horse-power of, 885 
 
 incrustation of, 721, 927-932 
 
 locomotive, 1113 
 
 natural gas as fuel for, 847 
 
 of the "Lusitania," 1381 
 
 steam, 885-944 (see Steam- 
 boilers) 
 Boiling-point of water, 719 
 
 of substances, 559 
 Boiling, resistance to, 570 
 Bolts and nuts, 231-238 
 
 and pins, taper, 1318 
 
 effect of initial strain in, 347 
 
 hanger, 243 
 
 holding power of in white pine, 
 346 
 
 square-head, table of weights 
 of, 242 
 
 strength of, tables, 348 
 
 stud, 237 
 
 track, weight of, 244, 245 
 Bonds, rail, electric resistance of, 
 
 1416 
 
 Boosters, 1456 
 Boyle's or Mariotte's law, 600, 
 
 603 
 Braces, diagonal, stresses in, 542, 
 
 545 
 
 Brackets, cast-iron, strength of, 292 
 Brake horse-power, 970 
 
 horse-power, definition of, 1017 
 
 Prony, 1333 
 Brakes, band, design of, 1240 
 
 electric, 1240 
 
 friction, 1239 
 
 magnetic, 1240 
 Brass alloys, 390 
 
 and copper-lined iron pipe, 227 
 
 and copper tubes, coils and 
 bends, 222 
 
 influence of lead on, 394 
 
 Brass plates, bars, and wire, tables, 
 228, 229 
 
 rolled, composition of, 391 
 
 sheets and bars, table, 228, 229 
 
 tube, seamless, table, 224, 225 
 
 wire, weight of, table, 229 
 Brazing metal, composition of, 390 
 
 of aluminum bronze, 397 
 
 solder, composition of, 390 
 Brick, absorption of water by, 370 
 
 fire, number required for vari- 
 ous circles, table, 267 
 
 fire, sizes and shapes of, 266 
 
 kiln, temperature in, 555 
 
 magnesia, 269 
 
 piers, safe strength of, 1386 
 
 sand-lime, tests of, 371 
 
 specific gravity of, 177 
 
 strength of, 358, 370-372 
 
 weight of, 180, 370 
 
 zirconia, 270 
 
 Bricks and blocks, slag, 268 
 Brickwork, allowable pressures 
 on, 1386 
 
 measure of, 180 
 
 weight of, 180 
 Bridge iron, durability of, 466 
 
 links, steel, strength of, 353 
 
 members, strains allowed in, 
 287 
 
 trusses, 543-547 
 Brine, boiling of, 570 
 
 properties of, 570, 571, 1343 
 Brinell's tests of hardness, 364 
 Briquettes, coal, 831 
 Britannia metal, composition of, 
 
 407 
 British thermal unit (B.T.U.), 
 
 560, 867 
 
 Brittleness of steel (see Steel) 
 Bronze, aluminum, strength, ot, 
 396 
 
 ancient, composition of, 388 
 
 deoxidized, composition of, 395 
 
 Gurley's, composition of, 390 
 
 manganese, 401 
 
 navy-yard, strength of, 398 
 
 phosphor, 394 
 
 strength of, 356 
 
 Tobin, 391, 392 
 
 variation in strength of, 386 
 Buffing and polishing, 1310 
 Building-laws, New York City, 
 1388-1390 
 
 -laws on columns, New York, 
 Boston, and Chicago, 292 
 
 -materials, coefficients of fric- 
 tion of, 1220 
 
 -materials, sizes and weights, 
 
 177, 180, 191 
 
 Buildings, construction of, 1385- 
 1395 
 
 fire-proof, 1389 
 
 heating and ventilation of, 684 
 
 mill, approximate cost of, 1394 
 
 transmission of heat through 
 walls of, 688 
 
 walls of, 1388 
 
1484 
 
 hill-car 
 
 INDEX. 
 
 rar-oas 
 
 Bulkheads, plating and framing 
 
 for, table, 339 
 
 stresses in due to water-pres- 
 sure, 338 
 Buoyancy, 719 
 Burners, acetylene, 857 
 
 fuel oil, 842 
 Burning of steel, 481 
 Burr truss, stresses in, 544 
 Bush-metal, composition of, 390 
 Bushel of coal and of coke, weight 
 
 of, 834 
 Butt-joints, riveted, 428 
 
 CG. S. system of measure- 
 ments, 1396 
 COa, (see also carbon dioxide, 
 
 carbonic acid) 
 
 COa recorders, autographic, 891 
 CO2, temperature required for 
 
 production of, 852 
 Cable, formula for deflection of, 
 
 1207 
 
 traction ropes, 256 
 Cables (see Wire rope) 
 
 chain, proving tests of, 264 
 chain, wrought-iron, 264, 265 
 galvanized steel, 255 
 suspension-bridge, 255 
 Cable-ways, suspension, 1205 
 Cadmium, properties of, 178 
 Calcium carbide and acetylene, 
 
 855 
 chloride in refrigerating-ma- 
 
 chines, 1343 
 Calculus, 73-82 
 Caloric engines, 1095 
 Calorie, definition of, 560 
 Calorimeter for coal, Mahler 
 
 bomb, 826 
 steam, 942-944 
 steam, coil, 943 
 steam, separating, 943 
 steam, throttling, 943 
 Calorimetric tests of coal, 826, 827 
 Cam, 537 
 Campbell's formulae for strength 
 
 of steel, 477 
 Canals, irrigation, 755 
 Candle-power, definition of, 1469 
 of electric lights, 1468-1476 
 of gas lights, 860 
 per watt of lamps, 1475 
 Canvas, strength of, 357 
 Cap screws, dimensions of, 238 
 
 table of standard, 238 
 Capacity, electrical, 1440 
 
 electrical, of conductors, 1445 
 Car heating by steam, 702 
 journals, friction of, 1228 
 wheel, irons used for. 453 
 Cars, steel plate for, 507 
 Carbon, burning out of steel, 485 
 dioxide (see also CO 2) 
 dioxide exhaled by a man, 687 
 dioxide in air, 687 
 dioxide, pressure, volume, etc., 
 1341 
 
 Carbon, effect of, on strength of 
 steel, 476 
 
 gas, 845 
 Carbonic acid, allowable in air, 
 
 681, 685 
 
 Carbonizing (see Case-hardening) 
 Carborundum* made in the elec- 
 tric furnace, 1425 
 Cargo hoisting by rope, 414 
 Carnegie steel sections, proper- 
 ties of, 305-321 
 Carnot cycle, 598, 600 
 
 cycle, efficiency of steam in, 881 
 Carriages, resistance of, on roads, 
 
 534 
 
 Carriers, bucket, 1197 
 Case-hardening of iron and steel, 
 
 510, 1291 
 
 Casks, volume of, 65 
 Cast copper, strength of, 356, 384 
 Cast-iron, 437-454 
 
 addition to, of ferro-silicon, 
 titanium, vanadium, and 
 manganese, 450 
 
 analyses of, 439-450 
 
 bad, 453 
 
 bars, tests of, 444 
 
 beams, strength of, 451 
 
 Bessemeri zed, 453 
 
 chemistry of, 438-443 
 
 columns, eccentric loading of, 
 296 
 
 columns, strength of, 289-292 
 
 columns, tests of, 290 
 
 columns, weight of, table, 200 
 
 combined carbon changed to 
 graphite by heating, 448 
 
 compressive strength of, 283 
 
 corrosion of, 466 
 
 cylinders, bursting strength of, 
 452 
 
 durability of, 466 
 
 effect of cupola melting, 450 
 
 expansion in cooling, 448 
 
 growth of by heating, 1254 
 
 hard, due to excessive silicon, 
 1254 
 
 influence of length of bar on 
 strength, 446 
 
 influence of phosphorus, sul- 
 phur, etc., 438 
 
 journal bearings, 1223 
 
 malleable, 454 
 
 manufacture of, 437 
 
 mixture of, with steel, 453 
 
 mobility of molecules of, 449 
 
 permanent expansion of, by 
 heating, 453 
 
 pipe, 196-200 (see Pipe, cast- 
 iron) 
 
 pipe-fittings, sizes and weights, 
 206-216 
 
 relation of chemical composi- 
 tion to fracture, 446 
 
 shrinkage of, 438, 447, 1254 
 
 specific gravity and strength, 
 452 
 
 specifications for, 441 
 
cas-cha 
 
 INDEX. 
 
 cha-chl 
 
 1485 
 
 Cast-iron strength in relation to 
 silicon and cross-section, 447 
 
 strength in relation to size of 
 bar and to chemical consti- 
 tution, 446 
 
 strength of, 445-447 
 
 tests of, 352, 444-447 
 
 theory of relation of strength 
 to composition, 446 
 
 variation of density and te- 
 nacity, 452 
 
 water pipe, transverse strength 
 of, 452 
 
 white, converted into gray by 
 
 heating, 448 
 
 Castings, deformation of, by 
 shrinkage, 448 
 
 from blast-furnace metal, 450 
 
 hard, from soft pig, 450 
 
 hard to drill, due to low Mn, 
 450 
 
 iron, analysis of, 439 
 
 iron, chemical standards for, 
 441 
 
 iron, strength of, 352 
 
 made in permanent cast-iron 
 molds, 1255 
 
 shrinkage of, 1254 
 
 specifications for, 441 
 
 steel, 489, 510 
 
 steel, specifications for, 489, 510 
 
 steel, strength of, 355 
 
 weakness of large, 1253 
 
 weight of, from pattern, 1256 
 Catenary, to plot, 52 
 Cement as a preservative coating, 
 471 
 
 for leather belts, 1152 
 
 Portland, strength of. 358 
 
 Portland, tests of, 373 
 
 weight and specific gravity of, 
 
 Cements, mortar, strength of, 372 
 Cementation or case-hardening, 
 
 510, 1291 
 
 Cementite, 439, 480 
 Center of gravity, 516 
 
 of gravity, of regular figures, 
 
 516 
 
 of gyration, 518 
 of oscillation, 518 
 of percussion, 518 
 Centigrade-Fahrenheit conver- 
 sion table, 550, 551 
 Centigrade, thermometer scale, 
 
 550, 551 
 Centrifugal air compressors, 648, 
 
 649 
 
 fans (see Fans, centrifugal) 
 fans, high-pressure, 648, 649 
 force, 521 
 
 force in fly-wheels, 1047 
 pumps (see Pumps, centrifugal), 
 
 796-802 
 
 tension of belts, 1139 
 Chain-blocks, efficiency of, 1181 
 Chain-cables, proving tests of, 264 
 weight and strength of, 264 
 
 Chain-drives, 1153 
 
 silent, 1156 
 
 vs. belting, 1155 
 Cham-hoists, 1181 
 Chains, formulae for safe load on, 
 348 
 
 link-belt, 1196 
 
 monobar, 1199 
 
 pin, 1199 
 
 pitch, breaking and working 
 strains of, 265 
 
 roller, 1199 
 
 sizes, weights and properties, 
 264, 265 
 
 specifications for, 264 
 
 strength of, tables, 264, 265 
 
 tests of, 264, 265 
 Chalk, strength of, 371 
 Change gears for lathes, 1260 
 Channels, Carnegie steel, proper- 
 ties of, table, 312-313 
 
 open, velocity of water in, 755 
 
 safe loads, table, 313 
 
 strength of, 352 
 Charcoal, 836-837 
 
 absorption of gases and water 
 
 by, 837 
 mshe' 
 
 bushel of, 180 
 
 composition of, 836 
 
 pig iron, 440, 452 
 
 results from different methods 
 of making, 837 
 
 weights per cubic foot, 180 
 Charles's law, 600, 604 
 Chatter in tools, 1264 
 Chemical elements, table, 173 
 
 symbols, 173 
 
 Chemistry of cast iron, 438-443 
 Chezy's formula for flow of water, 
 
 728 
 
 Chilling cast iron, 441 
 Chimneys, 944-958 
 
 anchor bolts for, 957 
 
 draught intensity in, 945 
 
 draught, power of, 946 
 
 draught, theory, 944 
 
 draught with oil fuel, 952 
 
 effect of flues on draught, 947 
 
 for ventilating, 712 
 
 height of, 948 
 
 height of water column due to 
 unbalanced pressure in, 946 
 
 interior, of Equitable building, 
 954 
 
 largest in the world, 952, 954 
 
 lightning protection of, 949 
 
 radial brick, 954 
 
 rate of combustion due to 
 height of, 947 
 
 reinforced concrete, 958 
 
 sheet iron, 958 
 
 size of, table, 950 
 
 size of, for oil fuel, 951 
 
 stability of, 954 
 
 steel, 956 
 
 steel, design of, 956 
 
 steel, foundation for, 957-, 958 
 
 tall brick, 953 
 
1486 
 
 chi-cla 
 
 INDEX. 
 
 cla-coe 
 
 Chimneys, velocity of air in, 946 
 velocity of gas in, 951 
 with forced draught, 952 
 Chisels, cold, cutting angle of, 
 
 1261 
 
 Chord of circle, 58 
 Chords of trusses, strains in, 545 
 Chrome paints, anti-corrosive, 469 
 Chrome steel, 496 
 Chromium- vanadium steels, 500- 
 
 502 
 
 Cippoleti weir, 764 
 Circle, 57-60 
 area of, 57 
 
 circumferences in feet, diam- 
 eters in inches, table, 1310 
 circumferences of, 1 inch to 32 
 
 feet, 120 
 
 diameter of to enclose a num- 
 ber of rings, 51 
 equation of, 71 
 
 large, to describe an arc of, 51 
 length of arc of, 58 
 length of arc of, Huyghen's 
 
 approximation, 58 
 length of chord of, 58 
 problems, 37-44 
 properties of, 57, 58 
 relation of arc, chord, etc., of, 
 
 58 
 
 relations of, to equal, inscribed 
 and circumscribed square, 59 
 sectors and segments of, 60 
 Circles, area in square feet, diam- 
 eter in inches (table of cyl- 
 inders), 131, 132 
 circumference and area of, 
 
 table, 111-119 
 
 diameter of and sides of equiva- 
 lent square, 125 
 number inscribed in a larger 
 
 circle, 125 
 ^Circuits, alternating current (see 
 
 Alternating Current) 
 electric (see Electric circuits) 
 electric, e.m.f. in, 1406 
 electric, polyphase, 1445 (see 
 
 Alternating currents) 
 electric, power of, 1408 
 magnetic, 1430 
 Circular arcs, lengths of, 58 
 arcs, lengths of, tables, 122-124 
 curve, formulae for, 59 
 functions, Calculus, 81 
 inch, 18 
 measure, 20 
 mil, 18, 29, 30 
 mil wire gage, 29, 30 
 pitch of gears, 1158 
 ring, 60 
 
 segments, areas of, 121, 122 
 Circumference of circles, 1 inch 
 
 to 32 feet, table, 120 
 of circles, table, 111-119 
 Cisterns and tanks, number of 
 
 barrels in, 134 
 capacity of, 132-134 
 Classification of iron and steel, 436 
 
 Clay, cubic feet per ton, 181 
 
 fire, analysis, 269 
 
 melting point of, 556 
 Clearance between journal and 
 bearing, 1230 
 
 in steam-engines, 966, 1021 
 
 of rivet heads, 322 
 Clutches, friction, 1179, 1239 
 Coal, analysis of, 821-830 
 
 analyses and heating values of 
 various, tables, 828-830 
 
 and coke, Connellsville, 824 
 
 anthracite, sizes of, 823 
 
 approximate heating value of, 
 822 
 
 bituminous, classification of, 
 819 
 
 briquets, 831 
 
 burning, Illinois without smoke, 
 921 
 
 caking and non-caking, 820 
 
 calorimeter, 826 
 
 calorimetric tests of, 826, 827 
 
 cannel, 821 
 
 classification of, 819-821 
 
 conveyors, 1197 
 
 cost of for steam power, 1010 
 
 cubic feet per ton, 180 
 
 Dulong's formula for heating 
 value of, 827 
 
 efficiencies of, in gas-engine 
 tests, 853 
 
 foreign, analysis of, 825 
 
 -gas, composition of, 860 
 
 -gas, manufacture, 858 
 
 heating value of, 821-824, 828- 
 830 
 
 products of distillation of, 834 
 
 purchase of, by specification, 830 
 
 Rhode Island graphitic, 821 
 
 sampling, for analysis, 825, 900 
 
 semi-anthracite, 824 
 
 semi-bituminous, composition 
 of, 819-823, 828 
 
 space occupied by anthracite,- 
 823 
 
 spontaneous combustion of, 832 
 
 steam, relative value of, 826 
 
 storage bins, 1196 
 
 tests of, 822, 823 
 
 vs. oil as fuel, 842, 843 
 
 washing, 833 
 
 weathering of, 830 
 
 weight of bushel of, 834 
 
 Welsh, analysis of, 825 
 Coals, furnaces for different, 827 
 Coatings, preservative, 471-474 
 Coatings, protective, for pipe, 206 
 Coefficient of elasticity, 274, 374 
 
 expansion, 566 (see Expansion 
 by heat) 
 
 fineness, 1369 
 
 friction, definition, 1219 
 
 friction of journals, 1220 
 
 friction, rolling, 1220 
 
 friction, tables, 1220-1223 
 
 performance of ships, 1370 
 
 propellers, 1378 
 
INDEX. 
 
 corn-corn 
 
 1487 
 
 Coefficient of transverse strength, 
 
 297 
 
 water lines, 1369 
 Coils and. bends of brass tubes, 
 
 222 
 
 electric, heating of, 1409 
 heat radiated from, in blower 
 
 system, 708 
 Coiled pipes, 221 
 Coke, analyses of, 833 
 
 by-products of manufacture of, 
 
 833, 834 
 
 foundry, quality of, 1255 
 ovens, generation of steam 
 
 from waste heat of, 834 
 weight of, 180, 834 
 Coking, experiments in, 833 
 Cold-chisels, form of, 1261 
 
 -drawing, effect of, on steel, 361 
 -drawn steel, tests of, 361 
 effect of, on railroad axles, 465 
 effect of, on strength of iron and 
 
 steel, 464 
 
 -rolled steel, tests of, 361 
 -rolling, effect of, on steel, 479 
 -saw, 1309 
 Collapse of corrugated furnaces, 
 
 342 
 
 of tubes, tests of, 341-344 
 resistance of hollow cylinders 
 
 to, 341-345 
 
 Collars for shafting, 1133 
 Cologarithm, 137 
 Color determination of tempera- 
 ture, 558 
 Color scale for steel tempering, 
 
 493 
 Color values of various illumi- 
 
 nants, 1469 
 
 Columns, built steel, tests of, 287 
 Carnegie channel, dimensions 
 
 and safe loads, 323-327 
 Carnegie plate and angle, 323, 
 
 328-330 
 
 cast-iron, strength of, 289-292 
 cast-iron, tests of, 290 
 cast-iron, weight of, table, 200 
 comparison of formulae for, 286 
 eccentric, loading of, 296 
 Gordon's formula for, 284 
 Hodgkinson's formula for, 283 
 made of old boiler tubes, tests 
 
 of, 363 
 mill, 1393 
 
 permissible stresses in, 286 
 strength of, by New York 
 
 building laws, 1389 
 wrought-iron, tests of, 360 
 wrought-iron, ultimate strength 
 
 of, table, 285 
 Combination, 10 
 Combined stresses, 335 
 Combustion, analyses of gases of, 
 
 817 
 
 heat of, 560 
 of fuels, 816 
 
 of gases, rise of temperature in, 
 818 
 
 Combustion, rate of, due to chim- 
 neys, 947 
 
 spontaneous, of coal, 832 
 theory of, 816 
 
 Commutating-pole motors, 1437 
 Composition of forces, 513 
 Compound engines (sec Steam- 
 engines, compound), 976-983 
 interest, 13, 14 
 locomotives, 1122, 1124 
 proportion, 7 
 numbers, 5 
 units of weights and measures, 
 
 27 
 
 Compressed-air, 623, 632-653 
 adiabatic and isothermal com- 
 pression, 633 
 cranes, 1192 
 diagrams, curve of, 636 
 drills driven by, 645 
 engines, adiabatic expansion in, 
 
 638 
 
 engines, efficiency, 641 
 flow of, in pipes, 618-624 
 for motors, effect of heating, 
 
 639-641 
 formulae, 633 
 for street railways, 652 
 gain due to reheating, 647 
 hoisting engines, 646 
 horse-power required to com- 
 press air, 637 
 locomotives, 1128 
 loss of energy in, 632 
 losses due to heating, 633 
 machines, air required to run, 
 
 645, 647 
 mean effective pressures, tables, 
 
 636, 637 
 
 mine pumps, 652 
 moisture in, 611 
 motors, 639-641 
 motors with return-air circuit, 
 
 648 
 
 Popp system, 639-641 
 practical applications of, 647 
 pumping with (see also Air-lift), 
 
 645 
 
 reheating of, 641 
 table for pumping plants, 645 
 tramways, 652 
 
 transmission, efficiencies of, 641 
 two-stage compression, 635 
 volumes, pressures, tempera- 
 tures, table, 636 
 work of adiabatic compression, 
 
 634 
 
 Compressed steel, 488 
 Compressibility of liquids, 175 
 
 of water, 721 
 Compression, adiabatic, formulae 
 
 for, 633 
 
 and flexure combined, 335 
 and shear combined, 335 
 and torsion combined, 335 
 in steam-engines, 965 
 of air, tables, 635-638 
 Compressive strength, 281-283 
 
1488 
 
 coin-con 
 
 INDEX. 
 
 con-cop 
 
 Compressive strength of iron bars, 
 
 359 
 
 strength of woods, 366 
 tests, specimens for, 282 
 Compressor volume in refrigerat- 
 ing, 1341 
 Compressors, air, effect of intake 
 
 temperature, 647 
 air, tables of, 641-643 
 Concrete, crushing strength of 
 
 12-in. cubes, 1386 
 durability of iron in, 466 
 reinforced, allowable working 
 
 stresses, 1386 
 
 Condenser, barometric, 1069 
 the Leblanc, 1056 
 tubes, heat transmission in, 
 
 589 
 
 Condensers, 1069-1079 
 air-pump for, 1071, 1073 
 calculation of surface of, 939 
 choice of, 1078 
 circulating pump for, 1075 
 continuous use of cooling water 
 
 in, 1076 
 
 contraflow, 1071 
 cooling- towers for, 1079 
 cooling water required, 1068 
 ejector, 1069 
 
 evaporative surface, 1076 
 for refrigerating machines, 1353 
 heat transference in, 1070 
 increase of power due to, 1077 
 jet, 1068 
 surface, 1069 
 tubes and tube plates of, 1072, 
 
 1073 
 Condensing apparatus, power 
 
 used by, 1071 
 
 Conductance, electrical, 1401 
 Conduction of heat, 580 
 
 of heat, external and internal, 
 
 580 
 Conductivity, electrical, of metal, 
 
 1401 
 
 electric, of steel, 477 
 Conductors, electrical, heating of, 
 
 1408 
 electrical, in series or parallel, 
 
 resistance of, 1407 
 Conduit, water, efficiency of, 766 
 Cone, measures of, 62 
 
 pulleys, 1136 
 Conic sections, 73 
 Connecting - rods , steam - engine, 
 
 1025 
 
 tapered, 1026 
 
 Connections, transformer, 1452 
 Conoid, parabolic, 65 
 Conoidal fans, 666 
 Conservation of energy, 531 
 Constantan, copper-nickel alloy, 
 
 403 
 
 Constants, steam-engine, 971-974 
 Construction of buildings, 1385- 
 
 1395 
 
 Controllers, for electric motors, 
 1462 
 
 Convection, Dulong's law of, 
 
 table of factors, for, 597 
 loss of heat due to, 596 
 of heat, 580 
 
 Conversion tables, metric, 23-26 
 Converter, Bessemer, tempera- 
 ture in, 555 
 Converters, electric, 1453 
 
 synchronous, 1453 
 Conveying of coal in mines, 1203 
 Conveyors, belt, 1198-1201 
 cable-hoist, 1205 
 coal, 1197 
 horse-power required for, 1198, 
 
 1200 
 
 screw, 1198 
 Cooling agents in refrigeration, 
 
 1342 
 
 air for ventilation, 710 
 effect, in refrigerating, 1341 
 of air, 594 
 
 of air by washing, 687 
 Cooling-tower, air per pound of 
 circulating water, table, 1081 
 air supply required for, 1080 
 for condensers, 1079 
 practice in refrigerating plants, 
 
 1354 
 
 water evaporated per pound of 
 . air, 1080 
 water vapor mixed with air, 
 
 table, 1081 
 Co-ordinate axes, 70 
 Copper, 178 
 
 and brass-lined iron pipe, 227 
 
 ball pyrometer, 553 
 
 balls, hollow, 345 
 
 cast, strength of, 356, 384 
 
 castings of high conductivity, 
 
 368 
 
 density of, 1406 
 drawn, strength of, 356 
 effect of on cast-iron, 438 
 electric conductivity of, 1402 
 -manganese alloys, 401 
 -nickel alloys, 402 
 plates, strength of, 356 
 resistivity of, 1403 
 temperature coefficient of, 1403 
 tubing, bends and coils, 222 
 rods, weight of, table, 230 
 steels, 499 
 
 strength of at high tempera- 
 tures, 368 
 -tin alloys, 384 
 
 -tin alloys, properties and com- 
 position of, 384 
 -tin-zinc alloys, law of variation 
 
 of strength of, 388 
 -tin-zinc alloys, properties and 
 
 composition, 387 
 -vanadium alloys, 395 
 weight required in different sys- 
 tems of transmission, 1459 
 Copper-wire and plates, weight of, 
 
 table, 229 
 
 carrying capacity of, Under- 
 writer's table, 1410 
 
cop-era 
 
 INDEX. 
 
 cra-eur 
 
 1489 
 
 Copper-wire, cross-section required 
 
 for a given current, 1410 
 electrical resistance, table, 1404 
 stranded, 253 
 table of electrical resistance, 
 
 1404 
 weight of for electric circuits, 
 
 1410 
 Copper-zinc alloys, strength of, 
 
 386 
 -zinc alloys, table of composition 
 
 and properties, 386 
 -zinc-iron alloys, 393 
 Cord of wood, weight of, 181 
 yield of charcoal from, 836 
 Cordage, technical terms relating 
 
 to, 411 
 
 weight of, 411, 415, 
 Cork, properties of, 377 
 Corrosion by stray electric cur- 
 rents, 470 
 
 due to overstrain, 470 
 electrolytic theory of, 468 
 of iron, 467 
 of pipe in hot-water heating, 
 
 708 
 
 of steam-boilers, 467, 927-932 
 prevention of, 468 
 resistance of aluminum alloys 
 
 to, 401 
 
 resistance to of nickel steel, 498 
 Corrosive agents in atmosphere, 
 
 466 
 
 Corrugated arches, 195 
 furnaces, 342, 917 
 plates, properties of Carnegie 
 
 steel, table, 310 
 sheets, sizes and weights, 194 
 Cosecant of an angle, table, 170- 
 
 172 
 Cosine of an angle, 66 
 
 of an angle, table, 170-172 
 Cost of coal for steam-power, 1010 
 
 of steam-power, 1009-1011 
 Cotangent of an angle, 66 
 Cotangents of angles, table, 170- 
 
 172 
 
 Cotton ropes, strength of, 357 
 Coulomb, definition of, 1397 
 Counterbalancing of hoisting- 
 engines, 1188 
 of locomotives, 1126 
 of steam-engines, 1008 
 Counterpoise system of hoisting, 
 
 1189 
 
 Couples, 515 
 Couplings, flange, 1133 
 
 hose, standard sizes, 218 
 Coverings for steam-pipe, tests of, 
 
 584-587 
 Coversed sine of angles, table, 170- 
 
 172 
 Cox's formula for loss of head, 
 
 . 734 
 Crane chains, 264, 265 
 
 installations, notable, 1192 
 pillar, 150-ton, 1192 
 Cranes, 1189-1193 
 
 Cranes and hoists, power required 
 
 for, 1193 
 
 classification of, 1189 
 compressed air, 1192 
 electric, 1190-1192 
 electric, loads and speeds of, 
 
 1191 
 
 guyed, stresses in, 542 
 jib, 1190 
 
 power required for, 1191 
 quay, 1193 
 
 simple, stresses in, 541 
 traveling, 1190-1193 
 Crank angles, steam-engine, table, 
 
 1058 
 
 arm, dimensions of, 1029 
 pins, steam-engine, 1027-1029 
 pins, steel, specifications for, 
 
 507 
 shaft, steam-engine, torsion and 
 
 flexure of, 1038 
 shafts, steam-engines, 1030- 
 
 1038 
 
 Cranks, steam-engines, 1029 
 Critical point in heat treatment 
 
 of steel, 480 
 temperature and pressure of 
 
 gases and liquids, 606 
 Cross-head guides, 1025 
 
 pin, 1029 
 Cross-sections of materials, for 
 
 draftsmen, 271 
 Crucible steel, 475, 490-494 (see 
 
 Steel, crucible) 
 Crushing strength of masonry 
 
 materials, 371 
 Crystallization of iron by fatigue, 
 
 466 
 
 Cubature of volumes, 77 
 Cube root, 9 
 
 roots, table of, 93-108 
 Cubes of decimals, table, 108 
 
 of numbers, table, 93-108 
 Cubic feet and gallons, table, 130 
 
 measure, 18 
 Cupola fan, power required for, 
 
 1253 
 
 gases, utilization of, 1253 
 loss in melting iron in, 1253 
 practice, 1247-1257 
 practice, improvement of, 1249 
 results of increased driving, 
 
 1252 
 
 Cupolas, blast-pipes for, 671 
 blast-pressure in, 1247-1251 
 blowers for, 661, 662 
 charges for, 1247-1250 
 charges in stove foundries, 1250 
 dimensions of, 1247 
 rotary blowers for, 678 
 slag in, 1248 
 Current motors, 765 
 Currents, electric (see Electric 
 
 currents) 
 
 Curve, railway degree of, 54 
 Curve of P V n , construction of , 602 
 Curves in pipe-lines, resistance of, 
 747 
 
1490 
 
 cut-dif 
 
 INDEX. 
 
 dif-dyn 
 
 Cut-off for various laps and travel 
 
 9f slide valves, 1060 
 Cutting metal by oxy-acetylene 
 
 flame, 488 
 metal, resistance overcome in, 
 
 1292 
 speeds of machine tools, (see also 
 
 Tools, cutting), 1258 
 speeds of tools, 1268 
 stone with wire, 1309 
 Cycloid, construction of, 50 
 differential equations of, 81 
 integration of, 81 
 measures of, 61 
 Cycloidal gear-teeth, 1162 
 Cylinder condensation in steam- 
 engines, 966-968 
 lubrication, 1245 
 measures of, 62 
 
 Cylinders, cast-iron, weight of, 200 
 hollow, resistance of to collapse, 
 
 341-345 
 
 hollow, under tension, 339 
 hooped, 340 
 hydraulic press, thickness of, 
 
 340, 813 
 
 locomotive, 1112 
 steam-engine (see Steam-engines) 
 tables of capacities of, 131 
 thick hollow, under tension, 339 
 thin hollow, under tension, 340 
 Cylindrical ring, 64 
 
 tanks, capacities of, table, 132 
 
 D ALTON'S law of gaseous 
 pressures, 604 
 Dam, stability of, 515 
 Darcy's formula, flow of water, 732 
 formula, table, of flow of water 
 
 in pipes, 740, 741 
 Decimal equivalents of feet and 
 
 inches, 5 
 
 equivalents of fractions, 3 
 gage, 32, 
 Decimals, 3 
 
 square and cubes of, 108 
 Delta connection for alternating 
 
 currents, 1447 
 Delta connection transformers, 
 
 1452 
 
 metal wire, 248, 393 
 Denominate numbers, 5 
 Deoxidized bronze, 395 
 Derrick, stresses in, 542 
 Detrick and Harvey key, 1330 
 Diagonals, formulae for strains in, 
 
 545 
 
 Diametral pitch, 1158 
 Diesel oil engine, 1102 
 Differential calculus, 73-82 
 coefficient, 75 
 coefficient, sign of, 78 
 gearing, 1169 
 
 of exponential function, 79, 80 
 partial, 75 
 pulley, 539 
 screw, 540, 541 
 second, third, etc., 77 
 
 Differential windlass, 540 
 Differentials of algebraic func- 
 tions, 74 
 
 Differentiation, formulae for, 74 
 Discount, 12 
 
 Disk fans (see Fans, disk) 
 Displacement of ships, 1369, 1374 
 Distillation of coal, 834 
 Distiller for marine engines, 1082 
 Distilling apparatus, multiple 
 
 system, 570 
 Doble motor, tests of, 782 
 
 nozzle, efficiency of, 782 
 Domed heads of boilers, 339 
 Domes on steam boilers, 918 
 Draught, chimney .intensity of, 945 
 
 chimney, with oil fuel, 952 
 
 forced, chimneys with, 952 
 
 forced for steam boilers, 923 
 
 power of chimneys, 945, 946 
 
 theory of chimneys, 944 
 Drawing-press, blanks for, 1322 
 Dressings, belt, 1151 
 Driers and drying, 574 
 
 performance of, 575 
 Drift bolts, resistance of in timber, 
 
 346 
 
 Drill gage, table, 30 
 Drills, feeds and speeds for, 1288 
 
 for pipe taps, 201 
 
 high-speed steel, 1285 
 
 performance of, 1289 
 
 rock, air required for, 645 
 
 speed of, 1285 
 
 tap, sizes of, 236, 1320 
 
 twist, experiments with, 1289 
 Drilling compounds, 1286 
 
 high-speed, data on, 1289 
 
 holes, speed of, 1287 
 
 steel and cast iron, power re- 
 quired for, 1286, 1287 
 Drop hi electric circuits, 1407 
 
 press, pressures obtainable by, 
 
 1322 
 
 Drums, steam-boiler, 913 
 Dry measure, 19 
 Drying and evaporation, 569-577 
 
 apparatus, design of, 576 
 
 in a vacuum, 573 
 
 of different materials, 574 
 Ductility of metals, table, 180 
 Dulong's formula for heating 
 value of coal, 827 
 
 law of convection, table of fac- 
 tors for, 597 
 
 law of radiation, table of factors 
 
 for, 596 
 Durability of cutting tools, 1268 
 
 of iron, 465-467 
 Durand's rule for areas, 56 
 Dust explosions, 837 
 
 fuel, 837 
 Duty, measure of, 27 
 
 of pumping-engines, 802 
 
 trials of pumping-engines, 802- 
 
 806 
 
 Dynamics, fundamental equations 
 of, 525 
 
dyn-ele 
 
 INDEX. 
 
 ele-ele 
 
 1491 
 
 Dynamo-electric machines, classi- 
 fication of, 1437 
 
 e.m.f. of armature circuit, 1436 
 
 moving force of, 1435 
 
 torque of armature, 1435 
 
 strength of field, 1436 
 Dynamometers, 1333 
 
 Alden absorption, 1334 
 
 hydraulic absorption, 6000 H.P., 
 1335 
 
 Prony brake, 1333 
 
 traction, 1333 
 
 transmission, 1335 
 Dynamotors, 1457 
 Dyne, definition of, 512 
 
 EARTH, cubic feet per ton, 181 
 Eccentric loading of columns, 
 296 
 
 Eccentric, steam-engine, 1039 
 Economical angle of framed 
 
 structures, 548 
 
 Economics of power-plants, 1011 
 Economizers, fuel (see Fuel econ- 
 omizers), 924 
 Edison wire gage, 29, 30 
 Efficiency, definition of, 12 
 
 of a machine, 532 
 
 of compressed-air engines, 641 
 
 of compressed-air transmission, 
 641 
 
 of differential screw, 541 
 
 of electric systems, 1412 
 
 of fans, 656, 657 
 
 of hydraulic turbines, 7715 
 
 of injector, 937 
 
 of pumps, 790 
 
 of riveted joints, 428-434 
 
 of screw, 538 
 
 of screw bolts, 538 
 
 of steam-boilers, 891 
 
 of steam-engines, 964 
 Ejector condensers, 1069 
 Elastic Limit, 273-278 
 
 apparent, 273 
 
 Bauschinger's definition of, 275 
 
 elevation of, 275 
 
 relation of, to endurance, 275 
 
 Wohler's experiments on, 275 
 Elastic resilience, 274 
 
 resistance to torsion, 334 
 Elasticity, coefficient of, 274 
 
 moduli of, of materials, 374 
 
 modulus of, 274 
 Electric brakes, 1240 
 
 circuits (see Circuits, electric) 
 
 conductivity of steel, 477 
 
 current, alternating, 1440-1461 
 (see Alternating currents) 
 
 current, cost of fuel for, 796 
 
 current determining the direc- 
 tion of, 1432 
 
 current required to fuse wires, 
 1409 
 
 currents, direct, 1406 
 
 currents, heating due to, 1408 
 
 currents, short-circuiting of, 
 1411 
 
 Electric furnaces, 1422 
 
 heaters, 713, 1420 
 
 heating, 713 
 
 lighting, 1468-1477 
 
 lighting, cost of, 1475 
 
 lighting, terms used in, 1468 
 
 locomotive, 1416 
 
 Electric Motors (see also Motors) , 
 1461 
 
 alternating current, variable 
 speed, 1463 
 
 changing the number of poles, 
 1463 
 
 for the machine-shop, 1294- 
 1303, 1466 
 
 for machine tools, 1294-1303, 
 1467 
 
 for wood-working tools, 1303- 
 1305 
 
 selection of, for different ser- 
 vice, 1464 
 
 speed control of, 1462 
 
 types used for various purposes, 
 
 1464 
 Electric power, cost of, 1012 
 
 process of treating iron sur- 
 faces, 473 
 Electric Railways, 1414 
 
 adhesion between wheel and 
 rail, 1416 
 
 cars, resistance of, 1110 
 
 efficiency of distributing sys- 
 tems, 1417 
 
 safe speed on curves, 1416 
 
 steam railroads electrified, 1418 
 Eectric resistanceof steel rails. 1416 
 
 smelting of pig iron, 1424 
 
 stations, economy of engines 
 in, 992 
 
 storage batteries, 1425-1428 
 
 transmission, direct current, 
 1410-1413 
 
 transmission, high tension, 
 notes on, 1459 
 
 transmission, lines, spacing for 
 high voltages, 1460 
 
 transmission, sag of wires, 1461 
 
 vs. steam heating, 1421 
 
 welding, 1419 
 
 wires (see Wires and Copper 
 
 wires) 
 Electrical and mechanical units, 
 
 equivalent values of, 1399 
 Electrical engineering, 1396-1477 
 
 horse-power, 970, 1408 
 
 machinery, shaft fits, allow- 
 ances for, 1326 
 
 resistance, 1400 
 
 resistance of different metals 
 
 and alloys, 1401 
 . resistance of rail bonds, 1416 
 
 symbols, 1477 
 
 units, relations of, 1397, 1399 
 Electricity, analogies to flow of 
 water, 1400 
 
 standardsof measurements, 1396 
 
 units used in, 1396 
 Electro-chemical equivalents, 1429 
 
1492 
 
 ele-ent 
 
 INDEX. 
 
 ent-eye 
 
 Electro - magnetic measurements, 
 
 1398 
 
 -magnets, 1430^1437 
 -magnets, polarity of, 1432 
 -magnets, strength of, 1431 
 -motive force of armature cir- 
 cuit, 1436 
 Electrolysis, 1428 
 Electrolytic theory of corrosion, 
 
 468 
 Elements, chemical, table, 173 
 
 of machines, 535-541 
 Elevators, coal, 1196 
 gravity discharge, 1197 
 perfect discharge, 1197 
 Ellipse, construction of, 45-48 
 equations of, 71 
 measures of, 60 
 Ellipsoid, 64 
 
 Elongation, measurement of, 279 
 Emery, grades of, 1311 
 
 wheels, safe speeds, 1316, 1317 
 wheels, speed and selection of, 
 
 1310-1315 
 
 wheels, stress in, 1310 
 wheels, truing and dressing, 
 
 1317 
 
 E.M.P. of electric circuits, 1407 
 Endless screw, 540 
 Endurance of materials, relation 
 
 of, to elastic limit, 275 
 Energy, available, of expanding 
 
 steam, 870 
 conservation of, 531 
 definition of, 528 
 intrinsic or internal, 600 
 measure of, 528 
 mechanical, of steam expanded 
 
 to various pressures, 963 
 of recoil of guns, 531 
 of water flowing in a tube, 746, 
 
 765 
 
 sources of, 531 
 Engines, alcohol, 1102 
 
 alcohol consumption in, 844 
 automobile, capacity of, 1101 
 blowing, 680 
 compressed air, efficiency of, 
 
 639-641 
 
 fire, capacities of, 752 
 gas, 1095-1108 (see G as-engines) 
 hoisting (see Hoisting engines), 
 
 1186 
 
 hot-air or caloric, 1095 
 hydraulic, 815 
 
 internal combustion, 1095-1108 
 marine, steam-pipes for, 880 
 oil and gasoline, 1101 
 petroleum, 1102 
 pumping, 802-806 (see Pump- 
 ing-engines) 
 
 steam, 959-1095 (see Steam- 
 engines) 
 solar, 1015 
 winding (see Hoisting engines), 
 
 1186 
 
 Entropy, definition of, 599 
 of water and steam, 602 
 
 Entropy of water and steam, 
 tables, 869, 871-873 
 
 -temperature diagram, 599 
 Epicycloid, 50 
 
 Equalization of pipes, 625, 884 
 Equation of payments, 14 
 Equation of pipes, 884 
 Equations, algebraic, 34-36 
 
 of circle, 71 
 
 of ellipse, 71 
 
 of hyberbola, 72 
 
 of parabola, 72 
 
 quadratic, 35 
 
 referred to co-ordinate axes, 70 
 Equilibrium of forces, 516 
 Equivalent orifice, mine ventila- 
 tion, 715 
 
 E qui valen ts , electro-chemical ,1429 
 Erosion of soils by water, 755 
 Ether, petroleum, as fuel, 841 
 Euler's formula for long columns, 
 
 284 
 Evaporation, 569-577 
 
 by exhaust steam, 572 
 
 by multiple system, 570 
 
 factors of, 908-912 
 
 in a vacuum, 573 
 
 in salt manufacture, 570 
 
 latent heat of, 569 
 
 of sugar solutions, 572 
 
 of water from reservoirs and 
 channels, 569 
 
 total heat of, 569- 
 
 unit of, 886 
 Evaporator, for marine engines, 
 
 1082 
 
 Evolution, 8 
 Exciters, 1449 
 Exhauster, steam-jet, 679 
 Exhaust-steam, evaporation by, 
 572 
 
 for heating, 1009 
 
 Expansion, adiabatic, formulae for, 
 638 
 
 by heat, 565 
 
 coefficients of, 566 
 Expansion of air, adiabatic, 638 
 
 cast iron, permanent by heat- 
 ing, 453 
 
 gases, construction of curve of, 
 602 
 
 gases, curve of, 73 
 
 iron and steel by heat, 465 
 
 liquids, 567 
 
 nickel steel, 499 
 
 solids by heat, 566 
 
 steam, 959 
 
 steam, actual ratios of, 965 
 
 timber, 367 
 
 water, 716 
 Explosions, dust, 837 
 
 of fuel economizers. 927 
 Explosive energy of steam-boilers, 
 
 932 
 Exponential function, differential 
 
 of, 79, 80 
 
 Exponents, theory of, 36 
 Eye-bars, tests of, 360 
 
fac-fec 
 
 INDEX. 
 
 fee-fla 
 
 1493 
 
 FACTOR of evaporation, 908 
 of safety, 374-377 
 of safety, formulae for, 376 
 of safety in steam-boilers, 918 
 Factory heating by fan system, 
 
 708, 710 
 Fahrenheit-Centigrade conversion 
 
 table, 550, 551 
 Failures of stand-pipes, 350 
 
 of steel, 486 
 
 Fairbairn's experiments on riv- 
 eted joints, 424 
 Fall increaser for turbines, 780 
 Falling bodies, graphic represen- 
 tation, 522 
 height and velocity of tables, 
 
 523, 524 
 laws of, 521 
 Fan blowers, types of, 654 
 
 tables, caution in regard to, 662 
 Fans (see also Blowers) 
 and blowers, 653-681 
 and chimneys for ventilation, 
 
 712 
 
 and rotary blowers, compara- 
 tive efficiencies, 657 
 best proportions of, 653 
 blast-area of, 655 
 centrifugal, 648, 649, 653 
 centrifugal, high-pressure, 648 
 conoidal, 666 
 
 cupola, power required for, 1253 
 design of, 653 
 disk, 675-677 
 
 disk, influence of speed on effi- 
 ciency, 675, 677 
 effect of resistance on capacity 
 
 of, 664 
 
 efficiency of, 656, 657, 668 
 electric motors for, 1464 
 experiments on, 657 
 for cupolas, 661 
 high-pressure, capacity of, 663 
 horse-power of, 668 
 influence of spiral casings, 674 
 methods of testing, 667 
 multiblade, 655, 658 
 multiblade, characteristics of, 
 
 656 
 
 pipe lines for, 670 
 pressure characteristics of, 655 
 pressure due to velocity of, 653 
 quantity of air delivered by, 
 
 655 
 
 relation of speed volume, pres- 
 sure and power, 656 
 Farad, definition and value of, 
 
 1397 
 Fatigue, crystallization of iron by, 
 
 465 
 
 effect of, on iron, 465 
 Feed and depth of cut, effect of, 
 
 on speed of tools, 1264 
 -pump (see Pumps) 
 Feeds and speeds of drills, 1288 
 Feed-water, cold, strains caused 
 
 by, 939 
 heaters, 938-940 
 
 Feed-water heaters, capacity of, 
 
 939 
 
 heaters: closed vs. open, 940 
 heaters, proportions of, 940 
 heaters, transmission of heat 
 
 in, 590 
 
 heating, Nordberg system, 1003 
 heating, saving due to, 938 
 purification of, 723-726 
 to boilers by gravity, 938 
 Feet and inches, decimal equiva- 
 lents of, table, 5 
 Fellows stub tooth gear, 1167 
 Fence wires, corrosion of, 468 
 Ferrite, 439. 480 
 
 Ferro-alloys for foundry use, 1255 
 manufacture of, 1424 
 silicon, addition of, to cast-iron, 
 
 450 
 
 silicon, dangerous, 1255 
 Field, magnetic, 1398 
 Fifth roots and fifth powers of 
 
 numbers, 109 
 
 powers, square roots of, 110 
 Fineness, coefficient of, 1369 
 Finishing temperature, effect of 
 
 in steel rolling, 478 
 Fink roof truss, 547 
 Fire, temperature of, 817, 818 
 Fire-brick arches in locomotives, 
 
 1115 
 number required for various 
 
 circles, table, 267 
 refractoriness of, 268 
 sizes and shapes of, 266 
 weight of, 266 
 Fire-clay, analysis of, 269 
 
 pyrometer, 553, 556 
 Fire-engines, capacities of, 752 
 Fire-proof buildings, 1389 
 Fire-streams. 749-752 
 
 discharge from nozzles at differ- 
 ent pressures, 750, 753 
 effect of increased hose length, 
 
 750 
 
 friction loss in hose, 752 
 hydrant pressure required for, 
 
 table, 750 
 
 Fireless locomotive, 1127 
 Fits, force and shrink, 1324-1327 
 force and shrink, pressure re- 
 quired to start, 1327 
 limits of diameter for, 1325 
 press, pressure required for, 
 
 1324-1326 
 running, 1325 
 stresses due to, 1326 
 Fittings (see Pipe-fittings), 206- 
 
 216 
 
 Flagging, strength of, 373 
 Flanges, brass, 214, 215 
 
 cast-iron, forms of, 210, 214- 
 
 216 
 
 forged and rolled steel, 211 
 forged steel, for riveted pipe, 211 
 for riveted pipe, 211 
 pipe, extra heavy, tables, 210, 
 212 
 
1494 
 
 fla-flo 
 
 INDEX. 
 
 flo-fou 
 
 , is, pipe, tables, 209-213 
 
 __ during, dimensions of, 214 
 Flanged fittings, cast-iron, 208- 
 
 210 
 Flat plates in steam-boilers, 916 
 
 plates, strength of, 336 
 
 steel ropes, 258, 261 
 
 surfaces in steam-boilers, 916 
 .Flattened strand rope, 258, 261 
 Flexure and compression com- 
 bined, 335 
 
 and tension combined, 335 
 
 and torsion combined, 335 
 
 of beams, formula for, 297, 299 
 Flight conveyors, 1197 
 Flights, sizes and weights of, 1 199 
 Floors, maximum load on, 1390- 
 1393 
 
 strength of, 1390-1393 
 Flow of air in long pipes, 618-624 
 
 air in pipes, 617-624 
 
 air through orifices, 615-617, 
 670 
 
 compressed air, 618-624 
 
 gas in pipes, 864-866 
 
 gas in pipes, tables, 865, 866 
 
 gases, 605 
 
 metals, 1323 
 
 Flow of steam at low pressure, 
 699 
 
 capacities of pipes, 877-878 
 
 in long pipes, 877 
 
 in pipes, 877-879 
 
 into atmosphere, 876 
 
 loss of pressure due to friction, 
 877 
 
 loss of pressure due to radiation, 
 880 
 
 Napier's rule, 876 
 
 resistance of bends, valves, etc., 
 
 . 879 
 
 tables of, 699, 877-879 
 
 through a nozzle, 876, 1085 
 
 through safety valves, 934 
 Flow of water, 726-746 
 
 approximate formulae, 734, 737, 
 746 
 
 Chezy's formula, 728 
 
 D'Arcy's formula, 732 
 
 experiments and tables, 737- 
 753 
 
 exponential formula, 736 
 
 fall per mile and slope, table, 
 
 formulae for, 726-746 
 
 in cast-iron pipe, 737 
 
 in house service pipes, table, 744 
 
 in pipes at uniform velocity, 
 
 table, 739 
 in pipes, table from D'Arcy's 
 
 formula, 740, 741 
 table from Hazen & Williams' 
 
 formula, 742, 743 
 table from Kutter's formula, 
 
 738, 739 
 
 in riveted steel pipes, 734-736 
 in 20-in. pipe, 737 
 Kutter's formula, 730 
 
 Flow of water over weirs, 726, 762 
 through nozzles, table, 753 
 through orifices, 726 
 through rectangular orifices, 
 
 760 
 
 values of c, 732, 736 
 values of coefficient of friction, 
 
 734 
 
 Flowing water, horse-power of, 765 
 water, measurement of, 757-764 
 Flues, collapsing pressure of, 341 
 corrugated, 341, 917 (see also 
 
 Tubes and Boilers) 
 Flux, magnetic, 1398 
 Fly-wheels, arms of, 1050 
 centrifugal force in, 1047 
 diameters for various speeds, 
 
 1048 
 for presses, punches, shears, etc., 
 
 1323 
 for steam-engines, 1040, 1044- 
 
 1052 
 
 speed, variation in, 1044-1049 
 strains in, 1049 
 thickness of rim of, 1052 
 weight of, 1045-1048 
 weight of, for alternating cur- 
 rent units, 1047 
 wire wound, for extreme speeds, 
 
 1052 
 
 wooden rim, 1051 
 Foaming or priming of steam- 
 boilers, 721, 930 
 Foot-pound, unit of work, 528 
 Force, centrifugal, 521 
 definitions of, 512 
 graphic representation of, 513 
 moment of, 514 
 of a blow, 529, 1322 
 of acceleration, 526 
 units of, 512 
 work, power, etc., 528 
 Forces, composition of, 513 
 equilibrium of, 516 
 parallel, 515 
 parallelogram of, 513 
 parallelopipedon of, 514 
 polygon of, 513 
 resolution of, 513 
 Forced draught, chimneys with, 
 
 952 
 
 draught in steam-boilers, 923 
 Forcing and shrinking fits, 1323- 
 
 1327 (see Fits) 
 Forging and grinding of tools, 
 
 1263 
 
 heating of steel for, 492 
 hydraulic, 814, 815 
 of tool steel, 488, 492, 1263 
 Forgings, steel, annealing of, 482 
 
 strength of, 353 
 Forging-press, hydraulic, 814 
 Fottinger transformer or hy- 
 draulic pinion, 1095 
 Foundation walls, thickness of, 
 
 13S6 
 
 Foundations, masonry, allowable 
 pressures on, 1386 
 
fou-fru 
 
 INDEX. 
 
 fru-fur 
 
 1495 
 
 Foundations of buildings, 1386 
 Foundry coke, quality of, 1255 
 
 irons (see Pig iron and Cast 
 iron) 
 
 ladles, dimensions of, 1257 
 
 molding-sand, 1256 
 
 practice, 1247-1257 
 
 practice, shrinkage of castings, 
 
 practice, use of softeners, 1253 
 use of ferro alloys in, 1255 
 Fractions, 2 
 
 product of, in decimals, 4 
 Framed structures, stresses in, 
 
 541-548 
 
 Frames, steam-engine, 1043 
 Framing, for tanks with flat sides, 
 
 339 
 
 Francis's formulae for weirs, 762 
 Freezing point of brine, 1343 
 
 point of water, 719 
 French measures and weights, 21 
 
 26 
 
 thermal, unit, 560 
 Frequency changers, 1457 
 of alternating currents, 1440 
 standard, in electric currents, 
 
 1440 
 Friction and lubrication, 1219- 
 
 1246 
 brakes and friction clutches, 
 
 1239 
 
 brakes, capacity of, 1334 
 clutches, 1179 
 
 coefficient of, definition, 1219 
 coefficient of, in water-pipes, 
 
 734 
 
 coefficients of, tables, 1219-1221 
 drives, power transmitted by, 
 
 1178 
 
 fluid, laws of, 1220 
 laws of, of lubricated journals, 
 
 1225 
 loss of head by, in water-pipes, 
 
 728, 735, 745 
 moment of, 1229 
 Morin's laws of, 1223 
 of air in mine passages, 714 
 of car journals, 1228 
 of hydraulic packing, 813, 1241 
 of lubricated journals, 1220- 
 
 1232 
 of metals, under steam pressure, 
 
 1223 
 
 of motion, 1219-1222 
 of pivot bearings, 1229, 1232 
 of rest, 1219 
 of solids, 1219 
 of steam-engines, 1238 
 of steel tires on rails, 1219 
 rollers, 1233 
 rolling, 1219 
 
 unlubricated, law of, 1219 
 work of, 1229 
 Frictional gearing, 1 178 
 
 resistance of surfaces moved in 
 
 water, 756 
 Frustum of cone, 62 
 
 Frustum of parabolic conoid, 65 
 
 of pyramid, 62 
 
 of spheroid, 64 
 
 of spindle, 65 
 Fuel, 816-858 
 
 bagasse, 839 
 
 charcoal, 836-837 (sec Char- 
 coal) 
 
 coke, 824, 832-834 (see Coke) 
 
 combustion of, 816 
 
 dust, 837 
 Fuel, economizers, 924-927 
 
 equation of, 925 
 
 explosions of, 927 
 
 heating surface of, 925 
 
 heat transmission in, 925 
 
 saving due to, 925 
 
 tests of, 926 
 Fuel for cupolas, 1248, 1255 
 
 gas, 845 (see Gas) 
 
 gas, for small furnaces, 854 
 eat of combustion of, 560, 817 
 liquid, 840-844 
 peat, 838 
 pressed, 831 
 sawdust, 838 
 
 solid, classification of, 818 
 straw, 839 
 
 theory of combustion of, 816 
 turf, 838 
 
 value of illuminating gas, 863 
 weight of, 180 
 wet tan bark, 838 
 wood, 835, 836 
 Fuel-oil, burners for, 842 
 
 California, heating values of, 
 
 842 
 
 chimney draught with, 952 
 chimney table for, 951 
 specifications for purchaseof , 843 
 Functions, trigonometric, tables 
 
 of, 170-172 
 trigonometric, of half an angle, 
 
 69 
 of sum and difference of angles, 
 
 68 
 
 of twice an angle, 69 
 Furnace for melting iron for 
 
 malleable castings, 454 
 flues, steam-boiler, formulae for, 
 
 917 
 
 heating (see Heating) 
 Furnaces, blast, gases of, 855 
 blast, temperature in, 555 
 corrugated, 342 917 
 down draught, 919 
 electric, 1422 
 for different coals, 827 
 for house heating, 690 
 gas, fuel for, 854 
 hot-air, heating by, 690 
 industrial, temperatures in, 554 
 open hearth, temperature in, 
 
 554, 555 
 
 steam-boiler (see Boiler-fur- 
 naces) 
 steam-boiler, combustion space 
 
 in, 889 
 
1496 
 
 ffns-gas 
 
 INDEX. 
 
 gas-gca 
 
 Fusible alloys, 404 
 
 plugs in boilers, 404, 918 
 Fusibility of metals, 180 
 Fusing-disk, 1309 
 
 temperatures of substances, 554, 
 
 559 
 Fusion, latent heat of, 568 
 
 of electrical wires, 1409 
 
 g, value of, 522, 525 
 
 GAGE, decimal, 32 
 lines for steel angles, 321 
 sheet metal, 28, 29, 31, 32 
 
 Stub's wire, 28, 
 
 Gages, limit, for iron for screw 
 threads, 232 ' . 
 
 wire, 28-30 
 
 Gallon, British and American, 27 
 Gallons and cubic feet, table, 130 
 
 per minute, cubic feet per 
 
 second, 130 
 
 Galvanic action, corrosion by, 467 
 Galvanized sheets, weights of, 192 
 
 wire, test for, 474 
 
 wire rope, 255, 262 
 Galvanizing by cementation, 474 
 
 iron surfaces, 473. 474 
 
 of welded pipe 206 
 Gas (see also Fuel-gas, Water-gas, 
 Producer gas, Illuminating- 
 gas) 
 
 ammonia, properties of, 1339 
 
 analyses by volume and weight, 
 854 
 
 and electric lighting, 1468 
 
 and oil engines, rules for testing, 
 1105 
 
 and vapor mixtures, laws of, 
 604 
 
 anthracite, 845 
 
 bituminous, 846 
 
 carbon, 845 
 
 coal, 858 
 
 exhausters, rotary, 679 
 
 fuel (see also Water-gas) 
 
 fuel, cost of, 863 
 
 fuel for small furnaces, 854 
 
 flow of, in pipes, 864-866 (see 
 Flow of gas) 
 
 illuminating, 858-866 (see Il- 
 luminating-gas ) 
 
 lamps, pipe services for, 864 
 
 lights, candle-power of, 860 
 
 lights, Welsbach, standard sizes, 
 1474 
 
 meter, Thomas electric, 667, 
 669 
 
 natural, 847-848 
 
 perfect, equations of a, 600 
 
 pipe, cast-iron, weights and 
 dimensions, 198, 199 
 
 produced from ton of coal, 848 
 
 producer, 848-855 (see also Gas- 
 Producers) 
 
 sulphur-dioxide, properties of, 
 1338, 1341 
 
 table of factors for equivalent 
 volumes of, 865 
 
 Gas, water, 846, 859-864 (see 
 
 Water-gas) 
 Gases, absorption of, 605 
 
 Avogadrp's law of, 604 
 
 combustion of, rise of tempera- 
 ture in, 818 
 
 cupola, utilization of, 1253 
 
 densities of, 604 
 _ expansion of, 601, 603 
 
 expansion of by heat, table, 565 
 
 flow of, 605 
 
 heat of combustion of, 560 
 
 ignition temperature of, 858 
 
 law of Charles, 600, 604 
 
 liquefaction of, 605 
 
 Mariotte's law of, 603 
 
 of combustion, analyses of, 817 
 
 physical properties of, 603-606 
 
 specific heats of, 563, 564 
 
 waste, use of, under boilers, 
 898, 899 
 
 weight and specific gravity of, 
 
 table, 176 
 Gas-engine, 1095-1108 
 
 calculation of the power of, 1097 
 
 conditions of maximum effi- 
 ciency, 1103 
 
 economical performance of, 1104 
 
 efficiency of, 1103 
 
 four-cycle and two-cycle, 1096 
 
 governing, 1103 
 
 heat losses in, 1104 
 
 horse-power, estimate of, 1101 
 
 ignition in, 1102 
 
 mean effective pressure in, 1098 
 
 pressures developed in, 1097 
 
 pumps, 808 
 
 sizes of, 1100 
 
 temperatures and pressures in, 
 1096, 1099 
 
 tests of, 1105-1108 
 
 tests with different coals, 853 
 Gas-producers, capacity of. 851 
 
 and scrubbers, proportions of, 
 849 
 
 combustion in, 849 
 
 practice, 851 
 
 use of steam in, 854 
 Gasoline engines, 1101 
 
 fuel value of, 841 
 
 vapor pressures of, 844 
 Gauss, definition and value of, 
 
 1398 
 
 Gear, reduction, for steam tur- 
 bines, 1095 
 
 reversing, 1039 
 
 stub- tooth, 1167, 
 
 wheels, calculation of speed of, 
 1162 
 
 wheels, formulae for dimensions 
 of, 1160 
 
 wheels, milling cutters for, 1162 
 
 wheels, proportions of, 1161 
 
 worm, 540 
 
 Gears, automobile, efficiency of, 
 1172 
 
 lathe, for screw cutting, 1259 
 
 of lathes, quick change, 1260 
 
gea-gor 
 
 INDEX. 
 
 goY-har 
 
 1497 
 
 Gears, spur, machine-cut, 1178 
 
 with short teeth, 1160 
 Gear-box drive for machine tools, 
 
 1308 
 -cutting, speeds and feeds for, 
 
 1284 
 
 Gearing, annular, 1169 
 bevel, 1169 
 chordal, pitch, 1159 
 comparison of formulae, 1174- 
 
 1177 
 
 cycloidal teeth, 1162 
 diameters for 1-inch circular 
 
 pitch, 1159 
 differential, 1169 
 efficiency of , 1170-1172 
 forms of teeth, 1162-1167 
 f Fictional. 1178 
 involute teeth, 1165 
 pitch, pitch-circle, etc., 1157 
 proportions of teeth, 1159, 1161 
 racks, 1165 
 raw-hide, 1177 
 
 relation of diametral and cir- 
 cular pitch, 1158 
 speed of, 1177 
 spiral, 1168 
 stepped, 1168 
 strength of, 1172-1177 
 stub- tooth, 1167 
 toothed-wheel, 539, 1157-1180 
 twisted, 1168 
 worm, 1168 
 
 worm, efficiency of, 1171 
 Generator sets, standard dimen- 
 sions of, 1007 
 Generators, acetylene, 857 
 
 alternating-current, 1448 (see 
 
 Dynamo electric machines) 
 electric, 1437, 1448 
 Geometrical problems, 37-53 
 progression, 11 
 propositions, 53 
 Geometry, analytical, 70-73 
 German silver, 356, 402 
 conductivity of, 1401 
 Gesner process, treating iron sur- 
 faces, 473 
 Gib keys, 1332 
 Gilbert, unit of magneto-motive 
 
 force, 1398 
 
 Girder beams, Bethlehem steel/331 
 Girders, allowed stresses in plate 
 
 and lattice, 289 
 and beams, safe load on, 1387 
 and beams, New York building 
 
 laws, 1390 
 
 plate, strength of, 353 
 Warren, stresses in, 546 
 Glass, skylight, sizes and weights, 
 
 196 
 
 strength of, 365 
 weight of, 177 
 Gold, melting temperature of, 
 
 554, 559 
 
 properties of, 178 
 Gordon's formula for columns, 
 284 
 
 Governor, inertia, 1066 
 Governors, steam-engine, 1065 
 
 impulse wheel, 782 
 Governing of gas-engines, 1103 
 Grade line, hydraulic, 748 
 Grain, weight of, 180 
 Granite, strength of, 357, 370 
 Graphite, Acheson's defloccu- 
 lated, 1246 
 
 lubricant, 1246 
 
 paint, 471 
 
 Grate-surface, for house heating, 
 boilers and furnaces, 693 
 
 in locomotives, 1115 
 
 of a steam-boiler, 888 
 Gravel, cubic feet per ton, 181 
 Gravity, acceleration due to, 521, 
 525 
 
 boiler-feeders, 938 
 
 center of, 516 
 
 specific (see Specific gravity), 
 
 Grease lubricants, 1244 
 Greatest common measure or 
 
 divisor, 2 
 Greek letters, 1 
 Greenhouses, hot-water, heating 
 
 of, 703 
 
 steam-heating of, 702 
 Grinding as a substitute for finish 
 
 turning, 1317 
 of tools, 1263 
 wheel (see Grindstones and 
 
 Emery wheels) 
 wheel for high-speed tools, 1263, 
 
 1314 
 Grindstones, speed of, 1317 
 
 strains in, 1318 
 Guest's formula for combined 
 
 stresses, 335 
 Gun-bronze, variation in strength 
 
 of, 386 
 Gun-iron, variation in strength 
 
 of, 452 
 Gun-metal (bronze), composition 
 
 of, 390 
 
 Guns, energy of recoil of, 531 
 Gurley's bronze, composition of, 
 
 390 
 Guy ropes for stand-pipes, 349 
 
 ropes, wire, 255 
 Gyration, center of, 518 
 radius of, 293 
 table of radii of, 519 
 
 H- COLUMNS, Bethlehem 
 steel, 333 
 Halpin heat storage system, 
 927, 1014 
 Hammering, effect of, on steel, 
 
 488 
 
 Hanger bolts, 243 
 Hardening and tempering, change 
 
 of shape due to, 1291 
 of soft steel, 479 
 Hardness, electro-magnetic tests 
 
 of, 365 
 of copper-tin alloys, 385 
 
1498 
 
 har-hea 
 
 INDEX. 
 
 hea-hea 
 
 Hardness of metals, Brinell's tests, 
 364 
 
 of water, 723 
 
 scleroscope tests of, 365 
 Harvey process of hardening steel, 
 
 1291 
 Harveyizing steel armor-plate, 
 
 1291 
 Haulage, wire-rope, 1202-1205 
 
 wire-rope, endless rope system, 
 1203 
 
 wire-rope, engine-plane, 1203 
 
 wire-rope, inclined-plane, 1202 
 
 wire-rope, tail-rope system, 1203 
 
 wire-rope tramway, 1204 
 Hauling capacity of locomotives, 
 
 1111 
 Hawley down-draught furnace, 
 
 919 
 
 Hawsers, steel wire, 262 
 Hazen & Williams' formula, table 
 
 of flow of water, 742, 743 
 Head, loss of, 728, 735, 745 (see 
 Loss of head) 
 
 of air, due to temperature differ- 
 ences, 716 
 
 of water, 728 
 
 of water, comparison of, with 
 
 various units, 718 
 Heads of boilers, 914 
 
 of boilers, unbraced, wrought 
 
 iron, strength of, 337 
 Heat, 549-597 
 
 conducting power of metals, 
 580 
 
 conduction by various sub- 
 stances, 580-587 
 
 conduction of, 579 
 
 convection of, 579 
 
 effect of on gram of steel, 479 
 
 expansion due to, 565 
 
 generated by electric current, 
 1408 
 
 -insulating materials, tests of, 
 581 
 
 latent, 568 (see Latent heat) 
 
 loss by convection, 596 
 
 losses in steam-power plants, 
 1012 
 
 mechanical equivalent of, 560, 
 868 
 
 of combustion, 560 
 
 of combustion of fuels, 560, 817 
 
 produced by human beings, 686 
 
 quantitative measurement of, 
 560 
 
 radiating power of substances, 
 578 
 
 radiation of, 578 (see also Ra- 
 diation) 
 
 reflecting power of substances, 
 578 
 
 resistance, coefficients of, 583 
 
 resistance, reciprocal of con- 
 ductivity, 582 
 
 specific, 562-565 (see Specific 
 heat) 
 
 steam, storing of, 927, 1014 
 
 Heat storage, Halpin system, 927, 
 
 1014 
 Heat transmission, Blechynden's 
 
 tests of, 593 
 
 from flame to water, 592 
 from gases to water, 592 
 from steam to water, 587 
 in condenser tubes, 589 
 in feed-water heater, 590 
 in radiators, 698 
 resistance of metals to, 580 
 through building walls, etc., 582, 
 
 688 
 
 through plates, 580, 591 
 through plates from steam or 
 
 hot water to air, 595 
 Heat treatment of a motor-truck 
 
 axle, 479 
 treatment of high speed tool 
 
 steel, 1265 
 
 treatment of steel (see Steel) 
 unit of, 560, 867 
 units per pound of water, 717 
 Heaters and condensers, calcula- 
 tion of surface of, 939 
 cast iron, for hot-blast heating, 
 
 709 
 
 cast iron, tests of, 709 
 electric, 1420 
 feed-water, 938-940 
 feed- water, open-type, 940 
 feed-water, transmission of heat 
 
 in, 590 
 
 Heating and Ventilation, 681-716 
 allowance for exposure and 
 
 leakage, 688 
 blower system, 708710 
 boiler heating surface, 694 
 computation of radiating sur- 
 face, 698 
 
 heating surface, indirect, 698 
 heating value of radiators, 684, 
 
 697 
 
 quantity of heat required, 690 
 steam-heating, 694-703 (see 
 
 Steam-heating) 
 transmission of heat through 
 
 building walls, 688 
 Heating a building to 70 in zero 
 
 weather, 711 
 
 air, heat absorbed in, 691 
 and ventilating by electric cur- 
 rent, 1421 
 by blower system, capacity of 
 
 fans for, 711 
 by electricity, 713 
 by exhaust steam, 1009 
 by hot-air furnaces, 690 
 by hot water, 703- 708 (see Hot- 
 water heating) 
 
 by overhead steam pipes, 702 
 by steam (see Steam-heating) 
 domestic, by electricity, 1421 
 furnace, size of air pipes for, 692 
 furnace, with forced air supply, 
 
 690 
 
 guarantees, performance of, 712 
 of electrical conductors, 1408 
 
bca-liol 
 
 INDEX. 
 
 hoi-how 
 
 1499 
 
 Heating of factories by blower sys- 
 tem, 708, 710 
 of greenhouses, 702 
 of large buildings, 684 
 of steel for forging, 492 
 of tool steel, 492 
 problems, standard values in, 
 
 687 
 
 steam and electric, 1421 
 value of coals, 826-830 
 value of wood, 835 
 water by steam coils, 591 
 Seating-surface of steam-boiler, 
 
 887, 888 
 Height, table of, corresponding to 
 
 a given velocity, 523 
 Helical steel springs, 418 
 Helix, 61 
 
 Hemp rope, strength of, 357 
 rope, table of strength and 
 
 Weight of, 410, 415 
 Henry, definition and value of, 
 
 1397 
 High-speed tool steel (see Steel, 
 
 and Tools) 
 
 Hindley worm gear, 1169 
 Hobson's hot-blast pyrometer, 
 
 555 
 
 Hodgkinson's column formula, 283 
 Hoist, hydraulic, 783 
 Hoists, electric motors for, 1464 
 Hoisting by hydraulic pressure, 
 
 813 
 
 counterpoise system, 1189 
 cranes, 1189-1193 (see Cranes) 
 effect of slack rope, 1186 
 endless rope system, 1189 
 engines, 1186 
 
 engines, compressed-air, 646 
 engines, counterbalancing of, 
 
 1188 
 
 horse-power required for, 1184 
 Koepe system, 1189 
 loaded wagon system, 1189 
 limit of depth for, 1186 
 of cargoes, 414 
 pneumatic, 1187 
 suspension cable ways, 1205 
 with tapering ropes, 1188 
 Hoisting-rope, 410-415 
 flexible steel wire, 258, 259 
 iron or steel, tables, 255-261 
 ion-spinning, 258, 261 
 tresses in, on inclined planes, 
 
 1204 
 tension required to prevent 
 
 slipping, 1206 
 
 wire, sizes and strength of, 410 
 Holding power of bolts in white 
 
 pine, 346 
 
 of expanded boiler tubes, 364 
 of lag-screws, 347 
 of nails in wood, 347 
 f nails, spikes and screws, 346, 
 
 347 
 of tubes expanded into sheets, 
 
 364 
 of wood screws, 346 
 
 Holes, tube, in steam-boilers, 916 
 Hollow cylinders, resistance of to 
 
 collapse, 341-345 
 shafts, torsional strength of, 334 
 Homogeneity test for fire-box 
 
 steel, 508 
 Hooks and shackles, strength of, 
 
 1184 
 
 heavy crane, 1183 
 proportions of, 1182 
 Horse gin, 534 
 work of, 533 
 
 Horse-power (see also Power) 
 brake, 970 
 
 brake, definition of, 1017 
 computed from torque, 1436 
 constants, of steam-engines, 
 
 971-974 
 
 definition of, 27, 528 
 electrical, 970, 1408 
 electrical, brake and indicated, 
 
 1408 
 
 hours, definition of, 528 
 nominal, definition of, 974 
 of compound engine, estimat- 
 ing, 971 
 
 of flowing water, 765 
 of marine and locomotive boil- 
 ers, 888 
 
 of steam-boilers, 885 
 of steam-boilers, builders' rat- 
 ing, 888 
 
 of steam-engines, 970-976 
 water and steam, cost of, 767 
 Hose couplings, national standard, 
 
 218 
 
 fire, friction losses in, 752 
 hydrant pressures required with 
 
 different lengths of, 750 
 rubber-lined, friction loss in, 
 
 752 
 
 specifications for, 379 
 Hot-air engines, 1095 
 
 heating (see Heating) 
 Hot-blast pyrometer, Hobson's, 
 
 555 
 Hot-blast system of heating, 708 
 
 (see Heating) 
 Hot boxes, 1228 
 Hot-water Heating (see Heating), 
 
 703-708 
 
 arrangement of mains, 703 
 computing radiating surface, 
 
 704-706 
 
 corrosion of pipe in, 708 
 indirect, 705 
 of greenhouses, 703 
 rules for, 703 
 size of pipes for, 704 
 sizes of flow and return pipes, 
 
 707 
 
 velocity of flow, 703 
 with forced circulation, 707 
 House-heating (see Heating) 
 House-service pipes, flow of water 
 
 in, table, 744 
 
 Howden system of forced draught, 
 923 
 
1500 
 
 How-Ill 
 
 INDEX. 
 
 ill-Int 
 
 Howe truss, stresses in, 546 
 .tumidity and temperature, com- 
 fortable, 685 
 relative, table of, 610 
 Humphrey gas pump, 808 
 Hyatt roller bearings, 1235 
 Hydraesfer process, treating iron 
 
 surfaces, 473 
 
 Hydrant pressures required with 
 different lengths of hose, 750 
 Hydraulic air compressor, 650 
 apparatus, efficiency of, 812 
 cylinders, thickness of, 813 
 engine, 815 
 forging, 814, 815 
 formulae, 726-746 
 formulae, approximate, 734, 737, 
 
 746 
 
 grade-line, 748 
 packing, friction of, 813 
 pipe, riveted, table, 219 
 power in London, 814 
 press, thickness of cylinders 
 
 for, 340 
 
 presses hi iron works, 813 
 ram, 810-812 
 riveting machines, 814 
 turbines (see Turbines, hy- 
 draulic) 
 
 Hydraulics (see Flow of water) 
 Hydraulic pressure, hoisting by, 
 
 813 
 
 transmission, 812-816 
 transmission, energy of, 812 
 transmission, speed of water 
 through pipes and valves, 813 
 transmission, references, 816 
 Hydrometer, 175 
 Hygrometer, dry and wet bulb, 
 
 610 
 
 Hyperbola, asymptotes of, 73 
 construction of, 49 
 equations of, 72 
 Hyperbolic curve on indicator 
 
 diagrams, 974 
 
 logarithms, tables of, 164-166 
 Hypocycloid, 50 
 
 I-BEAMS (see also Beams) 
 Bethlehem steel, 332 
 Carnegie, table of, 307-310 
 safe loads on, 309 
 spacing, for uniform load, 311 
 Ice-making, absorption evapora- 
 tor system, 1367 
 machines, 1336-1367 (see Re- 
 frigerating machines) 
 plant, test of, 1367 
 tons of ice per ton of coal, 1367 
 with exhaust steam, 1367 
 Ice, manufacture, 1366 
 -melting effect, 1343 
 properties of, 720 
 strength of, 368 
 Ignition in gas engines, 1102 
 temperature of gases, 858 
 Illuminants, relative color values 
 of, 1469 
 
 Illuminants, relative efficiency of, 
 
 1472 
 
 Illuminating coal-gas, 858 
 Illuminating-gas, 858-866 
 
 calorific equivalents of constit- 
 uents, 860 
 fuel value of, 863 
 space required for plants, 862 
 Illuminating water-gas, 859 
 Illumination by arc lamps at 
 
 different distances, 1471 
 definition of, 1468 
 electric and gas lighting, 1468 
 interior, 1473 
 of buildings, watts per square 
 
 foot, required for, 1369 
 relation of, to vision, 1469 
 Impact, 530 
 Impedance, 1441 
 polygons, 1442 
 Impulse water wheels, 780 (see 
 
 Water wheel, tangential) 
 Impurities of water, 720 
 Incandescent lamps (see Lamps), 
 
 1470 
 Inches and fractions as decimals 
 
 of a foot, table, 5 
 Inclined plane, 527, 537 
 motion on, 527 
 stresses in hoisting ropes on, 
 
 1204 
 
 wire-rope haulage, 1202 
 Incrustation and scale, 721, 927 
 
 932 
 
 India rubber, action under ten- 
 sion, 378 
 
 vulcanized, tests of, 378 
 Indicated horse-power, 970-976 
 Indicator diagrams, analysis of, 
 
 1017 
 diagrams, to draw clearance 
 
 line on, 974 
 diagrams, to draw expansion 
 
 curve, 974 
 diagrams, tests of locomotives, 
 
 1122 
 rig, 969 
 Indicators, steam-engine, 968-976 
 
 (see Steam-engines) 
 steam-engine, errors of, 969 
 Indirect heating radiators, 698 
 Inductance, 1440 
 
 of lines and circuits, 1445 
 Induction, magnetic, 1398 
 
 motors, 1463 
 Inertia, definition of, 513 
 
 moment, of, 293, 517 
 Ingot iron, "Armco," 477 
 Injector, 807 
 
 efficiency of, 937 
 equation of, 936 
 performance of, 937 
 Inspection of steam-boilers, 932 
 Insulation, underwriters', 1410 
 Insulators, electrical value of, 1402 
 
 heat, 581 
 Integrals, 75 
 table of, 80, 81 
 
Int-iro 
 
 INDEX. 
 
 irr-Iam 
 
 1501 
 
 Integration, 76 
 
 Intensity of magnetization, 1398 
 
 Interest, 12 
 
 compound, 13, 14 
 Intercoolers for air compressors, 
 
 648 
 
 Interpolation, formula for, 86 
 Invar, iron-nickel alloy, 499, 567 
 Involute, 52 
 
 gear-teeth, 1165 
 
 gear-teeth, approximation of, 
 
 1166 
 
 Involution, 7 
 
 Iridium, properties of, 178 
 Iron and steel, 178, 436-511 
 classification of, 436 
 effect of cold on strength of, 
 
 464 
 
 electric furnaces, 1423 
 inoxidizable surface for, 472 
 preservative coatings for, 471- 
 
 474 
 
 relative corrosion of, 468 
 rustless coatings for, 471-474 
 sheets, weight of, 183 
 tensile strength at high tem- 
 peratures, 463 
 Iron bars (see Bars) 
 
 bars, weight of square and 
 
 round, 181, 184 
 bridges, durability of, 466 
 cast, 437-454 (see Cast-iron) 
 castings, chemical standards for, 
 
 441 
 
 coated with aluminum, 473 
 coated with lead, 474 
 coefficients of expansion of, 465 
 color of at various tempera- 
 tures, 558 
 
 -copper-zinc alloys, 393 
 corrosion of, 467 
 corrugated, sizes and weights, 
 
 194 
 
 durability of, 465-467 
 electrolytic, properties of, 460 
 flat-rolled, weight of, 188, 189 
 for stay-bolts, 462 
 inoxidizable surfaces, produc- 
 tion of, 472 
 
 latent heat of fusion of, 568 
 malleable, 454 (see Malleable 
 
 iron) 
 
 pig (see Pig-iron and Cast-iron) 
 plates, approximating weight'of , 
 
 486 
 
 plates, weight of, table, 187 
 properties of, 178 
 rivets, shearing resistance of, 
 
 430 
 
 rope, table of strength of, 410 
 shearing strength of. 362 
 sheets, weights, 31, 32, 183 
 -silicon-aluminum alloys, 398 
 specific heat of, 562, 563 
 tubes, collapsing pressure of, 
 
 341 
 
 wrought, 459-463 (see Wrought 
 iron) ^ 
 
 Irregular figure, area of, 56, 57 
 
 solid, volume of, 65 
 Irrigation canals, 755 
 Isothermal compression of air, 633 
 
 expansion, 601 
 
 expansion of steam, 959 
 
 JAPANESE alloys, composition 
 of, 393 
 Jarno tapers, 1319 
 Jet condensers, 1068 
 
 propulsion of ships, 1384 
 reaction of a, 1385 
 water wheels, 781 
 Jets, steam (see Steam jets) 
 
 vertical water, 749 
 Joints, pipe (see Pipe joints) 
 riveted, 424-435 (see Riveted 
 
 joints) 
 
 Joists, contents of, 21 
 Joule, definition and value of, 
 
 1396, 1397 
 
 Joule's equivalent, 560 
 Journals (see also Shafts and 
 
 Bearings) 
 
 coefficients of friction of, 1220 
 Journal-bearings, cast-iron, 1223 
 friction of, 1220-1232 
 of engines, 1034 
 
 KAOLIN, melting point of, 556 
 Kelvin's rule for electric 
 transmission, 1411 
 Kennedy key, 1330 
 Kerosene as fuel, 841 
 
 for scale in boilers, 929 
 Keys, dimensions of, 1328 
 gib, 1332 
 
 holding power of, 1332 
 various forms of, 1328 
 Key-seats, depth of, 1329 
 Keyways for milling cutters, 1277 
 Kinetic energy, 528 
 King-post truss, stresses in, 543 
 Kirkaldy's tests of strength of 
 
 materials, 352-358 
 Knife-edge bearings, 1238 
 Koepe's system of hoisting, 1189 
 Knot, on nautical mile, 17 
 Knots, varieties of, 415, 416 
 Krupp steel tires and axles, 354 
 Kutter's formula, flow of water, 730 
 formula, tables of flow of water, 
 738, 739 
 
 LACING of belts, 1147 
 Ladles, foundry, sizes of, 
 1257 
 Lag screws, holding power of, 347 
 
 screws, sizes and weights, 241 
 Lamps, arc, 1470 
 arc, data of, 1471 
 arc, illumination by, at differ- 
 ent distances, 1471 
 arrangement of, in rooms, 1475 
 electric, life of, 1476 
 incandescent, characteristics of, 
 
 1474 
 incandescent electric, 1470 
 
1502 
 
 lam-Jin 
 
 INDEX. 
 
 lin-Ioc 
 
 Lamps, mercury vapor, 1470 
 
 tungsten, 1473 
 Land measure, 17 
 Lang-lay wire-rope, 254 
 Lap and lead in slide valves, 1052- 
 
 1054 
 
 Lap joints, riveted, 426, 427 
 Laps and lapping, 1310 
 Latent heat of evaporation, 569 
 
 of fusion of iron, 568 
 
 of fusion of various substances, 
 
 568 
 Lathe, change-gears for, 1260 
 
 cutting speed of, 1259 
 
 horse-power to run, 1292, 1293 
 
 power required for, 1293 
 
 rules for screw-cutting gears, 
 1259 
 
 setting taper in, 1261 
 
 topis, forms of, 1261 
 Lattice girders, allowed stresses 
 
 in, 289 
 Laws of falling bodies, 521 
 
 of motion, 513 
 Lead and tin tubing, 226, 227 
 
 coatings on iron surfaces, 474 
 
 effect of, on copper alloys, 394 
 
 -lined iron pipes, 227 
 
 paint as a preservative, 471 
 
 pipe, tin-lined, sizes and weights, 
 table, 226 
 
 pipe, weights and sizes of, 
 table, 226, 227 
 
 properties of, 178 
 
 sheet, weight of, 228 
 
 waste-pipe, weights and sizes 
 
 of, 227 
 
 Leakage of steam in engines, 976 
 Least common multiple, 2 
 Leather, strength of, 357 
 Lea-Deagan two-stage pump, test 
 
 of, 801 
 
 Le Chatelier's pyrometer, 554 
 Lentz compound, engine, 997 
 Leveling by barometer, 607 
 
 by boiling water, 607 
 Lever, 535 
 
 bent, 514, 536 
 Lewis's key, 1329 
 Lighting, electric and gas, 1468 
 
 electric, cost of, 1475 
 
 of streets, 1471 
 
 quantity of gas and electricity 
 required for different rooms, 
 1473 
 
 street, recent installations, 1476 
 Lightning protection of chimneys, 
 
 949 
 
 Lights (see Lamps) 
 Lignites, analysis of, 829 
 Lime and cement mortar, strength 
 of, 372 
 
 and cement, weight of, 180 
 Limestone, strength of, 371 
 Limit, elastic, 273-278 
 
 gages for screw-thread iron, 232 
 Lines of force, 1430 
 Links, steel bridge, strength of, 353 
 
 Link-belting, sizes and weights, 
 
 1199 
 Link-motion, locomotive, 1119 
 
 steam-engine, 1062-1065 
 Lintels in buildings, 1390 
 Liquation of metals in alloys, 388 
 Liquefaction of gases, 605 
 Liquid air and other gases, 605, 606 
 
 measure, 18 
 
 Liquids, absorption of gases by, 
 605 
 
 Compressibility of, 175 
 
 expansion of, 567 
 
 specific gravity of, 175 
 
 specific heats of, 563 
 Loading and storage machinery, 
 
 1193 
 
 Lock- joints for pipes, 212 
 Locomotive boilers, 1113 
 
 boiler tubes, seamless, 222 
 
 boilers, size of, 1113 
 
 crank-pin, quantity of oil used 
 on, 1246 
 
 engine performance, 1122 
 
 forgings, strength of, 353 
 Locomotives, 1108-1129 
 
 boiler pressure, 1117 
 
 classification of, 1116 
 
 compounding of, 1125 
 
 compressed-air, 1128 
 
 compressed-air, with compound 
 cylinders, 1129 
 
 counterbalancing of, 1126 
 
 dimensions of, 1120-1122 
 
 drivers, sizes of, 1118 
 
 economy of high pressure in, 
 1116 
 
 effect of speed on cylinder pres- 
 sure, 1117 
 
 efficiency of, 1111 
 
 exhaust-nozzles, 1115 
 
 fire-brick arches in, 1115 
 
 fireless, 1127 
 
 fuel efficiency of, 1119 
 
 fuel waste of, 1125 
 
 grate-surface of, 1115 
 
 hauling capacity of, 1111 
 
 horse-power of, 1113 
 
 indicator tests of, 1122 
 
 leading types of, 1116 
 
 light, 1127 
 
 link-motion, 1119 
 
 Mallet compound, 1120 
 
 narrow gage, 1127 
 
 performance of high speed, 1118 
 
 petroleum burning, 1127 
 
 safety valves for, 935 
 
 smoke-stacks, 1115 
 
 speed of, 1118 
 
 steam distribution of, 1117 
 
 steam-ports, size of, 1118 
 
 superheating in, 1126 
 
 testing, 1123 
 
 tractive force of, 1112. 1125 
 
 types of, 1116 
 
 valve travel, 1118 
 
 water consumption of, 1122 
 
 weight of, 1124 
 
loc-mac 
 
 INDEX. 
 
 mac-man 
 
 1503 
 
 Locomotives, Wootten, 1114 
 Logarithmic curve, 73 
 
 ruled paper, 84 
 
 sines, etc., table, 167 
 Logarithms, 79 
 
 four-place, table, 168 
 
 hyperbolic, tables of, 164-166 
 
 six-place, table, 137-164 
 
 use of, 135-137 
 
 Logs, area of water required to 
 store, 181 
 
 lumber, etc., weight Of, 181 
 
 weight of, 181 
 Long measure, 17 
 Loop, steam, 883 
 Loops of force, 1430 
 Lord and Haas's tests of coal, 
 
 822, 823 
 Loss and profit, 12 
 
 of head, Cox's formula, 734 
 
 of head in cast-iron pipe, tables, 
 745 
 
 of head in flow of water, 728, 
 735, 745 
 
 of head in riveted steel pipes, 735 
 Lowmoor iron bars, strength of, 
 
 352 
 
 Lubricant, water as a, 1246 
 Lubricants, examination of, 1242 
 
 grease, 1244 
 
 measurement of durability, 1241 
 
 oil, specifications for, 1242 
 
 qualifications of good, 1242 
 
 relative value of, 1242 
 
 soda mixture, 1246 
 
 solid, 1246 
 
 specifications for petroleum, 
 
 1242 
 Lubrication, 1241-1246 
 
 of engines, quantity of oil 
 needed for, 1245 
 
 of steam-engine cylinders, 1245 
 Lumber, weight of, 181 
 Lumen, definition of, 1469 
 "Lusitania, " performance of, 
 1376, 1381 
 
 turbines and boilers of, 1381 
 Lux, definition of, 1469 
 
 MACHINE screws, A. S. M. 
 E. standard, table, 234- 
 237 
 
 screws, taps for, 1320 
 shop, 1258-1333 
 shops, electric motors for, 1294- 
 
 1308, 1466 
 Machine tools, drives, feeds and 
 
 speeds, 1307 
 electric motors for, 1294-1308, 
 
 1466 
 gear connections of, to motors, 
 
 1301 
 individual motors for driving, 
 
 1308 
 
 methods of driving, 1307 
 power required for, 1270, 1278, 
 
 1286, 1293 
 sizes of motors for, 1294 
 
 Machine tools, soda mixture for, 
 1246 
 
 speed of, 1258 
 
 Machines, dynamo-electric (see 
 Dynamo-electric-machines) 
 
 efficiency of, 532 
 
 elements of, 535-541 
 
 in groups, power required for 
 
 driving, 1305 
 
 Machinery, coal-handling, 1196- 
 1199 
 
 horse-power required to run, 
 
 1292-1308 
 
 Maclaurin's theorem, 78 
 Magnalium, magnesium-alumi- 
 num alloy, 399 
 Magnesia bricks, 269 
 Magnesite, analysis of, 270 
 Magnesium, properties of, 179 
 Magnet, electro, 1430 
 Magnets, lifting, 1193 
 Magnetic alloys, 402 
 
 balance, for testing steel, 483 
 
 brakes, 1240 
 
 capacity of iron and steel, ef- 
 fect of annealing on, 483 
 
 circuit, 1430 
 
 circuit, units of, 1398 
 
 field, 1398 
 
 field, strength of, 1436 
 
 flux, magnetic induction, 1398 
 
 moment, 1398 
 
 pole, unit of, definition, 1398 
 Magnetization, intensity of, 1398 
 Magneto-motive force, 1398 
 Magnolia metal, composition of, 
 
 405 
 
 Mahler's calorimeter, 826 
 Malleability of metals, table, 180 
 Malleable cast iron, 454 
 
 castings, annealing, 455 
 
 castings, design of, 457 
 
 castings, tests of, 458 
 
 iron, pig iron for, 454 
 
 iron, composition and strength 
 of, 454, 458 
 
 iron, improvement in quality, 
 458 
 
 iron, physical characteristics, 45 6 
 
 iron, shrinkage of, 455 
 
 iron, specifications, 457 
 
 iron, strength of, 454, 458 
 
 iron test bars, 457 
 Mandrels, standard steel, 1318 
 Manganese bronze, 401 
 
 -copper alloys, 401 
 
 effect of, on cast iron, 438, 450 
 
 effect of, on steel, 476 
 
 properties of, 179 
 
 steel, 494 
 
 sulphide, dangerous in steel, 486 
 Manganin, high resistance alloy, 
 
 404, 1402 
 
 Manhole openings in steam- 
 boilers, 914 
 Manila rope, 411 
 
 rope, weight and strength of, 
 410-415 
 
1504 
 
 man-mer 
 
 INDEX. 
 
 mer-mod 
 
 Manograph, a high-speed engine- 
 indicator, 969 
 Manometer, air, 607 
 
 work of, tables, 532, 533 
 Man-wheel, 533 
 Marble, strength of, 357 
 Marine engineering, 1368-1385 
 (see Ships and Steam-engines) 
 engine, internal combustion, 
 
 1374 
 
 engine practice, advance in, 1380 
 Mariotte's law of gases, 603 
 Martensite, 439, 480 
 Masonry, allowable pressures on, 
 
 1386 
 
 crushing strength of, 371 
 materials,, weight and specific 
 
 gravity of, 177 
 Mass, definition of, 511 
 Materials, 173-273 
 
 standard cross-sections, for 
 
 draftsmen, 271 
 strength of, 272-379 
 strength of, Kirkaldy's tests, 
 
 352-358 
 
 various, weights of, table, 181 
 Maxima and minima, 78, 79 
 Maxwell, definition and value of, 
 
 1398 
 Measures and weights, compound 
 
 units, 27 
 and weights, metric system, 21- 
 
 26 
 
 apothecaries, 19 
 board and timber, 20 
 circular, 20 
 dry, 19 
 liquid, 18 
 long, 17 
 nautical, 17 
 
 of work, power and duty, 27 
 old land, 17 
 shipping, 19, 1316 
 solid or cubic, 18 
 square, 18 
 surface, 18 
 time, 20 
 
 Measurement of air velocity, 624 
 of elongation, 279 
 of flowing water, 757-764 
 of vessels, 1368 
 
 Measurements, miner's inch, 761 
 Mechanics, 511-548 
 Mechanical equivalent of heat, 
 
 560, 868 
 and electrical units, equivalent 
 
 values of, 1399 
 powers, 535 
 stokers, 918 
 
 Mekarski compressed-air tram- 
 way, 652 
 
 Melting-points of substances, tem- 
 peratures, 554, 559 
 Mensuration, 54-66 
 Mercurial thermometer, 549 
 Mercury-arc rectifier, 1456 
 Mercury-bath pivot, 1233 
 properties of, 179 
 
 Mercury vapor lamp, 1460 
 Mesure and Nonet's pyrometric 
 
 telescope, 556 
 
 Metacenter, definition of, 719 
 Metals, anti-friction, 1223 
 
 coefficients of expansion of, 566 
 coefficients of friction of, 1220 
 electrical conductivity of, 1401 
 flow of, 1323 
 
 heat-conducting power of, 580 
 life of, under shocks, 276 
 properties of, 177-180 
 resistance overcome in cutting 
 
 of, 1292 
 
 specific gravity of, 174 
 specific heats of, 562, 563 
 table of ductility, infusibility, 
 malleability and tenacity, 180 
 tenacity of, at various tempera- 
 tures, 463 
 weight of, 174 
 Metaline lubricant, 1246 
 Metallography, 480 
 Meter, Thomas electric, for meas- 
 uring gas, 667, 669 
 Venturi, 758 
 
 water, V-notch recording, 759 
 Meters, water delivered through, 
 
 749 
 
 Methane gas, physical laws of, 604 
 Metric conversion tables, meas- 
 ures and weights, 21-26 
 screw-threads, cutting of, 1261 
 Microscopic constituents of cast 
 
 iron and steel, 439, 480 
 Mil, circular, 18, 29, 
 Mill buildings, columns, 1393 
 buildings, approximate cost of, 
 
 1394 
 
 power, 766 
 
 Milling cutters, diameter, clear- 
 ance and rake of, 1278 
 for gear-wheels, 1162 
 inserted teeth, 1276 
 keyways in, 1277 
 lubricant for, 1281 
 number of teeth in, 1276 
 side, 1275 
 spiral, 1275 
 
 Milling, high-speed, 1282 
 jobs, typical, 1281 
 machines, cutting speed of, 
 
 1280, 1284 
 machines, high results with, 
 
 1282 
 
 machines, typical jobs on, 1281 
 power required for, 1278 
 practice, modern, 1279, 1283 
 with or against the feed, 128O 
 Mine fans, experiments on, 673 
 ventilating fans, 673 
 ventilation, 714 
 
 Mines, centrifugal fans for, 672 
 Miner's inch, 18 
 
 inch measurements, 761 
 Modulus of elasticity, 274 
 
 of elasticity of various materials 
 374 
 
moci-nal 
 
 INDEX. 
 
 nap-orl 
 
 1505 
 
 Modulus of resistance, or section 
 modulus, 294 
 
 of rupture, 297 
 Moisture in atmosphere, 609-613 
 
 in steam, determination of, 942- 
 944 
 
 in steam escaping from boilers, 
 
 944 
 
 Molding-sand, 1256 
 Molds, cast-iron, for iron castings, 
 
 analysis of, 1256 
 Moment of a couple, 515 
 
 of a force, 514 
 
 of friction, 1229 
 
 of inertia, 293, 295, 517 
 
 statical, 514 
 
 Moments, method of, for deter- 
 mining stresses, 545 
 
 of inertia of regular solids, 517 
 
 of inertia of structural shapes, 
 
 295 
 
 Momentum, 527 
 Mond gas producer, 852 
 Monel metal, copper-nickel alloy, 
 
 403 
 
 Monobar chain conveyor, 1197 
 Morin's laws of friction, 1223 
 Morse tapers, 1319 
 Mortar, strength of, 372 
 Motion, accelerated, formulae for. 
 527 
 
 friction of, 1219, 1221 
 
 Newton's laws of, 513 
 
 on inclined planes, 527 
 
 perpetual, 532 
 
 retarded, 521 
 Motor applications, 1464-1468 
 
 boats, power of engines for, 1374 
 
 -driven machine tools, 1308 
 
 generators, 1456 
 
 repulsion, induction, 1464 
 
 squirrel-cage, 1463 
 
 temperatures, limits of, 1432 
 Motors, alternating-current, 1463 
 
 commutating pole, 1437 
 
 compressed-air, 639-641 
 
 electric (see Electric motors) 
 
 electric, classification of, 1461 
 
 gear connections of, for machine 
 tools, 1301 
 
 sizes of, for machine tools, 1294 
 
 water current, 765 
 Moving strut, 536 
 Mule, work of, 534 
 Multiphase electric currents, 1445 
 Multiple system of evaporation, 
 
 570 
 
 Multivane fans, 658 
 Muntz metal, composition of, 390 
 Mushet steel, 496 
 
 NAILS, cut, table of sizes and 
 weights, 244 
 cut vs. wire, 347 
 holding power of, 346 
 wire, table of sizes and weights, 
 
 246, 247 
 Nail-holding power of wood, 347 
 
 Naphtha as fuel, 841 
 
 Napier's rule for flow of steam, 
 
 876 
 
 Natural gas, 847, 848 
 Nautical measure, 17 
 
 mile, 17 
 
 Newton's laws of motion, 513 
 Nickel, effect .of on properties of 
 
 steel, 498 
 
 Nickel, properties of, 179, 379 
 steel, 497 
 steel, tests of, 497 
 steel, uses of, 498 
 Nickel-copper alloys, 402 
 
 -vanadium steels, 499 
 Niter process, treating iron sur- 
 faces, 473 
 
 Nordberg feed-water heating sys- 
 tem, 1003 
 key, 1331 
 
 pumping-engine, 805 
 Nozzle, efficiency of Doble, 782 
 Nozzles, flow of steam through; 
 
 876, 1085 
 
 flow of water in, 753 
 for measuring discharge of 
 
 pumping-engines, 759 
 water, efficiency of, 784 
 Nut and bolt heads, 231 
 
 OATS, weight of, 180 
 Ocean waves, power of, 784 
 Oersted, unit of magnetic 
 
 reluctance, 1398 
 
 Ohm, definition and value of, 1397 
 Ohm's law, 1406 
 
 law applied to alternating cur- 
 rents, 1442 
 law applied to parallel circuits, 
 
 1407 
 law applied to series circuits, 
 
 1407 
 
 Oil as fuel (see Fuel oil), 842, 843 
 engines, 1102 
 fire-test of, 1243 
 for scale removal in boilers, 930 
 for steam turbines, 1244 
 fuel, chimney draught with, 952 
 fuel, chimney table for, 951 
 lubricating, 1242-1245 (see Lub- 
 ricants) 
 paraffine, 1243 
 pressure in a bearing, 1228 
 quantity needed for engines, 
 
 1245 
 
 tempering of steel forgings 482 
 vs. coal as fuel, 842, 843 
 well, 1243 
 
 we.ls, air-lift pump for, 809 
 Open-hearth steel (see Steel, 
 
 open-hearth), 475 
 furnace, temperatures in, 554 
 Ordinates and abscissas, 70 
 Ores, cubic feet per ton, 181 
 Orifice, equivalent, in mine ven- 
 tilation, 715 
 
 flow of air through, 615-617, 
 670 
 
1506 
 
 ori-pew 
 
 INDEX 
 
 pho-pip 
 
 Orifice, flow of water through, 726 
 rectangular, flow of water 
 
 through, table, 760 
 Oscillation, center of, 518 
 
 radius of, 518 
 Overhead steam-pipe radiators, 
 
 702 
 
 Ox, work of, 534 
 Oxy-acetylene welding, 488 
 Oxygen, effect of on strength of 
 
 steel, 477 
 
 7T value and relations of, 57 
 
 PACKING, hydraulic, friction 
 of, 1241 
 -rings of engines, 1023 
 Paddle-wheels, 1383 
 Paint, 471 
 
 chrome, preventing corrosion, 
 469 
 
 for roofs,' 192 
 
 qualities of, 472 
 
 quantity of, for surface, 472 
 Paper, logarithmic ruled, 84 
 Parabola, area of by calculus, 76 
 
 construction of, 48, 49 
 
 equations of, 72 
 
 path of a projectile, 525 
 Parabolic conoid, 65 
 
 spindle, 65 
 Parallel forces, 515 , 
 
 operation of motors, 1439, 1450 
 Parallelogram area of, 54 
 
 of forces, 513 
 
 of velocities, 523 
 Parallelopipedon of forces, 514 
 Parentheses in algebra, 34 
 Partial payments, 14 
 Part-ing and threading tools, speed 
 
 of, 1268 
 Patterns, weight of, for castings, 
 
 1256 
 
 Payments, equation of, 14 
 Pearlite, 439, 480 
 Peat, 838 
 
 Pelton water-wheel, 780 
 Pendulum, 520 
 
 conical, 520 
 Percentage, 12 
 Percussion, center of, 518 
 Perforated plates, strength of, 425 
 Permeability, magnetic, 1400, 
 
 1430 
 
 Permeance, magnetic, 1400 
 Permutation, 10 
 Perpetual motion, 532 
 Petroleum as a metallurgical fuel, 
 843 
 
 -burning locomotives, 1127 
 
 cost of as fuel, 842 
 
 engines, 1102 
 
 for scale removal in boilers, 930 
 
 Lima, 841 
 
 products of distillation of, 840 
 
 products, specifications for, 1242 
 
 value of as fuel, 841 
 Pewter, composition of, 407 
 
 Phosphor-bronze, composition of, 
 
 390 
 
 specifications for, 395 
 springs, 424 
 strength of, 395 
 Phosphorus, influence on steel, 476 
 
 influence of, on cast iron, 438 
 Piano-wire, strength of, 250 
 Pictet fluid, for refrigerating, 1337 
 Piezometer, 757 
 Pig Iron (see also Cast iron) 
 analysis of, 439 
 charcoal, strength of, 452 
 distribution of silicon in, 448 
 electric smelting of, 1424 
 for malleable castings, 454 
 grading of, 437 
 
 influence of silicon, etc., on, 438 
 sampling, 443 
 specifications for, 443 
 Piles, bearing power of, 1386 
 Pillars, strength of, 283 
 Pine, strength of, 366 
 Pinions, raw-hide, 1177 
 Pins, forcing fits of by hydraulic 
 
 pressure, 1324 
 Pins, taper, 1321 
 Pipe bends, flexibility of, 221 
 branches, compound pipes, for- 
 mula for, 746 
 cast-iron, friction loss in, table, 
 
 747, 748 
 cast-iron , specifications for 
 
 metal for, 441 
 cast-iron, threaded, 199 
 corrosion of in hot- water heat- 
 ing, 708 
 
 coverings, tests of, 584-587 
 dimensions, Briggs standard, 
 
 221, 222 
 
 fittings, flanged, 208-214 
 fittings, screwed, 207, 216 
 fittings, strength of, 216 
 fittings, valves, etc., resistance 
 
 of, 701 
 flanges, extra heavy, tables, 
 
 210, 212 
 
 flanges, tables, 209-213 
 iron and steel, strength of, 363 
 iron, lead-, brass- and copper- 
 lined, 227 
 
 iron, lead-covered, 228 
 iron, tin- and lead-lined, 227 
 joints, bell and spigot, lead re- 
 quired for, 199 
 
 lines for fans and blowers, 670 
 lines, long, 743 
 specialties, 205 
 threading of, force required for, 
 
 363 
 welded, weight and bursting 
 
 strength of, 205 
 wooden stave, 218, 735 
 Pipes, see also Tubes 
 air-bound, 748 
 
 air, loss of pressure in, 617-624 
 and valves for superheated 
 steam, 882 
 
pip-pip 
 
 INDEX. 
 
 pis-pla 
 
 1507 
 
 Pipes, bent and coiled, 221, 222 
 block-tin, weights and sizes of, 
 
 2^7 
 
 coiled, table of, 221 
 Pipes, cast-iron, bell and spigot 
 
 for gas, 198 
 flanged, for gas, 199 
 for high-pressure service, 198 
 formulae for thickness of, 196 
 safe pressures for, tables, 196-198 
 thickness of, for various heads, 
 
 196-200 
 
 transverse strength of, 452 
 underground, weight of, 197 
 weight and dimensions, 196-200 
 Pipes, effects of bends in, 624, 747 
 equalization of, table 625 
 equation of, 884 
 flow of air in, 617-624 
 flow of gas in, 864-866 
 flow of steam in, 877-879 
 flow of water in, 728-746 
 for steam heating, 698 
 house-service, flow of water in, 
 
 table, 744 
 iron and steel, corrosion of, 466, 
 
 467 
 
 lead, safe heads for, 226 
 lead, (tin-lined, sizes and weights, 
 
 table, 227 
 lead, weights and sizes of, 
 
 table, 226 
 maximum and mean velocities 
 
 in, 758 
 
 proportioning to radiating sur- 
 face, 699, 700 ' 
 rectangular, flow of air in, 622 
 resistance of the inlet, 735 
 rifled, for conveying heavy oils, 
 
 746 
 
 riveted, flanges for, table, 211 
 riveted hydraulic, weights and 
 
 safe heads, table, 219 
 riveted iron, dimensions of, 
 
 table, 220 
 riveted steel, loss of head in, 
 
 734 
 
 riveted steel, water, 351 
 sizes of threads on, 201, 217 
 spiral riveted, table of, 220 
 steam (see Steam-pipes) 
 steam, sizes of in steam heat- 
 ing, 699-701 
 
 table of capacities of, 131 
 used as columns, 363 
 volume of air transmitted in, 
 
 table, 623, 624 
 water, loss of head in, 728, 735, 
 
 745 (see Loss of head) 
 welded, extra strong, 203, 204 
 welded, standard, table of di- 
 mensions, 202 
 Pipe-joint, Converse lock-joint, 
 
 212 
 
 Matheson, 212 
 Rockwood, 212 
 
 Piping, power-house, identifica- 
 tion of by different colors, 885 
 
 Piston rings, steam-engine, 1023 
 rods, steam-engine, 1024 
 valves, steam-engine, 1061 
 Pistons, steam-engine, 1023 
 Pitch, diametral, 1158 
 of gearing, 1157 
 of rivets, 427 
 of screw-propeller, 1377 
 Pitot tube, best form of, 667 
 gage, 757 
 
 measurements, accuracy of* 669. 
 use in testing fans, 667 
 Pivot-bearings, 1229, 1232 
 
 mercury bath, 1233 
 Plane, inclined, 527, 537 (see In- 
 clined plane) 
 
 surfaces, mensuration of, 54 
 Planer, horse-power required to 
 
 run, 1302 
 
 tools, standard, 1271-1274 
 work, 1270-1274 
 Planers, feeds and speeds of, 1270 
 
 power requirements of, 1302 
 Planing, time required for, 1271 
 
 work requiring, 1270 
 Planished and Russia iron, 473 
 Plank, wooden, maximum spans 
 
 for, 1392 
 Plants, high pressure water-power, 
 
 782 
 Plate-girder, strength of, 353 
 
 -girders, allowed stresses in, 289 
 Plates (see also Sheets) 
 
 acid pickled, heat transmission 
 
 through, 591 
 areas of, in square feet, table, 
 
 128, 129 
 
 brass, weight of, tables, 228, 229 
 Carnegie trough, properties of, 
 
 table, 308 
 
 circular, strength of, 336 
 copper, strength of, 356 
 copper, weight of, table. 229 
 corrugated steel, properties of, 
 
 table, 310 
 
 flat, cast-iron, strength of, 336 
 flat, for steam-boilers, 916 
 flat, unstayed, strength of, 337 
 for stand-pipes, 349 
 iron and steel, approximating 
 
 weight of, 486 
 
 iron, weight of, table, 187, 188 
 of different materials, table for 
 
 calculating weights of, 181 
 perforated, strength of, 425 < 
 punched, loss of strength in, 
 
 424 
 
 stayed, strength of, 338 
 steel boiler, specifications for, 
 
 507 
 steel, for cars, specifications for, 
 
 507 
 
 steel, specifications for, 507 
 steel, tests of, 353, 355 
 transmission of heat through, 
 
 587 
 
 transmission of heat through, 
 from air to water, 592 
 
1508 
 
 pla-prc 
 
 INDEX. 
 
 pre-pum 
 
 Plates, transmission of heat 
 through, from steam to w air, 
 595 
 
 Plating for bulkheads, table, 339 
 steel, stresses in, due to water 
 
 pressure, 338 
 for tanks, table, 338 
 Platinite, 499, 567 
 Platinum, properties of, 179 
 pyrometer, 553 
 wire, 248 
 
 Plenum system of heating, 708 
 Plow-steel wire, 250 
 
 -steel wire-rope, 257, 259 
 Plugs, fusible, in steam boilers, 
 
 918 
 
 Plunger packing, hydraulic, fric- 
 tion of, 1239 
 
 Pneumatic conveying, 1201 
 hoisting, 1187 
 postal transmission, 1201 
 Polarity of electro-magnets, 1432 
 Poles, tubular, 206 
 Polishing and buffing, 1310 
 
 wheels, speed of, 1310 
 Polyedron, 63 
 Polygon, area of, 55 
 construction of, 42-45 
 of forces, 513 
 Polygons, impedance, 1442 
 
 table of, 45, 55 
 Polyphase circuits, 1445 
 Popp system of compressed-air, 
 
 639-641 
 Population of the United States, 
 
 11 
 Port opening in steam-engines, 
 
 1057 
 
 Portland cement, strength of, 358 
 Postal transmission, pneumatic, 
 
 1201 
 
 Potential energy, 528 
 Pound, British avoirdupois, 26 
 
 -calorie, definition of, 560 
 Pounds per square inch, equiva- 
 lents of, 27 
 Power, animal, 532 
 
 and work, definition of, 528 
 
 electrical, cost of, 1012 
 
 factor of alternating currents, 
 
 1440 
 
 hydraulic, in London, 814 
 measures of, 27 
 of a waterfall, 765 
 of electric circuits, 1408 
 of ocean waves, 784 
 required for machine tools, 
 
 1292-1302 
 required to drive machines in 
 
 groups, 1305 
 tidal, 787 
 unit of, 528 
 
 Powers of numbers, algebraic, 33 
 of numbers, tables, 7, 8, 93- 
 
 110 
 
 Power-plant economics, 1011 
 Pratt truss, stresses in, 544 
 Preservative coatings, 471-474 
 
 Press fits, pressure required for, 
 1324-1326 
 
 forging, high-speed, steani hy- 
 draulic, 815 
 
 hydraulic forging, 814 
 
 hydraulic, thickness of cylinders 
 
 for, 340 
 
 Presses, hydraulic, in iron works, 
 813 
 
 punches and shears, fly-wheels 
 for, 1323 
 
 punches, etc., 1321 
 Pressed fuel, 831 
 Pressure, collapsing of flues, 342 
 
 collapsing of hollow cylinders, 
 
 341 
 Pressures of fluids, conversion 
 
 table for, 607 
 Priming, or foaming, of steam 
 
 boilers, 721, 930 
 Prism, 62 
 Prismoid, 63 
 
 rectangular, 62 
 Prismoidal formula, 63 
 Problems, geometrical, 37-53 
 
 in circles, 39-44 
 
 in lines and angles, 37-39 
 
 in polygons, 42-45 
 
 in triangles, 41 
 Process, the Thermit, 400 
 Producer-gas, 848-855 (see Gas) 
 Producers, gas (see Gas-producers) 
 
 gas, use of steam in, 854 
 Profit and loss, 12 
 Progression, arithmetical and geo- 
 metrical, 10, 11 
 
 Projectile, parabola path of, 525 
 Prony brake, 1333 
 Propeller, screw (see Screw-pro- 
 peirer) 1377 
 
 shafts, strength of, 354 
 Proportion, 6 
 
 compound, 7 
 Protective coatings for pipes, 
 
 206 
 Pulleys, 1135-1138 
 
 arms of, 1050 
 
 cone, 1136 
 
 cone, on machine tools, 1307 
 
 convexity of, 1136 
 
 differential, 539 
 
 for rope-driving, 1217 
 
 or blocks, 538 
 
 proportions of, 1111 
 
 speed of, 1148, 1162 
 Pulsometer, 806 
 
 tests of, 807 
 
 Pumps, air-, for condensers, 1071, 
 1073 
 
 air-lift, 808 
 
 and pumping-engines, 788-812' 
 
 boiler-feed, 792 
 
 boiler-feed, efficiency of, 937 
 
 centrifugal, 796-802 
 
 centrifugal, combination single 
 stage and two stage, 798 
 
 centrifugal, design of, 797 
 
 centrifugal, multi-stage, 797 
 
pum-pyr 
 
 INDEX. 
 
 qua-rca 
 
 1509 
 
 Pumps, centrifugal, relation of 
 
 height of lift to velocity, 797 
 centrifugal, tests of, 798, 800, 
 
 802 
 
 circulating, for condensers, 1075 
 depth of suction of, 788 
 direct-acting, efficiency of, 790 
 direct-acting, proportion of 
 
 steam cylinder, 790 
 electric motors for, 1463 
 feed, for marine engines, 1076 
 gas-engine, 808 
 high-duty, 793 
 horse-power of, 788 
 jet, 807 
 
 leakage, test of, 803 
 lift, water raised by, 790 
 mine, operated by compressed 
 
 air, 652 
 
 piston speed of, 791, 792 
 rotary, 801 
 rotary, tests of, 802 
 speed of water in passages of, 
 
 790 
 
 steam, sizes of, tables, 789, 791 
 suction of, with hot water, 788 
 theoretical capacity of, 788 
 underwriters', sizes of, 792 
 vacuum, 806 
 valves of, 792, 793 
 Pump-inspection table, 751 
 Pumping by compressed air, 645, 
 
 808 (see also Air-lift) 
 by gas-engines, cost of, 795 
 by steam pumps, cost of fuel 
 
 for, 795 
 
 cost of electric current for, 794 
 Pumping-engine, 72,000,000 gal., 
 
 screw, 794 
 
 the d'Auria, 793 
 
 Pumping-engines, duty trials of, 
 802-806 
 
 economy of, 794 
 
 high-duty records, 806 
 
 table of data for duty trials of, 
 803-805 
 
 use of nozzles to measure dis- 
 charge of, 759 
 Punches and dies, clearance of, 1321 
 
 spiral, 1322 
 
 Punched plates, strength of, 425 
 Punching and drilling of steel, 483, 
 
 485 
 
 Purification of water, 723-726 
 Pyramid, 62 
 
 frustum of, 62 
 Pyrometer, air, Wiborgh's, 555 
 
 copper-ball, 553 
 
 fire-clay, Seger's, 555 
 
 Hobson's hot-blast, 555 
 
 Le Chatelier's, 554 
 
 principles of, 549 
 
 thermo-electric, 553 
 
 Uehling-Steinbart, 557 
 Pyrometers, graduation of, 554 
 Pyrometric telescope, 556 
 Pyrometry, 549 
 
 Q 
 
 UARTER-TWIST belt, 1147 
 Queen-post truss, inverted, 
 
 stresses in, 544 
 truss, stresses in, 543 
 Quenching test for soft steel, 507 
 
 RACK, gearing. 1165 
 Radian, definition of, 523 
 Radiating power of sub- 
 stances, 578 
 surface, computation of, for 
 
 hot-water heating, 704 
 surface, computation of, for 
 
 steam heating, 698 
 surface, proportioning pipes for, 
 
 700 
 
 Radiation, black body, 579 
 of heat, 578 
 
 of various substances, 578, 595 
 Stefan and Boltzman's law, 579 
 table of factors for Dulong's 
 
 laws of, 596 
 Radiators, experiments with, 697, 
 
 708 
 
 indirect, 698 
 
 overhead steam-pipe, 702 
 steam and hot-water, 697 
 steam, removal of air from, 
 
 702 
 
 transmission of heat in, 697 
 Radius of gyration, 293, 518 
 of gyration, graphical method 
 
 for finding, 294 
 of gyration of structural shapes, 
 
 293, 294 
 
 of oscillation, 518 
 Rails, steel, electric resistance of, 
 
 1416 
 
 steel, specifications for, 508 ! 
 steel, strength of, 353 
 Railroad axles, effect of cold on, 
 
 465 
 steam, electrifications of, table, 
 
 1418 
 track, material required for one 
 
 mile of, 244, 245 
 trains, resistance of, 1108-1111 
 trains, speed of, 1118 
 Railway curve, degree of a, 54 
 street, compressed-air, 652 
 track bolts and nuts, 244, 245 
 Railways, electric (sec Electric 
 
 railways), 1414 
 narrow-gage, 1127 
 Ram, hydraulic, 810 
 Rankine cycle efficiency for differ- 
 ent conditions, 1091 
 cycle, efficiency of, 996, 1089 
 Rankine's formula for columns, 
 
 284 
 
 Ratio, 6 
 
 Raw-hide pinions, 1177 
 Reactance of alternating currents, 
 
 1441 
 
 in transformers, 1452 
 Reaction of a jet, 1385 
 Reamers, taper, 1318 
 Reaumur thermometer-scale, 549 
 
1510 
 
 INDEX. 
 
 ref-riv 
 
 Recalescence of steel, 480 
 Receiver-space in engines, 980 
 Receivers on steam pipe lines, 884 
 Reciprocals of numbers, tables of, 
 
 87-92 
 use of, 92 
 Recorder, carbon dioxide, or CO*. 
 
 890 
 continuous, of water pr steam 
 
 consumption, 970 
 Rectangle, definition of, 54 
 
 value of diagonal of, 54 
 Rectangular prismoid, 62 
 Rectifier, in absorption refrigerat- 
 ing machine, 1346 
 mercury arc, 1456 
 Reduction, ascending and de- 
 scending, 5 
 
 Reese's fusing disk, 1309 
 Reflecting power of substances, 
 
 578 
 
 Refrigerating (see also Ice-mak- 
 ing), 1336-1367 
 air-machines, 1343 
 direct-expansion method, 1365 
 Refrigerating - machines, actual 
 and theoretical capacity, 1355 
 ammonia absorption, 1346, 1364 
 ammonia compression, 1345, 
 
 1356 
 
 condensers for, 1353 
 cylinder-heating, 1349 
 diagrams of, 1348 
 dry, wet, and flooded systems, 
 
 1345 
 
 ether-machines, 1343 
 heat-balance, 1359 
 ice-melting effect, 1343 
 liquids for, pressure and boiling 
 
 points of, 1337 
 mean effective pressure and 
 
 horse-power, 1350 
 operations of, 1336 
 performance of, 1364 
 pipe-coils for, 1354 
 pounds of ammonia per minute, 
 
 1350 
 
 properties of brine, 1343 
 properties of vapor, 1337 
 quantity of ammonia required 
 
 for, 1351 
 
 rated capacity of, 1353 
 relative efficiency of, 1348 
 relative performance of am- 
 monia-compression and ab- 
 sorption machines, 1347 
 sizes and capacities, 1352 
 speed of, 1353 
 sulphur-dioxide, 1345 
 temperature range, 1360 
 test reports of, 1358 
 tests of, 1355 
 using water vapor, 1345 
 volumetric efficiency, 1349 
 Vqorhees multiple-effect, 1351 
 Refrigerating plants, cooling-tower 
 
 practice in, 1354 
 systems, efficiency of, 1349 
 
 Refrigeration, 1336-1367 
 a reversed heat cycle, 600 
 cooling effect, compressor vol- 
 ume, and power required, 
 1341 
 
 cubic feet space per ton of, 1308 
 means of applying the cold, 
 
 1365 
 
 Regenerator, heat, 1014 
 Regnault's experiments on steam, 
 
 870 
 Reinforced concrete, working 
 
 stresses of, 1387 
 
 Reluctance, magnetic, 1398, 1430 
 Reluctivity, magnetic, 1400 
 Reservoirs, evaporation of water 
 
 in, 569 
 Resilience, elastic, 274 
 
 of materials, 274 
 
 Resistance, elastic to torsion, 334 
 Resistance, electrical (see also 
 
 Electrical resistance), 1400 
 effect of annealing on, 1402 
 effect of temperature on, 1402 
 in circuits, 1406 
 internal, 1408 
 of copper wire, 1402, 1404 
 .of copper wire, rule for, 1406 
 of steel, 477 
 of steel rails, 1416 
 standard of, 1402 
 Resistance, elevation of ultimate, 
 
 275 
 frictional, of surfaces moved in 
 
 water, 756 
 
 moment of, and section mod- 
 ulus, 294, 295 
 
 of metals to repeated shocks, 276. 
 of ships, 1369 
 of trains, 1108-1111 
 tractive, of an electric car, 1415 
 work of, of a material, 274 
 Resistivity, definition of, 1403 
 
 of copper, 1403, 1406 
 Resolution of forces, 513 
 Retarded motion, 521 
 Reversing-gear for steam-engines, 
 
 dimensions of, 1039 
 Rhomboid, definition and area of, 
 
 54 
 Rhombus, definition and area of, 
 
 54 
 
 Rivet-iron and steel, shearing re- 
 sistance of, 430 
 spacing for structural work, 321, 
 
 322 
 
 Rivets, bearing pressure on, 426 
 center distances, of staggered, 
 
 322 
 
 cone-head, 239 
 diameters of, for riveted joints, 
 
 table, 429 
 in steam-boilers, rules for, 913, 
 
 914 
 length required for various 
 
 grips, 241 
 
 minimum spacing and clear- 
 ance, 322 
 
rlv-rop 
 
 IN&EX. 
 
 rop-sca 
 
 1511 
 
 Rivets, oval head, sizes and 
 
 weights, 238 
 pitch of, 426 
 
 pressure required to drive, 435 
 round head, weight of, 243 
 shearing value, area of rivets, 
 
 and bearing value, 240 
 steel, chemical and physical 
 
 tests of, 435 
 
 steel, specifications for, 505 
 tinners', table, 239 
 Riveted iron pipe, dimensions of, 
 
 table, 220 
 
 Riveted joints, 355, 424-435 
 British rules for, 433 
 drilled, vs. punch holes, 424 
 efficiencies of, 428-434, 914 
 notes on, 425 
 
 of maximum efficiency, 431 
 proportions of, 427-434 
 single riveted lap, 427 
 table of proportions, 434 
 tests of double-riveted lap and 
 
 butt, 429 
 
 tests of, table, 359 
 triple and quadruple, 431 
 triple, working pressures on 
 
 steam-boilers with, 917 
 Riveted pipe, flow of water in, 
 
 734-736 
 
 pipe, weight of steel for, 221 
 Riveting, cold, pressure required 
 
 for, 435 
 efficiency of different methods, 
 
 425 
 hand and hydraulic, strength of, 
 
 425 
 
 machines, hydraulic, 814 
 of structural steel, 484 
 pressure required for, 435 
 Roads, resistance of wagons on, 534 
 Rock-drills, air required for, 645 
 requirements of air-driven, 645 
 Rods of different materials, tables 
 for calculating weights of, 181 
 Roller bearings, 1233 
 
 chain and sprocket drives, 1153 
 Rollers and balls, steel, carrying 
 
 capacity of, 340 
 Rolling of steel, effect of finishing 
 
 temperature, 478 
 Roof construction, 191-195 
 paints, 192 
 
 -truss, stresses in, 547 
 snow and wind loads on, 191 
 strength jof, 1389 
 Roofing materials and roof con- 
 struction, 191-195 
 materials, weight of various, 191 
 Rope-driving, 1214-1218 
 English practice, 1218 
 horse-power of, 1215 
 pulleys for, 1217 
 sag of rope, 1216 
 tension of rope, 1214 
 weight of rope, 1218 
 Ropes and cables, 410-415 
 cotton and hemp, strength of ,357 
 
 Ropes, cotton, -for transmission, 
 
 1218 
 for hoisting or transmission, 
 
 410-415 
 hemp, iron and steel, table of 
 
 strength and weight of, 410 
 hoisting (see Hoisting-rope) 
 locked-wire, 262 
 manila, 411 
 
 manila, data of, 1214-1218 
 manila, hoisting and trans- 
 mission, life of, 415 
 manila, weight and strength of, 
 
 410-415 
 splicing of, 412 
 table of strength of iron, steel 
 
 and hemp, 410 
 
 taper, of uniform strength, 1208 
 technical terms relating to, 411 
 wire, "Lang Lay," 254 
 wire (see also Wire-rope) 
 wire, track cable for aerial tram- 
 ways, 260 
 Rotary blowers, 677 
 
 steam-engines, 1082 
 Rotation, accelerated, work of, 529 
 Rubber belting, 1152 
 goods, analysis of, 378 
 vulcanized, tests of, 378 
 Rule of three, 6, 7 
 Runnel's, hydraulic turbine, de- 
 termination of dimensions, 
 769a 
 
 Running fits, 1325 
 Rupture, modulus of, 297 
 Russia and planished iron, 473 
 
 SAFETY, factor of, 374-377 
 valves for locomotives, 935 
 valves for boilers, 932-935 
 valves, spring-loaded, 933 
 
 Sag of rope between pulleys, 1216 
 of wires between poles, 1461 
 
 Salt, solubility of, 571 
 weight of, 180 
 
 Salt-brine manufacture, evapora- 
 tion in, 570 
 
 properties of, 570, 571, 1343 
 solution, specific heat of, 564 
 solution test of hydraulic tur- 
 bine discharge, 774 
 
 Sampling coal for analysis, 825 
 
 Sand, cubic feet per ton, 181 
 molding, 1256' 
 
 Sand-blast, 1309 
 
 Sand-lime brick, tests of, 371 
 
 Sandstone, strength of, 371 
 
 Saturation point of vapors, 604 
 
 Sawdust as fuel, 838 
 
 Sawing metal, 1309 
 
 -machines for metals, 1291 
 metals, speeds and feeds for,1291 
 
 Scale, boiler, 721, 927-932 
 boiler, analyses of, 722 
 effect of, on boiler efficiency, 928 
 removal of, from boilers, 930 
 
 Scales, thermometer comparison 
 of,_550, 551 
 
1512 
 
 sca-sha 
 
 JNDEX. 
 
 sha-she 
 
 Scantling, table of contents of, 21 
 Schiele pivot bearing, 1233 
 Schiele's anti-friction curve, 50 
 Scleroscope, for testing hardness, 
 
 365 
 Screw, 61 
 
 -bolts* efficiency of, 538 
 
 conveyors, 1198 
 
 differential, 540 
 
 efficiency of a, 538 
 
 (element of machine) , 537 
 
 heads, machine, dimensions of, 
 237 
 
 -propeller, 1377 
 
 -propeller, coefficients of, 1378 
 
 -propeller, efficiency of, 1379 
 
 -propeller, slip of, 1379 
 Screws and nuts for automobiles, 
 table, 233 
 
 cap, table of standard, 238 
 
 lag, holding power of, 347 
 
 lag, table of, 241 
 
 machine, A. S. M. E. standard, 
 234 
 
 machine, dimensions of, 234-238 
 
 set, table of standard, 238 
 
 wood, 236 
 
 wood, holding power of, 346 
 Screw-threads, 231-238 
 
 Acme, 234 
 
 A. S. M. E. standard, table, 237 
 
 British Association standard, 
 232 
 
 English or Whit worth standard, 
 table, 232 
 
 International (metric) standard, 
 232 
 
 limit gages for, 232 
 
 metric, cutting of, 1261 
 
 standard sizes for bolts and 
 taps, 235, 236 
 
 U.S. or Sellers standard, table 
 
 of, 231 
 
 Scrubbers for gas producers, 849 
 Sea-water, freezing-point of, 719 
 Secant of an angle, 66 
 
 of an arc, 67 
 Secants of angles, table of, 170- 
 
 172 
 Section modulus of structural 
 
 shapes, 294, 295 
 Sector of circle, 60 
 Sediment in steam-boilers, 928 
 Seger pyrometer cones, 555 
 Segment of circle, 60 
 Segments, circular, areas of, 121, 
 
 122 
 
 Segregation in steel ingots, 487 
 Self-inductance of lines and cir- 
 cuits, 1445 
 "Semi-steel," 453 
 Separators, steam 941 
 
 steam, efficiency of, 941 
 Set-screws, dimensions of, 238 
 
 holding power of, 1332 
 
 standard table of, 238 
 Sewers, grade of, 757 
 Shackles, strength of, 1184 
 
 Shaft bearings, 1034 
 
 bearings, large, tests of, 1230 
 couplings, flange, 1133 
 fit, allowances for electrical ma- 
 chinery, 1326 
 -governors, 1066 
 speeds in geometrical progres- 
 sion, 1138 
 Shafts and bearings of engines, 
 
 1042-1044 
 bearings for, 1034 
 bending resistance of, 1032 
 dimensions of, 1030-1033 
 equivalent twisting moment of, 
 
 1032 
 
 fly-wheel, 1033 
 hollow, 1133 
 hollow, torsi onal strength of, 
 
 334 
 
 steam-engine, 1030-1038 
 steel propeller, strength of, 354 
 twisting resistance of, 1030 
 Shafting, 1130-1134 
 collars for, 1133 
 deflection of, 1131 
 formulae for, 1130 
 horse-power transmitted by, 
 
 1130 
 
 keys for, 1328 
 laying out, 1134 
 power required to drive, 1305 
 torsion tests of, 361 
 Shaku-do, Japanese alloy, 393 
 Shapers, motors required to run, 
 
 1296 
 
 Shapes of test specimens, 280 
 structural steel, dimensions and 
 
 weights, 302-305 
 Shear and compression combined, 
 
 335 
 
 and tension combined, 335 
 poles, stresses in, 542 
 Shearing, effect of on structural 
 
 steel, 483 
 
 resistance of rivets, 430 
 strength of iron and steel, 362 
 strength of rivets, 240 
 strength of woods, table, 367 
 strength, relation to tensile 
 
 strength, 362 
 
 Sheaves, diameter of, for wire- 
 rope, 1211 
 for wire-rope transmission, 1208, 
 
 1211 
 
 size of for manila rope, 414 
 Sheet aluminum, weight of, 230 
 brass, weight of, table, 228 
 copper, weight of, 229 
 iron and steel, weight of, 183 
 metal gage, 28, 29, 31, 32 
 metal, weight of, by decimal 
 
 gage, 32 
 
 metals, strength of various, 356 
 Sheets (see Plates) 
 Shelby cold-drawn tubing, 223 
 Shells for steam-boilers, material 
 
 for, 908 
 spherical, strength, of, 339 
 
she-sin 
 
 INDEX. 
 
 sin-spe 
 
 1513 
 
 tiherardizing, 474 
 
 Shibu-ichi, Japanese alloy, 393 
 
 Shingles, weights and areas of, 
 
 196 
 Ship " Lusitania," performance of, 
 
 1376, 1381 
 
 Ships, Atlantic steam, perform- 
 ance of, 1376, 1383 
 coefficient of fineness of, 1369 
 coefficient of performance, 1370 
 C9efficient of water-lines, 1369 
 displacement of, 1369, 1374 
 horse-power for given speeds, 
 
 horse-power of, from wetted 
 
 surface, 1372 
 
 horse-power of internal com- 
 bustion engines for, 1374 
 horse-power required for, 1373- 
 
 1375 
 
 jet propulsion of, 1384 
 relation of horse-power to speed, 
 
 1373/1376 
 resistance of, 1369 
 resistance of, per horse-power, 
 
 1373 
 
 resistance of, Rankine's for- 
 mula, 137O 
 
 rules for measuring, 1368 
 rules for tonnage, 1369 
 small sizes, engine power re- 
 quired for, 1374 
 wetted surface of, 1371' 
 wetted surface, empirical equa- 
 tions for, 1371 
 with reciprocating engine, and 
 
 turbine combined, 1383 
 Shipbuilding, steel for, 507 
 Shipping measure, 19, 1368 
 Shocks, resistance of metals to 
 
 repeated, 276 
 stresses produced by, 276 
 Short circuits, electric, 1411 
 Shrinkage fits (see Fits, 1324) 
 of alloys, 409 
 of castings, 1254 
 of cast iron, 438, 447 
 of malleable iron castings, 455 
 strains relieved by uniform 
 
 cooling, 448 
 
 Sign of differential coefficients, 78 
 of trigonometrical functions, 67 
 Signs, arithmetical, 1 
 Silicon-aluminum-iron alloys, 398 
 -bronze, 395 
 -bronze wire, 248, 395 
 distribution of, in pig iron, 448 
 excessive, making cast iron 
 
 hard, 1254 
 influence of, on cast iron, 438, 
 
 447 
 
 influence of, on steel, 476 
 Silundum, 1425 
 Silver, melting temperature, 554, 
 
 559 
 
 properties of, 179 
 
 Simpson's rule for areas, 56 * 
 
 Sine of an angle, 66 4 
 
 Sines of angles, table, 170-172 
 
 Single-phase circuits, 1445 
 
 Sinking fund, 17 
 
 Siphon, 754 
 
 Sirocco fans, 653, 664-666 
 
 Skin effect in alternating currents, 
 
 1442 
 Skylight glass, sizes and weights, 
 
 196 
 
 Slag bricks and slag blocks, 268 
 in cupolas, 1248 
 in wrought iroh, 460 
 Slate roofing, sizes, areas, and 
 
 weights, 195 
 Slide rule, 82 
 
 Slide-valve, cut-off for various' laps 
 and travels, table, 1060, 1061 
 definitions, 1052 
 diagrams, 1053-1055 
 effect of lap and lead, 1052- 
 
 1057 
 
 lead, 1057 
 port opening, 1057 
 ratio of lap to travel, 1058 
 relative motion of cross-head 
 
 and crank, 1060 
 steam-engine, .^1052-1062 
 Slope, table of, and fall in feet per 
 
 mile, 729 
 
 Slotters, power required for, 1295 
 Smoke-prevention, 92O-922 
 Smoke-stacks, locomotive, 1115 
 
 sheet-iron, 958 
 Snow load on roofs, 191 
 
 weight of, 720 
 Soapstone lubricant, 1246 
 
 strength of, 371 
 Soda mixture for machine tools, 
 
 1246 
 
 Softeners in foundry work, 1253 
 Softening of water, 724 
 Soils, bearing power of, 1385 
 
 resistance of, to erosion, 755 
 Solar engines, 1015 
 Solder, brazing, composition of, 
 
 390 
 
 for aluminum, 382, 383 
 Solders, composition of various, 
 
 383, 409 
 
 Soldering aluminum-bronze, 397- 
 Solid bodies, mensuration of, 61- 
 
 66 
 
 measure, 18 
 of revolution, 64 
 I Solubility of common salt, 571 
 | of sulphate of lime, 571 
 Soot, effect of on boiler tubes, 931 
 Sorbite, 480 
 
 i Sources of energy, 531 
 i Specific discharge of hydraulic 
 < turbine, 7706 
 
 Specific gravity, 173-175 
 i and Baume's hydrometer com- 
 pared, table, 175 
 and strength of cast iron, 452 
 of brine, 571 
 of cast iron, 452 
 of copper-tin alloys, 384 
 
1514 
 
 spe-sph 
 
 INDEX. 
 
 sph-sta 
 
 Specific gravity of coppor-zilic al- 
 loys, 388 
 
 of gases, 170 
 
 of ice, 7 HO 
 
 of li(|iiids, table, 175 
 
 of metals, table, 1 / I 
 
 of steel, ISC) 
 
 of stones, brick, etc., 177 
 Specific heal, 502 505. 720 
 
 determination of, 502 
 
 of air, 502, 614. 
 of gases, 503, 504 
 of k-e, 720 
 
 of iron and steel, 502, 563 
 of liquids, 503 
 of superheated strain 809 
 Of metals, 502. 503 
 of solids, 502. 503 
 of saturated steam, 807 
 of water. 50-1. 720 
 of woods. 503 
 
 Specifications for boiler-plate, 507 
 castings. I II 
 cast iron, 441 
 chains. 20-1 
 
 elliptical steel springs, 423 
 foundry pig iron, 443 
 fuel oil. 8-13 
 gal\ani/,ed \\ire, 250 
 helical steel springs, 423 
 liose. 379 
 
 malleable iron, 157 
 metal for cast-iron pipe, 441 
 oils. 12-12 
 petroleum lubricants. 1212 
 
 phosphor-bronze, 395 
 
 purchase of coal. 830 
 
 spring steel. 507 
 
 steel axles. 5O7. 5O9 
 
 steel billets. 5O7 
 
 steel castings. -189. 510 
 
 steel crank-pins, 507 
 
 steel for automobiles, 510 
 
 steel forgings, 500 
 
 steel for ships, 507 
 
 steel rails. 5OS 
 
 steel ri\ ets, 505 
 
 steel splice-bars, 509 
 
 steel tires. 5O9 
 
 structural steel. 501 
 
 tin and (erne-plate, 191 
 
 \\ rought iron. 101 . 102 
 Sjieed of cut ting. elVect of feed and 
 dept li of cut on. 120-1 
 
 of cutting tools, 1258 
 
 vessels. 1373 
 Speeds in geometrical progression, 
 
 L807 
 
 Spelter, (.svc /inc) 
 Sphere, measures of. 02 
 
 Spheres of different materials, table 
 
 for calculating weight of. IS I 
 (able of volumes and surfaces, 
 
 120. 127 
 
 Spherical pol>gon. area, of, 03 
 segment , volume of. (VI 
 shells and domed boiler heads, 
 
 339 
 
 Spherical polvgon shells, strength 
 of. 339 
 
 shells, thickness of, to resist a 
 giren pressure, 339 
 
 t riangle, area of. 03 
 
 /one, area, and volume of, 0-1 
 Spheroid, <> 1 
 Spikes, holding power of, 3-10 
 
 railroad and boat, 215, 2 IS 
 
 wrought-, 215 
 Spindle, surface and volume of, 
 
 0-1. 05 
 Spiral. 51. 01 
 
 conical, 01 
 
 construction of, 51 
 
 gears, 1 108 
 
 plane, 01 
 
 -rivet (vl pipe-fittings, table, 220 
 
 -riveted pipe, table of, 220 
 Splice-bars, steel, specifications 
 
 for, 509 
 
 Splices, railroad track, tables, 245 
 Splicing of ropes. -112 
 
 Of wire i-o pe. 203 
 Spontaneous combustion of coal, 
 
 832 
 Springs, 117 -121 
 
 elliptical, si/es of. 123 
 
 elliptical, specifications for. -123 
 
 for engine-governors, 1000 loos 
 
 helical, 118 -122 
 
 helical, formula' for deflection 
 
 and strength, 1 18 
 helical, specification for. 123 
 helical, steel, tables of capacity 
 
 and dellection. 1 IS 122 
 laminated steel. 1 17 
 
 phosphor-bronze, -12 1 
 
 semi-ellipt ical, 1 17 
 
 steel, chromium-vanadium, 121 
 
 steel, strength of. 355 
 
 to resist torsion, 123 
 Sprocket wheels. 1 15-1. 1 150 
 Spruce, strength of, 307 
 Square, definition of, 5-1 
 
 measure, 18 
 
 root. 8 
 
 roots of lift h powers. 1 1O 
 
 roots, tables of, 93 108 
 
 side of. equivalent, to circle of 
 same area. 125 
 
 \alue of diagonal of. 5 1 
 
 Squares of decimals, table, HIS 
 
 of numbers, table. 93 I OS 
 Squirrel-cage motor, 1-103 
 Stability 
 
 of chimneys. 9;"> 1 
 
 of dam, 515 
 .Stand-pipes. 3-19 351 
 
 at Yonkers. N. V.. 350 
 
 failures of. 35O 
 
 guy-ropes for. 3-19 
 
 heights of. for various diam- 
 eters and plates, table. 351 
 
 thickness of plates of. table. 
 35 1 
 
 thickness of side plates. 3-19 
 
 wind-strain on, 319 
 
sta-ste 
 
 INDEX. 
 
 >tc->te 
 
 
 . transformers, 
 
 1 \^-2 
 
 ;tl moment. ")l") 
 -holt iron. 462 
 May-bolts in steam-boilers, 916 
 
 steam-boiler, loads on. 91 1> 
 
 steam-boiler, material for 
 Stayed surfaces, strength of, 338 
 .Steam, 867-885 
 
 boilers (see Steam-boilers beloic) 
 
 calorimeters, 942-944 
 
 consumption, continuous re- 
 corder for, 970 
 
 consumption in engines, Wil- 
 lan's law, 991 
 
 determining moisture in, 942- 
 945 
 
 -domes on boilers, 918 
 
 -drums, 913 
 
 dry, definition, 867 
 
 dry. identification of. 944 
 
 energy of, expanded to various 
 pressures, 963 
 
 engines (see Steam-engines, be- 
 lou:) 
 
 entropy of. tables. -S7 1-874 
 
 expanding, available energy of, 
 870 
 
 expansion of, 959 
 
 fire-engines, capacity and econ- 
 omy of. 993, 994 ' 
 
 flow of. 876-882 (see Flow of 
 steam) 
 ous, 870 
 
 generation of. from waste heat 
 of coke-ovens. 834 
 
 heat required to generate 1 
 pound of, 867 
 
 heating, 694-703 
 
 heating, diameter of supply- 
 mains, 699. 701 
 
 heating, indiree' 
 
 heating of greenhouses, 7o2 
 
 heating, pipes for, 699-701 
 
 heating, vacuum systems of, 
 . 
 
 jackets on engines, 1004 
 
 -jet bio we; 
 
 -jet exhauster. 679 
 
 -jet ventilator, 679 
 
 latent heat of. 867 
 
 loop. 883 
 
 loss of pressure in pipes, 880 
 
 maximum efficiency of, in Car- 
 not cyel. 
 
 mean pressure of expanded, 960 
 
 -metal (bronze alloy;. 39O. 
 
 moisture in, escaping from 
 boilers. 945 
 
 pipe coverings, tests of, 584- 
 587 
 
 pipes (sec Steam -Pipes below) 
 
 ports, area of. 880 
 
 power, cost of. 1009-1011 
 
 receivers on pipelines, 884 
 
 Regnault's experiments on, 870 
 
 sampling for moisture. 942 
 
 saturated, definition, 867 
 
 strain, satu i olume 
 
 and latent heat of. M;<.I. s, i 
 
 saturated, properties of at high 
 temperatures. 
 
 saturated, properties of. table, 
 869, 871-874 
 
 saturated, specific heat of, 867 
 
 saturated. temperature and 
 pressure of, 868 
 
 saturated, total heat of, 867 
 
 separators. 941 
 
 separators, efficiency of, 941 
 
 -ships. Atlantic, performances 
 of. 1376. ! 
 
 superheated (see also Super- 
 heated steam) 
 
 superheated, definition, 867 
 
 superheated, economy of steam- 
 engines with, 998 
 
 superheated, pipes and valves 
 for, 882 
 
 superheated, properties of, 870, 
 875 
 
 superheated, specific heat of, 869 
 
 superheated, volume of , 869 
 
 temperature of, 867 
 
 vessels (see Ships) 
 
 weight of, per cubic foot, table, 
 871 
 
 wet. definition, 867 
 Steam-boilers, 885-944 (see also 
 Boilers) 
 
 air-leakage in, 891 
 
 braces in 916 
 
 bumped heads, rules for, 914 
 
 combustion space in furnaces 
 of, 889 
 
 compounds, 929 
 
 conditions to secure fuel econ- 
 omy in, 890, 893 
 
 construction of, 908-918 
 
 corrosion of, 4G7, 927-932 
 
 curves of performance of, 894, 
 895 
 
 dangerous, 932 
 
 domes on, 918 
 
 down-draught furnace for. 919 
 
 effect of rate of driving, 893 
 
 effect of soot on, 931 
 Steam-boiler efficiency, at differ- 
 ent rates of driving, 898 
 
 computation of, 687, 891 
 
 effect of excess air supply, 896' 
 
 effect of imperfect combustion, 
 896 
 
 effect of quality of coal, 895 
 
 maximum, 898 
 
 obtained in practice. 897 
 
 relation of, to rate of driving, 
 air-supply, etc., 893 
 
 straight line formula for. 896 
 Steam-boilers, evaporative tests 
 of. 898, 899-908 
 
 excess air supply to, 896 
 
 explosive energy of. 932 
 
 factors of evaporation, 908-912 
 
 factors of safety of. 918 
 
 feed-pumps for, efficiency of, 937 
 
1516 
 
 ste-ste 
 
 INDEX. 
 
 ste-ste 
 
 Steam-boilers, feed- water heaters 
 for, 938-940 (see Feed-water 
 heaters) 
 
 feed-water, saving due to heat- 
 ing of, 938 
 
 flat plates in, rules for, 916 
 flues and gas passages, propor- 
 tions of, 889 
 
 foaming or priming of, 721, 930 
 for blast-furnaces, 899 
 forced combustion in, 923 
 fuel economizers, 924 
 furnace formulae, 917 
 furnaces, height of, 889 
 fusible plugs in, 918 
 grate-surface, 887, 888 
 grate-surface, relation to heat- 
 ing surface, 887 
 gravity feeders, 938 
 heating-surface in, 887, 888 
 heating-surface, relation of, to 
 
 grate-surface, 887 
 heat losses in, 892 
 height of chimney for, 948, 950 
 high rates of evaporation, 898 
 horse-power of, 885 
 hydrostatic test of, 918 
 imperfect combustion in, 896 
 incrustation of, 927-932 
 injectors on, 936-938 (see In- 
 jectors) 
 
 man-hole openings in, 914 
 marine, corrosion of, 930 
 measure of duty of, 886 
 t mechanical stokers for, 918 
 moisture in steam escaping 
 
 from, 944 
 
 performance of, 889 
 ' plates, ductility of, 913 
 plates, tensile strength of, 908, 
 
 913 
 
 pressure allowable in, 917, 918 
 proportions of, 887-889 
 proportions of grate- and heat- 
 ing-surface for given horse- 
 power, 887, 888 
 proportions of grate-spacing, 
 
 889 
 quench-bend tests of steel 'for, 
 
 913 
 
 riveting rules for, 914 
 safety-valves, 932-935 
 safety-valves, discharge of steam 
 
 through, 934 
 
 safety-valves, formulae for, 932 
 safety-valves, spring-loaded, 933 
 safe working-pressure, 918 
 scale compounds, 929 
 scale in, 927-932 
 sediment in, 928 
 shells, material for, 908> 
 smoke prevention, 920-923 
 stay-bolts in, 916 
 stays, loads on, 916 
 stays, material for, 908 
 steel for, 913 
 
 strain caused by cold feed- 
 water, 939 
 
 Steam-boilers, strength of, 9C8- 
 
 918 
 strength of circumferential 
 
 seams, 913 
 
 strength of rivets, 914 
 tests, heat-balance in, 907 
 tests, rules for, 899-9O8 
 thickness of plates, 913 
 tube holes, 916 
 tube-plates, rules for, 914 
 tube spacing in, 916 
 tubes, holding power of, 916 
 tubes, iron and steel, 916, 
 
 917 
 
 tubes, material for, 913 
 tubes, size of, 917 
 use of kerosene in, 929 
 use of zinc in, 931 
 using waste gases, 898, 899 
 working pressures on with triple 
 
 riveted joints, 917 
 Steam-engines, 959-1095 
 
 advantages of compounding, 
 
 976 
 advantages of high initial and 
 
 low back pressure, 996 
 and turbine, best economy of, 
 
 in 1904, 1005 
 bearings, size of, 1034 
 bed-plates, dimensions of, 1044 
 clearance in, 966 
 Steam-engines, compound, 976- 
 
 983 
 
 best cylinder ratios, 982 
 calculation of cylinders of, 982 
 combined indicator diagram, 
 
 979 
 
 cylinder proportions, 980 
 economy of, 997 
 estimating horse-power of, 971 
 formulae for expansion and 
 
 work in, 031 
 high-speed, performance of, 
 
 989, 990 
 
 high-speed, sizes of, 989, 990 
 non-condensing, efficiency of, 
 
 1000 
 
 receiver, ideal diagram, 977 
 receiver space in, 980 
 receiver type, 977 
 steam- jacketed, performances 
 
 of, 989 
 
 steam-jacketed, tost of, 1005 
 Sulzer, water-consumption of, 
 
 998 
 test of with and without jackets, 
 
 1005 
 two-cylinder vs. three-cylinder, 
 
 997 
 velocity of steam in passages of, 
 
 986 
 
 water consumption of, 988 
 Woolf, ideal diagram, 977 
 Steam-engines, compression, ef- 
 fect of, 965 
 
 condensers, 1069-1079 (see Con- 
 densers) 
 connecting-rod ends, 1026 
 
ste-ste 
 
 INDEX. 
 
 ste-ste 
 
 1517 
 
 dteam- engines, connecting-rods, 
 dimensions of, 1025, 1040, 1041 
 cost of power from, 1009-1011 
 counterbalancing of, 1008 
 crank-angles, table, 1058 
 crank-piiis,dimensions of, 1027, 
 
 1040, 1041 
 
 crank-pins, pressure on, 1028 
 crank-pins, strength of, 1027 
 cranks, dimensions of, 1027 
 crank-shafts, dimensions of, 
 
 1030-1038, 1040, 1041 
 crank-shaft^, formulae for torsion 
 
 and flexure, 1038 
 crank-shafts for triple-expan- 
 sion, 1038 
 
 crank-shafts, three-throw, 1038 
 cross-head and crank, relative 
 
 motion of, 1060 
 cross-head, dimensions of, 1040, 
 
 1041 
 cross-head pin, dimensions of, 
 
 1029, 1040, 1041 
 cut-off, most economical point 
 
 of, 1009 
 
 cylinder condensation, experi- 
 ments on, 967 
 cylinder condensation, loss by, 
 
 966 
 
 cylinder, finding size of, 970 
 cylinders, dimensions of, 1021, 
 
 1022, 1039, 1041 
 cylinders, ratios of, 980, 982, 986 
 cylinder-head bolts, size of, 
 
 1022, 1039, 1041 
 cylinder-heads, dimensions of, 
 
 1022, 1039 
 design, current practice, 1039- 
 
 1041 
 dimensions of parts of, 1007, 
 
 1021-1042 
 eccentric-rods, dimensions of, 
 
 1039 
 
 eccentrics, dimensions of, 1039 
 economic performance of, 987 
 
 1007 
 
 Steam-engines, economy at vari- 
 ous loads and speeds, 992, 993 
 effect on of wet steam, 1001 
 of in central stations, 992 
 of simple and compound com- 
 pared, 997 
 tests of high speed, 994 
 under variable loads, 992 
 with superheated steam, 998 
 Steam-engines, effect of leakage 
 
 on indicator diagram, 976 
 effect on, of moisture in steam, 
 
 1001 
 efficiency in thermal units per 
 
 minute, 964 
 
 estimating I.H.P. of single 
 
 cylinder and compound, 970 
 
 exhaust sjteam used for heating, 
 
 1009 
 
 expansions in, table, 965 
 fly-wheels (see Fly-wheels), 
 1040, 1041, 1044-X052 
 
 Steam-engines, foundations em- 
 bedded in air, 1009 
 frames, dimensions of, 1044 
 friction of, 1238 
 governors, fly-ball, 1066 
 governors, fly-wheel, 1066 
 governors, shaft, 1066 
 governors, springs for, 1066-" 
 
 1068 
 
 guides, sizes of, 1024 
 highest economy of, 1003 
 high piston speed in, 995 
 high-speed, British, 995 
 high-speed Corliss, 995 
 high-speed, economy of, 994 
 high-speed, performance of, 
 
 988, 989, 992 
 
 high-speed, sizes of, 988-992 
 high-speed throttling, 996 
 horse-power constants, 971-974 
 indicated horse-power, 970-976 
 indicator diagrams, (see Indi- 
 cator), 968-976 
 indicator rigs, 969 
 indicators, errors of, 969 
 influence of vacuum and super- 
 heat on economy, 1001 
 Lentz compound, 997 
 limitations of speed of, 995 
 link motions, 1062-1065 
 mean and terminal pressures, 960 
 mean effective pressure, calcula- 
 tions of, 961 
 measures of duty of, 963 
 non-condensing, 998990 
 oil required for, 1245 
 pipes for, 879, 1039, 1040 
 piston-rings, size of, 1023 
 piston-rod guides, size of, 1024 
 piston-rods, fit of, 1024 
 piston-rods, size of, 1024, 1040, 
 
 1041 
 
 pistons, clearance of, 1021 
 pistons, dimensions of, 1022, 
 
 1040, 1041 
 piston-valves, 1061 
 prevention of vibration in, 1008 
 proportions, current practice, 
 
 1039-1041 
 
 proportions of, 1021 1042 
 quadruple-expansion, 986 
 quadruple, performance of, 1003 
 Rankine cycle efficiencies, 996 
 ratio of cylinder capacity in 
 
 compound marine, 980 
 ratio of expansion in, 962 
 reciprocating parts, weight of, 
 
 1040, 1041 
 
 relative cost of, 1011 
 reversing gear, dimensions of, 
 
 1039 
 
 rolling-mill, sizes of, 1008 
 rotary, 1082 
 rules for tests of, 1015 
 setting the valves of, 1061 
 shafts and bearings (see Snafts) , 
 
 1030-1033, 1040, 1041 
 single-cylinder, economy of, 987 
 
1518 
 
 ste-ste 
 
 INDEX. 
 
 ste-ste 
 
 Steam - engines , single - cylinder, 
 high-speed, sizes and perform- 
 ance of, 989 
 
 single-cylinder, water consump- 
 tion of, 987-1007 
 slide valves (see Slide Valves), 
 
 1053-1055 
 
 small, coal consumption of, 993 
 small, water consumption of, 992 
 Sulzer compound and triple- 
 expansion, 998 
 superheated steam in, 998 
 steam consumption of differ- 
 ent types, 999 
 
 steam-jackets, influence of, 1004 
 steam-turbines and gas-engines 
 
 compared, 1013 
 Stumpf uniflow, 997 
 test of with superheated steam. 
 
 998 
 
 three-cylinder, 1038 
 to change speed of, 1066 
 to put on center, 1061 
 Steam-engines, triple-expansion, 
 
 983-986 
 
 crank-shafts for, 1038 
 cylinder proportions, 983-985 
 cylinder ratios, 986 
 high-speed, sizes and perform- 
 ances of, 990, 991 
 non-condensing, 990 
 sequence of cranks in, 986 
 steam-jacketed, performance of, 
 
 990, 991 
 
 theoretical mean effective pres- 
 sures, 984 
 types of, 986 
 
 water consumption of, 998 
 Steam-engines, using superheated 
 
 steam, 998-1002 
 use of reheaters in, 1004 
 valve-rods, dimensions of, 1038 
 Walschaerts valve-gear, 1064 
 water consumption of, 967, 975, 
 
 987-1006 
 
 water consumption from indi- 
 cator-cards, 975 
 
 with variable loads, wasteful, 964 
 with sulphur-dioxide adden- 
 dum, 1007 
 
 wrist-pin, dimensions of, 1029 
 Steam-pipes, 882-885 
 copper, strength of, 882 
 copper, tests of, 882 
 failures of, 882 
 for engines, 879 
 for marine engines, 880 
 proportioning for minimum loss 
 by radiation and friction, 880 
 riveted-steel, 883 
 uncovered, loss from, 884 
 underground, condensation in, 
 
 884 
 
 valves in, 883 
 wire-wound, 882 
 Steam turbines, 1083-1095 
 and gas-engine, combined plant 
 of, 10 14 
 
 Steam turbines and steam-engines 
 
 compared, 1005, 1092 
 effect of pressure, vacuum and 
 
 superheat, 1090 
 effect of vacuum on, 1088 
 efficiency of, 1087 
 heat consumption of ideal 
 
 engine, 1091 
 
 impulse and reaction, 1082, 1087 
 low-pressure, 1069 
 low - pressure, combined with 
 
 high - pressure reciprocating 
 
 engine, 1383 
 most economical vacuum, 1075 
 Rankine cycle ratio of, 1089 
 reduction gear for, 1095 
 speed of the blades, 1086 
 steam consumption of, 1088, 
 
 1092 
 
 testing oil for, 1244 
 tests of, 1088 
 theory of, 1084 
 
 using exhaust, from reciprocat- 
 ing engines, 1093, 1383 
 30,000 K.W., 1092 
 Steel, 475-511 
 
 analyses and properties of, 476 
 and iron, classification of, 436 
 alloy, heat treatment of, 502- 
 
 504 
 
 aluminum, 496 
 annealing of, 484, 492 
 axle, effect of heat treatment 
 
 on, 479 
 axles, specifications for, 507, 
 
 509 
 
 axles, strength of, 354 
 bars, effect of nicking, 485 
 beams, safe load on, 298 
 bending tests of, 478 
 Bessemer basic, ultimate 
 
 strength of, 476 
 Bessemer, range of strength of, 
 
 478 
 
 blooms, weight of, table, 190 
 bridge-links, strength of, 353 
 brittleness due to heating. 483 
 burning carbon out of, 485 
 burning, overheating, and re- 
 storing, 481 
 Campbell's formulae for strength 
 
 of, 477 
 
 castings, 489, 510 
 castings, specifications for, 489, 
 
 510 
 
 castings, strength of, 355 
 cementation or case-hardening 
 
 of, 1291 
 chrome, 496 
 chromium nickel, 501 
 chromium-vanadium, 500-502 
 chromium -vanadium spring, 
 
 424 
 
 cold-drawn, tests of, 361 
 cold-rolled, tests of, 361 
 color-scale for tempering, 493 
 comparative tests of large and 
 
 small pieces, 480 
 
ste-ste 
 
 INDEX. 
 
 ste-stc 
 
 1519 
 
 Steel, copper-, 499 
 corrosion of, 467, 468 
 crank-pins, specifications for, 
 
 507 
 critical point in heat treatment 
 
 of, 480 
 
 crucible, 475, 490-494 
 crucible, analyses of, 490, 494 
 crucible, effect of heat treat- 
 ment, 481, 491 
 crucible, selection of grades of, 
 
 490 
 crucible, specific gravities of, 
 
 490 
 
 dangerous, containing mangan- 
 ese sulphide, 486 
 effect of annealing, 47.9 
 effect of annealing on grain of, 
 
 479 
 effect of annealing on magnetic 
 
 capacity, 483 
 
 effect of cold on strength of, 464 
 effect of finishing temperature 
 
 in rolling, 478 
 effect of heating, 481 
 effect of heat on grain, 479, 491 
 effect of oxygen on strength of, 
 
 477 
 effect of vibration and load on, 
 
 278 
 
 electric conductivity of, 477 
 endurance of, under repeated 
 
 stresses, 487 
 
 expansion of, by heat, 566 
 eye-bars, test of, 360 
 failures of, 486 
 fatigue resistance of, 500 
 fire-box, homogeneity test for, 
 
 508 
 
 fluid-compressed, 488 
 for bridges, specifications of, 
 
 504, 505 
 for car-axles, specifications, 507, 
 
 509 
 for different uses, analyses of, 
 
 505-510 
 
 forgings, annealing of, 482 
 forgings, oil-tempering of, 482 
 forgings, specifications for, 506 
 for rails, specifications, 508 
 for ships, specifications of, 507 
 for steam boilers, 913 
 hardening of soft, 479 
 Harvey i/ing, 1291 
 heating in a lead bath, 492 
 heating in melted salts by an 
 
 electric current, 492 
 heating of, for forging, 492 
 heat treatment of Cr-Va steel, 
 
 .502 
 high carbon, resistance of, to 
 
 shock, 277 
 high-speed tool, 494 
 high-speed tool, emery wheel 
 
 for grinding, 1263, 1314 
 high-speed tool, Taylor's experi- 
 ments, 1261 
 high-speed tool, tests of, 1369 
 
 Steel, high-strength, for shipbuild- 
 ing, 507 
 
 ingots, segregation in, 487 
 
 life of, under shock, 276 
 
 low strength of, 477 
 
 low strength of, due to insuffi- 
 cient work, 478 
 
 manganese, 494 
 
 manganese, resistance to abra- 
 sion of, 495 
 
 manufacture of, 475 
 
 melting temperature of, 555 
 
 mixture of, with cast iron, 
 453 
 
 Mushet, 490 
 
 nickel, 497 
 
 nickel, tests of, 497 
 
 nickel-vanadium, 499 
 
 of different carbons, uses of, 494 
 
 open-hearth, range of strength 
 of, 478 
 
 plates (see Plates, steel) 
 
 quench-bend tests of, for boilers, 
 913 
 
 rails, electric resistance of, 1416 
 . rails, specifications for, 508 
 
 rails, strength of, 353 
 
 range of strength in, 478 
 
 recalescence of, 480 
 
 relation between chemical com- 
 position and physical char- 
 acter of, 476 
 
 rivet, shearing resistance of, 430 
 
 rivets, specifications for, 505 
 
 shearing strength of, 362 
 
 sheets, weight of, 183 
 
 soft, quenching test for, 507 
 
 specific gravity of, 486 
 
 specifications for, 504-511 
 
 splice-bars, specifications for, 
 509 
 
 spring, strength of, 355 
 
 springs (see Springs, steel) 
 
 static and dynamic properties 
 of, 500 
 
 strength of, Campbell's formulae 
 for, 477 
 
 strength of, Kirkaldy's tests, 
 353 
 
 strength of, variation in, 478 
 Steel, structural, annealing of, 484 
 
 effect of punching and shearing, 
 
 483 
 
 ' punching of, 483 
 punching and drilling of, 485 
 
 riveting of, 484 
 
 shapes, properties of, 305-321 
 
 specifications for, 504 
 
 treatment of, 483-485 
 
 upsetting of, 484 
 
 welding of, forbidden, 484 
 Steel struts, formulae for, 285 
 
 tempering of, 493 
 
 tensile strength of, at high 
 temperatures, 463 
 
 tensile strength of, pure, 477 
 
 tires, .specifications for, 509 
 
 tires, strength of, 354 
 
1520 
 
 ste-str 
 
 INDEX. 
 
 str-str 
 
 Steel tool, composition and heat 
 
 treatment of, 1265 
 tool, heating of, 492 
 tool, high-speed, 1265 
 tungsten, 496 
 
 used in automobile construc- 
 tion, 510 
 
 very pure, low strength of, 477 
 water-pipe, 351 
 welding of, 484, 498 
 wire gage, tables, 30 
 working of, at blue heat, 482 
 working stresses in bridge 
 
 members, 287 
 Stefan and Boltzman law of 
 
 radiation, 579 
 Stellite, alloy for cutting tools, 
 
 1269 
 
 Sterro metal, 393 
 St. Gothard tunnel, loss of pres- 
 sure in air-pipes in, 620 
 Stoker, Riley, 919 
 
 Taylor gravity underfeed, 919 
 Stokers, mechanical, for steam- 
 boilers, 918 
 underfeed, 919 
 
 Stone-cutting with wire, 1309 
 strength of, 357, 370 
 weight and specific gravity of, 
 
 table, 177 
 
 Storage batteries, 1425-1428 
 batteries, Edison alkaline, 1428 
 batteries, rules for care of, 1427 
 of steam heat, 927, 1014 
 Storms, pressure of wind in, 627 
 Stove foundries, cupola charges 
 
 in, 1250 
 
 Stoves, for heating compressed- 
 air, efficiency of, 641 
 Straight-line formula for columns, 
 
 285 
 
 formula for boiler efficiency, 896 
 Strain and stress, 272 
 Strand, steel wire, for guys, 255 
 Straw as fuel, 839 
 Stream, open, measurement of 
 
 flow, 760 
 Streams, fire, 749-752 (see Fire 
 
 streams) 
 
 running, horse-power of, 765 
 Street-lighting installations, 1476 
 
 kinds of, 1472 
 Strength and specific gravity of 
 
 cast iron, 452 
 compressive, 281-283 
 compressive, of woods, 368 
 loss of, in punched plates, 424 
 Strength of aluminum, 381 
 aluminum-copper alloys, 396 
 anchor forgings, 353 
 basic Bessemer steel, 476 
 belting, 357 
 
 blocks for hoisting, 1 181 
 boiler-heads, 337, 338 
 boiler-plate at high tempera- 
 tures, 463 
 bolts, 348 
 brick, 358 
 
 Strength of brick and stone, 370- 
 
 372 
 
 bridge-links, 353 
 bronze, 356, 384 
 canvas, 357 
 castings, 352 
 cast iron, 444-447 
 cast-iron beams, 451 
 cast-iron columns, 289 
 cast-iron cylinders, 452 
 cast-iron flanged fittings, 452 
 cast iron, relation to size of bar, 
 
 444 
 
 cast-iron water-pipes, 196, 452 
 cement mortar, 372 
 chain cables, tables, 264, 265 
 chains, table, 264, 265 
 chalk, 371 
 
 columns, 283-293, 1389 
 copper at high temperatures, 
 
 368 
 
 copper plates, 356 
 copper- tin alloys, 385 
 copper-tin-zinc alloys, graphic 
 
 representation, 388 
 copper-zinc alloys, 388 
 cordage, table, 410, 415, 1218 
 crank-pins, 1027 
 electro-magnet, 1431 
 flagging, 373 
 flat plates, 336 
 floors, 1390-1393 
 German silver, 356 
 glass, 365 
 granite, 357 
 gun-bronze, 386 
 hand and hydraulic riveted 
 
 joints, 425 
 ice, 368 
 iron and steel, effect of cold on, 
 
 464 
 
 iron and steel pipe, 363 
 lime-cement mortar, 372 
 limestone, 371 
 locomotive forcings, 353 
 Lowmoor iron bars, 352 
 malleable iron, 454, 45S 
 marble, 357 
 masonry materials, 371 
 materials, 272-379 
 materials, Kirkaldy's tests, 352- 
 
 358 
 
 perforated plates, 425 
 phosphor-bronze, 395 
 Portland cement, 358 
 riveted joints, 359, 424-435 
 roof trusses, 547 
 rope, 357, 411, 1218 
 sandstone, 371 
 silicon-bronze wire, 395 
 soapstone, 371 
 spring steel, 355 
 spruce timber, 367 
 stayed surfaces, 338 
 steam-boilers, 908-918 
 steel axles, 354 
 steel castings, 355 
 steel, formulae for, 476, 477 
 
str-sul 
 
 INDEX. 
 
 sul-tay 
 
 1521 
 
 Strength of steel propeller-shafts, 
 
 354 
 
 steel rails, 353 
 steel tires, 354 
 structural shapes, 305-321 
 timber, 368 
 twisted iron, 280 
 unstayed surfaces, 337 
 various sheet metals, 356 
 welds, 264, 355 
 wire, 357, 358 
 
 wire and hemp rope, 356, 357 
 wrought-iron columns, 285 
 yellow pine, 368 
 zinc plates, 370 
 
 Strength, range of, in steel, 478 
 shearing, of iron and steel, 
 
 362 
 
 shearing, of woods, table, 367 
 tensile, 278 
 tensile, of iron -and steel at high 
 
 temperatures, 463 
 tensile, of pure steel, 477 
 torsional, 334 
 transverse, 297-300 
 Stress and strain, 272 
 
 due to temperature, 335 
 Stresses allowed in bridge mem- 
 bers, 287 
 combined, 335 
 effect of, 272 
 
 in framed structures, 541-548 
 in plating of bulkheads, etc., 
 
 due to water-pressure, 338 
 in steel plating due to water 
 
 pressure, 338 
 produced by shocks, 276 
 Structural materials, permissible 
 
 stresses in, 1387, 1388 
 shapes, elements of, 294 
 shapes, moment of inertia of, 
 
 295 
 shapes, radius of gyration of, 
 
 295 
 
 shapes, steel (sec Steel, struc- 
 tural, also Beams, angles, 
 etc.) 
 steel shapes, dimensions and 
 
 weights, 302-305 
 steel shapes, properties of, 305- 
 
 321 
 
 work, rivet spacing for, 321, 322 
 Structures, framed, stresses in. ' 
 
 541-548 
 
 Strut, moving, 536 
 Struts, steel, formulae for, 285 
 strength of, 283 
 wrought-iron, formulae for, 285 
 Stub gear teeth, 1167 
 Stud bolts, 237 
 Stumpf uniflow engine, 997 
 Suction lift of pumps, 788 
 Sugar manufacture, 839 
 Sugar solutions, concentration of, 
 
 572 
 
 Sulphate of lime, solubility of, 571 
 S ulpliur-dioxide refrigerating-ma- 
 chine, 1345 
 
 Sulphur - dioxide - addendum to 
 
 steam-engine, 1007 
 dioxide, properties of, 1338 
 influence of, on cast iron, 438 
 influence of, on steel, 476 
 Sum and difference of angles, 
 
 functions of, 68 
 Sun, heat of, as a source of power, 
 
 1015 
 Superheated steam, economy of 
 
 steam-engines with, 998 * 
 steam, effect of on steam con- 
 sumption, 998 
 steam, practical application of, 
 
 1002 
 Superheating, economy duo to, 
 
 1006 
 
 in locomotives, 1126 
 Surface condensers, 1069 
 
 of sphere, table, 126, 127 
 Surfaces of geometrical solids, 61- 
 
 66 
 of revolution, quadrature of, 
 
 unstayed flat, 337 
 Suspension cableways, 1205 
 Sweet's slide-valve diagram, 1054 
 Symbols, chemical, 173 
 
 electrical, 1477 
 Synchronous converters, 1453 
 
 generators, 1448, 1453 
 
 -motor, 1463 
 
 T -CONNECTIONS, trans- 
 formers, 1452 
 T-shapes, properties of Car- 
 negie steel, table, 313-315 
 T-slots, T-bolts and T-nuts, 1321 
 Tackle, hoisting, 1182 
 Tackles, rope, efficiency of, 415 
 Taggers, tin, 192 
 
 Tail-rope, system of haulage, 1203 
 Tanbark as fuel, 838 
 Tangent of an angle, 66 
 Tangents of angles, table of, 170- 
 
 172 
 Tangential or* impulse water 
 
 wheels, tables of, 785 
 Tanks and cisterns, number of 
 
 barrels in, 134 
 
 capacities of, tables, 132-134 
 with flat sides, plating and 
 
 framing for, 339 
 Tap-drills, sizes of, 235, 23, i:*2O 
 
 for pipe taps, 201 
 Taper pins, 1321 
 
 to set in a lathe, 1261 
 Tapers, Jarno, 1319 
 
 Morse, 1319 
 Tapered wire rope, 1208 
 Taps, A. S. M. E. standard, 235, 
 
 236 
 Tapping and threading, speeds 
 
 for, 1290 
 
 Taylor's experiments on cutting 
 tools of high-speed steel, 1261 
 Taylor's rules for belting, 1143 
 Taylor's theorem, 78 
 
1522 
 
 tay-thr 
 
 INDEX. 
 
 thr-too 
 
 Taylor -White high-speed tools, 
 
 cutting speeds of, 1266 
 Teeth of gears, forms of, 1 162-1 167 
 of gears, proportions, 1159, 
 
 1161 
 Telegraph poles, tubular, 206 
 
 -wire, tests of, table, 250 
 Telpherage, 1196 
 Temperature, absolute, 567 
 
 and humidity, comfortable, 685 
 coefficient of resistance of 
 
 copper, 1403 
 conversion table, 552 
 determination of by color, 558 
 determinations of melting- 
 points, 554, 559 
 effect of on strength, 368, 463- 
 
 465 
 
 -entropy diagram, 600 
 -entropy diagram of water and 
 
 steam, 602 
 of fire, 817, 818 
 rise of, in combustion of gases, 
 
 818 
 
 stress due to, 335 
 Temper carbon, in cast-iron, 439 
 Tempering, effect of, on steel, 493 
 oil, of steel forgings, 482 
 steel, change of shape due to, 
 
 1291 
 
 Tenacity of different metals, 180 
 of metals at various tempera- 
 tures, 368, 463-465 
 Tensile strength (see Strength) 
 strength, increase of, by twist- 
 ing, 280 
 tests, precautions in making, 
 
 279 
 
 tests, specimens for, 280 
 Tension and flexure, combined, 335 
 
 and shear, combined, 335 
 Terne-plate, or roofing tin, 193 
 Terra cotta, weight of, 196 
 Tests, compressive (see Compres- 
 
 sive strength) 
 of steam-boilers, rules for, 899- 
 
 908 
 
 of steam-engines, rules for, 1015 
 of strength of materials (see 
 
 Strength) 
 
 quench-bend, of steel 913 
 tensile (see Strength and Ten- 
 sile strength) 
 Thermal capacity, 562 
 storage, 927, 1014 
 units, 560 
 Thermit process, 401 
 
 welding process, 488 
 Thermodynamics, 597-603 
 
 laws of, 598 
 Thermometer, air, 557 
 
 centigrade and Fahrenheit com- 
 pared, tables, 550 
 Threads, pipe, standard, 201, 217 
 Threading and parting tools, 
 
 speed of, 1268 
 
 and tapping, speeds for, 1290 
 pipe, force required for, 3(a 
 
 Three-phase circuits, 1445 
 
 transmission, rule for sizes of 
 
 wires, 1459 
 
 Throttle valves, size of, 880 
 Thrust bearings, 1232 
 Tides, utilization of power of, 787 
 Ties, railroad, required per mile 
 
 of track, 245 
 Tiles, weight of, 196 
 Timber (see also Wood) 
 
 beams, safe loads, 1387, 1393 
 beams, strength of, 368- 
 expansion of, 367 
 measure, 20 
 preservation of, 368 
 strength of, 368-369 
 table of contents in feet, 21 
 to compute volume of square, 
 
 21 
 
 Time, measures of, 20 
 Tin, alloys of (see Alloys) 
 lined iron pipe, 227 
 plates, 192-194 
 properties of, 179 
 Tires, locomotive, shrinkage fits, 
 
 1324 
 
 steel, friction of on rails, 1219 
 steel, specifications for, 509 
 steel, strength of, 354 
 Titanium, additions to cast-iron, 
 
 439, 451 
 
 -aluminum alloy, 401 
 Tobin bronze, 392 
 Toggle-joint, 536 
 Tonnage of vessels, 1369 
 Tons per mile, equivalent of, in 
 
 Ibs. per yard, 27 
 
 Tools, cutting, durability of, 1268 
 cutting, effect of feed and depth 
 
 of cut on speed of, 1264 
 cutting, in small shops, best 
 
 method of treatment, 1268 
 cutting, interval between grind- 
 ings of, 1264 
 
 cutting, pressure on, 1264 
 cutting, use of water on, 1264 
 economical cutting speed of, 
 
 1268 
 
 forging and grinding of, 1263 
 high speed, table of cutting 
 
 speeds, 1266 
 
 machine (see Machine tools) 
 parting and thread - cutting , 
 
 speed of, 1268 
 standard planing, 1271 
 Tool-steel (see also Steel) 
 best quality, 1265 
 high-speed, composition and 
 
 heat-treatment of, 1265 
 high-speed, new (1909), tests of, 
 
 1269 
 
 high-speed, Taylor's experi- 
 ments, 1265 
 in small shops, best treatment 
 
 of, 1268 
 
 of different qualities, 1268 
 Toothed-wheel gearing, 539, 11 57-. 
 1180 
 
tor-tri 
 
 INDEX. 
 
 tro-iur 
 
 1523 
 
 Torque computed from watts and 
 
 revolutions, 1436 
 horse -power and revolutions, 
 
 1436 
 
 of an armature, 1435 
 Torsion and compression com- 
 bined, 335 
 
 and flexure combined, 335 
 elastic resistance to, 334 
 of shafts, 1030, 1130 
 tests of shafting, 361 
 Torsional strength, 334 
 Track bolts, 244, 245 
 
 spikes, 245 
 
 Tractive force of locomotive, 1112 
 Tractrix, Schiele's anti-friction 
 
 curve, 50 
 Train resistance, electric cars, 1415 
 
 loads, average, 1125 
 Trains, railroad, resistance of, 
 
 1108 
 
 railroad, speed of, 1187 
 Trammels, to describe an ellipse 
 
 with, 45 
 Tramways, compressed-air, 652 
 
 wire-rope, 1204 
 Transformers, constant current, 
 
 1453 
 
 efficiency of, 1451 
 electrical, 1451 
 
 primary and secondary of, 1451 
 Transmission, compressed-air (see 
 
 Compressed-air) 
 electric, 1410, 1457 
 electric, area of wires, 1410, 1457 
 electric, economy of, 1411 
 electric, efficiency of, 1411 
 electric, weight of copper for, 
 
 1411, 1457 
 
 electric, wire table for, 1413, 1457 
 hydraulic-pressure (see Hydrau- 
 lic-pressure transmission) 
 of heat (see Heat) 
 of power by wire-rope (see 
 
 Wire-rope), 1208-1213 
 pneumatic postal, 1201 
 rope (see Rope-driving) 
 rope, iron and steel, 256, 257 
 
 > wire-rope (see Wire-rope) 
 Transporting power of water, 755 
 Transverse strength, 297-300 
 Trapezium and Trapezoid, 54 
 Trapezoidal rule, 56 
 Triangles, mensuration of, 54 
 problems in, 41 
 solution of, 69 
 spherical, 63 
 Trigonometrical computations by 
 
 slide rule, 83 
 formulae, 68 
 
 functions, logarithmic, 167 
 functions, table, 170-172 
 Trigonometry, 66-70 
 Triple effect evaporators, 570 
 Triple-expansion engine (see 
 
 Steam-engines) 
 
 Triple-riveted joints, working 
 pressures on boilers with, 917 
 
 Troostite, 480 
 
 Trough plates, properties of, 308 
 
 Troy weight, 19 
 
 Trusses, bridge, stresses in, 543- 
 
 547 
 
 roof, stresses in, 547 
 Tubes (see also Pipe) 
 aluminum 226 
 aluminum bronze, 397 
 boiler (see Steam-boiler tubes) 
 boiler, table, 204 
 boiler, used as columns, 336 
 brass, seamless, 224, 225 
 collapse of, formulae for, 341-344 
 collapse of, tests of, 341-344 
 collapsing pressure of, table, 
 
 334 
 
 copper, 225 
 expanded, holding power of, 364, 
 
 916 
 
 lead and tin, 227 
 of different materials, weight 
 
 of, 181 
 
 seamless, 222-225 
 steel, cold-drawn, Shelby, 223 
 surface per foot of length, 224 
 Tube-plates, steam-boiler, rules 
 
 for, 914 
 Tube-spacing in steam-boilers, 
 
 916 
 Tungsten and aluminum alloy, 
 
 399 
 
 electric lamps, 1473 
 steel. 496 
 
 Turbines, hydraulic, 768-780 
 American high-speed runners, 
 
 comparison of, 770 
 capacity criterion, 770 
 capacity of, 769B 
 determination of dimensions of 
 
 runners, 7 69 A 
 determination of sizes, 770, 
 
 770B, 771A 
 
 discharge loss of, 769B 
 draft tubes for, 778 
 efficiency of 77 IB 
 estimating weights of, 771 A 
 fall increaser for, 780 
 gate opening, relation of to 
 
 efficiency, 772 
 10,000 H.P. machine at Sno- 
 
 qualmie Falls, 779 
 13,500 H.P. machine at Du- 
 
 luth, 779 
 limiting profiles of runners, 
 
 769B 
 
 power table for, 776, 777 
 recent practice, 778 
 selection of, 771, 771 A 
 some large, 779 
 specific discharge, 770, 770B 
 specific speed, 770 
 speed criterion, 770 
 tests of discharge by salt solu- 
 tion, 774 
 
 type characteristics, 770 
 Turbines, steam (see Steam- 
 turbines) 
 
1524 
 
 tur-vaii 
 
 INDEX, 
 
 van-wat 
 
 Turf or peat, as fuel, 838 
 Turnbuckles, 243 
 Tuyeres for cupolas, 1247 
 Twist-drill (see Drills) 
 
 and steel wire gages, 1286 
 
 gage, table, 30 
 
 sizes and speeds, 1285 
 Twisted steel bars, strength of, 280 
 Two-phase currents, 1445 
 Type characteristic of turbines, 
 770 
 
 -metal, 408 
 
 UEHLING and Steinbart 
 pyrometer, 557 
 Underwriters' rules for elec- 
 trical wiring, 1410 
 Unequal arms on balances, 20 
 U inflow steam-engines, Stumpf, 
 
 997 
 
 Unions, pipe fittings, 207 
 Unit of evaporation, 886 
 . of force, 512 
 of heat, 560 
 of power, 528 
 of work, 528 
 Units, electrical and mechanical, 
 
 equivalent values of, 1399 
 electrical, relations of, 1397 
 of the magnetic circuit, 1399 
 united States, population of, 11 
 
 standard sheet metal gage, 29, 
 Unstayed surfaces, strength of, 
 
 337 
 Upsetting of structural steel, 484 
 
 V -NOTCH recording water 
 meter, 759 
 Vacuum at different tem- 
 peratures, 788 
 drying in, 573 
 for turbines, most economical, 
 
 1075 
 
 high, advantage of, 1078 
 high, influence of on steam-en- 
 gine economy, 1001 
 inches of mercury and absolute 
 
 pressure, 1071 
 pumps, 806 
 
 systems of steam heating, 702 
 Valves and elbows, friction of air 
 
 in, 624 
 and fittings, loss of pressure due 
 
 to, 747, 748 
 and pipe fittings, description 
 
 and sizes, 206-208 
 for superheated steam, 882 
 in steam pipes, 883 
 pump, 792, 793 
 straight-way gate, 217, 218 
 Valve-gear, Stephenson, 1062 
 
 Walschaerts, 1064 
 Valve-stem or rod, design of (see 
 
 Steam-engines) , 1038 
 Vanadium-chrome steel, 500-502 
 -copper alloys, 395 
 effect of on cast iron, 439, 450 
 -nickel steels, 499 
 
 Vanadium steel spring, 424. 
 
 Vapor and gases, mixtures of, 604 
 pressures of various liquids, 844 
 saturation point of, 604 
 water, and air mixture, weight 
 of, 610-613 
 
 Vapors used in refrigerating, 
 properties of, 1341 
 
 Varnishes, 471 
 
 Velocity, angular, 522 
 
 due to falling a given height, 
 
 of gas in chimneys, 951 
 
 parallelogram of, 523 
 
 table of height corresponding 
 
 to a given, 523 
 Ventilating ducts, quantity of air 
 
 carried by, 683 
 fans, 653-660, 672 
 Ventilation (see also Heating and 
 
 Ventilation) 
 by chimneys, 712 
 by steam-jet, 679 
 cooling air for, 710 
 of mines (see Mine- ventilation) 
 of mines, equivalent orifice. 715 
 problems, standard values in, 
 
 687 
 
 standards of, 686 
 Ventilators, centrifugal for mines, 
 
 672 
 
 Venturi meter, 758 
 Versed sine of an arc, 67 
 
 sines, table, 170-172 
 Verticals, formulae for strains in, 
 
 545 
 Vessels (see also Ships) 
 
 framing of, table, 339 
 Vibrations in engines, preventing, 
 
 1008 
 
 Vis-viva, 528 
 Volt, definition of, 1397 
 Voltages used in long-distance 
 
 transmission, 1459 
 Volumes of revolution, cubature 
 
 of, 77 
 Vulcanized India rubber, 378 
 
 WALLS of buildings, thick- 
 ness of, 1388 
 of warehouses, factories, 
 etc., 1388 
 windows, etc., heat loss through, 
 
 688 
 
 Walschaerts valve-gear, 1064 j 
 Warren girder, stresses in, 546 
 Washers, cast and wrought, tables 
 
 of, 242, 243 
 Washing of coal, 833 
 Water, 716-726 
 
 abrading power of, 755 
 amount of to develop a given 
 
 horse-power, 783 
 analysis 9f , 722 
 as a lubricant, 1246 
 boiling-point at various baro- 
 metric pressures, 608 
 boiling-point of, 719 
 
wat-wat 
 
 INDEX. 
 
 wat-wlr 
 
 1525 
 
 Water, comparison of head in feet 
 
 with various units, 718 
 compressibility of, 720 
 conduits, long, efficiency of, 766 
 consumption of locomotives 
 
 1122 
 consumption of steam-engines 
 
 (sec Steam-engines) 
 current motors, 765 
 drums for boilers, 913 
 erosion and abrading by, 755 
 flow of (sec Flow of water) 
 flowing in a tube, power of, 
 
 765 
 flowing, measurement of, 757- 
 
 764 
 
 freezing-point of, 719 
 frictional resistance of surfaces 
 
 moved in, 756 
 -gas, 846, 859-864 
 -gas analyses of, 860 
 -gas, manufacture of, 859 
 -gas plant, efficiency of, 861 
 -gas plant, space required for, 
 
 862 
 
 hammer, 749 
 hardness of, 723 
 head of, 718 
 
 heating of, by steam coils, 591 
 heat-units per pound of, 717 
 horse-power required to raise, 
 
 788 
 
 impurities of, 720 
 in pipes, loss of energy in, 812 
 jets, vertical, 749 
 meter, V-notch recording, 759 
 meters, capacity of, 749 
 pipe, cast-iron, transverse 
 
 strength of, 452 
 pipes, compound with branches, 
 
 746 
 
 -power, 765 
 
 -power plants, high pressure, 782 
 -power, value of, 766 
 pressure on vertical surfaces, 
 
 719 
 
 pressure per square inch, equiv- 
 alents of, 27, 718 
 pressures and heads, table, 718 
 prices charged for in cities, 749 
 pumping by compressed air, 808 
 purification of, 723-726 
 -softening apparatus, 724 
 specific heat of, 564, 720 
 total heat and entropy of, 869, 
 
 87 1-873 
 
 tower (see Stand-pipe) 
 lower at Yonkers, N. Y., 350 
 transporting power of, 755 
 under pressure, energy of, 765 
 units of pressure and head, 718 
 vapor and air mixture, weight of, 
 
 610-613 
 velocity of, in open channels, 
 
 755 
 
 weight at different tempera- 
 tures, 716, 717 
 weight of one cubic foot, 27 
 
 Waterfall, power of a, 765 
 Water-wheels, 768 
 
 impulse, 780 
 
 jet, power of, 784 
 
 Pelt-on, 780 
 
 tangential, choice of, 781 
 
 tangential, governing, 782 
 
 tangential, power of, 784, 785 
 
 tangential, reversible, 781 
 Waves, ocean, power of, 784 
 Weathering of coal, 830 
 Wedge, 537 
 Wedge, volume of, 62 
 Weighing on incorrect balance, 20 
 Weight and specific gravity of 
 materials, 174-177 (see also 
 Material in question) 
 . definition of, 511 
 
 measures of, 19 
 Weights and measures, 17-27 
 Weir dam measurement, 762 
 
 flow of water over, 762 
 
 trapezoidal, 764 
 
 triangular or V-notch, 759 
 Welds, strength of, 355 
 
 electric, 1419 
 
 electric arc, 1419 
 
 of steel, 484, 487 
 Welding, oxy-acetylene, 488 
 
 process, the thermit, 488 
 Well, artesian, pumping by com- 
 pressed air, 810 
 Welsbach gas lights, standard 
 
 sizes, 1474 
 
 Wheat, weight of, 180 
 Wheel and axle, 539 
 Wheels, turbine (see Turbine 
 
 wheel) 
 
 Whipple truss, 544 
 White-metal alloys, 407 
 Whitworth process of compressing 
 
 steel, 488 
 
 Wiborgh air-pyrometer, 555 
 Wild wood pumping-engine, high 
 
 economy of, 805 
 
 Willans law of steam consump- 
 tion. 991 
 Wind, 626, 627 
 
 force of, 627 
 
 loads on roofs, 191 
 
 pressure of, in storms, 627 
 
 strain on stand-pipes, 349 
 Winding engines (see Hoisting 
 
 engines) 1186 
 Windlass, 539 
 
 differential, 540 
 
 Windows, heat-loss through, 688 
 Windmills, 627-632 
 
 capacity and economy, 627-632 
 Wire, aluminum, properties of, 
 248, 1414 
 
 aluminum-bronze, 248 
 
 brass, properties of, 248 
 
 brass, weight of, table, 229 
 
 copper, hard-drawn specifica- 
 tion for, 251, 252 
 
 copper, rule for resistance of, 
 140G 
 
1526 
 
 wir-wlr 
 
 INDEX. 
 
 Woh-zon 
 
 Wire, copper, stranded, 253 
 
 copper, telegraph and tele- 
 phone, 251, 252 
 
 copper, weight of bare and in- 
 sulated, 252 
 
 gages, tables, 28 
 
 galvanized, for telegraph and 
 telephone lines, 250 
 
 galvanized iron, specifications 
 for, 250 
 
 galvanized steel strand, 255 
 
 insulated copper, 252 
 
 nails, 246, 247 
 
 of different metals, 248 
 
 phosphor-bronze, 248 
 
 piano, strength of, 250 
 
 platinum, properties of, 248 
 
 plow steel, 250 
 
 silicon-bronze, 248, 395 
 
 steel, properties of, 249 
 
 stranded feed, table, 253 
 
 telegraph, tests of, 250 
 
 weight per mile-ohm, 250 
 
 -wound fly-wheels, 1052 
 Wires of various metals, strength 
 of, 358 
 
 sag of between poles, 1461 
 Wire-rope, 253-263 
 
 bending curvature of, 1213 
 
 bending of, 254 
 
 breaking strength of, 254, 1209 
 
 exposure to heat, 256 
 
 extra flexible, 258, 259 
 
 flat, 260, 261 
 
 flattened strand, 258, 261 
 
 flexible hoisting, 258, 259 
 
 galvanized, 255, 262 
 
 galvanized steel hawser, 262 
 
 haulage (see Haulage) 
 
 horse-power transmitted by, 
 1210 
 
 iron and steel, table of strength 
 of, 261, 410 
 
 locked, 262 
 
 notes on use of, 254, 256 
 
 plow steel, 257-259 
 
 protection of, 256 
 
 radius of curvature of, 1213 
 
 sag or deflection of, 1211 
 
 sheaves for, 1208, 1211 
 
 splicing of, 263 
 
 steel-clad hoisting, 260 
 
 strength of, 356 
 
 table of strength of, 410 
 
 tapered, 1208 
 
 tramways, 1204 
 
 varieties and uses, 254, 256 
 Wire-rope transmission, deflec- 
 tion of rope, 1207, 1211 
 
 inclined, 1212 
 
 limits of span, 1212 
 
 long distance, 1212 
 
 of power by, 1208 
 
 sheaves for, 1211 
 Wiring rules, Underwriters', 1410 
 
 table for direct currents, 1413 
 
 table for three-phase transmis- 
 sion lines, 1459 
 
 Wohlor's experiments on strength 
 
 of materials, 275 
 Wood (sec also Timber) 
 
 as fuel, 835, 836 
 
 composition of, 835 
 
 drying of, 368 
 
 expansion of, by heat, 368 
 
 expansion of, by water, 368 
 
 heating value of, 835 
 
 holding power of bolts in, 346 
 
 nail-holding power of, 346, 347 
 
 screws, 236 
 
 screws, holding power of, 346 
 
 strength of, 368, 369 
 
 strength of, Kirkaldy 's tests, 358 
 
 weight of, 181 
 
 weight and specific gravity of, 
 table, 176 
 
 weight and heating values of, 
 835 
 
 weight per cord, 181 
 Woods, American shearing 
 strength of, 367 
 
 tests of, 366 
 Wood-working machinery, power 
 
 required for, 1303 
 Wooden fly-wheels, 1051 
 
 stave pipe, 218, 735 
 Woodruff key, 1331, 1332 
 Woolf compound engines, 977 
 Wootten locomotive, 1114 
 Work, definition of, 27, 528 
 
 energy, power, 528 
 
 of accelerated rotation, 529 
 
 of acceleration, 529 
 
 of a man, horse, etc., 532-534 
 
 of friction, 1229 
 Worm gearing, 540, 1168 
 Wrist-pins, dimensions of, 1029 
 Wrought-iron, chemical composi- 
 tion of, 460 
 
 effect of rolling on strength of, 
 460 
 
 manufacture of, 459 
 
 slag in, 460 
 
 specifications, 461, 462 
 
 strength of, 352, 359, 459-463 
 
 strength of, at high tempera- 
 tures, 463 
 
 strength of, Kirkaldy 's tests, 352 
 
 ACHT rigging,' galvanized 
 
 steel rope, 255 
 Yield point, 273 
 
 Z-BARS, Carnegie, properties 
 of, 316 
 Zero, absolute, 567, 868 
 Zeuner's slide-valve diagram, 1055 
 Zinc alloys (see Alloys) 
 plates, strength of, 370 
 properties of, 179 
 sheet, weight of, table, 228 
 use of in steam-boilers, 931 
 Zirconia, 270 
 Zone of spheroid, 64 
 of spindle, 65 
 spherical, 64 
 
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